[libc-commits] [libc] [libc][math] Implement powf function correctly rounded to all rounding modes. (PR #71188)
via libc-commits
libc-commits at lists.llvm.org
Mon Nov 6 09:27:24 PST 2023
https://github.com/lntue updated https://github.com/llvm/llvm-project/pull/71188
>From d8f84ec8850c8c1ff710be542e23ac85eef67fce Mon Sep 17 00:00:00 2001
From: Tue Ly <lntue.h at gmail.com>
Date: Fri, 3 Nov 2023 14:17:00 +0000
Subject: [PATCH 1/3] [libc][math] Implement powf function correctly rounded to
all rounding modes.
---
libc/config/darwin/arm/entrypoints.txt | 1 +
libc/config/linux/aarch64/entrypoints.txt | 1 +
libc/config/linux/riscv/entrypoints.txt | 1 +
libc/config/linux/x86_64/entrypoints.txt | 1 +
libc/config/windows/entrypoints.txt | 1 +
libc/docs/math/index.rst | 3 +-
libc/spec/stdc.td | 1 +
libc/src/math/generic/CMakeLists.txt | 30 +
libc/src/math/generic/common_constants.cpp | 87 +++
libc/src/math/generic/common_constants.h | 5 +
libc/src/math/generic/log2f.cpp | 46 --
libc/src/math/generic/powf.cpp | 840 +++++++++++++++++++++
libc/test/UnitTest/FPMatcher.h | 7 +
libc/test/src/math/CMakeLists.txt | 13 +
libc/test/src/math/powf_test.cpp | 123 +++
libc/test/src/math/smoke/CMakeLists.txt | 12 +
libc/test/src/math/smoke/powf_test.cpp | 189 +++++
libc/utils/MPFRWrapper/MPFRUtils.cpp | 8 +
libc/utils/MPFRWrapper/MPFRUtils.h | 1 +
19 files changed, 1323 insertions(+), 47 deletions(-)
create mode 100644 libc/src/math/generic/powf.cpp
create mode 100644 libc/test/src/math/powf_test.cpp
create mode 100644 libc/test/src/math/smoke/powf_test.cpp
diff --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt
index ecdd2d0624fcf5d..362138c92a6869f 100644
--- a/libc/config/darwin/arm/entrypoints.txt
+++ b/libc/config/darwin/arm/entrypoints.txt
@@ -199,6 +199,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 52e9e8036a3fae3..096e2afb06e5a9d 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -316,6 +316,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
index 52ca12121812d12..7dadbc7f8285477 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/libc/config/linux/riscv/entrypoints.txt
@@ -325,6 +325,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index ab105e1d6344725..31ea282edb59126 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -329,6 +329,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt
index 1ee088e399438b7..5611b399e8bca8b 100644
--- a/libc/config/windows/entrypoints.txt
+++ b/libc/config/windows/entrypoints.txt
@@ -198,6 +198,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
index 77b3c8b99a0c2bc..7c83691c0d9c801 100644
--- a/libc/docs/math/index.rst
+++ b/libc/docs/math/index.rst
@@ -420,7 +420,7 @@ Higher Math Functions
+------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
| pow | | | | | | | | | | | | |
+------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
-| powf | | | | | | | | | | | | |
+| powf | |check| | |check| | | |check| | |check| | | | |check| | | | | |
+------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
| powl | | | | | | | | | | | | |
+------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
@@ -493,6 +493,7 @@ log |check| |check|
log10 |check| |check|
log1p |check| |check|
log2 |check| |check|
+pow |check|
sin |check| large
sincos |check| large
sinh |check|
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
index 1e9043b841ff1d8..239d8f9843cfc0f 100644
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -491,6 +491,7 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"nextafter", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
FunctionSpec<"nextafterl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoubleType>]>,
+ FunctionSpec<"powf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
FunctionSpec<"pow", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
FunctionSpec<"coshf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 843349ccdc196a7..8fc2b0850fbc077 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -747,6 +747,36 @@ add_entrypoint_object(
-O3
)
+add_entrypoint_object(
+ powf
+ SRCS
+ powf.cpp
+ HDRS
+ ../powf.h
+ DEPENDS
+ .common_constants
+ .explogxf
+ .exp2f
+ .exp10f
+ libc.src.__support.builtin_wrappers
+ libc.src.__support.CPP.bit
+ libc.src.__support.CPP.optional
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.nearest_integer
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.rounding_mode
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.FPUtil.triple_double
+ libc.src.__support.macros.optimization
+ libc.include.errno
+ libc.src.errno.errno
+ libc.include.math
+ COMPILE_OPTIONS
+ -O3
+)
+
add_entrypoint_object(
copysign
SRCS
diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp
index 737d2ab77121adb..1a23d00297105f7 100644
--- a/libc/src/math/generic/common_constants.cpp
+++ b/libc/src/math/generic/common_constants.cpp
@@ -227,6 +227,51 @@ alignas(64) const double LOG_R[128] = {
0x1.5707a26bb8c66p-1, 0x1.5af405c3649ep-1, 0x1.5af405c3649ep-1,
0x1.5ee82aa24192p-1, 0x0.000000000000p0};
+alignas(64) const double LOG2_R[128] = {
+ 0x0.0000000000000p+0, 0x1.72c7ba20f7327p-7, 0x1.743ee861f3556p-6,
+ 0x1.184b8e4c56af8p-5, 0x1.77394c9d958d5p-5, 0x1.d6ebd1f1febfep-5,
+ 0x1.1bb32a600549dp-4, 0x1.4c560fe68af88p-4, 0x1.7d60496cfbb4cp-4,
+ 0x1.960caf9abb7cap-4, 0x1.c7b528b70f1c5p-4, 0x1.f9c95dc1d1165p-4,
+ 0x1.097e38ce60649p-3, 0x1.22dadc2ab3497p-3, 0x1.3c6fb650cde51p-3,
+ 0x1.494f863b8df35p-3, 0x1.633a8bf437ce1p-3, 0x1.7046031c79f85p-3,
+ 0x1.8a8980abfbd32p-3, 0x1.97c1cb13c7ec1p-3, 0x1.b2602497d5346p-3,
+ 0x1.bfc67a7fff4ccp-3, 0x1.dac22d3e441d3p-3, 0x1.e857d3d361368p-3,
+ 0x1.01d9bbcfa61d4p-2, 0x1.08bce0d95fa38p-2, 0x1.169c05363f158p-2,
+ 0x1.1d982c9d52708p-2, 0x1.249cd2b13cd6cp-2, 0x1.32bfee370ee68p-2,
+ 0x1.39de8e1559f6fp-2, 0x1.4106017c3eca3p-2, 0x1.4f6fbb2cec598p-2,
+ 0x1.56b22e6b578e5p-2, 0x1.5dfdcf1eeae0ep-2, 0x1.6552b49986277p-2,
+ 0x1.6cb0f6865c8eap-2, 0x1.7b89f02cf2aadp-2, 0x1.8304d90c11fd3p-2,
+ 0x1.8a8980abfbd32p-2, 0x1.921800924dd3bp-2, 0x1.99b072a96c6b2p-2,
+ 0x1.a8ff971810a5ep-2, 0x1.b0b67f4f4681p-2, 0x1.b877c57b1b07p-2,
+ 0x1.c043859e2fdb3p-2, 0x1.c819dc2d45fe4p-2, 0x1.cffae611ad12bp-2,
+ 0x1.d7e6c0abc3579p-2, 0x1.dfdd89d586e2bp-2, 0x1.e7df5fe538ab3p-2,
+ 0x1.efec61b011f85p-2, 0x1.f804ae8d0cd02p-2, 0x1.0014332be0033p-1,
+ 0x1.042bd4b9a7c99p-1, 0x1.08494c66b8efp-1, 0x1.0c6caaf0c5597p-1,
+ 0x1.1096015dee4dap-1, 0x1.14c560fe68af9p-1, 0x1.18fadb6e2d3c2p-1,
+ 0x1.1d368296b5255p-1, 0x1.217868b0c37e8p-1, 0x1.25c0a0463bebp-1,
+ 0x1.2a0f3c340705cp-1, 0x1.2e644fac04fd8p-1, 0x1.2e644fac04fd8p-1,
+ 0x1.32bfee370ee68p-1, 0x1.37222bb70747cp-1, 0x1.3b8b1c68fa6edp-1,
+ 0x1.3ffad4e74f1d6p-1, 0x1.44716a2c08262p-1, 0x1.44716a2c08262p-1,
+ 0x1.48eef19317991p-1, 0x1.4d7380dcc422dp-1, 0x1.51ff2e30214bcp-1,
+ 0x1.5692101d9b4a6p-1, 0x1.5b2c3da19723bp-1, 0x1.5b2c3da19723bp-1,
+ 0x1.5fcdce2727ddbp-1, 0x1.6476d98ad990ap-1, 0x1.6927781d932a8p-1,
+ 0x1.6927781d932a8p-1, 0x1.6ddfc2a78fc63p-1, 0x1.729fd26b707c8p-1,
+ 0x1.7767c12967a45p-1, 0x1.7767c12967a45p-1, 0x1.7c37a9227e7fbp-1,
+ 0x1.810fa51bf65fdp-1, 0x1.810fa51bf65fdp-1, 0x1.85efd062c656dp-1,
+ 0x1.8ad846cf369a4p-1, 0x1.8ad846cf369a4p-1, 0x1.8fc924c89ac84p-1,
+ 0x1.94c287492c4dbp-1, 0x1.94c287492c4dbp-1, 0x1.99c48be2063c8p-1,
+ 0x1.9ecf50bf43f13p-1, 0x1.9ecf50bf43f13p-1, 0x1.a3e2f4ac43f6p-1,
+ 0x1.a8ff971810a5ep-1, 0x1.a8ff971810a5ep-1, 0x1.ae255819f022dp-1,
+ 0x1.b35458761d479p-1, 0x1.b35458761d479p-1, 0x1.b88cb9a2ab521p-1,
+ 0x1.b88cb9a2ab521p-1, 0x1.bdce9dcc96187p-1, 0x1.c31a27dd00b4ap-1,
+ 0x1.c31a27dd00b4ap-1, 0x1.c86f7b7ea4a89p-1, 0x1.c86f7b7ea4a89p-1,
+ 0x1.cdcebd2373995p-1, 0x1.d338120a6dd9dp-1, 0x1.d338120a6dd9dp-1,
+ 0x1.d8aba045b01c8p-1, 0x1.d8aba045b01c8p-1, 0x1.de298ec0bac0dp-1,
+ 0x1.de298ec0bac0dp-1, 0x1.e3b20546f554ap-1, 0x1.e3b20546f554ap-1,
+ 0x1.e9452c8a71028p-1, 0x1.e9452c8a71028p-1, 0x1.eee32e2aeccbfp-1,
+ 0x1.eee32e2aeccbfp-1, 0x1.f48c34bd1e96fp-1, 0x1.f48c34bd1e96fp-1,
+ 0x1.fa406bd2443dfp-1, 0x1.0000000000000p0};
+
// Generated by Sollya with:
// for i from 0 to 127 do {
// r = 2^-8 * ceil( 2^8 * (1 - 2^(-8)) / (1 + i*2^-7) );
@@ -395,6 +440,48 @@ alignas(64) const int S2[193] = {
-0x1cd, -0x1d1, -0x1d5, -0x1d9, -0x1dd, -0x1e0, -0x1e4, -0x1e8, -0x1ec,
-0x1f0, -0x1f4, -0x1f8, -0x1fc};
+alignas(64) const double R2[193] = {
+ 0x1.0101p0, 0x1.00fdp0, 0x1.00f9p0, 0x1.00f5p0, 0x1.00f1p0,
+ 0x1.00edp0, 0x1.00e9p0, 0x1.00e5p0, 0x1.00e1p0, 0x1.00ddp0,
+ 0x1.00d9p0, 0x1.00d5p0, 0x1.00d1p0, 0x1.00cdp0, 0x1.00c9p0,
+ 0x1.00c5p0, 0x1.00c1p0, 0x1.00bdp0, 0x1.00b9p0, 0x1.00b4p0,
+ 0x1.00bp0, 0x1.00acp0, 0x1.00a8p0, 0x1.00a4p0, 0x1.00ap0,
+ 0x1.009cp0, 0x1.0098p0, 0x1.0094p0, 0x1.009p0, 0x1.008cp0,
+ 0x1.0088p0, 0x1.0084p0, 0x1.008p0, 0x1.007cp0, 0x1.0078p0,
+ 0x1.0074p0, 0x1.007p0, 0x1.006cp0, 0x1.0068p0, 0x1.0064p0,
+ 0x1.006p0, 0x1.005cp0, 0x1.0058p0, 0x1.0054p0, 0x1.005p0,
+ 0x1.004cp0, 0x1.0048p0, 0x1.0044p0, 0x1.004p0, 0x1.003cp0,
+ 0x1.0038p0, 0x1.0034p0, 0x1.003p0, 0x1.002cp0, 0x1.0028p0,
+ 0x1.0024p0, 0x1.002p0, 0x1.001cp0, 0x1.0018p0, 0x1.0014p0,
+ 0x1.001p0, 0x1.000cp0, 0x1.0008p0, 0x1.0004p0, 0x1p0,
+ 0x1.fff8p-1, 0x1.fffp-1, 0x1.ffe8p-1, 0x1.ffep-1, 0x1.ffd8p-1,
+ 0x1.ffdp-1, 0x1.ffc8p-1, 0x1.ffcp-1, 0x1.ffb8p-1, 0x1.ffbp-1,
+ 0x1.ffa8p-1, 0x1.ffap-1, 0x1.ff98p-1, 0x1.ff9p-1, 0x1.ff88p-1,
+ 0x1.ff8p-1, 0x1.ff78p-1, 0x1.ff7p-1, 0x1.ff68p-1, 0x1.ff6p-1,
+ 0x1.ff58p-1, 0x1.ff5p-1, 0x1.ff48p-1, 0x1.ff4p-1, 0x1.ff38p-1,
+ 0x1.ff3p-1, 0x1.ff28p-1, 0x1.ff2p-1, 0x1.ff18p-1, 0x1.ff1p-1,
+ 0x1.ff08p-1, 0x1.ffp-1, 0x1.fef8p-1, 0x1.fefp-1, 0x1.fee8p-1,
+ 0x1.feep-1, 0x1.fed8p-1, 0x1.fedp-1, 0x1.fec8p-1, 0x1.fecp-1,
+ 0x1.feb8p-1, 0x1.febp-1, 0x1.fea8p-1, 0x1.feap-1, 0x1.fe98p-1,
+ 0x1.fe92p-1, 0x1.fe8ap-1, 0x1.fe82p-1, 0x1.fe7ap-1, 0x1.fe72p-1,
+ 0x1.fe6ap-1, 0x1.fe62p-1, 0x1.fe5ap-1, 0x1.fe52p-1, 0x1.fe4ap-1,
+ 0x1.fe42p-1, 0x1.fe3ap-1, 0x1.fe32p-1, 0x1.fe2ap-1, 0x1.fe22p-1,
+ 0x1.fe1ap-1, 0x1.fe12p-1, 0x1.fe0ap-1, 0x1.fe02p-1, 0x1.fdfap-1,
+ 0x1.fdf2p-1, 0x1.fdeap-1, 0x1.fde2p-1, 0x1.fddap-1, 0x1.fdd2p-1,
+ 0x1.fdcap-1, 0x1.fdc2p-1, 0x1.fdbap-1, 0x1.fdb2p-1, 0x1.fdaap-1,
+ 0x1.fda2p-1, 0x1.fd9ap-1, 0x1.fd92p-1, 0x1.fd8cp-1, 0x1.fd84p-1,
+ 0x1.fd7cp-1, 0x1.fd74p-1, 0x1.fd6cp-1, 0x1.fd64p-1, 0x1.fd5cp-1,
+ 0x1.fd54p-1, 0x1.fd4cp-1, 0x1.fd44p-1, 0x1.fd3cp-1, 0x1.fd34p-1,
+ 0x1.fd2cp-1, 0x1.fd24p-1, 0x1.fd1cp-1, 0x1.fd14p-1, 0x1.fd0cp-1,
+ 0x1.fd04p-1, 0x1.fcfcp-1, 0x1.fcf4p-1, 0x1.fcecp-1, 0x1.fce4p-1,
+ 0x1.fcdcp-1, 0x1.fcd6p-1, 0x1.fccep-1, 0x1.fcc6p-1, 0x1.fcbep-1,
+ 0x1.fcb6p-1, 0x1.fcaep-1, 0x1.fca6p-1, 0x1.fc9ep-1, 0x1.fc96p-1,
+ 0x1.fc8ep-1, 0x1.fc86p-1, 0x1.fc7ep-1, 0x1.fc76p-1, 0x1.fc6ep-1,
+ 0x1.fc66p-1, 0x1.fc5ep-1, 0x1.fc56p-1, 0x1.fc4ep-1, 0x1.fc46p-1,
+ 0x1.fc4p-1, 0x1.fc38p-1, 0x1.fc3p-1, 0x1.fc28p-1, 0x1.fc2p-1,
+ 0x1.fc18p-1, 0x1.fc1p-1, 0x1.fc08p-1,
+};
+
// Logarithm range reduction - Step 3:
// r(k) = 2^-21 round(2^21 / (1 + k*2^-21)) for k = -80 .. 80.
// Output range:
diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h
index df9d7828bf1609d..13fc8d757cb8ca3 100644
--- a/libc/src/math/generic/common_constants.h
+++ b/libc/src/math/generic/common_constants.h
@@ -34,6 +34,9 @@ extern const double CD[128];
extern const double LOG_R[128];
extern const NumberPair<double> LOG_R_DD[128];
+// Lookup table for -log2(r)
+extern const double LOG2_R[128];
+
// Minimax polynomial for (log(1 + x) - x)/x^2, generated by sollya with:
// > P = fpminimax((log(1 + x) - x)/x^2, 5, [|D...|], [-2^-8, 2^-7]);
constexpr double LOG_COEFFS[6] = {-0x1.fffffffffffffp-2, 0x1.5555555554a9bp-2,
@@ -45,6 +48,8 @@ extern const int S2[193];
extern const int S3[161];
extern const int S4[130];
+extern const double R2[193];
+
// log(2) generated by Sollya with:
// > a = 2^-43 * nearestint(2^43*log(2));
// LSB = 2^-43 is chosen so that e_x * LOG_2_HI is exact for -1075 < e_x < 1024.
diff --git a/libc/src/math/generic/log2f.cpp b/libc/src/math/generic/log2f.cpp
index cbb71fb91b10705..7665a90f092359f 100644
--- a/libc/src/math/generic/log2f.cpp
+++ b/libc/src/math/generic/log2f.cpp
@@ -53,52 +53,6 @@
namespace LIBC_NAMESPACE {
-// Lookup table for log2(f) = log2(1 + n*2^(-7)) where n = 0..127.
-static constexpr double LOG2_R[128] = {
- 0x0.0000000000000p+0, 0x1.72c7ba20f7327p-7, 0x1.743ee861f3556p-6,
- 0x1.184b8e4c56af8p-5, 0x1.77394c9d958d5p-5, 0x1.d6ebd1f1febfep-5,
- 0x1.1bb32a600549dp-4, 0x1.4c560fe68af88p-4, 0x1.7d60496cfbb4cp-4,
- 0x1.960caf9abb7cap-4, 0x1.c7b528b70f1c5p-4, 0x1.f9c95dc1d1165p-4,
- 0x1.097e38ce60649p-3, 0x1.22dadc2ab3497p-3, 0x1.3c6fb650cde51p-3,
- 0x1.494f863b8df35p-3, 0x1.633a8bf437ce1p-3, 0x1.7046031c79f85p-3,
- 0x1.8a8980abfbd32p-3, 0x1.97c1cb13c7ec1p-3, 0x1.b2602497d5346p-3,
- 0x1.bfc67a7fff4ccp-3, 0x1.dac22d3e441d3p-3, 0x1.e857d3d361368p-3,
- 0x1.01d9bbcfa61d4p-2, 0x1.08bce0d95fa38p-2, 0x1.169c05363f158p-2,
- 0x1.1d982c9d52708p-2, 0x1.249cd2b13cd6cp-2, 0x1.32bfee370ee68p-2,
- 0x1.39de8e1559f6fp-2, 0x1.4106017c3eca3p-2, 0x1.4f6fbb2cec598p-2,
- 0x1.56b22e6b578e5p-2, 0x1.5dfdcf1eeae0ep-2, 0x1.6552b49986277p-2,
- 0x1.6cb0f6865c8eap-2, 0x1.7b89f02cf2aadp-2, 0x1.8304d90c11fd3p-2,
- 0x1.8a8980abfbd32p-2, 0x1.921800924dd3bp-2, 0x1.99b072a96c6b2p-2,
- 0x1.a8ff971810a5ep-2, 0x1.b0b67f4f4681p-2, 0x1.b877c57b1b07p-2,
- 0x1.c043859e2fdb3p-2, 0x1.c819dc2d45fe4p-2, 0x1.cffae611ad12bp-2,
- 0x1.d7e6c0abc3579p-2, 0x1.dfdd89d586e2bp-2, 0x1.e7df5fe538ab3p-2,
- 0x1.efec61b011f85p-2, 0x1.f804ae8d0cd02p-2, 0x1.0014332be0033p-1,
- 0x1.042bd4b9a7c99p-1, 0x1.08494c66b8efp-1, 0x1.0c6caaf0c5597p-1,
- 0x1.1096015dee4dap-1, 0x1.14c560fe68af9p-1, 0x1.18fadb6e2d3c2p-1,
- 0x1.1d368296b5255p-1, 0x1.217868b0c37e8p-1, 0x1.25c0a0463bebp-1,
- 0x1.2a0f3c340705cp-1, 0x1.2e644fac04fd8p-1, 0x1.2e644fac04fd8p-1,
- 0x1.32bfee370ee68p-1, 0x1.37222bb70747cp-1, 0x1.3b8b1c68fa6edp-1,
- 0x1.3ffad4e74f1d6p-1, 0x1.44716a2c08262p-1, 0x1.44716a2c08262p-1,
- 0x1.48eef19317991p-1, 0x1.4d7380dcc422dp-1, 0x1.51ff2e30214bcp-1,
- 0x1.5692101d9b4a6p-1, 0x1.5b2c3da19723bp-1, 0x1.5b2c3da19723bp-1,
- 0x1.5fcdce2727ddbp-1, 0x1.6476d98ad990ap-1, 0x1.6927781d932a8p-1,
- 0x1.6927781d932a8p-1, 0x1.6ddfc2a78fc63p-1, 0x1.729fd26b707c8p-1,
- 0x1.7767c12967a45p-1, 0x1.7767c12967a45p-1, 0x1.7c37a9227e7fbp-1,
- 0x1.810fa51bf65fdp-1, 0x1.810fa51bf65fdp-1, 0x1.85efd062c656dp-1,
- 0x1.8ad846cf369a4p-1, 0x1.8ad846cf369a4p-1, 0x1.8fc924c89ac84p-1,
- 0x1.94c287492c4dbp-1, 0x1.94c287492c4dbp-1, 0x1.99c48be2063c8p-1,
- 0x1.9ecf50bf43f13p-1, 0x1.9ecf50bf43f13p-1, 0x1.a3e2f4ac43f6p-1,
- 0x1.a8ff971810a5ep-1, 0x1.a8ff971810a5ep-1, 0x1.ae255819f022dp-1,
- 0x1.b35458761d479p-1, 0x1.b35458761d479p-1, 0x1.b88cb9a2ab521p-1,
- 0x1.b88cb9a2ab521p-1, 0x1.bdce9dcc96187p-1, 0x1.c31a27dd00b4ap-1,
- 0x1.c31a27dd00b4ap-1, 0x1.c86f7b7ea4a89p-1, 0x1.c86f7b7ea4a89p-1,
- 0x1.cdcebd2373995p-1, 0x1.d338120a6dd9dp-1, 0x1.d338120a6dd9dp-1,
- 0x1.d8aba045b01c8p-1, 0x1.d8aba045b01c8p-1, 0x1.de298ec0bac0dp-1,
- 0x1.de298ec0bac0dp-1, 0x1.e3b20546f554ap-1, 0x1.e3b20546f554ap-1,
- 0x1.e9452c8a71028p-1, 0x1.e9452c8a71028p-1, 0x1.eee32e2aeccbfp-1,
- 0x1.eee32e2aeccbfp-1, 0x1.f48c34bd1e96fp-1, 0x1.f48c34bd1e96fp-1,
- 0x1.fa406bd2443dfp-1, 0x1.0000000000000p0};
-
LLVM_LIBC_FUNCTION(float, log2f, (float x)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
diff --git a/libc/src/math/generic/powf.cpp b/libc/src/math/generic/powf.cpp
new file mode 100644
index 000000000000000..c432a4fa372f24b
--- /dev/null
+++ b/libc/src/math/generic/powf.cpp
@@ -0,0 +1,840 @@
+//===-- Single-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 "src/math/powf.h"
+#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
+#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/optional.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/builtin_wrappers.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/math/exp10f.h"
+#include "src/math/exp2f.h"
+
+#include <errno.h>
+
+namespace LIBC_NAMESPACE {
+
+using fputil::DoubleDouble;
+using fputil::TripleDouble;
+
+namespace {
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+constexpr uint64_t ERR = 64;
+#else
+constexpr uint64_t ERR = 128;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
+// We choose the precision of the high part to be 53 - 24 - 8, so that when
+// y * (e_x + LOG2_R_DD[i].hi) is exact.
+// Generated by Sollya with:
+// > for i from 0 to 127 do {
+// r = 2^-8 * ceil(2^8 * (1 - 2^-8) / (1 + i * 2^-7) );
+// a = -log2(r);
+// b = round(1 + a, 53 - 24 - 8, RN) - 1;
+// c = round(a - b, D, RN);
+// d = round(a - b - c, D, RN);
+// print("{", d, ",", c, ", ", b, "},");
+// };
+static constexpr TripleDouble LOG2_R_TD[128] = {
+ {0.0, 0.0, 0.0},
+ {0x1.84a2c615b70adp-79, -0x1.177c23362928cp-25, 0x1.72c8p-7},
+ {-0x1.f27b820fd03eap-76, -0x1.179e0caa9c9abp-22, 0x1.744p-6},
+ {-0x1.f27ef487c8f34p-77, -0x1.c6cea541f5b7p-23, 0x1.184cp-5},
+ {-0x1.e3f80fbc71454p-76, -0x1.66c4d4e554434p-22, 0x1.773ap-5},
+ {-0x1.9f8ef14d5f6eep-79, -0x1.70700a00fdd55p-24, 0x1.d6ecp-5},
+ {0x1.452bbce7398c1p-77, 0x1.53002a4e86631p-23, 0x1.1bb3p-4},
+ {-0x1.990555535afdp-81, 0x1.fcd15f101c142p-25, 0x1.4c56p-4},
+ {0x1.447e30ad393eep-78, 0x1.25b3eed319cedp-22, 0x1.7d6p-4},
+ {0x1.b7759da88a2dap-76, -0x1.4195120d8486fp-22, 0x1.960dp-4},
+ {0x1.cee7766ece702p-78, 0x1.45b878e27d0d9p-23, 0x1.c7b5p-4},
+ {-0x1.a55c745ecdc2fp-77, 0x1.770744593a4cbp-22, 0x1.f9c9p-4},
+ {0x1.f7ec992caa67fp-77, 0x1.c673032495d24p-22, 0x1.097ep-3},
+ {-0x1.433638c6ece3ep-77, -0x1.1eaa65b49696ep-22, 0x1.22dbp-3},
+ {0x1.58f27b6518824p-76, 0x1.b2866f2850b22p-22, 0x1.3c6f8p-3},
+ {-0x1.86bdcfdfd4a4cp-79, 0x1.8ee37cd2ea9d3p-25, 0x1.494f8p-3},
+ {-0x1.ff7044a68a7fap-80, 0x1.7e86f9c2154fbp-24, 0x1.633a8p-3},
+ {-0x1.aa21694561327p-81, 0x1.8e3cfc25f0ce6p-26, 0x1.7046p-3},
+ {-0x1.d209f2d4239c6p-87, 0x1.57f7a64ccd537p-28, 0x1.8a898p-3},
+ {-0x1.a55e97e60e632p-76, -0x1.a761c09fbd2aep-22, 0x1.97c2p-3},
+ {0x1.261179225541ep-76, 0x1.24bea9a2c66f3p-22, 0x1.b26p-3},
+ {-0x1.08fa30510fca9p-82, -0x1.60002ccfe43f5p-25, 0x1.bfc68p-3},
+ {-0x1.63ec8d56242f9p-76, 0x1.69f220e97f22cp-22, 0x1.dac2p-3},
+ {0x1.8bcdaf0534365p-76, -0x1.6164f64c210ep-22, 0x1.e858p-3},
+ {0x1.1003282896056p-78, -0x1.0c1678ae89767p-24, 0x1.01d9cp-2},
+ {0x1.01bcc7025fa92p-78, -0x1.f26a05c813d57p-22, 0x1.08bdp-2},
+ {-0x1.fe8a8648e9ebcp-80, 0x1.4d8fc561c8d44p-24, 0x1.169cp-2},
+ {0x1.08dfb23650c75p-79, -0x1.362ad8f7ca2dp-22, 0x1.1d984p-2},
+ {-0x1.f8d5a89861a5ep-79, 0x1.2b13cd6c4d042p-22, 0x1.249ccp-2},
+ {-0x1.a1c872983511ep-76, -0x1.1c8f11979a5dbp-22, 0x1.32cp-2},
+ {0x1.e8e21bff3336bp-77, 0x1.c2ab3edefe569p-23, 0x1.39de8p-2},
+ {0x1.fd1994fb2c4a1p-80, 0x1.7c3eca28e69cap-26, 0x1.4106p-2},
+ {0x1.6b94b51cf76b1p-80, -0x1.34c4e99e1c6c6p-24, 0x1.4f6fcp-2},
+ {-0x1.31d55da1d0f66p-76, -0x1.194a871b63619p-22, 0x1.56b24p-2},
+ {-0x1.378b22691e28bp-77, 0x1.e3dd5c1c885aep-23, 0x1.5dfdcp-2},
+ {0x1.99e302970e411p-83, -0x1.6ccf3b1129b7cp-23, 0x1.6552cp-2},
+ {0x1.20164a049664dp-82, -0x1.2f346e2bf924bp-23, 0x1.6cb1p-2},
+ {-0x1.d14aac4d864c3p-77, -0x1.fa61aaa59c1d8p-23, 0x1.7b8ap-2},
+ {0x1.496ab4e4b293fp-79, 0x1.90c11fd32a3abp-22, 0x1.8304cp-2},
+ {-0x1.d209f2d4239c6p-86, 0x1.57f7a64ccd537p-27, 0x1.8a898p-2},
+ {0x1.eae3326327babp-81, 0x1.249ba76fee235p-27, 0x1.9218p-2},
+ {0x1.fa05bddfded8cp-77, -0x1.aad2729b21ae5p-23, 0x1.99b08p-2},
+ {-0x1.624140d175ba2p-77, 0x1.71810a5e1818p-22, 0x1.a8ff8p-2},
+ {0x1.f1c5160c515c1p-81, -0x1.6172fe015e13cp-27, 0x1.b0b68p-2},
+ {-0x1.86a6204eec8cp-79, 0x1.5ec6c1bfbf89ap-24, 0x1.b877cp-2},
+ {0x1.718f761dd3915p-78, 0x1.678bf6cdedf51p-24, 0x1.c0438p-2},
+ {-0x1.d4ee66c3700e4p-76, 0x1.c2d45fe43895ep-22, 0x1.c819cp-2},
+ {-0x1.7d14533586306p-77, -0x1.9ee52ed49d71dp-22, 0x1.cffbp-2},
+ {0x1.5ce9fb5a7bb5bp-81, 0x1.5786af187a96bp-27, 0x1.d7e6cp-2},
+ {-0x1.ae6face57ad3bp-77, 0x1.3ab0dc56138c9p-23, 0x1.dfdd8p-2},
+ {0x1.5ac93b443d55fp-78, 0x1.fe538ab34efb5p-22, 0x1.e7df4p-2},
+ {0x1.f1753e0ae1e8fp-76, -0x1.e4fee07aa4b68p-22, 0x1.efec8p-2},
+ {0x1.cdfd4c297069bp-76, -0x1.172f32fe67287p-22, 0x1.f804cp-2},
+ {0x1.97a0e8f3ba742p-79, -0x1.9a83ff9ab9cc8p-22, 0x1.00144p-1},
+ {-0x1.800450f5b2357p-78, -0x1.68cb06cece193p-22, 0x1.042bep-1},
+ {-0x1.a839041241fe7p-78, 0x1.8cd71ddf82e2p-22, 0x1.08494p-1},
+ {0x1.ed0b8eeccca86p-78, 0x1.5e18ab2df3ae6p-22, 0x1.0c6cap-1},
+ {0x1.3dd41df9689b3p-79, 0x1.5dee4d9d8a273p-25, 0x1.1096p-1},
+ {-0x1.990555535afdp-82, 0x1.fcd15f101c142p-26, 0x1.14c56p-1},
+ {-0x1.1773d02c9055cp-77, -0x1.2474b0f992ba1p-23, 0x1.18faep-1},
+ {-0x1.4aeef330c53c1p-78, 0x1.4b5a92a606047p-24, 0x1.1d368p-1},
+ {0x1.8e6ff749ebacbp-77, 0x1.16186fcf54bbdp-22, 0x1.21786p-1},
+ {0x1.c09d761c548ebp-84, 0x1.18efabeb7d722p-27, 0x1.25c0ap-1},
+ {0x1.aaa73a428e1e4p-78, -0x1.e5fc7d238691dp-24, 0x1.2a0f4p-1},
+ {-0x1.af2f3d8b63fbap-79, 0x1.f5809faf6283cp-22, 0x1.2e644p-1},
+ {-0x1.af2f3d8b63fbap-79, 0x1.f5809faf6283cp-22, 0x1.2e644p-1},
+ {0x1.78de359f2bb88p-77, 0x1.c6e1dcd0cb449p-22, 0x1.32bfep-1},
+ {-0x1.415ae1a715618p-76, 0x1.76e0e8f74b4d5p-22, 0x1.37222p-1},
+ {-0x1.4991b5375621fp-79, -0x1.cb82c89692d99p-24, 0x1.3b8b2p-1},
+ {-0x1.827d37deb2236p-76, -0x1.63161c5432aebp-22, 0x1.3ffaep-1},
+ {0x1.9576edac01c78p-77, 0x1.458104c41b901p-22, 0x1.44716p-1},
+ {0x1.9576edac01c78p-77, 0x1.458104c41b901p-22, 0x1.44716p-1},
+ {-0x1.05a27b81e2219p-77, -0x1.cd9d0cde578d5p-22, 0x1.48efp-1},
+ {0x1.237616778b4bap-82, 0x1.b9884591add87p-26, 0x1.4d738p-1},
+ {0x1.3b7d7e5d148bbp-76, 0x1.c6042978605ffp-22, 0x1.51ff2p-1},
+ {-0x1.cc3f936a5977cp-79, -0x1.fc4c96b37dcf6p-22, 0x1.56922p-1},
+ {0x1.20164a049664dp-83, -0x1.2f346e2bf924bp-24, 0x1.5b2c4p-1},
+ {0x1.20164a049664dp-83, -0x1.2f346e2bf924bp-24, 0x1.5b2c4p-1},
+ {-0x1.a212919a92f7ap-77, 0x1.c4e4fbb68a4d1p-22, 0x1.5fcdcp-1},
+ {-0x1.b64b03f7230ddp-77, -0x1.9d499bd9b3226p-23, 0x1.6476ep-1},
+ {-0x1.1ec6379e6e3b9p-77, -0x1.f89b355ede26fp-23, 0x1.69278p-1},
+ {-0x1.1ec6379e6e3b9p-77, -0x1.f89b355ede26fp-23, 0x1.69278p-1},
+ {-0x1.4ba44c03bfbbdp-78, 0x1.53c7e319f6e92p-24, 0x1.6ddfcp-1},
+ {-0x1.c36fc650d030fp-77, -0x1.b291f070528c7p-22, 0x1.729fep-1},
+ {-0x1.69e5693a7f067p-80, 0x1.2967a451a7b48p-25, 0x1.7767cp-1},
+ {-0x1.69e5693a7f067p-80, 0x1.2967a451a7b48p-25, 0x1.7767cp-1},
+ {0x1.6598aae91499ap-76, 0x1.244fcff690fcep-22, 0x1.7c37ap-1},
+ {0x1.99d61ec432837p-77, 0x1.46fd97f5dc572p-23, 0x1.810fap-1},
+ {0x1.99d61ec432837p-77, 0x1.46fd97f5dc572p-23, 0x1.810fap-1},
+ {0x1.855c42078f81bp-76, -0x1.f3a7352663e5p-22, 0x1.85efep-1},
+ {-0x1.59408e815107p-77, 0x1.b3cda690370b5p-23, 0x1.8ad84p-1},
+ {-0x1.59408e815107p-77, 0x1.b3cda690370b5p-23, 0x1.8ad84p-1},
+ {0x1.33b318085e50ap-78, 0x1.3226b211bf1d9p-23, 0x1.8fc92p-1},
+ {0x1.343fe7c9cb4aep-79, 0x1.d24b136c101eep-23, 0x1.94c28p-1},
+ {0x1.343fe7c9cb4aep-79, 0x1.d24b136c101eep-23, 0x1.94c28p-1},
+ {-0x1.d19522e56fe6p-76, 0x1.7c40c7907e82ap-22, 0x1.99c48p-1},
+ {-0x1.23b9d8ea55c3ep-77, -0x1.e81781d97ee91p-22, 0x1.9ecf6p-1},
+ {-0x1.23b9d8ea55c3ep-77, -0x1.e81781d97ee91p-22, 0x1.9ecf6p-1},
+ {0x1.829440c24aeb6p-78, -0x1.6a77813f94e01p-22, 0x1.a3e3p-1},
+ {-0x1.624140d175ba2p-76, -0x1.1cfdeb43cfdp-22, 0x1.a8ffap-1},
+ {-0x1.624140d175ba2p-76, -0x1.1cfdeb43cfdp-22, 0x1.a8ffap-1},
+ {0x1.afa6f024fb045p-77, -0x1.f983f74d3138fp-23, 0x1.ae256p-1},
+ {-0x1.603ad3a5d326dp-78, -0x1.e278ae1a1f51fp-23, 0x1.b3546p-1},
+ {-0x1.603ad3a5d326dp-78, -0x1.e278ae1a1f51fp-23, 0x1.b3546p-1},
+ {-0x1.0c1e0e5855d6ap-77, -0x1.97552b7b5ea45p-23, 0x1.b88ccp-1},
+ {-0x1.0c1e0e5855d6ap-77, -0x1.97552b7b5ea45p-23, 0x1.b88ccp-1},
+ {0x1.c817ad56baa16p-78, -0x1.19b4f3c72c4f8p-24, 0x1.bdceap-1},
+ {0x1.44c47ac1bf62bp-77, 0x1.f7402d26f1a12p-23, 0x1.c31a2p-1},
+ {0x1.44c47ac1bf62bp-77, 0x1.f7402d26f1a12p-23, 0x1.c31a2p-1},
+ {-0x1.69b9465eae1e6p-78, -0x1.2056d5dd31d96p-23, 0x1.c86f8p-1},
+ {-0x1.69b9465eae1e6p-78, -0x1.2056d5dd31d96p-23, 0x1.c86f8p-1},
+ {-0x1.24a6d9d1d1904p-79, -0x1.6e46335aae723p-24, 0x1.cdcecp-1},
+ {-0x1.3826144575ac4p-76, -0x1.beb244c59f331p-22, 0x1.d3382p-1},
+ {-0x1.3826144575ac4p-76, -0x1.beb244c59f331p-22, 0x1.d3382p-1},
+ {0x1.dbc96b3b12b25p-81, 0x1.16c071e93fd97p-27, 0x1.d8abap-1},
+ {0x1.dbc96b3b12b25p-81, 0x1.16c071e93fd97p-27, 0x1.d8abap-1},
+ {0x1.68a8ccdbd1f33p-77, 0x1.d8175819530c2p-22, 0x1.de298p-1},
+ {0x1.68a8ccdbd1f33p-77, 0x1.d8175819530c2p-22, 0x1.de298p-1},
+ {0x1.e586711df5ea1p-79, 0x1.51bd552842c1cp-23, 0x1.e3b2p-1},
+ {0x1.e586711df5ea1p-79, 0x1.51bd552842c1cp-23, 0x1.e3b2p-1},
+ {-0x1.bc25adf042483p-79, 0x1.914e204f19d94p-22, 0x1.e9452p-1},
+ {-0x1.bc25adf042483p-79, 0x1.914e204f19d94p-22, 0x1.e9452p-1},
+ {0x1.d7d82b65c5686p-76, 0x1.c55d997da24fdp-22, 0x1.eee32p-1},
+ {0x1.d7d82b65c5686p-76, 0x1.c55d997da24fdp-22, 0x1.eee32p-1},
+ {-0x1.3f108c0857ca3p-77, -0x1.685c2d2298a6ep-22, 0x1.f48c4p-1},
+ {-0x1.3f108c0857ca3p-77, -0x1.685c2d2298a6ep-22, 0x1.f48c4p-1},
+ {-0x1.bd800bca7a221p-78, 0x1.7a4887bd74039p-22, 0x1.fa406p-1},
+ {0.0, 0.0, 1.0},
+};
+
+// Look up table for the second range reduction step:
+// Generated by Sollya with:
+// > for i from -64 to 128 do {
+// r = 2^-16 * nearestint(2^16 / (1 + i * 2^-14) );
+// a = -log2(r);
+// b = round(a, D, RN);
+// c = round(a - b, D, RN);
+// print("{", c, ", ", b, "},");
+// };
+static constexpr DoubleDouble LOG2_R2_DD[] = {
+ {0x1.ff25180953e64p-62, -0x1.720c2ab2312a9p-8},
+ {-0x1.15ffd79560d8fp-62, -0x1.6c4c92b1478ffp-8},
+ {0x1.b8d6d6f2e3579p-62, -0x1.668ce3c873549p-8},
+ {-0x1.5bfc3f0d5ef71p-62, -0x1.60cd1df6fde91p-8},
+ {-0x1.d1f7a8777984ap-64, -0x1.5b0d413c30b5ep-8},
+ {0x1.8e858515b8343p-66, -0x1.554d4d97551abp-8},
+ {0x1.e165c4014c1f2p-62, -0x1.4f8d4307b46ecp-8},
+ {0x1.0f84b2cc14c7ep-63, -0x1.49cd218c9800bp-8},
+ {0x1.de618ed0db9a6p-62, -0x1.440ce9254916cp-8},
+ {-0x1.f6b8587e64f22p-62, -0x1.3e4c99d110ee7p-8},
+ {-0x1.7f793c84cfa63p-64, -0x1.388c338f38bdp-8},
+ {-0x1.7d7ecf6258c9ap-65, -0x1.32cbb65f09aeep-8},
+ {-0x1.810bc5ac188f5p-62, -0x1.2d0b223fcce81p-8},
+ {-0x1.950035fc5b67cp-62, -0x1.274a7730cb841p-8},
+ {0x1.4f47f3048cdadp-62, -0x1.2189b5314e95dp-8},
+ {0x1.269519861e298p-68, -0x1.1bc8dc409f279p-8},
+ {-0x1.5c2b0a46a7e2fp-62, -0x1.1607ec5e063b3p-8},
+ {0x1.5001ac8f0bda8p-63, -0x1.1046e588cccap-8},
+ {0x1.106f246af5d41p-62, -0x1.0a85c7c03bc4ap-8},
+ {0x1.82a00583b34bap-66, -0x1.0354423e3c666p-8},
+ {0x1.b6f37deb3137p-65, -0x1.fb25e19f11aecp-9},
+ {-0x1.44a2140444811p-63, -0x1.efa310d6550ecp-9},
+ {0x1.f5e68a763133fp-63, -0x1.e4201220d4858p-9},
+ {0x1.692083115f0b9p-63, -0x1.d89ce57d219a6p-9},
+ {0x1.144bb17b9ac9cp-63, -0x1.cd198ae9cdc3dp-9},
+ {0x1.ee7f086d32c05p-63, -0x1.c19602656a671p-9},
+ {-0x1.d4f1167538dbep-63, -0x1.b6124bee88d82p-9},
+ {0x1.7df8d226c67ep-63, -0x1.aa8e6783ba5a2p-9},
+ {0x1.60545d61b9512p-63, -0x1.9f0a5523901ebp-9},
+ {0x1.54c99c291702p-63, -0x1.938614cc9b468p-9},
+ {-0x1.a7e678d7280dep-64, -0x1.8801a67d6ce1p-9},
+ {-0x1.6d419bbeb223ap-64, -0x1.7c7d0a3495ec9p-9},
+ {0x1.ce2b9892e27e9p-64, -0x1.70f83ff0a7565p-9},
+ {-0x1.a4db4eff7bd61p-63, -0x1.657347b031fa2p-9},
+ {0x1.5bb04682fab82p-63, -0x1.59ee2171c6a2fp-9},
+ {-0x1.78b8bfe6a3adep-64, -0x1.4e68cd33f60a3p-9},
+ {0x1.574c3ce9b89b1p-63, -0x1.42e34af550d87p-9},
+ {0x1.08fb216647b7bp-63, -0x1.375d9ab467a4dp-9},
+ {0x1.ed5a50e7b919cp-66, -0x1.2bd7bc6fcaf56p-9},
+ {0x1.91ad7a23f86fep-63, -0x1.2051b0260b3fp-9},
+ {0x1.3ab2c932b8b0ap-64, -0x1.14cb75d5b8e54p-9},
+ {-0x1.c63bcdf120f7ap-63, -0x1.09450d7d643a9p-9},
+ {0x1.8af8c4ab4e82dp-64, -0x1.fb7cee373b008p-10},
+ {0x1.a52c2ca9d8b9bp-65, -0x1.e46f655de9cc6p-10},
+ {-0x1.460b177a58742p-64, -0x1.cd61806bf5166p-10},
+ {0x1.611089de8d12ap-66, -0x1.b6533f5e7cf9bp-10},
+ {-0x1.4209853cee70cp-69, -0x1.9f44a232a16eep-10},
+ {0x1.964e032541a28p-64, -0x1.8835a8e5824c3p-10},
+ {-0x1.fa9f94392637bp-66, -0x1.712653743f454p-10},
+ {-0x1.3293693721a53p-64, -0x1.5a16a1dbf7eb6p-10},
+ {-0x1.6e2af03c83c6ep-68, -0x1.43069419cbad5p-10},
+ {-0x1.b5f05b9d5bd29p-65, -0x1.2bf62a2ad9d74p-10},
+ {0x1.3db883c072f72p-64, -0x1.14e5640c4193p-10},
+ {-0x1.a675a1c045304p-68, -0x1.fba8837643cf6p-11},
+ {0x1.3b9c2aeb00068p-66, -0x1.cd85866933743p-11},
+ {-0x1.2911a381901ebp-66, -0x1.9f61d0eb8f98bp-11},
+ {-0x1.5ea75a74def03p-68, -0x1.713d62f7957c3p-11},
+ {-0x1.305b92f93ffep-67, -0x1.43183c878218dp-11},
+ {0x1.b7c8c8dd40d35p-68, -0x1.14f25d959223ap-11},
+ {0x1.dc915d58a62f6p-66, -0x1.cd978c3804191p-12},
+ {0x1.c7bc3fe53cd94p-66, -0x1.7148ec2a1bfc9p-12},
+ {-0x1.427ce595cc53cp-67, -0x1.14f8daf5e3bcfp-12},
+ {-0x1.d523885ac824cp-67, -0x1.714eb11fa5363p-13},
+ {-0x1.945957f63330ap-69, -0x1.715193b17d35dp-14},
+ {0, 0},
+ {-0x1.88fb2ea8bf9eap-70, 0x1.7157590356aeep-14},
+ {-0x1.5aeaee345d04ep-68, 0x1.715a3bc3593d5p-13},
+ {-0x1.7fce430230132p-66, 0x1.1505d6ee104c5p-12},
+ {-0x1.9a480f204ff09p-70, 0x1.716001718cb2bp-12},
+ {-0x1.00e7233f2d8bdp-68, 0x1.cdbb9d77ae5a8p-12},
+ {0x1.09d379fa18c5dp-67, 0x1.150c5586012b8p-11},
+ {0x1.b6b9d90a104d3p-65, 0x1.433b951d0b231p-11},
+ {0x1.4d9a3ea651885p-65, 0x1.716b8d86bc285p-11},
+ {-0x1.7590b3a76f0f9p-67, 0x1.9f9c3ec8db94fp-11},
+ {0x1.f183ca5b21bfep-65, 0x1.cdcda8e93107fp-11},
+ {-0x1.a7e3465ba127p-66, 0x1.fbffcbed8465fp-11},
+ {-0x1.7821f738d1221p-64, 0x1.151953edceec6p-10},
+ {0x1.3bb4c0fb95359p-65, 0x1.2c331e5ca2e7dp-10},
+ {0x1.236028e962f8p-64, 0x1.434d4546227fcp-10},
+ {0x1.aaaa64d30f184p-66, 0x1.5a67c8ad32315p-10},
+ {-0x1.a821b7cc57a7ap-64, 0x1.7182a894b69c6p-10},
+ {-0x1.13d9d78aace21p-64, 0x1.889de4ff94838p-10},
+ {-0x1.2f249a6b923ap-64, 0x1.9fb97df0b0cc2p-10},
+ {-0x1.d47dc3664be7ap-68, 0x1.b6d5736af07e6p-10},
+ {0x1.bd1522c6418fbp-64, 0x1.cdf1c57138c53p-10},
+ {-0x1.bacdbb22d2163p-64, 0x1.e50e74066eee6p-10},
+ {-0x1.ca7604812d77bp-64, 0x1.fc2b7f2d786a5p-10},
+ {-0x1.2b6832f8830bfp-63, 0x1.09a473749d663p-9},
+ {0x1.4e712033d0457p-65, 0x1.1533559e4de55p-9},
+ {-0x1.473dd044017b5p-66, 0x1.20c26615409f1p-9},
+ {-0x1.e033bcac726d3p-63, 0x1.2c51a4dae8915p-9},
+ {-0x1.4a47a2b18a0fap-63, 0x1.37e111f0b8cb5p-9},
+ {0x1.6f3615771c17bp-66, 0x1.4370ad58246ddp-9},
+ {0x1.c0ee6c32d6236p-65, 0x1.4f0077129eabp-9},
+ {0x1.fa94c99761b8fp-64, 0x1.5a906f219ac67p-9},
+ {-0x1.979e6b473fbf8p-64, 0x1.662095868c153p-9},
+ {0x1.30edde8d24c7bp-64, 0x1.71b0ea42e5fdap-9},
+ {-0x1.d01594fe1421cp-64, 0x1.7d416d581bf7cp-9},
+ {0x1.50bf7b995b49ap-63, 0x1.88d21ec7a18cdp-9},
+ {-0x1.28ea2bcec5018p-63, 0x1.9462fe92ea57cp-9},
+ {0x1.ed6add489c30bp-65, 0x1.9ff40cbb6a04bp-9},
+ {0x1.201d5c3bbeb69p-64, 0x1.ab85494294517p-9},
+ {-0x1.a05d0d4461ea9p-64, 0x1.b716b429dd0d3p-9},
+ {-0x1.7c974c8a392fdp-63, 0x1.c2a84d72b8189p-9},
+ {-0x1.f068238451bdep-64, 0x1.ce3a151e9965bp-9},
+ {-0x1.5e4d95c6259c3p-66, 0x1.d9cc0b2ef4f83p-9},
+ {-0x1.1fc262efaad6cp-63, 0x1.e55e2fa53ee53p-9},
+ {0x1.49eee7abc7716p-63, 0x1.f0f08282eb533p-9},
+ {-0x1.903de284d2782p-65, 0x1.fc8303c96e7a6p-9},
+ {-0x1.ec564845134cbp-63, 0x1.040ad9bd1e522p-8},
+ {-0x1.7692b7791cf1fp-66, 0x1.0861eadabc3dcp-8},
+ {-0x1.37829afb11c1p-62, 0x1.0e2b6b51e4f7ep-8},
+ {0x1.6706b91c3b0bap-62, 0x1.13f5030033459p-8},
+ {-0x1.7558ccd710756p-62, 0x1.19beb1e6616c9p-8},
+ {0x1.79f72a5bbe9dep-62, 0x1.1f88780529bb1p-8},
+ {-0x1.e1297c110b25p-62, 0x1.2552555d46886p-8},
+ {0x1.29930d567ca26p-62, 0x1.2b1c49ef72343p-8},
+ {0x1.a08cbd7592a17p-65, 0x1.30e655bc67275p-8},
+ {0x1.e4f9d4ac5db83p-62, 0x1.36b078c4dfd31p-8},
+ {-0x1.ed1b0aafd30c2p-62, 0x1.3c7ab30996b1cp-8},
+ {0x1.e78f0aa014b32p-62, 0x1.4245048b46462p-8},
+ {0x1.8594548038a0fp-69, 0x1.480f6d4aa91c2p-8},
+ {0x1.3df498168a333p-63, 0x1.4dd9ed4879c82p-8},
+ {0x1.b1c502544f82ap-62, 0x1.53a4848572e77p-8},
+ {-0x1.dc50552fe0da9p-63, 0x1.596f33024f203p-8},
+ {-0x1.671d85c357d5ep-62, 0x1.5f39f8bfc9212p-8},
+ {0x1.1c670cabccefap-64, 0x1.6504d5be9ba1ep-8},
+ {-0x1.9983a9e98f318p-62, 0x1.6acfc9ff8162fp-8},
+ {0x1.ae1a26af3eebep-62, 0x1.709ad583352d6p-8},
+ {0x1.655eb510bfda3p-62, 0x1.7665f84a71d35p-8},
+ {-0x1.e287bc0192e15p-64, 0x1.7c313255f22f8p-8},
+ {0x1.cc4944139ccbfp-63, 0x1.81fc83a671257p-8},
+ {0x1.4e09b4cb8645bp-62, 0x1.87c7ec3ca9a19p-8},
+ {-0x1.5becc991e3a5fp-64, 0x1.8d936c1956991p-8},
+ {-0x1.ddfa3f1e15ba8p-62, 0x1.935f033d3309ep-8},
+ {-0x1.b7b06ea3fb362p-62, 0x1.992ab1a8f9facp-8},
+ {0x1.32d614904e46cp-62, 0x1.9ef6775d667b4p-8},
+ {-0x1.7186892b5bfaep-64, 0x1.a4c2545b33a3ep-8},
+ {-0x1.d4de10b28dfd8p-62, 0x1.aa8e48a31c95cp-8},
+ {0x1.4bb4b3bdc8175p-62, 0x1.b05a5435dc7adp-8},
+ {0x1.9cedbd1d7fba5p-62, 0x1.b62677142e86p-8},
+ {-0x1.0ed3379beaffdp-66, 0x1.bbf2b13ecdf2fp-8},
+ {0x1.6e86a125567a6p-62, 0x1.c1bf02b67606p-8},
+ {-0x1.35038e0c0a52cp-62, 0x1.c6184f1b326d9p-8},
+ {0x1.05ef8bf5adf5ep-67, 0x1.cbe4c95b6c5abp-8},
+ {-0x1.b7338b99a6b26p-65, 0x1.d1b15aeab217cp-8},
+ {0x1.9e901c30c427ep-63, 0x1.d77e03c9bf0a4p-8},
+ {-0x1.1f28a9c0b3d47p-62, 0x1.dd4ac3f94ea0ap-8},
+ {-0x1.140ef760d3b63p-62, 0x1.e3179b7a1c52p-8},
+ {-0x1.ab65b1037f517p-63, 0x1.e8e48a4ce39e7p-8},
+ {-0x1.76940c457ce6dp-63, 0x1.eeb19072600edp-8},
+ {0x1.da3ae65a605cfp-64, 0x1.f47eadeb4d34dp-8},
+ {0x1.b15d0bce2ede6p-62, 0x1.fa4be2b866abp-8},
+ {0x1.e02aa1fa9dc57p-61, 0x1.000c976d340a6p-7},
+ {0x1.6be971a5565b9p-62, 0x1.02f34929068f3p-7},
+ {-0x1.8a9319a6ed164p-64, 0x1.05da069008be7p-7},
+ {0x1.825079f1e0ec5p-62, 0x1.08c0cfa298771p-7},
+ {0x1.60d5749321466p-63, 0x1.0ba7a461139c8p-7},
+ {-0x1.5b8f4c479e2ep-61, 0x1.0e8e84cbd8169p-7},
+ {-0x1.e3e1248004e29p-62, 0x1.117570e343d17p-7},
+ {0x1.9ac06487c375p-63, 0x1.145c68a7b4bddp-7},
+ {0x1.f657ea5c03ea4p-62, 0x1.17436c1988d0dp-7},
+ {-0x1.5a965659a05e2p-61, 0x1.1a2a7b391e04p-7},
+ {-0x1.21ce9b9bfc512p-61, 0x1.1d119606d2554p-7},
+ {-0x1.30fda247ad0e1p-61, 0x1.1ff8bc8303c7p-7},
+ {-0x1.382c78a45cdeap-62, 0x1.22dfeeae10601p-7},
+ {0x1.46ae4a64073d4p-61, 0x1.250d5bf952374p-7},
+ {-0x1.dcad2cec3b84bp-62, 0x1.27f4a29740a2fp-7},
+ {-0x1.413fbeb0b0635p-61, 0x1.2adbf4e50cdf9p-7},
+ {0x1.f28e6a48bcb9p-61, 0x1.2dc352e315049p-7},
+ {-0x1.96f286e1eb086p-61, 0x1.30aabc91b72ep-7},
+ {-0x1.f88c04206dfa1p-61, 0x1.339231f1517c1p-7},
+ {-0x1.11ea20e195841p-61, 0x1.3679b30242139p-7},
+ {-0x1.d6e71452b674ap-63, 0x1.39613fc4e71dcp-7},
+ {-0x1.57c578233b1b3p-61, 0x1.3c48d8399ec85p-7},
+ {-0x1.ec430f03b76ep-63, 0x1.3f307c60c7455p-7},
+ {0x1.e00dd1902ffb9p-61, 0x1.42182c3abecb5p-7},
+ {-0x1.f22bcd96afe38p-61, 0x1.44ffe7c7e3957p-7},
+ {0x1.08fd90f841d3p-61, 0x1.47e7af0893e2fp-7},
+ {0x1.09594c5552bccp-62, 0x1.4acf81fd2df7ep-7},
+ {-0x1.01a8a652e5602p-61, 0x1.4db760a6101c9p-7},
+ {-0x1.826168febb3dp-64, 0x1.509f4b03989dcp-7},
+ {-0x1.7eb21a35021e3p-62, 0x1.5387411625cccp-7},
+ {-0x1.66cbc818e175p-61, 0x1.566f42de15ff4p-7},
+ {0x1.9b784dd6cebdap-64, 0x1.5957505bc78f6p-7},
+ {0x1.2b121ab482456p-61, 0x1.5b8562298c65bp-7},
+ {-0x1.5d29869dd8233p-62, 0x1.5e6d842633702p-7},
+ {-0x1.572a1b6cd63cfp-61, 0x1.6155b1d99f672p-7},
+ {-0x1.a1f355360e877p-62, 0x1.643deb442eb59p-7},
+ {-0x1.b6f1cd2e1c03fp-61, 0x1.672630663fcadp-7},
+ {-0x1.2aaa11ccddcaep-61, 0x1.6a0e8140311aap-7},
+ {0x1.3d979ddf4746cp-61, 0x1.6cf6ddd2611d4p-7},
+ {-0x1.dc930484501f8p-63, 0x1.6fdf461d2e4f8p-7},
+};
+
+LIBC_INLINE bool is_odd_integer(float x) {
+ using FloatProp = typename fputil::FloatProperties<float>;
+ uint32_t x_u = cpp::bit_cast<uint32_t>(x);
+ int x_e = static_cast<int>((x_u & FloatProp::EXPONENT_MASK) >>
+ FloatProp::MANTISSA_WIDTH);
+ int lsb = unsafe_ctz(x_u | FloatProp::EXPONENT_MASK);
+ constexpr int UNIT_EXPONENT =
+ static_cast<int>(FloatProp::EXPONENT_BIAS + FloatProp::MANTISSA_WIDTH);
+ return (x_e + lsb == UNIT_EXPONENT);
+}
+
+LIBC_INLINE bool is_integer(float x) {
+ using FloatProp = typename fputil::FloatProperties<float>;
+ uint32_t x_u = cpp::bit_cast<uint32_t>(x);
+ int x_e = static_cast<int>((x_u & FloatProp::EXPONENT_MASK) >>
+ FloatProp::MANTISSA_WIDTH);
+ int lsb = unsafe_ctz(x_u | FloatProp::EXPONENT_MASK);
+ constexpr int UNIT_EXPONENT =
+ static_cast<int>(FloatProp::EXPONENT_BIAS + FloatProp::MANTISSA_WIDTH);
+ return (x_e + lsb >= UNIT_EXPONENT);
+}
+
+LIBC_INLINE bool larger_exponent(double a, double b) {
+ using DoubleBits = typename fputil::FPBits<double>;
+ return DoubleBits(a).get_unbiased_exponent() >=
+ DoubleBits(b).get_unbiased_exponent();
+}
+
+// Calculate 2^(y * log2(x)) in double-double precision.
+// At this point we can reuse the following values:
+// idx_x: index for extra precision of log2 for the middle part of log2(x).
+// dx: the reduced argument for log2(x)
+// y6: 2^6 * y.
+// lo6_hi: the high part of 2^6 * (y - (hi + mid))
+// exp2_hi_mid: high part of 2^(hi + mid)
+double powf_double_double(int idx_x, double dx, double y6, double lo6_hi,
+ const DoubleDouble &exp2_hi_mid) {
+ using DoubleBits = typename fputil::FPBits<double>;
+ using DoubleProp = typename fputil::FloatProperties<double>;
+ // Perform a second range reduction step:
+ // idx2 = round(2^14 * (dx + 2^-8)) = round ( dx * 2^14 + 2^6)
+ // dx2 = (1 + dx) * r2 - 1
+ // Output range:
+ // -0x1.3ffcp-15 <= dx2 <= 0x1.3e3dp-15
+ int idx2 = static_cast<int>(
+ fputil::nearest_integer(fputil::multiply_add(dx, 0x1.0p14, 0x1.0p6)));
+ double dx2 = fputil::multiply_add(1.0 + dx, R2[idx2], -1.0); // Exact
+
+ // Degree-5 polynomial approximation of log2(1 + x)/x in double-double
+ // precision. Generate by Solya with:
+ // > P = fpminimax(log2(1 + x)/x, 5, [|DD...|],
+ // [-0x1.3ffcp-15, 0x1.3e3dp-15]);
+ // > dirtyinfnorm(log2(1 + x)/x - P, [-0x1.3ffcp-15, 0x1.3e3dp-15]);
+ // 0x1.8be5...p-96.
+ constexpr DoubleDouble COEFFS[] = {
+ {0x1.777d0ffda25ep-56, 0x1.71547652b82fep0},
+ {-0x1.777d101cf0a84p-57, -0x1.71547652b82fep-1},
+ {0x1.ce04b5140d867p-56, 0x1.ec709dc3a03fdp-2},
+ {0x1.137b47e635be5p-56, -0x1.71547652b82fbp-2},
+ {-0x1.b5a30b3bdb318p-58, 0x1.2776c516a92a2p-2},
+ {0x1.2d2fbd081e657p-57, -0x1.ec70af1929ca6p-3},
+ };
+
+ DoubleDouble dx_dd({0.0, dx2});
+ DoubleDouble p = fputil::polyeval(dx_dd, COEFFS[0], COEFFS[1], COEFFS[2],
+ COEFFS[3], COEFFS[4], COEFFS[5]);
+ // log2(1 + dx2) ~ dx2 * P(dx2)
+ DoubleDouble log2_x_lo = fputil::quick_mult(dx2, p);
+ // Lower parts of (e_x - log2(r1)) of the first range reduction constant
+ DoubleDouble log2_x_mid({LOG2_R_TD[idx_x].lo, LOG2_R_TD[idx_x].mid});
+ // -log2(r2) + lower part of (e_x - log2(r1))
+ DoubleDouble log2_x_m = fputil::add(LOG2_R2_DD[idx2], log2_x_mid);
+ // log2(1 + dx2) - log2(r2) + lower part of (e_x - log2(r1))
+ // Since we don't know which one has larger exponent to apply Fast2Sum
+ // algorithm, we need to check them before calling double-double addition.
+ DoubleDouble log2_x = larger_exponent(log2_x_m.hi, log2_x_lo.hi)
+ ? fputil::add(log2_x_m, log2_x_lo)
+ : fputil::add(log2_x_lo, log2_x_m);
+ DoubleDouble lo6_hi_dd({0.0, lo6_hi});
+ // 2^6 * y * (log2(1 + dx2) - log2(r2) + lower part of (e_x - log2(r1)))
+ DoubleDouble prod = fputil::quick_mult(y6, log2_x);
+ // 2^6 * (y * log2(x) - (hi + mid)) = 2^6 * lo
+ DoubleDouble lo6 = larger_exponent(prod.hi, lo6_hi)
+ ? fputil::add(prod, lo6_hi_dd)
+ : fputil::add(lo6_hi_dd, prod);
+
+ constexpr DoubleDouble EXP2_COEFFS[] = {
+ {0, 0x1p0},
+ {0x1.abc9e3b398024p-62, 0x1.62e42fefa39efp-7},
+ {-0x1.5e43a5429bddbp-69, 0x1.ebfbdff82c58fp-15},
+ {-0x1.d33162491268fp-77, 0x1.c6b08d704a0cp-23},
+ {0x1.4fb32d240a14ep-86, 0x1.3b2ab6fba4e77p-31},
+ {0x1.e84e916be83ep-97, 0x1.5d87fe78a6731p-40},
+ {-0x1.9a447bfddc5e6p-103, 0x1.430912f86bfb8p-49},
+ {-0x1.31a55719de47fp-113, 0x1.ffcbfc588ded9p-59},
+ {-0x1.0ba57164eb36bp-122, 0x1.62c034beb8339p-68},
+ {-0x1.8483eabd9642dp-132, 0x1.b5251ff97bee1p-78},
+ };
+
+ DoubleDouble pp = fputil::polyeval(
+ lo6, EXP2_COEFFS[0], EXP2_COEFFS[1], EXP2_COEFFS[2], EXP2_COEFFS[3],
+ EXP2_COEFFS[4], EXP2_COEFFS[5], EXP2_COEFFS[6], EXP2_COEFFS[7],
+ EXP2_COEFFS[8], EXP2_COEFFS[9]);
+ DoubleDouble rr = fputil::quick_mult(exp2_hi_mid, pp);
+
+ // Make sure the sum is normalized:
+ DoubleDouble r = fputil::exact_add(rr.hi, rr.lo);
+ // Round to odd.
+ uint64_t r_bits = cpp::bit_cast<uint64_t>(r.hi);
+ if (LIBC_UNLIKELY(((r_bits & 0xfff'ffff) == 0) && (r.lo != 0.0))) {
+ bool hi_sign = DoubleBits(r.hi).get_sign();
+ bool lo_sign = DoubleBits(r.lo).get_sign();
+ if (hi_sign == lo_sign) {
+ ++r_bits;
+ } else if ((r_bits & DoubleProp::MANTISSA_MASK) > 0) {
+ --r_bits;
+ }
+ }
+
+ return cpp::bit_cast<double>(r_bits);
+}
+
+} // namespace
+
+LLVM_LIBC_FUNCTION(float, powf, (float x, float y)) {
+ using FloatBits = typename fputil::FPBits<float>;
+ using FloatProp = typename fputil::FloatProperties<float>;
+ using DoubleProp = typename fputil::FloatProperties<double>;
+ FloatBits xbits(x), ybits(y);
+
+ uint32_t x_u = xbits.uintval();
+ uint32_t x_abs = x_u & FloatProp::EXP_MANT_MASK;
+ uint32_t y_u = ybits.uintval();
+ uint32_t y_abs = y_u & FloatProp::EXP_MANT_MASK;
+
+ ///////// BEGIN - Check exceptional cases ////////////////////////////////////
+
+ // The single precision number that is closest to 1 is (1 - 2^-24), which has
+ // log2(1 - 2^-24) ~ -1.715...p-24.
+ // So if |y| > 151 * 2^24, and x is finite:
+ // |y * log2(x)| = 0 or > 151.
+ // Hence x^y will either overflow or underflow if x is not zero.
+ if (LIBC_UNLIKELY((y_abs & 0x007f'ffff) == 0) || (y_abs > 0x4f170000)) {
+ // Exceptional exponents.
+ switch (y_abs) {
+ case 0x0000'0000: { // y = +-0.0f
+ return 1.0f;
+ }
+ case 0x7f80'0000: { // y = +-Inf
+ if (x_abs > 0x7f80'0000) {
+ // pow(NaN, +-Inf) = NaN
+ return x;
+ }
+ if (x_abs == 0x3f80'0000) {
+ // pow(+-1, +-Inf) = 1.0f
+ return 1.0f;
+ }
+ if (x_abs == 0 && y_u == 0xff80'0000) {
+ // pow(+-0, -Inf) = +inf and raise FE_DIVBYZERO
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_DIVBYZERO);
+ return FloatBits::inf().get_val();
+ }
+ // pow (|x| < 1, -inf) = +inf
+ // pow (|x| < 1, +inf) = 0.0f
+ // pow (|x| > 1, -inf) = 0.0f
+ // pow (|x| > 1, +inf) = +inf
+ return ((x_abs < 0x3f80'0000) == (y_u == 0xff80'0000))
+ ? FloatBits::inf().get_val()
+ : 0.0f;
+ }
+ default:
+ // Speed up for common exponents
+ switch (y_u) {
+ case 0x3f00'0000: // y = 0.5f
+ // pow(x, 1/2) = sqrt(x)
+ return fputil::sqrt(x);
+ case 0x3f80'0000: // y = 1.0f
+ return x;
+ case 0x4000'0000: // y = 2.0f
+ // pow(x, 2) = x^2
+ return x * x;
+ // TODO: Enable special case speed-up for x^(-1/2) when rsqrt is ready.
+ // case 0xbf00'0000: // pow(x, -1/2) = rsqrt(x)
+ // return rsqrt(x);
+ }
+ if (y_abs > 0x4f17'0000) {
+ if (y_abs > 0x7f80'0000) {
+ // y is NaN
+ if (x_u == 0x3f80'0000) { // x = 1.0f
+ // pow(1, NaN) = 1
+ return 1.0f;
+ }
+ // pow(x, NaN) = NaN
+ return y;
+ }
+ // x^y will be overflow / underflow in single precision. Set y to a
+ // large enough exponent but not too large, so that the computations
+ // won't be overflow in double precision.
+ y = cpp::bit_cast<float>((y_u & FloatProp::SIGN_MASK) + 0x4f800000U);
+ }
+ }
+ }
+
+ int ex = -FloatBits::EXPONENT_BIAS;
+ uint64_t sign = 0;
+
+ // y is finite and non-zero.
+ if (LIBC_UNLIKELY(((x_u & 0x801f'ffffU) == 0) || x_u >= 0x7f80'0000U ||
+ x_u < 0x0080'0000U)) {
+ switch (x_u) {
+ case 0x3f80'0000: // x = 1.0f
+ return 1.0f;
+ // TODO: Put these 2 entrypoint dependency under control flag.
+ case 0x4000'0000: // x = 2.0f
+ // pow(2, y) = exp2(y)
+ return exp2f(y);
+ case 0x4120'0000: // x = 10.0f
+ // pow(10, y) = exp10(y)
+ return exp10f(y);
+ }
+
+ bool x_sign = x_u >= FloatProp::SIGN_MASK;
+
+ switch (x_abs) {
+ case 0x0000'0000: { // x = +-0.0f
+ bool x_sign = (x_u >= FloatProp::SIGN_MASK);
+ bool out_sign = x_sign && is_odd_integer(FloatBits(y_u).get_val());
+ if (y_u > 0x8000'0000U) {
+ // pow(0, negative number) = inf
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_DIVBYZERO);
+ return FloatBits::inf(out_sign).get_val();
+ }
+ // pow(0, positive number) = 0
+ return out_sign ? -0.0f : 0.0f;
+ }
+ case 0x7f80'0000: { // x = +-Inf
+ bool x_sign = (x_u >= FloatProp::SIGN_MASK);
+ bool out_sign = x_sign && is_odd_integer(FloatBits(y_u).get_val());
+ if (y_u >= FloatProp::SIGN_MASK) {
+ return out_sign ? -0.0f : 0.0f;
+ }
+ return FloatBits::inf(out_sign).get_val();
+ }
+ }
+
+ if (x_abs > 0x7f80'0000) {
+ // x is NaN.
+ // pow (aNaN, 0) is already taken care above.
+ return x;
+ }
+
+ // Normalize denormal inputs.
+ if (x_abs < 0x0080'0000U) {
+ ex -= 64;
+ x *= 0x1.0p64f;
+ }
+
+ // x is finite and negative, and y is a finite integer.
+ if (x_sign) {
+ if (is_integer(y)) {
+ x = -x;
+ if (is_odd_integer(y)) {
+ // sign = -1.0;
+ sign = 0x8000'0000'0000'0000ULL;
+ }
+ } else {
+ // pow( negative, non-integer ) = NaN
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ return FloatBits::build_quiet_nan(0);
+ }
+ }
+ }
+
+ ///////// END - Check exceptional cases //////////////////////////////////////
+
+ // x^y = 2^( y * log2(x) )
+ // = 2^( y * ( e_x + log2(m_x) ) )
+ // First we compute log2(x) = e_x + log2(m_x)
+ x_u = FloatBits(x).uintval();
+
+ // Extract exponent field of x.
+ ex += (x_u >> FloatProp::MANTISSA_WIDTH);
+ double e_x = static_cast<double>(ex);
+ // Use the highest 7 fractional bits of m_x as the index for look up tables.
+ uint32_t x_mant = x_u & FloatProp::MANTISSA_MASK;
+ int idx_x = static_cast<int>(x_mant >> (FloatProp::MANTISSA_WIDTH - 7));
+ // Add the hidden bit to the mantissa.
+ // 1 <= m_x < 2
+ float m_x = cpp::bit_cast<float>(x_mant | 0x3f800000);
+
+ // Reduced argument for log2(m_x):
+ // dx = r * m_x - 1.
+ // The computation is exact, and -2^-8 <= dx < 2^-7.
+ // Then m_x = (1 + dx) / r, and
+ // log2(m_x) = log2( (1 + dx) / r )
+ // = log2(1 + dx) - log2(r).
+ double dx;
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+ dx = static_cast<double>(fputil::multiply_add(m_x, R[idx_x], -1.0f)); // Exact
+#else
+ dx = fputil::multiply_add(static_cast<double>(m_x), RD[idx_x], -1.0); // Exact
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
+ // Degree-5 polynomial approximation:
+ // dx * P(dx) ~ log2(1 + dx)
+ // Generated by Sollya with:
+ // > P = fpminimax(log2(1 + x)/x, 5, [|D...|], [-2^-8, 2^-7]);
+ // > dirtyinfnorm(log2(1 + x)/x - P, [-2^-8, 2^-7]);
+ // 0x1.653...p-52
+ constexpr double COEFFS[] = {0x1.71547652b82fep0, -0x1.71547652b7a07p-1,
+ 0x1.ec709dc458db1p-2, -0x1.715479c2266c9p-2,
+ 0x1.2776ae1ddf8fp-2, -0x1.e7b2178870157p-3};
+
+ double dx2 = dx * dx; // Exact
+ double c0 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]);
+ double c1 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]);
+ double c2 = fputil::multiply_add(dx, COEFFS[5], COEFFS[4]);
+
+ double p = fputil::polyeval(dx2, c0, c1, c2);
+
+ //////////////////////////////////////////////////////////////////////////////
+ // NOTE: For some reason, this is significantly less efficient than above!
+ //
+ // > P = fpminimax(log2(1 + x)/x, 4, [|D...|], [-2^-8, 2^-7]);
+ // > dirtyinfnorm(log2(1 + x)/x - P, [-2^-8, 2^-7]);
+ // 0x1.d04...p-44
+ // constexpr double COEFFS[] = {0x1.71547652b8133p0, -0x1.71547652d1e33p-1,
+ // 0x1.ec70a098473dep-2, -0x1.7154c5ccdf121p-2,
+ // 0x1.2514fd90a130ap-2};
+ //
+ // double dx2 = dx * dx;
+ // double c0 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]);
+ // double c1 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]);
+ // double p = fputil::polyeval(dx2, c0, c1, COEFFS[4]);
+ //////////////////////////////////////////////////////////////////////////////
+
+ // s = e_x - log2(r) + dx * P(dx)
+ // Approximation errors:
+ // |log2(x) - s| < ulp(e_x) + (bounds on dx) * (error bounds of P(dx))
+ // = ulp(e_x) + 2^-7 * 2^-51
+ // < 2^8 * 2^-52 + 2^-7 * 2^-43
+ // ~ 2^-44 + 2^-50
+ double s = fputil::multiply_add(dx, p, LOG2_R[idx_x] + e_x);
+
+ // To compute 2^(y * log2(x)), we break the exponent into 3 parts:
+ // y * log(2) = hi + mid + lo, where
+ // hi is an integer
+ // mid * 2^6 is an integer
+ // |lo| <= 2^-7
+ // Then:
+ // x^y = 2^(y * log2(x)) = 2^hi * 2^mid * 2^lo,
+ // In which 2^mid is obtained from a look-up table of size 2^6 = 64 elements,
+ // and 2^lo ~ 1 + lo * P(lo).
+ // Thus, we have:
+ // hi + mid = 2^-6 * round( 2^6 * y * log2(x) )
+ // If we restrict the output such that |hi| < 150, (hi + mid) uses (8 + 6)
+ // bits, hence, if we use double precision to perform
+ // round( 2^6 * y * log2(x))
+ // the lo part is bounded by 2^-7 + 2^(-(52 - 14)) = 2^-7 + 2^-38
+
+ // In the following computations:
+ // y6 = 2^6 * y
+ // hm = 2^6 * (hi + mid) = round(2^6 * y * log2(x)) ~ round(y6 * s)
+ // lo6 = 2^6 * lo = 2^6 * (y - (hi + mid)) = y6 * log2(x) - hm.
+ double y6 = static_cast<double>(y * 0x1.0p6f); // Exact.
+ double hm = fputil::nearest_integer(s * y6);
+ // lo6 = 2^6 * lo.
+ double lo6_hi =
+ fputil::multiply_add(y6, e_x + LOG2_R_TD[idx_x].hi, -hm); // Exact
+ // Error bounds:
+ // | (y*log2(x) - hm * 2^-6 - lo) / y| < err(dx * p) + err(LOG2_R_DD.lo)
+ // < 2^-51 + 2^-75
+ double lo6 = fputil::multiply_add(
+ y6, fputil::multiply_add(dx, p, LOG2_R_TD[idx_x].mid), lo6_hi);
+
+ // |2^(hi + mid) - exp2_hi_mid| <= ulp(exp2_hi_mid) / 2
+ // Clamp the exponent part into smaller range that fits double precision.
+ // For those exponents that are out of range, the final conversion will round
+ // them correctly to inf/max float or 0/min float accordingly.
+ int64_t hm_i = static_cast<int64_t>(hm);
+ hm_i = (hm_i > (1 << 15)) ? (1 << 15)
+ : (hm_i < (-(1 << 15)) ? -(1 << 15) : hm_i);
+
+ int idx_y = hm_i & 0x3f;
+
+ // 2^hi
+ int64_t exp_hi_i = (hm_i >> 6) << DoubleProp::MANTISSA_WIDTH;
+ // 2^mid
+ int64_t exp_mid_i = cpp::bit_cast<uint64_t>(EXP2_MID1[idx_y].hi);
+ // (-1)^sign * 2^hi * 2^mid
+ // Error <= 2^hi * 2^-53
+ uint64_t exp2_hi_mid_i = static_cast<uint64_t>(exp_hi_i + exp_mid_i) + sign;
+ double exp2_hi_mid = cpp::bit_cast<double>(exp2_hi_mid_i);
+
+ // Degree-5 polynomial approximation P(lo6) ~ 2^(lo6 / 2^6) = 2^(lo).
+ // Generated by Sollya with:
+ // > P = fpminimax(2^(x/64), 5, [|1, D...|], [-2^-1, 2^-1]);
+ // > dirtyinfnorm(2^(x/64) - P, [-0.5, 0.5]);
+ // 0x1.a2b77e618f5c4c176fd11b7659016cde5de83cb72p-60
+ constexpr double EXP2_COEFFS[] = {0x1p0,
+ 0x1.62e42fefa39efp-7,
+ 0x1.ebfbdff82a23ap-15,
+ 0x1.c6b08d7076268p-23,
+ 0x1.3b2ad33f8b48bp-31,
+ 0x1.5d870c4d84445p-40};
+
+ double lo6_sqr = lo6 * lo6;
+ double d0 = fputil::multiply_add(lo6, EXP2_COEFFS[1], EXP2_COEFFS[0]);
+ double d1 = fputil::multiply_add(lo6, EXP2_COEFFS[3], EXP2_COEFFS[2]);
+ double d2 = fputil::multiply_add(lo6, EXP2_COEFFS[5], EXP2_COEFFS[4]);
+ double pp = fputil::polyeval(lo6_sqr, d0, d1, d2);
+
+ double r = pp * exp2_hi_mid;
+
+ // Ziv accuracy test.
+ uint64_t r_u = cpp::bit_cast<uint64_t>(r);
+ float r_upper = static_cast<float>(cpp::bit_cast<double>(r_u + ERR));
+ float r_lower = static_cast<float>(cpp::bit_cast<double>(r_u - ERR));
+
+ if (LIBC_LIKELY(r_upper == r_lower)) {
+ // Check for overflow or underflow.
+ if (LIBC_UNLIKELY(FloatBits(r_upper).get_mantissa() == 0)) {
+ if (FloatBits(r_upper).is_inf()) {
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ } else if (r_upper == 0.0f) {
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_UNDERFLOW);
+ }
+ }
+ return r_upper;
+ }
+
+ // Scale lower part of 2^(hi + mid)
+ DoubleDouble exp2_hi_mid_dd;
+ exp2_hi_mid_dd.lo =
+ (idx_y != 0)
+ ? cpp::bit_cast<double>(exp_hi_i +
+ cpp::bit_cast<int64_t>(EXP2_MID1[idx_y].mid))
+ : 0.0;
+ exp2_hi_mid_dd.hi = exp2_hi_mid;
+
+ return static_cast<float>(
+ powf_double_double(idx_x, dx, y6, lo6_hi, exp2_hi_mid_dd)) +
+ 0.0f;
+ // return static_cast<float>(r);
+}
+
+} // namespace LIBC_NAMESPACE
diff --git a/libc/test/UnitTest/FPMatcher.h b/libc/test/UnitTest/FPMatcher.h
index 14c8a85ba7ad480..132952e6532b816 100644
--- a/libc/test/UnitTest/FPMatcher.h
+++ b/libc/test/UnitTest/FPMatcher.h
@@ -67,6 +67,13 @@ template <typename T> struct FPTest : public Test {
static constexpr T aNaN = T(FPBits::build_quiet_nan(1));
static constexpr T inf = T(FPBits::inf());
static constexpr T neg_inf = T(FPBits::neg_inf());
+ static constexpr int N_ROUNDING_MODES = 4;
+ static constexpr fputil::testing::RoundingMode ROUNDING_MODES[4] = {
+ fputil::testing::RoundingMode::Nearest,
+ fputil::testing::RoundingMode::Upward,
+ fputil::testing::RoundingMode::Downward,
+ fputil::testing::RoundingMode::TowardZero,
+ };
};
} // namespace testing
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index 2ba03676a633fff..47ea0a9639b033d 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -1696,6 +1696,19 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
+add_fp_unittest(
+ powf_test
+ NEED_MPFR
+ SUITE
+ libc-math-unittests
+ SRCS
+ powf_test.cpp
+ DEPENDS
+ libc.include.math
+ libc.src.math.powf
+ libc.src.__support.FPUtil.fp_bits
+)
+
add_subdirectory(generic)
add_subdirectory(smoke)
diff --git a/libc/test/src/math/powf_test.cpp b/libc/test/src/math/powf_test.cpp
new file mode 100644
index 000000000000000..36773970baed4d7
--- /dev/null
+++ b/libc/test/src/math/powf_test.cpp
@@ -0,0 +1,123 @@
+//===-- Unittests 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 "src/__support/FPUtil/FPBits.h"
+#include "src/math/powf.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+#include <math.h>
+
+#include <errno.h>
+#include <stdint.h>
+
+using LlvmLibcPowfTest = LIBC_NAMESPACE::testing::FPTest<float>;
+using LIBC_NAMESPACE::testing::tlog;
+
+namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
+
+TEST_F(LlvmLibcPowfTest, TrickyInputs) {
+ constexpr int N = 11;
+ constexpr mpfr::BinaryInput<float> INPUTS[2] = {
+ {0x1.290bbp-124f, 0x1.1e6d92p-25f}, {0x1.2e9fb6p+5f, -0x1.1b82b6p-18f},
+ {0x1.6877f6p+60f, -0x1.75f1c6p-4f}, {0x1.0936acp-63f, -0x1.55200ep-15f},
+ {0x1.d6d72ap+43f, -0x1.749ccap-5f}, {0x1.4afb2ap-40f, 0x1.063198p+0f},
+ {0x1.0124dep+0f, -0x1.fdb016p+9f}, {0x1.1058p+0f, 0x1.ap+64f},
+ {0x1.1058p+0f, -0x1.ap+64f}, {0x1.1058p+0f, 0x1.ap+64f},
+ {0x1.fa32d4p-1f, 0x1.67a62ep+12f},
+ };
+
+ for (int i = 0; i < N; ++i) {
+ float x = INPUTS[i].x;
+ float y = INPUTS[i].y;
+ EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Pow, INPUTS[i],
+ LIBC_NAMESPACE::powf(x, y), 0.5);
+ }
+}
+
+TEST_F(LlvmLibcPowfTest, InFloatRange) {
+ constexpr uint32_t X_COUNT = 1'23;
+ constexpr uint32_t X_START = FPBits(0.25f).uintval();
+ constexpr uint32_t X_STOP = FPBits(4.0f).uintval();
+ constexpr uint32_t X_STEP = (X_STOP - X_START) / X_COUNT;
+
+ constexpr uint32_t Y_COUNT = 1'37;
+ constexpr uint32_t Y_START = FPBits(0.25f).uintval();
+ constexpr uint32_t Y_STOP = FPBits(4.0f).uintval();
+ constexpr uint32_t Y_STEP = (Y_STOP - Y_START) / Y_COUNT;
+
+ auto test = [&](mpfr::RoundingMode rounding_mode) {
+ mpfr::ForceRoundingMode __r(rounding_mode);
+ if (!__r.success)
+ return;
+
+ uint64_t fails = 0;
+ uint64_t count = 0;
+ uint64_t cc = 0;
+ float mx, my, mr = 0.0;
+ double tol = 0.5;
+
+ for (uint32_t i = 0, v = X_START; i <= X_COUNT; ++i, v += X_STEP) {
+ float x = FPBits(v).get_val();
+ if (isnan(x) || isinf(x) || x < 0.0)
+ continue;
+
+ for (uint32_t j = 0, w = Y_START; j <= Y_COUNT; ++j, w += Y_STEP) {
+ float y = FPBits(w).get_val();
+ if (isnan(y) || isinf(y))
+ continue;
+
+ libc_errno = 0;
+ float result = LIBC_NAMESPACE::powf(x, y);
+ ++cc;
+ if (isnan(result) || isinf(result))
+ continue;
+
+ ++count;
+ mpfr::BinaryInput<float> inputs{x, y};
+
+ if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Pow, inputs,
+ result, 0.5, rounding_mode)) {
+ ++fails;
+ while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(
+ mpfr::Operation::Pow, inputs, result, tol, rounding_mode)) {
+ mx = x;
+ my = y;
+ mr = result;
+
+ if (tol > 1000.0)
+ break;
+
+ tol *= 2.0;
+ }
+ }
+ }
+ }
+ if (fails || (count < cc)) {
+ tlog << " Powf failed: " << fails << "/" << count << "/" << cc
+ << " tests.\n"
+ << " Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
+ }
+ if (fails) {
+ mpfr::BinaryInput<float> inputs{mx, my};
+ EXPECT_MPFR_MATCH(mpfr::Operation::Pow, inputs, mr, 0.5, rounding_mode);
+ }
+ };
+
+ tlog << " Test Rounding To Nearest...\n";
+ test(mpfr::RoundingMode::Nearest);
+
+ tlog << " Test Rounding Downward...\n";
+ test(mpfr::RoundingMode::Downward);
+
+ tlog << " Test Rounding Upward...\n";
+ test(mpfr::RoundingMode::Upward);
+
+ tlog << " Test Rounding Toward Zero...\n";
+ test(mpfr::RoundingMode::TowardZero);
+}
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index a9b31eaf6a4944c..75508752a41fd8e 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -1534,3 +1534,15 @@ add_fp_unittest(
libc.src.math.erff
libc.src.__support.FPUtil.fp_bits
)
+
+add_fp_unittest(
+ powf_test
+ SUITE
+ libc-math-smoke-tests
+ SRCS
+ powf_test.cpp
+ DEPENDS
+ libc.include.math
+ libc.src.math.powf
+ libc.src.__support.FPUtil.fp_bits
+)
diff --git a/libc/test/src/math/smoke/powf_test.cpp b/libc/test/src/math/smoke/powf_test.cpp
new file mode 100644
index 000000000000000..1867dde0ac3beab
--- /dev/null
+++ b/libc/test/src/math/smoke/powf_test.cpp
@@ -0,0 +1,189 @@
+//===-- Unittests 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 "src/__support/FPUtil/FPBits.h"
+#include "src/math/powf.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include <math.h>
+
+#include <errno.h>
+#include <stdint.h>
+
+using LlvmLibcPowfTest = LIBC_NAMESPACE::testing::FPTest<float>;
+using LIBC_NAMESPACE::fputil::testing::ForceRoundingMode;
+using LIBC_NAMESPACE::fputil::testing::RoundingMode;
+
+TEST_F(LlvmLibcPowfTest, SpecialNumbers) {
+ constexpr float neg_odd_integer = -3.0f;
+ constexpr float neg_even_integer = -6.0f;
+ constexpr float neg_non_integer = -1.1f;
+ constexpr float pos_odd_integer = 5.0f;
+ constexpr float pos_even_integer = 8.0f;
+ constexpr float pos_non_integer = 1.1f;
+
+ for (int i = 0; i < N_ROUNDING_MODES; ++i) {
+ ForceRoundingMode __r(ROUNDING_MODES[i]);
+ if (!__r.success)
+ continue;
+
+ // pow( 0.0f, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf(zero, neg_odd_integer), FE_DIVBYZERO);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf(zero, neg_even_integer), FE_DIVBYZERO);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf(zero, neg_non_integer), FE_DIVBYZERO);
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(zero, pos_odd_integer));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(zero, pos_even_integer));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(zero, pos_non_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(zero, zero));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(zero, neg_zero));
+ EXPECT_FP_EQ(0.0f, LIBC_NAMESPACE::powf(zero, inf));
+ EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf(zero, neg_inf),
+ FE_DIVBYZERO);
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(zero, aNaN));
+
+ // pow( -0.0f, exponent )
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ neg_inf, LIBC_NAMESPACE::powf(neg_zero, neg_odd_integer), FE_DIVBYZERO);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf(neg_zero, neg_even_integer), FE_DIVBYZERO);
+ EXPECT_FP_EQ_WITH_EXCEPTION(
+ inf, LIBC_NAMESPACE::powf(neg_zero, neg_non_integer), FE_DIVBYZERO);
+ EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::powf(neg_zero, pos_odd_integer));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(neg_zero, pos_even_integer));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(neg_zero, pos_non_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(neg_zero, zero));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(neg_zero, neg_zero));
+ EXPECT_FP_EQ(0.0f, LIBC_NAMESPACE::powf(neg_zero, inf));
+ EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf(neg_zero, neg_inf),
+ FE_DIVBYZERO);
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(neg_zero, aNaN));
+
+ // pow( 1.0f, exponent )
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, zero));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, neg_zero));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, 1.0f));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, -1.0f));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, neg_odd_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, neg_even_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, neg_non_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, pos_odd_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, pos_even_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, pos_non_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, inf));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, neg_inf));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(1.0f, aNaN));
+
+ // pow( 1.0f, exponent )
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(-1.0f, zero));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(-1.0f, neg_zero));
+ EXPECT_FP_EQ(-1.0f, LIBC_NAMESPACE::powf(-1.0f, 1.0f));
+ EXPECT_FP_EQ(-1.0f, LIBC_NAMESPACE::powf(-1.0f, -1.0f));
+ EXPECT_FP_EQ(-1.0f, LIBC_NAMESPACE::powf(-1.0f, neg_odd_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(-1.0f, neg_even_integer));
+ EXPECT_FP_IS_NAN_WITH_EXCEPTION(
+ LIBC_NAMESPACE::powf(-1.0f, neg_non_integer), FE_INVALID);
+ EXPECT_FP_EQ(-1.0f, LIBC_NAMESPACE::powf(-1.0f, pos_odd_integer));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(-1.0f, pos_even_integer));
+ EXPECT_FP_IS_NAN_WITH_EXCEPTION(
+ LIBC_NAMESPACE::powf(-1.0f, pos_non_integer), FE_INVALID);
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(-1.0f, inf));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(-1.0f, neg_inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(-1.0f, aNaN));
+
+ // pow( inf, exponent )
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(inf, zero));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(inf, neg_zero));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(inf, 1.0f));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(inf, -1.0f));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(inf, neg_odd_integer));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(inf, neg_even_integer));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(inf, neg_non_integer));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(inf, pos_odd_integer));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(inf, pos_even_integer));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(inf, pos_non_integer));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(inf, inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(inf, neg_inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(inf, aNaN));
+
+ // pow( -inf, exponent )
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(neg_inf, zero));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(neg_inf, neg_zero));
+ EXPECT_FP_EQ(neg_inf, LIBC_NAMESPACE::powf(neg_inf, 1.0f));
+ EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::powf(neg_inf, -1.0f));
+ EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::powf(neg_inf, neg_odd_integer));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(neg_inf, neg_even_integer));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(neg_inf, neg_non_integer));
+ EXPECT_FP_EQ(neg_inf, LIBC_NAMESPACE::powf(neg_inf, pos_odd_integer));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(neg_inf, pos_even_integer));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(neg_inf, pos_non_integer));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(neg_inf, inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(neg_inf, neg_inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(neg_inf, aNaN));
+
+ // pow ( aNaN, exponent )
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(aNaN, zero));
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(aNaN, neg_zero));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, 1.0f));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, -1.0f));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, neg_odd_integer));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, neg_even_integer));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, neg_non_integer));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, pos_odd_integer));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, pos_even_integer));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, pos_non_integer));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, neg_inf));
+ EXPECT_FP_IS_NAN(LIBC_NAMESPACE::powf(aNaN, aNaN));
+
+ // pow ( base, inf )
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(0.1f, inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(-0.1f, inf));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(1.1f, inf));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(-1.1f, inf));
+
+ // pow ( base, -inf )
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(0.1f, neg_inf));
+ EXPECT_FP_EQ(inf, LIBC_NAMESPACE::powf(-0.1f, neg_inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(1.1f, neg_inf));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::powf(-1.1f, neg_inf));
+
+ // Exact powers of 2:
+ EXPECT_FP_EQ(0x1.0p15f, LIBC_NAMESPACE::powf(2.0f, 15.0f));
+ EXPECT_FP_EQ(0x1.0p126f, LIBC_NAMESPACE::powf(2.0f, 126.0f));
+ EXPECT_FP_EQ(0x1.0p-45f, LIBC_NAMESPACE::powf(2.0f, -45.0f));
+ EXPECT_FP_EQ(0x1.0p-126f, LIBC_NAMESPACE::powf(2.0f, -126.0f));
+ EXPECT_FP_EQ(0x1.0p-149f, LIBC_NAMESPACE::powf(2.0f, -149.0f));
+
+ // Exact powers of 10:
+ EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::powf(10.0f, 0.0f));
+ EXPECT_FP_EQ(10.0f, LIBC_NAMESPACE::powf(10.0f, 1.0f));
+ EXPECT_FP_EQ(100.0f, LIBC_NAMESPACE::powf(10.0f, 2.0f));
+ EXPECT_FP_EQ(1000.0f, LIBC_NAMESPACE::powf(10.0f, 3.0f));
+ EXPECT_FP_EQ(10000.0f, LIBC_NAMESPACE::powf(10.0f, 4.0f));
+ EXPECT_FP_EQ(100000.0f, LIBC_NAMESPACE::powf(10.0f, 5.0f));
+ EXPECT_FP_EQ(1000000.0f, LIBC_NAMESPACE::powf(10.0f, 6.0f));
+ EXPECT_FP_EQ(10000000.0f, LIBC_NAMESPACE::powf(10.0f, 7.0f));
+ EXPECT_FP_EQ(100000000.0f, LIBC_NAMESPACE::powf(10.0f, 8.0f));
+ EXPECT_FP_EQ(1000000000.0f, LIBC_NAMESPACE::powf(10.0f, 9.0f));
+ EXPECT_FP_EQ(10000000000.0f, LIBC_NAMESPACE::powf(10.0f, 10.0f));
+
+ // Overflow / Underflow:
+ if (ROUNDING_MODES[i] != RoundingMode::Downward &&
+ ROUNDING_MODES[i] != RoundingMode::TowardZero) {
+ EXPECT_FP_EQ_WITH_EXCEPTION(inf, LIBC_NAMESPACE::powf(3.1f, 201.0f),
+ FE_OVERFLOW);
+ }
+ if (ROUNDING_MODES[i] != RoundingMode::Upward) {
+ EXPECT_FP_EQ_WITH_EXCEPTION(0.0f, LIBC_NAMESPACE::powf(3.1f, -201.0f),
+ FE_UNDERFLOW);
+ }
+ }
+}
diff --git a/libc/utils/MPFRWrapper/MPFRUtils.cpp b/libc/utils/MPFRWrapper/MPFRUtils.cpp
index 0818955f14de7d3..cc100f6938f033e 100644
--- a/libc/utils/MPFRWrapper/MPFRUtils.cpp
+++ b/libc/utils/MPFRWrapper/MPFRUtils.cpp
@@ -287,6 +287,12 @@ class MPFRNumber {
return result;
}
+ MPFRNumber pow(const MPFRNumber &b) {
+ MPFRNumber result(*this);
+ mpfr_pow(result.value, value, b.value, mpfr_rounding);
+ return result;
+ }
+
MPFRNumber remquo(const MPFRNumber &divisor, int "ient) {
MPFRNumber remainder(*this);
long q;
@@ -626,6 +632,8 @@ binary_operation_one_output(Operation op, InputType x, InputType y,
return inputX.fmod(inputY);
case Operation::Hypot:
return inputX.hypot(inputY);
+ case Operation::Pow:
+ return inputX.pow(inputY);
default:
__builtin_unreachable();
}
diff --git a/libc/utils/MPFRWrapper/MPFRUtils.h b/libc/utils/MPFRWrapper/MPFRUtils.h
index b9573e89f25a4a9..25e6b0ba9ac08bc 100644
--- a/libc/utils/MPFRWrapper/MPFRUtils.h
+++ b/libc/utils/MPFRWrapper/MPFRUtils.h
@@ -70,6 +70,7 @@ enum class Operation : int {
BeginBinaryOperationsSingleOutput,
Fmod,
Hypot,
+ Pow,
EndBinaryOperationsSingleOutput,
// Operations which take two floating point numbers of the same type as
>From e01e3f3de95315d13266d10b2ed64e8a2246e654 Mon Sep 17 00:00:00 2001
From: Tue Ly <lntue.h at gmail.com>
Date: Fri, 3 Nov 2023 14:38:03 +0000
Subject: [PATCH 2/3] Fix hard-coded number of test cases in powf_test.
---
libc/test/src/math/powf_test.cpp | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/libc/test/src/math/powf_test.cpp b/libc/test/src/math/powf_test.cpp
index 36773970baed4d7..608bd85bbf0c790 100644
--- a/libc/test/src/math/powf_test.cpp
+++ b/libc/test/src/math/powf_test.cpp
@@ -23,7 +23,7 @@ namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
TEST_F(LlvmLibcPowfTest, TrickyInputs) {
constexpr int N = 11;
- constexpr mpfr::BinaryInput<float> INPUTS[2] = {
+ constexpr mpfr::BinaryInput<float> INPUTS[N] = {
{0x1.290bbp-124f, 0x1.1e6d92p-25f}, {0x1.2e9fb6p+5f, -0x1.1b82b6p-18f},
{0x1.6877f6p+60f, -0x1.75f1c6p-4f}, {0x1.0936acp-63f, -0x1.55200ep-15f},
{0x1.d6d72ap+43f, -0x1.749ccap-5f}, {0x1.4afb2ap-40f, 0x1.063198p+0f},
>From baca7eed204f42153c901e0b8ed8adfd99aecb76 Mon Sep 17 00:00:00 2001
From: Tue Ly <lntue.h at gmail.com>
Date: Mon, 6 Nov 2023 17:26:05 +0000
Subject: [PATCH 3/3] Move exp2f and exp10f implementations to header libraries
to be shared with powf and remove dependency between entrypoints.
---
libc/src/math/generic/CMakeLists.txt | 44 +++++--
libc/src/math/generic/exp10f.cpp | 123 +-------------------
libc/src/math/generic/exp10f_impl.h | 141 +++++++++++++++++++++++
libc/src/math/generic/exp2f.cpp | 150 +-----------------------
libc/src/math/generic/exp2f_impl.h | 165 +++++++++++++++++++++++++++
libc/src/math/generic/powf.cpp | 10 +-
6 files changed, 349 insertions(+), 284 deletions(-)
create mode 100644 libc/src/math/generic/exp10f_impl.h
create mode 100644 libc/src/math/generic/exp2f_impl.h
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 8fc2b0850fbc077..693887c165ce98c 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -625,12 +625,10 @@ add_entrypoint_object(
-O3
)
-add_entrypoint_object(
- exp2f
- SRCS
- exp2f.cpp
+add_header_library(
+ exp2f_impl
HDRS
- ../exp2f.h
+ exp2f_impl.h
DEPENDS
.explogxf
libc.src.__support.FPUtil.except_value_utils
@@ -641,9 +639,20 @@ add_entrypoint_object(
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
+ libc.src.__support.common
libc.include.errno
libc.src.errno.errno
libc.include.math
+)
+
+add_entrypoint_object(
+ exp2f
+ SRCS
+ exp2f.cpp
+ HDRS
+ ../exp2f.h
+ DEPENDS
+ .exp2f_impl
COMPILE_OPTIONS
-O3
)
@@ -675,12 +684,10 @@ add_entrypoint_object(
-O3
)
-add_entrypoint_object(
- exp10f
- SRCS
- exp10f.cpp
+add_header_library(
+ exp10f_impl
HDRS
- ../exp10f.h
+ exp10f_impl.h
DEPENDS
.explogxf
libc.src.__support.FPUtil.fenv_impl
@@ -690,6 +697,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
+ libc.src.__support.common
libc.include.errno
libc.src.errno.errno
libc.include.math
@@ -697,6 +705,18 @@ add_entrypoint_object(
-O3
)
+add_entrypoint_object(
+ exp10f
+ SRCS
+ exp10f.cpp
+ HDRS
+ ../exp10f.h
+ DEPENDS
+ .exp10f_impl
+ COMPILE_OPTIONS
+ -O3
+)
+
add_entrypoint_object(
expm1
SRCS
@@ -756,8 +776,8 @@ add_entrypoint_object(
DEPENDS
.common_constants
.explogxf
- .exp2f
- .exp10f
+ .exp2f_impl
+ .exp10f_impl
libc.src.__support.builtin_wrappers
libc.src.__support.CPP.bit
libc.src.__support.CPP.optional
diff --git a/libc/src/math/generic/exp10f.cpp b/libc/src/math/generic/exp10f.cpp
index 52190fb92405e7b..273b583df8e50f8 100644
--- a/libc/src/math/generic/exp10f.cpp
+++ b/libc/src/math/generic/exp10f.cpp
@@ -7,130 +7,11 @@
//===----------------------------------------------------------------------===//
#include "src/math/exp10f.h"
-#include "explogxf.h"
-#include "src/__support/FPUtil/BasicOperations.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/nearest_integer.h"
-#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/common.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-
-#include <errno.h>
+#include "src/math/generic/exp10f_impl.h"
namespace LIBC_NAMESPACE {
-LLVM_LIBC_FUNCTION(float, exp10f, (float x)) {
- using FPBits = typename fputil::FPBits<float>;
- FPBits xbits(x);
-
- uint32_t x_u = xbits.uintval();
- uint32_t x_abs = x_u & 0x7fff'ffffU;
-
- // When |x| >= log10(2^128), or x is nan
- if (LIBC_UNLIKELY(x_abs >= 0x421a'209bU)) {
- // When x < log10(2^-150) or nan
- if (x_u > 0xc234'9e35U) {
- // exp(-Inf) = 0
- if (xbits.is_inf())
- return 0.0f;
- // exp(nan) = nan
- if (xbits.is_nan())
- return x;
- if (fputil::fenv_is_round_up())
- return static_cast<float>(FPBits(FPBits::MIN_SUBNORMAL));
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_UNDERFLOW);
- return 0.0f;
- }
- // x >= log10(2^128) or nan
- if (!xbits.get_sign() && (x_u >= 0x421a'209bU)) {
- // x is finite
- if (x_u < 0x7f80'0000U) {
- int rounding = fputil::quick_get_round();
- if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
- return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
-
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_OVERFLOW);
- }
- // x is +inf or nan
- return x + static_cast<float>(FPBits::inf());
- }
- }
-
- // When |x| <= log10(2)*2^-6
- if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) {
- if (LIBC_UNLIKELY(x_u == 0xb25e'5bd9U)) { // x = -0x1.bcb7b2p-27f
- if (fputil::fenv_is_round_to_nearest())
- return 0x1.fffffep-1f;
- }
- // |x| < 2^-25
- // 10^x ~ 1 + log(10) * x
- if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
- return fputil::multiply_add(x, 0x1.26bb1cp+1f, 1.0f);
- }
-
- return static_cast<float>(Exp10Base::powb_lo(x));
- }
-
- // Exceptional value.
- if (LIBC_UNLIKELY(x_u == 0x3d14'd956U)) { // x = 0x1.29b2acp-5f
- if (fputil::fenv_is_round_up())
- return 0x1.1657c4p+0f;
- }
-
- // Exact outputs when x = 1, 2, ..., 10.
- // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)
- if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) {
- switch (x_u) {
- case 0x3f800000U: // x = 1.0f
- return 10.0f;
- case 0x40000000U: // x = 2.0f
- return 100.0f;
- case 0x40400000U: // x = 3.0f
- return 1'000.0f;
- case 0x40800000U: // x = 4.0f
- return 10'000.0f;
- case 0x40a00000U: // x = 5.0f
- return 100'000.0f;
- case 0x40c00000U: // x = 6.0f
- return 1'000'000.0f;
- case 0x40e00000U: // x = 7.0f
- return 10'000'000.0f;
- case 0x41000000U: // x = 8.0f
- return 100'000'000.0f;
- case 0x41100000U: // x = 9.0f
- return 1'000'000'000.0f;
- case 0x41200000U: // x = 10.0f
- return 10'000'000'000.0f;
- }
- }
-
- // Range reduction: 10^x = 2^(mid + hi) * 10^lo
- // rr = (2^(mid + hi), lo)
- auto rr = exp_b_range_reduc<Exp10Base>(x);
-
- // The low part is approximated by a degree-5 minimax polynomial.
- // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
- using fputil::multiply_add;
- double lo2 = rr.lo * rr.lo;
- // c0 = 1 + COEFFS[0] * lo
- double c0 = multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0);
- // c1 = COEFFS[1] + COEFFS[2] * lo
- double c1 = multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);
- // c2 = COEFFS[3] + COEFFS[4] * lo
- double c2 = multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);
- // p = c1 + c2 * lo^2
- // = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3
- double p = multiply_add(lo2, c2, c1);
- // 10^lo ~ c0 + p * lo^2
- // 10^x = 2^(mid + hi) * 10^lo
- // ~ mh * (c0 + p * lo^2)
- // = (mh * c0) + p * (mh * lo^2)
- return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh));
-}
+LLVM_LIBC_FUNCTION(float, exp10f, (float x)) { return generic::exp10f(x); }
} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/exp10f_impl.h b/libc/src/math/generic/exp10f_impl.h
new file mode 100644
index 000000000000000..1d632b160265e3f
--- /dev/null
+++ b/libc/src/math/generic/exp10f_impl.h
@@ -0,0 +1,141 @@
+//===-- Single-precision 10^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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
+#define LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
+
+#include "explogxf.h"
+#include "src/__support/FPUtil/BasicOperations.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/math/exp10f.h"
+
+#include <errno.h>
+
+namespace LIBC_NAMESPACE::generic {
+
+LIBC_INLINE float exp10f(float x) {
+ using FPBits = typename fputil::FPBits<float>;
+ FPBits xbits(x);
+
+ uint32_t x_u = xbits.uintval();
+ uint32_t x_abs = x_u & 0x7fff'ffffU;
+
+ // When |x| >= log10(2^128), or x is nan
+ if (LIBC_UNLIKELY(x_abs >= 0x421a'209bU)) {
+ // When x < log10(2^-150) or nan
+ if (x_u > 0xc234'9e35U) {
+ // exp(-Inf) = 0
+ if (xbits.is_inf())
+ return 0.0f;
+ // exp(nan) = nan
+ if (xbits.is_nan())
+ return x;
+ if (fputil::fenv_is_round_up())
+ return static_cast<float>(FPBits(FPBits::MIN_SUBNORMAL));
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_UNDERFLOW);
+ return 0.0f;
+ }
+ // x >= log10(2^128) or nan
+ if (!xbits.get_sign() && (x_u >= 0x421a'209bU)) {
+ // x is finite
+ if (x_u < 0x7f80'0000U) {
+ int rounding = fputil::quick_get_round();
+ if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
+ return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
+
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ }
+ // x is +inf or nan
+ return x + static_cast<float>(FPBits::inf());
+ }
+ }
+
+ // When |x| <= log10(2)*2^-6
+ if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) {
+ if (LIBC_UNLIKELY(x_u == 0xb25e'5bd9U)) { // x = -0x1.bcb7b2p-27f
+ if (fputil::fenv_is_round_to_nearest())
+ return 0x1.fffffep-1f;
+ }
+ // |x| < 2^-25
+ // 10^x ~ 1 + log(10) * x
+ if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
+ return fputil::multiply_add(x, 0x1.26bb1cp+1f, 1.0f);
+ }
+
+ return static_cast<float>(Exp10Base::powb_lo(x));
+ }
+
+ // Exceptional value.
+ if (LIBC_UNLIKELY(x_u == 0x3d14'd956U)) { // x = 0x1.29b2acp-5f
+ if (fputil::fenv_is_round_up())
+ return 0x1.1657c4p+0f;
+ }
+
+ // Exact outputs when x = 1, 2, ..., 10.
+ // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)
+ if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) {
+ switch (x_u) {
+ case 0x3f800000U: // x = 1.0f
+ return 10.0f;
+ case 0x40000000U: // x = 2.0f
+ return 100.0f;
+ case 0x40400000U: // x = 3.0f
+ return 1'000.0f;
+ case 0x40800000U: // x = 4.0f
+ return 10'000.0f;
+ case 0x40a00000U: // x = 5.0f
+ return 100'000.0f;
+ case 0x40c00000U: // x = 6.0f
+ return 1'000'000.0f;
+ case 0x40e00000U: // x = 7.0f
+ return 10'000'000.0f;
+ case 0x41000000U: // x = 8.0f
+ return 100'000'000.0f;
+ case 0x41100000U: // x = 9.0f
+ return 1'000'000'000.0f;
+ case 0x41200000U: // x = 10.0f
+ return 10'000'000'000.0f;
+ }
+ }
+
+ // Range reduction: 10^x = 2^(mid + hi) * 10^lo
+ // rr = (2^(mid + hi), lo)
+ auto rr = exp_b_range_reduc<Exp10Base>(x);
+
+ // The low part is approximated by a degree-5 minimax polynomial.
+ // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
+ using fputil::multiply_add;
+ double lo2 = rr.lo * rr.lo;
+ // c0 = 1 + COEFFS[0] * lo
+ double c0 = multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0);
+ // c1 = COEFFS[1] + COEFFS[2] * lo
+ double c1 = multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);
+ // c2 = COEFFS[3] + COEFFS[4] * lo
+ double c2 = multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);
+ // p = c1 + c2 * lo^2
+ // = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3
+ double p = multiply_add(lo2, c2, c1);
+ // 10^lo ~ c0 + p * lo^2
+ // 10^x = 2^(mid + hi) * 10^lo
+ // ~ mh * (c0 + p * lo^2)
+ // = (mh * c0) + p * (mh * lo^2)
+ return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh));
+}
+
+} // namespace LIBC_NAMESPACE::generic
+
+#endif // LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
diff --git a/libc/src/math/generic/exp2f.cpp b/libc/src/math/generic/exp2f.cpp
index fc91dfdfe95afa0..e6cb9383dfa2e1b 100644
--- a/libc/src/math/generic/exp2f.cpp
+++ b/libc/src/math/generic/exp2f.cpp
@@ -7,155 +7,11 @@
//===----------------------------------------------------------------------===//
#include "src/math/exp2f.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/except_value_utils.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/nearest_integer.h"
-#include "src/__support/FPUtil/rounding_mode.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-#include "src/__support/macros/properties/cpu_features.h"
-
-#include <errno.h>
-
-#include "explogxf.h"
+#include "src/__support/common.h" // for LLVM_LIBC_FUNCTION
+#include "src/math/generic/exp2f_impl.h"
namespace LIBC_NAMESPACE {
-constexpr uint32_t EXVAL1 = 0x3b42'9d37U;
-constexpr uint32_t EXVAL2 = 0xbcf3'a937U;
-constexpr uint32_t EXVAL_MASK = EXVAL1 & EXVAL2;
-
-LLVM_LIBC_FUNCTION(float, exp2f, (float x)) {
- using FPBits = typename fputil::FPBits<float>;
- FPBits xbits(x);
-
- uint32_t x_u = xbits.uintval();
- uint32_t x_abs = x_u & 0x7fff'ffffU;
-
- // When |x| >= 128, or x is nan, or |x| <= 2^-5
- if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) {
- // |x| <= 2^-5
- if (x_abs <= 0x3d00'0000) {
- // |x| < 2^-25
- if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
- return 1.0f + x;
- }
-
- // Check exceptional values.
- if (LIBC_UNLIKELY((x_u & EXVAL_MASK) == EXVAL_MASK)) {
- if (LIBC_UNLIKELY(x_u == EXVAL1)) { // x = 0x1.853a6ep-9f
- return fputil::round_result_slightly_down(0x1.00870ap+0f);
- } else if (LIBC_UNLIKELY(x_u == EXVAL2)) { // x = -0x1.e7526ep-6f
- return fputil::round_result_slightly_down(0x1.f58d62p-1f);
- }
- }
-
- // Minimax polynomial generated by Sollya with:
- // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]);
- constexpr double COEFFS[] = {
- 0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3, 0x1.c6b08d6f2d7aap-5,
- 0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13};
- double xd = static_cast<double>(x);
- double xsq = xd * xd;
- double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
- double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
- double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
- double p = fputil::polyeval(xsq, c0, c1, c2);
- double r = fputil::multiply_add(p, xd, 1.0);
- return static_cast<float>(r);
- }
-
- // x >= 128
- if (!xbits.get_sign()) {
- // x is finite
- if (x_u < 0x7f80'0000U) {
- int rounding = fputil::quick_get_round();
- if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
- return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
-
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_OVERFLOW);
- }
- // x is +inf or nan
- return x + FPBits::inf().get_val();
- }
- // x <= -150
- if (x_u >= 0xc316'0000U) {
- // exp(-Inf) = 0
- if (xbits.is_inf())
- return 0.0f;
- // exp(nan) = nan
- if (xbits.is_nan())
- return x;
- if (fputil::fenv_is_round_up())
- return FPBits(FPBits::MIN_SUBNORMAL).get_val();
- if (x != 0.0f) {
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_UNDERFLOW);
- }
- return 0.0f;
- }
- }
-
- // For -150 < x < 128, to compute 2^x, we perform the following range
- // reduction: find hi, mid, lo such that:
- // x = hi + mid + lo, in which
- // hi is an integer,
- // 0 <= mid * 2^5 < 32 is an integer
- // -2^(-6) <= lo <= 2^-6.
- // In particular,
- // hi + mid = round(x * 2^5) * 2^(-5).
- // Then,
- // 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
- // 2^mid is stored in the lookup table of 32 elements.
- // 2^lo is computed using a degree-5 minimax polynomial
- // generated by Sollya.
- // We perform 2^hi * 2^mid by simply add hi to the exponent field
- // of 2^mid.
-
- // kf = (hi + mid) * 2^5 = round(x * 2^5)
- float kf;
- int k;
-#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
- kf = fputil::nearest_integer(x * 32.0f);
- k = static_cast<int>(kf);
-#else
- constexpr float HALF[2] = {0.5f, -0.5f};
- k = static_cast<int>(fputil::multiply_add(x, 32.0f, HALF[x < 0.0f]));
- kf = static_cast<float>(k);
-#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
-
- // dx = lo = x - (hi + mid) = x - kf * 2^(-5)
- double dx = fputil::multiply_add(-0x1.0p-5f, kf, x);
-
- // hi = floor(kf * 2^(-4))
- // exp_hi = shift hi to the exponent field of double precision.
- int64_t exp_hi =
- static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS)
- << fputil::FloatProperties<double>::MANTISSA_WIDTH);
- // mh = 2^hi * 2^mid
- // mh_bits = bit field of mh
- int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp_hi;
- double mh = fputil::FPBits<double>(uint64_t(mh_bits)).get_val();
-
- // Degree-5 polynomial approximating (2^x - 1)/x generating by Sollya with:
- // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32. 1/32]);
- constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
- 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
- 0x1.5d88091198529p-10};
- double dx_sq = dx * dx;
- double c1 = fputil::multiply_add(dx, COEFFS[0], 1.0);
- double c2 = fputil::multiply_add(dx, COEFFS[2], COEFFS[1]);
- double c3 = fputil::multiply_add(dx, COEFFS[4], COEFFS[3]);
- double p = fputil::multiply_add(dx_sq, c3, c2);
- // 2^x = 2^(hi + mid + lo)
- // = 2^(hi + mid) * 2^lo
- // ~ mh * (1 + lo * P(lo))
- // = mh + (mh*lo) * P(lo)
- return static_cast<float>(fputil::multiply_add(p, dx_sq * mh, c1 * mh));
-}
+LLVM_LIBC_FUNCTION(float, exp2f, (float x)) { return generic::exp2f(x); }
} // namespace LIBC_NAMESPACE
diff --git a/libc/src/math/generic/exp2f_impl.h b/libc/src/math/generic/exp2f_impl.h
new file mode 100644
index 000000000000000..447bd43398b2bce
--- /dev/null
+++ b/libc/src/math/generic/exp2f_impl.h
@@ -0,0 +1,165 @@
+//===-- 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_MATH_GENERIC_EXP2F_IMPL_H
+#define LLVM_LIBC_SRC_MATH_GENERIC_EXP2F_IMPL_H
+
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/macros/properties/cpu_features.h"
+
+#include <errno.h>
+
+#include "explogxf.h"
+
+namespace LIBC_NAMESPACE::generic {
+
+LIBC_INLINE float exp2f(float x) {
+ constexpr uint32_t EXVAL1 = 0x3b42'9d37U;
+ constexpr uint32_t EXVAL2 = 0xbcf3'a937U;
+ constexpr uint32_t EXVAL_MASK = EXVAL1 & EXVAL2;
+
+ using FPBits = typename fputil::FPBits<float>;
+ FPBits xbits(x);
+
+ uint32_t x_u = xbits.uintval();
+ uint32_t x_abs = x_u & 0x7fff'ffffU;
+
+ // When |x| >= 128, or x is nan, or |x| <= 2^-5
+ if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) {
+ // |x| <= 2^-5
+ if (x_abs <= 0x3d00'0000) {
+ // |x| < 2^-25
+ if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
+ return 1.0f + x;
+ }
+
+ // Check exceptional values.
+ if (LIBC_UNLIKELY((x_u & EXVAL_MASK) == EXVAL_MASK)) {
+ if (LIBC_UNLIKELY(x_u == EXVAL1)) { // x = 0x1.853a6ep-9f
+ return fputil::round_result_slightly_down(0x1.00870ap+0f);
+ } else if (LIBC_UNLIKELY(x_u == EXVAL2)) { // x = -0x1.e7526ep-6f
+ return fputil::round_result_slightly_down(0x1.f58d62p-1f);
+ }
+ }
+
+ // Minimax polynomial generated by Sollya with:
+ // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]);
+ constexpr double COEFFS[] = {
+ 0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3, 0x1.c6b08d6f2d7aap-5,
+ 0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13};
+ double xd = static_cast<double>(x);
+ double xsq = xd * xd;
+ double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
+ double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
+ double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
+ double p = fputil::polyeval(xsq, c0, c1, c2);
+ double r = fputil::multiply_add(p, xd, 1.0);
+ return static_cast<float>(r);
+ }
+
+ // x >= 128
+ if (!xbits.get_sign()) {
+ // x is finite
+ if (x_u < 0x7f80'0000U) {
+ int rounding = fputil::quick_get_round();
+ if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
+ return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
+
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ }
+ // x is +inf or nan
+ return x + FPBits::inf().get_val();
+ }
+ // x <= -150
+ if (x_u >= 0xc316'0000U) {
+ // exp(-Inf) = 0
+ if (xbits.is_inf())
+ return 0.0f;
+ // exp(nan) = nan
+ if (xbits.is_nan())
+ return x;
+ if (fputil::fenv_is_round_up())
+ return FPBits(FPBits::MIN_SUBNORMAL).get_val();
+ if (x != 0.0f) {
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_UNDERFLOW);
+ }
+ return 0.0f;
+ }
+ }
+
+ // For -150 < x < 128, to compute 2^x, we perform the following range
+ // reduction: find hi, mid, lo such that:
+ // x = hi + mid + lo, in which
+ // hi is an integer,
+ // 0 <= mid * 2^5 < 32 is an integer
+ // -2^(-6) <= lo <= 2^-6.
+ // In particular,
+ // hi + mid = round(x * 2^5) * 2^(-5).
+ // Then,
+ // 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
+ // 2^mid is stored in the lookup table of 32 elements.
+ // 2^lo is computed using a degree-5 minimax polynomial
+ // generated by Sollya.
+ // We perform 2^hi * 2^mid by simply add hi to the exponent field
+ // of 2^mid.
+
+ // kf = (hi + mid) * 2^5 = round(x * 2^5)
+ float kf;
+ int k;
+#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
+ kf = fputil::nearest_integer(x * 32.0f);
+ k = static_cast<int>(kf);
+#else
+ constexpr float HALF[2] = {0.5f, -0.5f};
+ k = static_cast<int>(fputil::multiply_add(x, 32.0f, HALF[x < 0.0f]));
+ kf = static_cast<float>(k);
+#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
+
+ // dx = lo = x - (hi + mid) = x - kf * 2^(-5)
+ double dx = fputil::multiply_add(-0x1.0p-5f, kf, x);
+
+ // hi = floor(kf * 2^(-4))
+ // exp_hi = shift hi to the exponent field of double precision.
+ int64_t exp_hi =
+ static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS)
+ << fputil::FloatProperties<double>::MANTISSA_WIDTH);
+ // mh = 2^hi * 2^mid
+ // mh_bits = bit field of mh
+ int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp_hi;
+ double mh = fputil::FPBits<double>(uint64_t(mh_bits)).get_val();
+
+ // Degree-5 polynomial approximating (2^x - 1)/x generating by Sollya with:
+ // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32. 1/32]);
+ constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
+ 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
+ 0x1.5d88091198529p-10};
+ double dx_sq = dx * dx;
+ double c1 = fputil::multiply_add(dx, COEFFS[0], 1.0);
+ double c2 = fputil::multiply_add(dx, COEFFS[2], COEFFS[1]);
+ double c3 = fputil::multiply_add(dx, COEFFS[4], COEFFS[3]);
+ double p = fputil::multiply_add(dx_sq, c3, c2);
+ // 2^x = 2^(hi + mid + lo)
+ // = 2^(hi + mid) * 2^lo
+ // ~ mh * (1 + lo * P(lo))
+ // = mh + (mh*lo) * P(lo)
+ return static_cast<float>(fputil::multiply_add(p, dx_sq * mh, c1 * mh));
+}
+
+} // namespace LIBC_NAMESPACE::generic
+
+#endif // LLVM_LIBC_SRC_MATH_GENERIC_EXP2F_IMPL_H
diff --git a/libc/src/math/generic/powf.cpp b/libc/src/math/generic/powf.cpp
index c432a4fa372f24b..9612f3d05316441 100644
--- a/libc/src/math/generic/powf.cpp
+++ b/libc/src/math/generic/powf.cpp
@@ -17,12 +17,14 @@
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/FPUtil/rounding_mode.h"
-#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/FPUtil/sqrt.h" // Speedup for powf(x, 1/2) = sqrtf(x)
#include "src/__support/builtin_wrappers.h"
#include "src/__support/common.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/math/exp10f.h"
-#include "src/math/exp2f.h"
+
+#include "exp10f_impl.h" // Speedup for powf(10, y) = exp10f(y)
+#include "exp2f_impl.h" // Speedup for powf(2, y) = exp2f(y)
#include <errno.h>
@@ -602,10 +604,10 @@ LLVM_LIBC_FUNCTION(float, powf, (float x, float y)) {
// TODO: Put these 2 entrypoint dependency under control flag.
case 0x4000'0000: // x = 2.0f
// pow(2, y) = exp2(y)
- return exp2f(y);
+ return generic::exp2f(y);
case 0x4120'0000: // x = 10.0f
// pow(10, y) = exp10(y)
- return exp10f(y);
+ return generic::exp10f(y);
}
bool x_sign = x_u >= FloatProp::SIGN_MASK;
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