[libc-commits] [libc] 0928368 - [libc] Provide Arm Optimized Routines for the LLVM libc project.
Siva Chandra Reddy via libc-commits
libc-commits at lists.llvm.org
Mon Mar 16 12:19:57 PDT 2020
Author: Kristof Beyls
Date: 2020-03-16T12:19:31-07:00
New Revision: 0928368f623a0f885894f9c3ef1b740b060c0d9c
URL: https://github.com/llvm/llvm-project/commit/0928368f623a0f885894f9c3ef1b740b060c0d9c
DIFF: https://github.com/llvm/llvm-project/commit/0928368f623a0f885894f9c3ef1b740b060c0d9c.diff
LOG: [libc] Provide Arm Optimized Routines for the LLVM libc project.
This adds the Arm Optimized Routines (see
https://github.com/ARM-software/optimized-routines) source code under the
the LLVM license. The version of the code provided in this patch is v20.02
of the Arm Optimized Routines project.
This entire contribution is being committed as is even though it does
not currently fit the LLVM libc model and does not follow the LLVM
coding style. In the near future, implementations from this patch will be
moved over to their right place in the LLVM-libc tree. This will be done
over many small patches, all of which will go through the normal LLVM code
review process. See this libc-dev post for the plan:
http://lists.llvm.org/pipermail/libc-dev/2020-March/000044.html
Differential revision of the original upload: https://reviews.llvm.org/D75355
Added:
libc/AOR_v20.02/Makefile
libc/AOR_v20.02/config.mk.dist
libc/AOR_v20.02/math/Dir.mk
libc/AOR_v20.02/math/cosf.c
libc/AOR_v20.02/math/exp.c
libc/AOR_v20.02/math/exp2.c
libc/AOR_v20.02/math/exp2f.c
libc/AOR_v20.02/math/exp2f_data.c
libc/AOR_v20.02/math/exp_data.c
libc/AOR_v20.02/math/expf.c
libc/AOR_v20.02/math/include/mathlib.h
libc/AOR_v20.02/math/log.c
libc/AOR_v20.02/math/log2.c
libc/AOR_v20.02/math/log2_data.c
libc/AOR_v20.02/math/log2f.c
libc/AOR_v20.02/math/log2f_data.c
libc/AOR_v20.02/math/log_data.c
libc/AOR_v20.02/math/logf.c
libc/AOR_v20.02/math/logf_data.c
libc/AOR_v20.02/math/math_config.h
libc/AOR_v20.02/math/math_err.c
libc/AOR_v20.02/math/math_errf.c
libc/AOR_v20.02/math/pow.c
libc/AOR_v20.02/math/pow_log_data.c
libc/AOR_v20.02/math/powf.c
libc/AOR_v20.02/math/powf_log2_data.c
libc/AOR_v20.02/math/s_cos.c
libc/AOR_v20.02/math/s_cosf.c
libc/AOR_v20.02/math/s_exp.c
libc/AOR_v20.02/math/s_exp2f.c
libc/AOR_v20.02/math/s_exp2f_1u.c
libc/AOR_v20.02/math/s_expf.c
libc/AOR_v20.02/math/s_expf_1u.c
libc/AOR_v20.02/math/s_log.c
libc/AOR_v20.02/math/s_logf.c
libc/AOR_v20.02/math/s_pow.c
libc/AOR_v20.02/math/s_powf.c
libc/AOR_v20.02/math/s_sin.c
libc/AOR_v20.02/math/s_sinf.c
libc/AOR_v20.02/math/sincosf.c
libc/AOR_v20.02/math/sincosf.h
libc/AOR_v20.02/math/sincosf_data.c
libc/AOR_v20.02/math/sinf.c
libc/AOR_v20.02/math/test/mathbench.c
libc/AOR_v20.02/math/test/mathtest.c
libc/AOR_v20.02/math/test/rtest/dotest.c
libc/AOR_v20.02/math/test/rtest/intern.h
libc/AOR_v20.02/math/test/rtest/main.c
libc/AOR_v20.02/math/test/rtest/random.c
libc/AOR_v20.02/math/test/rtest/random.h
libc/AOR_v20.02/math/test/rtest/semi.c
libc/AOR_v20.02/math/test/rtest/semi.h
libc/AOR_v20.02/math/test/rtest/types.h
libc/AOR_v20.02/math/test/rtest/wrappers.c
libc/AOR_v20.02/math/test/rtest/wrappers.h
libc/AOR_v20.02/math/test/runulp.sh
libc/AOR_v20.02/math/test/testcases/directed/cosf.tst
libc/AOR_v20.02/math/test/testcases/directed/exp.tst
libc/AOR_v20.02/math/test/testcases/directed/exp2.tst
libc/AOR_v20.02/math/test/testcases/directed/exp2f.tst
libc/AOR_v20.02/math/test/testcases/directed/expf.tst
libc/AOR_v20.02/math/test/testcases/directed/log.tst
libc/AOR_v20.02/math/test/testcases/directed/log2.tst
libc/AOR_v20.02/math/test/testcases/directed/log2f.tst
libc/AOR_v20.02/math/test/testcases/directed/logf.tst
libc/AOR_v20.02/math/test/testcases/directed/pow.tst
libc/AOR_v20.02/math/test/testcases/directed/powf.tst
libc/AOR_v20.02/math/test/testcases/directed/sincosf.tst
libc/AOR_v20.02/math/test/testcases/directed/sinf.tst
libc/AOR_v20.02/math/test/testcases/random/double.tst
libc/AOR_v20.02/math/test/testcases/random/float.tst
libc/AOR_v20.02/math/test/traces/exp.txt
libc/AOR_v20.02/math/test/traces/sincosf.txt
libc/AOR_v20.02/math/test/ulp.c
libc/AOR_v20.02/math/test/ulp.h
libc/AOR_v20.02/math/tools/cos.sollya
libc/AOR_v20.02/math/tools/exp.sollya
libc/AOR_v20.02/math/tools/exp2.sollya
libc/AOR_v20.02/math/tools/log.sollya
libc/AOR_v20.02/math/tools/log2.sollya
libc/AOR_v20.02/math/tools/log2_abs.sollya
libc/AOR_v20.02/math/tools/log_abs.sollya
libc/AOR_v20.02/math/tools/plot.py
libc/AOR_v20.02/math/tools/remez.jl
libc/AOR_v20.02/math/tools/sin.sollya
libc/AOR_v20.02/math/tools/v_exp.sollya
libc/AOR_v20.02/math/tools/v_log.sollya
libc/AOR_v20.02/math/tools/v_sin.sollya
libc/AOR_v20.02/math/v_cos.c
libc/AOR_v20.02/math/v_cosf.c
libc/AOR_v20.02/math/v_exp.c
libc/AOR_v20.02/math/v_exp.h
libc/AOR_v20.02/math/v_exp2f.c
libc/AOR_v20.02/math/v_exp2f_1u.c
libc/AOR_v20.02/math/v_exp_data.c
libc/AOR_v20.02/math/v_expf.c
libc/AOR_v20.02/math/v_expf_1u.c
libc/AOR_v20.02/math/v_log.c
libc/AOR_v20.02/math/v_log.h
libc/AOR_v20.02/math/v_log_data.c
libc/AOR_v20.02/math/v_logf.c
libc/AOR_v20.02/math/v_math.h
libc/AOR_v20.02/math/v_pow.c
libc/AOR_v20.02/math/v_powf.c
libc/AOR_v20.02/math/v_sin.c
libc/AOR_v20.02/math/v_sinf.c
libc/AOR_v20.02/math/vn_cos.c
libc/AOR_v20.02/math/vn_cosf.c
libc/AOR_v20.02/math/vn_exp.c
libc/AOR_v20.02/math/vn_exp2f.c
libc/AOR_v20.02/math/vn_exp2f_1u.c
libc/AOR_v20.02/math/vn_expf.c
libc/AOR_v20.02/math/vn_expf_1u.c
libc/AOR_v20.02/math/vn_log.c
libc/AOR_v20.02/math/vn_logf.c
libc/AOR_v20.02/math/vn_pow.c
libc/AOR_v20.02/math/vn_powf.c
libc/AOR_v20.02/math/vn_sin.c
libc/AOR_v20.02/math/vn_sinf.c
libc/AOR_v20.02/networking/Dir.mk
libc/AOR_v20.02/networking/aarch64/chksum_simd.c
libc/AOR_v20.02/networking/arm/chksum_simd.c
libc/AOR_v20.02/networking/chksum.c
libc/AOR_v20.02/networking/chksum_common.h
libc/AOR_v20.02/networking/include/networking.h
libc/AOR_v20.02/networking/test/chksum.c
libc/AOR_v20.02/string/Dir.mk
libc/AOR_v20.02/string/aarch64/check-arch.S
libc/AOR_v20.02/string/aarch64/memchr-sve.S
libc/AOR_v20.02/string/aarch64/memchr.S
libc/AOR_v20.02/string/aarch64/memcmp-sve.S
libc/AOR_v20.02/string/aarch64/memcmp.S
libc/AOR_v20.02/string/aarch64/memcpy-advsimd.S
libc/AOR_v20.02/string/aarch64/memcpy.S
libc/AOR_v20.02/string/aarch64/memset.S
libc/AOR_v20.02/string/aarch64/stpcpy-sve.S
libc/AOR_v20.02/string/aarch64/stpcpy.S
libc/AOR_v20.02/string/aarch64/strchr-mte.S
libc/AOR_v20.02/string/aarch64/strchr-sve.S
libc/AOR_v20.02/string/aarch64/strchr.S
libc/AOR_v20.02/string/aarch64/strchrnul-sve.S
libc/AOR_v20.02/string/aarch64/strchrnul.S
libc/AOR_v20.02/string/aarch64/strcmp-sve.S
libc/AOR_v20.02/string/aarch64/strcmp.S
libc/AOR_v20.02/string/aarch64/strcpy-sve.S
libc/AOR_v20.02/string/aarch64/strcpy.S
libc/AOR_v20.02/string/aarch64/strlen-mte.S
libc/AOR_v20.02/string/aarch64/strlen-sve.S
libc/AOR_v20.02/string/aarch64/strlen.S
libc/AOR_v20.02/string/aarch64/strncmp-sve.S
libc/AOR_v20.02/string/aarch64/strncmp.S
libc/AOR_v20.02/string/aarch64/strnlen-sve.S
libc/AOR_v20.02/string/aarch64/strnlen.S
libc/AOR_v20.02/string/aarch64/strrchr-sve.S
libc/AOR_v20.02/string/aarch64/strrchr.S
libc/AOR_v20.02/string/arm/check-arch.S
libc/AOR_v20.02/string/arm/memchr.S
libc/AOR_v20.02/string/arm/memcpy.S
libc/AOR_v20.02/string/arm/memset.S
libc/AOR_v20.02/string/arm/strcmp-armv6m.S
libc/AOR_v20.02/string/arm/strcmp.S
libc/AOR_v20.02/string/arm/strcpy.c
libc/AOR_v20.02/string/arm/strlen-armv6t2.S
libc/AOR_v20.02/string/asmdefs.h
libc/AOR_v20.02/string/include/stringlib.h
libc/AOR_v20.02/string/test/memchr.c
libc/AOR_v20.02/string/test/memcmp.c
libc/AOR_v20.02/string/test/memcpy.c
libc/AOR_v20.02/string/test/memmove.c
libc/AOR_v20.02/string/test/memset.c
libc/AOR_v20.02/string/test/stpcpy.c
libc/AOR_v20.02/string/test/strchr.c
libc/AOR_v20.02/string/test/strchrnul.c
libc/AOR_v20.02/string/test/strcmp.c
libc/AOR_v20.02/string/test/strcpy.c
libc/AOR_v20.02/string/test/strlen.c
libc/AOR_v20.02/string/test/strncmp.c
libc/AOR_v20.02/string/test/strnlen.c
libc/AOR_v20.02/string/test/strrchr.c
libc/AOR_v20.02/string/x86_64/check-arch.S
Modified:
Removed:
################################################################################
diff --git a/libc/AOR_v20.02/Makefile b/libc/AOR_v20.02/Makefile
new file mode 100644
index 000000000000..53e0245f82c4
--- /dev/null
+++ b/libc/AOR_v20.02/Makefile
@@ -0,0 +1,90 @@
+# Makefile - requires GNU make
+#
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+srcdir = .
+prefix = /usr
+bindir = $(prefix)/bin
+libdir = $(prefix)/lib
+includedir = $(prefix)/include
+
+# Configure these in config.mk, do not make changes in this file.
+SUBS = math string networking
+HOST_CC = cc
+HOST_CFLAGS = -std=c99 -O2
+HOST_LDFLAGS =
+HOST_LDLIBS =
+EMULATOR =
+CPPFLAGS =
+CFLAGS = -std=c99 -O2
+CFLAGS_SHARED = -fPIC
+CFLAGS_ALL = -Ibuild/include $(CPPFLAGS) $(CFLAGS)
+LDFLAGS =
+LDLIBS =
+AR = $(CROSS_COMPILE)ar
+RANLIB = $(CROSS_COMPILE)ranlib
+INSTALL = install
+
+all:
+
+-include config.mk
+
+$(foreach sub,$(SUBS),$(eval include $(srcdir)/$(sub)/Dir.mk))
+
+# Required targets of subproject foo:
+# all-foo
+# check-foo
+# clean-foo
+# install-foo
+# Required make variables of subproject foo:
+# foo-files: Built files (all in build/).
+# Make variables used by subproject foo:
+# foo-...: Variables defined in foo/Dir.mk or by config.mk.
+
+all: $(SUBS:%=all-%)
+
+ALL_FILES = $(foreach sub,$(SUBS),$($(sub)-files))
+DIRS = $(sort $(patsubst %/,%,$(dir $(ALL_FILES))))
+$(ALL_FILES): | $(DIRS)
+$(DIRS):
+ mkdir -p $@
+
+$(filter %.os,$(ALL_FILES)): CFLAGS_ALL += $(CFLAGS_SHARED)
+
+build/%.o: $(srcdir)/%.S
+ $(CC) $(CFLAGS_ALL) -c -o $@ $<
+
+build/%.o: $(srcdir)/%.c
+ $(CC) $(CFLAGS_ALL) -c -o $@ $<
+
+build/%.os: $(srcdir)/%.S
+ $(CC) $(CFLAGS_ALL) -c -o $@ $<
+
+build/%.os: $(srcdir)/%.c
+ $(CC) $(CFLAGS_ALL) -c -o $@ $<
+
+clean: $(SUBS:%=clean-%)
+ rm -rf build
+
+distclean: clean
+ rm -f config.mk
+
+$(DESTDIR)$(bindir)/%: build/bin/%
+ $(INSTALL) -D $< $@
+
+$(DESTDIR)$(libdir)/%.so: build/lib/%.so
+ $(INSTALL) -D $< $@
+
+$(DESTDIR)$(libdir)/%: build/lib/%
+ $(INSTALL) -m 644 -D $< $@
+
+$(DESTDIR)$(includedir)/%: build/include/%
+ $(INSTALL) -m 644 -D $< $@
+
+install: $(SUBS:%=install-%)
+
+check: $(SUBS:%=check-%)
+
+.PHONY: all clean distclean install check
diff --git a/libc/AOR_v20.02/config.mk.dist b/libc/AOR_v20.02/config.mk.dist
new file mode 100644
index 000000000000..240d4b6f4b4c
--- /dev/null
+++ b/libc/AOR_v20.02/config.mk.dist
@@ -0,0 +1,68 @@
+# Example config.mk
+#
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+# Subprojects to build
+SUBS = math string networking
+
+# Target architecture: aarch64, arm or x86_64
+ARCH = aarch64
+
+# Compiler for the target
+CC = $(CROSS_COMPILE)gcc
+CFLAGS = -std=c99 -pipe -O3
+CFLAGS += -Wall -Wno-missing-braces
+CFLAGS += -Werror=implicit-function-declaration
+
+# Used for test case generator that is executed on the host
+HOST_CC = gcc
+HOST_CFLAGS = -std=c99 -O2
+HOST_CFLAGS += -Wall -Wno-unused-function
+
+# Enable debug info.
+HOST_CFLAGS += -g
+CFLAGS += -g
+
+# Optimize the shared libraries on aarch64 assuming they fit in 1M.
+#CFLAGS_SHARED = -fPIC -mcmodel=tiny
+
+# Use for cross compilation with gcc.
+#CROSS_COMPILE = aarch64-none-linux-gnu-
+
+# Use with cross testing.
+#EMULATOR = qemu-aarch64-static
+#EMULATOR = sh -c 'scp $$1 user at host:/dir && ssh user at host /dir/"$$@"' --
+
+# Additional flags for subprojects.
+math-cflags =
+math-ldlibs =
+math-ulpflags =
+math-testflags =
+string-cflags =
+networking-cflags =
+
+# Use if mpfr is available on the target for ulp error checking.
+#math-ldlibs += -lmpfr -lgmp
+#math-cflags += -DUSE_MPFR
+
+# Use with gcc.
+math-cflags += -frounding-math -fexcess-precision=standard -fno-stack-protector
+math-cflags += -ffp-contract=fast -fno-math-errno
+
+# Use with clang.
+#math-cflags += -ffp-contract=fast
+
+# Disable vector math code
+#math-cflags += -DWANT_VMATH=0
+
+# Disable fenv checks
+#math-ulpflags = -q -f
+#math-testflags = -nostatus
+
+# Enable assertion checks.
+#networking-cflags += -DWANT_ASSERT
+
+# Avoid auto-vectorization of scalar code and unroll loops
+networking-cflags += -O2 -fno-tree-vectorize -funroll-loops
diff --git a/libc/AOR_v20.02/math/Dir.mk b/libc/AOR_v20.02/math/Dir.mk
new file mode 100644
index 000000000000..6be9115e86b0
--- /dev/null
+++ b/libc/AOR_v20.02/math/Dir.mk
@@ -0,0 +1,111 @@
+# Makefile fragment - requires GNU make
+#
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+S := $(srcdir)/math
+B := build/math
+
+math-lib-srcs := $(wildcard $(S)/*.[cS])
+math-test-srcs := \
+ $(S)/test/mathtest.c \
+ $(S)/test/mathbench.c \
+ $(S)/test/ulp.c \
+
+math-test-host-srcs := $(wildcard $(S)/test/rtest/*.[cS])
+
+math-includes := $(patsubst $(S)/%,build/%,$(wildcard $(S)/include/*.h))
+
+math-libs := \
+ build/lib/libmathlib.so \
+ build/lib/libmathlib.a \
+
+math-tools := \
+ build/bin/mathtest \
+ build/bin/mathbench \
+ build/bin/mathbench_libc \
+ build/bin/runulp.sh \
+ build/bin/ulp \
+
+math-host-tools := \
+ build/bin/rtest \
+
+math-lib-objs := $(patsubst $(S)/%,$(B)/%.o,$(basename $(math-lib-srcs)))
+math-test-objs := $(patsubst $(S)/%,$(B)/%.o,$(basename $(math-test-srcs)))
+math-host-objs := $(patsubst $(S)/%,$(B)/%.o,$(basename $(math-test-host-srcs)))
+math-target-objs := $(math-lib-objs) $(math-test-objs)
+math-objs := $(math-target-objs) $(math-target-objs:%.o=%.os) $(math-host-objs)
+
+math-files := \
+ $(math-objs) \
+ $(math-libs) \
+ $(math-tools) \
+ $(math-host-tools) \
+ $(math-includes) \
+
+all-math: $(math-libs) $(math-tools) $(math-includes)
+
+$(math-objs): $(math-includes)
+$(math-objs): CFLAGS_ALL += $(math-cflags)
+$(B)/test/mathtest.o: CFLAGS_ALL += -fmath-errno
+$(math-host-objs): CC = $(HOST_CC)
+$(math-host-objs): CFLAGS_ALL = $(HOST_CFLAGS)
+
+$(B)/test/ulp.o: $(S)/test/ulp.h
+
+build/lib/libmathlib.so: $(math-lib-objs:%.o=%.os)
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS) -shared -o $@ $^
+
+build/lib/libmathlib.a: $(math-lib-objs)
+ rm -f $@
+ $(AR) rc $@ $^
+ $(RANLIB) $@
+
+$(math-host-tools): HOST_LDLIBS += -lm -lmpfr -lmpc
+$(math-tools): LDLIBS += $(math-ldlibs) -lm
+
+build/bin/rtest: $(math-host-objs)
+ $(HOST_CC) $(HOST_CFLAGS) $(HOST_LDFLAGS) -o $@ $^ $(HOST_LDLIBS)
+
+build/bin/mathtest: $(B)/test/mathtest.o build/lib/libmathlib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS) -static -o $@ $^ $(LDLIBS)
+
+build/bin/mathbench: $(B)/test/mathbench.o build/lib/libmathlib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS) -static -o $@ $^ $(LDLIBS)
+
+# This is not ideal, but allows custom symbols in mathbench to get resolved.
+build/bin/mathbench_libc: $(B)/test/mathbench.o build/lib/libmathlib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS) -static -o $@ $< $(LDLIBS) -lc build/lib/libmathlib.a -lm
+
+build/bin/ulp: $(B)/test/ulp.o build/lib/libmathlib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS) -static -o $@ $^ $(LDLIBS)
+
+build/include/%.h: $(S)/include/%.h
+ cp $< $@
+
+build/bin/%.sh: $(S)/test/%.sh
+ cp $< $@
+
+math-tests := $(wildcard $(S)/test/testcases/directed/*.tst)
+math-rtests := $(wildcard $(S)/test/testcases/random/*.tst)
+
+check-math-test: $(math-tools)
+ cat $(math-tests) | $(EMULATOR) build/bin/mathtest $(math-testflags)
+
+check-math-rtest: $(math-host-tools) $(math-tools)
+ cat $(math-rtests) | build/bin/rtest | $(EMULATOR) build/bin/mathtest $(math-testflags)
+
+check-math-ulp: $(math-tools)
+ ULPFLAGS="$(math-ulpflags)" build/bin/runulp.sh $(EMULATOR)
+
+check-math: check-math-test check-math-rtest check-math-ulp
+
+install-math: \
+ $(math-libs:build/lib/%=$(DESTDIR)$(libdir)/%) \
+ $(math-includes:build/include/%=$(DESTDIR)$(includedir)/%)
+
+clean-math:
+ rm -f $(math-files)
+
+.PHONY: all-math check-math-test check-math-rtest check-math-ulp check-math install-math clean-math
diff --git a/libc/AOR_v20.02/math/cosf.c b/libc/AOR_v20.02/math/cosf.c
new file mode 100644
index 000000000000..1ab98a1dd60f
--- /dev/null
+++ b/libc/AOR_v20.02/math/cosf.c
@@ -0,0 +1,64 @@
+/*
+ * Single-precision cos function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <math.h>
+#include "math_config.h"
+#include "sincosf.h"
+
+/* Fast cosf implementation. Worst-case ULP is 0.5607, maximum relative
+ error is 0.5303 * 2^-23. A single-step range reduction is used for
+ small values. Large inputs have their range reduced using fast integer
+ arithmetic. */
+float
+cosf (float y)
+{
+ double x = y;
+ double s;
+ int n;
+ const sincos_t *p = &__sincosf_table[0];
+
+ if (abstop12 (y) < abstop12 (pio4))
+ {
+ double x2 = x * x;
+
+ if (unlikely (abstop12 (y) < abstop12 (0x1p-12f)))
+ return 1.0f;
+
+ return sinf_poly (x, x2, p, 1);
+ }
+ else if (likely (abstop12 (y) < abstop12 (120.0f)))
+ {
+ x = reduce_fast (x, p, &n);
+
+ /* Setup the signs for sin and cos. */
+ s = p->sign[n & 3];
+
+ if (n & 2)
+ p = &__sincosf_table[1];
+
+ return sinf_poly (x * s, x * x, p, n ^ 1);
+ }
+ else if (abstop12 (y) < abstop12 (INFINITY))
+ {
+ uint32_t xi = asuint (y);
+ int sign = xi >> 31;
+
+ x = reduce_large (xi, &n);
+
+ /* Setup signs for sin and cos - include original sign. */
+ s = p->sign[(n + sign) & 3];
+
+ if ((n + sign) & 2)
+ p = &__sincosf_table[1];
+
+ return sinf_poly (x * s, x * x, p, n ^ 1);
+ }
+ else
+ return __math_invalidf (y);
+}
diff --git a/libc/AOR_v20.02/math/exp.c b/libc/AOR_v20.02/math/exp.c
new file mode 100644
index 000000000000..d0996023188c
--- /dev/null
+++ b/libc/AOR_v20.02/math/exp.c
@@ -0,0 +1,177 @@
+/*
+ * Double-precision e^x function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <float.h>
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define N (1 << EXP_TABLE_BITS)
+#define InvLn2N __exp_data.invln2N
+#define NegLn2hiN __exp_data.negln2hiN
+#define NegLn2loN __exp_data.negln2loN
+#define Shift __exp_data.shift
+#define T __exp_data.tab
+#define C2 __exp_data.poly[5 - EXP_POLY_ORDER]
+#define C3 __exp_data.poly[6 - EXP_POLY_ORDER]
+#define C4 __exp_data.poly[7 - EXP_POLY_ORDER]
+#define C5 __exp_data.poly[8 - EXP_POLY_ORDER]
+#define C6 __exp_data.poly[9 - EXP_POLY_ORDER]
+
+/* Handle cases that may overflow or underflow when computing the result that
+ is scale*(1+TMP) without intermediate rounding. The bit representation of
+ scale is in SBITS, however it has a computed exponent that may have
+ overflown into the sign bit so that needs to be adjusted before using it as
+ a double. (int32_t)KI is the k used in the argument reduction and exponent
+ adjustment of scale, positive k here means the result may overflow and
+ negative k means the result may underflow. */
+static inline double
+specialcase (double_t tmp, uint64_t sbits, uint64_t ki)
+{
+ double_t scale, y;
+
+ if ((ki & 0x80000000) == 0)
+ {
+ /* k > 0, the exponent of scale might have overflowed by <= 460. */
+ sbits -= 1009ull << 52;
+ scale = asdouble (sbits);
+ y = 0x1p1009 * (scale + scale * tmp);
+ return check_oflow (eval_as_double (y));
+ }
+ /* k < 0, need special care in the subnormal range. */
+ sbits += 1022ull << 52;
+ scale = asdouble (sbits);
+ y = scale + scale * tmp;
+ if (y < 1.0)
+ {
+ /* Round y to the right precision before scaling it into the subnormal
+ range to avoid double rounding that can cause 0.5+E/2 ulp error where
+ E is the worst-case ulp error outside the subnormal range. So this
+ is only useful if the goal is better than 1 ulp worst-case error. */
+ double_t hi, lo;
+ lo = scale - y + scale * tmp;
+ hi = 1.0 + y;
+ lo = 1.0 - hi + y + lo;
+ y = eval_as_double (hi + lo) - 1.0;
+ /* Avoid -0.0 with downward rounding. */
+ if (WANT_ROUNDING && y == 0.0)
+ y = 0.0;
+ /* The underflow exception needs to be signaled explicitly. */
+ force_eval_double (opt_barrier_double (0x1p-1022) * 0x1p-1022);
+ }
+ y = 0x1p-1022 * y;
+ return check_uflow (eval_as_double (y));
+}
+
+/* Top 12 bits of a double (sign and exponent bits). */
+static inline uint32_t
+top12 (double x)
+{
+ return asuint64 (x) >> 52;
+}
+
+/* Computes exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|.
+ If hastail is 0 then xtail is assumed to be 0 too. */
+static inline double
+exp_inline (double x, double xtail, int hastail)
+{
+ uint32_t abstop;
+ uint64_t ki, idx, top, sbits;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, z, r, r2, scale, tail, tmp;
+
+ abstop = top12 (x) & 0x7ff;
+ if (unlikely (abstop - top12 (0x1p-54) >= top12 (512.0) - top12 (0x1p-54)))
+ {
+ if (abstop - top12 (0x1p-54) >= 0x80000000)
+ /* Avoid spurious underflow for tiny x. */
+ /* Note: 0 is common input. */
+ return WANT_ROUNDING ? 1.0 + x : 1.0;
+ if (abstop >= top12 (1024.0))
+ {
+ if (asuint64 (x) == asuint64 (-INFINITY))
+ return 0.0;
+ if (abstop >= top12 (INFINITY))
+ return 1.0 + x;
+ if (asuint64 (x) >> 63)
+ return __math_uflow (0);
+ else
+ return __math_oflow (0);
+ }
+ /* Large x is special cased below. */
+ abstop = 0;
+ }
+
+ /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */
+ /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */
+ z = InvLn2N * x;
+#if TOINT_INTRINSICS
+ kd = roundtoint (z);
+ ki = converttoint (z);
+#elif EXP_USE_TOINT_NARROW
+ /* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
+ kd = eval_as_double (z + Shift);
+ ki = asuint64 (kd) >> 16;
+ kd = (double_t) (int32_t) ki;
+#else
+ /* z - kd is in [-1, 1] in non-nearest rounding modes. */
+ kd = eval_as_double (z + Shift);
+ ki = asuint64 (kd);
+ kd -= Shift;
+#endif
+ r = x + kd * NegLn2hiN + kd * NegLn2loN;
+ /* The code assumes 2^-200 < |xtail| < 2^-8/N. */
+ if (hastail)
+ r += xtail;
+ /* 2^(k/N) ~= scale * (1 + tail). */
+ idx = 2 * (ki % N);
+ top = ki << (52 - EXP_TABLE_BITS);
+ tail = asdouble (T[idx]);
+ /* This is only a valid scale when -1023*N < k < 1024*N. */
+ sbits = T[idx + 1] + top;
+ /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ r2 = r * r;
+ /* Without fma the worst case error is 0.25/N ulp larger. */
+ /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */
+#if EXP_POLY_ORDER == 4
+ tmp = tail + r + r2 * C2 + r * r2 * (C3 + r * C4);
+#elif EXP_POLY_ORDER == 5
+ tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5);
+#elif EXP_POLY_ORDER == 6
+ tmp = tail + r + r2 * (0.5 + r * C3) + r2 * r2 * (C4 + r * C5 + r2 * C6);
+#endif
+ if (unlikely (abstop == 0))
+ return specialcase (tmp, sbits, ki);
+ scale = asdouble (sbits);
+ /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there
+ is no spurious underflow here even without fma. */
+ return eval_as_double (scale + scale * tmp);
+}
+
+double
+exp (double x)
+{
+ return exp_inline (x, 0, 0);
+}
+
+/* May be useful for implementing pow where more than double
+ precision input is needed. */
+double
+__exp_dd (double x, double xtail)
+{
+ return exp_inline (x, xtail, 1);
+}
+#if USE_GLIBC_ABI
+strong_alias (exp, __exp_finite)
+hidden_alias (exp, __ieee754_exp)
+hidden_alias (__exp_dd, __exp1)
+# if LDBL_MANT_DIG == 53
+long double expl (long double x) { return exp (x); }
+# endif
+#endif
diff --git a/libc/AOR_v20.02/math/exp2.c b/libc/AOR_v20.02/math/exp2.c
new file mode 100644
index 000000000000..53296ab7c581
--- /dev/null
+++ b/libc/AOR_v20.02/math/exp2.c
@@ -0,0 +1,144 @@
+/*
+ * Double-precision 2^x function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <float.h>
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define N (1 << EXP_TABLE_BITS)
+#define Shift __exp_data.exp2_shift
+#define T __exp_data.tab
+#define C1 __exp_data.exp2_poly[0]
+#define C2 __exp_data.exp2_poly[1]
+#define C3 __exp_data.exp2_poly[2]
+#define C4 __exp_data.exp2_poly[3]
+#define C5 __exp_data.exp2_poly[4]
+#define C6 __exp_data.exp2_poly[5]
+
+/* Handle cases that may overflow or underflow when computing the result that
+ is scale*(1+TMP) without intermediate rounding. The bit representation of
+ scale is in SBITS, however it has a computed exponent that may have
+ overflown into the sign bit so that needs to be adjusted before using it as
+ a double. (int32_t)KI is the k used in the argument reduction and exponent
+ adjustment of scale, positive k here means the result may overflow and
+ negative k means the result may underflow. */
+static inline double
+specialcase (double_t tmp, uint64_t sbits, uint64_t ki)
+{
+ double_t scale, y;
+
+ if ((ki & 0x80000000) == 0)
+ {
+ /* k > 0, the exponent of scale might have overflowed by 1. */
+ sbits -= 1ull << 52;
+ scale = asdouble (sbits);
+ y = 2 * (scale + scale * tmp);
+ return check_oflow (eval_as_double (y));
+ }
+ /* k < 0, need special care in the subnormal range. */
+ sbits += 1022ull << 52;
+ scale = asdouble (sbits);
+ y = scale + scale * tmp;
+ if (y < 1.0)
+ {
+ /* Round y to the right precision before scaling it into the subnormal
+ range to avoid double rounding that can cause 0.5+E/2 ulp error where
+ E is the worst-case ulp error outside the subnormal range. So this
+ is only useful if the goal is better than 1 ulp worst-case error. */
+ double_t hi, lo;
+ lo = scale - y + scale * tmp;
+ hi = 1.0 + y;
+ lo = 1.0 - hi + y + lo;
+ y = eval_as_double (hi + lo) - 1.0;
+ /* Avoid -0.0 with downward rounding. */
+ if (WANT_ROUNDING && y == 0.0)
+ y = 0.0;
+ /* The underflow exception needs to be signaled explicitly. */
+ force_eval_double (opt_barrier_double (0x1p-1022) * 0x1p-1022);
+ }
+ y = 0x1p-1022 * y;
+ return check_uflow (eval_as_double (y));
+}
+
+/* Top 12 bits of a double (sign and exponent bits). */
+static inline uint32_t
+top12 (double x)
+{
+ return asuint64 (x) >> 52;
+}
+
+double
+exp2 (double x)
+{
+ uint32_t abstop;
+ uint64_t ki, idx, top, sbits;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, r, r2, scale, tail, tmp;
+
+ abstop = top12 (x) & 0x7ff;
+ if (unlikely (abstop - top12 (0x1p-54) >= top12 (512.0) - top12 (0x1p-54)))
+ {
+ if (abstop - top12 (0x1p-54) >= 0x80000000)
+ /* Avoid spurious underflow for tiny x. */
+ /* Note: 0 is common input. */
+ return WANT_ROUNDING ? 1.0 + x : 1.0;
+ if (abstop >= top12 (1024.0))
+ {
+ if (asuint64 (x) == asuint64 (-INFINITY))
+ return 0.0;
+ if (abstop >= top12 (INFINITY))
+ return 1.0 + x;
+ if (!(asuint64 (x) >> 63))
+ return __math_oflow (0);
+ else if (asuint64 (x) >= asuint64 (-1075.0))
+ return __math_uflow (0);
+ }
+ if (2 * asuint64 (x) > 2 * asuint64 (928.0))
+ /* Large x is special cased below. */
+ abstop = 0;
+ }
+
+ /* exp2(x) = 2^(k/N) * 2^r, with 2^r in [2^(-1/2N),2^(1/2N)]. */
+ /* x = k/N + r, with int k and r in [-1/2N, 1/2N]. */
+ kd = eval_as_double (x + Shift);
+ ki = asuint64 (kd); /* k. */
+ kd -= Shift; /* k/N for int k. */
+ r = x - kd;
+ /* 2^(k/N) ~= scale * (1 + tail). */
+ idx = 2 * (ki % N);
+ top = ki << (52 - EXP_TABLE_BITS);
+ tail = asdouble (T[idx]);
+ /* This is only a valid scale when -1023*N < k < 1024*N. */
+ sbits = T[idx + 1] + top;
+ /* exp2(x) = 2^(k/N) * 2^r ~= scale + scale * (tail + 2^r - 1). */
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ r2 = r * r;
+ /* Without fma the worst case error is 0.5/N ulp larger. */
+ /* Worst case error is less than 0.5+0.86/N+(abs poly error * 2^53) ulp. */
+#if EXP2_POLY_ORDER == 4
+ tmp = tail + r * C1 + r2 * C2 + r * r2 * (C3 + r * C4);
+#elif EXP2_POLY_ORDER == 5
+ tmp = tail + r * C1 + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5);
+#elif EXP2_POLY_ORDER == 6
+ tmp = tail + r * C1 + r2 * (0.5 + r * C3) + r2 * r2 * (C4 + r * C5 + r2 * C6);
+#endif
+ if (unlikely (abstop == 0))
+ return specialcase (tmp, sbits, ki);
+ scale = asdouble (sbits);
+ /* Note: tmp == 0 or |tmp| > 2^-65 and scale > 2^-928, so there
+ is no spurious underflow here even without fma. */
+ return eval_as_double (scale + scale * tmp);
+}
+#if USE_GLIBC_ABI
+strong_alias (exp2, __exp2_finite)
+hidden_alias (exp2, __ieee754_exp2)
+# if LDBL_MANT_DIG == 53
+long double exp2l (long double x) { return exp2 (x); }
+# endif
+#endif
diff --git a/libc/AOR_v20.02/math/exp2f.c b/libc/AOR_v20.02/math/exp2f.c
new file mode 100644
index 000000000000..4259e29777e1
--- /dev/null
+++ b/libc/AOR_v20.02/math/exp2f.c
@@ -0,0 +1,81 @@
+/*
+ * Single-precision 2^x function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+EXP2F_TABLE_BITS = 5
+EXP2F_POLY_ORDER = 3
+
+ULP error: 0.502 (nearest rounding.)
+Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
+Wrong count: 168353 (all nearest rounding wrong results with fma.)
+Non-nearest ULP error: 1 (rounded ULP error)
+*/
+
+#define N (1 << EXP2F_TABLE_BITS)
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly
+#define SHIFT __exp2f_data.shift_scaled
+
+static inline uint32_t
+top12 (float x)
+{
+ return asuint (x) >> 20;
+}
+
+float
+exp2f (float x)
+{
+ uint32_t abstop;
+ uint64_t ki, t;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, xd, z, r, r2, y, s;
+
+ xd = (double_t) x;
+ abstop = top12 (x) & 0x7ff;
+ if (unlikely (abstop >= top12 (128.0f)))
+ {
+ /* |x| >= 128 or x is nan. */
+ if (asuint (x) == asuint (-INFINITY))
+ return 0.0f;
+ if (abstop >= top12 (INFINITY))
+ return x + x;
+ if (x > 0.0f)
+ return __math_oflowf (0);
+ if (x <= -150.0f)
+ return __math_uflowf (0);
+#if WANT_ERRNO_UFLOW
+ if (x < -149.0f)
+ return __math_may_uflowf (0);
+#endif
+ }
+
+ /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */
+ kd = eval_as_double (xd + SHIFT);
+ ki = asuint64 (kd);
+ kd -= SHIFT; /* k/N for int k. */
+ r = xd - kd;
+
+ /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+ t = T[ki % N];
+ t += ki << (52 - EXP2F_TABLE_BITS);
+ s = asdouble (t);
+ z = C[0] * r + C[1];
+ r2 = r * r;
+ y = C[2] * r + 1;
+ y = z * r2 + y;
+ y = y * s;
+ return eval_as_float (y);
+}
+#if USE_GLIBC_ABI
+strong_alias (exp2f, __exp2f_finite)
+hidden_alias (exp2f, __ieee754_exp2f)
+#endif
diff --git a/libc/AOR_v20.02/math/exp2f_data.c b/libc/AOR_v20.02/math/exp2f_data.c
new file mode 100644
index 000000000000..063075006328
--- /dev/null
+++ b/libc/AOR_v20.02/math/exp2f_data.c
@@ -0,0 +1,79 @@
+/*
+ * Shared data between expf, exp2f and powf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+#define N (1 << EXP2F_TABLE_BITS)
+
+const struct exp2f_data __exp2f_data = {
+ /* tab[i] = uint(2^(i/N)) - (i << 52-BITS)
+ used for computing 2^(k/N) for an int |k| < 150 N as
+ double(tab[k%N] + (k << 52-BITS)) */
+ .tab = {
+#if N == 8
+0x3ff0000000000000, 0x3fef72b83c7d517b, 0x3fef06fe0a31b715, 0x3feebfdad5362a27,
+0x3feea09e667f3bcd, 0x3feeace5422aa0db, 0x3feee89f995ad3ad, 0x3fef5818dcfba487,
+#elif N == 16
+0x3ff0000000000000, 0x3fefb5586cf9890f, 0x3fef72b83c7d517b, 0x3fef387a6e756238,
+0x3fef06fe0a31b715, 0x3feedea64c123422, 0x3feebfdad5362a27, 0x3feeab07dd485429,
+0x3feea09e667f3bcd, 0x3feea11473eb0187, 0x3feeace5422aa0db, 0x3feec49182a3f090,
+0x3feee89f995ad3ad, 0x3fef199bdd85529c, 0x3fef5818dcfba487, 0x3fefa4afa2a490da,
+#elif N == 32
+0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
+0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
+0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
+0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
+0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
+0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
+0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
+0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
+#elif N == 64
+0x3ff0000000000000, 0x3fefec9a3e778061, 0x3fefd9b0d3158574, 0x3fefc74518759bc8,
+0x3fefb5586cf9890f, 0x3fefa3ec32d3d1a2, 0x3fef9301d0125b51, 0x3fef829aaea92de0,
+0x3fef72b83c7d517b, 0x3fef635beb6fcb75, 0x3fef54873168b9aa, 0x3fef463b88628cd6,
+0x3fef387a6e756238, 0x3fef2b4565e27cdd, 0x3fef1e9df51fdee1, 0x3fef1285a6e4030b,
+0x3fef06fe0a31b715, 0x3feefc08b26416ff, 0x3feef1a7373aa9cb, 0x3feee7db34e59ff7,
+0x3feedea64c123422, 0x3feed60a21f72e2a, 0x3feece086061892d, 0x3feec6a2b5c13cd0,
+0x3feebfdad5362a27, 0x3feeb9b2769d2ca7, 0x3feeb42b569d4f82, 0x3feeaf4736b527da,
+0x3feeab07dd485429, 0x3feea76f15ad2148, 0x3feea47eb03a5585, 0x3feea23882552225,
+0x3feea09e667f3bcd, 0x3fee9fb23c651a2f, 0x3fee9f75e8ec5f74, 0x3fee9feb564267c9,
+0x3feea11473eb0187, 0x3feea2f336cf4e62, 0x3feea589994cce13, 0x3feea8d99b4492ed,
+0x3feeace5422aa0db, 0x3feeb1ae99157736, 0x3feeb737b0cdc5e5, 0x3feebd829fde4e50,
+0x3feec49182a3f090, 0x3feecc667b5de565, 0x3feed503b23e255d, 0x3feede6b5579fdbf,
+0x3feee89f995ad3ad, 0x3feef3a2b84f15fb, 0x3feeff76f2fb5e47, 0x3fef0c1e904bc1d2,
+0x3fef199bdd85529c, 0x3fef27f12e57d14b, 0x3fef3720dcef9069, 0x3fef472d4a07897c,
+0x3fef5818dcfba487, 0x3fef69e603db3285, 0x3fef7c97337b9b5f, 0x3fef902ee78b3ff6,
+0x3fefa4afa2a490da, 0x3fefba1bee615a27, 0x3fefd0765b6e4540, 0x3fefe7c1819e90d8,
+#endif
+ },
+ .shift_scaled = 0x1.8p+52 / N,
+ .poly = {
+#if N == 8
+ 0x1.c6a00335106e2p-5, 0x1.ec0c313449f55p-3, 0x1.62e431111f69fp-1,
+#elif N == 16
+ 0x1.c6ac6aa313963p-5, 0x1.ebfff4532d9bap-3, 0x1.62e43001bc49fp-1,
+#elif N == 32
+ 0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1,
+#elif N == 64
+ 0x1.c6b04b4221b2ap-5, 0x1.ebfc213e184d7p-3, 0x1.62e42fefb5b7fp-1,
+#endif
+ },
+ .shift = 0x1.8p+52,
+ .invln2_scaled = 0x1.71547652b82fep+0 * N,
+ .poly_scaled = {
+#if N == 8
+ 0x1.c6a00335106e2p-5/N/N/N, 0x1.ec0c313449f55p-3/N/N, 0x1.62e431111f69fp-1/N,
+#elif N == 16
+ 0x1.c6ac6aa313963p-5/N/N/N, 0x1.ebfff4532d9bap-3/N/N, 0x1.62e43001bc49fp-1/N,
+#elif N == 32
+ 0x1.c6af84b912394p-5/N/N/N, 0x1.ebfce50fac4f3p-3/N/N, 0x1.62e42ff0c52d6p-1/N,
+#elif N == 64
+ 0x1.c6b04b4221b2ap-5/N/N/N, 0x1.ebfc213e184d7p-3/N/N, 0x1.62e42fefb5b7fp-1/N,
+#endif
+ },
+};
diff --git a/libc/AOR_v20.02/math/exp_data.c b/libc/AOR_v20.02/math/exp_data.c
new file mode 100644
index 000000000000..682eee860070
--- /dev/null
+++ b/libc/AOR_v20.02/math/exp_data.c
@@ -0,0 +1,1121 @@
+/*
+ * Shared data between exp, exp2 and pow.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+#define N (1 << EXP_TABLE_BITS)
+
+const struct exp_data __exp_data = {
+// N/ln2
+.invln2N = 0x1.71547652b82fep0 * N,
+// -ln2/N
+#if N == 64
+.negln2hiN = -0x1.62e42fefa0000p-7,
+.negln2loN = -0x1.cf79abc9e3b3ap-46,
+#elif N == 128
+.negln2hiN = -0x1.62e42fefa0000p-8,
+.negln2loN = -0x1.cf79abc9e3b3ap-47,
+#elif N == 256
+.negln2hiN = -0x1.62e42fefc0000p-9,
+.negln2loN = 0x1.c610ca86c3899p-45,
+#elif N == 512
+.negln2hiN = -0x1.62e42fef80000p-10,
+.negln2loN = -0x1.1cf79abc9e3b4p-45,
+#endif
+// Used for rounding when !TOINT_INTRINSICS
+#if EXP_USE_TOINT_NARROW
+.shift = 0x1800000000.8p0,
+#else
+.shift = 0x1.8p52,
+#endif
+// exp polynomial coefficients.
+.poly = {
+#if N == 64 && EXP_POLY_ORDER == 5 && !EXP_POLY_WIDE
+// abs error: 1.5543*2^-60
+// ulp error: 0.529 (0.533 without fma)
+// if |x| < ln2/128+eps
+// abs error if |x| < ln2/64: 1.7157*2^-50
+0x1.fffffffffdbcdp-2,
+0x1.555555555444cp-3,
+0x1.555573c6a9f7dp-5,
+0x1.1111266d28935p-7,
+#elif N == 64 && EXP_POLY_ORDER == 6 && EXP_POLY_WIDE
+// abs error: 1.6735*2^-64
+// ulp error: 0.518 (0.522 without fma)
+// if |x| < ln2/64
+0x1.5555555548f9ap-3,
+0x1.555555554bf5dp-5,
+0x1.11115b75f0f4dp-7,
+0x1.6c171a6b6303ep-10,
+#elif N == 128 && EXP_POLY_ORDER == 5 && !EXP_POLY_WIDE
+// abs error: 1.555*2^-66
+// ulp error: 0.509 (0.511 without fma)
+// if |x| < ln2/256+eps
+// abs error if |x| < ln2/256+0x1p-15: 1.09*2^-65
+// abs error if |x| < ln2/128: 1.7145*2^-56
+0x1.ffffffffffdbdp-2,
+0x1.555555555543cp-3,
+0x1.55555cf172b91p-5,
+0x1.1111167a4d017p-7,
+#elif N == 128 && EXP_POLY_ORDER == 5 && EXP_POLY_WIDE
+// abs error: 1.5542*2^-60
+// ulp error: 0.521 (0.523 without fma)
+// if |x| < ln2/128
+0x1.fffffffffdbcep-2,
+0x1.55555555543c2p-3,
+0x1.555573c64f2e3p-5,
+0x1.111126b4eff73p-7,
+#elif N == 128 && EXP_POLY_ORDER == 6 && EXP_POLY_WIDE
+// abs error: 1.6861*2^-71
+// ulp error: 0.509 (0.511 without fma)
+// if |x| < ln2/128
+0x1.55555555548fdp-3,
+0x1.555555555658fp-5,
+0x1.111123a859bb6p-7,
+0x1.6c16ba6920cabp-10,
+#elif N == 256 && EXP_POLY_ORDER == 4 && !EXP_POLY_WIDE
+// abs error: 1.43*2^-58
+// ulp error: 0.549 (0.550 without fma)
+// if |x| < ln2/512
+0x1p0, // unused
+0x1.fffffffffffd4p-2,
+0x1.5555571d6ef9p-3,
+0x1.5555576a5adcep-5,
+#elif N == 256 && EXP_POLY_ORDER == 5 && EXP_POLY_WIDE
+// abs error: 1.5547*2^-66
+// ulp error: 0.505 (0.506 without fma)
+// if |x| < ln2/256
+0x1.ffffffffffdbdp-2,
+0x1.555555555543cp-3,
+0x1.55555cf16e1edp-5,
+0x1.1111167a4b553p-7,
+#elif N == 512 && EXP_POLY_ORDER == 4 && !EXP_POLY_WIDE
+// abs error: 1.4300*2^-63
+// ulp error: 0.504
+// if |x| < ln2/1024
+// abs error if |x| < ln2/512: 1.0689*2^-55
+0x1p0, // unused
+0x1.ffffffffffffdp-2,
+0x1.555555c75bb6p-3,
+0x1.555555dec04a8p-5,
+#endif
+},
+.exp2_shift = 0x1.8p52 / N,
+// exp2 polynomial coefficients.
+.exp2_poly = {
+#if N == 64 && EXP2_POLY_ORDER == 6 && EXP2_POLY_WIDE
+// abs error: 1.3054*2^-63
+// ulp error: 0.515
+// if |x| < 1/64
+0x1.62e42fefa39efp-1,
+0x1.ebfbdff82c58fp-3,
+0x1.c6b08d7045cf1p-5,
+0x1.3b2ab6fb8fd0ep-7,
+0x1.5d884afec48d7p-10,
+0x1.43097dc684ae1p-13,
+#elif N == 128 && EXP2_POLY_ORDER == 5 && !EXP2_POLY_WIDE
+// abs error: 1.2195*2^-65
+// ulp error: 0.507 (0.511 without fma)
+// if |x| < 1/256
+// abs error if |x| < 1/128: 1.9941*2^-56
+0x1.62e42fefa39efp-1,
+0x1.ebfbdff82c424p-3,
+0x1.c6b08d70cf4b5p-5,
+0x1.3b2abd24650ccp-7,
+0x1.5d7e09b4e3a84p-10,
+#elif N == 256 && EXP2_POLY_ORDER == 5 && EXP2_POLY_WIDE
+// abs error: 1.2195*2^-65
+// ulp error: 0.504 (0.508 without fma)
+// if |x| < 1/256
+0x1.62e42fefa39efp-1,
+0x1.ebfbdff82c424p-3,
+0x1.c6b08d70cf4b5p-5,
+0x1.3b2abd24650ccp-7,
+0x1.5d7e09b4e3a84p-10,
+#elif N == 512 && EXP2_POLY_ORDER == 4 && !EXP2_POLY_WIDE
+// abs error: 1.4411*2^-64
+// ulp error: 0.5024 (0.5063 without fma)
+// if |x| < 1/1024
+// abs error if |x| < 1/512: 1.9430*2^-56
+0x1.62e42fefa39ecp-1,
+0x1.ebfbdff82c58bp-3,
+0x1.c6b08e46de41fp-5,
+0x1.3b2ab786ee1dap-7,
+#endif
+},
+// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N)
+// tab[2*k] = asuint64(T[k])
+// tab[2*k+1] = asuint64(H[k]) - (k << 52)/N
+.tab = {
+#if N == 64
+0x0, 0x3ff0000000000000,
+0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
+0x3c8cd2523567f613, 0x3fefd9b0d3158574,
+0x3c60f74e61e6c861, 0x3fefc74518759bc8,
+0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
+0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
+0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
+0xbc91c923b9d5f416, 0x3fef829aaea92de0,
+0xbc801b15eaa59348, 0x3fef72b83c7d517b,
+0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
+0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
+0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
+0x3c968efde3a8a894, 0x3fef387a6e756238,
+0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
+0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
+0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
+0x3c834d754db0abb6, 0x3fef06fe0a31b715,
+0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
+0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
+0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
+0x3c859f48a72a4c6d, 0x3feedea64c123422,
+0xbc58a78f4817895b, 0x3feed60a21f72e2a,
+0x3c4363ed60c2ac11, 0x3feece086061892d,
+0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
+0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
+0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
+0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
+0x3c93350518fdd78e, 0x3feeaf4736b527da,
+0x3c9063e1e21c5409, 0x3feeab07dd485429,
+0x3c9432e62b64c035, 0x3feea76f15ad2148,
+0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
+0xbc93cedd78565858, 0x3feea23882552225,
+0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
+0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
+0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
+0xbc8619321e55e68a, 0x3fee9feb564267c9,
+0xbc7b32dcb94da51d, 0x3feea11473eb0187,
+0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
+0xbc9369b6f13b3734, 0x3feea589994cce13,
+0xbc94d450d872576e, 0x3feea8d99b4492ed,
+0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
+0x3c7bf68359f35f44, 0x3feeb1ae99157736,
+0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
+0xbc92434322f4f9aa, 0x3feebd829fde4e50,
+0x3c71affc2b91ce27, 0x3feec49182a3f090,
+0xbc87c50422622263, 0x3feecc667b5de565,
+0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
+0x3c8469846e735ab3, 0x3feede6b5579fdbf,
+0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
+0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
+0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
+0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
+0x3c736eae30af0cb3, 0x3fef199bdd85529c,
+0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
+0x3c676b2c6c921968, 0x3fef3720dcef9069,
+0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
+0x3c74a385a63d07a7, 0x3fef5818dcfba487,
+0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
+0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
+0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
+0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
+0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
+0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
+0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
+#elif N == 128
+0x0, 0x3ff0000000000000,
+0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
+0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
+0xbc905e7a108766d1, 0x3fefe315e86e7f85,
+0x3c8cd2523567f613, 0x3fefd9b0d3158574,
+0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
+0x3c60f74e61e6c861, 0x3fefc74518759bc8,
+0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
+0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
+0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
+0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
+0xbc6a033489906e0b, 0x3fef9b66affed31b,
+0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
+0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
+0xbc91c923b9d5f416, 0x3fef829aaea92de0,
+0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
+0xbc801b15eaa59348, 0x3fef72b83c7d517b,
+0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
+0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
+0xbc96d99c7611eb26, 0x3fef5be084045cd4,
+0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
+0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
+0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
+0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
+0x3c968efde3a8a894, 0x3fef387a6e756238,
+0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
+0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
+0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
+0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
+0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
+0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
+0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
+0x3c834d754db0abb6, 0x3fef06fe0a31b715,
+0x3c864201e2ac744c, 0x3fef0170fc4cd831,
+0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
+0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
+0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
+0xbc9907f81b512d8e, 0x3feeecae6d05d866,
+0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
+0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
+0x3c859f48a72a4c6d, 0x3feedea64c123422,
+0xbc9312607a28698a, 0x3feeda4504ac801c,
+0xbc58a78f4817895b, 0x3feed60a21f72e2a,
+0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
+0x3c4363ed60c2ac11, 0x3feece086061892d,
+0x3c9666093b0664ef, 0x3feeca41ed1d0057,
+0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
+0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
+0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
+0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
+0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
+0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
+0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
+0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
+0x3c93350518fdd78e, 0x3feeaf4736b527da,
+0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
+0x3c9063e1e21c5409, 0x3feeab07dd485429,
+0x3c34c7855019c6ea, 0x3feea9268a5946b7,
+0x3c9432e62b64c035, 0x3feea76f15ad2148,
+0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
+0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
+0xbc845378892be9ae, 0x3feea34634ccc320,
+0xbc93cedd78565858, 0x3feea23882552225,
+0x3c5710aa807e1964, 0x3feea155d44ca973,
+0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
+0xbc6a12ad8734b982, 0x3feea012750bdabf,
+0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
+0xbc80dc3d54e08851, 0x3fee9f7df9519484,
+0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
+0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
+0xbc8619321e55e68a, 0x3fee9feb564267c9,
+0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
+0xbc7b32dcb94da51d, 0x3feea11473eb0187,
+0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
+0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
+0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
+0xbc9369b6f13b3734, 0x3feea589994cce13,
+0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
+0xbc94d450d872576e, 0x3feea8d99b4492ed,
+0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
+0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
+0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
+0x3c7bf68359f35f44, 0x3feeb1ae99157736,
+0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
+0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
+0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
+0xbc92434322f4f9aa, 0x3feebd829fde4e50,
+0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
+0x3c71affc2b91ce27, 0x3feec49182a3f090,
+0x3c6dd235e10a73bb, 0x3feec86319e32323,
+0xbc87c50422622263, 0x3feecc667b5de565,
+0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
+0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
+0x3c90cc319cee31d2, 0x3feed99e1330b358,
+0x3c8469846e735ab3, 0x3feede6b5579fdbf,
+0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
+0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
+0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
+0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
+0xbc90a40e3da6f640, 0x3feef9728de5593a,
+0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
+0xbc91eee26b588a35, 0x3fef05b030a1064a,
+0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
+0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
+0x3c736eae30af0cb3, 0x3fef199bdd85529c,
+0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
+0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
+0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
+0x3c676b2c6c921968, 0x3fef3720dcef9069,
+0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
+0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
+0xbc900dae3875a949, 0x3fef4f87080d89f2,
+0x3c74a385a63d07a7, 0x3fef5818dcfba487,
+0xbc82919e2040220f, 0x3fef60e316c98398,
+0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
+0x3c843a59ac016b4b, 0x3fef7321f301b460,
+0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
+0xbc892ab93b470dc9, 0x3fef864614f5a129,
+0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
+0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
+0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
+0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
+0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
+0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
+0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
+0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
+0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
+0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
+#elif N == 256
+0x0, 0x3ff0000000000000,
+0xbc84e82fc61851ac, 0x3feffb1afa5abcbf,
+0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
+0xbc82985dd8521d32, 0x3feff168143b0281,
+0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
+0x3c651e617061bfbd, 0x3fefe7d42e11bbcc,
+0xbc905e7a108766d1, 0x3fefe315e86e7f85,
+0x3c845fad437fa426, 0x3fefde5f72f654b1,
+0x3c8cd2523567f613, 0x3fefd9b0d3158574,
+0xbc954529642b232f, 0x3fefd50a0e3c1f89,
+0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
+0x3c8293708ef5c32e, 0x3fefcbd42b72a836,
+0x3c60f74e61e6c861, 0x3fefc74518759bc8,
+0xbc95b9280905b2a4, 0x3fefc2bdf66607e0,
+0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
+0x3c84f31f32c4b7e7, 0x3fefb9c79b1f3919,
+0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
+0x3c9407fb30d06420, 0x3fefb0f145e46c85,
+0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
+0xbc9a5d04b3b9911b, 0x3fefa83b23395dec,
+0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
+0xbc937a01f0739546, 0x3fef9fa55fdfa9c5,
+0xbc6a033489906e0b, 0x3fef9b66affed31b,
+0x3c8b8268b04ef0a5, 0x3fef973028d7233e,
+0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
+0xbc9ac46e44a2ebcc, 0x3fef8edbab5e2ab6,
+0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
+0xbc65704e90c9f860, 0x3fef86a814f204ab,
+0xbc91c923b9d5f416, 0x3fef829aaea92de0,
+0xbc897cea57e46280, 0x3fef7e95934f312e,
+0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
+0x3c56f01429e2b9d2, 0x3fef76a45471c3c2,
+0xbc801b15eaa59348, 0x3fef72b83c7d517b,
+0x3c6e653b2459034b, 0x3fef6ed48695bbc0,
+0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
+0x3c92cc7ea345b7dc, 0x3fef672658375d2f,
+0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
+0x3c957bfb2876ea9e, 0x3fef5f99f8138a1c,
+0xbc96d99c7611eb26, 0x3fef5be084045cd4,
+0x3c8cdc1873af2155, 0x3fef582f95281c6b,
+0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
+0xbc9493684653a131, 0x3fef50e75eb44027,
+0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
+0xbc98e2899077520a, 0x3fef49c18438ce4d,
+0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
+0x3c9120fcd4f59273, 0x3fef42be3578a819,
+0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
+0x3c89b788c188c9b8, 0x3fef3bdda27912d1,
+0x3c968efde3a8a894, 0x3fef387a6e756238,
+0x3c877afbca90ef84, 0x3fef351ffb82140a,
+0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
+0x3c91512f082876ee, 0x3fef2e85711ece75,
+0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
+0x3c9a02f0c7d75ec6, 0x3fef280e341ddf29,
+0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
+0xbc803297e78260bf, 0x3fef21ba7591bb70,
+0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
+0xbc95b77e5ccd9fbf, 0x3fef1b8a66d10f13,
+0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
+0xbc91e75c40b4251e, 0x3fef157e39771b2f,
+0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
+0x3c98a911f1f7785a, 0x3fef0f961f641589,
+0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
+0xbc61e7c998db7dbb, 0x3fef09d24abd886b,
+0x3c834d754db0abb6, 0x3fef06fe0a31b715,
+0x3c85425c11faadf4, 0x3fef0432edeeb2fd,
+0x3c864201e2ac744c, 0x3fef0170fc4cd831,
+0xbc979517a03e2847, 0x3feefeb83ba8ea32,
+0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
+0xbc800e2a46da4bee, 0x3feef96266e3fa2d,
+0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
+0xbc87430803972b34, 0x3feef431a2de883b,
+0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
+0xbc954de30ae02d94, 0x3feeef26231e754a,
+0xbc9907f81b512d8e, 0x3feeecae6d05d866,
+0xbc94f2487e1c03ec, 0x3feeea401b7140ef,
+0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
+0x3c914a5432fcb2f4, 0x3feee57fbfec6cf4,
+0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
+0x3c79c3bba5562a2f, 0x3feee0e544ede173,
+0x3c859f48a72a4c6d, 0x3feedea64c123422,
+0xbc85a71612e21658, 0x3feedc70df1c5175,
+0xbc9312607a28698a, 0x3feeda4504ac801c,
+0x3c86421f6f1d24d6, 0x3feed822c367a024,
+0xbc58a78f4817895b, 0x3feed60a21f72e2a,
+0xbc9348a6815fce65, 0x3feed3fb2709468a,
+0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
+0x3c835c43984d9871, 0x3feecffa3f84b9d4,
+0x3c4363ed60c2ac11, 0x3feece086061892d,
+0xbc632afc8d9473a0, 0x3feecc2042a7d232,
+0x3c9666093b0664ef, 0x3feeca41ed1d0057,
+0xbc95fc5e44de020e, 0x3feec86d668b3237,
+0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
+0xbc7ea0148327c42f, 0x3feec4e1e192aed2,
+0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
+0xbc7a843ad1a88022, 0x3feec17dea6db7d7,
+0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
+0x3c892ca3bf144e63, 0x3feebe41b817c114,
+0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
+0xbc902c99b04aa8b0, 0x3feebb2d81d8abff,
+0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
+0x3c73e34f67e67118, 0x3feeb8417f4531ee,
+0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
+0xbc75a3b1197ba0f0, 0x3feeb57de83f4eef,
+0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
+0x3c81bd2888075068, 0x3feeb2e2f4f6ad27,
+0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
+0xbc896be8ae89ef8f, 0x3feeb070dde910d2,
+0x3c93350518fdd78e, 0x3feeaf4736b527da,
+0xbc88e6ac90348602, 0x3feeae27dbe2c4cf,
+0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
+0xbc91af7f1365c3ac, 0x3feeac0827ff07cc,
+0x3c9063e1e21c5409, 0x3feeab07dd485429,
+0xbc943a3540d1898a, 0x3feeaa11fba87a03,
+0x3c34c7855019c6ea, 0x3feea9268a5946b7,
+0xbc951f58ddaa8090, 0x3feea84590998b93,
+0x3c9432e62b64c035, 0x3feea76f15ad2148,
+0xbc82e1648e50a17c, 0x3feea6a320dceb71,
+0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
+0x3c95f30eda98a575, 0x3feea52ae6cdf6f4,
+0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
+0x3c917ecda8a72159, 0x3feea3dd1d1929fd,
+0xbc845378892be9ae, 0x3feea34634ccc320,
+0xbc9345f3cee1ae6e, 0x3feea2b9febc8fb7,
+0xbc93cedd78565858, 0x3feea23882552225,
+0xbc85c33fdf910406, 0x3feea1c1c70833f6,
+0x3c5710aa807e1964, 0x3feea155d44ca973,
+0x3c81079ab5789604, 0x3feea0f4b19e9538,
+0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
+0x3c727df161cd7778, 0x3feea052fa75173e,
+0xbc6a12ad8734b982, 0x3feea012750bdabf,
+0x3c93f9924a05b767, 0x3fee9fdcddd47645,
+0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
+0xbc87557939a8b5ef, 0x3fee9f9298593ae5,
+0xbc80dc3d54e08851, 0x3fee9f7df9519484,
+0x3c51ed2f56fa9d1a, 0x3fee9f7466f42e87,
+0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
+0xbc88e67a9006c909, 0x3fee9f8286ead08a,
+0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
+0x3c86597566977ac8, 0x3fee9fbd35d7cbfd,
+0xbc8619321e55e68a, 0x3fee9feb564267c9,
+0x3c92c0b7028a5c3a, 0x3feea024b1ab6e09,
+0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
+0x3c8a30faf49cc78c, 0x3feea0b938ac1cf6,
+0xbc7b32dcb94da51d, 0x3feea11473eb0187,
+0xbc92dad3519d7b5b, 0x3feea17b0976cfdb,
+0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
+0x3c87d51410fd15c2, 0x3feea26a62ff86f0,
+0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
+0xbc760a3629969871, 0x3feea3878491c491,
+0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
+0x3c8b18c6e3fdef5d, 0x3feea4d2add106d9,
+0xbc9369b6f13b3734, 0x3feea589994cce13,
+0x3c90ec1ddcb1390a, 0x3feea64c1eb941f7,
+0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
+0xbc522cea4f3afa1e, 0x3feea7f4179f5b21,
+0xbc94d450d872576e, 0x3feea8d99b4492ed,
+0x3c7c88549b958471, 0x3feea9cad931a436,
+0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
+0x3c931143962f7877, 0x3feeabd0a478580f,
+0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
+0x3c93e9e96f112479, 0x3feeae05bad61778,
+0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
+0xbc8dac42a4a38df0, 0x3feeb06a5e0866d9,
+0x3c7bf68359f35f44, 0x3feeb1ae99157736,
+0x3c8b99dd98b1ed84, 0x3feeb2fed0282c8a,
+0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
+0xbc7885ad50cbb750, 0x3feeb5c353aa2fe2,
+0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
+0xbc82d5e85f3e0301, 0x3feeb8b82b5f98e5,
+0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
+0xbc51669428996971, 0x3feebbdd9a7670b3,
+0xbc92434322f4f9aa, 0x3feebd829fde4e50,
+0x3c71f2b2c1c4c014, 0x3feebf33e47a22a2,
+0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
+0xbc9294f304f166b6, 0x3feec2bb4d53fe0d,
+0x3c71affc2b91ce27, 0x3feec49182a3f090,
+0xbc8a1e58414c07d3, 0x3feec674194bb8d5,
+0x3c6dd235e10a73bb, 0x3feec86319e32323,
+0xbc79740b58a20091, 0x3feeca5e8d07f29e,
+0xbc87c50422622263, 0x3feecc667b5de565,
+0x3c9165830a2b96c2, 0x3feece7aed8eb8bb,
+0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
+0xbc903d5cbe27874b, 0x3feed2c980460ad8,
+0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
+0x3c5986178980fce0, 0x3feed74a8af46052,
+0x3c90cc319cee31d2, 0x3feed99e1330b358,
+0xbc89472975b1f2a5, 0x3feedbfe53c12e59,
+0x3c8469846e735ab3, 0x3feede6b5579fdbf,
+0x3c7d8157a34b7e7f, 0x3feee0e521356eba,
+0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
+0x3c8c8a4e231ebb7d, 0x3feee5ff3a3c2774,
+0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
+0xbc888c8d11a142e5, 0x3feeeb4ce622f2ff,
+0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
+0x3c889c2ea41433c7, 0x3feef0ce6c9a8952,
+0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
+0xbc7274aedac8ff80, 0x3feef68415b749b1,
+0xbc90a40e3da6f640, 0x3feef9728de5593a,
+0x3c85c620ce76df06, 0x3feefc6e29f1c52a,
+0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
+0xbc8fda52e1b51e41, 0x3fef028cf22749e4,
+0xbc91eee26b588a35, 0x3fef05b030a1064a,
+0xbc32141a7b3e2cd8, 0x3fef08e0b79a6f1f,
+0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
+0xbc302899507554e5, 0x3fef0f69c3f3a207,
+0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
+0xbc80dda2d4c0010c, 0x3fef16286141b33d,
+0x3c736eae30af0cb3, 0x3fef199bdd85529c,
+0xbc8a007daadf8d68, 0x3fef1d1cd9fa652c,
+0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
+0x3c836909391181d3, 0x3fef244778fafb22,
+0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
+0xbc811cd7dbdf9547, 0x3fef2ba88988c933,
+0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
+0xbc7ac28b7bef6621, 0x3fef33405751c4db,
+0x3c676b2c6c921968, 0x3fef3720dcef9069,
+0xbc7030587207b9e1, 0x3fef3b0f2e6d1675,
+0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
+0xbc8cc734592af7fc, 0x3fef43155b5bab74,
+0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
+0x3c87752a44f587e8, 0x3fef4b532b08c968,
+0xbc900dae3875a949, 0x3fef4f87080d89f2,
+0x3c85b66fefeef52e, 0x3fef53c8eacaa1d6,
+0x3c74a385a63d07a7, 0x3fef5818dcfba487,
+0x3c5159d9d908a96e, 0x3fef5c76e862e6d3,
+0xbc82919e2040220f, 0x3fef60e316c98398,
+0x3c8c254d16117a68, 0x3fef655d71ff6075,
+0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
+0xbc8d8c329fbd0e03, 0x3fef6e7cd63a8315,
+0x3c843a59ac016b4b, 0x3fef7321f301b460,
+0xbc8ea6e6fbd5f2a6, 0x3fef77d5641c0658,
+0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
+0xbc63e8e3eab2cbb4, 0x3fef81676b197d17,
+0xbc892ab93b470dc9, 0x3fef864614f5a129,
+0xbc8b7966cd0d2cd9, 0x3fef8b333b16ee12,
+0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
+0xbc776caa4c2ff1cf, 0x3fef953924676d76,
+0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
+0xbc81d5fc525d9940, 0x3fef9f7977cdb740,
+0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
+0x3c855cd8aaea3d21, 0x3fefa9f4867cca6e,
+0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
+0x3c8269947c2bed4a, 0x3fefb4aaa2188510,
+0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
+0xbc83b6137e9afe9e, 0x3fefbf9c1cb6412a,
+0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
+0xbc69fa74878ba7c7, 0x3fefcac948dd7274,
+0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
+0x3c901f3a75ee0efe, 0x3fefd632798844f8,
+0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
+0xbc516a9ce6ed84fa, 0x3fefe1d802243c89,
+0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
+0xbc699c7db2effc76, 0x3fefedba3692d514,
+0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
+0x3c64b458677f9840, 0x3feff9d96b2a23d9,
+#elif N == 512
+0x0, 0x3ff0000000000000,
+0xbc75d87ade1f60d5, 0x3feffd8c86da1c0a,
+0xbc84e82fc61851ac, 0x3feffb1afa5abcbf,
+0x3c9bffdaa7ac4bac, 0x3feff8ab5b2cbd11,
+0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
+0x3c75c18e5ae0563a, 0x3feff3d1e77170b4,
+0xbc82985dd8521d32, 0x3feff168143b0281,
+0xbc705b1125cf49a5, 0x3fefef003103b10e,
+0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
+0x3c9f879abbff3f87, 0x3fefea363d42b027,
+0x3c651e617061bfbd, 0x3fefe7d42e11bbcc,
+0x3c9b14003824712a, 0x3fefe57411915a8a,
+0xbc905e7a108766d1, 0x3fefe315e86e7f85,
+0x3c61cbf0f38af658, 0x3fefe0b9b35659d8,
+0x3c845fad437fa426, 0x3fefde5f72f654b1,
+0xbc9a3316383dcbc5, 0x3fefdc0727fc1762,
+0x3c8cd2523567f613, 0x3fefd9b0d3158574,
+0x3c9901c9e0e797fd, 0x3fefd75c74f0bec2,
+0xbc954529642b232f, 0x3fefd50a0e3c1f89,
+0xbc89b3236d111646, 0x3fefd2b99fa6407c,
+0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
+0xbc8cb191be99b1b0, 0x3fefce1ead925493,
+0x3c8293708ef5c32e, 0x3fefcbd42b72a836,
+0xbc9acb71e83765b7, 0x3fefc98ba42e7d30,
+0x3c60f74e61e6c861, 0x3fefc74518759bc8,
+0x3c5cd3e58b03697e, 0x3fefc50088f8093f,
+0xbc95b9280905b2a4, 0x3fefc2bdf66607e0,
+0xbc8bfb07d4755452, 0x3fefc07d61701716,
+0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
+0x3c8aedeb3e7b14cd, 0x3fefbc02331b9715,
+0x3c84f31f32c4b7e7, 0x3fefb9c79b1f3919,
+0x3c9a8eb1f3d914b4, 0x3fefb78f03834e52,
+0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
+0xbc85b9eb0402507b, 0x3fefb323d833d93f,
+0x3c9407fb30d06420, 0x3fefb0f145e46c85,
+0xbc93f0f225bbf3ee, 0x3fefaec0b6bdae53,
+0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
+0xbc9c3fe7282d1784, 0x3fefaa65a4b520ba,
+0xbc9a5d04b3b9911b, 0x3fefa83b23395dec,
+0x3c9c8be44bf4cde8, 0x3fefa612a7b26300,
+0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
+0x3c820c5444c93c44, 0x3fefa1c7c55189c6,
+0xbc937a01f0739546, 0x3fef9fa55fdfa9c5,
+0xbc84c6baeb580d7a, 0x3fef9d8503328e6d,
+0xbc6a033489906e0b, 0x3fef9b66affed31b,
+0x3c8657aa1b0d9f83, 0x3fef994a66f951ce,
+0x3c8b8268b04ef0a5, 0x3fef973028d7233e,
+0x3c62f2c7fd6ee145, 0x3fef9517f64d9ef1,
+0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
+0xbc6b0b2789925e90, 0x3fef90edb6db2dc1,
+0xbc9ac46e44a2ebcc, 0x3fef8edbab5e2ab6,
+0xbc93aad17d197fae, 0x3fef8ccbae51a5c8,
+0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
+0xbc989c464a07ad70, 0x3fef88b1e264a0e9,
+0xbc65704e90c9f860, 0x3fef86a814f204ab,
+0xbc72c338fce197f4, 0x3fef84a058cbae1e,
+0xbc91c923b9d5f416, 0x3fef829aaea92de0,
+0xbc6dca724cea0eb6, 0x3fef809717425438,
+0xbc897cea57e46280, 0x3fef7e95934f312e,
+0x3c464770b955d34d, 0x3fef7c962388149e,
+0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
+0xbc962811c114424f, 0x3fef789d83606e12,
+0x3c56f01429e2b9d2, 0x3fef76a45471c3c2,
+0x3c8ec58e74904dd4, 0x3fef74ad3c92df73,
+0xbc801b15eaa59348, 0x3fef72b83c7d517b,
+0x3c8d63b0ab2d5bbf, 0x3fef70c554eaea89,
+0x3c6e653b2459034b, 0x3fef6ed48695bbc0,
+0xbc9ca9effbeeac92, 0x3fef6ce5d23816c9,
+0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
+0x3c8bda920de0f6e2, 0x3fef690eba4df41f,
+0x3c92cc7ea345b7dc, 0x3fef672658375d2f,
+0xbc9a597f9a5ff71c, 0x3fef654013041dc2,
+0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
+0x3c50835b125aa573, 0x3fef6179e2363cf8,
+0x3c957bfb2876ea9e, 0x3fef5f99f8138a1c,
+0x3c8aaa13d61aec1f, 0x3fef5dbc2dc40bf0,
+0xbc96d99c7611eb26, 0x3fef5be084045cd4,
+0x3c8a4f81aa7110bd, 0x3fef5a06fb91588f,
+0x3c8cdc1873af2155, 0x3fef582f95281c6b,
+0xbc6817fd6a313e3e, 0x3fef565a51860746,
+0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
+0xbc96236af85fd26a, 0x3fef52b6358e15e8,
+0xbc9493684653a131, 0x3fef50e75eb44027,
+0x3c7795eb4523abe7, 0x3fef4f1aad999e82,
+0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
+0x3c8fe58b91b40095, 0x3fef4b87bf9cda38,
+0xbc98e2899077520a, 0x3fef49c18438ce4d,
+0x3c91ecaa860c614a, 0x3fef47fd7190241e,
+0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
+0xbc3e45c83ba0bbcb, 0x3fef447bc96ffc18,
+0x3c9120fcd4f59273, 0x3fef42be3578a819,
+0xbc29fd3bea07b4ee, 0x3fef4102cd3d09b9,
+0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
+0x3c87f1c7350e256d, 0x3fef3d9282fc1f27,
+0x3c89b788c188c9b8, 0x3fef3bdda27912d1,
+0x3c420dac6c124f4f, 0x3fef3a2af0b63bff,
+0x3c968efde3a8a894, 0x3fef387a6e756238,
+0xbc99501d09bc09fd, 0x3fef36cc1c78903a,
+0x3c877afbca90ef84, 0x3fef351ffb82140a,
+0x3c73baf864dc8675, 0x3fef33760c547f15,
+0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
+0x3c91b0575c1eaf54, 0x3fef3028c65fa1ff,
+0x3c91512f082876ee, 0x3fef2e85711ece75,
+0xbc90364bc9ce33ab, 0x3fef2ce450b3cb82,
+0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
+0xbc7548165d85ed32, 0x3fef29a8b16f0a30,
+0x3c9a02f0c7d75ec6, 0x3fef280e341ddf29,
+0x3c7c3b977a68e32c, 0x3fef2675eeb3ab98,
+0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
+0xbc93a255f697ecfe, 0x3fef234c0ea83f36,
+0xbc803297e78260bf, 0x3fef21ba7591bb70,
+0x3c8d2d19edc1e550, 0x3fef202b17779965,
+0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
+0xbc76b2173113dd8c, 0x3fef1d130f50d65c,
+0xbc95b77e5ccd9fbf, 0x3fef1b8a66d10f13,
+0x3c811aa5f853590b, 0x3fef1a03fc675d1f,
+0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
+0x3c61d61a34c8aa02, 0x3fef16fde4f2e280,
+0xbc91e75c40b4251e, 0x3fef157e39771b2f,
+0xbc91f892bf6b286d, 0x3fef1400cf2f6c18,
+0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
+0x3c7590c65c20e680, 0x3fef110cc15d5346,
+0x3c98a911f1f7785a, 0x3fef0f961f641589,
+0x3c86fe320b5c1e9d, 0x3fef0e21c1c14833,
+0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
+0xbc903cd8b2f25790, 0x3fef0b3fd6a454d2,
+0xbc61e7c998db7dbb, 0x3fef09d24abd886b,
+0x3c7b3bf786a54a87, 0x3fef08670653dfe4,
+0x3c834d754db0abb6, 0x3fef06fe0a31b715,
+0x3c74bb6c41732885, 0x3fef05975721b004,
+0x3c85425c11faadf4, 0x3fef0432edeeb2fd,
+0xbc99d7399abb9a8b, 0x3fef02d0cf63eeac,
+0x3c864201e2ac744c, 0x3fef0170fc4cd831,
+0xbc5451d60c6ac9eb, 0x3fef001375752b40,
+0xbc979517a03e2847, 0x3feefeb83ba8ea32,
+0x3c8787a210ceafd9, 0x3feefd5f4fb45e20,
+0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
+0xbc888d1e4629943d, 0x3feefab46484ebb4,
+0xbc800e2a46da4bee, 0x3feef96266e3fa2d,
+0xbc93369c544088b6, 0x3feef812ba4ea77d,
+0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
+0x3c85373ce4eb6dfb, 0x3feef57a577dd72b,
+0xbc87430803972b34, 0x3feef431a2de883b,
+0x3c83adec8265a67f, 0x3feef2eb428335b4,
+0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
+0xbc835388bcac6bc5, 0x3feef06581d3f669,
+0xbc954de30ae02d94, 0x3feeef26231e754a,
+0x3c727cdb4e4b6640, 0x3feeede91be9c811,
+0xbc9907f81b512d8e, 0x3feeecae6d05d866,
+0x3c86c2696a26af35, 0x3feeeb761742d808,
+0xbc94f2487e1c03ec, 0x3feeea401b7140ef,
+0x3c888f6ff06b979a, 0x3feee90c7a61d55b,
+0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
+0xbc89d5efaabc2030, 0x3feee6ac4bcdf3ea,
+0x3c914a5432fcb2f4, 0x3feee57fbfec6cf4,
+0xbc76b8867f91c9d6, 0x3feee4559212ef89,
+0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
+0x3c94c9c0b5157fe6, 0x3feee20853c10f28,
+0x3c79c3bba5562a2f, 0x3feee0e544ede173,
+0xbc62455345b51c8e, 0x3feedfc4976d27fa,
+0x3c859f48a72a4c6d, 0x3feedea64c123422,
+0xbc93331de45477d0, 0x3feedd8a63b0a09b,
+0xbc85a71612e21658, 0x3feedc70df1c5175,
+0xbc95f84d39b39b16, 0x3feedb59bf29743f,
+0xbc9312607a28698a, 0x3feeda4504ac801c,
+0xbc72ba4dc7c4d562, 0x3feed932b07a35df,
+0x3c86421f6f1d24d6, 0x3feed822c367a024,
+0xbc844f25dc02691f, 0x3feed7153e4a136a,
+0xbc58a78f4817895b, 0x3feed60a21f72e2a,
+0xbc888d328eb9b501, 0x3feed5016f44d8f5,
+0xbc9348a6815fce65, 0x3feed3fb2709468a,
+0x3c7f0bec42ddb15a, 0x3feed2f74a1af3f1,
+0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
+0xbc615f0a2b9cd452, 0x3feed0f6d5817663,
+0x3c835c43984d9871, 0x3feecffa3f84b9d4,
+0xbc8c2e465a919e1d, 0x3feecf0018321a1a,
+0x3c4363ed60c2ac11, 0x3feece086061892d,
+0xbc865dfd02bd08f1, 0x3feecd1318eb43ec,
+0xbc632afc8d9473a0, 0x3feecc2042a7d232,
+0xbc8e68cec89b1762, 0x3feecb2fde7006f4,
+0x3c9666093b0664ef, 0x3feeca41ed1d0057,
+0xbc48ae858eb682ca, 0x3feec9566f8827d0,
+0xbc95fc5e44de020e, 0x3feec86d668b3237,
+0x3c5dd71277c0915f, 0x3feec786d3001fe5,
+0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
+0x3c92001325ecd7fb, 0x3feec5c10fa920a1,
+0xbc7ea0148327c42f, 0x3feec4e1e192aed2,
+0x3c65ace6e2870332, 0x3feec4052c5916c4,
+0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
+0xbc9595c55690ffaf, 0x3feec2532feaada6,
+0xbc7a843ad1a88022, 0x3feec17dea6db7d7,
+0xbc8b401ba9fb5199, 0x3feec0ab213d5283,
+0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
+0x3c6df82bf324cc57, 0x3feebf0d073537ca,
+0x3c892ca3bf144e63, 0x3feebe41b817c114,
+0x3c97cae38641c7bb, 0x3feebd78e8bb586b,
+0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
+0x3c62d80c5c4a2b67, 0x3feebbeeccbd7b2a,
+0xbc902c99b04aa8b0, 0x3feebb2d81d8abff,
+0x3c8f39c10d12eaf0, 0x3feeba6eba2e35f0,
+0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
+0xbc80b582d74a55d9, 0x3feeb8f8b804f127,
+0x3c73e34f67e67118, 0x3feeb8417f4531ee,
+0xbc6b4e327ff434ca, 0x3feeb78ccd3deb0d,
+0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
+0xbc592dca38593e20, 0x3feeb62b00da3b14,
+0xbc75a3b1197ba0f0, 0x3feeb57de83f4eef,
+0xbc85daca9994833e, 0x3feeb4d359dfd53d,
+0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
+0xbc980b4321bc6dae, 0x3feeb385df598d78,
+0x3c81bd2888075068, 0x3feeb2e2f4f6ad27,
+0xbc8390afec5241c5, 0x3feeb24298571b06,
+0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
+0x3c8f15cdafe7d586, 0x3feeb1098bed1bdf,
+0xbc896be8ae89ef8f, 0x3feeb070dde910d2,
+0xbc910aa91ae9b67f, 0x3feeafdac1351819,
+0x3c93350518fdd78e, 0x3feeaf4736b527da,
+0x3c957e1b67462375, 0x3feeaeb63f4d854c,
+0xbc88e6ac90348602, 0x3feeae27dbe2c4cf,
+0x3c8124d5051552a7, 0x3feead9c0d59ca07,
+0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
+0xbc3ca103952ecf1f, 0x3feeac8c32824135,
+0xbc91af7f1365c3ac, 0x3feeac0827ff07cc,
+0x3c773345c02a4fd6, 0x3feeab86b5f43d92,
+0x3c9063e1e21c5409, 0x3feeab07dd485429,
+0xbc909d2a0fce20f2, 0x3feeaa8b9ee20d1e,
+0xbc943a3540d1898a, 0x3feeaa11fba87a03,
+0xbc924f2cb4f81746, 0x3feea99af482fc8f,
+0x3c34c7855019c6ea, 0x3feea9268a5946b7,
+0xbc943592a0a9846b, 0x3feea8b4be135acc,
+0xbc951f58ddaa8090, 0x3feea84590998b93,
+0xbc956bc85d444f4f, 0x3feea7d902d47c65,
+0x3c9432e62b64c035, 0x3feea76f15ad2148,
+0x3c914d1e4218319f, 0x3feea707ca0cbf0f,
+0xbc82e1648e50a17c, 0x3feea6a320dceb71,
+0x3c971c93709313f4, 0x3feea6411b078d26,
+0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
+0x3c7f88303b60d222, 0x3feea584fd15612a,
+0x3c95f30eda98a575, 0x3feea52ae6cdf6f4,
+0x3c70125ca18d4b5b, 0x3feea4d3778bc944,
+0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
+0x3c9592ea73798b11, 0x3feea42c91c56acd,
+0x3c917ecda8a72159, 0x3feea3dd1d1929fd,
+0xbc9371d6d7d75739, 0x3feea390532205d8,
+0xbc845378892be9ae, 0x3feea34634ccc320,
+0xbc8ac05fd996f807, 0x3feea2fec30678b7,
+0xbc9345f3cee1ae6e, 0x3feea2b9febc8fb7,
+0xbc91f5067d03653a, 0x3feea277e8dcc390,
+0xbc93cedd78565858, 0x3feea23882552225,
+0x3c917339c86ce3ad, 0x3feea1fbcc140be7,
+0xbc85c33fdf910406, 0x3feea1c1c70833f6,
+0xbc77e66065ba2500, 0x3feea18a7420a036,
+0x3c5710aa807e1964, 0x3feea155d44ca973,
+0x3c964c827ee6b49a, 0x3feea123e87bfb7a,
+0x3c81079ab5789604, 0x3feea0f4b19e9538,
+0xbc928311a3c73480, 0x3feea0c830a4c8d4,
+0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
+0x3c882c79e185e981, 0x3feea077541ee718,
+0x3c727df161cd7778, 0x3feea052fa75173e,
+0xbc8b48cea80b043b, 0x3feea0315a736c75,
+0xbc6a12ad8734b982, 0x3feea012750bdabf,
+0xbc4f4863bc8e5180, 0x3fee9ff64b30aa09,
+0x3c93f9924a05b767, 0x3fee9fdcddd47645,
+0x3c954835dd4b7548, 0x3fee9fc62dea2f8a,
+0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
+0xbc8bf41f59b59f8a, 0x3fee9fa10a38cee8,
+0xbc87557939a8b5ef, 0x3fee9f9298593ae5,
+0xbc8f652fde52775c, 0x3fee9f86e7ba9fef,
+0xbc80dc3d54e08851, 0x3fee9f7df9519484,
+0xbc7b0300defbcf98, 0x3fee9f77ce1303f6,
+0x3c51ed2f56fa9d1a, 0x3fee9f7466f42e87,
+0xbc89dab646035dc0, 0x3fee9f73c4eaa988,
+0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
+0xbc91f0c230588dde, 0x3fee9f7ad3ef9011,
+0xbc88e67a9006c909, 0x3fee9f8286ead08a,
+0x3c9106450507a28c, 0x3fee9f8d02d50b8f,
+0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
+0xbc9129729a10f3a0, 0x3fee9faa5953c849,
+0x3c86597566977ac8, 0x3fee9fbd35d7cbfd,
+0x3c781a70a5124f67, 0x3fee9fd2df29ce7c,
+0xbc8619321e55e68a, 0x3fee9feb564267c9,
+0x3c941626ea62646d, 0x3feea0069c1a861d,
+0x3c92c0b7028a5c3a, 0x3feea024b1ab6e09,
+0xbc940b9f54365b7c, 0x3feea04597eeba8f,
+0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
+0x3c873455e0e826c1, 0x3feea08fda749e5d,
+0x3c8a30faf49cc78c, 0x3feea0b938ac1cf6,
+0x3c94f006ad874e3e, 0x3feea0e56b7fcf03,
+0xbc7b32dcb94da51d, 0x3feea11473eb0187,
+0xbc8f6d693d0973bb, 0x3feea14652e958aa,
+0xbc92dad3519d7b5b, 0x3feea17b0976cfdb,
+0x3c58c5ee2b7e7848, 0x3feea1b2988fb9ec,
+0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
+0xbc88b25e045d207b, 0x3feea22a4456e7a3,
+0x3c87d51410fd15c2, 0x3feea26a62ff86f0,
+0xbc69cb3314060ca7, 0x3feea2ad5e2850ac,
+0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
+0x3c87a0b15d19e0bb, 0x3feea33bedf2e1b9,
+0xbc760a3629969871, 0x3feea3878491c491,
+0x3c94aa7212bfa73c, 0x3feea3d5fbab091f,
+0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
+0xbc81e688272a8a12, 0x3feea47b8f4abaa9,
+0x3c8b18c6e3fdef5d, 0x3feea4d2add106d9,
+0x3c4ab7b7112ec9d5, 0x3feea52cb0d1736a,
+0xbc9369b6f13b3734, 0x3feea589994cce13,
+0x3c8a1e274eed4476, 0x3feea5e968443d9a,
+0x3c90ec1ddcb1390a, 0x3feea64c1eb941f7,
+0x3c94a533a59324da, 0x3feea6b1bdadb46d,
+0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
+0x3c7a56d2760d087d, 0x3feea785b91e07f1,
+0xbc522cea4f3afa1e, 0x3feea7f4179f5b21,
+0x3c91682c1c6e8b05, 0x3feea86562ab00ec,
+0xbc94d450d872576e, 0x3feea8d99b4492ed,
+0x3c89ea99cf7a9591, 0x3feea950c27004c2,
+0x3c7c88549b958471, 0x3feea9cad931a436,
+0xbc59e57d8f92ff8e, 0x3feeaa47e08e1957,
+0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
+0x3c909b176e05a9cd, 0x3feeab4ac52be8f7,
+0x3c931143962f7877, 0x3feeabd0a478580f,
+0x3c711607f1952c95, 0x3feeac597875c644,
+0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
+0x3c869608f0f86431, 0x3feead74029db01e,
+0x3c93e9e96f112479, 0x3feeae05bad61778,
+0xbc7f1ced15c5c5c0, 0x3feeae9a6bdb5598,
+0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
+0x3c614b97be3f7b4e, 0x3feeafccbc6c19e6,
+0xbc8dac42a4a38df0, 0x3feeb06a5e0866d9,
+0x3c81c1701c359530, 0x3feeb10afc931857,
+0x3c7bf68359f35f44, 0x3feeb1ae99157736,
+0xbc8edb1bf6809287, 0x3feeb2553499284b,
+0x3c8b99dd98b1ed84, 0x3feeb2fed0282c8a,
+0xbc8ba58ce7a736d3, 0x3feeb3ab6ccce12c,
+0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
+0xbc93fc025e1db9ce, 0x3feeb50dad829e70,
+0xbc7885ad50cbb750, 0x3feeb5c353aa2fe2,
+0xbc8d737c7d71382e, 0x3feeb67bff148396,
+0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
+0x3c6ae88c43905293, 0x3feeb7f669e2802b,
+0xbc82d5e85f3e0301, 0x3feeb8b82b5f98e5,
+0xbc93d1f7661fe51b, 0x3feeb97cf65253d1,
+0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
+0x3c651b68797ffc1c, 0x3feebb0faccf9243,
+0xbc51669428996971, 0x3feebbdd9a7670b3,
+0x3c54579c5ceed70b, 0x3feebcae95cba768,
+0xbc92434322f4f9aa, 0x3feebd829fde4e50,
+0x3c87298413381667, 0x3feebe59b9bddb5b,
+0x3c71f2b2c1c4c014, 0x3feebf33e47a22a2,
+0xbc905000be64e965, 0x3feec01121235681,
+0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
+0xbc89fb12e3454b73, 0x3feec1d4d47f2598,
+0xbc9294f304f166b6, 0x3feec2bb4d53fe0d,
+0x3c7be2a03697693b, 0x3feec3a4dc5a3dd3,
+0x3c71affc2b91ce27, 0x3feec49182a3f090,
+0x3c90622b15810eea, 0x3feec581414380f2,
+0xbc8a1e58414c07d3, 0x3feec674194bb8d5,
+0x3be9a5ecc875d327, 0x3feec76a0bcfc15e,
+0x3c6dd235e10a73bb, 0x3feec86319e32323,
+0x3c88ea486a3350ef, 0x3feec95f4499c647,
+0xbc79740b58a20091, 0x3feeca5e8d07f29e,
+0xbc7a2ee551d4c40f, 0x3feecb60f4424fcb,
+0xbc87c50422622263, 0x3feecc667b5de565,
+0x3c89c31f7e38028b, 0x3feecd6f23701b15,
+0x3c9165830a2b96c2, 0x3feece7aed8eb8bb,
+0xbc5fac13f4e005a3, 0x3feecf89dacfe68c,
+0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
+0x3c7d8aced7162e89, 0x3feed1b1231475f7,
+0xbc903d5cbe27874b, 0x3feed2c980460ad8,
+0xbc848f50cea7269f, 0x3feed3e504f696b1,
+0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
+0x3c821eb9a08a0542, 0x3feed625893523d4,
+0x3c5986178980fce0, 0x3feed74a8af46052,
+0xbc6133a953131cfd, 0x3feed872b8950a73,
+0x3c90cc319cee31d2, 0x3feed99e1330b358,
+0x3c89e95e6f4a0ae4, 0x3feedacc9be14dca,
+0xbc89472975b1f2a5, 0x3feedbfe53c12e59,
+0xbc90260cf07cb311, 0x3feedd333beb0b7e,
+0x3c8469846e735ab3, 0x3feede6b5579fdbf,
+0x3c1bca400a7b939d, 0x3feedfa6a1897fd2,
+0x3c7d8157a34b7e7f, 0x3feee0e521356eba,
+0x3c9140bc34dfc19f, 0x3feee226d59a09ee,
+0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
+0xbc8c9b1da461ab87, 0x3feee4b3e100301e,
+0x3c8c8a4e231ebb7d, 0x3feee5ff3a3c2774,
+0x3c8c115f23ebea8e, 0x3feee74dcca5a413,
+0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
+0xbc6dcab99f23f84e, 0x3feee9f4a17a4735,
+0xbc888c8d11a142e5, 0x3feeeb4ce622f2ff,
+0x3c60a43e8b7e4bfe, 0x3feeeca868742ee4,
+0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
+0x3c915b1397075f04, 0x3feeef692a8fa8cd,
+0x3c889c2ea41433c7, 0x3feef0ce6c9a8952,
+0xbc839f7a1f04d2b0, 0x3feef236f0cf3f3a,
+0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
+0xbc86a510f31e13e6, 0x3feef511c43bbd62,
+0xbc7274aedac8ff80, 0x3feef68415b749b1,
+0xbc92887ea88e7340, 0x3feef7f9ade433c6,
+0xbc90a40e3da6f640, 0x3feef9728de5593a,
+0xbc6e57ac604759ba, 0x3feefaeeb6ddfc87,
+0x3c85c620ce76df06, 0x3feefc6e29f1c52a,
+0x3c8e6c6db4f83226, 0x3feefdf0e844bfc6,
+0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
+0xbc8d1bf10460dba0, 0x3fef01004b3a7804,
+0xbc8fda52e1b51e41, 0x3fef028cf22749e4,
+0x3c8e5d80813dddfc, 0x3fef041ce8e77680,
+0xbc91eee26b588a35, 0x3fef05b030a1064a,
+0x3c8caff9640f2dcb, 0x3fef0746ca7a67a7,
+0xbc32141a7b3e2cd8, 0x3fef08e0b79a6f1f,
+0x3c7a77557fd62db3, 0x3fef0a7df9285775,
+0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
+0xbc651ba6128db749, 0x3fef0dc27e2cb5e5,
+0xbc302899507554e5, 0x3fef0f69c3f3a207,
+0xbc7c0ffefdc5e251, 0x3fef111462c95b60,
+0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
+0xbc8b6cd058bfd6fa, 0x3fef1473b0468d30,
+0xbc80dda2d4c0010c, 0x3fef16286141b33d,
+0x3c923759b8aca76d, 0x3fef17e06ff301f4,
+0x3c736eae30af0cb3, 0x3fef199bdd85529c,
+0xbc895498a73dac7d, 0x3fef1b5aab23e61e,
+0xbc8a007daadf8d68, 0x3fef1d1cd9fa652c,
+0x3c851de924583108, 0x3fef1ee26b34e065,
+0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
+0xbc8c5fe4051ba06c, 0x3fef2277b9881650,
+0x3c836909391181d3, 0x3fef244778fafb22,
+0xbc6d1816c0a9ac07, 0x3fef261a9f8630ad,
+0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
+0xbc7af5c67c4e8235, 0x3fef29cb269e601f,
+0xbc811cd7dbdf9547, 0x3fef2ba88988c933,
+0xbc8304ef0045d575, 0x3fef2d89584661a1,
+0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
+0x3c8725f94f910375, 0x3fef31553dfa8313,
+0xbc7ac28b7bef6621, 0x3fef33405751c4db,
+0x3c7b53e99f9191e8, 0x3fef352ee13da7cb,
+0x3c676b2c6c921968, 0x3fef3720dcef9069,
+0xbc810a79e6d7e2b8, 0x3fef39164b994d23,
+0xbc7030587207b9e1, 0x3fef3b0f2e6d1675,
+0x3c840635f6d2a9c0, 0x3fef3d0b869d8f0f,
+0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
+0x3c549eeef9ec910c, 0x3fef410e9be12cb9,
+0xbc8cc734592af7fc, 0x3fef43155b5bab74,
+0xbc8335827ffb9dce, 0x3fef451f95018d17,
+0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
+0x3c645563980ef762, 0x3fef493e7ba2c38c,
+0x3c87752a44f587e8, 0x3fef4b532b08c968,
+0xbc8cd0205eb2aab2, 0x3fef4d6b596f948c,
+0xbc900dae3875a949, 0x3fef4f87080d89f2,
+0xbc8aab80ceab2b4a, 0x3fef51a638197a3c,
+0x3c85b66fefeef52e, 0x3fef53c8eacaa1d6,
+0xbc8f870f40a8ba1b, 0x3fef55ef2158a91f,
+0x3c74a385a63d07a7, 0x3fef5818dcfba487,
+0x3c83c119f18464c5, 0x3fef5a461eec14be,
+0x3c5159d9d908a96e, 0x3fef5c76e862e6d3,
+0xbc5a628c2be4e7c7, 0x3fef5eab3a99745b,
+0xbc82919e2040220f, 0x3fef60e316c98398,
+0xbc72550d76be719a, 0x3fef631e7e2d479d,
+0x3c8c254d16117a68, 0x3fef655d71ff6075,
+0xbc82090274667d12, 0x3fef679ff37adb4a,
+0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
+0x3c75f7d28150cac4, 0x3fef6c2fa45c4dfd,
+0xbc8d8c329fbd0e03, 0x3fef6e7cd63a8315,
+0x3c890de9296f4cd1, 0x3fef70cd9ab294e4,
+0x3c843a59ac016b4b, 0x3fef7321f301b460,
+0x3c832ff9978b34bc, 0x3fef7579e065807d,
+0xbc8ea6e6fbd5f2a6, 0x3fef77d5641c0658,
+0xbc7303b63dda1980, 0x3fef7a347f63c159,
+0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
+0xbc81f2ba385f2f95, 0x3fef7efd81a2ece1,
+0xbc63e8e3eab2cbb4, 0x3fef81676b197d17,
+0x3c768d9144ae12fc, 0x3fef83d4f11f8220,
+0xbc892ab93b470dc9, 0x3fef864614f5a129,
+0x3c853687f542403b, 0x3fef88bad7dcee90,
+0xbc8b7966cd0d2cd9, 0x3fef8b333b16ee12,
+0xbc736ed2de40b407, 0x3fef8daf3fe592e8,
+0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
+0xbc614ef56c770f3b, 0x3fef92b2334ac7ee,
+0xbc776caa4c2ff1cf, 0x3fef953924676d76,
+0x3c8df7d1353d8e88, 0x3fef97c3bc24e350,
+0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
+0xbc850bed64091b8a, 0x3fef9ce3e4933c7e,
+0xbc81d5fc525d9940, 0x3fef9f7977cdb740,
+0x3c89d852381c317f, 0x3fefa212b6bc3181,
+0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
+0x3c68a00e3cca04c4, 0x3fefa7503ccd2be5,
+0x3c855cd8aaea3d21, 0x3fefa9f4867cca6e,
+0xbc5a1f25ce94cae7, 0x3fefac9c80faa594,
+0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
+0xbc6fb5f3ee307976, 0x3fefb1f78d802dc2,
+0x3c8269947c2bed4a, 0x3fefb4aaa2188510,
+0x3c737e8ae802b851, 0x3fefb7616ca06dd6,
+0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
+0x3c875119560e34af, 0x3fefbcda28a52e59,
+0xbc83b6137e9afe9e, 0x3fefbf9c1cb6412a,
+0xbc7431c3840929c6, 0x3fefc261cbdf5be7,
+0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
+0xbc8cb472d2e86b99, 0x3fefc7f860a70c22,
+0xbc69fa74878ba7c7, 0x3fefcac948dd7274,
+0x3c83f5df2fde16a8, 0x3fefcd9df15b82ac,
+0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
+0x3c8eef18336b62e3, 0x3fefd35288633625,
+0x3c901f3a75ee0efe, 0x3fefd632798844f8,
+0x3c80d23f87b50a2a, 0x3fefd916302bd526,
+0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
+0x3c8302dee657c8e6, 0x3fefdee8f32a4b45,
+0xbc516a9ce6ed84fa, 0x3fefe1d802243c89,
+0xbc7b0caa080df170, 0x3fefe4cadbdac61d,
+0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
+0x3c7617a9f2fd24e5, 0x3fefeabbf4c0ba54,
+0xbc699c7db2effc76, 0x3fefedba3692d514,
+0x3c75f103b8fd5ca7, 0x3feff0bc4866e8ad,
+0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
+0x3c8e70b094fa075a, 0x3feff6cbe15f6314,
+0x3c64b458677f9840, 0x3feff9d96b2a23d9,
+0xbc72ec9a3e5d680a, 0x3feffceaca4391b6,
+#endif
+},
+};
diff --git a/libc/AOR_v20.02/math/expf.c b/libc/AOR_v20.02/math/expf.c
new file mode 100644
index 000000000000..035cb4519163
--- /dev/null
+++ b/libc/AOR_v20.02/math/expf.c
@@ -0,0 +1,92 @@
+/*
+ * Single-precision e^x function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+EXP2F_TABLE_BITS = 5
+EXP2F_POLY_ORDER = 3
+
+ULP error: 0.502 (nearest rounding.)
+Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
+Wrong count: 170635 (all nearest rounding wrong results with fma.)
+Non-nearest ULP error: 1 (rounded ULP error)
+*/
+
+#define N (1 << EXP2F_TABLE_BITS)
+#define InvLn2N __exp2f_data.invln2_scaled
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly_scaled
+
+static inline uint32_t
+top12 (float x)
+{
+ return asuint (x) >> 20;
+}
+
+float
+expf (float x)
+{
+ uint32_t abstop;
+ uint64_t ki, t;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, xd, z, r, r2, y, s;
+
+ xd = (double_t) x;
+ abstop = top12 (x) & 0x7ff;
+ if (unlikely (abstop >= top12 (88.0f)))
+ {
+ /* |x| >= 88 or x is nan. */
+ if (asuint (x) == asuint (-INFINITY))
+ return 0.0f;
+ if (abstop >= top12 (INFINITY))
+ return x + x;
+ if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
+ return __math_oflowf (0);
+ if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
+ return __math_uflowf (0);
+#if WANT_ERRNO_UFLOW
+ if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
+ return __math_may_uflowf (0);
+#endif
+ }
+
+ /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
+ z = InvLn2N * xd;
+
+ /* Round and convert z to int, the result is in [-150*N, 128*N] and
+ ideally nearest int is used, otherwise the magnitude of r can be
+ bigger which gives larger approximation error. */
+#if TOINT_INTRINSICS
+ kd = roundtoint (z);
+ ki = converttoint (z);
+#else
+# define SHIFT __exp2f_data.shift
+ kd = eval_as_double (z + SHIFT);
+ ki = asuint64 (kd);
+ kd -= SHIFT;
+#endif
+ r = z - kd;
+
+ /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+ t = T[ki % N];
+ t += ki << (52 - EXP2F_TABLE_BITS);
+ s = asdouble (t);
+ z = C[0] * r + C[1];
+ r2 = r * r;
+ y = C[2] * r + 1;
+ y = z * r2 + y;
+ y = y * s;
+ return eval_as_float (y);
+}
+#if USE_GLIBC_ABI
+strong_alias (expf, __expf_finite)
+hidden_alias (expf, __ieee754_expf)
+#endif
diff --git a/libc/AOR_v20.02/math/include/mathlib.h b/libc/AOR_v20.02/math/include/mathlib.h
new file mode 100644
index 000000000000..4765ff4106f2
--- /dev/null
+++ b/libc/AOR_v20.02/math/include/mathlib.h
@@ -0,0 +1,101 @@
+/*
+ * Public API.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef _MATHLIB_H
+#define _MATHLIB_H
+
+float expf (float);
+float exp2f (float);
+float logf (float);
+float log2f (float);
+float powf (float, float);
+float sinf (float);
+float cosf (float);
+void sincosf (float, float*, float*);
+
+double exp (double);
+double exp2 (double);
+double log (double);
+double log2 (double);
+double pow (double, double);
+
+/* Scalar functions using the vector algorithm with identical result. */
+float __s_sinf (float);
+float __s_cosf (float);
+float __s_expf (float);
+float __s_expf_1u (float);
+float __s_exp2f (float);
+float __s_exp2f_1u (float);
+float __s_logf (float);
+float __s_powf (float, float);
+double __s_sin (double);
+double __s_cos (double);
+double __s_exp (double);
+double __s_log (double);
+double __s_pow (double, double);
+
+#if __aarch64__
+#if __GNUC__ >= 5
+typedef __Float32x4_t __f32x4_t;
+typedef __Float64x2_t __f64x2_t;
+#elif __clang_major__*100+__clang_minor__ >= 305
+typedef __attribute__((__neon_vector_type__(4))) float __f32x4_t;
+typedef __attribute__((__neon_vector_type__(2))) double __f64x2_t;
+#else
+#error Unsupported compiler
+#endif
+
+/* Vector functions following the base PCS. */
+__f32x4_t __v_sinf (__f32x4_t);
+__f32x4_t __v_cosf (__f32x4_t);
+__f32x4_t __v_expf (__f32x4_t);
+__f32x4_t __v_expf_1u (__f32x4_t);
+__f32x4_t __v_exp2f (__f32x4_t);
+__f32x4_t __v_exp2f_1u (__f32x4_t);
+__f32x4_t __v_logf (__f32x4_t);
+__f32x4_t __v_powf (__f32x4_t, __f32x4_t);
+__f64x2_t __v_sin (__f64x2_t);
+__f64x2_t __v_cos (__f64x2_t);
+__f64x2_t __v_exp (__f64x2_t);
+__f64x2_t __v_log (__f64x2_t);
+__f64x2_t __v_pow (__f64x2_t, __f64x2_t);
+
+#if __GNUC__ >= 9 || __clang_major__ >= 8
+#define __vpcs __attribute__((__aarch64_vector_pcs__))
+
+/* Vector functions following the vector PCS. */
+__vpcs __f32x4_t __vn_sinf (__f32x4_t);
+__vpcs __f32x4_t __vn_cosf (__f32x4_t);
+__vpcs __f32x4_t __vn_expf (__f32x4_t);
+__vpcs __f32x4_t __vn_expf_1u (__f32x4_t);
+__vpcs __f32x4_t __vn_exp2f (__f32x4_t);
+__vpcs __f32x4_t __vn_exp2f_1u (__f32x4_t);
+__vpcs __f32x4_t __vn_logf (__f32x4_t);
+__vpcs __f32x4_t __vn_powf (__f32x4_t, __f32x4_t);
+__vpcs __f64x2_t __vn_sin (__f64x2_t);
+__vpcs __f64x2_t __vn_cos (__f64x2_t);
+__vpcs __f64x2_t __vn_exp (__f64x2_t);
+__vpcs __f64x2_t __vn_log (__f64x2_t);
+__vpcs __f64x2_t __vn_pow (__f64x2_t, __f64x2_t);
+
+/* Vector functions following the vector PCS using ABI names. */
+__vpcs __f32x4_t _ZGVnN4v_sinf (__f32x4_t);
+__vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t);
+__vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t);
+__vpcs __f32x4_t _ZGVnN4v_exp2f (__f32x4_t);
+__vpcs __f32x4_t _ZGVnN4v_logf (__f32x4_t);
+__vpcs __f32x4_t _ZGVnN4vv_powf (__f32x4_t, __f32x4_t);
+__vpcs __f64x2_t _ZGVnN2v_sin (__f64x2_t);
+__vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t);
+__vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t);
+__vpcs __f64x2_t _ZGVnN2v_log (__f64x2_t);
+__vpcs __f64x2_t _ZGVnN2vv_pow (__f64x2_t, __f64x2_t);
+#endif
+#endif
+
+#endif
diff --git a/libc/AOR_v20.02/math/log.c b/libc/AOR_v20.02/math/log.c
new file mode 100644
index 000000000000..c546b694099d
--- /dev/null
+++ b/libc/AOR_v20.02/math/log.c
@@ -0,0 +1,163 @@
+/*
+ * Double-precision log(x) function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <float.h>
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define T __log_data.tab
+#define T2 __log_data.tab2
+#define B __log_data.poly1
+#define A __log_data.poly
+#define Ln2hi __log_data.ln2hi
+#define Ln2lo __log_data.ln2lo
+#define N (1 << LOG_TABLE_BITS)
+#define OFF 0x3fe6000000000000
+
+/* Top 16 bits of a double. */
+static inline uint32_t
+top16 (double x)
+{
+ return asuint64 (x) >> 48;
+}
+
+double
+log (double x)
+{
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
+ uint64_t ix, iz, tmp;
+ uint32_t top;
+ int k, i;
+
+ ix = asuint64 (x);
+ top = top16 (x);
+
+#if LOG_POLY1_ORDER == 10 || LOG_POLY1_ORDER == 11
+# define LO asuint64 (1.0 - 0x1p-5)
+# define HI asuint64 (1.0 + 0x1.1p-5)
+#elif LOG_POLY1_ORDER == 12
+# define LO asuint64 (1.0 - 0x1p-4)
+# define HI asuint64 (1.0 + 0x1.09p-4)
+#endif
+ if (unlikely (ix - LO < HI - LO))
+ {
+ /* Handle close to 1.0 inputs separately. */
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
+ return 0;
+ r = x - 1.0;
+ r2 = r * r;
+ r3 = r * r2;
+#if LOG_POLY1_ORDER == 10
+ /* Worst-case error is around 0.516 ULP. */
+ y = r3 * (B[1] + r * B[2] + r2 * B[3]
+ + r3 * (B[4] + r * B[5] + r2 * B[6] + r3 * (B[7] + r * B[8])));
+ w = B[0] * r2; /* B[0] == -0.5. */
+ hi = r + w;
+ y += r - hi + w;
+ y += hi;
+#elif LOG_POLY1_ORDER == 11
+ /* Worst-case error is around 0.516 ULP. */
+ y = r3 * (B[1] + r * B[2]
+ + r2 * (B[3] + r * B[4] + r2 * B[5]
+ + r3 * (B[6] + r * B[7] + r2 * B[8] + r3 * B[9])));
+ w = B[0] * r2; /* B[0] == -0.5. */
+ hi = r + w;
+ y += r - hi + w;
+ y += hi;
+#elif LOG_POLY1_ORDER == 12
+ y = r3 * (B[1] + r * B[2] + r2 * B[3]
+ + r3 * (B[4] + r * B[5] + r2 * B[6]
+ + r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
+# if N <= 64
+ /* Worst-case error is around 0.532 ULP. */
+ w = B[0] * r2; /* B[0] == -0.5. */
+ hi = r + w;
+ y += r - hi + w;
+ y += hi;
+# else
+ /* Worst-case error is around 0.507 ULP. */
+ w = r * 0x1p27;
+ double_t rhi = r + w - w;
+ double_t rlo = r - rhi;
+ w = rhi * rhi * B[0]; /* B[0] == -0.5. */
+ hi = r + w;
+ lo = r - hi + w;
+ lo += B[0] * rlo * (rhi + r);
+ y += lo;
+ y += hi;
+# endif
+#endif
+ return eval_as_double (y);
+ }
+ if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
+ {
+ /* x < 0x1p-1022 or inf or nan. */
+ if (ix * 2 == 0)
+ return __math_divzero (1);
+ if (ix == asuint64 (INFINITY)) /* log(inf) == inf. */
+ return x;
+ if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
+ return __math_invalid (x);
+ /* x is subnormal, normalize it. */
+ ix = asuint64 (x * 0x1p52);
+ ix -= 52ULL << 52;
+ }
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
+ k = (int64_t) tmp >> 52; /* arithmetic shift */
+ iz = ix - (tmp & 0xfffULL << 52);
+ invc = T[i].invc;
+ logc = T[i].logc;
+ z = asdouble (iz);
+
+ /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
+ /* r ~= z/c - 1, |r| < 1/(2*N). */
+#if HAVE_FAST_FMA
+ /* rounding error: 0x1p-55/N. */
+ r = fma (z, invc, -1.0);
+#else
+ /* rounding error: 0x1p-55/N + 0x1p-66. */
+ r = (z - T2[i].chi - T2[i].clo) * invc;
+#endif
+ kd = (double_t) k;
+
+ /* hi + lo = r + log(c) + k*Ln2. */
+ w = kd * Ln2hi + logc;
+ hi = w + r;
+ lo = w - hi + r + kd * Ln2lo;
+
+ /* log(x) = lo + (log1p(r) - r) + hi. */
+ r2 = r * r; /* rounding error: 0x1p-54/N^2. */
+ /* Worst case error if |y| > 0x1p-5:
+ 0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma)
+ Worst case error if |y| > 0x1p-4:
+ 0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma). */
+#if LOG_POLY_ORDER == 6
+ y = lo + r2 * A[0] + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi;
+#elif LOG_POLY_ORDER == 7
+ y = lo
+ + r2 * (A[0] + r * A[1] + r2 * (A[2] + r * A[3])
+ + r2 * r2 * (A[4] + r * A[5]))
+ + hi;
+#endif
+ return eval_as_double (y);
+}
+#if USE_GLIBC_ABI
+strong_alias (log, __log_finite)
+hidden_alias (log, __ieee754_log)
+# if LDBL_MANT_DIG == 53
+long double logl (long double x) { return log (x); }
+# endif
+#endif
diff --git a/libc/AOR_v20.02/math/log2.c b/libc/AOR_v20.02/math/log2.c
new file mode 100644
index 000000000000..a1e20b0118a5
--- /dev/null
+++ b/libc/AOR_v20.02/math/log2.c
@@ -0,0 +1,142 @@
+/*
+ * Double-precision log2(x) function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <float.h>
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+#define T __log2_data.tab
+#define T2 __log2_data.tab2
+#define B __log2_data.poly1
+#define A __log2_data.poly
+#define InvLn2hi __log2_data.invln2hi
+#define InvLn2lo __log2_data.invln2lo
+#define N (1 << LOG2_TABLE_BITS)
+#define OFF 0x3fe6000000000000
+
+/* Top 16 bits of a double. */
+static inline uint32_t
+top16 (double x)
+{
+ return asuint64 (x) >> 48;
+}
+
+double
+log2 (double x)
+{
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
+ uint64_t ix, iz, tmp;
+ uint32_t top;
+ int k, i;
+
+ ix = asuint64 (x);
+ top = top16 (x);
+
+#if LOG2_POLY1_ORDER == 11
+# define LO asuint64 (1.0 - 0x1.5b51p-5)
+# define HI asuint64 (1.0 + 0x1.6ab2p-5)
+#endif
+ if (unlikely (ix - LO < HI - LO))
+ {
+ /* Handle close to 1.0 inputs separately. */
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
+ return 0;
+ r = x - 1.0;
+#if HAVE_FAST_FMA
+ hi = r * InvLn2hi;
+ lo = r * InvLn2lo + fma (r, InvLn2hi, -hi);
+#else
+ double_t rhi, rlo;
+ rhi = asdouble (asuint64 (r) & -1ULL << 32);
+ rlo = r - rhi;
+ hi = rhi * InvLn2hi;
+ lo = rlo * InvLn2hi + r * InvLn2lo;
+#endif
+ r2 = r * r; /* rounding error: 0x1p-62. */
+ r4 = r2 * r2;
+#if LOG2_POLY1_ORDER == 11
+ /* Worst-case error is less than 0.54 ULP (0.55 ULP without fma). */
+ p = r2 * (B[0] + r * B[1]);
+ y = hi + p;
+ lo += hi - y + p;
+ lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5])
+ + r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9])));
+ y += lo;
+#endif
+ return eval_as_double (y);
+ }
+ if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
+ {
+ /* x < 0x1p-1022 or inf or nan. */
+ if (ix * 2 == 0)
+ return __math_divzero (1);
+ if (ix == asuint64 (INFINITY)) /* log(inf) == inf. */
+ return x;
+ if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
+ return __math_invalid (x);
+ /* x is subnormal, normalize it. */
+ ix = asuint64 (x * 0x1p52);
+ ix -= 52ULL << 52;
+ }
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (52 - LOG2_TABLE_BITS)) % N;
+ k = (int64_t) tmp >> 52; /* arithmetic shift */
+ iz = ix - (tmp & 0xfffULL << 52);
+ invc = T[i].invc;
+ logc = T[i].logc;
+ z = asdouble (iz);
+ kd = (double_t) k;
+
+ /* log2(x) = log2(z/c) + log2(c) + k. */
+ /* r ~= z/c - 1, |r| < 1/(2*N). */
+#if HAVE_FAST_FMA
+ /* rounding error: 0x1p-55/N. */
+ r = fma (z, invc, -1.0);
+ t1 = r * InvLn2hi;
+ t2 = r * InvLn2lo + fma (r, InvLn2hi, -t1);
+#else
+ double_t rhi, rlo;
+ /* rounding error: 0x1p-55/N + 0x1p-65. */
+ r = (z - T2[i].chi - T2[i].clo) * invc;
+ rhi = asdouble (asuint64 (r) & -1ULL << 32);
+ rlo = r - rhi;
+ t1 = rhi * InvLn2hi;
+ t2 = rlo * InvLn2hi + r * InvLn2lo;
+#endif
+
+ /* hi + lo = r/ln2 + log2(c) + k. */
+ t3 = kd + logc;
+ hi = t3 + t1;
+ lo = t3 - hi + t1 + t2;
+
+ /* log2(r+1) = r/ln2 + r^2*poly(r). */
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ r2 = r * r; /* rounding error: 0x1p-54/N^2. */
+ r4 = r2 * r2;
+#if LOG2_POLY_ORDER == 7
+ /* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
+ ~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma). */
+ p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]);
+ y = lo + r2 * p + hi;
+#endif
+ return eval_as_double (y);
+}
+#if USE_GLIBC_ABI
+strong_alias (log2, __log2_finite)
+hidden_alias (log2, __ieee754_log2)
+# if LDBL_MANT_DIG == 53
+long double log2l (long double x) { return log2 (x); }
+# endif
+#endif
diff --git a/libc/AOR_v20.02/math/log2_data.c b/libc/AOR_v20.02/math/log2_data.c
new file mode 100644
index 000000000000..a487dbfb9856
--- /dev/null
+++ b/libc/AOR_v20.02/math/log2_data.c
@@ -0,0 +1,210 @@
+/*
+ * Data for log2.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+#define N (1 << LOG2_TABLE_BITS)
+
+const struct log2_data __log2_data = {
+// First coefficient: 0x1.71547652b82fe1777d0ffda0d24p0
+.invln2hi = 0x1.7154765200000p+0,
+.invln2lo = 0x1.705fc2eefa200p-33,
+.poly1 = {
+#if LOG2_POLY1_ORDER == 11
+// relative error: 0x1.2fad8188p-63
+// in -0x1.5b51p-5 0x1.6ab2p-5
+-0x1.71547652b82fep-1,
+0x1.ec709dc3a03f7p-2,
+-0x1.71547652b7c3fp-2,
+0x1.2776c50f05be4p-2,
+-0x1.ec709dd768fe5p-3,
+0x1.a61761ec4e736p-3,
+-0x1.7153fbc64a79bp-3,
+0x1.484d154f01b4ap-3,
+-0x1.289e4a72c383cp-3,
+0x1.0b32f285aee66p-3,
+#endif
+},
+.poly = {
+#if N == 64 && LOG2_POLY_ORDER == 7
+// relative error: 0x1.a72c2bf8p-58
+// abs error: 0x1.67a552c8p-66
+// in -0x1.f45p-8 0x1.f45p-8
+-0x1.71547652b8339p-1,
+0x1.ec709dc3a04bep-2,
+-0x1.7154764702ffbp-2,
+0x1.2776c50034c48p-2,
+-0x1.ec7b328ea92bcp-3,
+0x1.a6225e117f92ep-3,
+#endif
+},
+/* Algorithm:
+
+ x = 2^k z
+ log2(x) = k + log2(c) + log2(z/c)
+ log2(z/c) = poly(z/c - 1)
+
+where z is in [1.6p-1; 1.6p0] which is split into N subintervals and z falls
+into the ith one, then table entries are computed as
+
+ tab[i].invc = 1/c
+ tab[i].logc = (double)log2(c)
+ tab2[i].chi = (double)c
+ tab2[i].clo = (double)(c - (double)c)
+
+where c is near the center of the subinterval and is chosen by trying +-2^29
+floating point invc candidates around 1/center and selecting one for which
+
+ 1) the rounding error in 0x1.8p10 + logc is 0,
+ 2) the rounding error in z - chi - clo is < 0x1p-64 and
+ 3) the rounding error in (double)log2(c) is minimized (< 0x1p-68).
+
+Note: 1) ensures that k + logc can be computed without rounding error, 2)
+ensures that z/c - 1 can be computed as (z - chi - clo)*invc with close to a
+single rounding error when there is no fast fma for z*invc - 1, 3) ensures
+that logc + poly(z/c - 1) has small error, however near x == 1 when
+|log2(x)| < 0x1p-4, this is not enough so that is special cased. */
+.tab = {
+#if N == 64
+{0x1.724286bb1acf8p+0, -0x1.1095feecdb000p-1},
+{0x1.6e1f766d2cca1p+0, -0x1.08494bd76d000p-1},
+{0x1.6a13d0e30d48ap+0, -0x1.00143aee8f800p-1},
+{0x1.661ec32d06c85p+0, -0x1.efec5360b4000p-2},
+{0x1.623fa951198f8p+0, -0x1.dfdd91ab7e000p-2},
+{0x1.5e75ba4cf026cp+0, -0x1.cffae0cc79000p-2},
+{0x1.5ac055a214fb8p+0, -0x1.c043811fda000p-2},
+{0x1.571ed0f166e1ep+0, -0x1.b0b67323ae000p-2},
+{0x1.53909590bf835p+0, -0x1.a152f5a2db000p-2},
+{0x1.5014fed61adddp+0, -0x1.9217f5af86000p-2},
+{0x1.4cab88e487bd0p+0, -0x1.8304db0719000p-2},
+{0x1.49539b4334feep+0, -0x1.74189f9a9e000p-2},
+{0x1.460cbdfafd569p+0, -0x1.6552bb5199000p-2},
+{0x1.42d664ee4b953p+0, -0x1.56b23a29b1000p-2},
+{0x1.3fb01111dd8a6p+0, -0x1.483650f5fa000p-2},
+{0x1.3c995b70c5836p+0, -0x1.39de937f6a000p-2},
+{0x1.3991c4ab6fd4ap+0, -0x1.2baa1538d6000p-2},
+{0x1.3698e0ce099b5p+0, -0x1.1d98340ca4000p-2},
+{0x1.33ae48213e7b2p+0, -0x1.0fa853a40e000p-2},
+{0x1.30d191985bdb1p+0, -0x1.01d9c32e73000p-2},
+{0x1.2e025cab271d7p+0, -0x1.e857da2fa6000p-3},
+{0x1.2b404cf13cd82p+0, -0x1.cd3c8633d8000p-3},
+{0x1.288b02c7ccb50p+0, -0x1.b26034c14a000p-3},
+{0x1.25e2263944de5p+0, -0x1.97c1c2f4fe000p-3},
+{0x1.234563d8615b1p+0, -0x1.7d6023f800000p-3},
+{0x1.20b46e33eaf38p+0, -0x1.633a71a05e000p-3},
+{0x1.1e2eefdcda3ddp+0, -0x1.494f5e9570000p-3},
+{0x1.1bb4a580b3930p+0, -0x1.2f9e424e0a000p-3},
+{0x1.19453847f2200p+0, -0x1.162595afdc000p-3},
+{0x1.16e06c0d5d73cp+0, -0x1.f9c9a75bd8000p-4},
+{0x1.1485f47b7e4c2p+0, -0x1.c7b575bf9c000p-4},
+{0x1.12358ad0085d1p+0, -0x1.960c60ff48000p-4},
+{0x1.0fef00f532227p+0, -0x1.64ce247b60000p-4},
+{0x1.0db2077d03a8fp+0, -0x1.33f78b2014000p-4},
+{0x1.0b7e6d65980d9p+0, -0x1.0387d1a42c000p-4},
+{0x1.0953efe7b408dp+0, -0x1.a6f9208b50000p-5},
+{0x1.07325cac53b83p+0, -0x1.47a954f770000p-5},
+{0x1.05197e40d1b5cp+0, -0x1.d23a8c50c0000p-6},
+{0x1.03091c1208ea2p+0, -0x1.16a2629780000p-6},
+{0x1.0101025b37e21p+0, -0x1.720f8d8e80000p-8},
+{0x1.fc07ef9caa76bp-1, 0x1.6fe53b1500000p-7},
+{0x1.f4465d3f6f184p-1, 0x1.11ccce10f8000p-5},
+{0x1.ecc079f84107fp-1, 0x1.c4dfc8c8b8000p-5},
+{0x1.e573a99975ae8p-1, 0x1.3aa321e574000p-4},
+{0x1.de5d6f0bd3de6p-1, 0x1.918a0d08b8000p-4},
+{0x1.d77b681ff38b3p-1, 0x1.e72e9da044000p-4},
+{0x1.d0cb5724de943p-1, 0x1.1dcd2507f6000p-3},
+{0x1.ca4b2dc0e7563p-1, 0x1.476ab03dea000p-3},
+{0x1.c3f8ee8d6cb51p-1, 0x1.7074377e22000p-3},
+{0x1.bdd2b4f020c4cp-1, 0x1.98ede8ba94000p-3},
+{0x1.b7d6c006015cap-1, 0x1.c0db86ad2e000p-3},
+{0x1.b20366e2e338fp-1, 0x1.e840aafcee000p-3},
+{0x1.ac57026295039p-1, 0x1.0790ab4678000p-2},
+{0x1.a6d01bc2731ddp-1, 0x1.1ac056801c000p-2},
+{0x1.a16d3bc3ff18bp-1, 0x1.2db11d4fee000p-2},
+{0x1.9c2d14967feadp-1, 0x1.406464ec58000p-2},
+{0x1.970e4f47c9902p-1, 0x1.52dbe093af000p-2},
+{0x1.920fb3982bcf2p-1, 0x1.651902050d000p-2},
+{0x1.8d30187f759f1p-1, 0x1.771d2cdeaf000p-2},
+{0x1.886e5ebb9f66dp-1, 0x1.88e9c857d9000p-2},
+{0x1.83c97b658b994p-1, 0x1.9a80155e16000p-2},
+{0x1.7f405ffc61022p-1, 0x1.abe186ed3d000p-2},
+{0x1.7ad22181415cap-1, 0x1.bd0f2aea0e000p-2},
+{0x1.767dcf99eff8cp-1, 0x1.ce0a43dbf4000p-2},
+#endif
+},
+#if !HAVE_FAST_FMA
+.tab2 = {
+# if N == 64
+{0x1.6200012b90a8ep-1, 0x1.904ab0644b605p-55},
+{0x1.66000045734a6p-1, 0x1.1ff9bea62f7a9p-57},
+{0x1.69fffc325f2c5p-1, 0x1.27ecfcb3c90bap-55},
+{0x1.6e00038b95a04p-1, 0x1.8ff8856739326p-55},
+{0x1.71fffe09994e3p-1, 0x1.afd40275f82b1p-55},
+{0x1.7600015590e1p-1, -0x1.2fd75b4238341p-56},
+{0x1.7a00012655bd5p-1, 0x1.808e67c242b76p-56},
+{0x1.7e0003259e9a6p-1, -0x1.208e426f622b7p-57},
+{0x1.81fffedb4b2d2p-1, -0x1.402461ea5c92fp-55},
+{0x1.860002dfafcc3p-1, 0x1.df7f4a2f29a1fp-57},
+{0x1.89ffff78c6b5p-1, -0x1.e0453094995fdp-55},
+{0x1.8e00039671566p-1, -0x1.a04f3bec77b45p-55},
+{0x1.91fffe2bf1745p-1, -0x1.7fa34400e203cp-56},
+{0x1.95fffcc5c9fd1p-1, -0x1.6ff8005a0695dp-56},
+{0x1.9a0003bba4767p-1, 0x1.0f8c4c4ec7e03p-56},
+{0x1.9dfffe7b92da5p-1, 0x1.e7fd9478c4602p-55},
+{0x1.a1fffd72efdafp-1, -0x1.a0c554dcdae7ep-57},
+{0x1.a5fffde04ff95p-1, 0x1.67da98ce9b26bp-55},
+{0x1.a9fffca5e8d2bp-1, -0x1.284c9b54c13dep-55},
+{0x1.adfffddad03eap-1, 0x1.812c8ea602e3cp-58},
+{0x1.b1ffff10d3d4dp-1, -0x1.efaddad27789cp-55},
+{0x1.b5fffce21165ap-1, 0x1.3cb1719c61237p-58},
+{0x1.b9fffd950e674p-1, 0x1.3f7d94194cep-56},
+{0x1.be000139ca8afp-1, 0x1.50ac4215d9bcp-56},
+{0x1.c20005b46df99p-1, 0x1.beea653e9c1c9p-57},
+{0x1.c600040b9f7aep-1, -0x1.c079f274a70d6p-56},
+{0x1.ca0006255fd8ap-1, -0x1.a0b4076e84c1fp-56},
+{0x1.cdfffd94c095dp-1, 0x1.8f933f99ab5d7p-55},
+{0x1.d1ffff975d6cfp-1, -0x1.82c08665fe1bep-58},
+{0x1.d5fffa2561c93p-1, -0x1.b04289bd295f3p-56},
+{0x1.d9fff9d228b0cp-1, 0x1.70251340fa236p-55},
+{0x1.de00065bc7e16p-1, -0x1.5011e16a4d80cp-56},
+{0x1.e200002f64791p-1, 0x1.9802f09ef62ep-55},
+{0x1.e600057d7a6d8p-1, -0x1.e0b75580cf7fap-56},
+{0x1.ea00027edc00cp-1, -0x1.c848309459811p-55},
+{0x1.ee0006cf5cb7cp-1, -0x1.f8027951576f4p-55},
+{0x1.f2000782b7dccp-1, -0x1.f81d97274538fp-55},
+{0x1.f6000260c450ap-1, -0x1.071002727ffdcp-59},
+{0x1.f9fffe88cd533p-1, -0x1.81bdce1fda8bp-58},
+{0x1.fdfffd50f8689p-1, 0x1.7f91acb918e6ep-55},
+{0x1.0200004292367p+0, 0x1.b7ff365324681p-54},
+{0x1.05fffe3e3d668p+0, 0x1.6fa08ddae957bp-55},
+{0x1.0a0000a85a757p+0, -0x1.7e2de80d3fb91p-58},
+{0x1.0e0001a5f3fccp+0, -0x1.1823305c5f014p-54},
+{0x1.11ffff8afbaf5p+0, -0x1.bfabb6680bac2p-55},
+{0x1.15fffe54d91adp+0, -0x1.d7f121737e7efp-54},
+{0x1.1a00011ac36e1p+0, 0x1.c000a0516f5ffp-54},
+{0x1.1e00019c84248p+0, -0x1.082fbe4da5dap-54},
+{0x1.220000ffe5e6ep+0, -0x1.8fdd04c9cfb43p-55},
+{0x1.26000269fd891p+0, 0x1.cfe2a7994d182p-55},
+{0x1.2a00029a6e6dap+0, -0x1.00273715e8bc5p-56},
+{0x1.2dfffe0293e39p+0, 0x1.b7c39dab2a6f9p-54},
+{0x1.31ffff7dcf082p+0, 0x1.df1336edc5254p-56},
+{0x1.35ffff05a8b6p+0, -0x1.e03564ccd31ebp-54},
+{0x1.3a0002e0eaeccp+0, 0x1.5f0e74bd3a477p-56},
+{0x1.3e000043bb236p+0, 0x1.c7dcb149d8833p-54},
+{0x1.4200002d187ffp+0, 0x1.e08afcf2d3d28p-56},
+{0x1.460000d387cb1p+0, 0x1.20837856599a6p-55},
+{0x1.4a00004569f89p+0, -0x1.9fa5c904fbcd2p-55},
+{0x1.4e000043543f3p+0, -0x1.81125ed175329p-56},
+{0x1.51fffcc027f0fp+0, 0x1.883d8847754dcp-54},
+{0x1.55ffffd87b36fp+0, -0x1.709e731d02807p-55},
+{0x1.59ffff21df7bap+0, 0x1.7f79f68727b02p-55},
+{0x1.5dfffebfc3481p+0, -0x1.180902e30e93ep-54},
+# endif
+},
+#endif /* !HAVE_FAST_FMA */
+};
diff --git a/libc/AOR_v20.02/math/log2f.c b/libc/AOR_v20.02/math/log2f.c
new file mode 100644
index 000000000000..a43814f9827c
--- /dev/null
+++ b/libc/AOR_v20.02/math/log2f.c
@@ -0,0 +1,81 @@
+/*
+ * Single-precision log2 function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+LOG2F_TABLE_BITS = 4
+LOG2F_POLY_ORDER = 4
+
+ULP error: 0.752 (nearest rounding.)
+Relative error: 1.9 * 2^-26 (before rounding.)
+*/
+
+#define N (1 << LOG2F_TABLE_BITS)
+#define T __log2f_data.tab
+#define A __log2f_data.poly
+#define OFF 0x3f330000
+
+float
+log2f (float x)
+{
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t z, r, r2, p, y, y0, invc, logc;
+ uint32_t ix, iz, top, tmp;
+ int k, i;
+
+ ix = asuint (x);
+#if WANT_ROUNDING
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (unlikely (ix == 0x3f800000))
+ return 0;
+#endif
+ if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
+ {
+ /* x < 0x1p-126 or inf or nan. */
+ if (ix * 2 == 0)
+ return __math_divzerof (1);
+ if (ix == 0x7f800000) /* log2(inf) == inf. */
+ return x;
+ if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
+ return __math_invalidf (x);
+ /* x is subnormal, normalize it. */
+ ix = asuint (x * 0x1p23f);
+ ix -= 23 << 23;
+ }
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
+ top = tmp & 0xff800000;
+ iz = ix - top;
+ k = (int32_t) tmp >> 23; /* arithmetic shift */
+ invc = T[i].invc;
+ logc = T[i].logc;
+ z = (double_t) asfloat (iz);
+
+ /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
+ r = z * invc - 1;
+ y0 = logc + (double_t) k;
+
+ /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
+ r2 = r * r;
+ y = A[1] * r + A[2];
+ y = A[0] * r2 + y;
+ p = A[3] * r + y0;
+ y = y * r2 + p;
+ return eval_as_float (y);
+}
+#if USE_GLIBC_ABI
+strong_alias (log2f, __log2f_finite)
+hidden_alias (log2f, __ieee754_log2f)
+#endif
diff --git a/libc/AOR_v20.02/math/log2f_data.c b/libc/AOR_v20.02/math/log2f_data.c
new file mode 100644
index 000000000000..f8f270db4015
--- /dev/null
+++ b/libc/AOR_v20.02/math/log2f_data.c
@@ -0,0 +1,34 @@
+/*
+ * Data definition for log2f.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+const struct log2f_data __log2f_data = {
+ .tab = {
+ { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 },
+ { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 },
+ { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 },
+ { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 },
+ { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 },
+ { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 },
+ { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 },
+ { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 },
+ { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 },
+ { 0x1p+0, 0x0p+0 },
+ { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 },
+ { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 },
+ { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 },
+ { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 },
+ { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 },
+ { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 },
+ },
+ .poly = {
+ -0x1.712b6f70a7e4dp-2, 0x1.ecabf496832ep-2, -0x1.715479ffae3dep-1,
+ 0x1.715475f35c8b8p0,
+ }
+};
diff --git a/libc/AOR_v20.02/math/log_data.c b/libc/AOR_v20.02/math/log_data.c
new file mode 100644
index 000000000000..26fc9dfca60c
--- /dev/null
+++ b/libc/AOR_v20.02/math/log_data.c
@@ -0,0 +1,512 @@
+/*
+ * Data for log.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+#define N (1 << LOG_TABLE_BITS)
+
+const struct log_data __log_data = {
+.ln2hi = 0x1.62e42fefa3800p-1,
+.ln2lo = 0x1.ef35793c76730p-45,
+.poly1 = {
+#if LOG_POLY1_ORDER == 10
+// relative error: 0x1.32eccc6p-62
+// in -0x1p-5 0x1.1p-5 (|log(1+x)| > 0x1p-5 outside this interval)
+-0x1p-1,
+0x1.55555555554e5p-2,
+-0x1.0000000000af2p-2,
+0x1.9999999bbe436p-3,
+-0x1.55555537f9cdep-3,
+0x1.24922fc8127cfp-3,
+-0x1.0000b7d6bb612p-3,
+0x1.c806ee1ddbcafp-4,
+-0x1.972335a9c2d6ep-4,
+#elif LOG_POLY1_ORDER == 11
+// relative error: 0x1.52c8b708p-68
+// in -0x1p-5 0x1.1p-5 (|log(1+x)| > 0x1p-5 outside this interval)
+-0x1p-1,
+0x1.5555555555555p-2,
+-0x1.ffffffffffea9p-3,
+0x1.999999999c4d4p-3,
+-0x1.55555557f5541p-3,
+0x1.249248fbe33e4p-3,
+-0x1.ffffc9a3c825bp-4,
+0x1.c71e1f204435dp-4,
+-0x1.9a7f26377d06ep-4,
+0x1.71c30cf8f7364p-4,
+#elif LOG_POLY1_ORDER == 12
+// relative error: 0x1.c04d76cp-63
+// in -0x1p-4 0x1.09p-4 (|log(1+x)| > 0x1p-4 outside the interval)
+-0x1p-1,
+0x1.5555555555577p-2,
+-0x1.ffffffffffdcbp-3,
+0x1.999999995dd0cp-3,
+-0x1.55555556745a7p-3,
+0x1.24924a344de3p-3,
+-0x1.fffffa4423d65p-4,
+0x1.c7184282ad6cap-4,
+-0x1.999eb43b068ffp-4,
+0x1.78182f7afd085p-4,
+-0x1.5521375d145cdp-4,
+#endif
+},
+.poly = {
+#if N == 64 && LOG_POLY_ORDER == 7
+// relative error: 0x1.906eb8ap-58
+// abs error: 0x1.d2cad5a8p-67
+// in -0x1.fp-8 0x1.fp-8
+-0x1.0000000000027p-1,
+0x1.555555555556ap-2,
+-0x1.fffffff0440bap-3,
+0x1.99999991906c3p-3,
+-0x1.555c8d7e8201ep-3,
+0x1.24978c59151fap-3,
+#elif N == 128 && LOG_POLY_ORDER == 6
+// relative error: 0x1.926199e8p-56
+// abs error: 0x1.882ff33p-65
+// in -0x1.fp-9 0x1.fp-9
+-0x1.0000000000001p-1,
+0x1.555555551305bp-2,
+-0x1.fffffffeb459p-3,
+0x1.999b324f10111p-3,
+-0x1.55575e506c89fp-3,
+#elif N == 128 && LOG_POLY_ORDER == 7
+// relative error: 0x1.649fc4bp-64
+// abs error: 0x1.c3b5769p-74
+// in -0x1.fp-9 0x1.fp-9
+-0x1.0000000000001p-1,
+0x1.5555555555556p-2,
+-0x1.fffffffea1a8p-3,
+0x1.99999998e9139p-3,
+-0x1.555776801b968p-3,
+0x1.2493c29331a5cp-3,
+#endif
+},
+/* Algorithm:
+
+ x = 2^k z
+ log(x) = k ln2 + log(c) + log(z/c)
+ log(z/c) = poly(z/c - 1)
+
+where z is in [1.6p-1; 1.6p0] which is split into N subintervals and z falls
+into the ith one, then table entries are computed as
+
+ tab[i].invc = 1/c
+ tab[i].logc = (double)log(c)
+ tab2[i].chi = (double)c
+ tab2[i].clo = (double)(c - (double)c)
+
+where c is near the center of the subinterval and is chosen by trying +-2^29
+floating point invc candidates around 1/center and selecting one for which
+
+ 1) the rounding error in 0x1.8p9 + logc is 0,
+ 2) the rounding error in z - chi - clo is < 0x1p-66 and
+ 3) the rounding error in (double)log(c) is minimized (< 0x1p-66).
+
+Note: 1) ensures that k*ln2hi + logc can be computed without rounding error,
+2) ensures that z/c - 1 can be computed as (z - chi - clo)*invc with close to
+a single rounding error when there is no fast fma for z*invc - 1, 3) ensures
+that logc + poly(z/c - 1) has small error, however near x == 1 when
+|log(x)| < 0x1p-4, this is not enough so that is special cased. */
+.tab = {
+#if N == 64
+{0x1.7242886495cd8p+0, -0x1.79e267bdfe000p-2},
+{0x1.6e1f769340dc9p+0, -0x1.6e60ee0ecb000p-2},
+{0x1.6a13ccc8f195cp+0, -0x1.63002fdbf6000p-2},
+{0x1.661ec72e86f3ap+0, -0x1.57bf76c597000p-2},
+{0x1.623fa6c447b16p+0, -0x1.4c9e07f0d2000p-2},
+{0x1.5e75bbca31702p+0, -0x1.419b42f027000p-2},
+{0x1.5ac05655adb10p+0, -0x1.36b67660e6000p-2},
+{0x1.571ed3e940191p+0, -0x1.2bef0839e4800p-2},
+{0x1.539094ac0fbbfp+0, -0x1.21445727cb000p-2},
+{0x1.5015007e7fc42p+0, -0x1.16b5ca3c3d000p-2},
+{0x1.4cab877c31cf9p+0, -0x1.0c42d3805f800p-2},
+{0x1.49539e76a88d3p+0, -0x1.01eae61b60800p-2},
+{0x1.460cbc12211dap+0, -0x1.ef5adb9fb0000p-3},
+{0x1.42d6624debe3ap+0, -0x1.db13daab99000p-3},
+{0x1.3fb0144f0d462p+0, -0x1.c6ffbe896e000p-3},
+{0x1.3c995a1f9a9b4p+0, -0x1.b31d84722d000p-3},
+{0x1.3991c23952500p+0, -0x1.9f6c3cf6eb000p-3},
+{0x1.3698df35eaa14p+0, -0x1.8beafe7f13000p-3},
+{0x1.33ae463091760p+0, -0x1.7898db878d000p-3},
+{0x1.30d190aae3d72p+0, -0x1.6574efe4ec000p-3},
+{0x1.2e025c9203c89p+0, -0x1.527e620845000p-3},
+{0x1.2b404a7244988p+0, -0x1.3fb457d798000p-3},
+{0x1.288b01dc19544p+0, -0x1.2d1615a077000p-3},
+{0x1.25e2268085f69p+0, -0x1.1aa2b431e5000p-3},
+{0x1.23456812abb74p+0, -0x1.08598f1d2b000p-3},
+{0x1.20b4703174157p+0, -0x1.ec738fee40000p-4},
+{0x1.1e2ef308b4e9bp+0, -0x1.c885768862000p-4},
+{0x1.1bb4a36b70a3fp+0, -0x1.a4e75b6a46000p-4},
+{0x1.194538e960658p+0, -0x1.8197efba9a000p-4},
+{0x1.16e0692a10ac8p+0, -0x1.5e95ad734e000p-4},
+{0x1.1485f1ba1568bp+0, -0x1.3bdf67117c000p-4},
+{0x1.12358e123ed6fp+0, -0x1.1973b744f0000p-4},
+{0x1.0fef01de37c8dp+0, -0x1.eea33446bc000p-5},
+{0x1.0db20b82be414p+0, -0x1.aaef4ab304000p-5},
+{0x1.0b7e6f67f69b3p+0, -0x1.67c962fd2c000p-5},
+{0x1.0953f342fc108p+0, -0x1.252f29acf8000p-5},
+{0x1.0732604ec956bp+0, -0x1.c63d19e9c0000p-6},
+{0x1.051980117f9b0p+0, -0x1.432ab6a388000p-6},
+{0x1.03091aa6810f1p+0, -0x1.8244357f50000p-7},
+{0x1.01010152cf066p+0, -0x1.0080a711c0000p-8},
+{0x1.fc07ef6b6e30bp-1, 0x1.fe03018e80000p-8},
+{0x1.f4465aa1024afp-1, 0x1.7b91986450000p-6},
+{0x1.ecc07a8fd3f5ep-1, 0x1.39e88608c8000p-5},
+{0x1.e573ad856b537p-1, 0x1.b42dc6e624000p-5},
+{0x1.de5d6dc7b8057p-1, 0x1.165372ec20000p-4},
+{0x1.d77b6498bddf7p-1, 0x1.51b07a0170000p-4},
+{0x1.d0cb580315c0fp-1, 0x1.8c3465c7ea000p-4},
+{0x1.ca4b30d1cf449p-1, 0x1.c5e544a290000p-4},
+{0x1.c3f8ef4810d8ep-1, 0x1.fec91aa0a6000p-4},
+{0x1.bdd2b8b311f44p-1, 0x1.1b72acdc5c000p-3},
+{0x1.b7d6c2eeac054p-1, 0x1.371fc65a98000p-3},
+{0x1.b20363474c8f5p-1, 0x1.526e61c1aa000p-3},
+{0x1.ac570165eeab1p-1, 0x1.6d60ffc240000p-3},
+{0x1.a6d019f331df4p-1, 0x1.87fa08a013000p-3},
+{0x1.a16d3ebc9e3c3p-1, 0x1.a23bc630c3000p-3},
+{0x1.9c2d14567ef45p-1, 0x1.bc286a3512000p-3},
+{0x1.970e4efae9169p-1, 0x1.d5c2195697000p-3},
+{0x1.920fb3bd0b802p-1, 0x1.ef0ae132d3000p-3},
+{0x1.8d3018b58699ap-1, 0x1.040259974e000p-2},
+{0x1.886e5ff170ee6p-1, 0x1.1058bd40e2000p-2},
+{0x1.83c977ad35d27p-1, 0x1.1c898c1137800p-2},
+{0x1.7f405ed16c520p-1, 0x1.2895a3e65b000p-2},
+{0x1.7ad220d0335c4p-1, 0x1.347dd8f6bd000p-2},
+{0x1.767dce53474fdp-1, 0x1.4043083cb3800p-2},
+#elif N == 128
+{0x1.734f0c3e0de9fp+0, -0x1.7cc7f79e69000p-2},
+{0x1.713786a2ce91fp+0, -0x1.76feec20d0000p-2},
+{0x1.6f26008fab5a0p+0, -0x1.713e31351e000p-2},
+{0x1.6d1a61f138c7dp+0, -0x1.6b85b38287800p-2},
+{0x1.6b1490bc5b4d1p+0, -0x1.65d5590807800p-2},
+{0x1.69147332f0cbap+0, -0x1.602d076180000p-2},
+{0x1.6719f18224223p+0, -0x1.5a8ca86909000p-2},
+{0x1.6524f99a51ed9p+0, -0x1.54f4356035000p-2},
+{0x1.63356aa8f24c4p+0, -0x1.4f637c36b4000p-2},
+{0x1.614b36b9ddc14p+0, -0x1.49da7fda85000p-2},
+{0x1.5f66452c65c4cp+0, -0x1.445923989a800p-2},
+{0x1.5d867b5912c4fp+0, -0x1.3edf439b0b800p-2},
+{0x1.5babccb5b90dep+0, -0x1.396ce448f7000p-2},
+{0x1.59d61f2d91a78p+0, -0x1.3401e17bda000p-2},
+{0x1.5805612465687p+0, -0x1.2e9e2ef468000p-2},
+{0x1.56397cee76bd3p+0, -0x1.2941b3830e000p-2},
+{0x1.54725e2a77f93p+0, -0x1.23ec58cda8800p-2},
+{0x1.52aff42064583p+0, -0x1.1e9e129279000p-2},
+{0x1.50f22dbb2bddfp+0, -0x1.1956d2b48f800p-2},
+{0x1.4f38f4734ded7p+0, -0x1.141679ab9f800p-2},
+{0x1.4d843cfde2840p+0, -0x1.0edd094ef9800p-2},
+{0x1.4bd3ec078a3c8p+0, -0x1.09aa518db1000p-2},
+{0x1.4a27fc3e0258ap+0, -0x1.047e65263b800p-2},
+{0x1.4880524d48434p+0, -0x1.feb224586f000p-3},
+{0x1.46dce1b192d0bp+0, -0x1.f474a7517b000p-3},
+{0x1.453d9d3391854p+0, -0x1.ea4443d103000p-3},
+{0x1.43a2744b4845ap+0, -0x1.e020d44e9b000p-3},
+{0x1.420b54115f8fbp+0, -0x1.d60a22977f000p-3},
+{0x1.40782da3ef4b1p+0, -0x1.cc00104959000p-3},
+{0x1.3ee8f5d57fe8fp+0, -0x1.c202956891000p-3},
+{0x1.3d5d9a00b4ce9p+0, -0x1.b81178d811000p-3},
+{0x1.3bd60c010c12bp+0, -0x1.ae2c9ccd3d000p-3},
+{0x1.3a5242b75dab8p+0, -0x1.a45402e129000p-3},
+{0x1.38d22cd9fd002p+0, -0x1.9a877681df000p-3},
+{0x1.3755bc5847a1cp+0, -0x1.90c6d69483000p-3},
+{0x1.35dce49ad36e2p+0, -0x1.87120a645c000p-3},
+{0x1.34679984dd440p+0, -0x1.7d68fb4143000p-3},
+{0x1.32f5cceffcb24p+0, -0x1.73cb83c627000p-3},
+{0x1.3187775a10d49p+0, -0x1.6a39a9b376000p-3},
+{0x1.301c8373e3990p+0, -0x1.60b3154b7a000p-3},
+{0x1.2eb4ebb95f841p+0, -0x1.5737d76243000p-3},
+{0x1.2d50a0219a9d1p+0, -0x1.4dc7b8fc23000p-3},
+{0x1.2bef9a8b7fd2ap+0, -0x1.4462c51d20000p-3},
+{0x1.2a91c7a0c1babp+0, -0x1.3b08abc830000p-3},
+{0x1.293726014b530p+0, -0x1.31b996b490000p-3},
+{0x1.27dfa5757a1f5p+0, -0x1.2875490a44000p-3},
+{0x1.268b39b1d3bbfp+0, -0x1.1f3b9f879a000p-3},
+{0x1.2539d838ff5bdp+0, -0x1.160c8252ca000p-3},
+{0x1.23eb7aac9083bp+0, -0x1.0ce7f57f72000p-3},
+{0x1.22a012ba940b6p+0, -0x1.03cdc49fea000p-3},
+{0x1.2157996cc4132p+0, -0x1.f57bdbc4b8000p-4},
+{0x1.201201dd2fc9bp+0, -0x1.e370896404000p-4},
+{0x1.1ecf4494d480bp+0, -0x1.d17983ef94000p-4},
+{0x1.1d8f5528f6569p+0, -0x1.bf9674ed8a000p-4},
+{0x1.1c52311577e7cp+0, -0x1.adc79202f6000p-4},
+{0x1.1b17c74cb26e9p+0, -0x1.9c0c3e7288000p-4},
+{0x1.19e010c2c1ab6p+0, -0x1.8a646b372c000p-4},
+{0x1.18ab07bb670bdp+0, -0x1.78d01b3ac0000p-4},
+{0x1.1778a25efbcb6p+0, -0x1.674f145380000p-4},
+{0x1.1648d354c31dap+0, -0x1.55e0e6d878000p-4},
+{0x1.151b990275fddp+0, -0x1.4485cdea1e000p-4},
+{0x1.13f0ea432d24cp+0, -0x1.333d94d6aa000p-4},
+{0x1.12c8b7210f9dap+0, -0x1.22079f8c56000p-4},
+{0x1.11a3028ecb531p+0, -0x1.10e4698622000p-4},
+{0x1.107fbda8434afp+0, -0x1.ffa6c6ad20000p-5},
+{0x1.0f5ee0f4e6bb3p+0, -0x1.dda8d4a774000p-5},
+{0x1.0e4065d2a9fcep+0, -0x1.bbcece4850000p-5},
+{0x1.0d244632ca521p+0, -0x1.9a1894012c000p-5},
+{0x1.0c0a77ce2981ap+0, -0x1.788583302c000p-5},
+{0x1.0af2f83c636d1p+0, -0x1.5715e67d68000p-5},
+{0x1.09ddb98a01339p+0, -0x1.35c8a49658000p-5},
+{0x1.08cabaf52e7dfp+0, -0x1.149e364154000p-5},
+{0x1.07b9f2f4e28fbp+0, -0x1.e72c082eb8000p-6},
+{0x1.06ab58c358f19p+0, -0x1.a55f152528000p-6},
+{0x1.059eea5ecf92cp+0, -0x1.63d62cf818000p-6},
+{0x1.04949cdd12c90p+0, -0x1.228fb8caa0000p-6},
+{0x1.038c6c6f0ada9p+0, -0x1.c317b20f90000p-7},
+{0x1.02865137932a9p+0, -0x1.419355daa0000p-7},
+{0x1.0182427ea7348p+0, -0x1.81203c2ec0000p-8},
+{0x1.008040614b195p+0, -0x1.0040979240000p-9},
+{0x1.fe01ff726fa1ap-1, 0x1.feff384900000p-9},
+{0x1.fa11cc261ea74p-1, 0x1.7dc41353d0000p-7},
+{0x1.f6310b081992ep-1, 0x1.3cea3c4c28000p-6},
+{0x1.f25f63ceeadcdp-1, 0x1.b9fc114890000p-6},
+{0x1.ee9c8039113e7p-1, 0x1.1b0d8ce110000p-5},
+{0x1.eae8078cbb1abp-1, 0x1.58a5bd001c000p-5},
+{0x1.e741aa29d0c9bp-1, 0x1.95c8340d88000p-5},
+{0x1.e3a91830a99b5p-1, 0x1.d276aef578000p-5},
+{0x1.e01e009609a56p-1, 0x1.07598e598c000p-4},
+{0x1.dca01e577bb98p-1, 0x1.253f5e30d2000p-4},
+{0x1.d92f20b7c9103p-1, 0x1.42edd8b380000p-4},
+{0x1.d5cac66fb5ccep-1, 0x1.606598757c000p-4},
+{0x1.d272caa5ede9dp-1, 0x1.7da76356a0000p-4},
+{0x1.cf26e3e6b2ccdp-1, 0x1.9ab434e1c6000p-4},
+{0x1.cbe6da2a77902p-1, 0x1.b78c7bb0d6000p-4},
+{0x1.c8b266d37086dp-1, 0x1.d431332e72000p-4},
+{0x1.c5894bd5d5804p-1, 0x1.f0a3171de6000p-4},
+{0x1.c26b533bb9f8cp-1, 0x1.067152b914000p-3},
+{0x1.bf583eeece73fp-1, 0x1.147858292b000p-3},
+{0x1.bc4fd75db96c1p-1, 0x1.2266ecdca3000p-3},
+{0x1.b951e0c864a28p-1, 0x1.303d7a6c55000p-3},
+{0x1.b65e2c5ef3e2cp-1, 0x1.3dfc33c331000p-3},
+{0x1.b374867c9888bp-1, 0x1.4ba366b7a8000p-3},
+{0x1.b094b211d304ap-1, 0x1.5933928d1f000p-3},
+{0x1.adbe885f2ef7ep-1, 0x1.66acd2418f000p-3},
+{0x1.aaf1d31603da2p-1, 0x1.740f8ec669000p-3},
+{0x1.a82e63fd358a7p-1, 0x1.815c0f51af000p-3},
+{0x1.a5740ef09738bp-1, 0x1.8e92954f68000p-3},
+{0x1.a2c2a90ab4b27p-1, 0x1.9bb3602f84000p-3},
+{0x1.a01a01393f2d1p-1, 0x1.a8bed1c2c0000p-3},
+{0x1.9d79f24db3c1bp-1, 0x1.b5b515c01d000p-3},
+{0x1.9ae2505c7b190p-1, 0x1.c2967ccbcc000p-3},
+{0x1.9852ef297ce2fp-1, 0x1.cf635d5486000p-3},
+{0x1.95cbaeea44b75p-1, 0x1.dc1bd3446c000p-3},
+{0x1.934c69de74838p-1, 0x1.e8c01b8cfe000p-3},
+{0x1.90d4f2f6752e6p-1, 0x1.f5509c0179000p-3},
+{0x1.8e6528effd79dp-1, 0x1.00e6c121fb800p-2},
+{0x1.8bfce9fcc007cp-1, 0x1.071b80e93d000p-2},
+{0x1.899c0dabec30ep-1, 0x1.0d46b9e867000p-2},
+{0x1.87427aa2317fbp-1, 0x1.13687334bd000p-2},
+{0x1.84f00acb39a08p-1, 0x1.1980d67234800p-2},
+{0x1.82a49e8653e55p-1, 0x1.1f8ffe0cc8000p-2},
+{0x1.8060195f40260p-1, 0x1.2595fd7636800p-2},
+{0x1.7e22563e0a329p-1, 0x1.2b9300914a800p-2},
+{0x1.7beb377dcb5adp-1, 0x1.3187210436000p-2},
+{0x1.79baa679725c2p-1, 0x1.377266dec1800p-2},
+{0x1.77907f2170657p-1, 0x1.3d54ffbaf3000p-2},
+{0x1.756cadbd6130cp-1, 0x1.432eee32fe000p-2},
+#endif
+},
+#if !HAVE_FAST_FMA
+.tab2 = {
+# if N == 64
+{0x1.61ffff94c4fecp-1, -0x1.9fe4fc998f325p-56},
+{0x1.66000020377ddp-1, 0x1.e804c7a9519f2p-55},
+{0x1.6a00004c41678p-1, 0x1.902c675d9ecfep-55},
+{0x1.6dffff7384f87p-1, -0x1.2fd6b95e55043p-56},
+{0x1.720000b37216ep-1, 0x1.802bc8d437043p-55},
+{0x1.75ffffbeb3c9dp-1, 0x1.6047ad0a0d4e4p-57},
+{0x1.7a0000628daep-1, -0x1.e00434b49313dp-56},
+{0x1.7dffffd7abd1ap-1, -0x1.6015f8a083576p-56},
+{0x1.81ffffdf40c54p-1, 0x1.7f54bf76a42c9p-57},
+{0x1.860000f334e11p-1, 0x1.60054cb5344d7p-56},
+{0x1.8a0001238aca7p-1, 0x1.c03c9bd132f55p-57},
+{0x1.8dffffb81d212p-1, -0x1.001e519f2764fp-55},
+{0x1.92000086adc7cp-1, 0x1.1fe40f88f49c6p-55},
+{0x1.960000135d8eap-1, -0x1.f832268dc3095p-55},
+{0x1.99ffff9435acp-1, 0x1.7031d8b835edcp-56},
+{0x1.9e00003478565p-1, -0x1.0030b221ce3eep-58},
+{0x1.a20000b592948p-1, 0x1.8fd2f1dbd4639p-55},
+{0x1.a600000ad0bcfp-1, 0x1.901d6a974e6bep-55},
+{0x1.a9ffff55953a5p-1, 0x1.a07556192db98p-57},
+{0x1.adffff29ce03dp-1, -0x1.fff0717ec71c2p-56},
+{0x1.b1ffff34f3ac8p-1, 0x1.8005573de89d1p-57},
+{0x1.b60000894c55bp-1, -0x1.ff2fb51b044c7p-57},
+{0x1.b9fffef45ec7dp-1, -0x1.9ff7c4e8730fp-56},
+{0x1.be0000cda7b2ap-1, 0x1.57d058dbf3c1dp-55},
+{0x1.c1ffff2c57917p-1, 0x1.7e66d7e48dbc9p-58},
+{0x1.c60000ea5b82ap-1, -0x1.47f5e132ed4bep-55},
+{0x1.ca0001121ae98p-1, -0x1.40958c8d5e00ap-58},
+{0x1.ce0000f9241cbp-1, -0x1.7da063caa81c8p-59},
+{0x1.d1fffe8be95a4p-1, -0x1.82e3a411afcd9p-59},
+{0x1.d5ffff035932bp-1, -0x1.00f901b3fe87dp-58},
+{0x1.d9fffe8b54ba7p-1, 0x1.ffef55d6e3a4p-55},
+{0x1.de0000ad95d19p-1, 0x1.5feb2efd4c7c7p-55},
+{0x1.e1fffe925ce47p-1, 0x1.c8085484eaf08p-55},
+{0x1.e5fffe3ddf853p-1, -0x1.fd5ed02c5cadp-60},
+{0x1.e9fffed0a0e5fp-1, -0x1.a80aaef411586p-55},
+{0x1.ee00008f82eep-1, -0x1.b000aeaf97276p-55},
+{0x1.f20000a22d2f4p-1, -0x1.8f8906e13eba3p-56},
+{0x1.f5fffee35b57dp-1, 0x1.1fdd33b2d3714p-57},
+{0x1.fa00014eec3a6p-1, -0x1.3ee0b7a18c1a5p-58},
+{0x1.fdffff5daa89fp-1, -0x1.c1e24c8e3b503p-58},
+{0x1.0200005b93349p+0, -0x1.50197fe6bedcap-54},
+{0x1.05ffff9d597acp+0, 0x1.20160d062d0dcp-55},
+{0x1.0a00005687a63p+0, -0x1.27f3f9307696ep-54},
+{0x1.0dffff779164ep+0, 0x1.b7eb40bb9c4f4p-54},
+{0x1.12000044a0aa8p+0, 0x1.efbc914d512c4p-55},
+{0x1.16000069685bcp+0, -0x1.c0bea3eb2d82cp-57},
+{0x1.1a000093f0d78p+0, 0x1.1fecbf1e8c52p-54},
+{0x1.1dffffb2b1457p+0, -0x1.3fc91365637d6p-55},
+{0x1.2200008824a1p+0, -0x1.dff7e9feb578ap-54},
+{0x1.25ffffeef953p+0, -0x1.b00a61ec912f7p-55},
+{0x1.2a0000a1e7783p+0, 0x1.60048318b0483p-56},
+{0x1.2e0000853d4c7p+0, -0x1.77fbedf2c8cf3p-54},
+{0x1.320000324c55bp+0, 0x1.f81983997354fp-54},
+{0x1.360000594f796p+0, -0x1.cfe4beff900a9p-54},
+{0x1.3a0000a4c1c0fp+0, 0x1.07dbb2e268d0ep-54},
+{0x1.3e0000751c61bp+0, 0x1.80583ed1c566ep-56},
+{0x1.42000069e8a9fp+0, 0x1.f01f1edf82045p-54},
+{0x1.460000b5a1e34p+0, -0x1.dfdf0cf45c14ap-55},
+{0x1.4a0000187e513p+0, 0x1.401306b83a98dp-55},
+{0x1.4dffff3ba420bp+0, 0x1.9fc6539a6454ep-56},
+{0x1.51fffffe391c9p+0, -0x1.601ef3353ac83p-54},
+{0x1.560000e342455p+0, 0x1.3fb7fac8ac151p-55},
+{0x1.59ffffc39676fp+0, 0x1.4fe7dd6659cc2p-55},
+{0x1.5dfffff10ef42p+0, -0x1.48154cb592bcbp-54},
+# elif N == 128
+{0x1.61000014fb66bp-1, 0x1.e026c91425b3cp-56},
+{0x1.63000034db495p-1, 0x1.dbfea48005d41p-55},
+{0x1.650000d94d478p-1, 0x1.e7fa786d6a5b7p-55},
+{0x1.67000074e6fadp-1, 0x1.1fcea6b54254cp-57},
+{0x1.68ffffedf0faep-1, -0x1.c7e274c590efdp-56},
+{0x1.6b0000763c5bcp-1, -0x1.ac16848dcda01p-55},
+{0x1.6d0001e5cc1f6p-1, 0x1.33f1c9d499311p-55},
+{0x1.6efffeb05f63ep-1, -0x1.e80041ae22d53p-56},
+{0x1.710000e86978p-1, 0x1.bff6671097952p-56},
+{0x1.72ffffc67e912p-1, 0x1.c00e226bd8724p-55},
+{0x1.74fffdf81116ap-1, -0x1.e02916ef101d2p-57},
+{0x1.770000f679c9p-1, -0x1.7fc71cd549c74p-57},
+{0x1.78ffffa7ec835p-1, 0x1.1bec19ef50483p-55},
+{0x1.7affffe20c2e6p-1, -0x1.07e1729cc6465p-56},
+{0x1.7cfffed3fc9p-1, -0x1.08072087b8b1cp-55},
+{0x1.7efffe9261a76p-1, 0x1.dc0286d9df9aep-55},
+{0x1.81000049ca3e8p-1, 0x1.97fd251e54c33p-55},
+{0x1.8300017932c8fp-1, -0x1.afee9b630f381p-55},
+{0x1.850000633739cp-1, 0x1.9bfbf6b6535bcp-55},
+{0x1.87000204289c6p-1, -0x1.bbf65f3117b75p-55},
+{0x1.88fffebf57904p-1, -0x1.9006ea23dcb57p-55},
+{0x1.8b00022bc04dfp-1, -0x1.d00df38e04b0ap-56},
+{0x1.8cfffe50c1b8ap-1, -0x1.8007146ff9f05p-55},
+{0x1.8effffc918e43p-1, 0x1.3817bd07a7038p-55},
+{0x1.910001efa5fc7p-1, 0x1.93e9176dfb403p-55},
+{0x1.9300013467bb9p-1, 0x1.f804e4b980276p-56},
+{0x1.94fffe6ee076fp-1, -0x1.f7ef0d9ff622ep-55},
+{0x1.96fffde3c12d1p-1, -0x1.082aa962638bap-56},
+{0x1.98ffff4458a0dp-1, -0x1.7801b9164a8efp-55},
+{0x1.9afffdd982e3ep-1, -0x1.740e08a5a9337p-55},
+{0x1.9cfffed49fb66p-1, 0x1.fce08c19bep-60},
+{0x1.9f00020f19c51p-1, -0x1.a3faa27885b0ap-55},
+{0x1.a10001145b006p-1, 0x1.4ff489958da56p-56},
+{0x1.a300007bbf6fap-1, 0x1.cbeab8a2b6d18p-55},
+{0x1.a500010971d79p-1, 0x1.8fecadd78793p-55},
+{0x1.a70001df52e48p-1, -0x1.f41763dd8abdbp-55},
+{0x1.a90001c593352p-1, -0x1.ebf0284c27612p-55},
+{0x1.ab0002a4f3e4bp-1, -0x1.9fd043cff3f5fp-57},
+{0x1.acfffd7ae1ed1p-1, -0x1.23ee7129070b4p-55},
+{0x1.aefffee510478p-1, 0x1.a063ee00edea3p-57},
+{0x1.b0fffdb650d5bp-1, 0x1.a06c8381f0ab9p-58},
+{0x1.b2ffffeaaca57p-1, -0x1.9011e74233c1dp-56},
+{0x1.b4fffd995badcp-1, -0x1.9ff1068862a9fp-56},
+{0x1.b7000249e659cp-1, 0x1.aff45d0864f3ep-55},
+{0x1.b8ffff987164p-1, 0x1.cfe7796c2c3f9p-56},
+{0x1.bafffd204cb4fp-1, -0x1.3ff27eef22bc4p-57},
+{0x1.bcfffd2415c45p-1, -0x1.cffb7ee3bea21p-57},
+{0x1.beffff86309dfp-1, -0x1.14103972e0b5cp-55},
+{0x1.c0fffe1b57653p-1, 0x1.bc16494b76a19p-55},
+{0x1.c2ffff1fa57e3p-1, -0x1.4feef8d30c6edp-57},
+{0x1.c4fffdcbfe424p-1, -0x1.43f68bcec4775p-55},
+{0x1.c6fffed54b9f7p-1, 0x1.47ea3f053e0ecp-55},
+{0x1.c8fffeb998fd5p-1, 0x1.383068df992f1p-56},
+{0x1.cb0002125219ap-1, -0x1.8fd8e64180e04p-57},
+{0x1.ccfffdd94469cp-1, 0x1.e7ebe1cc7ea72p-55},
+{0x1.cefffeafdc476p-1, 0x1.ebe39ad9f88fep-55},
+{0x1.d1000169af82bp-1, 0x1.57d91a8b95a71p-56},
+{0x1.d30000d0ff71dp-1, 0x1.9c1906970c7dap-55},
+{0x1.d4fffea790fc4p-1, -0x1.80e37c558fe0cp-58},
+{0x1.d70002edc87e5p-1, -0x1.f80d64dc10f44p-56},
+{0x1.d900021dc82aap-1, -0x1.47c8f94fd5c5cp-56},
+{0x1.dafffd86b0283p-1, 0x1.c7f1dc521617ep-55},
+{0x1.dd000296c4739p-1, 0x1.8019eb2ffb153p-55},
+{0x1.defffe54490f5p-1, 0x1.e00d2c652cc89p-57},
+{0x1.e0fffcdabf694p-1, -0x1.f8340202d69d2p-56},
+{0x1.e2fffdb52c8ddp-1, 0x1.b00c1ca1b0864p-56},
+{0x1.e4ffff24216efp-1, 0x1.2ffa8b094ab51p-56},
+{0x1.e6fffe88a5e11p-1, -0x1.7f673b1efbe59p-58},
+{0x1.e9000119eff0dp-1, -0x1.4808d5e0bc801p-55},
+{0x1.eafffdfa51744p-1, 0x1.80006d54320b5p-56},
+{0x1.ed0001a127fa1p-1, -0x1.002f860565c92p-58},
+{0x1.ef00007babcc4p-1, -0x1.540445d35e611p-55},
+{0x1.f0ffff57a8d02p-1, -0x1.ffb3139ef9105p-59},
+{0x1.f30001ee58ac7p-1, 0x1.a81acf2731155p-55},
+{0x1.f4ffff5823494p-1, 0x1.a3f41d4d7c743p-55},
+{0x1.f6ffffca94c6bp-1, -0x1.202f41c987875p-57},
+{0x1.f8fffe1f9c441p-1, 0x1.77dd1f477e74bp-56},
+{0x1.fafffd2e0e37ep-1, -0x1.f01199a7ca331p-57},
+{0x1.fd0001c77e49ep-1, 0x1.181ee4bceacb1p-56},
+{0x1.feffff7e0c331p-1, -0x1.e05370170875ap-57},
+{0x1.00ffff465606ep+0, -0x1.a7ead491c0adap-55},
+{0x1.02ffff3867a58p+0, -0x1.77f69c3fcb2ep-54},
+{0x1.04ffffdfc0d17p+0, 0x1.7bffe34cb945bp-54},
+{0x1.0700003cd4d82p+0, 0x1.20083c0e456cbp-55},
+{0x1.08ffff9f2cbe8p+0, -0x1.dffdfbe37751ap-57},
+{0x1.0b000010cda65p+0, -0x1.13f7faee626ebp-54},
+{0x1.0d00001a4d338p+0, 0x1.07dfa79489ff7p-55},
+{0x1.0effffadafdfdp+0, -0x1.7040570d66bcp-56},
+{0x1.110000bbafd96p+0, 0x1.e80d4846d0b62p-55},
+{0x1.12ffffae5f45dp+0, 0x1.dbffa64fd36efp-54},
+{0x1.150000dd59ad9p+0, 0x1.a0077701250aep-54},
+{0x1.170000f21559ap+0, 0x1.dfdf9e2e3deeep-55},
+{0x1.18ffffc275426p+0, 0x1.10030dc3b7273p-54},
+{0x1.1b000123d3c59p+0, 0x1.97f7980030188p-54},
+{0x1.1cffff8299eb7p+0, -0x1.5f932ab9f8c67p-57},
+{0x1.1effff48ad4p+0, 0x1.37fbf9da75bebp-54},
+{0x1.210000c8b86a4p+0, 0x1.f806b91fd5b22p-54},
+{0x1.2300003854303p+0, 0x1.3ffc2eb9fbf33p-54},
+{0x1.24fffffbcf684p+0, 0x1.601e77e2e2e72p-56},
+{0x1.26ffff52921d9p+0, 0x1.ffcbb767f0c61p-56},
+{0x1.2900014933a3cp+0, -0x1.202ca3c02412bp-56},
+{0x1.2b00014556313p+0, -0x1.2808233f21f02p-54},
+{0x1.2cfffebfe523bp+0, -0x1.8ff7e384fdcf2p-55},
+{0x1.2f0000bb8ad96p+0, -0x1.5ff51503041c5p-55},
+{0x1.30ffffb7ae2afp+0, -0x1.10071885e289dp-55},
+{0x1.32ffffeac5f7fp+0, -0x1.1ff5d3fb7b715p-54},
+{0x1.350000ca66756p+0, 0x1.57f82228b82bdp-54},
+{0x1.3700011fbf721p+0, 0x1.000bac40dd5ccp-55},
+{0x1.38ffff9592fb9p+0, -0x1.43f9d2db2a751p-54},
+{0x1.3b00004ddd242p+0, 0x1.57f6b707638e1p-55},
+{0x1.3cffff5b2c957p+0, 0x1.a023a10bf1231p-56},
+{0x1.3efffeab0b418p+0, 0x1.87f6d66b152bp-54},
+{0x1.410001532aff4p+0, 0x1.7f8375f198524p-57},
+{0x1.4300017478b29p+0, 0x1.301e672dc5143p-55},
+{0x1.44fffe795b463p+0, 0x1.9ff69b8b2895ap-55},
+{0x1.46fffe80475ep+0, -0x1.5c0b19bc2f254p-54},
+{0x1.48fffef6fc1e7p+0, 0x1.b4009f23a2a72p-54},
+{0x1.4afffe5bea704p+0, -0x1.4ffb7bf0d7d45p-54},
+{0x1.4d000171027dep+0, -0x1.9c06471dc6a3dp-54},
+{0x1.4f0000ff03ee2p+0, 0x1.77f890b85531cp-54},
+{0x1.5100012dc4bd1p+0, 0x1.004657166a436p-57},
+{0x1.530001605277ap+0, -0x1.6bfcece233209p-54},
+{0x1.54fffecdb704cp+0, -0x1.902720505a1d7p-55},
+{0x1.56fffef5f54a9p+0, 0x1.bbfe60ec96412p-54},
+{0x1.5900017e61012p+0, 0x1.87ec581afef9p-55},
+{0x1.5b00003c93e92p+0, -0x1.f41080abf0ccp-54},
+{0x1.5d0001d4919bcp+0, -0x1.8812afb254729p-54},
+{0x1.5efffe7b87a89p+0, -0x1.47eb780ed6904p-54},
+#endif
+},
+#endif /* !HAVE_FAST_FMA */
+};
diff --git a/libc/AOR_v20.02/math/logf.c b/libc/AOR_v20.02/math/logf.c
new file mode 100644
index 000000000000..5afe629d68e7
--- /dev/null
+++ b/libc/AOR_v20.02/math/logf.c
@@ -0,0 +1,80 @@
+/*
+ * Single-precision log function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+LOGF_TABLE_BITS = 4
+LOGF_POLY_ORDER = 4
+
+ULP error: 0.818 (nearest rounding.)
+Relative error: 1.957 * 2^-26 (before rounding.)
+*/
+
+#define T __logf_data.tab
+#define A __logf_data.poly
+#define Ln2 __logf_data.ln2
+#define N (1 << LOGF_TABLE_BITS)
+#define OFF 0x3f330000
+
+float
+logf (float x)
+{
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t z, r, r2, y, y0, invc, logc;
+ uint32_t ix, iz, tmp;
+ int k, i;
+
+ ix = asuint (x);
+#if WANT_ROUNDING
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (unlikely (ix == 0x3f800000))
+ return 0;
+#endif
+ if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
+ {
+ /* x < 0x1p-126 or inf or nan. */
+ if (ix * 2 == 0)
+ return __math_divzerof (1);
+ if (ix == 0x7f800000) /* log(inf) == inf. */
+ return x;
+ if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
+ return __math_invalidf (x);
+ /* x is subnormal, normalize it. */
+ ix = asuint (x * 0x1p23f);
+ ix -= 23 << 23;
+ }
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
+ k = (int32_t) tmp >> 23; /* arithmetic shift */
+ iz = ix - (tmp & 0x1ff << 23);
+ invc = T[i].invc;
+ logc = T[i].logc;
+ z = (double_t) asfloat (iz);
+
+ /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
+ r = z * invc - 1;
+ y0 = logc + (double_t) k * Ln2;
+
+ /* Pipelined polynomial evaluation to approximate log1p(r). */
+ r2 = r * r;
+ y = A[1] * r + A[2];
+ y = A[0] * r2 + y;
+ y = y * r2 + (y0 + r);
+ return eval_as_float (y);
+}
+#if USE_GLIBC_ABI
+strong_alias (logf, __logf_finite)
+hidden_alias (logf, __ieee754_logf)
+#endif
diff --git a/libc/AOR_v20.02/math/logf_data.c b/libc/AOR_v20.02/math/logf_data.c
new file mode 100644
index 000000000000..e4de10f58e67
--- /dev/null
+++ b/libc/AOR_v20.02/math/logf_data.c
@@ -0,0 +1,34 @@
+/*
+ * Data definition for logf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+const struct logf_data __logf_data = {
+ .tab = {
+ { 0x1.661ec79f8f3bep+0, -0x1.57bf7808caadep-2 },
+ { 0x1.571ed4aaf883dp+0, -0x1.2bef0a7c06ddbp-2 },
+ { 0x1.49539f0f010bp+0, -0x1.01eae7f513a67p-2 },
+ { 0x1.3c995b0b80385p+0, -0x1.b31d8a68224e9p-3 },
+ { 0x1.30d190c8864a5p+0, -0x1.6574f0ac07758p-3 },
+ { 0x1.25e227b0b8eap+0, -0x1.1aa2bc79c81p-3 },
+ { 0x1.1bb4a4a1a343fp+0, -0x1.a4e76ce8c0e5ep-4 },
+ { 0x1.12358f08ae5bap+0, -0x1.1973c5a611cccp-4 },
+ { 0x1.0953f419900a7p+0, -0x1.252f438e10c1ep-5 },
+ { 0x1p+0, 0x0p+0 },
+ { 0x1.e608cfd9a47acp-1, 0x1.aa5aa5df25984p-5 },
+ { 0x1.ca4b31f026aap-1, 0x1.c5e53aa362eb4p-4 },
+ { 0x1.b2036576afce6p-1, 0x1.526e57720db08p-3 },
+ { 0x1.9c2d163a1aa2dp-1, 0x1.bc2860d22477p-3 },
+ { 0x1.886e6037841edp-1, 0x1.1058bc8a07ee1p-2 },
+ { 0x1.767dcf5534862p-1, 0x1.4043057b6ee09p-2 },
+ },
+ .ln2 = 0x1.62e42fefa39efp-1,
+ .poly = {
+ -0x1.00ea348b88334p-2, 0x1.5575b0be00b6ap-2, -0x1.ffffef20a4123p-2,
+ }
+};
diff --git a/libc/AOR_v20.02/math/math_config.h b/libc/AOR_v20.02/math/math_config.h
new file mode 100644
index 000000000000..ea2d59e94ff0
--- /dev/null
+++ b/libc/AOR_v20.02/math/math_config.h
@@ -0,0 +1,420 @@
+/*
+ * Configuration for math routines.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef _MATH_CONFIG_H
+#define _MATH_CONFIG_H
+
+#include <math.h>
+#include <stdint.h>
+
+#ifndef WANT_ROUNDING
+/* If defined to 1, return correct results for special cases in non-nearest
+ rounding modes (logf (1.0f) returns 0.0f with FE_DOWNWARD rather than -0.0f).
+ This may be set to 0 if there is no fenv support or if math functions only
+ get called in round to nearest mode. */
+# define WANT_ROUNDING 1
+#endif
+#ifndef WANT_ERRNO
+/* If defined to 1, set errno in math functions according to ISO C. Many math
+ libraries do not set errno, so this is 0 by default. It may need to be
+ set to 1 if math.h has (math_errhandling & MATH_ERRNO) != 0. */
+# define WANT_ERRNO 0
+#endif
+#ifndef WANT_ERRNO_UFLOW
+/* Set errno to ERANGE if result underflows to 0 (in all rounding modes). */
+# define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
+#endif
+
+/* Compiler can inline round as a single instruction. */
+#ifndef HAVE_FAST_ROUND
+# if __aarch64__
+# define HAVE_FAST_ROUND 1
+# else
+# define HAVE_FAST_ROUND 0
+# endif
+#endif
+
+/* Compiler can inline lround, but not (long)round(x). */
+#ifndef HAVE_FAST_LROUND
+# if __aarch64__ && (100*__GNUC__ + __GNUC_MINOR__) >= 408 && __NO_MATH_ERRNO__
+# define HAVE_FAST_LROUND 1
+# else
+# define HAVE_FAST_LROUND 0
+# endif
+#endif
+
+/* Compiler can inline fma as a single instruction. */
+#ifndef HAVE_FAST_FMA
+# if defined FP_FAST_FMA || __aarch64__
+# define HAVE_FAST_FMA 1
+# else
+# define HAVE_FAST_FMA 0
+# endif
+#endif
+
+/* Provide *_finite symbols and some of the glibc hidden symbols
+ so libmathlib can be used with binaries compiled against glibc
+ to interpose math functions with both static and dynamic linking. */
+#ifndef USE_GLIBC_ABI
+# if __GNUC__
+# define USE_GLIBC_ABI 1
+# else
+# define USE_GLIBC_ABI 0
+# endif
+#endif
+
+/* Optionally used extensions. */
+#ifdef __GNUC__
+# define HIDDEN __attribute__ ((__visibility__ ("hidden")))
+# define NOINLINE __attribute__ ((noinline))
+# define UNUSED __attribute__ ((unused))
+# define likely(x) __builtin_expect (!!(x), 1)
+# define unlikely(x) __builtin_expect (x, 0)
+# if __GNUC__ >= 9
+# define attribute_copy(f) __attribute__ ((copy (f)))
+# else
+# define attribute_copy(f)
+# endif
+# define strong_alias(f, a) \
+ extern __typeof (f) a __attribute__ ((alias (#f))) attribute_copy (f);
+# define hidden_alias(f, a) \
+ extern __typeof (f) a __attribute__ ((alias (#f), visibility ("hidden"))) \
+ attribute_copy (f);
+#else
+# define HIDDEN
+# define NOINLINE
+# define UNUSED
+# define likely(x) (x)
+# define unlikely(x) (x)
+#endif
+
+#if HAVE_FAST_ROUND
+/* When set, the roundtoint and converttoint functions are provided with
+ the semantics documented below. */
+# define TOINT_INTRINSICS 1
+
+/* Round x to nearest int in all rounding modes, ties have to be rounded
+ consistently with converttoint so the results match. If the result
+ would be outside of [-2^31, 2^31-1] then the semantics is unspecified. */
+static inline double_t
+roundtoint (double_t x)
+{
+ return round (x);
+}
+
+/* Convert x to nearest int in all rounding modes, ties have to be rounded
+ consistently with roundtoint. If the result is not representible in an
+ int32_t then the semantics is unspecified. */
+static inline int32_t
+converttoint (double_t x)
+{
+# if HAVE_FAST_LROUND
+ return lround (x);
+# else
+ return (long) round (x);
+# endif
+}
+#endif
+
+static inline uint32_t
+asuint (float f)
+{
+ union
+ {
+ float f;
+ uint32_t i;
+ } u = {f};
+ return u.i;
+}
+
+static inline float
+asfloat (uint32_t i)
+{
+ union
+ {
+ uint32_t i;
+ float f;
+ } u = {i};
+ return u.f;
+}
+
+static inline uint64_t
+asuint64 (double f)
+{
+ union
+ {
+ double f;
+ uint64_t i;
+ } u = {f};
+ return u.i;
+}
+
+static inline double
+asdouble (uint64_t i)
+{
+ union
+ {
+ uint64_t i;
+ double f;
+ } u = {i};
+ return u.f;
+}
+
+#ifndef IEEE_754_2008_SNAN
+# define IEEE_754_2008_SNAN 1
+#endif
+static inline int
+issignalingf_inline (float x)
+{
+ uint32_t ix = asuint (x);
+ if (!IEEE_754_2008_SNAN)
+ return (ix & 0x7fc00000) == 0x7fc00000;
+ return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
+}
+
+static inline int
+issignaling_inline (double x)
+{
+ uint64_t ix = asuint64 (x);
+ if (!IEEE_754_2008_SNAN)
+ return (ix & 0x7ff8000000000000) == 0x7ff8000000000000;
+ return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL;
+}
+
+#if __aarch64__ && __GNUC__
+/* Prevent the optimization of a floating-point expression. */
+static inline float
+opt_barrier_float (float x)
+{
+ __asm__ __volatile__ ("" : "+w" (x));
+ return x;
+}
+static inline double
+opt_barrier_double (double x)
+{
+ __asm__ __volatile__ ("" : "+w" (x));
+ return x;
+}
+/* Force the evaluation of a floating-point expression for its side-effect. */
+static inline void
+force_eval_float (float x)
+{
+ __asm__ __volatile__ ("" : "+w" (x));
+}
+static inline void
+force_eval_double (double x)
+{
+ __asm__ __volatile__ ("" : "+w" (x));
+}
+#else
+static inline float
+opt_barrier_float (float x)
+{
+ volatile float y = x;
+ return y;
+}
+static inline double
+opt_barrier_double (double x)
+{
+ volatile double y = x;
+ return y;
+}
+static inline void
+force_eval_float (float x)
+{
+ volatile float y UNUSED = x;
+}
+static inline void
+force_eval_double (double x)
+{
+ volatile double y UNUSED = x;
+}
+#endif
+
+/* Evaluate an expression as the specified type, normally a type
+ cast should be enough, but compilers implement non-standard
+ excess-precision handling, so when FLT_EVAL_METHOD != 0 then
+ these functions may need to be customized. */
+static inline float
+eval_as_float (float x)
+{
+ return x;
+}
+static inline double
+eval_as_double (double x)
+{
+ return x;
+}
+
+/* Error handling tail calls for special cases, with a sign argument.
+ The sign of the return value is set if the argument is non-zero. */
+
+/* The result overflows. */
+HIDDEN float __math_oflowf (uint32_t);
+/* The result underflows to 0 in nearest rounding mode. */
+HIDDEN float __math_uflowf (uint32_t);
+/* The result underflows to 0 in some directed rounding mode only. */
+HIDDEN float __math_may_uflowf (uint32_t);
+/* Division by zero. */
+HIDDEN float __math_divzerof (uint32_t);
+/* The result overflows. */
+HIDDEN double __math_oflow (uint32_t);
+/* The result underflows to 0 in nearest rounding mode. */
+HIDDEN double __math_uflow (uint32_t);
+/* The result underflows to 0 in some directed rounding mode only. */
+HIDDEN double __math_may_uflow (uint32_t);
+/* Division by zero. */
+HIDDEN double __math_divzero (uint32_t);
+
+/* Error handling using input checking. */
+
+/* Invalid input unless it is a quiet NaN. */
+HIDDEN float __math_invalidf (float);
+/* Invalid input unless it is a quiet NaN. */
+HIDDEN double __math_invalid (double);
+
+/* Error handling using output checking, only for errno setting. */
+
+/* Check if the result overflowed to infinity. */
+HIDDEN double __math_check_oflow (double);
+/* Check if the result underflowed to 0. */
+HIDDEN double __math_check_uflow (double);
+
+/* Check if the result overflowed to infinity. */
+static inline double
+check_oflow (double x)
+{
+ return WANT_ERRNO ? __math_check_oflow (x) : x;
+}
+
+/* Check if the result underflowed to 0. */
+static inline double
+check_uflow (double x)
+{
+ return WANT_ERRNO ? __math_check_uflow (x) : x;
+}
+
+
+/* Shared between expf, exp2f and powf. */
+#define EXP2F_TABLE_BITS 5
+#define EXP2F_POLY_ORDER 3
+extern const struct exp2f_data
+{
+ uint64_t tab[1 << EXP2F_TABLE_BITS];
+ double shift_scaled;
+ double poly[EXP2F_POLY_ORDER];
+ double shift;
+ double invln2_scaled;
+ double poly_scaled[EXP2F_POLY_ORDER];
+} __exp2f_data HIDDEN;
+
+#define LOGF_TABLE_BITS 4
+#define LOGF_POLY_ORDER 4
+extern const struct logf_data
+{
+ struct
+ {
+ double invc, logc;
+ } tab[1 << LOGF_TABLE_BITS];
+ double ln2;
+ double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */
+} __logf_data HIDDEN;
+
+#define LOG2F_TABLE_BITS 4
+#define LOG2F_POLY_ORDER 4
+extern const struct log2f_data
+{
+ struct
+ {
+ double invc, logc;
+ } tab[1 << LOG2F_TABLE_BITS];
+ double poly[LOG2F_POLY_ORDER];
+} __log2f_data HIDDEN;
+
+#define POWF_LOG2_TABLE_BITS 4
+#define POWF_LOG2_POLY_ORDER 5
+#if TOINT_INTRINSICS
+# define POWF_SCALE_BITS EXP2F_TABLE_BITS
+#else
+# define POWF_SCALE_BITS 0
+#endif
+#define POWF_SCALE ((double) (1 << POWF_SCALE_BITS))
+extern const struct powf_log2_data
+{
+ struct
+ {
+ double invc, logc;
+ } tab[1 << POWF_LOG2_TABLE_BITS];
+ double poly[POWF_LOG2_POLY_ORDER];
+} __powf_log2_data HIDDEN;
+
+
+#define EXP_TABLE_BITS 7
+#define EXP_POLY_ORDER 5
+/* Use polynomial that is optimized for a wider input range. This may be
+ needed for good precision in non-nearest rounding and !TOINT_INTRINSICS. */
+#define EXP_POLY_WIDE 0
+/* Use close to nearest rounding toint when !TOINT_INTRINSICS. This may be
+ needed for good precision in non-nearest rouning and !EXP_POLY_WIDE. */
+#define EXP_USE_TOINT_NARROW 0
+#define EXP2_POLY_ORDER 5
+#define EXP2_POLY_WIDE 0
+extern const struct exp_data
+{
+ double invln2N;
+ double shift;
+ double negln2hiN;
+ double negln2loN;
+ double poly[4]; /* Last four coefficients. */
+ double exp2_shift;
+ double exp2_poly[EXP2_POLY_ORDER];
+ uint64_t tab[2*(1 << EXP_TABLE_BITS)];
+} __exp_data HIDDEN;
+
+#define LOG_TABLE_BITS 7
+#define LOG_POLY_ORDER 6
+#define LOG_POLY1_ORDER 12
+extern const struct log_data
+{
+ double ln2hi;
+ double ln2lo;
+ double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
+ double poly1[LOG_POLY1_ORDER - 1];
+ struct {double invc, logc;} tab[1 << LOG_TABLE_BITS];
+#if !HAVE_FAST_FMA
+ struct {double chi, clo;} tab2[1 << LOG_TABLE_BITS];
+#endif
+} __log_data HIDDEN;
+
+#define LOG2_TABLE_BITS 6
+#define LOG2_POLY_ORDER 7
+#define LOG2_POLY1_ORDER 11
+extern const struct log2_data
+{
+ double invln2hi;
+ double invln2lo;
+ double poly[LOG2_POLY_ORDER - 1];
+ double poly1[LOG2_POLY1_ORDER - 1];
+ struct {double invc, logc;} tab[1 << LOG2_TABLE_BITS];
+#if !HAVE_FAST_FMA
+ struct {double chi, clo;} tab2[1 << LOG2_TABLE_BITS];
+#endif
+} __log2_data HIDDEN;
+
+#define POW_LOG_TABLE_BITS 7
+#define POW_LOG_POLY_ORDER 8
+extern const struct pow_log_data
+{
+ double ln2hi;
+ double ln2lo;
+ double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
+ /* Note: the pad field is unused, but allows slightly faster indexing. */
+ struct {double invc, pad, logc, logctail;} tab[1 << POW_LOG_TABLE_BITS];
+} __pow_log_data HIDDEN;
+
+#endif
diff --git a/libc/AOR_v20.02/math/math_err.c b/libc/AOR_v20.02/math/math_err.c
new file mode 100644
index 000000000000..77d8a940efee
--- /dev/null
+++ b/libc/AOR_v20.02/math/math_err.c
@@ -0,0 +1,81 @@
+/*
+ * Double-precision math error handling.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+#if WANT_ERRNO
+#include <errno.h>
+/* NOINLINE reduces code size and avoids making math functions non-leaf
+ when the error handling is inlined. */
+NOINLINE static double
+with_errno (double y, int e)
+{
+ errno = e;
+ return y;
+}
+#else
+#define with_errno(x, e) (x)
+#endif
+
+/* NOINLINE reduces code size. */
+NOINLINE static double
+xflow (uint32_t sign, double y)
+{
+ y = eval_as_double (opt_barrier_double (sign ? -y : y) * y);
+ return with_errno (y, ERANGE);
+}
+
+HIDDEN double
+__math_uflow (uint32_t sign)
+{
+ return xflow (sign, 0x1p-767);
+}
+
+#if WANT_ERRNO_UFLOW
+/* Underflows to zero in some non-nearest rounding mode, setting errno
+ is valid even if the result is non-zero, but in the subnormal range. */
+HIDDEN double
+__math_may_uflow (uint32_t sign)
+{
+ return xflow (sign, 0x1.8p-538);
+}
+#endif
+
+HIDDEN double
+__math_oflow (uint32_t sign)
+{
+ return xflow (sign, 0x1p769);
+}
+
+HIDDEN double
+__math_divzero (uint32_t sign)
+{
+ double y = opt_barrier_double (sign ? -1.0 : 1.0) / 0.0;
+ return with_errno (y, ERANGE);
+}
+
+HIDDEN double
+__math_invalid (double x)
+{
+ double y = (x - x) / (x - x);
+ return isnan (x) ? y : with_errno (y, EDOM);
+}
+
+/* Check result and set errno if necessary. */
+
+HIDDEN double
+__math_check_uflow (double y)
+{
+ return y == 0.0 ? with_errno (y, ERANGE) : y;
+}
+
+HIDDEN double
+__math_check_oflow (double y)
+{
+ return isinf (y) ? with_errno (y, ERANGE) : y;
+}
diff --git a/libc/AOR_v20.02/math/math_errf.c b/libc/AOR_v20.02/math/math_errf.c
new file mode 100644
index 000000000000..0837463af4fd
--- /dev/null
+++ b/libc/AOR_v20.02/math/math_errf.c
@@ -0,0 +1,67 @@
+/*
+ * Single-precision math error handling.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+#if WANT_ERRNO
+#include <errno.h>
+/* NOINLINE reduces code size and avoids making math functions non-leaf
+ when the error handling is inlined. */
+NOINLINE static float
+with_errnof (float y, int e)
+{
+ errno = e;
+ return y;
+}
+#else
+#define with_errnof(x, e) (x)
+#endif
+
+/* NOINLINE reduces code size. */
+NOINLINE static float
+xflowf (uint32_t sign, float y)
+{
+ y = eval_as_float (opt_barrier_float (sign ? -y : y) * y);
+ return with_errnof (y, ERANGE);
+}
+
+HIDDEN float
+__math_uflowf (uint32_t sign)
+{
+ return xflowf (sign, 0x1p-95f);
+}
+
+#if WANT_ERRNO_UFLOW
+/* Underflows to zero in some non-nearest rounding mode, setting errno
+ is valid even if the result is non-zero, but in the subnormal range. */
+HIDDEN float
+__math_may_uflowf (uint32_t sign)
+{
+ return xflowf (sign, 0x1.4p-75f);
+}
+#endif
+
+HIDDEN float
+__math_oflowf (uint32_t sign)
+{
+ return xflowf (sign, 0x1p97f);
+}
+
+HIDDEN float
+__math_divzerof (uint32_t sign)
+{
+ float y = opt_barrier_float (sign ? -1.0f : 1.0f) / 0.0f;
+ return with_errnof (y, ERANGE);
+}
+
+HIDDEN float
+__math_invalidf (float x)
+{
+ float y = (x - x) / (x - x);
+ return isnan (x) ? y : with_errnof (y, EDOM);
+}
diff --git a/libc/AOR_v20.02/math/pow.c b/libc/AOR_v20.02/math/pow.c
new file mode 100644
index 000000000000..acdb23da138e
--- /dev/null
+++ b/libc/AOR_v20.02/math/pow.c
@@ -0,0 +1,381 @@
+/*
+ * Double-precision x^y function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <float.h>
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+Worst-case error: 0.54 ULP (~= ulperr_exp + 1024*Ln2*relerr_log*2^53)
+relerr_log: 1.3 * 2^-68 (Relative error of log, 1.5 * 2^-68 without fma)
+ulperr_exp: 0.509 ULP (ULP error of exp, 0.511 ULP without fma)
+*/
+
+#define T __pow_log_data.tab
+#define A __pow_log_data.poly
+#define Ln2hi __pow_log_data.ln2hi
+#define Ln2lo __pow_log_data.ln2lo
+#define N (1 << POW_LOG_TABLE_BITS)
+#define OFF 0x3fe6955500000000
+
+/* Top 12 bits of a double (sign and exponent bits). */
+static inline uint32_t
+top12 (double x)
+{
+ return asuint64 (x) >> 52;
+}
+
+/* Compute y+TAIL = log(x) where the rounded result is y and TAIL has about
+ additional 15 bits precision. IX is the bit representation of x, but
+ normalized in the subnormal range using the sign bit for the exponent. */
+static inline double_t
+log_inline (uint64_t ix, double_t *tail)
+{
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t z, r, y, invc, logc, logctail, kd, hi, t1, t2, lo, lo1, lo2, p;
+ uint64_t iz, tmp;
+ int k, i;
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (52 - POW_LOG_TABLE_BITS)) % N;
+ k = (int64_t) tmp >> 52; /* arithmetic shift */
+ iz = ix - (tmp & 0xfffULL << 52);
+ z = asdouble (iz);
+ kd = (double_t) k;
+
+ /* log(x) = k*Ln2 + log(c) + log1p(z/c-1). */
+ invc = T[i].invc;
+ logc = T[i].logc;
+ logctail = T[i].logctail;
+
+ /* Note: 1/c is j/N or j/N/2 where j is an integer in [N,2N) and
+ |z/c - 1| < 1/N, so r = z/c - 1 is exactly representible. */
+#if HAVE_FAST_FMA
+ r = fma (z, invc, -1.0);
+#else
+ /* Split z such that rhi, rlo and rhi*rhi are exact and |rlo| <= |r|. */
+ double_t zhi = asdouble ((iz + (1ULL << 31)) & (-1ULL << 32));
+ double_t zlo = z - zhi;
+ double_t rhi = zhi * invc - 1.0;
+ double_t rlo = zlo * invc;
+ r = rhi + rlo;
+#endif
+
+ /* k*Ln2 + log(c) + r. */
+ t1 = kd * Ln2hi + logc;
+ t2 = t1 + r;
+ lo1 = kd * Ln2lo + logctail;
+ lo2 = t1 - t2 + r;
+
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ double_t ar, ar2, ar3, lo3, lo4;
+ ar = A[0] * r; /* A[0] = -0.5. */
+ ar2 = r * ar;
+ ar3 = r * ar2;
+ /* k*Ln2 + log(c) + r + A[0]*r*r. */
+#if HAVE_FAST_FMA
+ hi = t2 + ar2;
+ lo3 = fma (ar, r, -ar2);
+ lo4 = t2 - hi + ar2;
+#else
+ double_t arhi = A[0] * rhi;
+ double_t arhi2 = rhi * arhi;
+ hi = t2 + arhi2;
+ lo3 = rlo * (ar + arhi);
+ lo4 = t2 - hi + arhi2;
+#endif
+ /* p = log1p(r) - r - A[0]*r*r. */
+#if POW_LOG_POLY_ORDER == 8
+ p = (ar3
+ * (A[1] + r * A[2] + ar2 * (A[3] + r * A[4] + ar2 * (A[5] + r * A[6]))));
+#endif
+ lo = lo1 + lo2 + lo3 + lo4 + p;
+ y = hi + lo;
+ *tail = hi - y + lo;
+ return y;
+}
+
+#undef N
+#undef T
+#define N (1 << EXP_TABLE_BITS)
+#define InvLn2N __exp_data.invln2N
+#define NegLn2hiN __exp_data.negln2hiN
+#define NegLn2loN __exp_data.negln2loN
+#define Shift __exp_data.shift
+#define T __exp_data.tab
+#define C2 __exp_data.poly[5 - EXP_POLY_ORDER]
+#define C3 __exp_data.poly[6 - EXP_POLY_ORDER]
+#define C4 __exp_data.poly[7 - EXP_POLY_ORDER]
+#define C5 __exp_data.poly[8 - EXP_POLY_ORDER]
+#define C6 __exp_data.poly[9 - EXP_POLY_ORDER]
+
+/* Handle cases that may overflow or underflow when computing the result that
+ is scale*(1+TMP) without intermediate rounding. The bit representation of
+ scale is in SBITS, however it has a computed exponent that may have
+ overflown into the sign bit so that needs to be adjusted before using it as
+ a double. (int32_t)KI is the k used in the argument reduction and exponent
+ adjustment of scale, positive k here means the result may overflow and
+ negative k means the result may underflow. */
+static inline double
+specialcase (double_t tmp, uint64_t sbits, uint64_t ki)
+{
+ double_t scale, y;
+
+ if ((ki & 0x80000000) == 0)
+ {
+ /* k > 0, the exponent of scale might have overflowed by <= 460. */
+ sbits -= 1009ull << 52;
+ scale = asdouble (sbits);
+ y = 0x1p1009 * (scale + scale * tmp);
+ return check_oflow (eval_as_double (y));
+ }
+ /* k < 0, need special care in the subnormal range. */
+ sbits += 1022ull << 52;
+ /* Note: sbits is signed scale. */
+ scale = asdouble (sbits);
+ y = scale + scale * tmp;
+ if (fabs (y) < 1.0)
+ {
+ /* Round y to the right precision before scaling it into the subnormal
+ range to avoid double rounding that can cause 0.5+E/2 ulp error where
+ E is the worst-case ulp error outside the subnormal range. So this
+ is only useful if the goal is better than 1 ulp worst-case error. */
+ double_t hi, lo, one = 1.0;
+ if (y < 0.0)
+ one = -1.0;
+ lo = scale - y + scale * tmp;
+ hi = one + y;
+ lo = one - hi + y + lo;
+ y = eval_as_double (hi + lo) - one;
+ /* Fix the sign of 0. */
+ if (y == 0.0)
+ y = asdouble (sbits & 0x8000000000000000);
+ /* The underflow exception needs to be signaled explicitly. */
+ force_eval_double (opt_barrier_double (0x1p-1022) * 0x1p-1022);
+ }
+ y = 0x1p-1022 * y;
+ return check_uflow (eval_as_double (y));
+}
+
+#define SIGN_BIAS (0x800 << EXP_TABLE_BITS)
+
+/* Computes sign*exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|.
+ The sign_bias argument is SIGN_BIAS or 0 and sets the sign to -1 or 1. */
+static inline double
+exp_inline (double_t x, double_t xtail, uint32_t sign_bias)
+{
+ uint32_t abstop;
+ uint64_t ki, idx, top, sbits;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, z, r, r2, scale, tail, tmp;
+
+ abstop = top12 (x) & 0x7ff;
+ if (unlikely (abstop - top12 (0x1p-54) >= top12 (512.0) - top12 (0x1p-54)))
+ {
+ if (abstop - top12 (0x1p-54) >= 0x80000000)
+ {
+ /* Avoid spurious underflow for tiny x. */
+ /* Note: 0 is common input. */
+ double_t one = WANT_ROUNDING ? 1.0 + x : 1.0;
+ return sign_bias ? -one : one;
+ }
+ if (abstop >= top12 (1024.0))
+ {
+ /* Note: inf and nan are already handled. */
+ if (asuint64 (x) >> 63)
+ return __math_uflow (sign_bias);
+ else
+ return __math_oflow (sign_bias);
+ }
+ /* Large x is special cased below. */
+ abstop = 0;
+ }
+
+ /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */
+ /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */
+ z = InvLn2N * x;
+#if TOINT_INTRINSICS
+ kd = roundtoint (z);
+ ki = converttoint (z);
+#elif EXP_USE_TOINT_NARROW
+ /* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
+ kd = eval_as_double (z + Shift);
+ ki = asuint64 (kd) >> 16;
+ kd = (double_t) (int32_t) ki;
+#else
+ /* z - kd is in [-1, 1] in non-nearest rounding modes. */
+ kd = eval_as_double (z + Shift);
+ ki = asuint64 (kd);
+ kd -= Shift;
+#endif
+ r = x + kd * NegLn2hiN + kd * NegLn2loN;
+ /* The code assumes 2^-200 < |xtail| < 2^-8/N. */
+ r += xtail;
+ /* 2^(k/N) ~= scale * (1 + tail). */
+ idx = 2 * (ki % N);
+ top = (ki + sign_bias) << (52 - EXP_TABLE_BITS);
+ tail = asdouble (T[idx]);
+ /* This is only a valid scale when -1023*N < k < 1024*N. */
+ sbits = T[idx + 1] + top;
+ /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */
+ /* Evaluation is optimized assuming superscalar pipelined execution. */
+ r2 = r * r;
+ /* Without fma the worst case error is 0.25/N ulp larger. */
+ /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */
+#if EXP_POLY_ORDER == 4
+ tmp = tail + r + r2 * C2 + r * r2 * (C3 + r * C4);
+#elif EXP_POLY_ORDER == 5
+ tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5);
+#elif EXP_POLY_ORDER == 6
+ tmp = tail + r + r2 * (0.5 + r * C3) + r2 * r2 * (C4 + r * C5 + r2 * C6);
+#endif
+ if (unlikely (abstop == 0))
+ return specialcase (tmp, sbits, ki);
+ scale = asdouble (sbits);
+ /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there
+ is no spurious underflow here even without fma. */
+ return eval_as_double (scale + scale * tmp);
+}
+
+/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is
+ the bit representation of a non-zero finite floating-point value. */
+static inline int
+checkint (uint64_t iy)
+{
+ int e = iy >> 52 & 0x7ff;
+ if (e < 0x3ff)
+ return 0;
+ if (e > 0x3ff + 52)
+ return 2;
+ if (iy & ((1ULL << (0x3ff + 52 - e)) - 1))
+ return 0;
+ if (iy & (1ULL << (0x3ff + 52 - e)))
+ return 1;
+ return 2;
+}
+
+/* Returns 1 if input is the bit representation of 0, infinity or nan. */
+static inline int
+zeroinfnan (uint64_t i)
+{
+ return 2 * i - 1 >= 2 * asuint64 (INFINITY) - 1;
+}
+
+double
+pow (double x, double y)
+{
+ uint32_t sign_bias = 0;
+ uint64_t ix, iy;
+ uint32_t topx, topy;
+
+ ix = asuint64 (x);
+ iy = asuint64 (y);
+ topx = top12 (x);
+ topy = top12 (y);
+ if (unlikely (topx - 0x001 >= 0x7ff - 0x001
+ || (topy & 0x7ff) - 0x3be >= 0x43e - 0x3be))
+ {
+ /* Note: if |y| > 1075 * ln2 * 2^53 ~= 0x1.749p62 then pow(x,y) = inf/0
+ and if |y| < 2^-54 / 1075 ~= 0x1.e7b6p-65 then pow(x,y) = +-1. */
+ /* Special cases: (x < 0x1p-126 or inf or nan) or
+ (|y| < 0x1p-65 or |y| >= 0x1p63 or nan). */
+ if (unlikely (zeroinfnan (iy)))
+ {
+ if (2 * iy == 0)
+ return issignaling_inline (x) ? x + y : 1.0;
+ if (ix == asuint64 (1.0))
+ return issignaling_inline (y) ? x + y : 1.0;
+ if (2 * ix > 2 * asuint64 (INFINITY)
+ || 2 * iy > 2 * asuint64 (INFINITY))
+ return x + y;
+ if (2 * ix == 2 * asuint64 (1.0))
+ return 1.0;
+ if ((2 * ix < 2 * asuint64 (1.0)) == !(iy >> 63))
+ return 0.0; /* |x|<1 && y==inf or |x|>1 && y==-inf. */
+ return y * y;
+ }
+ if (unlikely (zeroinfnan (ix)))
+ {
+ double_t x2 = x * x;
+ if (ix >> 63 && checkint (iy) == 1)
+ {
+ x2 = -x2;
+ sign_bias = 1;
+ }
+ if (WANT_ERRNO && 2 * ix == 0 && iy >> 63)
+ return __math_divzero (sign_bias);
+ /* Without the barrier some versions of clang hoist the 1/x2 and
+ thus division by zero exception can be signaled spuriously. */
+ return iy >> 63 ? opt_barrier_double (1 / x2) : x2;
+ }
+ /* Here x and y are non-zero finite. */
+ if (ix >> 63)
+ {
+ /* Finite x < 0. */
+ int yint = checkint (iy);
+ if (yint == 0)
+ return __math_invalid (x);
+ if (yint == 1)
+ sign_bias = SIGN_BIAS;
+ ix &= 0x7fffffffffffffff;
+ topx &= 0x7ff;
+ }
+ if ((topy & 0x7ff) - 0x3be >= 0x43e - 0x3be)
+ {
+ /* Note: sign_bias == 0 here because y is not odd. */
+ if (ix == asuint64 (1.0))
+ return 1.0;
+ if ((topy & 0x7ff) < 0x3be)
+ {
+ /* |y| < 2^-65, x^y ~= 1 + y*log(x). */
+ if (WANT_ROUNDING)
+ return ix > asuint64 (1.0) ? 1.0 + y : 1.0 - y;
+ else
+ return 1.0;
+ }
+ return (ix > asuint64 (1.0)) == (topy < 0x800) ? __math_oflow (0)
+ : __math_uflow (0);
+ }
+ if (topx == 0)
+ {
+ /* Normalize subnormal x so exponent becomes negative. */
+ /* Without the barrier some versions of clang evalutate the mul
+ unconditionally causing spurious overflow exceptions. */
+ ix = asuint64 (opt_barrier_double (x) * 0x1p52);
+ ix &= 0x7fffffffffffffff;
+ ix -= 52ULL << 52;
+ }
+ }
+
+ double_t lo;
+ double_t hi = log_inline (ix, &lo);
+ double_t ehi, elo;
+#if HAVE_FAST_FMA
+ ehi = y * hi;
+ elo = y * lo + fma (y, hi, -ehi);
+#else
+ double_t yhi = asdouble (iy & -1ULL << 27);
+ double_t ylo = y - yhi;
+ double_t lhi = asdouble (asuint64 (hi) & -1ULL << 27);
+ double_t llo = hi - lhi + lo;
+ ehi = yhi * lhi;
+ elo = ylo * lhi + y * llo; /* |elo| < |ehi| * 2^-25. */
+#endif
+ return exp_inline (ehi, elo, sign_bias);
+}
+#if USE_GLIBC_ABI
+strong_alias (pow, __pow_finite)
+hidden_alias (pow, __ieee754_pow)
+# if LDBL_MANT_DIG == 53
+long double powl (long double x, long double y) { return pow (x, y); }
+# endif
+#endif
diff --git a/libc/AOR_v20.02/math/pow_log_data.c b/libc/AOR_v20.02/math/pow_log_data.c
new file mode 100644
index 000000000000..445d605228f8
--- /dev/null
+++ b/libc/AOR_v20.02/math/pow_log_data.c
@@ -0,0 +1,185 @@
+/*
+ * Data for the log part of pow.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+#define N (1 << POW_LOG_TABLE_BITS)
+
+const struct pow_log_data __pow_log_data = {
+.ln2hi = 0x1.62e42fefa3800p-1,
+.ln2lo = 0x1.ef35793c76730p-45,
+.poly = {
+#if N == 128 && POW_LOG_POLY_ORDER == 8
+// relative error: 0x1.11922ap-70
+// in -0x1.6bp-8 0x1.6bp-8
+// Coefficients are scaled to match the scaling during evaluation.
+-0x1p-1,
+0x1.555555555556p-2 * -2,
+-0x1.0000000000006p-2 * -2,
+0x1.999999959554ep-3 * 4,
+-0x1.555555529a47ap-3 * 4,
+0x1.2495b9b4845e9p-3 * -8,
+-0x1.0002b8b263fc3p-3 * -8,
+#endif
+},
+/* Algorithm:
+
+ x = 2^k z
+ log(x) = k ln2 + log(c) + log(z/c)
+ log(z/c) = poly(z/c - 1)
+
+where z is in [0x1.69555p-1; 0x1.69555p0] which is split into N subintervals
+and z falls into the ith one, then table entries are computed as
+
+ tab[i].invc = 1/c
+ tab[i].logc = round(0x1p43*log(c))/0x1p43
+ tab[i].logctail = (double)(log(c) - logc)
+
+where c is chosen near the center of the subinterval such that 1/c has only a
+few precision bits so z/c - 1 is exactly representible as double:
+
+ 1/c = center < 1 ? round(N/center)/N : round(2*N/center)/N/2
+
+Note: |z/c - 1| < 1/N for the chosen c, |log(c) - logc - logctail| < 0x1p-97,
+the last few bits of logc are rounded away so k*ln2hi + logc has no rounding
+error and the interval for z is selected such that near x == 1, where log(x)
+is tiny, large cancellation error is avoided in logc + poly(z/c - 1). */
+.tab = {
+#if N == 128
+#define A(a, b, c) {a, 0, b, c},
+A(0x1.6a00000000000p+0, -0x1.62c82f2b9c800p-2, 0x1.ab42428375680p-48)
+A(0x1.6800000000000p+0, -0x1.5d1bdbf580800p-2, -0x1.ca508d8e0f720p-46)
+A(0x1.6600000000000p+0, -0x1.5767717455800p-2, -0x1.362a4d5b6506dp-45)
+A(0x1.6400000000000p+0, -0x1.51aad872df800p-2, -0x1.684e49eb067d5p-49)
+A(0x1.6200000000000p+0, -0x1.4be5f95777800p-2, -0x1.41b6993293ee0p-47)
+A(0x1.6000000000000p+0, -0x1.4618bc21c6000p-2, 0x1.3d82f484c84ccp-46)
+A(0x1.5e00000000000p+0, -0x1.404308686a800p-2, 0x1.c42f3ed820b3ap-50)
+A(0x1.5c00000000000p+0, -0x1.3a64c55694800p-2, 0x1.0b1c686519460p-45)
+A(0x1.5a00000000000p+0, -0x1.347dd9a988000p-2, 0x1.5594dd4c58092p-45)
+A(0x1.5800000000000p+0, -0x1.2e8e2bae12000p-2, 0x1.67b1e99b72bd8p-45)
+A(0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46)
+A(0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46)
+A(0x1.5400000000000p+0, -0x1.22941fbcf7800p-2, -0x1.65a242853da76p-46)
+A(0x1.5200000000000p+0, -0x1.1c898c1699800p-2, -0x1.fafbc68e75404p-46)
+A(0x1.5000000000000p+0, -0x1.1675cababa800p-2, 0x1.f1fc63382a8f0p-46)
+A(0x1.4e00000000000p+0, -0x1.1058bf9ae4800p-2, -0x1.6a8c4fd055a66p-45)
+A(0x1.4c00000000000p+0, -0x1.0a324e2739000p-2, -0x1.c6bee7ef4030ep-47)
+A(0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48)
+A(0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48)
+A(0x1.4800000000000p+0, -0x1.fb9186d5e4000p-3, 0x1.d572aab993c87p-47)
+A(0x1.4600000000000p+0, -0x1.ef0adcbdc6000p-3, 0x1.b26b79c86af24p-45)
+A(0x1.4400000000000p+0, -0x1.e27076e2af000p-3, -0x1.72f4f543fff10p-46)
+A(0x1.4200000000000p+0, -0x1.d5c216b4fc000p-3, 0x1.1ba91bbca681bp-45)
+A(0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45)
+A(0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45)
+A(0x1.3e00000000000p+0, -0x1.bc286742d9000p-3, 0x1.94eb0318bb78fp-46)
+A(0x1.3c00000000000p+0, -0x1.af3c94e80c000p-3, 0x1.a4e633fcd9066p-52)
+A(0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45)
+A(0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45)
+A(0x1.3800000000000p+0, -0x1.9525a9cf45000p-3, -0x1.ad1d904c1d4e3p-45)
+A(0x1.3600000000000p+0, -0x1.87fa06520d000p-3, 0x1.bbdbf7fdbfa09p-45)
+A(0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45)
+A(0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45)
+A(0x1.3200000000000p+0, -0x1.6d60fe719d000p-3, -0x1.0e46aa3b2e266p-46)
+A(0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46)
+A(0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46)
+A(0x1.2e00000000000p+0, -0x1.526e5e3a1b000p-3, -0x1.0de8b90075b8fp-45)
+A(0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46)
+A(0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46)
+A(0x1.2a00000000000p+0, -0x1.371fc201e9000p-3, 0x1.178864d27543ap-48)
+A(0x1.2800000000000p+0, -0x1.29552f81ff000p-3, -0x1.48d301771c408p-45)
+A(0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45)
+A(0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45)
+A(0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47)
+A(0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47)
+A(0x1.2200000000000p+0, -0x1.fec9131dbe000p-4, -0x1.575545ca333f2p-45)
+A(0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45)
+A(0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45)
+A(0x1.1e00000000000p+0, -0x1.c5e548f5bc000p-4, -0x1.d0c57585fbe06p-46)
+A(0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45)
+A(0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45)
+A(0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46)
+A(0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46)
+A(0x1.1800000000000p+0, -0x1.6f0d28ae56000p-4, -0x1.69737c93373dap-45)
+A(0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46)
+A(0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46)
+A(0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45)
+A(0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45)
+A(0x1.1200000000000p+0, -0x1.16536eea38000p-4, 0x1.47c5e768fa309p-46)
+A(0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45)
+A(0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45)
+A(0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46)
+A(0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46)
+A(0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45)
+A(0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45)
+A(0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48)
+A(0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48)
+A(0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45)
+A(0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45)
+A(0x1.0600000000000p+0, -0x1.7b91b07d58000p-6, -0x1.88d5493faa639p-45)
+A(0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50)
+A(0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50)
+A(0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46)
+A(0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46)
+A(0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0)
+A(0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0)
+A(0x1.fc00000000000p-1, 0x1.0101575890000p-7, -0x1.0c76b999d2be8p-46)
+A(0x1.f800000000000p-1, 0x1.0205658938000p-6, -0x1.3dc5b06e2f7d2p-45)
+A(0x1.f400000000000p-1, 0x1.8492528c90000p-6, -0x1.aa0ba325a0c34p-45)
+A(0x1.f000000000000p-1, 0x1.0415d89e74000p-5, 0x1.111c05cf1d753p-47)
+A(0x1.ec00000000000p-1, 0x1.466aed42e0000p-5, -0x1.c167375bdfd28p-45)
+A(0x1.e800000000000p-1, 0x1.894aa149fc000p-5, -0x1.97995d05a267dp-46)
+A(0x1.e400000000000p-1, 0x1.ccb73cdddc000p-5, -0x1.a68f247d82807p-46)
+A(0x1.e200000000000p-1, 0x1.eea31c006c000p-5, -0x1.e113e4fc93b7bp-47)
+A(0x1.de00000000000p-1, 0x1.1973bd1466000p-4, -0x1.5325d560d9e9bp-45)
+A(0x1.da00000000000p-1, 0x1.3bdf5a7d1e000p-4, 0x1.cc85ea5db4ed7p-45)
+A(0x1.d600000000000p-1, 0x1.5e95a4d97a000p-4, -0x1.c69063c5d1d1ep-45)
+A(0x1.d400000000000p-1, 0x1.700d30aeac000p-4, 0x1.c1e8da99ded32p-49)
+A(0x1.d000000000000p-1, 0x1.9335e5d594000p-4, 0x1.3115c3abd47dap-45)
+A(0x1.cc00000000000p-1, 0x1.b6ac88dad6000p-4, -0x1.390802bf768e5p-46)
+A(0x1.ca00000000000p-1, 0x1.c885801bc4000p-4, 0x1.646d1c65aacd3p-45)
+A(0x1.c600000000000p-1, 0x1.ec739830a2000p-4, -0x1.dc068afe645e0p-45)
+A(0x1.c400000000000p-1, 0x1.fe89139dbe000p-4, -0x1.534d64fa10afdp-45)
+A(0x1.c000000000000p-1, 0x1.1178e8227e000p-3, 0x1.1ef78ce2d07f2p-45)
+A(0x1.be00000000000p-1, 0x1.1aa2b7e23f000p-3, 0x1.ca78e44389934p-45)
+A(0x1.ba00000000000p-1, 0x1.2d1610c868000p-3, 0x1.39d6ccb81b4a1p-47)
+A(0x1.b800000000000p-1, 0x1.365fcb0159000p-3, 0x1.62fa8234b7289p-51)
+A(0x1.b400000000000p-1, 0x1.4913d8333b000p-3, 0x1.5837954fdb678p-45)
+A(0x1.b200000000000p-1, 0x1.527e5e4a1b000p-3, 0x1.633e8e5697dc7p-45)
+A(0x1.ae00000000000p-1, 0x1.6574ebe8c1000p-3, 0x1.9cf8b2c3c2e78p-46)
+A(0x1.ac00000000000p-1, 0x1.6f0128b757000p-3, -0x1.5118de59c21e1p-45)
+A(0x1.aa00000000000p-1, 0x1.7898d85445000p-3, -0x1.c661070914305p-46)
+A(0x1.a600000000000p-1, 0x1.8beafeb390000p-3, -0x1.73d54aae92cd1p-47)
+A(0x1.a400000000000p-1, 0x1.95a5adcf70000p-3, 0x1.7f22858a0ff6fp-47)
+A(0x1.a000000000000p-1, 0x1.a93ed3c8ae000p-3, -0x1.8724350562169p-45)
+A(0x1.9e00000000000p-1, 0x1.b31d8575bd000p-3, -0x1.c358d4eace1aap-47)
+A(0x1.9c00000000000p-1, 0x1.bd087383be000p-3, -0x1.d4bc4595412b6p-45)
+A(0x1.9a00000000000p-1, 0x1.c6ffbc6f01000p-3, -0x1.1ec72c5962bd2p-48)
+A(0x1.9600000000000p-1, 0x1.db13db0d49000p-3, -0x1.aff2af715b035p-45)
+A(0x1.9400000000000p-1, 0x1.e530effe71000p-3, 0x1.212276041f430p-51)
+A(0x1.9200000000000p-1, 0x1.ef5ade4dd0000p-3, -0x1.a211565bb8e11p-51)
+A(0x1.9000000000000p-1, 0x1.f991c6cb3b000p-3, 0x1.bcbecca0cdf30p-46)
+A(0x1.8c00000000000p-1, 0x1.07138604d5800p-2, 0x1.89cdb16ed4e91p-48)
+A(0x1.8a00000000000p-1, 0x1.0c42d67616000p-2, 0x1.7188b163ceae9p-45)
+A(0x1.8800000000000p-1, 0x1.1178e8227e800p-2, -0x1.c210e63a5f01cp-45)
+A(0x1.8600000000000p-1, 0x1.16b5ccbacf800p-2, 0x1.b9acdf7a51681p-45)
+A(0x1.8400000000000p-1, 0x1.1bf99635a6800p-2, 0x1.ca6ed5147bdb7p-45)
+A(0x1.8200000000000p-1, 0x1.214456d0eb800p-2, 0x1.a87deba46baeap-47)
+A(0x1.7e00000000000p-1, 0x1.2bef07cdc9000p-2, 0x1.a9cfa4a5004f4p-45)
+A(0x1.7c00000000000p-1, 0x1.314f1e1d36000p-2, -0x1.8e27ad3213cb8p-45)
+A(0x1.7a00000000000p-1, 0x1.36b6776be1000p-2, 0x1.16ecdb0f177c8p-46)
+A(0x1.7800000000000p-1, 0x1.3c25277333000p-2, 0x1.83b54b606bd5cp-46)
+A(0x1.7600000000000p-1, 0x1.419b423d5e800p-2, 0x1.8e436ec90e09dp-47)
+A(0x1.7400000000000p-1, 0x1.4718dc271c800p-2, -0x1.f27ce0967d675p-45)
+A(0x1.7200000000000p-1, 0x1.4c9e09e173000p-2, -0x1.e20891b0ad8a4p-45)
+A(0x1.7000000000000p-1, 0x1.522ae0738a000p-2, 0x1.ebe708164c759p-45)
+A(0x1.6e00000000000p-1, 0x1.57bf753c8d000p-2, 0x1.fadedee5d40efp-46)
+A(0x1.6c00000000000p-1, 0x1.5d5bddf596000p-2, -0x1.a0b2a08a465dcp-47)
+#endif
+},
+};
diff --git a/libc/AOR_v20.02/math/powf.c b/libc/AOR_v20.02/math/powf.c
new file mode 100644
index 000000000000..3cb70c0b6288
--- /dev/null
+++ b/libc/AOR_v20.02/math/powf.c
@@ -0,0 +1,222 @@
+/*
+ * Single-precision pow function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+POWF_LOG2_POLY_ORDER = 5
+EXP2F_TABLE_BITS = 5
+
+ULP error: 0.82 (~ 0.5 + relerr*2^24)
+relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2)
+relerr_log2: 1.83 * 2^-33 (Relative error of logx.)
+relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).)
+*/
+
+#define N (1 << POWF_LOG2_TABLE_BITS)
+#define T __powf_log2_data.tab
+#define A __powf_log2_data.poly
+#define OFF 0x3f330000
+
+/* Subnormal input is normalized so ix has negative biased exponent.
+ Output is multiplied by N (POWF_SCALE) if TOINT_INTRINICS is set. */
+static inline double_t
+log2_inline (uint32_t ix)
+{
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t z, r, r2, r4, p, q, y, y0, invc, logc;
+ uint32_t iz, top, tmp;
+ int k, i;
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (23 - POWF_LOG2_TABLE_BITS)) % N;
+ top = tmp & 0xff800000;
+ iz = ix - top;
+ k = (int32_t) top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */
+ invc = T[i].invc;
+ logc = T[i].logc;
+ z = (double_t) asfloat (iz);
+
+ /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
+ r = z * invc - 1;
+ y0 = logc + (double_t) k;
+
+ /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
+ r2 = r * r;
+ y = A[0] * r + A[1];
+ p = A[2] * r + A[3];
+ r4 = r2 * r2;
+ q = A[4] * r + y0;
+ q = p * r2 + q;
+ y = y * r4 + q;
+ return y;
+}
+
+#undef N
+#undef T
+#define N (1 << EXP2F_TABLE_BITS)
+#define T __exp2f_data.tab
+#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11))
+
+/* The output of log2 and thus the input of exp2 is either scaled by N
+ (in case of fast toint intrinsics) or not. The unscaled xd must be
+ in [-1021,1023], sign_bias sets the sign of the result. */
+static inline float
+exp2_inline (double_t xd, uint32_t sign_bias)
+{
+ uint64_t ki, ski, t;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, z, r, r2, y, s;
+
+#if TOINT_INTRINSICS
+# define C __exp2f_data.poly_scaled
+ /* N*x = k + r with r in [-1/2, 1/2] */
+ kd = roundtoint (xd); /* k */
+ ki = converttoint (xd);
+#else
+# define C __exp2f_data.poly
+# define SHIFT __exp2f_data.shift_scaled
+ /* x = k/N + r with r in [-1/(2N), 1/(2N)] */
+ kd = eval_as_double (xd + SHIFT);
+ ki = asuint64 (kd);
+ kd -= SHIFT; /* k/N */
+#endif
+ r = xd - kd;
+
+ /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+ t = T[ki % N];
+ ski = ki + sign_bias;
+ t += ski << (52 - EXP2F_TABLE_BITS);
+ s = asdouble (t);
+ z = C[0] * r + C[1];
+ r2 = r * r;
+ y = C[2] * r + 1;
+ y = z * r2 + y;
+ y = y * s;
+ return eval_as_float (y);
+}
+
+/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is
+ the bit representation of a non-zero finite floating-point value. */
+static inline int
+checkint (uint32_t iy)
+{
+ int e = iy >> 23 & 0xff;
+ if (e < 0x7f)
+ return 0;
+ if (e > 0x7f + 23)
+ return 2;
+ if (iy & ((1 << (0x7f + 23 - e)) - 1))
+ return 0;
+ if (iy & (1 << (0x7f + 23 - e)))
+ return 1;
+ return 2;
+}
+
+static inline int
+zeroinfnan (uint32_t ix)
+{
+ return 2 * ix - 1 >= 2u * 0x7f800000 - 1;
+}
+
+float
+powf (float x, float y)
+{
+ uint32_t sign_bias = 0;
+ uint32_t ix, iy;
+
+ ix = asuint (x);
+ iy = asuint (y);
+ if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000 || zeroinfnan (iy)))
+ {
+ /* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan). */
+ if (unlikely (zeroinfnan (iy)))
+ {
+ if (2 * iy == 0)
+ return issignalingf_inline (x) ? x + y : 1.0f;
+ if (ix == 0x3f800000)
+ return issignalingf_inline (y) ? x + y : 1.0f;
+ if (2 * ix > 2u * 0x7f800000 || 2 * iy > 2u * 0x7f800000)
+ return x + y;
+ if (2 * ix == 2 * 0x3f800000)
+ return 1.0f;
+ if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000))
+ return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf. */
+ return y * y;
+ }
+ if (unlikely (zeroinfnan (ix)))
+ {
+ float_t x2 = x * x;
+ if (ix & 0x80000000 && checkint (iy) == 1)
+ {
+ x2 = -x2;
+ sign_bias = 1;
+ }
+#if WANT_ERRNO
+ if (2 * ix == 0 && iy & 0x80000000)
+ return __math_divzerof (sign_bias);
+#endif
+ /* Without the barrier some versions of clang hoist the 1/x2 and
+ thus division by zero exception can be signaled spuriously. */
+ return iy & 0x80000000 ? opt_barrier_float (1 / x2) : x2;
+ }
+ /* x and y are non-zero finite. */
+ if (ix & 0x80000000)
+ {
+ /* Finite x < 0. */
+ int yint = checkint (iy);
+ if (yint == 0)
+ return __math_invalidf (x);
+ if (yint == 1)
+ sign_bias = SIGN_BIAS;
+ ix &= 0x7fffffff;
+ }
+ if (ix < 0x00800000)
+ {
+ /* Normalize subnormal x so exponent becomes negative. */
+ ix = asuint (x * 0x1p23f);
+ ix &= 0x7fffffff;
+ ix -= 23 << 23;
+ }
+ }
+ double_t logx = log2_inline (ix);
+ double_t ylogx = y * logx; /* Note: cannot overflow, y is single prec. */
+ if (unlikely ((asuint64 (ylogx) >> 47 & 0xffff)
+ >= asuint64 (126.0 * POWF_SCALE) >> 47))
+ {
+ /* |y*log(x)| >= 126. */
+ if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE)
+ /* |x^y| > 0x1.ffffffp127. */
+ return __math_oflowf (sign_bias);
+ if (WANT_ROUNDING && WANT_ERRNO
+ && ylogx > 0x1.fffffffa3aae2p+6 * POWF_SCALE)
+ /* |x^y| > 0x1.fffffep127, check if we round away from 0. */
+ if ((!sign_bias
+ && eval_as_float (1.0f + opt_barrier_float (0x1p-25f)) != 1.0f)
+ || (sign_bias
+ && eval_as_float (-1.0f - opt_barrier_float (0x1p-25f))
+ != -1.0f))
+ return __math_oflowf (sign_bias);
+ if (ylogx <= -150.0 * POWF_SCALE)
+ return __math_uflowf (sign_bias);
+#if WANT_ERRNO_UFLOW
+ if (ylogx < -149.0 * POWF_SCALE)
+ return __math_may_uflowf (sign_bias);
+#endif
+ }
+ return exp2_inline (ylogx, sign_bias);
+}
+#if USE_GLIBC_ABI
+strong_alias (powf, __powf_finite)
+hidden_alias (powf, __ieee754_powf)
+#endif
diff --git a/libc/AOR_v20.02/math/powf_log2_data.c b/libc/AOR_v20.02/math/powf_log2_data.c
new file mode 100644
index 000000000000..d7c74b3d19e8
--- /dev/null
+++ b/libc/AOR_v20.02/math/powf_log2_data.c
@@ -0,0 +1,35 @@
+/*
+ * Data definition for powf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "math_config.h"
+
+const struct powf_log2_data __powf_log2_data = {
+ .tab = {
+ { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * POWF_SCALE },
+ { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * POWF_SCALE },
+ { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * POWF_SCALE },
+ { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * POWF_SCALE },
+ { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * POWF_SCALE },
+ { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * POWF_SCALE },
+ { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * POWF_SCALE },
+ { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * POWF_SCALE },
+ { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * POWF_SCALE },
+ { 0x1p+0, 0x0p+0 * POWF_SCALE },
+ { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * POWF_SCALE },
+ { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * POWF_SCALE },
+ { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * POWF_SCALE },
+ { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * POWF_SCALE },
+ { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * POWF_SCALE },
+ { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * POWF_SCALE },
+ },
+ .poly = {
+ 0x1.27616c9496e0bp-2 * POWF_SCALE, -0x1.71969a075c67ap-2 * POWF_SCALE,
+ 0x1.ec70a6ca7baddp-2 * POWF_SCALE, -0x1.7154748bef6c8p-1 * POWF_SCALE,
+ 0x1.71547652ab82bp0 * POWF_SCALE,
+ }
+};
diff --git a/libc/AOR_v20.02/math/s_cos.c b/libc/AOR_v20.02/math/s_cos.c
new file mode 100644
index 000000000000..c0176c70e3d3
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_cos.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_cos.c"
diff --git a/libc/AOR_v20.02/math/s_cosf.c b/libc/AOR_v20.02/math/s_cosf.c
new file mode 100644
index 000000000000..8bea8ec96b60
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_cosf.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_cosf.c"
diff --git a/libc/AOR_v20.02/math/s_exp.c b/libc/AOR_v20.02/math/s_exp.c
new file mode 100644
index 000000000000..2c9dbe7dde9b
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_exp.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_exp.c"
diff --git a/libc/AOR_v20.02/math/s_exp2f.c b/libc/AOR_v20.02/math/s_exp2f.c
new file mode 100644
index 000000000000..de566753922d
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_exp2f.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_exp2f.c"
diff --git a/libc/AOR_v20.02/math/s_exp2f_1u.c b/libc/AOR_v20.02/math/s_exp2f_1u.c
new file mode 100644
index 000000000000..53d557fb4aea
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_exp2f_1u.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_exp2f_1u.c"
diff --git a/libc/AOR_v20.02/math/s_expf.c b/libc/AOR_v20.02/math/s_expf.c
new file mode 100644
index 000000000000..6340895920fe
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_expf.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_expf.c"
diff --git a/libc/AOR_v20.02/math/s_expf_1u.c b/libc/AOR_v20.02/math/s_expf_1u.c
new file mode 100644
index 000000000000..127ae3bdd47b
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_expf_1u.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_expf_1u.c"
diff --git a/libc/AOR_v20.02/math/s_log.c b/libc/AOR_v20.02/math/s_log.c
new file mode 100644
index 000000000000..22fd46c48819
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_log.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_log.c"
diff --git a/libc/AOR_v20.02/math/s_logf.c b/libc/AOR_v20.02/math/s_logf.c
new file mode 100644
index 000000000000..3066f381482f
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_logf.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_logf.c"
diff --git a/libc/AOR_v20.02/math/s_pow.c b/libc/AOR_v20.02/math/s_pow.c
new file mode 100644
index 000000000000..bf0910bfef02
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_pow.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_pow.c"
diff --git a/libc/AOR_v20.02/math/s_powf.c b/libc/AOR_v20.02/math/s_powf.c
new file mode 100644
index 000000000000..48319a22db52
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_powf.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_powf.c"
diff --git a/libc/AOR_v20.02/math/s_sin.c b/libc/AOR_v20.02/math/s_sin.c
new file mode 100644
index 000000000000..969714f996e3
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_sin.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_sin.c"
diff --git a/libc/AOR_v20.02/math/s_sinf.c b/libc/AOR_v20.02/math/s_sinf.c
new file mode 100644
index 000000000000..55d45677c642
--- /dev/null
+++ b/libc/AOR_v20.02/math/s_sinf.c
@@ -0,0 +1,7 @@
+/*
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#define SCALAR 1
+#include "v_sinf.c"
diff --git a/libc/AOR_v20.02/math/sincosf.c b/libc/AOR_v20.02/math/sincosf.c
new file mode 100644
index 000000000000..819b05b21080
--- /dev/null
+++ b/libc/AOR_v20.02/math/sincosf.c
@@ -0,0 +1,80 @@
+/*
+ * Single-precision sin/cos function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <math.h>
+#include "math_config.h"
+#include "sincosf.h"
+
+/* Fast sincosf implementation. Worst-case ULP is 0.5607, maximum relative
+ error is 0.5303 * 2^-23. A single-step range reduction is used for
+ small values. Large inputs have their range reduced using fast integer
+ arithmetic. */
+void
+sincosf (float y, float *sinp, float *cosp)
+{
+ double x = y;
+ double s;
+ int n;
+ const sincos_t *p = &__sincosf_table[0];
+
+ if (abstop12 (y) < abstop12 (pio4))
+ {
+ double x2 = x * x;
+
+ if (unlikely (abstop12 (y) < abstop12 (0x1p-12f)))
+ {
+ if (unlikely (abstop12 (y) < abstop12 (0x1p-126f)))
+ /* Force underflow for tiny y. */
+ force_eval_float (x2);
+ *sinp = y;
+ *cosp = 1.0f;
+ return;
+ }
+
+ sincosf_poly (x, x2, p, 0, sinp, cosp);
+ }
+ else if (abstop12 (y) < abstop12 (120.0f))
+ {
+ x = reduce_fast (x, p, &n);
+
+ /* Setup the signs for sin and cos. */
+ s = p->sign[n & 3];
+
+ if (n & 2)
+ p = &__sincosf_table[1];
+
+ sincosf_poly (x * s, x * x, p, n, sinp, cosp);
+ }
+ else if (likely (abstop12 (y) < abstop12 (INFINITY)))
+ {
+ uint32_t xi = asuint (y);
+ int sign = xi >> 31;
+
+ x = reduce_large (xi, &n);
+
+ /* Setup signs for sin and cos - include original sign. */
+ s = p->sign[(n + sign) & 3];
+
+ if ((n + sign) & 2)
+ p = &__sincosf_table[1];
+
+ sincosf_poly (x * s, x * x, p, n, sinp, cosp);
+ }
+ else
+ {
+ /* Return NaN if Inf or NaN for both sin and cos. */
+ *sinp = *cosp = y - y;
+#if WANT_ERRNO
+ /* Needed to set errno for +-Inf, the add is a hack to work
+ around a gcc register allocation issue: just passing y
+ affects code generation in the fast path. */
+ __math_invalidf (y + y);
+#endif
+ }
+}
diff --git a/libc/AOR_v20.02/math/sincosf.h b/libc/AOR_v20.02/math/sincosf.h
new file mode 100644
index 000000000000..ef40d708acde
--- /dev/null
+++ b/libc/AOR_v20.02/math/sincosf.h
@@ -0,0 +1,154 @@
+/*
+ * Header for sinf, cosf and sincosf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <math.h>
+#include "math_config.h"
+
+/* 2PI * 2^-64. */
+static const double pi63 = 0x1.921FB54442D18p-62;
+/* PI / 4. */
+static const double pio4 = 0x1.921FB54442D18p-1;
+
+/* The constants and polynomials for sine and cosine. */
+typedef struct
+{
+ double sign[4]; /* Sign of sine in quadrants 0..3. */
+ double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
+ double hpi; /* PI / 2. */
+ double c0, c1, c2, c3, c4; /* Cosine polynomial. */
+ double s1, s2, s3; /* Sine polynomial. */
+} sincos_t;
+
+/* Polynomial data (the cosine polynomial is negated in the 2nd entry). */
+extern const sincos_t __sincosf_table[2] HIDDEN;
+
+/* Table with 4/PI to 192 bit precision. */
+extern const uint32_t __inv_pio4[] HIDDEN;
+
+/* Top 12 bits of the float representation with the sign bit cleared. */
+static inline uint32_t
+abstop12 (float x)
+{
+ return (asuint (x) >> 20) & 0x7ff;
+}
+
+/* Compute the sine and cosine of inputs X and X2 (X squared), using the
+ polynomial P and store the results in SINP and COSP. N is the quadrant,
+ if odd the cosine and sine polynomials are swapped. */
+static inline void
+sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
+ float *cosp)
+{
+ double x3, x4, x5, x6, s, c, c1, c2, s1;
+
+ x4 = x2 * x2;
+ x3 = x2 * x;
+ c2 = p->c3 + x2 * p->c4;
+ s1 = p->s2 + x2 * p->s3;
+
+ /* Swap sin/cos result based on quadrant. */
+ float *tmp = (n & 1 ? cosp : sinp);
+ cosp = (n & 1 ? sinp : cosp);
+ sinp = tmp;
+
+ c1 = p->c0 + x2 * p->c1;
+ x5 = x3 * x2;
+ x6 = x4 * x2;
+
+ s = x + x3 * p->s1;
+ c = c1 + x4 * p->c2;
+
+ *sinp = s + x5 * s1;
+ *cosp = c + x6 * c2;
+}
+
+/* Return the sine of inputs X and X2 (X squared) using the polynomial P.
+ N is the quadrant, and if odd the cosine polynomial is used. */
+static inline float
+sinf_poly (double x, double x2, const sincos_t *p, int n)
+{
+ double x3, x4, x6, x7, s, c, c1, c2, s1;
+
+ if ((n & 1) == 0)
+ {
+ x3 = x * x2;
+ s1 = p->s2 + x2 * p->s3;
+
+ x7 = x3 * x2;
+ s = x + x3 * p->s1;
+
+ return s + x7 * s1;
+ }
+ else
+ {
+ x4 = x2 * x2;
+ c2 = p->c3 + x2 * p->c4;
+ c1 = p->c0 + x2 * p->c1;
+
+ x6 = x4 * x2;
+ c = c1 + x4 * p->c2;
+
+ return c + x6 * c2;
+ }
+}
+
+/* Fast range reduction using single multiply-subtract. Return the modulo of
+ X as a value between -PI/4 and PI/4 and store the quadrant in NP.
+ The values for PI/2 and 2/PI are accessed via P. Since PI/2 as a double
+ is accurate to 55 bits and the worst-case cancellation happens at 6 * PI/4,
+ the result is accurate for |X| <= 120.0. */
+static inline double
+reduce_fast (double x, const sincos_t *p, int *np)
+{
+ double r;
+#if TOINT_INTRINSICS
+ /* Use fast round and lround instructions when available. */
+ r = x * p->hpi_inv;
+ *np = converttoint (r);
+ return x - roundtoint (r) * p->hpi;
+#else
+ /* Use scaled float to int conversion with explicit rounding.
+ hpi_inv is prescaled by 2^24 so the quadrant ends up in bits 24..31.
+ This avoids inaccuracies introduced by truncating negative values. */
+ r = x * p->hpi_inv;
+ int n = ((int32_t)r + 0x800000) >> 24;
+ *np = n;
+ return x - n * p->hpi;
+#endif
+}
+
+/* Reduce the range of XI to a multiple of PI/2 using fast integer arithmetic.
+ XI is a reinterpreted float and must be >= 2.0f (the sign bit is ignored).
+ Return the modulo between -PI/4 and PI/4 and store the quadrant in NP.
+ Reduction uses a table of 4/PI with 192 bits of precision. A 32x96->128 bit
+ multiply computes the exact 2.62-bit fixed-point modulo. Since the result
+ can have at most 29 leading zeros after the binary point, the double
+ precision result is accurate to 33 bits. */
+static inline double
+reduce_large (uint32_t xi, int *np)
+{
+ const uint32_t *arr = &__inv_pio4[(xi >> 26) & 15];
+ int shift = (xi >> 23) & 7;
+ uint64_t n, res0, res1, res2;
+
+ xi = (xi & 0xffffff) | 0x800000;
+ xi <<= shift;
+
+ res0 = xi * arr[0];
+ res1 = (uint64_t)xi * arr[4];
+ res2 = (uint64_t)xi * arr[8];
+ res0 = (res2 >> 32) | (res0 << 32);
+ res0 += res1;
+
+ n = (res0 + (1ULL << 61)) >> 62;
+ res0 -= n << 62;
+ double x = (int64_t)res0;
+ *np = n;
+ return x * pi63;
+}
diff --git a/libc/AOR_v20.02/math/sincosf_data.c b/libc/AOR_v20.02/math/sincosf_data.c
new file mode 100644
index 000000000000..a3d5efda6f4c
--- /dev/null
+++ b/libc/AOR_v20.02/math/sincosf_data.c
@@ -0,0 +1,64 @@
+/*
+ * Data definition for sinf, cosf and sincosf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <math.h>
+#include "math_config.h"
+#include "sincosf.h"
+
+/* The constants and polynomials for sine and cosine. The 2nd entry
+ computes -cos (x) rather than cos (x) to get negation for free. */
+const sincos_t __sincosf_table[2] =
+{
+ {
+ { 1.0, -1.0, -1.0, 1.0 },
+#if TOINT_INTRINSICS
+ 0x1.45F306DC9C883p-1,
+#else
+ 0x1.45F306DC9C883p+23,
+#endif
+ 0x1.921FB54442D18p0,
+ 0x1p0,
+ -0x1.ffffffd0c621cp-2,
+ 0x1.55553e1068f19p-5,
+ -0x1.6c087e89a359dp-10,
+ 0x1.99343027bf8c3p-16,
+ -0x1.555545995a603p-3,
+ 0x1.1107605230bc4p-7,
+ -0x1.994eb3774cf24p-13
+ },
+ {
+ { 1.0, -1.0, -1.0, 1.0 },
+#if TOINT_INTRINSICS
+ 0x1.45F306DC9C883p-1,
+#else
+ 0x1.45F306DC9C883p+23,
+#endif
+ 0x1.921FB54442D18p0,
+ -0x1p0,
+ 0x1.ffffffd0c621cp-2,
+ -0x1.55553e1068f19p-5,
+ 0x1.6c087e89a359dp-10,
+ -0x1.99343027bf8c3p-16,
+ -0x1.555545995a603p-3,
+ 0x1.1107605230bc4p-7,
+ -0x1.994eb3774cf24p-13
+ }
+};
+
+/* Table with 4/PI to 192 bit precision. To avoid unaligned accesses
+ only 8 new bits are added per entry, making the table 4 times larger. */
+const uint32_t __inv_pio4[24] =
+{
+ 0xa2, 0xa2f9, 0xa2f983, 0xa2f9836e,
+ 0xf9836e4e, 0x836e4e44, 0x6e4e4415, 0x4e441529,
+ 0x441529fc, 0x1529fc27, 0x29fc2757, 0xfc2757d1,
+ 0x2757d1f5, 0x57d1f534, 0xd1f534dd, 0xf534ddc0,
+ 0x34ddc0db, 0xddc0db62, 0xc0db6295, 0xdb629599,
+ 0x6295993c, 0x95993c43, 0x993c4390, 0x3c439041
+};
diff --git a/libc/AOR_v20.02/math/sinf.c b/libc/AOR_v20.02/math/sinf.c
new file mode 100644
index 000000000000..644b82dd94da
--- /dev/null
+++ b/libc/AOR_v20.02/math/sinf.c
@@ -0,0 +1,68 @@
+/*
+ * Single-precision sin function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <math.h>
+#include "math_config.h"
+#include "sincosf.h"
+
+/* Fast sinf implementation. Worst-case ULP is 0.5607, maximum relative
+ error is 0.5303 * 2^-23. A single-step range reduction is used for
+ small values. Large inputs have their range reduced using fast integer
+ arithmetic. */
+float
+sinf (float y)
+{
+ double x = y;
+ double s;
+ int n;
+ const sincos_t *p = &__sincosf_table[0];
+
+ if (abstop12 (y) < abstop12 (pio4))
+ {
+ s = x * x;
+
+ if (unlikely (abstop12 (y) < abstop12 (0x1p-12f)))
+ {
+ if (unlikely (abstop12 (y) < abstop12 (0x1p-126f)))
+ /* Force underflow for tiny y. */
+ force_eval_float (s);
+ return y;
+ }
+
+ return sinf_poly (x, s, p, 0);
+ }
+ else if (likely (abstop12 (y) < abstop12 (120.0f)))
+ {
+ x = reduce_fast (x, p, &n);
+
+ /* Setup the signs for sin and cos. */
+ s = p->sign[n & 3];
+
+ if (n & 2)
+ p = &__sincosf_table[1];
+
+ return sinf_poly (x * s, x * x, p, n);
+ }
+ else if (abstop12 (y) < abstop12 (INFINITY))
+ {
+ uint32_t xi = asuint (y);
+ int sign = xi >> 31;
+
+ x = reduce_large (xi, &n);
+
+ /* Setup signs for sin and cos - include original sign. */
+ s = p->sign[(n + sign) & 3];
+
+ if ((n + sign) & 2)
+ p = &__sincosf_table[1];
+
+ return sinf_poly (x * s, x * x, p, n);
+ }
+ else
+ return __math_invalidf (y);
+}
diff --git a/libc/AOR_v20.02/math/test/mathbench.c b/libc/AOR_v20.02/math/test/mathbench.c
new file mode 100644
index 000000000000..a57eddb2b481
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/mathbench.c
@@ -0,0 +1,772 @@
+/*
+ * Microbenchmark for math functions.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#undef _GNU_SOURCE
+#define _GNU_SOURCE 1
+#include <stdint.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include <time.h>
+#include <math.h>
+#include "mathlib.h"
+
+#ifndef WANT_VMATH
+/* Enable the build of vector math code. */
+# define WANT_VMATH 1
+#endif
+
+/* Number of measurements, best result is reported. */
+#define MEASURE 60
+/* Array size. */
+#define N 8000
+/* Iterations over the array. */
+#define ITER 125
+
+static double *Trace;
+static size_t trace_size;
+static double A[N];
+static float Af[N];
+static long measurecount = MEASURE;
+static long itercount = ITER;
+
+#if __aarch64__ && WANT_VMATH
+typedef __f64x2_t v_double;
+
+#define v_double_len() 2
+
+static inline v_double
+v_double_load (const double *p)
+{
+ return (v_double){p[0], p[1]};
+}
+
+static inline v_double
+v_double_dup (double x)
+{
+ return (v_double){x, x};
+}
+
+typedef __f32x4_t v_float;
+
+#define v_float_len() 4
+
+static inline v_float
+v_float_load (const float *p)
+{
+ return (v_float){p[0], p[1], p[2], p[3]};
+}
+
+static inline v_float
+v_float_dup (float x)
+{
+ return (v_float){x, x, x, x};
+}
+#else
+/* dummy definitions to make things compile. */
+typedef double v_double;
+typedef float v_float;
+#define v_double_len(x) 1
+#define v_double_load(x) (x)[0]
+#define v_double_dup(x) (x)
+#define v_float_len(x) 1
+#define v_float_load(x) (x)[0]
+#define v_float_dup(x) (x)
+#endif
+
+static double
+dummy (double x)
+{
+ return x;
+}
+
+static float
+dummyf (float x)
+{
+ return x;
+}
+
+#if WANT_VMATH
+#if __aarch64__
+static v_double
+__v_dummy (v_double x)
+{
+ return x;
+}
+
+static v_float
+__v_dummyf (v_float x)
+{
+ return x;
+}
+
+#ifdef __vpcs
+__vpcs static v_double
+__vn_dummy (v_double x)
+{
+ return x;
+}
+
+__vpcs static v_float
+__vn_dummyf (v_float x)
+{
+ return x;
+}
+
+__vpcs static v_float
+xy__vn_powf (v_float x)
+{
+ return __vn_powf (x, x);
+}
+
+__vpcs static v_float
+xy_Z_powf (v_float x)
+{
+ return _ZGVnN4vv_powf (x, x);
+}
+
+__vpcs static v_double
+xy__vn_pow (v_double x)
+{
+ return __vn_pow (x, x);
+}
+
+__vpcs static v_double
+xy_Z_pow (v_double x)
+{
+ return _ZGVnN2vv_pow (x, x);
+}
+#endif
+
+static v_float
+xy__v_powf (v_float x)
+{
+ return __v_powf (x, x);
+}
+
+static v_double
+xy__v_pow (v_double x)
+{
+ return __v_pow (x, x);
+}
+#endif
+
+static float
+xy__s_powf (float x)
+{
+ return __s_powf (x, x);
+}
+
+static double
+xy__s_pow (double x)
+{
+ return __s_pow (x, x);
+}
+#endif
+
+static double
+xypow (double x)
+{
+ return pow (x, x);
+}
+
+static float
+xypowf (float x)
+{
+ return powf (x, x);
+}
+
+static double
+xpow (double x)
+{
+ return pow (x, 23.4);
+}
+
+static float
+xpowf (float x)
+{
+ return powf (x, 23.4f);
+}
+
+static double
+ypow (double x)
+{
+ return pow (2.34, x);
+}
+
+static float
+ypowf (float x)
+{
+ return powf (2.34f, x);
+}
+
+static float
+sincosf_wrap (float x)
+{
+ float s, c;
+ sincosf (x, &s, &c);
+ return s + c;
+}
+
+static const struct fun
+{
+ const char *name;
+ int prec;
+ int vec;
+ double lo;
+ double hi;
+ union
+ {
+ double (*d) (double);
+ float (*f) (float);
+ v_double (*vd) (v_double);
+ v_float (*vf) (v_float);
+#ifdef __vpcs
+ __vpcs v_double (*vnd) (v_double);
+ __vpcs v_float (*vnf) (v_float);
+#endif
+ } fun;
+} funtab[] = {
+#define D(func, lo, hi) {#func, 'd', 0, lo, hi, {.d = func}},
+#define F(func, lo, hi) {#func, 'f', 0, lo, hi, {.f = func}},
+#define VD(func, lo, hi) {#func, 'd', 'v', lo, hi, {.vd = func}},
+#define VF(func, lo, hi) {#func, 'f', 'v', lo, hi, {.vf = func}},
+#define VND(func, lo, hi) {#func, 'd', 'n', lo, hi, {.vnd = func}},
+#define VNF(func, lo, hi) {#func, 'f', 'n', lo, hi, {.vnf = func}},
+D (dummy, 1.0, 2.0)
+D (exp, -9.9, 9.9)
+D (exp, 0.5, 1.0)
+D (exp2, -9.9, 9.9)
+D (log, 0.01, 11.1)
+D (log, 0.999, 1.001)
+D (log2, 0.01, 11.1)
+D (log2, 0.999, 1.001)
+{"pow", 'd', 0, 0.01, 11.1, {.d = xypow}},
+D (xpow, 0.01, 11.1)
+D (ypow, -9.9, 9.9)
+
+F (dummyf, 1.0, 2.0)
+F (expf, -9.9, 9.9)
+F (exp2f, -9.9, 9.9)
+F (logf, 0.01, 11.1)
+F (log2f, 0.01, 11.1)
+{"powf", 'f', 0, 0.01, 11.1, {.f = xypowf}},
+F (xpowf, 0.01, 11.1)
+F (ypowf, -9.9, 9.9)
+{"sincosf", 'f', 0, 0.1, 0.7, {.f = sincosf_wrap}},
+{"sincosf", 'f', 0, 0.8, 3.1, {.f = sincosf_wrap}},
+{"sincosf", 'f', 0, -3.1, 3.1, {.f = sincosf_wrap}},
+{"sincosf", 'f', 0, 3.3, 33.3, {.f = sincosf_wrap}},
+{"sincosf", 'f', 0, 100, 1000, {.f = sincosf_wrap}},
+{"sincosf", 'f', 0, 1e6, 1e32, {.f = sincosf_wrap}},
+F (sinf, 0.1, 0.7)
+F (sinf, 0.8, 3.1)
+F (sinf, -3.1, 3.1)
+F (sinf, 3.3, 33.3)
+F (sinf, 100, 1000)
+F (sinf, 1e6, 1e32)
+F (cosf, 0.1, 0.7)
+F (cosf, 0.8, 3.1)
+F (cosf, -3.1, 3.1)
+F (cosf, 3.3, 33.3)
+F (cosf, 100, 1000)
+F (cosf, 1e6, 1e32)
+#if WANT_VMATH
+D (__s_sin, -3.1, 3.1)
+D (__s_cos, -3.1, 3.1)
+D (__s_exp, -9.9, 9.9)
+D (__s_log, 0.01, 11.1)
+{"__s_pow", 'd', 0, 0.01, 11.1, {.d = xy__s_pow}},
+F (__s_expf, -9.9, 9.9)
+F (__s_expf_1u, -9.9, 9.9)
+F (__s_exp2f, -9.9, 9.9)
+F (__s_exp2f_1u, -9.9, 9.9)
+F (__s_logf, 0.01, 11.1)
+{"__s_powf", 'f', 0, 0.01, 11.1, {.f = xy__s_powf}},
+F (__s_sinf, -3.1, 3.1)
+F (__s_cosf, -3.1, 3.1)
+#if __aarch64__
+VD (__v_dummy, 1.0, 2.0)
+VD (__v_sin, -3.1, 3.1)
+VD (__v_cos, -3.1, 3.1)
+VD (__v_exp, -9.9, 9.9)
+VD (__v_log, 0.01, 11.1)
+{"__v_pow", 'd', 'v', 0.01, 11.1, {.vd = xy__v_pow}},
+VF (__v_dummyf, 1.0, 2.0)
+VF (__v_expf, -9.9, 9.9)
+VF (__v_expf_1u, -9.9, 9.9)
+VF (__v_exp2f, -9.9, 9.9)
+VF (__v_exp2f_1u, -9.9, 9.9)
+VF (__v_logf, 0.01, 11.1)
+{"__v_powf", 'f', 'v', 0.01, 11.1, {.vf = xy__v_powf}},
+VF (__v_sinf, -3.1, 3.1)
+VF (__v_cosf, -3.1, 3.1)
+#ifdef __vpcs
+VND (__vn_dummy, 1.0, 2.0)
+VND (__vn_exp, -9.9, 9.9)
+VND (_ZGVnN2v_exp, -9.9, 9.9)
+VND (__vn_log, 0.01, 11.1)
+VND (_ZGVnN2v_log, 0.01, 11.1)
+{"__vn_pow", 'd', 'n', 0.01, 11.1, {.vnd = xy__vn_pow}},
+{"_ZGVnN2vv_pow", 'd', 'n', 0.01, 11.1, {.vnd = xy_Z_pow}},
+VND (__vn_sin, -3.1, 3.1)
+VND (_ZGVnN2v_sin, -3.1, 3.1)
+VND (__vn_cos, -3.1, 3.1)
+VND (_ZGVnN2v_cos, -3.1, 3.1)
+VNF (__vn_dummyf, 1.0, 2.0)
+VNF (__vn_expf, -9.9, 9.9)
+VNF (_ZGVnN4v_expf, -9.9, 9.9)
+VNF (__vn_expf_1u, -9.9, 9.9)
+VNF (__vn_exp2f, -9.9, 9.9)
+VNF (_ZGVnN4v_exp2f, -9.9, 9.9)
+VNF (__vn_exp2f_1u, -9.9, 9.9)
+VNF (__vn_logf, 0.01, 11.1)
+VNF (_ZGVnN4v_logf, 0.01, 11.1)
+{"__vn_powf", 'f', 'n', 0.01, 11.1, {.vnf = xy__vn_powf}},
+{"_ZGVnN4vv_powf", 'f', 'n', 0.01, 11.1, {.vnf = xy_Z_powf}},
+VNF (__vn_sinf, -3.1, 3.1)
+VNF (_ZGVnN4v_sinf, -3.1, 3.1)
+VNF (__vn_cosf, -3.1, 3.1)
+VNF (_ZGVnN4v_cosf, -3.1, 3.1)
+#endif
+#endif
+#endif
+{0},
+#undef F
+#undef D
+#undef VF
+#undef VD
+#undef VNF
+#undef VND
+};
+
+static void
+gen_linear (double lo, double hi)
+{
+ for (int i = 0; i < N; i++)
+ A[i] = (lo * (N - i) + hi * i) / N;
+}
+
+static void
+genf_linear (double lo, double hi)
+{
+ for (int i = 0; i < N; i++)
+ Af[i] = (float)(lo * (N - i) + hi * i) / N;
+}
+
+static inline double
+asdouble (uint64_t i)
+{
+ union
+ {
+ uint64_t i;
+ double f;
+ } u = {i};
+ return u.f;
+}
+
+static uint64_t seed = 0x0123456789abcdef;
+
+static double
+frand (double lo, double hi)
+{
+ seed = 6364136223846793005ULL * seed + 1;
+ return lo + (hi - lo) * (asdouble (seed >> 12 | 0x3ffULL << 52) - 1.0);
+}
+
+static void
+gen_rand (double lo, double hi)
+{
+ for (int i = 0; i < N; i++)
+ A[i] = frand (lo, hi);
+}
+
+static void
+genf_rand (double lo, double hi)
+{
+ for (int i = 0; i < N; i++)
+ Af[i] = (float)frand (lo, hi);
+}
+
+static void
+gen_trace (int index)
+{
+ for (int i = 0; i < N; i++)
+ A[i] = Trace[index + i];
+}
+
+static void
+genf_trace (int index)
+{
+ for (int i = 0; i < N; i++)
+ Af[i] = (float)Trace[index + i];
+}
+
+static void
+run_thruput (double f (double))
+{
+ for (int i = 0; i < N; i++)
+ f (A[i]);
+}
+
+static void
+runf_thruput (float f (float))
+{
+ for (int i = 0; i < N; i++)
+ f (Af[i]);
+}
+
+volatile double zero = 0;
+
+static void
+run_latency (double f (double))
+{
+ double z = zero;
+ double prev = z;
+ for (int i = 0; i < N; i++)
+ prev = f (A[i] + prev * z);
+}
+
+static void
+runf_latency (float f (float))
+{
+ float z = (float)zero;
+ float prev = z;
+ for (int i = 0; i < N; i++)
+ prev = f (Af[i] + prev * z);
+}
+
+static void
+run_v_thruput (v_double f (v_double))
+{
+ for (int i = 0; i < N; i += v_double_len ())
+ f (v_double_load (A+i));
+}
+
+static void
+runf_v_thruput (v_float f (v_float))
+{
+ for (int i = 0; i < N; i += v_float_len ())
+ f (v_float_load (Af+i));
+}
+
+static void
+run_v_latency (v_double f (v_double))
+{
+ v_double z = v_double_dup (zero);
+ v_double prev = z;
+ for (int i = 0; i < N; i += v_double_len ())
+ prev = f (v_double_load (A+i) + prev * z);
+}
+
+static void
+runf_v_latency (v_float f (v_float))
+{
+ v_float z = v_float_dup (zero);
+ v_float prev = z;
+ for (int i = 0; i < N; i += v_float_len ())
+ prev = f (v_float_load (Af+i) + prev * z);
+}
+
+#ifdef __vpcs
+static void
+run_vn_thruput (__vpcs v_double f (v_double))
+{
+ for (int i = 0; i < N; i += v_double_len ())
+ f (v_double_load (A+i));
+}
+
+static void
+runf_vn_thruput (__vpcs v_float f (v_float))
+{
+ for (int i = 0; i < N; i += v_float_len ())
+ f (v_float_load (Af+i));
+}
+
+static void
+run_vn_latency (__vpcs v_double f (v_double))
+{
+ v_double z = v_double_dup (zero);
+ v_double prev = z;
+ for (int i = 0; i < N; i += v_double_len ())
+ prev = f (v_double_load (A+i) + prev * z);
+}
+
+static void
+runf_vn_latency (__vpcs v_float f (v_float))
+{
+ v_float z = v_float_dup (zero);
+ v_float prev = z;
+ for (int i = 0; i < N; i += v_float_len ())
+ prev = f (v_float_load (Af+i) + prev * z);
+}
+#endif
+
+static uint64_t
+tic (void)
+{
+ struct timespec ts;
+ if (clock_gettime (CLOCK_REALTIME, &ts))
+ abort ();
+ return ts.tv_sec * 1000000000ULL + ts.tv_nsec;
+}
+
+#define TIMEIT(run, f) do { \
+ dt = -1; \
+ run (f); /* Warm up. */ \
+ for (int j = 0; j < measurecount; j++) \
+ { \
+ uint64_t t0 = tic (); \
+ for (int i = 0; i < itercount; i++) \
+ run (f); \
+ uint64_t t1 = tic (); \
+ if (t1 - t0 < dt) \
+ dt = t1 - t0; \
+ } \
+} while (0)
+
+static void
+bench1 (const struct fun *f, int type, double lo, double hi)
+{
+ uint64_t dt = 0;
+ uint64_t ns100;
+ const char *s = type == 't' ? "rthruput" : "latency";
+ int vlen = 1;
+
+ if (f->vec && f->prec == 'd')
+ vlen = v_double_len();
+ else if (f->vec && f->prec == 'f')
+ vlen = v_float_len();
+
+ if (f->prec == 'd' && type == 't' && f->vec == 0)
+ TIMEIT (run_thruput, f->fun.d);
+ else if (f->prec == 'd' && type == 'l' && f->vec == 0)
+ TIMEIT (run_latency, f->fun.d);
+ else if (f->prec == 'f' && type == 't' && f->vec == 0)
+ TIMEIT (runf_thruput, f->fun.f);
+ else if (f->prec == 'f' && type == 'l' && f->vec == 0)
+ TIMEIT (runf_latency, f->fun.f);
+ else if (f->prec == 'd' && type == 't' && f->vec == 'v')
+ TIMEIT (run_v_thruput, f->fun.vd);
+ else if (f->prec == 'd' && type == 'l' && f->vec == 'v')
+ TIMEIT (run_v_latency, f->fun.vd);
+ else if (f->prec == 'f' && type == 't' && f->vec == 'v')
+ TIMEIT (runf_v_thruput, f->fun.vf);
+ else if (f->prec == 'f' && type == 'l' && f->vec == 'v')
+ TIMEIT (runf_v_latency, f->fun.vf);
+#ifdef __vpcs
+ else if (f->prec == 'd' && type == 't' && f->vec == 'n')
+ TIMEIT (run_vn_thruput, f->fun.vnd);
+ else if (f->prec == 'd' && type == 'l' && f->vec == 'n')
+ TIMEIT (run_vn_latency, f->fun.vnd);
+ else if (f->prec == 'f' && type == 't' && f->vec == 'n')
+ TIMEIT (runf_vn_thruput, f->fun.vnf);
+ else if (f->prec == 'f' && type == 'l' && f->vec == 'n')
+ TIMEIT (runf_vn_latency, f->fun.vnf);
+#endif
+
+ if (type == 't')
+ {
+ ns100 = (100 * dt + itercount * N / 2) / (itercount * N);
+ printf ("%9s %8s: %4u.%02u ns/elem %10llu ns in [%g %g]\n", f->name, s,
+ (unsigned) (ns100 / 100), (unsigned) (ns100 % 100),
+ (unsigned long long) dt, lo, hi);
+ }
+ else if (type == 'l')
+ {
+ ns100 = (100 * dt + itercount * N / vlen / 2) / (itercount * N / vlen);
+ printf ("%9s %8s: %4u.%02u ns/call %10llu ns in [%g %g]\n", f->name, s,
+ (unsigned) (ns100 / 100), (unsigned) (ns100 % 100),
+ (unsigned long long) dt, lo, hi);
+ }
+ fflush (stdout);
+}
+
+static void
+bench (const struct fun *f, double lo, double hi, int type, int gen)
+{
+ if (f->prec == 'd' && gen == 'r')
+ gen_rand (lo, hi);
+ else if (f->prec == 'd' && gen == 'l')
+ gen_linear (lo, hi);
+ else if (f->prec == 'd' && gen == 't')
+ gen_trace (0);
+ else if (f->prec == 'f' && gen == 'r')
+ genf_rand (lo, hi);
+ else if (f->prec == 'f' && gen == 'l')
+ genf_linear (lo, hi);
+ else if (f->prec == 'f' && gen == 't')
+ genf_trace (0);
+
+ if (gen == 't')
+ hi = trace_size / N;
+
+ if (type == 'b' || type == 't')
+ bench1 (f, 't', lo, hi);
+
+ if (type == 'b' || type == 'l')
+ bench1 (f, 'l', lo, hi);
+
+ for (int i = N; i < trace_size; i += N)
+ {
+ if (f->prec == 'd')
+ gen_trace (i);
+ else
+ genf_trace (i);
+
+ lo = i / N;
+ if (type == 'b' || type == 't')
+ bench1 (f, 't', lo, hi);
+
+ if (type == 'b' || type == 'l')
+ bench1 (f, 'l', lo, hi);
+ }
+}
+
+static void
+readtrace (const char *name)
+{
+ int n = 0;
+ FILE *f = strcmp (name, "-") == 0 ? stdin : fopen (name, "r");
+ if (!f)
+ {
+ printf ("openning \"%s\" failed: %m\n", name);
+ exit (1);
+ }
+ for (;;)
+ {
+ if (n >= trace_size)
+ {
+ trace_size += N;
+ Trace = realloc (Trace, trace_size * sizeof (Trace[0]));
+ if (Trace == NULL)
+ {
+ printf ("out of memory\n");
+ exit (1);
+ }
+ }
+ if (fscanf (f, "%lf", Trace + n) != 1)
+ break;
+ n++;
+ }
+ if (ferror (f) || n == 0)
+ {
+ printf ("reading \"%s\" failed: %m\n", name);
+ exit (1);
+ }
+ fclose (f);
+ if (n % N == 0)
+ trace_size = n;
+ for (int i = 0; n < trace_size; n++, i++)
+ Trace[n] = Trace[i];
+}
+
+static void
+usage (void)
+{
+ printf ("usage: ./mathbench [-g rand|linear|trace] [-t latency|thruput|both] "
+ "[-i low high] [-f tracefile] [-m measurements] [-c iterations] func "
+ "[func2 ..]\n");
+ printf ("func:\n");
+ printf ("%7s [run all benchmarks]\n", "all");
+ for (const struct fun *f = funtab; f->name; f++)
+ printf ("%7s [low: %g high: %g]\n", f->name, f->lo, f->hi);
+ exit (1);
+}
+
+int
+main (int argc, char *argv[])
+{
+ int usergen = 0, gen = 'r', type = 'b', all = 0;
+ double lo = 0, hi = 0;
+ const char *tracefile = "-";
+
+ argv++;
+ argc--;
+ for (;;)
+ {
+ if (argc <= 0)
+ usage ();
+ if (argv[0][0] != '-')
+ break;
+ else if (argc >= 3 && strcmp (argv[0], "-i") == 0)
+ {
+ usergen = 1;
+ lo = strtod (argv[1], 0);
+ hi = strtod (argv[2], 0);
+ argv += 3;
+ argc -= 3;
+ }
+ else if (argc >= 2 && strcmp (argv[0], "-m") == 0)
+ {
+ measurecount = strtol (argv[1], 0, 0);
+ argv += 2;
+ argc -= 2;
+ }
+ else if (argc >= 2 && strcmp (argv[0], "-c") == 0)
+ {
+ itercount = strtol (argv[1], 0, 0);
+ argv += 2;
+ argc -= 2;
+ }
+ else if (argc >= 2 && strcmp (argv[0], "-g") == 0)
+ {
+ gen = argv[1][0];
+ if (strchr ("rlt", gen) == 0)
+ usage ();
+ argv += 2;
+ argc -= 2;
+ }
+ else if (argc >= 2 && strcmp (argv[0], "-f") == 0)
+ {
+ gen = 't'; /* -f implies -g trace. */
+ tracefile = argv[1];
+ argv += 2;
+ argc -= 2;
+ }
+ else if (argc >= 2 && strcmp (argv[0], "-t") == 0)
+ {
+ type = argv[1][0];
+ if (strchr ("ltb", type) == 0)
+ usage ();
+ argv += 2;
+ argc -= 2;
+ }
+ else
+ usage ();
+ }
+ if (gen == 't')
+ {
+ readtrace (tracefile);
+ lo = hi = 0;
+ usergen = 1;
+ }
+ while (argc > 0)
+ {
+ int found = 0;
+ all = strcmp (argv[0], "all") == 0;
+ for (const struct fun *f = funtab; f->name; f++)
+ if (all || strcmp (argv[0], f->name) == 0)
+ {
+ found = 1;
+ if (!usergen)
+ {
+ lo = f->lo;
+ hi = f->hi;
+ }
+ bench (f, lo, hi, type, gen);
+ if (usergen && !all)
+ break;
+ }
+ if (!found)
+ printf ("unknown function: %s\n", argv[0]);
+ argv++;
+ argc--;
+ }
+ return 0;
+}
diff --git a/libc/AOR_v20.02/math/test/mathtest.c b/libc/AOR_v20.02/math/test/mathtest.c
new file mode 100644
index 000000000000..efe0a8a744bc
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/mathtest.c
@@ -0,0 +1,1702 @@
+/*
+ * mathtest.c - test rig for mathlib
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <assert.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <setjmp.h>
+#include <ctype.h>
+#include <math.h>
+#include <errno.h>
+#include <limits.h>
+#include <fenv.h>
+#include "mathlib.h"
+
+#ifndef math_errhandling
+# define math_errhandling 0
+#endif
+
+#ifdef __cplusplus
+ #define EXTERN_C extern "C"
+#else
+ #define EXTERN_C extern
+#endif
+
+#ifndef TRUE
+#define TRUE 1
+#endif
+#ifndef FALSE
+#define FALSE 0
+#endif
+
+#ifdef IMPORT_SYMBOL
+#define STR2(x) #x
+#define STR(x) STR2(x)
+_Pragma(STR(import IMPORT_SYMBOL))
+#endif
+
+int dmsd, dlsd;
+int quiet = 0;
+int doround = 0;
+unsigned statusmask = FE_ALL_EXCEPT;
+
+#define EXTRABITS (12)
+#define ULPUNIT (1<<EXTRABITS)
+
+typedef int (*test) (void);
+
+/*
+ struct to hold info about a function (which could actually be a macro)
+*/
+typedef struct {
+ enum {
+ t_func, t_macro
+ } type;
+ enum {
+ at_d, at_s, /* double or single precision float */
+ at_d2, at_s2, /* same, but taking two args */
+ at_di, at_si, /* double/single and an int */
+ at_dip, at_sip, /* double/single and an int ptr */
+ at_ddp, at_ssp, /* d/s and a d/s ptr */
+ at_dc, at_sc, /* double or single precision complex */
+ at_dc2, at_sc2 /* same, but taking two args */
+ } argtype;
+ enum {
+ rt_d, rt_s, rt_i, /* double, single, int */
+ rt_dc, rt_sc, /* double, single precision complex */
+ rt_d2, rt_s2 /* also use res2 */
+ } rettype;
+ union {
+ void* ptr;
+ double (*d_d_ptr)(double);
+ float (*s_s_ptr)(float);
+ int (*d_i_ptr)(double);
+ int (*s_i_ptr)(float);
+ double (*d2_d_ptr)(double, double);
+ float (*s2_s_ptr)(float, float);
+ double (*di_d_ptr)(double,int);
+ float (*si_s_ptr)(float,int);
+ double (*dip_d_ptr)(double,int*);
+ float (*sip_s_ptr)(float,int*);
+ double (*ddp_d_ptr)(double,double*);
+ float (*ssp_s_ptr)(float,float*);
+ } func;
+ enum {
+ m_none,
+ m_isfinite, m_isfinitef,
+ m_isgreater, m_isgreaterequal,
+ m_isgreaterequalf, m_isgreaterf,
+ m_isinf, m_isinff,
+ m_isless, m_islessequal,
+ m_islessequalf, m_islessf,
+ m_islessgreater, m_islessgreaterf,
+ m_isnan, m_isnanf,
+ m_isnormal, m_isnormalf,
+ m_isunordered, m_isunorderedf,
+ m_fpclassify, m_fpclassifyf,
+ m_signbit, m_signbitf,
+ /* not actually a macro, but makes things easier */
+ m_rred, m_rredf,
+ m_cadd, m_csub, m_cmul, m_cdiv,
+ m_caddf, m_csubf, m_cmulf, m_cdivf
+ } macro_name; /* only used if a macro/something that can't be done using func */
+ long long tolerance;
+ const char* name;
+} test_func;
+
+/* used in qsort */
+int compare_tfuncs(const void* a, const void* b) {
+ return strcmp(((test_func*)a)->name, ((test_func*)b)->name);
+}
+
+int is_double_argtype(int argtype) {
+ switch(argtype) {
+ case at_d:
+ case at_d2:
+ case at_dc:
+ case at_dc2:
+ return 1;
+ default:
+ return 0;
+ }
+}
+
+int is_single_argtype(int argtype) {
+ switch(argtype) {
+ case at_s:
+ case at_s2:
+ case at_sc:
+ case at_sc2:
+ return 1;
+ default:
+ return 0;
+ }
+}
+
+int is_double_rettype(int rettype) {
+ switch(rettype) {
+ case rt_d:
+ case rt_dc:
+ case rt_d2:
+ return 1;
+ default:
+ return 0;
+ }
+}
+
+int is_single_rettype(int rettype) {
+ switch(rettype) {
+ case rt_s:
+ case rt_sc:
+ case rt_s2:
+ return 1;
+ default:
+ return 0;
+ }
+}
+
+int is_complex_argtype(int argtype) {
+ switch(argtype) {
+ case at_dc:
+ case at_sc:
+ case at_dc2:
+ case at_sc2:
+ return 1;
+ default:
+ return 0;
+ }
+}
+
+int is_complex_rettype(int rettype) {
+ switch(rettype) {
+ case rt_dc:
+ case rt_sc:
+ return 1;
+ default:
+ return 0;
+ }
+}
+
+/*
+ * Special-case flags indicating that some functions' error
+ * tolerance handling is more complicated than a fixed relative
+ * error bound.
+ */
+#define ABSLOWERBOUND 0x4000000000000000LL
+#define PLUSMINUSPIO2 0x1000000000000000LL
+
+#define ARM_PREFIX(x) x
+
+#define TFUNC(arg,ret,name,tolerance) { t_func, arg, ret, (void*)&name, m_none, tolerance, #name }
+#define TFUNCARM(arg,ret,name,tolerance) { t_func, arg, ret, (void*)& ARM_PREFIX(name), m_none, tolerance, #name }
+#define MFUNC(arg,ret,name,tolerance) { t_macro, arg, ret, NULL, m_##name, tolerance, #name }
+
+/* sincosf wrappers for easier testing. */
+static float sincosf_sinf(float x) { float s,c; sincosf(x, &s, &c); return s; }
+static float sincosf_cosf(float x) { float s,c; sincosf(x, &s, &c); return c; }
+
+test_func tfuncs[] = {
+ /* trigonometric */
+ TFUNC(at_d,rt_d, acos, 4*ULPUNIT),
+ TFUNC(at_d,rt_d, asin, 4*ULPUNIT),
+ TFUNC(at_d,rt_d, atan, 4*ULPUNIT),
+ TFUNC(at_d2,rt_d, atan2, 4*ULPUNIT),
+
+ TFUNC(at_d,rt_d, tan, 2*ULPUNIT),
+ TFUNC(at_d,rt_d, sin, 2*ULPUNIT),
+ TFUNC(at_d,rt_d, cos, 2*ULPUNIT),
+
+ TFUNC(at_s,rt_s, acosf, 4*ULPUNIT),
+ TFUNC(at_s,rt_s, asinf, 4*ULPUNIT),
+ TFUNC(at_s,rt_s, atanf, 4*ULPUNIT),
+ TFUNC(at_s2,rt_s, atan2f, 4*ULPUNIT),
+ TFUNCARM(at_s,rt_s, tanf, 4*ULPUNIT),
+ TFUNCARM(at_s,rt_s, sinf, 3*ULPUNIT/4),
+ TFUNCARM(at_s,rt_s, cosf, 3*ULPUNIT/4),
+ TFUNCARM(at_s,rt_s, sincosf_sinf, 3*ULPUNIT/4),
+ TFUNCARM(at_s,rt_s, sincosf_cosf, 3*ULPUNIT/4),
+
+ /* hyperbolic */
+ TFUNC(at_d, rt_d, atanh, 4*ULPUNIT),
+ TFUNC(at_d, rt_d, asinh, 4*ULPUNIT),
+ TFUNC(at_d, rt_d, acosh, 4*ULPUNIT),
+ TFUNC(at_d,rt_d, tanh, 4*ULPUNIT),
+ TFUNC(at_d,rt_d, sinh, 4*ULPUNIT),
+ TFUNC(at_d,rt_d, cosh, 4*ULPUNIT),
+
+ TFUNC(at_s, rt_s, atanhf, 4*ULPUNIT),
+ TFUNC(at_s, rt_s, asinhf, 4*ULPUNIT),
+ TFUNC(at_s, rt_s, acoshf, 4*ULPUNIT),
+ TFUNC(at_s,rt_s, tanhf, 4*ULPUNIT),
+ TFUNC(at_s,rt_s, sinhf, 4*ULPUNIT),
+ TFUNC(at_s,rt_s, coshf, 4*ULPUNIT),
+
+ /* exponential and logarithmic */
+ TFUNC(at_d,rt_d, log, 3*ULPUNIT/4),
+ TFUNC(at_d,rt_d, log10, 3*ULPUNIT),
+ TFUNC(at_d,rt_d, log2, 3*ULPUNIT/4),
+ TFUNC(at_d,rt_d, log1p, 2*ULPUNIT),
+ TFUNC(at_d,rt_d, exp, 3*ULPUNIT/4),
+ TFUNC(at_d,rt_d, exp2, 3*ULPUNIT/4),
+ TFUNC(at_d,rt_d, expm1, ULPUNIT),
+ TFUNCARM(at_s,rt_s, logf, ULPUNIT),
+ TFUNC(at_s,rt_s, log10f, 3*ULPUNIT),
+ TFUNCARM(at_s,rt_s, log2f, ULPUNIT),
+ TFUNC(at_s,rt_s, log1pf, 2*ULPUNIT),
+ TFUNCARM(at_s,rt_s, expf, 3*ULPUNIT/4),
+ TFUNCARM(at_s,rt_s, exp2f, 3*ULPUNIT/4),
+ TFUNC(at_s,rt_s, expm1f, ULPUNIT),
+
+ /* power */
+ TFUNC(at_d2,rt_d, pow, 3*ULPUNIT/4),
+ TFUNC(at_d,rt_d, sqrt, ULPUNIT/2),
+ TFUNC(at_d,rt_d, cbrt, 2*ULPUNIT),
+ TFUNC(at_d2, rt_d, hypot, 4*ULPUNIT),
+
+ TFUNCARM(at_s2,rt_s, powf, ULPUNIT),
+ TFUNC(at_s,rt_s, sqrtf, ULPUNIT/2),
+ TFUNC(at_s,rt_s, cbrtf, 2*ULPUNIT),
+ TFUNC(at_s2, rt_s, hypotf, 4*ULPUNIT),
+
+ /* error function */
+ TFUNC(at_d,rt_d, erf, 16*ULPUNIT),
+ TFUNC(at_s,rt_s, erff, 16*ULPUNIT),
+ TFUNC(at_d,rt_d, erfc, 16*ULPUNIT),
+ TFUNC(at_s,rt_s, erfcf, 16*ULPUNIT),
+
+ /* gamma functions */
+ TFUNC(at_d,rt_d, tgamma, 16*ULPUNIT),
+ TFUNC(at_s,rt_s, tgammaf, 16*ULPUNIT),
+ TFUNC(at_d,rt_d, lgamma, 16*ULPUNIT | ABSLOWERBOUND),
+ TFUNC(at_s,rt_s, lgammaf, 16*ULPUNIT | ABSLOWERBOUND),
+
+ TFUNC(at_d,rt_d, ceil, 0),
+ TFUNC(at_s,rt_s, ceilf, 0),
+ TFUNC(at_d2,rt_d, copysign, 0),
+ TFUNC(at_s2,rt_s, copysignf, 0),
+ TFUNC(at_d,rt_d, floor, 0),
+ TFUNC(at_s,rt_s, floorf, 0),
+ TFUNC(at_d2,rt_d, fmax, 0),
+ TFUNC(at_s2,rt_s, fmaxf, 0),
+ TFUNC(at_d2,rt_d, fmin, 0),
+ TFUNC(at_s2,rt_s, fminf, 0),
+ TFUNC(at_d2,rt_d, fmod, 0),
+ TFUNC(at_s2,rt_s, fmodf, 0),
+ MFUNC(at_d, rt_i, fpclassify, 0),
+ MFUNC(at_s, rt_i, fpclassifyf, 0),
+ TFUNC(at_dip,rt_d, frexp, 0),
+ TFUNC(at_sip,rt_s, frexpf, 0),
+ MFUNC(at_d, rt_i, isfinite, 0),
+ MFUNC(at_s, rt_i, isfinitef, 0),
+ MFUNC(at_d, rt_i, isgreater, 0),
+ MFUNC(at_d, rt_i, isgreaterequal, 0),
+ MFUNC(at_s, rt_i, isgreaterequalf, 0),
+ MFUNC(at_s, rt_i, isgreaterf, 0),
+ MFUNC(at_d, rt_i, isinf, 0),
+ MFUNC(at_s, rt_i, isinff, 0),
+ MFUNC(at_d, rt_i, isless, 0),
+ MFUNC(at_d, rt_i, islessequal, 0),
+ MFUNC(at_s, rt_i, islessequalf, 0),
+ MFUNC(at_s, rt_i, islessf, 0),
+ MFUNC(at_d, rt_i, islessgreater, 0),
+ MFUNC(at_s, rt_i, islessgreaterf, 0),
+ MFUNC(at_d, rt_i, isnan, 0),
+ MFUNC(at_s, rt_i, isnanf, 0),
+ MFUNC(at_d, rt_i, isnormal, 0),
+ MFUNC(at_s, rt_i, isnormalf, 0),
+ MFUNC(at_d, rt_i, isunordered, 0),
+ MFUNC(at_s, rt_i, isunorderedf, 0),
+ TFUNC(at_di,rt_d, ldexp, 0),
+ TFUNC(at_si,rt_s, ldexpf, 0),
+ TFUNC(at_ddp,rt_d2, modf, 0),
+ TFUNC(at_ssp,rt_s2, modff, 0),
+#ifndef BIGRANGERED
+ MFUNC(at_d, rt_d, rred, 2*ULPUNIT),
+#else
+ MFUNC(at_d, rt_d, m_rred, ULPUNIT),
+#endif
+ MFUNC(at_d, rt_i, signbit, 0),
+ MFUNC(at_s, rt_i, signbitf, 0),
+};
+
+/*
+ * keywords are: func size op1 op2 result res2 errno op1r op1i op2r op2i resultr resulti
+ * also we ignore: wrongresult wrongres2 wrongerrno
+ * op1 equivalent to op1r, same with op2 and result
+ */
+
+typedef struct {
+ test_func *func;
+ unsigned op1r[2]; /* real part, also used for non-complex numbers */
+ unsigned op1i[2]; /* imaginary part */
+ unsigned op2r[2];
+ unsigned op2i[2];
+ unsigned resultr[3];
+ unsigned resulti[3];
+ enum {
+ rc_none, rc_zero, rc_infinity, rc_nan, rc_finite
+ } resultc; /* special complex results, rc_none means use resultr and resulti as normal */
+ unsigned res2[2];
+ unsigned status; /* IEEE status return, if any */
+ unsigned maybestatus; /* for optional status, or allowance for spurious */
+ int nresult; /* number of result words */
+ int in_err, in_err_limit;
+ int err;
+ int maybeerr;
+ int valid;
+ int comment;
+ int random;
+} testdetail;
+
+enum { /* keywords */
+ k_errno, k_errno_in, k_error, k_func, k_maybeerror, k_maybestatus, k_op1, k_op1i, k_op1r, k_op2, k_op2i, k_op2r,
+ k_random, k_res2, k_result, k_resultc, k_resulti, k_resultr, k_status,
+ k_wrongres2, k_wrongresult, k_wrongstatus, k_wrongerrno
+};
+char *keywords[] = {
+ "errno", "errno_in", "error", "func", "maybeerror", "maybestatus", "op1", "op1i", "op1r", "op2", "op2i", "op2r",
+ "random", "res2", "result", "resultc", "resulti", "resultr", "status",
+ "wrongres2", "wrongresult", "wrongstatus", "wrongerrno"
+};
+
+enum {
+ e_0, e_EDOM, e_ERANGE,
+
+ /*
+ * This enum makes sure that we have the right number of errnos in the
+ * errno[] array
+ */
+ e_number_of_errnos
+};
+char *errnos[] = {
+ "0", "EDOM", "ERANGE"
+};
+
+enum {
+ e_none, e_divbyzero, e_domain, e_overflow, e_underflow
+};
+char *errors[] = {
+ "0", "divbyzero", "domain", "overflow", "underflow"
+};
+
+static int verbose, fo, strict;
+
+/* state toggled by random=on / random=off */
+static int randomstate;
+
+/* Canonify a double NaN: SNaNs all become 7FF00000.00000001 and QNaNs
+ * all become 7FF80000.00000001 */
+void canon_dNaN(unsigned a[2]) {
+ if ((a[0] & 0x7FF00000) != 0x7FF00000)
+ return; /* not Inf or NaN */
+ if (!(a[0] & 0xFFFFF) && !a[1])
+ return; /* Inf */
+ a[0] &= 0x7FF80000; /* canonify top word */
+ a[1] = 0x00000001; /* canonify bottom word */
+}
+
+/* Canonify a single NaN: SNaNs all become 7F800001 and QNaNs
+ * all become 7FC00001. Returns classification of the NaN. */
+void canon_sNaN(unsigned a[1]) {
+ if ((a[0] & 0x7F800000) != 0x7F800000)
+ return; /* not Inf or NaN */
+ if (!(a[0] & 0x7FFFFF))
+ return; /* Inf */
+ a[0] &= 0x7FC00000; /* canonify most bits */
+ a[0] |= 0x00000001; /* canonify bottom bit */
+}
+
+/*
+ * Detect
diff icult operands for FO mode.
+ */
+int is_dhard(unsigned a[2])
+{
+ if ((a[0] & 0x7FF00000) == 0x7FF00000)
+ return TRUE; /* inf or NaN */
+ if ((a[0] & 0x7FF00000) == 0 &&
+ ((a[0] & 0x7FFFFFFF) | a[1]) != 0)
+ return TRUE; /* denormal */
+ return FALSE;
+}
+int is_shard(unsigned a[1])
+{
+ if ((a[0] & 0x7F800000) == 0x7F800000)
+ return TRUE; /* inf or NaN */
+ if ((a[0] & 0x7F800000) == 0 &&
+ (a[0] & 0x7FFFFFFF) != 0)
+ return TRUE; /* denormal */
+ return FALSE;
+}
+
+/*
+ * Normalise all zeroes into +0, for FO mode.
+ */
+void dnormzero(unsigned a[2])
+{
+ if (a[0] == 0x80000000 && a[1] == 0)
+ a[0] = 0;
+}
+void snormzero(unsigned a[1])
+{
+ if (a[0] == 0x80000000)
+ a[0] = 0;
+}
+
+static int find(char *word, char **array, int asize) {
+ int i, j;
+
+ asize /= sizeof(char *);
+
+ i = -1; j = asize; /* strictly between i and j */
+ while (j-i > 1) {
+ int k = (i+j) / 2;
+ int c = strcmp(word, array[k]);
+ if (c > 0)
+ i = k;
+ else if (c < 0)
+ j = k;
+ else /* found it! */
+ return k;
+ }
+ return -1; /* not found */
+}
+
+static test_func* find_testfunc(char *word) {
+ int i, j, asize;
+
+ asize = sizeof(tfuncs)/sizeof(test_func);
+
+ i = -1; j = asize; /* strictly between i and j */
+ while (j-i > 1) {
+ int k = (i+j) / 2;
+ int c = strcmp(word, tfuncs[k].name);
+ if (c > 0)
+ i = k;
+ else if (c < 0)
+ j = k;
+ else /* found it! */
+ return tfuncs + k;
+ }
+ return NULL; /* not found */
+}
+
+static long long calc_error(unsigned a[2], unsigned b[3], int shift, int rettype) {
+ unsigned r0, r1, r2;
+ int sign, carry;
+ long long result;
+
+ /*
+ * If either number is infinite, require exact equality. If
+ * either number is NaN, require that both are NaN. If either
+ * of these requirements is broken, return INT_MAX.
+ */
+ if (is_double_rettype(rettype)) {
+ if ((a[0] & 0x7FF00000) == 0x7FF00000 ||
+ (b[0] & 0x7FF00000) == 0x7FF00000) {
+ if (((a[0] & 0x800FFFFF) || a[1]) &&
+ ((b[0] & 0x800FFFFF) || b[1]) &&
+ (a[0] & 0x7FF00000) == 0x7FF00000 &&
+ (b[0] & 0x7FF00000) == 0x7FF00000)
+ return 0; /* both NaN - OK */
+ if (!((a[0] & 0xFFFFF) || a[1]) &&
+ !((b[0] & 0xFFFFF) || b[1]) &&
+ a[0] == b[0])
+ return 0; /* both same sign of Inf - OK */
+ return LLONG_MAX;
+ }
+ } else {
+ if ((a[0] & 0x7F800000) == 0x7F800000 ||
+ (b[0] & 0x7F800000) == 0x7F800000) {
+ if ((a[0] & 0x807FFFFF) &&
+ (b[0] & 0x807FFFFF) &&
+ (a[0] & 0x7F800000) == 0x7F800000 &&
+ (b[0] & 0x7F800000) == 0x7F800000)
+ return 0; /* both NaN - OK */
+ if (!(a[0] & 0x7FFFFF) &&
+ !(b[0] & 0x7FFFFF) &&
+ a[0] == b[0])
+ return 0; /* both same sign of Inf - OK */
+ return LLONG_MAX;
+ }
+ }
+
+ /*
+ * Both finite. Return INT_MAX if the signs
diff er.
+ */
+ if ((a[0] ^ b[0]) & 0x80000000)
+ return LLONG_MAX;
+
+ /*
+ * Now it's just straight multiple-word subtraction.
+ */
+ if (is_double_rettype(rettype)) {
+ r2 = -b[2]; carry = (r2 == 0);
+ r1 = a[1] + ~b[1] + carry; carry = (r1 < a[1] || (carry && r1 == a[1]));
+ r0 = a[0] + ~b[0] + carry;
+ } else {
+ r2 = -b[1]; carry = (r2 == 0);
+ r1 = a[0] + ~b[0] + carry; carry = (r1 < a[0] || (carry && r1 == a[0]));
+ r0 = ~0 + carry;
+ }
+
+ /*
+ * Forgive larger errors in specialised cases.
+ */
+ if (shift > 0) {
+ if (shift > 32*3)
+ return 0; /* all errors are forgiven! */
+ while (shift >= 32) {
+ r2 = r1;
+ r1 = r0;
+ r0 = -(r0 >> 31);
+ shift -= 32;
+ }
+
+ if (shift > 0) {
+ r2 = (r2 >> shift) | (r1 << (32-shift));
+ r1 = (r1 >> shift) | (r0 << (32-shift));
+ r0 = (r0 >> shift) | ((-(r0 >> 31)) << (32-shift));
+ }
+ }
+
+ if (r0 & 0x80000000) {
+ sign = 1;
+ r2 = ~r2; carry = (r2 == 0);
+ r1 = 0 + ~r1 + carry; carry = (carry && (r2 == 0));
+ r0 = 0 + ~r0 + carry;
+ } else {
+ sign = 0;
+ }
+
+ if (r0 >= (1LL<<(31-EXTRABITS)))
+ return LLONG_MAX; /* many ulps out */
+
+ result = (r2 >> (32-EXTRABITS)) & (ULPUNIT-1);
+ result |= r1 << EXTRABITS;
+ result |= (long long)r0 << (32+EXTRABITS);
+ if (sign)
+ result = -result;
+ return result;
+}
+
+/* special named operands */
+
+typedef struct {
+ unsigned op1, op2;
+ char* name;
+} special_op;
+
+static special_op special_ops_double[] = {
+ {0x00000000,0x00000000,"0"},
+ {0x3FF00000,0x00000000,"1"},
+ {0x7FF00000,0x00000000,"inf"},
+ {0x7FF80000,0x00000001,"qnan"},
+ {0x7FF00000,0x00000001,"snan"},
+ {0x3ff921fb,0x54442d18,"pi2"},
+ {0x400921fb,0x54442d18,"pi"},
+ {0x3fe921fb,0x54442d18,"pi4"},
+ {0x4002d97c,0x7f3321d2,"3pi4"},
+};
+
+static special_op special_ops_float[] = {
+ {0x00000000,0,"0"},
+ {0x3f800000,0,"1"},
+ {0x7f800000,0,"inf"},
+ {0x7fc00000,0,"qnan"},
+ {0x7f800001,0,"snan"},
+ {0x3fc90fdb,0,"pi2"},
+ {0x40490fdb,0,"pi"},
+ {0x3f490fdb,0,"pi4"},
+ {0x4016cbe4,0,"3pi4"},
+};
+
+/*
+ This is what is returned by the below functions.
+ We need it to handle the sign of the number
+*/
+static special_op tmp_op = {0,0,0};
+
+special_op* find_special_op_from_op(unsigned op1, unsigned op2, int is_double) {
+ int i;
+ special_op* sop;
+ if(is_double) {
+ sop = special_ops_double;
+ } else {
+ sop = special_ops_float;
+ }
+ for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) {
+ if(sop->op1 == (op1&0x7fffffff) && sop->op2 == op2) {
+ if(tmp_op.name) free(tmp_op.name);
+ tmp_op.name = malloc(strlen(sop->name)+2);
+ if(op1>>31) {
+ sprintf(tmp_op.name,"-%s",sop->name);
+ } else {
+ strcpy(tmp_op.name,sop->name);
+ }
+ return &tmp_op;
+ }
+ sop++;
+ }
+ return NULL;
+}
+
+special_op* find_special_op_from_name(const char* name, int is_double) {
+ int i, neg=0;
+ special_op* sop;
+ if(is_double) {
+ sop = special_ops_double;
+ } else {
+ sop = special_ops_float;
+ }
+ if(*name=='-') {
+ neg=1;
+ name++;
+ } else if(*name=='+') {
+ name++;
+ }
+ for(i = 0; i < sizeof(special_ops_double)/sizeof(special_op); i++) {
+ if(0 == strcmp(name,sop->name)) {
+ tmp_op.op1 = sop->op1;
+ if(neg) {
+ tmp_op.op1 |= 0x80000000;
+ }
+ tmp_op.op2 = sop->op2;
+ return &tmp_op;
+ }
+ sop++;
+ }
+ return NULL;
+}
+
+/*
+ helper function for the below
+ type=0 for single, 1 for double, 2 for no sop
+*/
+int do_op(char* q, unsigned* op, const char* name, int num, int sop_type) {
+ int i;
+ int n=num;
+ special_op* sop = NULL;
+ for(i = 0; i < num; i++) {
+ op[i] = 0;
+ }
+ if(sop_type<2) {
+ sop = find_special_op_from_name(q,sop_type);
+ }
+ if(sop != NULL) {
+ op[0] = sop->op1;
+ op[1] = sop->op2;
+ } else {
+ switch(num) {
+ case 1: n = sscanf(q, "%x", &op[0]); break;
+ case 2: n = sscanf(q, "%x.%x", &op[0], &op[1]); break;
+ case 3: n = sscanf(q, "%x.%x.%x", &op[0], &op[1], &op[2]); break;
+ default: return -1;
+ }
+ }
+ if (verbose) {
+ printf("%s=",name);
+ for (i = 0; (i < n); ++i) printf("%x.", op[i]);
+ printf(" (n=%d)\n", n);
+ }
+ return n;
+}
+
+testdetail parsetest(char *testbuf, testdetail oldtest) {
+ char *p; /* Current part of line: Option name */
+ char *q; /* Current part of line: Option value */
+ testdetail ret; /* What we return */
+ int k; /* Function enum from k_* */
+ int n; /* Used as returns for scanfs */
+ int argtype=2, rettype=2; /* for do_op */
+
+ /* clear ret */
+ memset(&ret, 0, sizeof(ret));
+
+ if (verbose) printf("Parsing line: %s\n", testbuf);
+ while (*testbuf && isspace(*testbuf)) testbuf++;
+ if (testbuf[0] == ';' || testbuf[0] == '#' || testbuf[0] == '!' ||
+ testbuf[0] == '>' || testbuf[0] == '\0') {
+ ret.comment = 1;
+ if (verbose) printf("Line is a comment\n");
+ return ret;
+ }
+ ret.comment = 0;
+
+ if (*testbuf == '+') {
+ if (oldtest.valid) {
+ ret = oldtest; /* structure copy */
+ } else {
+ fprintf(stderr, "copy from invalid: ignored\n");
+ }
+ testbuf++;
+ }
+
+ ret.random = randomstate;
+
+ ret.in_err = 0;
+ ret.in_err_limit = e_number_of_errnos;
+
+ p = strtok(testbuf, " \t");
+ while (p != NULL) {
+ q = strchr(p, '=');
+ if (!q)
+ goto balderdash;
+ *q++ = '\0';
+ k = find(p, keywords, sizeof(keywords));
+ switch (k) {
+ case k_random:
+ randomstate = (!strcmp(q, "on"));
+ ret.comment = 1;
+ return ret; /* otherwise ignore this line */
+ case k_func:
+ if (verbose) printf("func=%s ", q);
+ //ret.func = find(q, funcs, sizeof(funcs));
+ ret.func = find_testfunc(q);
+ if (ret.func == NULL)
+ {
+ if (verbose) printf("(id=unknown)\n");
+ goto balderdash;
+ }
+ if(is_single_argtype(ret.func->argtype))
+ argtype = 0;
+ else if(is_double_argtype(ret.func->argtype))
+ argtype = 1;
+ if(is_single_rettype(ret.func->rettype))
+ rettype = 0;
+ else if(is_double_rettype(ret.func->rettype))
+ rettype = 1;
+ //ret.size = sizes[ret.func];
+ if (verbose) printf("(name=%s) (size=%d)\n", ret.func->name, ret.func->argtype);
+ break;
+ case k_op1:
+ case k_op1r:
+ n = do_op(q,ret.op1r,"op1r",2,argtype);
+ if (n < 1)
+ goto balderdash;
+ break;
+ case k_op1i:
+ n = do_op(q,ret.op1i,"op1i",2,argtype);
+ if (n < 1)
+ goto balderdash;
+ break;
+ case k_op2:
+ case k_op2r:
+ n = do_op(q,ret.op2r,"op2r",2,argtype);
+ if (n < 1)
+ goto balderdash;
+ break;
+ case k_op2i:
+ n = do_op(q,ret.op2i,"op2i",2,argtype);
+ if (n < 1)
+ goto balderdash;
+ break;
+ case k_resultc:
+ puts(q);
+ if(strncmp(q,"inf",3)==0) {
+ ret.resultc = rc_infinity;
+ } else if(strcmp(q,"zero")==0) {
+ ret.resultc = rc_zero;
+ } else if(strcmp(q,"nan")==0) {
+ ret.resultc = rc_nan;
+ } else if(strcmp(q,"finite")==0) {
+ ret.resultc = rc_finite;
+ } else {
+ goto balderdash;
+ }
+ break;
+ case k_result:
+ case k_resultr:
+ n = (do_op)(q,ret.resultr,"resultr",3,rettype);
+ if (n < 1)
+ goto balderdash;
+ ret.nresult = n; /* assume real and imaginary have same no. words */
+ break;
+ case k_resulti:
+ n = do_op(q,ret.resulti,"resulti",3,rettype);
+ if (n < 1)
+ goto balderdash;
+ break;
+ case k_res2:
+ n = do_op(q,ret.res2,"res2",2,rettype);
+ if (n < 1)
+ goto balderdash;
+ break;
+ case k_status:
+ while (*q) {
+ if (*q == 'i') ret.status |= FE_INVALID;
+ if (*q == 'z') ret.status |= FE_DIVBYZERO;
+ if (*q == 'o') ret.status |= FE_OVERFLOW;
+ if (*q == 'u') ret.status |= FE_UNDERFLOW;
+ q++;
+ }
+ break;
+ case k_maybeerror:
+ n = find(q, errors, sizeof(errors));
+ if (n < 0)
+ goto balderdash;
+ if(math_errhandling&MATH_ERREXCEPT) {
+ switch(n) {
+ case e_domain: ret.maybestatus |= FE_INVALID; break;
+ case e_divbyzero: ret.maybestatus |= FE_DIVBYZERO; break;
+ case e_overflow: ret.maybestatus |= FE_OVERFLOW; break;
+ case e_underflow: ret.maybestatus |= FE_UNDERFLOW; break;
+ }
+ }
+ {
+ switch(n) {
+ case e_domain:
+ ret.maybeerr = e_EDOM; break;
+ case e_divbyzero:
+ case e_overflow:
+ case e_underflow:
+ ret.maybeerr = e_ERANGE; break;
+ }
+ }
+ case k_maybestatus:
+ while (*q) {
+ if (*q == 'i') ret.maybestatus |= FE_INVALID;
+ if (*q == 'z') ret.maybestatus |= FE_DIVBYZERO;
+ if (*q == 'o') ret.maybestatus |= FE_OVERFLOW;
+ if (*q == 'u') ret.maybestatus |= FE_UNDERFLOW;
+ q++;
+ }
+ break;
+ case k_error:
+ n = find(q, errors, sizeof(errors));
+ if (n < 0)
+ goto balderdash;
+ if(math_errhandling&MATH_ERREXCEPT) {
+ switch(n) {
+ case e_domain: ret.status |= FE_INVALID; break;
+ case e_divbyzero: ret.status |= FE_DIVBYZERO; break;
+ case e_overflow: ret.status |= FE_OVERFLOW; break;
+ case e_underflow: ret.status |= FE_UNDERFLOW; break;
+ }
+ }
+ if(math_errhandling&MATH_ERRNO) {
+ switch(n) {
+ case e_domain:
+ ret.err = e_EDOM; break;
+ case e_divbyzero:
+ case e_overflow:
+ case e_underflow:
+ ret.err = e_ERANGE; break;
+ }
+ }
+ if(!(math_errhandling&MATH_ERRNO)) {
+ switch(n) {
+ case e_domain:
+ ret.maybeerr = e_EDOM; break;
+ case e_divbyzero:
+ case e_overflow:
+ case e_underflow:
+ ret.maybeerr = e_ERANGE; break;
+ }
+ }
+ break;
+ case k_errno:
+ ret.err = find(q, errnos, sizeof(errnos));
+ if (ret.err < 0)
+ goto balderdash;
+ break;
+ case k_errno_in:
+ ret.in_err = find(q, errnos, sizeof(errnos));
+ if (ret.err < 0)
+ goto balderdash;
+ ret.in_err_limit = ret.in_err + 1;
+ break;
+ case k_wrongresult:
+ case k_wrongstatus:
+ case k_wrongres2:
+ case k_wrongerrno:
+ /* quietly ignore these keys */
+ break;
+ default:
+ goto balderdash;
+ }
+ p = strtok(NULL, " \t");
+ }
+ ret.valid = 1;
+ return ret;
+
+ /* come here from almost any error */
+ balderdash:
+ ret.valid = 0;
+ return ret;
+}
+
+typedef enum {
+ test_comment, /* deliberately not a test */
+ test_invalid, /* accidentally not a test */
+ test_decline, /* was a test, and wasn't run */
+ test_fail, /* was a test, and failed */
+ test_pass /* was a test, and passed */
+} testresult;
+
+char failtext[512];
+
+typedef union {
+ unsigned i[2];
+ double f;
+ double da[2];
+} dbl;
+
+typedef union {
+ unsigned i;
+ float f;
+ float da[2];
+} sgl;
+
+/* helper function for runtest */
+void print_error(int rettype, unsigned *result, char* text, char** failp) {
+ special_op *sop;
+ char *str;
+
+ if(result) {
+ *failp += sprintf(*failp," %s=",text);
+ sop = find_special_op_from_op(result[0],result[1],is_double_rettype(rettype));
+ if(sop) {
+ *failp += sprintf(*failp,"%s",sop->name);
+ } else {
+ if(is_double_rettype(rettype)) {
+ str="%08x.%08x";
+ } else {
+ str="%08x";
+ }
+ *failp += sprintf(*failp,str,result[0],result[1]);
+ }
+ }
+}
+
+
+void print_ulps_helper(const char *name, long long ulps, char** failp) {
+ if(ulps == LLONG_MAX) {
+ *failp += sprintf(*failp, " %s=HUGE", name);
+ } else {
+ *failp += sprintf(*failp, " %s=%.3f", name, (double)ulps / ULPUNIT);
+ }
+}
+
+/* for complex args make ulpsr or ulpsri = 0 to not print */
+void print_ulps(int rettype, long long ulpsr, long long ulpsi, char** failp) {
+ if(is_complex_rettype(rettype)) {
+ if (ulpsr) print_ulps_helper("ulpsr",ulpsr,failp);
+ if (ulpsi) print_ulps_helper("ulpsi",ulpsi,failp);
+ } else {
+ if (ulpsr) print_ulps_helper("ulps",ulpsr,failp);
+ }
+}
+
+int runtest(testdetail t) {
+ int err, status;
+
+ dbl d_arg1, d_arg2, d_res, d_res2;
+ sgl s_arg1, s_arg2, s_res, s_res2;
+
+ int deferred_decline = FALSE;
+ char *failp = failtext;
+
+ unsigned int intres=0;
+
+ int res2_adjust = 0;
+
+ if (t.comment)
+ return test_comment;
+ if (!t.valid)
+ return test_invalid;
+
+ /* Set IEEE status to mathlib-normal */
+ feclearexcept(FE_ALL_EXCEPT);
+
+ /* Deal with operands */
+#define DO_DOP(arg,op) arg.i[dmsd] = t.op[0]; arg.i[dlsd] = t.op[1]
+ DO_DOP(d_arg1,op1r);
+ DO_DOP(d_arg2,op2r);
+ s_arg1.i = t.op1r[0]; s_arg2.i = t.op2r[0];
+
+ /*
+ * Detect NaNs, infinities and denormals on input, and set a
+ * deferred decline flag if we're in FO mode.
+ *
+ * (We defer the decline rather than doing it immediately
+ * because even in FO mode the operation is not permitted to
+ * crash or tight-loop; so we _run_ the test, and then ignore
+ * all the results.)
+ */
+ if (fo) {
+ if (is_double_argtype(t.func->argtype) && is_dhard(t.op1r))
+ deferred_decline = TRUE;
+ if (t.func->argtype==at_d2 && is_dhard(t.op2r))
+ deferred_decline = TRUE;
+ if (is_single_argtype(t.func->argtype) && is_shard(t.op1r))
+ deferred_decline = TRUE;
+ if (t.func->argtype==at_s2 && is_shard(t.op2r))
+ deferred_decline = TRUE;
+ if (is_double_rettype(t.func->rettype) && is_dhard(t.resultr))
+ deferred_decline = TRUE;
+ if (t.func->rettype==rt_d2 && is_dhard(t.res2))
+ deferred_decline = TRUE;
+ if (is_single_argtype(t.func->rettype) && is_shard(t.resultr))
+ deferred_decline = TRUE;
+ if (t.func->rettype==rt_s2 && is_shard(t.res2))
+ deferred_decline = TRUE;
+ if (t.err == e_ERANGE)
+ deferred_decline = TRUE;
+ }
+
+ /*
+ * Perform the operation
+ */
+
+ errno = t.in_err == e_EDOM ? EDOM : t.in_err == e_ERANGE ? ERANGE : 0;
+ if (t.err == e_0)
+ t.err = t.in_err;
+ if (t.maybeerr == e_0)
+ t.maybeerr = t.in_err;
+
+ if(t.func->type == t_func) {
+ switch(t.func->argtype) {
+ case at_d: d_res.f = t.func->func.d_d_ptr(d_arg1.f); break;
+ case at_s: s_res.f = t.func->func.s_s_ptr(s_arg1.f); break;
+ case at_d2: d_res.f = t.func->func.d2_d_ptr(d_arg1.f, d_arg2.f); break;
+ case at_s2: s_res.f = t.func->func.s2_s_ptr(s_arg1.f, s_arg2.f); break;
+ case at_di: d_res.f = t.func->func.di_d_ptr(d_arg1.f, d_arg2.i[dmsd]); break;
+ case at_si: s_res.f = t.func->func.si_s_ptr(s_arg1.f, s_arg2.i); break;
+ case at_dip: d_res.f = t.func->func.dip_d_ptr(d_arg1.f, (int*)&intres); break;
+ case at_sip: s_res.f = t.func->func.sip_s_ptr(s_arg1.f, (int*)&intres); break;
+ case at_ddp: d_res.f = t.func->func.ddp_d_ptr(d_arg1.f, &d_res2.f); break;
+ case at_ssp: s_res.f = t.func->func.ssp_s_ptr(s_arg1.f, &s_res2.f); break;
+ default:
+ printf("unhandled function: %s\n",t.func->name);
+ return test_fail;
+ }
+ } else {
+ /* printf("macro: name=%s, num=%i, s1.i=0x%08x s1.f=%f\n",t.func->name, t.func->macro_name, s_arg1.i, (double)s_arg1.f); */
+ switch(t.func->macro_name) {
+ case m_isfinite: intres = isfinite(d_arg1.f); break;
+ case m_isinf: intres = isinf(d_arg1.f); break;
+ case m_isnan: intres = isnan(d_arg1.f); break;
+ case m_isnormal: intres = isnormal(d_arg1.f); break;
+ case m_signbit: intres = signbit(d_arg1.f); break;
+ case m_fpclassify: intres = fpclassify(d_arg1.f); break;
+ case m_isgreater: intres = isgreater(d_arg1.f, d_arg2.f); break;
+ case m_isgreaterequal: intres = isgreaterequal(d_arg1.f, d_arg2.f); break;
+ case m_isless: intres = isless(d_arg1.f, d_arg2.f); break;
+ case m_islessequal: intres = islessequal(d_arg1.f, d_arg2.f); break;
+ case m_islessgreater: intres = islessgreater(d_arg1.f, d_arg2.f); break;
+ case m_isunordered: intres = isunordered(d_arg1.f, d_arg2.f); break;
+
+ case m_isfinitef: intres = isfinite(s_arg1.f); break;
+ case m_isinff: intres = isinf(s_arg1.f); break;
+ case m_isnanf: intres = isnan(s_arg1.f); break;
+ case m_isnormalf: intres = isnormal(s_arg1.f); break;
+ case m_signbitf: intres = signbit(s_arg1.f); break;
+ case m_fpclassifyf: intres = fpclassify(s_arg1.f); break;
+ case m_isgreaterf: intres = isgreater(s_arg1.f, s_arg2.f); break;
+ case m_isgreaterequalf: intres = isgreaterequal(s_arg1.f, s_arg2.f); break;
+ case m_islessf: intres = isless(s_arg1.f, s_arg2.f); break;
+ case m_islessequalf: intres = islessequal(s_arg1.f, s_arg2.f); break;
+ case m_islessgreaterf: intres = islessgreater(s_arg1.f, s_arg2.f); break;
+ case m_isunorderedf: intres = isunordered(s_arg1.f, s_arg2.f); break;
+
+ default:
+ printf("unhandled macro: %s\n",t.func->name);
+ return test_fail;
+ }
+ }
+
+ /*
+ * Decline the test if the deferred decline flag was set above.
+ */
+ if (deferred_decline)
+ return test_decline;
+
+ /* printf("intres=%i\n",intres); */
+
+ /* Clear the fail text (indicating a pass unless we change it) */
+ failp[0] = '\0';
+
+ /* Check the IEEE status bits (except INX, which we disregard).
+ * We don't bother with this for complex numbers, because the
+ * complex functions are hard to get exactly right and we don't
+ * have to anyway (C99 annex G is only informative). */
+ if (!(is_complex_argtype(t.func->argtype) || is_complex_rettype(t.func->rettype))) {
+ status = fetestexcept(FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW);
+ if ((status|t.maybestatus|~statusmask) != (t.status|t.maybestatus|~statusmask)) {
+ if (quiet) failtext[0]='x';
+ else {
+ failp += sprintf(failp,
+ " wrongstatus=%s%s%s%s%s",
+ (status & FE_INVALID ? "i" : ""),
+ (status & FE_DIVBYZERO ? "z" : ""),
+ (status & FE_OVERFLOW ? "o" : ""),
+ (status & FE_UNDERFLOW ? "u" : ""),
+ (status ? "" : "OK"));
+ }
+ }
+ }
+
+ /* Check the result */
+ {
+ unsigned resultr[2], resulti[2];
+ unsigned tresultr[3], tresulti[3], wres;
+
+ switch(t.func->rettype) {
+ case rt_d:
+ case rt_d2:
+ tresultr[0] = t.resultr[0];
+ tresultr[1] = t.resultr[1];
+ resultr[0] = d_res.i[dmsd]; resultr[1] = d_res.i[dlsd];
+ wres = 2;
+ break;
+ case rt_i:
+ tresultr[0] = t.resultr[0];
+ resultr[0] = intres;
+ wres = 1;
+ break;
+ case rt_s:
+ case rt_s2:
+ tresultr[0] = t.resultr[0];
+ resultr[0] = s_res.i;
+ wres = 1;
+ break;
+ default:
+ puts("unhandled rettype in runtest");
+ wres = 0;
+ }
+ if(t.resultc != rc_none) {
+ int err = 0;
+ switch(t.resultc) {
+ case rc_zero:
+ if(resultr[0] != 0 || resulti[0] != 0 ||
+ (wres==2 && (resultr[1] != 0 || resulti[1] != 0))) {
+ err = 1;
+ }
+ break;
+ case rc_infinity:
+ if(wres==1) {
+ if(!((resultr[0]&0x7fffffff)==0x7f800000 ||
+ (resulti[0]&0x7fffffff)==0x7f800000)) {
+ err = 1;
+ }
+ } else {
+ if(!(((resultr[0]&0x7fffffff)==0x7ff00000 && resultr[1]==0) ||
+ ((resulti[0]&0x7fffffff)==0x7ff00000 && resulti[1]==0))) {
+ err = 1;
+ }
+ }
+ break;
+ case rc_nan:
+ if(wres==1) {
+ if(!((resultr[0]&0x7fffffff)>0x7f800000 ||
+ (resulti[0]&0x7fffffff)>0x7f800000)) {
+ err = 1;
+ }
+ } else {
+ canon_dNaN(resultr);
+ canon_dNaN(resulti);
+ if(!(((resultr[0]&0x7fffffff)>0x7ff00000 && resultr[1]==1) ||
+ ((resulti[0]&0x7fffffff)>0x7ff00000 && resulti[1]==1))) {
+ err = 1;
+ }
+ }
+ break;
+ case rc_finite:
+ if(wres==1) {
+ if(!((resultr[0]&0x7fffffff)<0x7f800000 ||
+ (resulti[0]&0x7fffffff)<0x7f800000)) {
+ err = 1;
+ }
+ } else {
+ if(!((resultr[0]&0x7fffffff)<0x7ff00000 ||
+ (resulti[0]&0x7fffffff)<0x7ff00000)) {
+ err = 1;
+ }
+ }
+ break;
+ default:
+ break;
+ }
+ if(err) {
+ print_error(t.func->rettype,resultr,"wrongresultr",&failp);
+ print_error(t.func->rettype,resulti,"wrongresulti",&failp);
+ }
+ } else if (t.nresult > wres) {
+ /*
+ * The test case data has provided the result to more
+ * than double precision. Instead of testing exact
+ * equality, we test against our maximum error
+ * tolerance.
+ */
+ int rshift, ishift;
+ long long ulpsr, ulpsi, ulptolerance;
+
+ tresultr[wres] = t.resultr[wres] << (32-EXTRABITS);
+ tresulti[wres] = t.resulti[wres] << (32-EXTRABITS);
+ if(strict) {
+ ulptolerance = 4096; /* one ulp */
+ } else {
+ ulptolerance = t.func->tolerance;
+ }
+ rshift = ishift = 0;
+ if (ulptolerance & ABSLOWERBOUND) {
+ /*
+ * Hack for the lgamma functions, which have an
+ * error behaviour that can't conveniently be
+ * characterised in pure ULPs. Really, we want to
+ * say that the error in lgamma is "at most N ULPs,
+ * or at most an absolute error of X, whichever is
+ * larger", for appropriately chosen N,X. But since
+ * these two functions are the only cases where it
+ * arises, I haven't bothered to do it in a nice way
+ * in the function table above.
+ *
+ * (The
diff icult cases arise with negative input
+ * values such that |gamma(x)| is very near to 1; in
+ * this situation implementations tend to separately
+ * compute lgamma(|x|) and the log of the correction
+ * term from the Euler reflection formula, and
+ * subtract - which catastrophically loses
+ * significance.)
+ *
+ * As far as I can tell, nobody cares about this:
+ * GNU libm doesn't get those cases right either,
+ * and OpenCL explicitly doesn't state a ULP error
+ * limit for lgamma. So my guess is that this is
+ * simply considered acceptable error behaviour for
+ * this particular function, and hence I feel free
+ * to allow for it here.
+ */
+ ulptolerance &= ~ABSLOWERBOUND;
+ if (t.op1r[0] & 0x80000000) {
+ if (t.func->rettype == rt_d)
+ rshift = 0x400 - ((tresultr[0] >> 20) & 0x7ff);
+ else if (t.func->rettype == rt_s)
+ rshift = 0x80 - ((tresultr[0] >> 23) & 0xff);
+ if (rshift < 0)
+ rshift = 0;
+ }
+ }
+ if (ulptolerance & PLUSMINUSPIO2) {
+ ulptolerance &= ~PLUSMINUSPIO2;
+ /*
+ * Hack for range reduction, which can reduce
+ * borderline cases in the wrong direction, i.e.
+ * return a value just outside one end of the interval
+ * [-pi/4,+pi/4] when it could have returned a value
+ * just inside the other end by subtracting an
+ * adjacent multiple of pi/2.
+ *
+ * We tolerate this, up to a point, because the
+ * trigonometric functions making use of the output of
+ * rred can cope and because making the range reducer
+ * do the exactly right thing in every case would be
+ * more expensive.
+ */
+ if (wres == 1) {
+ /* Upper bound of overshoot derived in rredf.h */
+ if ((resultr[0]&0x7FFFFFFF) <= 0x3f494b02 &&
+ (resultr[0]&0x7FFFFFFF) > 0x3f490fda &&
+ (resultr[0]&0x80000000) != (tresultr[0]&0x80000000)) {
+ unsigned long long val;
+ val = tresultr[0];
+ val = (val << 32) | tresultr[1];
+ /*
+ * Compute the alternative permitted result by
+ * subtracting from the sum of the extended
+ * single-precision bit patterns of +pi/4 and
+ * -pi/4. This is a horrible hack which only
+ * works because we can be confident that
+ * numbers in this range all have the same
+ * exponent!
+ */
+ val = 0xfe921fb54442d184ULL - val;
+ tresultr[0] = val >> 32;
+ tresultr[1] = (val >> (32-EXTRABITS)) << (32-EXTRABITS);
+ /*
+ * Also, expect a correspondingly
diff erent
+ * value of res2 as a result of this change.
+ * The adjustment depends on whether we just
+ * flipped the result from + to - or vice
+ * versa.
+ */
+ if (resultr[0] & 0x80000000) {
+ res2_adjust = +1;
+ } else {
+ res2_adjust = -1;
+ }
+ }
+ }
+ }
+ ulpsr = calc_error(resultr, tresultr, rshift, t.func->rettype);
+ if(is_complex_rettype(t.func->rettype)) {
+ ulpsi = calc_error(resulti, tresulti, ishift, t.func->rettype);
+ } else {
+ ulpsi = 0;
+ }
+ unsigned *rr = (ulpsr > ulptolerance || ulpsr < -ulptolerance) ? resultr : NULL;
+ unsigned *ri = (ulpsi > ulptolerance || ulpsi < -ulptolerance) ? resulti : NULL;
+/* printf("tolerance=%i, ulpsr=%i, ulpsi=%i, rr=%p, ri=%p\n",ulptolerance,ulpsr,ulpsi,rr,ri); */
+ if (rr || ri) {
+ if (quiet) failtext[0]='x';
+ else {
+ print_error(t.func->rettype,rr,"wrongresultr",&failp);
+ print_error(t.func->rettype,ri,"wrongresulti",&failp);
+ print_ulps(t.func->rettype,rr ? ulpsr : 0, ri ? ulpsi : 0,&failp);
+ }
+ }
+ } else {
+ if(is_complex_rettype(t.func->rettype))
+ /*
+ * Complex functions are not fully supported,
+ * this is unreachable, but prevents warnings.
+ */
+ abort();
+ /*
+ * The test case data has provided the result in
+ * exactly the output precision. Therefore we must
+ * complain about _any_ violation.
+ */
+ switch(t.func->rettype) {
+ case rt_dc:
+ canon_dNaN(tresulti);
+ canon_dNaN(resulti);
+ if (fo) {
+ dnormzero(tresulti);
+ dnormzero(resulti);
+ }
+ /* deliberate fall-through */
+ case rt_d:
+ canon_dNaN(tresultr);
+ canon_dNaN(resultr);
+ if (fo) {
+ dnormzero(tresultr);
+ dnormzero(resultr);
+ }
+ break;
+ case rt_sc:
+ canon_sNaN(tresulti);
+ canon_sNaN(resulti);
+ if (fo) {
+ snormzero(tresulti);
+ snormzero(resulti);
+ }
+ /* deliberate fall-through */
+ case rt_s:
+ canon_sNaN(tresultr);
+ canon_sNaN(resultr);
+ if (fo) {
+ snormzero(tresultr);
+ snormzero(resultr);
+ }
+ break;
+ default:
+ break;
+ }
+ if(is_complex_rettype(t.func->rettype)) {
+ unsigned *rr, *ri;
+ if(resultr[0] != tresultr[0] ||
+ (wres > 1 && resultr[1] != tresultr[1])) {
+ rr = resultr;
+ } else {
+ rr = NULL;
+ }
+ if(resulti[0] != tresulti[0] ||
+ (wres > 1 && resulti[1] != tresulti[1])) {
+ ri = resulti;
+ } else {
+ ri = NULL;
+ }
+ if(rr || ri) {
+ if (quiet) failtext[0]='x';
+ print_error(t.func->rettype,rr,"wrongresultr",&failp);
+ print_error(t.func->rettype,ri,"wrongresulti",&failp);
+ }
+ } else if (resultr[0] != tresultr[0] ||
+ (wres > 1 && resultr[1] != tresultr[1])) {
+ if (quiet) failtext[0]='x';
+ print_error(t.func->rettype,resultr,"wrongresult",&failp);
+ }
+ }
+ /*
+ * Now test res2, for those functions (frexp, modf, rred)
+ * which use it.
+ */
+ if (t.func->func.ptr == &frexp || t.func->func.ptr == &frexpf ||
+ t.func->macro_name == m_rred || t.func->macro_name == m_rredf) {
+ unsigned tres2 = t.res2[0];
+ if (res2_adjust) {
+ /* Fix for range reduction, propagated from further up */
+ tres2 = (tres2 + res2_adjust) & 3;
+ }
+ if (tres2 != intres) {
+ if (quiet) failtext[0]='x';
+ else {
+ failp += sprintf(failp,
+ " wrongres2=%08x", intres);
+ }
+ }
+ } else if (t.func->func.ptr == &modf || t.func->func.ptr == &modff) {
+ tresultr[0] = t.res2[0];
+ tresultr[1] = t.res2[1];
+ if (is_double_rettype(t.func->rettype)) {
+ canon_dNaN(tresultr);
+ resultr[0] = d_res2.i[dmsd];
+ resultr[1] = d_res2.i[dlsd];
+ canon_dNaN(resultr);
+ if (fo) {
+ dnormzero(tresultr);
+ dnormzero(resultr);
+ }
+ } else {
+ canon_sNaN(tresultr);
+ resultr[0] = s_res2.i;
+ resultr[1] = s_res2.i;
+ canon_sNaN(resultr);
+ if (fo) {
+ snormzero(tresultr);
+ snormzero(resultr);
+ }
+ }
+ if (resultr[0] != tresultr[0] ||
+ (wres > 1 && resultr[1] != tresultr[1])) {
+ if (quiet) failtext[0]='x';
+ else {
+ if (is_double_rettype(t.func->rettype))
+ failp += sprintf(failp, " wrongres2=%08x.%08x",
+ resultr[0], resultr[1]);
+ else
+ failp += sprintf(failp, " wrongres2=%08x",
+ resultr[0]);
+ }
+ }
+ }
+ }
+
+ /* Check errno */
+ err = (errno == EDOM ? e_EDOM : errno == ERANGE ? e_ERANGE : e_0);
+ if (err != t.err && err != t.maybeerr) {
+ if (quiet) failtext[0]='x';
+ else {
+ failp += sprintf(failp, " wrongerrno=%s expecterrno=%s ", errnos[err], errnos[t.err]);
+ }
+ }
+
+ return *failtext ? test_fail : test_pass;
+}
+
+int passed, failed, declined;
+
+void runtests(char *name, FILE *fp) {
+ char testbuf[512], linebuf[512];
+ int lineno = 1;
+ testdetail test;
+
+ test.valid = 0;
+
+ if (verbose) printf("runtests: %s\n", name);
+ while (fgets(testbuf, sizeof(testbuf), fp)) {
+ int res, print_errno;
+ testbuf[strcspn(testbuf, "\r\n")] = '\0';
+ strcpy(linebuf, testbuf);
+ test = parsetest(testbuf, test);
+ print_errno = 0;
+ while (test.in_err < test.in_err_limit) {
+ res = runtest(test);
+ if (res == test_pass) {
+ if (verbose)
+ printf("%s:%d: pass\n", name, lineno);
+ ++passed;
+ } else if (res == test_decline) {
+ if (verbose)
+ printf("%s:%d: declined\n", name, lineno);
+ ++declined;
+ } else if (res == test_fail) {
+ if (!quiet)
+ printf("%s:%d: FAIL%s: %s%s%s%s\n", name, lineno,
+ test.random ? " (random)" : "",
+ linebuf,
+ print_errno ? " errno_in=" : "",
+ print_errno ? errnos[test.in_err] : "",
+ failtext);
+ ++failed;
+ } else if (res == test_invalid) {
+ printf("%s:%d: malformed: %s\n", name, lineno, linebuf);
+ ++failed;
+ }
+ test.in_err++;
+ print_errno = 1;
+ }
+ lineno++;
+ }
+}
+
+int main(int ac, char **av) {
+ char **files;
+ int i, nfiles = 0;
+ dbl d;
+
+#ifdef MICROLIB
+ /*
+ * Invent argc and argv ourselves.
+ */
+ char *argv[256];
+ char args[256];
+ {
+ int sargs[2];
+ char *p;
+
+ ac = 0;
+
+ sargs[0]=(int)args;
+ sargs[1]=(int)sizeof(args);
+ if (!__semihost(0x15, sargs)) {
+ args[sizeof(args)-1] = '\0'; /* just in case */
+ p = args;
+ while (1) {
+ while (*p == ' ' || *p == '\t') p++;
+ if (!*p) break;
+ argv[ac++] = p;
+ while (*p && *p != ' ' && *p != '\t') p++;
+ if (*p) *p++ = '\0';
+ }
+ }
+
+ av = argv;
+ }
+#endif
+
+ /* Sort tfuncs */
+ qsort(tfuncs, sizeof(tfuncs)/sizeof(test_func), sizeof(test_func), &compare_tfuncs);
+
+ /*
+ * Autodetect the `double' endianness.
+ */
+ dmsd = 0;
+ d.f = 1.0; /* 0x3ff00000 / 0x00000000 */
+ if (d.i[dmsd] == 0) {
+ dmsd = 1;
+ }
+ /*
+ * Now dmsd denotes what the compiler thinks we're at. Let's
+ * check that it agrees with what the runtime thinks.
+ */
+ d.i[0] = d.i[1] = 0x11111111;/* a random +ve number */
+ d.f /= d.f; /* must now be one */
+ if (d.i[dmsd] == 0) {
+ fprintf(stderr, "YIKES! Compiler and runtime disagree on endianness"
+ " of `double'. Bailing out\n");
+ return 1;
+ }
+ dlsd = !dmsd;
+
+ /* default is terse */
+ verbose = 0;
+ fo = 0;
+ strict = 0;
+
+ files = (char **)malloc((ac+1) * sizeof(char *));
+ if (!files) {
+ fprintf(stderr, "initial malloc failed!\n");
+ return 1;
+ }
+#ifdef NOCMDLINE
+ files[nfiles++] = "testfile";
+#endif
+
+ while (--ac) {
+ char *p = *++av;
+ if (*p == '-') {
+ static char *options[] = {
+ "-fo",
+#if 0
+ "-noinexact",
+ "-noround",
+#endif
+ "-nostatus",
+ "-quiet",
+ "-strict",
+ "-v",
+ "-verbose",
+ };
+ enum {
+ op_fo,
+#if 0
+ op_noinexact,
+ op_noround,
+#endif
+ op_nostatus,
+ op_quiet,
+ op_strict,
+ op_v,
+ op_verbose,
+ };
+ switch (find(p, options, sizeof(options))) {
+ case op_quiet:
+ quiet = 1;
+ break;
+#if 0
+ case op_noinexact:
+ statusmask &= 0x0F; /* remove bit 4 */
+ break;
+ case op_noround:
+ doround = 0;
+ break;
+#endif
+ case op_nostatus: /* no status word => noinx,noround */
+ statusmask = 0;
+ doround = 0;
+ break;
+ case op_v:
+ case op_verbose:
+ verbose = 1;
+ break;
+ case op_fo:
+ fo = 1;
+ break;
+ case op_strict: /* tolerance is 1 ulp */
+ strict = 1;
+ break;
+ default:
+ fprintf(stderr, "unrecognised option: %s\n", p);
+ break;
+ }
+ } else {
+ files[nfiles++] = p;
+ }
+ }
+
+ passed = failed = declined = 0;
+
+ if (nfiles) {
+ for (i = 0; i < nfiles; i++) {
+ FILE *fp = fopen(files[i], "r");
+ if (!fp) {
+ fprintf(stderr, "Couldn't open %s\n", files[i]);
+ } else
+ runtests(files[i], fp);
+ }
+ } else
+ runtests("(stdin)", stdin);
+
+ printf("Completed. Passed %d, failed %d (total %d",
+ passed, failed, passed+failed);
+ if (declined)
+ printf(" plus %d declined", declined);
+ printf(")\n");
+ if (failed || passed == 0)
+ return 1;
+ printf("** TEST PASSED OK **\n");
+ return 0;
+}
+
+void undef_func() {
+ failed++;
+ puts("ERROR: undefined function called");
+}
diff --git a/libc/AOR_v20.02/math/test/rtest/dotest.c b/libc/AOR_v20.02/math/test/rtest/dotest.c
new file mode 100644
index 000000000000..43278626e75e
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/dotest.c
@@ -0,0 +1,2168 @@
+/*
+ * dotest.c - actually generate mathlib test cases
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <assert.h>
+#include <limits.h>
+
+#include "semi.h"
+#include "intern.h"
+#include "random.h"
+
+#define MPFR_PREC 96 /* good enough for float or double + a few extra bits */
+
+extern int lib_fo, lib_no_arith, ntests;
+
+/*
+ * Prototypes.
+ */
+static void cases_biased(uint32 *, uint32, uint32);
+static void cases_biased_positive(uint32 *, uint32, uint32);
+static void cases_biased_float(uint32 *, uint32, uint32);
+static void cases_uniform(uint32 *, uint32, uint32);
+static void cases_uniform_positive(uint32 *, uint32, uint32);
+static void cases_uniform_float(uint32 *, uint32, uint32);
+static void cases_uniform_float_positive(uint32 *, uint32, uint32);
+static void log_cases(uint32 *, uint32, uint32);
+static void log_cases_float(uint32 *, uint32, uint32);
+static void log1p_cases(uint32 *, uint32, uint32);
+static void log1p_cases_float(uint32 *, uint32, uint32);
+static void minmax_cases(uint32 *, uint32, uint32);
+static void minmax_cases_float(uint32 *, uint32, uint32);
+static void atan2_cases(uint32 *, uint32, uint32);
+static void atan2_cases_float(uint32 *, uint32, uint32);
+static void pow_cases(uint32 *, uint32, uint32);
+static void pow_cases_float(uint32 *, uint32, uint32);
+static void rred_cases(uint32 *, uint32, uint32);
+static void rred_cases_float(uint32 *, uint32, uint32);
+static void cases_semi1(uint32 *, uint32, uint32);
+static void cases_semi1_float(uint32 *, uint32, uint32);
+static void cases_semi2(uint32 *, uint32, uint32);
+static void cases_semi2_float(uint32 *, uint32, uint32);
+static void cases_ldexp(uint32 *, uint32, uint32);
+static void cases_ldexp_float(uint32 *, uint32, uint32);
+
+static void complex_cases_uniform(uint32 *, uint32, uint32);
+static void complex_cases_uniform_float(uint32 *, uint32, uint32);
+static void complex_cases_biased(uint32 *, uint32, uint32);
+static void complex_cases_biased_float(uint32 *, uint32, uint32);
+static void complex_log_cases(uint32 *, uint32, uint32);
+static void complex_log_cases_float(uint32 *, uint32, uint32);
+static void complex_pow_cases(uint32 *, uint32, uint32);
+static void complex_pow_cases_float(uint32 *, uint32, uint32);
+static void complex_arithmetic_cases(uint32 *, uint32, uint32);
+static void complex_arithmetic_cases_float(uint32 *, uint32, uint32);
+
+static uint32 doubletop(int x, int scale);
+static uint32 floatval(int x, int scale);
+
+/*
+ * Convert back and forth between IEEE bit patterns and the
+ * mpfr_t/mpc_t types.
+ */
+static void set_mpfr_d(mpfr_t x, uint32 h, uint32 l)
+{
+ uint64_t hl = ((uint64_t)h << 32) | l;
+ uint32 exp = (hl >> 52) & 0x7ff;
+ int64_t mantissa = hl & (((uint64_t)1 << 52) - 1);
+ int sign = (hl >> 63) ? -1 : +1;
+ if (exp == 0x7ff) {
+ if (mantissa == 0)
+ mpfr_set_inf(x, sign);
+ else
+ mpfr_set_nan(x);
+ } else if (exp == 0 && mantissa == 0) {
+ mpfr_set_ui(x, 0, GMP_RNDN);
+ mpfr_setsign(x, x, sign < 0, GMP_RNDN);
+ } else {
+ if (exp != 0)
+ mantissa |= ((uint64_t)1 << 52);
+ else
+ exp++;
+ mpfr_set_sj_2exp(x, mantissa * sign, (int)exp - 0x3ff - 52, GMP_RNDN);
+ }
+}
+static void set_mpfr_f(mpfr_t x, uint32 f)
+{
+ uint32 exp = (f >> 23) & 0xff;
+ int32 mantissa = f & ((1 << 23) - 1);
+ int sign = (f >> 31) ? -1 : +1;
+ if (exp == 0xff) {
+ if (mantissa == 0)
+ mpfr_set_inf(x, sign);
+ else
+ mpfr_set_nan(x);
+ } else if (exp == 0 && mantissa == 0) {
+ mpfr_set_ui(x, 0, GMP_RNDN);
+ mpfr_setsign(x, x, sign < 0, GMP_RNDN);
+ } else {
+ if (exp != 0)
+ mantissa |= (1 << 23);
+ else
+ exp++;
+ mpfr_set_sj_2exp(x, mantissa * sign, (int)exp - 0x7f - 23, GMP_RNDN);
+ }
+}
+static void set_mpc_d(mpc_t z, uint32 rh, uint32 rl, uint32 ih, uint32 il)
+{
+ mpfr_t x, y;
+ mpfr_init2(x, MPFR_PREC);
+ mpfr_init2(y, MPFR_PREC);
+ set_mpfr_d(x, rh, rl);
+ set_mpfr_d(y, ih, il);
+ mpc_set_fr_fr(z, x, y, MPC_RNDNN);
+ mpfr_clear(x);
+ mpfr_clear(y);
+}
+static void set_mpc_f(mpc_t z, uint32 r, uint32 i)
+{
+ mpfr_t x, y;
+ mpfr_init2(x, MPFR_PREC);
+ mpfr_init2(y, MPFR_PREC);
+ set_mpfr_f(x, r);
+ set_mpfr_f(y, i);
+ mpc_set_fr_fr(z, x, y, MPC_RNDNN);
+ mpfr_clear(x);
+ mpfr_clear(y);
+}
+static void get_mpfr_d(const mpfr_t x, uint32 *h, uint32 *l, uint32 *extra)
+{
+ uint32_t sign, expfield, mantfield;
+ mpfr_t significand;
+ int exp;
+
+ if (mpfr_nan_p(x)) {
+ *h = 0x7ff80000;
+ *l = 0;
+ *extra = 0;
+ return;
+ }
+
+ sign = mpfr_signbit(x) ? 0x80000000U : 0;
+
+ if (mpfr_inf_p(x)) {
+ *h = 0x7ff00000 | sign;
+ *l = 0;
+ *extra = 0;
+ return;
+ }
+
+ if (mpfr_zero_p(x)) {
+ *h = 0x00000000 | sign;
+ *l = 0;
+ *extra = 0;
+ return;
+ }
+
+ mpfr_init2(significand, MPFR_PREC);
+ mpfr_set(significand, x, GMP_RNDN);
+ exp = mpfr_get_exp(significand);
+ mpfr_set_exp(significand, 0);
+
+ /* Now significand is in [1/2,1), and significand * 2^exp == x.
+ * So the IEEE exponent corresponding to exp==0 is 0x3fe. */
+ if (exp > 0x400) {
+ /* overflow to infinity anyway */
+ *h = 0x7ff00000 | sign;
+ *l = 0;
+ *extra = 0;
+ mpfr_clear(significand);
+ return;
+ }
+
+ if (exp <= -0x3fe || mpfr_zero_p(x))
+ exp = -0x3fd; /* denormalise */
+ expfield = exp + 0x3fd; /* offset to cancel leading mantissa bit */
+
+ mpfr_div_2si(significand, x, exp - 21, GMP_RNDN);
+ mpfr_abs(significand, significand, GMP_RNDN);
+ mantfield = mpfr_get_ui(significand, GMP_RNDZ);
+ *h = sign + ((uint64_t)expfield << 20) + mantfield;
+ mpfr_sub_ui(significand, significand, mantfield, GMP_RNDN);
+ mpfr_mul_2ui(significand, significand, 32, GMP_RNDN);
+ mantfield = mpfr_get_ui(significand, GMP_RNDZ);
+ *l = mantfield;
+ mpfr_sub_ui(significand, significand, mantfield, GMP_RNDN);
+ mpfr_mul_2ui(significand, significand, 32, GMP_RNDN);
+ mantfield = mpfr_get_ui(significand, GMP_RNDZ);
+ *extra = mantfield;
+
+ mpfr_clear(significand);
+}
+static void get_mpfr_f(const mpfr_t x, uint32 *f, uint32 *extra)
+{
+ uint32_t sign, expfield, mantfield;
+ mpfr_t significand;
+ int exp;
+
+ if (mpfr_nan_p(x)) {
+ *f = 0x7fc00000;
+ *extra = 0;
+ return;
+ }
+
+ sign = mpfr_signbit(x) ? 0x80000000U : 0;
+
+ if (mpfr_inf_p(x)) {
+ *f = 0x7f800000 | sign;
+ *extra = 0;
+ return;
+ }
+
+ if (mpfr_zero_p(x)) {
+ *f = 0x00000000 | sign;
+ *extra = 0;
+ return;
+ }
+
+ mpfr_init2(significand, MPFR_PREC);
+ mpfr_set(significand, x, GMP_RNDN);
+ exp = mpfr_get_exp(significand);
+ mpfr_set_exp(significand, 0);
+
+ /* Now significand is in [1/2,1), and significand * 2^exp == x.
+ * So the IEEE exponent corresponding to exp==0 is 0x7e. */
+ if (exp > 0x80) {
+ /* overflow to infinity anyway */
+ *f = 0x7f800000 | sign;
+ *extra = 0;
+ mpfr_clear(significand);
+ return;
+ }
+
+ if (exp <= -0x7e || mpfr_zero_p(x))
+ exp = -0x7d; /* denormalise */
+ expfield = exp + 0x7d; /* offset to cancel leading mantissa bit */
+
+ mpfr_div_2si(significand, x, exp - 24, GMP_RNDN);
+ mpfr_abs(significand, significand, GMP_RNDN);
+ mantfield = mpfr_get_ui(significand, GMP_RNDZ);
+ *f = sign + ((uint64_t)expfield << 23) + mantfield;
+ mpfr_sub_ui(significand, significand, mantfield, GMP_RNDN);
+ mpfr_mul_2ui(significand, significand, 32, GMP_RNDN);
+ mantfield = mpfr_get_ui(significand, GMP_RNDZ);
+ *extra = mantfield;
+
+ mpfr_clear(significand);
+}
+static void get_mpc_d(const mpc_t z,
+ uint32 *rh, uint32 *rl, uint32 *rextra,
+ uint32 *ih, uint32 *il, uint32 *iextra)
+{
+ mpfr_t x, y;
+ mpfr_init2(x, MPFR_PREC);
+ mpfr_init2(y, MPFR_PREC);
+ mpc_real(x, z, GMP_RNDN);
+ mpc_imag(y, z, GMP_RNDN);
+ get_mpfr_d(x, rh, rl, rextra);
+ get_mpfr_d(y, ih, il, iextra);
+ mpfr_clear(x);
+ mpfr_clear(y);
+}
+static void get_mpc_f(const mpc_t z,
+ uint32 *r, uint32 *rextra,
+ uint32 *i, uint32 *iextra)
+{
+ mpfr_t x, y;
+ mpfr_init2(x, MPFR_PREC);
+ mpfr_init2(y, MPFR_PREC);
+ mpc_real(x, z, GMP_RNDN);
+ mpc_imag(y, z, GMP_RNDN);
+ get_mpfr_f(x, r, rextra);
+ get_mpfr_f(y, i, iextra);
+ mpfr_clear(x);
+ mpfr_clear(y);
+}
+
+/*
+ * Implementation of mathlib functions that aren't trivially
+ * implementable using an existing mpfr or mpc function.
+ */
+int test_rred(mpfr_t ret, const mpfr_t x, int *quadrant)
+{
+ mpfr_t halfpi;
+ long quo;
+ int status;
+
+ /*
+ * In the worst case of range reduction, we get an input of size
+ * around 2^1024, and must find its remainder mod pi, which means
+ * we need 1024 bits of pi at least. Plus, the remainder might
+ * happen to come out very very small if we're unlucky. How
+ * unlucky can we be? Well, conveniently, I once went through and
+ * actually worked that out using Paxson's modular minimisation
+ * algorithm, and it turns out that the smallest exponent you can
+ * get out of a nontrivial[1] double precision range reduction is
+ * 0x3c2, i.e. of the order of 2^-61. So we need 1024 bits of pi
+ * to get us down to the units digit, another 61 or so bits (say
+ * 64) to get down to the highest set bit of the output, and then
+ * some bits to make the actual mantissa big enough.
+ *
+ * [1] of course the output of range reduction can have an
+ * arbitrarily small exponent in the trivial case, where the
+ * input is so small that it's the identity function. That
+ * doesn't count.
+ */
+ mpfr_init2(halfpi, MPFR_PREC + 1024 + 64);
+ mpfr_const_pi(halfpi, GMP_RNDN);
+ mpfr_div_ui(halfpi, halfpi, 2, GMP_RNDN);
+
+ status = mpfr_remquo(ret, &quo, x, halfpi, GMP_RNDN);
+ *quadrant = quo & 3;
+
+ mpfr_clear(halfpi);
+
+ return status;
+}
+int test_lgamma(mpfr_t ret, const mpfr_t x, mpfr_rnd_t rnd)
+{
+ /*
+ * mpfr_lgamma takes an extra int * parameter to hold the output
+ * sign. We don't bother testing that, so this wrapper throws away
+ * the sign and hence fits into the same function prototype as all
+ * the other real->real mpfr functions.
+ *
+ * There is also mpfr_lngamma which has no sign output and hence
+ * has the right prototype already, but unfortunately it returns
+ * NaN in cases where gamma(x) < 0, so it's no use to us.
+ */
+ int sign;
+ return mpfr_lgamma(ret, &sign, x, rnd);
+}
+int test_cpow(mpc_t ret, const mpc_t x, const mpc_t y, mpc_rnd_t rnd)
+{
+ /*
+ * For complex pow, we must bump up the precision by a huge amount
+ * if we want it to get the really
diff icult cases right. (Not
+ * that we expect the library under test to be getting those cases
+ * right itself, but we'd at least like the test suite to report
+ * them as wrong for the _right reason_.)
+ *
+ * This works around a bug in mpc_pow(), fixed by r1455 in the MPC
+ * svn repository (2014-10-14) and expected to be in any MPC
+ * release after 1.0.2 (which was the latest release already made
+ * at the time of the fix). So as and when we update to an MPC
+ * with the fix in it, we could remove this workaround.
+ *
+ * For the reasons for choosing this amount of extra precision,
+ * see analysis in complex/cpownotes.txt for the rationale for the
+ * amount.
+ */
+ mpc_t xbig, ybig, retbig;
+ int status;
+
+ mpc_init2(xbig, 1034 + 53 + 60 + MPFR_PREC);
+ mpc_init2(ybig, 1034 + 53 + 60 + MPFR_PREC);
+ mpc_init2(retbig, 1034 + 53 + 60 + MPFR_PREC);
+
+ mpc_set(xbig, x, MPC_RNDNN);
+ mpc_set(ybig, y, MPC_RNDNN);
+ status = mpc_pow(retbig, xbig, ybig, rnd);
+ mpc_set(ret, retbig, rnd);
+
+ mpc_clear(xbig);
+ mpc_clear(ybig);
+ mpc_clear(retbig);
+
+ return status;
+}
+
+/*
+ * Identify 'hard' values (NaN, Inf, nonzero denormal) for deciding
+ * whether microlib will decline to run a test.
+ */
+#define is_shard(in) ( \
+ (((in)[0] & 0x7F800000) == 0x7F800000 || \
+ (((in)[0] & 0x7F800000) == 0 && ((in)[0]&0x7FFFFFFF) != 0)))
+
+#define is_dhard(in) ( \
+ (((in)[0] & 0x7FF00000) == 0x7FF00000 || \
+ (((in)[0] & 0x7FF00000) == 0 && (((in)[0] & 0xFFFFF) | (in)[1]) != 0)))
+
+/*
+ * Identify integers.
+ */
+int is_dinteger(uint32 *in)
+{
+ uint32 out[3];
+ if ((0x7FF00000 & ~in[0]) == 0)
+ return 0; /* not finite, hence not integer */
+ test_ceil(in, out);
+ return in[0] == out[0] && in[1] == out[1];
+}
+int is_sinteger(uint32 *in)
+{
+ uint32 out[3];
+ if ((0x7F800000 & ~in[0]) == 0)
+ return 0; /* not finite, hence not integer */
+ test_ceilf(in, out);
+ return in[0] == out[0];
+}
+
+/*
+ * Identify signalling NaNs.
+ */
+int is_dsnan(const uint32 *in)
+{
+ if ((in[0] & 0x7FF00000) != 0x7FF00000)
+ return 0; /* not the inf/nan exponent */
+ if ((in[0] << 12) == 0 && in[1] == 0)
+ return 0; /* inf */
+ if (in[0] & 0x00080000)
+ return 0; /* qnan */
+ return 1;
+}
+int is_ssnan(const uint32 *in)
+{
+ if ((in[0] & 0x7F800000) != 0x7F800000)
+ return 0; /* not the inf/nan exponent */
+ if ((in[0] << 9) == 0)
+ return 0; /* inf */
+ if (in[0] & 0x00400000)
+ return 0; /* qnan */
+ return 1;
+}
+int is_snan(const uint32 *in, int size)
+{
+ return size == 2 ? is_dsnan(in) : is_ssnan(in);
+}
+
+/*
+ * Wrapper functions called to fix up unusual results after the main
+ * test function has run.
+ */
+void universal_wrapper(wrapperctx *ctx)
+{
+ /*
+ * Any SNaN input gives rise to a QNaN output.
+ */
+ int op;
+ for (op = 0; op < wrapper_get_nops(ctx); op++) {
+ int size = wrapper_get_size(ctx, op);
+
+ if (!wrapper_is_complex(ctx, op) &&
+ is_snan(wrapper_get_ieee(ctx, op), size)) {
+ wrapper_set_nan(ctx);
+ }
+ }
+}
+
+Testable functions[] = {
+ /*
+ * Trig functions: sin, cos, tan. We test the core function
+ * between -16 and +16: we assume that range reduction exists
+ * and will be used for larger arguments, and we'll test that
+ * separately. Also we only go down to 2^-27 in magnitude,
+ * because below that sin(x)=tan(x)=x and cos(x)=1 as far as
+ * double precision can tell, which is boring.
+ */
+ {"sin", (funcptr)mpfr_sin, args1, {NULL},
+ cases_uniform, 0x3e400000, 0x40300000},
+ {"sinf", (funcptr)mpfr_sin, args1f, {NULL},
+ cases_uniform_float, 0x39800000, 0x41800000},
+ {"cos", (funcptr)mpfr_cos, args1, {NULL},
+ cases_uniform, 0x3e400000, 0x40300000},
+ {"cosf", (funcptr)mpfr_cos, args1f, {NULL},
+ cases_uniform_float, 0x39800000, 0x41800000},
+ {"tan", (funcptr)mpfr_tan, args1, {NULL},
+ cases_uniform, 0x3e400000, 0x40300000},
+ {"tanf", (funcptr)mpfr_tan, args1f, {NULL},
+ cases_uniform_float, 0x39800000, 0x41800000},
+ {"sincosf_sinf", (funcptr)mpfr_sin, args1f, {NULL},
+ cases_uniform_float, 0x39800000, 0x41800000},
+ {"sincosf_cosf", (funcptr)mpfr_cos, args1f, {NULL},
+ cases_uniform_float, 0x39800000, 0x41800000},
+ /*
+ * Inverse trig: asin, acos. Between 1 and -1, of course. acos
+ * goes down to 2^-54, asin to 2^-27.
+ */
+ {"asin", (funcptr)mpfr_asin, args1, {NULL},
+ cases_uniform, 0x3e400000, 0x3fefffff},
+ {"asinf", (funcptr)mpfr_asin, args1f, {NULL},
+ cases_uniform_float, 0x39800000, 0x3f7fffff},
+ {"acos", (funcptr)mpfr_acos, args1, {NULL},
+ cases_uniform, 0x3c900000, 0x3fefffff},
+ {"acosf", (funcptr)mpfr_acos, args1f, {NULL},
+ cases_uniform_float, 0x33800000, 0x3f7fffff},
+ /*
+ * Inverse trig: atan. atan is stable (in double prec) with
+ * argument magnitude past 2^53, so we'll test up to there.
+ * atan(x) is boringly just x below 2^-27.
+ */
+ {"atan", (funcptr)mpfr_atan, args1, {NULL},
+ cases_uniform, 0x3e400000, 0x43400000},
+ {"atanf", (funcptr)mpfr_atan, args1f, {NULL},
+ cases_uniform_float, 0x39800000, 0x4b800000},
+ /*
+ * atan2. Interesting cases arise when the exponents of the
+ * arguments
diff er by at most about 50.
+ */
+ {"atan2", (funcptr)mpfr_atan2, args2, {NULL},
+ atan2_cases, 0},
+ {"atan2f", (funcptr)mpfr_atan2, args2f, {NULL},
+ atan2_cases_float, 0},
+ /*
+ * The exponentials: exp, sinh, cosh. They overflow at around
+ * 710. exp and sinh are boring below 2^-54, cosh below 2^-27.
+ */
+ {"exp", (funcptr)mpfr_exp, args1, {NULL},
+ cases_uniform, 0x3c900000, 0x40878000},
+ {"expf", (funcptr)mpfr_exp, args1f, {NULL},
+ cases_uniform_float, 0x33800000, 0x42dc0000},
+ {"sinh", (funcptr)mpfr_sinh, args1, {NULL},
+ cases_uniform, 0x3c900000, 0x40878000},
+ {"sinhf", (funcptr)mpfr_sinh, args1f, {NULL},
+ cases_uniform_float, 0x33800000, 0x42dc0000},
+ {"cosh", (funcptr)mpfr_cosh, args1, {NULL},
+ cases_uniform, 0x3e400000, 0x40878000},
+ {"coshf", (funcptr)mpfr_cosh, args1f, {NULL},
+ cases_uniform_float, 0x39800000, 0x42dc0000},
+ /*
+ * tanh is stable past around 20. It's boring below 2^-27.
+ */
+ {"tanh", (funcptr)mpfr_tanh, args1, {NULL},
+ cases_uniform, 0x3e400000, 0x40340000},
+ {"tanhf", (funcptr)mpfr_tanh, args1f, {NULL},
+ cases_uniform, 0x39800000, 0x41100000},
+ /*
+ * log must be tested only on positive numbers, but can cover
+ * the whole range of positive nonzero finite numbers. It never
+ * gets boring.
+ */
+ {"log", (funcptr)mpfr_log, args1, {NULL}, log_cases, 0},
+ {"logf", (funcptr)mpfr_log, args1f, {NULL}, log_cases_float, 0},
+ {"log10", (funcptr)mpfr_log10, args1, {NULL}, log_cases, 0},
+ {"log10f", (funcptr)mpfr_log10, args1f, {NULL}, log_cases_float, 0},
+ /*
+ * pow.
+ */
+ {"pow", (funcptr)mpfr_pow, args2, {NULL}, pow_cases, 0},
+ {"powf", (funcptr)mpfr_pow, args2f, {NULL}, pow_cases_float, 0},
+ /*
+ * Trig range reduction. We are able to test this for all
+ * finite values, but will only bother for things between 2^-3
+ * and 2^+52.
+ */
+ {"rred", (funcptr)test_rred, rred, {NULL}, rred_cases, 0},
+ {"rredf", (funcptr)test_rred, rredf, {NULL}, rred_cases_float, 0},
+ /*
+ * Square and cube root.
+ */
+ {"sqrt", (funcptr)mpfr_sqrt, args1, {NULL}, log_cases, 0},
+ {"sqrtf", (funcptr)mpfr_sqrt, args1f, {NULL}, log_cases_float, 0},
+ {"cbrt", (funcptr)mpfr_cbrt, args1, {NULL}, log_cases, 0},
+ {"cbrtf", (funcptr)mpfr_cbrt, args1f, {NULL}, log_cases_float, 0},
+ {"hypot", (funcptr)mpfr_hypot, args2, {NULL}, atan2_cases, 0},
+ {"hypotf", (funcptr)mpfr_hypot, args2f, {NULL}, atan2_cases_float, 0},
+ /*
+ * Seminumerical functions.
+ */
+ {"ceil", (funcptr)test_ceil, semi1, {NULL}, cases_semi1},
+ {"ceilf", (funcptr)test_ceilf, semi1f, {NULL}, cases_semi1_float},
+ {"floor", (funcptr)test_floor, semi1, {NULL}, cases_semi1},
+ {"floorf", (funcptr)test_floorf, semi1f, {NULL}, cases_semi1_float},
+ {"fmod", (funcptr)test_fmod, semi2, {NULL}, cases_semi2},
+ {"fmodf", (funcptr)test_fmodf, semi2f, {NULL}, cases_semi2_float},
+ {"ldexp", (funcptr)test_ldexp, t_ldexp, {NULL}, cases_ldexp},
+ {"ldexpf", (funcptr)test_ldexpf, t_ldexpf, {NULL}, cases_ldexp_float},
+ {"frexp", (funcptr)test_frexp, t_frexp, {NULL}, cases_semi1},
+ {"frexpf", (funcptr)test_frexpf, t_frexpf, {NULL}, cases_semi1_float},
+ {"modf", (funcptr)test_modf, t_modf, {NULL}, cases_semi1},
+ {"modff", (funcptr)test_modff, t_modff, {NULL}, cases_semi1_float},
+
+ /*
+ * Classification and more semi-numericals
+ */
+ {"copysign", (funcptr)test_copysign, semi2, {NULL}, cases_semi2},
+ {"copysignf", (funcptr)test_copysignf, semi2f, {NULL}, cases_semi2_float},
+ {"isfinite", (funcptr)test_isfinite, classify, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"isfinitef", (funcptr)test_isfinitef, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"isinf", (funcptr)test_isinf, classify, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"isinff", (funcptr)test_isinff, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"isnan", (funcptr)test_isnan, classify, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"isnanf", (funcptr)test_isnanf, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"isnormal", (funcptr)test_isnormal, classify, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"isnormalf", (funcptr)test_isnormalf, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"signbit", (funcptr)test_signbit, classify, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"signbitf", (funcptr)test_signbitf, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"fpclassify", (funcptr)test_fpclassify, classify, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"fpclassifyf", (funcptr)test_fpclassifyf, classifyf, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ /*
+ * Comparisons
+ */
+ {"isgreater", (funcptr)test_isgreater, compare, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"isgreaterequal", (funcptr)test_isgreaterequal, compare, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"isless", (funcptr)test_isless, compare, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"islessequal", (funcptr)test_islessequal, compare, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"islessgreater", (funcptr)test_islessgreater, compare, {NULL}, cases_uniform, 0, 0x7fffffff},
+ {"isunordered", (funcptr)test_isunordered, compare, {NULL}, cases_uniform, 0, 0x7fffffff},
+
+ {"isgreaterf", (funcptr)test_isgreaterf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"isgreaterequalf", (funcptr)test_isgreaterequalf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"islessf", (funcptr)test_islessf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"islessequalf", (funcptr)test_islessequalf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"islessgreaterf", (funcptr)test_islessgreaterf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+ {"isunorderedf", (funcptr)test_isunorderedf, comparef, {NULL}, cases_uniform_float, 0, 0x7fffffff},
+
+ /*
+ * Inverse Hyperbolic functions
+ */
+ {"atanh", (funcptr)mpfr_atanh, args1, {NULL}, cases_uniform, 0x3e400000, 0x3fefffff},
+ {"asinh", (funcptr)mpfr_asinh, args1, {NULL}, cases_uniform, 0x3e400000, 0x3fefffff},
+ {"acosh", (funcptr)mpfr_acosh, args1, {NULL}, cases_uniform_positive, 0x3ff00000, 0x7fefffff},
+
+ {"atanhf", (funcptr)mpfr_atanh, args1f, {NULL}, cases_uniform_float, 0x32000000, 0x3f7fffff},
+ {"asinhf", (funcptr)mpfr_asinh, args1f, {NULL}, cases_uniform_float, 0x32000000, 0x3f7fffff},
+ {"acoshf", (funcptr)mpfr_acosh, args1f, {NULL}, cases_uniform_float_positive, 0x3f800000, 0x7f800000},
+
+ /*
+ * Everything else (sitting in a section down here at the bottom
+ * because historically they were not tested because we didn't
+ * have reference implementations for them)
+ */
+ {"csin", (funcptr)mpc_sin, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"csinf", (funcptr)mpc_sin, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+ {"ccos", (funcptr)mpc_cos, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"ccosf", (funcptr)mpc_cos, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+ {"ctan", (funcptr)mpc_tan, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"ctanf", (funcptr)mpc_tan, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+
+ {"casin", (funcptr)mpc_asin, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"casinf", (funcptr)mpc_asin, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+ {"cacos", (funcptr)mpc_acos, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"cacosf", (funcptr)mpc_acos, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+ {"catan", (funcptr)mpc_atan, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"catanf", (funcptr)mpc_atan, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+
+ {"csinh", (funcptr)mpc_sinh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"csinhf", (funcptr)mpc_sinh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+ {"ccosh", (funcptr)mpc_cosh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"ccoshf", (funcptr)mpc_cosh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+ {"ctanh", (funcptr)mpc_tanh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"ctanhf", (funcptr)mpc_tanh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+
+ {"casinh", (funcptr)mpc_asinh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"casinhf", (funcptr)mpc_asinh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+ {"cacosh", (funcptr)mpc_acosh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"cacoshf", (funcptr)mpc_acosh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+ {"catanh", (funcptr)mpc_atanh, args1c, {NULL}, complex_cases_uniform, 0x3f000000, 0x40300000},
+ {"catanhf", (funcptr)mpc_atanh, args1fc, {NULL}, complex_cases_uniform_float, 0x38000000, 0x41800000},
+
+ {"cexp", (funcptr)mpc_exp, args1c, {NULL}, complex_cases_uniform, 0x3c900000, 0x40862000},
+ {"cpow", (funcptr)test_cpow, args2c, {NULL}, complex_pow_cases, 0x3fc00000, 0x40000000},
+ {"clog", (funcptr)mpc_log, args1c, {NULL}, complex_log_cases, 0, 0},
+ {"csqrt", (funcptr)mpc_sqrt, args1c, {NULL}, complex_log_cases, 0, 0},
+
+ {"cexpf", (funcptr)mpc_exp, args1fc, {NULL}, complex_cases_uniform_float, 0x24800000, 0x42b00000},
+ {"cpowf", (funcptr)test_cpow, args2fc, {NULL}, complex_pow_cases_float, 0x3e000000, 0x41000000},
+ {"clogf", (funcptr)mpc_log, args1fc, {NULL}, complex_log_cases_float, 0, 0},
+ {"csqrtf", (funcptr)mpc_sqrt, args1fc, {NULL}, complex_log_cases_float, 0, 0},
+
+ {"cdiv", (funcptr)mpc_div, args2c, {NULL}, complex_arithmetic_cases, 0, 0},
+ {"cmul", (funcptr)mpc_mul, args2c, {NULL}, complex_arithmetic_cases, 0, 0},
+ {"cadd", (funcptr)mpc_add, args2c, {NULL}, complex_arithmetic_cases, 0, 0},
+ {"csub", (funcptr)mpc_sub, args2c, {NULL}, complex_arithmetic_cases, 0, 0},
+
+ {"cdivf", (funcptr)mpc_div, args2fc, {NULL}, complex_arithmetic_cases_float, 0, 0},
+ {"cmulf", (funcptr)mpc_mul, args2fc, {NULL}, complex_arithmetic_cases_float, 0, 0},
+ {"caddf", (funcptr)mpc_add, args2fc, {NULL}, complex_arithmetic_cases_float, 0, 0},
+ {"csubf", (funcptr)mpc_sub, args2fc, {NULL}, complex_arithmetic_cases_float, 0, 0},
+
+ {"cabsf", (funcptr)mpc_abs, args1fcr, {NULL}, complex_arithmetic_cases_float, 0, 0},
+ {"cabs", (funcptr)mpc_abs, args1cr, {NULL}, complex_arithmetic_cases, 0, 0},
+ {"cargf", (funcptr)mpc_arg, args1fcr, {NULL}, complex_arithmetic_cases_float, 0, 0},
+ {"carg", (funcptr)mpc_arg, args1cr, {NULL}, complex_arithmetic_cases, 0, 0},
+ {"cimagf", (funcptr)mpc_imag, args1fcr, {NULL}, complex_arithmetic_cases_float, 0, 0},
+ {"cimag", (funcptr)mpc_imag, args1cr, {NULL}, complex_arithmetic_cases, 0, 0},
+ {"conjf", (funcptr)mpc_conj, args1fc, {NULL}, complex_arithmetic_cases_float, 0, 0},
+ {"conj", (funcptr)mpc_conj, args1c, {NULL}, complex_arithmetic_cases, 0, 0},
+ {"cprojf", (funcptr)mpc_proj, args1fc, {NULL}, complex_arithmetic_cases_float, 0, 0},
+ {"cproj", (funcptr)mpc_proj, args1c, {NULL}, complex_arithmetic_cases, 0, 0},
+ {"crealf", (funcptr)mpc_real, args1fcr, {NULL}, complex_arithmetic_cases_float, 0, 0},
+ {"creal", (funcptr)mpc_real, args1cr, {NULL}, complex_arithmetic_cases, 0, 0},
+ {"erfcf", (funcptr)mpfr_erfc, args1f, {NULL}, cases_biased_float, 0x1e800000, 0x41000000},
+ {"erfc", (funcptr)mpfr_erfc, args1, {NULL}, cases_biased, 0x3bd00000, 0x403c0000},
+ {"erff", (funcptr)mpfr_erf, args1f, {NULL}, cases_biased_float, 0x03800000, 0x40700000},
+ {"erf", (funcptr)mpfr_erf, args1, {NULL}, cases_biased, 0x00800000, 0x40200000},
+ {"exp2f", (funcptr)mpfr_exp2, args1f, {NULL}, cases_uniform_float, 0x33800000, 0x43c00000},
+ {"exp2", (funcptr)mpfr_exp2, args1, {NULL}, cases_uniform, 0x3ca00000, 0x40a00000},
+ {"expm1f", (funcptr)mpfr_expm1, args1f, {NULL}, cases_uniform_float, 0x33000000, 0x43800000},
+ {"expm1", (funcptr)mpfr_expm1, args1, {NULL}, cases_uniform, 0x3c900000, 0x409c0000},
+ {"fmaxf", (funcptr)mpfr_max, args2f, {NULL}, minmax_cases_float, 0, 0x7f7fffff},
+ {"fmax", (funcptr)mpfr_max, args2, {NULL}, minmax_cases, 0, 0x7fefffff},
+ {"fminf", (funcptr)mpfr_min, args2f, {NULL}, minmax_cases_float, 0, 0x7f7fffff},
+ {"fmin", (funcptr)mpfr_min, args2, {NULL}, minmax_cases, 0, 0x7fefffff},
+ {"lgammaf", (funcptr)test_lgamma, args1f, {NULL}, cases_uniform_float, 0x01800000, 0x7f800000},
+ {"lgamma", (funcptr)test_lgamma, args1, {NULL}, cases_uniform, 0x00100000, 0x7ff00000},
+ {"log1pf", (funcptr)mpfr_log1p, args1f, {NULL}, log1p_cases_float, 0, 0},
+ {"log1p", (funcptr)mpfr_log1p, args1, {NULL}, log1p_cases, 0, 0},
+ {"log2f", (funcptr)mpfr_log2, args1f, {NULL}, log_cases_float, 0, 0},
+ {"log2", (funcptr)mpfr_log2, args1, {NULL}, log_cases, 0, 0},
+ {"tgammaf", (funcptr)mpfr_gamma, args1f, {NULL}, cases_uniform_float, 0x2f800000, 0x43000000},
+ {"tgamma", (funcptr)mpfr_gamma, args1, {NULL}, cases_uniform, 0x3c000000, 0x40800000},
+};
+
+const int nfunctions = ( sizeof(functions)/sizeof(*functions) );
+
+#define random_sign ( random_upto(1) ? 0x80000000 : 0 )
+
+static int iszero(uint32 *x) {
+ return !((x[0] & 0x7FFFFFFF) || x[1]);
+}
+
+
+static void complex_log_cases(uint32 *out, uint32 param1,
+ uint32 param2) {
+ cases_uniform(out,0x00100000,0x7fefffff);
+ cases_uniform(out+2,0x00100000,0x7fefffff);
+}
+
+
+static void complex_log_cases_float(uint32 *out, uint32 param1,
+ uint32 param2) {
+ cases_uniform_float(out,0x00800000,0x7f7fffff);
+ cases_uniform_float(out+2,0x00800000,0x7f7fffff);
+}
+
+static void complex_cases_biased(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ cases_biased(out,lowbound,highbound);
+ cases_biased(out+2,lowbound,highbound);
+}
+
+static void complex_cases_biased_float(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ cases_biased_float(out,lowbound,highbound);
+ cases_biased_float(out+2,lowbound,highbound);
+}
+
+static void complex_cases_uniform(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ cases_uniform(out,lowbound,highbound);
+ cases_uniform(out+2,lowbound,highbound);
+}
+
+static void complex_cases_uniform_float(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ cases_uniform_float(out,lowbound,highbound);
+ cases_uniform(out+2,lowbound,highbound);
+}
+
+static void complex_pow_cases(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ /*
+ * Generating non-overflowing cases for complex pow:
+ *
+ * Our base has both parts within the range [1/2,2], and hence
+ * its magnitude is within [1/2,2*sqrt(2)]. The magnitude of its
+ * logarithm in base 2 is therefore at most the magnitude of
+ * (log2(2*sqrt(2)) + i*pi/log(2)), or in other words
+ * hypot(3/2,pi/log(2)) = 4.77. So the magnitude of the exponent
+ * input must be at most our output magnitude limit (as a power
+ * of two) divided by that.
+ *
+ * I also set the output magnitude limit a bit low, because we
+ * don't guarantee (and neither does glibc) to prevent internal
+ * overflow in cases where the output _magnitude_ overflows but
+ * scaling it back down by cos and sin of the argument brings it
+ * back in range.
+ */
+ cases_uniform(out,0x3fe00000, 0x40000000);
+ cases_uniform(out+2,0x3fe00000, 0x40000000);
+ cases_uniform(out+4,0x3f800000, 0x40600000);
+ cases_uniform(out+6,0x3f800000, 0x40600000);
+}
+
+static void complex_pow_cases_float(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ /*
+ * Reasoning as above, though of course the detailed numbers are
+ * all
diff erent.
+ */
+ cases_uniform_float(out,0x3f000000, 0x40000000);
+ cases_uniform_float(out+2,0x3f000000, 0x40000000);
+ cases_uniform_float(out+4,0x3d600000, 0x41900000);
+ cases_uniform_float(out+6,0x3d600000, 0x41900000);
+}
+
+static void complex_arithmetic_cases(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ cases_uniform(out,0,0x7fefffff);
+ cases_uniform(out+2,0,0x7fefffff);
+ cases_uniform(out+4,0,0x7fefffff);
+ cases_uniform(out+6,0,0x7fefffff);
+}
+
+static void complex_arithmetic_cases_float(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ cases_uniform_float(out,0,0x7f7fffff);
+ cases_uniform_float(out+2,0,0x7f7fffff);
+ cases_uniform_float(out+4,0,0x7f7fffff);
+ cases_uniform_float(out+6,0,0x7f7fffff);
+}
+
+/*
+ * Included from fplib test suite, in a compact self-contained
+ * form.
+ */
+
+void float32_case(uint32 *ret) {
+ int n, bits;
+ uint32 f;
+ static int premax, preptr;
+ static uint32 *specifics = NULL;
+
+ if (!ret) {
+ if (specifics)
+ free(specifics);
+ specifics = NULL;
+ premax = preptr = 0;
+ return;
+ }
+
+ if (!specifics) {
+ int exps[] = {
+ -127, -126, -125, -24, -4, -3, -2, -1, 0, 1, 2, 3, 4,
+ 24, 29, 30, 31, 32, 61, 62, 63, 64, 126, 127, 128
+ };
+ int sign, eptr;
+ uint32 se, j;
+ /*
+ * We want a cross product of:
+ * - each of two sign bits (2)
+ * - each of the above (unbiased) exponents (25)
+ * - the following list of fraction parts:
+ * * zero (1)
+ * * all bits (1)
+ * * one-bit-set (23)
+ * * one-bit-clear (23)
+ * * one-bit-and-above (20: 3 are duplicates)
+ * * one-bit-and-below (20: 3 are duplicates)
+ * (total 88)
+ * (total 4400)
+ */
+ specifics = malloc(4400 * sizeof(*specifics));
+ preptr = 0;
+ for (sign = 0; sign <= 1; sign++) {
+ for (eptr = 0; eptr < sizeof(exps)/sizeof(*exps); eptr++) {
+ se = (sign ? 0x80000000 : 0) | ((exps[eptr]+127) << 23);
+ /*
+ * Zero.
+ */
+ specifics[preptr++] = se | 0;
+ /*
+ * All bits.
+ */
+ specifics[preptr++] = se | 0x7FFFFF;
+ /*
+ * One-bit-set.
+ */
+ for (j = 1; j && j <= 0x400000; j <<= 1)
+ specifics[preptr++] = se | j;
+ /*
+ * One-bit-clear.
+ */
+ for (j = 1; j && j <= 0x400000; j <<= 1)
+ specifics[preptr++] = se | (0x7FFFFF ^ j);
+ /*
+ * One-bit-and-everything-below.
+ */
+ for (j = 2; j && j <= 0x100000; j <<= 1)
+ specifics[preptr++] = se | (2*j-1);
+ /*
+ * One-bit-and-everything-above.
+ */
+ for (j = 4; j && j <= 0x200000; j <<= 1)
+ specifics[preptr++] = se | (0x7FFFFF ^ (j-1));
+ /*
+ * Done.
+ */
+ }
+ }
+ assert(preptr == 4400);
+ premax = preptr;
+ }
+
+ /*
+ * Decide whether to return a pre or a random case.
+ */
+ n = random32() % (premax+1);
+ if (n < preptr) {
+ /*
+ * Return pre[n].
+ */
+ uint32 t;
+ t = specifics[n];
+ specifics[n] = specifics[preptr-1];
+ specifics[preptr-1] = t; /* (not really needed) */
+ preptr--;
+ *ret = t;
+ } else {
+ /*
+ * Random case.
+ * Sign and exponent:
+ * - FIXME
+ * Significand:
+ * - with prob 1/5, a totally random bit pattern
+ * - with prob 1/5, all 1s down to some point and then random
+ * - with prob 1/5, all 1s up to some point and then random
+ * - with prob 1/5, all 0s down to some point and then random
+ * - with prob 1/5, all 0s up to some point and then random
+ */
+ n = random32() % 5;
+ f = random32(); /* some random bits */
+ bits = random32() % 22 + 1; /* 1-22 */
+ switch (n) {
+ case 0:
+ break; /* leave f alone */
+ case 1:
+ f |= (1<<bits)-1;
+ break;
+ case 2:
+ f &= ~((1<<bits)-1);
+ break;
+ case 3:
+ f |= ~((1<<bits)-1);
+ break;
+ case 4:
+ f &= (1<<bits)-1;
+ break;
+ }
+ f &= 0x7FFFFF;
+ f |= (random32() & 0xFF800000);/* FIXME - do better */
+ *ret = f;
+ }
+}
+static void float64_case(uint32 *ret) {
+ int n, bits;
+ uint32 f, g;
+ static int premax, preptr;
+ static uint32 (*specifics)[2] = NULL;
+
+ if (!ret) {
+ if (specifics)
+ free(specifics);
+ specifics = NULL;
+ premax = preptr = 0;
+ return;
+ }
+
+ if (!specifics) {
+ int exps[] = {
+ -1023, -1022, -1021, -129, -128, -127, -126, -53, -4, -3, -2,
+ -1, 0, 1, 2, 3, 4, 29, 30, 31, 32, 53, 61, 62, 63, 64, 127,
+ 128, 129, 1022, 1023, 1024
+ };
+ int sign, eptr;
+ uint32 se, j;
+ /*
+ * We want a cross product of:
+ * - each of two sign bits (2)
+ * - each of the above (unbiased) exponents (32)
+ * - the following list of fraction parts:
+ * * zero (1)
+ * * all bits (1)
+ * * one-bit-set (52)
+ * * one-bit-clear (52)
+ * * one-bit-and-above (49: 3 are duplicates)
+ * * one-bit-and-below (49: 3 are duplicates)
+ * (total 204)
+ * (total 13056)
+ */
+ specifics = malloc(13056 * sizeof(*specifics));
+ preptr = 0;
+ for (sign = 0; sign <= 1; sign++) {
+ for (eptr = 0; eptr < sizeof(exps)/sizeof(*exps); eptr++) {
+ se = (sign ? 0x80000000 : 0) | ((exps[eptr]+1023) << 20);
+ /*
+ * Zero.
+ */
+ specifics[preptr][0] = 0;
+ specifics[preptr][1] = 0;
+ specifics[preptr++][0] |= se;
+ /*
+ * All bits.
+ */
+ specifics[preptr][0] = 0xFFFFF;
+ specifics[preptr][1] = ~0;
+ specifics[preptr++][0] |= se;
+ /*
+ * One-bit-set.
+ */
+ for (j = 1; j && j <= 0x80000000; j <<= 1) {
+ specifics[preptr][0] = 0;
+ specifics[preptr][1] = j;
+ specifics[preptr++][0] |= se;
+ if (j & 0xFFFFF) {
+ specifics[preptr][0] = j;
+ specifics[preptr][1] = 0;
+ specifics[preptr++][0] |= se;
+ }
+ }
+ /*
+ * One-bit-clear.
+ */
+ for (j = 1; j && j <= 0x80000000; j <<= 1) {
+ specifics[preptr][0] = 0xFFFFF;
+ specifics[preptr][1] = ~j;
+ specifics[preptr++][0] |= se;
+ if (j & 0xFFFFF) {
+ specifics[preptr][0] = 0xFFFFF ^ j;
+ specifics[preptr][1] = ~0;
+ specifics[preptr++][0] |= se;
+ }
+ }
+ /*
+ * One-bit-and-everything-below.
+ */
+ for (j = 2; j && j <= 0x80000000; j <<= 1) {
+ specifics[preptr][0] = 0;
+ specifics[preptr][1] = 2*j-1;
+ specifics[preptr++][0] |= se;
+ }
+ for (j = 1; j && j <= 0x20000; j <<= 1) {
+ specifics[preptr][0] = 2*j-1;
+ specifics[preptr][1] = ~0;
+ specifics[preptr++][0] |= se;
+ }
+ /*
+ * One-bit-and-everything-above.
+ */
+ for (j = 4; j && j <= 0x80000000; j <<= 1) {
+ specifics[preptr][0] = 0xFFFFF;
+ specifics[preptr][1] = ~(j-1);
+ specifics[preptr++][0] |= se;
+ }
+ for (j = 1; j && j <= 0x40000; j <<= 1) {
+ specifics[preptr][0] = 0xFFFFF ^ (j-1);
+ specifics[preptr][1] = 0;
+ specifics[preptr++][0] |= se;
+ }
+ /*
+ * Done.
+ */
+ }
+ }
+ assert(preptr == 13056);
+ premax = preptr;
+ }
+
+ /*
+ * Decide whether to return a pre or a random case.
+ */
+ n = (uint32) random32() % (uint32) (premax+1);
+ if (n < preptr) {
+ /*
+ * Return pre[n].
+ */
+ uint32 t;
+ t = specifics[n][0];
+ specifics[n][0] = specifics[preptr-1][0];
+ specifics[preptr-1][0] = t; /* (not really needed) */
+ ret[0] = t;
+ t = specifics[n][1];
+ specifics[n][1] = specifics[preptr-1][1];
+ specifics[preptr-1][1] = t; /* (not really needed) */
+ ret[1] = t;
+ preptr--;
+ } else {
+ /*
+ * Random case.
+ * Sign and exponent:
+ * - FIXME
+ * Significand:
+ * - with prob 1/5, a totally random bit pattern
+ * - with prob 1/5, all 1s down to some point and then random
+ * - with prob 1/5, all 1s up to some point and then random
+ * - with prob 1/5, all 0s down to some point and then random
+ * - with prob 1/5, all 0s up to some point and then random
+ */
+ n = random32() % 5;
+ f = random32(); /* some random bits */
+ g = random32(); /* some random bits */
+ bits = random32() % 51 + 1; /* 1-51 */
+ switch (n) {
+ case 0:
+ break; /* leave f alone */
+ case 1:
+ if (bits <= 32)
+ f |= (1<<bits)-1;
+ else {
+ bits -= 32;
+ g |= (1<<bits)-1;
+ f = ~0;
+ }
+ break;
+ case 2:
+ if (bits <= 32)
+ f &= ~((1<<bits)-1);
+ else {
+ bits -= 32;
+ g &= ~((1<<bits)-1);
+ f = 0;
+ }
+ break;
+ case 3:
+ if (bits <= 32)
+ g &= (1<<bits)-1;
+ else {
+ bits -= 32;
+ f &= (1<<bits)-1;
+ g = 0;
+ }
+ break;
+ case 4:
+ if (bits <= 32)
+ g |= ~((1<<bits)-1);
+ else {
+ bits -= 32;
+ f |= ~((1<<bits)-1);
+ g = ~0;
+ }
+ break;
+ }
+ g &= 0xFFFFF;
+ g |= (random32() & 0xFFF00000);/* FIXME - do better */
+ ret[0] = g;
+ ret[1] = f;
+ }
+}
+
+static void cases_biased(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ do {
+ out[0] = highbound - random_upto_biased(highbound-lowbound, 8);
+ out[1] = random_upto(0xFFFFFFFF);
+ out[0] |= random_sign;
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void cases_biased_positive(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ do {
+ out[0] = highbound - random_upto_biased(highbound-lowbound, 8);
+ out[1] = random_upto(0xFFFFFFFF);
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void cases_biased_float(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ do {
+ out[0] = highbound - random_upto_biased(highbound-lowbound, 8);
+ out[1] = 0;
+ out[0] |= random_sign;
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void cases_semi1(uint32 *out, uint32 param1,
+ uint32 param2) {
+ float64_case(out);
+}
+
+static void cases_semi1_float(uint32 *out, uint32 param1,
+ uint32 param2) {
+ float32_case(out);
+}
+
+static void cases_semi2(uint32 *out, uint32 param1,
+ uint32 param2) {
+ float64_case(out);
+ float64_case(out+2);
+}
+
+static void cases_semi2_float(uint32 *out, uint32 param1,
+ uint32 param2) {
+ float32_case(out);
+ float32_case(out+2);
+}
+
+static void cases_ldexp(uint32 *out, uint32 param1,
+ uint32 param2) {
+ float64_case(out);
+ out[2] = random_upto(2048)-1024;
+}
+
+static void cases_ldexp_float(uint32 *out, uint32 param1,
+ uint32 param2) {
+ float32_case(out);
+ out[2] = random_upto(256)-128;
+}
+
+static void cases_uniform(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ do {
+ out[0] = highbound - random_upto(highbound-lowbound);
+ out[1] = random_upto(0xFFFFFFFF);
+ out[0] |= random_sign;
+ } while (iszero(out)); /* rule out zero */
+}
+static void cases_uniform_float(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ do {
+ out[0] = highbound - random_upto(highbound-lowbound);
+ out[1] = 0;
+ out[0] |= random_sign;
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void cases_uniform_positive(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ do {
+ out[0] = highbound - random_upto(highbound-lowbound);
+ out[1] = random_upto(0xFFFFFFFF);
+ } while (iszero(out)); /* rule out zero */
+}
+static void cases_uniform_float_positive(uint32 *out, uint32 lowbound,
+ uint32 highbound) {
+ do {
+ out[0] = highbound - random_upto(highbound-lowbound);
+ out[1] = 0;
+ } while (iszero(out)); /* rule out zero */
+}
+
+
+static void log_cases(uint32 *out, uint32 param1,
+ uint32 param2) {
+ do {
+ out[0] = random_upto(0x7FEFFFFF);
+ out[1] = random_upto(0xFFFFFFFF);
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void log_cases_float(uint32 *out, uint32 param1,
+ uint32 param2) {
+ do {
+ out[0] = random_upto(0x7F7FFFFF);
+ out[1] = 0;
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void log1p_cases(uint32 *out, uint32 param1, uint32 param2)
+{
+ uint32 sign = random_sign;
+ if (sign == 0) {
+ cases_uniform_positive(out, 0x3c700000, 0x43400000);
+ } else {
+ cases_uniform_positive(out, 0x3c000000, 0x3ff00000);
+ }
+ out[0] |= sign;
+}
+
+static void log1p_cases_float(uint32 *out, uint32 param1, uint32 param2)
+{
+ uint32 sign = random_sign;
+ if (sign == 0) {
+ cases_uniform_float_positive(out, 0x32000000, 0x4c000000);
+ } else {
+ cases_uniform_float_positive(out, 0x30000000, 0x3f800000);
+ }
+ out[0] |= sign;
+}
+
+static void minmax_cases(uint32 *out, uint32 param1, uint32 param2)
+{
+ do {
+ out[0] = random_upto(0x7FEFFFFF);
+ out[1] = random_upto(0xFFFFFFFF);
+ out[0] |= random_sign;
+ out[2] = random_upto(0x7FEFFFFF);
+ out[3] = random_upto(0xFFFFFFFF);
+ out[2] |= random_sign;
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void minmax_cases_float(uint32 *out, uint32 param1, uint32 param2)
+{
+ do {
+ out[0] = random_upto(0x7F7FFFFF);
+ out[1] = 0;
+ out[0] |= random_sign;
+ out[2] = random_upto(0x7F7FFFFF);
+ out[3] = 0;
+ out[2] |= random_sign;
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void rred_cases(uint32 *out, uint32 param1,
+ uint32 param2) {
+ do {
+ out[0] = ((0x3fc00000 + random_upto(0x036fffff)) |
+ (random_upto(1) << 31));
+ out[1] = random_upto(0xFFFFFFFF);
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void rred_cases_float(uint32 *out, uint32 param1,
+ uint32 param2) {
+ do {
+ out[0] = ((0x3e000000 + random_upto(0x0cffffff)) |
+ (random_upto(1) << 31));
+ out[1] = 0; /* for iszero */
+ } while (iszero(out)); /* rule out zero */
+}
+
+static void atan2_cases(uint32 *out, uint32 param1,
+ uint32 param2) {
+ do {
+ int exp
diff = random_upto(101)-51;
+ int swap;
+ if (exp
diff < 0) {
+ exp
diff = -exp
diff ;
+ swap = 2;
+ } else
+ swap = 0;
+ out[swap ^ 0] = random_upto(0x7FEFFFFF-((exp
diff +1)<<20));
+ out[swap ^ 2] = random_upto(((exp
diff +1)<<20)-1) + out[swap ^ 0];
+ out[1] = random_upto(0xFFFFFFFF);
+ out[3] = random_upto(0xFFFFFFFF);
+ out[0] |= random_sign;
+ out[2] |= random_sign;
+ } while (iszero(out) || iszero(out+2));/* rule out zero */
+}
+
+static void atan2_cases_float(uint32 *out, uint32 param1,
+ uint32 param2) {
+ do {
+ int exp
diff = random_upto(44)-22;
+ int swap;
+ if (exp
diff < 0) {
+ exp
diff = -exp
diff ;
+ swap = 2;
+ } else
+ swap = 0;
+ out[swap ^ 0] = random_upto(0x7F7FFFFF-((exp
diff +1)<<23));
+ out[swap ^ 2] = random_upto(((exp
diff +1)<<23)-1) + out[swap ^ 0];
+ out[0] |= random_sign;
+ out[2] |= random_sign;
+ out[1] = out[3] = 0; /* for iszero */
+ } while (iszero(out) || iszero(out+2));/* rule out zero */
+}
+
+static void pow_cases(uint32 *out, uint32 param1,
+ uint32 param2) {
+ /*
+ * Pick an exponent e (-0x33 to +0x7FE) for x, and here's the
+ * range of numbers we can use as y:
+ *
+ * For e < 0x3FE, the range is [-0x400/(0x3FE-e),+0x432/(0x3FE-e)]
+ * For e > 0x3FF, the range is [-0x432/(e-0x3FF),+0x400/(e-0x3FF)]
+ *
+ * For e == 0x3FE or e == 0x3FF, the range gets infinite at one
+ * end or the other, so we have to be cleverer: pick a number n
+ * of useful bits in the mantissa (1 thru 52, so 1 must imply
+ * 0x3ff00000.00000001 whereas 52 is anything at least as big
+ * as 0x3ff80000.00000000; for e == 0x3fe, 1 necessarily means
+ * 0x3fefffff.ffffffff and 52 is anything at most as big as
+ * 0x3fe80000.00000000). Then, as it happens, a sensible
+ * maximum power is 2^(63-n) for e == 0x3fe, and 2^(62-n) for
+ * e == 0x3ff.
+ *
+ * We inevitably get some overflows in approximating the log
+ * curves by these nasty step functions, but that's all right -
+ * we do want _some_ overflows to be tested.
+ *
+ * Having got that, then, it's just a matter of inventing a
+ * probability distribution for all of this.
+ */
+ int e, n;
+ uint32 dmin, dmax;
+ const uint32 pmin = 0x3e100000;
+
+ /*
+ * Generate exponents in a slightly biased fashion.
+ */
+ e = (random_upto(1) ? /* is exponent small or big? */
+ 0x3FE - random_upto_biased(0x431,2) : /* small */
+ 0x3FF + random_upto_biased(0x3FF,2)); /* big */
+
+ /*
+ * Now split into cases.
+ */
+ if (e < 0x3FE || e > 0x3FF) {
+ uint32 imin, imax;
+ if (e < 0x3FE)
+ imin = 0x40000 / (0x3FE - e), imax = 0x43200 / (0x3FE - e);
+ else
+ imin = 0x43200 / (e - 0x3FF), imax = 0x40000 / (e - 0x3FF);
+ /* Power range runs from -imin to imax. Now convert to doubles */
+ dmin = doubletop(imin, -8);
+ dmax = doubletop(imax, -8);
+ /* Compute the number of mantissa bits. */
+ n = (e > 0 ? 53 : 52+e);
+ } else {
+ /* Critical exponents. Generate a top bit index. */
+ n = 52 - random_upto_biased(51, 4);
+ if (e == 0x3FE)
+ dmax = 63 - n;
+ else
+ dmax = 62 - n;
+ dmax = (dmax << 20) + 0x3FF00000;
+ dmin = dmax;
+ }
+ /* Generate a mantissa. */
+ if (n <= 32) {
+ out[0] = 0;
+ out[1] = random_upto((1 << (n-1)) - 1) + (1 << (n-1));
+ } else if (n == 33) {
+ out[0] = 1;
+ out[1] = random_upto(0xFFFFFFFF);
+ } else if (n > 33) {
+ out[0] = random_upto((1 << (n-33)) - 1) + (1 << (n-33));
+ out[1] = random_upto(0xFFFFFFFF);
+ }
+ /* Negate the mantissa if e == 0x3FE. */
+ if (e == 0x3FE) {
+ out[1] = -out[1];
+ out[0] = -out[0];
+ if (out[1]) out[0]--;
+ }
+ /* Put the exponent on. */
+ out[0] &= 0xFFFFF;
+ out[0] |= ((e > 0 ? e : 0) << 20);
+ /* Generate a power. Powers don't go below 2^-30. */
+ if (random_upto(1)) {
+ /* Positive power */
+ out[2] = dmax - random_upto_biased(dmax-pmin, 10);
+ } else {
+ /* Negative power */
+ out[2] = (dmin - random_upto_biased(dmin-pmin, 10)) | 0x80000000;
+ }
+ out[3] = random_upto(0xFFFFFFFF);
+}
+static void pow_cases_float(uint32 *out, uint32 param1,
+ uint32 param2) {
+ /*
+ * Pick an exponent e (-0x16 to +0xFE) for x, and here's the
+ * range of numbers we can use as y:
+ *
+ * For e < 0x7E, the range is [-0x80/(0x7E-e),+0x95/(0x7E-e)]
+ * For e > 0x7F, the range is [-0x95/(e-0x7F),+0x80/(e-0x7F)]
+ *
+ * For e == 0x7E or e == 0x7F, the range gets infinite at one
+ * end or the other, so we have to be cleverer: pick a number n
+ * of useful bits in the mantissa (1 thru 23, so 1 must imply
+ * 0x3f800001 whereas 23 is anything at least as big as
+ * 0x3fc00000; for e == 0x7e, 1 necessarily means 0x3f7fffff
+ * and 23 is anything at most as big as 0x3f400000). Then, as
+ * it happens, a sensible maximum power is 2^(31-n) for e ==
+ * 0x7e, and 2^(30-n) for e == 0x7f.
+ *
+ * We inevitably get some overflows in approximating the log
+ * curves by these nasty step functions, but that's all right -
+ * we do want _some_ overflows to be tested.
+ *
+ * Having got that, then, it's just a matter of inventing a
+ * probability distribution for all of this.
+ */
+ int e, n;
+ uint32 dmin, dmax;
+ const uint32 pmin = 0x38000000;
+
+ /*
+ * Generate exponents in a slightly biased fashion.
+ */
+ e = (random_upto(1) ? /* is exponent small or big? */
+ 0x7E - random_upto_biased(0x94,2) : /* small */
+ 0x7F + random_upto_biased(0x7f,2)); /* big */
+
+ /*
+ * Now split into cases.
+ */
+ if (e < 0x7E || e > 0x7F) {
+ uint32 imin, imax;
+ if (e < 0x7E)
+ imin = 0x8000 / (0x7e - e), imax = 0x9500 / (0x7e - e);
+ else
+ imin = 0x9500 / (e - 0x7f), imax = 0x8000 / (e - 0x7f);
+ /* Power range runs from -imin to imax. Now convert to doubles */
+ dmin = floatval(imin, -8);
+ dmax = floatval(imax, -8);
+ /* Compute the number of mantissa bits. */
+ n = (e > 0 ? 24 : 23+e);
+ } else {
+ /* Critical exponents. Generate a top bit index. */
+ n = 23 - random_upto_biased(22, 4);
+ if (e == 0x7E)
+ dmax = 31 - n;
+ else
+ dmax = 30 - n;
+ dmax = (dmax << 23) + 0x3F800000;
+ dmin = dmax;
+ }
+ /* Generate a mantissa. */
+ out[0] = random_upto((1 << (n-1)) - 1) + (1 << (n-1));
+ out[1] = 0;
+ /* Negate the mantissa if e == 0x7E. */
+ if (e == 0x7E) {
+ out[0] = -out[0];
+ }
+ /* Put the exponent on. */
+ out[0] &= 0x7FFFFF;
+ out[0] |= ((e > 0 ? e : 0) << 23);
+ /* Generate a power. Powers don't go below 2^-15. */
+ if (random_upto(1)) {
+ /* Positive power */
+ out[2] = dmax - random_upto_biased(dmax-pmin, 10);
+ } else {
+ /* Negative power */
+ out[2] = (dmin - random_upto_biased(dmin-pmin, 10)) | 0x80000000;
+ }
+ out[3] = 0;
+}
+
+void vet_for_decline(Testable *fn, uint32 *args, uint32 *result, int got_errno_in) {
+ int declined = 0;
+
+ switch (fn->type) {
+ case args1:
+ case rred:
+ case semi1:
+ case t_frexp:
+ case t_modf:
+ case classify:
+ case t_ldexp:
+ declined |= lib_fo && is_dhard(args+0);
+ break;
+ case args1f:
+ case rredf:
+ case semi1f:
+ case t_frexpf:
+ case t_modff:
+ case classifyf:
+ declined |= lib_fo && is_shard(args+0);
+ break;
+ case args2:
+ case semi2:
+ case args1c:
+ case args1cr:
+ case compare:
+ declined |= lib_fo && is_dhard(args+0);
+ declined |= lib_fo && is_dhard(args+2);
+ break;
+ case args2f:
+ case semi2f:
+ case t_ldexpf:
+ case comparef:
+ case args1fc:
+ case args1fcr:
+ declined |= lib_fo && is_shard(args+0);
+ declined |= lib_fo && is_shard(args+2);
+ break;
+ case args2c:
+ declined |= lib_fo && is_dhard(args+0);
+ declined |= lib_fo && is_dhard(args+2);
+ declined |= lib_fo && is_dhard(args+4);
+ declined |= lib_fo && is_dhard(args+6);
+ break;
+ case args2fc:
+ declined |= lib_fo && is_shard(args+0);
+ declined |= lib_fo && is_shard(args+2);
+ declined |= lib_fo && is_shard(args+4);
+ declined |= lib_fo && is_shard(args+6);
+ break;
+ }
+
+ switch (fn->type) {
+ case args1: /* return an extra-precise result */
+ case args2:
+ case rred:
+ case semi1: /* return a double result */
+ case semi2:
+ case t_ldexp:
+ case t_frexp: /* return double * int */
+ case args1cr:
+ declined |= lib_fo && is_dhard(result);
+ break;
+ case args1f:
+ case args2f:
+ case rredf:
+ case semi1f:
+ case semi2f:
+ case t_ldexpf:
+ case args1fcr:
+ declined |= lib_fo && is_shard(result);
+ break;
+ case t_modf: /* return double * double */
+ declined |= lib_fo && is_dhard(result+0);
+ declined |= lib_fo && is_dhard(result+2);
+ break;
+ case t_modff: /* return float * float */
+ declined |= lib_fo && is_shard(result+2);
+ /* fall through */
+ case t_frexpf: /* return float * int */
+ declined |= lib_fo && is_shard(result+0);
+ break;
+ case args1c:
+ case args2c:
+ declined |= lib_fo && is_dhard(result+0);
+ declined |= lib_fo && is_dhard(result+4);
+ break;
+ case args1fc:
+ case args2fc:
+ declined |= lib_fo && is_shard(result+0);
+ declined |= lib_fo && is_shard(result+4);
+ break;
+ }
+
+ /* Expect basic arithmetic tests to be declined if the command
+ * line said that would happen */
+ declined |= (lib_no_arith && (fn->func == (funcptr)mpc_add ||
+ fn->func == (funcptr)mpc_sub ||
+ fn->func == (funcptr)mpc_mul ||
+ fn->func == (funcptr)mpc_div));
+
+ if (!declined) {
+ if (got_errno_in)
+ ntests++;
+ else
+ ntests += 3;
+ }
+}
+
+void docase(Testable *fn, uint32 *args) {
+ uint32 result[8]; /* real part in first 4, imaginary part in last 4 */
+ char *errstr = NULL;
+ mpfr_t a, b, r;
+ mpc_t ac, bc, rc;
+ int rejected, printextra;
+ wrapperctx ctx;
+
+ mpfr_init2(a, MPFR_PREC);
+ mpfr_init2(b, MPFR_PREC);
+ mpfr_init2(r, MPFR_PREC);
+ mpc_init2(ac, MPFR_PREC);
+ mpc_init2(bc, MPFR_PREC);
+ mpc_init2(rc, MPFR_PREC);
+
+ printf("func=%s", fn->name);
+
+ rejected = 0; /* FIXME */
+
+ switch (fn->type) {
+ case args1:
+ case rred:
+ case semi1:
+ case t_frexp:
+ case t_modf:
+ case classify:
+ printf(" op1=%08x.%08x", args[0], args[1]);
+ break;
+ case args1f:
+ case rredf:
+ case semi1f:
+ case t_frexpf:
+ case t_modff:
+ case classifyf:
+ printf(" op1=%08x", args[0]);
+ break;
+ case args2:
+ case semi2:
+ case compare:
+ printf(" op1=%08x.%08x", args[0], args[1]);
+ printf(" op2=%08x.%08x", args[2], args[3]);
+ break;
+ case args2f:
+ case semi2f:
+ case t_ldexpf:
+ case comparef:
+ printf(" op1=%08x", args[0]);
+ printf(" op2=%08x", args[2]);
+ break;
+ case t_ldexp:
+ printf(" op1=%08x.%08x", args[0], args[1]);
+ printf(" op2=%08x", args[2]);
+ break;
+ case args1c:
+ case args1cr:
+ printf(" op1r=%08x.%08x", args[0], args[1]);
+ printf(" op1i=%08x.%08x", args[2], args[3]);
+ break;
+ case args2c:
+ printf(" op1r=%08x.%08x", args[0], args[1]);
+ printf(" op1i=%08x.%08x", args[2], args[3]);
+ printf(" op2r=%08x.%08x", args[4], args[5]);
+ printf(" op2i=%08x.%08x", args[6], args[7]);
+ break;
+ case args1fc:
+ case args1fcr:
+ printf(" op1r=%08x", args[0]);
+ printf(" op1i=%08x", args[2]);
+ break;
+ case args2fc:
+ printf(" op1r=%08x", args[0]);
+ printf(" op1i=%08x", args[2]);
+ printf(" op2r=%08x", args[4]);
+ printf(" op2i=%08x", args[6]);
+ break;
+ default:
+ fprintf(stderr, "internal inconsistency?!\n");
+ abort();
+ }
+
+ if (rejected == 2) {
+ printf(" - test case rejected\n");
+ goto cleanup;
+ }
+
+ wrapper_init(&ctx);
+
+ if (rejected == 0) {
+ switch (fn->type) {
+ case args1:
+ set_mpfr_d(a, args[0], args[1]);
+ wrapper_op_real(&ctx, a, 2, args);
+ ((testfunc1)(fn->func))(r, a, GMP_RNDN);
+ get_mpfr_d(r, &result[0], &result[1], &result[2]);
+ wrapper_result_real(&ctx, r, 2, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpfr_d(r, &result[0], &result[1], &result[2]);
+ break;
+ case args1cr:
+ set_mpc_d(ac, args[0], args[1], args[2], args[3]);
+ wrapper_op_complex(&ctx, ac, 2, args);
+ ((testfunc1cr)(fn->func))(r, ac, GMP_RNDN);
+ get_mpfr_d(r, &result[0], &result[1], &result[2]);
+ wrapper_result_real(&ctx, r, 2, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpfr_d(r, &result[0], &result[1], &result[2]);
+ break;
+ case args1f:
+ set_mpfr_f(a, args[0]);
+ wrapper_op_real(&ctx, a, 1, args);
+ ((testfunc1)(fn->func))(r, a, GMP_RNDN);
+ get_mpfr_f(r, &result[0], &result[1]);
+ wrapper_result_real(&ctx, r, 1, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpfr_f(r, &result[0], &result[1]);
+ break;
+ case args1fcr:
+ set_mpc_f(ac, args[0], args[2]);
+ wrapper_op_complex(&ctx, ac, 1, args);
+ ((testfunc1cr)(fn->func))(r, ac, GMP_RNDN);
+ get_mpfr_f(r, &result[0], &result[1]);
+ wrapper_result_real(&ctx, r, 1, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpfr_f(r, &result[0], &result[1]);
+ break;
+ case args2:
+ set_mpfr_d(a, args[0], args[1]);
+ wrapper_op_real(&ctx, a, 2, args);
+ set_mpfr_d(b, args[2], args[3]);
+ wrapper_op_real(&ctx, b, 2, args+2);
+ ((testfunc2)(fn->func))(r, a, b, GMP_RNDN);
+ get_mpfr_d(r, &result[0], &result[1], &result[2]);
+ wrapper_result_real(&ctx, r, 2, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpfr_d(r, &result[0], &result[1], &result[2]);
+ break;
+ case args2f:
+ set_mpfr_f(a, args[0]);
+ wrapper_op_real(&ctx, a, 1, args);
+ set_mpfr_f(b, args[2]);
+ wrapper_op_real(&ctx, b, 1, args+2);
+ ((testfunc2)(fn->func))(r, a, b, GMP_RNDN);
+ get_mpfr_f(r, &result[0], &result[1]);
+ wrapper_result_real(&ctx, r, 1, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpfr_f(r, &result[0], &result[1]);
+ break;
+ case rred:
+ set_mpfr_d(a, args[0], args[1]);
+ wrapper_op_real(&ctx, a, 2, args);
+ ((testrred)(fn->func))(r, a, (int *)&result[3]);
+ get_mpfr_d(r, &result[0], &result[1], &result[2]);
+ wrapper_result_real(&ctx, r, 2, result);
+ /* We never need to mess about with the integer auxiliary
+ * output. */
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpfr_d(r, &result[0], &result[1], &result[2]);
+ break;
+ case rredf:
+ set_mpfr_f(a, args[0]);
+ wrapper_op_real(&ctx, a, 1, args);
+ ((testrred)(fn->func))(r, a, (int *)&result[3]);
+ get_mpfr_f(r, &result[0], &result[1]);
+ wrapper_result_real(&ctx, r, 1, result);
+ /* We never need to mess about with the integer auxiliary
+ * output. */
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpfr_f(r, &result[0], &result[1]);
+ break;
+ case semi1:
+ case semi1f:
+ errstr = ((testsemi1)(fn->func))(args, result);
+ break;
+ case semi2:
+ case compare:
+ errstr = ((testsemi2)(fn->func))(args, args+2, result);
+ break;
+ case semi2f:
+ case comparef:
+ case t_ldexpf:
+ errstr = ((testsemi2f)(fn->func))(args, args+2, result);
+ break;
+ case t_ldexp:
+ errstr = ((testldexp)(fn->func))(args, args+2, result);
+ break;
+ case t_frexp:
+ errstr = ((testfrexp)(fn->func))(args, result, result+2);
+ break;
+ case t_frexpf:
+ errstr = ((testfrexp)(fn->func))(args, result, result+2);
+ break;
+ case t_modf:
+ errstr = ((testmodf)(fn->func))(args, result, result+2);
+ break;
+ case t_modff:
+ errstr = ((testmodf)(fn->func))(args, result, result+2);
+ break;
+ case classify:
+ errstr = ((testclassify)(fn->func))(args, &result[0]);
+ break;
+ case classifyf:
+ errstr = ((testclassifyf)(fn->func))(args, &result[0]);
+ break;
+ case args1c:
+ set_mpc_d(ac, args[0], args[1], args[2], args[3]);
+ wrapper_op_complex(&ctx, ac, 2, args);
+ ((testfunc1c)(fn->func))(rc, ac, MPC_RNDNN);
+ get_mpc_d(rc, &result[0], &result[1], &result[2], &result[4], &result[5], &result[6]);
+ wrapper_result_complex(&ctx, rc, 2, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpc_d(rc, &result[0], &result[1], &result[2], &result[4], &result[5], &result[6]);
+ break;
+ case args2c:
+ set_mpc_d(ac, args[0], args[1], args[2], args[3]);
+ wrapper_op_complex(&ctx, ac, 2, args);
+ set_mpc_d(bc, args[4], args[5], args[6], args[7]);
+ wrapper_op_complex(&ctx, bc, 2, args+4);
+ ((testfunc2c)(fn->func))(rc, ac, bc, MPC_RNDNN);
+ get_mpc_d(rc, &result[0], &result[1], &result[2], &result[4], &result[5], &result[6]);
+ wrapper_result_complex(&ctx, rc, 2, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpc_d(rc, &result[0], &result[1], &result[2], &result[4], &result[5], &result[6]);
+ break;
+ case args1fc:
+ set_mpc_f(ac, args[0], args[2]);
+ wrapper_op_complex(&ctx, ac, 1, args);
+ ((testfunc1c)(fn->func))(rc, ac, MPC_RNDNN);
+ get_mpc_f(rc, &result[0], &result[1], &result[4], &result[5]);
+ wrapper_result_complex(&ctx, rc, 1, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpc_f(rc, &result[0], &result[1], &result[4], &result[5]);
+ break;
+ case args2fc:
+ set_mpc_f(ac, args[0], args[2]);
+ wrapper_op_complex(&ctx, ac, 1, args);
+ set_mpc_f(bc, args[4], args[6]);
+ wrapper_op_complex(&ctx, bc, 1, args+4);
+ ((testfunc2c)(fn->func))(rc, ac, bc, MPC_RNDNN);
+ get_mpc_f(rc, &result[0], &result[1], &result[4], &result[5]);
+ wrapper_result_complex(&ctx, rc, 1, result);
+ if (wrapper_run(&ctx, fn->wrappers))
+ get_mpc_f(rc, &result[0], &result[1], &result[4], &result[5]);
+ break;
+ default:
+ fprintf(stderr, "internal inconsistency?!\n");
+ abort();
+ }
+ }
+
+ switch (fn->type) {
+ case args1: /* return an extra-precise result */
+ case args2:
+ case args1cr:
+ case rred:
+ printextra = 1;
+ if (rejected == 0) {
+ errstr = NULL;
+ if (!mpfr_zero_p(a)) {
+ if ((result[0] & 0x7FFFFFFF) == 0 && result[1] == 0) {
+ /*
+ * If the output is +0 or -0 apart from the extra
+ * precision in result[2], then there's a tricky
+ * judgment call about what we require in the
+ * output. If we output the extra bits and set
+ * errstr="?underflow" then mathtest will tolerate
+ * the function under test rounding down to zero
+ * _or_ up to the minimum denormal; whereas if we
+ * suppress the extra bits and set
+ * errstr="underflow", then mathtest will enforce
+ * that the function really does underflow to zero.
+ *
+ * But where to draw the line? It seems clear to
+ * me that numbers along the lines of
+ * 00000000.00000000.7ff should be treated
+ * similarly to 00000000.00000000.801, but on the
+ * other hand, we must surely be prepared to
+ * enforce a genuine underflow-to-zero in _some_
+ * case where the true mathematical output is
+ * nonzero but absurdly tiny.
+ *
+ * I think a reasonable place to draw the
+ * distinction is at 00000000.00000000.400, i.e.
+ * one quarter of the minimum positive denormal.
+ * If a value less than that rounds up to the
+ * minimum denormal, that must mean the function
+ * under test has managed to make an error of an
+ * entire factor of two, and that's something we
+ * should fix. Above that, you can misround within
+ * the limits of your accuracy bound if you have
+ * to.
+ */
+ if (result[2] < 0x40000000) {
+ /* Total underflow (ERANGE + UFL) is required,
+ * and we suppress the extra bits to make
+ * mathtest enforce that the output is really
+ * zero. */
+ errstr = "underflow";
+ printextra = 0;
+ } else {
+ /* Total underflow is not required, but if the
+ * function rounds down to zero anyway, then
+ * we should be prepared to tolerate it. */
+ errstr = "?underflow";
+ }
+ } else if (!(result[0] & 0x7ff00000)) {
+ /*
+ * If the output is denormal, we usually expect a
+ * UFL exception, warning the user of partial
+ * underflow. The exception is if the denormal
+ * being returned is just one of the input values,
+ * unchanged even in principle. I bodgily handle
+ * this by just special-casing the functions in
+ * question below.
+ */
+ if (!strcmp(fn->name, "fmax") ||
+ !strcmp(fn->name, "fmin") ||
+ !strcmp(fn->name, "creal") ||
+ !strcmp(fn->name, "cimag")) {
+ /* no error expected */
+ } else {
+ errstr = "u";
+ }
+ } else if ((result[0] & 0x7FFFFFFF) > 0x7FEFFFFF) {
+ /*
+ * Infinite results are usually due to overflow,
+ * but one exception is lgamma of a negative
+ * integer.
+ */
+ if (!strcmp(fn->name, "lgamma") &&
+ (args[0] & 0x80000000) != 0 && /* negative */
+ is_dinteger(args)) {
+ errstr = "ERANGE status=z";
+ } else {
+ errstr = "overflow";
+ }
+ printextra = 0;
+ }
+ } else {
+ /* lgamma(0) is also a pole. */
+ if (!strcmp(fn->name, "lgamma")) {
+ errstr = "ERANGE status=z";
+ printextra = 0;
+ }
+ }
+ }
+
+ if (!printextra || (rejected && !(rejected==1 && result[2]!=0))) {
+ printf(" result=%08x.%08x",
+ result[0], result[1]);
+ } else {
+ printf(" result=%08x.%08x.%03x",
+ result[0], result[1], (result[2] >> 20) & 0xFFF);
+ }
+ if (fn->type == rred) {
+ printf(" res2=%08x", result[3]);
+ }
+ break;
+ case args1f:
+ case args2f:
+ case args1fcr:
+ case rredf:
+ printextra = 1;
+ if (rejected == 0) {
+ errstr = NULL;
+ if (!mpfr_zero_p(a)) {
+ if ((result[0] & 0x7FFFFFFF) == 0) {
+ /*
+ * Decide whether to print the extra bits based on
+ * just how close to zero the number is. See the
+ * big comment in the double-precision case for
+ * discussion.
+ */
+ if (result[1] < 0x40000000) {
+ errstr = "underflow";
+ printextra = 0;
+ } else {
+ errstr = "?underflow";
+ }
+ } else if (!(result[0] & 0x7f800000)) {
+ /*
+ * Functions which do not report partial overflow
+ * are listed here as special cases. (See the
+ * corresponding double case above for a fuller
+ * comment.)
+ */
+ if (!strcmp(fn->name, "fmaxf") ||
+ !strcmp(fn->name, "fminf") ||
+ !strcmp(fn->name, "crealf") ||
+ !strcmp(fn->name, "cimagf")) {
+ /* no error expected */
+ } else {
+ errstr = "u";
+ }
+ } else if ((result[0] & 0x7FFFFFFF) > 0x7F7FFFFF) {
+ /*
+ * Infinite results are usually due to overflow,
+ * but one exception is lgamma of a negative
+ * integer.
+ */
+ if (!strcmp(fn->name, "lgammaf") &&
+ (args[0] & 0x80000000) != 0 && /* negative */
+ is_sinteger(args)) {
+ errstr = "ERANGE status=z";
+ } else {
+ errstr = "overflow";
+ }
+ printextra = 0;
+ }
+ } else {
+ /* lgamma(0) is also a pole. */
+ if (!strcmp(fn->name, "lgammaf")) {
+ errstr = "ERANGE status=z";
+ printextra = 0;
+ }
+ }
+ }
+
+ if (!printextra || (rejected && !(rejected==1 && result[1]!=0))) {
+ printf(" result=%08x",
+ result[0]);
+ } else {
+ printf(" result=%08x.%03x",
+ result[0], (result[1] >> 20) & 0xFFF);
+ }
+ if (fn->type == rredf) {
+ printf(" res2=%08x", result[3]);
+ }
+ break;
+ case semi1: /* return a double result */
+ case semi2:
+ case t_ldexp:
+ printf(" result=%08x.%08x", result[0], result[1]);
+ break;
+ case semi1f:
+ case semi2f:
+ case t_ldexpf:
+ printf(" result=%08x", result[0]);
+ break;
+ case t_frexp: /* return double * int */
+ printf(" result=%08x.%08x res2=%08x", result[0], result[1],
+ result[2]);
+ break;
+ case t_modf: /* return double * double */
+ printf(" result=%08x.%08x res2=%08x.%08x",
+ result[0], result[1], result[2], result[3]);
+ break;
+ case t_modff: /* return float * float */
+ /* fall through */
+ case t_frexpf: /* return float * int */
+ printf(" result=%08x res2=%08x", result[0], result[2]);
+ break;
+ case classify:
+ case classifyf:
+ case compare:
+ case comparef:
+ printf(" result=%x", result[0]);
+ break;
+ case args1c:
+ case args2c:
+ if (0/* errstr */) {
+ printf(" resultr=%08x.%08x", result[0], result[1]);
+ printf(" resulti=%08x.%08x", result[4], result[5]);
+ } else {
+ printf(" resultr=%08x.%08x.%03x",
+ result[0], result[1], (result[2] >> 20) & 0xFFF);
+ printf(" resulti=%08x.%08x.%03x",
+ result[4], result[5], (result[6] >> 20) & 0xFFF);
+ }
+ /* Underflow behaviour doesn't seem to be specified for complex arithmetic */
+ errstr = "?underflow";
+ break;
+ case args1fc:
+ case args2fc:
+ if (0/* errstr */) {
+ printf(" resultr=%08x", result[0]);
+ printf(" resulti=%08x", result[4]);
+ } else {
+ printf(" resultr=%08x.%03x",
+ result[0], (result[1] >> 20) & 0xFFF);
+ printf(" resulti=%08x.%03x",
+ result[4], (result[5] >> 20) & 0xFFF);
+ }
+ /* Underflow behaviour doesn't seem to be specified for complex arithmetic */
+ errstr = "?underflow";
+ break;
+ }
+
+ if (errstr && *(errstr+1) == '\0') {
+ printf(" errno=0 status=%c",*errstr);
+ } else if (errstr && *errstr == '?') {
+ printf(" maybeerror=%s", errstr+1);
+ } else if (errstr && errstr[0] == 'E') {
+ printf(" errno=%s", errstr);
+ } else {
+ printf(" error=%s", errstr && *errstr ? errstr : "0");
+ }
+
+ printf("\n");
+
+ vet_for_decline(fn, args, result, 0);
+
+ cleanup:
+ mpfr_clear(a);
+ mpfr_clear(b);
+ mpfr_clear(r);
+ mpc_clear(ac);
+ mpc_clear(bc);
+ mpc_clear(rc);
+}
+
+void gencases(Testable *fn, int number) {
+ int i;
+ uint32 args[8];
+
+ float32_case(NULL);
+ float64_case(NULL);
+
+ printf("random=on\n"); /* signal to runtests.pl that the following tests are randomly generated */
+ for (i = 0; i < number; i++) {
+ /* generate test point */
+ fn->cases(args, fn->caseparam1, fn->caseparam2);
+ docase(fn, args);
+ }
+ printf("random=off\n");
+}
+
+static uint32 doubletop(int x, int scale) {
+ int e = 0x412 + scale;
+ while (!(x & 0x100000))
+ x <<= 1, e--;
+ return (e << 20) + x;
+}
+
+static uint32 floatval(int x, int scale) {
+ int e = 0x95 + scale;
+ while (!(x & 0x800000))
+ x <<= 1, e--;
+ return (e << 23) + x;
+}
diff --git a/libc/AOR_v20.02/math/test/rtest/intern.h b/libc/AOR_v20.02/math/test/rtest/intern.h
new file mode 100644
index 000000000000..8b1cc4f3176c
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/intern.h
@@ -0,0 +1,92 @@
+/*
+ * intern.h
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef mathtest_intern_h
+#define mathtest_intern_h
+
+#include <mpfr.h>
+#include <mpc.h>
+
+#include "types.h"
+#include "wrappers.h"
+
+/* Generic function pointer. */
+typedef void (*funcptr)(void);
+
+/* Pointers to test function types. */
+typedef int (*testfunc1)(mpfr_t, mpfr_t, mpfr_rnd_t);
+typedef int (*testfunc2)(mpfr_t, mpfr_t, mpfr_t, mpfr_rnd_t);
+typedef int (*testrred)(mpfr_t, mpfr_t, int *);
+typedef char * (*testsemi1)(uint32 *, uint32 *);
+typedef char * (*testsemi2)(uint32 *, uint32 *, uint32 *);
+typedef char * (*testsemi2f)(uint32 *, uint32 *, uint32 *);
+typedef char * (*testldexp)(uint32 *, uint32 *, uint32 *);
+typedef char * (*testfrexp)(uint32 *, uint32 *, uint32 *);
+typedef char * (*testmodf)(uint32 *, uint32 *, uint32 *);
+typedef char * (*testclassify)(uint32 *, uint32 *);
+typedef char * (*testclassifyf)(uint32 *, uint32 *);
+
+typedef int (*testfunc1c)(mpc_t, mpc_t, mpc_rnd_t);
+typedef int (*testfunc2c)(mpc_t, mpc_t, mpc_t, mpc_rnd_t);
+
+typedef int (*testfunc1cr)(mpfr_t, mpc_t, mpfr_rnd_t);
+
+/* Pointer to a function that generates random test cases. */
+typedef void (*casegen)(uint32 *, uint32, uint32);
+
+/*
+ * List of testable functions, their types, and their testable range.
+ */
+enum {
+ args1, /* afloat-based, one argument */
+ args1f, /* same as args1 but in single prec */
+ args2, /* afloat-based, two arguments */
+ args2f, /* same as args2 but in single prec */
+ rred, /* afloat-based, one arg, aux return */
+ rredf, /* same as rred but in single prec */
+ semi1, /* seminumerical, one argument */
+ semi1f, /* seminumerical, 1 arg, float */
+ semi2, /* seminumerical, two arguments */
+ semi2f, /* seminumerical, 2 args, floats */
+ t_ldexp, /* dbl * int -> dbl */
+ t_ldexpf, /* sgl * int -> sgl */
+ t_frexp, /* dbl -> dbl * int */
+ t_frexpf, /* sgl -> sgl * int */
+ t_modf, /* dbl -> dbl * dbl */
+ t_modff, /* sgl -> sgl * sgl */
+ classify, /* classify double: dbl -> int */
+ classifyf, /* classify float: flt -> int */
+ compare, /* compare doubles, returns int */
+ comparef, /* compare floats, returns int */
+
+ args1c, /* acomplex-base, one argument */
+ args2c,
+ args1fc,
+ args2fc,
+ args1cr, /* dbl-complex -> complex */
+ args1fcr /* sgl-complex -> complex */
+};
+
+typedef struct __testable Testable;
+struct __testable {
+ char *name;
+ funcptr func;
+ int type;
+ wrapperfunc wrappers[MAXWRAPPERS];
+ casegen cases; /* complex functions use the same casegen for both real and complex args */
+ uint32 caseparam1, caseparam2;
+};
+
+extern Testable functions[];
+extern const int nfunctions;
+
+extern void init_pi(void);
+
+int nargs_(Testable* f);
+
+#endif
diff --git a/libc/AOR_v20.02/math/test/rtest/main.c b/libc/AOR_v20.02/math/test/rtest/main.c
new file mode 100644
index 000000000000..c4ddd0f86fcb
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/main.c
@@ -0,0 +1,335 @@
+/*
+ * main.c
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <assert.h>
+#include <stdio.h>
+#include <string.h>
+#include <ctype.h>
+#include <stdlib.h>
+#include <time.h>
+
+#include "intern.h"
+
+void gencases(Testable *fn, int number);
+void docase(Testable *fn, uint32 *args);
+void vet_for_decline(Testable *fn, uint32 *args, uint32 *result, int got_errno_in);
+void seed_random(uint32 seed);
+
+int check_declines = 0;
+int lib_fo = 0;
+int lib_no_arith = 0;
+int ntests = 0;
+
+int nargs_(Testable* f) {
+ switch((f)->type) {
+ case args2:
+ case args2f:
+ case semi2:
+ case semi2f:
+ case t_ldexp:
+ case t_ldexpf:
+ case args1c:
+ case args1fc:
+ case args1cr:
+ case args1fcr:
+ case compare:
+ case comparef:
+ return 2;
+ case args2c:
+ case args2fc:
+ return 4;
+ default:
+ return 1;
+ }
+}
+
+static int isdouble(Testable *f)
+{
+ switch (f->type) {
+ case args1:
+ case rred:
+ case semi1:
+ case t_frexp:
+ case t_modf:
+ case classify:
+ case t_ldexp:
+ case args2:
+ case semi2:
+ case args1c:
+ case args1cr:
+ case compare:
+ case args2c:
+ return 1;
+ case args1f:
+ case rredf:
+ case semi1f:
+ case t_frexpf:
+ case t_modff:
+ case classifyf:
+ case args2f:
+ case semi2f:
+ case t_ldexpf:
+ case comparef:
+ case args1fc:
+ case args1fcr:
+ case args2fc:
+ return 0;
+ default:
+ assert(0 && "Bad function type");
+ }
+}
+
+Testable *find_function(const char *func)
+{
+ int i;
+ for (i = 0; i < nfunctions; i++) {
+ if (func && !strcmp(func, functions[i].name)) {
+ return &functions[i];
+ }
+ }
+ return NULL;
+}
+
+void get_operand(const char *str, Testable *f, uint32 *word0, uint32 *word1)
+{
+ struct special {
+ unsigned dblword0, dblword1, sglword;
+ const char *name;
+ } specials[] = {
+ {0x00000000,0x00000000,0x00000000,"0"},
+ {0x3FF00000,0x00000000,0x3f800000,"1"},
+ {0x7FF00000,0x00000000,0x7f800000,"inf"},
+ {0x7FF80000,0x00000001,0x7fc00000,"qnan"},
+ {0x7FF00000,0x00000001,0x7f800001,"snan"},
+ {0x3ff921fb,0x54442d18,0x3fc90fdb,"pi2"},
+ {0x400921fb,0x54442d18,0x40490fdb,"pi"},
+ {0x3fe921fb,0x54442d18,0x3f490fdb,"pi4"},
+ {0x4002d97c,0x7f3321d2,0x4016cbe4,"3pi4"},
+ };
+ int i;
+
+ for (i = 0; i < (int)(sizeof(specials)/sizeof(*specials)); i++) {
+ if (!strcmp(str, specials[i].name) ||
+ ((str[0] == '-' || str[0] == '+') &&
+ !strcmp(str+1, specials[i].name))) {
+ assert(f);
+ if (isdouble(f)) {
+ *word0 = specials[i].dblword0;
+ *word1 = specials[i].dblword1;
+ } else {
+ *word0 = specials[i].sglword;
+ *word1 = 0;
+ }
+ if (str[0] == '-')
+ *word0 |= 0x80000000U;
+ return;
+ }
+ }
+
+ sscanf(str, "%"I32"x.%"I32"x", word0, word1);
+}
+
+void dofile(FILE *fp, int translating) {
+ char buf[1024], sparebuf[1024], *p;
+
+ /*
+ * Command syntax is:
+ *
+ * - "seed <integer>" sets a random seed
+ *
+ * - "test <function> <ntests>" generates random test lines
+ *
+ * - "<function> op1=foo [op2=bar]" generates a specific test
+ * - "func=<function> op1=foo [op2=bar]" does the same
+ * - "func=<function> op1=foo result=bar" will just output the line as-is
+ *
+ * - a semicolon or a blank line is ignored
+ */
+ while (fgets(buf, sizeof(buf), fp)) {
+ buf[strcspn(buf, "\r\n")] = '\0';
+ strcpy(sparebuf, buf);
+ p = buf;
+ while (*p && isspace(*p)) p++;
+ if (!*p || *p == ';') {
+ /* Comment or blank line. Only print if `translating' is set. */
+ if (translating)
+ printf("%s\n", buf);
+ continue;
+ }
+ if (!strncmp(buf, "seed ", 5)) {
+ seed_random(atoi(buf+5));
+ } else if (!strncmp(buf, "random=", 7)) {
+ /*
+ * Copy 'random=on' / 'random=off' lines unconditionally
+ * to the output, so that random test failures can be
+ * accumulated into a recent-failures-list file and
+ * still identified as random-in-origin when re-run the
+ * next day.
+ */
+ printf("%s\n", buf);
+ } else if (!strncmp(buf, "test ", 5)) {
+ char *p = buf+5;
+ char *q;
+ int ntests, i;
+ q = p;
+ while (*p && !isspace(*p)) p++;
+ if (*p) *p++ = '\0';
+ while (*p && isspace(*p)) p++;
+ if (*p)
+ ntests = atoi(p);
+ else
+ ntests = 100; /* *shrug* */
+ for (i = 0; i < nfunctions; i++) {
+ if (!strcmp(q, functions[i].name)) {
+ gencases(&functions[i], ntests);
+ break;
+ }
+ }
+ if (i == nfunctions) {
+ fprintf(stderr, "unknown test `%s'\n", q);
+ }
+ } else {
+ /*
+ * Parse a specific test line.
+ */
+ uint32 ops[8], result[8];
+ int got_op = 0; /* &1 for got_op1, &4 for got_op3 etc. */
+ Testable *f = 0;
+ char *q, *r;
+ int got_result = 0, got_errno_in = 0;
+
+ for (q = strtok(p, " \t"); q; q = strtok(NULL, " \t")) {
+ r = strchr(q, '=');
+ if (!r) {
+ f = find_function(q);
+ } else {
+ *r++ = '\0';
+
+ if (!strcmp(q, "func"))
+ f = find_function(r);
+ else if (!strcmp(q, "op1") || !strcmp(q, "op1r")) {
+ get_operand(r, f, &ops[0], &ops[1]);
+ got_op |= 1;
+ } else if (!strcmp(q, "op2") || !strcmp(q, "op1i")) {
+ get_operand(r, f, &ops[2], &ops[3]);
+ got_op |= 2;
+ } else if (!strcmp(q, "op2r")) {
+ get_operand(r, f, &ops[4], &ops[5]);
+ got_op |= 4;
+ } else if (!strcmp(q, "op2i")) {
+ get_operand(r, f, &ops[6], &ops[7]);
+ got_op |= 8;
+ } else if (!strcmp(q, "result") || !strcmp(q, "resultr")) {
+ get_operand(r, f, &result[0], &result[1]);
+ got_result |= 1;
+ } else if (!strcmp(q, "resulti")) {
+ get_operand(r, f, &result[4], &result[5]);
+ got_result |= 2;
+ } else if (!strcmp(q, "res2")) {
+ get_operand(r, f, &result[2], &result[3]);
+ got_result |= 4;
+ } else if (!strcmp(q, "errno_in")) {
+ got_errno_in = 1;
+ }
+ }
+ }
+
+ /*
+ * Test cases already set up by the input are not
+ * reprocessed by default, unlike the fplib tests. (This
+ * is mostly for historical reasons, because we used to
+ * use a very slow and incomplete internal reference
+ * implementation; now our ref impl is MPFR/MPC it
+ * probably wouldn't be such a bad idea, though we'd still
+ * have to make sure all the special cases came out
+ * right.) If translating==2 (corresponding to the -T
+ * command-line option) then we regenerate everything
+ * regardless.
+ */
+ if (got_result && translating < 2) {
+ if (f)
+ vet_for_decline(f, ops, result, got_errno_in);
+ puts(sparebuf);
+ continue;
+ }
+
+ if (f && got_op==(1<<nargs_(f))-1) {
+ /*
+ * And do it!
+ */
+ docase(f, ops);
+ }
+ }
+ }
+}
+
+int main(int argc, char **argv) {
+ int errs = 0, opts = 1, files = 0, translating = 0;
+ unsigned int seed = 1; /* in case no explicit seed provided */
+
+ seed_random(seed);
+
+ setvbuf(stdout, NULL, _IOLBF, BUFSIZ); /* stops incomplete lines being printed when out of time */
+
+ while (--argc) {
+ FILE *fp;
+ char *p = *++argv;
+
+ if (opts && *p == '-') {
+ if(*(p+1) == 0) { /* single -, read from stdin */
+ break;
+ } else if (!strcmp(p, "-t")) {
+ translating = 1;
+ } else if (!strcmp(p, "-T")) {
+ translating = 2;
+ } else if (!strcmp(p, "-c")) {
+ check_declines = 1;
+ } else if (!strcmp(p, "--")) {
+ opts = 0;
+ } else if (!strcmp(p,"--seed") && argc > 1 && 1==sscanf(*(argv+1),"%u",&seed)) {
+ seed_random(seed);
+ argv++; /* next in argv is seed value, so skip */
+ --argc;
+ } else if (!strcmp(p, "-fo")) {
+ lib_fo = 1;
+ } else if (!strcmp(p, "-noarith")) {
+ lib_no_arith = 1;
+ } else {
+ fprintf(stderr,
+ "rtest: ignoring unrecognised option '%s'\n", p);
+ errs = 1;
+ }
+ } else {
+ files = 1;
+ if (!errs) {
+ fp = fopen(p, "r");
+ if (fp) {
+ dofile(fp, translating);
+ fclose(fp);
+ } else {
+ perror(p);
+ errs = 1;
+ }
+ }
+ }
+ }
+
+ /*
+ * If no filename arguments, use stdin.
+ */
+ if (!files && !errs) {
+ dofile(stdin, translating);
+ }
+
+ if (check_declines) {
+ fprintf(stderr, "Tests expected to run: %d\n", ntests);
+ fflush(stderr);
+ }
+
+ return errs;
+}
diff --git a/libc/AOR_v20.02/math/test/rtest/random.c b/libc/AOR_v20.02/math/test/rtest/random.c
new file mode 100644
index 000000000000..b6ad6a79a722
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/random.c
@@ -0,0 +1,100 @@
+/*
+ * random.c - random number generator for producing mathlib test cases
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "types.h"
+#include "random.h"
+
+static uint32 seedbuf[55];
+static int seedptr;
+
+void seed_random(uint32 seed) {
+ int i;
+
+ seedptr = 0;
+ for (i = 0; i < 55; i++) {
+ seed = seed % 44488 * 48271 - seed / 44488 * 3399;
+ seedbuf[i] = seed - 1;
+ }
+}
+
+uint32 base_random(void) {
+ seedptr %= 55;
+ seedbuf[seedptr] += seedbuf[(seedptr+31)%55];
+ return seedbuf[seedptr++];
+}
+
+uint32 random32(void) {
+ uint32 a, b, b1, b2;
+ a = base_random();
+ b = base_random();
+ for (b1 = 0x80000000, b2 = 1; b1 > b2; b1 >>= 1, b2 <<= 1) {
+ uint32 b3 = b1 | b2;
+ if ((b & b3) != 0 && (b & b3) != b3)
+ b ^= b3;
+ }
+ return a ^ b;
+}
+
+/*
+ * random_upto: generate a uniformly randomised number in the range
+ * 0,...,limit-1. (Precondition: limit > 0.)
+ *
+ * random_upto_biased: generate a number in the same range, but with
+ * the probability skewed towards the high end by means of taking the
+ * maximum of 8*bias+1 samples from the uniform distribution on the
+ * same range. (I don't know why bias is given in that curious way -
+ * historical reasons, I expect.)
+ *
+ * For speed, I separate the implementation of random_upto into the
+ * two stages of (a) generate a bitmask which reduces a 32-bit random
+ * number to within a factor of two of the right range, (b) repeatedly
+ * generate numbers in that range until one is small enough. Splitting
+ * it up like that means that random_upto_biased can do (a) only once
+ * even when it does (b) lots of times.
+ */
+
+static uint32 random_upto_makemask(uint32 limit) {
+ uint32 mask = 0xFFFFFFFF;
+ int i;
+ for (i = 16; i > 0; i >>= 1)
+ if ((limit & (mask >> i)) == limit)
+ mask >>= i;
+ return mask;
+}
+
+static uint32 random_upto_internal(uint32 limit, uint32 mask) {
+ uint32 ret;
+ do {
+ ret = random32() & mask;
+ } while (ret > limit);
+ return ret;
+}
+
+uint32 random_upto(uint32 limit) {
+ uint32 mask = random_upto_makemask(limit);
+ return random_upto_internal(limit, mask);
+}
+
+uint32 random_upto_biased(uint32 limit, int bias) {
+ uint32 mask = random_upto_makemask(limit);
+
+ uint32 ret = random_upto_internal(limit, mask);
+ while (bias--) {
+ uint32 tmp;
+ tmp = random_upto_internal(limit, mask); if (tmp < ret) ret = tmp;
+ tmp = random_upto_internal(limit, mask); if (tmp < ret) ret = tmp;
+ tmp = random_upto_internal(limit, mask); if (tmp < ret) ret = tmp;
+ tmp = random_upto_internal(limit, mask); if (tmp < ret) ret = tmp;
+ tmp = random_upto_internal(limit, mask); if (tmp < ret) ret = tmp;
+ tmp = random_upto_internal(limit, mask); if (tmp < ret) ret = tmp;
+ tmp = random_upto_internal(limit, mask); if (tmp < ret) ret = tmp;
+ tmp = random_upto_internal(limit, mask); if (tmp < ret) ret = tmp;
+ }
+
+ return ret;
+}
diff --git a/libc/AOR_v20.02/math/test/rtest/random.h b/libc/AOR_v20.02/math/test/rtest/random.h
new file mode 100644
index 000000000000..5ab0c0f0dfcb
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/random.h
@@ -0,0 +1,13 @@
+/*
+ * random.h - header for random.c
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "types.h"
+
+uint32 random32(void);
+uint32 random_upto(uint32 limit);
+uint32 random_upto_biased(uint32 limit, int bias);
diff --git a/libc/AOR_v20.02/math/test/rtest/semi.c b/libc/AOR_v20.02/math/test/rtest/semi.c
new file mode 100644
index 000000000000..aefb2b81d4a5
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/semi.c
@@ -0,0 +1,906 @@
+/*
+ * semi.c: test implementations of mathlib seminumerical functions
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdio.h>
+#include "semi.h"
+
+static void test_rint(uint32 *in, uint32 *out,
+ int isfloor, int isceil) {
+ int sign = in[0] & 0x80000000;
+ int roundup = (isfloor && sign) || (isceil && !sign);
+ uint32 xh, xl, roundword;
+ int ex = (in[0] >> 20) & 0x7FF; /* exponent */
+ int i;
+
+ if ((ex > 0x3ff + 52 - 1) || /* things this big can't be fractional */
+ ((in[0] & 0x7FFFFFFF) == 0 && in[1] == 0)) { /* zero */
+ /* NaN, Inf, a large integer, or zero: just return the input */
+ out[0] = in[0];
+ out[1] = in[1];
+ return;
+ }
+
+ /*
+ * Special case: ex < 0x3ff, ie our number is in (0,1). Return
+ * 1 or 0 according to roundup.
+ */
+ if (ex < 0x3ff) {
+ out[0] = sign | (roundup ? 0x3FF00000 : 0);
+ out[1] = 0;
+ return;
+ }
+
+ /*
+ * We're not short of time here, so we'll do this the hideously
+ * inefficient way. Shift bit by bit so that the units place is
+ * somewhere predictable, round, and shift back again.
+ */
+ xh = in[0];
+ xl = in[1];
+ roundword = 0;
+ for (i = ex; i < 0x3ff + 52; i++) {
+ if (roundword & 1)
+ roundword |= 2; /* preserve sticky bit */
+ roundword = (roundword >> 1) | ((xl & 1) << 31);
+ xl = (xl >> 1) | ((xh & 1) << 31);
+ xh = xh >> 1;
+ }
+ if (roundword && roundup) {
+ xl++;
+ xh += (xl==0);
+ }
+ for (i = ex; i < 0x3ff + 52; i++) {
+ xh = (xh << 1) | ((xl >> 31) & 1);
+ xl = (xl & 0x7FFFFFFF) << 1;
+ }
+ out[0] = xh;
+ out[1] = xl;
+}
+
+char *test_ceil(uint32 *in, uint32 *out) {
+ test_rint(in, out, 0, 1);
+ return NULL;
+}
+
+char *test_floor(uint32 *in, uint32 *out) {
+ test_rint(in, out, 1, 0);
+ return NULL;
+}
+
+static void test_rintf(uint32 *in, uint32 *out,
+ int isfloor, int isceil) {
+ int sign = *in & 0x80000000;
+ int roundup = (isfloor && sign) || (isceil && !sign);
+ uint32 x, roundword;
+ int ex = (*in >> 23) & 0xFF; /* exponent */
+ int i;
+
+ if ((ex > 0x7f + 23 - 1) || /* things this big can't be fractional */
+ (*in & 0x7FFFFFFF) == 0) { /* zero */
+ /* NaN, Inf, a large integer, or zero: just return the input */
+ *out = *in;
+ return;
+ }
+
+ /*
+ * Special case: ex < 0x7f, ie our number is in (0,1). Return
+ * 1 or 0 according to roundup.
+ */
+ if (ex < 0x7f) {
+ *out = sign | (roundup ? 0x3F800000 : 0);
+ return;
+ }
+
+ /*
+ * We're not short of time here, so we'll do this the hideously
+ * inefficient way. Shift bit by bit so that the units place is
+ * somewhere predictable, round, and shift back again.
+ */
+ x = *in;
+ roundword = 0;
+ for (i = ex; i < 0x7F + 23; i++) {
+ if (roundword & 1)
+ roundword |= 2; /* preserve sticky bit */
+ roundword = (roundword >> 1) | ((x & 1) << 31);
+ x = x >> 1;
+ }
+ if (roundword && roundup) {
+ x++;
+ }
+ for (i = ex; i < 0x7F + 23; i++) {
+ x = x << 1;
+ }
+ *out = x;
+}
+
+char *test_ceilf(uint32 *in, uint32 *out) {
+ test_rintf(in, out, 0, 1);
+ return NULL;
+}
+
+char *test_floorf(uint32 *in, uint32 *out) {
+ test_rintf(in, out, 1, 0);
+ return NULL;
+}
+
+char *test_fmod(uint32 *a, uint32 *b, uint32 *out) {
+ int sign;
+ int32 aex, bex;
+ uint32 am[2], bm[2];
+
+ if (((a[0] & 0x7FFFFFFF) << 1) + !!a[1] > 0xFFE00000 ||
+ ((b[0] & 0x7FFFFFFF) << 1) + !!b[1] > 0xFFE00000) {
+ /* a or b is NaN: return QNaN, optionally with IVO */
+ uint32 an, bn;
+ out[0] = 0x7ff80000;
+ out[1] = 1;
+ an = ((a[0] & 0x7FFFFFFF) << 1) + !!a[1];
+ bn = ((b[0] & 0x7FFFFFFF) << 1) + !!b[1];
+ if ((an > 0xFFE00000 && an < 0xFFF00000) ||
+ (bn > 0xFFE00000 && bn < 0xFFF00000))
+ return "i"; /* at least one SNaN: IVO */
+ else
+ return NULL; /* no SNaNs, but at least 1 QNaN */
+ }
+ if ((b[0] & 0x7FFFFFFF) == 0 && b[1] == 0) { /* b==0: EDOM */
+ out[0] = 0x7ff80000;
+ out[1] = 1;
+ return "EDOM status=i";
+ }
+ if ((a[0] & 0x7FF00000) == 0x7FF00000) { /* a==Inf: EDOM */
+ out[0] = 0x7ff80000;
+ out[1] = 1;
+ return "EDOM status=i";
+ }
+ if ((b[0] & 0x7FF00000) == 0x7FF00000) { /* b==Inf: return a */
+ out[0] = a[0];
+ out[1] = a[1];
+ return NULL;
+ }
+ if ((a[0] & 0x7FFFFFFF) == 0 && a[1] == 0) { /* a==0: return a */
+ out[0] = a[0];
+ out[1] = a[1];
+ return NULL;
+ }
+
+ /*
+ * OK. That's the special cases cleared out of the way. Now we
+ * have finite (though not necessarily normal) a and b.
+ */
+ sign = a[0] & 0x80000000; /* we discard sign of b */
+ test_frexp(a, am, (uint32 *)&aex);
+ test_frexp(b, bm, (uint32 *)&bex);
+ am[0] &= 0xFFFFF, am[0] |= 0x100000;
+ bm[0] &= 0xFFFFF, bm[0] |= 0x100000;
+
+ while (aex >= bex) {
+ if (am[0] > bm[0] || (am[0] == bm[0] && am[1] >= bm[1])) {
+ am[1] -= bm[1];
+ am[0] = am[0] - bm[0] - (am[1] > ~bm[1]);
+ }
+ if (aex > bex) {
+ am[0] = (am[0] << 1) | ((am[1] & 0x80000000) >> 31);
+ am[1] <<= 1;
+ aex--;
+ } else
+ break;
+ }
+
+ /*
+ * Renormalise final result; this can be cunningly done by
+ * passing a denormal to ldexp.
+ */
+ aex += 0x3fd;
+ am[0] |= sign;
+ test_ldexp(am, (uint32 *)&aex, out);
+
+ return NULL; /* FIXME */
+}
+
+char *test_fmodf(uint32 *a, uint32 *b, uint32 *out) {
+ int sign;
+ int32 aex, bex;
+ uint32 am, bm;
+
+ if ((*a & 0x7FFFFFFF) > 0x7F800000 ||
+ (*b & 0x7FFFFFFF) > 0x7F800000) {
+ /* a or b is NaN: return QNaN, optionally with IVO */
+ uint32 an, bn;
+ *out = 0x7fc00001;
+ an = *a & 0x7FFFFFFF;
+ bn = *b & 0x7FFFFFFF;
+ if ((an > 0x7f800000 && an < 0x7fc00000) ||
+ (bn > 0x7f800000 && bn < 0x7fc00000))
+ return "i"; /* at least one SNaN: IVO */
+ else
+ return NULL; /* no SNaNs, but at least 1 QNaN */
+ }
+ if ((*b & 0x7FFFFFFF) == 0) { /* b==0: EDOM */
+ *out = 0x7fc00001;
+ return "EDOM status=i";
+ }
+ if ((*a & 0x7F800000) == 0x7F800000) { /* a==Inf: EDOM */
+ *out = 0x7fc00001;
+ return "EDOM status=i";
+ }
+ if ((*b & 0x7F800000) == 0x7F800000) { /* b==Inf: return a */
+ *out = *a;
+ return NULL;
+ }
+ if ((*a & 0x7FFFFFFF) == 0) { /* a==0: return a */
+ *out = *a;
+ return NULL;
+ }
+
+ /*
+ * OK. That's the special cases cleared out of the way. Now we
+ * have finite (though not necessarily normal) a and b.
+ */
+ sign = a[0] & 0x80000000; /* we discard sign of b */
+ test_frexpf(a, &am, (uint32 *)&aex);
+ test_frexpf(b, &bm, (uint32 *)&bex);
+ am &= 0x7FFFFF, am |= 0x800000;
+ bm &= 0x7FFFFF, bm |= 0x800000;
+
+ while (aex >= bex) {
+ if (am >= bm) {
+ am -= bm;
+ }
+ if (aex > bex) {
+ am <<= 1;
+ aex--;
+ } else
+ break;
+ }
+
+ /*
+ * Renormalise final result; this can be cunningly done by
+ * passing a denormal to ldexp.
+ */
+ aex += 0x7d;
+ am |= sign;
+ test_ldexpf(&am, (uint32 *)&aex, out);
+
+ return NULL; /* FIXME */
+}
+
+char *test_ldexp(uint32 *x, uint32 *np, uint32 *out) {
+ int n = *np;
+ int32 n2;
+ uint32 y[2];
+ int ex = (x[0] >> 20) & 0x7FF; /* exponent */
+ int sign = x[0] & 0x80000000;
+
+ if (ex == 0x7FF) { /* inf/NaN; just return x */
+ out[0] = x[0];
+ out[1] = x[1];
+ return NULL;
+ }
+ if ((x[0] & 0x7FFFFFFF) == 0 && x[1] == 0) { /* zero: return x */
+ out[0] = x[0];
+ out[1] = x[1];
+ return NULL;
+ }
+
+ test_frexp(x, y, (uint32 *)&n2);
+ ex = n + n2;
+ if (ex > 0x400) { /* overflow */
+ out[0] = sign | 0x7FF00000;
+ out[1] = 0;
+ return "overflow";
+ }
+ /*
+ * Underflow. 2^-1074 is 00000000.00000001; so if ex == -1074
+ * then we have something [2^-1075,2^-1074). Under round-to-
+ * nearest-even, this whole interval rounds up to 2^-1074,
+ * except for the bottom endpoint which rounds to even and is
+ * an underflow condition.
+ *
+ * So, ex < -1074 is definite underflow, and ex == -1074 is
+ * underflow iff all mantissa bits are zero.
+ */
+ if (ex < -1074 || (ex == -1074 && (y[0] & 0xFFFFF) == 0 && y[1] == 0)) {
+ out[0] = sign; /* underflow: correctly signed zero */
+ out[1] = 0;
+ return "underflow";
+ }
+
+ /*
+ * No overflow or underflow; should be nice and simple, unless
+ * we have to denormalise and round the result.
+ */
+ if (ex < -1021) { /* denormalise and round */
+ uint32 roundword;
+ y[0] &= 0x000FFFFF;
+ y[0] |= 0x00100000; /* set leading bit */
+ roundword = 0;
+ while (ex < -1021) {
+ if (roundword & 1)
+ roundword |= 2; /* preserve sticky bit */
+ roundword = (roundword >> 1) | ((y[1] & 1) << 31);
+ y[1] = (y[1] >> 1) | ((y[0] & 1) << 31);
+ y[0] = y[0] >> 1;
+ ex++;
+ }
+ if (roundword > 0x80000000 || /* round up */
+ (roundword == 0x80000000 && (y[1] & 1))) { /* round up to even */
+ y[1]++;
+ y[0] += (y[1] == 0);
+ }
+ out[0] = sign | y[0];
+ out[1] = y[1];
+ /* Proper ERANGE underflow was handled earlier, but we still
+ * expect an IEEE Underflow exception if this partially
+ * underflowed result is not exact. */
+ if (roundword)
+ return "u";
+ return NULL; /* underflow was handled earlier */
+ } else {
+ out[0] = y[0] + (ex << 20);
+ out[1] = y[1];
+ return NULL;
+ }
+}
+
+char *test_ldexpf(uint32 *x, uint32 *np, uint32 *out) {
+ int n = *np;
+ int32 n2;
+ uint32 y;
+ int ex = (*x >> 23) & 0xFF; /* exponent */
+ int sign = *x & 0x80000000;
+
+ if (ex == 0xFF) { /* inf/NaN; just return x */
+ *out = *x;
+ return NULL;
+ }
+ if ((*x & 0x7FFFFFFF) == 0) { /* zero: return x */
+ *out = *x;
+ return NULL;
+ }
+
+ test_frexpf(x, &y, (uint32 *)&n2);
+ ex = n + n2;
+ if (ex > 0x80) { /* overflow */
+ *out = sign | 0x7F800000;
+ return "overflow";
+ }
+ /*
+ * Underflow. 2^-149 is 00000001; so if ex == -149 then we have
+ * something [2^-150,2^-149). Under round-to- nearest-even,
+ * this whole interval rounds up to 2^-149, except for the
+ * bottom endpoint which rounds to even and is an underflow
+ * condition.
+ *
+ * So, ex < -149 is definite underflow, and ex == -149 is
+ * underflow iff all mantissa bits are zero.
+ */
+ if (ex < -149 || (ex == -149 && (y & 0x7FFFFF) == 0)) {
+ *out = sign; /* underflow: correctly signed zero */
+ return "underflow";
+ }
+
+ /*
+ * No overflow or underflow; should be nice and simple, unless
+ * we have to denormalise and round the result.
+ */
+ if (ex < -125) { /* denormalise and round */
+ uint32 roundword;
+ y &= 0x007FFFFF;
+ y |= 0x00800000; /* set leading bit */
+ roundword = 0;
+ while (ex < -125) {
+ if (roundword & 1)
+ roundword |= 2; /* preserve sticky bit */
+ roundword = (roundword >> 1) | ((y & 1) << 31);
+ y = y >> 1;
+ ex++;
+ }
+ if (roundword > 0x80000000 || /* round up */
+ (roundword == 0x80000000 && (y & 1))) { /* round up to even */
+ y++;
+ }
+ *out = sign | y;
+ /* Proper ERANGE underflow was handled earlier, but we still
+ * expect an IEEE Underflow exception if this partially
+ * underflowed result is not exact. */
+ if (roundword)
+ return "u";
+ return NULL; /* underflow was handled earlier */
+ } else {
+ *out = y + (ex << 23);
+ return NULL;
+ }
+}
+
+char *test_frexp(uint32 *x, uint32 *out, uint32 *nout) {
+ int ex = (x[0] >> 20) & 0x7FF; /* exponent */
+ if (ex == 0x7FF) { /* inf/NaN; return x/0 */
+ out[0] = x[0];
+ out[1] = x[1];
+ nout[0] = 0;
+ return NULL;
+ }
+ if (ex == 0) { /* denormals/zeros */
+ int sign;
+ uint32 xh, xl;
+ if ((x[0] & 0x7FFFFFFF) == 0 && x[1] == 0) {
+ /* zero: return x/0 */
+ out[0] = x[0];
+ out[1] = x[1];
+ nout[0] = 0;
+ return NULL;
+ }
+ sign = x[0] & 0x80000000;
+ xh = x[0] & 0x7FFFFFFF;
+ xl = x[1];
+ ex = 1;
+ while (!(xh & 0x100000)) {
+ ex--;
+ xh = (xh << 1) | ((xl >> 31) & 1);
+ xl = (xl & 0x7FFFFFFF) << 1;
+ }
+ out[0] = sign | 0x3FE00000 | (xh & 0xFFFFF);
+ out[1] = xl;
+ nout[0] = ex - 0x3FE;
+ return NULL;
+ }
+ out[0] = 0x3FE00000 | (x[0] & 0x800FFFFF);
+ out[1] = x[1];
+ nout[0] = ex - 0x3FE;
+ return NULL; /* ordinary number; no error */
+}
+
+char *test_frexpf(uint32 *x, uint32 *out, uint32 *nout) {
+ int ex = (*x >> 23) & 0xFF; /* exponent */
+ if (ex == 0xFF) { /* inf/NaN; return x/0 */
+ *out = *x;
+ nout[0] = 0;
+ return NULL;
+ }
+ if (ex == 0) { /* denormals/zeros */
+ int sign;
+ uint32 xv;
+ if ((*x & 0x7FFFFFFF) == 0) {
+ /* zero: return x/0 */
+ *out = *x;
+ nout[0] = 0;
+ return NULL;
+ }
+ sign = *x & 0x80000000;
+ xv = *x & 0x7FFFFFFF;
+ ex = 1;
+ while (!(xv & 0x800000)) {
+ ex--;
+ xv = xv << 1;
+ }
+ *out = sign | 0x3F000000 | (xv & 0x7FFFFF);
+ nout[0] = ex - 0x7E;
+ return NULL;
+ }
+ *out = 0x3F000000 | (*x & 0x807FFFFF);
+ nout[0] = ex - 0x7E;
+ return NULL; /* ordinary number; no error */
+}
+
+char *test_modf(uint32 *x, uint32 *fout, uint32 *iout) {
+ int ex = (x[0] >> 20) & 0x7FF; /* exponent */
+ int sign = x[0] & 0x80000000;
+ uint32 fh, fl;
+
+ if (((x[0] & 0x7FFFFFFF) | (!!x[1])) > 0x7FF00000) {
+ /*
+ * NaN input: return the same in _both_ outputs.
+ */
+ fout[0] = iout[0] = x[0];
+ fout[1] = iout[1] = x[1];
+ return NULL;
+ }
+
+ test_rint(x, iout, 0, 0);
+ fh = x[0] - iout[0];
+ fl = x[1] - iout[1];
+ if (!fh && !fl) { /* no fraction part */
+ fout[0] = sign;
+ fout[1] = 0;
+ return NULL;
+ }
+ if (!(iout[0] & 0x7FFFFFFF) && !iout[1]) { /* no integer part */
+ fout[0] = x[0];
+ fout[1] = x[1];
+ return NULL;
+ }
+ while (!(fh & 0x100000)) {
+ ex--;
+ fh = (fh << 1) | ((fl >> 31) & 1);
+ fl = (fl & 0x7FFFFFFF) << 1;
+ }
+ fout[0] = sign | (ex << 20) | (fh & 0xFFFFF);
+ fout[1] = fl;
+ return NULL;
+}
+
+char *test_modff(uint32 *x, uint32 *fout, uint32 *iout) {
+ int ex = (*x >> 23) & 0xFF; /* exponent */
+ int sign = *x & 0x80000000;
+ uint32 f;
+
+ if ((*x & 0x7FFFFFFF) > 0x7F800000) {
+ /*
+ * NaN input: return the same in _both_ outputs.
+ */
+ *fout = *iout = *x;
+ return NULL;
+ }
+
+ test_rintf(x, iout, 0, 0);
+ f = *x - *iout;
+ if (!f) { /* no fraction part */
+ *fout = sign;
+ return NULL;
+ }
+ if (!(*iout & 0x7FFFFFFF)) { /* no integer part */
+ *fout = *x;
+ return NULL;
+ }
+ while (!(f & 0x800000)) {
+ ex--;
+ f = f << 1;
+ }
+ *fout = sign | (ex << 23) | (f & 0x7FFFFF);
+ return NULL;
+}
+
+char *test_copysign(uint32 *x, uint32 *y, uint32 *out)
+{
+ int ysign = y[0] & 0x80000000;
+ int xhigh = x[0] & 0x7fffffff;
+
+ out[0] = ysign | xhigh;
+ out[1] = x[1];
+
+ /* There can be no error */
+ return NULL;
+}
+
+char *test_copysignf(uint32 *x, uint32 *y, uint32 *out)
+{
+ int ysign = y[0] & 0x80000000;
+ int xhigh = x[0] & 0x7fffffff;
+
+ out[0] = ysign | xhigh;
+
+ /* There can be no error */
+ return NULL;
+}
+
+char *test_isfinite(uint32 *x, uint32 *out)
+{
+ int xhigh = x[0];
+ /* Being finite means that the exponent is not 0x7ff */
+ if ((xhigh & 0x7ff00000) == 0x7ff00000) out[0] = 0;
+ else out[0] = 1;
+ return NULL;
+}
+
+char *test_isfinitef(uint32 *x, uint32 *out)
+{
+ /* Being finite means that the exponent is not 0xff */
+ if ((x[0] & 0x7f800000) == 0x7f800000) out[0] = 0;
+ else out[0] = 1;
+ return NULL;
+}
+
+char *test_isinff(uint32 *x, uint32 *out)
+{
+ /* Being infinite means that our bottom 30 bits equate to 0x7f800000 */
+ if ((x[0] & 0x7fffffff) == 0x7f800000) out[0] = 1;
+ else out[0] = 0;
+ return NULL;
+}
+
+char *test_isinf(uint32 *x, uint32 *out)
+{
+ int xhigh = x[0];
+ int xlow = x[1];
+ /* Being infinite means that our fraction is zero and exponent is 0x7ff */
+ if (((xhigh & 0x7fffffff) == 0x7ff00000) && (xlow == 0)) out[0] = 1;
+ else out[0] = 0;
+ return NULL;
+}
+
+char *test_isnanf(uint32 *x, uint32 *out)
+{
+ /* Being NaN means that our exponent is 0xff and non-0 fraction */
+ int exponent = x[0] & 0x7f800000;
+ int fraction = x[0] & 0x007fffff;
+ if ((exponent == 0x7f800000) && (fraction != 0)) out[0] = 1;
+ else out[0] = 0;
+ return NULL;
+}
+
+char *test_isnan(uint32 *x, uint32 *out)
+{
+ /* Being NaN means that our exponent is 0x7ff and non-0 fraction */
+ int exponent = x[0] & 0x7ff00000;
+ int fractionhigh = x[0] & 0x000fffff;
+ if ((exponent == 0x7ff00000) && ((fractionhigh != 0) || x[1] != 0))
+ out[0] = 1;
+ else out[0] = 0;
+ return NULL;
+}
+
+char *test_isnormalf(uint32 *x, uint32 *out)
+{
+ /* Being normal means exponent is not 0 and is not 0xff */
+ int exponent = x[0] & 0x7f800000;
+ if (exponent == 0x7f800000) out[0] = 0;
+ else if (exponent == 0) out[0] = 0;
+ else out[0] = 1;
+ return NULL;
+}
+
+char *test_isnormal(uint32 *x, uint32 *out)
+{
+ /* Being normal means exponent is not 0 and is not 0x7ff */
+ int exponent = x[0] & 0x7ff00000;
+ if (exponent == 0x7ff00000) out[0] = 0;
+ else if (exponent == 0) out[0] = 0;
+ else out[0] = 1;
+ return NULL;
+}
+
+char *test_signbitf(uint32 *x, uint32 *out)
+{
+ /* Sign bit is bit 31 */
+ out[0] = (x[0] >> 31) & 1;
+ return NULL;
+}
+
+char *test_signbit(uint32 *x, uint32 *out)
+{
+ /* Sign bit is bit 31 */
+ out[0] = (x[0] >> 31) & 1;
+ return NULL;
+}
+
+char *test_fpclassify(uint32 *x, uint32 *out)
+{
+ int exponent = (x[0] & 0x7ff00000) >> 20;
+ int fraction = (x[0] & 0x000fffff) | x[1];
+
+ if ((exponent == 0x00) && (fraction == 0)) out[0] = 0;
+ else if ((exponent == 0x00) && (fraction != 0)) out[0] = 4;
+ else if ((exponent == 0x7ff) && (fraction == 0)) out[0] = 3;
+ else if ((exponent == 0x7ff) && (fraction != 0)) out[0] = 7;
+ else out[0] = 5;
+ return NULL;
+}
+
+char *test_fpclassifyf(uint32 *x, uint32 *out)
+{
+ int exponent = (x[0] & 0x7f800000) >> 23;
+ int fraction = x[0] & 0x007fffff;
+
+ if ((exponent == 0x000) && (fraction == 0)) out[0] = 0;
+ else if ((exponent == 0x000) && (fraction != 0)) out[0] = 4;
+ else if ((exponent == 0xff) && (fraction == 0)) out[0] = 3;
+ else if ((exponent == 0xff) && (fraction != 0)) out[0] = 7;
+ else out[0] = 5;
+ return NULL;
+}
+
+/*
+ * Internal function that compares doubles in x & y and returns -3, -2, -1, 0,
+ * 1 if they compare to be signaling, unordered, less than, equal or greater
+ * than.
+ */
+static int fpcmp4(uint32 *x, uint32 *y)
+{
+ int result = 0;
+
+ /*
+ * Sort out whether results are ordered or not to begin with
+ * NaNs have exponent 0x7ff, and non-zero fraction. Signaling NaNs take
+ * higher priority than quiet ones.
+ */
+ if ((x[0] & 0x7fffffff) >= 0x7ff80000) result = -2;
+ else if ((x[0] & 0x7fffffff) > 0x7ff00000) result = -3;
+ else if (((x[0] & 0x7fffffff) == 0x7ff00000) && (x[1] != 0)) result = -3;
+ if ((y[0] & 0x7fffffff) >= 0x7ff80000 && result != -3) result = -2;
+ else if ((y[0] & 0x7fffffff) > 0x7ff00000) result = -3;
+ else if (((y[0] & 0x7fffffff) == 0x7ff00000) && (y[1] != 0)) result = -3;
+ if (result != 0) return result;
+
+ /*
+ * The two forms of zero are equal
+ */
+ if (((x[0] & 0x7fffffff) == 0) && x[1] == 0 &&
+ ((y[0] & 0x7fffffff) == 0) && y[1] == 0)
+ return 0;
+
+ /*
+ * If x and y have
diff erent signs we can tell that they're not equal
+ * If x is +ve we have x > y return 1 - otherwise y is +ve return -1
+ */
+ if ((x[0] >> 31) != (y[0] >> 31))
+ return ((x[0] >> 31) == 0) - ((y[0] >> 31) == 0);
+
+ /*
+ * Now we have both signs the same, let's do an initial compare of the
+ * values.
+ *
+ * Whoever designed IEEE754's floating point formats is very clever and
+ * earns my undying admiration. Once you remove the sign-bit, the
+ * floating point numbers can be ordered using the standard <, ==, >
+ * operators will treating the fp-numbers as integers with that bit-
+ * pattern.
+ */
+ if ((x[0] & 0x7fffffff) < (y[0] & 0x7fffffff)) result = -1;
+ else if ((x[0] & 0x7fffffff) > (y[0] & 0x7fffffff)) result = 1;
+ else if (x[1] < y[1]) result = -1;
+ else if (x[1] > y[1]) result = 1;
+ else result = 0;
+
+ /*
+ * Now we return the result - is x is positive (and therefore so is y) we
+ * return the plain result - otherwise we negate it and return.
+ */
+ if ((x[0] >> 31) == 0) return result;
+ else return -result;
+}
+
+/*
+ * Internal function that compares floats in x & y and returns -3, -2, -1, 0,
+ * 1 if they compare to be signaling, unordered, less than, equal or greater
+ * than.
+ */
+static int fpcmp4f(uint32 *x, uint32 *y)
+{
+ int result = 0;
+
+ /*
+ * Sort out whether results are ordered or not to begin with
+ * NaNs have exponent 0xff, and non-zero fraction - we have to handle all
+ * signaling cases over the quiet ones
+ */
+ if ((x[0] & 0x7fffffff) >= 0x7fc00000) result = -2;
+ else if ((x[0] & 0x7fffffff) > 0x7f800000) result = -3;
+ if ((y[0] & 0x7fffffff) >= 0x7fc00000 && result != -3) result = -2;
+ else if ((y[0] & 0x7fffffff) > 0x7f800000) result = -3;
+ if (result != 0) return result;
+
+ /*
+ * The two forms of zero are equal
+ */
+ if (((x[0] & 0x7fffffff) == 0) && ((y[0] & 0x7fffffff) == 0))
+ return 0;
+
+ /*
+ * If x and y have
diff erent signs we can tell that they're not equal
+ * If x is +ve we have x > y return 1 - otherwise y is +ve return -1
+ */
+ if ((x[0] >> 31) != (y[0] >> 31))
+ return ((x[0] >> 31) == 0) - ((y[0] >> 31) == 0);
+
+ /*
+ * Now we have both signs the same, let's do an initial compare of the
+ * values.
+ *
+ * Whoever designed IEEE754's floating point formats is very clever and
+ * earns my undying admiration. Once you remove the sign-bit, the
+ * floating point numbers can be ordered using the standard <, ==, >
+ * operators will treating the fp-numbers as integers with that bit-
+ * pattern.
+ */
+ if ((x[0] & 0x7fffffff) < (y[0] & 0x7fffffff)) result = -1;
+ else if ((x[0] & 0x7fffffff) > (y[0] & 0x7fffffff)) result = 1;
+ else result = 0;
+
+ /*
+ * Now we return the result - is x is positive (and therefore so is y) we
+ * return the plain result - otherwise we negate it and return.
+ */
+ if ((x[0] >> 31) == 0) return result;
+ else return -result;
+}
+
+char *test_isgreater(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4(x, y);
+ *out = (result == 1);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_isgreaterequal(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4(x, y);
+ *out = (result >= 0);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_isless(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4(x, y);
+ *out = (result == -1);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_islessequal(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4(x, y);
+ *out = (result == -1) || (result == 0);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_islessgreater(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4(x, y);
+ *out = (result == -1) || (result == 1);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_isunordered(uint32 *x, uint32 *y, uint32 *out)
+{
+ int normal = 0;
+ int result = fpcmp4(x, y);
+
+ test_isnormal(x, out);
+ normal |= *out;
+ test_isnormal(y, out);
+ normal |= *out;
+ *out = (result == -2) || (result == -3);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_isgreaterf(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4f(x, y);
+ *out = (result == 1);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_isgreaterequalf(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4f(x, y);
+ *out = (result >= 0);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_islessf(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4f(x, y);
+ *out = (result == -1);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_islessequalf(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4f(x, y);
+ *out = (result == -1) || (result == 0);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_islessgreaterf(uint32 *x, uint32 *y, uint32 *out)
+{
+ int result = fpcmp4f(x, y);
+ *out = (result == -1) || (result == 1);
+ return result == -3 ? "i" : NULL;
+}
+
+char *test_isunorderedf(uint32 *x, uint32 *y, uint32 *out)
+{
+ int normal = 0;
+ int result = fpcmp4f(x, y);
+
+ test_isnormalf(x, out);
+ normal |= *out;
+ test_isnormalf(y, out);
+ normal |= *out;
+ *out = (result == -2) || (result == -3);
+ return result == -3 ? "i" : NULL;
+}
diff --git a/libc/AOR_v20.02/math/test/rtest/semi.h b/libc/AOR_v20.02/math/test/rtest/semi.h
new file mode 100644
index 000000000000..0aaeee7a0acb
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/semi.h
@@ -0,0 +1,54 @@
+/*
+ * semi.h: header for semi.c
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef test_semi_h
+#define test_semi_h
+
+#include "types.h"
+
+char *test_ceil(uint32 *in, uint32 *out);
+char *test_floor(uint32 *in, uint32 *out);
+char *test_fmod(uint32 *a, uint32 *b, uint32 *out);
+char *test_ldexp(uint32 *x, uint32 *n, uint32 *out);
+char *test_frexp(uint32 *x, uint32 *out, uint32 *nout);
+char *test_modf(uint32 *x, uint32 *iout, uint32 *fout);
+char *test_ceilf(uint32 *in, uint32 *out);
+char *test_floorf(uint32 *in, uint32 *out);
+char *test_fmodf(uint32 *a, uint32 *b, uint32 *out);
+char *test_ldexpf(uint32 *x, uint32 *n, uint32 *out);
+char *test_frexpf(uint32 *x, uint32 *out, uint32 *nout);
+char *test_modff(uint32 *x, uint32 *iout, uint32 *fout);
+
+char *test_copysign(uint32 *x, uint32 *y, uint32 *out);
+char *test_copysignf(uint32 *x, uint32 *y, uint32 *out);
+char *test_isfinite(uint32 *x, uint32 *out);
+char *test_isfinitef(uint32 *x, uint32 *out);
+char *test_isinf(uint32 *x, uint32 *out);
+char *test_isinff(uint32 *x, uint32 *out);
+char *test_isnan(uint32 *x, uint32 *out);
+char *test_isnanf(uint32 *x, uint32 *out);
+char *test_isnormal(uint32 *x, uint32 *out);
+char *test_isnormalf(uint32 *x, uint32 *out);
+char *test_signbit(uint32 *x, uint32 *out);
+char *test_signbitf(uint32 *x, uint32 *out);
+char *test_fpclassify(uint32 *x, uint32 *out);
+char *test_fpclassifyf(uint32 *x, uint32 *out);
+
+char *test_isgreater(uint32 *x, uint32 *y, uint32 *out);
+char *test_isgreaterequal(uint32 *x, uint32 *y, uint32 *out);
+char *test_isless(uint32 *x, uint32 *y, uint32 *out);
+char *test_islessequal(uint32 *x, uint32 *y, uint32 *out);
+char *test_islessgreater(uint32 *x, uint32 *y, uint32 *out);
+char *test_isunordered(uint32 *x, uint32 *y, uint32 *out);
+char *test_isgreaterf(uint32 *x, uint32 *y, uint32 *out);
+char *test_isgreaterequalf(uint32 *x, uint32 *y, uint32 *out);
+char *test_islessf(uint32 *x, uint32 *y, uint32 *out);
+char *test_islessequalf(uint32 *x, uint32 *y, uint32 *out);
+char *test_islessgreaterf(uint32 *x, uint32 *y, uint32 *out);
+char *test_isunorderedf(uint32 *x, uint32 *y, uint32 *out);
+#endif
diff --git a/libc/AOR_v20.02/math/test/rtest/types.h b/libc/AOR_v20.02/math/test/rtest/types.h
new file mode 100644
index 000000000000..36806a68dcab
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/types.h
@@ -0,0 +1,26 @@
+/*
+ * types.h
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef mathtest_types_h
+#define mathtest_types_h
+
+#include <limits.h>
+
+#if UINT_MAX == 4294967295
+typedef unsigned int uint32;
+typedef int int32;
+#define I32 ""
+#elif ULONG_MAX == 4294967295
+typedef unsigned long uint32;
+typedef long int32;
+#define I32 "l"
+#else
+#error Could not find an unsigned 32-bit integer type
+#endif
+
+#endif
diff --git a/libc/AOR_v20.02/math/test/rtest/wrappers.c b/libc/AOR_v20.02/math/test/rtest/wrappers.c
new file mode 100644
index 000000000000..71b90ea47fad
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/wrappers.c
@@ -0,0 +1,262 @@
+/*
+ * wrappers.c - wrappers to modify output of MPFR/MPC test functions
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <assert.h>
+#include <stddef.h>
+#include <stdint.h>
+
+#include "intern.h"
+
+void wrapper_init(wrapperctx *ctx)
+{
+ int i;
+ ctx->nops = ctx->nresults = 0;
+ for (i = 0; i < 2; i++) {
+ ctx->mpfr_ops[i] = NULL;
+ ctx->mpc_ops[i] = NULL;
+ ctx->ieee_ops[i] = NULL;
+ }
+ ctx->mpfr_result = NULL;
+ ctx->mpc_result = NULL;
+ ctx->ieee_result = NULL;
+ ctx->need_regen = 0;
+}
+
+void wrapper_op_real(wrapperctx *ctx, const mpfr_t r,
+ int size, const uint32 *ieee)
+{
+ assert(ctx->nops < 2);
+ ctx->mpfr_ops[ctx->nops] = r;
+ ctx->ieee_ops[ctx->nops] = ieee;
+ ctx->size_ops[ctx->nops] = size;
+ ctx->nops++;
+}
+
+void wrapper_op_complex(wrapperctx *ctx, const mpc_t c,
+ int size, const uint32 *ieee)
+{
+ assert(ctx->nops < 2);
+ ctx->mpc_ops[ctx->nops] = c;
+ ctx->ieee_ops[ctx->nops] = ieee;
+ ctx->size_ops[ctx->nops] = size;
+ ctx->nops++;
+}
+
+void wrapper_result_real(wrapperctx *ctx, mpfr_t r,
+ int size, uint32 *ieee)
+{
+ assert(ctx->nresults < 1);
+ ctx->mpfr_result = r;
+ ctx->ieee_result = ieee;
+ ctx->size_result = size;
+ ctx->nresults++;
+}
+
+void wrapper_result_complex(wrapperctx *ctx, mpc_t c,
+ int size, uint32 *ieee)
+{
+ assert(ctx->nresults < 1);
+ ctx->mpc_result = c;
+ ctx->ieee_result = ieee;
+ ctx->size_result = size;
+ ctx->nresults++;
+}
+
+int wrapper_run(wrapperctx *ctx, wrapperfunc wrappers[MAXWRAPPERS])
+{
+ int i;
+ for (i = 0; i < MAXWRAPPERS && wrappers[i]; i++)
+ wrappers[i](ctx);
+ universal_wrapper(ctx);
+ return ctx->need_regen;
+}
+
+mpfr_srcptr wrapper_get_mpfr(wrapperctx *ctx, int op)
+{
+ if (op < 0) {
+ assert(ctx->mpfr_result);
+ return ctx->mpfr_result;
+ } else {
+ assert(ctx->mpfr_ops[op]);
+ return ctx->mpfr_ops[op];
+ }
+}
+
+const uint32 *wrapper_get_ieee(wrapperctx *ctx, int op)
+{
+ if (op < 0) {
+ assert(ctx->mpfr_result);
+ return ctx->ieee_result;
+ } else {
+ assert(ctx->mpfr_ops[op]);
+ return ctx->ieee_ops[op];
+ }
+}
+
+int wrapper_get_nops(wrapperctx *ctx)
+{
+ return ctx->nops;
+}
+
+int wrapper_get_size(wrapperctx *ctx, int op)
+{
+ if (op < 0) {
+ assert(ctx->mpfr_result || ctx->mpc_result);
+ return ctx->size_result;
+ } else {
+ assert(ctx->mpfr_ops[op] || ctx->mpc_ops[op]);
+ return ctx->size_ops[op];
+ }
+}
+
+int wrapper_is_complex(wrapperctx *ctx, int op)
+{
+ if (op < 0) {
+ assert(ctx->mpfr_result || ctx->mpc_result);
+ return ctx->mpc_result != NULL;
+ } else {
+ assert(ctx->mpfr_ops[op] || ctx->mpc_ops[op]);
+ return ctx->mpc_ops[op] != NULL;
+ }
+}
+
+mpc_srcptr wrapper_get_mpc(wrapperctx *ctx, int op)
+{
+ if (op < 0) {
+ assert(ctx->mpc_result);
+ return ctx->mpc_result;
+ } else {
+ assert(ctx->mpc_ops[op]);
+ return ctx->mpc_ops[op];
+ }
+}
+
+mpfr_srcptr wrapper_get_mpfr_r(wrapperctx *ctx, int op)
+{
+ if (op < 0) {
+ assert(ctx->mpc_result);
+ return mpc_realref(ctx->mpc_result);
+ } else {
+ assert(ctx->mpc_ops[op]);
+ return mpc_realref(ctx->mpc_ops[op]);
+ }
+}
+
+mpfr_srcptr wrapper_get_mpfr_i(wrapperctx *ctx, int op)
+{
+ if (op < 0) {
+ assert(ctx->mpc_result);
+ return mpc_imagref(ctx->mpc_result);
+ } else {
+ assert(ctx->mpc_ops[op]);
+ return mpc_imagref(ctx->mpc_ops[op]);
+ }
+}
+
+const uint32 *wrapper_get_ieee_r(wrapperctx *ctx, int op)
+{
+ if (op < 0) {
+ assert(ctx->mpc_result);
+ return ctx->ieee_result;
+ } else {
+ assert(ctx->mpc_ops[op]);
+ return ctx->ieee_ops[op];
+ }
+}
+
+const uint32 *wrapper_get_ieee_i(wrapperctx *ctx, int op)
+{
+ if (op < 0) {
+ assert(ctx->mpc_result);
+ return ctx->ieee_result + 4;
+ } else {
+ assert(ctx->mpc_ops[op]);
+ return ctx->ieee_ops[op] + 2;
+ }
+}
+
+void wrapper_set_sign(wrapperctx *ctx, uint32 sign)
+{
+ assert(ctx->mpfr_result);
+ ctx->ieee_result[0] |= (sign & 0x80000000U);
+}
+
+void wrapper_set_sign_r(wrapperctx *ctx, uint32 sign)
+{
+ assert(ctx->mpc_result);
+ ctx->ieee_result[0] |= (sign & 0x80000000U);
+}
+
+void wrapper_set_sign_i(wrapperctx *ctx, uint32 sign)
+{
+ assert(ctx->mpc_result);
+ ctx->ieee_result[4] |= (sign & 0x80000000U);
+}
+
+void wrapper_set_nan(wrapperctx *ctx)
+{
+ assert(ctx->mpfr_result);
+ mpfr_set_nan(ctx->mpfr_result);
+ ctx->need_regen = 1;
+}
+
+void wrapper_set_nan_r(wrapperctx *ctx)
+{
+ assert(ctx->mpc_result);
+ mpfr_set_nan(mpc_realref(ctx->mpc_result)); /* FIXME: better way? */
+ ctx->need_regen = 1;
+}
+
+void wrapper_set_nan_i(wrapperctx *ctx)
+{
+ assert(ctx->mpc_result);
+ mpfr_set_nan(mpc_imagref(ctx->mpc_result)); /* FIXME: better way? */
+ ctx->need_regen = 1;
+}
+
+void wrapper_set_int(wrapperctx *ctx, int val)
+{
+ assert(ctx->mpfr_result);
+ mpfr_set_si(ctx->mpfr_result, val, GMP_RNDN);
+ ctx->need_regen = 1;
+}
+
+void wrapper_set_int_r(wrapperctx *ctx, int val)
+{
+ assert(ctx->mpc_result);
+ mpfr_set_si(mpc_realref(ctx->mpc_result), val, GMP_RNDN);
+ ctx->need_regen = 1;
+}
+
+void wrapper_set_int_i(wrapperctx *ctx, int val)
+{
+ assert(ctx->mpc_result);
+ mpfr_set_si(mpc_realref(ctx->mpc_result), val, GMP_RNDN);
+ ctx->need_regen = 1;
+}
+
+void wrapper_set_mpfr(wrapperctx *ctx, const mpfr_t val)
+{
+ assert(ctx->mpfr_result);
+ mpfr_set(ctx->mpfr_result, val, GMP_RNDN);
+ ctx->need_regen = 1;
+}
+
+void wrapper_set_mpfr_r(wrapperctx *ctx, const mpfr_t val)
+{
+ assert(ctx->mpc_result);
+ mpfr_set(mpc_realref(ctx->mpc_result), val, GMP_RNDN);
+ ctx->need_regen = 1;
+}
+
+void wrapper_set_mpfr_i(wrapperctx *ctx, const mpfr_t val)
+{
+ assert(ctx->mpc_result);
+ mpfr_set(mpc_realref(ctx->mpc_result), val, GMP_RNDN);
+ ctx->need_regen = 1;
+}
diff --git a/libc/AOR_v20.02/math/test/rtest/wrappers.h b/libc/AOR_v20.02/math/test/rtest/wrappers.h
new file mode 100644
index 000000000000..e2e653a0f01e
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/rtest/wrappers.h
@@ -0,0 +1,115 @@
+/*
+ * wrappers.h - wrappers to modify output of MPFR/MPC test functions
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+typedef struct {
+ /* Structure type should be considered opaque outside wrappers.c,
+ * though we have to define it here so its size is known. */
+ int nops;
+ int nresults;
+ mpfr_srcptr mpfr_ops[2];
+ mpfr_ptr mpfr_result;
+ mpc_srcptr mpc_ops[2];
+ mpc_ptr mpc_result;
+ const uint32 *ieee_ops[2];
+ uint32 *ieee_result;
+ int size_ops[2];
+ int size_result;
+ int need_regen;
+} wrapperctx;
+
+typedef void (*wrapperfunc)(wrapperctx *ctx);
+#define MAXWRAPPERS 3
+
+/*
+ * Functions for the test harness to call.
+ *
+ * When the test harness executes a test function, it should
+ * initialise a wrapperctx with wrapper_init, then provide all the
+ * operands and results in both mpfr/mpc and IEEE (+ extrabits)
+ * formats via wrapper_op_* and wrapper_result_*. Then it should run
+ * the function's wrappers using wrapper_run(), and if that returns
+ * true then the primary result has been rewritten in mpfr/mpc format
+ * and it should therefore retranslate into IEEE.
+ *
+ * 'size' in all prototypes below represents an FP type by giving the
+ * number of 32-bit words it requires, so 1=float and 2=double. Input
+ * operands will be that many words (or that many for both their real
+ * and imag parts); outputs will have one extra word for 'extrabits'.
+ *
+ * This system only applies at all to reference functions using
+ * mpfr/mpc. The seminumerical functions we implement in pure IEEE
+ * form are expected to handle all their own special cases correctly.
+ */
+
+void wrapper_init(wrapperctx *ctx);
+
+/* Real operand. */
+void wrapper_op_real(wrapperctx *ctx, const mpfr_t r,
+ int size, const uint32 *ieee);
+
+/* Complex operand. Real part starts at ieee[0], the imag part at ieee[2]. */
+void wrapper_op_complex(wrapperctx *ctx, const mpc_t c,
+ int size, const uint32 *ieee);
+
+/* Real result. ieee contains size+1 words, as discussed above. */
+void wrapper_result_real(wrapperctx *ctx, mpfr_t r,
+ int size, uint32 *ieee);
+
+/* Complex result. ieee contains size+1 words of real part starting at
+ * ieee[0], and another size+1 of imag part starting at ieee[4]. */
+void wrapper_result_complex(wrapperctx *ctx, mpc_t c,
+ int size, uint32 *ieee);
+
+int wrapper_run(wrapperctx *ctx, wrapperfunc wrappers[MAXWRAPPERS]);
+
+/*
+ * Functions for wrappers to call. 'op' indicates which operand is
+ * being requested: 0,1 means first and second, and -1 means the
+ * result.
+ */
+
+mpfr_srcptr wrapper_get_mpfr(wrapperctx *ctx, int op);
+const uint32 *wrapper_get_ieee(wrapperctx *ctx, int op);
+
+mpc_srcptr wrapper_get_mpc(wrapperctx *ctx, int op);
+mpfr_srcptr wrapper_get_mpfr_r(wrapperctx *ctx, int op);
+mpfr_srcptr wrapper_get_mpfr_i(wrapperctx *ctx, int op);
+const uint32 *wrapper_get_ieee_r(wrapperctx *ctx, int op);
+const uint32 *wrapper_get_ieee_i(wrapperctx *ctx, int op);
+
+/* Query operand count + types */
+int wrapper_get_nops(wrapperctx *ctx);
+int wrapper_get_size(wrapperctx *ctx, int op);
+int wrapper_is_complex(wrapperctx *ctx, int op);
+
+/* Change just the sign of the result. Only the top bit of 'sign' is used. */
+void wrapper_set_sign(wrapperctx *ctx, uint32 sign);
+void wrapper_set_sign_r(wrapperctx *ctx, uint32 sign);
+void wrapper_set_sign_i(wrapperctx *ctx, uint32 sign);
+
+/* Set a result to NaN. */
+void wrapper_set_nan(wrapperctx *ctx);
+void wrapper_set_nan_r(wrapperctx *ctx);
+void wrapper_set_nan_i(wrapperctx *ctx);
+
+/* Set a result to an integer value (converted to the appropriate
+ * float format). */
+void wrapper_set_int(wrapperctx *ctx, int val);
+void wrapper_set_int_r(wrapperctx *ctx, int val);
+void wrapper_set_int_i(wrapperctx *ctx, int val);
+
+/* Set a result to a new MPFR float. */
+void wrapper_set_mpfr(wrapperctx *ctx, const mpfr_t val);
+void wrapper_set_mpfr_r(wrapperctx *ctx, const mpfr_t val);
+void wrapper_set_mpfr_i(wrapperctx *ctx, const mpfr_t val);
+
+/*
+ * A universal wrapper called for _all_ functions, that doesn't have
+ * to be specified individually everywhere.
+ */
+void universal_wrapper(wrapperctx *ctx);
diff --git a/libc/AOR_v20.02/math/test/runulp.sh b/libc/AOR_v20.02/math/test/runulp.sh
new file mode 100755
index 000000000000..431829bfc52f
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/runulp.sh
@@ -0,0 +1,295 @@
+#!/bin/bash
+
+# ULP error check script.
+#
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+#set -x
+set -eu
+
+# cd to bin directory.
+cd "${0%/*}"
+
+rmodes='n u d z'
+#rmodes=n
+flags="${ULPFLAGS:--q}"
+emu="$@"
+
+FAIL=0
+PASS=0
+
+t() {
+ [ $r = "n" ] && Lt=$L || Lt=$Ldir
+ $emu ./ulp -r $r -e $Lt $flags "$@" && PASS=$((PASS+1)) || FAIL=$((FAIL+1))
+}
+
+check() {
+ $emu ./ulp -f -q "$@" >/dev/null
+}
+
+Ldir=0.5
+for r in $rmodes
+do
+L=0.01
+t exp 0 0xffff000000000000 10000
+t exp 0x1p-6 0x1p6 40000
+t exp -0x1p-6 -0x1p6 40000
+t exp 633.3 733.3 10000
+t exp -633.3 -777.3 10000
+
+L=0.01
+t exp2 0 0xffff000000000000 10000
+t exp2 0x1p-6 0x1p6 40000
+t exp2 -0x1p-6 -0x1p6 40000
+t exp2 633.3 733.3 10000
+t exp2 -633.3 -777.3 10000
+
+L=0.02
+t log 0 0xffff000000000000 10000
+t log 0x1p-4 0x1p4 40000
+t log 0 inf 40000
+
+L=0.05
+t log2 0 0xffff000000000000 10000
+t log2 0x1p-4 0x1p4 40000
+t log2 0 inf 40000
+
+L=0.05
+t pow 0.5 2.0 x 0 inf 20000
+t pow -0.5 -2.0 x 0 inf 20000
+t pow 0.5 2.0 x -0 -inf 20000
+t pow -0.5 -2.0 x -0 -inf 20000
+t pow 0.5 2.0 x 0x1p-10 0x1p10 40000
+t pow 0.5 2.0 x -0x1p-10 -0x1p10 40000
+t pow 0 inf x 0.5 2.0 80000
+t pow 0 inf x -0.5 -2.0 80000
+t pow 0x1.fp-1 0x1.08p0 x 0x1p8 0x1p17 80000
+t pow 0x1.fp-1 0x1.08p0 x -0x1p8 -0x1p17 80000
+t pow 0 0x1p-1000 x 0 1.0 50000
+t pow 0x1p1000 inf x 0 1.0 50000
+t pow 0x1.ffffffffffff0p-1 0x1.0000000000008p0 x 0x1p60 0x1p68 50000
+t pow 0x1.ffffffffff000p-1 0x1p0 x 0x1p50 0x1p52 50000
+t pow -0x1.ffffffffff000p-1 -0x1p0 x 0x1p50 0x1p52 50000
+
+L=0.01
+t expf 0 0xffff0000 10000
+t expf 0x1p-14 0x1p8 50000
+t expf -0x1p-14 -0x1p8 50000
+
+L=0.01
+t exp2f 0 0xffff0000 10000
+t exp2f 0x1p-14 0x1p8 50000
+t exp2f -0x1p-14 -0x1p8 50000
+
+L=0.32
+t logf 0 0xffff0000 10000
+t logf 0x1p-4 0x1p4 50000
+t logf 0 inf 50000
+
+L=0.26
+t log2f 0 0xffff0000 10000
+t log2f 0x1p-4 0x1p4 50000
+t log2f 0 inf 50000
+
+L=0.06
+t sinf 0 0xffff0000 10000
+t sinf 0x1p-14 0x1p54 50000
+t sinf -0x1p-14 -0x1p54 50000
+
+L=0.06
+t cosf 0 0xffff0000 10000
+t cosf 0x1p-14 0x1p54 50000
+t cosf -0x1p-14 -0x1p54 50000
+
+L=0.06
+t sincosf_sinf 0 0xffff0000 10000
+t sincosf_sinf 0x1p-14 0x1p54 50000
+t sincosf_sinf -0x1p-14 -0x1p54 50000
+
+L=0.06
+t sincosf_cosf 0 0xffff0000 10000
+t sincosf_cosf 0x1p-14 0x1p54 50000
+t sincosf_cosf -0x1p-14 -0x1p54 50000
+
+L=0.4
+t powf 0x1p-1 0x1p1 x 0x1p-7 0x1p7 50000
+t powf 0x1p-1 0x1p1 x -0x1p-7 -0x1p7 50000
+t powf 0x1p-70 0x1p70 x 0x1p-1 0x1p1 50000
+t powf 0x1p-70 0x1p70 x -0x1p-1 -0x1p1 50000
+t powf 0x1.ep-1 0x1.1p0 x 0x1p8 0x1p14 50000
+t powf 0x1.ep-1 0x1.1p0 x -0x1p8 -0x1p14 50000
+done
+
+# vector functions
+Ldir=0.5
+r='n'
+flags="${ULPFLAGS:--q} -f"
+runs=
+check __s_exp 1 && runs=1
+runv=
+check __v_exp 1 && runv=1
+runvn=
+check __vn_exp 1 && runvn=1
+
+range_exp='
+ 0 0xffff000000000000 10000
+ 0x1p-6 0x1p6 400000
+ -0x1p-6 -0x1p6 400000
+ 633.3 733.3 10000
+ -633.3 -777.3 10000
+'
+
+range_log='
+ 0 0xffff000000000000 10000
+ 0x1p-4 0x1p4 400000
+ 0 inf 400000
+'
+
+range_pow='
+ 0x1p-1 0x1p1 x 0x1p-10 0x1p10 50000
+ 0x1p-1 0x1p1 x -0x1p-10 -0x1p10 50000
+ 0x1p-500 0x1p500 x 0x1p-1 0x1p1 50000
+ 0x1p-500 0x1p500 x -0x1p-1 -0x1p1 50000
+ 0x1.ep-1 0x1.1p0 x 0x1p8 0x1p16 50000
+ 0x1.ep-1 0x1.1p0 x -0x1p8 -0x1p16 50000
+'
+
+range_sin='
+ 0 0xffff000000000000 10000
+ 0x1p-4 0x1p4 400000
+ -0x1p-23 0x1p23 400000
+'
+range_cos="$range_sin"
+
+range_expf='
+ 0 0xffff0000 10000
+ 0x1p-14 0x1p8 500000
+ -0x1p-14 -0x1p8 500000
+'
+
+range_expf_1u="$range_expf"
+range_exp2f="$range_expf"
+range_exp2f_1u="$range_expf"
+
+range_logf='
+ 0 0xffff0000 10000
+ 0x1p-4 0x1p4 500000
+'
+
+range_sinf='
+ 0 0xffff0000 10000
+ 0x1p-4 0x1p4 300000
+-0x1p-9 -0x1p9 300000
+'
+range_cosf="$range_sinf"
+
+range_powf='
+ 0x1p-1 0x1p1 x 0x1p-7 0x1p7 50000
+ 0x1p-1 0x1p1 x -0x1p-7 -0x1p7 50000
+ 0x1p-70 0x1p70 x 0x1p-1 0x1p1 50000
+ 0x1p-70 0x1p70 x -0x1p-1 -0x1p1 50000
+ 0x1.ep-1 0x1.1p0 x 0x1p8 0x1p14 50000
+ 0x1.ep-1 0x1.1p0 x -0x1p8 -0x1p14 50000
+'
+
+# error limits
+L_exp=1.9
+L_log=1.2
+L_pow=0.05
+L_sin=3.0
+L_cos=3.0
+L_expf=1.49
+L_expf_1u=0.4
+L_exp2f=1.49
+L_exp2f_1u=0.4
+L_logf=2.9
+L_sinf=1.4
+L_cosf=1.4
+L_powf=2.1
+
+while read G F R
+do
+ [ "$R" = 1 ] || continue
+ case "$G" in \#*) continue ;; esac
+ eval range="\${range_$G}"
+ eval L="\${L_$G}"
+ while read X
+ do
+ [ -n "$X" ] || continue
+ case "$X" in \#*) continue ;; esac
+ t $F $X
+ done << EOF
+$range
+EOF
+done << EOF
+# group symbol run
+exp __s_exp $runs
+exp __v_exp $runv
+exp __vn_exp $runvn
+exp _ZGVnN2v_exp $runvn
+
+log __s_log $runs
+log __v_log $runv
+log __vn_log $runvn
+log _ZGVnN2v_log $runvn
+
+pow __s_pow $runs
+pow __v_pow $runv
+pow __vn_pow $runvn
+pow _ZGVnN2vv_pow $runvn
+
+sin __s_sin $runs
+sin __v_sin $runv
+sin __vn_sin $runvn
+sin _ZGVnN2v_sin $runvn
+
+cos __s_cos $runs
+cos __v_cos $runv
+cos __vn_cos $runvn
+cos _ZGVnN2v_cos $runvn
+
+expf __s_expf $runs
+expf __v_expf $runv
+expf __vn_expf $runvn
+expf _ZGVnN4v_expf $runvn
+
+expf_1u __s_expf_1u $runs
+expf_1u __v_expf_1u $runv
+expf_1u __vn_expf_1u $runvn
+
+exp2f __s_exp2f $runs
+exp2f __v_exp2f $runv
+exp2f __vn_exp2f $runvn
+exp2f _ZGVnN4v_exp2f $runvn
+
+exp2f_1u __s_exp2f_1u $runs
+exp2f_1u __v_exp2f_1u $runv
+exp2f_1u __vn_exp2f_1u $runvn
+
+logf __s_logf $runs
+logf __v_logf $runv
+logf __vn_logf $runvn
+logf _ZGVnN4v_logf $runvn
+
+sinf __s_sinf $runs
+sinf __v_sinf $runv
+sinf __vn_sinf $runvn
+sinf _ZGVnN4v_sinf $runvn
+
+cosf __s_cosf $runs
+cosf __v_cosf $runv
+cosf __vn_cosf $runvn
+cosf _ZGVnN4v_cosf $runvn
+
+powf __s_powf $runs
+powf __v_powf $runv
+powf __vn_powf $runvn
+powf _ZGVnN4vv_powf $runvn
+EOF
+
+[ 0 -eq $FAIL ] || {
+ echo "FAILED $FAIL PASSED $PASS"
+ exit 1
+}
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/cosf.tst b/libc/AOR_v20.02/math/test/testcases/directed/cosf.tst
new file mode 100644
index 000000000000..8c7621a4550c
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/cosf.tst
@@ -0,0 +1,26 @@
+; cosf.tst - Directed test cases for SP cosine
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=cosf op1=7fc00001 result=7fc00001 errno=0
+func=cosf op1=ffc00001 result=7fc00001 errno=0
+func=cosf op1=7f800001 result=7fc00001 errno=0 status=i
+func=cosf op1=ff800001 result=7fc00001 errno=0 status=i
+func=cosf op1=7f800000 result=7fc00001 errno=EDOM status=i
+func=cosf op1=ff800000 result=7fc00001 errno=EDOM status=i
+func=cosf op1=00000000 result=3f800000 errno=0
+func=cosf op1=80000000 result=3f800000 errno=0
+; SDCOMP-26094: check cosf in the cases for which the range reducer
+; returns values furthest beyond its nominal upper bound of pi/4.
+func=cosf op1=46427f1b result=3f34dc5c.565 error=0
+func=cosf op1=4647e568 result=3f34dc33.c1f error=0
+func=cosf op1=46428bac result=bf34dbf2.8e3 error=0
+func=cosf op1=4647f1f9 result=bf34dbc9.f9b error=0
+func=cosf op1=4647fe8a result=3f34db60.313 error=0
+func=cosf op1=45d8d7f1 result=bf35006a.7fd error=0
+func=cosf op1=45d371a4 result=3f350056.39b error=0
+func=cosf op1=45ce0b57 result=bf350041.f38 error=0
+func=cosf op1=45d35882 result=bf34ffec.868 error=0
+func=cosf op1=45cdf235 result=3f34ffd8.404 error=0
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/exp.tst b/libc/AOR_v20.02/math/test/testcases/directed/exp.tst
new file mode 100644
index 000000000000..7c466d6b6ca9
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/exp.tst
@@ -0,0 +1,32 @@
+; Directed test cases for exp
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=exp op1=7ff80000.00000001 result=7ff80000.00000001 errno=0
+func=exp op1=fff80000.00000001 result=7ff80000.00000001 errno=0
+func=exp op1=7ff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=exp op1=fff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=exp op1=7ff00000.00000000 result=7ff00000.00000000 errno=0
+func=exp op1=fff00000.00000000 result=00000000.00000000 errno=0
+func=exp op1=7fefffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=ox
+func=exp op1=ffefffff.ffffffff result=00000000.00000000 errno=ERANGE status=ux
+func=exp op1=00000000.00000000 result=3ff00000.00000000 errno=0
+func=exp op1=80000000.00000000 result=3ff00000.00000000 errno=0
+func=exp op1=00000000.00000001 result=3ff00000.00000000 errno=0
+func=exp op1=80000000.00000001 result=3ff00000.00000000 errno=0
+func=exp op1=3c900000.00000000 result=3ff00000.00000000.400 errno=0
+func=exp op1=bc900000.00000000 result=3fefffff.ffffffff.800 errno=0
+func=exp op1=3fe00000.00000000 result=3ffa6129.8e1e069b.c97 errno=0
+func=exp op1=bfe00000.00000000 result=3fe368b2.fc6f9609.fe8 errno=0
+func=exp op1=3ff00000.00000000 result=4005bf0a.8b145769.535 errno=0
+func=exp op1=bff00000.00000000 result=3fd78b56.362cef37.c6b errno=0
+func=exp op1=40000000.00000000 result=401d8e64.b8d4ddad.cc3 errno=0
+func=exp op1=c0000000.00000000 result=3fc152aa.a3bf81cb.9fe errno=0
+func=exp op1=3ff12345.6789abcd result=40075955.c34718ed.6e3 errno=0
+func=exp op1=40862e42.fefa39ef result=7fefffff.ffffff2a.1b1 errno=0
+func=exp op1=40862e42.fefa39f0 result=7ff00000.00000000 errno=ERANGE status=ox
+func=exp op1=c0874910.d52d3051 result=00000000.00000001 status=ux
+func=exp op1=c0874910.d52d3052 result=00000000.00000000 errno=ERANGE status=ux
+func=exp op1=c085d589.f2fe5107 result=00f00000.000000f1.46b errno=0
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/exp2.tst b/libc/AOR_v20.02/math/test/testcases/directed/exp2.tst
new file mode 100644
index 000000000000..b8bcef0e7fca
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/exp2.tst
@@ -0,0 +1,31 @@
+; Directed test cases for exp2
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=exp2 op1=7ff80000.00000001 result=7ff80000.00000001 errno=0
+func=exp2 op1=fff80000.00000001 result=7ff80000.00000001 errno=0
+func=exp2 op1=7ff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=exp2 op1=fff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=exp2 op1=7ff00000.00000000 result=7ff00000.00000000 errno=0
+func=exp2 op1=fff00000.00000000 result=00000000.00000000 errno=0
+func=exp2 op1=7fefffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=ox
+func=exp2 op1=ffefffff.ffffffff result=00000000.00000000 errno=ERANGE status=ux
+func=exp2 op1=00000000.00000000 result=3ff00000.00000000 errno=0
+func=exp2 op1=80000000.00000000 result=3ff00000.00000000 errno=0
+func=exp2 op1=00000000.00000001 result=3ff00000.00000000 errno=0
+func=exp2 op1=80000000.00000001 result=3ff00000.00000000 errno=0
+func=exp2 op1=3ca00000.00000000 result=3ff00000.00000000.58c errno=0
+func=exp2 op1=bc900000.00000000 result=3fefffff.ffffffff.a74 errno=0
+func=exp2 op1=3fe00000.00000000 result=3ff6a09e.667f3bcc.909 errno=0
+func=exp2 op1=bfe00000.00000000 result=3fe6a09e.667f3bcc.909 errno=0
+func=exp2 op1=3ff00000.00000000 result=40000000.00000000 errno=0
+func=exp2 op1=bff00000.00000000 result=3fe00000.00000000 errno=0
+func=exp2 op1=40000000.00000000 result=40100000.00000000 errno=0
+func=exp2 op1=c0000000.00000000 result=3fd00000.00000000 errno=0
+func=exp2 op1=3ff12345.6789abcd result=4000cef3.c5d12321.663 errno=0
+func=exp2 op1=408fffff.ffffffff result=7fefffff.fffffd3a.37a errno=0
+func=exp2 op1=40900000.00000000 result=7ff00000.00000000 errno=ERANGE status=ox
+func=exp2 op1=c090ca00.00000000 result=00000000.00000000.b50 status=ux
+func=exp2 op1=c090cc00.00000000 result=00000000.00000000 errno=ERANGE status=ux
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/exp2f.tst b/libc/AOR_v20.02/math/test/testcases/directed/exp2f.tst
new file mode 100644
index 000000000000..2a7cc2b256b5
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/exp2f.tst
@@ -0,0 +1,26 @@
+; exp2f.tst - Directed test cases for exp2f
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=exp2f op1=7fc00001 result=7fc00001 errno=0
+func=exp2f op1=ffc00001 result=7fc00001 errno=0
+func=exp2f op1=7f800001 result=7fc00001 errno=0 status=i
+func=exp2f op1=ff800001 result=7fc00001 errno=0 status=i
+func=exp2f op1=7f800000 result=7f800000 errno=0
+func=exp2f op1=7f7fffff result=7f800000 errno=ERANGE status=ox
+func=exp2f op1=ff800000 result=00000000 errno=0
+func=exp2f op1=ff7fffff result=00000000 errno=ERANGE status=ux
+func=exp2f op1=00000000 result=3f800000 errno=0
+func=exp2f op1=80000000 result=3f800000 errno=0
+func=exp2f op1=42fa0001 result=7e00002c.5c8 errno=0
+func=exp2f op1=42ffffff result=7f7fffa7.470 errno=0
+func=exp2f op1=43000000 result=7f800000 errno=ERANGE status=ox
+func=exp2f op1=43000001 result=7f800000 errno=ERANGE status=ox
+func=exp2f op1=c2fa0001 result=00ffffa7.470 errno=0
+func=exp2f op1=c2fc0000 result=00800000 errno=0
+func=exp2f op1=c2fc0001 result=007fffd3.a38 errno=0 status=ux
+func=exp2f op1=c3150000 result=00000001 errno=0
+func=exp2f op1=c3158000 result=00000000.800 errno=ERANGE status=ux
+func=exp2f op1=c3165432 result=00000000.4bd errno=ERANGE status=ux
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/expf.tst b/libc/AOR_v20.02/math/test/testcases/directed/expf.tst
new file mode 100644
index 000000000000..13ce50418f66
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/expf.tst
@@ -0,0 +1,24 @@
+; expf.tst - Directed test cases for expf
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=expf op1=7fc00001 result=7fc00001 errno=0
+func=expf op1=ffc00001 result=7fc00001 errno=0
+func=expf op1=7f800001 result=7fc00001 errno=0 status=i
+func=expf op1=ff800001 result=7fc00001 errno=0 status=i
+func=expf op1=7f800000 result=7f800000 errno=0
+func=expf op1=7f7fffff result=7f800000 errno=ERANGE status=ox
+func=expf op1=ff800000 result=00000000 errno=0
+func=expf op1=ff7fffff result=00000000 errno=ERANGE status=ux
+func=expf op1=00000000 result=3f800000 errno=0
+func=expf op1=80000000 result=3f800000 errno=0
+func=expf op1=42affff8 result=7ef87ed4.e0c errno=0
+func=expf op1=42b00008 result=7ef88698.f67 errno=0
+func=expf op1=42cffff8 result=7f800000 errno=ERANGE status=ox
+func=expf op1=42d00008 result=7f800000 errno=ERANGE status=ox
+func=expf op1=c2affff8 result=0041eecc.041 errno=0 status=ux
+func=expf op1=c2b00008 result=0041ecbc.95e errno=0 status=ux
+func=expf op1=c2cffff8 result=00000000 errno=ERANGE status=ux
+func=expf op1=c2d00008 result=00000000 errno=ERANGE status=ux
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/log.tst b/libc/AOR_v20.02/math/test/testcases/directed/log.tst
new file mode 100644
index 000000000000..f0cb8008a121
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/log.tst
@@ -0,0 +1,22 @@
+; Directed test cases for log
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=log op1=7ff80000.00000001 result=7ff80000.00000001 errno=0
+func=log op1=fff80000.00000001 result=7ff80000.00000001 errno=0
+func=log op1=7ff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=log op1=fff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=log op1=7ff00000.00000000 result=7ff00000.00000000 errno=0
+func=log op1=fff00000.00000000 result=7ff80000.00000001 errno=EDOM status=i
+func=log op1=7fefffff.ffffffff result=40862e42.fefa39ef.354 errno=0
+func=log op1=ffefffff.ffffffff result=7ff80000.00000001 errno=EDOM status=i
+func=log op1=3ff00000.00000000 result=00000000.00000000 errno=0
+func=log op1=bff00000.00000000 result=7ff80000.00000001 errno=EDOM status=i
+func=log op1=00000000.00000000 result=fff00000.00000000 errno=ERANGE status=z
+func=log op1=80000000.00000000 result=fff00000.00000000 errno=ERANGE status=z
+func=log op1=00000000.00000001 result=c0874385.446d71c3.639 errno=0
+func=log op1=80000000.00000001 result=7ff80000.00000001 errno=EDOM status=i
+func=log op1=40000000.00000000 result=3fe62e42.fefa39ef.358 errno=0
+func=log op1=3fe00000.00000000 result=bfe62e42.fefa39ef.358 errno=0
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/log2.tst b/libc/AOR_v20.02/math/test/testcases/directed/log2.tst
new file mode 100644
index 000000000000..702f2779b400
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/log2.tst
@@ -0,0 +1,22 @@
+; Directed test cases for log2
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=log2 op1=7ff80000.00000001 result=7ff80000.00000001 errno=0
+func=log2 op1=fff80000.00000001 result=7ff80000.00000001 errno=0
+func=log2 op1=7ff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=log2 op1=fff00000.00000001 result=7ff80000.00000001 errno=0 status=i
+func=log2 op1=7ff00000.00000000 result=7ff00000.00000000 errno=0
+func=log2 op1=fff00000.00000000 result=7ff80000.00000001 errno=EDOM status=i
+func=log2 op1=7fefffff.ffffffff result=408fffff.ffffffff.ffa errno=0
+func=log2 op1=ffefffff.ffffffff result=7ff80000.00000001 errno=EDOM status=i
+func=log2 op1=3ff00000.00000000 result=00000000.00000000 errno=0
+func=log2 op1=bff00000.00000000 result=7ff80000.00000001 errno=EDOM status=i
+func=log2 op1=00000000.00000000 result=fff00000.00000000 errno=ERANGE status=z
+func=log2 op1=80000000.00000000 result=fff00000.00000000 errno=ERANGE status=z
+func=log2 op1=00000000.00000001 result=c090c800.00000000 errno=0
+func=log2 op1=80000000.00000001 result=7ff80000.00000001 errno=EDOM status=i
+func=log2 op1=40000000.00000000 result=3ff00000.00000000 errno=0
+func=log2 op1=3fe00000.00000000 result=bff00000.00000000 errno=0
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/log2f.tst b/libc/AOR_v20.02/math/test/testcases/directed/log2f.tst
new file mode 100644
index 000000000000..2f1a01e93ee9
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/log2f.tst
@@ -0,0 +1,28 @@
+; log2f.tst - Directed test cases for log2f
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=log2f op1=7fc00001 result=7fc00001 errno=0
+func=log2f op1=ffc00001 result=7fc00001 errno=0
+func=log2f op1=7f800001 result=7fc00001 errno=0 status=i
+func=log2f op1=ff800001 result=7fc00001 errno=0 status=i
+func=log2f op1=ff810000 result=7fc00001 errno=0 status=i
+func=log2f op1=7f800000 result=7f800000 errno=0
+func=log2f op1=ff800000 result=7fc00001 errno=EDOM status=i
+func=log2f op1=3f800000 result=00000000 errno=0
+func=log2f op1=00000000 result=ff800000 errno=ERANGE status=z
+func=log2f op1=80000000 result=ff800000 errno=ERANGE status=z
+func=log2f op1=80000001 result=7fc00001 errno=EDOM status=i
+
+func=log2f op1=3f7d70a4 result=bc6d8f8b.7d4 error=0
+func=log2f op1=3f604189 result=be4394c8.395 error=0
+func=log2f op1=3f278034 result=bf1caa73.88e error=0
+func=log2f op1=3edd3c36 result=bf9af3b9.619 error=0
+func=log2f op1=3e61259a result=c00bdb95.650 error=0
+func=log2f op1=3f8147ae result=3c6b3267.d6a error=0
+func=log2f op1=3f8fbe77 result=3e2b5fe2.a1c error=0
+func=log2f op1=3fac3eea result=3edb4d5e.1fc error=0
+func=log2f op1=3fd6e632 result=3f3f5d3a.827 error=0
+func=log2f op1=40070838 result=3f89e055.a0a error=0
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/logf.tst b/libc/AOR_v20.02/math/test/testcases/directed/logf.tst
new file mode 100644
index 000000000000..d19cc154f363
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/logf.tst
@@ -0,0 +1,70 @@
+; logf.tst - Directed test cases for logf
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=logf op1=7fc00001 result=7fc00001 errno=0
+func=logf op1=ffc00001 result=7fc00001 errno=0
+func=logf op1=7f800001 result=7fc00001 errno=0 status=i
+func=logf op1=ff800001 result=7fc00001 errno=0 status=i
+func=logf op1=ff810000 result=7fc00001 errno=0 status=i
+func=logf op1=7f800000 result=7f800000 errno=0
+func=logf op1=ff800000 result=7fc00001 errno=EDOM status=i
+func=logf op1=3f800000 result=00000000 errno=0
+func=logf op1=00000000 result=ff800000 errno=ERANGE status=z
+func=logf op1=80000000 result=ff800000 errno=ERANGE status=z
+func=logf op1=80000001 result=7fc00001 errno=EDOM status=i
+
+; Directed tests for the special-case handling of log of things
+; very near 1
+func=logf op1=3f781e49 result=bd0016d9.4ae error=0
+func=logf op1=3f78e602 result=bce675e5.f31 error=0
+func=logf op1=3f844a18 result=3d07030e.ae1 error=0
+func=logf op1=3f79b55b result=bccbd88a.6cb error=0
+func=logf op1=3f7e2f5f result=bbe92452.74a error=0
+func=logf op1=3f7f1c03 result=bb6462c1.c2c error=0
+func=logf op1=3f78b213 result=bced23e2.f56 error=0
+func=logf op1=3f87d5c0 result=3d735847.b7a error=0
+func=logf op1=3f7fa6ad result=bab2c532.12d error=0
+func=logf op1=3f87c06a result=3d70d4b6.b5e error=0
+func=logf op1=3f79cf30 result=bcc88942.6e9 error=0
+func=logf op1=3f794c77 result=bcd94c6f.b1e error=0
+func=logf op1=3f835655 result=3cd2d8a0.0bf error=0
+func=logf op1=3f81b5c0 result=3c596d08.520 error=0
+func=logf op1=3f805e2f result=3b3c18d4.d2b error=0
+func=logf op1=3f7aa609 result=bcad0f90.fdb error=0
+func=logf op1=3f7a9091 result=bcafcd59.f83 error=0
+func=logf op1=3f7a7475 result=bcb36490.a0f error=0
+func=logf op1=3f823417 result=3c8bd287.fa6 error=0
+func=logf op1=3f7fbcc3 result=ba868bac.14c error=0
+func=logf op1=3f805fc9 result=3b3f4a76.169 error=0
+func=logf op1=3f833d43 result=3cccbc4f.cb7 error=0
+func=logf op1=3f7cb1de result=bc54e91e.6b5 error=0
+func=logf op1=3f7f2793 result=bb58c8af.bfc error=0
+func=logf op1=3f7bb8c3 result=bc8a0fc9.93c error=0
+func=logf op1=3f81d349 result=3c67fe09.42e error=0
+func=logf op1=3f7c254d result=bc788cf4.610 error=0
+func=logf op1=3f7f789d result=bb0786d9.6c6 error=0
+func=logf op1=3f7ed1f2 result=bb97605f.963 error=0
+func=logf op1=3f826067 result=3c96b4af.5e1 error=0
+func=logf op1=3f821a68 result=3c8581f9.dac error=0
+func=logf op1=3f864e1a result=3d44f368.e66 error=0
+func=logf op1=3f7fea3d result=b9ae1f66.b58 error=0
+func=logf op1=3f7cf4f5 result=bc43ed76.1c5 error=0
+func=logf op1=3f84c223 result=3d15814e.36d error=0
+func=logf op1=3f7dae6d result=bc1511d5.0aa error=0
+func=logf op1=3f7c0a3c result=bc7f6c0d.758 error=0
+func=logf op1=3f858b22 result=3d2da861.f36 error=0
+func=logf op1=3f85d7c7 result=3d36d490.ee9 error=0
+func=logf op1=3f7f2109 result=bb5f5851.2ed error=0
+func=logf op1=3f83809c result=3cdd23f7.6b1 error=0
+func=logf op1=3f83d96e result=3cf2b9c8.0b1 error=0
+func=logf op1=3f86ca84 result=3d53bee8.53f error=0
+func=logf op1=3f83548e result=3cd269c3.39d error=0
+func=logf op1=3f7c199c result=bc7b84b6.0da error=0
+func=logf op1=3f83133f result=3cc27c0a.9dd error=0
+func=logf op1=3f7c97b4 result=bc5b89dd.399 error=0
+func=logf op1=3f810bc1 result=3c05553c.011 error=0
+func=logf op1=3f7dadb8 result=bc153f7e.fbb error=0
+func=logf op1=3f87be56 result=3d709602.538 error=0
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/pow.tst b/libc/AOR_v20.02/math/test/testcases/directed/pow.tst
new file mode 100644
index 000000000000..474cc377e5f0
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/pow.tst
@@ -0,0 +1,1419 @@
+; Directed test cases for pow
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=pow op1=00000000.00000000 op2=00000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=00000000.00000001 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=00100000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=1fffffff.ffffffff result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=3bdfffff.ffffffff result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=3be00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=3fe00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=3ff00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=40000000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=40080000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=40120000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=40180000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=407ff800.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=408ff800.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=43dfffff.ffffffff result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=43e00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=7fefffff.ffffffff result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=7ff00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=7ff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=00000000.00000000 op2=7ff80000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=80000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=80000000.00000001 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=80100000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=9fffffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=bbdfffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=bbe00000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=bfe00000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=bff00000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=c0000000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=c0080000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=c0120000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=c0180000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=c07f3000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=c090ce00.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=c3dfffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=c3e00000.00000000 result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=ffefffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=z
+func=pow op1=00000000.00000000 op2=fff00000.00000000 result=7ff00000.00000000 errno=0
+func=pow op1=00000000.00000000 op2=fff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=00000000.00000000 op2=fff80000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=00000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=00000000.00000001 result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=00100000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=1fffffff.ffffffff result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=3bdfffff.ffffffff result=3fefffff.ffffffff.d17 errno=0
+func=pow op1=00000000.00000001 op2=3be00000.00000000 result=3fefffff.ffffffff.d17 errno=0
+func=pow op1=00000000.00000001 op2=3fe00000.00000000 result=1e600000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=3ff00000.00000000 result=00000000.00000001 errno=0 status=u
+func=pow op1=00000000.00000001 op2=40000000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00000000.00000001 op2=40080000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00000000.00000001 op2=40120000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00000000.00000001 op2=40180000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00000000.00000001 op2=407ff800.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00000000.00000001 op2=408ff800.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00000000.00000001 op2=43dfffff.ffffffff result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00000000.00000001 op2=43e00000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00000000.00000001 op2=7fefffff.ffffffff result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00000000.00000001 op2=7ff00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=7ff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=00000000.00000001 op2=7ff80000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=80000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=80000000.00000001 result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=80100000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=9fffffff.ffffffff result=3ff00000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=bbdfffff.ffffffff result=3ff00000.00000000.174 errno=0
+func=pow op1=00000000.00000001 op2=bbe00000.00000000 result=3ff00000.00000000.174 errno=0
+func=pow op1=00000000.00000001 op2=bfe00000.00000000 result=61800000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=bff00000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=c0000000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=c0080000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=c0120000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=c0180000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=c07f3000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=c090ce00.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=c3dfffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=c3e00000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=ffefffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00000000.00000001 op2=fff00000.00000000 result=7ff00000.00000000 errno=0
+func=pow op1=00000000.00000001 op2=fff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=00000000.00000001 op2=fff80000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=00000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=00000000.00000001 result=3ff00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=00100000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=1fffffff.ffffffff result=3ff00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=3bdfffff.ffffffff result=3fefffff.ffffffff.d3b errno=0
+func=pow op1=00100000.00000000 op2=3be00000.00000000 result=3fefffff.ffffffff.d3b errno=0
+func=pow op1=00100000.00000000 op2=3fe00000.00000000 result=20000000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=3ff00000.00000000 result=00100000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=40000000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00100000.00000000 op2=40080000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00100000.00000000 op2=40120000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00100000.00000000 op2=40180000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00100000.00000000 op2=407ff800.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00100000.00000000 op2=408ff800.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00100000.00000000 op2=43dfffff.ffffffff result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00100000.00000000 op2=43e00000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00100000.00000000 op2=7fefffff.ffffffff result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=00100000.00000000 op2=7ff00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=7ff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=00100000.00000000 op2=7ff80000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=80000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=80000000.00000001 result=3ff00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=80100000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=9fffffff.ffffffff result=3ff00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=bbdfffff.ffffffff result=3ff00000.00000000.162 errno=0
+func=pow op1=00100000.00000000 op2=bbe00000.00000000 result=3ff00000.00000000.162 errno=0
+func=pow op1=00100000.00000000 op2=bfe00000.00000000 result=5fe00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=bff00000.00000000 result=7fd00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=c0000000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00100000.00000000 op2=c0080000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00100000.00000000 op2=c0120000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00100000.00000000 op2=c0180000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00100000.00000000 op2=c07f3000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00100000.00000000 op2=c090ce00.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00100000.00000000 op2=c3dfffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00100000.00000000 op2=c3e00000.00000000 result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00100000.00000000 op2=ffefffff.ffffffff result=7ff00000.00000000 errno=ERANGE status=o
+func=pow op1=00100000.00000000 op2=fff00000.00000000 result=7ff00000.00000000 errno=0
+func=pow op1=00100000.00000000 op2=fff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=00100000.00000000 op2=fff80000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=00000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=00000000.00000001 result=3ff00000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=00100000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=1fffffff.ffffffff result=3ff00000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=3bdfffff.ffffffff result=3fefffff.ffffffff.e9d errno=0
+func=pow op1=1fffffff.ffffffff op2=3be00000.00000000 result=3fefffff.ffffffff.e9d errno=0
+func=pow op1=1fffffff.ffffffff op2=3fe00000.00000000 result=2ff6a09e.667f3bcc.360 errno=0
+func=pow op1=1fffffff.ffffffff op2=3ff00000.00000000 result=1fffffff.ffffffff errno=0
+func=pow op1=1fffffff.ffffffff op2=40000000.00000000 result=000fffff.ffffffff errno=0 status=u
+func=pow op1=1fffffff.ffffffff op2=40080000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=1fffffff.ffffffff op2=40120000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=1fffffff.ffffffff op2=40180000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=1fffffff.ffffffff op2=407ff800.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=1fffffff.ffffffff op2=408ff800.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=1fffffff.ffffffff op2=43dfffff.ffffffff result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=1fffffff.ffffffff op2=43e00000.00000000 result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=1fffffff.ffffffff op2=7fefffff.ffffffff result=00000000.00000000 errno=ERANGE status=u
+func=pow op1=1fffffff.ffffffff op2=7ff00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=7ff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=1fffffff.ffffffff op2=7ff80000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=80000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=80000000.00000001 result=3ff00000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=80100000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=9fffffff.ffffffff result=3ff00000.00000000 errno=0
+func=pow op1=1fffffff.ffffffff op2=bbdfffff.ffffffff result=3ff00000.00000000.0b1 errno=0
+func=pow op1=1fffffff.ffffffff op2=bbe00000.00000000 result=3ff00000.00000000.0b1 errno=0
+func=pow op1=1fffffff.ffffffff op2=bfe00000.00000000 result=4fe6a09e.667f3bcc.eb0 errno=0
+func=pow op1=1fffffff.ffffffff op2=bff00000.00000000 result=5fe00000.00000000.800 errno=0
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+func=pow op1=fff00000.00000000 op2=80000000.00000001 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=80100000.00000000 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=9fffffff.ffffffff result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=bbdfffff.ffffffff result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=bbe00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=bfe00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=bff00000.00000000 result=80000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=c0000000.00000000 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=c0080000.00000000 result=80000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=c0120000.00000000 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=c0180000.00000000 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=c07f3000.00000000 result=80000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=c090ce00.00000000 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=c3dfffff.ffffffff result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=c3e00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=ffefffff.ffffffff result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=fff00000.00000000 result=00000000.00000000 errno=0
+func=pow op1=fff00000.00000000 op2=fff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000000 op2=fff80000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=fff00000.00000001 op2=00000000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=00000000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=00100000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=1fffffff.ffffffff result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=3bdfffff.ffffffff result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=3be00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=3fe00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=3ff00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=40000000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=40080000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=40120000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=40180000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=407ff800.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=408ff800.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=43dfffff.ffffffff result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=43e00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=7fefffff.ffffffff result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=7ff00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=7ff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=7ff80000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=80000000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=80000000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=80100000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=9fffffff.ffffffff result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=bbdfffff.ffffffff result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=bbe00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=bfe00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=bff00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=c0000000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=c0080000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=c0120000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=c0180000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=c07f3000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=c090ce00.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=c3dfffff.ffffffff result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=c3e00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=ffefffff.ffffffff result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=fff00000.00000000 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=fff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff00000.00000001 op2=fff80000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff80000.00000001 op2=00000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=00000000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=00100000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=1fffffff.ffffffff result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=3bdfffff.ffffffff result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=3be00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=3fe00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=3ff00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=40000000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=40080000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=40120000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=40180000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=407ff800.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=408ff800.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=43dfffff.ffffffff result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=43e00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=7fefffff.ffffffff result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=7ff00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=7ff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff80000.00000001 op2=7ff80000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=80000000.00000000 result=3ff00000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=80000000.00000001 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=80100000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=9fffffff.ffffffff result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=bbdfffff.ffffffff result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=bbe00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=bfe00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=bff00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=c0000000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=c0080000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=c0120000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=c0180000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=c07f3000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=c090ce00.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=c3dfffff.ffffffff result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=c3e00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=ffefffff.ffffffff result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=fff00000.00000000 result=7ff80000.00000000 errno=0
+func=pow op1=fff80000.00000001 op2=fff00000.00000001 result=7ff80000.00000000 errno=0 status=i
+func=pow op1=fff80000.00000001 op2=fff80000.00000001 result=7ff80000.00000000 errno=0
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/powf.tst b/libc/AOR_v20.02/math/test/testcases/directed/powf.tst
new file mode 100644
index 000000000000..9719b1f991ed
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/powf.tst
@@ -0,0 +1,247 @@
+; powf.tst - Directed test cases for powf
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+func=powf op1=7f800001 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=7fc00001 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=ffc00001 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=7f800000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=40800000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=40400000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=3f000000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=00000000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=80000000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=bf000000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=c0400000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=c0800000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=ff800000 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=7f800001 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=7fc00001 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=ffc00001 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=7f800000 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=40800000 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=40400000 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=3f000000 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=00000000 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=80000000 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=bf000000 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=c0400000 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=c0800000 result=7fc00001 errno=0 status=i
+func=powf op1=ff800001 op2=ff800000 result=7fc00001 errno=0 status=i
+func=powf op1=7fc00001 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=7fc00001 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=7fc00001 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=7fc00001 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=7fc00001 op2=7f800000 result=7fc00001 errno=0
+func=powf op1=7fc00001 op2=40800000 result=7fc00001 errno=0
+func=powf op1=7fc00001 op2=40400000 result=7fc00001 errno=0
+func=powf op1=7fc00001 op2=3f000000 result=7fc00001 errno=0
+func=powf op1=7fc00001 op2=00000000 result=3f800000 errno=0
+func=powf op1=7fc00001 op2=80000000 result=3f800000 errno=0
+func=powf op1=7fc00001 op2=bf000000 result=7fc00001 errno=0
+func=powf op1=7fc00001 op2=c0400000 result=7fc00001 errno=0
+func=powf op1=7fc00001 op2=c0800000 result=7fc00001 errno=0
+func=powf op1=7fc00001 op2=ff800000 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=ffc00001 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=ffc00001 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=7f800000 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=40800000 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=40400000 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=3f000000 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=00000000 result=3f800000 errno=0
+func=powf op1=ffc00001 op2=80000000 result=3f800000 errno=0
+func=powf op1=ffc00001 op2=bf000000 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=c0400000 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=c0800000 result=7fc00001 errno=0
+func=powf op1=ffc00001 op2=ff800000 result=7fc00001 errno=0
+func=powf op1=7f800000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=7f800000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=7f800000 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=7f800000 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=7f800000 op2=7f800000 result=7f800000 errno=0
+func=powf op1=7f800000 op2=40800000 result=7f800000 errno=0
+func=powf op1=7f800000 op2=40400000 result=7f800000 errno=0
+func=powf op1=7f800000 op2=3f000000 result=7f800000 errno=0
+func=powf op1=7f800000 op2=00000001 result=7f800000 errno=0
+func=powf op1=7f800000 op2=00000000 result=3f800000 errno=0
+func=powf op1=7f800000 op2=80000000 result=3f800000 errno=0
+func=powf op1=7f800000 op2=bf000000 result=00000000 errno=0
+func=powf op1=7f800000 op2=c0400000 result=00000000 errno=0
+func=powf op1=7f800000 op2=c0800000 result=00000000 errno=0
+func=powf op1=7f800000 op2=ff800000 result=00000000 errno=0
+func=powf op1=40800000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=40800000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=40800000 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=40800000 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=40800000 op2=7f800000 result=7f800000 errno=0
+func=powf op1=40800000 op2=40800000 result=43800000 errno=0
+func=powf op1=40800000 op2=40400000 result=42800000 errno=0
+func=powf op1=40800000 op2=3f000000 result=40000000 errno=0
+func=powf op1=40800000 op2=00000000 result=3f800000 errno=0
+func=powf op1=40800000 op2=80000000 result=3f800000 errno=0
+func=powf op1=40800000 op2=bf000000 result=3f000000 errno=0
+func=powf op1=40800000 op2=c0400000 result=3c800000 errno=0
+func=powf op1=40800000 op2=c0800000 result=3b800000 errno=0
+func=powf op1=40800000 op2=ff800000 result=00000000 errno=0
+func=powf op1=3f800000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=3f800000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=3f800000 op2=7fc00001 result=3f800000 errno=0
+func=powf op1=3f800000 op2=ffc00001 result=3f800000 errno=0
+func=powf op1=3f800000 op2=7f800000 result=3f800000 errno=0
+func=powf op1=3f800000 op2=40800000 result=3f800000 errno=0
+func=powf op1=3f800000 op2=40400000 result=3f800000 errno=0
+func=powf op1=3f800000 op2=3f000000 result=3f800000 errno=0
+func=powf op1=3f800000 op2=00000000 result=3f800000 errno=0
+func=powf op1=3f800000 op2=80000000 result=3f800000 errno=0
+func=powf op1=3f800000 op2=bf000000 result=3f800000 errno=0
+func=powf op1=3f800000 op2=c0400000 result=3f800000 errno=0
+func=powf op1=3f800000 op2=c0800000 result=3f800000 errno=0
+func=powf op1=3f800000 op2=ff800000 result=3f800000 errno=0
+func=powf op1=3e800000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=3e800000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=3e800000 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=3e800000 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=3e800000 op2=7f800000 result=00000000 errno=0
+func=powf op1=3e800000 op2=40800000 result=3b800000 errno=0
+func=powf op1=3e800000 op2=40400000 result=3c800000 errno=0
+func=powf op1=3e800000 op2=3f000000 result=3f000000 errno=0
+func=powf op1=3e800000 op2=00000000 result=3f800000 errno=0
+func=powf op1=3e800000 op2=80000000 result=3f800000 errno=0
+func=powf op1=3e800000 op2=bf000000 result=40000000 errno=0
+func=powf op1=3e800000 op2=c0400000 result=42800000 errno=0
+func=powf op1=3e800000 op2=c0800000 result=43800000 errno=0
+func=powf op1=3e800000 op2=ff800000 result=7f800000 errno=0
+func=powf op1=00000001 op2=bf800000 result=7f800000 errno=ERANGE status=ox
+func=powf op1=00000000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=00000000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=00000000 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=00000000 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=00000000 op2=7f800000 result=00000000 errno=0
+func=powf op1=00000000 op2=40800000 result=00000000 errno=0
+func=powf op1=00000000 op2=40400000 result=00000000 errno=0
+func=powf op1=00000000 op2=3f000000 result=00000000 errno=0
+func=powf op1=00000000 op2=00000000 result=3f800000 errno=0
+func=powf op1=00000000 op2=80000000 result=3f800000 errno=0
+func=powf op1=00000000 op2=bf000000 result=7f800000 errno=ERANGE status=z
+func=powf op1=00000000 op2=c0400000 result=7f800000 errno=ERANGE status=z
+func=powf op1=00000000 op2=c0800000 result=7f800000 errno=ERANGE status=z
+func=powf op1=00000000 op2=ff800000 result=7f800000 errno=ERANGE
+func=powf op1=80000000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=80000000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=80000000 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=80000000 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=80000000 op2=7f800000 result=00000000 errno=0
+func=powf op1=80000000 op2=40800000 result=00000000 errno=0
+func=powf op1=80000000 op2=40400000 result=80000000 errno=0
+func=powf op1=80000000 op2=3f000000 result=00000000 errno=0
+func=powf op1=80000000 op2=00000000 result=3f800000 errno=0
+func=powf op1=80000000 op2=80000000 result=3f800000 errno=0
+func=powf op1=80000000 op2=bf000000 result=7f800000 errno=ERANGE status=z
+func=powf op1=80000000 op2=c0400000 result=ff800000 errno=ERANGE status=z
+func=powf op1=80000000 op2=c0800000 result=7f800000 errno=ERANGE status=z
+func=powf op1=80000000 op2=ff800000 result=7f800000 errno=ERANGE
+func=powf op1=be800000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=be800000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=be800000 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=be800000 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=be800000 op2=7f800000 result=00000000 errno=0
+func=powf op1=be800000 op2=40800000 result=3b800000 errno=0
+func=powf op1=be800000 op2=40400000 result=bc800000 errno=0
+func=powf op1=be800000 op2=3f000000 result=7fc00001 errno=EDOM status=i
+func=powf op1=be800000 op2=00000000 result=3f800000 errno=0
+func=powf op1=be800000 op2=80000000 result=3f800000 errno=0
+func=powf op1=be800000 op2=bf000000 result=7fc00001 errno=EDOM status=i
+func=powf op1=be800000 op2=c0400000 result=c2800000 errno=0
+func=powf op1=be800000 op2=c0800000 result=43800000 errno=0
+func=powf op1=be800000 op2=ff800000 result=7f800000 errno=0
+func=powf op1=bf800000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=bf800000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=bf800000 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=bf800000 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=bf800000 op2=7f800000 result=3f800000 errno=0
+func=powf op1=bf800000 op2=40800000 result=3f800000 errno=0
+func=powf op1=bf800000 op2=40400000 result=bf800000 errno=0
+func=powf op1=bf800000 op2=3f000000 result=7fc00001 errno=EDOM status=i
+func=powf op1=bf800000 op2=00000000 result=3f800000 errno=0
+func=powf op1=bf800000 op2=80000000 result=3f800000 errno=0
+func=powf op1=bf800000 op2=bf000000 result=7fc00001 errno=EDOM status=i
+func=powf op1=bf800000 op2=c0400000 result=bf800000 errno=0
+func=powf op1=bf800000 op2=c0800000 result=3f800000 errno=0
+func=powf op1=bf800000 op2=ff800000 result=3f800000 errno=0
+func=powf op1=c0800000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=c0800000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=c0800000 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=c0800000 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=c0800000 op2=7f800000 result=7f800000 errno=0
+func=powf op1=c0800000 op2=40800000 result=43800000 errno=0
+func=powf op1=c0800000 op2=40400000 result=c2800000 errno=0
+func=powf op1=c0800000 op2=3f000000 result=7fc00001 errno=EDOM status=i
+func=powf op1=c0800000 op2=00000000 result=3f800000 errno=0
+func=powf op1=c0800000 op2=80000000 result=3f800000 errno=0
+func=powf op1=c0800000 op2=bf000000 result=7fc00001 errno=EDOM status=i
+func=powf op1=c0800000 op2=c0400000 result=bc800000 errno=0
+func=powf op1=c0800000 op2=c0800000 result=3b800000 errno=0
+func=powf op1=c0800000 op2=ff800000 result=00000000 errno=0
+func=powf op1=ff800000 op2=7f800001 result=7fc00001 errno=0 status=i
+func=powf op1=ff800000 op2=ff800001 result=7fc00001 errno=0 status=i
+func=powf op1=ff800000 op2=7fc00001 result=7fc00001 errno=0
+func=powf op1=ff800000 op2=ffc00001 result=7fc00001 errno=0
+func=powf op1=ff800000 op2=7f800000 result=7f800000 errno=0
+func=powf op1=ff800000 op2=40800000 result=7f800000 errno=0
+func=powf op1=ff800000 op2=40400000 result=ff800000 errno=0
+func=powf op1=ff800000 op2=3f000000 result=7f800000 errno=0
+func=powf op1=ff800000 op2=00000000 result=3f800000 errno=0
+func=powf op1=ff800000 op2=80000000 result=3f800000 errno=0
+func=powf op1=ff800000 op2=bf000000 result=00000000 errno=0
+func=powf op1=ff800000 op2=c0400000 result=80000000 errno=0
+func=powf op1=ff800000 op2=c0800000 result=00000000 errno=0
+func=powf op1=ff800000 op2=ff800000 result=00000000 errno=0
+
+
+func=powf op1=36c27f9d op2=4109fa51 result=00000000 errno=ERANGE status=ux
+func=powf op1=351738cd op2=c0c55691 result=7f800000 errno=ERANGE status=ox
+func=powf op1=42836035 op2=41a99f40 result=7f800000 errno=ERANGE status=ox
+func=powf op1=32bd53f3 op2=40bcba58 result=00000000 errno=ERANGE status=ux
+func=powf op1=32dc5bff op2=40be62ea result=00000000 errno=ERANGE status=ux
+func=powf op1=3a8a3f66 op2=4172bd43 result=00000000 errno=ERANGE status=ux
+func=powf op1=28f0e770 op2=c035b4ca result=7f800000 errno=ERANGE status=ox
+func=powf op1=40886699 op2=c28f703a result=00000000 errno=ERANGE status=ux
+func=powf op1=414bd593 op2=c22370cf result=00000000 errno=ERANGE status=ux
+func=powf op1=3a2f1163 op2=c1422d45 result=7f800000 errno=ERANGE status=ox
+func=powf op1=434f5cf3 op2=41851272 result=7f800000 errno=ERANGE status=ox
+func=powf op1=2e0e27a4 op2=c06b13f5 result=7f800000 errno=ERANGE status=ox
+func=powf op1=39aef7a6 op2=414fd60a result=00000000 errno=ERANGE status=ux
+func=powf op1=21c80729 op2=c00a04ab result=7f800000 errno=ERANGE status=ox
+func=powf op1=42455a4b op2=c1d55905 result=00000000 errno=ERANGE status=ux
+func=powf op1=2d173e0b op2=c05ee797 result=7f800000 errno=ERANGE status=ox
+func=powf op1=452edf9a op2=4132dd7f result=7f800000 errno=ERANGE status=ox
+func=powf op1=406bf67b op2=c29f5f12 result=00000000 errno=ERANGE status=ux
+func=powf op1=2d82a6fc op2=4085779e result=00000000 errno=ERANGE status=ux
+func=powf op1=4551f827 op2=41304516 result=7f800000 errno=ERANGE status=ox
+func=powf op1=3a917c51 op2=41726c0a result=00000001.37f errno=0 status=ux
+; iso c allows both errno=ERANGE and errno=0
+;func=powf op1=3b19bbaa op2=4188e6fb result=00000000.b5f errno=0 status=ux
+;func=powf op1=4088bd18 op2=c28ef056 result=00000000.986 errno=0 status=ux
+func=powf op1=3f7ffd76 op2=4a09221e result=00aa9d24.3ad error=0
+
+func=powf op1=007fffff op2=bf000001 result=5f00002c.2b2 error=0
+func=powf op1=000007ff op2=bf000001 result=62000830.96f error=0
+func=powf op1=007fffff op2=80800001 result=3f800000.000 error=0
+func=powf op1=00000000 op2=800007ff result=7f800000 errno=ERANGE status=z
+func=powf op1=00000000 op2=000007ff result=00000000 error=0
+func=powf op1=bf800000 op2=ff7fffff result=3f800000 error=0
+func=powf op1=2e4e4f30 op2=406b0dc2 result=007e9c59.eb4 errno=0 status=u
+
+; SDCOMP-25549: ensure the biggest overflow case possible is not
+; mishandled. Also check the analogous underflow, and also ensure that
+; our massive-overflow checks do not affect numbers _just within_ the
+; range.
+func=powf op1=7f7fffff op2=7f7fffff result=7f800000 error=overflow
+func=powf op1=7f7fffff op2=ff7fffff result=00000000 error=underflow
+func=powf op1=54cb3000 op2=403fffff result=7f7fffb2.a95 error=0
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/sincosf.tst b/libc/AOR_v20.02/math/test/testcases/directed/sincosf.tst
new file mode 100644
index 000000000000..d22fd9802694
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/sincosf.tst
@@ -0,0 +1,52 @@
+; Directed test cases for SP sincos
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+
+func=sincosf_sinf op1=7fc00001 result=7fc00001 errno=0
+func=sincosf_sinf op1=ffc00001 result=7fc00001 errno=0
+func=sincosf_sinf op1=7f800001 result=7fc00001 errno=0 status=i
+func=sincosf_sinf op1=ff800001 result=7fc00001 errno=0 status=i
+func=sincosf_sinf op1=7f800000 result=7fc00001 errno=EDOM status=i
+func=sincosf_sinf op1=ff800000 result=7fc00001 errno=EDOM status=i
+func=sincosf_sinf op1=00000000 result=00000000 errno=0
+func=sincosf_sinf op1=80000000 result=80000000 errno=0
+func=sincosf_sinf op1=c70d39a1 result=be37fad5.7ed errno=0
+func=sincosf_sinf op1=46427f1b result=3f352d80.f9b error=0
+func=sincosf_sinf op1=4647e568 result=3f352da9.7be error=0
+func=sincosf_sinf op1=46428bac result=bf352dea.924 error=0
+func=sincosf_sinf op1=4647f1f9 result=bf352e13.146 error=0
+func=sincosf_sinf op1=4647fe8a result=3f352e7c.ac9 error=0
+func=sincosf_sinf op1=45d8d7f1 result=3f35097b.cb0 error=0
+func=sincosf_sinf op1=45d371a4 result=bf350990.102 error=0
+func=sincosf_sinf op1=45ce0b57 result=3f3509a4.554 error=0
+func=sincosf_sinf op1=45d35882 result=3f3509f9.bdb error=0
+func=sincosf_sinf op1=45cdf235 result=bf350a0e.02c error=0
+
+func=sincosf_cosf op1=7fc00001 result=7fc00001 errno=0
+func=sincosf_cosf op1=ffc00001 result=7fc00001 errno=0
+func=sincosf_cosf op1=7f800001 result=7fc00001 errno=0 status=i
+func=sincosf_cosf op1=ff800001 result=7fc00001 errno=0 status=i
+func=sincosf_cosf op1=7f800000 result=7fc00001 errno=EDOM status=i
+func=sincosf_cosf op1=ff800000 result=7fc00001 errno=EDOM status=i
+func=sincosf_cosf op1=00000000 result=3f800000 errno=0
+func=sincosf_cosf op1=80000000 result=3f800000 errno=0
+func=sincosf_cosf op1=46427f1b result=3f34dc5c.565 error=0
+func=sincosf_cosf op1=4647e568 result=3f34dc33.c1f error=0
+func=sincosf_cosf op1=46428bac result=bf34dbf2.8e3 error=0
+func=sincosf_cosf op1=4647f1f9 result=bf34dbc9.f9b error=0
+func=sincosf_cosf op1=4647fe8a result=3f34db60.313 error=0
+func=sincosf_cosf op1=45d8d7f1 result=bf35006a.7fd error=0
+func=sincosf_cosf op1=45d371a4 result=3f350056.39b error=0
+func=sincosf_cosf op1=45ce0b57 result=bf350041.f38 error=0
+func=sincosf_cosf op1=45d35882 result=bf34ffec.868 error=0
+func=sincosf_cosf op1=45cdf235 result=3f34ffd8.404 error=0
+
+; no underflow
+func=sincosf_sinf op1=17800000 result=17800000.000
+func=sincosf_cosf op1=17800000 result=3f800000.000
+; underflow
+func=sincosf_sinf op1=00400000 result=00400000.000 status=ux
+func=sincosf_cosf op1=00400000 result=3f800000.000 status=ux
diff --git a/libc/AOR_v20.02/math/test/testcases/directed/sinf.tst b/libc/AOR_v20.02/math/test/testcases/directed/sinf.tst
new file mode 100644
index 000000000000..022bf1424879
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/directed/sinf.tst
@@ -0,0 +1,29 @@
+; sinf.tst - Directed test cases for SP sine
+;
+; Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+; See https://llvm.org/LICENSE.txt for license information.
+; SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+
+func=sinf op1=7fc00001 result=7fc00001 errno=0
+func=sinf op1=ffc00001 result=7fc00001 errno=0
+func=sinf op1=7f800001 result=7fc00001 errno=0 status=i
+func=sinf op1=ff800001 result=7fc00001 errno=0 status=i
+func=sinf op1=7f800000 result=7fc00001 errno=EDOM status=i
+func=sinf op1=ff800000 result=7fc00001 errno=EDOM status=i
+func=sinf op1=00000000 result=00000000 errno=0
+func=sinf op1=80000000 result=80000000 errno=0
+; Directed test for a failure I found while developing mathbench
+func=sinf op1=c70d39a1 result=be37fad5.7ed errno=0
+; SDCOMP-26094: check sinf in the cases for which the range reducer
+; returns values furthest beyond its nominal upper bound of pi/4.
+func=sinf op1=46427f1b result=3f352d80.f9b error=0
+func=sinf op1=4647e568 result=3f352da9.7be error=0
+func=sinf op1=46428bac result=bf352dea.924 error=0
+func=sinf op1=4647f1f9 result=bf352e13.146 error=0
+func=sinf op1=4647fe8a result=3f352e7c.ac9 error=0
+func=sinf op1=45d8d7f1 result=3f35097b.cb0 error=0
+func=sinf op1=45d371a4 result=bf350990.102 error=0
+func=sinf op1=45ce0b57 result=3f3509a4.554 error=0
+func=sinf op1=45d35882 result=3f3509f9.bdb error=0
+func=sinf op1=45cdf235 result=bf350a0e.02c error=0
diff --git a/libc/AOR_v20.02/math/test/testcases/random/double.tst b/libc/AOR_v20.02/math/test/testcases/random/double.tst
new file mode 100644
index 000000000000..3c9ab6b16a71
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/random/double.tst
@@ -0,0 +1,11 @@
+!! double.tst - Random test case specification for DP functions
+!!
+!! Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+!! See https://llvm.org/LICENSE.txt for license information.
+!! SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+test exp 10000
+test exp2 10000
+test log 10000
+test log2 10000
+test pow 40000
diff --git a/libc/AOR_v20.02/math/test/testcases/random/float.tst b/libc/AOR_v20.02/math/test/testcases/random/float.tst
new file mode 100644
index 000000000000..c142d63cd594
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/testcases/random/float.tst
@@ -0,0 +1,16 @@
+!! single.tst - Random test case specification for SP functions
+!!
+!! Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+!! See https://llvm.org/LICENSE.txt for license information.
+!! SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+test sinf 10000
+test cosf 10000
+test sincosf_sinf 5000
+test sincosf_cosf 5000
+test tanf 10000
+test expf 10000
+test exp2f 10000
+test logf 10000
+test log2f 10000
+test powf 10000
diff --git a/libc/AOR_v20.02/math/test/traces/exp.txt b/libc/AOR_v20.02/math/test/traces/exp.txt
new file mode 100644
index 000000000000..cb067d5174b9
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/traces/exp.txt
@@ -0,0 +1,16000 @@
+0x1.0bc8e7ca4ae1bp+0
+0x1.f9a012f44a109p-1
+-0x1.87a0e64ca4704p-15
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+0x1.45fa2a0b71c2bp-1
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+0x1.55ed18823552ep-1
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diff --git a/libc/AOR_v20.02/math/test/traces/sincosf.txt b/libc/AOR_v20.02/math/test/traces/sincosf.txt
new file mode 100644
index 000000000000..33de0c7ab9e3
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/traces/sincosf.txt
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diff --git a/libc/AOR_v20.02/math/test/ulp.c b/libc/AOR_v20.02/math/test/ulp.c
new file mode 100644
index 000000000000..3821986f7cb4
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/ulp.c
@@ -0,0 +1,852 @@
+/*
+ * ULP error checking tool for math functions.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <ctype.h>
+#include <fenv.h>
+#include <float.h>
+#include <math.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "mathlib.h"
+
+/* Don't depend on mpfr by default. */
+#ifndef USE_MPFR
+# define USE_MPFR 0
+#endif
+#if USE_MPFR
+# include <mpfr.h>
+#endif
+
+#ifndef WANT_VMATH
+/* Enable the build of vector math code. */
+# define WANT_VMATH 1
+#endif
+
+static inline uint64_t
+asuint64 (double f)
+{
+ union
+ {
+ double f;
+ uint64_t i;
+ } u = {f};
+ return u.i;
+}
+
+static inline double
+asdouble (uint64_t i)
+{
+ union
+ {
+ uint64_t i;
+ double f;
+ } u = {i};
+ return u.f;
+}
+
+static inline uint32_t
+asuint (float f)
+{
+ union
+ {
+ float f;
+ uint32_t i;
+ } u = {f};
+ return u.i;
+}
+
+static inline float
+asfloat (uint32_t i)
+{
+ union
+ {
+ uint32_t i;
+ float f;
+ } u = {i};
+ return u.f;
+}
+
+static uint64_t seed = 0x0123456789abcdef;
+static uint64_t
+rand64 (void)
+{
+ seed = 6364136223846793005ull * seed + 1;
+ return seed ^ (seed >> 32);
+}
+
+/* Uniform random in [0,n]. */
+static uint64_t
+randn (uint64_t n)
+{
+ uint64_t r, m;
+
+ if (n == 0)
+ return 0;
+ n++;
+ if (n == 0)
+ return rand64 ();
+ for (;;)
+ {
+ r = rand64 ();
+ m = r % n;
+ if (r - m <= -n)
+ return m;
+ }
+}
+
+struct gen
+{
+ uint64_t start;
+ uint64_t len;
+ uint64_t start2;
+ uint64_t len2;
+ uint64_t off;
+ uint64_t step;
+ uint64_t cnt;
+};
+
+struct args_f1
+{
+ float x;
+};
+
+struct args_f2
+{
+ float x;
+ float x2;
+};
+
+struct args_d1
+{
+ double x;
+};
+
+struct args_d2
+{
+ double x;
+ double x2;
+};
+
+/* result = y + tail*2^ulpexp. */
+struct ret_f
+{
+ float y;
+ double tail;
+ int ulpexp;
+ int ex;
+ int ex_may;
+};
+
+struct ret_d
+{
+ double y;
+ double tail;
+ int ulpexp;
+ int ex;
+ int ex_may;
+};
+
+static inline uint64_t
+next1 (struct gen *g)
+{
+ /* For single argument use randomized incremental steps,
+ that produce dense sampling without collisions and allow
+ testing all inputs in a range. */
+ uint64_t r = g->start + g->off;
+ g->off += g->step + randn (g->step / 2);
+ if (g->off > g->len)
+ g->off -= g->len; /* hack. */
+ return r;
+}
+
+static inline uint64_t
+next2 (uint64_t *x2, struct gen *g)
+{
+ /* For two arguments use uniform random sampling. */
+ uint64_t r = g->start + randn (g->len);
+ *x2 = g->start2 + randn (g->len2);
+ return r;
+}
+
+static struct args_f1
+next_f1 (void *g)
+{
+ return (struct args_f1){asfloat (next1 (g))};
+}
+
+static struct args_f2
+next_f2 (void *g)
+{
+ uint64_t x2;
+ uint64_t x = next2 (&x2, g);
+ return (struct args_f2){asfloat (x), asfloat (x2)};
+}
+
+static struct args_d1
+next_d1 (void *g)
+{
+ return (struct args_d1){asdouble (next1 (g))};
+}
+
+static struct args_d2
+next_d2 (void *g)
+{
+ uint64_t x2;
+ uint64_t x = next2 (&x2, g);
+ return (struct args_d2){asdouble (x), asdouble (x2)};
+}
+
+struct conf
+{
+ int r;
+ int rc;
+ int quiet;
+ int mpfr;
+ int fenv;
+ unsigned long long n;
+ double softlim;
+ double errlim;
+};
+
+/* Wrappers for sincos. */
+static float sincosf_sinf(float x) {(void)cosf(x); return sinf(x);}
+static float sincosf_cosf(float x) {(void)sinf(x); return cosf(x);}
+static double sincos_sin(double x) {(void)cos(x); return sin(x);}
+static double sincos_cos(double x) {(void)sin(x); return cos(x);}
+#if USE_MPFR
+static int sincos_mpfr_sin(mpfr_t y, const mpfr_t x, mpfr_rnd_t r) { mpfr_cos(y,x,r); return mpfr_sin(y,x,r); }
+static int sincos_mpfr_cos(mpfr_t y, const mpfr_t x, mpfr_rnd_t r) { mpfr_sin(y,x,r); return mpfr_cos(y,x,r); }
+#endif
+
+/* A bit of a hack: call vector functions twice with the same
+ input in lane 0 but a
diff erent value in other lanes: once
+ with an in-range value and then with a special case value. */
+static int secondcall;
+
+/* Wrappers for vector functions. */
+#if __aarch64__ && WANT_VMATH
+typedef __f32x4_t v_float;
+typedef __f64x2_t v_double;
+static const float fv[2] = {1.0f, -INFINITY};
+static const double dv[2] = {1.0, -INFINITY};
+static inline v_float argf(float x) { return (v_float){x,x,x,fv[secondcall]}; }
+static inline v_double argd(double x) { return (v_double){x,dv[secondcall]}; }
+
+static float v_sinf(float x) { return __v_sinf(argf(x))[0]; }
+static float v_cosf(float x) { return __v_cosf(argf(x))[0]; }
+static float v_expf_1u(float x) { return __v_expf_1u(argf(x))[0]; }
+static float v_expf(float x) { return __v_expf(argf(x))[0]; }
+static float v_exp2f_1u(float x) { return __v_exp2f_1u(argf(x))[0]; }
+static float v_exp2f(float x) { return __v_exp2f(argf(x))[0]; }
+static float v_logf(float x) { return __v_logf(argf(x))[0]; }
+static float v_powf(float x, float y) { return __v_powf(argf(x),argf(y))[0]; }
+static double v_sin(double x) { return __v_sin(argd(x))[0]; }
+static double v_cos(double x) { return __v_cos(argd(x))[0]; }
+static double v_exp(double x) { return __v_exp(argd(x))[0]; }
+static double v_log(double x) { return __v_log(argd(x))[0]; }
+static double v_pow(double x, double y) { return __v_pow(argd(x),argd(y))[0]; }
+#ifdef __vpcs
+static float vn_sinf(float x) { return __vn_sinf(argf(x))[0]; }
+static float vn_cosf(float x) { return __vn_cosf(argf(x))[0]; }
+static float vn_expf_1u(float x) { return __vn_expf_1u(argf(x))[0]; }
+static float vn_expf(float x) { return __vn_expf(argf(x))[0]; }
+static float vn_exp2f_1u(float x) { return __vn_exp2f_1u(argf(x))[0]; }
+static float vn_exp2f(float x) { return __vn_exp2f(argf(x))[0]; }
+static float vn_logf(float x) { return __vn_logf(argf(x))[0]; }
+static float vn_powf(float x, float y) { return __vn_powf(argf(x),argf(y))[0]; }
+static double vn_sin(double x) { return __vn_sin(argd(x))[0]; }
+static double vn_cos(double x) { return __vn_cos(argd(x))[0]; }
+static double vn_exp(double x) { return __vn_exp(argd(x))[0]; }
+static double vn_log(double x) { return __vn_log(argd(x))[0]; }
+static double vn_pow(double x, double y) { return __vn_pow(argd(x),argd(y))[0]; }
+static float Z_sinf(float x) { return _ZGVnN4v_sinf(argf(x))[0]; }
+static float Z_cosf(float x) { return _ZGVnN4v_cosf(argf(x))[0]; }
+static float Z_expf(float x) { return _ZGVnN4v_expf(argf(x))[0]; }
+static float Z_exp2f(float x) { return _ZGVnN4v_exp2f(argf(x))[0]; }
+static float Z_logf(float x) { return _ZGVnN4v_logf(argf(x))[0]; }
+static float Z_powf(float x, float y) { return _ZGVnN4vv_powf(argf(x),argf(y))[0]; }
+static double Z_sin(double x) { return _ZGVnN2v_sin(argd(x))[0]; }
+static double Z_cos(double x) { return _ZGVnN2v_cos(argd(x))[0]; }
+static double Z_exp(double x) { return _ZGVnN2v_exp(argd(x))[0]; }
+static double Z_log(double x) { return _ZGVnN2v_log(argd(x))[0]; }
+static double Z_pow(double x, double y) { return _ZGVnN2vv_pow(argd(x),argd(y))[0]; }
+#endif
+#endif
+
+struct fun
+{
+ const char *name;
+ int arity;
+ int singleprec;
+ int twice;
+ union
+ {
+ float (*f1) (float);
+ float (*f2) (float, float);
+ double (*d1) (double);
+ double (*d2) (double, double);
+ } fun;
+ union
+ {
+ double (*f1) (double);
+ double (*f2) (double, double);
+ long double (*d1) (long double);
+ long double (*d2) (long double, long double);
+ } fun_long;
+#if USE_MPFR
+ union
+ {
+ int (*f1) (mpfr_t, const mpfr_t, mpfr_rnd_t);
+ int (*f2) (mpfr_t, const mpfr_t, const mpfr_t, mpfr_rnd_t);
+ int (*d1) (mpfr_t, const mpfr_t, mpfr_rnd_t);
+ int (*d2) (mpfr_t, const mpfr_t, const mpfr_t, mpfr_rnd_t);
+ } fun_mpfr;
+#endif
+};
+
+static const struct fun fun[] = {
+#if USE_MPFR
+# define F(x, x_wrap, x_long, x_mpfr, a, s, t, twice) \
+ {#x, a, s, twice, {.t = x_wrap}, {.t = x_long}, {.t = x_mpfr}},
+#else
+# define F(x, x_wrap, x_long, x_mpfr, a, s, t, twice) \
+ {#x, a, s, twice, {.t = x_wrap}, {.t = x_long}},
+#endif
+#define F1(x) F (x##f, x##f, x, mpfr_##x, 1, 1, f1, 0)
+#define F2(x) F (x##f, x##f, x, mpfr_##x, 2, 1, f2, 0)
+#define D1(x) F (x, x, x##l, mpfr_##x, 1, 0, d1, 0)
+#define D2(x) F (x, x, x##l, mpfr_##x, 2, 0, d2, 0)
+ F1 (sin)
+ F1 (cos)
+ F (sincosf_sinf, sincosf_sinf, sincos_sin, sincos_mpfr_sin, 1, 1, f1, 0)
+ F (sincosf_cosf, sincosf_cosf, sincos_cos, sincos_mpfr_cos, 1, 1, f1, 0)
+ F1 (exp)
+ F1 (exp2)
+ F1 (log)
+ F1 (log2)
+ F2 (pow)
+ D1 (exp)
+ D1 (exp2)
+ D1 (log)
+ D1 (log2)
+ D2 (pow)
+#if WANT_VMATH
+ F (__s_sinf, __s_sinf, sin, mpfr_sin, 1, 1, f1, 0)
+ F (__s_cosf, __s_cosf, cos, mpfr_cos, 1, 1, f1, 0)
+ F (__s_expf_1u, __s_expf_1u, exp, mpfr_exp, 1, 1, f1, 0)
+ F (__s_expf, __s_expf, exp, mpfr_exp, 1, 1, f1, 0)
+ F (__s_exp2f_1u, __s_exp2f_1u, exp2, mpfr_exp2, 1, 1, f1, 0)
+ F (__s_exp2f, __s_exp2f, exp2, mpfr_exp2, 1, 1, f1, 0)
+ F (__s_powf, __s_powf, pow, mpfr_pow, 2, 1, f2, 0)
+ F (__s_logf, __s_logf, log, mpfr_log, 1, 1, f1, 0)
+ F (__s_sin, __s_sin, sinl, mpfr_sin, 1, 0, d1, 0)
+ F (__s_cos, __s_cos, cosl, mpfr_cos, 1, 0, d1, 0)
+ F (__s_exp, __s_exp, expl, mpfr_exp, 1, 0, d1, 0)
+ F (__s_log, __s_log, logl, mpfr_log, 1, 0, d1, 0)
+ F (__s_pow, __s_pow, powl, mpfr_pow, 2, 0, d2, 0)
+#if __aarch64__
+ F (__v_sinf, v_sinf, sin, mpfr_sin, 1, 1, f1, 1)
+ F (__v_cosf, v_cosf, cos, mpfr_cos, 1, 1, f1, 1)
+ F (__v_expf_1u, v_expf_1u, exp, mpfr_exp, 1, 1, f1, 1)
+ F (__v_expf, v_expf, exp, mpfr_exp, 1, 1, f1, 1)
+ F (__v_exp2f_1u, v_exp2f_1u, exp2, mpfr_exp2, 1, 1, f1, 1)
+ F (__v_exp2f, v_exp2f, exp2, mpfr_exp2, 1, 1, f1, 1)
+ F (__v_logf, v_logf, log, mpfr_log, 1, 1, f1, 1)
+ F (__v_powf, v_powf, pow, mpfr_pow, 2, 1, f2, 1)
+ F (__v_sin, v_sin, sinl, mpfr_sin, 1, 0, d1, 1)
+ F (__v_cos, v_cos, cosl, mpfr_cos, 1, 0, d1, 1)
+ F (__v_exp, v_exp, expl, mpfr_exp, 1, 0, d1, 1)
+ F (__v_log, v_log, logl, mpfr_log, 1, 0, d1, 1)
+ F (__v_pow, v_pow, powl, mpfr_pow, 2, 0, d2, 1)
+#ifdef __vpcs
+ F (__vn_sinf, vn_sinf, sin, mpfr_sin, 1, 1, f1, 1)
+ F (__vn_cosf, vn_cosf, cos, mpfr_cos, 1, 1, f1, 1)
+ F (__vn_expf_1u, vn_expf_1u, exp, mpfr_exp, 1, 1, f1, 1)
+ F (__vn_expf, vn_expf, exp, mpfr_exp, 1, 1, f1, 1)
+ F (__vn_exp2f_1u, vn_exp2f_1u, exp2, mpfr_exp2, 1, 1, f1, 1)
+ F (__vn_exp2f, vn_exp2f, exp2, mpfr_exp2, 1, 1, f1, 1)
+ F (__vn_logf, vn_logf, log, mpfr_log, 1, 1, f1, 1)
+ F (__vn_powf, vn_powf, pow, mpfr_pow, 2, 1, f2, 1)
+ F (__vn_sin, vn_sin, sinl, mpfr_sin, 1, 0, d1, 1)
+ F (__vn_cos, vn_cos, cosl, mpfr_cos, 1, 0, d1, 1)
+ F (__vn_exp, vn_exp, expl, mpfr_exp, 1, 0, d1, 1)
+ F (__vn_log, vn_log, logl, mpfr_log, 1, 0, d1, 1)
+ F (__vn_pow, vn_pow, powl, mpfr_pow, 2, 0, d2, 1)
+ F (_ZGVnN4v_sinf, Z_sinf, sin, mpfr_sin, 1, 1, f1, 1)
+ F (_ZGVnN4v_cosf, Z_cosf, cos, mpfr_cos, 1, 1, f1, 1)
+ F (_ZGVnN4v_expf, Z_expf, exp, mpfr_exp, 1, 1, f1, 1)
+ F (_ZGVnN4v_exp2f, Z_exp2f, exp2, mpfr_exp2, 1, 1, f1, 1)
+ F (_ZGVnN4v_logf, Z_logf, log, mpfr_log, 1, 1, f1, 1)
+ F (_ZGVnN4vv_powf, Z_powf, pow, mpfr_pow, 2, 1, f2, 1)
+ F (_ZGVnN2v_sin, Z_sin, sinl, mpfr_sin, 1, 0, d1, 1)
+ F (_ZGVnN2v_cos, Z_cos, cosl, mpfr_cos, 1, 0, d1, 1)
+ F (_ZGVnN2v_exp, Z_exp, expl, mpfr_exp, 1, 0, d1, 1)
+ F (_ZGVnN2v_log, Z_log, logl, mpfr_log, 1, 0, d1, 1)
+ F (_ZGVnN2vv_pow, Z_pow, powl, mpfr_pow, 2, 0, d2, 1)
+#endif
+#endif
+#endif
+#undef F
+#undef F1
+#undef F2
+#undef D1
+#undef D2
+ {0}};
+
+/* Boilerplate for generic calls. */
+
+static inline int
+ulpscale_f (float x)
+{
+ int e = asuint (x) >> 23 & 0xff;
+ if (!e)
+ e++;
+ return e - 0x7f - 23;
+}
+static inline int
+ulpscale_d (double x)
+{
+ int e = asuint64 (x) >> 52 & 0x7ff;
+ if (!e)
+ e++;
+ return e - 0x3ff - 52;
+}
+static inline float
+call_f1 (const struct fun *f, struct args_f1 a)
+{
+ return f->fun.f1 (a.x);
+}
+static inline float
+call_f2 (const struct fun *f, struct args_f2 a)
+{
+ return f->fun.f2 (a.x, a.x2);
+}
+
+static inline double
+call_d1 (const struct fun *f, struct args_d1 a)
+{
+ return f->fun.d1 (a.x);
+}
+static inline double
+call_d2 (const struct fun *f, struct args_d2 a)
+{
+ return f->fun.d2 (a.x, a.x2);
+}
+static inline double
+call_long_f1 (const struct fun *f, struct args_f1 a)
+{
+ return f->fun_long.f1 (a.x);
+}
+static inline double
+call_long_f2 (const struct fun *f, struct args_f2 a)
+{
+ return f->fun_long.f2 (a.x, a.x2);
+}
+static inline long double
+call_long_d1 (const struct fun *f, struct args_d1 a)
+{
+ return f->fun_long.d1 (a.x);
+}
+static inline long double
+call_long_d2 (const struct fun *f, struct args_d2 a)
+{
+ return f->fun_long.d2 (a.x, a.x2);
+}
+static inline void
+printcall_f1 (const struct fun *f, struct args_f1 a)
+{
+ printf ("%s(%a)", f->name, a.x);
+}
+static inline void
+printcall_f2 (const struct fun *f, struct args_f2 a)
+{
+ printf ("%s(%a, %a)", f->name, a.x, a.x2);
+}
+static inline void
+printcall_d1 (const struct fun *f, struct args_d1 a)
+{
+ printf ("%s(%a)", f->name, a.x);
+}
+static inline void
+printcall_d2 (const struct fun *f, struct args_d2 a)
+{
+ printf ("%s(%a, %a)", f->name, a.x, a.x2);
+}
+static inline void
+printgen_f1 (const struct fun *f, struct gen *gen)
+{
+ printf ("%s in [%a;%a]", f->name, asfloat (gen->start),
+ asfloat (gen->start + gen->len));
+}
+static inline void
+printgen_f2 (const struct fun *f, struct gen *gen)
+{
+ printf ("%s in [%a;%a] x [%a;%a]", f->name, asfloat (gen->start),
+ asfloat (gen->start + gen->len), asfloat (gen->start2),
+ asfloat (gen->start2 + gen->len2));
+}
+static inline void
+printgen_d1 (const struct fun *f, struct gen *gen)
+{
+ printf ("%s in [%a;%a]", f->name, asdouble (gen->start),
+ asdouble (gen->start + gen->len));
+}
+static inline void
+printgen_d2 (const struct fun *f, struct gen *gen)
+{
+ printf ("%s in [%a;%a] x [%a;%a]", f->name, asdouble (gen->start),
+ asdouble (gen->start + gen->len), asdouble (gen->start2),
+ asdouble (gen->start2 + gen->len2));
+}
+
+#define reduce_f1(a, f, op) (f (a.x))
+#define reduce_f2(a, f, op) (f (a.x) op f (a.x2))
+#define reduce_d1(a, f, op) (f (a.x))
+#define reduce_d2(a, f, op) (f (a.x) op f (a.x2))
+
+#ifndef IEEE_754_2008_SNAN
+# define IEEE_754_2008_SNAN 1
+#endif
+static inline int
+issignaling_f (float x)
+{
+ uint32_t ix = asuint (x);
+ if (!IEEE_754_2008_SNAN)
+ return (ix & 0x7fc00000) == 0x7fc00000;
+ return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
+}
+static inline int
+issignaling_d (double x)
+{
+ uint64_t ix = asuint64 (x);
+ if (!IEEE_754_2008_SNAN)
+ return (ix & 0x7ff8000000000000) == 0x7ff8000000000000;
+ return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL;
+}
+
+#if USE_MPFR
+static mpfr_rnd_t
+rmap (int r)
+{
+ switch (r)
+ {
+ case FE_TONEAREST:
+ return MPFR_RNDN;
+ case FE_TOWARDZERO:
+ return MPFR_RNDZ;
+ case FE_UPWARD:
+ return MPFR_RNDU;
+ case FE_DOWNWARD:
+ return MPFR_RNDD;
+ }
+ return -1;
+}
+
+#define prec_mpfr_f 50
+#define prec_mpfr_d 80
+#define prec_f 24
+#define prec_d 53
+#define emin_f -148
+#define emin_d -1073
+#define emax_f 128
+#define emax_d 1024
+static inline int
+call_mpfr_f1 (mpfr_t y, const struct fun *f, struct args_f1 a, mpfr_rnd_t r)
+{
+ MPFR_DECL_INIT (x, prec_f);
+ mpfr_set_flt (x, a.x, MPFR_RNDN);
+ return f->fun_mpfr.f1 (y, x, r);
+}
+static inline int
+call_mpfr_f2 (mpfr_t y, const struct fun *f, struct args_f2 a, mpfr_rnd_t r)
+{
+ MPFR_DECL_INIT (x, prec_f);
+ MPFR_DECL_INIT (x2, prec_f);
+ mpfr_set_flt (x, a.x, MPFR_RNDN);
+ mpfr_set_flt (x2, a.x2, MPFR_RNDN);
+ return f->fun_mpfr.f2 (y, x, x2, r);
+}
+static inline int
+call_mpfr_d1 (mpfr_t y, const struct fun *f, struct args_d1 a, mpfr_rnd_t r)
+{
+ MPFR_DECL_INIT (x, prec_d);
+ mpfr_set_d (x, a.x, MPFR_RNDN);
+ return f->fun_mpfr.d1 (y, x, r);
+}
+static inline int
+call_mpfr_d2 (mpfr_t y, const struct fun *f, struct args_d2 a, mpfr_rnd_t r)
+{
+ MPFR_DECL_INIT (x, prec_d);
+ MPFR_DECL_INIT (x2, prec_d);
+ mpfr_set_d (x, a.x, MPFR_RNDN);
+ mpfr_set_d (x2, a.x2, MPFR_RNDN);
+ return f->fun_mpfr.d2 (y, x, x2, r);
+}
+#endif
+
+#define float_f float
+#define double_f double
+#define copysign_f copysignf
+#define nextafter_f nextafterf
+#define fabs_f fabsf
+#define asuint_f asuint
+#define asfloat_f asfloat
+#define scalbn_f scalbnf
+#define lscalbn_f scalbn
+#define halfinf_f 0x1p127f
+#define min_normal_f 0x1p-126f
+
+#define float_d double
+#define double_d long double
+#define copysign_d copysign
+#define nextafter_d nextafter
+#define fabs_d fabs
+#define asuint_d asuint64
+#define asfloat_d asdouble
+#define scalbn_d scalbn
+#define lscalbn_d scalbnl
+#define halfinf_d 0x1p1023
+#define min_normal_d 0x1p-1022
+
+#define NEW_RT
+#define RT(x) x##_f
+#define T(x) x##_f1
+#include "ulp.h"
+#undef T
+#define T(x) x##_f2
+#include "ulp.h"
+#undef T
+#undef RT
+
+#define NEW_RT
+#define RT(x) x##_d
+#define T(x) x##_d1
+#include "ulp.h"
+#undef T
+#define T(x) x##_d2
+#include "ulp.h"
+#undef T
+#undef RT
+
+static void
+usage (void)
+{
+ puts ("./ulp [-q] [-m] [-f] [-r nudz] [-l soft-ulplimit] [-e ulplimit] func "
+ "lo [hi [x lo2 hi2] [count]]");
+ puts ("Compares func against a higher precision implementation in [lo; hi].");
+ puts ("-q: quiet.");
+ puts ("-m: use mpfr even if faster method is available.");
+ puts ("-f: disable fenv testing (rounding modes and exceptions).");
+ puts ("Supported func:");
+ for (const struct fun *f = fun; f->name; f++)
+ printf ("\t%s\n", f->name);
+ exit (1);
+}
+
+static int
+cmp (const struct fun *f, struct gen *gen, const struct conf *conf)
+{
+ int r = 1;
+ if (f->arity == 1 && f->singleprec)
+ r = cmp_f1 (f, gen, conf);
+ else if (f->arity == 2 && f->singleprec)
+ r = cmp_f2 (f, gen, conf);
+ else if (f->arity == 1 && !f->singleprec)
+ r = cmp_d1 (f, gen, conf);
+ else if (f->arity == 2 && !f->singleprec)
+ r = cmp_d2 (f, gen, conf);
+ else
+ usage ();
+ return r;
+}
+
+static uint64_t
+getnum (const char *s, int singleprec)
+{
+ // int i;
+ uint64_t sign = 0;
+ // char buf[12];
+
+ if (s[0] == '+')
+ s++;
+ else if (s[0] == '-')
+ {
+ sign = singleprec ? 1ULL << 31 : 1ULL << 63;
+ s++;
+ }
+ /* 0xXXXX is treated as bit representation, '-' flips the sign bit. */
+ if (s[0] == '0' && tolower (s[1]) == 'x' && strchr (s, 'p') == 0)
+ return sign ^ strtoull (s, 0, 0);
+ // /* SNaN, QNaN, NaN, Inf. */
+ // for (i=0; s[i] && i < sizeof buf; i++)
+ // buf[i] = tolower(s[i]);
+ // buf[i] = 0;
+ // if (strcmp(buf, "snan") == 0)
+ // return sign | (singleprec ? 0x7fa00000 : 0x7ff4000000000000);
+ // if (strcmp(buf, "qnan") == 0 || strcmp(buf, "nan") == 0)
+ // return sign | (singleprec ? 0x7fc00000 : 0x7ff8000000000000);
+ // if (strcmp(buf, "inf") == 0 || strcmp(buf, "infinity") == 0)
+ // return sign | (singleprec ? 0x7f800000 : 0x7ff0000000000000);
+ /* Otherwise assume it's a floating-point literal. */
+ return sign
+ | (singleprec ? asuint (strtof (s, 0)) : asuint64 (strtod (s, 0)));
+}
+
+static void
+parsegen (struct gen *g, int argc, char *argv[], const struct fun *f)
+{
+ int singleprec = f->singleprec;
+ int arity = f->arity;
+ uint64_t a, b, a2, b2, n;
+ if (argc < 1)
+ usage ();
+ b = a = getnum (argv[0], singleprec);
+ n = 0;
+ if (argc > 1 && strcmp (argv[1], "x") == 0)
+ {
+ argc -= 2;
+ argv += 2;
+ }
+ else if (argc > 1)
+ {
+ b = getnum (argv[1], singleprec);
+ if (argc > 2 && strcmp (argv[2], "x") == 0)
+ {
+ argc -= 3;
+ argv += 3;
+ }
+ }
+ b2 = a2 = getnum (argv[0], singleprec);
+ if (argc > 1)
+ b2 = getnum (argv[1], singleprec);
+ if (argc > 2)
+ n = strtoull (argv[2], 0, 0);
+ if (argc > 3)
+ usage ();
+ //printf("ab %lx %lx ab2 %lx %lx n %lu\n", a, b, a2, b2, n);
+ if (arity == 1)
+ {
+ g->start = a;
+ g->len = b - a;
+ if (n - 1 > b - a)
+ n = b - a + 1;
+ g->off = 0;
+ g->step = n ? (g->len + 1) / n : 1;
+ g->start2 = g->len2 = 0;
+ g->cnt = n;
+ }
+ else if (arity == 2)
+ {
+ g->start = a;
+ g->len = b - a;
+ g->off = g->step = 0;
+ g->start2 = a2;
+ g->len2 = b2 - a2;
+ g->cnt = n;
+ }
+ else
+ usage ();
+}
+
+int
+main (int argc, char *argv[])
+{
+ const struct fun *f;
+ struct gen gen;
+ struct conf conf;
+ conf.rc = 'n';
+ conf.quiet = 0;
+ conf.mpfr = 0;
+ conf.fenv = 1;
+ conf.softlim = 0;
+ conf.errlim = INFINITY;
+ for (;;)
+ {
+ argc--;
+ argv++;
+ if (argc < 1)
+ usage ();
+ if (argv[0][0] != '-')
+ break;
+ switch (argv[0][1])
+ {
+ case 'e':
+ argc--;
+ argv++;
+ if (argc < 1)
+ usage ();
+ conf.errlim = strtod (argv[0], 0);
+ break;
+ case 'f':
+ conf.fenv = 0;
+ break;
+ case 'l':
+ argc--;
+ argv++;
+ if (argc < 1)
+ usage ();
+ conf.softlim = strtod (argv[0], 0);
+ break;
+ case 'm':
+ conf.mpfr = 1;
+ break;
+ case 'q':
+ conf.quiet = 1;
+ break;
+ case 'r':
+ conf.rc = argv[0][2];
+ if (!conf.rc)
+ {
+ argc--;
+ argv++;
+ if (argc < 1)
+ usage ();
+ conf.rc = argv[0][0];
+ }
+ break;
+ default:
+ usage ();
+ }
+ }
+ switch (conf.rc)
+ {
+ case 'n':
+ conf.r = FE_TONEAREST;
+ break;
+ case 'u':
+ conf.r = FE_UPWARD;
+ break;
+ case 'd':
+ conf.r = FE_DOWNWARD;
+ break;
+ case 'z':
+ conf.r = FE_TOWARDZERO;
+ break;
+ default:
+ usage ();
+ }
+ for (f = fun; f->name; f++)
+ if (strcmp (argv[0], f->name) == 0)
+ break;
+ if (!f->name)
+ usage ();
+ if (!f->singleprec && LDBL_MANT_DIG == DBL_MANT_DIG)
+ conf.mpfr = 1; /* Use mpfr if long double has no extra precision. */
+ if (!USE_MPFR && conf.mpfr)
+ {
+ puts ("mpfr is not available.");
+ return 0;
+ }
+ argc--;
+ argv++;
+ parsegen (&gen, argc, argv, f);
+ conf.n = gen.cnt;
+ return cmp (f, &gen, &conf);
+}
diff --git a/libc/AOR_v20.02/math/test/ulp.h b/libc/AOR_v20.02/math/test/ulp.h
new file mode 100644
index 000000000000..2743dc59b5a4
--- /dev/null
+++ b/libc/AOR_v20.02/math/test/ulp.h
@@ -0,0 +1,363 @@
+/*
+ * Generic functions for ULP error estimation.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* For each
diff erent math function type,
+ T(x) should add a
diff erent suffix to x.
+ RT(x) should add a return type specific suffix to x. */
+
+#ifdef NEW_RT
+#undef NEW_RT
+
+# if USE_MPFR
+static int RT(ulpscale_mpfr) (mpfr_t x, int t)
+{
+ /* TODO: pow of 2 cases. */
+ if (mpfr_regular_p (x))
+ {
+ mpfr_exp_t e = mpfr_get_exp (x) - RT(prec);
+ if (e < RT(emin))
+ e = RT(emin) - 1;
+ if (e > RT(emax) - RT(prec))
+ e = RT(emax) - RT(prec);
+ return e;
+ }
+ if (mpfr_zero_p (x))
+ return RT(emin) - 1;
+ if (mpfr_inf_p (x))
+ return RT(emax) - RT(prec);
+ /* NaN. */
+ return 0;
+}
+# endif
+
+/* Difference between exact result and closest real number that
+ gets rounded to got, i.e. error before rounding, for a correctly
+ rounded result the
diff erence is 0. */
+static double RT(ulperr) (RT(float) got, const struct RT(ret) * p, int r)
+{
+ RT(float) want = p->y;
+ RT(float) d;
+ double e;
+
+ if (RT(asuint) (got) == RT(asuint) (want))
+ return 0.0;
+ if (signbit (got) != signbit (want))
+ /* May have false positives with NaN. */
+ //return isnan(got) && isnan(want) ? 0 : INFINITY;
+ return INFINITY;
+ if (!isfinite (want) || !isfinite (got))
+ {
+ if (isnan (got) != isnan (want))
+ return INFINITY;
+ if (isnan (want))
+ return 0;
+ if (isinf (got))
+ {
+ got = RT(copysign) (RT(halfinf), got);
+ want *= 0.5f;
+ }
+ if (isinf (want))
+ {
+ want = RT(copysign) (RT(halfinf), want);
+ got *= 0.5f;
+ }
+ }
+ if (r == FE_TONEAREST)
+ {
+ // TODO: incorrect when got vs want cross a powof2 boundary
+ /* error = got > want
+ ? got - want - tail ulp - 0.5 ulp
+ : got - want - tail ulp + 0.5 ulp; */
+ d = got - want;
+ e = d > 0 ? -p->tail - 0.5 : -p->tail + 0.5;
+ }
+ else
+ {
+ if ((r == FE_DOWNWARD && got < want) || (r == FE_UPWARD && got > want)
+ || (r == FE_TOWARDZERO && fabs (got) < fabs (want)))
+ got = RT(nextafter) (got, want);
+ d = got - want;
+ e = -p->tail;
+ }
+ return RT(scalbn) (d, -p->ulpexp) + e;
+}
+
+static int RT(isok) (RT(float) ygot, int exgot, RT(float) ywant, int exwant,
+ int exmay)
+{
+ return RT(asuint) (ygot) == RT(asuint) (ywant)
+ && ((exgot ^ exwant) & ~exmay) == 0;
+}
+
+static int RT(isok_nofenv) (RT(float) ygot, RT(float) ywant)
+{
+ return RT(asuint) (ygot) == RT(asuint) (ywant);
+}
+#endif
+
+static inline void T(call_fenv) (const struct fun *f, struct T(args) a, int r,
+ RT(float) * y, int *ex)
+{
+ if (r != FE_TONEAREST)
+ fesetround (r);
+ feclearexcept (FE_ALL_EXCEPT);
+ *y = T(call) (f, a);
+ *ex = fetestexcept (FE_ALL_EXCEPT);
+ if (r != FE_TONEAREST)
+ fesetround (FE_TONEAREST);
+}
+
+static inline void T(call_nofenv) (const struct fun *f, struct T(args) a,
+ int r, RT(float) * y, int *ex)
+{
+ *y = T(call) (f, a);
+ *ex = 0;
+}
+
+static inline int T(call_long_fenv) (const struct fun *f, struct T(args) a,
+ int r, struct RT(ret) * p,
+ RT(float) ygot, int exgot)
+{
+ if (r != FE_TONEAREST)
+ fesetround (r);
+ feclearexcept (FE_ALL_EXCEPT);
+ volatile struct T(args) va = a; // TODO: barrier
+ a = va;
+ RT(double) yl = T(call_long) (f, a);
+ p->y = (RT(float)) yl;
+ volatile RT(float) vy = p->y; // TODO: barrier
+ (void) vy;
+ p->ex = fetestexcept (FE_ALL_EXCEPT);
+ if (r != FE_TONEAREST)
+ fesetround (FE_TONEAREST);
+ p->ex_may = FE_INEXACT;
+ if (RT(isok) (ygot, exgot, p->y, p->ex, p->ex_may))
+ return 1;
+ p->ulpexp = RT(ulpscale) (p->y);
+ if (isinf (p->y))
+ p->tail = RT(lscalbn) (yl - (RT(double)) 2 * RT(halfinf), -p->ulpexp);
+ else
+ p->tail = RT(lscalbn) (yl - p->y, -p->ulpexp);
+ if (RT(fabs) (p->y) < RT(min_normal))
+ {
+ /* TODO: subnormal result is treated as undeflow even if it's
+ exact since call_long may not raise inexact correctly. */
+ if (p->y != 0 || (p->ex & FE_INEXACT))
+ p->ex |= FE_UNDERFLOW | FE_INEXACT;
+ }
+ return 0;
+}
+static inline int T(call_long_nofenv) (const struct fun *f, struct T(args) a,
+ int r, struct RT(ret) * p,
+ RT(float) ygot, int exgot)
+{
+ RT(double) yl = T(call_long) (f, a);
+ p->y = (RT(float)) yl;
+ if (RT(isok_nofenv) (ygot, p->y))
+ return 1;
+ p->ulpexp = RT(ulpscale) (p->y);
+ if (isinf (p->y))
+ p->tail = RT(lscalbn) (yl - (RT(double)) 2 * RT(halfinf), -p->ulpexp);
+ else
+ p->tail = RT(lscalbn) (yl - p->y, -p->ulpexp);
+ return 0;
+}
+
+/* There are nan input args and all quiet. */
+static inline int T(qnanpropagation) (struct T(args) a)
+{
+ return T(reduce) (a, isnan, ||) && !T(reduce) (a, RT(issignaling), ||);
+}
+static inline RT(float) T(sum) (struct T(args) a)
+{
+ return T(reduce) (a, , +);
+}
+
+/* returns 1 if the got result is ok. */
+static inline int T(call_mpfr_fix) (const struct fun *f, struct T(args) a,
+ int r_fenv, struct RT(ret) * p,
+ RT(float) ygot, int exgot)
+{
+#if USE_MPFR
+ int t, t2;
+ mpfr_rnd_t r = rmap (r_fenv);
+ MPFR_DECL_INIT(my, RT(prec_mpfr));
+ MPFR_DECL_INIT(mr, RT(prec));
+ MPFR_DECL_INIT(me, RT(prec_mpfr));
+ mpfr_clear_flags ();
+ t = T(call_mpfr) (my, f, a, r);
+ /* Double rounding. */
+ t2 = mpfr_set (mr, my, r);
+ if (t2)
+ t = t2;
+ mpfr_set_emin (RT(emin));
+ mpfr_set_emax (RT(emax));
+ t = mpfr_check_range (mr, t, r);
+ t = mpfr_subnormalize (mr, t, r);
+ mpfr_set_emax (MPFR_EMAX_DEFAULT);
+ mpfr_set_emin (MPFR_EMIN_DEFAULT);
+ p->y = mpfr_get_d (mr, r);
+ p->ex = t ? FE_INEXACT : 0;
+ p->ex_may = FE_INEXACT;
+ if (mpfr_underflow_p () && (p->ex & FE_INEXACT))
+ /* TODO: handle before and after rounding uflow cases. */
+ p->ex |= FE_UNDERFLOW;
+ if (mpfr_overflow_p ())
+ p->ex |= FE_OVERFLOW | FE_INEXACT;
+ if (mpfr_divby0_p ())
+ p->ex |= FE_DIVBYZERO;
+ //if (mpfr_erangeflag_p ())
+ // p->ex |= FE_INVALID;
+ if (!mpfr_nanflag_p () && RT(isok) (ygot, exgot, p->y, p->ex, p->ex_may))
+ return 1;
+ if (mpfr_nanflag_p () && !T(qnanpropagation) (a))
+ p->ex |= FE_INVALID;
+ p->ulpexp = RT(ulpscale_mpfr) (my, t);
+ if (!isfinite (p->y))
+ {
+ p->tail = 0;
+ if (isnan (p->y))
+ {
+ /* If an input was nan keep its sign. */
+ p->y = T(sum) (a);
+ if (!isnan (p->y))
+ p->y = (p->y - p->y) / (p->y - p->y);
+ return RT(isok) (ygot, exgot, p->y, p->ex, p->ex_may);
+ }
+ mpfr_set_si_2exp (mr, signbit (p->y) ? -1 : 1, 1024, MPFR_RNDN);
+ if (mpfr_cmpabs (my, mr) >= 0)
+ return RT(isok) (ygot, exgot, p->y, p->ex, p->ex_may);
+ }
+ mpfr_sub (me, my, mr, MPFR_RNDN);
+ mpfr_mul_2si (me, me, -p->ulpexp, MPFR_RNDN);
+ p->tail = mpfr_get_d (me, MPFR_RNDN);
+ return 0;
+#else
+ abort ();
+#endif
+}
+
+static int T(cmp) (const struct fun *f, struct gen *gen,
+ const struct conf *conf)
+{
+ double maxerr = 0;
+ uint64_t cnt = 0;
+ uint64_t cnt1 = 0;
+ uint64_t cnt2 = 0;
+ uint64_t cntfail = 0;
+ int r = conf->r;
+ int use_mpfr = conf->mpfr;
+ int fenv = conf->fenv;
+ for (;;)
+ {
+ struct RT(ret) want;
+ struct T(args) a = T(next) (gen);
+ int exgot;
+ int exgot2;
+ RT(float) ygot;
+ RT(float) ygot2;
+ int fail = 0;
+ if (fenv)
+ T(call_fenv) (f, a, r, &ygot, &exgot);
+ else
+ T(call_nofenv) (f, a, r, &ygot, &exgot);
+ if (f->twice) {
+ secondcall = 1;
+ if (fenv)
+ T(call_fenv) (f, a, r, &ygot2, &exgot2);
+ else
+ T(call_nofenv) (f, a, r, &ygot2, &exgot2);
+ secondcall = 0;
+ if (RT(asuint) (ygot) != RT(asuint) (ygot2))
+ {
+ fail = 1;
+ cntfail++;
+ T(printcall) (f, a);
+ printf (" got %a then %a for same input\n", ygot, ygot2);
+ }
+ }
+ cnt++;
+ int ok = use_mpfr
+ ? T(call_mpfr_fix) (f, a, r, &want, ygot, exgot)
+ : (fenv ? T(call_long_fenv) (f, a, r, &want, ygot, exgot)
+ : T(call_long_nofenv) (f, a, r, &want, ygot, exgot));
+ if (!ok)
+ {
+ int print = 0;
+ double err = RT(ulperr) (ygot, &want, r);
+ double abserr = fabs (err);
+ // TODO: count errors below accuracy limit.
+ if (abserr > 0)
+ cnt1++;
+ if (abserr > 1)
+ cnt2++;
+ if (abserr > conf->errlim)
+ {
+ print = 1;
+ if (!fail)
+ {
+ fail = 1;
+ cntfail++;
+ }
+ }
+ if (abserr > maxerr)
+ {
+ maxerr = abserr;
+ if (!conf->quiet && abserr > conf->softlim)
+ print = 1;
+ }
+ if (print)
+ {
+ T(printcall) (f, a);
+ // TODO: inf ulp handling
+ printf (" got %a want %a %+g ulp err %g\n", ygot, want.y,
+ want.tail, err);
+ }
+ int
diff = fenv ? exgot ^ want.ex : 0;
+ if (fenv && (
diff & ~want.ex_may))
+ {
+ if (!fail)
+ {
+ fail = 1;
+ cntfail++;
+ }
+ T(printcall) (f, a);
+ printf (" is %a %+g ulp, got except 0x%0x", want.y, want.tail,
+ exgot);
+ if (
diff & exgot)
+ printf (" wrongly set: 0x%x",
diff & exgot);
+ if (
diff & ~exgot)
+ printf (" wrongly clear: 0x%x",
diff & ~exgot);
+ putchar ('\n');
+ }
+ }
+ if (cnt >= conf->n)
+ break;
+ if (!conf->quiet && cnt % 0x100000 == 0)
+ printf ("progress: %6.3f%% cnt %llu cnt1 %llu cnt2 %llu cntfail %llu "
+ "maxerr %g\n",
+ 100.0 * cnt / conf->n, (unsigned long long) cnt,
+ (unsigned long long) cnt1, (unsigned long long) cnt2,
+ (unsigned long long) cntfail, maxerr);
+ }
+ double cc = cnt;
+ if (cntfail)
+ printf ("FAIL ");
+ else
+ printf ("PASS ");
+ T(printgen) (f, gen);
+ printf (" round %c errlim %g maxerr %g %s cnt %llu cnt1 %llu %g%% cnt2 %llu "
+ "%g%% cntfail %llu %g%%\n",
+ conf->rc, conf->errlim,
+ maxerr, conf->r == FE_TONEAREST ? "+0.5" : "+1.0",
+ (unsigned long long) cnt,
+ (unsigned long long) cnt1, 100.0 * cnt1 / cc,
+ (unsigned long long) cnt2, 100.0 * cnt2 / cc,
+ (unsigned long long) cntfail, 100.0 * cntfail / cc);
+ return !!cntfail;
+}
diff --git a/libc/AOR_v20.02/math/tools/cos.sollya b/libc/AOR_v20.02/math/tools/cos.sollya
new file mode 100644
index 000000000000..71d45965decb
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/cos.sollya
@@ -0,0 +1,32 @@
+// polynomial for approximating cos(x)
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 8; // polynomial degree
+a = -pi/4; // interval
+b = pi/4;
+
+// find even polynomial with minimal abs error compared to cos(x)
+
+f = cos(x);
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg/2 do {
+ p = roundcoefficients(approx(poly,2*i), [|D ...|]);
+ poly = poly + x^(2*i)*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/exp.sollya b/libc/AOR_v20.02/math/tools/exp.sollya
new file mode 100644
index 000000000000..1877b0761197
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/exp.sollya
@@ -0,0 +1,36 @@
+// polynomial for approximating e^x
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 5; // poly degree
+N = 128; // table entries
+b = log(2)/(2*N); // interval
+b = b + b*0x1p-16; // increase interval for non-nearest rounding (TOINT_NARROW)
+a = -b;
+
+// find polynomial with minimal abs error
+
+// return p that minimizes |exp(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first 2 coeffs are fixed, iteratively find optimal double prec coeffs
+poly = 1 + x;
+for i from 2 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30));
+print("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30));
+print("in [",a,b,"]");
+// double interval error for non-nearest rounding
+print("rel2 error:", accurateinfnorm(1-poly(x)/exp(x), [2*a;2*b], 30));
+print("abs2 error:", accurateinfnorm(exp(x)-poly(x), [2*a;2*b], 30));
+print("in [",2*a,2*b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/exp2.sollya b/libc/AOR_v20.02/math/tools/exp2.sollya
new file mode 100644
index 000000000000..7980eefbff5f
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/exp2.sollya
@@ -0,0 +1,49 @@
+// polynomial for approximating 2^x
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+// exp2f parameters
+deg = 3; // poly degree
+N = 32; // table entries
+b = 1/(2*N); // interval
+a = -b;
+
+//// exp2 parameters
+//deg = 5; // poly degree
+//N = 128; // table entries
+//b = 1/(2*N); // interval
+//a = -b;
+
+// find polynomial with minimal relative error
+
+f = 2^x;
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
+approx = proc(poly,d) {
+ return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
+};
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx_abs = proc(poly,d) {
+ return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+// p = roundcoefficients(approx_abs(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/2^x, [a;b], 30));
+print("abs error:", accurateinfnorm(2^x-poly(x), [a;b], 30));
+print("in [",a,b,"]");
+// double interval error for non-nearest rounding:
+print("rel2 error:", accurateinfnorm(1-poly(x)/2^x, [2*a;2*b], 30));
+print("abs2 error:", accurateinfnorm(2^x-poly(x), [2*a;2*b], 30));
+print("in [",2*a,2*b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/log.sollya b/libc/AOR_v20.02/math/tools/log.sollya
new file mode 100644
index 000000000000..41072395eb92
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/log.sollya
@@ -0,0 +1,36 @@
+// polynomial for approximating log(1+x)
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 12; // poly degree
+// |log(1+x)| > 0x1p-4 outside the interval
+a = -0x1p-4;
+b = 0x1.09p-4;
+
+// find log(1+x)/x polynomial with minimal relative error
+// (minimal relative error polynomial for log(1+x) is the same * x)
+deg = deg-1; // because of /x
+
+// f = log(1+x)/x; using taylor series
+f = 0;
+for i from 0 to 60 do { f = f + (-x)^i/(i+1); };
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
+approx = proc(poly,d) {
+ return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/log2.sollya b/libc/AOR_v20.02/math/tools/log2.sollya
new file mode 100644
index 000000000000..6b3e867b77a9
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/log2.sollya
@@ -0,0 +1,43 @@
+// polynomial for approximating log2(1+x)
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 11; // poly degree
+// |log2(1+x)| > 0x1p-4 outside the interval
+a = -0x1.5b51p-5;
+b = 0x1.6ab2p-5;
+
+ln2 = evaluate(log(2),0);
+invln2hi = double(1/ln2 + 0x1p21) - 0x1p21; // round away last 21 bits
+invln2lo = double(1/ln2 - invln2hi);
+
+// find log2(1+x)/x polynomial with minimal relative error
+// (minimal relative error polynomial for log2(1+x) is the same * x)
+deg = deg-1; // because of /x
+
+// f = log(1+x)/x; using taylor series
+f = 0;
+for i from 0 to 60 do { f = f + (-x)^i/(i+1); };
+f = f/ln2;
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
+approx = proc(poly,d) {
+ return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = invln2hi + invln2lo;
+for i from 1 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("invln2hi:", invln2hi);
+print("invln2lo:", invln2lo);
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/log2_abs.sollya b/libc/AOR_v20.02/math/tools/log2_abs.sollya
new file mode 100644
index 000000000000..ecbc7e075003
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/log2_abs.sollya
@@ -0,0 +1,42 @@
+// polynomial for approximating log2(1+x)
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 7; // poly degree
+// interval ~= 1/(2*N), where N is the table entries
+a= -0x1.f45p-8;
+b= 0x1.f45p-8;
+
+ln2 = evaluate(log(2),0);
+invln2hi = double(1/ln2 + 0x1p21) - 0x1p21; // round away last 21 bits
+invln2lo = double(1/ln2 - invln2hi);
+
+// find log2(1+x) polynomial with minimal absolute error
+f = log(1+x)/ln2;
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = x*(invln2lo + invln2hi);
+for i from 2 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("invln2hi:", invln2hi);
+print("invln2lo:", invln2lo);
+print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30));
+//// relative error computation fails if f(0)==0
+//// g = f(x)/x = log2(1+x)/x; using taylor series
+//g = 0;
+//for i from 0 to 60 do { g = g + (-x)^i/(i+1)/ln2; };
+//print("rel error:", accurateinfnorm(1-(poly(x)/x)/g(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/log_abs.sollya b/libc/AOR_v20.02/math/tools/log_abs.sollya
new file mode 100644
index 000000000000..c12242364869
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/log_abs.sollya
@@ -0,0 +1,36 @@
+// polynomial for approximating log(1+x)
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 6; // poly degree
+// interval ~= 1/(2*N), where N is the table entries
+a = -0x1.fp-9;
+b = 0x1.fp-9;
+
+// find log(1+x) polynomial with minimal absolute error
+f = log(1+x);
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = x;
+for i from 2 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30));
+// relative error computation fails if f(0)==0
+// g = f(x)/x = log(1+x)/x; using taylor series
+g = 0;
+for i from 0 to 60 do { g = g + (-x)^i/(i+1); };
+print("rel error:", accurateinfnorm(1-poly(x)/x/g(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/plot.py b/libc/AOR_v20.02/math/tools/plot.py
new file mode 100755
index 000000000000..611c99a9e69f
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/plot.py
@@ -0,0 +1,62 @@
+#!/usr/bin/python
+
+# ULP error plot tool.
+#
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+import numpy as np
+import matplotlib.pyplot as plt
+import sys
+import re
+
+# example usage:
+# build/bin/ulp -e .0001 log 0.5 2.0 2345678 | math/tools/plot.py
+
+def fhex(s):
+ return float.fromhex(s)
+
+def parse(f):
+ xs = []
+ gs = []
+ ys = []
+ es = []
+ # Has to match the format used in ulp.c
+ r = re.compile(r'[^ (]+\(([^ )]*)\) got ([^ ]+) want ([^ ]+) [^ ]+ ulp err ([^ ]+)')
+ for line in f:
+ m = r.match(line)
+ if m:
+ x = fhex(m.group(1))
+ g = fhex(m.group(2))
+ y = fhex(m.group(3))
+ e = float(m.group(4))
+ xs.append(x)
+ gs.append(g)
+ ys.append(y)
+ es.append(e)
+ elif line.startswith('PASS') or line.startswith('FAIL'):
+ # Print the summary line
+ print(line)
+ return xs, gs, ys, es
+
+def plot(xs, gs, ys, es):
+ if len(xs) < 2:
+ print('not enough samples')
+ return
+ a = min(xs)
+ b = max(xs)
+ fig, (ax0,ax1) = plt.subplots(nrows=2)
+ es = np.abs(es) # ignore the sign
+ emax = max(es)
+ ax0.text(a+(b-a)*0.7, emax*0.8, '%s\n%g'%(emax.hex(),emax))
+ ax0.plot(xs,es,'r.')
+ ax0.grid()
+ ax1.plot(xs,ys,'r.',label='want')
+ ax1.plot(xs,gs,'b.',label='got')
+ ax1.grid()
+ ax1.legend()
+ plt.show()
+
+xs, gs, ys, es = parse(sys.stdin)
+plot(xs, gs, ys, es)
diff --git a/libc/AOR_v20.02/math/tools/remez.jl b/libc/AOR_v20.02/math/tools/remez.jl
new file mode 100755
index 000000000000..bf934f4a7c11
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/remez.jl
@@ -0,0 +1,1335 @@
+#!/usr/bin/env julia
+# -*- julia -*-
+
+# remez.jl - implementation of the Remez algorithm for polynomial approximation
+#
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+import Base.\
+
+# ----------------------------------------------------------------------
+# Helper functions to cope with
diff erent Julia versions.
+if VERSION >= v"0.7.0"
+ array1d(T, d) = Array{T, 1}(undef, d)
+ array2d(T, d1, d2) = Array{T, 2}(undef, d1, d2)
+else
+ array1d(T, d) = Array(T, d)
+ array2d(T, d1, d2) = Array(T, d1, d2)
+end
+if VERSION < v"0.5.0"
+ String = ASCIIString
+end
+if VERSION >= v"0.6.0"
+ # Use Base.invokelatest to run functions made using eval(), to
+ # avoid "world age" error
+ run(f, x...) = Base.invokelatest(f, x...)
+else
+ # Prior to 0.6.0, invokelatest doesn't exist (but fortunately the
+ # world age problem also doesn't seem to exist)
+ run(f, x...) = f(x...)
+end
+
+# ----------------------------------------------------------------------
+# Global variables configured by command-line options.
+floatsuffix = "" # adjusted by --floatsuffix
+xvarname = "x" # adjusted by --variable
+epsbits = 256 # adjusted by --bits
+debug_facilities = Set() # adjusted by --debug
+full_output = false # adjusted by --full
+array_format = false # adjusted by --array
+preliminary_commands = array1d(String, 0) # adjusted by --pre
+
+# ----------------------------------------------------------------------
+# Diagnostic and utility functions.
+
+# Enable debugging printouts from a particular subpart of this
+# program.
+#
+# Arguments:
+# facility Name of the facility to debug. For a list of facility names,
+# look through the code for calls to debug().
+#
+# Return value is a BigFloat.
+function enable_debug(facility)
+ push!(debug_facilities, facility)
+end
+
+# Print a diagnostic.
+#
+# Arguments:
+# facility Name of the facility for which this is a debug message.
+# printargs Arguments to println() if debugging of that facility is
+# enabled.
+macro debug(facility, printargs...)
+ printit = quote
+ print("[", $facility, "] ")
+ end
+ for arg in printargs
+ printit = quote
+ $printit
+ print($(esc(arg)))
+ end
+ end
+ return quote
+ if $facility in debug_facilities
+ $printit
+ println()
+ end
+ end
+end
+
+# Evaluate a polynomial.
+
+# Arguments:
+# coeffs Array of BigFloats giving the coefficients of the polynomial.
+# Starts with the constant term, i.e. coeffs[i] is the
+# coefficient of x^(i-1) (because Julia arrays are 1-based).
+# x Point at which to evaluate the polynomial.
+#
+# Return value is a BigFloat.
+function poly_eval(coeffs::Array{BigFloat}, x::BigFloat)
+ n = length(coeffs)
+ if n == 0
+ return BigFloat(0)
+ elseif n == 1
+ return coeffs[1]
+ else
+ return coeffs[1] + x * poly_eval(coeffs[2:n], x)
+ end
+end
+
+# Evaluate a rational function.
+
+# Arguments:
+# ncoeffs Array of BigFloats giving the coefficients of the numerator.
+# Starts with the constant term, and 1-based, as above.
+# dcoeffs Array of BigFloats giving the coefficients of the denominator.
+# Starts with the constant term, and 1-based, as above.
+# x Point at which to evaluate the function.
+#
+# Return value is a BigFloat.
+function ratfn_eval(ncoeffs::Array{BigFloat}, dcoeffs::Array{BigFloat},
+ x::BigFloat)
+ return poly_eval(ncoeffs, x) / poly_eval(dcoeffs, x)
+end
+
+# Format a BigFloat into an appropriate output format.
+# Arguments:
+# x BigFloat to format.
+#
+# Return value is a string.
+function float_to_str(x)
+ return string(x) * floatsuffix
+end
+
+# Format a polynomial into an arithmetic expression, for pasting into
+# other tools such as gnuplot.
+
+# Arguments:
+# coeffs Array of BigFloats giving the coefficients of the polynomial.
+# Starts with the constant term, and 1-based, as above.
+#
+# Return value is a string.
+function poly_to_string(coeffs::Array{BigFloat})
+ n = length(coeffs)
+ if n == 0
+ return "0"
+ elseif n == 1
+ return float_to_str(coeffs[1])
+ else
+ return string(float_to_str(coeffs[1]), "+", xvarname, "*(",
+ poly_to_string(coeffs[2:n]), ")")
+ end
+end
+
+# Format a rational function into a string.
+
+# Arguments:
+# ncoeffs Array of BigFloats giving the coefficients of the numerator.
+# Starts with the constant term, and 1-based, as above.
+# dcoeffs Array of BigFloats giving the coefficients of the denominator.
+# Starts with the constant term, and 1-based, as above.
+#
+# Return value is a string.
+function ratfn_to_string(ncoeffs::Array{BigFloat}, dcoeffs::Array{BigFloat})
+ if length(dcoeffs) == 1 && dcoeffs[1] == 1
+ # Special case: if the denominator is just 1, leave it out.
+ return poly_to_string(ncoeffs)
+ else
+ return string("(", poly_to_string(ncoeffs), ")/(",
+ poly_to_string(dcoeffs), ")")
+ end
+end
+
+# Format a list of x,y pairs into a string.
+
+# Arguments:
+# xys Array of (x,y) pairs of BigFloats.
+#
+# Return value is a string.
+function format_xylist(xys::Array{Tuple{BigFloat,BigFloat}})
+ return ("[\n" *
+ join([" "*string(x)*" -> "*string(y) for (x,y) in xys], "\n") *
+ "\n]")
+end
+
+# ----------------------------------------------------------------------
+# Matrix-equation solver for matrices of BigFloat.
+#
+# I had hoped that Julia's type-genericity would allow me to solve the
+# matrix equation Mx=V by just writing 'M \ V'. Unfortunately, that
+# works by translating the inputs into double precision and handing
+# off to an optimised library, which misses the point when I have a
+# matrix and vector of BigFloat and want my result in _better_ than
+# double precision. So I have to implement my own specialisation of
+# the \ operator for that case.
+#
+# Fortunately, the point of using BigFloats is that we have precision
+# to burn, so I can do completely naïve Gaussian elimination without
+# worrying about instability.
+
+# Arguments:
+# matrix_in 2-dimensional array of BigFloats, representing a matrix M
+# in row-first order, i.e. matrix_in[r,c] represents the
+# entry in row r col c.
+# vector_in 1-dimensional array of BigFloats, representing a vector V.
+#
+# Return value: a 1-dimensional array X of BigFloats, satisfying M X = V.
+#
+# Expects the input to be an invertible square matrix and a vector of
+# the corresponding size, on pain of failing an assertion.
+function \(matrix_in :: Array{BigFloat,2},
+ vector_in :: Array{BigFloat,1})
+ # Copy the inputs, because we'll be mutating them as we go.
+ M = copy(matrix_in)
+ V = copy(vector_in)
+
+ # Input consistency criteria: matrix is square, and vector has
+ # length to match.
+ n = length(V)
+ @assert(n > 0)
+ @assert(size(M) == (n,n))
+
+ @debug("gausselim", "starting, n=", n)
+
+ for i = 1:1:n
+ # Straightforward Gaussian elimination: find the largest
+ # non-zero entry in column i (and in a row we haven't sorted
+ # out already), swap it into row i, scale that row to
+ # normalise it to 1, then zero out the rest of the column by
+ # subtracting a multiple of that row from each other row.
+
+ @debug("gausselim", "matrix=", repr(M))
+ @debug("gausselim", "vector=", repr(V))
+
+ # Find the best pivot.
+ bestrow = 0
+ bestval = 0
+ for j = i:1:n
+ if abs(M[j,i]) > bestval
+ bestrow = j
+ bestval = M[j,i]
+ end
+ end
+ @assert(bestrow > 0) # make sure we did actually find one
+
+ @debug("gausselim", "bestrow=", bestrow)
+
+ # Swap it into row i.
+ if bestrow != i
+ for k = 1:1:n
+ M[bestrow,k],M[i,k] = M[i,k],M[bestrow,k]
+ end
+ V[bestrow],V[i] = V[i],V[bestrow]
+ end
+
+ # Scale that row so that M[i,i] becomes 1.
+ divisor = M[i,i]
+ for k = 1:1:n
+ M[i,k] = M[i,k] / divisor
+ end
+ V[i] = V[i] / divisor
+ @assert(M[i,i] == 1)
+
+ # Zero out all other entries in column i, by subtracting
+ # multiples of this row.
+ for j = 1:1:n
+ if j != i
+ factor = M[j,i]
+ for k = 1:1:n
+ M[j,k] = M[j,k] - M[i,k] * factor
+ end
+ V[j] = V[j] - V[i] * factor
+ @assert(M[j,i] == 0)
+ end
+ end
+ end
+
+ @debug("gausselim", "matrix=", repr(M))
+ @debug("gausselim", "vector=", repr(V))
+ @debug("gausselim", "done!")
+
+ # Now we're done: M is the identity matrix, so the equation Mx=V
+ # becomes just x=V, i.e. V is already exactly the vector we want
+ # to return.
+ return V
+end
+
+# ----------------------------------------------------------------------
+# Least-squares fitting of a rational function to a set of (x,y)
+# points.
+#
+# We use this to get an initial starting point for the Remez
+# iteration. Therefore, it doesn't really need to be particularly
+# accurate; it only needs to be good enough to wiggle back and forth
+# across the target function the right number of times (so as to give
+# enough error extrema to start optimising from) and not have any
+# poles in the target interval.
+#
+# Least-squares fitting of a _polynomial_ is actually a sensible thing
+# to do, and minimises the rms error. Doing the following trick with a
+# rational function P/Q is less sensible, because it cannot be made to
+# minimise the error function (P/Q-f)^2 that you actually wanted;
+# instead it minimises (P-fQ)^2. But that should be good enough to
+# have the properties described above.
+#
+# Some theory: suppose you're trying to choose a set of parameters a_i
+# so as to minimise the sum of squares of some error function E_i.
+# Basic calculus says, if you do this in one variable, just
+#
diff erentiate and solve for zero. In this case, that works fine even
+# with multiple variables, because you _partially_
diff erentiate with
+# respect to each a_i, giving a system of equations, and that system
+# turns out to be linear so we just solve it as a matrix.
+#
+# In this case, our parameters are the coefficients of P and Q; to
+# avoid underdetermining the system we'll fix Q's constant term at 1,
+# so that our error function (as described above) is
+#
+# E = \sum (p_0 + p_1 x + ... + p_n x^n - y - y q_1 x - ... - y q_d x^d)^2
+#
+# where the sum is over all (x,y) coordinate pairs. Setting dE/dp_j=0
+# (for each j) gives an equation of the form
+#
+# 0 = \sum 2(p_0 + p_1 x + ... + p_n x^n - y - y q_1 x - ... - y q_d x^d) x^j
+#
+# and setting dE/dq_j=0 gives one of the form
+#
+# 0 = \sum 2(p_0 + p_1 x + ... + p_n x^n - y - y q_1 x - ... - y q_d x^d) y x^j
+#
+# And both of those row types, treated as multivariate linear
+# equations in the p,q values, have each coefficient being a value of
+# the form \sum x^i, \sum y x^i or \sum y^2 x^i, for various i. (Times
+# a factor of 2, but we can throw that away.) So we can go through the
+# list of input coordinates summing all of those things, and then we
+# have enough information to construct our matrix and solve it
+# straight off for the rational function coefficients.
+
+# Arguments:
+# f The function to be approximated. Maps BigFloat -> BigFloat.
+# xvals Array of BigFloats, giving the list of x-coordinates at which
+# to evaluate f.
+# n Degree of the numerator polynomial of the desired rational
+# function.
+# d Degree of the denominator polynomial of the desired rational
+# function.
+# w Error-weighting function. Takes two BigFloat arguments x,y
+# and returns a scaling factor for the error at that location.
+# A larger value indicates that the error should be given
+# greater weight in the square sum we try to minimise.
+# If unspecified, defaults to giving everything the same weight.
+#
+# Return values: a pair of arrays of BigFloats (N,D) giving the
+# coefficients of the returned rational function. N has size n+1; D
+# has size d+1. Both start with the constant term, i.e. N[i] is the
+# coefficient of x^(i-1) (because Julia arrays are 1-based). D[1] will
+# be 1.
+function ratfn_leastsquares(f::Function, xvals::Array{BigFloat}, n, d,
+ w = (x,y)->BigFloat(1))
+ # Accumulate sums of x^i y^j, for j={0,1,2} and a range of x.
+ # Again because Julia arrays are 1-based, we'll have sums[i,j]
+ # being the sum of x^(i-1) y^(j-1).
+ maxpow = max(n,d) * 2 + 1
+ sums = zeros(BigFloat, maxpow, 3)
+ for x = xvals
+ y = f(x)
+ weight = w(x,y)
+ for i = 1:1:maxpow
+ for j = 1:1:3
+ sums[i,j] += x^(i-1) * y^(j-1) * weight
+ end
+ end
+ end
+
+ @debug("leastsquares", "sums=", repr(sums))
+
+ # Build the matrix. We're solving n+d+1 equations in n+d+1
+ # unknowns. (We actually have to return n+d+2 coefficients, but
+ # one of them is hardwired to 1.)
+ matrix = array2d(BigFloat, n+d+1, n+d+1)
+ vector = array1d(BigFloat, n+d+1)
+ for i = 0:1:n
+ # Equation obtained by
diff erentiating with respect to p_i,
+ # i.e. the numerator coefficient of x^i.
+ row = 1+i
+ for j = 0:1:n
+ matrix[row, 1+j] = sums[1+i+j, 1]
+ end
+ for j = 1:1:d
+ matrix[row, 1+n+j] = -sums[1+i+j, 2]
+ end
+ vector[row] = sums[1+i, 2]
+ end
+ for i = 1:1:d
+ # Equation obtained by
diff erentiating with respect to q_i,
+ # i.e. the denominator coefficient of x^i.
+ row = 1+n+i
+ for j = 0:1:n
+ matrix[row, 1+j] = sums[1+i+j, 2]
+ end
+ for j = 1:1:d
+ matrix[row, 1+n+j] = -sums[1+i+j, 3]
+ end
+ vector[row] = sums[1+i, 3]
+ end
+
+ @debug("leastsquares", "matrix=", repr(matrix))
+ @debug("leastsquares", "vector=", repr(vector))
+
+ # Solve the matrix equation.
+ all_coeffs = matrix \ vector
+
+ @debug("leastsquares", "all_coeffs=", repr(all_coeffs))
+
+ # And marshal the results into two separate polynomial vectors to
+ # return.
+ ncoeffs = all_coeffs[1:n+1]
+ dcoeffs = vcat([1], all_coeffs[n+2:n+d+1])
+ return (ncoeffs, dcoeffs)
+end
+
+# ----------------------------------------------------------------------
+# Golden-section search to find a maximum of a function.
+
+# Arguments:
+# f Function to be maximised/minimised. Maps BigFloat -> BigFloat.
+# a,b,c BigFloats bracketing a maximum of the function.
+#
+# Expects:
+# a,b,c are in order (either a<=b<=c or c<=b<=a)
+# a != c (but b can equal one or the other if it wants to)
+# f(a) <= f(b) >= f(c)
+#
+# Return value is an (x,y) pair of BigFloats giving the extremal input
+# and output. (That is, y=f(x).)
+function goldensection(f::Function, a::BigFloat, b::BigFloat, c::BigFloat)
+ # Decide on a 'good enough' threshold.
+ threshold = abs(c-a) * 2^(-epsbits/2)
+
+ # We'll need the golden ratio phi, of course. Or rather, in this
+ # case, we need 1/phi = 0.618...
+ one_over_phi = 2 / (1 + sqrt(BigFloat(5)))
+
+ # Flip round the interval endpoints so that the interval [a,b] is
+ # at least as large as [b,c]. (Then we can always pick our new
+ # point in [a,b] without having to handle lots of special cases.)
+ if abs(b-a) < abs(c-a)
+ a, c = c, a
+ end
+
+ # Evaluate the function at the initial points.
+ fa = f(a)
+ fb = f(b)
+ fc = f(c)
+
+ @debug("goldensection", "starting")
+
+ while abs(c-a) > threshold
+ @debug("goldensection", "a: ", a, " -> ", fa)
+ @debug("goldensection", "b: ", b, " -> ", fb)
+ @debug("goldensection", "c: ", c, " -> ", fc)
+
+ # Check invariants.
+ @assert(a <= b <= c || c <= b <= a)
+ @assert(fa <= fb >= fc)
+
+ # Subdivide the larger of the intervals [a,b] and [b,c]. We've
+ # arranged that this is always [a,b], for simplicity.
+ d = a + (b-a) * one_over_phi
+
+ # Now we have an interval looking like this (possibly
+ # reversed):
+ #
+ # a d b c
+ #
+ # and we know f(b) is bigger than either f(a) or f(c). We have
+ # two cases: either f(d) > f(b), or vice versa. In either
+ # case, we can narrow to an interval of 1/phi the size, and
+ # still satisfy all our invariants (three ordered points,
+ # [a,b] at least the width of [b,c], f(a)<=f(b)>=f(c)).
+ fd = f(d)
+ @debug("goldensection", "d: ", d, " -> ", fd)
+ if fd > fb
+ a, b, c = a, d, b
+ fa, fb, fc = fa, fd, fb
+ @debug("goldensection", "adb case")
+ else
+ a, b, c = c, b, d
+ fa, fb, fc = fc, fb, fd
+ @debug("goldensection", "cbd case")
+ end
+ end
+
+ @debug("goldensection", "done: ", b, " -> ", fb)
+ return (b, fb)
+end
+
+# ----------------------------------------------------------------------
+# Find the extrema of a function within a given interval.
+
+# Arguments:
+# f The function to be approximated. Maps BigFloat -> BigFloat.
+# grid A set of points at which to evaluate f. Must be high enough
+# resolution to make extrema obvious.
+#
+# Returns an array of (x,y) pairs of BigFloats, with each x,y giving
+# the extremum location and its value (i.e. y=f(x)).
+function find_extrema(f::Function, grid::Array{BigFloat})
+ len = length(grid)
+ extrema = array1d(Tuple{BigFloat, BigFloat}, 0)
+ for i = 1:1:len
+ # We have to provide goldensection() with three points
+ # bracketing the extremum. If the extremum is at one end of
+ # the interval, then the only way we can do that is to set two
+ # of the points equal (which goldensection() will cope with).
+ prev = max(1, i-1)
+ next = min(i+1, len)
+
+ # Find our three pairs of (x,y) coordinates.
+ xp, xi, xn = grid[prev], grid[i], grid[next]
+ yp, yi, yn = f(xp), f(xi), f(xn)
+
+ # See if they look like an extremum, and if so, ask
+ # goldensection() to give a more exact location for it.
+ if yp <= yi >= yn
+ push!(extrema, goldensection(f, xp, xi, xn))
+ elseif yp >= yi <= yn
+ x, y = goldensection(x->-f(x), xp, xi, xn)
+ push!(extrema, (x, -y))
+ end
+ end
+ return extrema
+end
+
+# ----------------------------------------------------------------------
+# Winnow a list of a function's extrema to give a subsequence of a
+# specified length, with the extrema in the subsequence alternating
+# signs, and with the smallest absolute value of an extremum in the
+# subsequence as large as possible.
+#
+# We do this using a dynamic-programming approach. We work along the
+# provided array of extrema, and at all times, we track the best set
+# of extrema we have so far seen for each possible (length, sign of
+# last extremum) pair. Each new extremum is evaluated to see whether
+# it can be added to any previously seen best subsequence to make a
+# new subsequence that beats the previous record holder in its slot.
+
+# Arguments:
+# extrema An array of (x,y) pairs of BigFloats giving the input extrema.
+# n Number of extrema required as output.
+#
+# Returns a new array of (x,y) pairs which is a subsequence of the
+# original sequence. (So, in particular, if the input was sorted by x
+# then so will the output be.)
+function winnow_extrema(extrema::Array{Tuple{BigFloat,BigFloat}}, n)
+ # best[i,j] gives the best sequence so far of length i and with
+ # sign j (where signs are coded as 1=positive, 2=negative), in the
+ # form of a tuple (cost, actual array of x,y pairs).
+ best = fill((BigFloat(0), array1d(Tuple{BigFloat,BigFloat}, 0)), n, 2)
+
+ for (x,y) = extrema
+ if y > 0
+ sign = 1
+ elseif y < 0
+ sign = 2
+ else
+ # A zero-valued extremum cannot possibly contribute to any
+ # optimal sequence, so we simply ignore it!
+ continue
+ end
+
+ for i = 1:1:n
+ # See if we can create a new entry for best[i,sign] by
+ # appending our current (x,y) to some previous thing.
+ if i == 1
+ # Special case: we don't store a best zero-length
+ # sequence :-)
+ candidate = (abs(y), [(x,y)])
+ else
+ othersign = 3-sign # map 1->2 and 2->1
+ oldscore, oldlist = best[i-1, othersign]
+ newscore = min(abs(y), oldscore)
+ newlist = vcat(oldlist, [(x,y)])
+ candidate = (newscore, newlist)
+ end
+ # If our new candidate improves on the previous value of
+ # best[i,sign], then replace it.
+ if candidate[1] > best[i,sign][1]
+ best[i,sign] = candidate
+ end
+ end
+ end
+
+ # Our ultimate return value has to be either best[n,1] or
+ # best[n,2], but it could be either. See which one has the higher
+ # score.
+ if best[n,1][1] > best[n,2][1]
+ ret = best[n,1][2]
+ else
+ ret = best[n,2][2]
+ end
+ # Make sure we did actually _find_ a good answer.
+ @assert(length(ret) == n)
+ return ret
+end
+
+# ----------------------------------------------------------------------
+# Construct a rational-function approximation with equal and
+# alternating weighted deviation at a specific set of x-coordinates.
+
+# Arguments:
+# f The function to be approximated. Maps BigFloat -> BigFloat.
+# coords An array of BigFloats giving the x-coordinates. There should
+# be n+d+2 of them.
+# n, d The degrees of the numerator and denominator of the desired
+# approximation.
+# prev_err A plausible value for the alternating weighted deviation.
+# (Required to kickstart a binary search in the nonlinear case;
+# see comments below.)
+# w Error-weighting function. Takes two BigFloat arguments x,y
+# and returns a scaling factor for the error at that location.
+# The returned approximation R should have the minimum possible
+# maximum value of abs((f(x)-R(x)) * w(x,f(x))). Optional
+# parameter, defaulting to the always-return-1 function.
+#
+# Return values: a pair of arrays of BigFloats (N,D) giving the
+# coefficients of the returned rational function. N has size n+1; D
+# has size d+1. Both start with the constant term, i.e. N[i] is the
+# coefficient of x^(i-1) (because Julia arrays are 1-based). D[1] will
+# be 1.
+function ratfn_equal_deviation(f::Function, coords::Array{BigFloat},
+ n, d, prev_err::BigFloat,
+ w = (x,y)->BigFloat(1))
+ @debug("equaldev", "n=", n, " d=", d, " coords=", repr(coords))
+ @assert(length(coords) == n+d+2)
+
+ if d == 0
+ # Special case: we're after a polynomial. In this case, we
+ # have the particularly easy job of just constructing and
+ # solving a system of n+2 linear equations, to find the n+1
+ # coefficients of the polynomial and also the amount of
+ # deviation at the specified coordinates. Each equation is of
+ # the form
+ #
+ # p_0 x^0 + p_1 x^1 + ... + p_n x^n ± e/w(x) = f(x)
+ #
+ # in which the p_i and e are the variables, and the powers of
+ # x and calls to w and f are the coefficients.
+
+ matrix = array2d(BigFloat, n+2, n+2)
+ vector = array1d(BigFloat, n+2)
+ currsign = +1
+ for i = 1:1:n+2
+ x = coords[i]
+ for j = 0:1:n
+ matrix[i,1+j] = x^j
+ end
+ y = f(x)
+ vector[i] = y
+ matrix[i, n+2] = currsign / w(x,y)
+ currsign = -currsign
+ end
+
+ @debug("equaldev", "matrix=", repr(matrix))
+ @debug("equaldev", "vector=", repr(vector))
+
+ outvector = matrix \ vector
+
+ @debug("equaldev", "outvector=", repr(outvector))
+
+ ncoeffs = outvector[1:n+1]
+ dcoeffs = [BigFloat(1)]
+ return ncoeffs, dcoeffs
+ else
+ # For a nontrivial rational function, the system of equations
+ # we need to solve becomes nonlinear, because each equation
+ # now takes the form
+ #
+ # p_0 x^0 + p_1 x^1 + ... + p_n x^n
+ # --------------------------------- ± e/w(x) = f(x)
+ # x^0 + q_1 x^1 + ... + q_d x^d
+ #
+ # and multiplying up by the denominator gives you a lot of
+ # terms containing e × q_i. So we can't do this the really
+ # easy way using a matrix equation as above.
+ #
+ # Fortunately, this is a fairly easy kind of nonlinear system.
+ # The equations all become linear if you switch to treating e
+ # as a constant, so a reasonably sensible approach is to pick
+ # a candidate value of e, solve all but one of the equations
+ # for the remaining unknowns, and then see what the error
+ # turns out to be in the final equation. The Chebyshev
+ # alternation theorem guarantees that that error in the last
+ # equation will be anti-monotonic in the input e, so we can
+ # just binary-search until we get the two as close to equal as
+ # we need them.
+
+ function try_e(e)
+ # Try a given value of e, derive the coefficients of the
+ # resulting rational function by setting up equations
+ # based on the first n+d+1 of the n+d+2 coordinates, and
+ # see what the error turns out to be at the final
+ # coordinate.
+ matrix = array2d(BigFloat, n+d+1, n+d+1)
+ vector = array1d(BigFloat, n+d+1)
+ currsign = +1
+ for i = 1:1:n+d+1
+ x = coords[i]
+ y = f(x)
+ y_adj = y - currsign * e / w(x,y)
+ for j = 0:1:n
+ matrix[i,1+j] = x^j
+ end
+ for j = 1:1:d
+ matrix[i,1+n+j] = -x^j * y_adj
+ end
+ vector[i] = y_adj
+ currsign = -currsign
+ end
+
+ @debug("equaldev", "trying e=", e)
+ @debug("equaldev", "matrix=", repr(matrix))
+ @debug("equaldev", "vector=", repr(vector))
+
+ outvector = matrix \ vector
+
+ @debug("equaldev", "outvector=", repr(outvector))
+
+ ncoeffs = outvector[1:n+1]
+ dcoeffs = vcat([BigFloat(1)], outvector[n+2:n+d+1])
+
+ x = coords[n+d+2]
+ y = f(x)
+ last_e = (ratfn_eval(ncoeffs, dcoeffs, x) - y) * w(x,y) * -currsign
+
+ @debug("equaldev", "last e=", last_e)
+
+ return ncoeffs, dcoeffs, last_e
+ end
+
+ threshold = 2^(-epsbits/2) # convergence threshold
+
+ # Start by trying our previous iteration's error value. This
+ # value (e0) will be one end of our binary-search interval,
+ # and whatever it caused the last point's error to be, that
+ # (e1) will be the other end.
+ e0 = prev_err
+ @debug("equaldev", "e0 = ", e0)
+ nc, dc, e1 = try_e(e0)
+ @debug("equaldev", "e1 = ", e1)
+ if abs(e1-e0) <= threshold
+ # If we're _really_ lucky, we hit the error right on the
+ # nose just by doing that!
+ return nc, dc
+ end
+ s = sign(e1-e0)
+ @debug("equaldev", "s = ", s)
+
+ # Verify by assertion that trying our other interval endpoint
+ # e1 gives a value that's wrong in the other direction.
+ # (Otherwise our binary search won't get a sensible answer at
+ # all.)
+ nc, dc, e2 = try_e(e1)
+ @debug("equaldev", "e2 = ", e2)
+ @assert(sign(e2-e1) == -s)
+
+ # Now binary-search until our two endpoints narrow enough.
+ local emid
+ while abs(e1-e0) > threshold
+ emid = (e1+e0)/2
+ nc, dc, enew = try_e(emid)
+ if sign(enew-emid) == s
+ e0 = emid
+ else
+ e1 = emid
+ end
+ end
+
+ @debug("equaldev", "final e=", emid)
+ return nc, dc
+ end
+end
+
+# ----------------------------------------------------------------------
+# Top-level function to find a minimax rational-function approximation.
+
+# Arguments:
+# f The function to be approximated. Maps BigFloat -> BigFloat.
+# interval A pair of BigFloats giving the endpoints of the interval
+# (in either order) on which to approximate f.
+# n, d The degrees of the numerator and denominator of the desired
+# approximation.
+# w Error-weighting function. Takes two BigFloat arguments x,y
+# and returns a scaling factor for the error at that location.
+# The returned approximation R should have the minimum possible
+# maximum value of abs((f(x)-R(x)) * w(x,f(x))). Optional
+# parameter, defaulting to the always-return-1 function.
+#
+# Return values: a tuple (N,D,E,X), where
+
+# N,D A pair of arrays of BigFloats giving the coefficients
+# of the returned rational function. N has size n+1; D
+# has size d+1. Both start with the constant term, i.e.
+# N[i] is the coefficient of x^(i-1) (because Julia
+# arrays are 1-based). D[1] will be 1.
+# E The maximum weighted error (BigFloat).
+# X An array of pairs of BigFloats giving the locations of n+2
+# points and the weighted error at each of those points. The
+# weighted error values will have alternating signs, which
+# means that the Chebyshev alternation theorem guarantees
+# that any other function of the same degree must exceed
+# the error of this one at at least one of those points.
+function ratfn_minimax(f::Function, interval::Tuple{BigFloat,BigFloat}, n, d,
+ w = (x,y)->BigFloat(1))
+ # We start off by finding a least-squares approximation. This
+ # doesn't need to be perfect, but if we can get it reasonably good
+ # then it'll save iterations in the refining stage.
+ #
+ # Least-squares approximations tend to look nicer in a minimax
+ # sense if you evaluate the function at a big pile of Chebyshev
+ # nodes rather than uniformly spaced points. These values will
+ # also make a good grid to use for the initial search for error
+ # extrema, so we'll keep them around for that reason too.
+
+ # Construct the grid.
+ lo, hi = minimum(interval), maximum(interval)
+ local grid
+ let
+ mid = (hi+lo)/2
+ halfwid = (hi-lo)/2
+ nnodes = 16 * (n+d+1)
+ pi = 2*asin(BigFloat(1))
+ grid = [ mid - halfwid * cos(pi*i/nnodes) for i=0:1:nnodes ]
+ end
+
+ # Find the initial least-squares approximation.
+ (nc, dc) = ratfn_leastsquares(f, grid, n, d, w)
+ @debug("minimax", "initial leastsquares approx = ",
+ ratfn_to_string(nc, dc))
+
+ # Threshold of convergence. We stop when the relative
diff erence
+ # between the min and max (winnowed) error extrema is less than
+ # this.
+ #
+ # This is set to the cube root of machine epsilon on a more or
+ # less empirical basis, because the rational-function case will
+ # not converge reliably if you set it to only the square root.
+ # (Repeatable by using the --test mode.) On the assumption that
+ # input and output error in each iteration can be expected to be
+ # related by a simple power law (because it'll just be down to how
+ # many leading terms of a Taylor series are zero), the cube root
+ # was the next thing to try.
+ threshold = 2^(-epsbits/3)
+
+ # Main loop.
+ while true
+ # Find all the error extrema we can.
+ function compute_error(x)
+ real_y = f(x)
+ approx_y = ratfn_eval(nc, dc, x)
+ return (approx_y - real_y) * w(x, real_y)
+ end
+ extrema = find_extrema(compute_error, grid)
+ @debug("minimax", "all extrema = ", format_xylist(extrema))
+
+ # Winnow the extrema down to the right number, and ensure they
+ # have alternating sign.
+ extrema = winnow_extrema(extrema, n+d+2)
+ @debug("minimax", "winnowed extrema = ", format_xylist(extrema))
+
+ # See if we've finished.
+ min_err = minimum([abs(y) for (x,y) = extrema])
+ max_err = maximum([abs(y) for (x,y) = extrema])
+ variation = (max_err - min_err) / max_err
+ @debug("minimax", "extremum variation = ", variation)
+ if variation < threshold
+ @debug("minimax", "done!")
+ return nc, dc, max_err, extrema
+ end
+
+ # If not, refine our function by equalising the error at the
+ # extrema points, and go round again.
+ (nc, dc) = ratfn_equal_deviation(f, map(x->x[1], extrema),
+ n, d, max_err, w)
+ @debug("minimax", "refined approx = ", ratfn_to_string(nc, dc))
+ end
+end
+
+# ----------------------------------------------------------------------
+# Check if a polynomial is well-conditioned for accurate evaluation in
+# a given interval by Horner's rule.
+#
+# This is true if at every step where Horner's rule computes
+# (coefficient + x*value_so_far), the constant coefficient you're
+# adding on is of larger magnitude than the x*value_so_far operand.
+# And this has to be true for every x in the interval.
+#
+# Arguments:
+# coeffs The coefficients of the polynomial under test. Starts with
+# the constant term, i.e. coeffs[i] is the coefficient of
+# x^(i-1) (because Julia arrays are 1-based).
+# lo, hi The bounds of the interval.
+#
+# Return value: the largest ratio (x*value_so_far / coefficient), at
+# any step of evaluation, for any x in the interval. If this is less
+# than 1, the polynomial is at least somewhat well-conditioned;
+# ideally you want it to be more like 1/8 or 1/16 or so, so that the
+# relative rounding error accumulated at each step are reduced by
+# several factors of 2 when the next coefficient is added on.
+
+function wellcond(coeffs, lo, hi)
+ x = max(abs(lo), abs(hi))
+ worst = 0
+ so_far = 0
+ for i = length(coeffs):-1:1
+ coeff = abs(coeffs[i])
+ so_far *= x
+ if coeff != 0
+ thisval = so_far / coeff
+ worst = max(worst, thisval)
+ so_far += coeff
+ end
+ end
+ return worst
+end
+
+# ----------------------------------------------------------------------
+# Small set of unit tests.
+
+function test()
+ passes = 0
+ fails = 0
+
+ function approx_eq(x, y, limit=1e-6)
+ return abs(x - y) < limit
+ end
+
+ function test(condition)
+ if condition
+ passes += 1
+ else
+ println("fail")
+ fails += 1
+ end
+ end
+
+ # Test Gaussian elimination.
+ println("Gaussian test 1:")
+ m = BigFloat[1 1 2; 3 5 8; 13 34 21]
+ v = BigFloat[1, -1, 2]
+ ret = m \ v
+ println(" ",repr(ret))
+ test(approx_eq(ret[1], 109/26))
+ test(approx_eq(ret[2], -105/130))
+ test(approx_eq(ret[3], -31/26))
+
+ # Test leastsquares rational functions.
+ println("Leastsquares test 1:")
+ n = 10000
+ a = array1d(BigFloat, n+1)
+ for i = 0:1:n
+ a[1+i] = i/BigFloat(n)
+ end
+ (nc, dc) = ratfn_leastsquares(x->exp(x), a, 2, 2)
+ println(" ",ratfn_to_string(nc, dc))
+ for x = a
+ test(approx_eq(exp(x), ratfn_eval(nc, dc, x), 1e-4))
+ end
+
+ # Test golden section search.
+ println("Golden section test 1:")
+ x, y = goldensection(x->sin(x),
+ BigFloat(0), BigFloat(1)/10, BigFloat(4))
+ println(" ", x, " -> ", y)
+ test(approx_eq(x, asin(BigFloat(1))))
+ test(approx_eq(y, 1))
+
+ # Test extrema-winnowing algorithm.
+ println("Winnow test 1:")
+ extrema = [(x, sin(20*x)*sin(197*x))
+ for x in BigFloat(0):BigFloat(1)/1000:BigFloat(1)]
+ winnowed = winnow_extrema(extrema, 12)
+ println(" ret = ", format_xylist(winnowed))
+ prevx, prevy = -1, 0
+ for (x,y) = winnowed
+ test(x > prevx)
+ test(y != 0)
+ test(prevy * y <= 0) # tolerates initial prevx having no sign
+ test(abs(y) > 0.9)
+ prevx, prevy = x, y
+ end
+
+ # Test actual minimax approximation.
+ println("Minimax test 1 (polynomial):")
+ (nc, dc, e, x) = ratfn_minimax(x->exp(x), (BigFloat(0), BigFloat(1)), 4, 0)
+ println(" ",e)
+ println(" ",ratfn_to_string(nc, dc))
+ test(0 < e < 1e-3)
+ for x = 0:BigFloat(1)/1000:1
+ test(abs(ratfn_eval(nc, dc, x) - exp(x)) <= e * 1.0000001)
+ end
+
+ println("Minimax test 2 (rational):")
+ (nc, dc, e, x) = ratfn_minimax(x->exp(x), (BigFloat(0), BigFloat(1)), 2, 2)
+ println(" ",e)
+ println(" ",ratfn_to_string(nc, dc))
+ test(0 < e < 1e-3)
+ for x = 0:BigFloat(1)/1000:1
+ test(abs(ratfn_eval(nc, dc, x) - exp(x)) <= e * 1.0000001)
+ end
+
+ println("Minimax test 3 (polynomial, weighted):")
+ (nc, dc, e, x) = ratfn_minimax(x->exp(x), (BigFloat(0), BigFloat(1)), 4, 0,
+ (x,y)->1/y)
+ println(" ",e)
+ println(" ",ratfn_to_string(nc, dc))
+ test(0 < e < 1e-3)
+ for x = 0:BigFloat(1)/1000:1
+ test(abs(ratfn_eval(nc, dc, x) - exp(x))/exp(x) <= e * 1.0000001)
+ end
+
+ println("Minimax test 4 (rational, weighted):")
+ (nc, dc, e, x) = ratfn_minimax(x->exp(x), (BigFloat(0), BigFloat(1)), 2, 2,
+ (x,y)->1/y)
+ println(" ",e)
+ println(" ",ratfn_to_string(nc, dc))
+ test(0 < e < 1e-3)
+ for x = 0:BigFloat(1)/1000:1
+ test(abs(ratfn_eval(nc, dc, x) - exp(x))/exp(x) <= e * 1.0000001)
+ end
+
+ println("Minimax test 5 (rational, weighted, odd degree):")
+ (nc, dc, e, x) = ratfn_minimax(x->exp(x), (BigFloat(0), BigFloat(1)), 2, 1,
+ (x,y)->1/y)
+ println(" ",e)
+ println(" ",ratfn_to_string(nc, dc))
+ test(0 < e < 1e-3)
+ for x = 0:BigFloat(1)/1000:1
+ test(abs(ratfn_eval(nc, dc, x) - exp(x))/exp(x) <= e * 1.0000001)
+ end
+
+ total = passes + fails
+ println(passes, " passes ", fails, " fails ", total, " total")
+end
+
+# ----------------------------------------------------------------------
+# Online help.
+function help()
+ print("""
+Usage:
+
+ remez.jl [options] <lo> <hi> <n> <d> <expr> [<weight>]
+
+Arguments:
+
+ <lo>, <hi>
+
+ Bounds of the interval on which to approximate the target
+ function. These are parsed and evaluated as Julia expressions,
+ so you can write things like '1/BigFloat(6)' to get an
+ accurate representation of 1/6, or '4*atan(BigFloat(1))' to
+ get pi. (Unfortunately, the obvious 'BigFloat(pi)' doesn't
+ work in Julia.)
+
+ <n>, <d>
+
+ The desired degree of polynomial(s) you want for your
+ approximation. These should be non-negative integers. If you
+ want a rational function as output, set <n> to the degree of
+ the numerator, and <d> the denominator. If you just want an
+ ordinary polynomial, set <d> to 0, and <n> to the degree of
+ the polynomial you want.
+
+ <expr>
+
+ A Julia expression giving the function to be approximated on
+ the interval. The input value is predefined as 'x' when this
+ expression is evaluated, so you should write something along
+ the lines of 'sin(x)' or 'sqrt(1+tan(x)^2)' etc.
+
+ <weight>
+
+ If provided, a Julia expression giving the weighting factor
+ for the approximation error. The output polynomial will
+ minimise the largest absolute value of (P-f) * w at any point
+ in the interval, where P is the value of the polynomial, f is
+ the value of the target function given by <expr>, and w is the
+ weight given by this function.
+
+ When this expression is evaluated, the input value to P and f
+ is predefined as 'x', and also the true output value f(x) is
+ predefined as 'y'. So you can minimise the relative error by
+ simply writing '1/y'.
+
+ If the <weight> argument is not provided, the default
+ weighting function always returns 1, so that the polynomial
+ will minimise the maximum absolute error |P-f|.
+
+Computation options:
+
+ --pre=<predef_expr>
+
+ Evaluate the Julia expression <predef_expr> before starting
+ the computation. This permits you to pre-define variables or
+ functions which the Julia expressions in your main arguments
+ can refer to. All of <lo>, <hi>, <expr> and <weight> can make
+ use of things defined by <predef_expr>.
+
+ One internal remez.jl function that you might sometimes find
+ useful in this expression is 'goldensection', which finds the
+ location and value of a maximum of a function. For example,
+ one implementation strategy for the gamma function involves
+ translating it to put its unique local minimum at the origin,
+ in which case you can write something like this
+
+ --pre='(m,my) = goldensection(x -> -gamma(x),
+ BigFloat(1), BigFloat(1.5), BigFloat(2))'
+
+ to predefine 'm' as the location of gamma's minimum, and 'my'
+ as the (negated) value that gamma actually takes at that
+ point, i.e. -gamma(m).
+
+ (Since 'goldensection' always finds a maximum, we had to
+ negate gamma in the input function to make it find a minimum
+ instead. Consult the comments in the source for more details
+ on the use of this function.)
+
+ If you use this option more than once, all the expressions you
+ provide will be run in sequence.
+
+ --bits=<bits>
+
+ Specify the accuracy to which you want the output polynomial,
+ in bits. Default 256, which should be more than enough.
+
+ --bigfloatbits=<bits>
+
+ Turn up the precision used by Julia for its BigFloat
+ evaluation. Default is Julia's default (also 256). You might
+ want to try setting this higher than the --bits value if the
+ algorithm is failing to converge for some reason.
+
+Output options:
+
+ --full
+
+ Instead of just printing the approximation function itself,
+ also print auxiliary information:
+ - the locations of the error extrema, and the actual
+ (weighted) error at each of those locations
+ - the overall maximum error of the function
+ - a 'well-conditioning quotient', giving the worst-case ratio
+ between any polynomial coefficient and the largest possible
+ value of the higher-order terms it will be added to.
+
+ The well-conditioning quotient should be less than 1, ideally
+ by several factors of two, for accurate evaluation in the
+ target precision. If you request a rational function, a
+ separate well-conditioning quotient will be printed for the
+ numerator and denominator.
+
+ Use this option when deciding how wide an interval to
+ approximate your function on, and what degree of polynomial
+ you need.
+
+ --variable=<identifier>
+
+ When writing the output polynomial or rational function in its
+ usual form as an arithmetic expression, use <identifier> as
+ the name of the input variable. Default is 'x'.
+
+ --suffix=<suffix>
+
+ When writing the output polynomial or rational function in its
+ usual form as an arithmetic expression, write <suffix> after
+ every floating-point literal. For example, '--suffix=F' will
+ generate a C expression in which the coefficients are literals
+ of type 'float' rather than 'double'.
+
+ --array
+
+ Instead of writing the output polynomial as an arithmetic
+ expression in Horner's rule form, write out just its
+ coefficients, one per line, each with a trailing comma.
+ Suitable for pasting into a C array declaration.
+
+ This option is not currently supported if the output is a
+ rational function, because you'd need two separate arrays for
+ the numerator and denominator coefficients and there's no
+ obviously right way to provide both of those together.
+
+Debug and test options:
+
+ --debug=<facility>
+
+ Enable debugging output from various parts of the Remez
+ calculation. <facility> should be the name of one of the
+ classes of diagnostic output implemented in the program.
+ Useful values include 'gausselim', 'leastsquares',
+ 'goldensection', 'equaldev', 'minimax'. This is probably
+ mostly useful to people debugging problems with the script, so
+ consult the source code for more information about what the
+ diagnostic output for each of those facilities will be.
+
+ If you want diagnostics from more than one facility, specify
+ this option multiple times with
diff erent arguments.
+
+ --test
+
+ Run remez.jl's internal test suite. No arguments needed.
+
+Miscellaneous options:
+
+ --help
+
+ Display this text and exit. No arguments needed.
+
+""")
+end
+
+# ----------------------------------------------------------------------
+# Main program.
+
+function main()
+ nargs = length(argwords)
+ if nargs != 5 && nargs != 6
+ error("usage: remez.jl <lo> <hi> <n> <d> <expr> [<weight>]\n" *
+ " run 'remez.jl --help' for more help")
+ end
+
+ for preliminary_command in preliminary_commands
+ eval(Meta.parse(preliminary_command))
+ end
+
+ lo = BigFloat(eval(Meta.parse(argwords[1])))
+ hi = BigFloat(eval(Meta.parse(argwords[2])))
+ n = parse(Int,argwords[3])
+ d = parse(Int,argwords[4])
+ f = eval(Meta.parse("x -> " * argwords[5]))
+
+ # Wrap the user-provided function with a function of our own. This
+ # arranges to detect silly FP values (inf,nan) early and diagnose
+ # them sensibly, and also lets us log all evaluations of the
+ # function in case you suspect it's doing the wrong thing at some
+ # special-case point.
+ function func(x)
+ y = run(f,x)
+ @debug("f", x, " -> ", y)
+ if !isfinite(y)
+ error("f(" * string(x) * ") returned non-finite value " * string(y))
+ end
+ return y
+ end
+
+ if nargs == 6
+ # Wrap the user-provided weight function similarly.
+ w = eval(Meta.parse("(x,y) -> " * argwords[6]))
+ function wrapped_weight(x,y)
+ ww = run(w,x,y)
+ if !isfinite(ww)
+ error("w(" * string(x) * "," * string(y) *
+ ") returned non-finite value " * string(ww))
+ end
+ return ww
+ end
+ weight = wrapped_weight
+ else
+ weight = (x,y)->BigFloat(1)
+ end
+
+ (nc, dc, e, extrema) = ratfn_minimax(func, (lo, hi), n, d, weight)
+ if array_format
+ if d == 0
+ functext = join([string(x)*",\n" for x=nc],"")
+ else
+ # It's unclear how you should best format an array of
+ # coefficients for a rational function, so I'll leave
+ # implementing this option until I have a use case.
+ error("--array unsupported for rational functions")
+ end
+ else
+ functext = ratfn_to_string(nc, dc) * "\n"
+ end
+ if full_output
+ # Print everything you might want to know about the function
+ println("extrema = ", format_xylist(extrema))
+ println("maxerror = ", string(e))
+ if length(dc) > 1
+ println("wellconditioning_numerator = ",
+ string(wellcond(nc, lo, hi)))
+ println("wellconditioning_denominator = ",
+ string(wellcond(dc, lo, hi)))
+ else
+ println("wellconditioning = ", string(wellcond(nc, lo, hi)))
+ end
+ print("function = ", functext)
+ else
+ # Just print the text people will want to paste into their code
+ print(functext)
+ end
+end
+
+# ----------------------------------------------------------------------
+# Top-level code: parse the argument list and decide what to do.
+
+what_to_do = main
+
+doing_opts = true
+argwords = array1d(String, 0)
+for arg = ARGS
+ global doing_opts, what_to_do, argwords
+ global full_output, array_format, xvarname, floatsuffix, epsbits
+ if doing_opts && startswith(arg, "-")
+ if arg == "--"
+ doing_opts = false
+ elseif arg == "--help"
+ what_to_do = help
+ elseif arg == "--test"
+ what_to_do = test
+ elseif arg == "--full"
+ full_output = true
+ elseif arg == "--array"
+ array_format = true
+ elseif startswith(arg, "--debug=")
+ enable_debug(arg[length("--debug=")+1:end])
+ elseif startswith(arg, "--variable=")
+ xvarname = arg[length("--variable=")+1:end]
+ elseif startswith(arg, "--suffix=")
+ floatsuffix = arg[length("--suffix=")+1:end]
+ elseif startswith(arg, "--bits=")
+ epsbits = parse(Int,arg[length("--bits=")+1:end])
+ elseif startswith(arg, "--bigfloatbits=")
+ set_bigfloat_precision(
+ parse(Int,arg[length("--bigfloatbits=")+1:end]))
+ elseif startswith(arg, "--pre=")
+ push!(preliminary_commands, arg[length("--pre=")+1:end])
+ else
+ error("unrecognised option: ", arg)
+ end
+ else
+ push!(argwords, arg)
+ end
+end
+
+what_to_do()
diff --git a/libc/AOR_v20.02/math/tools/sin.sollya b/libc/AOR_v20.02/math/tools/sin.sollya
new file mode 100644
index 000000000000..f5c11ec2f191
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/sin.sollya
@@ -0,0 +1,38 @@
+// polynomial for approximating sin(x)
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 7; // polynomial degree
+a = -pi/4; // interval
+b = pi/4;
+
+// find even polynomial with minimal abs error compared to sin(x)/x
+
+// account for /x
+deg = deg-1;
+
+// f = sin(x)/x;
+f = 1;
+c = 1;
+for i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; };
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg/2 do {
+ p = roundcoefficients(approx(poly,2*i), [|D ...|]);
+ poly = poly + x^(2*i)*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("abs error:", accurateinfnorm(sin(x)-x*poly(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/v_exp.sollya b/libc/AOR_v20.02/math/tools/v_exp.sollya
new file mode 100644
index 000000000000..4ef477f90020
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/v_exp.sollya
@@ -0,0 +1,31 @@
+// polynomial for approximating e^x
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 4; // poly degree
+N = 128; // table entries
+b = log(2)/(2*N); // interval
+a = -b;
+
+// find polynomial with minimal abs error
+
+// return p that minimizes |exp(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first 2 coeffs are fixed, iteratively find optimal double prec coeffs
+poly = 1 + x;
+for i from 2 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30));
+print("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/v_log.sollya b/libc/AOR_v20.02/math/tools/v_log.sollya
new file mode 100644
index 000000000000..d23b9da48460
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/v_log.sollya
@@ -0,0 +1,35 @@
+// polynomial used for __v_log(x)
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 6; // poly degree
+a = -0x1.fc1p-9;
+b = 0x1.009p-8;
+
+// find log(1+x)/x polynomial with minimal relative error
+// (minimal relative error polynomial for log(1+x) is the same * x)
+deg = deg-1; // because of /x
+
+// f = log(1+x)/x; using taylor series
+f = 0;
+for i from 0 to 60 do { f = f + (-x)^i/(i+1); };
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
+approx = proc(poly,d) {
+ return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/tools/v_sin.sollya b/libc/AOR_v20.02/math/tools/v_sin.sollya
new file mode 100644
index 000000000000..5c596427daab
--- /dev/null
+++ b/libc/AOR_v20.02/math/tools/v_sin.sollya
@@ -0,0 +1,37 @@
+// polynomial for approximating sin(x)
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+deg = 15; // polynomial degree
+a = -pi/2; // interval
+b = pi/2;
+
+// find even polynomial with minimal abs error compared to sin(x)/x
+
+// account for /x
+deg = deg-1;
+
+// f = sin(x)/x;
+f = 1;
+c = 1;
+for i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; };
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(f(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = 1;
+for i from 1 to deg/2 do {
+ p = roundcoefficients(approx(poly,2*i), [|D ...|]);
+ poly = poly + x^(2*i)*coeff(p,0);
+};
+
+display = hexadecimal;
+print("abs error:", accurateinfnorm(sin(x)-x*poly(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
diff --git a/libc/AOR_v20.02/math/v_cos.c b/libc/AOR_v20.02/math/v_cos.c
new file mode 100644
index 000000000000..1eebdbceeda0
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_cos.c
@@ -0,0 +1,88 @@
+/*
+ * Double-precision vector cos function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const double Poly[] = {
+/* worst-case error is 3.5 ulp.
+ abs error: 0x1.be222a58p-53 in [-pi/2, pi/2]. */
+-0x1.9f4a9c8b21dc9p-41,
+ 0x1.60e88a10163f2p-33,
+-0x1.ae6361b7254e7p-26,
+ 0x1.71de382e8d62bp-19,
+-0x1.a01a019aeb4ffp-13,
+ 0x1.111111110b25ep-7,
+-0x1.55555555554c3p-3,
+};
+
+#define C7 v_f64 (Poly[0])
+#define C6 v_f64 (Poly[1])
+#define C5 v_f64 (Poly[2])
+#define C4 v_f64 (Poly[3])
+#define C3 v_f64 (Poly[4])
+#define C2 v_f64 (Poly[5])
+#define C1 v_f64 (Poly[6])
+
+#define InvPi v_f64 (0x1.45f306dc9c883p-2)
+#define HalfPi v_f64 (0x1.921fb54442d18p+0)
+#define Pi1 v_f64 (0x1.921fb54442d18p+1)
+#define Pi2 v_f64 (0x1.1a62633145c06p-53)
+#define Pi3 v_f64 (0x1.c1cd129024e09p-106)
+#define Shift v_f64 (0x1.8p52)
+#define RangeVal v_f64 (0x1p23)
+#define AbsMask v_u64 (0x7fffffffffffffff)
+
+VPCS_ATTR
+__attribute__ ((noinline)) static v_f64_t
+specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
+{
+ return v_call_f64 (cos, x, y, cmp);
+}
+
+VPCS_ATTR
+v_f64_t
+V_NAME(cos) (v_f64_t x)
+{
+ v_f64_t n, r, r2, y;
+ v_u64_t odd, cmp;
+
+ r = v_as_f64_u64 (v_as_u64_f64 (x) & AbsMask);
+ cmp = v_cond_u64 (v_as_u64_f64 (r) >= v_as_u64_f64 (RangeVal));
+
+ /* n = rint((|x|+pi/2)/pi) - 0.5. */
+ n = v_fma_f64 (InvPi, r + HalfPi, Shift);
+ odd = v_as_u64_f64 (n) << 63;
+ n -= Shift;
+ n -= v_f64 (0.5);
+
+ /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
+ r = v_fma_f64 (-Pi1, n, r);
+ r = v_fma_f64 (-Pi2, n, r);
+ r = v_fma_f64 (-Pi3, n, r);
+
+ /* sin(r) poly approx. */
+ r2 = r * r;
+ y = v_fma_f64 (C7, r2, C6);
+ y = v_fma_f64 (y, r2, C5);
+ y = v_fma_f64 (y, r2, C4);
+ y = v_fma_f64 (y, r2, C3);
+ y = v_fma_f64 (y, r2, C2);
+ y = v_fma_f64 (y, r2, C1);
+ y = v_fma_f64 (y * r2, r, r);
+
+ /* sign. */
+ y = v_as_f64_u64 (v_as_u64_f64 (y) ^ odd);
+
+ if (unlikely (v_any_u64 (cmp)))
+ return specialcase (x, y, cmp);
+ return y;
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_cosf.c b/libc/AOR_v20.02/math/v_cosf.c
new file mode 100644
index 000000000000..b9dcd486f4b2
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_cosf.c
@@ -0,0 +1,77 @@
+/*
+ * Single-precision vector cos function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const float Poly[] = {
+ /* 1.886 ulp error */
+ 0x1.5b2e76p-19f,
+ -0x1.9f42eap-13f,
+ 0x1.110df4p-7f,
+ -0x1.555548p-3f,
+};
+#define Pi1 v_f32 (0x1.921fb6p+1f)
+#define Pi2 v_f32 (-0x1.777a5cp-24f)
+#define Pi3 v_f32 (-0x1.ee59dap-49f)
+#define A3 v_f32 (Poly[3])
+#define A5 v_f32 (Poly[2])
+#define A7 v_f32 (Poly[1])
+#define A9 v_f32 (Poly[0])
+#define RangeVal v_f32 (0x1p20f)
+#define InvPi v_f32 (0x1.45f306p-2f)
+#define Shift v_f32 (0x1.8p+23f)
+#define AbsMask v_u32 (0x7fffffff)
+#define HalfPi v_f32 (0x1.921fb6p0f)
+
+VPCS_ATTR
+static v_f32_t
+specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
+{
+ /* Fall back to scalar code. */
+ return v_call_f32 (cosf, x, y, cmp);
+}
+
+VPCS_ATTR
+v_f32_t
+V_NAME(cosf) (v_f32_t x)
+{
+ v_f32_t n, r, r2, y;
+ v_u32_t odd, cmp;
+
+ r = v_as_f32_u32 (v_as_u32_f32 (x) & AbsMask);
+ cmp = v_cond_u32 (v_as_u32_f32 (r) >= v_as_u32_f32 (RangeVal));
+
+ /* n = rint((|x|+pi/2)/pi) - 0.5 */
+ n = v_fma_f32 (InvPi, r + HalfPi, Shift);
+ odd = v_as_u32_f32 (n) << 31;
+ n -= Shift;
+ n -= v_f32 (0.5f);
+
+ /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2) */
+ r = v_fma_f32 (-Pi1, n, r);
+ r = v_fma_f32 (-Pi2, n, r);
+ r = v_fma_f32 (-Pi3, n, r);
+
+ /* y = sin(r) */
+ r2 = r * r;
+ y = v_fma_f32 (A9, r2, A7);
+ y = v_fma_f32 (y, r2, A5);
+ y = v_fma_f32 (y, r2, A3);
+ y = v_fma_f32 (y * r2, r, r);
+
+ /* sign fix */
+ y = v_as_f32_u32 (v_as_u32_f32 (y) ^ odd);
+
+ if (unlikely (v_any_u32 (cmp)))
+ return specialcase (x, y, cmp);
+ return y;
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_exp.c b/libc/AOR_v20.02/math/v_exp.c
new file mode 100644
index 000000000000..9074cecdd154
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_exp.c
@@ -0,0 +1,95 @@
+/*
+ * Double-precision vector e^x function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+#include "v_exp.h"
+
+#if V_EXP_TABLE_BITS == 7
+/* maxerr: 1.88 +0.5 ulp
+ rel error: 1.4337*2^-53
+ abs error: 1.4299*2^-53 in [ -ln2/256, ln2/256 ]. */
+#define C1 v_f64 (0x1.ffffffffffd43p-2)
+#define C2 v_f64 (0x1.55555c75adbb2p-3)
+#define C3 v_f64 (0x1.55555da646206p-5)
+#define InvLn2 v_f64 (0x1.71547652b82fep7) /* N/ln2. */
+#define Ln2hi v_f64 (0x1.62e42fefa39efp-8) /* ln2/N. */
+#define Ln2lo v_f64 (0x1.abc9e3b39803f3p-63)
+#elif V_EXP_TABLE_BITS == 8
+/* maxerr: 0.54 +0.5 ulp
+ rel error: 1.4318*2^-58
+ abs error: 1.4299*2^-58 in [ -ln2/512, ln2/512 ]. */
+#define C1 v_f64 (0x1.fffffffffffd4p-2)
+#define C2 v_f64 (0x1.5555571d6b68cp-3)
+#define C3 v_f64 (0x1.5555576a59599p-5)
+#define InvLn2 v_f64 (0x1.71547652b82fep8)
+#define Ln2hi v_f64 (0x1.62e42fefa39efp-9)
+#define Ln2lo v_f64 (0x1.abc9e3b39803f3p-64)
+#endif
+
+#define N (1 << V_EXP_TABLE_BITS)
+#define Tab __v_exp_data
+#define IndexMask v_u64 (N - 1)
+#define Shift v_f64 (0x1.8p+52)
+#define Thres v_f64 (704.0)
+
+VPCS_ATTR
+static v_f64_t
+specialcase (v_f64_t s, v_f64_t y, v_f64_t n)
+{
+ v_f64_t absn = v_abs_f64 (n);
+
+ /* 2^(n/N) may overflow, break it up into s1*s2. */
+ v_u64_t b = v_cond_u64 (n <= v_f64 (0.0)) & v_u64 (0x6000000000000000);
+ v_f64_t s1 = v_as_f64_u64 (v_u64 (0x7000000000000000) - b);
+ v_f64_t s2 = v_as_f64_u64 (v_as_u64_f64 (s) - v_u64 (0x3010000000000000) + b);
+ v_u64_t cmp = v_cond_u64 (absn > v_f64 (1280.0 * N));
+ v_f64_t r1 = s1 * s1;
+ v_f64_t r0 = v_fma_f64 (y, s2, s2) * s1;
+ return v_as_f64_u64 ((cmp & v_as_u64_f64 (r1)) | (~cmp & v_as_u64_f64 (r0)));
+}
+
+VPCS_ATTR
+v_f64_t
+V_NAME(exp) (v_f64_t x)
+{
+ v_f64_t n, r, r2, s, y, z;
+ v_u64_t cmp, u, e, i;
+
+ cmp = v_cond_u64 (v_abs_f64 (x) > Thres);
+
+ /* n = round(x/(ln2/N)). */
+ z = v_fma_f64 (x, InvLn2, Shift);
+ u = v_as_u64_f64 (z);
+ n = z - Shift;
+
+ /* r = x - n*ln2/N. */
+ r = x;
+ r = v_fma_f64 (-Ln2hi, n, r);
+ r = v_fma_f64 (-Ln2lo, n, r);
+
+ e = u << (52 - V_EXP_TABLE_BITS);
+ i = u & IndexMask;
+
+ /* y = exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */
+ r2 = r * r;
+ y = v_fma_f64 (C2, r, C1);
+ y = v_fma_f64 (C3, r2, y);
+ y = v_fma_f64 (y, r2, r);
+
+ /* s = 2^(n/N). */
+ u = v_lookup_u64 (Tab, i);
+ s = v_as_f64_u64 (u + e);
+
+ if (unlikely (v_any_u64 (cmp)))
+ return specialcase (s, y, n);
+ return v_fma_f64 (y, s, s);
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_exp.h b/libc/AOR_v20.02/math/v_exp.h
new file mode 100644
index 000000000000..251c85dc5255
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_exp.h
@@ -0,0 +1,15 @@
+/*
+ * Declarations for double-precision e^x vector function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "v_math.h"
+#if WANT_VMATH
+
+#define V_EXP_TABLE_BITS 7
+
+extern const u64_t __v_exp_data[1 << V_EXP_TABLE_BITS] HIDDEN;
+#endif
diff --git a/libc/AOR_v20.02/math/v_exp2f.c b/libc/AOR_v20.02/math/v_exp2f.c
new file mode 100644
index 000000000000..876298fea531
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_exp2f.c
@@ -0,0 +1,79 @@
+/*
+ * Single-precision vector 2^x function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const float Poly[] = {
+ /* maxerr: 1.962 ulp. */
+ 0x1.59977ap-10f,
+ 0x1.3ce9e4p-7f,
+ 0x1.c6bd32p-5f,
+ 0x1.ebf9bcp-3f,
+ 0x1.62e422p-1f,
+};
+#define C0 v_f32 (Poly[0])
+#define C1 v_f32 (Poly[1])
+#define C2 v_f32 (Poly[2])
+#define C3 v_f32 (Poly[3])
+#define C4 v_f32 (Poly[4])
+
+#define Shift v_f32 (0x1.8p23f)
+
+VPCS_ATTR
+static v_f32_t
+specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale)
+{
+ /* 2^n may overflow, break it up into s1*s2. */
+ v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000);
+ v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
+ v_f32_t s2 = v_as_f32_u32 (e - b);
+ v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f));
+ v_u32_t r2 = v_as_u32_f32 (s1 * s1);
+ v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);
+ /* Similar to r1 but avoids double rounding in the subnormal range. */
+ v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));
+ return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));
+}
+
+VPCS_ATTR
+v_f32_t
+V_NAME(exp2f) (v_f32_t x)
+{
+ v_f32_t n, r, r2, scale, p, q, poly, absn;
+ v_u32_t cmp, e;
+
+ /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
+ x = n + r, with r in [-1/2, 1/2]. */
+#if 0
+ v_f32_t z;
+ z = x + Shift;
+ n = z - Shift;
+ r = x - n;
+ e = v_as_u32_f32 (z) << 23;
+#else
+ n = v_round_f32 (x);
+ r = x - n;
+ e = v_as_u32_s32 (v_round_s32 (x)) << 23;
+#endif
+ scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
+ absn = v_abs_f32 (n);
+ cmp = v_cond_u32 (absn > v_f32 (126.0f));
+ r2 = r * r;
+ p = v_fma_f32 (C0, r, C1);
+ q = v_fma_f32 (C2, r, C3);
+ q = v_fma_f32 (p, r2, q);
+ p = C4 * r;
+ poly = v_fma_f32 (q, r2, p);
+ if (unlikely (v_any_u32 (cmp)))
+ return specialcase (poly, n, e, absn, cmp, scale);
+ return v_fma_f32 (poly, scale, scale);
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_exp2f_1u.c b/libc/AOR_v20.02/math/v_exp2f_1u.c
new file mode 100644
index 000000000000..d8b660e15f23
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_exp2f_1u.c
@@ -0,0 +1,76 @@
+/*
+ * Single-precision vector 2^x function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const float Poly[] = {
+ /* maxerr: 0.878 ulp. */
+ 0x1.416b5ep-13f, 0x1.5f082ep-10f, 0x1.3b2dep-7f, 0x1.c6af7cp-5f, 0x1.ebfbdcp-3f, 0x1.62e43p-1f
+};
+#define C0 v_f32 (Poly[0])
+#define C1 v_f32 (Poly[1])
+#define C2 v_f32 (Poly[2])
+#define C3 v_f32 (Poly[3])
+#define C4 v_f32 (Poly[4])
+#define C5 v_f32 (Poly[5])
+
+#define Shift v_f32 (0x1.8p23f)
+#define InvLn2 v_f32 (0x1.715476p+0f)
+#define Ln2hi v_f32 (0x1.62e4p-1f)
+#define Ln2lo v_f32 (0x1.7f7d1cp-20f)
+
+VPCS_ATTR
+static v_f32_t
+specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn)
+{
+ /* 2^n may overflow, break it up into s1*s2. */
+ v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x83000000);
+ v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
+ v_f32_t s2 = v_as_f32_u32 (e - b);
+ v_u32_t cmp = v_cond_u32 (absn > v_f32 (192.0f));
+ v_f32_t r1 = s1 * s1;
+ v_f32_t r0 = poly * s1 * s2;
+ return v_as_f32_u32 ((cmp & v_as_u32_f32 (r1)) | (~cmp & v_as_u32_f32 (r0)));
+}
+
+VPCS_ATTR
+v_f32_t
+V_NAME(exp2f_1u) (v_f32_t x)
+{
+ v_f32_t n, r, scale, poly, absn;
+ v_u32_t cmp, e;
+
+ /* exp2(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]
+ x = n + r, with r in [-1/2, 1/2]. */
+#if 0
+ v_f32_t z;
+ z = x + Shift;
+ n = z - Shift;
+ r = x - n;
+ e = v_as_u32_f32 (z) << 23;
+#else
+ n = v_round_f32 (x);
+ r = x - n;
+ e = v_as_u32_s32 (v_round_s32 (x)) << 23;
+#endif
+ scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
+ absn = v_abs_f32 (n);
+ cmp = v_cond_u32 (absn > v_f32 (126.0f));
+ poly = v_fma_f32 (C0, r, C1);
+ poly = v_fma_f32 (poly, r, C2);
+ poly = v_fma_f32 (poly, r, C3);
+ poly = v_fma_f32 (poly, r, C4);
+ poly = v_fma_f32 (poly, r, C5);
+ poly = v_fma_f32 (poly, r, v_f32 (1.0f));
+ if (unlikely (v_any_u32 (cmp)))
+ return specialcase (poly, n, e, absn);
+ return scale * poly;
+}
+#endif
diff --git a/libc/AOR_v20.02/math/v_exp_data.c b/libc/AOR_v20.02/math/v_exp_data.c
new file mode 100644
index 000000000000..fc248e3ce479
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_exp_data.c
@@ -0,0 +1,404 @@
+/*
+ * Lookup table for double-precision e^x vector function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "v_exp.h"
+#if WANT_VMATH
+
+#define N (1 << V_EXP_TABLE_BITS)
+
+/* 2^(j/N), j=0..N. */
+const u64_t __v_exp_data[] = {
+#if N == 128
+0x3ff0000000000000,
+0x3feff63da9fb3335,
+0x3fefec9a3e778061,
+0x3fefe315e86e7f85,
+0x3fefd9b0d3158574,
+0x3fefd06b29ddf6de,
+0x3fefc74518759bc8,
+0x3fefbe3ecac6f383,
+0x3fefb5586cf9890f,
+0x3fefac922b7247f7,
+0x3fefa3ec32d3d1a2,
+0x3fef9b66affed31b,
+0x3fef9301d0125b51,
+0x3fef8abdc06c31cc,
+0x3fef829aaea92de0,
+0x3fef7a98c8a58e51,
+0x3fef72b83c7d517b,
+0x3fef6af9388c8dea,
+0x3fef635beb6fcb75,
+0x3fef5be084045cd4,
+0x3fef54873168b9aa,
+0x3fef4d5022fcd91d,
+0x3fef463b88628cd6,
+0x3fef3f49917ddc96,
+0x3fef387a6e756238,
+0x3fef31ce4fb2a63f,
+0x3fef2b4565e27cdd,
+0x3fef24dfe1f56381,
+0x3fef1e9df51fdee1,
+0x3fef187fd0dad990,
+0x3fef1285a6e4030b,
+0x3fef0cafa93e2f56,
+0x3fef06fe0a31b715,
+0x3fef0170fc4cd831,
+0x3feefc08b26416ff,
+0x3feef6c55f929ff1,
+0x3feef1a7373aa9cb,
+0x3feeecae6d05d866,
+0x3feee7db34e59ff7,
+0x3feee32dc313a8e5,
+0x3feedea64c123422,
+0x3feeda4504ac801c,
+0x3feed60a21f72e2a,
+0x3feed1f5d950a897,
+0x3feece086061892d,
+0x3feeca41ed1d0057,
+0x3feec6a2b5c13cd0,
+0x3feec32af0d7d3de,
+0x3feebfdad5362a27,
+0x3feebcb299fddd0d,
+0x3feeb9b2769d2ca7,
+0x3feeb6daa2cf6642,
+0x3feeb42b569d4f82,
+0x3feeb1a4ca5d920f,
+0x3feeaf4736b527da,
+0x3feead12d497c7fd,
+0x3feeab07dd485429,
+0x3feea9268a5946b7,
+0x3feea76f15ad2148,
+0x3feea5e1b976dc09,
+0x3feea47eb03a5585,
+0x3feea34634ccc320,
+0x3feea23882552225,
+0x3feea155d44ca973,
+0x3feea09e667f3bcd,
+0x3feea012750bdabf,
+0x3fee9fb23c651a2f,
+0x3fee9f7df9519484,
+0x3fee9f75e8ec5f74,
+0x3fee9f9a48a58174,
+0x3fee9feb564267c9,
+0x3feea0694fde5d3f,
+0x3feea11473eb0187,
+0x3feea1ed0130c132,
+0x3feea2f336cf4e62,
+0x3feea427543e1a12,
+0x3feea589994cce13,
+0x3feea71a4623c7ad,
+0x3feea8d99b4492ed,
+0x3feeaac7d98a6699,
+0x3feeace5422aa0db,
+0x3feeaf3216b5448c,
+0x3feeb1ae99157736,
+0x3feeb45b0b91ffc6,
+0x3feeb737b0cdc5e5,
+0x3feeba44cbc8520f,
+0x3feebd829fde4e50,
+0x3feec0f170ca07ba,
+0x3feec49182a3f090,
+0x3feec86319e32323,
+0x3feecc667b5de565,
+0x3feed09bec4a2d33,
+0x3feed503b23e255d,
+0x3feed99e1330b358,
+0x3feede6b5579fdbf,
+0x3feee36bbfd3f37a,
+0x3feee89f995ad3ad,
+0x3feeee07298db666,
+0x3feef3a2b84f15fb,
+0x3feef9728de5593a,
+0x3feeff76f2fb5e47,
+0x3fef05b030a1064a,
+0x3fef0c1e904bc1d2,
+0x3fef12c25bd71e09,
+0x3fef199bdd85529c,
+0x3fef20ab5fffd07a,
+0x3fef27f12e57d14b,
+0x3fef2f6d9406e7b5,
+0x3fef3720dcef9069,
+0x3fef3f0b555dc3fa,
+0x3fef472d4a07897c,
+0x3fef4f87080d89f2,
+0x3fef5818dcfba487,
+0x3fef60e316c98398,
+0x3fef69e603db3285,
+0x3fef7321f301b460,
+0x3fef7c97337b9b5f,
+0x3fef864614f5a129,
+0x3fef902ee78b3ff6,
+0x3fef9a51fbc74c83,
+0x3fefa4afa2a490da,
+0x3fefaf482d8e67f1,
+0x3fefba1bee615a27,
+0x3fefc52b376bba97,
+0x3fefd0765b6e4540,
+0x3fefdbfdad9cbe14,
+0x3fefe7c1819e90d8,
+0x3feff3c22b8f71f1,
+#elif N == 256
+0x3ff0000000000000,
+0x3feffb1afa5abcbf,
+0x3feff63da9fb3335,
+0x3feff168143b0281,
+0x3fefec9a3e778061,
+0x3fefe7d42e11bbcc,
+0x3fefe315e86e7f85,
+0x3fefde5f72f654b1,
+0x3fefd9b0d3158574,
+0x3fefd50a0e3c1f89,
+0x3fefd06b29ddf6de,
+0x3fefcbd42b72a836,
+0x3fefc74518759bc8,
+0x3fefc2bdf66607e0,
+0x3fefbe3ecac6f383,
+0x3fefb9c79b1f3919,
+0x3fefb5586cf9890f,
+0x3fefb0f145e46c85,
+0x3fefac922b7247f7,
+0x3fefa83b23395dec,
+0x3fefa3ec32d3d1a2,
+0x3fef9fa55fdfa9c5,
+0x3fef9b66affed31b,
+0x3fef973028d7233e,
+0x3fef9301d0125b51,
+0x3fef8edbab5e2ab6,
+0x3fef8abdc06c31cc,
+0x3fef86a814f204ab,
+0x3fef829aaea92de0,
+0x3fef7e95934f312e,
+0x3fef7a98c8a58e51,
+0x3fef76a45471c3c2,
+0x3fef72b83c7d517b,
+0x3fef6ed48695bbc0,
+0x3fef6af9388c8dea,
+0x3fef672658375d2f,
+0x3fef635beb6fcb75,
+0x3fef5f99f8138a1c,
+0x3fef5be084045cd4,
+0x3fef582f95281c6b,
+0x3fef54873168b9aa,
+0x3fef50e75eb44027,
+0x3fef4d5022fcd91d,
+0x3fef49c18438ce4d,
+0x3fef463b88628cd6,
+0x3fef42be3578a819,
+0x3fef3f49917ddc96,
+0x3fef3bdda27912d1,
+0x3fef387a6e756238,
+0x3fef351ffb82140a,
+0x3fef31ce4fb2a63f,
+0x3fef2e85711ece75,
+0x3fef2b4565e27cdd,
+0x3fef280e341ddf29,
+0x3fef24dfe1f56381,
+0x3fef21ba7591bb70,
+0x3fef1e9df51fdee1,
+0x3fef1b8a66d10f13,
+0x3fef187fd0dad990,
+0x3fef157e39771b2f,
+0x3fef1285a6e4030b,
+0x3fef0f961f641589,
+0x3fef0cafa93e2f56,
+0x3fef09d24abd886b,
+0x3fef06fe0a31b715,
+0x3fef0432edeeb2fd,
+0x3fef0170fc4cd831,
+0x3feefeb83ba8ea32,
+0x3feefc08b26416ff,
+0x3feef96266e3fa2d,
+0x3feef6c55f929ff1,
+0x3feef431a2de883b,
+0x3feef1a7373aa9cb,
+0x3feeef26231e754a,
+0x3feeecae6d05d866,
+0x3feeea401b7140ef,
+0x3feee7db34e59ff7,
+0x3feee57fbfec6cf4,
+0x3feee32dc313a8e5,
+0x3feee0e544ede173,
+0x3feedea64c123422,
+0x3feedc70df1c5175,
+0x3feeda4504ac801c,
+0x3feed822c367a024,
+0x3feed60a21f72e2a,
+0x3feed3fb2709468a,
+0x3feed1f5d950a897,
+0x3feecffa3f84b9d4,
+0x3feece086061892d,
+0x3feecc2042a7d232,
+0x3feeca41ed1d0057,
+0x3feec86d668b3237,
+0x3feec6a2b5c13cd0,
+0x3feec4e1e192aed2,
+0x3feec32af0d7d3de,
+0x3feec17dea6db7d7,
+0x3feebfdad5362a27,
+0x3feebe41b817c114,
+0x3feebcb299fddd0d,
+0x3feebb2d81d8abff,
+0x3feeb9b2769d2ca7,
+0x3feeb8417f4531ee,
+0x3feeb6daa2cf6642,
+0x3feeb57de83f4eef,
+0x3feeb42b569d4f82,
+0x3feeb2e2f4f6ad27,
+0x3feeb1a4ca5d920f,
+0x3feeb070dde910d2,
+0x3feeaf4736b527da,
+0x3feeae27dbe2c4cf,
+0x3feead12d497c7fd,
+0x3feeac0827ff07cc,
+0x3feeab07dd485429,
+0x3feeaa11fba87a03,
+0x3feea9268a5946b7,
+0x3feea84590998b93,
+0x3feea76f15ad2148,
+0x3feea6a320dceb71,
+0x3feea5e1b976dc09,
+0x3feea52ae6cdf6f4,
+0x3feea47eb03a5585,
+0x3feea3dd1d1929fd,
+0x3feea34634ccc320,
+0x3feea2b9febc8fb7,
+0x3feea23882552225,
+0x3feea1c1c70833f6,
+0x3feea155d44ca973,
+0x3feea0f4b19e9538,
+0x3feea09e667f3bcd,
+0x3feea052fa75173e,
+0x3feea012750bdabf,
+0x3fee9fdcddd47645,
+0x3fee9fb23c651a2f,
+0x3fee9f9298593ae5,
+0x3fee9f7df9519484,
+0x3fee9f7466f42e87,
+0x3fee9f75e8ec5f74,
+0x3fee9f8286ead08a,
+0x3fee9f9a48a58174,
+0x3fee9fbd35d7cbfd,
+0x3fee9feb564267c9,
+0x3feea024b1ab6e09,
+0x3feea0694fde5d3f,
+0x3feea0b938ac1cf6,
+0x3feea11473eb0187,
+0x3feea17b0976cfdb,
+0x3feea1ed0130c132,
+0x3feea26a62ff86f0,
+0x3feea2f336cf4e62,
+0x3feea3878491c491,
+0x3feea427543e1a12,
+0x3feea4d2add106d9,
+0x3feea589994cce13,
+0x3feea64c1eb941f7,
+0x3feea71a4623c7ad,
+0x3feea7f4179f5b21,
+0x3feea8d99b4492ed,
+0x3feea9cad931a436,
+0x3feeaac7d98a6699,
+0x3feeabd0a478580f,
+0x3feeace5422aa0db,
+0x3feeae05bad61778,
+0x3feeaf3216b5448c,
+0x3feeb06a5e0866d9,
+0x3feeb1ae99157736,
+0x3feeb2fed0282c8a,
+0x3feeb45b0b91ffc6,
+0x3feeb5c353aa2fe2,
+0x3feeb737b0cdc5e5,
+0x3feeb8b82b5f98e5,
+0x3feeba44cbc8520f,
+0x3feebbdd9a7670b3,
+0x3feebd829fde4e50,
+0x3feebf33e47a22a2,
+0x3feec0f170ca07ba,
+0x3feec2bb4d53fe0d,
+0x3feec49182a3f090,
+0x3feec674194bb8d5,
+0x3feec86319e32323,
+0x3feeca5e8d07f29e,
+0x3feecc667b5de565,
+0x3feece7aed8eb8bb,
+0x3feed09bec4a2d33,
+0x3feed2c980460ad8,
+0x3feed503b23e255d,
+0x3feed74a8af46052,
+0x3feed99e1330b358,
+0x3feedbfe53c12e59,
+0x3feede6b5579fdbf,
+0x3feee0e521356eba,
+0x3feee36bbfd3f37a,
+0x3feee5ff3a3c2774,
+0x3feee89f995ad3ad,
+0x3feeeb4ce622f2ff,
+0x3feeee07298db666,
+0x3feef0ce6c9a8952,
+0x3feef3a2b84f15fb,
+0x3feef68415b749b1,
+0x3feef9728de5593a,
+0x3feefc6e29f1c52a,
+0x3feeff76f2fb5e47,
+0x3fef028cf22749e4,
+0x3fef05b030a1064a,
+0x3fef08e0b79a6f1f,
+0x3fef0c1e904bc1d2,
+0x3fef0f69c3f3a207,
+0x3fef12c25bd71e09,
+0x3fef16286141b33d,
+0x3fef199bdd85529c,
+0x3fef1d1cd9fa652c,
+0x3fef20ab5fffd07a,
+0x3fef244778fafb22,
+0x3fef27f12e57d14b,
+0x3fef2ba88988c933,
+0x3fef2f6d9406e7b5,
+0x3fef33405751c4db,
+0x3fef3720dcef9069,
+0x3fef3b0f2e6d1675,
+0x3fef3f0b555dc3fa,
+0x3fef43155b5bab74,
+0x3fef472d4a07897c,
+0x3fef4b532b08c968,
+0x3fef4f87080d89f2,
+0x3fef53c8eacaa1d6,
+0x3fef5818dcfba487,
+0x3fef5c76e862e6d3,
+0x3fef60e316c98398,
+0x3fef655d71ff6075,
+0x3fef69e603db3285,
+0x3fef6e7cd63a8315,
+0x3fef7321f301b460,
+0x3fef77d5641c0658,
+0x3fef7c97337b9b5f,
+0x3fef81676b197d17,
+0x3fef864614f5a129,
+0x3fef8b333b16ee12,
+0x3fef902ee78b3ff6,
+0x3fef953924676d76,
+0x3fef9a51fbc74c83,
+0x3fef9f7977cdb740,
+0x3fefa4afa2a490da,
+0x3fefa9f4867cca6e,
+0x3fefaf482d8e67f1,
+0x3fefb4aaa2188510,
+0x3fefba1bee615a27,
+0x3fefbf9c1cb6412a,
+0x3fefc52b376bba97,
+0x3fefcac948dd7274,
+0x3fefd0765b6e4540,
+0x3fefd632798844f8,
+0x3fefdbfdad9cbe14,
+0x3fefe1d802243c89,
+0x3fefe7c1819e90d8,
+0x3fefedba3692d514,
+0x3feff3c22b8f71f1,
+0x3feff9d96b2a23d9,
+#endif
+};
+#endif
diff --git a/libc/AOR_v20.02/math/v_expf.c b/libc/AOR_v20.02/math/v_expf.c
new file mode 100644
index 000000000000..b9223b2519b1
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_expf.c
@@ -0,0 +1,84 @@
+/*
+ * Single-precision vector e^x function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const float Poly[] = {
+ /* maxerr: 1.45358 +0.5 ulp. */
+ 0x1.0e4020p-7f,
+ 0x1.573e2ep-5f,
+ 0x1.555e66p-3f,
+ 0x1.fffdb6p-2f,
+ 0x1.ffffecp-1f,
+};
+#define C0 v_f32 (Poly[0])
+#define C1 v_f32 (Poly[1])
+#define C2 v_f32 (Poly[2])
+#define C3 v_f32 (Poly[3])
+#define C4 v_f32 (Poly[4])
+
+#define Shift v_f32 (0x1.8p23f)
+#define InvLn2 v_f32 (0x1.715476p+0f)
+#define Ln2hi v_f32 (0x1.62e4p-1f)
+#define Ln2lo v_f32 (0x1.7f7d1cp-20f)
+
+VPCS_ATTR
+static v_f32_t
+specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale)
+{
+ /* 2^n may overflow, break it up into s1*s2. */
+ v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000);
+ v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
+ v_f32_t s2 = v_as_f32_u32 (e - b);
+ v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f));
+ v_u32_t r2 = v_as_u32_f32 (s1 * s1);
+ v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);
+ /* Similar to r1 but avoids double rounding in the subnormal range. */
+ v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));
+ return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));
+}
+
+VPCS_ATTR
+v_f32_t
+V_NAME(expf) (v_f32_t x)
+{
+ v_f32_t n, r, r2, scale, p, q, poly, absn, z;
+ v_u32_t cmp, e;
+
+ /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
+ x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
+#if 1
+ z = v_fma_f32 (x, InvLn2, Shift);
+ n = z - Shift;
+ r = v_fma_f32 (n, -Ln2hi, x);
+ r = v_fma_f32 (n, -Ln2lo, r);
+ e = v_as_u32_f32 (z) << 23;
+#else
+ z = x * InvLn2;
+ n = v_round_f32 (z);
+ r = v_fma_f32 (n, -Ln2hi, x);
+ r = v_fma_f32 (n, -Ln2lo, r);
+ e = v_as_u32_s32 (v_round_s32 (z)) << 23;
+#endif
+ scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
+ absn = v_abs_f32 (n);
+ cmp = v_cond_u32 (absn > v_f32 (126.0f));
+ r2 = r * r;
+ p = v_fma_f32 (C0, r, C1);
+ q = v_fma_f32 (C2, r, C3);
+ q = v_fma_f32 (p, r2, q);
+ p = C4 * r;
+ poly = v_fma_f32 (q, r2, p);
+ if (unlikely (v_any_u32 (cmp)))
+ return specialcase (poly, n, e, absn, cmp, scale);
+ return v_fma_f32 (poly, scale, scale);
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_expf_1u.c b/libc/AOR_v20.02/math/v_expf_1u.c
new file mode 100644
index 000000000000..640ca1f5cad6
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_expf_1u.c
@@ -0,0 +1,81 @@
+/*
+ * Single-precision vector e^x function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const float Poly[] = {
+ /* maxerr: 0.36565 +0.5 ulp. */
+ 0x1.6a6000p-10f,
+ 0x1.12718ep-7f,
+ 0x1.555af0p-5f,
+ 0x1.555430p-3f,
+ 0x1.fffff4p-2f,
+};
+#define C0 v_f32 (Poly[0])
+#define C1 v_f32 (Poly[1])
+#define C2 v_f32 (Poly[2])
+#define C3 v_f32 (Poly[3])
+#define C4 v_f32 (Poly[4])
+
+#define Shift v_f32 (0x1.8p23f)
+#define InvLn2 v_f32 (0x1.715476p+0f)
+#define Ln2hi v_f32 (0x1.62e4p-1f)
+#define Ln2lo v_f32 (0x1.7f7d1cp-20f)
+
+VPCS_ATTR
+static v_f32_t
+specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn)
+{
+ /* 2^n may overflow, break it up into s1*s2. */
+ v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x83000000);
+ v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
+ v_f32_t s2 = v_as_f32_u32 (e - b);
+ v_u32_t cmp = v_cond_u32 (absn > v_f32 (192.0f));
+ v_f32_t r1 = s1 * s1;
+ v_f32_t r0 = poly * s1 * s2;
+ return v_as_f32_u32 ((cmp & v_as_u32_f32 (r1)) | (~cmp & v_as_u32_f32 (r0)));
+}
+
+VPCS_ATTR
+v_f32_t
+V_NAME(expf_1u) (v_f32_t x)
+{
+ v_f32_t n, r, scale, poly, absn, z;
+ v_u32_t cmp, e;
+
+ /* exp(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]
+ x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
+#if 1
+ z = v_fma_f32 (x, InvLn2, Shift);
+ n = z - Shift;
+ r = v_fma_f32 (n, -Ln2hi, x);
+ r = v_fma_f32 (n, -Ln2lo, r);
+ e = v_as_u32_f32 (z) << 23;
+#else
+ z = x * InvLn2;
+ n = v_round_f32 (z);
+ r = v_fma_f32 (n, -Ln2hi, x);
+ r = v_fma_f32 (n, -Ln2lo, r);
+ e = v_as_u32_s32 (v_round_s32 (z)) << 23;
+#endif
+ scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
+ absn = v_abs_f32 (n);
+ cmp = v_cond_u32 (absn > v_f32 (126.0f));
+ poly = v_fma_f32 (C0, r, C1);
+ poly = v_fma_f32 (poly, r, C2);
+ poly = v_fma_f32 (poly, r, C3);
+ poly = v_fma_f32 (poly, r, C4);
+ poly = v_fma_f32 (poly, r, v_f32 (1.0f));
+ poly = v_fma_f32 (poly, r, v_f32 (1.0f));
+ if (unlikely (v_any_u32 (cmp)))
+ return specialcase (poly, n, e, absn);
+ return scale * poly;
+}
+#endif
diff --git a/libc/AOR_v20.02/math/v_log.c b/libc/AOR_v20.02/math/v_log.c
new file mode 100644
index 000000000000..06340fe62584
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_log.c
@@ -0,0 +1,105 @@
+/*
+ * Double-precision vector log(x) function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#include "v_log.h"
+#if V_SUPPORTED
+
+/* Worst-case error: 1.17 + 0.5 ulp. */
+
+static const f64_t Poly[] = {
+ /* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */
+ -0x1.ffffffffffff7p-2,
+ 0x1.55555555170d4p-2,
+ -0x1.0000000399c27p-2,
+ 0x1.999b2e90e94cap-3,
+ -0x1.554e550bd501ep-3,
+};
+
+#define A0 v_f64 (Poly[0])
+#define A1 v_f64 (Poly[1])
+#define A2 v_f64 (Poly[2])
+#define A3 v_f64 (Poly[3])
+#define A4 v_f64 (Poly[4])
+#define Ln2 v_f64 (0x1.62e42fefa39efp-1)
+#define N (1 << V_LOG_TABLE_BITS)
+#define OFF v_u64 (0x3fe6900900000000)
+
+struct entry
+{
+ v_f64_t invc;
+ v_f64_t logc;
+};
+
+static inline struct entry
+lookup (v_u64_t i)
+{
+ struct entry e;
+#ifdef SCALAR
+ e.invc = __v_log_data[i].invc;
+ e.logc = __v_log_data[i].logc;
+#else
+ e.invc[0] = __v_log_data[i[0]].invc;
+ e.logc[0] = __v_log_data[i[0]].logc;
+ e.invc[1] = __v_log_data[i[1]].invc;
+ e.logc[1] = __v_log_data[i[1]].logc;
+#endif
+ return e;
+}
+
+VPCS_ATTR
+__attribute__ ((noinline)) static v_f64_t
+specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
+{
+ return v_call_f64 (log, x, y, cmp);
+}
+
+VPCS_ATTR
+v_f64_t
+V_NAME(log) (v_f64_t x)
+{
+ v_f64_t z, r, r2, p, y, kd, hi;
+ v_u64_t ix, iz, tmp, top, i, cmp;
+ v_s64_t k;
+ struct entry e;
+
+ ix = v_as_u64_f64 (x);
+ top = ix >> 48;
+ cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010));
+
+ /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+ The range is split into N subintervals.
+ The ith subinterval contains z and c is near its center. */
+ tmp = ix - OFF;
+ i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N;
+ k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */
+ iz = ix - (tmp & v_u64 (0xfffULL << 52));
+ z = v_as_f64_u64 (iz);
+ e = lookup (i);
+
+ /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
+ r = v_fma_f64 (z, e.invc, v_f64 (-1.0));
+ kd = v_to_f64_s64 (k);
+
+ /* hi = r + log(c) + k*Ln2. */
+ hi = v_fma_f64 (kd, Ln2, e.logc + r);
+ /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
+ r2 = r * r;
+ y = v_fma_f64 (A3, r, A2);
+ p = v_fma_f64 (A1, r, A0);
+ y = v_fma_f64 (A4, r2, y);
+ y = v_fma_f64 (y, r2, p);
+ y = v_fma_f64 (y, r2, hi);
+
+ if (unlikely (v_any_u64 (cmp)))
+ return specialcase (x, y, cmp);
+ return y;
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_log.h b/libc/AOR_v20.02/math/v_log.h
new file mode 100644
index 000000000000..a50fe9e4671b
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_log.h
@@ -0,0 +1,19 @@
+/*
+ * Declarations for double-precision log(x) vector function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "v_math.h"
+#if WANT_VMATH
+
+#define V_LOG_TABLE_BITS 7
+
+extern const struct v_log_data
+{
+ f64_t invc;
+ f64_t logc;
+} __v_log_data[1 << V_LOG_TABLE_BITS] HIDDEN;
+#endif
diff --git a/libc/AOR_v20.02/math/v_log_data.c b/libc/AOR_v20.02/math/v_log_data.c
new file mode 100644
index 000000000000..a7da633648a8
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_log_data.c
@@ -0,0 +1,159 @@
+/*
+ * Lookup table for double-precision log(x) vector function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "v_log.h"
+#if WANT_VMATH
+
+#define N (1 << V_LOG_TABLE_BITS)
+
+/* Algorithm:
+
+ x = 2^k z
+ log(x) = k ln2 + log(c) + poly(z/c - 1)
+
+where z is in [a;2a) which is split into N subintervals (a=0x1.69009p-1,N=128)
+and log(c) and 1/c for the ith subinterval comes from a lookup table:
+
+ tab[i].invc = 1/c
+ tab[i].logc = (double)log(c)
+
+where c is near the center of the subinterval and is chosen by trying several
+floating point invc candidates around 1/center and selecting one for which
+the error in (double)log(c) is minimized (< 0x1p-74), except the subinterval
+that contains 1 and the previous one got tweaked to avoid cancellation. */
+const struct v_log_data __v_log_data[N] = {
+{0x1.6a133d0dec120p+0, -0x1.62fe995eb963ap-2},
+{0x1.6815f2f3e42edp+0, -0x1.5d5a48dad6b67p-2},
+{0x1.661e39be1ac9ep+0, -0x1.57bde257d2769p-2},
+{0x1.642bfa30ac371p+0, -0x1.52294fbf2af55p-2},
+{0x1.623f1d916f323p+0, -0x1.4c9c7b598aa38p-2},
+{0x1.60578da220f65p+0, -0x1.47174fc5ff560p-2},
+{0x1.5e75349dea571p+0, -0x1.4199b7fa7b5cap-2},
+{0x1.5c97fd387a75ap+0, -0x1.3c239f48cfb99p-2},
+{0x1.5abfd2981f200p+0, -0x1.36b4f154d2aebp-2},
+{0x1.58eca051dc99cp+0, -0x1.314d9a0ff32fbp-2},
+{0x1.571e526d9df12p+0, -0x1.2bed85cca3cffp-2},
+{0x1.5554d555b3fcbp+0, -0x1.2694a11421af9p-2},
+{0x1.539015e2a20cdp+0, -0x1.2142d8d014fb2p-2},
+{0x1.51d0014ee0164p+0, -0x1.1bf81a2c77776p-2},
+{0x1.50148538cd9eep+0, -0x1.16b452a39c6a4p-2},
+{0x1.4e5d8f9f698a1p+0, -0x1.11776ffa6c67ep-2},
+{0x1.4cab0edca66bep+0, -0x1.0c416035020e0p-2},
+{0x1.4afcf1a9db874p+0, -0x1.071211aa10fdap-2},
+{0x1.495327136e16fp+0, -0x1.01e972e293b1bp-2},
+{0x1.47ad9e84af28fp+0, -0x1.f98ee587fd434p-3},
+{0x1.460c47b39ae15p+0, -0x1.ef5800ad716fbp-3},
+{0x1.446f12b278001p+0, -0x1.e52e160484698p-3},
+{0x1.42d5efdd720ecp+0, -0x1.db1104b19352ep-3},
+{0x1.4140cfe001a0fp+0, -0x1.d100ac59e0bd6p-3},
+{0x1.3fafa3b421f69p+0, -0x1.c6fced287c3bdp-3},
+{0x1.3e225c9c8ece5p+0, -0x1.bd05a7b317c29p-3},
+{0x1.3c98ec29a211ap+0, -0x1.b31abd229164fp-3},
+{0x1.3b13442a413fep+0, -0x1.a93c0edadb0a3p-3},
+{0x1.399156baa3c54p+0, -0x1.9f697ee30d7ddp-3},
+{0x1.38131639b4cdbp+0, -0x1.95a2efa9aa40ap-3},
+{0x1.36987540fbf53p+0, -0x1.8be843d796044p-3},
+{0x1.352166b648f61p+0, -0x1.82395ecc477edp-3},
+{0x1.33adddb3eb575p+0, -0x1.7896240966422p-3},
+{0x1.323dcd99fc1d3p+0, -0x1.6efe77aca8c55p-3},
+{0x1.30d129fefc7d2p+0, -0x1.65723e117ec5cp-3},
+{0x1.2f67e6b72fe7dp+0, -0x1.5bf15c0955706p-3},
+{0x1.2e01f7cf8b187p+0, -0x1.527bb6c111da1p-3},
+{0x1.2c9f518ddc86ep+0, -0x1.491133c939f8fp-3},
+{0x1.2b3fe86e5f413p+0, -0x1.3fb1b90c7fc58p-3},
+{0x1.29e3b1211b25cp+0, -0x1.365d2cc485f8dp-3},
+{0x1.288aa08b373cfp+0, -0x1.2d13758970de7p-3},
+{0x1.2734abcaa8467p+0, -0x1.23d47a721fd47p-3},
+{0x1.25e1c82459b81p+0, -0x1.1aa0229f25ec2p-3},
+{0x1.2491eb1ad59c5p+0, -0x1.117655ddebc3bp-3},
+{0x1.23450a54048b5p+0, -0x1.0856fbf83ab6bp-3},
+{0x1.21fb1bb09e578p+0, -0x1.fe83fabbaa106p-4},
+{0x1.20b415346d8f7p+0, -0x1.ec6e8507a56cdp-4},
+{0x1.1f6fed179a1acp+0, -0x1.da6d68c7cc2eap-4},
+{0x1.1e2e99b93c7b3p+0, -0x1.c88078462be0cp-4},
+{0x1.1cf011a7a882ap+0, -0x1.b6a786a423565p-4},
+{0x1.1bb44b97dba5ap+0, -0x1.a4e2676ac7f85p-4},
+{0x1.1a7b3e66cdd4fp+0, -0x1.9330eea777e76p-4},
+{0x1.1944e11dc56cdp+0, -0x1.8192f134d5ad9p-4},
+{0x1.18112aebb1a6ep+0, -0x1.70084464f0538p-4},
+{0x1.16e013231b7e9p+0, -0x1.5e90bdec5cb1fp-4},
+{0x1.15b1913f156cfp+0, -0x1.4d2c3433c5536p-4},
+{0x1.14859cdedde13p+0, -0x1.3bda7e219879ap-4},
+{0x1.135c2dc68cfa4p+0, -0x1.2a9b732d27194p-4},
+{0x1.12353bdb01684p+0, -0x1.196eeb2b10807p-4},
+{0x1.1110bf25b85b4p+0, -0x1.0854be8ef8a7ep-4},
+{0x1.0feeafd2f8577p+0, -0x1.ee998cb277432p-5},
+{0x1.0ecf062c51c3bp+0, -0x1.ccadb79919fb9p-5},
+{0x1.0db1baa076c8bp+0, -0x1.aae5b1d8618b0p-5},
+{0x1.0c96c5bb3048ep+0, -0x1.89413015d7442p-5},
+{0x1.0b7e20263e070p+0, -0x1.67bfe7bf158dep-5},
+{0x1.0a67c2acd0ce3p+0, -0x1.46618f83941bep-5},
+{0x1.0953a6391e982p+0, -0x1.2525df1b0618ap-5},
+{0x1.0841c3caea380p+0, -0x1.040c8e2f77c6ap-5},
+{0x1.07321489b13eap+0, -0x1.c62aad39f738ap-6},
+{0x1.062491aee9904p+0, -0x1.847fe3bdead9cp-6},
+{0x1.05193497a7cc5p+0, -0x1.43183683400acp-6},
+{0x1.040ff6b5f5e9fp+0, -0x1.01f31c4e1d544p-6},
+{0x1.0308d19aa6127p+0, -0x1.82201d1e6b69ap-7},
+{0x1.0203beedb0c67p+0, -0x1.00dd0f3e1bfd6p-7},
+{0x1.010037d38bcc2p+0, -0x1.ff6fe1feb4e53p-9},
+{1.0, 0.0},
+{0x1.fc06d493cca10p-1, 0x1.fe91885ec8e20p-8},
+{0x1.f81e6ac3b918fp-1, 0x1.fc516f716296dp-7},
+{0x1.f44546ef18996p-1, 0x1.7bb4dd70a015bp-6},
+{0x1.f07b10382c84bp-1, 0x1.f84c99b34b674p-6},
+{0x1.ecbf7070e59d4p-1, 0x1.39f9ce4fb2d71p-5},
+{0x1.e91213f715939p-1, 0x1.7756c0fd22e78p-5},
+{0x1.e572a9a75f7b7p-1, 0x1.b43ee82db8f3ap-5},
+{0x1.e1e0e2c530207p-1, 0x1.f0b3fced60034p-5},
+{0x1.de5c72d8a8be3p-1, 0x1.165bd78d4878ep-4},
+{0x1.dae50fa5658ccp-1, 0x1.3425d2715ebe6p-4},
+{0x1.d77a71145a2dap-1, 0x1.51b8bd91b7915p-4},
+{0x1.d41c51166623ep-1, 0x1.6f15632c76a47p-4},
+{0x1.d0ca6ba0bb29fp-1, 0x1.8c3c88ecbe503p-4},
+{0x1.cd847e8e59681p-1, 0x1.a92ef077625dap-4},
+{0x1.ca4a499693e00p-1, 0x1.c5ed5745fa006p-4},
+{0x1.c71b8e399e821p-1, 0x1.e27876de1c993p-4},
+{0x1.c3f80faf19077p-1, 0x1.fed104fce4cdcp-4},
+{0x1.c0df92dc2b0ecp-1, 0x1.0d7bd9c17d78bp-3},
+{0x1.bdd1de3cbb542p-1, 0x1.1b76986cef97bp-3},
+{0x1.baceb9e1007a3p-1, 0x1.295913d24f750p-3},
+{0x1.b7d5ef543e55ep-1, 0x1.37239fa295d17p-3},
+{0x1.b4e749977d953p-1, 0x1.44d68dd78714bp-3},
+{0x1.b20295155478ep-1, 0x1.52722ebe5d780p-3},
+{0x1.af279f8e82be2p-1, 0x1.5ff6d12671f98p-3},
+{0x1.ac5638197fdf3p-1, 0x1.6d64c2389484bp-3},
+{0x1.a98e2f102e087p-1, 0x1.7abc4da40fddap-3},
+{0x1.a6cf5606d05c1p-1, 0x1.87fdbda1e8452p-3},
+{0x1.a4197fc04d746p-1, 0x1.95295b06a5f37p-3},
+{0x1.a16c80293dc01p-1, 0x1.a23f6d34abbc5p-3},
+{0x1.9ec82c4dc5bc9p-1, 0x1.af403a28e04f2p-3},
+{0x1.9c2c5a491f534p-1, 0x1.bc2c06a85721ap-3},
+{0x1.9998e1480b618p-1, 0x1.c903161240163p-3},
+{0x1.970d9977c6c2dp-1, 0x1.d5c5aa93287ebp-3},
+{0x1.948a5c023d212p-1, 0x1.e274051823fa9p-3},
+{0x1.920f0303d6809p-1, 0x1.ef0e656300c16p-3},
+{0x1.8f9b698a98b45p-1, 0x1.fb9509f05aa2ap-3},
+{0x1.8d2f6b81726f6p-1, 0x1.04041821f37afp-2},
+{0x1.8acae5bb55badp-1, 0x1.0a340a49b3029p-2},
+{0x1.886db5d9275b8p-1, 0x1.105a7918a126dp-2},
+{0x1.8617ba567c13cp-1, 0x1.1677819812b84p-2},
+{0x1.83c8d27487800p-1, 0x1.1c8b405b40c0ep-2},
+{0x1.8180de3c5dbe7p-1, 0x1.2295d16cfa6b1p-2},
+{0x1.7f3fbe71cdb71p-1, 0x1.28975066318a2p-2},
+{0x1.7d055498071c1p-1, 0x1.2e8fd855d86fcp-2},
+{0x1.7ad182e54f65ap-1, 0x1.347f83d605e59p-2},
+{0x1.78a42c3c90125p-1, 0x1.3a666d1244588p-2},
+{0x1.767d342f76944p-1, 0x1.4044adb6f8ec4p-2},
+{0x1.745c7ef26b00ap-1, 0x1.461a5f077558cp-2},
+{0x1.7241f15769d0fp-1, 0x1.4be799e20b9c8p-2},
+{0x1.702d70d396e41p-1, 0x1.51ac76a6b79dfp-2},
+{0x1.6e1ee3700cd11p-1, 0x1.57690d5744a45p-2},
+{0x1.6c162fc9cbe02p-1, 0x1.5d1d758e45217p-2},
+};
+#endif
diff --git a/libc/AOR_v20.02/math/v_logf.c b/libc/AOR_v20.02/math/v_logf.c
new file mode 100644
index 000000000000..dbe2acef8c04
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_logf.c
@@ -0,0 +1,74 @@
+/*
+ * Single-precision vector log function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const float Poly[] = {
+ /* 3.34 ulp error */
+ -0x1.3e737cp-3f, 0x1.5a9aa2p-3f, -0x1.4f9934p-3f, 0x1.961348p-3f,
+ -0x1.00187cp-2f, 0x1.555d7cp-2f, -0x1.ffffc8p-2f,
+};
+#define P7 v_f32 (Poly[0])
+#define P6 v_f32 (Poly[1])
+#define P5 v_f32 (Poly[2])
+#define P4 v_f32 (Poly[3])
+#define P3 v_f32 (Poly[4])
+#define P2 v_f32 (Poly[5])
+#define P1 v_f32 (Poly[6])
+
+#define Ln2 v_f32 (0x1.62e43p-1f) /* 0x3f317218 */
+#define Min v_u32 (0x00800000)
+#define Max v_u32 (0x7f800000)
+#define Mask v_u32 (0x007fffff)
+#define Off v_u32 (0x3f2aaaab) /* 0.666667 */
+
+VPCS_ATTR
+__attribute__ ((noinline)) static v_f32_t
+specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
+{
+ /* Fall back to scalar code. */
+ return v_call_f32 (logf, x, y, cmp);
+}
+
+VPCS_ATTR
+v_f32_t
+V_NAME(logf) (v_f32_t x)
+{
+ v_f32_t n, p, q, r, r2, y;
+ v_u32_t u, cmp;
+
+ u = v_as_u32_f32 (x);
+ cmp = v_cond_u32 (u - Min >= Max - Min);
+
+ /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3 */
+ u -= Off;
+ n = v_to_f32_s32 (v_as_s32_u32 (u) >> 23); /* signextend */
+ u &= Mask;
+ u += Off;
+ r = v_as_f32_u32 (u) - v_f32 (1.0f);
+
+ /* y = log(1+r) + n*ln2. */
+ r2 = r * r;
+ /* n*ln2 + r + r2*(P1 + r*P2 + r2*(P3 + r*P4 + r2*(P5 + r*P6 + r2*P7))). */
+ p = v_fma_f32 (P6, r, P5);
+ q = v_fma_f32 (P4, r, P3);
+ y = v_fma_f32 (P2, r, P1);
+ p = v_fma_f32 (P7, r2, p);
+ q = v_fma_f32 (p, r2, q);
+ y = v_fma_f32 (q, r2, y);
+ p = v_fma_f32 (Ln2, n, r);
+ y = v_fma_f32 (y, r2, p);
+
+ if (unlikely (v_any_u32 (cmp)))
+ return specialcase (x, y, cmp);
+ return y;
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_math.h b/libc/AOR_v20.02/math/v_math.h
new file mode 100644
index 000000000000..4b2a6d19faaf
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_math.h
@@ -0,0 +1,642 @@
+/*
+ * Vector math abstractions.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef _V_MATH_H
+#define _V_MATH_H
+
+#ifndef WANT_VMATH
+/* Enable the build of vector math code. */
+# define WANT_VMATH 1
+#endif
+#if WANT_VMATH
+
+/* The goal of this header is to allow vector and scalar
+ build of the same algorithm, the provided intrinsic
+ wrappers are also vector length agnostic so they can
+ be implemented for SVE too (or other simd architectures)
+ and then the code should work on those targets too. */
+
+#if SCALAR
+#define V_NAME(x) __s_##x
+#elif VPCS && __aarch64__
+#define V_NAME(x) __vn_##x
+#define VPCS_ATTR __attribute__ ((aarch64_vector_pcs))
+#else
+#define V_NAME(x) __v_##x
+#endif
+
+#ifndef VPCS_ATTR
+#define VPCS_ATTR
+#endif
+#ifndef VPCS_ALIAS
+#define VPCS_ALIAS
+#endif
+
+#include <stdint.h>
+#include "math_config.h"
+
+typedef float f32_t;
+typedef uint32_t u32_t;
+typedef int32_t s32_t;
+typedef double f64_t;
+typedef uint64_t u64_t;
+typedef int64_t s64_t;
+
+/* reinterpret as type1 from type2. */
+static inline u32_t
+as_u32_f32 (f32_t x)
+{
+ union { f32_t f; u32_t u; } r = {x};
+ return r.u;
+}
+static inline f32_t
+as_f32_u32 (u32_t x)
+{
+ union { u32_t u; f32_t f; } r = {x};
+ return r.f;
+}
+static inline s32_t
+as_s32_u32 (u32_t x)
+{
+ union { u32_t u; s32_t i; } r = {x};
+ return r.i;
+}
+static inline u32_t
+as_u32_s32 (s32_t x)
+{
+ union { s32_t i; u32_t u; } r = {x};
+ return r.u;
+}
+static inline u64_t
+as_u64_f64 (f64_t x)
+{
+ union { f64_t f; u64_t u; } r = {x};
+ return r.u;
+}
+static inline f64_t
+as_f64_u64 (u64_t x)
+{
+ union { u64_t u; f64_t f; } r = {x};
+ return r.f;
+}
+static inline s64_t
+as_s64_u64 (u64_t x)
+{
+ union { u64_t u; s64_t i; } r = {x};
+ return r.i;
+}
+static inline u64_t
+as_u64_s64 (s64_t x)
+{
+ union { s64_t i; u64_t u; } r = {x};
+ return r.u;
+}
+
+#if SCALAR
+#define V_SUPPORTED 1
+typedef f32_t v_f32_t;
+typedef u32_t v_u32_t;
+typedef s32_t v_s32_t;
+typedef f64_t v_f64_t;
+typedef u64_t v_u64_t;
+typedef s64_t v_s64_t;
+
+static inline int
+v_lanes32 (void)
+{
+ return 1;
+}
+
+static inline v_f32_t
+v_f32 (f32_t x)
+{
+ return x;
+}
+static inline v_u32_t
+v_u32 (u32_t x)
+{
+ return x;
+}
+static inline v_s32_t
+v_s32 (s32_t x)
+{
+ return x;
+}
+
+static inline f32_t
+v_get_f32 (v_f32_t x, int i)
+{
+ return x;
+}
+static inline u32_t
+v_get_u32 (v_u32_t x, int i)
+{
+ return x;
+}
+static inline s32_t
+v_get_s32 (v_s32_t x, int i)
+{
+ return x;
+}
+
+static inline void
+v_set_f32 (v_f32_t *x, int i, f32_t v)
+{
+ *x = v;
+}
+static inline void
+v_set_u32 (v_u32_t *x, int i, u32_t v)
+{
+ *x = v;
+}
+static inline void
+v_set_s32 (v_s32_t *x, int i, s32_t v)
+{
+ *x = v;
+}
+
+/* true if any elements of a v_cond result is non-zero. */
+static inline int
+v_any_u32 (v_u32_t x)
+{
+ return x != 0;
+}
+/* to wrap the result of relational operators. */
+static inline v_u32_t
+v_cond_u32 (v_u32_t x)
+{
+ return x ? -1 : 0;
+}
+static inline v_f32_t
+v_abs_f32 (v_f32_t x)
+{
+ return __builtin_fabsf (x);
+}
+static inline v_f32_t
+v_fma_f32 (v_f32_t x, v_f32_t y, v_f32_t z)
+{
+ return __builtin_fmaf (x, y, z);
+}
+static inline v_f32_t
+v_round_f32 (v_f32_t x)
+{
+ return __builtin_roundf (x);
+}
+static inline v_s32_t
+v_round_s32 (v_f32_t x)
+{
+ return __builtin_lroundf (x); /* relies on -fno-math-errno. */
+}
+/* convert to type1 from type2. */
+static inline v_f32_t
+v_to_f32_s32 (v_s32_t x)
+{
+ return x;
+}
+static inline v_f32_t
+v_to_f32_u32 (v_u32_t x)
+{
+ return x;
+}
+/* reinterpret as type1 from type2. */
+static inline v_u32_t
+v_as_u32_f32 (v_f32_t x)
+{
+ union { v_f32_t f; v_u32_t u; } r = {x};
+ return r.u;
+}
+static inline v_f32_t
+v_as_f32_u32 (v_u32_t x)
+{
+ union { v_u32_t u; v_f32_t f; } r = {x};
+ return r.f;
+}
+static inline v_s32_t
+v_as_s32_u32 (v_u32_t x)
+{
+ union { v_u32_t u; v_s32_t i; } r = {x};
+ return r.i;
+}
+static inline v_u32_t
+v_as_u32_s32 (v_s32_t x)
+{
+ union { v_s32_t i; v_u32_t u; } r = {x};
+ return r.u;
+}
+static inline v_f32_t
+v_lookup_f32 (const f32_t *tab, v_u32_t idx)
+{
+ return tab[idx];
+}
+static inline v_u32_t
+v_lookup_u32 (const u32_t *tab, v_u32_t idx)
+{
+ return tab[idx];
+}
+static inline v_f32_t
+v_call_f32 (f32_t (*f) (f32_t), v_f32_t x, v_f32_t y, v_u32_t p)
+{
+ return f (x);
+}
+static inline v_f32_t
+v_call2_f32 (f32_t (*f) (f32_t, f32_t), v_f32_t x1, v_f32_t x2, v_f32_t y,
+ v_u32_t p)
+{
+ return f (x1, x2);
+}
+
+static inline int
+v_lanes64 (void)
+{
+ return 1;
+}
+static inline v_f64_t
+v_f64 (f64_t x)
+{
+ return x;
+}
+static inline v_u64_t
+v_u64 (u64_t x)
+{
+ return x;
+}
+static inline v_s64_t
+v_s64 (s64_t x)
+{
+ return x;
+}
+static inline f64_t
+v_get_f64 (v_f64_t x, int i)
+{
+ return x;
+}
+static inline void
+v_set_f64 (v_f64_t *x, int i, f64_t v)
+{
+ *x = v;
+}
+/* true if any elements of a v_cond result is non-zero. */
+static inline int
+v_any_u64 (v_u64_t x)
+{
+ return x != 0;
+}
+/* to wrap the result of relational operators. */
+static inline v_u64_t
+v_cond_u64 (v_u64_t x)
+{
+ return x ? -1 : 0;
+}
+static inline v_f64_t
+v_abs_f64 (v_f64_t x)
+{
+ return __builtin_fabs (x);
+}
+static inline v_f64_t
+v_fma_f64 (v_f64_t x, v_f64_t y, v_f64_t z)
+{
+ return __builtin_fma (x, y, z);
+}
+static inline v_f64_t
+v_round_f64 (v_f64_t x)
+{
+ return __builtin_round (x);
+}
+static inline v_s64_t
+v_round_s64 (v_f64_t x)
+{
+ return __builtin_lround (x); /* relies on -fno-math-errno. */
+}
+/* convert to type1 from type2. */
+static inline v_f64_t
+v_to_f64_s64 (v_s64_t x)
+{
+ return x;
+}
+static inline v_f64_t
+v_to_f64_u64 (v_u64_t x)
+{
+ return x;
+}
+/* reinterpret as type1 from type2. */
+static inline v_u64_t
+v_as_u64_f64 (v_f64_t x)
+{
+ union { v_f64_t f; v_u64_t u; } r = {x};
+ return r.u;
+}
+static inline v_f64_t
+v_as_f64_u64 (v_u64_t x)
+{
+ union { v_u64_t u; v_f64_t f; } r = {x};
+ return r.f;
+}
+static inline v_s64_t
+v_as_s64_u64 (v_u64_t x)
+{
+ union { v_u64_t u; v_s64_t i; } r = {x};
+ return r.i;
+}
+static inline v_u64_t
+v_as_u64_s64 (v_s64_t x)
+{
+ union { v_s64_t i; v_u64_t u; } r = {x};
+ return r.u;
+}
+static inline v_f64_t
+v_lookup_f64 (const f64_t *tab, v_u64_t idx)
+{
+ return tab[idx];
+}
+static inline v_u64_t
+v_lookup_u64 (const u64_t *tab, v_u64_t idx)
+{
+ return tab[idx];
+}
+static inline v_f64_t
+v_call_f64 (f64_t (*f) (f64_t), v_f64_t x, v_f64_t y, v_u64_t p)
+{
+ return f (x);
+}
+
+#elif __aarch64__
+#define V_SUPPORTED 1
+#include <arm_neon.h>
+typedef float32x4_t v_f32_t;
+typedef uint32x4_t v_u32_t;
+typedef int32x4_t v_s32_t;
+typedef float64x2_t v_f64_t;
+typedef uint64x2_t v_u64_t;
+typedef int64x2_t v_s64_t;
+
+static inline int
+v_lanes32 (void)
+{
+ return 4;
+}
+
+static inline v_f32_t
+v_f32 (f32_t x)
+{
+ return (v_f32_t){x, x, x, x};
+}
+static inline v_u32_t
+v_u32 (u32_t x)
+{
+ return (v_u32_t){x, x, x, x};
+}
+static inline v_s32_t
+v_s32 (s32_t x)
+{
+ return (v_s32_t){x, x, x, x};
+}
+
+static inline f32_t
+v_get_f32 (v_f32_t x, int i)
+{
+ return x[i];
+}
+static inline u32_t
+v_get_u32 (v_u32_t x, int i)
+{
+ return x[i];
+}
+static inline s32_t
+v_get_s32 (v_s32_t x, int i)
+{
+ return x[i];
+}
+
+static inline void
+v_set_f32 (v_f32_t *x, int i, f32_t v)
+{
+ (*x)[i] = v;
+}
+static inline void
+v_set_u32 (v_u32_t *x, int i, u32_t v)
+{
+ (*x)[i] = v;
+}
+static inline void
+v_set_s32 (v_s32_t *x, int i, s32_t v)
+{
+ (*x)[i] = v;
+}
+
+/* true if any elements of a v_cond result is non-zero. */
+static inline int
+v_any_u32 (v_u32_t x)
+{
+ /* assume elements in x are either 0 or -1u. */
+ return vpaddd_u64 (vreinterpretq_u64_u32 (x)) != 0;
+}
+/* to wrap the result of relational operators. */
+static inline v_u32_t
+v_cond_u32 (v_u32_t x)
+{
+ return x;
+}
+static inline v_f32_t
+v_abs_f32 (v_f32_t x)
+{
+ return vabsq_f32 (x);
+}
+static inline v_f32_t
+v_fma_f32 (v_f32_t x, v_f32_t y, v_f32_t z)
+{
+ return vfmaq_f32 (z, x, y);
+}
+static inline v_f32_t
+v_round_f32 (v_f32_t x)
+{
+ return vrndaq_f32 (x);
+}
+static inline v_s32_t
+v_round_s32 (v_f32_t x)
+{
+ return vcvtaq_s32_f32 (x);
+}
+/* convert to type1 from type2. */
+static inline v_f32_t
+v_to_f32_s32 (v_s32_t x)
+{
+ return (v_f32_t){x[0], x[1], x[2], x[3]};
+}
+static inline v_f32_t
+v_to_f32_u32 (v_u32_t x)
+{
+ return (v_f32_t){x[0], x[1], x[2], x[3]};
+}
+/* reinterpret as type1 from type2. */
+static inline v_u32_t
+v_as_u32_f32 (v_f32_t x)
+{
+ union { v_f32_t f; v_u32_t u; } r = {x};
+ return r.u;
+}
+static inline v_f32_t
+v_as_f32_u32 (v_u32_t x)
+{
+ union { v_u32_t u; v_f32_t f; } r = {x};
+ return r.f;
+}
+static inline v_s32_t
+v_as_s32_u32 (v_u32_t x)
+{
+ union { v_u32_t u; v_s32_t i; } r = {x};
+ return r.i;
+}
+static inline v_u32_t
+v_as_u32_s32 (v_s32_t x)
+{
+ union { v_s32_t i; v_u32_t u; } r = {x};
+ return r.u;
+}
+static inline v_f32_t
+v_lookup_f32 (const f32_t *tab, v_u32_t idx)
+{
+ return (v_f32_t){tab[idx[0]], tab[idx[1]], tab[idx[2]], tab[idx[3]]};
+}
+static inline v_u32_t
+v_lookup_u32 (const u32_t *tab, v_u32_t idx)
+{
+ return (v_u32_t){tab[idx[0]], tab[idx[1]], tab[idx[2]], tab[idx[3]]};
+}
+static inline v_f32_t
+v_call_f32 (f32_t (*f) (f32_t), v_f32_t x, v_f32_t y, v_u32_t p)
+{
+ return (v_f32_t){p[0] ? f (x[0]) : y[0], p[1] ? f (x[1]) : y[1],
+ p[2] ? f (x[2]) : y[2], p[3] ? f (x[3]) : y[3]};
+}
+static inline v_f32_t
+v_call2_f32 (f32_t (*f) (f32_t, f32_t), v_f32_t x1, v_f32_t x2, v_f32_t y,
+ v_u32_t p)
+{
+ return (
+ v_f32_t){p[0] ? f (x1[0], x2[0]) : y[0], p[1] ? f (x1[1], x2[1]) : y[1],
+ p[2] ? f (x1[2], x2[2]) : y[2], p[3] ? f (x1[3], x2[3]) : y[3]};
+}
+
+static inline int
+v_lanes64 (void)
+{
+ return 2;
+}
+static inline v_f64_t
+v_f64 (f64_t x)
+{
+ return (v_f64_t){x, x};
+}
+static inline v_u64_t
+v_u64 (u64_t x)
+{
+ return (v_u64_t){x, x};
+}
+static inline v_s64_t
+v_s64 (s64_t x)
+{
+ return (v_s64_t){x, x};
+}
+static inline f64_t
+v_get_f64 (v_f64_t x, int i)
+{
+ return x[i];
+}
+static inline void
+v_set_f64 (v_f64_t *x, int i, f64_t v)
+{
+ (*x)[i] = v;
+}
+/* true if any elements of a v_cond result is non-zero. */
+static inline int
+v_any_u64 (v_u64_t x)
+{
+ /* assume elements in x are either 0 or -1u. */
+ return vpaddd_u64 (x) != 0;
+}
+/* to wrap the result of relational operators. */
+static inline v_u64_t
+v_cond_u64 (v_u64_t x)
+{
+ return x;
+}
+static inline v_f64_t
+v_abs_f64 (v_f64_t x)
+{
+ return vabsq_f64 (x);
+}
+static inline v_f64_t
+v_fma_f64 (v_f64_t x, v_f64_t y, v_f64_t z)
+{
+ return vfmaq_f64 (z, x, y);
+}
+static inline v_f64_t
+v_round_f64 (v_f64_t x)
+{
+ return vrndaq_f64 (x);
+}
+static inline v_s64_t
+v_round_s64 (v_f64_t x)
+{
+ return vcvtaq_s64_f64 (x);
+}
+/* convert to type1 from type2. */
+static inline v_f64_t
+v_to_f64_s64 (v_s64_t x)
+{
+ return (v_f64_t){x[0], x[1]};
+}
+static inline v_f64_t
+v_to_f64_u64 (v_u64_t x)
+{
+ return (v_f64_t){x[0], x[1]};
+}
+/* reinterpret as type1 from type2. */
+static inline v_u64_t
+v_as_u64_f64 (v_f64_t x)
+{
+ union { v_f64_t f; v_u64_t u; } r = {x};
+ return r.u;
+}
+static inline v_f64_t
+v_as_f64_u64 (v_u64_t x)
+{
+ union { v_u64_t u; v_f64_t f; } r = {x};
+ return r.f;
+}
+static inline v_s64_t
+v_as_s64_u64 (v_u64_t x)
+{
+ union { v_u64_t u; v_s64_t i; } r = {x};
+ return r.i;
+}
+static inline v_u64_t
+v_as_u64_s64 (v_s64_t x)
+{
+ union { v_s64_t i; v_u64_t u; } r = {x};
+ return r.u;
+}
+static inline v_f64_t
+v_lookup_f64 (const f64_t *tab, v_u64_t idx)
+{
+ return (v_f64_t){tab[idx[0]], tab[idx[1]]};
+}
+static inline v_u64_t
+v_lookup_u64 (const u64_t *tab, v_u64_t idx)
+{
+ return (v_u64_t){tab[idx[0]], tab[idx[1]]};
+}
+static inline v_f64_t
+v_call_f64 (f64_t (*f) (f64_t), v_f64_t x, v_f64_t y, v_u64_t p)
+{
+ return (v_f64_t){p[0] ? f (x[0]) : y[0], p[1] ? f (x[1]) : y[1]};
+}
+#endif
+
+#endif
+#endif
diff --git a/libc/AOR_v20.02/math/v_pow.c b/libc/AOR_v20.02/math/v_pow.c
new file mode 100644
index 000000000000..e42873416f74
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_pow.c
@@ -0,0 +1,28 @@
+/*
+ * Double-precision vector pow function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+VPCS_ATTR
+v_f64_t
+V_NAME(pow) (v_f64_t x, v_f64_t y)
+{
+ v_f64_t z;
+ for (int lane = 0; lane < v_lanes64 (); lane++)
+ {
+ f64_t sx = v_get_f64 (x, lane);
+ f64_t sy = v_get_f64 (y, lane);
+ f64_t sz = pow (sx, sy);
+ v_set_f64 (&z, lane, sz);
+ }
+ return z;
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_powf.c b/libc/AOR_v20.02/math/v_powf.c
new file mode 100644
index 000000000000..c4d8db0e38fa
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_powf.c
@@ -0,0 +1,236 @@
+/*
+ * Single-precision vector powf function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+#define Min v_u32 (0x00800000)
+#define Max v_u32 (0x7f800000)
+#define SBITS 5
+#define Tlog v__powf_log2_data.tab
+#define Texp v__exp2f_data.tab
+#define A v__powf_log2_data.poly
+#define C v__exp2f_data.poly
+#define LOGDEG 4
+
+#if LOGDEG == 5
+/* 1.01 ulp */
+#define OFF v_u32 (0x3f330000)
+#define TBITS 4
+#elif LOGDEG == 4
+/* 2.6 ulp ~ 0.5 + 2^24 (128*Ln2*relerr_log2 + relerr_exp2) */
+#define OFF v_u32 (0x3f35d000)
+#define TBITS 5
+#endif
+
+#define V_EXP2F_TABLE_BITS SBITS
+#define V_EXP2F_POLY_ORDER 3
+struct v_exp2f_data
+{
+ uint64_t tab[1 << V_EXP2F_TABLE_BITS];
+ double poly[V_EXP2F_POLY_ORDER];
+};
+
+#define V_POWF_LOG2_TABLE_BITS TBITS
+#define V_POWF_LOG2_POLY_ORDER LOGDEG
+#define SCALE ((double) (1 << SBITS))
+struct v_powf_log2_data
+{
+ struct
+ {
+ double invc, logc;
+ } tab[1 << V_POWF_LOG2_TABLE_BITS];
+ double poly[V_POWF_LOG2_POLY_ORDER];
+};
+
+static const struct v_powf_log2_data v__powf_log2_data = {
+#if LOGDEG == 5
+ .tab = {
+{ 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * SCALE },
+{ 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * SCALE },
+{ 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * SCALE },
+{ 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * SCALE },
+{ 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * SCALE },
+{ 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * SCALE },
+{ 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * SCALE },
+{ 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * SCALE },
+{ 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * SCALE },
+{ 0x1p+0, 0x0p+0 * SCALE },
+{ 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * SCALE },
+{ 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * SCALE },
+{ 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * SCALE },
+{ 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * SCALE },
+{ 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * SCALE },
+{ 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * SCALE },
+ },
+/* rel err: 1.46 * 2^-32 */
+ .poly = {
+0x1.27616c9496e0bp-2 * SCALE, -0x1.71969a075c67ap-2 * SCALE,
+0x1.ec70a6ca7baddp-2 * SCALE, -0x1.7154748bef6c8p-1 * SCALE,
+0x1.71547652ab82bp0 * SCALE,
+ }
+#elif LOGDEG == 4
+ .tab = {
+{0x1.6489890582816p+0, -0x1.e960f97b22702p-2 * SCALE},
+{0x1.5cf19b35e3472p+0, -0x1.c993406cd4db6p-2 * SCALE},
+{0x1.55aac0e956d65p+0, -0x1.aa711d9a7d0f3p-2 * SCALE},
+{0x1.4eb0022977e01p+0, -0x1.8bf37bacdce9bp-2 * SCALE},
+{0x1.47fcccda1dd1fp+0, -0x1.6e13b3519946ep-2 * SCALE},
+{0x1.418ceabab68c1p+0, -0x1.50cb8281e4089p-2 * SCALE},
+{0x1.3b5c788f1edb3p+0, -0x1.341504a237e2bp-2 * SCALE},
+{0x1.3567de48e9c9ap+0, -0x1.17eaab624ffbbp-2 * SCALE},
+{0x1.2fabc80fd19bap+0, -0x1.f88e708f8c853p-3 * SCALE},
+{0x1.2a25200ce536bp+0, -0x1.c24b6da113914p-3 * SCALE},
+{0x1.24d108e0152e3p+0, -0x1.8d02ee397cb1dp-3 * SCALE},
+{0x1.1facd8ab2fbe1p+0, -0x1.58ac1223408b3p-3 * SCALE},
+{0x1.1ab614a03efdfp+0, -0x1.253e6fd190e89p-3 * SCALE},
+{0x1.15ea6d03af9ffp+0, -0x1.e5641882c12ffp-4 * SCALE},
+{0x1.1147b994bb776p+0, -0x1.81fea712926f7p-4 * SCALE},
+{0x1.0ccbf650593aap+0, -0x1.203e240de64a3p-4 * SCALE},
+{0x1.0875408477302p+0, -0x1.8029b86a78281p-5 * SCALE},
+{0x1.0441d42a93328p+0, -0x1.85d713190fb9p-6 * SCALE},
+{0x1p+0, 0x0p+0 * SCALE},
+{0x1.f1d006c855e86p-1, 0x1.4c1cc07312997p-5 * SCALE},
+{0x1.e28c3341aa301p-1, 0x1.5e1848ccec948p-4 * SCALE},
+{0x1.d4bdf9aa64747p-1, 0x1.04cfcb7f1196fp-3 * SCALE},
+{0x1.c7b45a24e5803p-1, 0x1.582813d463c21p-3 * SCALE},
+{0x1.bb5f5eb2ed60ap-1, 0x1.a936fa68760ccp-3 * SCALE},
+{0x1.afb0bff8fe6b4p-1, 0x1.f81bc31d6cc4ep-3 * SCALE},
+{0x1.a49badf7ab1f5p-1, 0x1.2279a09fae6b1p-2 * SCALE},
+{0x1.9a14a111fc4c9p-1, 0x1.47ec0b6df5526p-2 * SCALE},
+{0x1.901131f5b2fdcp-1, 0x1.6c71762280f1p-2 * SCALE},
+{0x1.8687f73f6d865p-1, 0x1.90155070798dap-2 * SCALE},
+{0x1.7d7067eb77986p-1, 0x1.b2e23b1d3068cp-2 * SCALE},
+{0x1.74c2c1cf97b65p-1, 0x1.d4e21b0daa86ap-2 * SCALE},
+{0x1.6c77f37cff2a1p-1, 0x1.f61e2a2f67f3fp-2 * SCALE},
+ },
+/* rel err: 1.5 * 2^-30 */
+ .poly = {
+ -0x1.6ff5daa3b3d7cp-2 * SCALE,
+ 0x1.ec81d03c01aebp-2 * SCALE,
+ -0x1.71547bb43f101p-1 * SCALE,
+ 0x1.7154764a815cbp0 * SCALE,
+ }
+#endif
+};
+
+static const struct v_exp2f_data v__exp2f_data = {
+ .tab = {
+0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
+0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
+0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
+0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
+0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
+0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
+0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
+0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
+ },
+/* rel err: 1.69 * 2^-34 */
+ .poly = {
+0x1.c6af84b912394p-5/SCALE/SCALE/SCALE, 0x1.ebfce50fac4f3p-3/SCALE/SCALE, 0x1.62e42ff0c52d6p-1/SCALE
+ },
+};
+
+VPCS_ATTR
+__attribute__ ((noinline)) static v_f32_t
+specialcase (v_f32_t x, v_f32_t y, v_f32_t ret, v_u32_t cmp)
+{
+ return v_call2_f32 (powf, x, y, ret, cmp);
+}
+
+VPCS_ATTR
+v_f32_t
+V_NAME(powf) (v_f32_t x, v_f32_t y)
+{
+ v_u32_t u, tmp, cmp, i, top, iz;
+ v_s32_t k;
+ v_f32_t ret;
+
+ u = v_as_u32_f32 (x);
+ cmp = v_cond_u32 (u - Min >= Max - Min);
+ tmp = u - OFF;
+ i = (tmp >> (23 - TBITS)) % (1 << TBITS);
+ top = tmp & 0xff800000;
+ iz = u - top;
+ k = v_as_s32_u32 (top) >> (23 - SBITS); /* arithmetic shift */
+
+ for (int lane = 0; lane < v_lanes32 (); lane++)
+ {
+ uint32_t si, siz;
+ int32_t sk;
+ float sy;
+
+ /* Use double precision for each lane. */
+ double invc, logc, z, r, p, y0, logx, ylogx, kd, s;
+ uint64_t ki, t;
+
+ si = v_get_u32 (i, lane);
+ siz = v_get_u32 (iz, lane);
+ sk = v_get_s32 (k, lane);
+ sy = v_get_f32 (y, lane);
+
+ invc = Tlog[si].invc;
+ logc = Tlog[si].logc;
+ z = (double) as_f32_u32 (siz);
+
+ /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
+ r = __builtin_fma (z, invc, -1.0);
+ y0 = logc + (double) sk;
+
+ /* Polynomial to approximate log1p(r)/ln2. */
+#if LOGDEG == 5
+ logx = A[0];
+ logx = r * logx + A[1];
+ logx = r * logx + A[2];
+ logx = r * logx + A[3];
+ logx = r * logx + A[4];
+ logx = r * logx + y0;
+#elif LOGDEG == 4
+ logx = A[0];
+ logx = r * logx + A[1];
+ logx = r * logx + A[2];
+ logx = r * logx + A[3];
+ logx = r * logx + y0;
+#endif
+ ylogx = sy * logx;
+ v_set_u32 (&cmp, lane,
+ (as_u64_f64 (ylogx) >> 47 & 0xffff)
+ >= as_u64_f64 (126.0 * (1 << SBITS)) >> 47
+ ? 1
+ : v_get_u32 (cmp, lane));
+
+ /* N*x = k + r with r in [-1/2, 1/2] */
+#if TOINT_INTRINSICS
+ kd = roundtoint (ylogx); /* k */
+ ki = converttoint (ylogx);
+#else
+# define SHIFT 0x1.8p52
+ kd = eval_as_double (ylogx + SHIFT);
+ ki = asuint64 (kd);
+ kd -= SHIFT;
+#endif
+ r = ylogx - kd;
+
+ /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+ t = Texp[ki % (1 << SBITS)];
+ t += ki << (52 - SBITS);
+ s = as_f64_u64 (t);
+ p = C[0];
+ p = __builtin_fma (p, r, C[1]);
+ p = __builtin_fma (p, r, C[2]);
+ p = __builtin_fma (p, s * r, s);
+
+ v_set_f32 (&ret, lane, p);
+ }
+ if (unlikely (v_any_u32 (cmp)))
+ return specialcase (x, y, ret, cmp);
+ return ret;
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_sin.c b/libc/AOR_v20.02/math/v_sin.c
new file mode 100644
index 000000000000..899d1f558089
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_sin.c
@@ -0,0 +1,87 @@
+/*
+ * Double-precision vector sin function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const double Poly[] = {
+/* worst-case error is 3.5 ulp.
+ abs error: 0x1.be222a58p-53 in [-pi/2, pi/2]. */
+-0x1.9f4a9c8b21dc9p-41,
+ 0x1.60e88a10163f2p-33,
+-0x1.ae6361b7254e7p-26,
+ 0x1.71de382e8d62bp-19,
+-0x1.a01a019aeb4ffp-13,
+ 0x1.111111110b25ep-7,
+-0x1.55555555554c3p-3,
+};
+
+#define C7 v_f64 (Poly[0])
+#define C6 v_f64 (Poly[1])
+#define C5 v_f64 (Poly[2])
+#define C4 v_f64 (Poly[3])
+#define C3 v_f64 (Poly[4])
+#define C2 v_f64 (Poly[5])
+#define C1 v_f64 (Poly[6])
+
+#define InvPi v_f64 (0x1.45f306dc9c883p-2)
+#define Pi1 v_f64 (0x1.921fb54442d18p+1)
+#define Pi2 v_f64 (0x1.1a62633145c06p-53)
+#define Pi3 v_f64 (0x1.c1cd129024e09p-106)
+#define Shift v_f64 (0x1.8p52)
+#define RangeVal v_f64 (0x1p23)
+#define AbsMask v_u64 (0x7fffffffffffffff)
+
+VPCS_ATTR
+__attribute__ ((noinline)) static v_f64_t
+specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
+{
+ return v_call_f64 (sin, x, y, cmp);
+}
+
+VPCS_ATTR
+v_f64_t
+V_NAME(sin) (v_f64_t x)
+{
+ v_f64_t n, r, r2, y;
+ v_u64_t sign, odd, cmp;
+
+ r = v_as_f64_u64 (v_as_u64_f64 (x) & AbsMask);
+ sign = v_as_u64_f64 (x) & ~AbsMask;
+ cmp = v_cond_u64 (v_as_u64_f64 (r) >= v_as_u64_f64 (RangeVal));
+
+ /* n = rint(|x|/pi). */
+ n = v_fma_f64 (InvPi, r, Shift);
+ odd = v_as_u64_f64 (n) << 63;
+ n -= Shift;
+
+ /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
+ r = v_fma_f64 (-Pi1, n, r);
+ r = v_fma_f64 (-Pi2, n, r);
+ r = v_fma_f64 (-Pi3, n, r);
+
+ /* sin(r) poly approx. */
+ r2 = r * r;
+ y = v_fma_f64 (C7, r2, C6);
+ y = v_fma_f64 (y, r2, C5);
+ y = v_fma_f64 (y, r2, C4);
+ y = v_fma_f64 (y, r2, C3);
+ y = v_fma_f64 (y, r2, C2);
+ y = v_fma_f64 (y, r2, C1);
+ y = v_fma_f64 (y * r2, r, r);
+
+ /* sign. */
+ y = v_as_f64_u64 (v_as_u64_f64 (y) ^ sign ^ odd);
+
+ if (unlikely (v_any_u64 (cmp)))
+ return specialcase (x, y, cmp);
+ return y;
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/v_sinf.c b/libc/AOR_v20.02/math/v_sinf.c
new file mode 100644
index 000000000000..de7a18f3e4ff
--- /dev/null
+++ b/libc/AOR_v20.02/math/v_sinf.c
@@ -0,0 +1,76 @@
+/*
+ * Single-precision vector sin function.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "mathlib.h"
+#include "v_math.h"
+#if V_SUPPORTED
+
+static const float Poly[] = {
+ /* 1.886 ulp error */
+ 0x1.5b2e76p-19f,
+ -0x1.9f42eap-13f,
+ 0x1.110df4p-7f,
+ -0x1.555548p-3f,
+};
+#define Pi1 v_f32 (0x1.921fb6p+1f)
+#define Pi2 v_f32 (-0x1.777a5cp-24f)
+#define Pi3 v_f32 (-0x1.ee59dap-49f)
+#define A3 v_f32 (Poly[3])
+#define A5 v_f32 (Poly[2])
+#define A7 v_f32 (Poly[1])
+#define A9 v_f32 (Poly[0])
+#define RangeVal v_f32 (0x1p20f)
+#define InvPi v_f32 (0x1.45f306p-2f)
+#define Shift v_f32 (0x1.8p+23f)
+#define AbsMask v_u32 (0x7fffffff)
+
+VPCS_ATTR
+static v_f32_t
+specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
+{
+ /* Fall back to scalar code. */
+ return v_call_f32 (sinf, x, y, cmp);
+}
+
+VPCS_ATTR
+v_f32_t
+V_NAME(sinf) (v_f32_t x)
+{
+ v_f32_t n, r, r2, y;
+ v_u32_t sign, odd, cmp;
+
+ r = v_as_f32_u32 (v_as_u32_f32 (x) & AbsMask);
+ sign = v_as_u32_f32 (x) & ~AbsMask;
+ cmp = v_cond_u32 (v_as_u32_f32 (r) >= v_as_u32_f32 (RangeVal));
+
+ /* n = rint(|x|/pi) */
+ n = v_fma_f32 (InvPi, r, Shift);
+ odd = v_as_u32_f32 (n) << 31;
+ n -= Shift;
+
+ /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2) */
+ r = v_fma_f32 (-Pi1, n, r);
+ r = v_fma_f32 (-Pi2, n, r);
+ r = v_fma_f32 (-Pi3, n, r);
+
+ /* y = sin(r) */
+ r2 = r * r;
+ y = v_fma_f32 (A9, r2, A7);
+ y = v_fma_f32 (y, r2, A5);
+ y = v_fma_f32 (y, r2, A3);
+ y = v_fma_f32 (y * r2, r, r);
+
+ /* sign fix */
+ y = v_as_f32_u32 (v_as_u32_f32 (y) ^ sign ^ odd);
+
+ if (unlikely (v_any_u32 (cmp)))
+ return specialcase (x, y, cmp);
+ return y;
+}
+VPCS_ALIAS
+#endif
diff --git a/libc/AOR_v20.02/math/vn_cos.c b/libc/AOR_v20.02/math/vn_cos.c
new file mode 100644
index 000000000000..76fc8b86657f
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_cos.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_cos.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_cos, _ZGVnN2v_cos)
+#include "v_cos.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_cosf.c b/libc/AOR_v20.02/math/vn_cosf.c
new file mode 100644
index 000000000000..2ed24ae05935
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_cosf.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_cosf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_cosf, _ZGVnN4v_cosf)
+#include "v_cosf.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_exp.c b/libc/AOR_v20.02/math/vn_exp.c
new file mode 100644
index 000000000000..7492014dca07
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_exp.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_exp.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_exp, _ZGVnN2v_exp)
+#include "v_exp.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_exp2f.c b/libc/AOR_v20.02/math/vn_exp2f.c
new file mode 100644
index 000000000000..df3d56fd17f7
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_exp2f.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_exp2f.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_exp2f, _ZGVnN4v_exp2f)
+#include "v_exp2f.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_exp2f_1u.c b/libc/AOR_v20.02/math/vn_exp2f_1u.c
new file mode 100644
index 000000000000..b974e5b18bcc
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_exp2f_1u.c
@@ -0,0 +1,12 @@
+/*
+ * AdvSIMD vector PCS variant of __v_exp2f_1u.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#include "v_exp2f_1u.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_expf.c b/libc/AOR_v20.02/math/vn_expf.c
new file mode 100644
index 000000000000..de5a8cf4f316
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_expf.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_expf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_expf, _ZGVnN4v_expf)
+#include "v_expf.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_expf_1u.c b/libc/AOR_v20.02/math/vn_expf_1u.c
new file mode 100644
index 000000000000..20b625b25aa7
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_expf_1u.c
@@ -0,0 +1,12 @@
+/*
+ * AdvSIMD vector PCS variant of __v_expf_1u.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#include "v_expf_1u.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_log.c b/libc/AOR_v20.02/math/vn_log.c
new file mode 100644
index 000000000000..c766d727d60d
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_log.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_log.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_log, _ZGVnN2v_log)
+#include "v_log.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_logf.c b/libc/AOR_v20.02/math/vn_logf.c
new file mode 100644
index 000000000000..03edb1961dc4
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_logf.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_logf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_logf, _ZGVnN4v_logf)
+#include "v_logf.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_pow.c b/libc/AOR_v20.02/math/vn_pow.c
new file mode 100644
index 000000000000..dbad0aaa4f27
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_pow.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_pow.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_pow, _ZGVnN2vv_pow)
+#include "v_pow.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_powf.c b/libc/AOR_v20.02/math/vn_powf.c
new file mode 100644
index 000000000000..6fd4c76527c7
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_powf.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_powf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_powf, _ZGVnN4vv_powf)
+#include "v_powf.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_sin.c b/libc/AOR_v20.02/math/vn_sin.c
new file mode 100644
index 000000000000..be0585be8ad9
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_sin.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_sin.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_sin, _ZGVnN2v_sin)
+#include "v_sin.c"
+#endif
diff --git a/libc/AOR_v20.02/math/vn_sinf.c b/libc/AOR_v20.02/math/vn_sinf.c
new file mode 100644
index 000000000000..32cd11e2fdba
--- /dev/null
+++ b/libc/AOR_v20.02/math/vn_sinf.c
@@ -0,0 +1,13 @@
+/*
+ * AdvSIMD vector PCS variant of __v_sinf.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+#include "mathlib.h"
+#ifdef __vpcs
+#define VPCS 1
+#define VPCS_ALIAS strong_alias (__vn_sinf, _ZGVnN4v_sinf)
+#include "v_sinf.c"
+#endif
diff --git a/libc/AOR_v20.02/networking/Dir.mk b/libc/AOR_v20.02/networking/Dir.mk
new file mode 100644
index 000000000000..68bc94b41e3d
--- /dev/null
+++ b/libc/AOR_v20.02/networking/Dir.mk
@@ -0,0 +1,77 @@
+# Makefile fragment - requires GNU make
+#
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+S := $(srcdir)/networking
+B := build/networking
+
+ifeq ($(ARCH),)
+all-networking check-networking install-networking clean-networking:
+ @echo "*** Please set ARCH in config.mk. ***"
+ @exit 1
+else
+
+networking-lib-srcs := $(wildcard $(S)/*.[cS]) $(wildcard $(S)/$(ARCH)/*.[cS])
+networking-test-srcs := $(wildcard $(S)/test/*.c)
+
+networking-includes := $(patsubst $(S)/%,build/%,$(wildcard $(S)/include/*.h))
+
+networking-libs := \
+ build/lib/libnetworking.so \
+ build/lib/libnetworking.a \
+
+networking-tools := \
+ build/bin/test/chksum
+
+networking-lib-objs := $(patsubst $(S)/%,$(B)/%.o,$(basename $(networking-lib-srcs)))
+networking-test-objs := $(patsubst $(S)/%,$(B)/%.o,$(basename $(networking-test-srcs)))
+
+networking-objs := \
+ $(networking-lib-objs) \
+ $(networking-lib-objs:%.o=%.os) \
+ $(networking-test-objs) \
+
+networking-files := \
+ $(networking-objs) \
+ $(networking-libs) \
+ $(networking-tools) \
+ $(networking-includes) \
+
+all-networking: $(networking-libs) $(networking-tools) $(networking-includes)
+
+$(networking-objs): $(networking-includes)
+$(networking-objs): CFLAGS_ALL += $(networking-cflags)
+
+build/lib/libnetworking.so: $(networking-lib-objs:%.o=%.os)
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS) -shared -o $@ $^
+
+build/lib/libnetworkinglib.a: $(networking-lib-objs)
+ rm -f $@
+ $(AR) rc $@ $^
+ $(RANLIB) $@
+
+build/bin/test/%: $(B)/test/%.o build/lib/libnetworkinglib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS) -static -o $@ $^ $(LDLIBS)
+
+build/include/%.h: $(S)/include/%.h
+ cp $< $@
+
+build/bin/%.sh: $(S)/test/%.sh
+ cp $< $@
+
+check-networking: $(networking-tools)
+ $(EMULATOR) build/bin/test/chksum -i simple
+ $(EMULATOR) build/bin/test/chksum -i scalar
+ $(EMULATOR) build/bin/test/chksum -i simd || true # simd is not always available
+
+install-networking: \
+ $(networking-libs:build/lib/%=$(DESTDIR)$(libdir)/%) \
+ $(networking-includes:build/include/%=$(DESTDIR)$(includedir)/%)
+
+clean-networking:
+ rm -f $(networking-files)
+endif
+
+.PHONY: all-networking check-networking install-networking clean-networking
diff --git a/libc/AOR_v20.02/networking/aarch64/chksum_simd.c b/libc/AOR_v20.02/networking/aarch64/chksum_simd.c
new file mode 100644
index 000000000000..eaa0f3bc3e17
--- /dev/null
+++ b/libc/AOR_v20.02/networking/aarch64/chksum_simd.c
@@ -0,0 +1,147 @@
+/*
+ * AArch64-specific checksum implementation using NEON
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "networking.h"
+#include "../chksum_common.h"
+
+#ifndef __ARM_NEON
+#pragma GCC target("+simd")
+#endif
+
+#include <arm_neon.h>
+
+always_inline
+static inline uint64_t
+slurp_head64(const void **pptr, uint32_t *nbytes)
+{
+ Assert(*nbytes >= 8);
+ uint64_t sum = 0;
+ uint32_t off = (uintptr_t) *pptr % 8;
+ if (likely(off != 0))
+ {
+ /* Get rid of bytes 0..off-1 */
+ const unsigned char *ptr64 = align_ptr(*pptr, 8);
+ uint64_t mask = ALL_ONES << (CHAR_BIT * off);
+ uint64_t val = load64(ptr64) & mask;
+ /* Fold 64-bit sum to 33 bits */
+ sum = val >> 32;
+ sum += (uint32_t) val;
+ *pptr = ptr64 + 8;
+ *nbytes -= 8 - off;
+ }
+ return sum;
+}
+
+always_inline
+static inline uint64_t
+slurp_tail64(uint64_t sum, const void *ptr, uint32_t nbytes)
+{
+ Assert(nbytes < 8);
+ if (likely(nbytes != 0))
+ {
+ /* Get rid of bytes 7..nbytes */
+ uint64_t mask = ALL_ONES >> (CHAR_BIT * (8 - nbytes));
+ Assert(__builtin_popcountl(mask) / CHAR_BIT == nbytes);
+ uint64_t val = load64(ptr) & mask;
+ sum += val >> 32;
+ sum += (uint32_t) val;
+ nbytes = 0;
+ }
+ Assert(nbytes == 0);
+ return sum;
+}
+
+unsigned short
+__chksum_aarch64_simd(const void *ptr, unsigned int nbytes)
+{
+ bool swap = (uintptr_t) ptr & 1;
+ uint64_t sum;
+
+ if (unlikely(nbytes < 50))
+ {
+ sum = slurp_small(ptr, nbytes);
+ swap = false;
+ goto fold;
+ }
+
+ /* 8-byte align pointer */
+ Assert(nbytes >= 8);
+ sum = slurp_head64(&ptr, &nbytes);
+ Assert(((uintptr_t) ptr & 7) == 0);
+
+ const uint32_t *may_alias ptr32 = ptr;
+
+ uint64x2_t vsum0 = { 0, 0 };
+ uint64x2_t vsum1 = { 0, 0 };
+ uint64x2_t vsum2 = { 0, 0 };
+ uint64x2_t vsum3 = { 0, 0 };
+
+ /* Sum groups of 64 bytes */
+ for (uint32_t i = 0; i < nbytes / 64; i++)
+ {
+ uint32x4_t vtmp0 = vld1q_u32(ptr32);
+ uint32x4_t vtmp1 = vld1q_u32(ptr32 + 4);
+ uint32x4_t vtmp2 = vld1q_u32(ptr32 + 8);
+ uint32x4_t vtmp3 = vld1q_u32(ptr32 + 12);
+ vsum0 = vpadalq_u32(vsum0, vtmp0);
+ vsum1 = vpadalq_u32(vsum1, vtmp1);
+ vsum2 = vpadalq_u32(vsum2, vtmp2);
+ vsum3 = vpadalq_u32(vsum3, vtmp3);
+ ptr32 += 16;
+ }
+ nbytes %= 64;
+
+ /* Fold vsum2 and vsum3 into vsum0 and vsum1 */
+ vsum0 = vpadalq_u32(vsum0, vreinterpretq_u32_u64(vsum2));
+ vsum1 = vpadalq_u32(vsum1, vreinterpretq_u32_u64(vsum3));
+
+ /* Add any trailing group of 32 bytes */
+ if (nbytes & 32)
+ {
+ uint32x4_t vtmp0 = vld1q_u32(ptr32);
+ uint32x4_t vtmp1 = vld1q_u32(ptr32 + 4);
+ vsum0 = vpadalq_u32(vsum0, vtmp0);
+ vsum1 = vpadalq_u32(vsum1, vtmp1);
+ ptr32 += 8;
+ nbytes -= 32;
+ }
+ Assert(nbytes < 32);
+
+ /* Fold vsum1 into vsum0 */
+ vsum0 = vpadalq_u32(vsum0, vreinterpretq_u32_u64(vsum1));
+
+ /* Add any trailing group of 16 bytes */
+ if (nbytes & 16)
+ {
+ uint32x4_t vtmp = vld1q_u32(ptr32);
+ vsum0 = vpadalq_u32(vsum0, vtmp);
+ ptr32 += 4;
+ nbytes -= 16;
+ }
+ Assert(nbytes < 16);
+
+ /* Add any trailing group of 8 bytes */
+ if (nbytes & 8)
+ {
+ uint32x2_t vtmp = vld1_u32(ptr32);
+ vsum0 = vaddw_u32(vsum0, vtmp);
+ ptr32 += 2;
+ nbytes -= 8;
+ }
+ Assert(nbytes < 8);
+
+ uint64_t val = vaddlvq_u32(vreinterpretq_u32_u64(vsum0));
+ sum += val >> 32;
+ sum += (uint32_t) val;
+
+ /* Handle any trailing 0..7 bytes */
+ sum = slurp_tail64(sum, ptr32, nbytes);
+
+fold:
+ return fold_and_swap(sum, swap);
+}
diff --git a/libc/AOR_v20.02/networking/arm/chksum_simd.c b/libc/AOR_v20.02/networking/arm/chksum_simd.c
new file mode 100644
index 000000000000..aa70a3c81e18
--- /dev/null
+++ b/libc/AOR_v20.02/networking/arm/chksum_simd.c
@@ -0,0 +1,150 @@
+/*
+ * Armv7-A specific checksum implementation using NEON
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "networking.h"
+#include "../chksum_common.h"
+
+#ifndef __ARM_NEON
+#pragma GCC target("+simd")
+#endif
+
+#include <arm_neon.h>
+
+unsigned short
+__chksum_arm_simd(const void *ptr, unsigned int nbytes)
+{
+ bool swap = (uintptr_t) ptr & 1;
+ uint64x1_t vsum = { 0 };
+
+ if (unlikely(nbytes < 40))
+ {
+ uint64_t sum = slurp_small(ptr, nbytes);
+ return fold_and_swap(sum, false);
+ }
+
+ /* 8-byte align pointer */
+ /* Inline slurp_head-like code since we use NEON here */
+ Assert(nbytes >= 8);
+ uint32_t off = (uintptr_t) ptr & 7;
+ if (likely(off != 0))
+ {
+ const uint64_t *may_alias ptr64 = align_ptr(ptr, 8);
+ uint64x1_t vword64 = vld1_u64(ptr64);
+ /* Get rid of bytes 0..off-1 */
+ uint64x1_t vmask = vdup_n_u64(ALL_ONES);
+ int64x1_t vshiftl = vdup_n_s64(CHAR_BIT * off);
+ vmask = vshl_u64(vmask, vshiftl);
+ vword64 = vand_u64(vword64, vmask);
+ uint32x2_t vtmp = vreinterpret_u32_u64(vword64);
+ /* Set accumulator */
+ vsum = vpaddl_u32(vtmp);
+ /* Update pointer and remaining size */
+ ptr = (char *) ptr64 + 8;
+ nbytes -= 8 - off;
+ }
+ Assert(((uintptr_t) ptr & 7) == 0);
+
+ /* Sum groups of 64 bytes */
+ uint64x2_t vsum0 = { 0, 0 };
+ uint64x2_t vsum1 = { 0, 0 };
+ uint64x2_t vsum2 = { 0, 0 };
+ uint64x2_t vsum3 = { 0, 0 };
+ const uint32_t *may_alias ptr32 = ptr;
+ for (uint32_t i = 0; i < nbytes / 64; i++)
+ {
+ uint32x4_t vtmp0 = vld1q_u32(ptr32);
+ uint32x4_t vtmp1 = vld1q_u32(ptr32 + 4);
+ uint32x4_t vtmp2 = vld1q_u32(ptr32 + 8);
+ uint32x4_t vtmp3 = vld1q_u32(ptr32 + 12);
+ vsum0 = vpadalq_u32(vsum0, vtmp0);
+ vsum1 = vpadalq_u32(vsum1, vtmp1);
+ vsum2 = vpadalq_u32(vsum2, vtmp2);
+ vsum3 = vpadalq_u32(vsum3, vtmp3);
+ ptr32 += 16;
+ }
+ nbytes %= 64;
+
+ /* Fold vsum1/vsum2/vsum3 into vsum0 */
+ vsum0 = vpadalq_u32(vsum0, vreinterpretq_u32_u64(vsum2));
+ vsum1 = vpadalq_u32(vsum1, vreinterpretq_u32_u64(vsum3));
+ vsum0 = vpadalq_u32(vsum0, vreinterpretq_u32_u64(vsum1));
+
+ /* Add any trailing 16-byte groups */
+ while (likely(nbytes >= 16))
+ {
+ uint32x4_t vtmp0 = vld1q_u32(ptr32);
+ vsum0 = vpadalq_u32(vsum0, vtmp0);
+ ptr32 += 4;
+ nbytes -= 16;
+ }
+ Assert(nbytes < 16);
+
+ /* Fold vsum0 into vsum */
+ {
+ /* 4xu32 (4x32b) -> 2xu64 (2x33b) */
+ vsum0 = vpaddlq_u32(vreinterpretq_u32_u64(vsum0));
+ /* 4xu32 (2x(1b+32b)) -> 2xu64 (2x(0b+32b)) */
+ vsum0 = vpaddlq_u32(vreinterpretq_u32_u64(vsum0));
+ /* 4xu32 (4x32b) -> 2xu64 (2x33b) */
+ Assert((vgetq_lane_u64(vsum0, 0) >> 32) == 0);
+ Assert((vgetq_lane_u64(vsum0, 1) >> 32) == 0);
+ uint32x2_t vtmp = vmovn_u64(vsum0);
+ /* Add to accumulator */
+ vsum = vpadal_u32(vsum, vtmp);
+ }
+
+ /* Add any trailing group of 8 bytes */
+ if (nbytes & 8)
+ {
+ uint32x2_t vtmp = vld1_u32(ptr32);
+ /* Add to accumulator */
+ vsum = vpadal_u32(vsum, vtmp);
+ ptr32 += 2;
+ nbytes -= 8;
+ }
+ Assert(nbytes < 8);
+
+ /* Handle any trailing 1..7 bytes */
+ if (likely(nbytes != 0))
+ {
+ Assert(((uintptr_t) ptr32 & 7) == 0);
+ Assert(nbytes < 8);
+ uint64x1_t vword64 = vld1_u64((const uint64_t *) ptr32);
+ /* Get rid of bytes 7..nbytes */
+ uint64x1_t vmask = vdup_n_u64(ALL_ONES);
+ int64x1_t vshiftr = vdup_n_s64(-CHAR_BIT * (8 - nbytes));
+ vmask = vshl_u64(vmask, vshiftr);/* Shift right */
+ vword64 = vand_u64(vword64, vmask);
+ /* Fold 64-bit sum to 33 bits */
+ vword64 = vpaddl_u32(vreinterpret_u32_u64(vword64));
+ /* Add to accumulator */
+ vsum = vpadal_u32(vsum, vreinterpret_u32_u64(vword64));
+ }
+
+ /* Fold 64-bit vsum to 32 bits */
+ vsum = vpaddl_u32(vreinterpret_u32_u64(vsum));
+ vsum = vpaddl_u32(vreinterpret_u32_u64(vsum));
+ Assert(vget_lane_u32(vreinterpret_u32_u64(vsum), 1) == 0);
+
+ /* Fold 32-bit vsum to 16 bits */
+ uint32x2_t vsum32 = vreinterpret_u32_u64(vsum);
+ vsum32 = vpaddl_u16(vreinterpret_u16_u32(vsum32));
+ vsum32 = vpaddl_u16(vreinterpret_u16_u32(vsum32));
+ Assert(vget_lane_u16(vreinterpret_u16_u32(vsum32), 1) == 0);
+ Assert(vget_lane_u16(vreinterpret_u16_u32(vsum32), 2) == 0);
+ Assert(vget_lane_u16(vreinterpret_u16_u32(vsum32), 3) == 0);
+
+ /* Convert to 16-bit scalar */
+ uint16_t sum = vget_lane_u16(vreinterpret_u16_u32(vsum32), 0);
+
+ if (unlikely(swap))/* Odd base pointer is unexpected */
+ {
+ sum = bswap16(sum);
+ }
+ return sum;
+}
diff --git a/libc/AOR_v20.02/networking/chksum.c b/libc/AOR_v20.02/networking/chksum.c
new file mode 100644
index 000000000000..5f9033402cd5
--- /dev/null
+++ b/libc/AOR_v20.02/networking/chksum.c
@@ -0,0 +1,82 @@
+/*
+ * Compute 16-bit sum in ones' complement arithmetic (with end-around carry).
+ * This sum is often used as a simple checksum in networking.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include "networking.h"
+#include "chksum_common.h"
+
+always_inline
+static inline uint32_t
+slurp_head32(const void **pptr, uint32_t *nbytes)
+{
+ uint32_t sum = 0;
+ Assert(*nbytes >= 4);
+ uint32_t off = (uintptr_t) *pptr % 4;
+ if (likely(off != 0))
+ {
+ /* Get rid of bytes 0..off-1 */
+ const unsigned char *ptr32 = align_ptr(*pptr, 4);
+ uint32_t mask = ~0U << (CHAR_BIT * off);
+ sum = load32(ptr32) & mask;
+ *pptr = ptr32 + 4;
+ *nbytes -= 4 - off;
+ }
+ return sum;
+}
+
+/* Additional loop unrolling would help when not auto-vectorizing */
+unsigned short
+__chksum(const void *ptr, unsigned int nbytes)
+{
+ bool swap = false;
+ uint64_t sum = 0;
+
+ if (nbytes > 300)
+ {
+ /* 4-byte align pointer */
+ swap = (uintptr_t) ptr & 1;
+ sum = slurp_head32(&ptr, &nbytes);
+ }
+ /* Else benefit of aligning not worth the overhead */
+
+ /* Sum all 16-byte chunks */
+ const char *cptr = ptr;
+ for (uint32_t nquads = nbytes / 16; nquads != 0; nquads--)
+ {
+ uint64_t h0 = load32(cptr + 0);
+ uint64_t h1 = load32(cptr + 4);
+ uint64_t h2 = load32(cptr + 8);
+ uint64_t h3 = load32(cptr + 12);
+ sum += h0 + h1 + h2 + h3;
+ cptr += 16;
+ }
+ nbytes %= 16;
+ Assert(nbytes < 16);
+
+ /* Handle any trailing 4-byte chunks */
+ while (nbytes >= 4)
+ {
+ sum += load32(cptr);
+ cptr += 4;
+ nbytes -= 4;
+ }
+ Assert(nbytes < 4);
+
+ if (nbytes & 2)
+ {
+ sum += load16(cptr);
+ cptr += 2;
+ }
+
+ if (nbytes & 1)
+ {
+ sum += *(uint8_t *)cptr;
+ }
+
+ return fold_and_swap(sum, swap);
+}
diff --git a/libc/AOR_v20.02/networking/chksum_common.h b/libc/AOR_v20.02/networking/chksum_common.h
new file mode 100644
index 000000000000..afb0552830f0
--- /dev/null
+++ b/libc/AOR_v20.02/networking/chksum_common.h
@@ -0,0 +1,133 @@
+/*
+ * Common code for checksum implementations
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef CHKSUM_COMMON_H
+#define CHKSUM_COMMON_H
+
+#if __BYTE_ORDER__ != __ORDER_LITTLE_ENDIAN__
+#error Only little endian supported
+#endif
+
+#include <limits.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <string.h>
+
+/* Assertions must be explicitly enabled */
+#if WANT_ASSERT
+#undef NDEBUG
+#include <assert.h>
+#define Assert(exp) assert(exp)
+#else
+#define Assert(exp) (void) (exp)
+#endif
+
+#ifdef __GNUC__
+#define likely(x) __builtin_expect(!!(x), 1)
+#define unlikely(x) __builtin_expect(!!(x), 0)
+#define may_alias __attribute__((__may_alias__))
+#define always_inline __attribute__((always_inline))
+#ifdef __clang__
+#define no_unroll_loops
+#else
+#define no_unroll_loops __attribute__((optimize("no-unroll-loops")))
+#endif
+#define bswap16(x) __builtin_bswap16((x))
+#else
+#define likely(x) (x)
+#define unlikely(x) (x)
+#define may_alias
+#define always_inline
+#define no_unroll_loops
+#define bswap16(x) ((uint8_t)((x) >> 8) | ((uint8_t)(x) << 8))
+#endif
+
+#define ALL_ONES ~UINT64_C(0)
+
+static inline
+uint64_t load64(const void *ptr)
+{
+ /* GCC will optimise this to a normal load instruction */
+ uint64_t v;
+ memcpy(&v, ptr, sizeof v);
+ return v;
+}
+
+static inline
+uint32_t load32(const void *ptr)
+{
+ /* GCC will optimise this to a normal load instruction */
+ uint32_t v;
+ memcpy(&v, ptr, sizeof v);
+ return v;
+}
+
+static inline
+uint16_t load16(const void *ptr)
+{
+ /* GCC will optimise this to a normal load instruction */
+ uint16_t v;
+ memcpy(&v, ptr, sizeof v);
+ return v;
+}
+
+/* slurp_small() is for small buffers, don't waste cycles on alignment */
+no_unroll_loops
+always_inline
+static inline uint64_t
+slurp_small(const void *ptr, uint32_t nbytes)
+{
+ const unsigned char *cptr = ptr;
+ uint64_t sum = 0;
+ while (nbytes >= 4)
+ {
+ sum += load32(cptr);
+ cptr += 4;
+ nbytes -= 4;
+ }
+ if (nbytes & 2)
+ {
+ sum += load16(cptr);
+ cptr += 2;
+ }
+ if (nbytes & 1)
+ {
+ sum += (uint8_t) *cptr;
+ }
+ return sum;
+}
+
+static inline const void *
+align_ptr(const void *ptr, size_t bytes)
+{
+ return (void *) ((uintptr_t) ptr & -(uintptr_t) bytes);
+}
+
+always_inline
+static inline uint16_t
+fold_and_swap(uint64_t sum, bool swap)
+{
+ /* Fold 64-bit sum to 32 bits */
+ sum = (sum & 0xffffffff) + (sum >> 32);
+ sum = (sum & 0xffffffff) + (sum >> 32);
+ Assert(sum == (uint32_t) sum);
+
+ /* Fold 32-bit sum to 16 bits */
+ sum = (sum & 0xffff) + (sum >> 16);
+ sum = (sum & 0xffff) + (sum >> 16);
+ Assert(sum == (uint16_t) sum);
+
+ if (unlikely(swap)) /* Odd base pointer is unexpected */
+ {
+ sum = bswap16(sum);
+ }
+
+ return (uint16_t) sum;
+}
+
+#endif
diff --git a/libc/AOR_v20.02/networking/include/networking.h b/libc/AOR_v20.02/networking/include/networking.h
new file mode 100644
index 000000000000..2f91a9efb883
--- /dev/null
+++ b/libc/AOR_v20.02/networking/include/networking.h
@@ -0,0 +1,15 @@
+/*
+ * Public API.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+unsigned short __chksum (const void *, unsigned int);
+#if __aarch64__ && __ARM_NEON
+unsigned short __chksum_aarch64_simd (const void *, unsigned int);
+#endif
+#if __arm__ && __ARM_NEON
+unsigned short __chksum_arm_simd (const void *, unsigned int);
+#endif
diff --git a/libc/AOR_v20.02/networking/test/chksum.c b/libc/AOR_v20.02/networking/test/chksum.c
new file mode 100644
index 000000000000..c4ac3fe6bf00
--- /dev/null
+++ b/libc/AOR_v20.02/networking/test/chksum.c
@@ -0,0 +1,382 @@
+/*
+ * Ones' complement checksum test & benchmark
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#define _GNU_SOURCE
+#include <inttypes.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <sys/mman.h>
+#include <time.h>
+#include <unistd.h>
+#include "../include/networking.h"
+
+#if WANT_ASSERT
+#undef NDEBUG
+#include <assert.h>
+#define Assert(exp) assert(exp)
+#else
+#define Assert(exp) (void) (exp)
+#endif
+
+#ifdef __GNUC__
+#define may_alias __attribute__((__may_alias__))
+#else
+#define may_alias
+#endif
+
+#define CACHE_LINE 64
+#define ALIGN(x, y) (((x) + (y) - 1) & ~((y) - 1))
+
+/* Reference implementation - do not modify! */
+static uint16_t
+checksum_simple(const void *ptr, uint32_t nbytes)
+{
+ const uint16_t *may_alias hptr = ptr;
+ uint64_t sum = 0;/* Need 64-bit accumulator when nbytes > 64K */
+
+ /* Sum all halfwords, assume misaligned accesses are handled in HW */
+ for (uint32_t nhalfs = nbytes >> 1; nhalfs != 0; nhalfs--)
+ {
+ sum += *hptr++;
+ }
+
+ /* Add any trailing odd byte */
+ if ((nbytes & 0x01) != 0)
+ {
+ sum += *(uint8_t *) hptr;
+ }
+
+ /* Fold 64-bit sum to 32 bits */
+ sum = (sum & 0xffffffff) + (sum >> 32);
+ sum = (sum & 0xffffffff) + (sum >> 32);
+ Assert(sum == (uint32_t) sum);
+
+ /* Fold 32-bit sum to 16 bits */
+ sum = (sum & 0xffff) + (sum >> 16);
+ sum = (sum & 0xffff) + (sum >> 16);
+ Assert(sum == (uint16_t) sum);
+
+ return (uint16_t) sum;
+}
+
+static struct
+{
+ uint16_t (*cksum_fp)(const void *, uint32_t);
+ const char *name;
+} implementations[] =
+{
+ { checksum_simple, "simple"},
+ { __chksum, "scalar"},
+#if __arm__
+ { __chksum_arm_simd, "simd" },
+#elif __aarch64__
+ { __chksum_aarch64_simd, "simd" },
+#endif
+ { NULL, NULL}
+};
+
+static int
+find_impl(const char *name)
+{
+ for (int i = 0; implementations[i].name != NULL; i++)
+ {
+ if (strcmp(implementations[i].name, name) == 0)
+ {
+ return i;
+ }
+ }
+ return -1;
+}
+
+static uint16_t (*CKSUM_FP)(const void *, uint32_t);
+static volatile uint16_t SINK;
+
+static bool
+verify(const void *data, uint32_t offset, uint32_t size)
+{
+
+ uint16_t csum_expected = checksum_simple(data, size);
+ uint16_t csum_actual = CKSUM_FP(data, size);
+ if (csum_actual != csum_expected)
+ {
+ fprintf(stderr, "\nInvalid checksum for offset %u size %u: "
+ "actual %04x expected %04x (valid)",
+ offset, size, csum_actual, csum_expected);
+ if (size < 65536)
+ {
+ /* Fatal error */
+ exit(EXIT_FAILURE);
+ }
+ /* Else some implementations only support sizes up to 2^16 */
+ return false;
+ }
+ return true;
+}
+
+static uint64_t
+clock_get_ns(void)
+{
+ struct timespec ts;
+ clock_gettime(CLOCK_MONOTONIC, &ts);
+ return ts.tv_sec * (uint64_t) 1000000000 + ts.tv_nsec;
+}
+
+static void
+benchmark(const uint8_t *base,
+ size_t poolsize,
+ uint32_t blksize,
+ uint32_t numops,
+ uint64_t cpufreq)
+{
+ printf("%11u ", (unsigned int) blksize); fflush(stdout);
+
+ uint64_t start = clock_get_ns();
+ for (uint32_t i = 0; i < numops; i ++)
+ {
+ /* Read a random value from the pool */
+ uint32_t random = ((uint32_t *) base)[i % (poolsize / 4)];
+ /* Generate a random starting address */
+ const void *data = &base[random % (poolsize - blksize)];
+ SINK = CKSUM_FP(data, blksize);
+ }
+ uint64_t end = clock_get_ns();
+
+#define MEGABYTE 1000000 /* Decimal megabyte (MB) */
+ uint64_t elapsed_ns = end - start;
+ uint64_t elapsed_ms = elapsed_ns / 1000000;
+ uint32_t blks_per_s = (uint32_t) ((numops / elapsed_ms) * 1000);
+ uint64_t accbytes = (uint64_t) numops * blksize;
+ printf("%11ju ", (uintmax_t) ((accbytes / elapsed_ms) * 1000) / MEGABYTE);
+ unsigned int cyc_per_blk = cpufreq / blks_per_s;
+ printf("%11u ", cyc_per_blk);
+ if (blksize != 0)
+ {
+ unsigned int cyc_per_byte = 1000 * cyc_per_blk / blksize;
+ printf("%7u.%03u ",
+ cyc_per_byte / 1000, cyc_per_byte % 1000);
+ }
+ printf("\n");
+}
+
+int main(int argc, char *argv[])
+{
+ int c;
+ bool DUMP = false;
+ uint32_t IMPL = 0;/* Simple implementation */
+ uint64_t CPUFREQ = 0;
+ uint32_t BLKSIZE = 0;
+ uint32_t NUMOPS = 1000000;
+ uint32_t POOLSIZE = 512 * 1024;/* Typical ARM L2 cache size */
+
+ setvbuf(stdout, NULL, _IOLBF, 160);
+ while ((c = getopt(argc, argv, "b:df:i:n:p:")) != -1)
+ {
+ switch (c)
+ {
+ case 'b' :
+ {
+ int blksize = atoi(optarg);
+ if (blksize < 1 || blksize > POOLSIZE / 2)
+ {
+ fprintf(stderr, "Invalid block size %d\n", blksize);
+ exit(EXIT_FAILURE);
+ }
+ BLKSIZE = (unsigned) blksize;
+ break;
+ }
+ case 'd' :
+ DUMP = true;
+ break;
+ case 'f' :
+ {
+ int64_t cpufreq = atoll(optarg);
+ if (cpufreq < 1)
+ {
+ fprintf(stderr, "Invalid CPU frequency %"PRId64"\n",
+ cpufreq);
+ exit(EXIT_FAILURE);
+ }
+ CPUFREQ = cpufreq;
+ break;
+ }
+ case 'i' :
+ {
+ int impl = find_impl(optarg);
+ if (impl < 0)
+ {
+ fprintf(stderr, "Invalid implementation %s\n", optarg);
+ goto usage;
+ }
+ IMPL = (unsigned) impl;
+ break;
+ }
+ case 'n' :
+ {
+ int numops = atoi(optarg);
+ if (numops < 1)
+ {
+ fprintf(stderr, "Invalid number of operations %d\n", numops);
+ exit(EXIT_FAILURE);
+ }
+ NUMOPS = (unsigned) numops;
+ break;
+ }
+ case 'p' :
+ {
+ int poolsize = atoi(optarg);
+ if (poolsize < 4096)
+ {
+ fprintf(stderr, "Invalid pool size %d\n", poolsize);
+ exit(EXIT_FAILURE);
+ }
+ char c = optarg[strlen(optarg) - 1];
+ if (c == 'M')
+ {
+ POOLSIZE = (unsigned) poolsize * 1024 * 1024;
+ }
+ else if (c == 'K')
+ {
+ POOLSIZE = (unsigned) poolsize * 1024;
+ }
+ else
+ {
+ POOLSIZE = (unsigned) poolsize;
+ }
+ break;
+ }
+ default :
+usage :
+ fprintf(stderr, "Usage: checksum <options>\n"
+ "-b <blksize> Block size\n"
+ "-d Dump first 96 bytes of data\n"
+ "-f <cpufreq> CPU frequency (Hz)\n"
+ "-i <impl> Implementation\n"
+ "-n <numops> Number of operations\n"
+ "-p <poolsize> Pool size (K or M suffix)\n"
+ );
+ printf("Implementations:");
+ for (int i = 0; implementations[i].name != NULL; i++)
+ {
+ printf(" %s", implementations[i].name);
+ }
+ printf("\n");
+ exit(EXIT_FAILURE);
+ }
+ }
+ if (optind > argc)
+ {
+ goto usage;
+ }
+
+ CKSUM_FP = implementations[IMPL].cksum_fp;
+ POOLSIZE = ALIGN(POOLSIZE, CACHE_LINE);
+ uint8_t *base = mmap(0, POOLSIZE, PROT_READ|PROT_WRITE,
+ MAP_PRIVATE|MAP_ANONYMOUS, -1, 0);
+ if (base == MAP_FAILED)
+ {
+ perror("aligned_alloc"), exit(EXIT_FAILURE);
+ }
+ for (size_t i = 0; i < POOLSIZE / 4; i++)
+ {
+ ((uint32_t *) base)[i] = rand();
+ }
+
+ printf("Implementation: %s\n", implementations[IMPL].name);
+ printf("numops %u, poolsize ", NUMOPS);
+ if (POOLSIZE % (1024 * 1024) == 0)
+ {
+ printf("%uMiB", POOLSIZE / (1024 * 1024));
+ }
+ else if (POOLSIZE % 1024 == 0)
+ {
+ printf("%uKiB", POOLSIZE / 1024);
+ }
+ else
+ {
+ printf("%uB", POOLSIZE);
+ }
+ printf(", blocksize %u, CPU frequency %juMHz\n",
+ BLKSIZE, (uintmax_t) (CPUFREQ / 1000000));
+#if WANT_ASSERT
+ printf("Warning: assertions are enabled\n");
+#endif
+
+ if (DUMP)
+ {
+ /* Print out first 96 bytes of data for human debugging */
+ for (int i = 0; i < 96; i++)
+ {
+ if (i % 8 == 0)
+ printf("%2u:", i);
+ printf(" %02x", base[i]);
+ if (i % 8 == 7)
+ printf("\n");
+ }
+ }
+
+ /* Verify that chosen algorithm handles all combinations of offsets and sizes */
+ printf("Verifying..."); fflush(stdout);
+ bool success = true;
+ /* Check all (relevant) combinations of size and offset */
+ for (int size = 0; size <= 256; size++)
+ {
+ for (int offset = 0; offset < 255; offset++)
+ {
+ /* Check at start of mapped memory */
+ success &= verify(&base[offset], offset, size);
+ /* Check at end of mapped memory */
+ uint8_t *p = base + POOLSIZE - (size + offset);
+ success &= verify(p, (uintptr_t) p % 64, size);
+ }
+ }
+ /* Check increasingly larger sizes */
+ for (size_t size = 1; size < POOLSIZE; size *= 2)
+ {
+ success &= verify(base, 0, size);
+ }
+ /* Check the full size, this can detect accumulator overflows */
+ success &= verify(base, 0, POOLSIZE);
+ printf("%s\n", success ? "OK" : "failure");
+
+ /* Print throughput in decimal megabyte (1000000B) per second */
+ if (CPUFREQ != 0)
+ {
+ printf("%11s %11s %11s %11s\n",
+ "block size", "MB/s", "cycles/blk", "cycles/byte");
+ }
+ else
+ {
+ printf("%11s %11s %11s %11s\n",
+ "block size", "MB/s", "ns/blk", "ns/byte");
+ CPUFREQ = 1000000000;
+ }
+ if (BLKSIZE != 0)
+ {
+ benchmark(base, POOLSIZE, BLKSIZE, NUMOPS, CPUFREQ);
+ }
+ else
+ {
+ static const uint16_t sizes[] =
+ { 20, 42, 102, 250, 612, 1500, 3674, 9000, 0 };
+ for (int i = 0; sizes[i] != 0; i++)
+ {
+ uint32_t numops = NUMOPS * 10000 / (40 + sizes[i]);
+ benchmark(base, POOLSIZE, sizes[i], numops, CPUFREQ);
+ }
+ }
+
+ if (munmap(base, POOLSIZE) != 0)
+ {
+ perror("munmap"), exit(EXIT_FAILURE);
+ }
+
+ return success ? EXIT_SUCCESS : EXIT_FAILURE;
+}
diff --git a/libc/AOR_v20.02/string/Dir.mk b/libc/AOR_v20.02/string/Dir.mk
new file mode 100644
index 000000000000..215452c8dc38
--- /dev/null
+++ b/libc/AOR_v20.02/string/Dir.mk
@@ -0,0 +1,101 @@
+# Makefile fragment - requires GNU make
+#
+# Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+# See https://llvm.org/LICENSE.txt for license information.
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+S := $(srcdir)/string
+B := build/string
+
+ifeq ($(ARCH),)
+all-string check-string install-string clean-string:
+ @echo "*** Please set ARCH in config.mk. ***"
+ @exit 1
+else
+
+string-lib-srcs := $(wildcard $(S)/$(ARCH)/*.[cS])
+string-test-srcs := $(wildcard $(S)/test/*.c)
+
+string-includes := $(patsubst $(S)/%,build/%,$(wildcard $(S)/include/*.h))
+
+string-libs := \
+ build/lib/libstringlib.so \
+ build/lib/libstringlib.a \
+
+string-tools := \
+ build/bin/test/memcpy \
+ build/bin/test/memmove \
+ build/bin/test/memset \
+ build/bin/test/memchr \
+ build/bin/test/memcmp \
+ build/bin/test/strcpy \
+ build/bin/test/stpcpy \
+ build/bin/test/strcmp \
+ build/bin/test/strchr \
+ build/bin/test/strrchr \
+ build/bin/test/strchrnul \
+ build/bin/test/strlen \
+ build/bin/test/strnlen \
+ build/bin/test/strncmp
+
+string-lib-objs := $(patsubst $(S)/%,$(B)/%.o,$(basename $(string-lib-srcs)))
+string-test-objs := $(patsubst $(S)/%,$(B)/%.o,$(basename $(string-test-srcs)))
+
+string-objs := \
+ $(string-lib-objs) \
+ $(string-lib-objs:%.o=%.os) \
+ $(string-test-objs) \
+
+string-files := \
+ $(string-objs) \
+ $(string-libs) \
+ $(string-tools) \
+ $(string-includes) \
+
+all-string: $(string-libs) $(string-tools) $(string-includes)
+
+$(string-objs): $(string-includes)
+$(string-objs): CFLAGS_ALL += $(string-cflags)
+
+build/lib/libstringlib.so: $(string-lib-objs:%.o=%.os)
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS) -shared -o $@ $^
+
+build/lib/libstringlib.a: $(string-lib-objs)
+ rm -f $@
+ $(AR) rc $@ $^
+ $(RANLIB) $@
+
+build/bin/test/%: $(B)/test/%.o build/lib/libstringlib.a
+ $(CC) $(CFLAGS_ALL) $(LDFLAGS) -static -o $@ $^ $(LDLIBS)
+
+build/include/%.h: $(S)/include/%.h
+ cp $< $@
+
+build/bin/%.sh: $(S)/test/%.sh
+ cp $< $@
+
+check-string: $(string-tools)
+ $(EMULATOR) build/bin/test/memcpy
+ $(EMULATOR) build/bin/test/memmove
+ $(EMULATOR) build/bin/test/memset
+ $(EMULATOR) build/bin/test/memchr
+ $(EMULATOR) build/bin/test/memcmp
+ $(EMULATOR) build/bin/test/strcpy
+ $(EMULATOR) build/bin/test/stpcpy
+ $(EMULATOR) build/bin/test/strcmp
+ $(EMULATOR) build/bin/test/strchr
+ $(EMULATOR) build/bin/test/strrchr
+ $(EMULATOR) build/bin/test/strchrnul
+ $(EMULATOR) build/bin/test/strlen
+ $(EMULATOR) build/bin/test/strnlen
+ $(EMULATOR) build/bin/test/strncmp
+
+install-string: \
+ $(string-libs:build/lib/%=$(DESTDIR)$(libdir)/%) \
+ $(string-includes:build/include/%=$(DESTDIR)$(includedir)/%)
+
+clean-string:
+ rm -f $(string-files)
+endif
+
+.PHONY: all-string check-string install-string clean-string
diff --git a/libc/AOR_v20.02/string/aarch64/check-arch.S b/libc/AOR_v20.02/string/aarch64/check-arch.S
new file mode 100644
index 000000000000..7783503b3c66
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/check-arch.S
@@ -0,0 +1,11 @@
+/*
+ * check ARCH setting.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if !__aarch64__
+# error ARCH setting does not match the compiler.
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/memchr-sve.S b/libc/AOR_v20.02/string/aarch64/memchr-sve.S
new file mode 100644
index 000000000000..d9c5fdd18673
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/memchr-sve.S
@@ -0,0 +1,65 @@
+/*
+ * memchr - find a character in a memory zone
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_FEATURE_SVE
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * SVE Available.
+ */
+
+ .arch armv8-a+sve
+ .text
+
+ .globl __memchr_aarch64_sve
+ .type __memchr_aarch64_sve, %function
+ .p2align 4
+__memchr_aarch64_sve:
+ dup z1.b, w1 /* duplicate c to a vector */
+ setffr /* initialize FFR */
+ mov x3, 0 /* initialize off */
+ nop
+
+0: whilelo p1.b, x3, x2 /* make sure off < max */
+ b.none 9f
+
+ /* Read a vector's worth of bytes, bounded by max,
+ stopping on first fault. */
+ ldff1b z0.b, p1/z, [x0, x3]
+ rdffrs p0.b, p1/z
+ b.nlast 2f
+
+ /* First fault did not fail: the vector bounded by max is valid.
+ Avoid depending on the contents of FFR beyond the branch. */
+ incb x3 /* speculate increment */
+ cmpeq p2.b, p1/z, z0.b, z1.b /* search for c */
+ b.none 0b
+ decb x3 /* undo speculate */
+
+ /* Found C. */
+1: brkb p2.b, p1/z, p2.b /* find the first c */
+ add x0, x0, x3 /* form partial pointer */
+ incp x0, p2.b /* form final pointer to c */
+ ret
+
+ /* First fault failed: only some of the vector is valid.
+ Perform the comparision only on the valid bytes. */
+2: cmpeq p2.b, p0/z, z0.b, z1.b
+ b.any 1b
+
+ /* No C found. Re-init FFR, increment, and loop. */
+ setffr
+ incp x3, p0.b
+ b 0b
+
+ /* Found end of count. */
+9: mov x0, 0 /* return null */
+ ret
+
+ .size __memchr_aarch64_sve, . - __memchr_aarch64_sve
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/memchr.S b/libc/AOR_v20.02/string/aarch64/memchr.S
new file mode 100644
index 000000000000..a454d6b896af
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/memchr.S
@@ -0,0 +1,144 @@
+/*
+ * memchr - find a character in a memory zone
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * Neon Available.
+ */
+
+#include "../asmdefs.h"
+
+/* Arguments and results. */
+#define srcin x0
+#define chrin w1
+#define cntin x2
+
+#define result x0
+
+#define src x3
+#define tmp x4
+#define wtmp2 w5
+#define synd x6
+#define soff x9
+#define cntrem x10
+
+#define vrepchr v0
+#define vdata1 v1
+#define vdata2 v2
+#define vhas_chr1 v3
+#define vhas_chr2 v4
+#define vrepmask v5
+#define vend v6
+
+/*
+ * Core algorithm:
+ *
+ * For each 32-byte chunk we calculate a 64-bit syndrome value, with two bits
+ * per byte. For each tuple, bit 0 is set if the relevant byte matched the
+ * requested character and bit 1 is not used (faster than using a 32bit
+ * syndrome). Since the bits in the syndrome reflect exactly the order in which
+ * things occur in the original string, counting trailing zeros allows to
+ * identify exactly which byte has matched.
+ */
+
+ENTRY (__memchr_aarch64)
+ /* Do not dereference srcin if no bytes to compare. */
+ cbz cntin, L(zero_length)
+ /*
+ * Magic constant 0x40100401 allows us to identify which lane matches
+ * the requested byte.
+ */
+ mov wtmp2, #0x0401
+ movk wtmp2, #0x4010, lsl #16
+ dup vrepchr.16b, chrin
+ /* Work with aligned 32-byte chunks */
+ bic src, srcin, #31
+ dup vrepmask.4s, wtmp2
+ ands soff, srcin, #31
+ and cntrem, cntin, #31
+ b.eq L(loop)
+
+ /*
+ * Input string is not 32-byte aligned. We calculate the syndrome
+ * value for the aligned 32 bytes block containing the first bytes
+ * and mask the irrelevant part.
+ */
+
+ ld1 {vdata1.16b, vdata2.16b}, [src], #32
+ sub tmp, soff, #32
+ adds cntin, cntin, tmp
+ cmeq vhas_chr1.16b, vdata1.16b, vrepchr.16b
+ cmeq vhas_chr2.16b, vdata2.16b, vrepchr.16b
+ and vhas_chr1.16b, vhas_chr1.16b, vrepmask.16b
+ and vhas_chr2.16b, vhas_chr2.16b, vrepmask.16b
+ addp vend.16b, vhas_chr1.16b, vhas_chr2.16b /* 256->128 */
+ addp vend.16b, vend.16b, vend.16b /* 128->64 */
+ mov synd, vend.d[0]
+ /* Clear the soff*2 lower bits */
+ lsl tmp, soff, #1
+ lsr synd, synd, tmp
+ lsl synd, synd, tmp
+ /* The first block can also be the last */
+ b.ls L(masklast)
+ /* Have we found something already? */
+ cbnz synd, L(tail)
+
+L(loop):
+ ld1 {vdata1.16b, vdata2.16b}, [src], #32
+ subs cntin, cntin, #32
+ cmeq vhas_chr1.16b, vdata1.16b, vrepchr.16b
+ cmeq vhas_chr2.16b, vdata2.16b, vrepchr.16b
+ /* If we're out of data we finish regardless of the result */
+ b.ls L(end)
+ /* Use a fast check for the termination condition */
+ orr vend.16b, vhas_chr1.16b, vhas_chr2.16b
+ addp vend.2d, vend.2d, vend.2d
+ mov synd, vend.d[0]
+ /* We're not out of data, loop if we haven't found the character */
+ cbz synd, L(loop)
+
+L(end):
+ /* Termination condition found, let's calculate the syndrome value */
+ and vhas_chr1.16b, vhas_chr1.16b, vrepmask.16b
+ and vhas_chr2.16b, vhas_chr2.16b, vrepmask.16b
+ addp vend.16b, vhas_chr1.16b, vhas_chr2.16b /* 256->128 */
+ addp vend.16b, vend.16b, vend.16b /* 128->64 */
+ mov synd, vend.d[0]
+ /* Only do the clear for the last possible block */
+ b.hi L(tail)
+
+L(masklast):
+ /* Clear the (32 - ((cntrem + soff) % 32)) * 2 upper bits */
+ add tmp, cntrem, soff
+ and tmp, tmp, #31
+ sub tmp, tmp, #32
+ neg tmp, tmp, lsl #1
+ lsl synd, synd, tmp
+ lsr synd, synd, tmp
+
+L(tail):
+ /* Count the trailing zeros using bit reversing */
+ rbit synd, synd
+ /* Compensate the last post-increment */
+ sub src, src, #32
+ /* Check that we have found a character */
+ cmp synd, #0
+ /* And count the leading zeros */
+ clz synd, synd
+ /* Compute the potential result */
+ add result, src, synd, lsr #1
+ /* Select result or NULL */
+ csel result, xzr, result, eq
+ ret
+
+L(zero_length):
+ mov result, #0
+ ret
+
+END (__memchr_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/memcmp-sve.S b/libc/AOR_v20.02/string/aarch64/memcmp-sve.S
new file mode 100644
index 000000000000..0a3962f587bf
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/memcmp-sve.S
@@ -0,0 +1,51 @@
+/*
+ * memcmp - compare memory
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_FEATURE_SVE
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * SVE Available.
+ */
+
+ .arch armv8-a+sve
+ .text
+
+ .globl __memcmp_aarch64_sve
+ .type __memcmp_aarch64_sve, %function
+ .p2align 4
+__memcmp_aarch64_sve:
+ mov x3, 0 /* initialize off */
+
+0: whilelo p0.b, x3, x2 /* while off < max */
+ b.none 9f
+
+ ld1b z0.b, p0/z, [x0, x3] /* read vectors bounded by max. */
+ ld1b z1.b, p0/z, [x1, x3]
+
+ /* Increment for a whole vector, even if we've only read a partial.
+ This is significantly cheaper than INCP, and since OFF is not
+ used after the loop it is ok to increment OFF past MAX. */
+ incb x3
+
+ cmpne p1.b, p0/z, z0.b, z1.b /* while no inequalities */
+ b.none 0b
+
+ /* Found inequality. */
+1: brkb p1.b, p0/z, p1.b /* find first such */
+ lasta w0, p1, z0.b /* extract each byte */
+ lasta w1, p1, z1.b
+ sub x0, x0, x1 /* return comparison */
+ ret
+
+ /* Found end-of-count. */
+9: mov x0, 0 /* return equality */
+ ret
+
+ .size __memcmp_aarch64_sve, . - __memcmp_aarch64_sve
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/memcmp.S b/libc/AOR_v20.02/string/aarch64/memcmp.S
new file mode 100644
index 000000000000..fab69b5320ee
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/memcmp.S
@@ -0,0 +1,134 @@
+/* memcmp - compare memory
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64, unaligned accesses.
+ */
+
+#include "../asmdefs.h"
+
+/* Parameters and result. */
+#define src1 x0
+#define src2 x1
+#define limit x2
+#define result w0
+
+/* Internal variables. */
+#define data1 x3
+#define data1w w3
+#define data1h x4
+#define data2 x5
+#define data2w w5
+#define data2h x6
+#define tmp1 x7
+#define tmp2 x8
+
+ENTRY (__memcmp_aarch64)
+ subs limit, limit, 8
+ b.lo L(less8)
+
+ ldr data1, [src1], 8
+ ldr data2, [src2], 8
+ cmp data1, data2
+ b.ne L(return)
+
+ subs limit, limit, 8
+ b.gt L(more16)
+
+ ldr data1, [src1, limit]
+ ldr data2, [src2, limit]
+ b L(return)
+
+L(more16):
+ ldr data1, [src1], 8
+ ldr data2, [src2], 8
+ cmp data1, data2
+ bne L(return)
+
+ /* Jump directly to comparing the last 16 bytes for 32 byte (or less)
+ strings. */
+ subs limit, limit, 16
+ b.ls L(last_bytes)
+
+ /* We overlap loads between 0-32 bytes at either side of SRC1 when we
+ try to align, so limit it only to strings larger than 128 bytes. */
+ cmp limit, 96
+ b.ls L(loop16)
+
+ /* Align src1 and adjust src2 with bytes not yet done. */
+ and tmp1, src1, 15
+ add limit, limit, tmp1
+ sub src1, src1, tmp1
+ sub src2, src2, tmp1
+
+ /* Loop performing 16 bytes per iteration using aligned src1.
+ Limit is pre-decremented by 16 and must be larger than zero.
+ Exit if <= 16 bytes left to do or if the data is not equal. */
+ .p2align 4
+L(loop16):
+ ldp data1, data1h, [src1], 16
+ ldp data2, data2h, [src2], 16
+ subs limit, limit, 16
+ ccmp data1, data2, 0, hi
+ ccmp data1h, data2h, 0, eq
+ b.eq L(loop16)
+
+ cmp data1, data2
+ bne L(return)
+ mov data1, data1h
+ mov data2, data2h
+ cmp data1, data2
+ bne L(return)
+
+ /* Compare last 1-16 bytes using unaligned access. */
+L(last_bytes):
+ add src1, src1, limit
+ add src2, src2, limit
+ ldp data1, data1h, [src1]
+ ldp data2, data2h, [src2]
+ cmp data1, data2
+ bne L(return)
+ mov data1, data1h
+ mov data2, data2h
+ cmp data1, data2
+
+ /* Compare data bytes and set return value to 0, -1 or 1. */
+L(return):
+#ifndef __AARCH64EB__
+ rev data1, data1
+ rev data2, data2
+#endif
+ cmp data1, data2
+L(ret_eq):
+ cset result, ne
+ cneg result, result, lo
+ ret
+
+ .p2align 4
+ /* Compare up to 8 bytes. Limit is [-8..-1]. */
+L(less8):
+ adds limit, limit, 4
+ b.lo L(less4)
+ ldr data1w, [src1], 4
+ ldr data2w, [src2], 4
+ cmp data1w, data2w
+ b.ne L(return)
+ sub limit, limit, 4
+L(less4):
+ adds limit, limit, 4
+ beq L(ret_eq)
+L(byte_loop):
+ ldrb data1w, [src1], 1
+ ldrb data2w, [src2], 1
+ subs limit, limit, 1
+ ccmp data1w, data2w, 0, ne /* NZCV = 0b0000. */
+ b.eq L(byte_loop)
+ sub result, data1w, data2w
+ ret
+
+END (__memcmp_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/memcpy-advsimd.S b/libc/AOR_v20.02/string/aarch64/memcpy-advsimd.S
new file mode 100644
index 000000000000..befd32bb98c7
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/memcpy-advsimd.S
@@ -0,0 +1,202 @@
+/*
+ * memcpy - copy memory area
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64, Advanced SIMD, unaligned accesses.
+ *
+ */
+
+#include "../asmdefs.h"
+
+#define dstin x0
+#define src x1
+#define count x2
+#define dst x3
+#define srcend x4
+#define dstend x5
+#define A_l x6
+#define A_lw w6
+#define A_h x7
+#define B_l x8
+#define B_lw w8
+#define B_h x9
+#define C_lw w10
+#define tmp1 x14
+
+#define A_q q0
+#define B_q q1
+#define C_q q2
+#define D_q q3
+#define E_q q4
+#define F_q q5
+#define G_q q6
+#define H_q q7
+
+/* This implementation handles overlaps and supports both memcpy and memmove
+ from a single entry point. It uses unaligned accesses and branchless
+ sequences to keep the code small, simple and improve performance.
+
+ Copies are split into 3 main cases: small copies of up to 32 bytes, medium
+ copies of up to 128 bytes, and large copies. The overhead of the overlap
+ check is negligible since it is only required for large copies.
+
+ Large copies use a software pipelined loop processing 64 bytes per iteration.
+ The source pointer is 16-byte aligned to minimize unaligned accesses.
+ The loop tail is handled by always copying 64 bytes from the end.
+*/
+
+ENTRY (__memcpy_aarch64_simd)
+ENTRY_ALIAS (__memmove_aarch64_simd)
+ add srcend, src, count
+ add dstend, dstin, count
+ cmp count, 128
+ b.hi L(copy_long)
+ cmp count, 32
+ b.hi L(copy32_128)
+
+ /* Small copies: 0..32 bytes. */
+ cmp count, 16
+ b.lo L(copy16)
+ ldr A_q, [src]
+ ldr B_q, [srcend, -16]
+ str A_q, [dstin]
+ str B_q, [dstend, -16]
+ ret
+
+ /* Copy 8-15 bytes. */
+L(copy16):
+ tbz count, 3, L(copy8)
+ ldr A_l, [src]
+ ldr A_h, [srcend, -8]
+ str A_l, [dstin]
+ str A_h, [dstend, -8]
+ ret
+
+ .p2align 3
+ /* Copy 4-7 bytes. */
+L(copy8):
+ tbz count, 2, L(copy4)
+ ldr A_lw, [src]
+ ldr B_lw, [srcend, -4]
+ str A_lw, [dstin]
+ str B_lw, [dstend, -4]
+ ret
+
+ /* Copy 0..3 bytes using a branchless sequence. */
+L(copy4):
+ cbz count, L(copy0)
+ lsr tmp1, count, 1
+ ldrb A_lw, [src]
+ ldrb C_lw, [srcend, -1]
+ ldrb B_lw, [src, tmp1]
+ strb A_lw, [dstin]
+ strb B_lw, [dstin, tmp1]
+ strb C_lw, [dstend, -1]
+L(copy0):
+ ret
+
+ .p2align 4
+ /* Medium copies: 33..128 bytes. */
+L(copy32_128):
+ ldp A_q, B_q, [src]
+ ldp C_q, D_q, [srcend, -32]
+ cmp count, 64
+ b.hi L(copy128)
+ stp A_q, B_q, [dstin]
+ stp C_q, D_q, [dstend, -32]
+ ret
+
+ .p2align 4
+ /* Copy 65..128 bytes. */
+L(copy128):
+ ldp E_q, F_q, [src, 32]
+ cmp count, 96
+ b.ls L(copy96)
+ ldp G_q, H_q, [srcend, -64]
+ stp G_q, H_q, [dstend, -64]
+L(copy96):
+ stp A_q, B_q, [dstin]
+ stp E_q, F_q, [dstin, 32]
+ stp C_q, D_q, [dstend, -32]
+ ret
+
+ /* Copy more than 128 bytes. */
+L(copy_long):
+ /* Use backwards copy if there is an overlap. */
+ sub tmp1, dstin, src
+ cmp tmp1, count
+ b.lo L(copy_long_backwards)
+
+ /* Copy 16 bytes and then align src to 16-byte alignment. */
+ ldr D_q, [src]
+ and tmp1, src, 15
+ bic src, src, 15
+ sub dst, dstin, tmp1
+ add count, count, tmp1 /* Count is now 16 too large. */
+ ldp A_q, B_q, [src, 16]
+ str D_q, [dstin]
+ ldp C_q, D_q, [src, 48]
+ subs count, count, 128 + 16 /* Test and readjust count. */
+ b.ls L(copy64_from_end)
+L(loop64):
+ stp A_q, B_q, [dst, 16]
+ ldp A_q, B_q, [src, 80]
+ stp C_q, D_q, [dst, 48]
+ ldp C_q, D_q, [src, 112]
+ add src, src, 64
+ add dst, dst, 64
+ subs count, count, 64
+ b.hi L(loop64)
+
+ /* Write the last iteration and copy 64 bytes from the end. */
+L(copy64_from_end):
+ ldp E_q, F_q, [srcend, -64]
+ stp A_q, B_q, [dst, 16]
+ ldp A_q, B_q, [srcend, -32]
+ stp C_q, D_q, [dst, 48]
+ stp E_q, F_q, [dstend, -64]
+ stp A_q, B_q, [dstend, -32]
+ ret
+
+ /* Large backwards copy for overlapping copies.
+ Copy 16 bytes and then align srcend to 16-byte alignment. */
+L(copy_long_backwards):
+ cbz tmp1, L(copy0)
+ ldr D_q, [srcend, -16]
+ and tmp1, srcend, 15
+ bic srcend, srcend, 15
+ sub count, count, tmp1
+ ldp A_q, B_q, [srcend, -32]
+ str D_q, [dstend, -16]
+ ldp C_q, D_q, [srcend, -64]
+ sub dstend, dstend, tmp1
+ subs count, count, 128
+ b.ls L(copy64_from_start)
+
+L(loop64_backwards):
+ stp A_q, B_q, [dstend, -32]
+ ldp A_q, B_q, [srcend, -96]
+ stp C_q, D_q, [dstend, -64]
+ ldp C_q, D_q, [srcend, -128]
+ sub srcend, srcend, 64
+ sub dstend, dstend, 64
+ subs count, count, 64
+ b.hi L(loop64_backwards)
+
+ /* Write the last iteration and copy 64 bytes from the start. */
+L(copy64_from_start):
+ ldp E_q, F_q, [src, 32]
+ stp A_q, B_q, [dstend, -32]
+ ldp A_q, B_q, [src]
+ stp C_q, D_q, [dstend, -64]
+ stp E_q, F_q, [dstin, 32]
+ stp A_q, B_q, [dstin]
+ ret
+
+END (__memcpy_aarch64_simd)
diff --git a/libc/AOR_v20.02/string/aarch64/memcpy.S b/libc/AOR_v20.02/string/aarch64/memcpy.S
new file mode 100644
index 000000000000..459e22848e25
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/memcpy.S
@@ -0,0 +1,240 @@
+/*
+ * memcpy - copy memory area
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64, unaligned accesses.
+ *
+ */
+
+#include "../asmdefs.h"
+
+#define dstin x0
+#define src x1
+#define count x2
+#define dst x3
+#define srcend x4
+#define dstend x5
+#define A_l x6
+#define A_lw w6
+#define A_h x7
+#define B_l x8
+#define B_lw w8
+#define B_h x9
+#define C_l x10
+#define C_lw w10
+#define C_h x11
+#define D_l x12
+#define D_h x13
+#define E_l x14
+#define E_h x15
+#define F_l x16
+#define F_h x17
+#define G_l count
+#define G_h dst
+#define H_l src
+#define H_h srcend
+#define tmp1 x14
+
+/* This implementation handles overlaps and supports both memcpy and memmove
+ from a single entry point. It uses unaligned accesses and branchless
+ sequences to keep the code small, simple and improve performance.
+
+ Copies are split into 3 main cases: small copies of up to 32 bytes, medium
+ copies of up to 128 bytes, and large copies. The overhead of the overlap
+ check is negligible since it is only required for large copies.
+
+ Large copies use a software pipelined loop processing 64 bytes per iteration.
+ The destination pointer is 16-byte aligned to minimize unaligned accesses.
+ The loop tail is handled by always copying 64 bytes from the end.
+*/
+
+ENTRY (__memcpy_aarch64)
+ENTRY_ALIAS (__memmove_aarch64)
+ add srcend, src, count
+ add dstend, dstin, count
+ cmp count, 128
+ b.hi L(copy_long)
+ cmp count, 32
+ b.hi L(copy32_128)
+
+ /* Small copies: 0..32 bytes. */
+ cmp count, 16
+ b.lo L(copy16)
+ ldp A_l, A_h, [src]
+ ldp D_l, D_h, [srcend, -16]
+ stp A_l, A_h, [dstin]
+ stp D_l, D_h, [dstend, -16]
+ ret
+
+ /* Copy 8-15 bytes. */
+L(copy16):
+ tbz count, 3, L(copy8)
+ ldr A_l, [src]
+ ldr A_h, [srcend, -8]
+ str A_l, [dstin]
+ str A_h, [dstend, -8]
+ ret
+
+ .p2align 3
+ /* Copy 4-7 bytes. */
+L(copy8):
+ tbz count, 2, L(copy4)
+ ldr A_lw, [src]
+ ldr B_lw, [srcend, -4]
+ str A_lw, [dstin]
+ str B_lw, [dstend, -4]
+ ret
+
+ /* Copy 0..3 bytes using a branchless sequence. */
+L(copy4):
+ cbz count, L(copy0)
+ lsr tmp1, count, 1
+ ldrb A_lw, [src]
+ ldrb C_lw, [srcend, -1]
+ ldrb B_lw, [src, tmp1]
+ strb A_lw, [dstin]
+ strb B_lw, [dstin, tmp1]
+ strb C_lw, [dstend, -1]
+L(copy0):
+ ret
+
+ .p2align 4
+ /* Medium copies: 33..128 bytes. */
+L(copy32_128):
+ ldp A_l, A_h, [src]
+ ldp B_l, B_h, [src, 16]
+ ldp C_l, C_h, [srcend, -32]
+ ldp D_l, D_h, [srcend, -16]
+ cmp count, 64
+ b.hi L(copy128)
+ stp A_l, A_h, [dstin]
+ stp B_l, B_h, [dstin, 16]
+ stp C_l, C_h, [dstend, -32]
+ stp D_l, D_h, [dstend, -16]
+ ret
+
+ .p2align 4
+ /* Copy 65..128 bytes. */
+L(copy128):
+ ldp E_l, E_h, [src, 32]
+ ldp F_l, F_h, [src, 48]
+ cmp count, 96
+ b.ls L(copy96)
+ ldp G_l, G_h, [srcend, -64]
+ ldp H_l, H_h, [srcend, -48]
+ stp G_l, G_h, [dstend, -64]
+ stp H_l, H_h, [dstend, -48]
+L(copy96):
+ stp A_l, A_h, [dstin]
+ stp B_l, B_h, [dstin, 16]
+ stp E_l, E_h, [dstin, 32]
+ stp F_l, F_h, [dstin, 48]
+ stp C_l, C_h, [dstend, -32]
+ stp D_l, D_h, [dstend, -16]
+ ret
+
+ .p2align 4
+ /* Copy more than 128 bytes. */
+L(copy_long):
+ /* Use backwards copy if there is an overlap. */
+ sub tmp1, dstin, src
+ cbz tmp1, L(copy0)
+ cmp tmp1, count
+ b.lo L(copy_long_backwards)
+
+ /* Copy 16 bytes and then align dst to 16-byte alignment. */
+
+ ldp D_l, D_h, [src]
+ and tmp1, dstin, 15
+ bic dst, dstin, 15
+ sub src, src, tmp1
+ add count, count, tmp1 /* Count is now 16 too large. */
+ ldp A_l, A_h, [src, 16]
+ stp D_l, D_h, [dstin]
+ ldp B_l, B_h, [src, 32]
+ ldp C_l, C_h, [src, 48]
+ ldp D_l, D_h, [src, 64]!
+ subs count, count, 128 + 16 /* Test and readjust count. */
+ b.ls L(copy64_from_end)
+
+L(loop64):
+ stp A_l, A_h, [dst, 16]
+ ldp A_l, A_h, [src, 16]
+ stp B_l, B_h, [dst, 32]
+ ldp B_l, B_h, [src, 32]
+ stp C_l, C_h, [dst, 48]
+ ldp C_l, C_h, [src, 48]
+ stp D_l, D_h, [dst, 64]!
+ ldp D_l, D_h, [src, 64]!
+ subs count, count, 64
+ b.hi L(loop64)
+
+ /* Write the last iteration and copy 64 bytes from the end. */
+L(copy64_from_end):
+ ldp E_l, E_h, [srcend, -64]
+ stp A_l, A_h, [dst, 16]
+ ldp A_l, A_h, [srcend, -48]
+ stp B_l, B_h, [dst, 32]
+ ldp B_l, B_h, [srcend, -32]
+ stp C_l, C_h, [dst, 48]
+ ldp C_l, C_h, [srcend, -16]
+ stp D_l, D_h, [dst, 64]
+ stp E_l, E_h, [dstend, -64]
+ stp A_l, A_h, [dstend, -48]
+ stp B_l, B_h, [dstend, -32]
+ stp C_l, C_h, [dstend, -16]
+ ret
+
+ .p2align 4
+
+ /* Large backwards copy for overlapping copies.
+ Copy 16 bytes and then align dst to 16-byte alignment. */
+L(copy_long_backwards):
+ ldp D_l, D_h, [srcend, -16]
+ and tmp1, dstend, 15
+ sub srcend, srcend, tmp1
+ sub count, count, tmp1
+ ldp A_l, A_h, [srcend, -16]
+ stp D_l, D_h, [dstend, -16]
+ ldp B_l, B_h, [srcend, -32]
+ ldp C_l, C_h, [srcend, -48]
+ ldp D_l, D_h, [srcend, -64]!
+ sub dstend, dstend, tmp1
+ subs count, count, 128
+ b.ls L(copy64_from_start)
+
+L(loop64_backwards):
+ stp A_l, A_h, [dstend, -16]
+ ldp A_l, A_h, [srcend, -16]
+ stp B_l, B_h, [dstend, -32]
+ ldp B_l, B_h, [srcend, -32]
+ stp C_l, C_h, [dstend, -48]
+ ldp C_l, C_h, [srcend, -48]
+ stp D_l, D_h, [dstend, -64]!
+ ldp D_l, D_h, [srcend, -64]!
+ subs count, count, 64
+ b.hi L(loop64_backwards)
+
+ /* Write the last iteration and copy 64 bytes from the start. */
+L(copy64_from_start):
+ ldp G_l, G_h, [src, 48]
+ stp A_l, A_h, [dstend, -16]
+ ldp A_l, A_h, [src, 32]
+ stp B_l, B_h, [dstend, -32]
+ ldp B_l, B_h, [src, 16]
+ stp C_l, C_h, [dstend, -48]
+ ldp C_l, C_h, [src]
+ stp D_l, D_h, [dstend, -64]
+ stp G_l, G_h, [dstin, 48]
+ stp A_l, A_h, [dstin, 32]
+ stp B_l, B_h, [dstin, 16]
+ stp C_l, C_h, [dstin]
+ ret
+
+END (__memcpy_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/memset.S b/libc/AOR_v20.02/string/aarch64/memset.S
new file mode 100644
index 000000000000..39c78dcd7694
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/memset.S
@@ -0,0 +1,115 @@
+/*
+ * memset - fill memory with a constant byte
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64, Advanced SIMD, unaligned accesses.
+ *
+ */
+
+#include "../asmdefs.h"
+
+#define dstin x0
+#define val x1
+#define valw w1
+#define count x2
+#define dst x3
+#define dstend x4
+#define zva_val x5
+
+ENTRY (__memset_aarch64)
+
+ dup v0.16B, valw
+ add dstend, dstin, count
+
+ cmp count, 96
+ b.hi L(set_long)
+ cmp count, 16
+ b.hs L(set_medium)
+ mov val, v0.D[0]
+
+ /* Set 0..15 bytes. */
+ tbz count, 3, 1f
+ str val, [dstin]
+ str val, [dstend, -8]
+ ret
+ nop
+1: tbz count, 2, 2f
+ str valw, [dstin]
+ str valw, [dstend, -4]
+ ret
+2: cbz count, 3f
+ strb valw, [dstin]
+ tbz count, 1, 3f
+ strh valw, [dstend, -2]
+3: ret
+
+ /* Set 17..96 bytes. */
+L(set_medium):
+ str q0, [dstin]
+ tbnz count, 6, L(set96)
+ str q0, [dstend, -16]
+ tbz count, 5, 1f
+ str q0, [dstin, 16]
+ str q0, [dstend, -32]
+1: ret
+
+ .p2align 4
+ /* Set 64..96 bytes. Write 64 bytes from the start and
+ 32 bytes from the end. */
+L(set96):
+ str q0, [dstin, 16]
+ stp q0, q0, [dstin, 32]
+ stp q0, q0, [dstend, -32]
+ ret
+
+ .p2align 4
+L(set_long):
+ and valw, valw, 255
+ bic dst, dstin, 15
+ str q0, [dstin]
+ cmp count, 160
+ ccmp valw, 0, 0, hs
+ b.ne L(no_zva)
+
+#ifndef SKIP_ZVA_CHECK
+ mrs zva_val, dczid_el0
+ and zva_val, zva_val, 31
+ cmp zva_val, 4 /* ZVA size is 64 bytes. */
+ b.ne L(no_zva)
+#endif
+ str q0, [dst, 16]
+ stp q0, q0, [dst, 32]
+ bic dst, dst, 63
+ sub count, dstend, dst /* Count is now 64 too large. */
+ sub count, count, 128 /* Adjust count and bias for loop. */
+
+ .p2align 4
+L(zva_loop):
+ add dst, dst, 64
+ dc zva, dst
+ subs count, count, 64
+ b.hi L(zva_loop)
+ stp q0, q0, [dstend, -64]
+ stp q0, q0, [dstend, -32]
+ ret
+
+L(no_zva):
+ sub count, dstend, dst /* Count is 16 too large. */
+ sub dst, dst, 16 /* Dst is biased by -32. */
+ sub count, count, 64 + 16 /* Adjust count and bias for loop. */
+L(no_zva_loop):
+ stp q0, q0, [dst, 32]
+ stp q0, q0, [dst, 64]!
+ subs count, count, 64
+ b.hi L(no_zva_loop)
+ stp q0, q0, [dstend, -64]
+ stp q0, q0, [dstend, -32]
+ ret
+
+END (__memset_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/stpcpy-sve.S b/libc/AOR_v20.02/string/aarch64/stpcpy-sve.S
new file mode 100644
index 000000000000..54afdab72529
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/stpcpy-sve.S
@@ -0,0 +1,11 @@
+/*
+ * stpcpy - copy a string returning pointer to end.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#define BUILD_STPCPY 1
+
+#include "strcpy-sve.S"
diff --git a/libc/AOR_v20.02/string/aarch64/stpcpy.S b/libc/AOR_v20.02/string/aarch64/stpcpy.S
new file mode 100644
index 000000000000..8cf98db4ba25
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/stpcpy.S
@@ -0,0 +1,11 @@
+/*
+ * stpcpy - copy a string returning pointer to end.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#define BUILD_STPCPY 1
+
+#include "strcpy.S"
diff --git a/libc/AOR_v20.02/string/aarch64/strchr-mte.S b/libc/AOR_v20.02/string/aarch64/strchr-mte.S
new file mode 100644
index 000000000000..7c517916212a
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strchr-mte.S
@@ -0,0 +1,131 @@
+/*
+ * strchr - find a character in a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * Neon Available.
+ */
+
+#include "../asmdefs.h"
+
+/* Arguments and results. */
+#define srcin x0
+#define chrin w1
+
+#define result x0
+
+#define src x2
+#define tmp1 x3
+#define wtmp2 w4
+#define tmp3 x5
+
+#define vrepchr v0
+#define qdata q1
+#define vdata v1
+#define vhas_nul v2
+#define vhas_chr v3
+#define vrepmask_0 v4
+#define vrepmask_c v5
+#define vend v6
+
+#define L(l) .L ## l
+
+/* Core algorithm.
+
+ For each 16-byte chunk we calculate a 64-bit syndrome value, with
+ four bits per byte (LSB is always in bits 0 and 1, for both big
+ and little-endian systems). For each tuple, bit 0 is set if
+ the relevant byte matched the requested character; bit 1 is set
+ if the relevant byte matched the NUL end of string (we trigger
+ off bit0 for the special case of looking for NUL) and bits 2 and 3
+ are not used.
+ Since the bits in the syndrome reflect exactly the order in which
+ things occur in the original string a count_trailing_zeros()
+ operation will identify exactly which byte is causing the termination,
+ and why. */
+
+/* Locals and temporaries. */
+
+ENTRY(__strchr_aarch64_mte)
+ /* Magic constant 0x10011001 to allow us to identify which lane
+ matches the requested byte. Magic constant 0x20022002 used
+ similarly for NUL termination. */
+ mov wtmp2, #0x1001
+ movk wtmp2, #0x1001, lsl #16
+ dup vrepchr.16b, chrin
+ bic src, srcin, #15 /* Work with aligned 16-byte chunks. */
+ dup vrepmask_c.4s, wtmp2
+ ands tmp1, srcin, #15
+ add vrepmask_0.4s, vrepmask_c.4s, vrepmask_c.4s /* equiv: lsl #1 */
+ b.eq L(loop)
+
+ /* Input string is not 16-byte aligned. Rather than forcing
+ the padding bytes to a safe value, we calculate the syndrome
+ for all the bytes, but then mask off those bits of the
+ syndrome that are related to the padding. */
+ ldr qdata, [src], #16
+ cmeq vhas_nul.16b, vdata.16b, #0
+ cmeq vhas_chr.16b, vdata.16b, vrepchr.16b
+ and vhas_nul.16b, vhas_nul.16b, vrepmask_0.16b
+ and vhas_chr.16b, vhas_chr.16b, vrepmask_c.16b
+ lsl tmp1, tmp1, #2
+ orr vend.16b, vhas_nul.16b, vhas_chr.16b
+ mov tmp3, #~0
+ addp vend.16b, vend.16b, vend.16b /* 128->64 */
+ lsl tmp1, tmp3, tmp1
+
+ mov tmp3, vend.d[0]
+ ands tmp1, tmp3, tmp1 /* Mask padding bits. */
+ b.ne L(tail)
+
+L(loop):
+ ldr qdata, [src], #32
+ cmeq vhas_nul.16b, vdata.16b, #0
+ cmeq vhas_chr.16b, vdata.16b, vrepchr.16b
+ /* Use a fast check for the termination condition. */
+ orr vend.16b, vhas_nul.16b, vhas_chr.16b
+ addp vend.16b, vend.16b, vend.16b /* 128->64 */
+ mov tmp1, vend.d[0]
+ cbnz tmp1, L(end)
+
+ ldr qdata, [src, #-16]
+ cmeq vhas_nul.16b, vdata.16b, #0
+ cmeq vhas_chr.16b, vdata.16b, vrepchr.16b
+ /* Use a fast check for the termination condition. */
+ orr vend.16b, vhas_nul.16b, vhas_chr.16b
+ addp vend.16b, vend.16b, vend.16b /* 128->64 */
+ mov tmp1, vend.d[0]
+ cbz tmp1, L(loop)
+
+ /* Adjust src for next two subtractions. */
+ add src, src, #16
+L(end):
+ /* Termination condition found. Now need to establish exactly why
+ we terminated. */
+ and vhas_nul.16b, vhas_nul.16b, vrepmask_0.16b
+ and vhas_chr.16b, vhas_chr.16b, vrepmask_c.16b
+ sub src, src, #16
+ orr vend.16b, vhas_nul.16b, vhas_chr.16b
+ addp vend.16b, vend.16b, vend.16b /* 128->64 */
+
+ mov tmp1, vend.d[0]
+L(tail):
+ /* Count the trailing zeros, by bit reversing... */
+ rbit tmp1, tmp1
+ /* Re-bias source. */
+ sub src, src, #16
+ clz tmp1, tmp1 /* And counting the leading zeros. */
+ /* Tmp1 is even if the target character was found first. Otherwise
+ we've found the end of string and we weren't looking for NUL. */
+ tst tmp1, #1
+ add result, src, tmp1, lsr #2
+ csel result, result, xzr, eq
+ ret
+
+END(__strchr_aarch64_mte)
diff --git a/libc/AOR_v20.02/string/aarch64/strchr-sve.S b/libc/AOR_v20.02/string/aarch64/strchr-sve.S
new file mode 100644
index 000000000000..3f7d782c0027
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strchr-sve.S
@@ -0,0 +1,72 @@
+/*
+ * strchr/strchrnul - find a character in a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_FEATURE_SVE
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * SVE Available.
+ */
+
+ .arch armv8-a+sve
+ .text
+
+/* To build as strchrnul, define BUILD_STRCHRNUL before compiling this file. */
+#ifdef BUILD_STRCHRNUL
+#define FUNC __strchrnul_aarch64_sve
+#else
+#define FUNC __strchr_aarch64_sve
+#endif
+
+ .globl FUNC
+ .type FUNC, %function
+ .p2align 4
+FUNC:
+ dup z1.b, w1 /* replicate byte across vector */
+ setffr /* initialize FFR */
+ ptrue p1.b /* all ones; loop invariant */
+
+ .p2align 4
+ /* Read a vector's worth of bytes, stopping on first fault. */
+0: ldff1b z0.b, p1/z, [x0, xzr]
+ rdffrs p0.b, p1/z
+ b.nlast 2f
+
+ /* First fault did not fail: the whole vector is valid.
+ Avoid depending on the contents of FFR beyond the branch. */
+ incb x0 /* speculate increment */
+ cmpeq p2.b, p1/z, z0.b, z1.b /* search for c */
+ cmpeq p3.b, p1/z, z0.b, 0 /* search for 0 */
+ orrs p4.b, p1/z, p2.b, p3.b /* c | 0 */
+ b.none 0b
+ decb x0 /* undo speculate */
+
+ /* Found C or 0. */
+1: brka p4.b, p1/z, p4.b /* find first such */
+ sub x0, x0, 1 /* adjust pointer for that byte */
+ incp x0, p4.b
+#ifndef BUILD_STRCHRNUL
+ ptest p4, p2.b /* was first in c? */
+ csel x0, xzr, x0, none /* if there was no c, return null */
+#endif
+ ret
+
+ /* First fault failed: only some of the vector is valid.
+ Perform the comparision only on the valid bytes. */
+2: cmpeq p2.b, p0/z, z0.b, z1.b /* search for c */
+ cmpeq p3.b, p0/z, z0.b, 0 /* search for 0 */
+ orrs p4.b, p0/z, p2.b, p3.b /* c | 0 */
+ b.any 1b
+
+ /* No C or 0 found. Re-init FFR, increment, and loop. */
+ setffr
+ incp x0, p0.b
+ b 0b
+
+ .size FUNC, . - FUNC
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/strchr.S b/libc/AOR_v20.02/string/aarch64/strchr.S
new file mode 100644
index 000000000000..4c7617f21948
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strchr.S
@@ -0,0 +1,132 @@
+/*
+ * strchr - find a character in a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * Neon Available.
+ */
+
+#include "../asmdefs.h"
+
+/* Arguments and results. */
+#define srcin x0
+#define chrin w1
+
+#define result x0
+
+#define src x2
+#define tmp1 x3
+#define wtmp2 w4
+#define tmp3 x5
+
+#define vrepchr v0
+#define vdata1 v1
+#define vdata2 v2
+#define vhas_nul1 v3
+#define vhas_nul2 v4
+#define vhas_chr1 v5
+#define vhas_chr2 v6
+#define vrepmask_0 v7
+#define vrepmask_c v16
+#define vend1 v17
+#define vend2 v18
+
+/* Core algorithm.
+
+ For each 32-byte hunk we calculate a 64-bit syndrome value, with
+ two bits per byte (LSB is always in bits 0 and 1, for both big
+ and little-endian systems). For each tuple, bit 0 is set iff
+ the relevant byte matched the requested character; bit 1 is set
+ iff the relevant byte matched the NUL end of string (we trigger
+ off bit0 for the special case of looking for NUL). Since the bits
+ in the syndrome reflect exactly the order in which things occur
+ in the original string a count_trailing_zeros() operation will
+ identify exactly which byte is causing the termination, and why. */
+
+/* Locals and temporaries. */
+
+ENTRY (__strchr_aarch64)
+ /* Magic constant 0x40100401 to allow us to identify which lane
+ matches the requested byte. Magic constant 0x80200802 used
+ similarly for NUL termination. */
+ mov wtmp2, #0x0401
+ movk wtmp2, #0x4010, lsl #16
+ dup vrepchr.16b, chrin
+ bic src, srcin, #31 /* Work with aligned 32-byte hunks. */
+ dup vrepmask_c.4s, wtmp2
+ ands tmp1, srcin, #31
+ add vrepmask_0.4s, vrepmask_c.4s, vrepmask_c.4s /* equiv: lsl #1 */
+ b.eq L(loop)
+
+ /* Input string is not 32-byte aligned. Rather than forcing
+ the padding bytes to a safe value, we calculate the syndrome
+ for all the bytes, but then mask off those bits of the
+ syndrome that are related to the padding. */
+ ld1 {vdata1.16b, vdata2.16b}, [src], #32
+ neg tmp1, tmp1
+ cmeq vhas_nul1.16b, vdata1.16b, #0
+ cmeq vhas_chr1.16b, vdata1.16b, vrepchr.16b
+ cmeq vhas_nul2.16b, vdata2.16b, #0
+ cmeq vhas_chr2.16b, vdata2.16b, vrepchr.16b
+ and vhas_nul1.16b, vhas_nul1.16b, vrepmask_0.16b
+ and vhas_nul2.16b, vhas_nul2.16b, vrepmask_0.16b
+ and vhas_chr1.16b, vhas_chr1.16b, vrepmask_c.16b
+ and vhas_chr2.16b, vhas_chr2.16b, vrepmask_c.16b
+ orr vend1.16b, vhas_nul1.16b, vhas_chr1.16b
+ orr vend2.16b, vhas_nul2.16b, vhas_chr2.16b
+ lsl tmp1, tmp1, #1
+ addp vend1.16b, vend1.16b, vend2.16b // 256->128
+ mov tmp3, #~0
+ addp vend1.16b, vend1.16b, vend2.16b // 128->64
+ lsr tmp1, tmp3, tmp1
+
+ mov tmp3, vend1.d[0]
+ bic tmp1, tmp3, tmp1 // Mask padding bits.
+ cbnz tmp1, L(tail)
+
+L(loop):
+ ld1 {vdata1.16b, vdata2.16b}, [src], #32
+ cmeq vhas_nul1.16b, vdata1.16b, #0
+ cmeq vhas_chr1.16b, vdata1.16b, vrepchr.16b
+ cmeq vhas_nul2.16b, vdata2.16b, #0
+ cmeq vhas_chr2.16b, vdata2.16b, vrepchr.16b
+ /* Use a fast check for the termination condition. */
+ orr vend1.16b, vhas_nul1.16b, vhas_chr1.16b
+ orr vend2.16b, vhas_nul2.16b, vhas_chr2.16b
+ orr vend1.16b, vend1.16b, vend2.16b
+ addp vend1.2d, vend1.2d, vend1.2d
+ mov tmp1, vend1.d[0]
+ cbz tmp1, L(loop)
+
+ /* Termination condition found. Now need to establish exactly why
+ we terminated. */
+ and vhas_nul1.16b, vhas_nul1.16b, vrepmask_0.16b
+ and vhas_nul2.16b, vhas_nul2.16b, vrepmask_0.16b
+ and vhas_chr1.16b, vhas_chr1.16b, vrepmask_c.16b
+ and vhas_chr2.16b, vhas_chr2.16b, vrepmask_c.16b
+ orr vend1.16b, vhas_nul1.16b, vhas_chr1.16b
+ orr vend2.16b, vhas_nul2.16b, vhas_chr2.16b
+ addp vend1.16b, vend1.16b, vend2.16b // 256->128
+ addp vend1.16b, vend1.16b, vend2.16b // 128->64
+
+ mov tmp1, vend1.d[0]
+L(tail):
+ /* Count the trailing zeros, by bit reversing... */
+ rbit tmp1, tmp1
+ /* Re-bias source. */
+ sub src, src, #32
+ clz tmp1, tmp1 /* And counting the leading zeros. */
+ /* Tmp1 is even if the target charager was found first. Otherwise
+ we've found the end of string and we weren't looking for NUL. */
+ tst tmp1, #1
+ add result, src, tmp1, lsr #1
+ csel result, result, xzr, eq
+ ret
+
+END (__strchr_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/strchrnul-sve.S b/libc/AOR_v20.02/string/aarch64/strchrnul-sve.S
new file mode 100644
index 000000000000..0a3a60bbece8
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strchrnul-sve.S
@@ -0,0 +1,10 @@
+/*
+ * strchrnul - find a character or nul in a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#define BUILD_STRCHRNUL
+#include "strchr-sve.S"
diff --git a/libc/AOR_v20.02/string/aarch64/strchrnul.S b/libc/AOR_v20.02/string/aarch64/strchrnul.S
new file mode 100644
index 000000000000..50bd90c56922
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strchrnul.S
@@ -0,0 +1,117 @@
+/*
+ * strchrnul - find a character or nul in a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * Neon Available.
+ */
+
+#include "../asmdefs.h"
+
+/* Arguments and results. */
+#define srcin x0
+#define chrin w1
+
+#define result x0
+
+#define src x2
+#define tmp1 x3
+#define wtmp2 w4
+#define tmp3 x5
+
+#define vrepchr v0
+#define vdata1 v1
+#define vdata2 v2
+#define vhas_nul1 v3
+#define vhas_nul2 v4
+#define vhas_chr1 v5
+#define vhas_chr2 v6
+#define vrepmask v7
+#define vend1 v16
+
+/* Core algorithm.
+
+ For each 32-byte hunk we calculate a 64-bit syndrome value, with
+ two bits per byte (LSB is always in bits 0 and 1, for both big
+ and little-endian systems). For each tuple, bit 0 is set iff
+ the relevant byte matched the requested character or nul. Since the
+ bits in the syndrome reflect exactly the order in which things occur
+ in the original string a count_trailing_zeros() operation will
+ identify exactly which byte is causing the termination. */
+
+/* Locals and temporaries. */
+
+ENTRY (__strchrnul_aarch64)
+ /* Magic constant 0x40100401 to allow us to identify which lane
+ matches the termination condition. */
+ mov wtmp2, #0x0401
+ movk wtmp2, #0x4010, lsl #16
+ dup vrepchr.16b, chrin
+ bic src, srcin, #31 /* Work with aligned 32-byte hunks. */
+ dup vrepmask.4s, wtmp2
+ ands tmp1, srcin, #31
+ b.eq L(loop)
+
+ /* Input string is not 32-byte aligned. Rather than forcing
+ the padding bytes to a safe value, we calculate the syndrome
+ for all the bytes, but then mask off those bits of the
+ syndrome that are related to the padding. */
+ ld1 {vdata1.16b, vdata2.16b}, [src], #32
+ neg tmp1, tmp1
+ cmeq vhas_nul1.16b, vdata1.16b, #0
+ cmeq vhas_chr1.16b, vdata1.16b, vrepchr.16b
+ cmeq vhas_nul2.16b, vdata2.16b, #0
+ cmeq vhas_chr2.16b, vdata2.16b, vrepchr.16b
+ orr vhas_chr1.16b, vhas_chr1.16b, vhas_nul1.16b
+ orr vhas_chr2.16b, vhas_chr2.16b, vhas_nul2.16b
+ and vhas_chr1.16b, vhas_chr1.16b, vrepmask.16b
+ and vhas_chr2.16b, vhas_chr2.16b, vrepmask.16b
+ lsl tmp1, tmp1, #1
+ addp vend1.16b, vhas_chr1.16b, vhas_chr2.16b // 256->128
+ mov tmp3, #~0
+ addp vend1.16b, vend1.16b, vend1.16b // 128->64
+ lsr tmp1, tmp3, tmp1
+
+ mov tmp3, vend1.d[0]
+ bic tmp1, tmp3, tmp1 // Mask padding bits.
+ cbnz tmp1, L(tail)
+
+L(loop):
+ ld1 {vdata1.16b, vdata2.16b}, [src], #32
+ cmeq vhas_nul1.16b, vdata1.16b, #0
+ cmeq vhas_chr1.16b, vdata1.16b, vrepchr.16b
+ cmeq vhas_nul2.16b, vdata2.16b, #0
+ cmeq vhas_chr2.16b, vdata2.16b, vrepchr.16b
+ /* Use a fast check for the termination condition. */
+ orr vhas_chr1.16b, vhas_nul1.16b, vhas_chr1.16b
+ orr vhas_chr2.16b, vhas_nul2.16b, vhas_chr2.16b
+ orr vend1.16b, vhas_chr1.16b, vhas_chr2.16b
+ addp vend1.2d, vend1.2d, vend1.2d
+ mov tmp1, vend1.d[0]
+ cbz tmp1, L(loop)
+
+ /* Termination condition found. Now need to establish exactly why
+ we terminated. */
+ and vhas_chr1.16b, vhas_chr1.16b, vrepmask.16b
+ and vhas_chr2.16b, vhas_chr2.16b, vrepmask.16b
+ addp vend1.16b, vhas_chr1.16b, vhas_chr2.16b // 256->128
+ addp vend1.16b, vend1.16b, vend1.16b // 128->64
+
+ mov tmp1, vend1.d[0]
+L(tail):
+ /* Count the trailing zeros, by bit reversing... */
+ rbit tmp1, tmp1
+ /* Re-bias source. */
+ sub src, src, #32
+ clz tmp1, tmp1 /* ... and counting the leading zeros. */
+ /* tmp1 is twice the offset into the fragment. */
+ add result, src, tmp1, lsr #1
+ ret
+
+END (__strchrnul_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/strcmp-sve.S b/libc/AOR_v20.02/string/aarch64/strcmp-sve.S
new file mode 100644
index 000000000000..35aac0b7d0d2
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strcmp-sve.S
@@ -0,0 +1,60 @@
+/*
+ * __strcmp_aarch64_sve - compare two strings
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_FEATURE_SVE
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * SVE Available.
+ */
+
+ .arch armv8-a+sve
+ .text
+
+ .globl __strcmp_aarch64_sve
+ .type __strcmp_aarch64_sve, %function
+ .p2align 4
+__strcmp_aarch64_sve:
+ setffr /* initialize FFR */
+ ptrue p1.b, all /* all ones; loop invariant */
+ mov x2, 0 /* initialize offset */
+ nop
+
+ /* Read a vector's worth of bytes, stopping on first fault. */
+0: ldff1b z0.b, p1/z, [x0, x2]
+ ldff1b z1.b, p1/z, [x1, x2]
+ rdffrs p0.b, p1/z
+ b.nlast 2f
+
+ /* First fault did not fail: the whole vector is valid.
+ Avoid depending on the contents of FFR beyond the branch. */
+ incb x2, all /* skip bytes for next round */
+ cmpeq p2.b, p1/z, z0.b, z1.b /* compare strings */
+ cmpne p3.b, p1/z, z0.b, 0 /* search for ~zero */
+ nands p2.b, p1/z, p2.b, p3.b /* ~(eq & ~zero) -> ne | zero */
+ b.none 0b
+
+ /* Found end-of-string or inequality. */
+1: brkb p2.b, p1/z, p2.b /* find first such */
+ lasta w0, p2, z0.b /* extract each char */
+ lasta w1, p2, z1.b
+ sub x0, x0, x1 /* return comparison */
+ ret
+
+ /* First fault failed: only some of the vector is valid.
+ Perform the comparison only on the valid bytes. */
+2: incp x2, p0.b /* skip bytes for next round */
+ setffr /* re-init FFR for next round */
+ cmpeq p2.b, p0/z, z0.b, z1.b /* compare strings, as above */
+ cmpne p3.b, p0/z, z0.b, 0
+ nands p2.b, p0/z, p2.b, p3.b
+ b.none 0b
+ b 1b
+
+ .size __strcmp_aarch64_sve, . - __strcmp_aarch64_sve
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/strcmp.S b/libc/AOR_v20.02/string/aarch64/strcmp.S
new file mode 100644
index 000000000000..0dc5031e7326
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strcmp.S
@@ -0,0 +1,171 @@
+/*
+ * strcmp - compare two strings
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ */
+
+#include "../asmdefs.h"
+
+#define REP8_01 0x0101010101010101
+#define REP8_7f 0x7f7f7f7f7f7f7f7f
+#define REP8_80 0x8080808080808080
+
+/* Parameters and result. */
+#define src1 x0
+#define src2 x1
+#define result x0
+
+/* Internal variables. */
+#define data1 x2
+#define data1w w2
+#define data2 x3
+#define data2w w3
+#define has_nul x4
+#define
diff x5
+#define syndrome x6
+#define tmp1 x7
+#define tmp2 x8
+#define tmp3 x9
+#define zeroones x10
+#define pos x11
+
+ /* Start of performance-critical section -- one 64B cache line. */
+ENTRY (__strcmp_aarch64)
+ eor tmp1, src1, src2
+ mov zeroones, #REP8_01
+ tst tmp1, #7
+ b.ne L(misaligned8)
+ ands tmp1, src1, #7
+ b.ne L(mutual_align)
+ /* NUL detection works on the principle that (X - 1) & (~X) & 0x80
+ (=> (X - 1) & ~(X | 0x7f)) is non-zero iff a byte is zero, and
+ can be done in parallel across the entire word. */
+L(loop_aligned):
+ ldr data1, [src1], #8
+ ldr data2, [src2], #8
+L(start_realigned):
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ eor
diff , data1, data2 /* Non-zero if
diff erences found. */
+ bic has_nul, tmp1, tmp2 /* Non-zero if NUL terminator. */
+ orr syndrome,
diff , has_nul
+ cbz syndrome, L(loop_aligned)
+ /* End of performance-critical section -- one 64B cache line. */
+
+L(end):
+#ifndef __AARCH64EB__
+ rev syndrome, syndrome
+ rev data1, data1
+ /* The MS-non-zero bit of the syndrome marks either the first bit
+ that is
diff erent, or the top bit of the first zero byte.
+ Shifting left now will bring the critical information into the
+ top bits. */
+ clz pos, syndrome
+ rev data2, data2
+ lsl data1, data1, pos
+ lsl data2, data2, pos
+ /* But we need to zero-extend (char is unsigned) the value and then
+ perform a signed 32-bit subtraction. */
+ lsr data1, data1, #56
+ sub result, data1, data2, lsr #56
+ ret
+#else
+ /* For big-endian we cannot use the trick with the syndrome value
+ as carry-propagation can corrupt the upper bits if the trailing
+ bytes in the string contain 0x01. */
+ /* However, if there is no NUL byte in the dword, we can generate
+ the result directly. We can't just subtract the bytes as the
+ MSB might be significant. */
+ cbnz has_nul, 1f
+ cmp data1, data2
+ cset result, ne
+ cneg result, result, lo
+ ret
+1:
+ /* Re-compute the NUL-byte detection, using a byte-reversed value. */
+ rev tmp3, data1
+ sub tmp1, tmp3, zeroones
+ orr tmp2, tmp3, #REP8_7f
+ bic has_nul, tmp1, tmp2
+ rev has_nul, has_nul
+ orr syndrome,
diff , has_nul
+ clz pos, syndrome
+ /* The MS-non-zero bit of the syndrome marks either the first bit
+ that is
diff erent, or the top bit of the first zero byte.
+ Shifting left now will bring the critical information into the
+ top bits. */
+ lsl data1, data1, pos
+ lsl data2, data2, pos
+ /* But we need to zero-extend (char is unsigned) the value and then
+ perform a signed 32-bit subtraction. */
+ lsr data1, data1, #56
+ sub result, data1, data2, lsr #56
+ ret
+#endif
+
+L(mutual_align):
+ /* Sources are mutually aligned, but are not currently at an
+ alignment boundary. Round down the addresses and then mask off
+ the bytes that preceed the start point. */
+ bic src1, src1, #7
+ bic src2, src2, #7
+ lsl tmp1, tmp1, #3 /* Bytes beyond alignment -> bits. */
+ ldr data1, [src1], #8
+ neg tmp1, tmp1 /* Bits to alignment -64. */
+ ldr data2, [src2], #8
+ mov tmp2, #~0
+#ifdef __AARCH64EB__
+ /* Big-endian. Early bytes are at MSB. */
+ lsl tmp2, tmp2, tmp1 /* Shift (tmp1 & 63). */
+#else
+ /* Little-endian. Early bytes are at LSB. */
+ lsr tmp2, tmp2, tmp1 /* Shift (tmp1 & 63). */
+#endif
+ orr data1, data1, tmp2
+ orr data2, data2, tmp2
+ b L(start_realigned)
+
+L(misaligned8):
+ /* Align SRC1 to 8 bytes and then compare 8 bytes at a time, always
+ checking to make sure that we don't access beyond page boundary in
+ SRC2. */
+ tst src1, #7
+ b.eq L(loop_misaligned)
+L(do_misaligned):
+ ldrb data1w, [src1], #1
+ ldrb data2w, [src2], #1
+ cmp data1w, #1
+ ccmp data1w, data2w, #0, cs /* NZCV = 0b0000. */
+ b.ne L(done)
+ tst src1, #7
+ b.ne L(do_misaligned)
+
+L(loop_misaligned):
+ /* Test if we are within the last dword of the end of a 4K page. If
+ yes then jump back to the misaligned loop to copy a byte at a time. */
+ and tmp1, src2, #0xff8
+ eor tmp1, tmp1, #0xff8
+ cbz tmp1, L(do_misaligned)
+ ldr data1, [src1], #8
+ ldr data2, [src2], #8
+
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ eor
diff , data1, data2 /* Non-zero if
diff erences found. */
+ bic has_nul, tmp1, tmp2 /* Non-zero if NUL terminator. */
+ orr syndrome,
diff , has_nul
+ cbz syndrome, L(loop_misaligned)
+ b L(end)
+
+L(done):
+ sub result, data1, data2
+ ret
+
+END (__strcmp_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/strcpy-sve.S b/libc/AOR_v20.02/string/aarch64/strcpy-sve.S
new file mode 100644
index 000000000000..43e7621b6261
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strcpy-sve.S
@@ -0,0 +1,72 @@
+/*
+ * strcpy/stpcpy - copy a string returning pointer to start/end.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_FEATURE_SVE
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * SVE Available.
+ */
+
+ .arch armv8-a+sve
+ .text
+
+/* To build as stpcpy, define BUILD_STPCPY before compiling this file. */
+#ifdef BUILD_STPCPY
+#define FUNC __stpcpy_aarch64_sve
+#else
+#define FUNC __strcpy_aarch64_sve
+#endif
+
+ .globl FUNC
+ .type FUNC, %function
+ .p2align 4
+FUNC:
+ setffr /* initialize FFR */
+ ptrue p2.b, all /* all ones; loop invariant */
+ mov x2, 0 /* initialize offset */
+
+ .p2align 4
+ /* Read a vector's worth of bytes, stopping on first fault. */
+0: ldff1b z0.b, p2/z, [x1, x2]
+ rdffrs p0.b, p2/z
+ b.nlast 1f
+
+ /* First fault did not fail: the whole vector is valid.
+ Avoid depending on the contexts of FFR beyond the branch. */
+ cmpeq p1.b, p2/z, z0.b, 0 /* search for zeros */
+ b.any 2f
+
+ /* No zero found. Store the whole vector and loop. */
+ st1b z0.b, p2, [x0, x2]
+ incb x2, all
+ b 0b
+
+ /* First fault failed: only some of the vector is valid.
+ Perform the comparison only on the valid bytes. */
+1: cmpeq p1.b, p0/z, z0.b, 0 /* search for zeros */
+ b.any 2f
+
+ /* No zero found. Store the valid portion of the vector and loop. */
+ setffr /* re-init FFR */
+ st1b z0.b, p0, [x0, x2]
+ incp x2, p0.b
+ b 0b
+
+ /* Zero found. Crop the vector to the found zero and finish. */
+2: brka p0.b, p2/z, p1.b
+ st1b z0.b, p0, [x0, x2]
+#ifdef BUILD_STPCPY
+ add x0, x0, x2
+ sub x0, x0, 1
+ incp x0, p0.b
+#endif
+ ret
+
+ .size FUNC, . - FUNC
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/strcpy.S b/libc/AOR_v20.02/string/aarch64/strcpy.S
new file mode 100644
index 000000000000..dde9afbb7fb1
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strcpy.S
@@ -0,0 +1,309 @@
+/*
+ * strcpy/stpcpy - copy a string returning pointer to start/end.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64, unaligned accesses, min page size 4k.
+ */
+
+#include "../asmdefs.h"
+
+/* To build as stpcpy, define BUILD_STPCPY before compiling this file.
+
+ To test the page crossing code path more thoroughly, compile with
+ -DSTRCPY_TEST_PAGE_CROSS - this will force all copies through the slower
+ entry path. This option is not intended for production use. */
+
+/* Arguments and results. */
+#define dstin x0
+#define srcin x1
+
+/* Locals and temporaries. */
+#define src x2
+#define dst x3
+#define data1 x4
+#define data1w w4
+#define data2 x5
+#define data2w w5
+#define has_nul1 x6
+#define has_nul2 x7
+#define tmp1 x8
+#define tmp2 x9
+#define tmp3 x10
+#define tmp4 x11
+#define zeroones x12
+#define data1a x13
+#define data2a x14
+#define pos x15
+#define len x16
+#define to_align x17
+
+#ifdef BUILD_STPCPY
+#define STRCPY __stpcpy_aarch64
+#else
+#define STRCPY __strcpy_aarch64
+#endif
+
+ /* NUL detection works on the principle that (X - 1) & (~X) & 0x80
+ (=> (X - 1) & ~(X | 0x7f)) is non-zero iff a byte is zero, and
+ can be done in parallel across the entire word. */
+
+#define REP8_01 0x0101010101010101
+#define REP8_7f 0x7f7f7f7f7f7f7f7f
+#define REP8_80 0x8080808080808080
+
+ /* AArch64 systems have a minimum page size of 4k. We can do a quick
+ page size check for crossing this boundary on entry and if we
+ do not, then we can short-circuit much of the entry code. We
+ expect early page-crossing strings to be rare (probability of
+ 16/MIN_PAGE_SIZE ~= 0.4%), so the branch should be quite
+ predictable, even with random strings.
+
+ We don't bother checking for larger page sizes, the cost of setting
+ up the correct page size is just not worth the extra gain from
+ a small reduction in the cases taking the slow path. Note that
+ we only care about whether the first fetch, which may be
+ misaligned, crosses a page boundary - after that we move to aligned
+ fetches for the remainder of the string. */
+
+#ifdef STRCPY_TEST_PAGE_CROSS
+ /* Make everything that isn't Qword aligned look like a page cross. */
+#define MIN_PAGE_P2 4
+#else
+#define MIN_PAGE_P2 12
+#endif
+
+#define MIN_PAGE_SIZE (1 << MIN_PAGE_P2)
+
+ENTRY (STRCPY)
+ /* For moderately short strings, the fastest way to do the copy is to
+ calculate the length of the string in the same way as strlen, then
+ essentially do a memcpy of the result. This avoids the need for
+ multiple byte copies and further means that by the time we
+ reach the bulk copy loop we know we can always use DWord
+ accesses. We expect __strcpy_aarch64 to rarely be called repeatedly
+ with the same source string, so branch prediction is likely to
+ always be
diff icult - we mitigate against this by preferring
+ conditional select operations over branches whenever this is
+ feasible. */
+ and tmp2, srcin, #(MIN_PAGE_SIZE - 1)
+ mov zeroones, #REP8_01
+ and to_align, srcin, #15
+ cmp tmp2, #(MIN_PAGE_SIZE - 16)
+ neg tmp1, to_align
+ /* The first fetch will straddle a (possible) page boundary iff
+ srcin + 15 causes bit[MIN_PAGE_P2] to change value. A 16-byte
+ aligned string will never fail the page align check, so will
+ always take the fast path. */
+ b.gt L(page_cross)
+
+L(page_cross_ok):
+ ldp data1, data2, [srcin]
+#ifdef __AARCH64EB__
+ /* Because we expect the end to be found within 16 characters
+ (profiling shows this is the most common case), it's worth
+ swapping the bytes now to save having to recalculate the
+ termination syndrome later. We preserve data1 and data2
+ so that we can re-use the values later on. */
+ rev tmp2, data1
+ sub tmp1, tmp2, zeroones
+ orr tmp2, tmp2, #REP8_7f
+ bics has_nul1, tmp1, tmp2
+ b.ne L(fp_le8)
+ rev tmp4, data2
+ sub tmp3, tmp4, zeroones
+ orr tmp4, tmp4, #REP8_7f
+#else
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ bics has_nul1, tmp1, tmp2
+ b.ne L(fp_le8)
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, #REP8_7f
+#endif
+ bics has_nul2, tmp3, tmp4
+ b.eq L(bulk_entry)
+
+ /* The string is short (<=16 bytes). We don't know exactly how
+ short though, yet. Work out the exact length so that we can
+ quickly select the optimal copy strategy. */
+L(fp_gt8):
+ rev has_nul2, has_nul2
+ clz pos, has_nul2
+ mov tmp2, #56
+ add dst, dstin, pos, lsr #3 /* Bits to bytes. */
+ sub pos, tmp2, pos
+#ifdef __AARCH64EB__
+ lsr data2, data2, pos
+#else
+ lsl data2, data2, pos
+#endif
+ str data2, [dst, #1]
+ str data1, [dstin]
+#ifdef BUILD_STPCPY
+ add dstin, dst, #8
+#endif
+ ret
+
+L(fp_le8):
+ rev has_nul1, has_nul1
+ clz pos, has_nul1
+ add dst, dstin, pos, lsr #3 /* Bits to bytes. */
+ subs tmp2, pos, #24 /* Pos in bits. */
+ b.lt L(fp_lt4)
+#ifdef __AARCH64EB__
+ mov tmp2, #56
+ sub pos, tmp2, pos
+ lsr data2, data1, pos
+ lsr data1, data1, #32
+#else
+ lsr data2, data1, tmp2
+#endif
+ /* 4->7 bytes to copy. */
+ str data2w, [dst, #-3]
+ str data1w, [dstin]
+#ifdef BUILD_STPCPY
+ mov dstin, dst
+#endif
+ ret
+L(fp_lt4):
+ cbz pos, L(fp_lt2)
+ /* 2->3 bytes to copy. */
+#ifdef __AARCH64EB__
+ lsr data1, data1, #48
+#endif
+ strh data1w, [dstin]
+ /* Fall-through, one byte (max) to go. */
+L(fp_lt2):
+ /* Null-terminated string. Last character must be zero! */
+ strb wzr, [dst]
+#ifdef BUILD_STPCPY
+ mov dstin, dst
+#endif
+ ret
+
+ .p2align 6
+ /* Aligning here ensures that the entry code and main loop all lies
+ within one 64-byte cache line. */
+L(bulk_entry):
+ sub to_align, to_align, #16
+ stp data1, data2, [dstin]
+ sub src, srcin, to_align
+ sub dst, dstin, to_align
+ b L(entry_no_page_cross)
+
+ /* The inner loop deals with two Dwords at a time. This has a
+ slightly higher start-up cost, but we should win quite quickly,
+ especially on cores with a high number of issue slots per
+ cycle, as we get much better parallelism out of the operations. */
+L(main_loop):
+ stp data1, data2, [dst], #16
+L(entry_no_page_cross):
+ ldp data1, data2, [src], #16
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, #REP8_7f
+ bic has_nul1, tmp1, tmp2
+ bics has_nul2, tmp3, tmp4
+ ccmp has_nul1, #0, #0, eq /* NZCV = 0000 */
+ b.eq L(main_loop)
+
+ /* Since we know we are copying at least 16 bytes, the fastest way
+ to deal with the tail is to determine the location of the
+ trailing NUL, then (re)copy the 16 bytes leading up to that. */
+ cmp has_nul1, #0
+#ifdef __AARCH64EB__
+ /* For big-endian, carry propagation (if the final byte in the
+ string is 0x01) means we cannot use has_nul directly. The
+ easiest way to get the correct byte is to byte-swap the data
+ and calculate the syndrome a second time. */
+ csel data1, data1, data2, ne
+ rev data1, data1
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ bic has_nul1, tmp1, tmp2
+#else
+ csel has_nul1, has_nul1, has_nul2, ne
+#endif
+ rev has_nul1, has_nul1
+ clz pos, has_nul1
+ add tmp1, pos, #72
+ add pos, pos, #8
+ csel pos, pos, tmp1, ne
+ add src, src, pos, lsr #3
+ add dst, dst, pos, lsr #3
+ ldp data1, data2, [src, #-32]
+ stp data1, data2, [dst, #-16]
+#ifdef BUILD_STPCPY
+ sub dstin, dst, #1
+#endif
+ ret
+
+L(page_cross):
+ bic src, srcin, #15
+ /* Start by loading two words at [srcin & ~15], then forcing the
+ bytes that precede srcin to 0xff. This means they never look
+ like termination bytes. */
+ ldp data1, data2, [src]
+ lsl tmp1, tmp1, #3 /* Bytes beyond alignment -> bits. */
+ tst to_align, #7
+ csetm tmp2, ne
+#ifdef __AARCH64EB__
+ lsl tmp2, tmp2, tmp1 /* Shift (tmp1 & 63). */
+#else
+ lsr tmp2, tmp2, tmp1 /* Shift (tmp1 & 63). */
+#endif
+ orr data1, data1, tmp2
+ orr data2a, data2, tmp2
+ cmp to_align, #8
+ csinv data1, data1, xzr, lt
+ csel data2, data2, data2a, lt
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, #REP8_7f
+ bic has_nul1, tmp1, tmp2
+ bics has_nul2, tmp3, tmp4
+ ccmp has_nul1, #0, #0, eq /* NZCV = 0000 */
+ b.eq L(page_cross_ok)
+ /* We now need to make data1 and data2 look like they've been
+ loaded directly from srcin. Do a rotate on the 128-bit value. */
+ lsl tmp1, to_align, #3 /* Bytes->bits. */
+ neg tmp2, to_align, lsl #3
+#ifdef __AARCH64EB__
+ lsl data1a, data1, tmp1
+ lsr tmp4, data2, tmp2
+ lsl data2, data2, tmp1
+ orr tmp4, tmp4, data1a
+ cmp to_align, #8
+ csel data1, tmp4, data2, lt
+ rev tmp2, data1
+ rev tmp4, data2
+ sub tmp1, tmp2, zeroones
+ orr tmp2, tmp2, #REP8_7f
+ sub tmp3, tmp4, zeroones
+ orr tmp4, tmp4, #REP8_7f
+#else
+ lsr data1a, data1, tmp1
+ lsl tmp4, data2, tmp2
+ lsr data2, data2, tmp1
+ orr tmp4, tmp4, data1a
+ cmp to_align, #8
+ csel data1, tmp4, data2, lt
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, #REP8_7f
+#endif
+ bic has_nul1, tmp1, tmp2
+ cbnz has_nul1, L(fp_le8)
+ bic has_nul2, tmp3, tmp4
+ b L(fp_gt8)
+
+END (STRCPY)
diff --git a/libc/AOR_v20.02/string/aarch64/strlen-mte.S b/libc/AOR_v20.02/string/aarch64/strlen-mte.S
new file mode 100644
index 000000000000..8037abff865c
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strlen-mte.S
@@ -0,0 +1,186 @@
+/*
+ * strlen - calculate the length of a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64.
+ */
+
+#include "../asmdefs.h"
+
+/* Arguments and results. */
+#define srcin x0
+#define len x0
+
+/* Locals and temporaries. */
+#define src x1
+#define data1 x2
+#define data2 x3
+#define has_nul1 x4
+#define has_nul2 x5
+#define tmp1 x4
+#define tmp2 x5
+#define tmp3 x6
+#define tmp4 x7
+#define zeroones x8
+#define offset x9
+
+ /* NUL detection works on the principle that (X - 1) & (~X) & 0x80
+ (=> (X - 1) & ~(X | 0x7f)) is non-zero iff a byte is zero, and
+ can be done in parallel across the entire word. A faster check
+ (X - 1) & 0x80 is zero for non-NUL ASCII characters, but gives
+ false hits for characters 129..255. */
+
+#define REP8_01 0x0101010101010101
+#define REP8_7f 0x7f7f7f7f7f7f7f7f
+
+ /* This implementation is compatible with Memory Tagging. All loads
+ are 16 bytes in size and 16 bytes aligned. This also avoids the
+ need for page boundary checks. This implementation is correct
+ even without Memory Tagging, but other implementations could be
+ more beneficial if Memory Tagging is not enabled.
+
+ First load is aligned down and can contain bytes that are located
+ before the string. This is handled by modifying the "zeroones"
+ mask. The bytes that need to be ignored are set to zero.
+ If the string is aligned in such a way that 8 or more bytes from
+ the first load should be ignored, there is a special case
+ (skip_first_8_bytes) which only compares the second 8 bytes.
+
+ If there is a NUL byte in the first load, we calculate the length
+ from the 2 8-byte words using conditional select to reduce branch
+ mispredictions.
+
+ If the string is longer than 16 bytes, we check 32 bytes per
+ iteration using the fast NUL check (main_loop). If we encounter
+ non-ASCII characters, we fallback to a second loop
+ (nonascii_loop) using the full NUL check. */
+
+ENTRY(__strlen_aarch64_mte)
+ bic src, srcin, 15 /* Align down to 16 bytes. */
+ mov zeroones, REP8_01
+ /* (offset & 63) holds number of bits to ignore in a register.*/
+ lsl offset, srcin, 3
+ ldp data1, data2, [src], -16
+ lsl tmp1, zeroones, offset /* Shift (offset & 63). */
+#ifdef __AARCH64EB__
+ /* For big-endian, carry propagation (if the final byte in the
+ string is 0x01) means we cannot use has_nul1/2 directly.
+ e.g. 0x0100 - 0x0101 = 0xffff, so 0x01 will be mistaken for NUL.
+ Since we expect strings to be small and early-exit,
+ byte-swap the data now so has_null1/2 will be correct. */
+ rev data1, data1
+ rev data2, data2
+#endif
+ tbnz srcin, 3, L(skip_first_8_bytes)
+ sub tmp1, data1, tmp1
+ orr tmp2, data1, REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, REP8_7f
+ bics has_nul1, tmp1, tmp2
+ bic has_nul2, tmp3, tmp4
+ /* If comparison happens, C flag is always set. */
+ ccmp has_nul2, 0, 0, eq
+ beq L(main_loop)
+
+ /* Enter with C = has_nul1 == 0. */
+ csel has_nul1, has_nul1, has_nul2, cc
+ and tmp2, srcin, 7 /* Bytes to ignore. */
+ rev has_nul1, has_nul1
+ neg tmp2, tmp2
+ clz tmp1, has_nul1 /* Count bits before NUL. */
+ /* Add 8 if NUL byte is not in first register. */
+ add tmp3, tmp2, 8
+ csel len, tmp2, tmp3, cc
+ add len, len, tmp1, lsr 3
+ ret
+
+L(skip_first_8_bytes):
+ sub tmp1, data2, tmp1
+ orr tmp2, data2, REP8_7f
+ bics has_nul1, tmp1, tmp2
+ beq L(main_loop)
+
+ rev has_nul1, has_nul1
+ lsl tmp1, has_nul1, offset /* Ignore bytes before string. */
+ clz tmp1, tmp1 /* Count bits before NUL. */
+ lsr len, tmp1, 3
+ ret
+
+ /* The inner loop processes 32 bytes per iteration and uses the fast
+ NUL check. If we encounter non-ASCII characters, use a second
+ loop with the accurate NUL check. */
+ .p2align 4
+L(main_loop):
+ ldp data1, data2, [src, 32]!
+ sub tmp1, data1, zeroones
+ sub tmp3, data2, zeroones
+ orr tmp2, tmp1, tmp3
+ tst tmp2, zeroones, lsl 7
+ bne 1f
+ ldp data1, data2, [src, 16]
+ sub tmp1, data1, zeroones
+ sub tmp3, data2, zeroones
+ orr tmp2, tmp1, tmp3
+ tst tmp2, zeroones, lsl 7
+ beq L(main_loop)
+ add src, src, 16
+1:
+ /* The fast check failed, so do the slower, accurate NUL check. */
+ orr tmp2, data1, REP8_7f
+ orr tmp4, data2, REP8_7f
+ bics has_nul1, tmp1, tmp2
+ bic has_nul2, tmp3, tmp4
+ ccmp has_nul2, 0, 0, eq
+ beq L(nonascii_loop)
+
+ /* Enter with C = has_nul1 == 0. */
+L(tail):
+#ifdef __AARCH64EB__
+ /* For big-endian, carry propagation (if the final byte in the
+ string is 0x01) means we cannot use has_nul1/2 directly. The
+ easiest way to get the correct byte is to byte-swap the data
+ and calculate the syndrome a second time. */
+ csel data1, data1, data2, cc
+ rev data1, data1
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, REP8_7f
+ bic has_nul1, tmp1, tmp2
+#else
+ csel has_nul1, has_nul1, has_nul2, cc
+#endif
+ sub len, src, srcin
+ rev has_nul1, has_nul1
+ add tmp2, len, 8
+ clz tmp1, has_nul1
+ csel len, len, tmp2, cc
+ add len, len, tmp1, lsr 3
+ ret
+
+L(nonascii_loop):
+ ldp data1, data2, [src, 16]!
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, REP8_7f
+ bics has_nul1, tmp1, tmp2
+ bic has_nul2, tmp3, tmp4
+ ccmp has_nul2, 0, 0, eq
+ bne L(tail)
+ ldp data1, data2, [src, 16]!
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, REP8_7f
+ bics has_nul1, tmp1, tmp2
+ bic has_nul2, tmp3, tmp4
+ ccmp has_nul2, 0, 0, eq
+ beq L(nonascii_loop)
+ b L(tail)
+
+END(__strlen_aarch64_mte)
diff --git a/libc/AOR_v20.02/string/aarch64/strlen-sve.S b/libc/AOR_v20.02/string/aarch64/strlen-sve.S
new file mode 100644
index 000000000000..88bf0ee91bcd
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strlen-sve.S
@@ -0,0 +1,58 @@
+/*
+ * __strlen_aarch64_sve - compute the length of a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_FEATURE_SVE
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * SVE Available.
+ */
+
+ .arch armv8-a+sve
+ .text
+
+ .globl __strlen_aarch64_sve
+ .type __strlen_aarch64_sve, %function
+ .p2align 4
+__strlen_aarch64_sve:
+ setffr /* initialize FFR */
+ ptrue p2.b /* all ones; loop invariant */
+ mov x1, 0 /* initialize length */
+ nop
+
+ /* Read a vector's worth of bytes, stopping on first fault. */
+0: ldff1b z0.b, p2/z, [x0, x1]
+ nop
+ rdffrs p0.b, p2/z
+ b.nlast 2f
+
+ /* First fault did not fail: the whole vector is valid.
+ Avoid depending on the contents of FFR beyond the branch. */
+ incb x1, all /* speculate increment */
+ cmpeq p1.b, p2/z, z0.b, 0 /* loop if no zeros */
+ b.none 0b
+ decb x1, all /* undo speculate */
+
+ /* Zero found. Select the bytes before the first and count them. */
+1: brkb p0.b, p2/z, p1.b
+ incp x1, p0.b
+ mov x0, x1
+ ret
+
+ /* First fault failed: only some of the vector is valid.
+ Perform the comparison only on the valid bytes. */
+2: cmpeq p1.b, p0/z, z0.b, 0
+ b.any 1b
+
+ /* No zero found. Re-init FFR, increment, and loop. */
+ setffr
+ incp x1, p0.b
+ b 0b
+
+ .size __strlen_aarch64_sve, . - __strlen_aarch64_sve
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/strlen.S b/libc/AOR_v20.02/string/aarch64/strlen.S
new file mode 100644
index 000000000000..2d560db2cfba
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strlen.S
@@ -0,0 +1,207 @@
+/*
+ * strlen - calculate the length of a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64, unaligned accesses, min page size 4k.
+ */
+
+#include "../asmdefs.h"
+
+/* To test the page crossing code path more thoroughly, compile with
+ -DTEST_PAGE_CROSS - this will force all calls through the slower
+ entry path. This option is not intended for production use. */
+
+/* Arguments and results. */
+#define srcin x0
+#define len x0
+
+/* Locals and temporaries. */
+#define src x1
+#define data1 x2
+#define data2 x3
+#define has_nul1 x4
+#define has_nul2 x5
+#define tmp1 x4
+#define tmp2 x5
+#define tmp3 x6
+#define tmp4 x7
+#define zeroones x8
+
+ /* NUL detection works on the principle that (X - 1) & (~X) & 0x80
+ (=> (X - 1) & ~(X | 0x7f)) is non-zero iff a byte is zero, and
+ can be done in parallel across the entire word. A faster check
+ (X - 1) & 0x80 is zero for non-NUL ASCII characters, but gives
+ false hits for characters 129..255. */
+
+#define REP8_01 0x0101010101010101
+#define REP8_7f 0x7f7f7f7f7f7f7f7f
+#define REP8_80 0x8080808080808080
+
+#ifdef TEST_PAGE_CROSS
+# define MIN_PAGE_SIZE 15
+#else
+# define MIN_PAGE_SIZE 4096
+#endif
+
+ /* Since strings are short on average, we check the first 16 bytes
+ of the string for a NUL character. In order to do an unaligned ldp
+ safely we have to do a page cross check first. If there is a NUL
+ byte we calculate the length from the 2 8-byte words using
+ conditional select to reduce branch mispredictions (it is unlikely
+ __strlen_aarch64 will be repeatedly called on strings with the same length).
+
+ If the string is longer than 16 bytes, we align src so don't need
+ further page cross checks, and process 32 bytes per iteration
+ using the fast NUL check. If we encounter non-ASCII characters,
+ fallback to a second loop using the full NUL check.
+
+ If the page cross check fails, we read 16 bytes from an aligned
+ address, remove any characters before the string, and continue
+ in the main loop using aligned loads. Since strings crossing a
+ page in the first 16 bytes are rare (probability of
+ 16/MIN_PAGE_SIZE ~= 0.4%), this case does not need to be optimized.
+
+ AArch64 systems have a minimum page size of 4k. We don't bother
+ checking for larger page sizes - the cost of setting up the correct
+ page size is just not worth the extra gain from a small reduction in
+ the cases taking the slow path. Note that we only care about
+ whether the first fetch, which may be misaligned, crosses a page
+ boundary. */
+
+ENTRY (__strlen_aarch64)
+ and tmp1, srcin, MIN_PAGE_SIZE - 1
+ mov zeroones, REP8_01
+ cmp tmp1, MIN_PAGE_SIZE - 16
+ b.gt L(page_cross)
+ ldp data1, data2, [srcin]
+#ifdef __AARCH64EB__
+ /* For big-endian, carry propagation (if the final byte in the
+ string is 0x01) means we cannot use has_nul1/2 directly.
+ Since we expect strings to be small and early-exit,
+ byte-swap the data now so has_null1/2 will be correct. */
+ rev data1, data1
+ rev data2, data2
+#endif
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, REP8_7f
+ bics has_nul1, tmp1, tmp2
+ bic has_nul2, tmp3, tmp4
+ ccmp has_nul2, 0, 0, eq
+ beq L(main_loop_entry)
+
+ /* Enter with C = has_nul1 == 0. */
+ csel has_nul1, has_nul1, has_nul2, cc
+ mov len, 8
+ rev has_nul1, has_nul1
+ clz tmp1, has_nul1
+ csel len, xzr, len, cc
+ add len, len, tmp1, lsr 3
+ ret
+
+ /* The inner loop processes 32 bytes per iteration and uses the fast
+ NUL check. If we encounter non-ASCII characters, use a second
+ loop with the accurate NUL check. */
+ .p2align 4
+L(main_loop_entry):
+ bic src, srcin, 15
+ sub src, src, 16
+L(main_loop):
+ ldp data1, data2, [src, 32]!
+L(page_cross_entry):
+ sub tmp1, data1, zeroones
+ sub tmp3, data2, zeroones
+ orr tmp2, tmp1, tmp3
+ tst tmp2, zeroones, lsl 7
+ bne 1f
+ ldp data1, data2, [src, 16]
+ sub tmp1, data1, zeroones
+ sub tmp3, data2, zeroones
+ orr tmp2, tmp1, tmp3
+ tst tmp2, zeroones, lsl 7
+ beq L(main_loop)
+ add src, src, 16
+1:
+ /* The fast check failed, so do the slower, accurate NUL check. */
+ orr tmp2, data1, REP8_7f
+ orr tmp4, data2, REP8_7f
+ bics has_nul1, tmp1, tmp2
+ bic has_nul2, tmp3, tmp4
+ ccmp has_nul2, 0, 0, eq
+ beq L(nonascii_loop)
+
+ /* Enter with C = has_nul1 == 0. */
+L(tail):
+#ifdef __AARCH64EB__
+ /* For big-endian, carry propagation (if the final byte in the
+ string is 0x01) means we cannot use has_nul1/2 directly. The
+ easiest way to get the correct byte is to byte-swap the data
+ and calculate the syndrome a second time. */
+ csel data1, data1, data2, cc
+ rev data1, data1
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, REP8_7f
+ bic has_nul1, tmp1, tmp2
+#else
+ csel has_nul1, has_nul1, has_nul2, cc
+#endif
+ sub len, src, srcin
+ rev has_nul1, has_nul1
+ add tmp2, len, 8
+ clz tmp1, has_nul1
+ csel len, len, tmp2, cc
+ add len, len, tmp1, lsr 3
+ ret
+
+L(nonascii_loop):
+ ldp data1, data2, [src, 16]!
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, REP8_7f
+ bics has_nul1, tmp1, tmp2
+ bic has_nul2, tmp3, tmp4
+ ccmp has_nul2, 0, 0, eq
+ bne L(tail)
+ ldp data1, data2, [src, 16]!
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, REP8_7f
+ bics has_nul1, tmp1, tmp2
+ bic has_nul2, tmp3, tmp4
+ ccmp has_nul2, 0, 0, eq
+ beq L(nonascii_loop)
+ b L(tail)
+
+ /* Load 16 bytes from [srcin & ~15] and force the bytes that precede
+ srcin to 0x7f, so we ignore any NUL bytes before the string.
+ Then continue in the aligned loop. */
+L(page_cross):
+ bic src, srcin, 15
+ ldp data1, data2, [src]
+ lsl tmp1, srcin, 3
+ mov tmp4, -1
+#ifdef __AARCH64EB__
+ /* Big-endian. Early bytes are at MSB. */
+ lsr tmp1, tmp4, tmp1 /* Shift (tmp1 & 63). */
+#else
+ /* Little-endian. Early bytes are at LSB. */
+ lsl tmp1, tmp4, tmp1 /* Shift (tmp1 & 63). */
+#endif
+ orr tmp1, tmp1, REP8_80
+ orn data1, data1, tmp1
+ orn tmp2, data2, tmp1
+ tst srcin, 8
+ csel data1, data1, tmp4, eq
+ csel data2, data2, tmp2, eq
+ b L(page_cross_entry)
+
+END (__strlen_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/strncmp-sve.S b/libc/AOR_v20.02/string/aarch64/strncmp-sve.S
new file mode 100644
index 000000000000..f5d4f95fdf0f
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strncmp-sve.S
@@ -0,0 +1,69 @@
+/*
+ * strncmp - compare two strings with limit
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_FEATURE_SVE
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * SVE Available.
+ */
+
+ .arch armv8-a+sve
+ .text
+
+ .globl __strncmp_aarch64_sve
+ .type __strncmp_aarch64_sve, %function
+ .p2align 4
+__strncmp_aarch64_sve:
+ setffr /* initialize FFR */
+ mov x3, 0 /* initialize off */
+
+0: whilelo p0.b, x3, x2 /* while off < max */
+ b.none 9f
+
+ ldff1b z0.b, p0/z, [x0, x3]
+ ldff1b z1.b, p0/z, [x1, x3]
+ rdffrs p1.b, p0/z
+ b.nlast 2f
+
+ /* First fault did not fail: the vector up to max is valid.
+ Avoid depending on the contents of FFR beyond the branch.
+ Increment for a whole vector, even if we've only read a partial.
+ This is significantly cheaper than INCP, and since OFF is not
+ used after the loop it is ok to increment OFF past MAX. */
+ incb x3
+ cmpeq p1.b, p0/z, z0.b, z1.b /* compare strings */
+ cmpne p2.b, p0/z, z0.b, 0 /* search for ~zero */
+ nands p2.b, p0/z, p1.b, p2.b /* ~(eq & ~zero) -> ne | zero */
+ b.none 0b
+
+ /* Found end-of-string or inequality. */
+1: brkb p2.b, p0/z, p2.b /* find first such */
+ lasta w0, p2, z0.b /* extract each char */
+ lasta w1, p2, z1.b
+ sub x0, x0, x1 /* return comparison */
+ ret
+
+ /* First fault failed: only some of the vector is valid.
+ Perform the comparison only on the valid bytes. */
+2: cmpeq p2.b, p1/z, z0.b, z1.b /* compare strings, as above */
+ cmpne p3.b, p1/z, z0.b, 0
+ nands p2.b, p1/z, p2.b, p3.b
+ b.any 1b
+
+ /* No inequality or zero found. Re-init FFR, incr and loop. */
+ setffr
+ incp x3, p1.b
+ b 0b
+
+ /* Found end-of-count. */
+9: mov x0, 0 /* return equal */
+ ret
+
+ .size __strncmp_aarch64_sve, . - __strncmp_aarch64_sve
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/strncmp.S b/libc/AOR_v20.02/string/aarch64/strncmp.S
new file mode 100644
index 000000000000..d5a2752324e3
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strncmp.S
@@ -0,0 +1,262 @@
+/*
+ * strncmp - compare two strings
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ */
+
+#include "../asmdefs.h"
+
+#define REP8_01 0x0101010101010101
+#define REP8_7f 0x7f7f7f7f7f7f7f7f
+#define REP8_80 0x8080808080808080
+
+/* Parameters and result. */
+#define src1 x0
+#define src2 x1
+#define limit x2
+#define result x0
+
+/* Internal variables. */
+#define data1 x3
+#define data1w w3
+#define data2 x4
+#define data2w w4
+#define has_nul x5
+#define
diff x6
+#define syndrome x7
+#define tmp1 x8
+#define tmp2 x9
+#define tmp3 x10
+#define zeroones x11
+#define pos x12
+#define limit_wd x13
+#define mask x14
+#define endloop x15
+#define count mask
+
+ .text
+ .p2align 6
+ .rep 7
+ nop /* Pad so that the loop below fits a cache line. */
+ .endr
+ENTRY_ALIGN (__strncmp_aarch64, 0)
+ cbz limit, L(ret0)
+ eor tmp1, src1, src2
+ mov zeroones, #REP8_01
+ tst tmp1, #7
+ and count, src1, #7
+ b.ne L(misaligned8)
+ cbnz count, L(mutual_align)
+ /* Calculate the number of full and partial words -1. */
+ sub limit_wd, limit, #1 /* limit != 0, so no underflow. */
+ lsr limit_wd, limit_wd, #3 /* Convert to Dwords. */
+
+ /* NUL detection works on the principle that (X - 1) & (~X) & 0x80
+ (=> (X - 1) & ~(X | 0x7f)) is non-zero iff a byte is zero, and
+ can be done in parallel across the entire word. */
+ /* Start of performance-critical section -- one 64B cache line. */
+L(loop_aligned):
+ ldr data1, [src1], #8
+ ldr data2, [src2], #8
+L(start_realigned):
+ subs limit_wd, limit_wd, #1
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ eor
diff , data1, data2 /* Non-zero if
diff erences found. */
+ csinv endloop,
diff , xzr, pl /* Last Dword or
diff erences. */
+ bics has_nul, tmp1, tmp2 /* Non-zero if NUL terminator. */
+ ccmp endloop, #0, #0, eq
+ b.eq L(loop_aligned)
+ /* End of performance-critical section -- one 64B cache line. */
+
+ /* Not reached the limit, must have found the end or a
diff . */
+ tbz limit_wd, #63, L(not_limit)
+
+ /* Limit % 8 == 0 => all bytes significant. */
+ ands limit, limit, #7
+ b.eq L(not_limit)
+
+ lsl limit, limit, #3 /* Bits -> bytes. */
+ mov mask, #~0
+#ifdef __AARCH64EB__
+ lsr mask, mask, limit
+#else
+ lsl mask, mask, limit
+#endif
+ bic data1, data1, mask
+ bic data2, data2, mask
+
+ /* Make sure that the NUL byte is marked in the syndrome. */
+ orr has_nul, has_nul, mask
+
+L(not_limit):
+ orr syndrome,
diff , has_nul
+
+#ifndef __AARCH64EB__
+ rev syndrome, syndrome
+ rev data1, data1
+ /* The MS-non-zero bit of the syndrome marks either the first bit
+ that is
diff erent, or the top bit of the first zero byte.
+ Shifting left now will bring the critical information into the
+ top bits. */
+ clz pos, syndrome
+ rev data2, data2
+ lsl data1, data1, pos
+ lsl data2, data2, pos
+ /* But we need to zero-extend (char is unsigned) the value and then
+ perform a signed 32-bit subtraction. */
+ lsr data1, data1, #56
+ sub result, data1, data2, lsr #56
+ ret
+#else
+ /* For big-endian we cannot use the trick with the syndrome value
+ as carry-propagation can corrupt the upper bits if the trailing
+ bytes in the string contain 0x01. */
+ /* However, if there is no NUL byte in the dword, we can generate
+ the result directly. We can't just subtract the bytes as the
+ MSB might be significant. */
+ cbnz has_nul, 1f
+ cmp data1, data2
+ cset result, ne
+ cneg result, result, lo
+ ret
+1:
+ /* Re-compute the NUL-byte detection, using a byte-reversed value. */
+ rev tmp3, data1
+ sub tmp1, tmp3, zeroones
+ orr tmp2, tmp3, #REP8_7f
+ bic has_nul, tmp1, tmp2
+ rev has_nul, has_nul
+ orr syndrome,
diff , has_nul
+ clz pos, syndrome
+ /* The MS-non-zero bit of the syndrome marks either the first bit
+ that is
diff erent, or the top bit of the first zero byte.
+ Shifting left now will bring the critical information into the
+ top bits. */
+ lsl data1, data1, pos
+ lsl data2, data2, pos
+ /* But we need to zero-extend (char is unsigned) the value and then
+ perform a signed 32-bit subtraction. */
+ lsr data1, data1, #56
+ sub result, data1, data2, lsr #56
+ ret
+#endif
+
+L(mutual_align):
+ /* Sources are mutually aligned, but are not currently at an
+ alignment boundary. Round down the addresses and then mask off
+ the bytes that precede the start point.
+ We also need to adjust the limit calculations, but without
+ overflowing if the limit is near ULONG_MAX. */
+ bic src1, src1, #7
+ bic src2, src2, #7
+ ldr data1, [src1], #8
+ neg tmp3, count, lsl #3 /* 64 - bits(bytes beyond align). */
+ ldr data2, [src2], #8
+ mov tmp2, #~0
+ sub limit_wd, limit, #1 /* limit != 0, so no underflow. */
+#ifdef __AARCH64EB__
+ /* Big-endian. Early bytes are at MSB. */
+ lsl tmp2, tmp2, tmp3 /* Shift (count & 63). */
+#else
+ /* Little-endian. Early bytes are at LSB. */
+ lsr tmp2, tmp2, tmp3 /* Shift (count & 63). */
+#endif
+ and tmp3, limit_wd, #7
+ lsr limit_wd, limit_wd, #3
+ /* Adjust the limit. Only low 3 bits used, so overflow irrelevant. */
+ add limit, limit, count
+ add tmp3, tmp3, count
+ orr data1, data1, tmp2
+ orr data2, data2, tmp2
+ add limit_wd, limit_wd, tmp3, lsr #3
+ b L(start_realigned)
+
+ .p2align 6
+ /* Don't bother with dwords for up to 16 bytes. */
+L(misaligned8):
+ cmp limit, #16
+ b.hs L(try_misaligned_words)
+
+L(byte_loop):
+ /* Perhaps we can do better than this. */
+ ldrb data1w, [src1], #1
+ ldrb data2w, [src2], #1
+ subs limit, limit, #1
+ ccmp data1w, #1, #0, hi /* NZCV = 0b0000. */
+ ccmp data1w, data2w, #0, cs /* NZCV = 0b0000. */
+ b.eq L(byte_loop)
+L(done):
+ sub result, data1, data2
+ ret
+ /* Align the SRC1 to a dword by doing a bytewise compare and then do
+ the dword loop. */
+L(try_misaligned_words):
+ lsr limit_wd, limit, #3
+ cbz count, L(do_misaligned)
+
+ neg count, count
+ and count, count, #7
+ sub limit, limit, count
+ lsr limit_wd, limit, #3
+
+L(page_end_loop):
+ ldrb data1w, [src1], #1
+ ldrb data2w, [src2], #1
+ cmp data1w, #1
+ ccmp data1w, data2w, #0, cs /* NZCV = 0b0000. */
+ b.ne L(done)
+ subs count, count, #1
+ b.hi L(page_end_loop)
+
+L(do_misaligned):
+ /* Prepare ourselves for the next page crossing. Unlike the aligned
+ loop, we fetch 1 less dword because we risk crossing bounds on
+ SRC2. */
+ mov count, #8
+ subs limit_wd, limit_wd, #1
+ b.lo L(done_loop)
+L(loop_misaligned):
+ and tmp2, src2, #0xff8
+ eor tmp2, tmp2, #0xff8
+ cbz tmp2, L(page_end_loop)
+
+ ldr data1, [src1], #8
+ ldr data2, [src2], #8
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ eor
diff , data1, data2 /* Non-zero if
diff erences found. */
+ bics has_nul, tmp1, tmp2 /* Non-zero if NUL terminator. */
+ ccmp
diff , #0, #0, eq
+ b.ne L(not_limit)
+ subs limit_wd, limit_wd, #1
+ b.pl L(loop_misaligned)
+
+L(done_loop):
+ /* We found a
diff erence or a NULL before the limit was reached. */
+ and limit, limit, #7
+ cbz limit, L(not_limit)
+ /* Read the last word. */
+ sub src1, src1, 8
+ sub src2, src2, 8
+ ldr data1, [src1, limit]
+ ldr data2, [src2, limit]
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ eor
diff , data1, data2 /* Non-zero if
diff erences found. */
+ bics has_nul, tmp1, tmp2 /* Non-zero if NUL terminator. */
+ ccmp
diff , #0, #0, eq
+ b.ne L(not_limit)
+
+L(ret0):
+ mov result, #0
+ ret
+
+END ( __strncmp_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/strnlen-sve.S b/libc/AOR_v20.02/string/aarch64/strnlen-sve.S
new file mode 100644
index 000000000000..5d3957348a0c
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strnlen-sve.S
@@ -0,0 +1,75 @@
+/*
+ * strnlen - calculate the length of a string with limit.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_FEATURE_SVE
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * SVE Available.
+ */
+
+ .arch armv8-a+sve
+ .text
+
+ .globl __strnlen_aarch64_sve
+ .type __strnlen_aarch64_sve, %function
+ .p2align 4
+__strnlen_aarch64_sve:
+ setffr /* initialize FFR */
+ mov x2, 0 /* initialize len */
+ b 1f
+
+ .p2align 4
+ /* We have off + vl <= max, and so may read the whole vector. */
+0: ldff1b z0.b, p0/z, [x0, x2]
+ rdffrs p1.b, p0/z
+ b.nlast 2f
+
+ /* First fault did not fail: the whole vector is valid.
+ Avoid depending on the contents of FFR beyond the branch. */
+ cmpeq p2.b, p0/z, z0.b, 0
+ b.any 8f
+ incb x2
+
+1: whilelo p0.b, x2, x1
+ b.last 0b
+
+ /* We have off + vl < max. Test for off == max before proceeding. */
+ b.none 9f
+
+ ldff1b z0.b, p0/z, [x0, x2]
+ rdffrs p1.b, p0/z
+ b.nlast 2f
+
+ /* First fault did not fail: the vector up to max is valid.
+ Avoid depending on the contents of FFR beyond the branch.
+ Compare for end-of-string, but there are no more bytes. */
+ cmpeq p2.b, p0/z, z0.b, 0
+
+ /* Found end-of-string or zero. */
+8: brkb p2.b, p0/z, p2.b
+ mov x0, x2
+ incp x0, p2.b
+ ret
+
+ /* First fault failed: only some of the vector is valid.
+ Perform the comparison only on the valid bytes. */
+2: cmpeq p2.b, p1/z, z0.b, 0
+ b.any 8b
+
+ /* No inequality or zero found. Re-init FFR, incr and loop. */
+ setffr
+ incp x2, p1.b
+ b 1b
+
+ /* End of count. Return max. */
+9: mov x0, x2
+ ret
+
+ .size __strnlen_aarch64_sve, . - __strnlen_aarch64_sve
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/strnlen.S b/libc/AOR_v20.02/string/aarch64/strnlen.S
new file mode 100644
index 000000000000..72b74563a5a7
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strnlen.S
@@ -0,0 +1,156 @@
+/*
+ * strnlen - calculate the length of a string with limit.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ */
+
+#include "../asmdefs.h"
+
+/* Arguments and results. */
+#define srcin x0
+#define len x0
+#define limit x1
+
+/* Locals and temporaries. */
+#define src x2
+#define data1 x3
+#define data2 x4
+#define data2a x5
+#define has_nul1 x6
+#define has_nul2 x7
+#define tmp1 x8
+#define tmp2 x9
+#define tmp3 x10
+#define tmp4 x11
+#define zeroones x12
+#define pos x13
+#define limit_wd x14
+
+#define REP8_01 0x0101010101010101
+#define REP8_7f 0x7f7f7f7f7f7f7f7f
+#define REP8_80 0x8080808080808080
+
+ .text
+ .p2align 6
+L(start):
+ /* Pre-pad to ensure critical loop begins an icache line. */
+ .rep 7
+ nop
+ .endr
+ /* Put this code here to avoid wasting more space with pre-padding. */
+L(hit_limit):
+ mov len, limit
+ ret
+
+ENTRY_ALIGN (__strnlen_aarch64, 0)
+ cbz limit, L(hit_limit)
+ mov zeroones, #REP8_01
+ bic src, srcin, #15
+ ands tmp1, srcin, #15
+ b.ne L(misaligned)
+ /* Calculate the number of full and partial words -1. */
+ sub limit_wd, limit, #1 /* Limit != 0, so no underflow. */
+ lsr limit_wd, limit_wd, #4 /* Convert to Qwords. */
+
+ /* NUL detection works on the principle that (X - 1) & (~X) & 0x80
+ (=> (X - 1) & ~(X | 0x7f)) is non-zero iff a byte is zero, and
+ can be done in parallel across the entire word. */
+ /* The inner loop deals with two Dwords at a time. This has a
+ slightly higher start-up cost, but we should win quite quickly,
+ especially on cores with a high number of issue slots per
+ cycle, as we get much better parallelism out of the operations. */
+
+ /* Start of critial section -- keep to one 64Byte cache line. */
+L(loop):
+ ldp data1, data2, [src], #16
+L(realigned):
+ sub tmp1, data1, zeroones
+ orr tmp2, data1, #REP8_7f
+ sub tmp3, data2, zeroones
+ orr tmp4, data2, #REP8_7f
+ bic has_nul1, tmp1, tmp2
+ bic has_nul2, tmp3, tmp4
+ subs limit_wd, limit_wd, #1
+ orr tmp1, has_nul1, has_nul2
+ ccmp tmp1, #0, #0, pl /* NZCV = 0000 */
+ b.eq L(loop)
+ /* End of critical section -- keep to one 64Byte cache line. */
+
+ orr tmp1, has_nul1, has_nul2
+ cbz tmp1, L(hit_limit) /* No null in final Qword. */
+
+ /* We know there's a null in the final Qword. The easiest thing
+ to do now is work out the length of the string and return
+ MIN (len, limit). */
+
+ sub len, src, srcin
+ cbz has_nul1, L(nul_in_data2)
+#ifdef __AARCH64EB__
+ mov data2, data1
+#endif
+ sub len, len, #8
+ mov has_nul2, has_nul1
+L(nul_in_data2):
+#ifdef __AARCH64EB__
+ /* For big-endian, carry propagation (if the final byte in the
+ string is 0x01) means we cannot use has_nul directly. The
+ easiest way to get the correct byte is to byte-swap the data
+ and calculate the syndrome a second time. */
+ rev data2, data2
+ sub tmp1, data2, zeroones
+ orr tmp2, data2, #REP8_7f
+ bic has_nul2, tmp1, tmp2
+#endif
+ sub len, len, #8
+ rev has_nul2, has_nul2
+ clz pos, has_nul2
+ add len, len, pos, lsr #3 /* Bits to bytes. */
+ cmp len, limit
+ csel len, len, limit, ls /* Return the lower value. */
+ ret
+
+L(misaligned):
+ /* Deal with a partial first word.
+ We're doing two things in parallel here;
+ 1) Calculate the number of words (but avoiding overflow if
+ limit is near ULONG_MAX) - to do this we need to work out
+ limit + tmp1 - 1 as a 65-bit value before shifting it;
+ 2) Load and mask the initial data words - we force the bytes
+ before the ones we are interested in to 0xff - this ensures
+ early bytes will not hit any zero detection. */
+ sub limit_wd, limit, #1
+ neg tmp4, tmp1
+ cmp tmp1, #8
+
+ and tmp3, limit_wd, #15
+ lsr limit_wd, limit_wd, #4
+ mov tmp2, #~0
+
+ ldp data1, data2, [src], #16
+ lsl tmp4, tmp4, #3 /* Bytes beyond alignment -> bits. */
+ add tmp3, tmp3, tmp1
+
+#ifdef __AARCH64EB__
+ /* Big-endian. Early bytes are at MSB. */
+ lsl tmp2, tmp2, tmp4 /* Shift (tmp1 & 63). */
+#else
+ /* Little-endian. Early bytes are at LSB. */
+ lsr tmp2, tmp2, tmp4 /* Shift (tmp1 & 63). */
+#endif
+ add limit_wd, limit_wd, tmp3, lsr #4
+
+ orr data1, data1, tmp2
+ orr data2a, data2, tmp2
+
+ csinv data1, data1, xzr, le
+ csel data2, data2, data2a, le
+ b L(realigned)
+
+END (__strnlen_aarch64)
diff --git a/libc/AOR_v20.02/string/aarch64/strrchr-sve.S b/libc/AOR_v20.02/string/aarch64/strrchr-sve.S
new file mode 100644
index 000000000000..0b4fcb065631
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strrchr-sve.S
@@ -0,0 +1,86 @@
+/*
+ * strrchr - find the last of a character in a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_FEATURE_SVE
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * SVE Available.
+ */
+
+ .arch armv8-a+sve
+ .text
+
+ .globl __strrchr_aarch64_sve
+ .type __strrchr_aarch64_sve, %function
+ .p2align 4
+__strrchr_aarch64_sve:
+ dup z1.b, w1 /* replicate byte across vector */
+ setffr /* initialize FFR */
+ ptrue p1.b /* all ones; loop invariant */
+ mov x2, 0 /* no match found so far */
+ pfalse p2.b
+
+ .p2align 4
+ /* Read a vector's worth of bytes, stopping on first fault. */
+0: ldff1b z0.b, p1/z, [x0, xzr]
+ rdffrs p0.b, p1/z
+ b.nlast 1f
+
+ /* First fault did not fail: the whole vector is valid.
+ Avoid depending on the contents of FFR beyond the branch. */
+ incb x0, all /* skip bytes this round */
+ cmpeq p3.b, p1/z, z0.b, 0 /* search for 0 */
+ b.any 3f
+
+ cmpeq p3.b, p1/z, z0.b, z1.b /* search for c; no eos */
+ b.none 0b
+
+ mov x2, x0 /* save advanced base */
+ mov p2.b, p3.b /* save current search */
+ b 0b
+
+ /* First fault failed: only some of the vector is valid.
+ Perform the comparisions only on the valid bytes. */
+1: cmpeq p3.b, p0/z, z0.b, 0 /* search for 0 */
+ b.any 2f
+
+ cmpeq p3.b, p0/z, z0.b, z1.b /* search for c; no eos */
+ mov x3, x0
+ incp x0, p0.b /* skip bytes this round */
+ setffr /* re-init FFR */
+ b.none 0b
+
+ addvl x2, x3, 1 /* save advanced base */
+ mov p2.b, p3.b /* save current search */
+ b 0b
+
+ /* Found end-of-string. */
+2: incb x0, all /* advance base */
+3: brka p3.b, p1/z, p3.b /* mask after first 0 */
+ cmpeq p3.b, p3/z, z0.b, z1.b /* search for c not after eos */
+ b.any 4f
+
+ /* No C within last vector. Did we have one before? */
+ cbz x2, 5f
+ mov x0, x2 /* restore advanced base */
+ mov p3.b, p2.b /* restore saved search */
+
+ /* Find the *last* match in the predicate. This is slightly
+ more complicated than finding the first match. */
+4: rev p3.b, p3.b /* reverse the bits */
+ brka p3.b, p1/z, p3.b /* find position of last match */
+ decp x0, p3.b /* retard pointer to last match */
+ ret
+
+ /* No C whatsoever. Return NULL. */
+5: mov x0, 0
+ ret
+
+ .size __strrchr_aarch64_sve, . - __strrchr_aarch64_sve
+#endif
diff --git a/libc/AOR_v20.02/string/aarch64/strrchr.S b/libc/AOR_v20.02/string/aarch64/strrchr.S
new file mode 100644
index 000000000000..48df4865064d
--- /dev/null
+++ b/libc/AOR_v20.02/string/aarch64/strrchr.S
@@ -0,0 +1,148 @@
+/*
+ * strrchr - find last position of a character in a string.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/* Assumptions:
+ *
+ * ARMv8-a, AArch64
+ * Neon Available.
+ */
+
+#include "../asmdefs.h"
+
+/* Arguments and results. */
+#define srcin x0
+#define chrin w1
+
+#define result x0
+
+#define src x2
+#define tmp1 x3
+#define wtmp2 w4
+#define tmp3 x5
+#define src_match x6
+#define src_offset x7
+#define const_m1 x8
+#define tmp4 x9
+#define nul_match x10
+#define chr_match x11
+
+#define vrepchr v0
+#define vdata1 v1
+#define vdata2 v2
+#define vhas_nul1 v3
+#define vhas_nul2 v4
+#define vhas_chr1 v5
+#define vhas_chr2 v6
+#define vrepmask_0 v7
+#define vrepmask_c v16
+#define vend1 v17
+#define vend2 v18
+
+/* Core algorithm.
+
+ For each 32-byte hunk we calculate a 64-bit syndrome value, with
+ two bits per byte (LSB is always in bits 0 and 1, for both big
+ and little-endian systems). For each tuple, bit 0 is set iff
+ the relevant byte matched the requested character; bit 1 is set
+ iff the relevant byte matched the NUL end of string (we trigger
+ off bit0 for the special case of looking for NUL). Since the bits
+ in the syndrome reflect exactly the order in which things occur
+ in the original string a count_trailing_zeros() operation will
+ identify exactly which byte is causing the termination, and why. */
+
+ENTRY (__strrchr_aarch64)
+ /* Magic constant 0x40100401 to allow us to identify which lane
+ matches the requested byte. Magic constant 0x80200802 used
+ similarly for NUL termination. */
+ mov wtmp2, #0x0401
+ movk wtmp2, #0x4010, lsl #16
+ dup vrepchr.16b, chrin
+ bic src, srcin, #31 /* Work with aligned 32-byte hunks. */
+ dup vrepmask_c.4s, wtmp2
+ mov src_offset, #0
+ ands tmp1, srcin, #31
+ add vrepmask_0.4s, vrepmask_c.4s, vrepmask_c.4s /* equiv: lsl #1 */
+ b.eq L(aligned)
+
+ /* Input string is not 32-byte aligned. Rather than forcing
+ the padding bytes to a safe value, we calculate the syndrome
+ for all the bytes, but then mask off those bits of the
+ syndrome that are related to the padding. */
+ ld1 {vdata1.16b, vdata2.16b}, [src], #32
+ neg tmp1, tmp1
+ cmeq vhas_nul1.16b, vdata1.16b, #0
+ cmeq vhas_chr1.16b, vdata1.16b, vrepchr.16b
+ cmeq vhas_nul2.16b, vdata2.16b, #0
+ cmeq vhas_chr2.16b, vdata2.16b, vrepchr.16b
+ and vhas_nul1.16b, vhas_nul1.16b, vrepmask_0.16b
+ and vhas_chr1.16b, vhas_chr1.16b, vrepmask_c.16b
+ and vhas_nul2.16b, vhas_nul2.16b, vrepmask_0.16b
+ and vhas_chr2.16b, vhas_chr2.16b, vrepmask_c.16b
+ addp vhas_nul1.16b, vhas_nul1.16b, vhas_nul2.16b // 256->128
+ addp vhas_chr1.16b, vhas_chr1.16b, vhas_chr2.16b // 256->128
+ addp vhas_nul1.16b, vhas_nul1.16b, vhas_nul1.16b // 128->64
+ addp vhas_chr1.16b, vhas_chr1.16b, vhas_chr1.16b // 128->64
+ mov nul_match, vhas_nul1.d[0]
+ lsl tmp1, tmp1, #1
+ mov const_m1, #~0
+ mov chr_match, vhas_chr1.d[0]
+ lsr tmp3, const_m1, tmp1
+
+ bic nul_match, nul_match, tmp3 // Mask padding bits.
+ bic chr_match, chr_match, tmp3 // Mask padding bits.
+ cbnz nul_match, L(tail)
+
+L(loop):
+ cmp chr_match, #0
+ csel src_match, src, src_match, ne
+ csel src_offset, chr_match, src_offset, ne
+L(aligned):
+ ld1 {vdata1.16b, vdata2.16b}, [src], #32
+ cmeq vhas_nul1.16b, vdata1.16b, #0
+ cmeq vhas_chr1.16b, vdata1.16b, vrepchr.16b
+ cmeq vhas_nul2.16b, vdata2.16b, #0
+ cmeq vhas_chr2.16b, vdata2.16b, vrepchr.16b
+ addp vend1.16b, vhas_nul1.16b, vhas_nul2.16b // 256->128
+ and vhas_chr1.16b, vhas_chr1.16b, vrepmask_c.16b
+ and vhas_chr2.16b, vhas_chr2.16b, vrepmask_c.16b
+ addp vhas_chr1.16b, vhas_chr1.16b, vhas_chr2.16b // 256->128
+ addp vend1.16b, vend1.16b, vend1.16b // 128->64
+ addp vhas_chr1.16b, vhas_chr1.16b, vhas_chr1.16b // 128->64
+ mov nul_match, vend1.d[0]
+ mov chr_match, vhas_chr1.d[0]
+ cbz nul_match, L(loop)
+
+ and vhas_nul1.16b, vhas_nul1.16b, vrepmask_0.16b
+ and vhas_nul2.16b, vhas_nul2.16b, vrepmask_0.16b
+ addp vhas_nul1.16b, vhas_nul1.16b, vhas_nul2.16b
+ addp vhas_nul1.16b, vhas_nul1.16b, vhas_nul1.16b
+ mov nul_match, vhas_nul1.d[0]
+
+L(tail):
+ /* Work out exactly where the string ends. */
+ sub tmp4, nul_match, #1
+ eor tmp4, tmp4, nul_match
+ ands chr_match, chr_match, tmp4
+ /* And pick the values corresponding to the last match. */
+ csel src_match, src, src_match, ne
+ csel src_offset, chr_match, src_offset, ne
+
+ /* Count down from the top of the syndrome to find the last match. */
+ clz tmp3, src_offset
+ /* Src_match points beyond the word containing the match, so we can
+ simply subtract half the bit-offset into the syndrome. Because
+ we are counting down, we need to go back one more character. */
+ add tmp3, tmp3, #2
+ sub result, src_match, tmp3, lsr #1
+ /* But if the syndrome shows no match was found, then return NULL. */
+ cmp src_offset, #0
+ csel result, result, xzr, ne
+
+ ret
+
+END (__strrchr_aarch64)
diff --git a/libc/AOR_v20.02/string/arm/check-arch.S b/libc/AOR_v20.02/string/arm/check-arch.S
new file mode 100644
index 000000000000..64ffdd0eec7a
--- /dev/null
+++ b/libc/AOR_v20.02/string/arm/check-arch.S
@@ -0,0 +1,11 @@
+/*
+ * check ARCH setting.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if !__arm__
+# error ARCH setting does not match the compiler.
+#endif
diff --git a/libc/AOR_v20.02/string/arm/memchr.S b/libc/AOR_v20.02/string/arm/memchr.S
new file mode 100644
index 000000000000..a9bba052fb7e
--- /dev/null
+++ b/libc/AOR_v20.02/string/arm/memchr.S
@@ -0,0 +1,134 @@
+/*
+ * memchr - scan memory for a character
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/*
+ Written by Dave Gilbert <david.gilbert at linaro.org>
+
+ This __memchr_arm routine is optimised on a Cortex-A9 and should work on
+ all ARMv7 processors. It has a fast past for short sizes, and has
+ an optimised path for large data sets; the worst case is finding the
+ match early in a large data set.
+
+ */
+
+@ 2011-02-07 david.gilbert at linaro.org
+@ Extracted from local git a5b438d861
+@ 2011-07-14 david.gilbert at linaro.org
+@ Import endianness fix from local git ea786f1b
+@ 2011-12-07 david.gilbert at linaro.org
+@ Removed unneeded cbz from align loop
+
+ .syntax unified
+ .arch armv7-a
+
+@ this lets us check a flag in a 00/ff byte easily in either endianness
+#ifdef __ARMEB__
+#define CHARTSTMASK(c) 1<<(31-(c*8))
+#else
+#define CHARTSTMASK(c) 1<<(c*8)
+#endif
+ .text
+ .thumb
+
+@ ---------------------------------------------------------------------------
+ .thumb_func
+ .align 2
+ .p2align 4,,15
+ .global __memchr_arm
+ .type __memchr_arm,%function
+__memchr_arm:
+ @ r0 = start of memory to scan
+ @ r1 = character to look for
+ @ r2 = length
+ @ returns r0 = pointer to character or NULL if not found
+ and r1,r1,#0xff @ Don't think we can trust the caller to actually pass a char
+
+ cmp r2,#16 @ If it's short don't bother with anything clever
+ blt 20f
+
+ tst r0, #7 @ If it's already aligned skip the next bit
+ beq 10f
+
+ @ Work up to an aligned point
+5:
+ ldrb r3, [r0],#1
+ subs r2, r2, #1
+ cmp r3, r1
+ beq 50f @ If it matches exit found
+ tst r0, #7
+ bne 5b @ If not aligned yet then do next byte
+
+10:
+ @ At this point, we are aligned, we know we have at least 8 bytes to work with
+ push {r4,r5,r6,r7}
+ orr r1, r1, r1, lsl #8 @ expand the match word across to all bytes
+ orr r1, r1, r1, lsl #16
+ bic r4, r2, #7 @ Number of double words to work with
+ mvns r7, #0 @ all F's
+ movs r3, #0
+
+15:
+ ldmia r0!,{r5,r6}
+ subs r4, r4, #8
+ eor r5,r5, r1 @ Get it so that r5,r6 have 00's where the bytes match the target
+ eor r6,r6, r1
+ uadd8 r5, r5, r7 @ Parallel add 0xff - sets the GE bits for anything that wasn't 0
+ sel r5, r3, r7 @ bytes are 00 for none-00 bytes, or ff for 00 bytes - NOTE INVERSION
+ uadd8 r6, r6, r7 @ Parallel add 0xff - sets the GE bits for anything that wasn't 0
+ sel r6, r5, r7 @ chained....bytes are 00 for none-00 bytes, or ff for 00 bytes - NOTE INVERSION
+ cbnz r6, 60f
+ bne 15b @ (Flags from the subs above) If not run out of bytes then go around again
+
+ pop {r4,r5,r6,r7}
+ and r1,r1,#0xff @ Get r1 back to a single character from the expansion above
+ and r2,r2,#7 @ Leave the count remaining as the number after the double words have been done
+
+20:
+ cbz r2, 40f @ 0 length or hit the end already then not found
+
+21: @ Post aligned section, or just a short call
+ ldrb r3,[r0],#1
+ subs r2,r2,#1
+ eor r3,r3,r1 @ r3 = 0 if match - doesn't break flags from sub
+ cbz r3, 50f
+ bne 21b @ on r2 flags
+
+40:
+ movs r0,#0 @ not found
+ bx lr
+
+50:
+ subs r0,r0,#1 @ found
+ bx lr
+
+60: @ We're here because the fast path found a hit - now we have to track down exactly which word it was
+ @ r0 points to the start of the double word after the one that was tested
+ @ r5 has the 00/ff pattern for the first word, r6 has the chained value
+ cmp r5, #0
+ itte eq
+ moveq r5, r6 @ the end is in the 2nd word
+ subeq r0,r0,#3 @ Points to 2nd byte of 2nd word
+ subne r0,r0,#7 @ or 2nd byte of 1st word
+
+ @ r0 currently points to the 3rd byte of the word containing the hit
+ tst r5, # CHARTSTMASK(0) @ 1st character
+ bne 61f
+ adds r0,r0,#1
+ tst r5, # CHARTSTMASK(1) @ 2nd character
+ ittt eq
+ addeq r0,r0,#1
+ tsteq r5, # (3<<15) @ 2nd & 3rd character
+ @ If not the 3rd must be the last one
+ addeq r0,r0,#1
+
+61:
+ pop {r4,r5,r6,r7}
+ subs r0,r0,#1
+ bx lr
+
+ .size __memchr_arm, . - __memchr_arm
diff --git a/libc/AOR_v20.02/string/arm/memcpy.S b/libc/AOR_v20.02/string/arm/memcpy.S
new file mode 100644
index 000000000000..a410be5ba0f4
--- /dev/null
+++ b/libc/AOR_v20.02/string/arm/memcpy.S
@@ -0,0 +1,588 @@
+/*
+ * memcpy - copy memory area
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/*
+ This memcpy routine is optimised for Cortex-A15 cores and takes advantage
+ of VFP or NEON when built with the appropriate flags.
+
+ Assumptions:
+
+ ARMv6 (ARMv7-a if using Neon)
+ ARM state
+ Unaligned accesses
+
+ */
+
+#include "../asmdefs.h"
+
+ .syntax unified
+ /* This implementation requires ARM state. */
+ .arm
+
+#ifdef __ARM_NEON__
+
+ .fpu neon
+ .arch armv7-a
+# define FRAME_SIZE 4
+# define USE_VFP
+# define USE_NEON
+
+#elif !defined (__SOFTFP__)
+
+ .arch armv6
+ .fpu vfpv2
+# define FRAME_SIZE 32
+# define USE_VFP
+
+#else
+ .arch armv6
+# define FRAME_SIZE 32
+
+#endif
+
+/* Old versions of GAS incorrectly implement the NEON align semantics. */
+#ifdef BROKEN_ASM_NEON_ALIGN
+#define ALIGN(addr, align) addr,:align
+#else
+#define ALIGN(addr, align) addr:align
+#endif
+
+#define PC_OFFSET 8 /* PC pipeline compensation. */
+#define INSN_SIZE 4
+
+/* Call parameters. */
+#define dstin r0
+#define src r1
+#define count r2
+
+/* Locals. */
+#define tmp1 r3
+#define dst ip
+#define tmp2 r10
+
+#ifndef USE_NEON
+/* For bulk copies using GP registers. */
+#define A_l r2 /* Call-clobbered. */
+#define A_h r3 /* Call-clobbered. */
+#define B_l r4
+#define B_h r5
+#define C_l r6
+#define C_h r7
+#define D_l r8
+#define D_h r9
+#endif
+
+/* Number of lines ahead to pre-fetch data. If you change this the code
+ below will need adjustment to compensate. */
+
+#define prefetch_lines 5
+
+#ifdef USE_VFP
+ .macro cpy_line_vfp vreg, base
+ vstr \vreg, [dst, #\base]
+ vldr \vreg, [src, #\base]
+ vstr d0, [dst, #\base + 8]
+ vldr d0, [src, #\base + 8]
+ vstr d1, [dst, #\base + 16]
+ vldr d1, [src, #\base + 16]
+ vstr d2, [dst, #\base + 24]
+ vldr d2, [src, #\base + 24]
+ vstr \vreg, [dst, #\base + 32]
+ vldr \vreg, [src, #\base + prefetch_lines * 64 - 32]
+ vstr d0, [dst, #\base + 40]
+ vldr d0, [src, #\base + 40]
+ vstr d1, [dst, #\base + 48]
+ vldr d1, [src, #\base + 48]
+ vstr d2, [dst, #\base + 56]
+ vldr d2, [src, #\base + 56]
+ .endm
+
+ .macro cpy_tail_vfp vreg, base
+ vstr \vreg, [dst, #\base]
+ vldr \vreg, [src, #\base]
+ vstr d0, [dst, #\base + 8]
+ vldr d0, [src, #\base + 8]
+ vstr d1, [dst, #\base + 16]
+ vldr d1, [src, #\base + 16]
+ vstr d2, [dst, #\base + 24]
+ vldr d2, [src, #\base + 24]
+ vstr \vreg, [dst, #\base + 32]
+ vstr d0, [dst, #\base + 40]
+ vldr d0, [src, #\base + 40]
+ vstr d1, [dst, #\base + 48]
+ vldr d1, [src, #\base + 48]
+ vstr d2, [dst, #\base + 56]
+ vldr d2, [src, #\base + 56]
+ .endm
+#endif
+
+ENTRY (__memcpy_arm)
+
+ mov dst, dstin /* Preserve dstin, we need to return it. */
+ cmp count, #64
+ bge L(cpy_not_short)
+ /* Deal with small copies quickly by dropping straight into the
+ exit block. */
+
+L(tail63unaligned):
+#ifdef USE_NEON
+ and tmp1, count, #0x38
+ rsb tmp1, tmp1, #(56 - PC_OFFSET + INSN_SIZE)
+ add pc, pc, tmp1
+ vld1.8 {d0}, [src]! /* 14 words to go. */
+ vst1.8 {d0}, [dst]!
+ vld1.8 {d0}, [src]! /* 12 words to go. */
+ vst1.8 {d0}, [dst]!
+ vld1.8 {d0}, [src]! /* 10 words to go. */
+ vst1.8 {d0}, [dst]!
+ vld1.8 {d0}, [src]! /* 8 words to go. */
+ vst1.8 {d0}, [dst]!
+ vld1.8 {d0}, [src]! /* 6 words to go. */
+ vst1.8 {d0}, [dst]!
+ vld1.8 {d0}, [src]! /* 4 words to go. */
+ vst1.8 {d0}, [dst]!
+ vld1.8 {d0}, [src]! /* 2 words to go. */
+ vst1.8 {d0}, [dst]!
+
+ tst count, #4
+ ldrne tmp1, [src], #4
+ strne tmp1, [dst], #4
+#else
+ /* Copy up to 15 full words of data. May not be aligned. */
+ /* Cannot use VFP for unaligned data. */
+ and tmp1, count, #0x3c
+ add dst, dst, tmp1
+ add src, src, tmp1
+ rsb tmp1, tmp1, #(60 - PC_OFFSET/2 + INSN_SIZE/2)
+ /* Jump directly into the sequence below at the correct offset. */
+ add pc, pc, tmp1, lsl #1
+
+ ldr tmp1, [src, #-60] /* 15 words to go. */
+ str tmp1, [dst, #-60]
+
+ ldr tmp1, [src, #-56] /* 14 words to go. */
+ str tmp1, [dst, #-56]
+ ldr tmp1, [src, #-52]
+ str tmp1, [dst, #-52]
+
+ ldr tmp1, [src, #-48] /* 12 words to go. */
+ str tmp1, [dst, #-48]
+ ldr tmp1, [src, #-44]
+ str tmp1, [dst, #-44]
+
+ ldr tmp1, [src, #-40] /* 10 words to go. */
+ str tmp1, [dst, #-40]
+ ldr tmp1, [src, #-36]
+ str tmp1, [dst, #-36]
+
+ ldr tmp1, [src, #-32] /* 8 words to go. */
+ str tmp1, [dst, #-32]
+ ldr tmp1, [src, #-28]
+ str tmp1, [dst, #-28]
+
+ ldr tmp1, [src, #-24] /* 6 words to go. */
+ str tmp1, [dst, #-24]
+ ldr tmp1, [src, #-20]
+ str tmp1, [dst, #-20]
+
+ ldr tmp1, [src, #-16] /* 4 words to go. */
+ str tmp1, [dst, #-16]
+ ldr tmp1, [src, #-12]
+ str tmp1, [dst, #-12]
+
+ ldr tmp1, [src, #-8] /* 2 words to go. */
+ str tmp1, [dst, #-8]
+ ldr tmp1, [src, #-4]
+ str tmp1, [dst, #-4]
+#endif
+
+ lsls count, count, #31
+ ldrhcs tmp1, [src], #2
+ ldrbne src, [src] /* Src is dead, use as a scratch. */
+ strhcs tmp1, [dst], #2
+ strbne src, [dst]
+ bx lr
+
+L(cpy_not_short):
+ /* At least 64 bytes to copy, but don't know the alignment yet. */
+ str tmp2, [sp, #-FRAME_SIZE]!
+ and tmp2, src, #7
+ and tmp1, dst, #7
+ cmp tmp1, tmp2
+ bne L(cpy_notaligned)
+
+#ifdef USE_VFP
+ /* Magic dust alert! Force VFP on Cortex-A9. Experiments show
+ that the FP pipeline is much better at streaming loads and
+ stores. This is outside the critical loop. */
+ vmov.f32 s0, s0
+#endif
+
+ /* SRC and DST have the same mutual 64-bit alignment, but we may
+ still need to pre-copy some bytes to get to natural alignment.
+ We bring SRC and DST into full 64-bit alignment. */
+ lsls tmp2, dst, #29
+ beq 1f
+ rsbs tmp2, tmp2, #0
+ sub count, count, tmp2, lsr #29
+ ldrmi tmp1, [src], #4
+ strmi tmp1, [dst], #4
+ lsls tmp2, tmp2, #2
+ ldrhcs tmp1, [src], #2
+ ldrbne tmp2, [src], #1
+ strhcs tmp1, [dst], #2
+ strbne tmp2, [dst], #1
+
+1:
+ subs tmp2, count, #64 /* Use tmp2 for count. */
+ blt L(tail63aligned)
+
+ cmp tmp2, #512
+ bge L(cpy_body_long)
+
+L(cpy_body_medium): /* Count in tmp2. */
+#ifdef USE_VFP
+1:
+ vldr d0, [src, #0]
+ subs tmp2, tmp2, #64
+ vldr d1, [src, #8]
+ vstr d0, [dst, #0]
+ vldr d0, [src, #16]
+ vstr d1, [dst, #8]
+ vldr d1, [src, #24]
+ vstr d0, [dst, #16]
+ vldr d0, [src, #32]
+ vstr d1, [dst, #24]
+ vldr d1, [src, #40]
+ vstr d0, [dst, #32]
+ vldr d0, [src, #48]
+ vstr d1, [dst, #40]
+ vldr d1, [src, #56]
+ vstr d0, [dst, #48]
+ add src, src, #64
+ vstr d1, [dst, #56]
+ add dst, dst, #64
+ bge 1b
+ tst tmp2, #0x3f
+ beq L(done)
+
+L(tail63aligned): /* Count in tmp2. */
+ and tmp1, tmp2, #0x38
+ add dst, dst, tmp1
+ add src, src, tmp1
+ rsb tmp1, tmp1, #(56 - PC_OFFSET + INSN_SIZE)
+ add pc, pc, tmp1
+
+ vldr d0, [src, #-56] /* 14 words to go. */
+ vstr d0, [dst, #-56]
+ vldr d0, [src, #-48] /* 12 words to go. */
+ vstr d0, [dst, #-48]
+ vldr d0, [src, #-40] /* 10 words to go. */
+ vstr d0, [dst, #-40]
+ vldr d0, [src, #-32] /* 8 words to go. */
+ vstr d0, [dst, #-32]
+ vldr d0, [src, #-24] /* 6 words to go. */
+ vstr d0, [dst, #-24]
+ vldr d0, [src, #-16] /* 4 words to go. */
+ vstr d0, [dst, #-16]
+ vldr d0, [src, #-8] /* 2 words to go. */
+ vstr d0, [dst, #-8]
+#else
+ sub src, src, #8
+ sub dst, dst, #8
+1:
+ ldrd A_l, A_h, [src, #8]
+ strd A_l, A_h, [dst, #8]
+ ldrd A_l, A_h, [src, #16]
+ strd A_l, A_h, [dst, #16]
+ ldrd A_l, A_h, [src, #24]
+ strd A_l, A_h, [dst, #24]
+ ldrd A_l, A_h, [src, #32]
+ strd A_l, A_h, [dst, #32]
+ ldrd A_l, A_h, [src, #40]
+ strd A_l, A_h, [dst, #40]
+ ldrd A_l, A_h, [src, #48]
+ strd A_l, A_h, [dst, #48]
+ ldrd A_l, A_h, [src, #56]
+ strd A_l, A_h, [dst, #56]
+ ldrd A_l, A_h, [src, #64]!
+ strd A_l, A_h, [dst, #64]!
+ subs tmp2, tmp2, #64
+ bge 1b
+ tst tmp2, #0x3f
+ bne 1f
+ ldr tmp2,[sp], #FRAME_SIZE
+ bx lr
+1:
+ add src, src, #8
+ add dst, dst, #8
+
+L(tail63aligned): /* Count in tmp2. */
+ /* Copy up to 7 d-words of data. Similar to Ltail63unaligned, but
+ we know that the src and dest are 64-bit aligned so we can use
+ LDRD/STRD to improve efficiency. */
+ /* TMP2 is now negative, but we don't care about that. The bottom
+ six bits still tell us how many bytes are left to copy. */
+
+ and tmp1, tmp2, #0x38
+ add dst, dst, tmp1
+ add src, src, tmp1
+ rsb tmp1, tmp1, #(56 - PC_OFFSET + INSN_SIZE)
+ add pc, pc, tmp1
+ ldrd A_l, A_h, [src, #-56] /* 14 words to go. */
+ strd A_l, A_h, [dst, #-56]
+ ldrd A_l, A_h, [src, #-48] /* 12 words to go. */
+ strd A_l, A_h, [dst, #-48]
+ ldrd A_l, A_h, [src, #-40] /* 10 words to go. */
+ strd A_l, A_h, [dst, #-40]
+ ldrd A_l, A_h, [src, #-32] /* 8 words to go. */
+ strd A_l, A_h, [dst, #-32]
+ ldrd A_l, A_h, [src, #-24] /* 6 words to go. */
+ strd A_l, A_h, [dst, #-24]
+ ldrd A_l, A_h, [src, #-16] /* 4 words to go. */
+ strd A_l, A_h, [dst, #-16]
+ ldrd A_l, A_h, [src, #-8] /* 2 words to go. */
+ strd A_l, A_h, [dst, #-8]
+
+#endif
+ tst tmp2, #4
+ ldrne tmp1, [src], #4
+ strne tmp1, [dst], #4
+ lsls tmp2, tmp2, #31 /* Count (tmp2) now dead. */
+ ldrhcs tmp1, [src], #2
+ ldrbne tmp2, [src]
+ strhcs tmp1, [dst], #2
+ strbne tmp2, [dst]
+
+L(done):
+ ldr tmp2, [sp], #FRAME_SIZE
+ bx lr
+
+L(cpy_body_long): /* Count in tmp2. */
+
+ /* Long copy. We know that there's at least (prefetch_lines * 64)
+ bytes to go. */
+#ifdef USE_VFP
+ /* Don't use PLD. Instead, read some data in advance of the current
+ copy position into a register. This should act like a PLD
+ operation but we won't have to repeat the transfer. */
+
+ vldr d3, [src, #0]
+ vldr d4, [src, #64]
+ vldr d5, [src, #128]
+ vldr d6, [src, #192]
+ vldr d7, [src, #256]
+
+ vldr d0, [src, #8]
+ vldr d1, [src, #16]
+ vldr d2, [src, #24]
+ add src, src, #32
+
+ subs tmp2, tmp2, #prefetch_lines * 64 * 2
+ blt 2f
+1:
+ cpy_line_vfp d3, 0
+ cpy_line_vfp d4, 64
+ cpy_line_vfp d5, 128
+ add dst, dst, #3 * 64
+ add src, src, #3 * 64
+ cpy_line_vfp d6, 0
+ cpy_line_vfp d7, 64
+ add dst, dst, #2 * 64
+ add src, src, #2 * 64
+ subs tmp2, tmp2, #prefetch_lines * 64
+ bge 1b
+
+2:
+ cpy_tail_vfp d3, 0
+ cpy_tail_vfp d4, 64
+ cpy_tail_vfp d5, 128
+ add src, src, #3 * 64
+ add dst, dst, #3 * 64
+ cpy_tail_vfp d6, 0
+ vstr d7, [dst, #64]
+ vldr d7, [src, #64]
+ vstr d0, [dst, #64 + 8]
+ vldr d0, [src, #64 + 8]
+ vstr d1, [dst, #64 + 16]
+ vldr d1, [src, #64 + 16]
+ vstr d2, [dst, #64 + 24]
+ vldr d2, [src, #64 + 24]
+ vstr d7, [dst, #64 + 32]
+ add src, src, #96
+ vstr d0, [dst, #64 + 40]
+ vstr d1, [dst, #64 + 48]
+ vstr d2, [dst, #64 + 56]
+ add dst, dst, #128
+ add tmp2, tmp2, #prefetch_lines * 64
+ b L(cpy_body_medium)
+#else
+ /* Long copy. Use an SMS style loop to maximize the I/O
+ bandwidth of the core. We don't have enough spare registers
+ to synthesise prefetching, so use PLD operations. */
+ /* Pre-bias src and dst. */
+ sub src, src, #8
+ sub dst, dst, #8
+ pld [src, #8]
+ pld [src, #72]
+ subs tmp2, tmp2, #64
+ pld [src, #136]
+ ldrd A_l, A_h, [src, #8]
+ strd B_l, B_h, [sp, #8]
+ ldrd B_l, B_h, [src, #16]
+ strd C_l, C_h, [sp, #16]
+ ldrd C_l, C_h, [src, #24]
+ strd D_l, D_h, [sp, #24]
+ pld [src, #200]
+ ldrd D_l, D_h, [src, #32]!
+ b 1f
+ .p2align 6
+2:
+ pld [src, #232]
+ strd A_l, A_h, [dst, #40]
+ ldrd A_l, A_h, [src, #40]
+ strd B_l, B_h, [dst, #48]
+ ldrd B_l, B_h, [src, #48]
+ strd C_l, C_h, [dst, #56]
+ ldrd C_l, C_h, [src, #56]
+ strd D_l, D_h, [dst, #64]!
+ ldrd D_l, D_h, [src, #64]!
+ subs tmp2, tmp2, #64
+1:
+ strd A_l, A_h, [dst, #8]
+ ldrd A_l, A_h, [src, #8]
+ strd B_l, B_h, [dst, #16]
+ ldrd B_l, B_h, [src, #16]
+ strd C_l, C_h, [dst, #24]
+ ldrd C_l, C_h, [src, #24]
+ strd D_l, D_h, [dst, #32]
+ ldrd D_l, D_h, [src, #32]
+ bcs 2b
+ /* Save the remaining bytes and restore the callee-saved regs. */
+ strd A_l, A_h, [dst, #40]
+ add src, src, #40
+ strd B_l, B_h, [dst, #48]
+ ldrd B_l, B_h, [sp, #8]
+ strd C_l, C_h, [dst, #56]
+ ldrd C_l, C_h, [sp, #16]
+ strd D_l, D_h, [dst, #64]
+ ldrd D_l, D_h, [sp, #24]
+ add dst, dst, #72
+ tst tmp2, #0x3f
+ bne L(tail63aligned)
+ ldr tmp2, [sp], #FRAME_SIZE
+ bx lr
+#endif
+
+L(cpy_notaligned):
+ pld [src]
+ pld [src, #64]
+ /* There's at least 64 bytes to copy, but there is no mutual
+ alignment. */
+ /* Bring DST to 64-bit alignment. */
+ lsls tmp2, dst, #29
+ pld [src, #(2 * 64)]
+ beq 1f
+ rsbs tmp2, tmp2, #0
+ sub count, count, tmp2, lsr #29
+ ldrmi tmp1, [src], #4
+ strmi tmp1, [dst], #4
+ lsls tmp2, tmp2, #2
+ ldrbne tmp1, [src], #1
+ ldrhcs tmp2, [src], #2
+ strbne tmp1, [dst], #1
+ strhcs tmp2, [dst], #2
+1:
+ pld [src, #(3 * 64)]
+ subs count, count, #64
+ ldrmi tmp2, [sp], #FRAME_SIZE
+ bmi L(tail63unaligned)
+ pld [src, #(4 * 64)]
+
+#ifdef USE_NEON
+ vld1.8 {d0-d3}, [src]!
+ vld1.8 {d4-d7}, [src]!
+ subs count, count, #64
+ bmi 2f
+1:
+ pld [src, #(4 * 64)]
+ vst1.8 {d0-d3}, [ALIGN (dst, 64)]!
+ vld1.8 {d0-d3}, [src]!
+ vst1.8 {d4-d7}, [ALIGN (dst, 64)]!
+ vld1.8 {d4-d7}, [src]!
+ subs count, count, #64
+ bpl 1b
+2:
+ vst1.8 {d0-d3}, [ALIGN (dst, 64)]!
+ vst1.8 {d4-d7}, [ALIGN (dst, 64)]!
+ ands count, count, #0x3f
+#else
+ /* Use an SMS style loop to maximize the I/O bandwidth. */
+ sub src, src, #4
+ sub dst, dst, #8
+ subs tmp2, count, #64 /* Use tmp2 for count. */
+ ldr A_l, [src, #4]
+ ldr A_h, [src, #8]
+ strd B_l, B_h, [sp, #8]
+ ldr B_l, [src, #12]
+ ldr B_h, [src, #16]
+ strd C_l, C_h, [sp, #16]
+ ldr C_l, [src, #20]
+ ldr C_h, [src, #24]
+ strd D_l, D_h, [sp, #24]
+ ldr D_l, [src, #28]
+ ldr D_h, [src, #32]!
+ b 1f
+ .p2align 6
+2:
+ pld [src, #(5 * 64) - (32 - 4)]
+ strd A_l, A_h, [dst, #40]
+ ldr A_l, [src, #36]
+ ldr A_h, [src, #40]
+ strd B_l, B_h, [dst, #48]
+ ldr B_l, [src, #44]
+ ldr B_h, [src, #48]
+ strd C_l, C_h, [dst, #56]
+ ldr C_l, [src, #52]
+ ldr C_h, [src, #56]
+ strd D_l, D_h, [dst, #64]!
+ ldr D_l, [src, #60]
+ ldr D_h, [src, #64]!
+ subs tmp2, tmp2, #64
+1:
+ strd A_l, A_h, [dst, #8]
+ ldr A_l, [src, #4]
+ ldr A_h, [src, #8]
+ strd B_l, B_h, [dst, #16]
+ ldr B_l, [src, #12]
+ ldr B_h, [src, #16]
+ strd C_l, C_h, [dst, #24]
+ ldr C_l, [src, #20]
+ ldr C_h, [src, #24]
+ strd D_l, D_h, [dst, #32]
+ ldr D_l, [src, #28]
+ ldr D_h, [src, #32]
+ bcs 2b
+
+ /* Save the remaining bytes and restore the callee-saved regs. */
+ strd A_l, A_h, [dst, #40]
+ add src, src, #36
+ strd B_l, B_h, [dst, #48]
+ ldrd B_l, B_h, [sp, #8]
+ strd C_l, C_h, [dst, #56]
+ ldrd C_l, C_h, [sp, #16]
+ strd D_l, D_h, [dst, #64]
+ ldrd D_l, D_h, [sp, #24]
+ add dst, dst, #72
+ ands count, tmp2, #0x3f
+#endif
+ ldr tmp2, [sp], #FRAME_SIZE
+ bne L(tail63unaligned)
+ bx lr
+
+END (__memcpy_arm)
diff --git a/libc/AOR_v20.02/string/arm/memset.S b/libc/AOR_v20.02/string/arm/memset.S
new file mode 100644
index 000000000000..a3185b957f2f
--- /dev/null
+++ b/libc/AOR_v20.02/string/arm/memset.S
@@ -0,0 +1,100 @@
+/*
+ * memset - fill memory with a constant
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+/*
+ Written by Dave Gilbert <david.gilbert at linaro.org>
+
+ This memset routine is optimised on a Cortex-A9 and should work on
+ all ARMv7 processors.
+
+ */
+
+ .syntax unified
+ .arch armv7-a
+
+@ 2011-08-30 david.gilbert at linaro.org
+@ Extracted from local git 2f11b436
+
+@ this lets us check a flag in a 00/ff byte easily in either endianness
+#ifdef __ARMEB__
+#define CHARTSTMASK(c) 1<<(31-(c*8))
+#else
+#define CHARTSTMASK(c) 1<<(c*8)
+#endif
+ .text
+ .thumb
+
+@ ---------------------------------------------------------------------------
+ .thumb_func
+ .align 2
+ .p2align 4,,15
+ .global __memset_arm
+ .type __memset_arm,%function
+__memset_arm:
+ @ r0 = address
+ @ r1 = character
+ @ r2 = count
+ @ returns original address in r0
+
+ mov r3, r0 @ Leave r0 alone
+ cbz r2, 10f @ Exit if 0 length
+
+ tst r0, #7
+ beq 2f @ Already aligned
+
+ @ Ok, so we're misaligned here
+1:
+ strb r1, [r3], #1
+ subs r2,r2,#1
+ tst r3, #7
+ cbz r2, 10f @ Exit if we hit the end
+ bne 1b @ go round again if still misaligned
+
+2:
+ @ OK, so we're aligned
+ push {r4,r5,r6,r7}
+ bics r4, r2, #15 @ if less than 16 bytes then need to finish it off
+ beq 5f
+
+3:
+ @ POSIX says that ch is cast to an unsigned char. A uxtb is one
+ @ byte and takes two cycles, where an AND is four bytes but one
+ @ cycle.
+ and r1, #0xFF
+ orr r1, r1, r1, lsl#8 @ Same character into all bytes
+ orr r1, r1, r1, lsl#16
+ mov r5,r1
+ mov r6,r1
+ mov r7,r1
+
+4:
+ subs r4,r4,#16
+ stmia r3!,{r1,r5,r6,r7}
+ bne 4b
+ and r2,r2,#15
+
+ @ At this point we're still aligned and we have upto align-1 bytes left to right
+ @ we can avoid some of the byte-at-a time now by testing for some big chunks
+ tst r2,#8
+ itt ne
+ subne r2,r2,#8
+ stmiane r3!,{r1,r5}
+
+5:
+ pop {r4,r5,r6,r7}
+ cbz r2, 10f
+
+ @ Got to do any last < alignment bytes
+6:
+ subs r2,r2,#1
+ strb r1,[r3],#1
+ bne 6b
+
+10:
+ bx lr @ goodbye
+ .size __memset_arm, . - __memset_arm
diff --git a/libc/AOR_v20.02/string/arm/strcmp-armv6m.S b/libc/AOR_v20.02/string/arm/strcmp-armv6m.S
new file mode 100644
index 000000000000..462233d06004
--- /dev/null
+++ b/libc/AOR_v20.02/string/arm/strcmp-armv6m.S
@@ -0,0 +1,118 @@
+/*
+ * strcmp for ARMv6-M (optimized for performance, not size)
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_ARCH == 6 && __ARM_ARCH_6M__ >= 1
+
+ .thumb_func
+ .syntax unified
+ .arch armv6-m
+
+ .macro DoSub n, label
+ subs r0, r0, r1
+#ifdef __ARM_BIG_ENDIAN
+ lsrs r1, r4, \n
+#else
+ lsls r1, r4, \n
+#endif
+ orrs r1, r0
+ bne \label
+ .endm
+
+ .macro Byte_Test n, label
+ lsrs r0, r2, \n
+ lsrs r1, r3, \n
+ DoSub \n, \label
+ .endm
+
+ENTRY_ALIGN (__strcmp_armv6m, 4)
+ mov r2, r0
+ push {r4, r5, r6, lr}
+ orrs r2, r1
+ lsls r2, r2, #30
+ bne 6f
+ ldr r5, =0x01010101
+ lsls r6, r5, #7
+1:
+ ldmia r0!, {r2}
+ ldmia r1!, {r3}
+ subs r4, r2, r5
+ bics r4, r2
+ ands r4, r6
+ beq 3f
+
+#ifdef __ARM_BIG_ENDIAN
+ Byte_Test #24, 4f
+ Byte_Test #16, 4f
+ Byte_Test #8, 4f
+
+ b 7f
+3:
+ cmp r2, r3
+ beq 1b
+ cmp r2, r3
+#else
+ uxtb r0, r2
+ uxtb r1, r3
+ DoSub #24, 2f
+
+ uxth r0, r2
+ uxth r1, r3
+ DoSub #16, 2f
+
+ lsls r0, r2, #8
+ lsls r1, r3, #8
+ lsrs r0, r0, #8
+ lsrs r1, r1, #8
+ DoSub #8, 2f
+
+ lsrs r0, r2, #24
+ lsrs r1, r3, #24
+ subs r0, r0, r1
+2:
+ pop {r4, r5, r6, pc}
+
+3:
+ cmp r2, r3
+ beq 1b
+ rev r0, r2
+ rev r1, r3
+ cmp r0, r1
+#endif
+
+ bls 5f
+ movs r0, #1
+4:
+ pop {r4, r5, r6, pc}
+5:
+ movs r0, #0
+ mvns r0, r0
+ pop {r4, r5, r6, pc}
+6:
+ ldrb r2, [r0, #0]
+ ldrb r3, [r1, #0]
+ adds r0, #1
+ adds r1, #1
+ cmp r2, #0
+ beq 7f
+ cmp r2, r3
+ bne 7f
+ ldrb r2, [r0, #0]
+ ldrb r3, [r1, #0]
+ adds r0, #1
+ adds r1, #1
+ cmp r2, #0
+ beq 7f
+ cmp r2, r3
+ beq 6b
+7:
+ subs r0, r2, r3
+ pop {r4, r5, r6, pc}
+
+END (__strcmp_armv6m)
+
+#endif /* __ARM_ARCH == 6 && __ARM_ARCH_6M__ >= 1 */
diff --git a/libc/AOR_v20.02/string/arm/strcmp.S b/libc/AOR_v20.02/string/arm/strcmp.S
new file mode 100644
index 000000000000..db7cc0549fe2
--- /dev/null
+++ b/libc/AOR_v20.02/string/arm/strcmp.S
@@ -0,0 +1,477 @@
+/*
+ * strcmp for ARMv7
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_ARCH >= 7 && __ARM_ARCH_ISA_ARM >= 1
+
+/* Implementation of strcmp for ARMv7 when DSP instructions are
+ available. Use ldrd to support wider loads, provided the data
+ is sufficiently aligned. Use saturating arithmetic to optimize
+ the compares. */
+
+#include "../asmdefs.h"
+
+/* Build Options:
+ STRCMP_NO_PRECHECK: Don't run a quick pre-check of the first
+ byte in the string. If comparing completely random strings
+ the pre-check will save time, since there is a very high
+ probability of a mismatch in the first character: we save
+ significant overhead if this is the common case. However,
+ if strings are likely to be identical (eg because we're
+ verifying a hit in a hash table), then this check is largely
+ redundant. */
+
+#define STRCMP_NO_PRECHECK 0
+
+ /* This version uses Thumb-2 code. */
+ .thumb
+ .syntax unified
+
+#ifdef __ARM_BIG_ENDIAN
+#define S2LO lsl
+#define S2LOEQ lsleq
+#define S2HI lsr
+#define MSB 0x000000ff
+#define LSB 0xff000000
+#define BYTE0_OFFSET 24
+#define BYTE1_OFFSET 16
+#define BYTE2_OFFSET 8
+#define BYTE3_OFFSET 0
+#else /* not __ARM_BIG_ENDIAN */
+#define S2LO lsr
+#define S2LOEQ lsreq
+#define S2HI lsl
+#define BYTE0_OFFSET 0
+#define BYTE1_OFFSET 8
+#define BYTE2_OFFSET 16
+#define BYTE3_OFFSET 24
+#define MSB 0xff000000
+#define LSB 0x000000ff
+#endif /* not __ARM_BIG_ENDIAN */
+
+/* Parameters and result. */
+#define src1 r0
+#define src2 r1
+#define result r0 /* Overlaps src1. */
+
+/* Internal variables. */
+#define tmp1 r4
+#define tmp2 r5
+#define const_m1 r12
+
+/* Additional internal variables for 64-bit aligned data. */
+#define data1a r2
+#define data1b r3
+#define data2a r6
+#define data2b r7
+#define syndrome_a tmp1
+#define syndrome_b tmp2
+
+/* Additional internal variables for 32-bit aligned data. */
+#define data1 r2
+#define data2 r3
+#define syndrome tmp2
+
+
+ /* Macro to compute and return the result value for word-aligned
+ cases. */
+ .macro strcmp_epilogue_aligned synd d1 d2 restore_r6
+#ifdef __ARM_BIG_ENDIAN
+ /* If data1 contains a zero byte, then syndrome will contain a 1 in
+ bit 7 of that byte. Otherwise, the highest set bit in the
+ syndrome will highlight the first
diff erent bit. It is therefore
+ sufficient to extract the eight bits starting with the syndrome
+ bit. */
+ clz tmp1, \synd
+ lsl r1, \d2, tmp1
+ .if \restore_r6
+ ldrd r6, r7, [sp, #8]
+ .endif
+ .cfi_restore 6
+ .cfi_restore 7
+ lsl \d1, \d1, tmp1
+ .cfi_remember_state
+ lsr result, \d1, #24
+ ldrd r4, r5, [sp], #16
+ .cfi_restore 4
+ .cfi_restore 5
+ sub result, result, r1, lsr #24
+ bx lr
+#else
+ /* To use the big-endian trick we'd have to reverse all three words.
+ that's slower than this approach. */
+ rev \synd, \synd
+ clz tmp1, \synd
+ bic tmp1, tmp1, #7
+ lsr r1, \d2, tmp1
+ .cfi_remember_state
+ .if \restore_r6
+ ldrd r6, r7, [sp, #8]
+ .endif
+ .cfi_restore 6
+ .cfi_restore 7
+ lsr \d1, \d1, tmp1
+ and result, \d1, #255
+ and r1, r1, #255
+ ldrd r4, r5, [sp], #16
+ .cfi_restore 4
+ .cfi_restore 5
+ sub result, result, r1
+
+ bx lr
+#endif
+ .endm
+
+ .text
+ .p2align 5
+L(strcmp_start_addr):
+#if STRCMP_NO_PRECHECK == 0
+L(fastpath_exit):
+ sub r0, r2, r3
+ bx lr
+ nop
+#endif
+ENTRY_ALIGN (__strcmp_arm, 0)
+#if STRCMP_NO_PRECHECK == 0
+ ldrb r2, [src1]
+ ldrb r3, [src2]
+ cmp r2, #1
+ it cs
+ cmpcs r2, r3
+ bne L(fastpath_exit)
+#endif
+ strd r4, r5, [sp, #-16]!
+ .cfi_def_cfa_offset 16
+ .cfi_offset 4, -16
+ .cfi_offset 5, -12
+ orr tmp1, src1, src2
+ strd r6, r7, [sp, #8]
+ .cfi_offset 6, -8
+ .cfi_offset 7, -4
+ mvn const_m1, #0
+ lsl r2, tmp1, #29
+ cbz r2, L(loop_aligned8)
+
+L(not_aligned):
+ eor tmp1, src1, src2
+ tst tmp1, #7
+ bne L(misaligned8)
+
+ /* Deal with mutual misalignment by aligning downwards and then
+ masking off the unwanted loaded data to prevent a
diff erence. */
+ and tmp1, src1, #7
+ bic src1, src1, #7
+ and tmp2, tmp1, #3
+ bic src2, src2, #7
+ lsl tmp2, tmp2, #3 /* Bytes -> bits. */
+ ldrd data1a, data1b, [src1], #16
+ tst tmp1, #4
+ ldrd data2a, data2b, [src2], #16
+ /* In thumb code we can't use MVN with a register shift, but
+ we do have ORN. */
+ S2HI tmp1, const_m1, tmp2
+ orn data1a, data1a, tmp1
+ orn data2a, data2a, tmp1
+ beq L(start_realigned8)
+ orn data1b, data1b, tmp1
+ mov data1a, const_m1
+ orn data2b, data2b, tmp1
+ mov data2a, const_m1
+ b L(start_realigned8)
+
+ /* Unwind the inner loop by a factor of 2, giving 16 bytes per
+ pass. */
+ .p2align 5,,12 /* Don't start in the tail bytes of a cache line. */
+ .p2align 2 /* Always word aligned. */
+L(loop_aligned8):
+ ldrd data1a, data1b, [src1], #16
+ ldrd data2a, data2b, [src2], #16
+L(start_realigned8):
+ uadd8 syndrome_b, data1a, const_m1 /* Only want GE bits, */
+ eor syndrome_a, data1a, data2a
+ sel syndrome_a, syndrome_a, const_m1
+ cbnz syndrome_a, L(
diff _in_a)
+ uadd8 syndrome_b, data1b, const_m1 /* Only want GE bits. */
+ eor syndrome_b, data1b, data2b
+ sel syndrome_b, syndrome_b, const_m1
+ cbnz syndrome_b, L(
diff _in_b)
+
+ ldrd data1a, data1b, [src1, #-8]
+ ldrd data2a, data2b, [src2, #-8]
+ uadd8 syndrome_b, data1a, const_m1 /* Only want GE bits, */
+ eor syndrome_a, data1a, data2a
+ sel syndrome_a, syndrome_a, const_m1
+ uadd8 syndrome_b, data1b, const_m1 /* Only want GE bits. */
+ eor syndrome_b, data1b, data2b
+ sel syndrome_b, syndrome_b, const_m1
+ /* Can't use CBZ for backwards branch. */
+ orrs syndrome_b, syndrome_b, syndrome_a /* Only need if s_a == 0 */
+ beq L(loop_aligned8)
+
+L(
diff _found):
+ cbnz syndrome_a, L(
diff _in_a)
+
+L(
diff _in_b):
+ strcmp_epilogue_aligned syndrome_b, data1b, data2b 1
+
+L(
diff _in_a):
+ .cfi_restore_state
+ strcmp_epilogue_aligned syndrome_a, data1a, data2a 1
+
+ .cfi_restore_state
+L(misaligned8):
+ tst tmp1, #3
+ bne L(misaligned4)
+ ands tmp1, src1, #3
+ bne L(mutual_align4)
+
+ /* Unrolled by a factor of 2, to reduce the number of post-increment
+ operations. */
+L(loop_aligned4):
+ ldr data1, [src1], #8
+ ldr data2, [src2], #8
+L(start_realigned4):
+ uadd8 syndrome, data1, const_m1 /* Only need GE bits. */
+ eor syndrome, data1, data2
+ sel syndrome, syndrome, const_m1
+ cbnz syndrome, L(aligned4_done)
+ ldr data1, [src1, #-4]
+ ldr data2, [src2, #-4]
+ uadd8 syndrome, data1, const_m1
+ eor syndrome, data1, data2
+ sel syndrome, syndrome, const_m1
+ cmp syndrome, #0
+ beq L(loop_aligned4)
+
+L(aligned4_done):
+ strcmp_epilogue_aligned syndrome, data1, data2, 0
+
+L(mutual_align4):
+ .cfi_restore_state
+ /* Deal with mutual misalignment by aligning downwards and then
+ masking off the unwanted loaded data to prevent a
diff erence. */
+ lsl tmp1, tmp1, #3 /* Bytes -> bits. */
+ bic src1, src1, #3
+ ldr data1, [src1], #8
+ bic src2, src2, #3
+ ldr data2, [src2], #8
+
+ /* In thumb code we can't use MVN with a register shift, but
+ we do have ORN. */
+ S2HI tmp1, const_m1, tmp1
+ orn data1, data1, tmp1
+ orn data2, data2, tmp1
+ b L(start_realigned4)
+
+L(misaligned4):
+ ands tmp1, src1, #3
+ beq L(src1_aligned)
+ sub src2, src2, tmp1
+ bic src1, src1, #3
+ lsls tmp1, tmp1, #31
+ ldr data1, [src1], #4
+ beq L(aligned_m2)
+ bcs L(aligned_m1)
+
+#if STRCMP_NO_PRECHECK == 1
+ ldrb data2, [src2, #1]
+ uxtb tmp1, data1, ror #BYTE1_OFFSET
+ subs tmp1, tmp1, data2
+ bne L(misaligned_exit)
+ cbz data2, L(misaligned_exit)
+
+L(aligned_m2):
+ ldrb data2, [src2, #2]
+ uxtb tmp1, data1, ror #BYTE2_OFFSET
+ subs tmp1, tmp1, data2
+ bne L(misaligned_exit)
+ cbz data2, L(misaligned_exit)
+
+L(aligned_m1):
+ ldrb data2, [src2, #3]
+ uxtb tmp1, data1, ror #BYTE3_OFFSET
+ subs tmp1, tmp1, data2
+ bne L(misaligned_exit)
+ add src2, src2, #4
+ cbnz data2, L(src1_aligned)
+#else /* STRCMP_NO_PRECHECK */
+ /* If we've done the pre-check, then we don't need to check the
+ first byte again here. */
+ ldrb data2, [src2, #2]
+ uxtb tmp1, data1, ror #BYTE2_OFFSET
+ subs tmp1, tmp1, data2
+ bne L(misaligned_exit)
+ cbz data2, L(misaligned_exit)
+
+L(aligned_m2):
+ ldrb data2, [src2, #3]
+ uxtb tmp1, data1, ror #BYTE3_OFFSET
+ subs tmp1, tmp1, data2
+ bne L(misaligned_exit)
+ cbnz data2, L(aligned_m1)
+#endif
+
+L(misaligned_exit):
+ .cfi_remember_state
+ mov result, tmp1
+ ldr r4, [sp], #16
+ .cfi_restore 4
+ bx lr
+
+#if STRCMP_NO_PRECHECK == 0
+L(aligned_m1):
+ add src2, src2, #4
+#endif
+L(src1_aligned):
+ .cfi_restore_state
+ /* src1 is word aligned, but src2 has no common alignment
+ with it. */
+ ldr data1, [src1], #4
+ lsls tmp1, src2, #31 /* C=src2[1], Z=src2[0]. */
+
+ bic src2, src2, #3
+ ldr data2, [src2], #4
+ bhi L(overlap1) /* C=1, Z=0 => src2[1:0] = 0b11. */
+ bcs L(overlap2) /* C=1, Z=1 => src2[1:0] = 0b10. */
+
+ /* (overlap3) C=0, Z=0 => src2[1:0] = 0b01. */
+L(overlap3):
+ bic tmp1, data1, #MSB
+ uadd8 syndrome, data1, const_m1
+ eors syndrome, tmp1, data2, S2LO #8
+ sel syndrome, syndrome, const_m1
+ bne 4f
+ cbnz syndrome, 5f
+ ldr data2, [src2], #4
+ eor tmp1, tmp1, data1
+ cmp tmp1, data2, S2HI #24
+ bne 6f
+ ldr data1, [src1], #4
+ b L(overlap3)
+4:
+ S2LO data2, data2, #8
+ b L(strcmp_tail)
+
+5:
+ bics syndrome, syndrome, #MSB
+ bne L(strcmp_done_equal)
+
+ /* We can only get here if the MSB of data1 contains 0, so
+ fast-path the exit. */
+ ldrb result, [src2]
+ .cfi_remember_state
+ ldrd r4, r5, [sp], #16
+ .cfi_restore 4
+ .cfi_restore 5
+ /* R6/7 Not used in this sequence. */
+ .cfi_restore 6
+ .cfi_restore 7
+ neg result, result
+ bx lr
+
+6:
+ .cfi_restore_state
+ S2LO data1, data1, #24
+ and data2, data2, #LSB
+ b L(strcmp_tail)
+
+ .p2align 5,,12 /* Ensure at least 3 instructions in cache line. */
+L(overlap2):
+ and tmp1, data1, const_m1, S2LO #16
+ uadd8 syndrome, data1, const_m1
+ eors syndrome, tmp1, data2, S2LO #16
+ sel syndrome, syndrome, const_m1
+ bne 4f
+ cbnz syndrome, 5f
+ ldr data2, [src2], #4
+ eor tmp1, tmp1, data1
+ cmp tmp1, data2, S2HI #16
+ bne 6f
+ ldr data1, [src1], #4
+ b L(overlap2)
+4:
+ S2LO data2, data2, #16
+ b L(strcmp_tail)
+5:
+ ands syndrome, syndrome, const_m1, S2LO #16
+ bne L(strcmp_done_equal)
+
+ ldrh data2, [src2]
+ S2LO data1, data1, #16
+#ifdef __ARM_BIG_ENDIAN
+ lsl data2, data2, #16
+#endif
+ b L(strcmp_tail)
+
+6:
+ S2LO data1, data1, #16
+ and data2, data2, const_m1, S2LO #16
+ b L(strcmp_tail)
+
+ .p2align 5,,12 /* Ensure at least 3 instructions in cache line. */
+L(overlap1):
+ and tmp1, data1, #LSB
+ uadd8 syndrome, data1, const_m1
+ eors syndrome, tmp1, data2, S2LO #24
+ sel syndrome, syndrome, const_m1
+ bne 4f
+ cbnz syndrome, 5f
+ ldr data2, [src2], #4
+ eor tmp1, tmp1, data1
+ cmp tmp1, data2, S2HI #8
+ bne 6f
+ ldr data1, [src1], #4
+ b L(overlap1)
+4:
+ S2LO data2, data2, #24
+ b L(strcmp_tail)
+5:
+ tst syndrome, #LSB
+ bne L(strcmp_done_equal)
+ ldr data2, [src2]
+6:
+ S2LO data1, data1, #8
+ bic data2, data2, #MSB
+ b L(strcmp_tail)
+
+L(strcmp_done_equal):
+ mov result, #0
+ .cfi_remember_state
+ ldrd r4, r5, [sp], #16
+ .cfi_restore 4
+ .cfi_restore 5
+ /* R6/7 not used in this sequence. */
+ .cfi_restore 6
+ .cfi_restore 7
+ bx lr
+
+L(strcmp_tail):
+ .cfi_restore_state
+#ifndef __ARM_BIG_ENDIAN
+ rev data1, data1
+ rev data2, data2
+ /* Now everything looks big-endian... */
+#endif
+ uadd8 tmp1, data1, const_m1
+ eor tmp1, data1, data2
+ sel syndrome, tmp1, const_m1
+ clz tmp1, syndrome
+ lsl data1, data1, tmp1
+ lsl data2, data2, tmp1
+ lsr result, data1, #24
+ ldrd r4, r5, [sp], #16
+ .cfi_restore 4
+ .cfi_restore 5
+ /* R6/7 not used in this sequence. */
+ .cfi_restore 6
+ .cfi_restore 7
+ sub result, result, data2, lsr #24
+ bx lr
+
+END (__strcmp_arm)
+
+#endif /* __ARM_ARCH >= 7 && __ARM_ARCH_ISA_ARM >= 1 */
diff --git a/libc/AOR_v20.02/string/arm/strcpy.c b/libc/AOR_v20.02/string/arm/strcpy.c
new file mode 100644
index 000000000000..ce472ced2c45
--- /dev/null
+++ b/libc/AOR_v20.02/string/arm/strcpy.c
@@ -0,0 +1,134 @@
+/*
+ * strcpy
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if defined (__thumb2__) && !defined (__thumb__)
+
+/* For GLIBC:
+#include <string.h>
+#include <memcopy.h>
+
+#undef strcmp
+*/
+
+#ifdef __thumb2__
+#define magic1(REG) "#0x01010101"
+#define magic2(REG) "#0x80808080"
+#else
+#define magic1(REG) #REG
+#define magic2(REG) #REG ", lsl #7"
+#endif
+
+char* __attribute__((naked))
+__strcpy_arm (char* dst, const char* src)
+{
+ __asm__ (
+ "pld [r1, #0]\n\t"
+ "eor r2, r0, r1\n\t"
+ "mov ip, r0\n\t"
+ "tst r2, #3\n\t"
+ "bne 4f\n\t"
+ "tst r1, #3\n\t"
+ "bne 3f\n"
+ "5:\n\t"
+# ifndef __thumb2__
+ "str r5, [sp, #-4]!\n\t"
+ "mov r5, #0x01\n\t"
+ "orr r5, r5, r5, lsl #8\n\t"
+ "orr r5, r5, r5, lsl #16\n\t"
+# endif
+
+ "str r4, [sp, #-4]!\n\t"
+ "tst r1, #4\n\t"
+ "ldr r3, [r1], #4\n\t"
+ "beq 2f\n\t"
+ "sub r2, r3, "magic1(r5)"\n\t"
+ "bics r2, r2, r3\n\t"
+ "tst r2, "magic2(r5)"\n\t"
+ "itt eq\n\t"
+ "streq r3, [ip], #4\n\t"
+ "ldreq r3, [r1], #4\n"
+ "bne 1f\n\t"
+ /* Inner loop. We now know that r1 is 64-bit aligned, so we
+ can safely fetch up to two words. This allows us to avoid
+ load stalls. */
+ ".p2align 2\n"
+ "2:\n\t"
+ "pld [r1, #8]\n\t"
+ "ldr r4, [r1], #4\n\t"
+ "sub r2, r3, "magic1(r5)"\n\t"
+ "bics r2, r2, r3\n\t"
+ "tst r2, "magic2(r5)"\n\t"
+ "sub r2, r4, "magic1(r5)"\n\t"
+ "bne 1f\n\t"
+ "str r3, [ip], #4\n\t"
+ "bics r2, r2, r4\n\t"
+ "tst r2, "magic2(r5)"\n\t"
+ "itt eq\n\t"
+ "ldreq r3, [r1], #4\n\t"
+ "streq r4, [ip], #4\n\t"
+ "beq 2b\n\t"
+ "mov r3, r4\n"
+ "1:\n\t"
+# ifdef __ARMEB__
+ "rors r3, r3, #24\n\t"
+# endif
+ "strb r3, [ip], #1\n\t"
+ "tst r3, #0xff\n\t"
+# ifdef __ARMEL__
+ "ror r3, r3, #8\n\t"
+# endif
+ "bne 1b\n\t"
+ "ldr r4, [sp], #4\n\t"
+# ifndef __thumb2__
+ "ldr r5, [sp], #4\n\t"
+# endif
+ "BX LR\n"
+
+ /* Strings have the same offset from word alignment, but it's
+ not zero. */
+ "3:\n\t"
+ "tst r1, #1\n\t"
+ "beq 1f\n\t"
+ "ldrb r2, [r1], #1\n\t"
+ "strb r2, [ip], #1\n\t"
+ "cmp r2, #0\n\t"
+ "it eq\n"
+ "BXEQ LR\n"
+ "1:\n\t"
+ "tst r1, #2\n\t"
+ "beq 5b\n\t"
+ "ldrh r2, [r1], #2\n\t"
+# ifdef __ARMEB__
+ "tst r2, #0xff00\n\t"
+ "iteet ne\n\t"
+ "strneh r2, [ip], #2\n\t"
+ "lsreq r2, r2, #8\n\t"
+ "streqb r2, [ip]\n\t"
+ "tstne r2, #0xff\n\t"
+# else
+ "tst r2, #0xff\n\t"
+ "itet ne\n\t"
+ "strneh r2, [ip], #2\n\t"
+ "streqb r2, [ip]\n\t"
+ "tstne r2, #0xff00\n\t"
+# endif
+ "bne 5b\n\t"
+ "BX LR\n"
+
+ /* src and dst do not have a common word-alignement. Fall back to
+ byte copying. */
+ "4:\n\t"
+ "ldrb r2, [r1], #1\n\t"
+ "strb r2, [ip], #1\n\t"
+ "cmp r2, #0\n\t"
+ "bne 4b\n\t"
+ "BX LR");
+}
+/* For GLIBC: libc_hidden_builtin_def (strcpy) */
+
+#endif /* defined (__thumb2__) && !defined (__thumb__) */
diff --git a/libc/AOR_v20.02/string/arm/strlen-armv6t2.S b/libc/AOR_v20.02/string/arm/strlen-armv6t2.S
new file mode 100644
index 000000000000..e368e6233614
--- /dev/null
+++ b/libc/AOR_v20.02/string/arm/strlen-armv6t2.S
@@ -0,0 +1,125 @@
+/*
+ * strlen - calculate the length of a string
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if __ARM_ARCH >= 6 && __ARM_ARCH_ISA_THUMB == 2
+
+/*
+ Assumes:
+ ARMv6T2, AArch32
+
+ */
+
+#include "../asmdefs.h"
+
+#ifdef __ARMEB__
+#define S2LO lsl
+#define S2HI lsr
+#else
+#define S2LO lsr
+#define S2HI lsl
+#endif
+
+ /* This code requires Thumb. */
+ .thumb
+ .syntax unified
+
+/* Parameters and result. */
+#define srcin r0
+#define result r0
+
+/* Internal variables. */
+#define src r1
+#define data1a r2
+#define data1b r3
+#define const_m1 r12
+#define const_0 r4
+#define tmp1 r4 /* Overlaps const_0 */
+#define tmp2 r5
+
+ENTRY (__strlen_armv6t2)
+ pld [srcin, #0]
+ strd r4, r5, [sp, #-8]!
+ bic src, srcin, #7
+ mvn const_m1, #0
+ ands tmp1, srcin, #7 /* (8 - bytes) to alignment. */
+ pld [src, #32]
+ bne.w L(misaligned8)
+ mov const_0, #0
+ mov result, #-8
+L(loop_aligned):
+ /* Bytes 0-7. */
+ ldrd data1a, data1b, [src]
+ pld [src, #64]
+ add result, result, #8
+L(start_realigned):
+ uadd8 data1a, data1a, const_m1 /* Saturating GE<0:3> set. */
+ sel data1a, const_0, const_m1 /* Select based on GE<0:3>. */
+ uadd8 data1b, data1b, const_m1
+ sel data1b, data1a, const_m1 /* Only used if d1a == 0. */
+ cbnz data1b, L(null_found)
+
+ /* Bytes 8-15. */
+ ldrd data1a, data1b, [src, #8]
+ uadd8 data1a, data1a, const_m1 /* Saturating GE<0:3> set. */
+ add result, result, #8
+ sel data1a, const_0, const_m1 /* Select based on GE<0:3>. */
+ uadd8 data1b, data1b, const_m1
+ sel data1b, data1a, const_m1 /* Only used if d1a == 0. */
+ cbnz data1b, L(null_found)
+
+ /* Bytes 16-23. */
+ ldrd data1a, data1b, [src, #16]
+ uadd8 data1a, data1a, const_m1 /* Saturating GE<0:3> set. */
+ add result, result, #8
+ sel data1a, const_0, const_m1 /* Select based on GE<0:3>. */
+ uadd8 data1b, data1b, const_m1
+ sel data1b, data1a, const_m1 /* Only used if d1a == 0. */
+ cbnz data1b, L(null_found)
+
+ /* Bytes 24-31. */
+ ldrd data1a, data1b, [src, #24]
+ add src, src, #32
+ uadd8 data1a, data1a, const_m1 /* Saturating GE<0:3> set. */
+ add result, result, #8
+ sel data1a, const_0, const_m1 /* Select based on GE<0:3>. */
+ uadd8 data1b, data1b, const_m1
+ sel data1b, data1a, const_m1 /* Only used if d1a == 0. */
+ cmp data1b, #0
+ beq L(loop_aligned)
+
+L(null_found):
+ cmp data1a, #0
+ itt eq
+ addeq result, result, #4
+ moveq data1a, data1b
+#ifndef __ARMEB__
+ rev data1a, data1a
+#endif
+ clz data1a, data1a
+ ldrd r4, r5, [sp], #8
+ add result, result, data1a, lsr #3 /* Bits -> Bytes. */
+ bx lr
+
+L(misaligned8):
+ ldrd data1a, data1b, [src]
+ and tmp2, tmp1, #3
+ rsb result, tmp1, #0
+ lsl tmp2, tmp2, #3 /* Bytes -> bits. */
+ tst tmp1, #4
+ pld [src, #64]
+ S2HI tmp2, const_m1, tmp2
+ orn data1a, data1a, tmp2
+ itt ne
+ ornne data1b, data1b, tmp2
+ movne data1a, const_m1
+ mov const_0, #0
+ b L(start_realigned)
+
+END (__strlen_armv6t2)
+
+#endif /* __ARM_ARCH >= 6 && __ARM_ARCH_ISA_THUMB == 2 */
diff --git a/libc/AOR_v20.02/string/asmdefs.h b/libc/AOR_v20.02/string/asmdefs.h
new file mode 100644
index 000000000000..dcdd109ca0c0
--- /dev/null
+++ b/libc/AOR_v20.02/string/asmdefs.h
@@ -0,0 +1,32 @@
+/*
+ * Macros for asm code.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#ifndef _ASMDEFS_H
+#define _ASMDEFS_H
+
+#define ENTRY_ALIGN(name, alignment) \
+ .global name; \
+ .type name,%function; \
+ .align alignment; \
+ name: \
+ .cfi_startproc;
+
+#define ENTRY(name) ENTRY_ALIGN(name, 6)
+
+#define ENTRY_ALIAS(name) \
+ .global name; \
+ .type name,%function; \
+ name:
+
+#define END(name) \
+ .cfi_endproc; \
+ .size name, .-name;
+
+#define L(l) .L ## l
+
+#endif
diff --git a/libc/AOR_v20.02/string/include/stringlib.h b/libc/AOR_v20.02/string/include/stringlib.h
new file mode 100644
index 000000000000..252df46cfab3
--- /dev/null
+++ b/libc/AOR_v20.02/string/include/stringlib.h
@@ -0,0 +1,58 @@
+/*
+ * Public API.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stddef.h>
+
+/* restrict is not needed, but kept for documenting the interface contract. */
+#ifndef __restrict
+# define __restrict
+#endif
+
+#if __aarch64__
+void *__memcpy_aarch64 (void *__restrict, const void *__restrict, size_t);
+void *__memmove_aarch64 (void *, const void *, size_t);
+void *__memset_aarch64 (void *, int, size_t);
+void *__memchr_aarch64 (const void *, int, size_t);
+int __memcmp_aarch64 (const void *, const void *, size_t);
+char *__strcpy_aarch64 (char *__restrict, const char *__restrict);
+char *__stpcpy_aarch64 (char *__restrict, const char *__restrict);
+int __strcmp_aarch64 (const char *, const char *);
+char *__strchr_aarch64 (const char *, int);
+char *__strrchr_aarch64 (const char *, int);
+char *__strchrnul_aarch64 (const char *, int );
+size_t __strlen_aarch64 (const char *);
+size_t __strnlen_aarch64 (const char *, size_t);
+int __strncmp_aarch64 (const char *, const char *, size_t);
+char *__strchr_aarch64_mte (const char *, int);
+size_t __strlen_aarch64_mte (const char *);
+#if __ARM_NEON
+void *__memcpy_aarch64_simd (void *__restrict, const void *__restrict, size_t);
+void *__memmove_aarch64_simd (void *, const void *, size_t);
+#endif
+# if __ARM_FEATURE_SVE
+void *__memchr_aarch64_sve (const void *, int, size_t);
+int __memcmp_aarch64_sve (const void *, const void *, size_t);
+char *__strchr_aarch64_sve (const char *, int);
+char *__strrchr_aarch64_sve (const char *, int);
+char *__strchrnul_aarch64_sve (const char *, int );
+int __strcmp_aarch64_sve (const char *, const char *);
+char *__strcpy_aarch64_sve (char *__restrict, const char *__restrict);
+char *__stpcpy_aarch64_sve (char *__restrict, const char *__restrict);
+size_t __strlen_aarch64_sve (const char *);
+size_t __strnlen_aarch64_sve (const char *, size_t);
+int __strncmp_aarch64_sve (const char *, const char *, size_t);
+# endif
+#elif __arm__
+void *__memcpy_arm (void *__restrict, const void *__restrict, size_t);
+void *__memset_arm (void *, int, size_t);
+void *__memchr_arm (const void *, int, size_t);
+char *__strcpy_arm (char *__restrict, const char *__restrict);
+int __strcmp_arm (const char *, const char *);
+int __strcmp_armv6m (const char *, const char *);
+size_t __strlen_armv6t2 (const char *);
+#endif
diff --git a/libc/AOR_v20.02/string/test/memchr.c b/libc/AOR_v20.02/string/test/memchr.c
new file mode 100644
index 000000000000..ee7f2131a458
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/memchr.c
@@ -0,0 +1,94 @@
+/*
+ * memchr test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ void *(*fun)(const void *, int c, size_t n);
+} funtab[] = {
+#define F(x) {#x, x},
+F(memchr)
+#if __aarch64__
+F(__memchr_aarch64)
+# if __ARM_FEATURE_SVE
+F(__memchr_aarch64_sve)
+# endif
+#elif __arm__
+F(__memchr_arm)
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define SP 512
+#define LEN 250000
+static unsigned char sbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int align, int seekpos, int len)
+{
+ unsigned char *src = alignup(sbuf);
+ unsigned char *s = src + align;
+ unsigned char *f = len ? s + seekpos : 0;
+ int seekchar = 0x1;
+ int i;
+ void *p;
+
+ if (len > LEN || seekpos >= len || align >= A)
+ abort();
+
+ for (i = 0; i < seekpos; i++)
+ s[i] = 'a' + i%23;
+ s[i++] = seekchar;
+ for (; i < len; i++)
+ s[i] = 'a' + i%23;
+
+ p = fun->fun(s, seekchar, len);
+
+ if (p != f) {
+ ERR("%s(%p,0x%02x,%d) returned %p\n", fun->name, s, seekchar, len, p);
+ ERR("expected: %p\n", f);
+ abort();
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int a = 0; a < A; a++) {
+ for (int n = 0; n < 100; n++)
+ for (int sp = 0; sp < n-1; sp++)
+ test(funtab+i, a, sp, n);
+ for (int n = 100; n < LEN; n *= 2) {
+ test(funtab+i, a, n-1, n);
+ test(funtab+i, a, n/2, n);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/memcmp.c b/libc/AOR_v20.02/string/test/memcmp.c
new file mode 100644
index 000000000000..ece23bc571b5
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/memcmp.c
@@ -0,0 +1,97 @@
+/*
+ * memcmp test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ int (*fun)(const void *s1, const void *s2, size_t n);
+} funtab[] = {
+#define F(x) {#x, x},
+F(memcmp)
+#if __aarch64__
+F(__memcmp_aarch64)
+# if __ARM_FEATURE_SVE
+F(__memcmp_aarch64_sve)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define LEN 250000
+static unsigned char s1buf[LEN+2*A];
+static unsigned char s2buf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int s1align, int s2align, int len, int
diff pos)
+{
+ unsigned char *src1 = alignup(s1buf);
+ unsigned char *src2 = alignup(s2buf);
+ unsigned char *s1 = src1 + s1align;
+ unsigned char *s2 = src2 + s2align;
+ int r;
+
+ if (len > LEN || s1align >= A || s2align >= A)
+ abort();
+ if (
diff pos &&
diff pos >= len)
+ abort();
+
+ for (int i = 0; i < len+A; i++)
+ src1[i] = src2[i] = '?';
+ for (int i = 0; i < len; i++)
+ s1[i] = s2[i] = 'a' + i%23;
+ if (
diff pos)
+ s1[
diff pos]++;
+
+ r = fun->fun(s1, s2, len);
+
+ if ((!
diff pos && r != 0) || (
diff pos && r == 0)) {
+ ERR("%s(align %d, align %d, %d) failed, returned %d\n",
+ fun->name, s1align, s2align, len, r);
+ ERR("src1: %.*s\n", s1align+len+1, src1);
+ ERR("src2: %.*s\n", s2align+len+1, src2);
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int d = 0; d < A; d++)
+ for (int s = 0; s < A; s++) {
+ int n;
+ for (n = 0; n < 100; n++) {
+ test(funtab+i, d, s, n, 0);
+ test(funtab+i, d, s, n, n / 2);
+ }
+ for (; n < LEN; n *= 2) {
+ test(funtab+i, d, s, n, 0);
+ test(funtab+i, d, s, n, n / 2);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/memcpy.c b/libc/AOR_v20.02/string/test/memcpy.c
new file mode 100644
index 000000000000..62823af331ee
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/memcpy.c
@@ -0,0 +1,99 @@
+/*
+ * memcpy test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ void *(*fun)(void *, const void *, size_t);
+} funtab[] = {
+#define F(x) {#x, x},
+F(memcpy)
+#if __aarch64__
+F(__memcpy_aarch64)
+# if __ARM_NEON
+F(__memcpy_aarch64_simd)
+# endif
+#elif __arm__
+F(__memcpy_arm)
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define LEN 250000
+static unsigned char dbuf[LEN+2*A];
+static unsigned char sbuf[LEN+2*A];
+static unsigned char wbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int dalign, int salign, int len)
+{
+ unsigned char *src = alignup(sbuf);
+ unsigned char *dst = alignup(dbuf);
+ unsigned char *want = wbuf;
+ unsigned char *s = src + salign;
+ unsigned char *d = dst + dalign;
+ unsigned char *w = want + dalign;
+ void *p;
+ int i;
+
+ if (len > LEN || dalign >= A || salign >= A)
+ abort();
+ for (i = 0; i < len+A; i++) {
+ src[i] = '?';
+ want[i] = dst[i] = '*';
+ }
+ for (i = 0; i < len; i++)
+ s[i] = w[i] = 'a' + i%23;
+
+ p = fun->fun(d, s, len);
+ if (p != d)
+ ERR("%s(%p,..) returned %p\n", fun->name, d, p);
+ for (i = 0; i < len+A; i++) {
+ if (dst[i] != want[i]) {
+ ERR("%s(align %d, align %d, %d) failed\n", fun->name, dalign, salign, len);
+ ERR("got : %.*s\n", dalign+len+1, dst);
+ ERR("want: %.*s\n", dalign+len+1, want);
+ break;
+ }
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int d = 0; d < A; d++)
+ for (int s = 0; s < A; s++) {
+ int n;
+ for (n = 0; n < 100; n++)
+ test(funtab+i, d, s, n);
+ for (; n < LEN; n *= 2)
+ test(funtab+i, d, s, n);
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/memmove.c b/libc/AOR_v20.02/string/test/memmove.c
new file mode 100644
index 000000000000..6bb9eee1c3d9
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/memmove.c
@@ -0,0 +1,145 @@
+/*
+ * memmove test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ void *(*fun)(void *, const void *, size_t);
+} funtab[] = {
+#define F(x) {#x, x},
+F(memmove)
+#if __aarch64__
+F(__memmove_aarch64)
+# if __ARM_NEON
+F(__memmove_aarch64_simd)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define LEN 250000
+static unsigned char dbuf[LEN+2*A];
+static unsigned char sbuf[LEN+2*A];
+static unsigned char wbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int dalign, int salign, int len)
+{
+ unsigned char *src = alignup(sbuf);
+ unsigned char *dst = alignup(dbuf);
+ unsigned char *want = wbuf;
+ unsigned char *s = src + salign;
+ unsigned char *d = dst + dalign;
+ unsigned char *w = want + dalign;
+ void *p;
+ int i;
+
+ if (len > LEN || dalign >= A || salign >= A)
+ abort();
+ for (i = 0; i < len+A; i++) {
+ src[i] = '?';
+ want[i] = dst[i] = '*';
+ }
+ for (i = 0; i < len; i++)
+ s[i] = w[i] = 'a' + i%23;
+
+ p = fun->fun(d, s, len);
+ if (p != d)
+ ERR("%s(%p,..) returned %p\n", fun->name, d, p);
+ for (i = 0; i < len+A; i++) {
+ if (dst[i] != want[i]) {
+ ERR("%s(align %d, align %d, %d) failed\n", fun->name, dalign, salign, len);
+ ERR("got : %.*s\n", dalign+len+1, dst);
+ ERR("want: %.*s\n", dalign+len+1, want);
+ break;
+ }
+ }
+}
+
+static void test_overlap(const struct fun *fun, int dalign, int salign, int len)
+{
+ unsigned char *src = alignup(sbuf);
+ unsigned char *dst = alignup(sbuf);
+ unsigned char *want = wbuf;
+ unsigned char *s = src + salign;
+ unsigned char *d = dst + dalign;
+ unsigned char *w = wbuf + dalign;
+ void *p;
+
+ if (len > LEN || dalign >= A || salign >= A)
+ abort();
+
+ for (int i = 0; i < len+A; i++)
+ src[i] = want[i] = '?';
+
+ for (int i = 0; i < len; i++)
+ s[i] = w[i] = 'a' + i%23;
+
+ /* Copy the potential overlap range. */
+ if (s < d) {
+ for (int i = 0; i < (uintptr_t)d-(uintptr_t)s; i++)
+ want[salign+i] = src[salign+i];
+ } else {
+ for (int i = 0; i < (uintptr_t)s-(uintptr_t)d; i++)
+ want[len + dalign + i] = src[len + dalign + i];
+ }
+
+ p = fun->fun(d, s, len);
+ if (p != d)
+ ERR("%s(%p,..) returned %p\n", fun->name, d, p);
+ for (int i = 0; i < len+A; i++) {
+ if (dst[i] != want[i]) {
+ ERR("%s(align %d, align %d, %d) failed\n", fun->name, dalign, salign, len);
+ ERR("got : %.*s\n", dalign+len+1, dst);
+ ERR("want: %.*s\n", dalign+len+1, want);
+ abort();
+ break;
+ }
+ }
+}
+
+int main()
+{
+ test_overlap(funtab+0, 2, 1, 1);
+
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int d = 0; d < A; d++)
+ for (int s = 0; s < A; s++) {
+ int n;
+ for (n = 0; n < 100; n++) {
+ test(funtab+i, d, s, n);
+ test_overlap(funtab+i, d, s, n);
+ }
+ for (; n < LEN; n *= 2) {
+ test(funtab+i, d, s, n);
+ test_overlap(funtab+i, d, s, n);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/memset.c b/libc/AOR_v20.02/string/test/memset.c
new file mode 100644
index 000000000000..b977ceeb3102
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/memset.c
@@ -0,0 +1,112 @@
+/*
+ * memset test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ void *(*fun)(void *s, int c, size_t n);
+} funtab[] = {
+#define F(x) {#x, x},
+F(memset)
+#if __aarch64__
+F(__memset_aarch64)
+#elif __arm__
+F(__memset_arm)
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define LEN 250000
+static unsigned char sbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void err(const char *name, unsigned char *src, int salign, int c, int len)
+{
+ ERR("%s(align %d, %d, %d) failed\n", name, salign, c, len);
+ ERR("got : %.*s\n", salign+len+1, src);
+}
+
+static void test(const struct fun *fun, int salign, int c, int len)
+{
+ unsigned char *src = alignup(sbuf);
+ unsigned char *s = src + salign;
+ void *p;
+ int i;
+
+ if (len > LEN || salign >= A)
+ abort();
+ for (i = 0; i < len+A; i++)
+ src[i] = '?';
+ for (i = 0; i < len; i++)
+ s[i] = 'a' + i%23;
+ for (; i<len%A; i++)
+ s[i] = '*';
+
+ p = fun->fun(s, c, len);
+ if (p != s)
+ ERR("%s(%p,..) returned %p\n", fun->name, s, p);
+
+ for (i = 0; i < salign; i++) {
+ if (src[i] != '?') {
+ err(fun->name, src, salign, c, len);
+ return;
+ }
+ }
+ for (i = salign; i < len; i++) {
+ if (src[i] != (unsigned char)c) {
+ err(fun->name, src, salign, c, len);
+ return;
+ }
+ }
+ for (; i < len%A; i++) {
+ if (src[i] != '*') {
+ err(fun->name, src, salign, c, len);
+ return;
+ }
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int s = 0; s < A; s++) {
+ int n;
+ for (n = 0; n < 100; n++) {
+ test(funtab+i, s, 0, n);
+ test(funtab+i, s, 0x25, n);
+ test(funtab+i, s, 0xaa25, n);
+ }
+ for (; n < LEN; n *= 2) {
+ test(funtab+i, s, 0, n);
+ test(funtab+i, s, 0x25, n);
+ test(funtab+i, s, 0xaa25, n);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/stpcpy.c b/libc/AOR_v20.02/string/test/stpcpy.c
new file mode 100644
index 000000000000..eea9be1cac6c
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/stpcpy.c
@@ -0,0 +1,99 @@
+/*
+ * stpcpy test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#define _GNU_SOURCE
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ char *(*fun)(char *dest, const char *src);
+} funtab[] = {
+#define F(x) {#x, x},
+F(stpcpy)
+#if __aarch64__
+F(__stpcpy_aarch64)
+# if __ARM_FEATURE_SVE
+F(__stpcpy_aarch64_sve)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define LEN 250000
+static char dbuf[LEN+2*A];
+static char sbuf[LEN+2*A];
+static char wbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int dalign, int salign, int len)
+{
+ char *src = alignup(sbuf);
+ char *dst = alignup(dbuf);
+ char *want = wbuf;
+ char *s = src + salign;
+ char *d = dst + dalign;
+ char *w = want + dalign;
+ void *p;
+ int i;
+
+ if (len > LEN || dalign >= A || salign >= A)
+ abort();
+ for (i = 0; i < len+A; i++) {
+ src[i] = '?';
+ want[i] = dst[i] = '*';
+ }
+ for (i = 0; i < len; i++)
+ s[i] = w[i] = 'a' + i%23;
+ s[i] = w[i] = '\0';
+
+ p = fun->fun(d, s);
+ if (p != d + len)
+ ERR("%s(%p,..) returned %p\n", fun->name, d, p);
+ for (i = 0; i < len+A; i++) {
+ if (dst[i] != want[i]) {
+ ERR("%s(align %d, align %d, %d) failed\n", fun->name, dalign, salign, len);
+ ERR("got : %.*s\n", dalign+len+1, dst);
+ ERR("want: %.*s\n", dalign+len+1, want);
+ break;
+ }
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int d = 0; d < A; d++)
+ for (int s = 0; s < A; s++) {
+ int n;
+ for (n = 0; n < 100; n++)
+ test(funtab+i, d, s, n);
+ for (; n < LEN; n *= 2)
+ test(funtab+i, d, s, n);
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/strchr.c b/libc/AOR_v20.02/string/test/strchr.c
new file mode 100644
index 000000000000..6076e0380955
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/strchr.c
@@ -0,0 +1,99 @@
+/*
+ * strchr test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ char *(*fun)(const char *s, int c);
+} funtab[] = {
+#define F(x) {#x, x},
+F(strchr)
+#if __aarch64__
+F(__strchr_aarch64)
+F(__strchr_aarch64_mte)
+# if __ARM_FEATURE_SVE
+F(__strchr_aarch64_sve)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define SP 512
+#define LEN 250000
+static char sbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int align, int seekpos, int len)
+{
+ char *src = alignup(sbuf);
+ char *s = src + align;
+ char *f = seekpos != -1 ? s + seekpos : 0;
+ int seekchar = 0x1;
+ void *p;
+
+ if (len > LEN || seekpos >= len - 1 || align >= A)
+ abort();
+ if (seekchar >= 'a' && seekchar <= 'a' + 23)
+ abort();
+
+ for (int i = 0; i < len + A; i++)
+ src[i] = '?';
+ for (int i = 0; i < len - 2; i++)
+ s[i] = 'a' + i%23;
+ if (seekpos != -1)
+ s[seekpos] = seekchar;
+ s[len - 1] = '\0';
+
+ p = fun->fun(s, seekchar);
+
+ if (p != f) {
+ ERR("%s(%p,0x%02x,%d) returned %p\n", fun->name, s, seekchar, len, p);
+ ERR("expected: %p\n", f);
+ abort();
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int a = 0; a < A; a++) {
+ int n;
+ for (n = 1; n < 100; n++) {
+ for (int sp = 0; sp < n - 1; sp++)
+ test(funtab+i, a, sp, n);
+ test(funtab+i, a, -1, n);
+ }
+ for (; n < LEN; n *= 2) {
+ test(funtab+i, a, -1, n);
+ test(funtab+i, a, n / 2, n);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/strchrnul.c b/libc/AOR_v20.02/string/test/strchrnul.c
new file mode 100644
index 000000000000..6be1ec6f1dc0
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/strchrnul.c
@@ -0,0 +1,100 @@
+/*
+ * strchrnul test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#define _GNU_SOURCE
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ char *(*fun)(const char *s, int c);
+} funtab[] = {
+#define F(x) {#x, x},
+F(strchrnul)
+#if __aarch64__
+F(__strchrnul_aarch64)
+# if __ARM_FEATURE_SVE
+F(__strchrnul_aarch64_sve)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define SP 512
+#define LEN 250000
+static char sbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int align, int seekpos, int len)
+{
+ char *src = alignup(sbuf);
+ char *s = src + align;
+ char *f = seekpos != -1 ? s + seekpos : s + len - 1;
+ int seekchar = 0x1;
+ void *p;
+
+ if (len > LEN || seekpos >= len - 1 || align >= A)
+ abort();
+ if (seekchar >= 'a' && seekchar <= 'a' + 23)
+ abort();
+
+ for (int i = 0; i < len + A; i++)
+ src[i] = '?';
+ for (int i = 0; i < len - 2; i++)
+ s[i] = 'a' + i%23;
+ if (seekpos != -1)
+ s[seekpos] = seekchar;
+ s[len - 1] = '\0';
+
+ p = fun->fun(s, seekchar);
+
+ if (p != f) {
+ ERR("%s(%p,0x%02x,%d) returned %p\n", fun->name, s, seekchar, len, p);
+ ERR("expected: %p\n", f);
+ abort();
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int a = 0; a < A; a++) {
+ int n;
+ for (n = 1; n < 100; n++) {
+ for (int sp = 0; sp < n - 1; sp++)
+ test(funtab+i, a, sp, n);
+ test(funtab+i, a, -1, n);
+ }
+ for (; n < LEN; n *= 2) {
+ test(funtab+i, a, -1, n);
+ test(funtab+i, a, n / 2, n);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/strcmp.c b/libc/AOR_v20.02/string/test/strcmp.c
new file mode 100644
index 000000000000..40aa6fdf6cdd
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/strcmp.c
@@ -0,0 +1,104 @@
+/*
+ * strcmp test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ int (*fun)(const char *s1, const char *s2);
+} funtab[] = {
+#define F(x) {#x, x},
+F(strcmp)
+#if __aarch64__
+F(__strcmp_aarch64)
+# if __ARM_FEATURE_SVE
+F(__strcmp_aarch64_sve)
+# endif
+#elif __arm__
+# if __ARM_ARCH >= 7 && __ARM_ARCH_ISA_ARM >= 1
+F(__strcmp_arm)
+# elif __ARM_ARCH == 6 && __ARM_ARCH_6M__ >= 1
+F(__strcmp_armv6m)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define LEN 250000
+static char s1buf[LEN+2*A];
+static char s2buf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int s1align, int s2align, int len, int
diff pos)
+{
+ char *src1 = alignup(s1buf);
+ char *src2 = alignup(s2buf);
+ char *s1 = src1 + s1align;
+ char *s2 = src2 + s2align;
+ int r;
+
+ if (len > LEN || s1align >= A || s2align >= A)
+ abort();
+ if (
diff pos > 1 &&
diff pos >= len-1)
+ abort();
+
+ for (int i = 0; i < len+A; i++)
+ src1[i] = src2[i] = '?';
+ for (int i = 0; i < len-1; i++)
+ s1[i] = s2[i] = 'a' + i%23;
+ if (
diff pos > 1)
+ s1[
diff pos]++;
+ s1[len] = s2[len] = '\0';
+
+ r = fun->fun(s1, s2);
+
+ if (((
diff pos <= 1) && r != 0) || (
diff pos > 1 && r == 0)) {
+ ERR("%s(align %d, align %d, %d) failed, returned %d\n",
+ fun->name, s1align, s2align, len, r);
+ ERR("src1: %.*s\n", s1align+len+1, src1);
+ ERR("src2: %.*s\n", s2align+len+1, src2);
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int d = 0; d < A; d++)
+ for (int s = 0; s < A; s++) {
+ int n;
+ for (n = 0; n < 100; n++) {
+ test(funtab+i, d, s, n, 0);
+ test(funtab+i, d, s, n, n / 2);
+ }
+ for (; n < LEN; n *= 2) {
+ test(funtab+i, d, s, n, 0);
+ test(funtab+i, d, s, n, n / 2);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/strcpy.c b/libc/AOR_v20.02/string/test/strcpy.c
new file mode 100644
index 000000000000..d00fbefd792d
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/strcpy.c
@@ -0,0 +1,100 @@
+/*
+ * strcpy test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ char *(*fun)(char *dest, const char *src);
+} funtab[] = {
+#define F(x) {#x, x},
+F(strcpy)
+#if __aarch64__
+F(__strcpy_aarch64)
+# if __ARM_FEATURE_SVE
+F(__strcpy_aarch64_sve)
+# endif
+#elif __arm__ && defined (__thumb2__) && !defined (__thumb__)
+F(__strcpy_arm)
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define LEN 250000
+static char dbuf[LEN+2*A];
+static char sbuf[LEN+2*A];
+static char wbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int dalign, int salign, int len)
+{
+ char *src = alignup(sbuf);
+ char *dst = alignup(dbuf);
+ char *want = wbuf;
+ char *s = src + salign;
+ char *d = dst + dalign;
+ char *w = want + dalign;
+ void *p;
+ int i;
+
+ if (len > LEN || dalign >= A || salign >= A)
+ abort();
+ for (i = 0; i < len+A; i++) {
+ src[i] = '?';
+ want[i] = dst[i] = '*';
+ }
+ for (i = 0; i < len; i++)
+ s[i] = w[i] = 'a' + i%23;
+ s[i] = w[i] = '\0';
+
+ p = fun->fun(d, s);
+ if (p != d)
+ ERR("%s(%p,..) returned %p\n", fun->name, d, p);
+ for (i = 0; i < len+A; i++) {
+ if (dst[i] != want[i]) {
+ ERR("%s(align %d, align %d, %d) failed\n", fun->name, dalign, salign, len);
+ ERR("got : %.*s\n", dalign+len+1, dst);
+ ERR("want: %.*s\n", dalign+len+1, want);
+ break;
+ }
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int d = 0; d < A; d++)
+ for (int s = 0; s < A; s++) {
+ int n;
+ for (n = 0; n < 100; n++)
+ test(funtab+i, d, s, n);
+ for (; n < LEN; n *= 2)
+ test(funtab+i, d, s, n);
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/strlen.c b/libc/AOR_v20.02/string/test/strlen.c
new file mode 100644
index 000000000000..16a9176495c5
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/strlen.c
@@ -0,0 +1,92 @@
+/*
+ * strlen test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ size_t (*fun)(const char *s);
+} funtab[] = {
+#define F(x) {#x, x},
+F(strlen)
+#if __aarch64__
+F(__strlen_aarch64)
+F(__strlen_aarch64_mte)
+# if __ARM_FEATURE_SVE
+F(__strlen_aarch64_sve)
+# endif
+#elif __arm__
+# if __ARM_ARCH >= 6 && __ARM_ARCH_ISA_THUMB == 2
+F(__strlen_armv6t2)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define SP 512
+#define LEN 250000
+static char sbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int align, int len)
+{
+ char *src = alignup(sbuf);
+ char *s = src + align;
+ size_t r;
+
+ if (len > LEN || align >= A)
+ abort();
+
+ for (int i = 0; i < len + A; i++)
+ src[i] = '?';
+ for (int i = 0; i < len - 2; i++)
+ s[i] = 'a' + i%23;
+ s[len - 1] = '\0';
+
+ r = fun->fun(s);
+ if (r != len-1) {
+ ERR("%s(%p) returned %zu\n", fun->name, s, r);
+ ERR("input: %.*s\n", align+len+1, src);
+ ERR("expected: %d\n", len);
+ abort();
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int a = 0; a < A; a++) {
+ int n;
+ for (n = 1; n < 100; n++)
+ test(funtab+i, a, n);
+ for (; n < LEN; n *= 2)
+ test(funtab+i, a, n);
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/strncmp.c b/libc/AOR_v20.02/string/test/strncmp.c
new file mode 100644
index 000000000000..db2ef264aca1
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/strncmp.c
@@ -0,0 +1,104 @@
+/*
+ * strncmp test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ int (*fun)(const char *, const char *, size_t);
+} funtab[] = {
+#define F(x) {#x, x},
+F(strncmp)
+#if __aarch64__
+F(__strncmp_aarch64)
+# if __ARM_FEATURE_SVE
+F(__strncmp_aarch64_sve)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define LEN 250000
+static char s1buf[LEN+2*A];
+static char s2buf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int s1align, int s2align, int maxlen, int
diff pos, int len)
+{
+ char *src1 = alignup(s1buf);
+ char *src2 = alignup(s2buf);
+ char *s1 = src1 + s1align;
+ char *s2 = src2 + s2align;
+ int r;
+
+ if (len > LEN || s1align >= A || s2align >= A)
+ abort();
+ if (
diff pos > 1 &&
diff pos >= len-1)
+ abort();
+
+ for (int i = 0; i < len+A; i++)
+ src1[i] = src2[i] = '?';
+ for (int i = 0; i < len-1; i++)
+ s1[i] = s2[i] = 'a' + i%23;
+ if (
diff pos > 1)
+ s1[
diff pos]++;
+ s1[len] = s2[len] = '\0';
+
+ r = fun->fun(s1, s2, maxlen);
+
+
diff pos = maxlen <=
diff pos ? 0 :
diff pos;
+
+ if (((
diff pos <= 1) && r != 0) || (
diff pos > 1 && r == 0)) {
+ ERR("%s(align %d, align %d, %d (%d)) failed, returned %d (%d)\n",
+ fun->name, s1align, s2align, maxlen, len, r,
diff pos);
+ ERR("src1: %.*s\n", s1align+len+1, src1);
+ ERR("src2: %.*s\n", s2align+len+1, src2);
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int d = 0; d < A; d++)
+ for (int s = 0; s < A; s++) {
+ int n;
+ for (n = 0; n < 100; n++) {
+ test(funtab+i, d, s, n, 0, n);
+ test(funtab+i, d, s, n, n/2, n);
+ test(funtab+i, d, s, n/2, 0, n);
+ test(funtab+i, d, s, n/2, n/2, n);
+ }
+ for (; n < LEN; n *= 2) {
+ test(funtab+i, d, s, n, 0, n);
+ test(funtab+i, d, s, n, n/2, n);
+ test(funtab+i, d, s, n/2, 0, n);
+ test(funtab+i, d, s, n/2, n/2, n);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/strnlen.c b/libc/AOR_v20.02/string/test/strnlen.c
new file mode 100644
index 000000000000..d71272f16db2
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/strnlen.c
@@ -0,0 +1,94 @@
+/*
+ * strnlen test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#define _POSIX_C_SOURCE 200809L
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ size_t (*fun)(const char *s, size_t m);
+} funtab[] = {
+#define F(x) {#x, x},
+F(strnlen)
+#if __aarch64__
+F(__strnlen_aarch64)
+# if __ARM_FEATURE_SVE
+F(__strnlen_aarch64_sve)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define SP 512
+#define LEN 250000
+static char sbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int align, int maxlen, int len)
+{
+ char *src = alignup(sbuf);
+ char *s = src + align;
+ size_t r;
+ size_t e = maxlen < len ? maxlen : len - 1;
+
+ if (len > LEN || align >= A)
+ abort();
+
+ for (int i = 0; i < len + A; i++)
+ src[i] = '?';
+ for (int i = 0; i < len - 2; i++)
+ s[i] = 'a' + i%23;
+ s[len - 1] = '\0';
+
+ r = fun->fun(s, maxlen);
+ if (r != e) {
+ ERR("%s(%p) returned %zu\n", fun->name, s, r);
+ ERR("input: %.*s\n", align+len+1, src);
+ ERR("expected: %d\n", len);
+ abort();
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int a = 0; a < A; a++) {
+ int n;
+ for (n = 1; n < 100; n++)
+ for (int maxlen = 0; maxlen < 100; maxlen++)
+ test(funtab+i, a, maxlen, n);
+ for (; n < LEN; n *= 2) {
+ test(funtab+i, a, n*2, n);
+ test(funtab+i, a, n, n);
+ test(funtab+i, a, n/2, n);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/test/strrchr.c b/libc/AOR_v20.02/string/test/strrchr.c
new file mode 100644
index 000000000000..b2c3c873fcb6
--- /dev/null
+++ b/libc/AOR_v20.02/string/test/strrchr.c
@@ -0,0 +1,98 @@
+/*
+ * strrchr test.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include "stringlib.h"
+
+static const struct fun
+{
+ const char *name;
+ char *(*fun)(const char *s, int c);
+} funtab[] = {
+#define F(x) {#x, x},
+F(strrchr)
+#if __aarch64__
+F(__strrchr_aarch64)
+# if __ARM_FEATURE_SVE
+F(__strrchr_aarch64_sve)
+# endif
+#endif
+#undef F
+ {0, 0}
+};
+
+static int test_status;
+#define ERR(...) (test_status=1, printf(__VA_ARGS__))
+
+#define A 32
+#define SP 512
+#define LEN 250000
+static char sbuf[LEN+2*A];
+
+static void *alignup(void *p)
+{
+ return (void*)(((uintptr_t)p + A-1) & -A);
+}
+
+static void test(const struct fun *fun, int align, int seekpos, int len)
+{
+ char *src = alignup(sbuf);
+ char *s = src + align;
+ char *f = seekpos != -1 ? s + seekpos : 0;
+ int seekchar = 0x1;
+ void *p;
+
+ if (len > LEN || seekpos >= len - 1 || align >= A)
+ abort();
+ if (seekchar >= 'a' && seekchar <= 'a' + 23)
+ abort();
+
+ for (int i = 0; i < len + A; i++)
+ src[i] = '?';
+ for (int i = 0; i < len - 2; i++)
+ s[i] = 'a' + i%23;
+ if (seekpos != -1)
+ s[seekpos/2] = s[seekpos] = seekchar;
+ s[len - 1] = '\0';
+
+ p = fun->fun(s, seekchar);
+
+ if (p != f) {
+ ERR("%s(%p,0x%02x,%d) returned %p\n", fun->name, s, seekchar, len, p);
+ ERR("expected: %p\n", f);
+ abort();
+ }
+}
+
+int main()
+{
+ int r = 0;
+ for (int i=0; funtab[i].name; i++) {
+ test_status = 0;
+ for (int a = 0; a < A; a++) {
+ int n;
+ for (n = 1; n < 100; n++) {
+ for (int sp = 0; sp < n - 1; sp++)
+ test(funtab+i, a, sp, n);
+ test(funtab+i, a, -1, n);
+ }
+ for (; n < LEN; n *= 2) {
+ test(funtab+i, a, -1, n);
+ test(funtab+i, a, n / 2, n);
+ }
+ }
+ printf("%s %s\n", test_status ? "FAIL" : "PASS", funtab[i].name);
+ if (test_status)
+ r = -1;
+ }
+ return r;
+}
diff --git a/libc/AOR_v20.02/string/x86_64/check-arch.S b/libc/AOR_v20.02/string/x86_64/check-arch.S
new file mode 100644
index 000000000000..8c29aa5a7b3f
--- /dev/null
+++ b/libc/AOR_v20.02/string/x86_64/check-arch.S
@@ -0,0 +1,11 @@
+/*
+ * check ARCH setting.
+ *
+ * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+ * See https://llvm.org/LICENSE.txt for license information.
+ * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+ */
+
+#if !__x86_64__
+# error ARCH setting does not match the compiler.
+#endif
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