[libc] [llvm] [libc][math] Refactor acoshf implementation to header-only in src/__support/math folder. (PR #148418)
Muhammad Bassiouni via llvm-commits
llvm-commits at lists.llvm.org
Sun Jul 13 22:41:42 PDT 2025
https://github.com/bassiounix updated https://github.com/llvm/llvm-project/pull/148418
>From addec87f0cd595b6dbe30e373c4b4ee80177afc6 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Thu, 10 Jul 2025 09:24:28 +0300
Subject: [PATCH 01/15] [libc][math] Refactor ldexpf128 implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/ldexpf128.h | 29 ++++++++++++++++
libc/src/__support/math/CMakeLists.txt | 10 ++++++
libc/src/__support/math/ldexpf128.h | 34 +++++++++++++++++++
libc/src/math/generic/CMakeLists.txt | 3 +-
libc/src/math/generic/ldexpf128.cpp | 7 ++--
.../llvm-project-overlay/libc/BUILD.bazel | 17 +++++++++-
7 files changed, 94 insertions(+), 7 deletions(-)
create mode 100644 libc/shared/math/ldexpf128.h
create mode 100644 libc/src/__support/math/ldexpf128.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index e2950e075a81d..7ad6b7ecb941f 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -16,5 +16,6 @@
#include "math/frexpf.h"
#include "math/frexpf128.h"
#include "math/frexpf16.h"
+#include "math/ldexpf128.h"
#endif // LLVM_LIBC_SHARED_MATH_H
diff --git a/libc/shared/math/ldexpf128.h b/libc/shared/math/ldexpf128.h
new file mode 100644
index 0000000000000..d4066beb809c7
--- /dev/null
+++ b/libc/shared/math/ldexpf128.h
@@ -0,0 +1,29 @@
+//===-- Shared ldexpf128 function -------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_LDEXPF128_H
+#define LLVM_LIBC_SHARED_MATH_LDEXPF128_H
+
+#include "include/llvm-libc-types/float128.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT128
+
+#include "shared/libc_common.h"
+#include "src/__support/math/ldexpf128.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::ldexpf128;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT128
+
+#endif // LLVM_LIBC_SHARED_MATH_LDEXPF128_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 0baf12a26a9d5..4adfc33507e5d 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -82,3 +82,13 @@ add_header_library(
DEPENDS
libc.src.__support.FPUtil.manipulation_functions
)
+
+add_header_library(
+ ldexpf128
+ HDRS
+ ldexpf128.h
+ DEPENDS
+ libc.src.__support.macros.properties.types
+ libc.src.__support.FPUtil.manipulation_functions
+ libc.include.llvm-libc-types.float128
+)
diff --git a/libc/src/__support/math/ldexpf128.h b/libc/src/__support/math/ldexpf128.h
new file mode 100644
index 0000000000000..362583093b2f3
--- /dev/null
+++ b/libc/src/__support/math/ldexpf128.h
@@ -0,0 +1,34 @@
+//===-- Implementation header for ldexpf ------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_LDEXPF128_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_LDEXPF128_H
+
+#include "include/llvm-libc-types/float128.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT128
+
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+static constexpr float128 ldexpf128(float128 x, int exp) {
+ return fputil::ldexp(x, exp);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT128
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_LDEXPF128_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 60b8f83f6101d..4ad7e71387e6c 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1944,8 +1944,7 @@ add_entrypoint_object(
HDRS
../ldexpf128.h
DEPENDS
- libc.src.__support.macros.properties.types
- libc.src.__support.FPUtil.manipulation_functions
+ libc.src.__support.math.ldexpf128
)
add_object_library(
diff --git a/libc/src/math/generic/ldexpf128.cpp b/libc/src/math/generic/ldexpf128.cpp
index 03b1a2d2032e2..40afa5b285bcd 100644
--- a/libc/src/math/generic/ldexpf128.cpp
+++ b/libc/src/math/generic/ldexpf128.cpp
@@ -7,14 +7,13 @@
//===----------------------------------------------------------------------===//
#include "src/math/ldexpf128.h"
-#include "src/__support/FPUtil/ManipulationFunctions.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
+
+#include "src/__support/math/ldexpf128.h"
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float128, ldexpf128, (float128 x, int exp)) {
- return fputil::ldexp(x, exp);
+ return math::ldexpf128(x, exp);
}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 11ea06897f822..b429d662c4d34 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2177,6 +2177,16 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_ldexpf128",
+ hdrs = ["src/__support/math/ldexpf128.h"],
+ deps = [
+ ":__support_fputil_manipulation_functions",
+ ":__support_macros_properties_types",
+ ":llvm_libc_types_float128"
+ ],
+)
+
############################### complex targets ################################
libc_function(
@@ -3330,7 +3340,12 @@ libc_math_function(name = "ldexpf")
libc_math_function(name = "ldexpl")
-libc_math_function(name = "ldexpf128")
+libc_math_function(
+ name = "ldexpf128",
+ additional_deps = [
+ ":__support_math_ldexpf128",
+ ],
+)
libc_math_function(name = "ldexpf16")
>From 697efcd8f4cd0a9e8009f4d97afd64b06575294b Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Thu, 10 Jul 2025 09:55:59 +0300
Subject: [PATCH 02/15] [libc][math] Refactor ldexpf16 implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/ldexpf16.h | 31 +++++++++++++++++
libc/src/__support/math/CMakeLists.txt | 10 ++++++
libc/src/__support/math/ldexpf16.h | 34 +++++++++++++++++++
libc/src/math/generic/CMakeLists.txt | 3 +-
libc/src/math/generic/ldexpf16.cpp | 7 ++--
.../llvm-project-overlay/libc/BUILD.bazel | 17 +++++++++-
7 files changed, 96 insertions(+), 7 deletions(-)
create mode 100644 libc/shared/math/ldexpf16.h
create mode 100644 libc/src/__support/math/ldexpf16.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 7ad6b7ecb941f..ba6b1c2a7e28e 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -17,5 +17,6 @@
#include "math/frexpf128.h"
#include "math/frexpf16.h"
#include "math/ldexpf128.h"
+#include "math/ldexpf16.h"
#endif // LLVM_LIBC_SHARED_MATH_H
diff --git a/libc/shared/math/ldexpf16.h b/libc/shared/math/ldexpf16.h
new file mode 100644
index 0000000000000..d4e39c449943e
--- /dev/null
+++ b/libc/shared/math/ldexpf16.h
@@ -0,0 +1,31 @@
+//===-- Shared ldexpf16 function --------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_ldexpf16_H
+#define LLVM_LIBC_SHARED_MATH_ldexpf16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "shared/libc_common.h"
+#include "src/__support/math/ldexpf16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace shared {
+
+using math::ldexpf16;
+
+} // namespace shared
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_ldexpf16_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 4adfc33507e5d..2215695bd9e5f 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -92,3 +92,13 @@ add_header_library(
libc.src.__support.FPUtil.manipulation_functions
libc.include.llvm-libc-types.float128
)
+
+add_header_library(
+ ldexpf16
+ HDRS
+ ldexpf16.h
+ DEPENDS
+ libc.src.__support.macros.properties.types
+ libc.src.__support.FPUtil.manipulation_functions
+ libc.include.llvm-libc-macros.float16_macros
+)
diff --git a/libc/src/__support/math/ldexpf16.h b/libc/src/__support/math/ldexpf16.h
new file mode 100644
index 0000000000000..fbead87d909a8
--- /dev/null
+++ b/libc/src/__support/math/ldexpf16.h
@@ -0,0 +1,34 @@
+//===-- Implementation header for ldexpf16 ----------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_LDEXPF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_LDEXPF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+static constexpr float16 ldexpf16(float16 x, int exp) {
+ return fputil::ldexp(x, exp);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_LDEXPF16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 4ad7e71387e6c..8be57cd97c3f3 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1933,8 +1933,7 @@ add_entrypoint_object(
HDRS
../ldexpf16.h
DEPENDS
- libc.src.__support.macros.properties.types
- libc.src.__support.FPUtil.manipulation_functions
+ libc.src.__support.math.ldexpf16
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/ldexpf16.cpp b/libc/src/math/generic/ldexpf16.cpp
index caa344b41476b..ecf16337ee79a 100644
--- a/libc/src/math/generic/ldexpf16.cpp
+++ b/libc/src/math/generic/ldexpf16.cpp
@@ -7,14 +7,13 @@
//===----------------------------------------------------------------------===//
#include "src/math/ldexpf16.h"
-#include "src/__support/FPUtil/ManipulationFunctions.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
+
+#include "src/__support/math/ldexpf16.h"
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float16, ldexpf16, (float16 x, int exp)) {
- return fputil::ldexp(x, exp);
+ return math::ldexpf16(x, exp);
}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index b429d662c4d34..5476a178bfc5a 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2187,6 +2187,16 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_ldexpf16",
+ hdrs = ["src/__support/math/ldexpf16.h"],
+ deps = [
+ ":__support_macros_properties_types",
+ ":__support_fputil_manipulation_functions",
+ ":llvm_libc_macros_float16_macros"
+ ],
+)
+
############################### complex targets ################################
libc_function(
@@ -3347,7 +3357,12 @@ libc_math_function(
],
)
-libc_math_function(name = "ldexpf16")
+libc_math_function(
+ name = "ldexpf16",
+ additional_deps = [
+ ":__support_math_ldexpf16",
+ ],
+)
libc_math_function(name = "llogb")
>From 363a701dc4a1c24353e2415f0e32cc9cdd93ff98 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Thu, 10 Jul 2025 10:26:02 +0300
Subject: [PATCH 03/15] [libc][math] Refactor ldexpf implementation to
header-only in src/__support/math folder
---
libc/shared/math.h | 1 +
libc/shared/math/ldexpf.h | 23 +++++++++++++++
libc/src/__support/math/CMakeLists.txt | 8 ++++++
libc/src/__support/math/ldexpf.h | 28 +++++++++++++++++++
libc/src/math/generic/CMakeLists.txt | 2 +-
libc/src/math/generic/ldexpf.cpp | 6 ++--
.../llvm-project-overlay/libc/BUILD.bazel | 15 +++++++++-
7 files changed, 77 insertions(+), 6 deletions(-)
create mode 100644 libc/shared/math/ldexpf.h
create mode 100644 libc/src/__support/math/ldexpf.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index ba6b1c2a7e28e..b2f1a03e0940d 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -16,6 +16,7 @@
#include "math/frexpf.h"
#include "math/frexpf128.h"
#include "math/frexpf16.h"
+#include "math/ldexpf.h"
#include "math/ldexpf128.h"
#include "math/ldexpf16.h"
diff --git a/libc/shared/math/ldexpf.h b/libc/shared/math/ldexpf.h
new file mode 100644
index 0000000000000..497933c47321f
--- /dev/null
+++ b/libc/shared/math/ldexpf.h
@@ -0,0 +1,23 @@
+//===-- Shared ldexpf function ----------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_LDEXPF_H
+#define LLVM_LIBC_SHARED_MATH_LDEXPF_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/ldexpf.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::ldexpf;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_LDEXPF_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 2215695bd9e5f..900c0ab04d3a3 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -102,3 +102,11 @@ add_header_library(
libc.src.__support.FPUtil.manipulation_functions
libc.include.llvm-libc-macros.float16_macros
)
+
+add_header_library(
+ ldexpf
+ HDRS
+ ldexpf.h
+ DEPENDS
+ libc.src.__support.FPUtil.manipulation_functions
+)
diff --git a/libc/src/__support/math/ldexpf.h b/libc/src/__support/math/ldexpf.h
new file mode 100644
index 0000000000000..3a5ec1d471337
--- /dev/null
+++ b/libc/src/__support/math/ldexpf.h
@@ -0,0 +1,28 @@
+//===-- Implementation header for ldexpf ------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_LDEXPF_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_LDEXPF_H
+
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+static constexpr float ldexpf(float x, int exp) {
+ return fputil::ldexp(x, exp);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_LDEXPF_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 8be57cd97c3f3..a9237741788ae 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1913,7 +1913,7 @@ add_entrypoint_object(
HDRS
../ldexpf.h
DEPENDS
- libc.src.__support.FPUtil.manipulation_functions
+ libc.src.__support.math.ldexpf
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/ldexpf.cpp b/libc/src/math/generic/ldexpf.cpp
index 63c5d219f7a79..c5f30bb725e6b 100644
--- a/libc/src/math/generic/ldexpf.cpp
+++ b/libc/src/math/generic/ldexpf.cpp
@@ -7,14 +7,12 @@
//===----------------------------------------------------------------------===//
#include "src/math/ldexpf.h"
-#include "src/__support/FPUtil/ManipulationFunctions.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
+#include "src/__support/math/ldexpf.h"
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float, ldexpf, (float x, int exp)) {
- return fputil::ldexp(x, exp);
+ return math::ldexpf(x, exp);
}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 5476a178bfc5a..cd608a1352a7a 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2197,6 +2197,14 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_ldexpf",
+ hdrs = ["src/__support/math/ldexpf.h"],
+ deps = [
+ ":__support_fputil_manipulation_functions",
+ ],
+)
+
############################### complex targets ################################
libc_function(
@@ -3346,7 +3354,12 @@ libc_math_function(name = "ilogbf16")
libc_math_function(name = "ldexp")
-libc_math_function(name = "ldexpf")
+libc_math_function(
+ name = "ldexpf",
+ additional_deps = [
+ ":__support_math_ldexpf",
+ ]
+)
libc_math_function(name = "ldexpl")
>From 5284b8ee97ee0ca66ffca663f89d9abd144bc256 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Fri, 11 Jul 2025 03:12:38 +0300
Subject: [PATCH 04/15] [libc][math] Refactor exp implementation to header-only
in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/exp.h | 23 +
libc/src/__support/math/CMakeLists.txt | 39 ++
libc/src/__support/math/exp.h | 449 ++++++++++++++++++
libc/src/__support/math/exp_constants.h | 174 +++++++
libc/src/__support/math/exp_utils.h | 73 +++
libc/src/math/generic/CMakeLists.txt | 22 +-
libc/src/math/generic/common_constants.cpp | 157 ------
libc/src/math/generic/common_constants.h | 8 +-
libc/src/math/generic/exp.cpp | 427 +----------------
libc/src/math/generic/explogxf.h | 57 +--
.../llvm-project-overlay/libc/BUILD.bazel | 57 ++-
12 files changed, 812 insertions(+), 675 deletions(-)
create mode 100644 libc/shared/math/exp.h
create mode 100644 libc/src/__support/math/exp.h
create mode 100644 libc/src/__support/math/exp_constants.h
create mode 100644 libc/src/__support/math/exp_utils.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index b2f1a03e0940d..51a95a96db3ce 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -19,5 +19,6 @@
#include "math/ldexpf.h"
#include "math/ldexpf128.h"
#include "math/ldexpf16.h"
+#include "math/exp.h"
#endif // LLVM_LIBC_SHARED_MATH_H
diff --git a/libc/shared/math/exp.h b/libc/shared/math/exp.h
new file mode 100644
index 0000000000000..7cdd6331e613a
--- /dev/null
+++ b/libc/shared/math/exp.h
@@ -0,0 +1,23 @@
+//===-- Shared exp function -------------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_EXP_H
+#define LLVM_LIBC_SHARED_MATH_EXP_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/exp.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::exp;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_EXP_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 900c0ab04d3a3..f7ef9e7694fe6 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -110,3 +110,42 @@ add_header_library(
DEPENDS
libc.src.__support.FPUtil.manipulation_functions
)
+
+add_header_library(
+ exp_constants
+ HDRS
+ exp_constants.h
+ DEPENDS
+ libc.src.__support.FPUtil.triple_double
+)
+
+add_header_library(
+ exp_utils
+ HDRS
+ exp_utils.h
+ DEPENDS
+ libc.src.__support.CPP.optional
+ libc.src.__support.CPP.bit
+ libc.src.__support.FPUtil.fp_bits
+)
+
+add_header_library(
+ exp
+ HDRS
+ exp.h
+ DEPENDS
+ .exp_constants
+ .exp_utils
+ libc.src.__support.CPP.bit
+ libc.src.__support.CPP.optional
+ libc.src.__support.FPUtil.dyadic_float
+ 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.triple_double
+ libc.src.__support.integer_literals
+ libc.src.__support.macros.optimization
+)
diff --git a/libc/src/__support/math/exp.h b/libc/src/__support/math/exp.h
new file mode 100644
index 0000000000000..6d9ac8d401e06
--- /dev/null
+++ b/libc/src/__support/math/exp.h
@@ -0,0 +1,449 @@
+//===-- Implementation header for exp ---------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_H
+
+#include "exp_constants.h"
+#include "exp_utils.h"
+#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/optional.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.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/triple_double.h"
+#include "src/__support/common.h"
+#include "src/__support/integer_literals.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+
+namespace LIBC_NAMESPACE_DECL {
+
+using fputil::DoubleDouble;
+using fputil::TripleDouble;
+using Float128 = typename fputil::DyadicFloat<128>;
+
+using LIBC_NAMESPACE::operator""_u128;
+
+// log2(e)
+static constexpr double LOG2_E = 0x1.71547652b82fep+0;
+
+// Error bounds:
+// Errors when using double precision.
+static constexpr double ERR_D = 0x1.8p-63;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+// Errors when using double-double precision.
+static constexpr double ERR_DD = 0x1.0p-99;
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+// -2^-12 * log(2)
+// > a = -2^-12 * log(2);
+// > b = round(a, 30, RN);
+// > c = round(a - b, 30, RN);
+// > d = round(a - b - c, D, RN);
+// Errors < 1.5 * 2^-133
+static constexpr double MLOG_2_EXP2_M12_HI = -0x1.62e42ffp-13;
+static constexpr double MLOG_2_EXP2_M12_MID = 0x1.718432a1b0e26p-47;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr double MLOG_2_EXP2_M12_MID_30 = 0x1.718432ap-47;
+static constexpr double MLOG_2_EXP2_M12_LO = 0x1.b0e2633fe0685p-79;
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+namespace {
+
+// Polynomial approximations with double precision:
+// Return expm1(dx) / x ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
+// For |dx| < 2^-13 + 2^-30:
+// | output - expm1(dx) / dx | < 2^-51.
+static constexpr double poly_approx_d(double dx) {
+ // dx^2
+ double dx2 = dx * dx;
+ // c0 = 1 + dx / 2
+ double c0 = fputil::multiply_add(dx, 0.5, 1.0);
+ // c1 = 1/6 + dx / 24
+ double c1 =
+ fputil::multiply_add(dx, 0x1.5555555555555p-5, 0x1.5555555555555p-3);
+ // p = dx^2 * c1 + c0 = 1 + dx / 2 + dx^2 / 6 + dx^3 / 24
+ double p = fputil::multiply_add(dx2, c1, c0);
+ return p;
+}
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+// Polynomial approximation with double-double precision:
+// Return exp(dx) ~ 1 + dx + dx^2 / 2 + ... + dx^6 / 720
+// For |dx| < 2^-13 + 2^-30:
+// | output - exp(dx) | < 2^-101
+static constexpr DoubleDouble poly_approx_dd(const DoubleDouble &dx) {
+ // Taylor polynomial.
+ constexpr DoubleDouble COEFFS[] = {
+ {0, 0x1p0}, // 1
+ {0, 0x1p0}, // 1
+ {0, 0x1p-1}, // 1/2
+ {0x1.5555555555555p-57, 0x1.5555555555555p-3}, // 1/6
+ {0x1.5555555555555p-59, 0x1.5555555555555p-5}, // 1/24
+ {0x1.1111111111111p-63, 0x1.1111111111111p-7}, // 1/120
+ {-0x1.f49f49f49f49fp-65, 0x1.6c16c16c16c17p-10}, // 1/720
+ };
+
+ DoubleDouble p = fputil::polyeval(dx, COEFFS[0], COEFFS[1], COEFFS[2],
+ COEFFS[3], COEFFS[4], COEFFS[5], COEFFS[6]);
+ return p;
+}
+
+// Polynomial approximation with 128-bit precision:
+// Return exp(dx) ~ 1 + dx + dx^2 / 2 + ... + dx^7 / 5040
+// For |dx| < 2^-13 + 2^-30:
+// | output - exp(dx) | < 2^-126.
+static constexpr Float128 poly_approx_f128(const Float128 &dx) {
+ constexpr Float128 COEFFS_128[]{
+ {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
+ {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
+ {Sign::POS, -128, 0x80000000'00000000'00000000'00000000_u128}, // 0.5
+ {Sign::POS, -130, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/6
+ {Sign::POS, -132, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/24
+ {Sign::POS, -134, 0x88888888'88888888'88888888'88888889_u128}, // 1/120
+ {Sign::POS, -137, 0xb60b60b6'0b60b60b'60b60b60'b60b60b6_u128}, // 1/720
+ {Sign::POS, -140, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // 1/5040
+ };
+
+ Float128 p = fputil::polyeval(dx, COEFFS_128[0], COEFFS_128[1], COEFFS_128[2],
+ COEFFS_128[3], COEFFS_128[4], COEFFS_128[5],
+ COEFFS_128[6], COEFFS_128[7]);
+ return p;
+}
+
+// Compute exp(x) using 128-bit precision.
+// TODO(lntue): investigate triple-double precision implementation for this
+// step.
+static constexpr Float128 exp_f128(double x, double kd, int idx1, int idx2) {
+ // Recalculate dx:
+
+ double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
+ double t2 = kd * MLOG_2_EXP2_M12_MID_30; // exact
+ double t3 = kd * MLOG_2_EXP2_M12_LO; // Error < 2^-133
+
+ Float128 dx = fputil::quick_add(
+ Float128(t1), fputil::quick_add(Float128(t2), Float128(t3)));
+
+ // TODO: Skip recalculating exp_mid1 and exp_mid2.
+ Float128 exp_mid1 =
+ fputil::quick_add(Float128(EXP2_MID1[idx1].hi),
+ fputil::quick_add(Float128(EXP2_MID1[idx1].mid),
+ Float128(EXP2_MID1[idx1].lo)));
+
+ Float128 exp_mid2 =
+ fputil::quick_add(Float128(EXP2_MID2[idx2].hi),
+ fputil::quick_add(Float128(EXP2_MID2[idx2].mid),
+ Float128(EXP2_MID2[idx2].lo)));
+
+ Float128 exp_mid = fputil::quick_mul(exp_mid1, exp_mid2);
+
+ Float128 p = poly_approx_f128(dx);
+
+ Float128 r = fputil::quick_mul(exp_mid, p);
+
+ r.exponent += static_cast<int>(kd) >> 12;
+
+ return r;
+}
+
+// Compute exp(x) with double-double precision.
+static constexpr DoubleDouble exp_double_double(double x, double kd,
+ const DoubleDouble &exp_mid) {
+ // Recalculate dx:
+ // dx = x - k * 2^-12 * log(2)
+ double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
+ double t2 = kd * MLOG_2_EXP2_M12_MID_30; // exact
+ double t3 = kd * MLOG_2_EXP2_M12_LO; // Error < 2^-130
+
+ DoubleDouble dx = fputil::exact_add(t1, t2);
+ dx.lo += t3;
+
+ // Degree-6 Taylor polynomial approximation in double-double precision.
+ // | p - exp(x) | < 2^-100.
+ DoubleDouble p = poly_approx_dd(dx);
+
+ // Error bounds: 2^-99.
+ DoubleDouble r = fputil::quick_mult(exp_mid, p);
+
+ return r;
+}
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+// Check for exceptional cases when
+// |x| <= 2^-53 or x < log(2^-1075) or x >= 0x1.6232bdd7abcd3p+9
+static constexpr double set_exceptional(double x) {
+ using FPBits = typename fputil::FPBits<double>;
+ FPBits xbits(x);
+
+ uint64_t x_u = xbits.uintval();
+ uint64_t x_abs = xbits.abs().uintval();
+
+ // |x| <= 2^-53
+ if (x_abs <= 0x3ca0'0000'0000'0000ULL) {
+ // exp(x) ~ 1 + x
+ return 1 + x;
+ }
+
+ // x <= log(2^-1075) || x >= 0x1.6232bdd7abcd3p+9 or inf/nan.
+
+ // x <= log(2^-1075) or -inf/nan
+ if (x_u >= 0xc087'4910'd52d'3052ULL) {
+ // exp(-Inf) = 0
+ if (xbits.is_inf())
+ return 0.0;
+
+ // exp(nan) = nan
+ if (xbits.is_nan())
+ return x;
+
+ if (fputil::quick_get_round() == FE_UPWARD)
+ return FPBits::min_subnormal().get_val();
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_UNDERFLOW);
+ return 0.0;
+ }
+
+ // x >= round(log(MAX_NORMAL), D, RU) = 0x1.62e42fefa39fp+9 or +inf/nan
+ // x is finite
+ if (x_u < 0x7ff0'0000'0000'0000ULL) {
+ int rounding = fputil::quick_get_round();
+ if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
+ return FPBits::max_normal().get_val();
+
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ }
+ // x is +inf or nan
+ return x + FPBits::inf().get_val();
+}
+
+} // namespace
+
+namespace math {
+
+static constexpr double exp(double x) {
+ using FPBits = typename fputil::FPBits<double>;
+ FPBits xbits(x);
+
+ uint64_t x_u = xbits.uintval();
+
+ // Upper bound: max normal number = 2^1023 * (2 - 2^-52)
+ // > round(log (2^1023 ( 2 - 2^-52 )), D, RU) = 0x1.62e42fefa39fp+9
+ // > round(log (2^1023 ( 2 - 2^-52 )), D, RD) = 0x1.62e42fefa39efp+9
+ // > round(log (2^1023 ( 2 - 2^-52 )), D, RN) = 0x1.62e42fefa39efp+9
+ // > round(exp(0x1.62e42fefa39fp+9), D, RN) = infty
+
+ // Lower bound: min denormal number / 2 = 2^-1075
+ // > round(log(2^-1075), D, RN) = -0x1.74910d52d3052p9
+
+ // Another lower bound: min normal number = 2^-1022
+ // > round(log(2^-1022), D, RN) = -0x1.6232bdd7abcd2p9
+
+ // x < log(2^-1075) or x >= 0x1.6232bdd7abcd3p+9 or |x| < 2^-53.
+ if (LIBC_UNLIKELY(x_u >= 0xc0874910d52d3052 ||
+ (x_u < 0xbca0000000000000 && x_u >= 0x40862e42fefa39f0) ||
+ x_u < 0x3ca0000000000000)) {
+ return set_exceptional(x);
+ }
+
+ // Now log(2^-1075) <= x <= -2^-53 or 2^-53 <= x < log(2^1023 * (2 - 2^-52))
+
+ // Range reduction:
+ // Let x = log(2) * (hi + mid1 + mid2) + lo
+ // in which:
+ // hi is an integer
+ // mid1 * 2^6 is an integer
+ // mid2 * 2^12 is an integer
+ // then:
+ // exp(x) = 2^hi * 2^(mid1) * 2^(mid2) * exp(lo).
+ // With this formula:
+ // - multiplying by 2^hi is exact and cheap, simply by adding the exponent
+ // field.
+ // - 2^(mid1) and 2^(mid2) are stored in 2 x 64-element tables.
+ // - exp(lo) ~ 1 + lo + a0 * lo^2 + ...
+ //
+ // They can be defined by:
+ // hi + mid1 + mid2 = 2^(-12) * round(2^12 * log_2(e) * x)
+ // If we store L2E = round(log2(e), D, RN), then:
+ // log2(e) - L2E ~ 1.5 * 2^(-56)
+ // So the errors when computing in double precision is:
+ // | x * 2^12 * log_2(e) - D(x * 2^12 * L2E) | <=
+ // <= | x * 2^12 * log_2(e) - x * 2^12 * L2E | +
+ // + | x * 2^12 * L2E - D(x * 2^12 * L2E) |
+ // <= 2^12 * ( |x| * 1.5 * 2^-56 + eps(x)) for RN
+ // 2^12 * ( |x| * 1.5 * 2^-56 + 2*eps(x)) for other rounding modes.
+ // So if:
+ // hi + mid1 + mid2 = 2^(-12) * round(x * 2^12 * L2E) is computed entirely
+ // in double precision, the reduced argument:
+ // lo = x - log(2) * (hi + mid1 + mid2) is bounded by:
+ // |lo| <= 2^-13 + (|x| * 1.5 * 2^-56 + 2*eps(x))
+ // < 2^-13 + (1.5 * 2^9 * 1.5 * 2^-56 + 2*2^(9 - 52))
+ // < 2^-13 + 2^-41
+ //
+
+ // The following trick computes the round(x * L2E) more efficiently
+ // than using the rounding instructions, with the tradeoff for less accuracy,
+ // and hence a slightly larger range for the reduced argument `lo`.
+ //
+ // To be precise, since |x| < |log(2^-1075)| < 1.5 * 2^9,
+ // |x * 2^12 * L2E| < 1.5 * 2^9 * 1.5 < 2^23,
+ // So we can fit the rounded result round(x * 2^12 * L2E) in int32_t.
+ // Thus, the goal is to be able to use an additional addition and fixed width
+ // shift to get an int32_t representing round(x * 2^12 * L2E).
+ //
+ // Assuming int32_t using 2-complement representation, since the mantissa part
+ // of a double precision is unsigned with the leading bit hidden, if we add an
+ // extra constant C = 2^e1 + 2^e2 with e1 > e2 >= 2^25 to the product, the
+ // part that are < 2^e2 in resulted mantissa of (x*2^12*L2E + C) can be
+ // considered as a proper 2-complement representations of x*2^12*L2E.
+ //
+ // One small problem with this approach is that the sum (x*2^12*L2E + C) in
+ // double precision is rounded to the least significant bit of the dorminant
+ // factor C. In order to minimize the rounding errors from this addition, we
+ // want to minimize e1. Another constraint that we want is that after
+ // shifting the mantissa so that the least significant bit of int32_t
+ // corresponds to the unit bit of (x*2^12*L2E), the sign is correct without
+ // any adjustment. So combining these 2 requirements, we can choose
+ // C = 2^33 + 2^32, so that the sign bit corresponds to 2^31 bit, and hence
+ // after right shifting the mantissa, the resulting int32_t has correct sign.
+ // With this choice of C, the number of mantissa bits we need to shift to the
+ // right is: 52 - 33 = 19.
+ //
+ // Moreover, since the integer right shifts are equivalent to rounding down,
+ // we can add an extra 0.5 so that it will become round-to-nearest, tie-to-
+ // +infinity. So in particular, we can compute:
+ // hmm = x * 2^12 * L2E + C,
+ // where C = 2^33 + 2^32 + 2^-1, then if
+ // k = int32_t(lower 51 bits of double(x * 2^12 * L2E + C) >> 19),
+ // the reduced argument:
+ // lo = x - log(2) * 2^-12 * k is bounded by:
+ // |lo| <= 2^-13 + 2^-41 + 2^-12*2^-19
+ // = 2^-13 + 2^-31 + 2^-41.
+ //
+ // Finally, notice that k only uses the mantissa of x * 2^12 * L2E, so the
+ // exponent 2^12 is not needed. So we can simply define
+ // C = 2^(33 - 12) + 2^(32 - 12) + 2^(-13 - 12), and
+ // k = int32_t(lower 51 bits of double(x * L2E + C) >> 19).
+
+ // Rounding errors <= 2^-31 + 2^-41.
+ double tmp = fputil::multiply_add(x, LOG2_E, 0x1.8000'0000'4p21);
+ int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
+ double kd = static_cast<double>(k);
+
+ uint32_t idx1 = (k >> 6) & 0x3f;
+ uint32_t idx2 = k & 0x3f;
+ int hi = k >> 12;
+
+ bool denorm = (hi <= -1022);
+
+ DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
+ DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
+
+ DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);
+
+ // |x - (hi + mid1 + mid2) * log(2) - dx| < 2^11 * eps(M_LOG_2_EXP2_M12.lo)
+ // = 2^11 * 2^-13 * 2^-52
+ // = 2^-54.
+ // |dx| < 2^-13 + 2^-30.
+ double lo_h = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
+ double dx = fputil::multiply_add(kd, MLOG_2_EXP2_M12_MID, lo_h);
+
+ // We use the degree-4 Taylor polynomial to approximate exp(lo):
+ // exp(lo) ~ 1 + lo + lo^2 / 2 + lo^3 / 6 + lo^4 / 24 = 1 + lo * P(lo)
+ // So that the errors are bounded by:
+ // |P(lo) - expm1(lo)/lo| < |lo|^4 / 64 < 2^(-13 * 4) / 64 = 2^-58
+ // Let P_ be an evaluation of P where all intermediate computations are in
+ // double precision. Using either Horner's or Estrin's schemes, the evaluated
+ // errors can be bounded by:
+ // |P_(dx) - P(dx)| < 2^-51
+ // => |dx * P_(dx) - expm1(lo) | < 1.5 * 2^-64
+ // => 2^(mid1 + mid2) * |dx * P_(dx) - expm1(lo)| < 1.5 * 2^-63.
+ // Since we approximate
+ // 2^(mid1 + mid2) ~ exp_mid.hi + exp_mid.lo,
+ // We use the expression:
+ // (exp_mid.hi + exp_mid.lo) * (1 + dx * P_(dx)) ~
+ // ~ exp_mid.hi + (exp_mid.hi * dx * P_(dx) + exp_mid.lo)
+ // with errors bounded by 1.5 * 2^-63.
+
+ double mid_lo = dx * exp_mid.hi;
+
+ // Approximate expm1(dx)/dx ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
+ double p = poly_approx_d(dx);
+
+ double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo);
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ if (LIBC_UNLIKELY(denorm)) {
+ return ziv_test_denorm</*SKIP_ZIV_TEST=*/true>(hi, exp_mid.hi, lo, ERR_D)
+ .value();
+ } else {
+ // to multiply by 2^hi, a fast way is to simply add hi to the exponent
+ // field.
+ int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
+ double r =
+ cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(exp_mid.hi + lo));
+ return r;
+ }
+#else
+ if (LIBC_UNLIKELY(denorm)) {
+ if (auto r = ziv_test_denorm(hi, exp_mid.hi, lo, ERR_D);
+ LIBC_LIKELY(r.has_value()))
+ return r.value();
+ } else {
+ double upper = exp_mid.hi + (lo + ERR_D);
+ double lower = exp_mid.hi + (lo - ERR_D);
+
+ if (LIBC_LIKELY(upper == lower)) {
+ // to multiply by 2^hi, a fast way is to simply add hi to the exponent
+ // field.
+ int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
+ double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper));
+ return r;
+ }
+ }
+
+ // Use double-double
+ DoubleDouble r_dd = exp_double_double(x, kd, exp_mid);
+
+ if (LIBC_UNLIKELY(denorm)) {
+ if (auto r = ziv_test_denorm(hi, r_dd.hi, r_dd.lo, ERR_DD);
+ LIBC_LIKELY(r.has_value()))
+ return r.value();
+ } else {
+ double upper_dd = r_dd.hi + (r_dd.lo + ERR_DD);
+ double lower_dd = r_dd.hi + (r_dd.lo - ERR_DD);
+
+ if (LIBC_LIKELY(upper_dd == lower_dd)) {
+ int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
+ double r =
+ cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper_dd));
+ return r;
+ }
+ }
+
+ // Use 128-bit precision
+ Float128 r_f128 = exp_f128(x, kd, idx1, idx2);
+
+ return static_cast<double>(r_f128);
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP_H
diff --git a/libc/src/__support/math/exp_constants.h b/libc/src/__support/math/exp_constants.h
new file mode 100644
index 0000000000000..32976a86a01ad
--- /dev/null
+++ b/libc/src/__support/math/exp_constants.h
@@ -0,0 +1,174 @@
+//===-- Constants for exp function ------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP_CONSTANTS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_CONSTANTS_H
+
+#include "src/__support/FPUtil/triple_double.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Lookup table for 2^(k * 2^-6) with k = 0..63.
+// Generated by Sollya with:
+// > display=hexadecimal;
+// > prec = 500;
+// > for i from 0 to 63 do {
+// a = 2^(i * 2^-6);
+// b = round(a, D, RN);
+// c = round(a - b, D, RN);
+// d = round(a - b - c, D, RN);
+// print("{", d, ",", c, ",", b, "},");
+// };
+alignas(16) static constexpr fputil::TripleDouble EXP2_MID1[64] = {
+ {0, 0, 0x1p0},
+ {-0x1.9085b0a3d74d5p-110, -0x1.19083535b085dp-56, 0x1.02c9a3e778061p0},
+ {0x1.05ff94f8d257ep-110, 0x1.d73e2a475b465p-55, 0x1.059b0d3158574p0},
+ {0x1.15820d96b414fp-111, 0x1.186be4bb284ffp-57, 0x1.0874518759bc8p0},
+ {-0x1.67c9bd6ebf74cp-108, 0x1.8a62e4adc610bp-54, 0x1.0b5586cf9890fp0},
+ {-0x1.5aa76994e9ddbp-113, 0x1.03a1727c57b53p-59, 0x1.0e3ec32d3d1a2p0},
+ {0x1.9d58b988f562dp-109, -0x1.6c51039449b3ap-54, 0x1.11301d0125b51p0},
+ {-0x1.2fe7bb4c76416p-108, -0x1.32fbf9af1369ep-54, 0x1.1429aaea92dep0},
+ {0x1.4f2406aa13ffp-109, -0x1.19041b9d78a76p-55, 0x1.172b83c7d517bp0},
+ {0x1.ad36183926ae8p-111, 0x1.e5b4c7b4968e4p-55, 0x1.1a35beb6fcb75p0},
+ {0x1.ea62d0881b918p-110, 0x1.e016e00a2643cp-54, 0x1.1d4873168b9aap0},
+ {-0x1.781dbc16f1ea4p-111, 0x1.dc775814a8495p-55, 0x1.2063b88628cd6p0},
+ {-0x1.4d89f9af532ep-109, 0x1.9b07eb6c70573p-54, 0x1.2387a6e756238p0},
+ {0x1.277393a461b77p-110, 0x1.2bd339940e9d9p-55, 0x1.26b4565e27cddp0},
+ {0x1.de5448560469p-111, 0x1.612e8afad1255p-55, 0x1.29e9df51fdee1p0},
+ {-0x1.ee9d8f8cb9307p-110, 0x1.0024754db41d5p-54, 0x1.2d285a6e4030bp0},
+ {0x1.7b7b2f09cd0d9p-110, 0x1.6f46ad23182e4p-55, 0x1.306fe0a31b715p0},
+ {-0x1.406a2ea6cfc6bp-108, 0x1.32721843659a6p-54, 0x1.33c08b26416ffp0},
+ {0x1.87e3e12516bfap-108, -0x1.63aeabf42eae2p-54, 0x1.371a7373aa9cbp0},
+ {0x1.9b0b1ff17c296p-111, -0x1.5e436d661f5e3p-56, 0x1.3a7db34e59ff7p0},
+ {-0x1.808ba68fa8fb7p-109, 0x1.ada0911f09ebcp-55, 0x1.3dea64c123422p0},
+ {-0x1.32b43eafc6518p-114, -0x1.ef3691c309278p-58, 0x1.4160a21f72e2ap0},
+ {-0x1.0ac312de3d922p-114, 0x1.89b7a04ef80dp-59, 0x1.44e086061892dp0},
+ {0x1.e1eebae743acp-111, 0x1.3c1a3b69062fp-56, 0x1.486a2b5c13cdp0},
+ {0x1.c06c7745c2b39p-113, 0x1.d4397afec42e2p-56, 0x1.4bfdad5362a27p0},
+ {-0x1.1aa1fd7b685cdp-112, -0x1.4b309d25957e3p-54, 0x1.4f9b2769d2ca7p0},
+ {0x1.fa733951f214cp-111, -0x1.07abe1db13cadp-55, 0x1.5342b569d4f82p0},
+ {-0x1.ff86852a613ffp-111, 0x1.9bb2c011d93adp-54, 0x1.56f4736b527dap0},
+ {-0x1.744ee506fdafep-109, 0x1.6324c054647adp-54, 0x1.5ab07dd485429p0},
+ {-0x1.95f9ab75fa7d6p-108, 0x1.ba6f93080e65ep-54, 0x1.5e76f15ad2148p0},
+ {0x1.5d8e757cfb991p-111, -0x1.383c17e40b497p-54, 0x1.6247eb03a5585p0},
+ {0x1.4a337f4dc0a3bp-108, -0x1.bb60987591c34p-54, 0x1.6623882552225p0},
+ {0x1.57d3e3adec175p-108, -0x1.bdd3413b26456p-54, 0x1.6a09e667f3bcdp0},
+ {0x1.a59f88abbe778p-115, -0x1.bbe3a683c88abp-57, 0x1.6dfb23c651a2fp0},
+ {-0x1.269796953a4c3p-109, -0x1.16e4786887a99p-55, 0x1.71f75e8ec5f74p0},
+ {-0x1.8f8e7fa19e5e8p-108, -0x1.0245957316dd3p-54, 0x1.75feb564267c9p0},
+ {-0x1.4217a932d10d4p-113, -0x1.41577ee04992fp-55, 0x1.7a11473eb0187p0},
+ {0x1.70a1427f8fcdfp-112, 0x1.05d02ba15797ep-56, 0x1.7e2f336cf4e62p0},
+ {0x1.0f6ad65cbbac1p-112, -0x1.d4c1dd41532d8p-54, 0x1.82589994cce13p0},
+ {-0x1.f16f65181d921p-109, -0x1.fc6f89bd4f6bap-54, 0x1.868d99b4492edp0},
+ {-0x1.30644a7836333p-110, 0x1.6e9f156864b27p-54, 0x1.8ace5422aa0dbp0},
+ {0x1.3bf26d2b85163p-114, 0x1.5cc13a2e3976cp-55, 0x1.8f1ae99157736p0},
+ {0x1.697e257ac0db2p-111, -0x1.75fc781b57ebcp-57, 0x1.93737b0cdc5e5p0},
+ {0x1.7edb9d7144b6fp-108, -0x1.d185b7c1b85d1p-54, 0x1.97d829fde4e5p0},
+ {0x1.6376b7943085cp-110, 0x1.c7c46b071f2bep-56, 0x1.9c49182a3f09p0},
+ {0x1.354084551b4fbp-109, -0x1.359495d1cd533p-54, 0x1.a0c667b5de565p0},
+ {-0x1.bfd7adfd63f48p-111, -0x1.d2f6edb8d41e1p-54, 0x1.a5503b23e255dp0},
+ {0x1.8b16ae39e8cb9p-109, 0x1.0fac90ef7fd31p-54, 0x1.a9e6b5579fdbfp0},
+ {0x1.a7fbc3ae675eap-108, 0x1.7a1cd345dcc81p-54, 0x1.ae89f995ad3adp0},
+ {0x1.2babc0edda4d9p-111, -0x1.2805e3084d708p-57, 0x1.b33a2b84f15fbp0},
+ {0x1.aa64481e1ab72p-111, -0x1.5584f7e54ac3bp-56, 0x1.b7f76f2fb5e47p0},
+ {0x1.9a164050e1258p-109, 0x1.23dd07a2d9e84p-55, 0x1.bcc1e904bc1d2p0},
+ {0x1.99e51125928dap-110, 0x1.11065895048ddp-55, 0x1.c199bdd85529cp0},
+ {-0x1.fc44c329d5cb2p-109, 0x1.2884dff483cadp-54, 0x1.c67f12e57d14bp0},
+ {0x1.d8765566b032ep-110, 0x1.503cbd1e949dbp-56, 0x1.cb720dcef9069p0},
+ {-0x1.e7044039da0f6p-108, -0x1.cbc3743797a9cp-54, 0x1.d072d4a07897cp0},
+ {-0x1.ab053b05531fcp-111, 0x1.2ed02d75b3707p-55, 0x1.d5818dcfba487p0},
+ {0x1.7f6246f0ec615p-108, 0x1.c2300696db532p-54, 0x1.da9e603db3285p0},
+ {0x1.b7225a944efd6p-108, -0x1.1a5cd4f184b5cp-54, 0x1.dfc97337b9b5fp0},
+ {0x1.1e92cb3c2d278p-109, 0x1.39e8980a9cc8fp-55, 0x1.e502ee78b3ff6p0},
+ {-0x1.fc0f242bbf3dep-109, -0x1.e9c23179c2893p-54, 0x1.ea4afa2a490dap0},
+ {0x1.f6dd5d229ff69p-108, 0x1.dc7f486a4b6bp-54, 0x1.efa1bee615a27p0},
+ {-0x1.4019bffc80ef3p-110, 0x1.9d3e12dd8a18bp-54, 0x1.f50765b6e454p0},
+ {0x1.dc060c36f7651p-112, 0x1.74853f3a5931ep-55, 0x1.fa7c1819e90d8p0},
+};
+
+// Lookup table for 2^(k * 2^-12) with k = 0..63.
+// Generated by Sollya with:
+// > display=hexadecimal;
+// > prec = 500;
+// > for i from 0 to 63 do {
+// a = 2^(i * 2^-12);
+// b = round(a, D, RN);
+// c = round(a - b, D, RN);
+// d = round(a - b - c, D, RN);
+// print("{", d, ",", c, ",", b, "},");
+// };
+alignas(16) static constexpr fputil::TripleDouble EXP2_MID2[64] = {
+ {0, 0, 0x1p0},
+ {0x1.39726694630e3p-108, 0x1.ae8e38c59c72ap-54, 0x1.000b175effdc7p0},
+ {0x1.e5e06ddd31156p-112, -0x1.7b5d0d58ea8f4p-58, 0x1.00162f3904052p0},
+ {0x1.5a0768b51f609p-111, 0x1.4115cb6b16a8ep-54, 0x1.0021478e11ce6p0},
+ {0x1.d008403605217p-111, -0x1.d7c96f201bb2fp-55, 0x1.002c605e2e8cfp0},
+ {0x1.89bc16f765708p-109, 0x1.84711d4c35e9fp-54, 0x1.003779a95f959p0},
+ {-0x1.4535b7f8c1e2dp-109, -0x1.0484245243777p-55, 0x1.0042936faa3d8p0},
+ {-0x1.8ba92f6b25456p-108, -0x1.4b237da2025f9p-54, 0x1.004dadb113dap0},
+ {-0x1.30c72e81f4294p-113, -0x1.5e00e62d6b30dp-56, 0x1.0058c86da1c0ap0},
+ {-0x1.34a5384e6f0b9p-110, 0x1.a1d6cedbb9481p-54, 0x1.0063e3a559473p0},
+ {0x1.f8d0580865d2ep-108, -0x1.4acf197a00142p-54, 0x1.006eff583fc3dp0},
+ {-0x1.002bcb3ae9a99p-111, -0x1.eaf2ea42391a5p-57, 0x1.007a1b865a8cap0},
+ {0x1.c3c5aedee9851p-111, 0x1.da93f90835f75p-56, 0x1.0085382faef83p0},
+ {0x1.7217851d1ec6ep-109, -0x1.6a79084ab093cp-55, 0x1.00905554425d4p0},
+ {-0x1.80cbca335a7c3p-110, 0x1.86364f8fbe8f8p-54, 0x1.009b72f41a12bp0},
+ {-0x1.706bd4eb22595p-110, -0x1.82e8e14e3110ep-55, 0x1.00a6910f3b6fdp0},
+ {-0x1.b55dd523f3c08p-111, -0x1.4f6b2a7609f71p-55, 0x1.00b1afa5abcbfp0},
+ {0x1.90a1e207cced1p-110, -0x1.e1a258ea8f71bp-56, 0x1.00bcceb7707ecp0},
+ {0x1.78d0472db37c5p-110, 0x1.4362ca5bc26f1p-56, 0x1.00c7ee448ee02p0},
+ {-0x1.bcd4db3cb52fep-109, 0x1.095a56c919d02p-54, 0x1.00d30e4d0c483p0},
+ {-0x1.cf1b131575ec2p-112, -0x1.406ac4e81a645p-57, 0x1.00de2ed0ee0f5p0},
+ {-0x1.6aaa1fa7ff913p-112, 0x1.b5a6902767e09p-54, 0x1.00e94fd0398ep0},
+ {0x1.68f236dff3218p-110, -0x1.91b2060859321p-54, 0x1.00f4714af41d3p0},
+ {-0x1.e8bb58067e60ap-109, 0x1.427068ab22306p-55, 0x1.00ff93412315cp0},
+ {0x1.d4cd5e1d71fdfp-108, 0x1.c1d0660524e08p-54, 0x1.010ab5b2cbd11p0},
+ {0x1.e4ecf350ebe88p-108, -0x1.e7bdfb3204be8p-54, 0x1.0115d89ff3a8bp0},
+ {0x1.6a2aa2c89c4f8p-109, 0x1.843aa8b9cbbc6p-55, 0x1.0120fc089ff63p0},
+ {0x1.1ca368a20ed05p-110, -0x1.34104ee7edae9p-56, 0x1.012c1fecd613bp0},
+ {0x1.edb1095d925cfp-114, -0x1.2b6aeb6176892p-56, 0x1.0137444c9b5b5p0},
+ {-0x1.488c78eded75fp-111, 0x1.a8cd33b8a1bb3p-56, 0x1.01426927f5278p0},
+ {-0x1.7480f5ea1b3c9p-113, 0x1.2edc08e5da99ap-56, 0x1.014d8e7ee8d2fp0},
+ {-0x1.ae45989a04dd5p-111, 0x1.57ba2dc7e0c73p-55, 0x1.0158b4517bb88p0},
+ {0x1.bf48007d80987p-109, 0x1.b61299ab8cdb7p-54, 0x1.0163da9fb3335p0},
+ {0x1.1aa91a059292cp-109, -0x1.90565902c5f44p-54, 0x1.016f0169949edp0},
+ {0x1.b6663292855f5p-110, 0x1.70fc41c5c2d53p-55, 0x1.017a28af25567p0},
+ {0x1.e7fbca6793d94p-108, 0x1.4b9a6e145d76cp-54, 0x1.018550706ab62p0},
+ {-0x1.5b9f5c7de3b93p-110, -0x1.008eff5142bf9p-56, 0x1.019078ad6a19fp0},
+ {0x1.4638bf2f6acabp-110, -0x1.77669f033c7dep-54, 0x1.019ba16628de2p0},
+ {-0x1.ab237b9a069c5p-109, -0x1.09bb78eeead0ap-54, 0x1.01a6ca9aac5f3p0},
+ {0x1.3ab358be97cefp-108, 0x1.371231477ece5p-54, 0x1.01b1f44af9f9ep0},
+ {-0x1.4027b2294bb64p-110, 0x1.5e7626621eb5bp-56, 0x1.01bd1e77170b4p0},
+ {0x1.656394426c99p-111, -0x1.bc72b100828a5p-54, 0x1.01c8491f08f08p0},
+ {0x1.bf9785189bdd8p-111, -0x1.ce39cbbab8bbep-57, 0x1.01d37442d507p0},
+ {0x1.7c12f86114fe3p-109, 0x1.16996709da2e2p-55, 0x1.01de9fe280ac8p0},
+ {-0x1.653d5d24b5d28p-109, -0x1.c11f5239bf535p-55, 0x1.01e9cbfe113efp0},
+ {0x1.04a0cdc1d86d7p-109, 0x1.e1d4eb5edc6b3p-55, 0x1.01f4f8958c1c6p0},
+ {0x1.c678c46149782p-109, -0x1.afb99946ee3fp-54, 0x1.020025a8f6a35p0},
+ {0x1.48524e1e9df7p-108, -0x1.8f06d8a148a32p-54, 0x1.020b533856324p0},
+ {0x1.9953ea727ff0bp-109, -0x1.2bf310fc54eb6p-55, 0x1.02168143b0281p0},
+ {-0x1.ccfbbec22d28ep-108, -0x1.c95a035eb4175p-54, 0x1.0221afcb09e3ep0},
+ {0x1.9e2bb6e181de1p-108, -0x1.491793e46834dp-54, 0x1.022cdece68c4fp0},
+ {0x1.f17609ae29308p-110, -0x1.3e8d0d9c49091p-56, 0x1.02380e4dd22adp0},
+ {-0x1.c7dc2c476bfb8p-110, -0x1.314aa16278aa3p-54, 0x1.02433e494b755p0},
+ {-0x1.fab994971d4a3p-109, 0x1.48daf888e9651p-55, 0x1.024e6ec0da046p0},
+ {0x1.848b62cbdd0afp-109, 0x1.56dc8046821f4p-55, 0x1.02599fb483385p0},
+ {-0x1.bf603ba715d0cp-109, 0x1.45b42356b9d47p-54, 0x1.0264d1244c719p0},
+ {0x1.89434e751e1aap-110, -0x1.082ef51b61d7ep-56, 0x1.027003103b10ep0},
+ {-0x1.03b54fd64e8acp-110, 0x1.2106ed0920a34p-56, 0x1.027b357854772p0},
+ {0x1.7785ea0acc486p-109, -0x1.fd4cf26ea5d0fp-54, 0x1.0286685c9e059p0},
+ {-0x1.ce447fdb35ff9p-109, -0x1.09f8775e78084p-54, 0x1.02919bbd1d1d8p0},
+ {0x1.5b884aab5642ap-112, 0x1.64cbba902ca27p-58, 0x1.029ccf99d720ap0},
+ {-0x1.cfb3e46d7c1cp-108, 0x1.4383ef231d207p-54, 0x1.02a803f2d170dp0},
+ {-0x1.0d40cee4b81afp-112, 0x1.4a47a505b3a47p-54, 0x1.02b338c811703p0},
+ {0x1.6ae7d36d7c1f7p-109, 0x1.e47120223467fp-54, 0x1.02be6e199c811p0},
+};
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP_CONSTANTS_H
diff --git a/libc/src/__support/math/exp_utils.h b/libc/src/__support/math/exp_utils.h
new file mode 100644
index 0000000000000..4bad6fa04b716
--- /dev/null
+++ b/libc/src/__support/math/exp_utils.h
@@ -0,0 +1,73 @@
+//===-- Common utils for exp function ---------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP_UTILS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_UTILS_H
+
+#include "src/__support/CPP/optional.h"
+#include "src/__support/CPP/bit.h"
+#include "src/__support/FPUtil/FPBits.h"
+
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Rounding tests for 2^hi * (mid + lo) when the output might be denormal. We
+// assume further that 1 <= mid < 2, mid + lo < 2, and |lo| << mid.
+// Notice that, if 0 < x < 2^-1022,
+// double(2^-1022 + x) - 2^-1022 = double(x).
+// So if we scale x up by 2^1022, we can use
+// double(1.0 + 2^1022 * x) - 1.0 to test how x is rounded in denormal range.
+template <bool SKIP_ZIV_TEST = false>
+static constexpr cpp::optional<double>
+ziv_test_denorm(int hi, double mid, double lo, double err) {
+ using FPBits = typename fputil::FPBits<double>;
+
+ // Scaling factor = 1/(min normal number) = 2^1022
+ int64_t exp_hi = static_cast<int64_t>(hi + 1022) << FPBits::FRACTION_LEN;
+ double mid_hi = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(mid));
+ double lo_scaled =
+ (lo != 0.0) ? cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(lo))
+ : 0.0;
+
+ double extra_factor = 0.0;
+ uint64_t scale_down = 0x3FE0'0000'0000'0000; // 1022 in the exponent field.
+
+ // Result is denormal if (mid_hi + lo_scale < 1.0).
+ if ((1.0 - mid_hi) > lo_scaled) {
+ // Extra rounding step is needed, which adds more rounding errors.
+ err += 0x1.0p-52;
+ extra_factor = 1.0;
+ scale_down = 0x3FF0'0000'0000'0000; // 1023 in the exponent field.
+ }
+
+ // By adding 1.0, the results will have similar rounding points as denormal
+ // outputs.
+ if constexpr (SKIP_ZIV_TEST) {
+ double r = extra_factor + (mid_hi + lo_scaled);
+ return cpp::bit_cast<double>(cpp::bit_cast<uint64_t>(r) - scale_down);
+ } else {
+ double err_scaled =
+ cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(err));
+
+ double lo_u = lo_scaled + err_scaled;
+ double lo_l = lo_scaled - err_scaled;
+
+ double upper = extra_factor + (mid_hi + lo_u);
+ double lower = extra_factor + (mid_hi + lo_l);
+
+ if (LIBC_LIKELY(upper == lower)) {
+ return cpp::bit_cast<double>(cpp::bit_cast<uint64_t>(upper) - scale_down);
+ }
+
+ return cpp::nullopt;
+ }
+}
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP_UTILS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index a9237741788ae..b59beacd94143 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1312,20 +1312,7 @@ add_entrypoint_object(
HDRS
../exp.h
DEPENDS
- .common_constants
- .explogxf
- libc.src.__support.CPP.bit
- libc.src.__support.CPP.optional
- libc.src.__support.FPUtil.dyadic_float
- 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.triple_double
- libc.src.__support.integer_literals
- libc.src.__support.macros.optimization
+ libc.src.__support.math.exp
libc.src.errno.errno
)
@@ -1953,8 +1940,8 @@ add_object_library(
SRCS
common_constants.cpp
DEPENDS
+ libc.src.__support.math.exp_constants
libc.src.__support.number_pair
- libc.src.__support.FPUtil.triple_double
)
add_header_library(
@@ -3818,16 +3805,13 @@ add_object_library(
explogxf.cpp
DEPENDS
.common_constants
- libc.src.__support.CPP.bit
- libc.src.__support.CPP.optional
- libc.src.__support.FPUtil.basic_operations
libc.src.__support.FPUtil.basic_operations
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.common
+ libc.src.__support.math.exp_utils
libc.src.errno.errno
)
diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp
index b2c1293c6326d..4dcf84d00ad50 100644
--- a/libc/src/math/generic/common_constants.cpp
+++ b/libc/src/math/generic/common_constants.cpp
@@ -7,7 +7,6 @@
//===----------------------------------------------------------------------===//
#include "common_constants.h"
-#include "src/__support/FPUtil/triple_double.h"
#include "src/__support/macros/config.h"
#include "src/__support/number_pair.h"
@@ -728,160 +727,4 @@ const double EXP_M2[128] = {
0x1.568bb722dd593p1, 0x1.593b7d72305bbp1,
};
-// Lookup table for 2^(k * 2^-6) with k = 0..63.
-// Generated by Sollya with:
-// > display=hexadecimal;
-// > prec = 500;
-// > for i from 0 to 63 do {
-// a = 2^(i * 2^-6);
-// b = round(a, D, RN);
-// c = round(a - b, D, RN);
-// d = round(a - b - c, D, RN);
-// print("{", d, ",", c, ",", b, "},");
-// };
-alignas(16) const fputil::TripleDouble EXP2_MID1[64] = {
- {0, 0, 0x1p0},
- {-0x1.9085b0a3d74d5p-110, -0x1.19083535b085dp-56, 0x1.02c9a3e778061p0},
- {0x1.05ff94f8d257ep-110, 0x1.d73e2a475b465p-55, 0x1.059b0d3158574p0},
- {0x1.15820d96b414fp-111, 0x1.186be4bb284ffp-57, 0x1.0874518759bc8p0},
- {-0x1.67c9bd6ebf74cp-108, 0x1.8a62e4adc610bp-54, 0x1.0b5586cf9890fp0},
- {-0x1.5aa76994e9ddbp-113, 0x1.03a1727c57b53p-59, 0x1.0e3ec32d3d1a2p0},
- {0x1.9d58b988f562dp-109, -0x1.6c51039449b3ap-54, 0x1.11301d0125b51p0},
- {-0x1.2fe7bb4c76416p-108, -0x1.32fbf9af1369ep-54, 0x1.1429aaea92dep0},
- {0x1.4f2406aa13ffp-109, -0x1.19041b9d78a76p-55, 0x1.172b83c7d517bp0},
- {0x1.ad36183926ae8p-111, 0x1.e5b4c7b4968e4p-55, 0x1.1a35beb6fcb75p0},
- {0x1.ea62d0881b918p-110, 0x1.e016e00a2643cp-54, 0x1.1d4873168b9aap0},
- {-0x1.781dbc16f1ea4p-111, 0x1.dc775814a8495p-55, 0x1.2063b88628cd6p0},
- {-0x1.4d89f9af532ep-109, 0x1.9b07eb6c70573p-54, 0x1.2387a6e756238p0},
- {0x1.277393a461b77p-110, 0x1.2bd339940e9d9p-55, 0x1.26b4565e27cddp0},
- {0x1.de5448560469p-111, 0x1.612e8afad1255p-55, 0x1.29e9df51fdee1p0},
- {-0x1.ee9d8f8cb9307p-110, 0x1.0024754db41d5p-54, 0x1.2d285a6e4030bp0},
- {0x1.7b7b2f09cd0d9p-110, 0x1.6f46ad23182e4p-55, 0x1.306fe0a31b715p0},
- {-0x1.406a2ea6cfc6bp-108, 0x1.32721843659a6p-54, 0x1.33c08b26416ffp0},
- {0x1.87e3e12516bfap-108, -0x1.63aeabf42eae2p-54, 0x1.371a7373aa9cbp0},
- {0x1.9b0b1ff17c296p-111, -0x1.5e436d661f5e3p-56, 0x1.3a7db34e59ff7p0},
- {-0x1.808ba68fa8fb7p-109, 0x1.ada0911f09ebcp-55, 0x1.3dea64c123422p0},
- {-0x1.32b43eafc6518p-114, -0x1.ef3691c309278p-58, 0x1.4160a21f72e2ap0},
- {-0x1.0ac312de3d922p-114, 0x1.89b7a04ef80dp-59, 0x1.44e086061892dp0},
- {0x1.e1eebae743acp-111, 0x1.3c1a3b69062fp-56, 0x1.486a2b5c13cdp0},
- {0x1.c06c7745c2b39p-113, 0x1.d4397afec42e2p-56, 0x1.4bfdad5362a27p0},
- {-0x1.1aa1fd7b685cdp-112, -0x1.4b309d25957e3p-54, 0x1.4f9b2769d2ca7p0},
- {0x1.fa733951f214cp-111, -0x1.07abe1db13cadp-55, 0x1.5342b569d4f82p0},
- {-0x1.ff86852a613ffp-111, 0x1.9bb2c011d93adp-54, 0x1.56f4736b527dap0},
- {-0x1.744ee506fdafep-109, 0x1.6324c054647adp-54, 0x1.5ab07dd485429p0},
- {-0x1.95f9ab75fa7d6p-108, 0x1.ba6f93080e65ep-54, 0x1.5e76f15ad2148p0},
- {0x1.5d8e757cfb991p-111, -0x1.383c17e40b497p-54, 0x1.6247eb03a5585p0},
- {0x1.4a337f4dc0a3bp-108, -0x1.bb60987591c34p-54, 0x1.6623882552225p0},
- {0x1.57d3e3adec175p-108, -0x1.bdd3413b26456p-54, 0x1.6a09e667f3bcdp0},
- {0x1.a59f88abbe778p-115, -0x1.bbe3a683c88abp-57, 0x1.6dfb23c651a2fp0},
- {-0x1.269796953a4c3p-109, -0x1.16e4786887a99p-55, 0x1.71f75e8ec5f74p0},
- {-0x1.8f8e7fa19e5e8p-108, -0x1.0245957316dd3p-54, 0x1.75feb564267c9p0},
- {-0x1.4217a932d10d4p-113, -0x1.41577ee04992fp-55, 0x1.7a11473eb0187p0},
- {0x1.70a1427f8fcdfp-112, 0x1.05d02ba15797ep-56, 0x1.7e2f336cf4e62p0},
- {0x1.0f6ad65cbbac1p-112, -0x1.d4c1dd41532d8p-54, 0x1.82589994cce13p0},
- {-0x1.f16f65181d921p-109, -0x1.fc6f89bd4f6bap-54, 0x1.868d99b4492edp0},
- {-0x1.30644a7836333p-110, 0x1.6e9f156864b27p-54, 0x1.8ace5422aa0dbp0},
- {0x1.3bf26d2b85163p-114, 0x1.5cc13a2e3976cp-55, 0x1.8f1ae99157736p0},
- {0x1.697e257ac0db2p-111, -0x1.75fc781b57ebcp-57, 0x1.93737b0cdc5e5p0},
- {0x1.7edb9d7144b6fp-108, -0x1.d185b7c1b85d1p-54, 0x1.97d829fde4e5p0},
- {0x1.6376b7943085cp-110, 0x1.c7c46b071f2bep-56, 0x1.9c49182a3f09p0},
- {0x1.354084551b4fbp-109, -0x1.359495d1cd533p-54, 0x1.a0c667b5de565p0},
- {-0x1.bfd7adfd63f48p-111, -0x1.d2f6edb8d41e1p-54, 0x1.a5503b23e255dp0},
- {0x1.8b16ae39e8cb9p-109, 0x1.0fac90ef7fd31p-54, 0x1.a9e6b5579fdbfp0},
- {0x1.a7fbc3ae675eap-108, 0x1.7a1cd345dcc81p-54, 0x1.ae89f995ad3adp0},
- {0x1.2babc0edda4d9p-111, -0x1.2805e3084d708p-57, 0x1.b33a2b84f15fbp0},
- {0x1.aa64481e1ab72p-111, -0x1.5584f7e54ac3bp-56, 0x1.b7f76f2fb5e47p0},
- {0x1.9a164050e1258p-109, 0x1.23dd07a2d9e84p-55, 0x1.bcc1e904bc1d2p0},
- {0x1.99e51125928dap-110, 0x1.11065895048ddp-55, 0x1.c199bdd85529cp0},
- {-0x1.fc44c329d5cb2p-109, 0x1.2884dff483cadp-54, 0x1.c67f12e57d14bp0},
- {0x1.d8765566b032ep-110, 0x1.503cbd1e949dbp-56, 0x1.cb720dcef9069p0},
- {-0x1.e7044039da0f6p-108, -0x1.cbc3743797a9cp-54, 0x1.d072d4a07897cp0},
- {-0x1.ab053b05531fcp-111, 0x1.2ed02d75b3707p-55, 0x1.d5818dcfba487p0},
- {0x1.7f6246f0ec615p-108, 0x1.c2300696db532p-54, 0x1.da9e603db3285p0},
- {0x1.b7225a944efd6p-108, -0x1.1a5cd4f184b5cp-54, 0x1.dfc97337b9b5fp0},
- {0x1.1e92cb3c2d278p-109, 0x1.39e8980a9cc8fp-55, 0x1.e502ee78b3ff6p0},
- {-0x1.fc0f242bbf3dep-109, -0x1.e9c23179c2893p-54, 0x1.ea4afa2a490dap0},
- {0x1.f6dd5d229ff69p-108, 0x1.dc7f486a4b6bp-54, 0x1.efa1bee615a27p0},
- {-0x1.4019bffc80ef3p-110, 0x1.9d3e12dd8a18bp-54, 0x1.f50765b6e454p0},
- {0x1.dc060c36f7651p-112, 0x1.74853f3a5931ep-55, 0x1.fa7c1819e90d8p0},
-};
-
-// Lookup table for 2^(k * 2^-12) with k = 0..63.
-// Generated by Sollya with:
-// > display=hexadecimal;
-// > prec = 500;
-// > for i from 0 to 63 do {
-// a = 2^(i * 2^-12);
-// b = round(a, D, RN);
-// c = round(a - b, D, RN);
-// d = round(a - b - c, D, RN);
-// print("{", d, ",", c, ",", b, "},");
-// };
-alignas(16) const fputil::TripleDouble EXP2_MID2[64] = {
- {0, 0, 0x1p0},
- {0x1.39726694630e3p-108, 0x1.ae8e38c59c72ap-54, 0x1.000b175effdc7p0},
- {0x1.e5e06ddd31156p-112, -0x1.7b5d0d58ea8f4p-58, 0x1.00162f3904052p0},
- {0x1.5a0768b51f609p-111, 0x1.4115cb6b16a8ep-54, 0x1.0021478e11ce6p0},
- {0x1.d008403605217p-111, -0x1.d7c96f201bb2fp-55, 0x1.002c605e2e8cfp0},
- {0x1.89bc16f765708p-109, 0x1.84711d4c35e9fp-54, 0x1.003779a95f959p0},
- {-0x1.4535b7f8c1e2dp-109, -0x1.0484245243777p-55, 0x1.0042936faa3d8p0},
- {-0x1.8ba92f6b25456p-108, -0x1.4b237da2025f9p-54, 0x1.004dadb113dap0},
- {-0x1.30c72e81f4294p-113, -0x1.5e00e62d6b30dp-56, 0x1.0058c86da1c0ap0},
- {-0x1.34a5384e6f0b9p-110, 0x1.a1d6cedbb9481p-54, 0x1.0063e3a559473p0},
- {0x1.f8d0580865d2ep-108, -0x1.4acf197a00142p-54, 0x1.006eff583fc3dp0},
- {-0x1.002bcb3ae9a99p-111, -0x1.eaf2ea42391a5p-57, 0x1.007a1b865a8cap0},
- {0x1.c3c5aedee9851p-111, 0x1.da93f90835f75p-56, 0x1.0085382faef83p0},
- {0x1.7217851d1ec6ep-109, -0x1.6a79084ab093cp-55, 0x1.00905554425d4p0},
- {-0x1.80cbca335a7c3p-110, 0x1.86364f8fbe8f8p-54, 0x1.009b72f41a12bp0},
- {-0x1.706bd4eb22595p-110, -0x1.82e8e14e3110ep-55, 0x1.00a6910f3b6fdp0},
- {-0x1.b55dd523f3c08p-111, -0x1.4f6b2a7609f71p-55, 0x1.00b1afa5abcbfp0},
- {0x1.90a1e207cced1p-110, -0x1.e1a258ea8f71bp-56, 0x1.00bcceb7707ecp0},
- {0x1.78d0472db37c5p-110, 0x1.4362ca5bc26f1p-56, 0x1.00c7ee448ee02p0},
- {-0x1.bcd4db3cb52fep-109, 0x1.095a56c919d02p-54, 0x1.00d30e4d0c483p0},
- {-0x1.cf1b131575ec2p-112, -0x1.406ac4e81a645p-57, 0x1.00de2ed0ee0f5p0},
- {-0x1.6aaa1fa7ff913p-112, 0x1.b5a6902767e09p-54, 0x1.00e94fd0398ep0},
- {0x1.68f236dff3218p-110, -0x1.91b2060859321p-54, 0x1.00f4714af41d3p0},
- {-0x1.e8bb58067e60ap-109, 0x1.427068ab22306p-55, 0x1.00ff93412315cp0},
- {0x1.d4cd5e1d71fdfp-108, 0x1.c1d0660524e08p-54, 0x1.010ab5b2cbd11p0},
- {0x1.e4ecf350ebe88p-108, -0x1.e7bdfb3204be8p-54, 0x1.0115d89ff3a8bp0},
- {0x1.6a2aa2c89c4f8p-109, 0x1.843aa8b9cbbc6p-55, 0x1.0120fc089ff63p0},
- {0x1.1ca368a20ed05p-110, -0x1.34104ee7edae9p-56, 0x1.012c1fecd613bp0},
- {0x1.edb1095d925cfp-114, -0x1.2b6aeb6176892p-56, 0x1.0137444c9b5b5p0},
- {-0x1.488c78eded75fp-111, 0x1.a8cd33b8a1bb3p-56, 0x1.01426927f5278p0},
- {-0x1.7480f5ea1b3c9p-113, 0x1.2edc08e5da99ap-56, 0x1.014d8e7ee8d2fp0},
- {-0x1.ae45989a04dd5p-111, 0x1.57ba2dc7e0c73p-55, 0x1.0158b4517bb88p0},
- {0x1.bf48007d80987p-109, 0x1.b61299ab8cdb7p-54, 0x1.0163da9fb3335p0},
- {0x1.1aa91a059292cp-109, -0x1.90565902c5f44p-54, 0x1.016f0169949edp0},
- {0x1.b6663292855f5p-110, 0x1.70fc41c5c2d53p-55, 0x1.017a28af25567p0},
- {0x1.e7fbca6793d94p-108, 0x1.4b9a6e145d76cp-54, 0x1.018550706ab62p0},
- {-0x1.5b9f5c7de3b93p-110, -0x1.008eff5142bf9p-56, 0x1.019078ad6a19fp0},
- {0x1.4638bf2f6acabp-110, -0x1.77669f033c7dep-54, 0x1.019ba16628de2p0},
- {-0x1.ab237b9a069c5p-109, -0x1.09bb78eeead0ap-54, 0x1.01a6ca9aac5f3p0},
- {0x1.3ab358be97cefp-108, 0x1.371231477ece5p-54, 0x1.01b1f44af9f9ep0},
- {-0x1.4027b2294bb64p-110, 0x1.5e7626621eb5bp-56, 0x1.01bd1e77170b4p0},
- {0x1.656394426c99p-111, -0x1.bc72b100828a5p-54, 0x1.01c8491f08f08p0},
- {0x1.bf9785189bdd8p-111, -0x1.ce39cbbab8bbep-57, 0x1.01d37442d507p0},
- {0x1.7c12f86114fe3p-109, 0x1.16996709da2e2p-55, 0x1.01de9fe280ac8p0},
- {-0x1.653d5d24b5d28p-109, -0x1.c11f5239bf535p-55, 0x1.01e9cbfe113efp0},
- {0x1.04a0cdc1d86d7p-109, 0x1.e1d4eb5edc6b3p-55, 0x1.01f4f8958c1c6p0},
- {0x1.c678c46149782p-109, -0x1.afb99946ee3fp-54, 0x1.020025a8f6a35p0},
- {0x1.48524e1e9df7p-108, -0x1.8f06d8a148a32p-54, 0x1.020b533856324p0},
- {0x1.9953ea727ff0bp-109, -0x1.2bf310fc54eb6p-55, 0x1.02168143b0281p0},
- {-0x1.ccfbbec22d28ep-108, -0x1.c95a035eb4175p-54, 0x1.0221afcb09e3ep0},
- {0x1.9e2bb6e181de1p-108, -0x1.491793e46834dp-54, 0x1.022cdece68c4fp0},
- {0x1.f17609ae29308p-110, -0x1.3e8d0d9c49091p-56, 0x1.02380e4dd22adp0},
- {-0x1.c7dc2c476bfb8p-110, -0x1.314aa16278aa3p-54, 0x1.02433e494b755p0},
- {-0x1.fab994971d4a3p-109, 0x1.48daf888e9651p-55, 0x1.024e6ec0da046p0},
- {0x1.848b62cbdd0afp-109, 0x1.56dc8046821f4p-55, 0x1.02599fb483385p0},
- {-0x1.bf603ba715d0cp-109, 0x1.45b42356b9d47p-54, 0x1.0264d1244c719p0},
- {0x1.89434e751e1aap-110, -0x1.082ef51b61d7ep-56, 0x1.027003103b10ep0},
- {-0x1.03b54fd64e8acp-110, 0x1.2106ed0920a34p-56, 0x1.027b357854772p0},
- {0x1.7785ea0acc486p-109, -0x1.fd4cf26ea5d0fp-54, 0x1.0286685c9e059p0},
- {-0x1.ce447fdb35ff9p-109, -0x1.09f8775e78084p-54, 0x1.02919bbd1d1d8p0},
- {0x1.5b884aab5642ap-112, 0x1.64cbba902ca27p-58, 0x1.029ccf99d720ap0},
- {-0x1.cfb3e46d7c1cp-108, 0x1.4383ef231d207p-54, 0x1.02a803f2d170dp0},
- {-0x1.0d40cee4b81afp-112, 0x1.4a47a505b3a47p-54, 0x1.02b338c811703p0},
- {0x1.6ae7d36d7c1f7p-109, 0x1.e47120223467fp-54, 0x1.02be6e199c811p0},
-};
-
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h
index e65f002845953..a70d53d7dec22 100644
--- a/libc/src/math/generic/common_constants.h
+++ b/libc/src/math/generic/common_constants.h
@@ -12,6 +12,8 @@
#include "src/__support/FPUtil/triple_double.h"
#include "src/__support/macros/config.h"
#include "src/__support/number_pair.h"
+#include "src/__support/math/exp_constants.h"
+
namespace LIBC_NAMESPACE_DECL {
@@ -80,12 +82,6 @@ extern const double EXP_M1[195];
// > for i from 0 to 127 do { D(exp(i / 128)); };
extern const double EXP_M2[128];
-// Lookup table for 2^(k * 2^-6) with k = 0..63.
-extern const fputil::TripleDouble EXP2_MID1[64];
-
-// Lookup table for 2^(k * 2^-12) with k = 0..63.
-extern const fputil::TripleDouble EXP2_MID2[64];
-
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H
diff --git a/libc/src/math/generic/exp.cpp b/libc/src/math/generic/exp.cpp
index 143800ca078a6..38a3cd1e6e915 100644
--- a/libc/src/math/generic/exp.cpp
+++ b/libc/src/math/generic/exp.cpp
@@ -7,434 +7,11 @@
//===----------------------------------------------------------------------===//
#include "src/math/exp.h"
-#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
-#include "explogxf.h" // ziv_test_denorm.
-#include "src/__support/CPP/bit.h"
-#include "src/__support/CPP/optional.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/double_double.h"
-#include "src/__support/FPUtil/dyadic_float.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/triple_double.h"
-#include "src/__support/common.h"
-#include "src/__support/integer_literals.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-
+#include "src/__support/math/exp.h"
namespace LIBC_NAMESPACE_DECL {
-using fputil::DoubleDouble;
-using fputil::TripleDouble;
-using Float128 = typename fputil::DyadicFloat<128>;
-
-using LIBC_NAMESPACE::operator""_u128;
-
-// log2(e)
-constexpr double LOG2_E = 0x1.71547652b82fep+0;
-
-// Error bounds:
-// Errors when using double precision.
-constexpr double ERR_D = 0x1.8p-63;
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-// Errors when using double-double precision.
-constexpr double ERR_DD = 0x1.0p-99;
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-// -2^-12 * log(2)
-// > a = -2^-12 * log(2);
-// > b = round(a, 30, RN);
-// > c = round(a - b, 30, RN);
-// > d = round(a - b - c, D, RN);
-// Errors < 1.5 * 2^-133
-constexpr double MLOG_2_EXP2_M12_HI = -0x1.62e42ffp-13;
-constexpr double MLOG_2_EXP2_M12_MID = 0x1.718432a1b0e26p-47;
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-constexpr double MLOG_2_EXP2_M12_MID_30 = 0x1.718432ap-47;
-constexpr double MLOG_2_EXP2_M12_LO = 0x1.b0e2633fe0685p-79;
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-namespace {
-
-// Polynomial approximations with double precision:
-// Return expm1(dx) / x ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
-// For |dx| < 2^-13 + 2^-30:
-// | output - expm1(dx) / dx | < 2^-51.
-LIBC_INLINE double poly_approx_d(double dx) {
- // dx^2
- double dx2 = dx * dx;
- // c0 = 1 + dx / 2
- double c0 = fputil::multiply_add(dx, 0.5, 1.0);
- // c1 = 1/6 + dx / 24
- double c1 =
- fputil::multiply_add(dx, 0x1.5555555555555p-5, 0x1.5555555555555p-3);
- // p = dx^2 * c1 + c0 = 1 + dx / 2 + dx^2 / 6 + dx^3 / 24
- double p = fputil::multiply_add(dx2, c1, c0);
- return p;
-}
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-// Polynomial approximation with double-double precision:
-// Return exp(dx) ~ 1 + dx + dx^2 / 2 + ... + dx^6 / 720
-// For |dx| < 2^-13 + 2^-30:
-// | output - exp(dx) | < 2^-101
-DoubleDouble poly_approx_dd(const DoubleDouble &dx) {
- // Taylor polynomial.
- constexpr DoubleDouble COEFFS[] = {
- {0, 0x1p0}, // 1
- {0, 0x1p0}, // 1
- {0, 0x1p-1}, // 1/2
- {0x1.5555555555555p-57, 0x1.5555555555555p-3}, // 1/6
- {0x1.5555555555555p-59, 0x1.5555555555555p-5}, // 1/24
- {0x1.1111111111111p-63, 0x1.1111111111111p-7}, // 1/120
- {-0x1.f49f49f49f49fp-65, 0x1.6c16c16c16c17p-10}, // 1/720
- };
-
- DoubleDouble p = fputil::polyeval(dx, COEFFS[0], COEFFS[1], COEFFS[2],
- COEFFS[3], COEFFS[4], COEFFS[5], COEFFS[6]);
- return p;
-}
-
-// Polynomial approximation with 128-bit precision:
-// Return exp(dx) ~ 1 + dx + dx^2 / 2 + ... + dx^7 / 5040
-// For |dx| < 2^-13 + 2^-30:
-// | output - exp(dx) | < 2^-126.
-Float128 poly_approx_f128(const Float128 &dx) {
- constexpr Float128 COEFFS_128[]{
- {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
- {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
- {Sign::POS, -128, 0x80000000'00000000'00000000'00000000_u128}, // 0.5
- {Sign::POS, -130, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/6
- {Sign::POS, -132, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/24
- {Sign::POS, -134, 0x88888888'88888888'88888888'88888889_u128}, // 1/120
- {Sign::POS, -137, 0xb60b60b6'0b60b60b'60b60b60'b60b60b6_u128}, // 1/720
- {Sign::POS, -140, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // 1/5040
- };
-
- Float128 p = fputil::polyeval(dx, COEFFS_128[0], COEFFS_128[1], COEFFS_128[2],
- COEFFS_128[3], COEFFS_128[4], COEFFS_128[5],
- COEFFS_128[6], COEFFS_128[7]);
- return p;
-}
-
-// Compute exp(x) using 128-bit precision.
-// TODO(lntue): investigate triple-double precision implementation for this
-// step.
-Float128 exp_f128(double x, double kd, int idx1, int idx2) {
- // Recalculate dx:
-
- double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
- double t2 = kd * MLOG_2_EXP2_M12_MID_30; // exact
- double t3 = kd * MLOG_2_EXP2_M12_LO; // Error < 2^-133
-
- Float128 dx = fputil::quick_add(
- Float128(t1), fputil::quick_add(Float128(t2), Float128(t3)));
-
- // TODO: Skip recalculating exp_mid1 and exp_mid2.
- Float128 exp_mid1 =
- fputil::quick_add(Float128(EXP2_MID1[idx1].hi),
- fputil::quick_add(Float128(EXP2_MID1[idx1].mid),
- Float128(EXP2_MID1[idx1].lo)));
-
- Float128 exp_mid2 =
- fputil::quick_add(Float128(EXP2_MID2[idx2].hi),
- fputil::quick_add(Float128(EXP2_MID2[idx2].mid),
- Float128(EXP2_MID2[idx2].lo)));
-
- Float128 exp_mid = fputil::quick_mul(exp_mid1, exp_mid2);
-
- Float128 p = poly_approx_f128(dx);
-
- Float128 r = fputil::quick_mul(exp_mid, p);
-
- r.exponent += static_cast<int>(kd) >> 12;
-
- return r;
-}
-
-// Compute exp(x) with double-double precision.
-DoubleDouble exp_double_double(double x, double kd,
- const DoubleDouble &exp_mid) {
- // Recalculate dx:
- // dx = x - k * 2^-12 * log(2)
- double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
- double t2 = kd * MLOG_2_EXP2_M12_MID_30; // exact
- double t3 = kd * MLOG_2_EXP2_M12_LO; // Error < 2^-130
-
- DoubleDouble dx = fputil::exact_add(t1, t2);
- dx.lo += t3;
-
- // Degree-6 Taylor polynomial approximation in double-double precision.
- // | p - exp(x) | < 2^-100.
- DoubleDouble p = poly_approx_dd(dx);
-
- // Error bounds: 2^-99.
- DoubleDouble r = fputil::quick_mult(exp_mid, p);
-
- return r;
-}
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-// Check for exceptional cases when
-// |x| <= 2^-53 or x < log(2^-1075) or x >= 0x1.6232bdd7abcd3p+9
-double set_exceptional(double x) {
- using FPBits = typename fputil::FPBits<double>;
- FPBits xbits(x);
-
- uint64_t x_u = xbits.uintval();
- uint64_t x_abs = xbits.abs().uintval();
-
- // |x| <= 2^-53
- if (x_abs <= 0x3ca0'0000'0000'0000ULL) {
- // exp(x) ~ 1 + x
- return 1 + x;
- }
-
- // x <= log(2^-1075) || x >= 0x1.6232bdd7abcd3p+9 or inf/nan.
-
- // x <= log(2^-1075) or -inf/nan
- if (x_u >= 0xc087'4910'd52d'3052ULL) {
- // exp(-Inf) = 0
- if (xbits.is_inf())
- return 0.0;
-
- // exp(nan) = nan
- if (xbits.is_nan())
- return x;
-
- if (fputil::quick_get_round() == FE_UPWARD)
- return FPBits::min_subnormal().get_val();
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_UNDERFLOW);
- return 0.0;
- }
-
- // x >= round(log(MAX_NORMAL), D, RU) = 0x1.62e42fefa39fp+9 or +inf/nan
- // x is finite
- if (x_u < 0x7ff0'0000'0000'0000ULL) {
- int rounding = fputil::quick_get_round();
- if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
- return FPBits::max_normal().get_val();
-
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_OVERFLOW);
- }
- // x is +inf or nan
- return x + FPBits::inf().get_val();
-}
-
-} // namespace
-
LLVM_LIBC_FUNCTION(double, exp, (double x)) {
- using FPBits = typename fputil::FPBits<double>;
- FPBits xbits(x);
-
- uint64_t x_u = xbits.uintval();
-
- // Upper bound: max normal number = 2^1023 * (2 - 2^-52)
- // > round(log (2^1023 ( 2 - 2^-52 )), D, RU) = 0x1.62e42fefa39fp+9
- // > round(log (2^1023 ( 2 - 2^-52 )), D, RD) = 0x1.62e42fefa39efp+9
- // > round(log (2^1023 ( 2 - 2^-52 )), D, RN) = 0x1.62e42fefa39efp+9
- // > round(exp(0x1.62e42fefa39fp+9), D, RN) = infty
-
- // Lower bound: min denormal number / 2 = 2^-1075
- // > round(log(2^-1075), D, RN) = -0x1.74910d52d3052p9
-
- // Another lower bound: min normal number = 2^-1022
- // > round(log(2^-1022), D, RN) = -0x1.6232bdd7abcd2p9
-
- // x < log(2^-1075) or x >= 0x1.6232bdd7abcd3p+9 or |x| < 2^-53.
- if (LIBC_UNLIKELY(x_u >= 0xc0874910d52d3052 ||
- (x_u < 0xbca0000000000000 && x_u >= 0x40862e42fefa39f0) ||
- x_u < 0x3ca0000000000000)) {
- return set_exceptional(x);
- }
-
- // Now log(2^-1075) <= x <= -2^-53 or 2^-53 <= x < log(2^1023 * (2 - 2^-52))
-
- // Range reduction:
- // Let x = log(2) * (hi + mid1 + mid2) + lo
- // in which:
- // hi is an integer
- // mid1 * 2^6 is an integer
- // mid2 * 2^12 is an integer
- // then:
- // exp(x) = 2^hi * 2^(mid1) * 2^(mid2) * exp(lo).
- // With this formula:
- // - multiplying by 2^hi is exact and cheap, simply by adding the exponent
- // field.
- // - 2^(mid1) and 2^(mid2) are stored in 2 x 64-element tables.
- // - exp(lo) ~ 1 + lo + a0 * lo^2 + ...
- //
- // They can be defined by:
- // hi + mid1 + mid2 = 2^(-12) * round(2^12 * log_2(e) * x)
- // If we store L2E = round(log2(e), D, RN), then:
- // log2(e) - L2E ~ 1.5 * 2^(-56)
- // So the errors when computing in double precision is:
- // | x * 2^12 * log_2(e) - D(x * 2^12 * L2E) | <=
- // <= | x * 2^12 * log_2(e) - x * 2^12 * L2E | +
- // + | x * 2^12 * L2E - D(x * 2^12 * L2E) |
- // <= 2^12 * ( |x| * 1.5 * 2^-56 + eps(x)) for RN
- // 2^12 * ( |x| * 1.5 * 2^-56 + 2*eps(x)) for other rounding modes.
- // So if:
- // hi + mid1 + mid2 = 2^(-12) * round(x * 2^12 * L2E) is computed entirely
- // in double precision, the reduced argument:
- // lo = x - log(2) * (hi + mid1 + mid2) is bounded by:
- // |lo| <= 2^-13 + (|x| * 1.5 * 2^-56 + 2*eps(x))
- // < 2^-13 + (1.5 * 2^9 * 1.5 * 2^-56 + 2*2^(9 - 52))
- // < 2^-13 + 2^-41
- //
-
- // The following trick computes the round(x * L2E) more efficiently
- // than using the rounding instructions, with the tradeoff for less accuracy,
- // and hence a slightly larger range for the reduced argument `lo`.
- //
- // To be precise, since |x| < |log(2^-1075)| < 1.5 * 2^9,
- // |x * 2^12 * L2E| < 1.5 * 2^9 * 1.5 < 2^23,
- // So we can fit the rounded result round(x * 2^12 * L2E) in int32_t.
- // Thus, the goal is to be able to use an additional addition and fixed width
- // shift to get an int32_t representing round(x * 2^12 * L2E).
- //
- // Assuming int32_t using 2-complement representation, since the mantissa part
- // of a double precision is unsigned with the leading bit hidden, if we add an
- // extra constant C = 2^e1 + 2^e2 with e1 > e2 >= 2^25 to the product, the
- // part that are < 2^e2 in resulted mantissa of (x*2^12*L2E + C) can be
- // considered as a proper 2-complement representations of x*2^12*L2E.
- //
- // One small problem with this approach is that the sum (x*2^12*L2E + C) in
- // double precision is rounded to the least significant bit of the dorminant
- // factor C. In order to minimize the rounding errors from this addition, we
- // want to minimize e1. Another constraint that we want is that after
- // shifting the mantissa so that the least significant bit of int32_t
- // corresponds to the unit bit of (x*2^12*L2E), the sign is correct without
- // any adjustment. So combining these 2 requirements, we can choose
- // C = 2^33 + 2^32, so that the sign bit corresponds to 2^31 bit, and hence
- // after right shifting the mantissa, the resulting int32_t has correct sign.
- // With this choice of C, the number of mantissa bits we need to shift to the
- // right is: 52 - 33 = 19.
- //
- // Moreover, since the integer right shifts are equivalent to rounding down,
- // we can add an extra 0.5 so that it will become round-to-nearest, tie-to-
- // +infinity. So in particular, we can compute:
- // hmm = x * 2^12 * L2E + C,
- // where C = 2^33 + 2^32 + 2^-1, then if
- // k = int32_t(lower 51 bits of double(x * 2^12 * L2E + C) >> 19),
- // the reduced argument:
- // lo = x - log(2) * 2^-12 * k is bounded by:
- // |lo| <= 2^-13 + 2^-41 + 2^-12*2^-19
- // = 2^-13 + 2^-31 + 2^-41.
- //
- // Finally, notice that k only uses the mantissa of x * 2^12 * L2E, so the
- // exponent 2^12 is not needed. So we can simply define
- // C = 2^(33 - 12) + 2^(32 - 12) + 2^(-13 - 12), and
- // k = int32_t(lower 51 bits of double(x * L2E + C) >> 19).
-
- // Rounding errors <= 2^-31 + 2^-41.
- double tmp = fputil::multiply_add(x, LOG2_E, 0x1.8000'0000'4p21);
- int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
- double kd = static_cast<double>(k);
-
- uint32_t idx1 = (k >> 6) & 0x3f;
- uint32_t idx2 = k & 0x3f;
- int hi = k >> 12;
-
- bool denorm = (hi <= -1022);
-
- DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
- DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
-
- DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);
-
- // |x - (hi + mid1 + mid2) * log(2) - dx| < 2^11 * eps(M_LOG_2_EXP2_M12.lo)
- // = 2^11 * 2^-13 * 2^-52
- // = 2^-54.
- // |dx| < 2^-13 + 2^-30.
- double lo_h = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
- double dx = fputil::multiply_add(kd, MLOG_2_EXP2_M12_MID, lo_h);
-
- // We use the degree-4 Taylor polynomial to approximate exp(lo):
- // exp(lo) ~ 1 + lo + lo^2 / 2 + lo^3 / 6 + lo^4 / 24 = 1 + lo * P(lo)
- // So that the errors are bounded by:
- // |P(lo) - expm1(lo)/lo| < |lo|^4 / 64 < 2^(-13 * 4) / 64 = 2^-58
- // Let P_ be an evaluation of P where all intermediate computations are in
- // double precision. Using either Horner's or Estrin's schemes, the evaluated
- // errors can be bounded by:
- // |P_(dx) - P(dx)| < 2^-51
- // => |dx * P_(dx) - expm1(lo) | < 1.5 * 2^-64
- // => 2^(mid1 + mid2) * |dx * P_(dx) - expm1(lo)| < 1.5 * 2^-63.
- // Since we approximate
- // 2^(mid1 + mid2) ~ exp_mid.hi + exp_mid.lo,
- // We use the expression:
- // (exp_mid.hi + exp_mid.lo) * (1 + dx * P_(dx)) ~
- // ~ exp_mid.hi + (exp_mid.hi * dx * P_(dx) + exp_mid.lo)
- // with errors bounded by 1.5 * 2^-63.
-
- double mid_lo = dx * exp_mid.hi;
-
- // Approximate expm1(dx)/dx ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
- double p = poly_approx_d(dx);
-
- double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo);
-
-#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- if (LIBC_UNLIKELY(denorm)) {
- return ziv_test_denorm</*SKIP_ZIV_TEST=*/true>(hi, exp_mid.hi, lo, ERR_D)
- .value();
- } else {
- // to multiply by 2^hi, a fast way is to simply add hi to the exponent
- // field.
- int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
- double r =
- cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(exp_mid.hi + lo));
- return r;
- }
-#else
- if (LIBC_UNLIKELY(denorm)) {
- if (auto r = ziv_test_denorm(hi, exp_mid.hi, lo, ERR_D);
- LIBC_LIKELY(r.has_value()))
- return r.value();
- } else {
- double upper = exp_mid.hi + (lo + ERR_D);
- double lower = exp_mid.hi + (lo - ERR_D);
-
- if (LIBC_LIKELY(upper == lower)) {
- // to multiply by 2^hi, a fast way is to simply add hi to the exponent
- // field.
- int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
- double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper));
- return r;
- }
- }
-
- // Use double-double
- DoubleDouble r_dd = exp_double_double(x, kd, exp_mid);
-
- if (LIBC_UNLIKELY(denorm)) {
- if (auto r = ziv_test_denorm(hi, r_dd.hi, r_dd.lo, ERR_DD);
- LIBC_LIKELY(r.has_value()))
- return r.value();
- } else {
- double upper_dd = r_dd.hi + (r_dd.lo + ERR_DD);
- double lower_dd = r_dd.hi + (r_dd.lo - ERR_DD);
-
- if (LIBC_LIKELY(upper_dd == lower_dd)) {
- int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
- double r =
- cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper_dd));
- return r;
- }
- }
-
- // Use 128-bit precision
- Float128 r_f128 = exp_f128(x, kd, idx1, idx2);
-
- return static_cast<double>(r_f128);
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ return math::exp(x);
}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/explogxf.h b/libc/src/math/generic/explogxf.h
index 212ede4758549..5ae1457ca780e 100644
--- a/libc/src/math/generic/explogxf.h
+++ b/libc/src/math/generic/explogxf.h
@@ -10,16 +10,15 @@
#define LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H
#include "common_constants.h"
-#include "src/__support/CPP/bit.h"
-#include "src/__support/CPP/optional.h"
#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/properties/cpu_features.h"
+#include "src/__support/math/exp_utils.h"
+
namespace LIBC_NAMESPACE_DECL {
struct ExpBase {
@@ -375,58 +374,6 @@ LIBC_INLINE static double log_eval(double x) {
return result;
}
-// Rounding tests for 2^hi * (mid + lo) when the output might be denormal. We
-// assume further that 1 <= mid < 2, mid + lo < 2, and |lo| << mid.
-// Notice that, if 0 < x < 2^-1022,
-// double(2^-1022 + x) - 2^-1022 = double(x).
-// So if we scale x up by 2^1022, we can use
-// double(1.0 + 2^1022 * x) - 1.0 to test how x is rounded in denormal range.
-template <bool SKIP_ZIV_TEST = false>
-LIBC_INLINE static cpp::optional<double>
-ziv_test_denorm(int hi, double mid, double lo, double err) {
- using FPBits = typename fputil::FPBits<double>;
-
- // Scaling factor = 1/(min normal number) = 2^1022
- int64_t exp_hi = static_cast<int64_t>(hi + 1022) << FPBits::FRACTION_LEN;
- double mid_hi = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(mid));
- double lo_scaled =
- (lo != 0.0) ? cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(lo))
- : 0.0;
-
- double extra_factor = 0.0;
- uint64_t scale_down = 0x3FE0'0000'0000'0000; // 1022 in the exponent field.
-
- // Result is denormal if (mid_hi + lo_scale < 1.0).
- if ((1.0 - mid_hi) > lo_scaled) {
- // Extra rounding step is needed, which adds more rounding errors.
- err += 0x1.0p-52;
- extra_factor = 1.0;
- scale_down = 0x3FF0'0000'0000'0000; // 1023 in the exponent field.
- }
-
- // By adding 1.0, the results will have similar rounding points as denormal
- // outputs.
- if constexpr (SKIP_ZIV_TEST) {
- double r = extra_factor + (mid_hi + lo_scaled);
- return cpp::bit_cast<double>(cpp::bit_cast<uint64_t>(r) - scale_down);
- } else {
- double err_scaled =
- cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(err));
-
- double lo_u = lo_scaled + err_scaled;
- double lo_l = lo_scaled - err_scaled;
-
- double upper = extra_factor + (mid_hi + lo_u);
- double lower = extra_factor + (mid_hi + lo_l);
-
- if (LIBC_LIKELY(upper == lower)) {
- return cpp::bit_cast<double>(cpp::bit_cast<uint64_t>(upper) - scale_down);
- }
-
- return cpp::nullopt;
- }
-}
-
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index cd608a1352a7a..4ab0126291276 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -1919,7 +1919,7 @@ libc_support_library(
srcs = ["src/math/generic/common_constants.cpp"],
hdrs = ["src/math/generic/common_constants.h"],
deps = [
- ":__support_fputil_triple_double",
+ ":__support_math_exp_constants",
":__support_number_pair",
],
)
@@ -2002,10 +2002,10 @@ libc_support_library(
":__support_common",
":__support_fputil_fenv_impl",
":__support_fputil_fma",
- ":__support_fputil_fp_bits",
":__support_fputil_multiply_add",
":__support_fputil_nearest_integer",
":__support_fputil_polyeval",
+ ":__support_math_exp_utils",
":common_constants",
],
)
@@ -2205,6 +2205,46 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_exp_constants",
+ hdrs = ["src/__support/math/exp_constants.h"],
+ deps = [
+ ":__support_fputil_triple_double",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_exp_utils",
+ hdrs = ["src/__support/math/exp_utils.h"],
+ deps = [
+ ":__support_cpp_optional",
+ ":__support_cpp_bit",
+ ":__support_fputil_fp_bits",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_exp",
+ hdrs = ["src/__support/math/exp.h"],
+ deps = [
+ ":__support_math_exp_constants",
+ ":__support_math_exp_utils",
+ ":__support_cpp_bit",
+ ":__support_cpp_optional",
+ ":__support_fputil_dyadic_float",
+ ":__support_fputil_fenv_impl",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_rounding_mode",
+ ":__support_fputil_triple_double",
+ ":__support_fputil_double_double",
+ ":__support_integer_literals",
+ ":__support_macros_optimization",
+ ],
+)
+
############################### complex targets ################################
libc_function(
@@ -2785,17 +2825,8 @@ libc_math_function(
libc_math_function(
name = "exp",
additional_deps = [
- ":__support_fputil_double_double",
- ":__support_fputil_dyadic_float",
- ":__support_fputil_multiply_add",
- ":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
- ":__support_fputil_rounding_mode",
- ":__support_fputil_triple_double",
- ":__support_integer_literals",
- ":__support_macros_optimization",
- ":common_constants",
- ":explogxf",
+ ":__support_math_exp",
+ ":errno",
],
)
>From b6503f0d19baac36fdc3e9058f7c9ae4efe715cc Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Fri, 11 Jul 2025 03:19:04 +0300
Subject: [PATCH 05/15] fix style
---
libc/shared/math.h | 2 +-
libc/src/__support/math/exp.h | 3 +--
libc/src/__support/math/exp_utils.h | 7 +++----
libc/src/math/generic/common_constants.h | 3 +--
libc/src/math/generic/exp.cpp | 4 +---
5 files changed, 7 insertions(+), 12 deletions(-)
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 51a95a96db3ce..3012cbb938816 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -11,6 +11,7 @@
#include "libc_common.h"
+#include "math/exp.h"
#include "math/expf.h"
#include "math/expf16.h"
#include "math/frexpf.h"
@@ -19,6 +20,5 @@
#include "math/ldexpf.h"
#include "math/ldexpf128.h"
#include "math/ldexpf16.h"
-#include "math/exp.h"
#endif // LLVM_LIBC_SHARED_MATH_H
diff --git a/libc/src/__support/math/exp.h b/libc/src/__support/math/exp.h
index 6d9ac8d401e06..5c43e753ea687 100644
--- a/libc/src/__support/math/exp.h
+++ b/libc/src/__support/math/exp.h
@@ -27,7 +27,6 @@
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-
namespace LIBC_NAMESPACE_DECL {
using fputil::DoubleDouble;
@@ -162,7 +161,7 @@ static constexpr Float128 exp_f128(double x, double kd, int idx1, int idx2) {
// Compute exp(x) with double-double precision.
static constexpr DoubleDouble exp_double_double(double x, double kd,
- const DoubleDouble &exp_mid) {
+ const DoubleDouble &exp_mid) {
// Recalculate dx:
// dx = x - k * 2^-12 * log(2)
double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
diff --git a/libc/src/__support/math/exp_utils.h b/libc/src/__support/math/exp_utils.h
index 4bad6fa04b716..fc9ab10d76cc4 100644
--- a/libc/src/__support/math/exp_utils.h
+++ b/libc/src/__support/math/exp_utils.h
@@ -9,11 +9,10 @@
#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP_UTILS_H
#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_UTILS_H
-#include "src/__support/CPP/optional.h"
#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/optional.h"
#include "src/__support/FPUtil/FPBits.h"
-
namespace LIBC_NAMESPACE_DECL {
// Rounding tests for 2^hi * (mid + lo) when the output might be denormal. We
@@ -23,8 +22,8 @@ namespace LIBC_NAMESPACE_DECL {
// So if we scale x up by 2^1022, we can use
// double(1.0 + 2^1022 * x) - 1.0 to test how x is rounded in denormal range.
template <bool SKIP_ZIV_TEST = false>
-static constexpr cpp::optional<double>
-ziv_test_denorm(int hi, double mid, double lo, double err) {
+static constexpr cpp::optional<double> ziv_test_denorm(int hi, double mid,
+ double lo, double err) {
using FPBits = typename fputil::FPBits<double>;
// Scaling factor = 1/(min normal number) = 2^1022
diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h
index a70d53d7dec22..291816a7889ad 100644
--- a/libc/src/math/generic/common_constants.h
+++ b/libc/src/math/generic/common_constants.h
@@ -11,9 +11,8 @@
#include "src/__support/FPUtil/triple_double.h"
#include "src/__support/macros/config.h"
-#include "src/__support/number_pair.h"
#include "src/__support/math/exp_constants.h"
-
+#include "src/__support/number_pair.h"
namespace LIBC_NAMESPACE_DECL {
diff --git a/libc/src/math/generic/exp.cpp b/libc/src/math/generic/exp.cpp
index 38a3cd1e6e915..dc4d2ca480cb8 100644
--- a/libc/src/math/generic/exp.cpp
+++ b/libc/src/math/generic/exp.cpp
@@ -10,8 +10,6 @@
#include "src/__support/math/exp.h"
namespace LIBC_NAMESPACE_DECL {
-LLVM_LIBC_FUNCTION(double, exp, (double x)) {
- return math::exp(x);
-}
+LLVM_LIBC_FUNCTION(double, exp, (double x)) { return math::exp(x); }
} // namespace LIBC_NAMESPACE_DECL
>From 3fc11407903fc1aa0da0f84cd0f645362fcaff34 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 00:40:16 +0300
Subject: [PATCH 06/15] [libc][math] Refactor exp10 implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/exp10.h | 23 +
libc/src/__support/FPUtil/double_double.h | 4 +-
libc/src/__support/math/CMakeLists.txt | 21 +
libc/src/__support/math/exp10.h | 505 ++++++++++++++++++
libc/src/math/generic/CMakeLists.txt | 15 +-
libc/src/math/generic/exp10.cpp | 485 +----------------
.../llvm-project-overlay/libc/BUILD.bazel | 31 +-
8 files changed, 575 insertions(+), 510 deletions(-)
create mode 100644 libc/shared/math/exp10.h
create mode 100644 libc/src/__support/math/exp10.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 3012cbb938816..b37aa46820523 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -12,6 +12,7 @@
#include "libc_common.h"
#include "math/exp.h"
+#include "math/exp10.h"
#include "math/expf.h"
#include "math/expf16.h"
#include "math/frexpf.h"
diff --git a/libc/shared/math/exp10.h b/libc/shared/math/exp10.h
new file mode 100644
index 0000000000000..3d36d9103705f
--- /dev/null
+++ b/libc/shared/math/exp10.h
@@ -0,0 +1,23 @@
+//===-- Shared exp10 function -----------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_EXP10_H
+#define LLVM_LIBC_SHARED_MATH_EXP10_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/exp10.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::exp10;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_EXP10_H
diff --git a/libc/src/__support/FPUtil/double_double.h b/libc/src/__support/FPUtil/double_double.h
index c27885aadc028..8e54e845de493 100644
--- a/libc/src/__support/FPUtil/double_double.h
+++ b/libc/src/__support/FPUtil/double_double.h
@@ -151,8 +151,8 @@ LIBC_INLINE DoubleDouble quick_mult(double a, const DoubleDouble &b) {
}
template <size_t SPLIT_B = 27>
-LIBC_INLINE DoubleDouble quick_mult(const DoubleDouble &a,
- const DoubleDouble &b) {
+LIBC_INLINE constexpr DoubleDouble quick_mult(const DoubleDouble &a,
+ const DoubleDouble &b) {
DoubleDouble r = exact_mult<double, SPLIT_B>(a.hi, b.hi);
double t1 = multiply_add(a.hi, b.lo, r.lo);
double t2 = multiply_add(a.lo, b.hi, t1);
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index f7ef9e7694fe6..0bfc996c44fc8 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -149,3 +149,24 @@ add_header_library(
libc.src.__support.integer_literals
libc.src.__support.macros.optimization
)
+
+add_header_library(
+ exp10
+ HDRS
+ exp10.h
+ DEPENDS
+ .exp_constants
+ .exp_utils
+ libc.src.__support.CPP.bit
+ libc.src.__support.CPP.optional
+ libc.src.__support.FPUtil.dyadic_float
+ 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.triple_double
+ libc.src.__support.integer_literals
+ libc.src.__support.macros.optimization
+)
diff --git a/libc/src/__support/math/exp10.h b/libc/src/__support/math/exp10.h
new file mode 100644
index 0000000000000..da94281c0c745
--- /dev/null
+++ b/libc/src/__support/math/exp10.h
@@ -0,0 +1,505 @@
+//===-- Implementation header for exp10 ------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP10_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10_H
+
+#include "exp_constants.h" // Lookup tables EXP2_MID1 and EXP_M2.
+#include "exp_utils.h" // ziv_test_denorm.
+#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/optional.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.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/triple_double.h"
+#include "src/__support/common.h"
+#include "src/__support/integer_literals.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+namespace LIBC_NAMESPACE_DECL {
+
+using fputil::DoubleDouble;
+using fputil::TripleDouble;
+using Float128 = typename fputil::DyadicFloat<128>;
+
+using LIBC_NAMESPACE::operator""_u128;
+
+// log2(10)
+constexpr double LOG2_10 = 0x1.a934f0979a371p+1;
+
+// -2^-12 * log10(2)
+// > a = -2^-12 * log10(2);
+// > b = round(a, 32, RN);
+// > c = round(a - b, 32, RN);
+// > d = round(a - b - c, D, RN);
+// Errors < 1.5 * 2^-144
+constexpr double MLOG10_2_EXP2_M12_HI = -0x1.3441350ap-14;
+constexpr double MLOG10_2_EXP2_M12_MID = 0x1.0c0219dc1da99p-51;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+constexpr double MLOG10_2_EXP2_M12_MID_32 = 0x1.0c0219dcp-51;
+constexpr double MLOG10_2_EXP2_M12_LO = 0x1.da994fd20dba2p-87;
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+// Error bounds:
+// Errors when using double precision.
+constexpr double ERR_D = 0x1.8p-63;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+// Errors when using double-double precision.
+constexpr double ERR_DD = 0x1.8p-99;
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+namespace {
+
+// Polynomial approximations with double precision. Generated by Sollya with:
+// > P = fpminimax((10^x - 1)/x, 3, [|D...|], [-2^-14, 2^-14]);
+// > P;
+// Error bounds:
+// | output - (10^dx - 1) / dx | < 2^-52.
+LIBC_INLINE static constexpr double poly_approx_d(double dx) {
+ // dx^2
+ double dx2 = dx * dx;
+ double c0 =
+ fputil::multiply_add(dx, 0x1.53524c73cea6ap+1, 0x1.26bb1bbb55516p+1);
+ double c1 =
+ fputil::multiply_add(dx, 0x1.2bd75cc6afc65p+0, 0x1.0470587aa264cp+1);
+ double p = fputil::multiply_add(dx2, c1, c0);
+ return p;
+}
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+// Polynomial approximation with double-double precision. Generated by Solya
+// with:
+// > P = fpminimax((10^x - 1)/x, 5, [|DD...|], [-2^-14, 2^-14]);
+// Error bounds:
+// | output - 10^(dx) | < 2^-101
+static constexpr DoubleDouble poly_approx_dd(const DoubleDouble &dx) {
+ // Taylor polynomial.
+ constexpr DoubleDouble COEFFS[] = {
+ {0, 0x1p0},
+ {-0x1.f48ad494e927bp-53, 0x1.26bb1bbb55516p1},
+ {-0x1.e2bfab3191cd2p-53, 0x1.53524c73cea69p1},
+ {0x1.80fb65ec3b503p-53, 0x1.0470591de2ca4p1},
+ {0x1.338fc05e21e55p-54, 0x1.2bd7609fd98c4p0},
+ {0x1.d4ea116818fbp-56, 0x1.1429ffd519865p-1},
+ {-0x1.872a8ff352077p-57, 0x1.a7ed70847c8b3p-3},
+
+ };
+
+ DoubleDouble p = fputil::polyeval(dx, COEFFS[0], COEFFS[1], COEFFS[2],
+ COEFFS[3], COEFFS[4], COEFFS[5], COEFFS[6]);
+ return p;
+}
+
+// Polynomial approximation with 128-bit precision:
+// Return exp(dx) ~ 1 + a0 * dx + a1 * dx^2 + ... + a6 * dx^7
+// For |dx| < 2^-14:
+// | output - 10^dx | < 1.5 * 2^-124.
+static constexpr Float128 poly_approx_f128(const Float128 &dx) {
+ constexpr Float128 COEFFS_128[]{
+ {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
+ {Sign::POS, -126, 0x935d8ddd'aaa8ac16'ea56d62b'82d30a2d_u128},
+ {Sign::POS, -126, 0xa9a92639'e753443a'80a99ce7'5f4d5bdb_u128},
+ {Sign::POS, -126, 0x82382c8e'f1652304'6a4f9d7d'bf6c9635_u128},
+ {Sign::POS, -124, 0x12bd7609'fd98c44c'34578701'9216c7af_u128},
+ {Sign::POS, -127, 0x450a7ff4'7535d889'cc41ed7e'0d27aee5_u128},
+ {Sign::POS, -130, 0xd3f6b844'702d636b'8326bb91'a6e7601d_u128},
+ {Sign::POS, -130, 0x45b937f0'd05bb1cd'fa7b46df'314112a9_u128},
+ };
+
+ Float128 p = fputil::polyeval(dx, COEFFS_128[0], COEFFS_128[1], COEFFS_128[2],
+ COEFFS_128[3], COEFFS_128[4], COEFFS_128[5],
+ COEFFS_128[6], COEFFS_128[7]);
+ return p;
+}
+
+// Compute 10^(x) using 128-bit precision.
+// TODO(lntue): investigate triple-double precision implementation for this
+// step.
+static constexpr Float128 exp10_f128(double x, double kd, int idx1, int idx2) {
+ double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
+ double t2 = kd * MLOG10_2_EXP2_M12_MID_32; // exact
+ double t3 = kd * MLOG10_2_EXP2_M12_LO; // Error < 2^-144
+
+ Float128 dx = fputil::quick_add(
+ Float128(t1), fputil::quick_add(Float128(t2), Float128(t3)));
+
+ // TODO: Skip recalculating exp_mid1 and exp_mid2.
+ Float128 exp_mid1 =
+ fputil::quick_add(Float128(EXP2_MID1[idx1].hi),
+ fputil::quick_add(Float128(EXP2_MID1[idx1].mid),
+ Float128(EXP2_MID1[idx1].lo)));
+
+ Float128 exp_mid2 =
+ fputil::quick_add(Float128(EXP2_MID2[idx2].hi),
+ fputil::quick_add(Float128(EXP2_MID2[idx2].mid),
+ Float128(EXP2_MID2[idx2].lo)));
+
+ Float128 exp_mid = fputil::quick_mul(exp_mid1, exp_mid2);
+
+ Float128 p = poly_approx_f128(dx);
+
+ Float128 r = fputil::quick_mul(exp_mid, p);
+
+ r.exponent += static_cast<int>(kd) >> 12;
+
+ return r;
+}
+
+// Compute 10^x with double-double precision.
+static constexpr DoubleDouble exp10_double_double(double x, double kd,
+ const DoubleDouble &exp_mid) {
+ // Recalculate dx:
+ // dx = x - k * 2^-12 * log10(2)
+ double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
+ double t2 = kd * MLOG10_2_EXP2_M12_MID_32; // exact
+ double t3 = kd * MLOG10_2_EXP2_M12_LO; // Error < 2^-140
+
+ DoubleDouble dx = fputil::exact_add(t1, t2);
+ dx.lo += t3;
+
+ // Degree-6 polynomial approximation in double-double precision.
+ // | p - 10^x | < 2^-103.
+ DoubleDouble p = poly_approx_dd(dx);
+
+ // Error bounds: 2^-102.
+ DoubleDouble r = fputil::quick_mult(exp_mid, p);
+
+ return r;
+}
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+// When output is denormal.
+static constexpr double exp10_denorm(double x) {
+ // Range reduction.
+ double tmp = fputil::multiply_add(x, LOG2_10, 0x1.8000'0000'4p21);
+ int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
+ double kd = static_cast<double>(k);
+
+ uint32_t idx1 = (k >> 6) & 0x3f;
+ uint32_t idx2 = k & 0x3f;
+
+ int hi = k >> 12;
+
+ DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
+ DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
+ DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);
+
+ // |dx| < 1.5 * 2^-15 + 2^-31 < 2^-14
+ double lo_h = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
+ double dx = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_MID, lo_h);
+
+ double mid_lo = dx * exp_mid.hi;
+
+ // Approximate (10^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4.
+ double p = poly_approx_d(dx);
+
+ double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo);
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ return ziv_test_denorm</*SKIP_ZIV_TEST=*/true>(hi, exp_mid.hi, lo, ERR_D)
+ .value();
+#else
+ if (auto r = ziv_test_denorm(hi, exp_mid.hi, lo, ERR_D);
+ LIBC_LIKELY(r.has_value()))
+ return r.value();
+
+ // Use double-double
+ DoubleDouble r_dd = exp10_double_double(x, kd, exp_mid);
+
+ if (auto r = ziv_test_denorm(hi, r_dd.hi, r_dd.lo, ERR_DD);
+ LIBC_LIKELY(r.has_value()))
+ return r.value();
+
+ // Use 128-bit precision
+ Float128 r_f128 = exp10_f128(x, kd, idx1, idx2);
+
+ return static_cast<double>(r_f128);
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+}
+
+// Check for exceptional cases when:
+// * log10(1 - 2^-54) < x < log10(1 + 2^-53)
+// * x >= log10(2^1024)
+// * x <= log10(2^-1022)
+// * x is inf or nan
+static constexpr double set_exceptional(double x) {
+ using FPBits = typename fputil::FPBits<double>;
+ FPBits xbits(x);
+
+ uint64_t x_u = xbits.uintval();
+ uint64_t x_abs = xbits.abs().uintval();
+
+ // |x| < log10(1 + 2^-53)
+ if (x_abs <= 0x3c8bcb7b1526e50e) {
+ // 10^(x) ~ 1 + x/2
+ return fputil::multiply_add(x, 0.5, 1.0);
+ }
+
+ // x <= log10(2^-1022) || x >= log10(2^1024) or inf/nan.
+ if (x_u >= 0xc0733a7146f72a42) {
+ // x <= log10(2^-1075) or -inf/nan
+ if (x_u > 0xc07439b746e36b52) {
+ // exp(-Inf) = 0
+ if (xbits.is_inf())
+ return 0.0;
+
+ // exp(nan) = nan
+ if (xbits.is_nan())
+ return x;
+
+ if (fputil::quick_get_round() == FE_UPWARD)
+ return FPBits::min_subnormal().get_val();
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_UNDERFLOW);
+ return 0.0;
+ }
+
+ return exp10_denorm(x);
+ }
+
+ // x >= log10(2^1024) or +inf/nan
+ // x is finite
+ if (x_u < 0x7ff0'0000'0000'0000ULL) {
+ int rounding = fputil::quick_get_round();
+ if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
+ return FPBits::max_normal().get_val();
+
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ }
+ // x is +inf or nan
+ return x + FPBits::inf().get_val();
+}
+
+} // namespace
+
+namespace math {
+
+static constexpr double exp10(double x) {
+ using FPBits = typename fputil::FPBits<double>;
+ FPBits xbits(x);
+
+ uint64_t x_u = xbits.uintval();
+
+ // x <= log10(2^-1022) or x >= log10(2^1024) or
+ // log10(1 - 2^-54) < x < log10(1 + 2^-53).
+ if (LIBC_UNLIKELY(x_u >= 0xc0733a7146f72a42 ||
+ (x_u <= 0xbc7bcb7b1526e50e && x_u >= 0x40734413509f79ff) ||
+ x_u < 0x3c8bcb7b1526e50e)) {
+ return set_exceptional(x);
+ }
+
+ // Now log10(2^-1075) < x <= log10(1 - 2^-54) or
+ // log10(1 + 2^-53) < x < log10(2^1024)
+
+ // Range reduction:
+ // Let x = log10(2) * (hi + mid1 + mid2) + lo
+ // in which:
+ // hi is an integer
+ // mid1 * 2^6 is an integer
+ // mid2 * 2^12 is an integer
+ // then:
+ // 10^(x) = 2^hi * 2^(mid1) * 2^(mid2) * 10^(lo).
+ // With this formula:
+ // - multiplying by 2^hi is exact and cheap, simply by adding the exponent
+ // field.
+ // - 2^(mid1) and 2^(mid2) are stored in 2 x 64-element tables.
+ // - 10^(lo) ~ 1 + a0*lo + a1 * lo^2 + ...
+ //
+ // We compute (hi + mid1 + mid2) together by perform the rounding on
+ // x * log2(10) * 2^12.
+ // Since |x| < |log10(2^-1075)| < 2^9,
+ // |x * 2^12| < 2^9 * 2^12 < 2^21,
+ // So we can fit the rounded result round(x * 2^12) in int32_t.
+ // Thus, the goal is to be able to use an additional addition and fixed width
+ // shift to get an int32_t representing round(x * 2^12).
+ //
+ // Assuming int32_t using 2-complement representation, since the mantissa part
+ // of a double precision is unsigned with the leading bit hidden, if we add an
+ // extra constant C = 2^e1 + 2^e2 with e1 > e2 >= 2^23 to the product, the
+ // part that are < 2^e2 in resulted mantissa of (x*2^12*L2E + C) can be
+ // considered as a proper 2-complement representations of x*2^12.
+ //
+ // One small problem with this approach is that the sum (x*2^12 + C) in
+ // double precision is rounded to the least significant bit of the dorminant
+ // factor C. In order to minimize the rounding errors from this addition, we
+ // want to minimize e1. Another constraint that we want is that after
+ // shifting the mantissa so that the least significant bit of int32_t
+ // corresponds to the unit bit of (x*2^12*L2E), the sign is correct without
+ // any adjustment. So combining these 2 requirements, we can choose
+ // C = 2^33 + 2^32, so that the sign bit corresponds to 2^31 bit, and hence
+ // after right shifting the mantissa, the resulting int32_t has correct sign.
+ // With this choice of C, the number of mantissa bits we need to shift to the
+ // right is: 52 - 33 = 19.
+ //
+ // Moreover, since the integer right shifts are equivalent to rounding down,
+ // we can add an extra 0.5 so that it will become round-to-nearest, tie-to-
+ // +infinity. So in particular, we can compute:
+ // hmm = x * 2^12 + C,
+ // where C = 2^33 + 2^32 + 2^-1, then if
+ // k = int32_t(lower 51 bits of double(x * 2^12 + C) >> 19),
+ // the reduced argument:
+ // lo = x - log10(2) * 2^-12 * k is bounded by:
+ // |lo| = |x - log10(2) * 2^-12 * k|
+ // = log10(2) * 2^-12 * | x * log2(10) * 2^12 - k |
+ // <= log10(2) * 2^-12 * (2^-1 + 2^-19)
+ // < 1.5 * 2^-2 * (2^-13 + 2^-31)
+ // = 1.5 * (2^-15 * 2^-31)
+ //
+ // Finally, notice that k only uses the mantissa of x * 2^12, so the
+ // exponent 2^12 is not needed. So we can simply define
+ // C = 2^(33 - 12) + 2^(32 - 12) + 2^(-13 - 12), and
+ // k = int32_t(lower 51 bits of double(x + C) >> 19).
+
+ // Rounding errors <= 2^-31.
+ double tmp = fputil::multiply_add(x, LOG2_10, 0x1.8000'0000'4p21);
+ int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
+ double kd = static_cast<double>(k);
+
+ uint32_t idx1 = (k >> 6) & 0x3f;
+ uint32_t idx2 = k & 0x3f;
+
+ int hi = k >> 12;
+
+ DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
+ DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
+ DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);
+
+ // |dx| < 1.5 * 2^-15 + 2^-31 < 2^-14
+ double lo_h = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
+ double dx = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_MID, lo_h);
+
+ // We use the degree-4 polynomial to approximate 10^(lo):
+ // 10^(lo) ~ 1 + a0 * lo + a1 * lo^2 + a2 * lo^3 + a3 * lo^4
+ // = 1 + lo * P(lo)
+ // So that the errors are bounded by:
+ // |P(lo) - (10^lo - 1)/lo| < |lo|^4 / 64 < 2^(-13 * 4) / 64 = 2^-58
+ // Let P_ be an evaluation of P where all intermediate computations are in
+ // double precision. Using either Horner's or Estrin's schemes, the evaluated
+ // errors can be bounded by:
+ // |P_(lo) - P(lo)| < 2^-51
+ // => |lo * P_(lo) - (2^lo - 1) | < 2^-65
+ // => 2^(mid1 + mid2) * |lo * P_(lo) - expm1(lo)| < 2^-64.
+ // Since we approximate
+ // 2^(mid1 + mid2) ~ exp_mid.hi + exp_mid.lo,
+ // We use the expression:
+ // (exp_mid.hi + exp_mid.lo) * (1 + dx * P_(dx)) ~
+ // ~ exp_mid.hi + (exp_mid.hi * dx * P_(dx) + exp_mid.lo)
+ // with errors bounded by 2^-64.
+
+ double mid_lo = dx * exp_mid.hi;
+
+ // Approximate (10^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4.
+ double p = poly_approx_d(dx);
+
+ double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo);
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
+ double r =
+ cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(exp_mid.hi + lo));
+ return r;
+#else
+ double upper = exp_mid.hi + (lo + ERR_D);
+ double lower = exp_mid.hi + (lo - ERR_D);
+
+ if (LIBC_LIKELY(upper == lower)) {
+ // To multiply by 2^hi, a fast way is to simply add hi to the exponent
+ // field.
+ int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
+ double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper));
+ return r;
+ }
+
+ // Exact outputs when x = 1, 2, ..., 22 + hard to round with x = 23.
+ // Quick check mask: 0x800f'ffffU = ~(bits of 1.0 | ... | bits of 23.0)
+ if (LIBC_UNLIKELY((x_u & 0x8000'ffff'ffff'ffffULL) == 0ULL)) {
+ switch (x_u) {
+ case 0x3ff0000000000000: // x = 1.0
+ return 10.0;
+ case 0x4000000000000000: // x = 2.0
+ return 100.0;
+ case 0x4008000000000000: // x = 3.0
+ return 1'000.0;
+ case 0x4010000000000000: // x = 4.0
+ return 10'000.0;
+ case 0x4014000000000000: // x = 5.0
+ return 100'000.0;
+ case 0x4018000000000000: // x = 6.0
+ return 1'000'000.0;
+ case 0x401c000000000000: // x = 7.0
+ return 10'000'000.0;
+ case 0x4020000000000000: // x = 8.0
+ return 100'000'000.0;
+ case 0x4022000000000000: // x = 9.0
+ return 1'000'000'000.0;
+ case 0x4024000000000000: // x = 10.0
+ return 10'000'000'000.0;
+ case 0x4026000000000000: // x = 11.0
+ return 100'000'000'000.0;
+ case 0x4028000000000000: // x = 12.0
+ return 1'000'000'000'000.0;
+ case 0x402a000000000000: // x = 13.0
+ return 10'000'000'000'000.0;
+ case 0x402c000000000000: // x = 14.0
+ return 100'000'000'000'000.0;
+ case 0x402e000000000000: // x = 15.0
+ return 1'000'000'000'000'000.0;
+ case 0x4030000000000000: // x = 16.0
+ return 10'000'000'000'000'000.0;
+ case 0x4031000000000000: // x = 17.0
+ return 100'000'000'000'000'000.0;
+ case 0x4032000000000000: // x = 18.0
+ return 1'000'000'000'000'000'000.0;
+ case 0x4033000000000000: // x = 19.0
+ return 10'000'000'000'000'000'000.0;
+ case 0x4034000000000000: // x = 20.0
+ return 100'000'000'000'000'000'000.0;
+ case 0x4035000000000000: // x = 21.0
+ return 1'000'000'000'000'000'000'000.0;
+ case 0x4036000000000000: // x = 22.0
+ return 10'000'000'000'000'000'000'000.0;
+ case 0x4037000000000000: // x = 23.0
+ return 0x1.52d02c7e14af6p76 + x;
+ }
+ }
+
+ // Use double-double
+ DoubleDouble r_dd = exp10_double_double(x, kd, exp_mid);
+
+ double upper_dd = r_dd.hi + (r_dd.lo + ERR_DD);
+ double lower_dd = r_dd.hi + (r_dd.lo - ERR_DD);
+
+ if (LIBC_LIKELY(upper_dd == lower_dd)) {
+ // To multiply by 2^hi, a fast way is to simply add hi to the exponent
+ // field.
+ int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
+ double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper_dd));
+ return r;
+ }
+
+ // Use 128-bit precision
+ Float128 r_f128 = exp10_f128(x, kd, idx1, idx2);
+
+ return static_cast<double>(r_f128);
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index b59beacd94143..352c2ad4ab22a 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1457,20 +1457,7 @@ add_entrypoint_object(
HDRS
../exp10.h
DEPENDS
- .common_constants
- .explogxf
- libc.src.__support.CPP.bit
- libc.src.__support.CPP.optional
- libc.src.__support.FPUtil.dyadic_float
- 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.triple_double
- libc.src.__support.integer_literals
- libc.src.__support.macros.optimization
+ libc.src.__support.math.exp10
libc.src.errno.errno
)
diff --git a/libc/src/math/generic/exp10.cpp b/libc/src/math/generic/exp10.cpp
index c464979b092c3..5c36d28c166ae 100644
--- a/libc/src/math/generic/exp10.cpp
+++ b/libc/src/math/generic/exp10.cpp
@@ -7,491 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/exp10.h"
-#include "common_constants.h" // Lookup tables EXP2_MID1 and EXP_M2.
-#include "explogxf.h" // ziv_test_denorm.
-#include "src/__support/CPP/bit.h"
-#include "src/__support/CPP/optional.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/double_double.h"
-#include "src/__support/FPUtil/dyadic_float.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/triple_double.h"
-#include "src/__support/common.h"
-#include "src/__support/integer_literals.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/math/exp10.h"
namespace LIBC_NAMESPACE_DECL {
-using fputil::DoubleDouble;
-using fputil::TripleDouble;
-using Float128 = typename fputil::DyadicFloat<128>;
-
-using LIBC_NAMESPACE::operator""_u128;
-
-// log2(10)
-constexpr double LOG2_10 = 0x1.a934f0979a371p+1;
-
-// -2^-12 * log10(2)
-// > a = -2^-12 * log10(2);
-// > b = round(a, 32, RN);
-// > c = round(a - b, 32, RN);
-// > d = round(a - b - c, D, RN);
-// Errors < 1.5 * 2^-144
-constexpr double MLOG10_2_EXP2_M12_HI = -0x1.3441350ap-14;
-constexpr double MLOG10_2_EXP2_M12_MID = 0x1.0c0219dc1da99p-51;
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-constexpr double MLOG10_2_EXP2_M12_MID_32 = 0x1.0c0219dcp-51;
-constexpr double MLOG10_2_EXP2_M12_LO = 0x1.da994fd20dba2p-87;
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-// Error bounds:
-// Errors when using double precision.
-constexpr double ERR_D = 0x1.8p-63;
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-// Errors when using double-double precision.
-constexpr double ERR_DD = 0x1.8p-99;
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-namespace {
-
-// Polynomial approximations with double precision. Generated by Sollya with:
-// > P = fpminimax((10^x - 1)/x, 3, [|D...|], [-2^-14, 2^-14]);
-// > P;
-// Error bounds:
-// | output - (10^dx - 1) / dx | < 2^-52.
-LIBC_INLINE double poly_approx_d(double dx) {
- // dx^2
- double dx2 = dx * dx;
- double c0 =
- fputil::multiply_add(dx, 0x1.53524c73cea6ap+1, 0x1.26bb1bbb55516p+1);
- double c1 =
- fputil::multiply_add(dx, 0x1.2bd75cc6afc65p+0, 0x1.0470587aa264cp+1);
- double p = fputil::multiply_add(dx2, c1, c0);
- return p;
-}
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-// Polynomial approximation with double-double precision. Generated by Solya
-// with:
-// > P = fpminimax((10^x - 1)/x, 5, [|DD...|], [-2^-14, 2^-14]);
-// Error bounds:
-// | output - 10^(dx) | < 2^-101
-DoubleDouble poly_approx_dd(const DoubleDouble &dx) {
- // Taylor polynomial.
- constexpr DoubleDouble COEFFS[] = {
- {0, 0x1p0},
- {-0x1.f48ad494e927bp-53, 0x1.26bb1bbb55516p1},
- {-0x1.e2bfab3191cd2p-53, 0x1.53524c73cea69p1},
- {0x1.80fb65ec3b503p-53, 0x1.0470591de2ca4p1},
- {0x1.338fc05e21e55p-54, 0x1.2bd7609fd98c4p0},
- {0x1.d4ea116818fbp-56, 0x1.1429ffd519865p-1},
- {-0x1.872a8ff352077p-57, 0x1.a7ed70847c8b3p-3},
-
- };
-
- DoubleDouble p = fputil::polyeval(dx, COEFFS[0], COEFFS[1], COEFFS[2],
- COEFFS[3], COEFFS[4], COEFFS[5], COEFFS[6]);
- return p;
-}
-
-// Polynomial approximation with 128-bit precision:
-// Return exp(dx) ~ 1 + a0 * dx + a1 * dx^2 + ... + a6 * dx^7
-// For |dx| < 2^-14:
-// | output - 10^dx | < 1.5 * 2^-124.
-Float128 poly_approx_f128(const Float128 &dx) {
- constexpr Float128 COEFFS_128[]{
- {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
- {Sign::POS, -126, 0x935d8ddd'aaa8ac16'ea56d62b'82d30a2d_u128},
- {Sign::POS, -126, 0xa9a92639'e753443a'80a99ce7'5f4d5bdb_u128},
- {Sign::POS, -126, 0x82382c8e'f1652304'6a4f9d7d'bf6c9635_u128},
- {Sign::POS, -124, 0x12bd7609'fd98c44c'34578701'9216c7af_u128},
- {Sign::POS, -127, 0x450a7ff4'7535d889'cc41ed7e'0d27aee5_u128},
- {Sign::POS, -130, 0xd3f6b844'702d636b'8326bb91'a6e7601d_u128},
- {Sign::POS, -130, 0x45b937f0'd05bb1cd'fa7b46df'314112a9_u128},
- };
-
- Float128 p = fputil::polyeval(dx, COEFFS_128[0], COEFFS_128[1], COEFFS_128[2],
- COEFFS_128[3], COEFFS_128[4], COEFFS_128[5],
- COEFFS_128[6], COEFFS_128[7]);
- return p;
-}
-
-// Compute 10^(x) using 128-bit precision.
-// TODO(lntue): investigate triple-double precision implementation for this
-// step.
-Float128 exp10_f128(double x, double kd, int idx1, int idx2) {
- double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
- double t2 = kd * MLOG10_2_EXP2_M12_MID_32; // exact
- double t3 = kd * MLOG10_2_EXP2_M12_LO; // Error < 2^-144
-
- Float128 dx = fputil::quick_add(
- Float128(t1), fputil::quick_add(Float128(t2), Float128(t3)));
-
- // TODO: Skip recalculating exp_mid1 and exp_mid2.
- Float128 exp_mid1 =
- fputil::quick_add(Float128(EXP2_MID1[idx1].hi),
- fputil::quick_add(Float128(EXP2_MID1[idx1].mid),
- Float128(EXP2_MID1[idx1].lo)));
-
- Float128 exp_mid2 =
- fputil::quick_add(Float128(EXP2_MID2[idx2].hi),
- fputil::quick_add(Float128(EXP2_MID2[idx2].mid),
- Float128(EXP2_MID2[idx2].lo)));
-
- Float128 exp_mid = fputil::quick_mul(exp_mid1, exp_mid2);
-
- Float128 p = poly_approx_f128(dx);
-
- Float128 r = fputil::quick_mul(exp_mid, p);
-
- r.exponent += static_cast<int>(kd) >> 12;
-
- return r;
-}
-
-// Compute 10^x with double-double precision.
-DoubleDouble exp10_double_double(double x, double kd,
- const DoubleDouble &exp_mid) {
- // Recalculate dx:
- // dx = x - k * 2^-12 * log10(2)
- double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
- double t2 = kd * MLOG10_2_EXP2_M12_MID_32; // exact
- double t3 = kd * MLOG10_2_EXP2_M12_LO; // Error < 2^-140
-
- DoubleDouble dx = fputil::exact_add(t1, t2);
- dx.lo += t3;
-
- // Degree-6 polynomial approximation in double-double precision.
- // | p - 10^x | < 2^-103.
- DoubleDouble p = poly_approx_dd(dx);
-
- // Error bounds: 2^-102.
- DoubleDouble r = fputil::quick_mult(exp_mid, p);
-
- return r;
-}
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-// When output is denormal.
-double exp10_denorm(double x) {
- // Range reduction.
- double tmp = fputil::multiply_add(x, LOG2_10, 0x1.8000'0000'4p21);
- int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
- double kd = static_cast<double>(k);
-
- uint32_t idx1 = (k >> 6) & 0x3f;
- uint32_t idx2 = k & 0x3f;
-
- int hi = k >> 12;
-
- DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
- DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
- DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);
-
- // |dx| < 1.5 * 2^-15 + 2^-31 < 2^-14
- double lo_h = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
- double dx = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_MID, lo_h);
-
- double mid_lo = dx * exp_mid.hi;
-
- // Approximate (10^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4.
- double p = poly_approx_d(dx);
-
- double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo);
-
-#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- return ziv_test_denorm</*SKIP_ZIV_TEST=*/true>(hi, exp_mid.hi, lo, ERR_D)
- .value();
-#else
- if (auto r = ziv_test_denorm(hi, exp_mid.hi, lo, ERR_D);
- LIBC_LIKELY(r.has_value()))
- return r.value();
-
- // Use double-double
- DoubleDouble r_dd = exp10_double_double(x, kd, exp_mid);
-
- if (auto r = ziv_test_denorm(hi, r_dd.hi, r_dd.lo, ERR_DD);
- LIBC_LIKELY(r.has_value()))
- return r.value();
-
- // Use 128-bit precision
- Float128 r_f128 = exp10_f128(x, kd, idx1, idx2);
-
- return static_cast<double>(r_f128);
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-}
-
-// Check for exceptional cases when:
-// * log10(1 - 2^-54) < x < log10(1 + 2^-53)
-// * x >= log10(2^1024)
-// * x <= log10(2^-1022)
-// * x is inf or nan
-double set_exceptional(double x) {
- using FPBits = typename fputil::FPBits<double>;
- FPBits xbits(x);
-
- uint64_t x_u = xbits.uintval();
- uint64_t x_abs = xbits.abs().uintval();
-
- // |x| < log10(1 + 2^-53)
- if (x_abs <= 0x3c8bcb7b1526e50e) {
- // 10^(x) ~ 1 + x/2
- return fputil::multiply_add(x, 0.5, 1.0);
- }
-
- // x <= log10(2^-1022) || x >= log10(2^1024) or inf/nan.
- if (x_u >= 0xc0733a7146f72a42) {
- // x <= log10(2^-1075) or -inf/nan
- if (x_u > 0xc07439b746e36b52) {
- // exp(-Inf) = 0
- if (xbits.is_inf())
- return 0.0;
-
- // exp(nan) = nan
- if (xbits.is_nan())
- return x;
-
- if (fputil::quick_get_round() == FE_UPWARD)
- return FPBits::min_subnormal().get_val();
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_UNDERFLOW);
- return 0.0;
- }
-
- return exp10_denorm(x);
- }
-
- // x >= log10(2^1024) or +inf/nan
- // x is finite
- if (x_u < 0x7ff0'0000'0000'0000ULL) {
- int rounding = fputil::quick_get_round();
- if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
- return FPBits::max_normal().get_val();
-
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_OVERFLOW);
- }
- // x is +inf or nan
- return x + FPBits::inf().get_val();
-}
-
-} // namespace
-
-LLVM_LIBC_FUNCTION(double, exp10, (double x)) {
- using FPBits = typename fputil::FPBits<double>;
- FPBits xbits(x);
-
- uint64_t x_u = xbits.uintval();
-
- // x <= log10(2^-1022) or x >= log10(2^1024) or
- // log10(1 - 2^-54) < x < log10(1 + 2^-53).
- if (LIBC_UNLIKELY(x_u >= 0xc0733a7146f72a42 ||
- (x_u <= 0xbc7bcb7b1526e50e && x_u >= 0x40734413509f79ff) ||
- x_u < 0x3c8bcb7b1526e50e)) {
- return set_exceptional(x);
- }
-
- // Now log10(2^-1075) < x <= log10(1 - 2^-54) or
- // log10(1 + 2^-53) < x < log10(2^1024)
-
- // Range reduction:
- // Let x = log10(2) * (hi + mid1 + mid2) + lo
- // in which:
- // hi is an integer
- // mid1 * 2^6 is an integer
- // mid2 * 2^12 is an integer
- // then:
- // 10^(x) = 2^hi * 2^(mid1) * 2^(mid2) * 10^(lo).
- // With this formula:
- // - multiplying by 2^hi is exact and cheap, simply by adding the exponent
- // field.
- // - 2^(mid1) and 2^(mid2) are stored in 2 x 64-element tables.
- // - 10^(lo) ~ 1 + a0*lo + a1 * lo^2 + ...
- //
- // We compute (hi + mid1 + mid2) together by perform the rounding on
- // x * log2(10) * 2^12.
- // Since |x| < |log10(2^-1075)| < 2^9,
- // |x * 2^12| < 2^9 * 2^12 < 2^21,
- // So we can fit the rounded result round(x * 2^12) in int32_t.
- // Thus, the goal is to be able to use an additional addition and fixed width
- // shift to get an int32_t representing round(x * 2^12).
- //
- // Assuming int32_t using 2-complement representation, since the mantissa part
- // of a double precision is unsigned with the leading bit hidden, if we add an
- // extra constant C = 2^e1 + 2^e2 with e1 > e2 >= 2^23 to the product, the
- // part that are < 2^e2 in resulted mantissa of (x*2^12*L2E + C) can be
- // considered as a proper 2-complement representations of x*2^12.
- //
- // One small problem with this approach is that the sum (x*2^12 + C) in
- // double precision is rounded to the least significant bit of the dorminant
- // factor C. In order to minimize the rounding errors from this addition, we
- // want to minimize e1. Another constraint that we want is that after
- // shifting the mantissa so that the least significant bit of int32_t
- // corresponds to the unit bit of (x*2^12*L2E), the sign is correct without
- // any adjustment. So combining these 2 requirements, we can choose
- // C = 2^33 + 2^32, so that the sign bit corresponds to 2^31 bit, and hence
- // after right shifting the mantissa, the resulting int32_t has correct sign.
- // With this choice of C, the number of mantissa bits we need to shift to the
- // right is: 52 - 33 = 19.
- //
- // Moreover, since the integer right shifts are equivalent to rounding down,
- // we can add an extra 0.5 so that it will become round-to-nearest, tie-to-
- // +infinity. So in particular, we can compute:
- // hmm = x * 2^12 + C,
- // where C = 2^33 + 2^32 + 2^-1, then if
- // k = int32_t(lower 51 bits of double(x * 2^12 + C) >> 19),
- // the reduced argument:
- // lo = x - log10(2) * 2^-12 * k is bounded by:
- // |lo| = |x - log10(2) * 2^-12 * k|
- // = log10(2) * 2^-12 * | x * log2(10) * 2^12 - k |
- // <= log10(2) * 2^-12 * (2^-1 + 2^-19)
- // < 1.5 * 2^-2 * (2^-13 + 2^-31)
- // = 1.5 * (2^-15 * 2^-31)
- //
- // Finally, notice that k only uses the mantissa of x * 2^12, so the
- // exponent 2^12 is not needed. So we can simply define
- // C = 2^(33 - 12) + 2^(32 - 12) + 2^(-13 - 12), and
- // k = int32_t(lower 51 bits of double(x + C) >> 19).
-
- // Rounding errors <= 2^-31.
- double tmp = fputil::multiply_add(x, LOG2_10, 0x1.8000'0000'4p21);
- int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
- double kd = static_cast<double>(k);
-
- uint32_t idx1 = (k >> 6) & 0x3f;
- uint32_t idx2 = k & 0x3f;
-
- int hi = k >> 12;
-
- DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
- DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
- DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);
-
- // |dx| < 1.5 * 2^-15 + 2^-31 < 2^-14
- double lo_h = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
- double dx = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_MID, lo_h);
-
- // We use the degree-4 polynomial to approximate 10^(lo):
- // 10^(lo) ~ 1 + a0 * lo + a1 * lo^2 + a2 * lo^3 + a3 * lo^4
- // = 1 + lo * P(lo)
- // So that the errors are bounded by:
- // |P(lo) - (10^lo - 1)/lo| < |lo|^4 / 64 < 2^(-13 * 4) / 64 = 2^-58
- // Let P_ be an evaluation of P where all intermediate computations are in
- // double precision. Using either Horner's or Estrin's schemes, the evaluated
- // errors can be bounded by:
- // |P_(lo) - P(lo)| < 2^-51
- // => |lo * P_(lo) - (2^lo - 1) | < 2^-65
- // => 2^(mid1 + mid2) * |lo * P_(lo) - expm1(lo)| < 2^-64.
- // Since we approximate
- // 2^(mid1 + mid2) ~ exp_mid.hi + exp_mid.lo,
- // We use the expression:
- // (exp_mid.hi + exp_mid.lo) * (1 + dx * P_(dx)) ~
- // ~ exp_mid.hi + (exp_mid.hi * dx * P_(dx) + exp_mid.lo)
- // with errors bounded by 2^-64.
-
- double mid_lo = dx * exp_mid.hi;
-
- // Approximate (10^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4.
- double p = poly_approx_d(dx);
-
- double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo);
-
-#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
- double r =
- cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(exp_mid.hi + lo));
- return r;
-#else
- double upper = exp_mid.hi + (lo + ERR_D);
- double lower = exp_mid.hi + (lo - ERR_D);
-
- if (LIBC_LIKELY(upper == lower)) {
- // To multiply by 2^hi, a fast way is to simply add hi to the exponent
- // field.
- int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
- double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper));
- return r;
- }
-
- // Exact outputs when x = 1, 2, ..., 22 + hard to round with x = 23.
- // Quick check mask: 0x800f'ffffU = ~(bits of 1.0 | ... | bits of 23.0)
- if (LIBC_UNLIKELY((x_u & 0x8000'ffff'ffff'ffffULL) == 0ULL)) {
- switch (x_u) {
- case 0x3ff0000000000000: // x = 1.0
- return 10.0;
- case 0x4000000000000000: // x = 2.0
- return 100.0;
- case 0x4008000000000000: // x = 3.0
- return 1'000.0;
- case 0x4010000000000000: // x = 4.0
- return 10'000.0;
- case 0x4014000000000000: // x = 5.0
- return 100'000.0;
- case 0x4018000000000000: // x = 6.0
- return 1'000'000.0;
- case 0x401c000000000000: // x = 7.0
- return 10'000'000.0;
- case 0x4020000000000000: // x = 8.0
- return 100'000'000.0;
- case 0x4022000000000000: // x = 9.0
- return 1'000'000'000.0;
- case 0x4024000000000000: // x = 10.0
- return 10'000'000'000.0;
- case 0x4026000000000000: // x = 11.0
- return 100'000'000'000.0;
- case 0x4028000000000000: // x = 12.0
- return 1'000'000'000'000.0;
- case 0x402a000000000000: // x = 13.0
- return 10'000'000'000'000.0;
- case 0x402c000000000000: // x = 14.0
- return 100'000'000'000'000.0;
- case 0x402e000000000000: // x = 15.0
- return 1'000'000'000'000'000.0;
- case 0x4030000000000000: // x = 16.0
- return 10'000'000'000'000'000.0;
- case 0x4031000000000000: // x = 17.0
- return 100'000'000'000'000'000.0;
- case 0x4032000000000000: // x = 18.0
- return 1'000'000'000'000'000'000.0;
- case 0x4033000000000000: // x = 19.0
- return 10'000'000'000'000'000'000.0;
- case 0x4034000000000000: // x = 20.0
- return 100'000'000'000'000'000'000.0;
- case 0x4035000000000000: // x = 21.0
- return 1'000'000'000'000'000'000'000.0;
- case 0x4036000000000000: // x = 22.0
- return 10'000'000'000'000'000'000'000.0;
- case 0x4037000000000000: // x = 23.0
- return 0x1.52d02c7e14af6p76 + x;
- }
- }
-
- // Use double-double
- DoubleDouble r_dd = exp10_double_double(x, kd, exp_mid);
-
- double upper_dd = r_dd.hi + (r_dd.lo + ERR_DD);
- double lower_dd = r_dd.hi + (r_dd.lo - ERR_DD);
-
- if (LIBC_LIKELY(upper_dd == lower_dd)) {
- // To multiply by 2^hi, a fast way is to simply add hi to the exponent
- // field.
- int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
- double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper_dd));
- return r;
- }
-
- // Use 128-bit precision
- Float128 r_f128 = exp10_f128(x, kd, idx1, idx2);
-
- return static_cast<double>(r_f128);
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-}
+LLVM_LIBC_FUNCTION(double, exp10, (double x)) { return math::exp10(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 4ab0126291276..26fc8b4cf6543 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2245,6 +2245,24 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_exp10",
+ hdrs = ["src/__support/math/exp10.h"],
+ deps = [
+ ":__support_math_exp_constants",
+ ":__support_math_exp_utils",
+ ":__support_fputil_double_double",
+ ":__support_fputil_dyadic_float",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_rounding_mode",
+ ":__support_fputil_triple_double",
+ ":__support_integer_literals",
+ ":__support_macros_optimization",
+ ],
+)
+
############################### complex targets ################################
libc_function(
@@ -2849,17 +2867,8 @@ libc_math_function(
libc_math_function(
name = "exp10",
additional_deps = [
- ":__support_fputil_double_double",
- ":__support_fputil_dyadic_float",
- ":__support_fputil_multiply_add",
- ":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
- ":__support_fputil_rounding_mode",
- ":__support_fputil_triple_double",
- ":__support_integer_literals",
- ":__support_macros_optimization",
- ":common_constants",
- ":explogxf",
+ ":__support_math_exp10",
+ ":errno",
],
)
>From 26646c5e745721331a8e5d4e7120594e2723854d Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 04:42:34 +0300
Subject: [PATCH 07/15] [libc][math] Refactor exp10f implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/exp10f.h | 24 +++
libc/src/__support/math/CMakeLists.txt | 28 +++
.../exp10f_impl.h => __support/math/exp10f.h} | 17 +-
libc/src/__support/math/exp10f_utils.h | 171 ++++++++++++++++++
libc/src/math/generic/CMakeLists.txt | 33 +---
libc/src/math/generic/atanhf.cpp | 1 +
libc/src/math/generic/coshf.cpp | 2 +-
libc/src/math/generic/exp10f.cpp | 7 +-
libc/src/math/generic/explogxf.h | 156 +---------------
libc/src/math/generic/powf.cpp | 7 +-
libc/src/math/generic/sinhf.cpp | 1 +
.../llvm-project-overlay/libc/BUILD.bazel | 53 ++++--
13 files changed, 281 insertions(+), 220 deletions(-)
create mode 100644 libc/shared/math/exp10f.h
rename libc/src/{math/generic/exp10f_impl.h => __support/math/exp10f.h} (91%)
create mode 100644 libc/src/__support/math/exp10f_utils.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index b37aa46820523..2ae7c1d58ae10 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -13,6 +13,7 @@
#include "math/exp.h"
#include "math/exp10.h"
+#include "math/exp10f.h"
#include "math/expf.h"
#include "math/expf16.h"
#include "math/frexpf.h"
diff --git a/libc/shared/math/exp10f.h b/libc/shared/math/exp10f.h
new file mode 100644
index 0000000000000..556e78ab3b7a7
--- /dev/null
+++ b/libc/shared/math/exp10f.h
@@ -0,0 +1,24 @@
+//===-- Shared exp10f function -----------------------------------*- C++
+//-*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_EXP10F_H
+#define LLVM_LIBC_SHARED_MATH_EXP10F_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/exp10f.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::exp10f;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_EXP10F_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 0bfc996c44fc8..ad36679409f89 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -170,3 +170,31 @@ add_header_library(
libc.src.__support.integer_literals
libc.src.__support.macros.optimization
)
+
+add_header_library(
+ exp10f_utils
+ HDRS
+ exp10f_utils.h
+ DEPENDS
+ libc.src.__support.FPUtil.basic_operations
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.nearest_integer
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.common
+ libc.src.__support.math.exp_utils
+)
+
+add_header_library(
+ exp10f
+ HDRS
+ exp10f.h
+ DEPENDS
+ .exp10f_utils
+ libc.src.__support.macros.config
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.rounding_mode
+ libc.src.__support.macros.optimization
+)
diff --git a/libc/src/math/generic/exp10f_impl.h b/libc/src/__support/math/exp10f.h
similarity index 91%
rename from libc/src/math/generic/exp10f_impl.h
rename to libc/src/__support/math/exp10f.h
index 975fd01a0a25c..807b4f0d6c109 100644
--- a/libc/src/math/generic/exp10f_impl.h
+++ b/libc/src/__support/math/exp10f.h
@@ -1,4 +1,4 @@
-//===-- Single-precision 10^x function ------------------------------------===//
+//===-- Implementation header for exp10f ------------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
@@ -6,22 +6,21 @@
//
//===----------------------------------------------------------------------===//
-#ifndef LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
-#define LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_H
-#include "explogxf.h"
+#include "exp10f_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/rounding_mode.h"
-#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
namespace LIBC_NAMESPACE_DECL {
-namespace generic {
+namespace math {
-LIBC_INLINE float exp10f(float x) {
+static constexpr float exp10f(float x) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
@@ -132,7 +131,7 @@ LIBC_INLINE float exp10f(float x) {
return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh));
}
-} // namespace generic
+} // namespace math
} // namespace LIBC_NAMESPACE_DECL
-#endif // LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_H
diff --git a/libc/src/__support/math/exp10f_utils.h b/libc/src/__support/math/exp10f_utils.h
new file mode 100644
index 0000000000000..c491872cc725c
--- /dev/null
+++ b/libc/src/__support/math/exp10f_utils.h
@@ -0,0 +1,171 @@
+//===-- Common utils for exp10f ---------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP_FLOAT_CONSTANTS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_FLOAT_CONSTANTS_H
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+struct ExpBase {
+ // Base = e
+ static constexpr int MID_BITS = 5;
+ static constexpr int MID_MASK = (1 << MID_BITS) - 1;
+ // log2(e) * 2^5
+ static constexpr double LOG2_B = 0x1.71547652b82fep+0 * (1 << MID_BITS);
+ // High and low parts of -log(2) * 2^(-5)
+ static constexpr double M_LOGB_2_HI = -0x1.62e42fefa0000p-1 / (1 << MID_BITS);
+ static constexpr double M_LOGB_2_LO =
+ -0x1.cf79abc9e3b3ap-40 / (1 << MID_BITS);
+ // Look up table for bit fields of 2^(i/32) for i = 0..31, generated by Sollya
+ // with:
+ // > for i from 0 to 31 do printdouble(round(2^(i/32), D, RN));
+ static constexpr int64_t EXP_2_MID[1 << MID_BITS] = {
+ 0x3ff0000000000000, 0x3ff059b0d3158574, 0x3ff0b5586cf9890f,
+ 0x3ff11301d0125b51, 0x3ff172b83c7d517b, 0x3ff1d4873168b9aa,
+ 0x3ff2387a6e756238, 0x3ff29e9df51fdee1, 0x3ff306fe0a31b715,
+ 0x3ff371a7373aa9cb, 0x3ff3dea64c123422, 0x3ff44e086061892d,
+ 0x3ff4bfdad5362a27, 0x3ff5342b569d4f82, 0x3ff5ab07dd485429,
+ 0x3ff6247eb03a5585, 0x3ff6a09e667f3bcd, 0x3ff71f75e8ec5f74,
+ 0x3ff7a11473eb0187, 0x3ff82589994cce13, 0x3ff8ace5422aa0db,
+ 0x3ff93737b0cdc5e5, 0x3ff9c49182a3f090, 0x3ffa5503b23e255d,
+ 0x3ffae89f995ad3ad, 0x3ffb7f76f2fb5e47, 0x3ffc199bdd85529c,
+ 0x3ffcb720dcef9069, 0x3ffd5818dcfba487, 0x3ffdfc97337b9b5f,
+ 0x3ffea4afa2a490da, 0x3fff50765b6e4540,
+ };
+
+ // Approximating e^dx with degree-5 minimax polynomial generated by Sollya:
+ // > Q = fpminimax(expm1(x)/x, 4, [|1, D...|], [-log(2)/64, log(2)/64]);
+ // Then:
+ // e^dx ~ P(dx) = 1 + dx + COEFFS[0] * dx^2 + ... + COEFFS[3] * dx^5.
+ static constexpr double COEFFS[4] = {
+ 0x1.ffffffffe5bc8p-2, 0x1.555555555cd67p-3, 0x1.5555c2a9b48b4p-5,
+ 0x1.11112a0e34bdbp-7};
+
+ LIBC_INLINE static double powb_lo(double dx) {
+ using fputil::multiply_add;
+ double dx2 = dx * dx;
+ double c0 = 1.0 + dx;
+ // c1 = COEFFS[0] + COEFFS[1] * dx
+ double c1 = multiply_add(dx, ExpBase::COEFFS[1], ExpBase::COEFFS[0]);
+ // c2 = COEFFS[2] + COEFFS[3] * dx
+ double c2 = multiply_add(dx, ExpBase::COEFFS[3], ExpBase::COEFFS[2]);
+ // r = c4 + c5 * dx^4
+ // = 1 + dx + COEFFS[0] * dx^2 + ... + COEFFS[5] * dx^7
+ return fputil::polyeval(dx2, c0, c1, c2);
+ }
+};
+
+struct Exp10Base : public ExpBase {
+ // log2(10) * 2^5
+ static constexpr double LOG2_B = 0x1.a934f0979a371p1 * (1 << MID_BITS);
+ // High and low parts of -log10(2) * 2^(-5).
+ // Notice that since |x * log2(10)| < 150:
+ // |k| = |round(x * log2(10) * 2^5)| < 2^8 * 2^5 = 2^13
+ // So when the FMA instructions are not available, in order for the product
+ // k * M_LOGB_2_HI
+ // to be exact, we only store the high part of log10(2) up to 38 bits
+ // (= 53 - 15) of precision.
+ // It is generated by Sollya with:
+ // > round(log10(2), 44, RN);
+ static constexpr double M_LOGB_2_HI = -0x1.34413509f8p-2 / (1 << MID_BITS);
+ // > round(log10(2) - 0x1.34413509f8p-2, D, RN);
+ static constexpr double M_LOGB_2_LO = 0x1.80433b83b532ap-44 / (1 << MID_BITS);
+
+ // Approximating 10^dx with degree-5 minimax polynomial generated by Sollya:
+ // > Q = fpminimax((10^x - 1)/x, 4, [|D...|], [-log10(2)/2^6, log10(2)/2^6]);
+ // Then:
+ // 10^dx ~ P(dx) = 1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5.
+ static constexpr double COEFFS[5] = {0x1.26bb1bbb55515p1, 0x1.53524c73bd3eap1,
+ 0x1.0470591dff149p1, 0x1.2bd7c0a9fbc4dp0,
+ 0x1.1429e74a98f43p-1};
+
+ static double powb_lo(double dx) {
+ using fputil::multiply_add;
+ double dx2 = dx * dx;
+ // c0 = 1 + COEFFS[0] * dx
+ double c0 = multiply_add(dx, Exp10Base::COEFFS[0], 1.0);
+ // c1 = COEFFS[1] + COEFFS[2] * dx
+ double c1 = multiply_add(dx, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);
+ // c2 = COEFFS[3] + COEFFS[4] * dx
+ double c2 = multiply_add(dx, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);
+ // r = c0 + dx^2 * (c1 + c2 * dx^2)
+ // = c0 + c1 * dx^2 + c2 * dx^4
+ // = 1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5.
+ return fputil::polyeval(dx2, c0, c1, c2);
+ }
+};
+
+constexpr int LOG_P1_BITS = 6;
+constexpr int LOG_P1_SIZE = 1 << LOG_P1_BITS;
+
+// N[Table[Log[2, 1 + x], {x, 0/64, 63/64, 1/64}], 40]
+extern const double LOG_P1_LOG2[LOG_P1_SIZE];
+
+// N[Table[1/(1 + x), {x, 0/64, 63/64, 1/64}], 40]
+extern const double LOG_P1_1_OVER[LOG_P1_SIZE];
+
+// Taylor series expansion for Log[2, 1 + x] splitted to EVEN AND ODD numbers
+// K_LOG2_ODD starts from x^3
+extern const double K_LOG2_ODD[4];
+extern const double K_LOG2_EVEN[4];
+
+// Output of range reduction for exp_b: (2^(mid + hi), lo)
+// where:
+// b^x = 2^(mid + hi) * b^lo
+struct exp_b_reduc_t {
+ double mh; // 2^(mid + hi)
+ double lo;
+};
+
+// The function correctly calculates b^x value with at least float precision
+// in a limited range.
+// Range reduction:
+// b^x = 2^(hi + mid) * b^lo
+// where:
+// x = (hi + mid) * log_b(2) + lo
+// hi is an integer,
+// 0 <= mid * 2^MID_BITS < 2^MID_BITS is an integer
+// -2^(-MID_BITS - 1) <= lo * log2(b) <= 2^(-MID_BITS - 1)
+// Base class needs to provide the following constants:
+// - MID_BITS : number of bits after decimal points used for mid
+// - MID_MASK : 2^MID_BITS - 1, mask to extract mid bits
+// - LOG2_B : log2(b) * 2^MID_BITS for scaling
+// - M_LOGB_2_HI : high part of -log_b(2) * 2^(-MID_BITS)
+// - M_LOGB_2_LO : low part of -log_b(2) * 2^(-MID_BITS)
+// - EXP_2_MID : look up table for bit fields of 2^mid
+// Return:
+// { 2^(hi + mid), lo }
+template <class Base>
+LIBC_INLINE static constexpr exp_b_reduc_t exp_b_range_reduc(float x) {
+ double xd = static_cast<double>(x);
+ // kd = round((hi + mid) * log2(b) * 2^MID_BITS)
+ double kd = fputil::nearest_integer(Base::LOG2_B * xd);
+ // k = round((hi + mid) * log2(b) * 2^MID_BITS)
+ int k = static_cast<int>(kd);
+ // hi = floor(kd * 2^(-MID_BITS))
+ // exp_hi = shift hi to the exponent field of double precision.
+ uint64_t exp_hi = static_cast<uint64_t>(k >> Base::MID_BITS)
+ << fputil::FPBits<double>::FRACTION_LEN;
+ // mh = 2^hi * 2^mid
+ // mh_bits = bit field of mh
+ uint64_t mh_bits = Base::EXP_2_MID[k & Base::MID_MASK] + exp_hi;
+ double mh = fputil::FPBits<double>(mh_bits).get_val();
+ // dx = lo = x - (hi + mid) * log(2)
+ double dx = fputil::multiply_add(
+ kd, Base::M_LOGB_2_LO, fputil::multiply_add(kd, Base::M_LOGB_2_HI, xd));
+ return {mh, dx};
+}
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP_FLOAT_CONSTANTS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 352c2ad4ab22a..ebdd3d7235141 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -358,7 +358,6 @@ add_entrypoint_object(
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fma
- libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.macros.optimization
)
@@ -448,7 +447,6 @@ add_entrypoint_object(
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.fma
- libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
@@ -1461,21 +1459,6 @@ add_entrypoint_object(
libc.src.errno.errno
)
-add_header_library(
- exp10f_impl
- HDRS
- exp10f_impl.h
- DEPENDS
- .explogxf
- libc.src.__support.FPUtil.fenv_impl
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.rounding_mode
- libc.src.__support.macros.optimization
- libc.src.__support.common
- libc.src.errno.errno
-)
-
add_entrypoint_object(
exp10f
SRCS
@@ -1483,7 +1466,8 @@ add_entrypoint_object(
HDRS
../exp10f.h
DEPENDS
- .exp10f_impl
+ libc.src.__support.math.exp10f
+ libc.src.errno.errno
)
add_entrypoint_object(
@@ -1620,17 +1604,15 @@ add_entrypoint_object(
../powf.h
DEPENDS
.common_constants
- .exp10f_impl
.exp2f_impl
.explogxf
+ libc.src.__support.math.exp10f
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
@@ -3792,13 +3774,9 @@ add_object_library(
explogxf.cpp
DEPENDS
.common_constants
- libc.src.__support.FPUtil.basic_operations
- libc.src.__support.FPUtil.fenv_impl
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.nearest_integer
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.common
libc.src.__support.math.exp_utils
+ libc.src.__support.math.exp10f_utils
+ libc.src.__support.macros.properties.cpu_features
libc.src.errno.errno
)
@@ -3981,6 +3959,7 @@ add_entrypoint_object(
DEPENDS
.explogxf
libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.fenv_impl
libc.src.__support.macros.optimization
)
diff --git a/libc/src/math/generic/atanhf.cpp b/libc/src/math/generic/atanhf.cpp
index 2149314d2f676..f6fde766ef785 100644
--- a/libc/src/math/generic/atanhf.cpp
+++ b/libc/src/math/generic/atanhf.cpp
@@ -7,6 +7,7 @@
//===----------------------------------------------------------------------===//
#include "src/math/atanhf.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
diff --git a/libc/src/math/generic/coshf.cpp b/libc/src/math/generic/coshf.cpp
index c869f7d9dec5f..9f87564d524a6 100644
--- a/libc/src/math/generic/coshf.cpp
+++ b/libc/src/math/generic/coshf.cpp
@@ -7,8 +7,8 @@
//===----------------------------------------------------------------------===//
#include "src/math/coshf.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
diff --git a/libc/src/math/generic/exp10f.cpp b/libc/src/math/generic/exp10f.cpp
index 5284c380f52ec..b2d4f097bc7ce 100644
--- a/libc/src/math/generic/exp10f.cpp
+++ b/libc/src/math/generic/exp10f.cpp
@@ -7,12 +7,11 @@
//===----------------------------------------------------------------------===//
#include "src/math/exp10f.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
-#include "src/math/generic/exp10f_impl.h"
+
+#include "src/__support/math/exp10f.h"
namespace LIBC_NAMESPACE_DECL {
-LLVM_LIBC_FUNCTION(float, exp10f, (float x)) { return generic::exp10f(x); }
+LLVM_LIBC_FUNCTION(float, exp10f, (float x)) { return math::exp10f(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/explogxf.h b/libc/src/math/generic/explogxf.h
index 5ae1457ca780e..d9f39a0d6080f 100644
--- a/libc/src/math/generic/explogxf.h
+++ b/libc/src/math/generic/explogxf.h
@@ -10,166 +10,14 @@
#define LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H
#include "common_constants.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/nearest_integer.h"
+
#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
#include "src/__support/macros/properties/cpu_features.h"
-
+#include "src/__support/math/exp10f_utils.h"
#include "src/__support/math/exp_utils.h"
namespace LIBC_NAMESPACE_DECL {
-struct ExpBase {
- // Base = e
- static constexpr int MID_BITS = 5;
- static constexpr int MID_MASK = (1 << MID_BITS) - 1;
- // log2(e) * 2^5
- static constexpr double LOG2_B = 0x1.71547652b82fep+0 * (1 << MID_BITS);
- // High and low parts of -log(2) * 2^(-5)
- static constexpr double M_LOGB_2_HI = -0x1.62e42fefa0000p-1 / (1 << MID_BITS);
- static constexpr double M_LOGB_2_LO =
- -0x1.cf79abc9e3b3ap-40 / (1 << MID_BITS);
- // Look up table for bit fields of 2^(i/32) for i = 0..31, generated by Sollya
- // with:
- // > for i from 0 to 31 do printdouble(round(2^(i/32), D, RN));
- static constexpr int64_t EXP_2_MID[1 << MID_BITS] = {
- 0x3ff0000000000000, 0x3ff059b0d3158574, 0x3ff0b5586cf9890f,
- 0x3ff11301d0125b51, 0x3ff172b83c7d517b, 0x3ff1d4873168b9aa,
- 0x3ff2387a6e756238, 0x3ff29e9df51fdee1, 0x3ff306fe0a31b715,
- 0x3ff371a7373aa9cb, 0x3ff3dea64c123422, 0x3ff44e086061892d,
- 0x3ff4bfdad5362a27, 0x3ff5342b569d4f82, 0x3ff5ab07dd485429,
- 0x3ff6247eb03a5585, 0x3ff6a09e667f3bcd, 0x3ff71f75e8ec5f74,
- 0x3ff7a11473eb0187, 0x3ff82589994cce13, 0x3ff8ace5422aa0db,
- 0x3ff93737b0cdc5e5, 0x3ff9c49182a3f090, 0x3ffa5503b23e255d,
- 0x3ffae89f995ad3ad, 0x3ffb7f76f2fb5e47, 0x3ffc199bdd85529c,
- 0x3ffcb720dcef9069, 0x3ffd5818dcfba487, 0x3ffdfc97337b9b5f,
- 0x3ffea4afa2a490da, 0x3fff50765b6e4540,
- };
-
- // Approximating e^dx with degree-5 minimax polynomial generated by Sollya:
- // > Q = fpminimax(expm1(x)/x, 4, [|1, D...|], [-log(2)/64, log(2)/64]);
- // Then:
- // e^dx ~ P(dx) = 1 + dx + COEFFS[0] * dx^2 + ... + COEFFS[3] * dx^5.
- static constexpr double COEFFS[4] = {
- 0x1.ffffffffe5bc8p-2, 0x1.555555555cd67p-3, 0x1.5555c2a9b48b4p-5,
- 0x1.11112a0e34bdbp-7};
-
- LIBC_INLINE static double powb_lo(double dx) {
- using fputil::multiply_add;
- double dx2 = dx * dx;
- double c0 = 1.0 + dx;
- // c1 = COEFFS[0] + COEFFS[1] * dx
- double c1 = multiply_add(dx, ExpBase::COEFFS[1], ExpBase::COEFFS[0]);
- // c2 = COEFFS[2] + COEFFS[3] * dx
- double c2 = multiply_add(dx, ExpBase::COEFFS[3], ExpBase::COEFFS[2]);
- // r = c4 + c5 * dx^4
- // = 1 + dx + COEFFS[0] * dx^2 + ... + COEFFS[5] * dx^7
- return fputil::polyeval(dx2, c0, c1, c2);
- }
-};
-
-struct Exp10Base : public ExpBase {
- // log2(10) * 2^5
- static constexpr double LOG2_B = 0x1.a934f0979a371p1 * (1 << MID_BITS);
- // High and low parts of -log10(2) * 2^(-5).
- // Notice that since |x * log2(10)| < 150:
- // |k| = |round(x * log2(10) * 2^5)| < 2^8 * 2^5 = 2^13
- // So when the FMA instructions are not available, in order for the product
- // k * M_LOGB_2_HI
- // to be exact, we only store the high part of log10(2) up to 38 bits
- // (= 53 - 15) of precision.
- // It is generated by Sollya with:
- // > round(log10(2), 44, RN);
- static constexpr double M_LOGB_2_HI = -0x1.34413509f8p-2 / (1 << MID_BITS);
- // > round(log10(2) - 0x1.34413509f8p-2, D, RN);
- static constexpr double M_LOGB_2_LO = 0x1.80433b83b532ap-44 / (1 << MID_BITS);
-
- // Approximating 10^dx with degree-5 minimax polynomial generated by Sollya:
- // > Q = fpminimax((10^x - 1)/x, 4, [|D...|], [-log10(2)/2^6, log10(2)/2^6]);
- // Then:
- // 10^dx ~ P(dx) = 1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5.
- static constexpr double COEFFS[5] = {0x1.26bb1bbb55515p1, 0x1.53524c73bd3eap1,
- 0x1.0470591dff149p1, 0x1.2bd7c0a9fbc4dp0,
- 0x1.1429e74a98f43p-1};
-
- static double powb_lo(double dx) {
- using fputil::multiply_add;
- double dx2 = dx * dx;
- // c0 = 1 + COEFFS[0] * dx
- double c0 = multiply_add(dx, Exp10Base::COEFFS[0], 1.0);
- // c1 = COEFFS[1] + COEFFS[2] * dx
- double c1 = multiply_add(dx, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);
- // c2 = COEFFS[3] + COEFFS[4] * dx
- double c2 = multiply_add(dx, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);
- // r = c0 + dx^2 * (c1 + c2 * dx^2)
- // = c0 + c1 * dx^2 + c2 * dx^4
- // = 1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5.
- return fputil::polyeval(dx2, c0, c1, c2);
- }
-};
-
-constexpr int LOG_P1_BITS = 6;
-constexpr int LOG_P1_SIZE = 1 << LOG_P1_BITS;
-
-// N[Table[Log[2, 1 + x], {x, 0/64, 63/64, 1/64}], 40]
-extern const double LOG_P1_LOG2[LOG_P1_SIZE];
-
-// N[Table[1/(1 + x), {x, 0/64, 63/64, 1/64}], 40]
-extern const double LOG_P1_1_OVER[LOG_P1_SIZE];
-
-// Taylor series expansion for Log[2, 1 + x] splitted to EVEN AND ODD numbers
-// K_LOG2_ODD starts from x^3
-extern const double K_LOG2_ODD[4];
-extern const double K_LOG2_EVEN[4];
-
-// Output of range reduction for exp_b: (2^(mid + hi), lo)
-// where:
-// b^x = 2^(mid + hi) * b^lo
-struct exp_b_reduc_t {
- double mh; // 2^(mid + hi)
- double lo;
-};
-
-// The function correctly calculates b^x value with at least float precision
-// in a limited range.
-// Range reduction:
-// b^x = 2^(hi + mid) * b^lo
-// where:
-// x = (hi + mid) * log_b(2) + lo
-// hi is an integer,
-// 0 <= mid * 2^MID_BITS < 2^MID_BITS is an integer
-// -2^(-MID_BITS - 1) <= lo * log2(b) <= 2^(-MID_BITS - 1)
-// Base class needs to provide the following constants:
-// - MID_BITS : number of bits after decimal points used for mid
-// - MID_MASK : 2^MID_BITS - 1, mask to extract mid bits
-// - LOG2_B : log2(b) * 2^MID_BITS for scaling
-// - M_LOGB_2_HI : high part of -log_b(2) * 2^(-MID_BITS)
-// - M_LOGB_2_LO : low part of -log_b(2) * 2^(-MID_BITS)
-// - EXP_2_MID : look up table for bit fields of 2^mid
-// Return:
-// { 2^(hi + mid), lo }
-template <class Base> LIBC_INLINE exp_b_reduc_t exp_b_range_reduc(float x) {
- double xd = static_cast<double>(x);
- // kd = round((hi + mid) * log2(b) * 2^MID_BITS)
- double kd = fputil::nearest_integer(Base::LOG2_B * xd);
- // k = round((hi + mid) * log2(b) * 2^MID_BITS)
- int k = static_cast<int>(kd);
- // hi = floor(kd * 2^(-MID_BITS))
- // exp_hi = shift hi to the exponent field of double precision.
- uint64_t exp_hi = static_cast<uint64_t>(k >> Base::MID_BITS)
- << fputil::FPBits<double>::FRACTION_LEN;
- // mh = 2^hi * 2^mid
- // mh_bits = bit field of mh
- uint64_t mh_bits = Base::EXP_2_MID[k & Base::MID_MASK] + exp_hi;
- double mh = fputil::FPBits<double>(mh_bits).get_val();
- // dx = lo = x - (hi + mid) * log(2)
- double dx = fputil::multiply_add(
- kd, Base::M_LOGB_2_LO, fputil::multiply_add(kd, Base::M_LOGB_2_HI, xd));
- return {mh, dx};
-}
-
// The function correctly calculates sinh(x) and cosh(x) by calculating exp(x)
// and exp(-x) simultaneously.
// To compute e^x, we perform the following range
diff --git a/libc/src/math/generic/powf.cpp b/libc/src/math/generic/powf.cpp
index dfdfd5d6d5760..a45ef511c9bad 100644
--- a/libc/src/math/generic/powf.cpp
+++ b/libc/src/math/generic/powf.cpp
@@ -9,20 +9,17 @@
#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" // Speedup for powf(x, 1/2) = sqrtf(x)
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/math/exp10f.h" // Speedup for powf(10, y) = exp10f(y)
-#include "exp10f_impl.h" // Speedup for powf(10, y) = exp10f(y)
#include "exp2f_impl.h" // Speedup for powf(2, y) = exp2f(y)
namespace LIBC_NAMESPACE_DECL {
@@ -781,7 +778,7 @@ LLVM_LIBC_FUNCTION(float, powf, (float x, float y)) {
return generic::exp2f(y);
case 0x4120'0000: // x = 10.0f
// pow(10, y) = exp10(y)
- return generic::exp10f(y);
+ return math::exp10f(y);
#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
}
diff --git a/libc/src/math/generic/sinhf.cpp b/libc/src/math/generic/sinhf.cpp
index d6158fd302536..63111f84de141 100644
--- a/libc/src/math/generic/sinhf.cpp
+++ b/libc/src/math/generic/sinhf.cpp
@@ -7,6 +7,7 @@
//===----------------------------------------------------------------------===//
#include "src/math/sinhf.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/macros/config.h"
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 26fc8b4cf6543..3351f753ca3d3 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -1999,13 +1999,13 @@ libc_support_library(
srcs = ["src/math/generic/explogxf.cpp"],
hdrs = ["src/math/generic/explogxf.h"],
deps = [
- ":__support_common",
":__support_fputil_fenv_impl",
":__support_fputil_fma",
":__support_fputil_multiply_add",
":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
":__support_math_exp_utils",
+ ":__support_math_exp10f_utils",
+ ":__support_macros_properties_cpu_features",
":common_constants",
],
)
@@ -2050,19 +2050,6 @@ libc_support_library(
],
)
-libc_support_library(
- name = "exp10f_impl",
- hdrs = ["src/math/generic/exp10f_impl.h"],
- deps = [
- ":__support_fputil_fma",
- ":__support_fputil_multiply_add",
- ":__support_fputil_rounding_mode",
- ":__support_macros_optimization",
- ":common_constants",
- ":explogxf",
- ],
-)
-
libc_support_library(
name = "exp2f_impl",
hdrs = ["src/math/generic/exp2f_impl.h"],
@@ -2263,6 +2250,33 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_exp10f_utils",
+ hdrs = ["src/__support/math/exp10f_utils.h"],
+ deps = [
+ ":__support_fputil_basic_operations",
+ ":__support_fputil_fenv_impl",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_polyeval",
+ ":__support_common",
+ ":__support_math_exp_utils",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_exp10f",
+ hdrs = ["src/__support/math/exp10f.h"],
+ deps = [
+ ":__support_math_exp10f_utils",
+ ":__support_fputil_fenv_impl",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_rounding_mode",
+ ":__support_macros_optimization",
+ ],
+)
+
############################### complex targets ################################
libc_function(
@@ -2726,10 +2740,10 @@ libc_math_function(
name = "cosf",
additional_deps = [
":__support_fputil_fma",
- ":__support_fputil_multiply_add",
":__support_macros_optimization",
":__support_macros_properties_cpu_features",
":sincosf_utils",
+ ":errno",
],
)
@@ -2875,7 +2889,8 @@ libc_math_function(
libc_math_function(
name = "exp10f",
additional_deps = [
- ":exp10f_impl",
+ ":__support_math_exp10f",
+ ":errno",
],
)
@@ -3724,14 +3739,13 @@ libc_math_function(
":__support_fputil_multiply_add",
":__support_fputil_nearest_integer",
":__support_fputil_polyeval",
- ":__support_fputil_rounding_mode",
":__support_fputil_sqrt",
":__support_fputil_triple_double",
":__support_macros_optimization",
+ ":__support_math_exp10f",
":common_constants",
":explogxf",
":exp2f_impl",
- ":exp10f_impl",
],
)
@@ -3840,7 +3854,6 @@ libc_math_function(
name = "sinf",
additional_deps = [
":__support_fputil_fma",
- ":__support_fputil_multiply_add",
":__support_fputil_polyeval",
":__support_fputil_rounding_mode",
":__support_macros_optimization",
>From 9d1279d0d8ed25c7154dec07be34303d040172cf Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 06:45:24 +0300
Subject: [PATCH 08/15] [libc][math] Refactor exp10f16 implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/exp10f16.h | 29 ++++
libc/src/__support/math/CMakeLists.txt | 34 +++++
.../__support/math/exp10_float16_constants.h | 43 ++++++
libc/src/__support/math/exp10f16.h | 141 ++++++++++++++++++
libc/src/__support/math/exp10f16_utils.h | 64 ++++++++
libc/src/math/generic/CMakeLists.txt | 21 +--
libc/src/math/generic/exp10f16.cpp | 122 +--------------
libc/src/math/generic/exp10m1f16.cpp | 2 +-
libc/src/math/generic/expxf16.h | 56 +------
.../llvm-project-overlay/libc/BUILD.bazel | 38 ++++-
11 files changed, 357 insertions(+), 194 deletions(-)
create mode 100644 libc/shared/math/exp10f16.h
create mode 100644 libc/src/__support/math/exp10_float16_constants.h
create mode 100644 libc/src/__support/math/exp10f16.h
create mode 100644 libc/src/__support/math/exp10f16_utils.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 2ae7c1d58ae10..26f69d6fa43ea 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -14,6 +14,7 @@
#include "math/exp.h"
#include "math/exp10.h"
#include "math/exp10f.h"
+#include "math/exp10f16.h"
#include "math/expf.h"
#include "math/expf16.h"
#include "math/frexpf.h"
diff --git a/libc/shared/math/exp10f16.h b/libc/shared/math/exp10f16.h
new file mode 100644
index 0000000000000..8acdbdb7c70a1
--- /dev/null
+++ b/libc/shared/math/exp10f16.h
@@ -0,0 +1,29 @@
+//===-- Shared exp10f16 function --------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_EXP10F_H
+#define LLVM_LIBC_SHARED_MATH_EXP10F_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "shared/libc_common.h"
+#include "src/__support/math/exp10f16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::exp10f16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_EXP10F_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index ad36679409f89..77a47c65489dd 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -198,3 +198,37 @@ add_header_library(
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
)
+
+add_header_library(
+ exp10_float16_constants
+ HDRS
+ exp10_float16_constants.h
+ DEPENDS
+ libc.src.__support.CPP.array
+)
+
+add_header_library(
+ exp10f16_utils
+ HDRS
+ exp10f16_utils.h
+ DEPENDS
+ .expf16_utils
+ .exp10_float16_constants
+ libc.src.__support.FPUtil.fp_bits
+)
+
+add_header_library(
+ exp10f16
+ HDRS
+ exp10f16.h
+ DEPENDS
+ .exp10f16_utils
+ libc.src.__support.FPUtil.fp_bits
+ src.__support.FPUtil.FEnvImpl
+ src.__support.FPUtil.FPBits
+ src.__support.FPUtil.cast
+ src.__support.FPUtil.rounding_mode
+ src.__support.FPUtil.except_value_utils
+ src.__support.macros.optimization
+ src.__support.macros.properties.cpu_features
+)
diff --git a/libc/src/__support/math/exp10_float16_constants.h b/libc/src/__support/math/exp10_float16_constants.h
new file mode 100644
index 0000000000000..f5928db740ee4
--- /dev/null
+++ b/libc/src/__support/math/exp10_float16_constants.h
@@ -0,0 +1,43 @@
+//===-- Constants for exp10f16 function -------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP10_FLOAT16_CONSTANTS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10_FLOAT16_CONSTANTS_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+#include <stdint.h>
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/CPP/array.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Generated by Sollya with the following commands:
+// > display = hexadecimal;
+// > for i from 0 to 7 do printsingle(round(2^(i * 2^-3), SG, RN));
+static constexpr cpp::array<uint32_t, 8> EXP2_MID_BITS = {
+ 0x3f80'0000U, 0x3f8b'95c2U, 0x3f98'37f0U, 0x3fa5'fed7U,
+ 0x3fb5'04f3U, 0x3fc5'672aU, 0x3fd7'44fdU, 0x3fea'c0c7U,
+};
+
+// Generated by Sollya with the following commands:
+// > display = hexadecimal;
+// > round(log2(10), SG, RN);
+static constexpr float LOG2F_10 = 0x1.a934fp+1f;
+
+// Generated by Sollya with the following commands:
+// > display = hexadecimal;
+// > round(log10(2), SG, RN);
+static constexpr float LOG10F_2 = 0x1.344136p-2f;
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_H
diff --git a/libc/src/__support/math/exp10f16.h b/libc/src/__support/math/exp10f16.h
new file mode 100644
index 0000000000000..0d8b125348844
--- /dev/null
+++ b/libc/src/__support/math/exp10f16.h
@@ -0,0 +1,141 @@
+//===-- Implementation header for exp10f16 ----------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "exp10f16_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h"
+#include "src/__support/macros/properties/cpu_features.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
+static constexpr size_t N_EXP10F16_EXCEPTS = 5;
+#else
+static constexpr size_t N_EXP10F16_EXCEPTS = 8;
+#endif
+
+static constexpr fputil::ExceptValues<float16, N_EXP10F16_EXCEPTS>
+ EXP10F16_EXCEPTS = {{
+ // x = 0x1.8f4p-2, exp10f16(x) = 0x1.3ap+1 (RZ)
+ {0x363dU, 0x40e8U, 1U, 0U, 1U},
+ // x = 0x1.95cp-2, exp10f16(x) = 0x1.3ecp+1 (RZ)
+ {0x3657U, 0x40fbU, 1U, 0U, 0U},
+ // x = -0x1.018p-4, exp10f16(x) = 0x1.bbp-1 (RZ)
+ {0xac06U, 0x3aecU, 1U, 0U, 0U},
+ // x = -0x1.c28p+0, exp10f16(x) = 0x1.1ccp-6 (RZ)
+ {0xbf0aU, 0x2473U, 1U, 0U, 0U},
+ // x = -0x1.e1cp+1, exp10f16(x) = 0x1.694p-13 (RZ)
+ {0xc387U, 0x09a5U, 1U, 0U, 0U},
+#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
+ // x = 0x1.0cp+1, exp10f16(x) = 0x1.f04p+6 (RZ)
+ {0x4030U, 0x57c1U, 1U, 0U, 1U},
+ // x = 0x1.1b8p+1, exp10f16(x) = 0x1.47cp+7 (RZ)
+ {0x406eU, 0x591fU, 1U, 0U, 1U},
+ // x = 0x1.1b8p+2, exp10f16(x) = 0x1.a4p+14 (RZ)
+ {0x446eU, 0x7690U, 1U, 0U, 1U},
+#endif
+ }};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+static constexpr float16 exp10f16(float16 x) {
+ using FPBits = fputil::FPBits<float16>;
+ FPBits x_bits(x);
+
+ uint16_t x_u = x_bits.uintval();
+ uint16_t x_abs = x_u & 0x7fffU;
+
+ // When |x| >= 5, or x is NaN.
+ if (LIBC_UNLIKELY(x_abs >= 0x4500U)) {
+ // exp10(NaN) = NaN
+ if (x_bits.is_nan()) {
+ if (x_bits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ return x;
+ }
+
+ // When x >= 5.
+ if (x_bits.is_pos()) {
+ // exp10(+inf) = +inf
+ if (x_bits.is_inf())
+ return FPBits::inf().get_val();
+
+ switch (fputil::quick_get_round()) {
+ case FE_TONEAREST:
+ case FE_UPWARD:
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ return FPBits::inf().get_val();
+ default:
+ return FPBits::max_normal().get_val();
+ }
+ }
+
+ // When x <= -8.
+ if (x_u >= 0xc800U) {
+ // exp10(-inf) = +0
+ if (x_bits.is_inf())
+ return FPBits::zero().get_val();
+
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
+
+ if (fputil::fenv_is_round_up())
+ return FPBits::min_subnormal().get_val();
+ return FPBits::zero().get_val();
+ }
+ }
+
+ // When x is 1, 2, 3, or 4. These are hard-to-round cases with exact results.
+ if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) {
+ switch (x_u) {
+ case 0x3c00U: // x = 1.0f16
+ return fputil::cast<float16>(10.0);
+ case 0x4000U: // x = 2.0f16
+ return fputil::cast<float16>(100.0);
+ case 0x4200U: // x = 3.0f16
+ return fputil::cast<float16>(1'000.0);
+ case 0x4400U: // x = 4.0f16
+ return fputil::cast<float16>(10'000.0);
+ }
+ }
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ if (auto r = EXP10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+ return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+ // 10^x = 2^((hi + mid) * log2(10)) * 10^lo
+ auto [exp2_hi_mid, exp10_lo] = exp10_range_reduction(x);
+ return fputil::cast<float16>(exp2_hi_mid * exp10_lo);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_H
diff --git a/libc/src/__support/math/exp10f16_utils.h b/libc/src/__support/math/exp10f16_utils.h
new file mode 100644
index 0000000000000..ae251fc7ce800
--- /dev/null
+++ b/libc/src/__support/math/exp10f16_utils.h
@@ -0,0 +1,64 @@
+//===-- Common utils for exp10f16 -------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP_FLOAT_CONSTANTS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_FLOAT_CONSTANTS_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "exp10_float16_constants.h"
+#include "expf16_utils.h"
+#include "src/__support/FPUtil/FPBits.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+LIBC_INLINE static constexpr ExpRangeReduction
+exp10_range_reduction(float16 x) {
+ // For -8 < x < 5, to compute 10^x, we perform the following range reduction:
+ // find hi, mid, lo, such that:
+ // x = (hi + mid) * log2(10) + lo, in which
+ // hi is an integer,
+ // mid * 2^3 is an integer,
+ // -2^(-4) <= lo < 2^(-4).
+ // In particular,
+ // hi + mid = round(x * 2^3) * 2^(-3).
+ // Then,
+ // 10^x = 10^(hi + mid + lo) = 2^((hi + mid) * log2(10)) + 10^lo
+ // We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid
+ // by adding hi to the exponent field of 2^mid. 10^lo is computed using a
+ // degree-4 minimax polynomial generated by Sollya.
+
+ float xf = x;
+ float kf = fputil::nearest_integer(xf * (LOG2F_10 * 0x1.0p+3f));
+ int x_hi_mid = static_cast<int>(kf);
+ unsigned x_hi = static_cast<unsigned>(x_hi_mid) >> 3;
+ unsigned x_mid = static_cast<unsigned>(x_hi_mid) & 0x7;
+ // lo = x - (hi + mid) = round(x * 2^3 * log2(10)) * log10(2) * (-2^(-3)) + x
+ float lo = fputil::multiply_add(kf, LOG10F_2 * -0x1.0p-3f, xf);
+
+ uint32_t exp2_hi_mid_bits =
+ EXP2_MID_BITS[x_mid] +
+ static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN);
+ float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val();
+ // Degree-4 minimax polynomial generated by Sollya with the following
+ // commands:
+ // > display = hexadecimal;
+ // > P = fpminimax((10^x - 1)/x, 3, [|SG...|], [-2^-4, 2^-4]);
+ // > 1 + x * P;
+ float exp10_lo = fputil::polyeval(lo, 0x1p+0f, 0x1.26bb14p+1f, 0x1.53526p+1f,
+ 0x1.04b434p+1f, 0x1.2bcf9ep+0f);
+ return {exp2_hi_mid, exp10_lo};
+}
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index ebdd3d7235141..2c158a18bc145 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1477,20 +1477,8 @@ add_entrypoint_object(
HDRS
../exp10f16.h
DEPENDS
- .expxf16
- libc.hdr.errno_macros
- libc.hdr.fenv_macros
- libc.src.__support.CPP.array
- libc.src.__support.FPUtil.cast
- libc.src.__support.FPUtil.except_value_utils
- 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.macros.optimization
- libc.src.__support.macros.properties.cpu_features
+ libc.src.__support.math.exp10f16
+ libc.src.errno.errno
)
add_entrypoint_object(
@@ -1519,7 +1507,6 @@ add_entrypoint_object(
HDRS
../exp10m1f16.h
DEPENDS
- .expxf16
libc.hdr.errno_macros
libc.hdr.fenv_macros
libc.src.__support.FPUtil.cast
@@ -1531,6 +1518,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
libc.src.__support.macros.properties.cpu_features
+ libc.src.__support.math.exp10f16_utils
)
add_entrypoint_object(
@@ -5025,10 +5013,11 @@ add_header_library(
HDRS
expxf16.h
DEPENDS
- libc.src.__support.FPUtil.cast
libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.cast
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.nearest_integer
libc.src.__support.macros.attributes
libc.src.__support.math.expf16_utils
+ libc.src.__support.math.exp10_float16_constants
)
diff --git a/libc/src/math/generic/exp10f16.cpp b/libc/src/math/generic/exp10f16.cpp
index 31abf3b4f89b2..cb3c8599c9231 100644
--- a/libc/src/math/generic/exp10f16.cpp
+++ b/libc/src/math/generic/exp10f16.cpp
@@ -7,128 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/exp10f16.h"
-#include "expxf16.h"
-#include "hdr/errno_macros.h"
-#include "hdr/fenv_macros.h"
-#include "src/__support/CPP/array.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/cast.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/config.h"
-#include "src/__support/macros/optimization.h"
-#include "src/__support/macros/properties/cpu_features.h"
+#include "src/__support/math/exp10f16.h"
namespace LIBC_NAMESPACE_DECL {
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
-static constexpr size_t N_EXP10F16_EXCEPTS = 5;
-#else
-static constexpr size_t N_EXP10F16_EXCEPTS = 8;
-#endif
-
-static constexpr fputil::ExceptValues<float16, N_EXP10F16_EXCEPTS>
- EXP10F16_EXCEPTS = {{
- // x = 0x1.8f4p-2, exp10f16(x) = 0x1.3ap+1 (RZ)
- {0x363dU, 0x40e8U, 1U, 0U, 1U},
- // x = 0x1.95cp-2, exp10f16(x) = 0x1.3ecp+1 (RZ)
- {0x3657U, 0x40fbU, 1U, 0U, 0U},
- // x = -0x1.018p-4, exp10f16(x) = 0x1.bbp-1 (RZ)
- {0xac06U, 0x3aecU, 1U, 0U, 0U},
- // x = -0x1.c28p+0, exp10f16(x) = 0x1.1ccp-6 (RZ)
- {0xbf0aU, 0x2473U, 1U, 0U, 0U},
- // x = -0x1.e1cp+1, exp10f16(x) = 0x1.694p-13 (RZ)
- {0xc387U, 0x09a5U, 1U, 0U, 0U},
-#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
- // x = 0x1.0cp+1, exp10f16(x) = 0x1.f04p+6 (RZ)
- {0x4030U, 0x57c1U, 1U, 0U, 1U},
- // x = 0x1.1b8p+1, exp10f16(x) = 0x1.47cp+7 (RZ)
- {0x406eU, 0x591fU, 1U, 0U, 1U},
- // x = 0x1.1b8p+2, exp10f16(x) = 0x1.a4p+14 (RZ)
- {0x446eU, 0x7690U, 1U, 0U, 1U},
-#endif
- }};
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-LLVM_LIBC_FUNCTION(float16, exp10f16, (float16 x)) {
- using FPBits = fputil::FPBits<float16>;
- FPBits x_bits(x);
-
- uint16_t x_u = x_bits.uintval();
- uint16_t x_abs = x_u & 0x7fffU;
-
- // When |x| >= 5, or x is NaN.
- if (LIBC_UNLIKELY(x_abs >= 0x4500U)) {
- // exp10(NaN) = NaN
- if (x_bits.is_nan()) {
- if (x_bits.is_signaling_nan()) {
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- return x;
- }
-
- // When x >= 5.
- if (x_bits.is_pos()) {
- // exp10(+inf) = +inf
- if (x_bits.is_inf())
- return FPBits::inf().get_val();
-
- switch (fputil::quick_get_round()) {
- case FE_TONEAREST:
- case FE_UPWARD:
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_OVERFLOW);
- return FPBits::inf().get_val();
- default:
- return FPBits::max_normal().get_val();
- }
- }
-
- // When x <= -8.
- if (x_u >= 0xc800U) {
- // exp10(-inf) = +0
- if (x_bits.is_inf())
- return FPBits::zero().get_val();
-
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
-
- if (fputil::fenv_is_round_up())
- return FPBits::min_subnormal().get_val();
- return FPBits::zero().get_val();
- }
- }
-
- // When x is 1, 2, 3, or 4. These are hard-to-round cases with exact results.
- if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) {
- switch (x_u) {
- case 0x3c00U: // x = 1.0f16
- return fputil::cast<float16>(10.0);
- case 0x4000U: // x = 2.0f16
- return fputil::cast<float16>(100.0);
- case 0x4200U: // x = 3.0f16
- return fputil::cast<float16>(1'000.0);
- case 0x4400U: // x = 4.0f16
- return fputil::cast<float16>(10'000.0);
- }
- }
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- if (auto r = EXP10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
- return r.value();
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
- // 10^x = 2^((hi + mid) * log2(10)) * 10^lo
- auto [exp2_hi_mid, exp10_lo] = exp10_range_reduction(x);
- return fputil::cast<float16>(exp2_hi_mid * exp10_lo);
-}
+LLVM_LIBC_FUNCTION(float16, exp10f16, (float16 x)) { return math::exp10f16(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/exp10m1f16.cpp b/libc/src/math/generic/exp10m1f16.cpp
index 545c479694811..6c2fdbea418df 100644
--- a/libc/src/math/generic/exp10m1f16.cpp
+++ b/libc/src/math/generic/exp10m1f16.cpp
@@ -7,7 +7,6 @@
//===----------------------------------------------------------------------===//
#include "src/math/exp10m1f16.h"
-#include "expxf16.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "src/__support/FPUtil/FEnvImpl.h"
@@ -21,6 +20,7 @@
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h"
#include "src/__support/macros/properties/cpu_features.h"
+#include "src/__support/math/exp10f16_utils.h"
namespace LIBC_NAMESPACE_DECL {
diff --git a/libc/src/math/generic/expxf16.h b/libc/src/math/generic/expxf16.h
index 05ac95d586823..b17b14fa2d756 100644
--- a/libc/src/math/generic/expxf16.h
+++ b/libc/src/math/generic/expxf16.h
@@ -17,18 +17,11 @@
#include "src/__support/macros/config.h"
#include <stdint.h>
+#include "src/__support/math/exp10_float16_constants.h"
#include "src/__support/math/expf16_utils.h"
namespace LIBC_NAMESPACE_DECL {
-// Generated by Sollya with the following commands:
-// > display = hexadecimal;
-// > for i from 0 to 7 do printsingle(round(2^(i * 2^-3), SG, RN));
-constexpr cpp::array<uint32_t, 8> EXP2_MID_BITS = {
- 0x3f80'0000U, 0x3f8b'95c2U, 0x3f98'37f0U, 0x3fa5'fed7U,
- 0x3fb5'04f3U, 0x3fc5'672aU, 0x3fd7'44fdU, 0x3fea'c0c7U,
-};
-
LIBC_INLINE ExpRangeReduction exp2_range_reduction(float16 x) {
// For -25 < x < 16, to compute 2^x, we perform the following range reduction:
// find hi, mid, lo, such that:
@@ -66,53 +59,6 @@ LIBC_INLINE ExpRangeReduction exp2_range_reduction(float16 x) {
return {exp2_hi_mid, exp2_lo};
}
-// Generated by Sollya with the following commands:
-// > display = hexadecimal;
-// > round(log2(10), SG, RN);
-static constexpr float LOG2F_10 = 0x1.a934fp+1f;
-
-// Generated by Sollya with the following commands:
-// > display = hexadecimal;
-// > round(log10(2), SG, RN);
-static constexpr float LOG10F_2 = 0x1.344136p-2f;
-
-LIBC_INLINE ExpRangeReduction exp10_range_reduction(float16 x) {
- // For -8 < x < 5, to compute 10^x, we perform the following range reduction:
- // find hi, mid, lo, such that:
- // x = (hi + mid) * log2(10) + lo, in which
- // hi is an integer,
- // mid * 2^3 is an integer,
- // -2^(-4) <= lo < 2^(-4).
- // In particular,
- // hi + mid = round(x * 2^3) * 2^(-3).
- // Then,
- // 10^x = 10^(hi + mid + lo) = 2^((hi + mid) * log2(10)) + 10^lo
- // We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid
- // by adding hi to the exponent field of 2^mid. 10^lo is computed using a
- // degree-4 minimax polynomial generated by Sollya.
-
- float xf = x;
- float kf = fputil::nearest_integer(xf * (LOG2F_10 * 0x1.0p+3f));
- int x_hi_mid = static_cast<int>(kf);
- unsigned x_hi = static_cast<unsigned>(x_hi_mid) >> 3;
- unsigned x_mid = static_cast<unsigned>(x_hi_mid) & 0x7;
- // lo = x - (hi + mid) = round(x * 2^3 * log2(10)) * log10(2) * (-2^(-3)) + x
- float lo = fputil::multiply_add(kf, LOG10F_2 * -0x1.0p-3f, xf);
-
- uint32_t exp2_hi_mid_bits =
- EXP2_MID_BITS[x_mid] +
- static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN);
- float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val();
- // Degree-4 minimax polynomial generated by Sollya with the following
- // commands:
- // > display = hexadecimal;
- // > P = fpminimax((10^x - 1)/x, 3, [|SG...|], [-2^-4, 2^-4]);
- // > 1 + x * P;
- float exp10_lo = fputil::polyeval(lo, 0x1p+0f, 0x1.26bb14p+1f, 0x1.53526p+1f,
- 0x1.04b434p+1f, 0x1.2bcf9ep+0f);
- return {exp2_hi_mid, exp10_lo};
-}
-
// Generated by Sollya with the following commands:
// > display = hexadecimal;
// > round(log2(exp(1)), SG, RN);
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 3351f753ca3d3..7a497f16cccc1 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2074,6 +2074,7 @@ libc_support_library(
":__support_fputil_fp_bits",
":__support_fputil_nearest_integer",
":__support_math_expf16_utils",
+ ":__support_math_exp10_float16_constants",
],
)
@@ -2277,6 +2278,38 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_exp10_float16_constants",
+ hdrs = ["src/__support/math/exp10_float16_constants.h"],
+ deps = [
+ ":__support_cpp_array",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_exp10f16_utils",
+ hdrs = ["src/__support/math/exp10f16_utils.h"],
+ deps = [
+ ":__support_math_exp10_float16_constants",
+ ":__support_math_expf16_utils",
+ ":__support_fputil_fp_bits",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_exp10f16",
+ hdrs = ["src/__support/math/exp10f16.h"],
+ deps = [
+ ":__support_math_exp10f16_utils",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_cast",
+ ":__support_fputil_rounding_mode",
+ ":__support_fputil_except_value_utils",
+ ":__support_macros_optimization",
+ ":__support_macros_properties_cpu_features",
+ ],
+)
+
############################### complex targets ################################
libc_function(
@@ -2897,14 +2930,15 @@ libc_math_function(
libc_math_function(
name = "exp10f16",
additional_deps = [
- ":expxf16",
+ ":__support_math_exp10f16",
+ ":errno",
],
)
libc_math_function(
name = "exp10m1f16",
additional_deps = [
- ":expxf16",
+ ":__support_math_exp10f16_utils",
],
)
>From b5d474e3d45d1917957bf55f8a46689c9b5c1075 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 08:03:36 +0300
Subject: [PATCH 09/15] [libc][math] Refactor acos implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/acos.h | 23 ++
libc/src/__support/math/CMakeLists.txt | 33 ++
libc/src/__support/math/acos.h | 285 ++++++++++++++++++
.../generic => __support/math}/asin_utils.h | 34 +--
libc/src/math/generic/CMakeLists.txt | 28 +-
libc/src/math/generic/acos.cpp | 266 +---------------
libc/src/math/generic/asin.cpp | 2 +-
.../llvm-project-overlay/libc/BUILD.bazel | 39 +++
9 files changed, 403 insertions(+), 308 deletions(-)
create mode 100644 libc/shared/math/acos.h
create mode 100644 libc/src/__support/math/acos.h
rename libc/src/{math/generic => __support/math}/asin_utils.h (96%)
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 26f69d6fa43ea..8dcfaf0352339 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -11,6 +11,7 @@
#include "libc_common.h"
+#include "math/acos.h"
#include "math/exp.h"
#include "math/exp10.h"
#include "math/exp10f.h"
diff --git a/libc/shared/math/acos.h b/libc/shared/math/acos.h
new file mode 100644
index 0000000000000..73c6b512e16f4
--- /dev/null
+++ b/libc/shared/math/acos.h
@@ -0,0 +1,23 @@
+//===-- Shared acos function ------------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_ACOS_H
+#define LLVM_LIBC_SHARED_MATH_ACOS_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/acos.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acos;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOS_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 77a47c65489dd..4a29c2975d523 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -1,3 +1,36 @@
+add_header_library(
+ acos
+ HDRS
+ acos.h
+ DEPENDS
+ .asin_utils
+ libc.src.__support.math.asin_utils
+ libc.src.__support.FPUtil.double_double
+ libc.src.__support.FPUtil.dyadic_float
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.macros.optimization
+ libc.src.__support.macros.properties.types
+ libc.src.__support.macros.properties.cpu_features
+)
+
+add_header_library(
+ asin_utils
+ HDRS
+ asin_utils.h
+ DEPENDS
+ libc.src.__support.integer_literals
+ libc.src.__support.FPUtil.double_double
+ libc.src.__support.FPUtil.dyadic_float
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.nearest_integer
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.macros.optimization
+)
+
add_header_library(
exp_float_constants
HDRS
diff --git a/libc/src/__support/math/acos.h b/libc/src/__support/math/acos.h
new file mode 100644
index 0000000000000..a7287f11aa302
--- /dev/null
+++ b/libc/src/__support/math/acos.h
@@ -0,0 +1,285 @@
+//===-- Implementation header for acos --------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_H
+
+#include "asin_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+using DoubleDouble = fputil::DoubleDouble;
+using Float128 = fputil::DyadicFloat<128>;
+
+static constexpr double acos(double x) {
+ using FPBits = fputil::FPBits<double>;
+
+ FPBits xbits(x);
+ int x_exp = xbits.get_biased_exponent();
+
+ // |x| < 0.5.
+ if (x_exp < FPBits::EXP_BIAS - 1) {
+ // |x| < 2^-55.
+ if (LIBC_UNLIKELY(x_exp < FPBits::EXP_BIAS - 55)) {
+ // When |x| < 2^-55, acos(x) = pi/2
+#if defined(LIBC_MATH_HAS_SKIP_ACCURATE_PASS)
+ return PI_OVER_TWO.hi;
+#else
+ // Force the evaluation and prevent constant propagation so that it
+ // is rounded correctly for FE_UPWARD rounding mode.
+ return (xbits.abs().get_val() + 0x1.0p-160) + PI_OVER_TWO.hi;
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ }
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ // acos(x) = pi/2 - asin(x)
+ // = pi/2 - x * P(x^2)
+ double p = asin_eval(x * x);
+ return PI_OVER_TWO.hi + fputil::multiply_add(-x, p, PI_OVER_TWO.lo);
+#else
+ unsigned idx = 0;
+ DoubleDouble x_sq = fputil::exact_mult(x, x);
+ double err = xbits.abs().get_val() * 0x1.0p-51;
+ // Polynomial approximation:
+ // p ~ asin(x)/x
+ DoubleDouble p = asin_eval(x_sq, idx, err);
+ // asin(x) ~ x * p
+ DoubleDouble r0 = fputil::exact_mult(x, p.hi);
+ // acos(x) = pi/2 - asin(x)
+ // ~ pi/2 - x * p
+ // = pi/2 - x * (p.hi + p.lo)
+ double r_hi = fputil::multiply_add(-x, p.hi, PI_OVER_TWO.hi);
+ // Use Dekker's 2SUM algorithm to compute the lower part.
+ double r_lo = ((PI_OVER_TWO.hi - r_hi) - r0.hi) - r0.lo;
+ r_lo = fputil::multiply_add(-x, p.lo, r_lo + PI_OVER_TWO.lo);
+
+ // Ziv's accuracy test.
+
+ double r_upper = r_hi + (r_lo + err);
+ double r_lower = r_hi + (r_lo - err);
+
+ if (LIBC_LIKELY(r_upper == r_lower))
+ return r_upper;
+
+ // Ziv's accuracy test failed, perform 128-bit calculation.
+
+ // Recalculate mod 1/64.
+ idx = static_cast<unsigned>(fputil::nearest_integer(x_sq.hi * 0x1.0p6));
+
+ // Get x^2 - idx/64 exactly. When FMA is available, double-double
+ // multiplication will be correct for all rounding modes. Otherwise we use
+ // Float128 directly.
+ Float128 x_f128(x);
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ // u = x^2 - idx/64
+ Float128 u_hi(
+ fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, x_sq.hi));
+ Float128 u = fputil::quick_add(u_hi, Float128(x_sq.lo));
+#else
+ Float128 x_sq_f128 = fputil::quick_mul(x_f128, x_f128);
+ Float128 u = fputil::quick_add(
+ x_sq_f128, Float128(static_cast<double>(idx) * (-0x1.0p-6)));
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+
+ Float128 p_f128 = asin_eval(u, idx);
+ // Flip the sign of x_f128 to perform subtraction.
+ x_f128.sign = x_f128.sign.negate();
+ Float128 r =
+ fputil::quick_add(PI_OVER_TWO_F128, fputil::quick_mul(x_f128, p_f128));
+
+ return static_cast<double>(r);
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ }
+ // |x| >= 0.5
+
+ double x_abs = xbits.abs().get_val();
+
+ // Maintaining the sign:
+ constexpr double SIGN[2] = {1.0, -1.0};
+ double x_sign = SIGN[xbits.is_neg()];
+ // |x| >= 1
+ if (LIBC_UNLIKELY(x_exp >= FPBits::EXP_BIAS)) {
+ // x = +-1, asin(x) = +- pi/2
+ if (x_abs == 1.0) {
+ // x = 1, acos(x) = 0,
+ // x = -1, acos(x) = pi
+ return x == 1.0 ? 0.0 : fputil::multiply_add(-x_sign, PI.hi, PI.lo);
+ }
+ // |x| > 1, return NaN.
+ if (xbits.is_quiet_nan())
+ return x;
+
+ // Set domain error for non-NaN input.
+ if (!xbits.is_nan())
+ fputil::set_errno_if_required(EDOM);
+
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ // When |x| >= 0.5, we perform range reduction as follow:
+ //
+ // When 0.5 <= x < 1, let:
+ // y = acos(x)
+ // We will use the double angle formula:
+ // cos(2y) = 1 - 2 sin^2(y)
+ // and the complement angle identity:
+ // x = cos(y) = 1 - 2 sin^2 (y/2)
+ // So:
+ // sin(y/2) = sqrt( (1 - x)/2 )
+ // And hence:
+ // y/2 = asin( sqrt( (1 - x)/2 ) )
+ // Equivalently:
+ // acos(x) = y = 2 * asin( sqrt( (1 - x)/2 ) )
+ // Let u = (1 - x)/2, then:
+ // acos(x) = 2 * asin( sqrt(u) )
+ // Moreover, since 0.5 <= x < 1:
+ // 0 < u <= 1/4, and 0 < sqrt(u) <= 0.5,
+ // And hence we can reuse the same polynomial approximation of asin(x) when
+ // |x| <= 0.5:
+ // acos(x) ~ 2 * sqrt(u) * P(u).
+ //
+ // When -1 < x <= -0.5, we reduce to the previous case using the formula:
+ // acos(x) = pi - acos(-x)
+ // = pi - 2 * asin ( sqrt( (1 + x)/2 ) )
+ // ~ pi - 2 * sqrt(u) * P(u),
+ // where u = (1 - |x|)/2.
+
+ // u = (1 - |x|)/2
+ double u = fputil::multiply_add(x_abs, -0.5, 0.5);
+ // v_hi + v_lo ~ sqrt(u).
+ // Let:
+ // h = u - v_hi^2 = (sqrt(u) - v_hi) * (sqrt(u) + v_hi)
+ // Then:
+ // sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
+ // ~ v_hi + h / (2 * v_hi)
+ // So we can use:
+ // v_lo = h / (2 * v_hi).
+ double v_hi = fputil::sqrt<double>(u);
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ constexpr DoubleDouble CONST_TERM[2] = {{0.0, 0.0}, PI};
+ DoubleDouble const_term = CONST_TERM[xbits.is_neg()];
+
+ double p = asin_eval(u);
+ double scale = x_sign * 2.0 * v_hi;
+ double r = const_term.hi + fputil::multiply_add(scale, p, const_term.lo);
+ return r;
+#else
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double h = fputil::multiply_add(v_hi, -v_hi, u);
+#else
+ DoubleDouble v_hi_sq = fputil::exact_mult(v_hi, v_hi);
+ double h = (u - v_hi_sq.hi) - v_hi_sq.lo;
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+
+ // Scale v_lo and v_hi by 2 from the formula:
+ // vh = v_hi * 2
+ // vl = 2*v_lo = h / v_hi.
+ double vh = v_hi * 2.0;
+ double vl = h / v_hi;
+
+ // Polynomial approximation:
+ // p ~ asin(sqrt(u))/sqrt(u)
+ unsigned idx = 0;
+ double err = vh * 0x1.0p-51;
+
+ DoubleDouble p = asin_eval(DoubleDouble{0.0, u}, idx, err);
+
+ // Perform computations in double-double arithmetic:
+ // asin(x) = pi/2 - (v_hi + v_lo) * (ASIN_COEFFS[idx][0] + p)
+ DoubleDouble r0 = fputil::quick_mult(DoubleDouble{vl, vh}, p);
+
+ double r_hi = 0, r_lo = 0;
+ if (xbits.is_pos()) {
+ r_hi = r0.hi;
+ r_lo = r0.lo;
+ } else {
+ DoubleDouble r = fputil::exact_add(PI.hi, -r0.hi);
+ r_hi = r.hi;
+ r_lo = (PI.lo - r0.lo) + r.lo;
+ }
+
+ // Ziv's accuracy test.
+
+ double r_upper = r_hi + (r_lo + err);
+ double r_lower = r_hi + (r_lo - err);
+
+ if (LIBC_LIKELY(r_upper == r_lower))
+ return r_upper;
+
+ // Ziv's accuracy test failed, we redo the computations in Float128.
+ // Recalculate mod 1/64.
+ idx = static_cast<unsigned>(fputil::nearest_integer(u * 0x1.0p6));
+
+ // After the first step of Newton-Raphson approximating v = sqrt(u), we have
+ // that:
+ // sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
+ // v_lo = h / (2 * v_hi)
+ // With error:
+ // sqrt(u) - (v_hi + v_lo) = h * ( 1/(sqrt(u) + v_hi) - 1/(2*v_hi) )
+ // = -h^2 / (2*v * (sqrt(u) + v)^2).
+ // Since:
+ // (sqrt(u) + v_hi)^2 ~ (2sqrt(u))^2 = 4u,
+ // we can add another correction term to (v_hi + v_lo) that is:
+ // v_ll = -h^2 / (2*v_hi * 4u)
+ // = -v_lo * (h / 4u)
+ // = -vl * (h / 8u),
+ // making the errors:
+ // sqrt(u) - (v_hi + v_lo + v_ll) = O(h^3)
+ // well beyond 128-bit precision needed.
+
+ // Get the rounding error of vl = 2 * v_lo ~ h / vh
+ // Get full product of vh * vl
+#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ double vl_lo = fputil::multiply_add(-v_hi, vl, h) / v_hi;
+#else
+ DoubleDouble vh_vl = fputil::exact_mult(v_hi, vl);
+ double vl_lo = ((h - vh_vl.hi) - vh_vl.lo) / v_hi;
+#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
+ // vll = 2*v_ll = -vl * (h / (4u)).
+ double t = h * (-0.25) / u;
+ double vll = fputil::multiply_add(vl, t, vl_lo);
+ // m_v = -(v_hi + v_lo + v_ll).
+ Float128 m_v = fputil::quick_add(
+ Float128(vh), fputil::quick_add(Float128(vl), Float128(vll)));
+ m_v.sign = xbits.sign();
+
+ // Perform computations in Float128:
+ // acos(x) = (v_hi + v_lo + vll) * P(u) , when 0.5 <= x < 1,
+ // = pi - (v_hi + v_lo + vll) * P(u) , when -1 < x <= -0.5.
+ Float128 y_f128(fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, u));
+
+ Float128 p_f128 = asin_eval(y_f128, idx);
+ Float128 r_f128 = fputil::quick_mul(m_v, p_f128);
+
+ if (xbits.is_neg())
+ r_f128 = fputil::quick_add(PI_F128, r_f128);
+
+ return static_cast<double>(r_f128);
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_H
diff --git a/libc/src/math/generic/asin_utils.h b/libc/src/__support/math/asin_utils.h
similarity index 96%
rename from libc/src/math/generic/asin_utils.h
rename to libc/src/__support/math/asin_utils.h
index 44913d573de2c..4e0179e43298b 100644
--- a/libc/src/math/generic/asin_utils.h
+++ b/libc/src/__support/math/asin_utils.h
@@ -6,8 +6,8 @@
//
//===----------------------------------------------------------------------===//
-#ifndef LLVM_LIBC_SRC_MATH_GENERIC_ASIN_UTILS_H
-#define LLVM_LIBC_SRC_MATH_GENERIC_ASIN_UTILS_H
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ASIN_UTILS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ASIN_UTILS_H
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/double_double.h"
@@ -16,7 +16,6 @@
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/integer_literals.h"
#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
@@ -25,10 +24,10 @@ namespace {
using DoubleDouble = fputil::DoubleDouble;
using Float128 = fputil::DyadicFloat<128>;
-constexpr DoubleDouble PI = {0x1.1a62633145c07p-53, 0x1.921fb54442d18p1};
+static constexpr DoubleDouble PI = {0x1.1a62633145c07p-53, 0x1.921fb54442d18p1};
-constexpr DoubleDouble PI_OVER_TWO = {0x1.1a62633145c07p-54,
- 0x1.921fb54442d18p0};
+static constexpr DoubleDouble PI_OVER_TWO = {0x1.1a62633145c07p-54,
+ 0x1.921fb54442d18p0};
#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
@@ -39,14 +38,14 @@ constexpr DoubleDouble PI_OVER_TWO = {0x1.1a62633145c07p-54,
// > dirtyinfnorm(asin(x)/x - P, [0, 0.5]);
// 0x1.1a71ef0a0f26a9fb7ed7e41dee788b13d1770db3dp-52
-constexpr double ASIN_COEFFS[12] = {
+static constexpr double ASIN_COEFFS[12] = {
0x1.0000000000000p0, 0x1.5555555556dcfp-3, 0x1.3333333082e11p-4,
0x1.6db6dd14099edp-5, 0x1.f1c69b35bf81fp-6, 0x1.6e97194225a67p-6,
0x1.1babddb82ce12p-6, 0x1.d55bd078600d6p-7, 0x1.33328959e63d6p-7,
0x1.2b5993bda1d9bp-6, -0x1.806aff270bf25p-7, 0x1.02614e5ed3936p-5,
};
-LIBC_INLINE double asin_eval(double u) {
+LIBC_INLINE static constexpr double asin_eval(double u) {
double u2 = u * u;
double c0 = fputil::multiply_add(u, ASIN_COEFFS[1], ASIN_COEFFS[0]);
double c1 = fputil::multiply_add(u, ASIN_COEFFS[3], ASIN_COEFFS[2]);
@@ -124,7 +123,7 @@ LIBC_INLINE double asin_eval(double u) {
// > dirtyinfnorm(asin(x)/x - P, [-1/64, 1/64]);
// 0x1.999075402cafp-83
-constexpr double ASIN_COEFFS[9][12] = {
+static constexpr double ASIN_COEFFS[9][12] = {
{1.0, 0.0, 0x1.5555555555555p-3, 0x1.5555555555555p-57,
0x1.3333333333333p-4, 0x1.6db6db6db6db7p-5, 0x1.f1c71c71c71c7p-6,
0x1.6e8ba2e8ba2e9p-6, 0x1.1c4ec4ec4ec4fp-6, 0x1.c99999999999ap-7,
@@ -164,8 +163,8 @@ constexpr double ASIN_COEFFS[9][12] = {
};
// We calculate the lower part of the approximation P(u).
-LIBC_INLINE DoubleDouble asin_eval(const DoubleDouble &u, unsigned &idx,
- double &err) {
+LIBC_INLINE static constexpr DoubleDouble
+asin_eval(const DoubleDouble &u, unsigned &idx, double &err) {
using fputil::multiply_add;
// k = round(u * 32).
double k = fputil::nearest_integer(u.hi * 0x1.0p5);
@@ -239,7 +238,7 @@ LIBC_INLINE DoubleDouble asin_eval(const DoubleDouble &u, unsigned &idx,
// + (676039 x^24)/104857600 + (1300075 x^26)/226492416 +
// + (5014575 x^28)/973078528 + (9694845 x^30)/2080374784.
-constexpr Float128 ASIN_COEFFS_F128[17][16] = {
+static constexpr Float128 ASIN_COEFFS_F128[17][16] = {
{
{Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128},
{Sign::POS, -130, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128},
@@ -548,13 +547,14 @@ constexpr Float128 ASIN_COEFFS_F128[17][16] = {
},
};
-constexpr Float128 PI_OVER_TWO_F128 = {
+static constexpr Float128 PI_OVER_TWO_F128 = {
Sign::POS, -127, 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
-constexpr Float128 PI_F128 = {Sign::POS, -126,
- 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
+static constexpr Float128 PI_F128 = {
+ Sign::POS, -126, 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
-LIBC_INLINE Float128 asin_eval(const Float128 &u, unsigned idx) {
+LIBC_INLINE static constexpr Float128 asin_eval(const Float128 &u,
+ unsigned idx) {
return fputil::polyeval(u, ASIN_COEFFS_F128[idx][0], ASIN_COEFFS_F128[idx][1],
ASIN_COEFFS_F128[idx][2], ASIN_COEFFS_F128[idx][3],
ASIN_COEFFS_F128[idx][4], ASIN_COEFFS_F128[idx][5],
@@ -571,4 +571,4 @@ LIBC_INLINE Float128 asin_eval(const Float128 &u, unsigned idx) {
} // namespace LIBC_NAMESPACE_DECL
-#endif // LLVM_LIBC_SRC_MATH_GENERIC_ASIN_UTILS_H
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ASIN_UTILS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 2c158a18bc145..ed6b317500062 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4018,20 +4018,6 @@ add_entrypoint_object(
libc.src.__support.macros.properties.types
)
-add_header_library(
- asin_utils
- HDRS
- atan_utils.h
- DEPENDS
- libc.src.__support.integer_literals
- libc.src.__support.FPUtil.double_double
- libc.src.__support.FPUtil.dyadic_float
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.nearest_integer
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.macros.optimization
-)
-
add_entrypoint_object(
asin
SRCS
@@ -4039,7 +4025,7 @@ add_entrypoint_object(
HDRS
../asin.h
DEPENDS
- .asin_utils
+ libc.src.__support.math.asin_utils
libc.src.__support.FPUtil.double_double
libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.fenv_impl
@@ -4094,17 +4080,7 @@ add_entrypoint_object(
HDRS
../acos.h
DEPENDS
- .asin_utils
- libc.src.__support.FPUtil.double_double
- libc.src.__support.FPUtil.dyadic_float
- libc.src.__support.FPUtil.fenv_impl
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.FPUtil.sqrt
- libc.src.__support.macros.optimization
- libc.src.__support.macros.properties.types
- libc.src.__support.macros.properties.cpu_features
+ libc.src.__support.math.acos
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/acos.cpp b/libc/src/math/generic/acos.cpp
index c14721faef3ce..3a5964290cdd3 100644
--- a/libc/src/math/generic/acos.cpp
+++ b/libc/src/math/generic/acos.cpp
@@ -7,272 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/acos.h"
-#include "asin_utils.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/double_double.h"
-#include "src/__support/FPUtil/dyadic_float.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/sqrt.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
+#include "src/__support/math/acos.h"
namespace LIBC_NAMESPACE_DECL {
-using DoubleDouble = fputil::DoubleDouble;
-using Float128 = fputil::DyadicFloat<128>;
-
-LLVM_LIBC_FUNCTION(double, acos, (double x)) {
- using FPBits = fputil::FPBits<double>;
-
- FPBits xbits(x);
- int x_exp = xbits.get_biased_exponent();
-
- // |x| < 0.5.
- if (x_exp < FPBits::EXP_BIAS - 1) {
- // |x| < 2^-55.
- if (LIBC_UNLIKELY(x_exp < FPBits::EXP_BIAS - 55)) {
- // When |x| < 2^-55, acos(x) = pi/2
-#if defined(LIBC_MATH_HAS_SKIP_ACCURATE_PASS)
- return PI_OVER_TWO.hi;
-#else
- // Force the evaluation and prevent constant propagation so that it
- // is rounded correctly for FE_UPWARD rounding mode.
- return (xbits.abs().get_val() + 0x1.0p-160) + PI_OVER_TWO.hi;
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- }
-
-#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- // acos(x) = pi/2 - asin(x)
- // = pi/2 - x * P(x^2)
- double p = asin_eval(x * x);
- return PI_OVER_TWO.hi + fputil::multiply_add(-x, p, PI_OVER_TWO.lo);
-#else
- unsigned idx;
- DoubleDouble x_sq = fputil::exact_mult(x, x);
- double err = xbits.abs().get_val() * 0x1.0p-51;
- // Polynomial approximation:
- // p ~ asin(x)/x
- DoubleDouble p = asin_eval(x_sq, idx, err);
- // asin(x) ~ x * p
- DoubleDouble r0 = fputil::exact_mult(x, p.hi);
- // acos(x) = pi/2 - asin(x)
- // ~ pi/2 - x * p
- // = pi/2 - x * (p.hi + p.lo)
- double r_hi = fputil::multiply_add(-x, p.hi, PI_OVER_TWO.hi);
- // Use Dekker's 2SUM algorithm to compute the lower part.
- double r_lo = ((PI_OVER_TWO.hi - r_hi) - r0.hi) - r0.lo;
- r_lo = fputil::multiply_add(-x, p.lo, r_lo + PI_OVER_TWO.lo);
-
- // Ziv's accuracy test.
-
- double r_upper = r_hi + (r_lo + err);
- double r_lower = r_hi + (r_lo - err);
-
- if (LIBC_LIKELY(r_upper == r_lower))
- return r_upper;
-
- // Ziv's accuracy test failed, perform 128-bit calculation.
-
- // Recalculate mod 1/64.
- idx = static_cast<unsigned>(fputil::nearest_integer(x_sq.hi * 0x1.0p6));
-
- // Get x^2 - idx/64 exactly. When FMA is available, double-double
- // multiplication will be correct for all rounding modes. Otherwise we use
- // Float128 directly.
- Float128 x_f128(x);
-
-#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
- // u = x^2 - idx/64
- Float128 u_hi(
- fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, x_sq.hi));
- Float128 u = fputil::quick_add(u_hi, Float128(x_sq.lo));
-#else
- Float128 x_sq_f128 = fputil::quick_mul(x_f128, x_f128);
- Float128 u = fputil::quick_add(
- x_sq_f128, Float128(static_cast<double>(idx) * (-0x1.0p-6)));
-#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
-
- Float128 p_f128 = asin_eval(u, idx);
- // Flip the sign of x_f128 to perform subtraction.
- x_f128.sign = x_f128.sign.negate();
- Float128 r =
- fputil::quick_add(PI_OVER_TWO_F128, fputil::quick_mul(x_f128, p_f128));
-
- return static_cast<double>(r);
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- }
- // |x| >= 0.5
-
- double x_abs = xbits.abs().get_val();
-
- // Maintaining the sign:
- constexpr double SIGN[2] = {1.0, -1.0};
- double x_sign = SIGN[xbits.is_neg()];
- // |x| >= 1
- if (LIBC_UNLIKELY(x_exp >= FPBits::EXP_BIAS)) {
- // x = +-1, asin(x) = +- pi/2
- if (x_abs == 1.0) {
- // x = 1, acos(x) = 0,
- // x = -1, acos(x) = pi
- return x == 1.0 ? 0.0 : fputil::multiply_add(-x_sign, PI.hi, PI.lo);
- }
- // |x| > 1, return NaN.
- if (xbits.is_quiet_nan())
- return x;
-
- // Set domain error for non-NaN input.
- if (!xbits.is_nan())
- fputil::set_errno_if_required(EDOM);
-
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- // When |x| >= 0.5, we perform range reduction as follow:
- //
- // When 0.5 <= x < 1, let:
- // y = acos(x)
- // We will use the double angle formula:
- // cos(2y) = 1 - 2 sin^2(y)
- // and the complement angle identity:
- // x = cos(y) = 1 - 2 sin^2 (y/2)
- // So:
- // sin(y/2) = sqrt( (1 - x)/2 )
- // And hence:
- // y/2 = asin( sqrt( (1 - x)/2 ) )
- // Equivalently:
- // acos(x) = y = 2 * asin( sqrt( (1 - x)/2 ) )
- // Let u = (1 - x)/2, then:
- // acos(x) = 2 * asin( sqrt(u) )
- // Moreover, since 0.5 <= x < 1:
- // 0 < u <= 1/4, and 0 < sqrt(u) <= 0.5,
- // And hence we can reuse the same polynomial approximation of asin(x) when
- // |x| <= 0.5:
- // acos(x) ~ 2 * sqrt(u) * P(u).
- //
- // When -1 < x <= -0.5, we reduce to the previous case using the formula:
- // acos(x) = pi - acos(-x)
- // = pi - 2 * asin ( sqrt( (1 + x)/2 ) )
- // ~ pi - 2 * sqrt(u) * P(u),
- // where u = (1 - |x|)/2.
-
- // u = (1 - |x|)/2
- double u = fputil::multiply_add(x_abs, -0.5, 0.5);
- // v_hi + v_lo ~ sqrt(u).
- // Let:
- // h = u - v_hi^2 = (sqrt(u) - v_hi) * (sqrt(u) + v_hi)
- // Then:
- // sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
- // ~ v_hi + h / (2 * v_hi)
- // So we can use:
- // v_lo = h / (2 * v_hi).
- double v_hi = fputil::sqrt<double>(u);
-
-#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- constexpr DoubleDouble CONST_TERM[2] = {{0.0, 0.0}, PI};
- DoubleDouble const_term = CONST_TERM[xbits.is_neg()];
-
- double p = asin_eval(u);
- double scale = x_sign * 2.0 * v_hi;
- double r = const_term.hi + fputil::multiply_add(scale, p, const_term.lo);
- return r;
-#else
-
-#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
- double h = fputil::multiply_add(v_hi, -v_hi, u);
-#else
- DoubleDouble v_hi_sq = fputil::exact_mult(v_hi, v_hi);
- double h = (u - v_hi_sq.hi) - v_hi_sq.lo;
-#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
-
- // Scale v_lo and v_hi by 2 from the formula:
- // vh = v_hi * 2
- // vl = 2*v_lo = h / v_hi.
- double vh = v_hi * 2.0;
- double vl = h / v_hi;
-
- // Polynomial approximation:
- // p ~ asin(sqrt(u))/sqrt(u)
- unsigned idx;
- double err = vh * 0x1.0p-51;
-
- DoubleDouble p = asin_eval(DoubleDouble{0.0, u}, idx, err);
-
- // Perform computations in double-double arithmetic:
- // asin(x) = pi/2 - (v_hi + v_lo) * (ASIN_COEFFS[idx][0] + p)
- DoubleDouble r0 = fputil::quick_mult(DoubleDouble{vl, vh}, p);
-
- double r_hi, r_lo;
- if (xbits.is_pos()) {
- r_hi = r0.hi;
- r_lo = r0.lo;
- } else {
- DoubleDouble r = fputil::exact_add(PI.hi, -r0.hi);
- r_hi = r.hi;
- r_lo = (PI.lo - r0.lo) + r.lo;
- }
-
- // Ziv's accuracy test.
-
- double r_upper = r_hi + (r_lo + err);
- double r_lower = r_hi + (r_lo - err);
-
- if (LIBC_LIKELY(r_upper == r_lower))
- return r_upper;
-
- // Ziv's accuracy test failed, we redo the computations in Float128.
- // Recalculate mod 1/64.
- idx = static_cast<unsigned>(fputil::nearest_integer(u * 0x1.0p6));
-
- // After the first step of Newton-Raphson approximating v = sqrt(u), we have
- // that:
- // sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
- // v_lo = h / (2 * v_hi)
- // With error:
- // sqrt(u) - (v_hi + v_lo) = h * ( 1/(sqrt(u) + v_hi) - 1/(2*v_hi) )
- // = -h^2 / (2*v * (sqrt(u) + v)^2).
- // Since:
- // (sqrt(u) + v_hi)^2 ~ (2sqrt(u))^2 = 4u,
- // we can add another correction term to (v_hi + v_lo) that is:
- // v_ll = -h^2 / (2*v_hi * 4u)
- // = -v_lo * (h / 4u)
- // = -vl * (h / 8u),
- // making the errors:
- // sqrt(u) - (v_hi + v_lo + v_ll) = O(h^3)
- // well beyond 128-bit precision needed.
-
- // Get the rounding error of vl = 2 * v_lo ~ h / vh
- // Get full product of vh * vl
-#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
- double vl_lo = fputil::multiply_add(-v_hi, vl, h) / v_hi;
-#else
- DoubleDouble vh_vl = fputil::exact_mult(v_hi, vl);
- double vl_lo = ((h - vh_vl.hi) - vh_vl.lo) / v_hi;
-#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
- // vll = 2*v_ll = -vl * (h / (4u)).
- double t = h * (-0.25) / u;
- double vll = fputil::multiply_add(vl, t, vl_lo);
- // m_v = -(v_hi + v_lo + v_ll).
- Float128 m_v = fputil::quick_add(
- Float128(vh), fputil::quick_add(Float128(vl), Float128(vll)));
- m_v.sign = xbits.sign();
-
- // Perform computations in Float128:
- // acos(x) = (v_hi + v_lo + vll) * P(u) , when 0.5 <= x < 1,
- // = pi - (v_hi + v_lo + vll) * P(u) , when -1 < x <= -0.5.
- Float128 y_f128(fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, u));
-
- Float128 p_f128 = asin_eval(y_f128, idx);
- Float128 r_f128 = fputil::quick_mul(m_v, p_f128);
-
- if (xbits.is_neg())
- r_f128 = fputil::quick_add(PI_F128, r_f128);
-
- return static_cast<double>(r_f128);
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-}
+LLVM_LIBC_FUNCTION(double, acos, (double x)) { return math::acos(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/asin.cpp b/libc/src/math/generic/asin.cpp
index ad77683d1f880..c033597334345 100644
--- a/libc/src/math/generic/asin.cpp
+++ b/libc/src/math/generic/asin.cpp
@@ -7,7 +7,6 @@
//===----------------------------------------------------------------------===//
#include "src/math/asin.h"
-#include "asin_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
@@ -18,6 +17,7 @@
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
+#include "src/__support/math/asin_utils.h"
namespace LIBC_NAMESPACE_DECL {
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 7a497f16cccc1..e1a6076fed2c6 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2078,6 +2078,38 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_acos",
+ hdrs = ["src/__support/math/acos.h"],
+ deps = [
+ ":__support_math_asin_utils",
+ ":__support_fputil_double_double",
+ ":__support_fputil_dyadic_float",
+ ":__support_fputil_fenv_impl",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_sqrt",
+ ":__support_macros_optimization",
+ ":__support_macros_properties_types",
+ ":__support_macros_properties_cpu_features",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_asin_utils",
+ hdrs = ["src/__support/math/asin_utils.h"],
+ deps = [
+ ":__support_integer_literals",
+ ":__support_fputil_double_double",
+ ":__support_fputil_dyadic_float",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_polyeval",
+ ":__support_macros_optimization",
+ ],
+)
+
libc_support_library(
name = "__support_math_exp_float_constants",
hdrs = ["src/__support/math/exp_float_constants.h"],
@@ -2555,6 +2587,13 @@ libc_function(
################################ math targets ##################################
+libc_math_function(
+ name = "acos",
+ additional_deps = [
+ ":__support_math_acos",
+ ],
+)
+
libc_math_function(
name = "acosf",
additional_deps = [
>From cfcd849575c5ed02821263f1164f11e64f791481 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 09:07:30 +0300
Subject: [PATCH 10/15] libc][math] Refactor acosf implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/acosf.h | 23 +++
libc/src/__support/math/CMakeLists.txt | 24 +++
libc/src/__support/math/acosf.h | 140 ++++++++++++++++++
.../math/inv_trigf_utils.h} | 100 ++++++++++++-
libc/src/math/generic/CMakeLists.txt | 26 +---
libc/src/math/generic/acosf.cpp | 121 +--------------
libc/src/math/generic/asinf.cpp | 2 +-
libc/src/math/generic/atan2f.cpp | 2 +-
libc/src/math/generic/atanf.cpp | 2 +-
libc/src/math/generic/inv_trigf_utils.h | 110 --------------
.../llvm-project-overlay/libc/BUILD.bazel | 58 ++++----
12 files changed, 324 insertions(+), 285 deletions(-)
create mode 100644 libc/shared/math/acosf.h
create mode 100644 libc/src/__support/math/acosf.h
rename libc/src/{math/generic/inv_trigf_utils.cpp => __support/math/inv_trigf_utils.h} (57%)
delete mode 100644 libc/src/math/generic/inv_trigf_utils.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 8dcfaf0352339..617e46602de8c 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -12,6 +12,7 @@
#include "libc_common.h"
#include "math/acos.h"
+#include "math/acosf.h"
#include "math/exp.h"
#include "math/exp10.h"
#include "math/exp10f.h"
diff --git a/libc/shared/math/acosf.h b/libc/shared/math/acosf.h
new file mode 100644
index 0000000000000..7cdd64e7b379a
--- /dev/null
+++ b/libc/shared/math/acosf.h
@@ -0,0 +1,23 @@
+//===-- Shared acosf function -----------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_ACOSF_H
+#define LLVM_LIBC_SHARED_MATH_ACOSF_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/acosf.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acosf;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOSF_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 4a29c2975d523..fbe7e2c3125ce 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -17,6 +17,20 @@ add_header_library(
libc.src.__support.macros.properties.cpu_features
)
+add_header_library(
+ acosf
+ HDRS
+ acosf.h
+ DEPENDS
+ .inv_trigf_utils
+ libc.src.__support.FPUtil.except_value_utils
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.macros.optimization
+)
+
add_header_library(
asin_utils
HDRS
@@ -98,6 +112,16 @@ add_header_library(
libc.src.__support.FPUtil.manipulation_functions
)
+add_header_library(
+ inv_trigf_utils
+ HDRS
+ inv_trigf_utils.h
+ DEPENDS
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.common
+)
+
add_header_library(
frexpf16
HDRS
diff --git a/libc/src/__support/math/acosf.h b/libc/src/__support/math/acosf.h
new file mode 100644
index 0000000000000..05c82330060a8
--- /dev/null
+++ b/libc/src/__support/math/acosf.h
@@ -0,0 +1,140 @@
+//===-- Implementation header for acosf -------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF_H
+
+#include "inv_trigf_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr size_t N_EXCEPTS = 4;
+
+// Exceptional values when |x| <= 0.5
+static constexpr fputil::ExceptValues<float, N_EXCEPTS> ACOSF_EXCEPTS = {{
+ // (inputs, RZ output, RU offset, RD offset, RN offset)
+ // x = 0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
+ {0x328885a3, 0x3fc90fda, 1, 0, 1},
+ // x = -0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
+ {0xb28885a3, 0x3fc90fda, 1, 0, 1},
+ // x = 0x1.04c444p-12, acosf(x) = 0x1.920f68p0 (RZ)
+ {0x39826222, 0x3fc907b4, 1, 0, 1},
+ // x = -0x1.04c444p-12, acosf(x) = 0x1.923p0 (RZ)
+ {0xb9826222, 0x3fc91800, 1, 0, 1},
+}};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+static constexpr float acosf(float x) {
+ using FPBits = typename fputil::FPBits<float>;
+
+ FPBits xbits(x);
+ uint32_t x_uint = xbits.uintval();
+ uint32_t x_abs = xbits.uintval() & 0x7fff'ffffU;
+ uint32_t x_sign = x_uint >> 31;
+
+ // |x| <= 0.5
+ if (LIBC_UNLIKELY(x_abs <= 0x3f00'0000U)) {
+ // |x| < 0x1p-10
+ if (LIBC_UNLIKELY(x_abs < 0x3a80'0000U)) {
+ // When |x| < 2^-10, we use the following approximation:
+ // acos(x) = pi/2 - asin(x)
+ // ~ pi/2 - x - x^3 / 6
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ // Check for exceptional values
+ if (auto r = ACOSF_EXCEPTS.lookup(x_uint); LIBC_UNLIKELY(r.has_value()))
+ return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+ double xd = static_cast<double>(x);
+ return static_cast<float>(fputil::multiply_add(
+ -0x1.5555555555555p-3 * xd, xd * xd, M_MATH_PI_2 - xd));
+ }
+
+ // For |x| <= 0.5, we approximate acosf(x) by:
+ // acos(x) = pi/2 - asin(x) = pi/2 - x * P(x^2)
+ // Where P(X^2) = Q(X) is a degree-20 minimax even polynomial approximating
+ // asin(x)/x on [0, 0.5] generated by Sollya with:
+ // > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
+ // [|1, D...|], [0, 0.5]);
+ double xd = static_cast<double>(x);
+ double xsq = xd * xd;
+ double x3 = xd * xsq;
+ double r = asin_eval(xsq);
+ return static_cast<float>(fputil::multiply_add(-x3, r, M_MATH_PI_2 - xd));
+ }
+
+ // |x| >= 1, return 0, 2pi, or NaNs.
+ if (LIBC_UNLIKELY(x_abs >= 0x3f80'0000U)) {
+ if (x_abs == 0x3f80'0000U)
+ return x_sign ? /* x == -1.0f */ fputil::round_result_slightly_down(
+ 0x1.921fb6p+1f)
+ : /* x == 1.0f */ 0.0f;
+
+ if (xbits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ // |x| <= +/-inf
+ if (x_abs <= 0x7f80'0000U) {
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ }
+
+ return x + FPBits::quiet_nan().get_val();
+ }
+
+ // When 0.5 < |x| < 1, we perform range reduction as follow:
+ //
+ // Assume further that 0.5 < x <= 1, and let:
+ // y = acos(x)
+ // We use the double angle formula:
+ // x = cos(y) = 1 - 2 sin^2(y/2)
+ // So:
+ // sin(y/2) = sqrt( (1 - x)/2 )
+ // And hence:
+ // y = 2 * asin( sqrt( (1 - x)/2 ) )
+ // Let u = (1 - x)/2, then
+ // acos(x) = 2 * asin( sqrt(u) )
+ // Moreover, since 0.5 < x <= 1,
+ // 0 <= u < 1/4, and 0 <= sqrt(u) < 0.5,
+ // And hence we can reuse the same polynomial approximation of asin(x) when
+ // |x| <= 0.5:
+ // acos(x) ~ 2 * sqrt(u) * P(u).
+ //
+ // When -1 < x <= -0.5, we use the identity:
+ // acos(x) = pi - acos(-x)
+ // which is reduced to the postive case.
+
+ xbits.set_sign(Sign::POS);
+ double xd = static_cast<double>(xbits.get_val());
+ double u = fputil::multiply_add(-0.5, xd, 0.5);
+ double cv = 2 * fputil::sqrt<double>(u);
+
+ double r3 = asin_eval(u);
+ double r = fputil::multiply_add(cv * u, r3, cv);
+ return static_cast<float>(x_sign ? M_MATH_PI - r : r);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_H
diff --git a/libc/src/math/generic/inv_trigf_utils.cpp b/libc/src/__support/math/inv_trigf_utils.h
similarity index 57%
rename from libc/src/math/generic/inv_trigf_utils.cpp
rename to libc/src/__support/math/inv_trigf_utils.h
index f23028bb86b5c..8c5f7c44ddadf 100644
--- a/libc/src/math/generic/inv_trigf_utils.cpp
+++ b/libc/src/__support/math/inv_trigf_utils.h
@@ -1,4 +1,4 @@
-//===-- Single-precision general exp/log functions ------------------------===//
+//===-- Single-precision general inverse trigonometric functions ----------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
@@ -6,11 +6,20 @@
//
//===----------------------------------------------------------------------===//
-#include "inv_trigf_utils.h"
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_INV_TRIGF_UTILS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_INV_TRIGF_UTILS_H
+
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/common.h"
#include "src/__support/macros/config.h"
namespace LIBC_NAMESPACE_DECL {
+// PI and PI / 2
+static constexpr double M_MATH_PI = 0x1.921fb54442d18p+1;
+static constexpr double M_MATH_PI_2 = 0x1.921fb54442d18p+0;
+
// Polynomial approximation for 0 <= x <= 1:
// atan(x) ~ atan((i/16) + (x - (i/16)) * Q(x - i/16)
// = P(x - i/16)
@@ -29,7 +38,7 @@ namespace LIBC_NAMESPACE_DECL {
// Notice that degree-7 is good enough for atanf, but degree-8 helps reduce the
// error bounds for atan2f's fast pass 16 times, and it does not affect the
// performance of atanf much.
-double ATAN_COEFFS[17][9] = {
+static constexpr double ATAN_COEFFS[17][9] = {
{0.0, 1.0, 0x1.3f8d76d26d61bp-47, -0x1.5555555574cd8p-2,
0x1.0dde5d06878eap-29, 0x1.99997738acc77p-3, 0x1.2c43eac9797cap-16,
-0x1.25fb020007dbdp-3, 0x1.c1b6c31d7b0aep-7},
@@ -83,4 +92,89 @@ double ATAN_COEFFS[17][9] = {
0x1.555e31a1e15e9p-6, -0x1.245240d65e629p-7, -0x1.fa9ba66478903p-11},
};
+// Look-up table for atan(k/16) with k = 0..16.
+static constexpr double ATAN_K_OVER_16[17] = {
+ 0.0,
+ 0x1.ff55bb72cfdeap-5,
+ 0x1.fd5ba9aac2f6ep-4,
+ 0x1.7b97b4bce5b02p-3,
+ 0x1.f5b75f92c80ddp-3,
+ 0x1.362773707ebccp-2,
+ 0x1.6f61941e4def1p-2,
+ 0x1.a64eec3cc23fdp-2,
+ 0x1.dac670561bb4fp-2,
+ 0x1.0657e94db30dp-1,
+ 0x1.1e00babdefeb4p-1,
+ 0x1.345f01cce37bbp-1,
+ 0x1.4978fa3269ee1p-1,
+ 0x1.5d58987169b18p-1,
+ 0x1.700a7c5784634p-1,
+ 0x1.819d0b7158a4dp-1,
+ 0x1.921fb54442d18p-1,
+};
+
+// For |x| <= 1/32 and 0 <= i <= 16, return Q(x) such that:
+// Q(x) ~ (atan(x + i/16) - atan(i/16)) / x.
+LIBC_INLINE static constexpr double atan_eval(double x, unsigned i) {
+ double x2 = x * x;
+
+ double c0 = fputil::multiply_add(x, ATAN_COEFFS[i][2], ATAN_COEFFS[i][1]);
+ double c1 = fputil::multiply_add(x, ATAN_COEFFS[i][4], ATAN_COEFFS[i][3]);
+ double c2 = fputil::multiply_add(x, ATAN_COEFFS[i][6], ATAN_COEFFS[i][5]);
+ double c3 = fputil::multiply_add(x, ATAN_COEFFS[i][8], ATAN_COEFFS[i][7]);
+
+ double x4 = x2 * x2;
+ double d1 = fputil::multiply_add(x2, c1, c0);
+ double d2 = fputil::multiply_add(x2, c3, c2);
+ double p = fputil::multiply_add(x4, d2, d1);
+ return p;
+}
+
+// Evaluate atan without big lookup table.
+// atan(n/d) - atan(k/16) = atan((n/d - k/16) / (1 + (n/d) * (k/16)))
+// = atan((n - d * k/16)) / (d + n * k/16))
+// So we let q = (n - d * k/16) / (d + n * k/16),
+// and approximate with Taylor polynomial:
+// atan(q) ~ q - q^3/3 + q^5/5 - q^7/7 + q^9/9
+LIBC_INLINE static constexpr double atan_eval_no_table(double num, double den,
+ double k_over_16) {
+ double num_r = fputil::multiply_add(den, -k_over_16, num);
+ double den_r = fputil::multiply_add(num, k_over_16, den);
+ double q = num_r / den_r;
+
+ constexpr double ATAN_TAYLOR[] = {
+ -0x1.5555555555555p-2,
+ 0x1.999999999999ap-3,
+ -0x1.2492492492492p-3,
+ 0x1.c71c71c71c71cp-4,
+ };
+ double q2 = q * q;
+ double q3 = q2 * q;
+ double q4 = q2 * q2;
+ double c0 = fputil::multiply_add(q2, ATAN_TAYLOR[1], ATAN_TAYLOR[0]);
+ double c1 = fputil::multiply_add(q2, ATAN_TAYLOR[3], ATAN_TAYLOR[2]);
+ double d = fputil::multiply_add(q4, c1, c0);
+ return fputil::multiply_add(q3, d, q);
+}
+
+// > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
+// [|1, D...|], [0, 0.5]);
+static constexpr double ASIN_COEFFS[10] = {
+ 0x1.5555555540fa1p-3, 0x1.333333512edc2p-4, 0x1.6db6cc1541b31p-5,
+ 0x1.f1caff324770ep-6, 0x1.6e43899f5f4f4p-6, 0x1.1f847cf652577p-6,
+ 0x1.9b60f47f87146p-7, 0x1.259e2634c494fp-6, -0x1.df946fa875ddp-8,
+ 0x1.02311ecf99c28p-5};
+
+// Evaluate P(x^2) - 1, where P(x^2) ~ asin(x)/x
+LIBC_INLINE static constexpr double asin_eval(double xsq) {
+ double x4 = xsq * xsq;
+ double r1 = fputil::polyeval(x4, ASIN_COEFFS[0], ASIN_COEFFS[2],
+ ASIN_COEFFS[4], ASIN_COEFFS[6], ASIN_COEFFS[8]);
+ double r2 = fputil::polyeval(x4, ASIN_COEFFS[1], ASIN_COEFFS[3],
+ ASIN_COEFFS[5], ASIN_COEFFS[7], ASIN_COEFFS[9]);
+ return fputil::multiply_add(xsq, r2, r1);
+}
+
} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_INV_TRIGF_UTILS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index ed6b317500062..fd980fb52c624 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -3971,18 +3971,6 @@ add_entrypoint_object(
libc.src.__support.macros.properties.types
)
-add_object_library(
- inv_trigf_utils
- HDRS
- inv_trigf_utils.h
- SRCS
- inv_trigf_utils.cpp
- DEPENDS
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.common
-)
-
add_entrypoint_object(
asinf
SRCS
@@ -3996,7 +3984,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.sqrt
libc.src.__support.macros.optimization
- .inv_trigf_utils
+ libc.src.__support.math.inv_trigf_utils
)
add_entrypoint_object(
@@ -4044,13 +4032,7 @@ add_entrypoint_object(
HDRS
../acosf.h
DEPENDS
- libc.src.__support.FPUtil.except_value_utils
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.FPUtil.sqrt
- libc.src.__support.macros.optimization
- .inv_trigf_utils
+ libc.src.__support.math.acosf
)
add_entrypoint_object(
@@ -4122,7 +4104,6 @@ add_entrypoint_object(
HDRS
../atanf.h
DEPENDS
- .inv_trigf_utils
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
@@ -4130,6 +4111,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
+ libc.src.__support.math.inv_trigf_utils
)
add_entrypoint_object(
@@ -4178,7 +4160,6 @@ add_entrypoint_object(
../atan2f.h
atan2f_float.h
DEPENDS
- .inv_trigf_utils
libc.hdr.fenv_macros
libc.src.__support.FPUtil.double_double
libc.src.__support.FPUtil.fenv_impl
@@ -4188,6 +4169,7 @@ add_entrypoint_object(
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
+ libc.src.__support.math.inv_trigf_utils
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/acosf.cpp b/libc/src/math/generic/acosf.cpp
index 8dd6de2ce7474..7afc7d661d552 100644
--- a/libc/src/math/generic/acosf.cpp
+++ b/libc/src/math/generic/acosf.cpp
@@ -7,127 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/acosf.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/sqrt.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-
-#include "inv_trigf_utils.h"
+#include "src/__support/math/acosf.h"
namespace LIBC_NAMESPACE_DECL {
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-static constexpr size_t N_EXCEPTS = 4;
-
-// Exceptional values when |x| <= 0.5
-static constexpr fputil::ExceptValues<float, N_EXCEPTS> ACOSF_EXCEPTS = {{
- // (inputs, RZ output, RU offset, RD offset, RN offset)
- // x = 0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
- {0x328885a3, 0x3fc90fda, 1, 0, 1},
- // x = -0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
- {0xb28885a3, 0x3fc90fda, 1, 0, 1},
- // x = 0x1.04c444p-12, acosf(x) = 0x1.920f68p0 (RZ)
- {0x39826222, 0x3fc907b4, 1, 0, 1},
- // x = -0x1.04c444p-12, acosf(x) = 0x1.923p0 (RZ)
- {0xb9826222, 0x3fc91800, 1, 0, 1},
-}};
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-LLVM_LIBC_FUNCTION(float, acosf, (float x)) {
- using FPBits = typename fputil::FPBits<float>;
-
- FPBits xbits(x);
- uint32_t x_uint = xbits.uintval();
- uint32_t x_abs = xbits.uintval() & 0x7fff'ffffU;
- uint32_t x_sign = x_uint >> 31;
-
- // |x| <= 0.5
- if (LIBC_UNLIKELY(x_abs <= 0x3f00'0000U)) {
- // |x| < 0x1p-10
- if (LIBC_UNLIKELY(x_abs < 0x3a80'0000U)) {
- // When |x| < 2^-10, we use the following approximation:
- // acos(x) = pi/2 - asin(x)
- // ~ pi/2 - x - x^3 / 6
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- // Check for exceptional values
- if (auto r = ACOSF_EXCEPTS.lookup(x_uint); LIBC_UNLIKELY(r.has_value()))
- return r.value();
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
- double xd = static_cast<double>(x);
- return static_cast<float>(fputil::multiply_add(
- -0x1.5555555555555p-3 * xd, xd * xd, M_MATH_PI_2 - xd));
- }
-
- // For |x| <= 0.5, we approximate acosf(x) by:
- // acos(x) = pi/2 - asin(x) = pi/2 - x * P(x^2)
- // Where P(X^2) = Q(X) is a degree-20 minimax even polynomial approximating
- // asin(x)/x on [0, 0.5] generated by Sollya with:
- // > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
- // [|1, D...|], [0, 0.5]);
- double xd = static_cast<double>(x);
- double xsq = xd * xd;
- double x3 = xd * xsq;
- double r = asin_eval(xsq);
- return static_cast<float>(fputil::multiply_add(-x3, r, M_MATH_PI_2 - xd));
- }
-
- // |x| >= 1, return 0, 2pi, or NaNs.
- if (LIBC_UNLIKELY(x_abs >= 0x3f80'0000U)) {
- if (x_abs == 0x3f80'0000U)
- return x_sign ? /* x == -1.0f */ fputil::round_result_slightly_down(
- 0x1.921fb6p+1f)
- : /* x == 1.0f */ 0.0f;
-
- if (xbits.is_signaling_nan()) {
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- // |x| <= +/-inf
- if (x_abs <= 0x7f80'0000U) {
- fputil::set_errno_if_required(EDOM);
- fputil::raise_except_if_required(FE_INVALID);
- }
-
- return x + FPBits::quiet_nan().get_val();
- }
-
- // When 0.5 < |x| < 1, we perform range reduction as follow:
- //
- // Assume further that 0.5 < x <= 1, and let:
- // y = acos(x)
- // We use the double angle formula:
- // x = cos(y) = 1 - 2 sin^2(y/2)
- // So:
- // sin(y/2) = sqrt( (1 - x)/2 )
- // And hence:
- // y = 2 * asin( sqrt( (1 - x)/2 ) )
- // Let u = (1 - x)/2, then
- // acos(x) = 2 * asin( sqrt(u) )
- // Moreover, since 0.5 < x <= 1,
- // 0 <= u < 1/4, and 0 <= sqrt(u) < 0.5,
- // And hence we can reuse the same polynomial approximation of asin(x) when
- // |x| <= 0.5:
- // acos(x) ~ 2 * sqrt(u) * P(u).
- //
- // When -1 < x <= -0.5, we use the identity:
- // acos(x) = pi - acos(-x)
- // which is reduced to the postive case.
-
- xbits.set_sign(Sign::POS);
- double xd = static_cast<double>(xbits.get_val());
- double u = fputil::multiply_add(-0.5, xd, 0.5);
- double cv = 2 * fputil::sqrt<double>(u);
-
- double r3 = asin_eval(u);
- double r = fputil::multiply_add(cv * u, r3, cv);
- return static_cast<float>(x_sign ? M_MATH_PI - r : r);
-}
+LLVM_LIBC_FUNCTION(float, acosf, (float x)) { return math::acosf(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/asinf.cpp b/libc/src/math/generic/asinf.cpp
index 12383bf6dacae..c8d6b38ab1560 100644
--- a/libc/src/math/generic/asinf.cpp
+++ b/libc/src/math/generic/asinf.cpp
@@ -17,7 +17,7 @@
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
-#include "inv_trigf_utils.h"
+#include "src/__support/math/inv_trigf_utils.h"
namespace LIBC_NAMESPACE_DECL {
diff --git a/libc/src/math/generic/atan2f.cpp b/libc/src/math/generic/atan2f.cpp
index c04b0eb1cc589..bdc0ce5b9dfc4 100644
--- a/libc/src/math/generic/atan2f.cpp
+++ b/libc/src/math/generic/atan2f.cpp
@@ -8,7 +8,7 @@
#include "src/math/atan2f.h"
#include "hdr/fenv_macros.h"
-#include "inv_trigf_utils.h"
+#include "src/__support/math/inv_trigf_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
diff --git a/libc/src/math/generic/atanf.cpp b/libc/src/math/generic/atanf.cpp
index 46196dbe4162c..7b609869a1ee9 100644
--- a/libc/src/math/generic/atanf.cpp
+++ b/libc/src/math/generic/atanf.cpp
@@ -7,7 +7,7 @@
//===----------------------------------------------------------------------===//
#include "src/math/atanf.h"
-#include "inv_trigf_utils.h"
+#include "src/__support/math/inv_trigf_utils.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/except_value_utils.h"
diff --git a/libc/src/math/generic/inv_trigf_utils.h b/libc/src/math/generic/inv_trigf_utils.h
deleted file mode 100644
index 8b47aba342995..0000000000000
--- a/libc/src/math/generic/inv_trigf_utils.h
+++ /dev/null
@@ -1,110 +0,0 @@
-//===-- Single-precision general inverse trigonometric functions ----------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-#ifndef LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H
-#define LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H
-
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
-
-namespace LIBC_NAMESPACE_DECL {
-
-// PI and PI / 2
-static constexpr double M_MATH_PI = 0x1.921fb54442d18p+1;
-static constexpr double M_MATH_PI_2 = 0x1.921fb54442d18p+0;
-
-extern double ATAN_COEFFS[17][9];
-
-// Look-up table for atan(k/16) with k = 0..16.
-static constexpr double ATAN_K_OVER_16[17] = {
- 0.0,
- 0x1.ff55bb72cfdeap-5,
- 0x1.fd5ba9aac2f6ep-4,
- 0x1.7b97b4bce5b02p-3,
- 0x1.f5b75f92c80ddp-3,
- 0x1.362773707ebccp-2,
- 0x1.6f61941e4def1p-2,
- 0x1.a64eec3cc23fdp-2,
- 0x1.dac670561bb4fp-2,
- 0x1.0657e94db30dp-1,
- 0x1.1e00babdefeb4p-1,
- 0x1.345f01cce37bbp-1,
- 0x1.4978fa3269ee1p-1,
- 0x1.5d58987169b18p-1,
- 0x1.700a7c5784634p-1,
- 0x1.819d0b7158a4dp-1,
- 0x1.921fb54442d18p-1,
-};
-
-// For |x| <= 1/32 and 0 <= i <= 16, return Q(x) such that:
-// Q(x) ~ (atan(x + i/16) - atan(i/16)) / x.
-LIBC_INLINE static double atan_eval(double x, unsigned i) {
- double x2 = x * x;
-
- double c0 = fputil::multiply_add(x, ATAN_COEFFS[i][2], ATAN_COEFFS[i][1]);
- double c1 = fputil::multiply_add(x, ATAN_COEFFS[i][4], ATAN_COEFFS[i][3]);
- double c2 = fputil::multiply_add(x, ATAN_COEFFS[i][6], ATAN_COEFFS[i][5]);
- double c3 = fputil::multiply_add(x, ATAN_COEFFS[i][8], ATAN_COEFFS[i][7]);
-
- double x4 = x2 * x2;
- double d1 = fputil::multiply_add(x2, c1, c0);
- double d2 = fputil::multiply_add(x2, c3, c2);
- double p = fputil::multiply_add(x4, d2, d1);
- return p;
-}
-
-// Evaluate atan without big lookup table.
-// atan(n/d) - atan(k/16) = atan((n/d - k/16) / (1 + (n/d) * (k/16)))
-// = atan((n - d * k/16)) / (d + n * k/16))
-// So we let q = (n - d * k/16) / (d + n * k/16),
-// and approximate with Taylor polynomial:
-// atan(q) ~ q - q^3/3 + q^5/5 - q^7/7 + q^9/9
-LIBC_INLINE static double atan_eval_no_table(double num, double den,
- double k_over_16) {
- double num_r = fputil::multiply_add(den, -k_over_16, num);
- double den_r = fputil::multiply_add(num, k_over_16, den);
- double q = num_r / den_r;
-
- constexpr double ATAN_TAYLOR[] = {
- -0x1.5555555555555p-2,
- 0x1.999999999999ap-3,
- -0x1.2492492492492p-3,
- 0x1.c71c71c71c71cp-4,
- };
- double q2 = q * q;
- double q3 = q2 * q;
- double q4 = q2 * q2;
- double c0 = fputil::multiply_add(q2, ATAN_TAYLOR[1], ATAN_TAYLOR[0]);
- double c1 = fputil::multiply_add(q2, ATAN_TAYLOR[3], ATAN_TAYLOR[2]);
- double d = fputil::multiply_add(q4, c1, c0);
- return fputil::multiply_add(q3, d, q);
-}
-
-// > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
-// [|1, D...|], [0, 0.5]);
-static constexpr double ASIN_COEFFS[10] = {
- 0x1.5555555540fa1p-3, 0x1.333333512edc2p-4, 0x1.6db6cc1541b31p-5,
- 0x1.f1caff324770ep-6, 0x1.6e43899f5f4f4p-6, 0x1.1f847cf652577p-6,
- 0x1.9b60f47f87146p-7, 0x1.259e2634c494fp-6, -0x1.df946fa875ddp-8,
- 0x1.02311ecf99c28p-5};
-
-// Evaluate P(x^2) - 1, where P(x^2) ~ asin(x)/x
-LIBC_INLINE static double asin_eval(double xsq) {
- double x4 = xsq * xsq;
- double r1 = fputil::polyeval(x4, ASIN_COEFFS[0], ASIN_COEFFS[2],
- ASIN_COEFFS[4], ASIN_COEFFS[6], ASIN_COEFFS[8]);
- double r2 = fputil::polyeval(x4, ASIN_COEFFS[1], ASIN_COEFFS[3],
- ASIN_COEFFS[5], ASIN_COEFFS[7], ASIN_COEFFS[9]);
- return fputil::multiply_add(xsq, r2, r1);
-}
-
-} // namespace LIBC_NAMESPACE_DECL
-
-#endif // LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index e1a6076fed2c6..2bc8e44d82a4b 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2010,22 +2010,6 @@ libc_support_library(
],
)
-libc_support_library(
- name = "inv_trigf_utils",
- srcs = ["src/math/generic/inv_trigf_utils.cpp"],
- hdrs = [
- "src/math/generic/inv_trigf_utils.h",
- ],
- deps = [
- ":__support_common",
- ":__support_fputil_double_double",
- ":__support_fputil_fma",
- ":__support_fputil_multiply_add",
- ":__support_fputil_polyeval",
- ":__support_integer_literals",
- ],
-)
-
libc_support_library(
name = "atan_utils",
hdrs = ["src/math/generic/atan_utils.h"],
@@ -2096,6 +2080,20 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_acosf",
+ hdrs = ["src/__support/math/acosf.h"],
+ deps = [
+ ":__support_math_inv_trigf_utils",
+ ":__support_fputil_except_value_utils",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_sqrt",
+ ":__support_macros_optimization",
+ ],
+)
+
libc_support_library(
name = "__support_math_asin_utils",
hdrs = ["src/__support/math/asin_utils.h"],
@@ -2178,6 +2176,16 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_inv_trigf_utils",
+ hdrs = ["src/__support/math/inv_trigf_utils.h"],
+ deps = [
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_polyeval",
+ ":__support_common",
+ ],
+)
+
libc_support_library(
name = "__support_math_frexpf16",
hdrs = ["src/__support/math/frexpf16.h"],
@@ -2597,13 +2605,7 @@ libc_math_function(
libc_math_function(
name = "acosf",
additional_deps = [
- ":__support_fputil_fma",
- ":__support_fputil_multiply_add",
- ":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
- ":__support_fputil_sqrt",
- ":__support_macros_optimization",
- ":inv_trigf_utils",
+ ":__support_math_acosf",
],
)
@@ -2617,7 +2619,7 @@ libc_math_function(
":__support_fputil_polyeval",
":__support_fputil_sqrt",
":__support_macros_optimization",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
@@ -2645,7 +2647,7 @@ libc_math_function(
":__support_fputil_sqrt",
":__support_macros_optimization",
":__support_macros_properties_cpu_features",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
@@ -2659,7 +2661,7 @@ libc_math_function(
":__support_fputil_polyeval",
":__support_fputil_sqrt",
":__support_macros_optimization",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
@@ -2686,7 +2688,7 @@ libc_math_function(
":__support_fputil_polyeval",
":__support_fputil_rounding_mode",
":__support_macros_optimization",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
@@ -2705,7 +2707,7 @@ libc_math_function(
additional_deps = [
":__support_fputil_double_double",
":__support_fputil_nearest_integer",
- ":inv_trigf_utils",
+ ":__support_math_inv_trigf_utils",
],
)
>From 2837d2fb4504edc7ea1e72acadfbcefd17e045b4 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 09:38:00 +0300
Subject: [PATCH 11/15] fix styles
---
libc/src/__support/math/acosf.h | 1 -
libc/src/__support/math/inv_trigf_utils.h | 2 +-
libc/src/math/generic/atan2f.cpp | 2 +-
libc/src/math/generic/atanf.cpp | 2 +-
4 files changed, 3 insertions(+), 4 deletions(-)
diff --git a/libc/src/__support/math/acosf.h b/libc/src/__support/math/acosf.h
index 05c82330060a8..941c39f6c3eb6 100644
--- a/libc/src/__support/math/acosf.h
+++ b/libc/src/__support/math/acosf.h
@@ -18,7 +18,6 @@
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-
namespace LIBC_NAMESPACE_DECL {
namespace math {
diff --git a/libc/src/__support/math/inv_trigf_utils.h b/libc/src/__support/math/inv_trigf_utils.h
index 8c5f7c44ddadf..a2811c09e9ee9 100644
--- a/libc/src/__support/math/inv_trigf_utils.h
+++ b/libc/src/__support/math/inv_trigf_utils.h
@@ -137,7 +137,7 @@ LIBC_INLINE static constexpr double atan_eval(double x, unsigned i) {
// and approximate with Taylor polynomial:
// atan(q) ~ q - q^3/3 + q^5/5 - q^7/7 + q^9/9
LIBC_INLINE static constexpr double atan_eval_no_table(double num, double den,
- double k_over_16) {
+ double k_over_16) {
double num_r = fputil::multiply_add(den, -k_over_16, num);
double den_r = fputil::multiply_add(num, k_over_16, den);
double q = num_r / den_r;
diff --git a/libc/src/math/generic/atan2f.cpp b/libc/src/math/generic/atan2f.cpp
index bdc0ce5b9dfc4..0a768494baa64 100644
--- a/libc/src/math/generic/atan2f.cpp
+++ b/libc/src/math/generic/atan2f.cpp
@@ -8,7 +8,6 @@
#include "src/math/atan2f.h"
#include "hdr/fenv_macros.h"
-#include "src/__support/math/inv_trigf_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
@@ -18,6 +17,7 @@
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/math/inv_trigf_utils.h"
#if defined(LIBC_MATH_HAS_SKIP_ACCURATE_PASS) && \
defined(LIBC_MATH_HAS_INTERMEDIATE_COMP_IN_FLOAT)
diff --git a/libc/src/math/generic/atanf.cpp b/libc/src/math/generic/atanf.cpp
index 7b609869a1ee9..d12456c591016 100644
--- a/libc/src/math/generic/atanf.cpp
+++ b/libc/src/math/generic/atanf.cpp
@@ -7,7 +7,6 @@
//===----------------------------------------------------------------------===//
#include "src/math/atanf.h"
-#include "src/__support/math/inv_trigf_utils.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/except_value_utils.h"
@@ -16,6 +15,7 @@
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/math/inv_trigf_utils.h"
namespace LIBC_NAMESPACE_DECL {
>From f1ebe57616bfeaf6c157d6b1ec937af06db39fec Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 09:38:39 +0300
Subject: [PATCH 12/15] [libc][math] Refactor acosf16 implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/acosf16.h | 29 ++++
libc/src/__support/math/CMakeLists.txt | 16 ++
libc/src/__support/math/acosf16.h | 164 ++++++++++++++++++
libc/src/math/generic/CMakeLists.txt | 13 +-
libc/src/math/generic/acosf16.cpp | 139 +--------------
.../llvm-project-overlay/libc/BUILD.bazel | 24 ++-
7 files changed, 231 insertions(+), 155 deletions(-)
create mode 100644 libc/shared/math/acosf16.h
create mode 100644 libc/src/__support/math/acosf16.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index 617e46602de8c..baec05b08a25d 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -13,6 +13,7 @@
#include "math/acos.h"
#include "math/acosf.h"
+#include "math/acosf16.h"
#include "math/exp.h"
#include "math/exp10.h"
#include "math/exp10f.h"
diff --git a/libc/shared/math/acosf16.h b/libc/shared/math/acosf16.h
new file mode 100644
index 0000000000000..aaf6ed9922556
--- /dev/null
+++ b/libc/shared/math/acosf16.h
@@ -0,0 +1,29 @@
+//===-- Shared acosf16 function ---------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_ACOSF16_H
+#define LLVM_LIBC_SHARED_MATH_ACOSF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "shared/libc_common.h"
+#include "src/__support/math/acosf16.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acosf16;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOSF16_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index fbe7e2c3125ce..fc2c8a65340cc 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -31,6 +31,22 @@ add_header_library(
libc.src.__support.macros.optimization
)
+add_header_library(
+ acosf16
+ HDRS
+ acosf16.h
+ DEPENDS
+ libc.src.__support.FPUtil.cast
+ libc.src.__support.FPUtil.except_value_utils
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.macros.optimization
+ libc.src.__support.macros.properties.types
+)
+
add_header_library(
asin_utils
HDRS
diff --git a/libc/src/__support/math/acosf16.h b/libc/src/__support/math/acosf16.h
new file mode 100644
index 0000000000000..8423fbb2c178c
--- /dev/null
+++ b/libc/src/__support/math/acosf16.h
@@ -0,0 +1,164 @@
+//===-- Implementation header for acosf16 -----------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/optimization.h"
+
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+// Generated by Sollya using the following command:
+// > round(pi/2, SG, RN);
+// > round(pi, SG, RN);
+static constexpr float PI_OVER_2 = 0x1.921fb6p0f;
+static constexpr float PI = 0x1.921fb6p1f;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr size_t N_EXCEPTS = 2;
+
+static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSF16_EXCEPTS{{
+ // (input, RZ output, RU offset, RD offset, RN offset)
+ {0xacaf, 0x3e93, 1, 0, 0},
+ {0xb874, 0x4052, 1, 0, 1},
+}};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+static constexpr float16 acosf16(float16 x) {
+ using FPBits = fputil::FPBits<float16>;
+ FPBits xbits(x);
+
+ uint16_t x_u = xbits.uintval();
+ uint16_t x_abs = x_u & 0x7fff;
+ uint16_t x_sign = x_u >> 15;
+
+ // |x| > 0x1p0, |x| > 1, or x is NaN.
+ if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
+ // acosf16(NaN) = NaN
+ if (xbits.is_nan()) {
+ if (xbits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ return x;
+ }
+
+ // 1 < |x| <= +/-inf
+ fputil::raise_except_if_required(FE_INVALID);
+ fputil::set_errno_if_required(EDOM);
+
+ return FPBits::quiet_nan().get_val();
+ }
+
+ float xf = x;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ // Handle exceptional values
+ if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+ return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+ // |x| == 0x1p0, x is 1 or -1
+ // if x is (-)1, return pi, else
+ // if x is (+)1, return 0
+ if (LIBC_UNLIKELY(x_abs == 0x3c00))
+ return fputil::cast<float16>(x_sign ? PI : 0.0f);
+
+ float xsq = xf * xf;
+
+ // |x| <= 0x1p-1, |x| <= 0.5
+ if (x_abs <= 0x3800) {
+ // if x is 0, return pi/2
+ if (LIBC_UNLIKELY(x_abs == 0))
+ return fputil::cast<float16>(PI_OVER_2);
+
+ // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
+ // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
+ // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+ float interm =
+ fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
+ 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+ return fputil::cast<float16>(fputil::multiply_add(-xf, interm, PI_OVER_2));
+ }
+
+ // When |x| > 0.5, assume that 0.5 < |x| <= 1
+ //
+ // Step-by-step range-reduction proof:
+ // 1: Let y = asin(x), such that, x = sin(y)
+ // 2: From complimentary angle identity:
+ // x = sin(y) = cos(pi/2 - y)
+ // 3: Let z = pi/2 - y, such that x = cos(z)
+ // 4: From double angle formula; cos(2A) = 1 - 2 * sin^2(A):
+ // z = 2A, z/2 = A
+ // cos(z) = 1 - 2 * sin^2(z/2)
+ // 5: Make sin(z/2) subject of the formula:
+ // sin(z/2) = sqrt((1 - cos(z))/2)
+ // 6: Recall [3]; x = cos(z). Therefore:
+ // sin(z/2) = sqrt((1 - x)/2)
+ // 7: Let u = (1 - x)/2
+ // 8: Therefore:
+ // asin(sqrt(u)) = z/2
+ // 2 * asin(sqrt(u)) = z
+ // 9: Recall [3]; z = pi/2 - y. Therefore:
+ // y = pi/2 - z
+ // y = pi/2 - 2 * asin(sqrt(u))
+ // 10: Recall [1], y = asin(x). Therefore:
+ // asin(x) = pi/2 - 2 * asin(sqrt(u))
+ // 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
+ // Therefore:
+ // acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u)))
+ // acos(x) = 2 * asin(sqrt(u))
+ //
+ // THE RANGE REDUCTION, HOW?
+ // 12: Recall [7], u = (1 - x)/2
+ // 13: Since 0.5 < x <= 1, therefore:
+ // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
+ //
+ // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
+ // Step [11] as `sqrt(u)` is in range.
+ // When -1 < x <= -0.5, the identity:
+ // acos(x) = pi - acos(-x)
+ // allows us to compute for the negative x value (lhs)
+ // with a positive x value instead (rhs).
+
+ float xf_abs = (xf < 0 ? -xf : xf);
+ float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
+ float sqrt_u = fputil::sqrt<float>(u);
+
+ // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
+ // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+ float asin_sqrt_u =
+ sqrt_u * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
+ 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+
+ return fputil::cast<float16>(
+ x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index fd980fb52c624..300aa85ac1272 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -4042,17 +4042,8 @@ add_entrypoint_object(
HDRS
../acosf16.h
DEPENDS
- libc.hdr.errno_macros
- libc.hdr.fenv_macros
- libc.src.__support.FPUtil.cast
- libc.src.__support.FPUtil.except_value_utils
- libc.src.__support.FPUtil.fenv_impl
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.FPUtil.sqrt
- libc.src.__support.macros.optimization
- libc.src.__support.macros.properties.types
+ libc.src.__support.math.acosf16
+ libc.src.errno.errno
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/acosf16.cpp b/libc/src/math/generic/acosf16.cpp
index 202a950fbb5dd..0fbfd9a688c2d 100644
--- a/libc/src/math/generic/acosf16.cpp
+++ b/libc/src/math/generic/acosf16.cpp
@@ -8,144 +8,11 @@
//===----------------------------------------------------------------------===//
#include "src/math/acosf16.h"
-#include "hdr/errno_macros.h"
-#include "hdr/fenv_macros.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/cast.h"
-#include "src/__support/FPUtil/except_value_utils.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/sqrt.h"
-#include "src/__support/macros/optimization.h"
+#include "src/__support/math/acosf16.h"
-namespace LIBC_NAMESPACE_DECL {
-
-// Generated by Sollya using the following command:
-// > round(pi/2, SG, RN);
-// > round(pi, SG, RN);
-static constexpr float PI_OVER_2 = 0x1.921fb6p0f;
-static constexpr float PI = 0x1.921fb6p1f;
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-static constexpr size_t N_EXCEPTS = 2;
-
-static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ACOSF16_EXCEPTS{{
- // (input, RZ output, RU offset, RD offset, RN offset)
- {0xacaf, 0x3e93, 1, 0, 0},
- {0xb874, 0x4052, 1, 0, 1},
-}};
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) {
- using FPBits = fputil::FPBits<float16>;
- FPBits xbits(x);
-
- uint16_t x_u = xbits.uintval();
- uint16_t x_abs = x_u & 0x7fff;
- uint16_t x_sign = x_u >> 15;
-
- // |x| > 0x1p0, |x| > 1, or x is NaN.
- if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
- // acosf16(NaN) = NaN
- if (xbits.is_nan()) {
- if (xbits.is_signaling_nan()) {
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- return x;
- }
-
- // 1 < |x| <= +/-inf
- fputil::raise_except_if_required(FE_INVALID);
- fputil::set_errno_if_required(EDOM);
- return FPBits::quiet_nan().get_val();
- }
-
- float xf = x;
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- // Handle exceptional values
- if (auto r = ACOSF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
- return r.value();
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
- // |x| == 0x1p0, x is 1 or -1
- // if x is (-)1, return pi, else
- // if x is (+)1, return 0
- if (LIBC_UNLIKELY(x_abs == 0x3c00))
- return fputil::cast<float16>(x_sign ? PI : 0.0f);
-
- float xsq = xf * xf;
-
- // |x| <= 0x1p-1, |x| <= 0.5
- if (x_abs <= 0x3800) {
- // if x is 0, return pi/2
- if (LIBC_UNLIKELY(x_abs == 0))
- return fputil::cast<float16>(PI_OVER_2);
-
- // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
- // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
- // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
- float interm =
- fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
- 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
- return fputil::cast<float16>(fputil::multiply_add(-xf, interm, PI_OVER_2));
- }
-
- // When |x| > 0.5, assume that 0.5 < |x| <= 1
- //
- // Step-by-step range-reduction proof:
- // 1: Let y = asin(x), such that, x = sin(y)
- // 2: From complimentary angle identity:
- // x = sin(y) = cos(pi/2 - y)
- // 3: Let z = pi/2 - y, such that x = cos(z)
- // 4: From double angle formula; cos(2A) = 1 - 2 * sin^2(A):
- // z = 2A, z/2 = A
- // cos(z) = 1 - 2 * sin^2(z/2)
- // 5: Make sin(z/2) subject of the formula:
- // sin(z/2) = sqrt((1 - cos(z))/2)
- // 6: Recall [3]; x = cos(z). Therefore:
- // sin(z/2) = sqrt((1 - x)/2)
- // 7: Let u = (1 - x)/2
- // 8: Therefore:
- // asin(sqrt(u)) = z/2
- // 2 * asin(sqrt(u)) = z
- // 9: Recall [3]; z = pi/2 - y. Therefore:
- // y = pi/2 - z
- // y = pi/2 - 2 * asin(sqrt(u))
- // 10: Recall [1], y = asin(x). Therefore:
- // asin(x) = pi/2 - 2 * asin(sqrt(u))
- // 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x)
- // Therefore:
- // acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u)))
- // acos(x) = 2 * asin(sqrt(u))
- //
- // THE RANGE REDUCTION, HOW?
- // 12: Recall [7], u = (1 - x)/2
- // 13: Since 0.5 < x <= 1, therefore:
- // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
- //
- // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
- // Step [11] as `sqrt(u)` is in range.
- // When -1 < x <= -0.5, the identity:
- // acos(x) = pi - acos(-x)
- // allows us to compute for the negative x value (lhs)
- // with a positive x value instead (rhs).
-
- float xf_abs = (xf < 0 ? -xf : xf);
- float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
- float sqrt_u = fputil::sqrt<float>(u);
+namespace LIBC_NAMESPACE_DECL {
- // Degree-6 minimax polynomial of asin(x) generated by Sollya with:
- // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
- float asin_sqrt_u =
- sqrt_u * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
- 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) { return math::acosf16(x); }
- return fputil::cast<float16>(
- x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, PI) : 2 * asin_sqrt_u);
-}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 2bc8e44d82a4b..9ab5b0e38ca97 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2094,6 +2094,20 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_acosf16",
+ hdrs = ["src/__support/math/acosf16.h"],
+ deps = [
+ ":__support_fputil_cast",
+ ":__support_fputil_fma",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_sqrt",
+ ":__support_macros_optimization",
+ ],
+)
+
libc_support_library(
name = "__support_math_asin_utils",
hdrs = ["src/__support/math/asin_utils.h"],
@@ -2612,14 +2626,8 @@ libc_math_function(
libc_math_function(
name = "acosf16",
additional_deps = [
- ":__support_fputil_cast",
- ":__support_fputil_fma",
- ":__support_fputil_multiply_add",
- ":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
- ":__support_fputil_sqrt",
- ":__support_macros_optimization",
- ":__support_math_inv_trigf_utils",
+ ":__support_math_acosf16",
+ ":errno",
],
)
>From 61b1190e78d3ebf6b28de91bede861da1bcf27b9 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 09:40:22 +0300
Subject: [PATCH 13/15] fix style
---
libc/src/__support/math/acosf16.h | 1 -
libc/src/math/generic/acosf16.cpp | 1 -
2 files changed, 2 deletions(-)
diff --git a/libc/src/__support/math/acosf16.h b/libc/src/__support/math/acosf16.h
index 8423fbb2c178c..47946704fe891 100644
--- a/libc/src/__support/math/acosf16.h
+++ b/libc/src/__support/math/acosf16.h
@@ -22,7 +22,6 @@
#include "src/__support/FPUtil/sqrt.h"
#include "src/__support/macros/optimization.h"
-
namespace LIBC_NAMESPACE_DECL {
namespace math {
diff --git a/libc/src/math/generic/acosf16.cpp b/libc/src/math/generic/acosf16.cpp
index 0fbfd9a688c2d..0bf85f84c842c 100644
--- a/libc/src/math/generic/acosf16.cpp
+++ b/libc/src/math/generic/acosf16.cpp
@@ -10,7 +10,6 @@
#include "src/math/acosf16.h"
#include "src/__support/math/acosf16.h"
-
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float16, acosf16, (float16 x)) { return math::acosf16(x); }
>From 0afc137ca58b3779e1d548bb51924091ce582b0d Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 10:00:50 +0300
Subject: [PATCH 14/15] [libc][math] Refactor erff implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/erff.h | 23 +++
libc/src/__support/math/CMakeLists.txt | 12 ++
libc/src/__support/math/erff.h | 192 ++++++++++++++++++
libc/src/math/generic/CMakeLists.txt | 8 +-
libc/src/math/generic/erff.cpp | 174 +---------------
.../llvm-project-overlay/libc/BUILD.bazel | 14 +-
7 files changed, 243 insertions(+), 181 deletions(-)
create mode 100644 libc/shared/math/erff.h
create mode 100644 libc/src/__support/math/erff.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index baec05b08a25d..f2ad0b09a392c 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -14,6 +14,7 @@
#include "math/acos.h"
#include "math/acosf.h"
#include "math/acosf16.h"
+#include "math/erff.h"
#include "math/exp.h"
#include "math/exp10.h"
#include "math/exp10f.h"
diff --git a/libc/shared/math/erff.h b/libc/shared/math/erff.h
new file mode 100644
index 0000000000000..d0cca15570988
--- /dev/null
+++ b/libc/shared/math/erff.h
@@ -0,0 +1,23 @@
+//===-- Shared erff function ------------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_ERFF_H
+#define LLVM_LIBC_SHARED_MATH_ERFF_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/erff.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::erff;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_ERFF_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index fc2c8a65340cc..91cbf379ba5fc 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -61,6 +61,18 @@ add_header_library(
libc.src.__support.macros.optimization
)
+add_header_library(
+ erff
+ HDRS
+ erff.h
+ DEPENDS
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.except_value_utils
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.macros.optimization
+)
+
add_header_library(
exp_float_constants
HDRS
diff --git a/libc/src/__support/math/erff.h b/libc/src/__support/math/erff.h
new file mode 100644
index 0000000000000..ebf002bc0929f
--- /dev/null
+++ b/libc/src/__support/math/erff.h
@@ -0,0 +1,192 @@
+//===-- Implementation header for erff --------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ERFF_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ERFF_H
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+// Polynomials approximating erf(x)/x on ( k/8, (k + 1)/8 ) generated by Sollya
+// with:
+// > P = fpminimax(erf(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], [|D...|],
+// [k/8, (k + 1)/8]);
+// for k = 0..31.
+static constexpr double COEFFS[32][8] = {
+ {0x1.20dd750429b6dp0, -0x1.812746b037753p-2, 0x1.ce2f219e8596ap-4,
+ -0x1.b82cdacb78fdap-6, 0x1.56479297dfda5p-8, -0x1.8b3ac5455ef02p-11,
+ -0x1.126fcac367e3bp-8, 0x1.2d0bdb3ba4984p-4},
+ {0x1.20dd750429b6dp0, -0x1.812746b0379a8p-2, 0x1.ce2f21a03cf2ap-4,
+ -0x1.b82ce30de083ep-6, 0x1.565bcad3eb60fp-8, -0x1.c02c66f659256p-11,
+ 0x1.f92f673385229p-14, -0x1.def402648ae9p-17},
+ {0x1.20dd750429b34p0, -0x1.812746b032dcep-2, 0x1.ce2f219d84aaep-4,
+ -0x1.b82ce22dcf139p-6, 0x1.565b9efcd4af1p-8, -0x1.c021f1af414bcp-11,
+ 0x1.f7c6d177eff82p-14, -0x1.c9e4410dcf865p-17},
+ {0x1.20dd750426eabp0, -0x1.812746ae592c7p-2, 0x1.ce2f211525f14p-4,
+ -0x1.b82ccc125e63fp-6, 0x1.56596f261cfd3p-8, -0x1.bfde1ff8eeecfp-11,
+ 0x1.f31a9d15dc5d8p-14, -0x1.a5a4362844b3cp-17},
+ {0x1.20dd75039c705p0, -0x1.812746777e74dp-2, 0x1.ce2f17af98a1bp-4,
+ -0x1.b82be4b817cbep-6, 0x1.564bec2e2962ep-8, -0x1.bee86f9da3558p-11,
+ 0x1.e9443689dc0ccp-14, -0x1.79c0f230805d8p-17},
+ {0x1.20dd74f811211p0, -0x1.81274371a3e8fp-2, 0x1.ce2ec038262e5p-4,
+ -0x1.b8265b82c5e1fp-6, 0x1.5615a2e239267p-8, -0x1.bc63ae023dcebp-11,
+ 0x1.d87c2102f7e06p-14, -0x1.49584bea41d62p-17},
+ {0x1.20dd746d063e3p0, -0x1.812729a8a950fp-2, 0x1.ce2cb0a2df232p-4,
+ -0x1.b80eca1f51278p-6, 0x1.5572e26c46815p-8, -0x1.b715e5638b65ep-11,
+ 0x1.bfbb195484968p-14, -0x1.177a565c15c52p-17},
+ {0x1.20dd701b44486p0, -0x1.812691145f237p-2, 0x1.ce23a06b8cfd9p-4,
+ -0x1.b7c1dc7245288p-6, 0x1.53e92f7f397ddp-8, -0x1.ad97cc4acf0b2p-11,
+ 0x1.9f028b2b09b71p-14, -0x1.cdc4da08da8c1p-18},
+ {0x1.20dd5715ac332p0, -0x1.8123e680bd0ebp-2, 0x1.ce0457aded691p-4,
+ -0x1.b6f52d52bed4p-6, 0x1.50c291b84414cp-8, -0x1.9ea246b1ad4a9p-11,
+ 0x1.77654674e0cap-14, -0x1.737c11a1bcebbp-18},
+ {0x1.20dce6593e114p0, -0x1.811a59c02eadcp-2, 0x1.cdab53c7cd7d5p-4,
+ -0x1.b526d2e321eedp-6, 0x1.4b1d32cd8b994p-8, -0x1.8963143ec0a1ep-11,
+ 0x1.4ad5700e4db91p-14, -0x1.231e100e43ef2p-18},
+ {0x1.20db48bfd5a62p0, -0x1.80fdd84f9e308p-2, 0x1.ccd340d462983p-4,
+ -0x1.b196a2928768p-6, 0x1.4210c2c13a0f7p-8, -0x1.6dbdfb4ff71aep-11,
+ 0x1.1bca2d17fbd71p-14, -0x1.bca36f90c7cf5p-19},
+ {0x1.20d64b2f8f508p0, -0x1.80b4d4f19fa8bp-2, 0x1.cb088197262e3p-4,
+ -0x1.ab51fd02e5b99p-6, 0x1.34e1e5e81a632p-8, -0x1.4c66377b502cep-11,
+ 0x1.d9ad25066213cp-15, -0x1.4b0df7dd0cfa1p-19},
+ {0x1.20c8fc1243576p0, -0x1.8010cb2009e27p-2, 0x1.c7a47e9299315p-4,
+ -0x1.a155be5683654p-6, 0x1.233502694997bp-8, -0x1.26c94b7d813p-11,
+ 0x1.8094f1de25fb9p-15, -0x1.e0e3d776c6eefp-20},
+ {0x1.20a9bd1611bc1p0, -0x1.7ec7fbce83f9p-2, 0x1.c1d757d7317b7p-4,
+ -0x1.92c160cd589fp-6, 0x1.0d307269cc5c2p-8, -0x1.fda5b0d2d1879p-12,
+ 0x1.2fdd7b3b14a7fp-15, -0x1.54eed4a26af5ap-20},
+ {0x1.20682834f943dp0, -0x1.7c73f747bf5a9p-2, 0x1.b8c2db4a9ffd1p-4,
+ -0x1.7f0e4ffe989ecp-6, 0x1.e7061eae4166ep-9, -0x1.ad36e873fff2dp-12,
+ 0x1.d39222396128ep-16, -0x1.d83dacec5ea6bp-21},
+ {0x1.1feb8d12676d7p0, -0x1.7898347284afep-2, 0x1.aba3466b34451p-4,
+ -0x1.663adc573e2f9p-6, 0x1.ae99fb17c3e08p-9, -0x1.602f950ad5535p-12,
+ 0x1.5e9717490609dp-16, -0x1.3fca107bbc8d5p-21},
+ {0x1.1f12fe3c536fap0, -0x1.72b1d1f22e6d3p-2, 0x1.99fc0eed4a896p-4,
+ -0x1.48db0a87bd8c6p-6, 0x1.73e368895aa61p-9, -0x1.19b35d5301fc8p-12,
+ 0x1.007987e4bb033p-16, -0x1.a7edcd4c2dc7p-22},
+ {0x1.1db7b0df84d5dp0, -0x1.6a4e4a41cde02p-2, 0x1.83bbded16455dp-4,
+ -0x1.2809b3b36977ep-6, 0x1.39c08bab44679p-9, -0x1.b7b45a70ed119p-13,
+ 0x1.6e99b36410e7bp-17, -0x1.13619bb7ebc0cp-22},
+ {0x1.1bb1c85c4a527p0, -0x1.5f23b99a249a3p-2, 0x1.694c91fa0d12cp-4,
+ -0x1.053e1ce11c72dp-6, 0x1.02bf72c50ea78p-9, -0x1.4f478fb56cb02p-13,
+ 0x1.005f80ecbe213p-17, -0x1.5f2446bde7f5bp-23},
+ {0x1.18dec3bd51f9dp0, -0x1.5123f58346186p-2, 0x1.4b8a1ca536ab4p-4,
+ -0x1.c4243015cc723p-7, 0x1.a1a8a01d351efp-10, -0x1.f466b34f1d86bp-14,
+ 0x1.5f835eea0bf6ap-18, -0x1.b83165b939234p-24},
+ {0x1.152804c3369f4p0, -0x1.4084cd4afd4bcp-2, 0x1.2ba2e836e47aap-4,
+ -0x1.800f2dfc6904bp-7, 0x1.4a6daf0669c59p-10, -0x1.6e326ab872317p-14,
+ 0x1.d9761a6a755a5p-19, -0x1.0fca33f9dd4b5p-24},
+ {0x1.1087ad68356aap0, -0x1.2dbb044707459p-2, 0x1.0aea8ceaa0384p-4,
+ -0x1.40b516d52b3d2p-7, 0x1.00c9e05f01d22p-10, -0x1.076afb0dc0ff7p-14,
+ 0x1.39fadec400657p-19, -0x1.4b5761352e7e3p-25},
+ {0x1.0b0a7a8ba4a22p0, -0x1.196990d22d4a1p-2, 0x1.d5551e6ac0c4dp-5,
+ -0x1.07cce1770bd1ap-7, 0x1.890347b8848bfp-11, -0x1.757ec96750b6ap-15,
+ 0x1.9b258a1e06bcep-20, -0x1.8fc6d22da7572p-26},
+ {0x1.04ce2be70fb47p0, -0x1.0449e4b0b9cacp-2, 0x1.97f7424f4b0e7p-5,
+ -0x1.ac825439c42f4p-8, 0x1.28f5f65426dfbp-11, -0x1.05b699a90f90fp-15,
+ 0x1.0a888eecf4593p-20, -0x1.deace2b32bb31p-27},
+ {0x1.fbf9fb0e11cc8p-1, -0x1.de2640856545ap-3, 0x1.5f5b1f47f851p-5,
+ -0x1.588bc71eb41b9p-8, 0x1.bc6a0a772f56dp-12, -0x1.6b9fad1f1657ap-16,
+ 0x1.573204ba66504p-21, -0x1.1d38065c94e44p-27},
+ {0x1.ed8f18c99e031p-1, -0x1.b4cb6acd903b4p-3, 0x1.2c7f3dddd6fc1p-5,
+ -0x1.13052067df4ep-8, 0x1.4a5027444082fp-12, -0x1.f672bab0e2554p-17,
+ 0x1.b83c756348cc9p-22, -0x1.534f1a1079499p-28},
+ {0x1.debd33044166dp-1, -0x1.8d7cd9053f7d8p-3, 0x1.ff9957fb3d6e7p-6,
+ -0x1.b50be55de0f36p-9, 0x1.e92c8ec53a628p-13, -0x1.5a4b88d508007p-17,
+ 0x1.1a27737559e26p-22, -0x1.942ae62cb2c14p-29},
+ {0x1.cfdbf0386f3bdp-1, -0x1.68e33d93b0dc4p-3, 0x1.b2683d58f53dep-6,
+ -0x1.5a9174e70d26fp-9, 0x1.69ddd326d49cdp-13, -0x1.dd8f397a8219cp-18,
+ 0x1.6a755016ad4ddp-23, -0x1.e366e0139187dp-30},
+ {0x1.c132adb8d7464p-1, -0x1.475a899f61b46p-3, 0x1.70a431397a77cp-6,
+ -0x1.12e3d35beeee2p-9, 0x1.0c16b05738333p-13, -0x1.4a47f873e144ep-18,
+ 0x1.d3d494c698c02p-24, -0x1.2302c59547fe5p-30},
+ {0x1.b2f5fd05555e7p-1, -0x1.28feefbe03ec7p-3, 0x1.3923acbb3a676p-6,
+ -0x1.b4ff793cd6358p-10, 0x1.8ea0eb8c913bcp-14, -0x1.cb31ec2baceb1p-19,
+ 0x1.30011e7e80c04p-24, -0x1.617710635cb1dp-31},
+ {0x1.a54853cd9593ep-1, -0x1.0dbdbaea4dc8ep-3, 0x1.0a93e2c20a0fdp-6,
+ -0x1.5c969ff401ea8p-10, 0x1.29e0cc64fe627p-14, -0x1.4160d8e9d3c2ap-19,
+ 0x1.8e7b67594624ap-25, -0x1.b1cf2c975b09bp-32},
+ {0x1.983ceece09ff8p-1, -0x1.eacc78f7a2dp-4, 0x1.c74418410655fp-7,
+ -0x1.1756a050e441ep-10, 0x1.bff3650f7f548p-15, -0x1.c56c0217d3adap-20,
+ 0x1.07b4918d0b489p-25, -0x1.0d4be8c1c50f8p-32},
+};
+
+static constexpr float erff(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;
+
+ if (LIBC_UNLIKELY(x_abs >= 0x4080'0000U)) {
+ const float ONE[2] = {1.0f, -1.0f};
+ const float SMALL[2] = {-0x1.0p-25f, 0x1.0p-25f};
+
+ int sign = xbits.is_neg() ? 1 : 0;
+
+ if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
+ if (xbits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+ return (x_abs > 0x7f80'0000) ? x : ONE[sign];
+ }
+
+ return ONE[sign] + SMALL[sign];
+ }
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ // Exceptional mask = common 0 bits of 2 exceptional values.
+ constexpr uint32_t EXCEPT_MASK = 0x809a'6184U;
+
+ if (LIBC_UNLIKELY((x_abs & EXCEPT_MASK) == 0)) {
+ // Exceptional values
+ if (LIBC_UNLIKELY(x_abs == 0x3f65'9229U)) // |x| = 0x1.cb2452p-1f
+ return x < 0.0f ? fputil::round_result_slightly_down(-0x1.972ea8p-1f)
+ : fputil::round_result_slightly_up(0x1.972ea8p-1f);
+ if (LIBC_UNLIKELY(x_abs == 0x4004'1e6aU)) // |x| = 0x1.083cd4p+1f
+ return x < 0.0f ? fputil::round_result_slightly_down(-0x1.fe3462p-1f)
+ : fputil::round_result_slightly_up(0x1.fe3462p-1f);
+ if (x_abs == 0U)
+ return x;
+ }
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+ // Polynomial approximation:
+ // erf(x) ~ x * (c0 + c1 * x^2 + c2 * x^4 + ... + c7 * x^14)
+ double xd = static_cast<double>(x);
+ double xsq = xd * xd;
+
+ const uint32_t EIGHT = 3 << FPBits::FRACTION_LEN;
+ int idx = static_cast<int>(FPBits(x_abs + EIGHT).get_val());
+
+ double x4 = xsq * xsq;
+ double c0 = fputil::multiply_add(xsq, COEFFS[idx][1], COEFFS[idx][0]);
+ double c1 = fputil::multiply_add(xsq, COEFFS[idx][3], COEFFS[idx][2]);
+ double c2 = fputil::multiply_add(xsq, COEFFS[idx][5], COEFFS[idx][4]);
+ double c3 = fputil::multiply_add(xsq, COEFFS[idx][7], COEFFS[idx][6]);
+
+ double x8 = x4 * x4;
+ double p0 = fputil::multiply_add(x4, c1, c0);
+ double p1 = fputil::multiply_add(x4, c3, c2);
+
+ return static_cast<float>(xd * fputil::multiply_add(x8, p1, p0));
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ERFF_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 300aa85ac1272..5fb82cd469451 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1295,12 +1295,8 @@ add_entrypoint_object(
HDRS
../erff.h
DEPENDS
- .common_constants
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.except_value_utils
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.macros.optimization
+ libc.src.__support.math.erff
+ libc.src.errno.errno
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/erff.cpp b/libc/src/math/generic/erff.cpp
index 44607a52a2e57..003b3465ac597 100644
--- a/libc/src/math/generic/erff.cpp
+++ b/libc/src/math/generic/erff.cpp
@@ -7,180 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/erff.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/common.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/math/erff.h"
namespace LIBC_NAMESPACE_DECL {
-// Polynomials approximating erf(x)/x on ( k/8, (k + 1)/8 ) generated by Sollya
-// with:
-// > P = fpminimax(erf(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], [|D...|],
-// [k/8, (k + 1)/8]);
-// for k = 0..31.
-constexpr double COEFFS[32][8] = {
- {0x1.20dd750429b6dp0, -0x1.812746b037753p-2, 0x1.ce2f219e8596ap-4,
- -0x1.b82cdacb78fdap-6, 0x1.56479297dfda5p-8, -0x1.8b3ac5455ef02p-11,
- -0x1.126fcac367e3bp-8, 0x1.2d0bdb3ba4984p-4},
- {0x1.20dd750429b6dp0, -0x1.812746b0379a8p-2, 0x1.ce2f21a03cf2ap-4,
- -0x1.b82ce30de083ep-6, 0x1.565bcad3eb60fp-8, -0x1.c02c66f659256p-11,
- 0x1.f92f673385229p-14, -0x1.def402648ae9p-17},
- {0x1.20dd750429b34p0, -0x1.812746b032dcep-2, 0x1.ce2f219d84aaep-4,
- -0x1.b82ce22dcf139p-6, 0x1.565b9efcd4af1p-8, -0x1.c021f1af414bcp-11,
- 0x1.f7c6d177eff82p-14, -0x1.c9e4410dcf865p-17},
- {0x1.20dd750426eabp0, -0x1.812746ae592c7p-2, 0x1.ce2f211525f14p-4,
- -0x1.b82ccc125e63fp-6, 0x1.56596f261cfd3p-8, -0x1.bfde1ff8eeecfp-11,
- 0x1.f31a9d15dc5d8p-14, -0x1.a5a4362844b3cp-17},
- {0x1.20dd75039c705p0, -0x1.812746777e74dp-2, 0x1.ce2f17af98a1bp-4,
- -0x1.b82be4b817cbep-6, 0x1.564bec2e2962ep-8, -0x1.bee86f9da3558p-11,
- 0x1.e9443689dc0ccp-14, -0x1.79c0f230805d8p-17},
- {0x1.20dd74f811211p0, -0x1.81274371a3e8fp-2, 0x1.ce2ec038262e5p-4,
- -0x1.b8265b82c5e1fp-6, 0x1.5615a2e239267p-8, -0x1.bc63ae023dcebp-11,
- 0x1.d87c2102f7e06p-14, -0x1.49584bea41d62p-17},
- {0x1.20dd746d063e3p0, -0x1.812729a8a950fp-2, 0x1.ce2cb0a2df232p-4,
- -0x1.b80eca1f51278p-6, 0x1.5572e26c46815p-8, -0x1.b715e5638b65ep-11,
- 0x1.bfbb195484968p-14, -0x1.177a565c15c52p-17},
- {0x1.20dd701b44486p0, -0x1.812691145f237p-2, 0x1.ce23a06b8cfd9p-4,
- -0x1.b7c1dc7245288p-6, 0x1.53e92f7f397ddp-8, -0x1.ad97cc4acf0b2p-11,
- 0x1.9f028b2b09b71p-14, -0x1.cdc4da08da8c1p-18},
- {0x1.20dd5715ac332p0, -0x1.8123e680bd0ebp-2, 0x1.ce0457aded691p-4,
- -0x1.b6f52d52bed4p-6, 0x1.50c291b84414cp-8, -0x1.9ea246b1ad4a9p-11,
- 0x1.77654674e0cap-14, -0x1.737c11a1bcebbp-18},
- {0x1.20dce6593e114p0, -0x1.811a59c02eadcp-2, 0x1.cdab53c7cd7d5p-4,
- -0x1.b526d2e321eedp-6, 0x1.4b1d32cd8b994p-8, -0x1.8963143ec0a1ep-11,
- 0x1.4ad5700e4db91p-14, -0x1.231e100e43ef2p-18},
- {0x1.20db48bfd5a62p0, -0x1.80fdd84f9e308p-2, 0x1.ccd340d462983p-4,
- -0x1.b196a2928768p-6, 0x1.4210c2c13a0f7p-8, -0x1.6dbdfb4ff71aep-11,
- 0x1.1bca2d17fbd71p-14, -0x1.bca36f90c7cf5p-19},
- {0x1.20d64b2f8f508p0, -0x1.80b4d4f19fa8bp-2, 0x1.cb088197262e3p-4,
- -0x1.ab51fd02e5b99p-6, 0x1.34e1e5e81a632p-8, -0x1.4c66377b502cep-11,
- 0x1.d9ad25066213cp-15, -0x1.4b0df7dd0cfa1p-19},
- {0x1.20c8fc1243576p0, -0x1.8010cb2009e27p-2, 0x1.c7a47e9299315p-4,
- -0x1.a155be5683654p-6, 0x1.233502694997bp-8, -0x1.26c94b7d813p-11,
- 0x1.8094f1de25fb9p-15, -0x1.e0e3d776c6eefp-20},
- {0x1.20a9bd1611bc1p0, -0x1.7ec7fbce83f9p-2, 0x1.c1d757d7317b7p-4,
- -0x1.92c160cd589fp-6, 0x1.0d307269cc5c2p-8, -0x1.fda5b0d2d1879p-12,
- 0x1.2fdd7b3b14a7fp-15, -0x1.54eed4a26af5ap-20},
- {0x1.20682834f943dp0, -0x1.7c73f747bf5a9p-2, 0x1.b8c2db4a9ffd1p-4,
- -0x1.7f0e4ffe989ecp-6, 0x1.e7061eae4166ep-9, -0x1.ad36e873fff2dp-12,
- 0x1.d39222396128ep-16, -0x1.d83dacec5ea6bp-21},
- {0x1.1feb8d12676d7p0, -0x1.7898347284afep-2, 0x1.aba3466b34451p-4,
- -0x1.663adc573e2f9p-6, 0x1.ae99fb17c3e08p-9, -0x1.602f950ad5535p-12,
- 0x1.5e9717490609dp-16, -0x1.3fca107bbc8d5p-21},
- {0x1.1f12fe3c536fap0, -0x1.72b1d1f22e6d3p-2, 0x1.99fc0eed4a896p-4,
- -0x1.48db0a87bd8c6p-6, 0x1.73e368895aa61p-9, -0x1.19b35d5301fc8p-12,
- 0x1.007987e4bb033p-16, -0x1.a7edcd4c2dc7p-22},
- {0x1.1db7b0df84d5dp0, -0x1.6a4e4a41cde02p-2, 0x1.83bbded16455dp-4,
- -0x1.2809b3b36977ep-6, 0x1.39c08bab44679p-9, -0x1.b7b45a70ed119p-13,
- 0x1.6e99b36410e7bp-17, -0x1.13619bb7ebc0cp-22},
- {0x1.1bb1c85c4a527p0, -0x1.5f23b99a249a3p-2, 0x1.694c91fa0d12cp-4,
- -0x1.053e1ce11c72dp-6, 0x1.02bf72c50ea78p-9, -0x1.4f478fb56cb02p-13,
- 0x1.005f80ecbe213p-17, -0x1.5f2446bde7f5bp-23},
- {0x1.18dec3bd51f9dp0, -0x1.5123f58346186p-2, 0x1.4b8a1ca536ab4p-4,
- -0x1.c4243015cc723p-7, 0x1.a1a8a01d351efp-10, -0x1.f466b34f1d86bp-14,
- 0x1.5f835eea0bf6ap-18, -0x1.b83165b939234p-24},
- {0x1.152804c3369f4p0, -0x1.4084cd4afd4bcp-2, 0x1.2ba2e836e47aap-4,
- -0x1.800f2dfc6904bp-7, 0x1.4a6daf0669c59p-10, -0x1.6e326ab872317p-14,
- 0x1.d9761a6a755a5p-19, -0x1.0fca33f9dd4b5p-24},
- {0x1.1087ad68356aap0, -0x1.2dbb044707459p-2, 0x1.0aea8ceaa0384p-4,
- -0x1.40b516d52b3d2p-7, 0x1.00c9e05f01d22p-10, -0x1.076afb0dc0ff7p-14,
- 0x1.39fadec400657p-19, -0x1.4b5761352e7e3p-25},
- {0x1.0b0a7a8ba4a22p0, -0x1.196990d22d4a1p-2, 0x1.d5551e6ac0c4dp-5,
- -0x1.07cce1770bd1ap-7, 0x1.890347b8848bfp-11, -0x1.757ec96750b6ap-15,
- 0x1.9b258a1e06bcep-20, -0x1.8fc6d22da7572p-26},
- {0x1.04ce2be70fb47p0, -0x1.0449e4b0b9cacp-2, 0x1.97f7424f4b0e7p-5,
- -0x1.ac825439c42f4p-8, 0x1.28f5f65426dfbp-11, -0x1.05b699a90f90fp-15,
- 0x1.0a888eecf4593p-20, -0x1.deace2b32bb31p-27},
- {0x1.fbf9fb0e11cc8p-1, -0x1.de2640856545ap-3, 0x1.5f5b1f47f851p-5,
- -0x1.588bc71eb41b9p-8, 0x1.bc6a0a772f56dp-12, -0x1.6b9fad1f1657ap-16,
- 0x1.573204ba66504p-21, -0x1.1d38065c94e44p-27},
- {0x1.ed8f18c99e031p-1, -0x1.b4cb6acd903b4p-3, 0x1.2c7f3dddd6fc1p-5,
- -0x1.13052067df4ep-8, 0x1.4a5027444082fp-12, -0x1.f672bab0e2554p-17,
- 0x1.b83c756348cc9p-22, -0x1.534f1a1079499p-28},
- {0x1.debd33044166dp-1, -0x1.8d7cd9053f7d8p-3, 0x1.ff9957fb3d6e7p-6,
- -0x1.b50be55de0f36p-9, 0x1.e92c8ec53a628p-13, -0x1.5a4b88d508007p-17,
- 0x1.1a27737559e26p-22, -0x1.942ae62cb2c14p-29},
- {0x1.cfdbf0386f3bdp-1, -0x1.68e33d93b0dc4p-3, 0x1.b2683d58f53dep-6,
- -0x1.5a9174e70d26fp-9, 0x1.69ddd326d49cdp-13, -0x1.dd8f397a8219cp-18,
- 0x1.6a755016ad4ddp-23, -0x1.e366e0139187dp-30},
- {0x1.c132adb8d7464p-1, -0x1.475a899f61b46p-3, 0x1.70a431397a77cp-6,
- -0x1.12e3d35beeee2p-9, 0x1.0c16b05738333p-13, -0x1.4a47f873e144ep-18,
- 0x1.d3d494c698c02p-24, -0x1.2302c59547fe5p-30},
- {0x1.b2f5fd05555e7p-1, -0x1.28feefbe03ec7p-3, 0x1.3923acbb3a676p-6,
- -0x1.b4ff793cd6358p-10, 0x1.8ea0eb8c913bcp-14, -0x1.cb31ec2baceb1p-19,
- 0x1.30011e7e80c04p-24, -0x1.617710635cb1dp-31},
- {0x1.a54853cd9593ep-1, -0x1.0dbdbaea4dc8ep-3, 0x1.0a93e2c20a0fdp-6,
- -0x1.5c969ff401ea8p-10, 0x1.29e0cc64fe627p-14, -0x1.4160d8e9d3c2ap-19,
- 0x1.8e7b67594624ap-25, -0x1.b1cf2c975b09bp-32},
- {0x1.983ceece09ff8p-1, -0x1.eacc78f7a2dp-4, 0x1.c74418410655fp-7,
- -0x1.1756a050e441ep-10, 0x1.bff3650f7f548p-15, -0x1.c56c0217d3adap-20,
- 0x1.07b4918d0b489p-25, -0x1.0d4be8c1c50f8p-32},
-};
-
-LLVM_LIBC_FUNCTION(float, erff, (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;
-
- if (LIBC_UNLIKELY(x_abs >= 0x4080'0000U)) {
- const float ONE[2] = {1.0f, -1.0f};
- const float SMALL[2] = {-0x1.0p-25f, 0x1.0p-25f};
-
- int sign = xbits.is_neg() ? 1 : 0;
-
- if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
- if (xbits.is_signaling_nan()) {
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
- return (x_abs > 0x7f80'0000) ? x : ONE[sign];
- }
-
- return ONE[sign] + SMALL[sign];
- }
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- // Exceptional mask = common 0 bits of 2 exceptional values.
- constexpr uint32_t EXCEPT_MASK = 0x809a'6184U;
-
- if (LIBC_UNLIKELY((x_abs & EXCEPT_MASK) == 0)) {
- // Exceptional values
- if (LIBC_UNLIKELY(x_abs == 0x3f65'9229U)) // |x| = 0x1.cb2452p-1f
- return x < 0.0f ? fputil::round_result_slightly_down(-0x1.972ea8p-1f)
- : fputil::round_result_slightly_up(0x1.972ea8p-1f);
- if (LIBC_UNLIKELY(x_abs == 0x4004'1e6aU)) // |x| = 0x1.083cd4p+1f
- return x < 0.0f ? fputil::round_result_slightly_down(-0x1.fe3462p-1f)
- : fputil::round_result_slightly_up(0x1.fe3462p-1f);
- if (x_abs == 0U)
- return x;
- }
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
- // Polynomial approximation:
- // erf(x) ~ x * (c0 + c1 * x^2 + c2 * x^4 + ... + c7 * x^14)
- double xd = static_cast<double>(x);
- double xsq = xd * xd;
-
- const uint32_t EIGHT = 3 << FPBits::FRACTION_LEN;
- int idx = static_cast<int>(FPBits(x_abs + EIGHT).get_val());
-
- double x4 = xsq * xsq;
- double c0 = fputil::multiply_add(xsq, COEFFS[idx][1], COEFFS[idx][0]);
- double c1 = fputil::multiply_add(xsq, COEFFS[idx][3], COEFFS[idx][2]);
- double c2 = fputil::multiply_add(xsq, COEFFS[idx][5], COEFFS[idx][4]);
- double c3 = fputil::multiply_add(xsq, COEFFS[idx][7], COEFFS[idx][6]);
-
- double x8 = x4 * x4;
- double p0 = fputil::multiply_add(x4, c1, c0);
- double p1 = fputil::multiply_add(x4, c3, c2);
-
- return static_cast<float>(xd * fputil::multiply_add(x8, p1, p0));
-}
+LLVM_LIBC_FUNCTION(float, erff, (float x)) { return math::erff(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 9ab5b0e38ca97..74e331c0171e4 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -2122,6 +2122,16 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_erff",
+ hdrs = ["src/__support/math/erff.h"],
+ deps = [
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_polyeval",
+ ":__support_macros_optimization",
+ ],
+)
+
libc_support_library(
name = "__support_math_exp_float_constants",
hdrs = ["src/__support/math/exp_float_constants.h"],
@@ -2930,9 +2940,7 @@ libc_math_function(name = "dsubf128")
libc_math_function(
name = "erff",
additional_deps = [
- ":__support_fputil_multiply_add",
- ":__support_fputil_polyeval",
- ":__support_macros_optimization",
+ ":__support_math_erff"
],
)
>From 3c92206153cd06ae6050f4fcda649a11af0484fe Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Sun, 13 Jul 2025 12:13:40 +0300
Subject: [PATCH 15/15] [libc][math] Refactor acoshf implementation to
header-only in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/acoshf.h | 23 ++++
libc/src/__support/math/CMakeLists.txt | 32 +++++
.../__support/math/acosh_float_constants.h | 110 ++++++++++++++++++
libc/src/__support/math/acoshf.h | 85 ++++++++++++++
libc/src/__support/math/acoshf_utils.h | 56 +++++++++
libc/src/math/generic/CMakeLists.txt | 10 +-
libc/src/math/generic/acoshf.cpp | 68 +----------
libc/src/math/generic/common_constants.cpp | 92 ---------------
libc/src/math/generic/common_constants.h | 7 +-
libc/src/math/generic/explogxf.h | 36 +-----
.../llvm-project-overlay/libc/BUILD.bazel | 42 +++++--
12 files changed, 350 insertions(+), 212 deletions(-)
create mode 100644 libc/shared/math/acoshf.h
create mode 100644 libc/src/__support/math/acosh_float_constants.h
create mode 100644 libc/src/__support/math/acoshf.h
create mode 100644 libc/src/__support/math/acoshf_utils.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index f2ad0b09a392c..33fe235c51824 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -14,6 +14,7 @@
#include "math/acos.h"
#include "math/acosf.h"
#include "math/acosf16.h"
+#include "math/acoshf.h"
#include "math/erff.h"
#include "math/exp.h"
#include "math/exp10.h"
diff --git a/libc/shared/math/acoshf.h b/libc/shared/math/acoshf.h
new file mode 100644
index 0000000000000..86bdbce3d905c
--- /dev/null
+++ b/libc/shared/math/acoshf.h
@@ -0,0 +1,23 @@
+//===-- Shared acoshf function ----------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SHARED_MATH_ACOSHF_H
+#define LLVM_LIBC_SHARED_MATH_ACOSHF_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/acoshf.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::acoshf;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_ACOSHF_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 91cbf379ba5fc..b0e562fb20d0d 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -47,6 +47,38 @@ add_header_library(
libc.src.__support.macros.properties.types
)
+add_header_library(
+ acosh_float_constants
+ HDRS
+ acosh_float_constants.h
+ DEPENDS
+ libc.src.__support.macros.config
+)
+
+add_header_library(
+ acoshf_utils
+ HDRS
+ acoshf_utils.h
+ DEPENDS
+ .acosh_float_constants
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.polyeval
+)
+
+add_header_library(
+ acoshf
+ HDRS
+ acoshf.h
+ DEPENDS
+ .acoshf_utils
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.macros.optimization
+)
+
add_header_library(
asin_utils
HDRS
diff --git a/libc/src/__support/math/acosh_float_constants.h b/libc/src/__support/math/acosh_float_constants.h
new file mode 100644
index 0000000000000..4a4c42c220537
--- /dev/null
+++ b/libc/src/__support/math/acosh_float_constants.h
@@ -0,0 +1,110 @@
+//===-- Common constants for acoshf function --------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSH_FLOAT_CONSTANTS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSH_FLOAT_CONSTANTS_H
+
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127.
+static const double ONE_OVER_F[128] = {
+ 0x1.0000000000000p+0, 0x1.fc07f01fc07f0p-1, 0x1.f81f81f81f820p-1,
+ 0x1.f44659e4a4271p-1, 0x1.f07c1f07c1f08p-1, 0x1.ecc07b301ecc0p-1,
+ 0x1.e9131abf0b767p-1, 0x1.e573ac901e574p-1, 0x1.e1e1e1e1e1e1ep-1,
+ 0x1.de5d6e3f8868ap-1, 0x1.dae6076b981dbp-1, 0x1.d77b654b82c34p-1,
+ 0x1.d41d41d41d41dp-1, 0x1.d0cb58f6ec074p-1, 0x1.cd85689039b0bp-1,
+ 0x1.ca4b3055ee191p-1, 0x1.c71c71c71c71cp-1, 0x1.c3f8f01c3f8f0p-1,
+ 0x1.c0e070381c0e0p-1, 0x1.bdd2b899406f7p-1, 0x1.bacf914c1bad0p-1,
+ 0x1.b7d6c3dda338bp-1, 0x1.b4e81b4e81b4fp-1, 0x1.b2036406c80d9p-1,
+ 0x1.af286bca1af28p-1, 0x1.ac5701ac5701bp-1, 0x1.a98ef606a63bep-1,
+ 0x1.a6d01a6d01a6dp-1, 0x1.a41a41a41a41ap-1, 0x1.a16d3f97a4b02p-1,
+ 0x1.9ec8e951033d9p-1, 0x1.9c2d14ee4a102p-1, 0x1.999999999999ap-1,
+ 0x1.970e4f80cb872p-1, 0x1.948b0fcd6e9e0p-1, 0x1.920fb49d0e229p-1,
+ 0x1.8f9c18f9c18fap-1, 0x1.8d3018d3018d3p-1, 0x1.8acb90f6bf3aap-1,
+ 0x1.886e5f0abb04ap-1, 0x1.8618618618618p-1, 0x1.83c977ab2beddp-1,
+ 0x1.8181818181818p-1, 0x1.7f405fd017f40p-1, 0x1.7d05f417d05f4p-1,
+ 0x1.7ad2208e0ecc3p-1, 0x1.78a4c8178a4c8p-1, 0x1.767dce434a9b1p-1,
+ 0x1.745d1745d1746p-1, 0x1.724287f46debcp-1, 0x1.702e05c0b8170p-1,
+ 0x1.6e1f76b4337c7p-1, 0x1.6c16c16c16c17p-1, 0x1.6a13cd1537290p-1,
+ 0x1.6816816816817p-1, 0x1.661ec6a5122f9p-1, 0x1.642c8590b2164p-1,
+ 0x1.623fa77016240p-1, 0x1.6058160581606p-1, 0x1.5e75bb8d015e7p-1,
+ 0x1.5c9882b931057p-1, 0x1.5ac056b015ac0p-1, 0x1.58ed2308158edp-1,
+ 0x1.571ed3c506b3ap-1, 0x1.5555555555555p-1, 0x1.5390948f40febp-1,
+ 0x1.51d07eae2f815p-1, 0x1.5015015015015p-1, 0x1.4e5e0a72f0539p-1,
+ 0x1.4cab88725af6ep-1, 0x1.4afd6a052bf5bp-1, 0x1.49539e3b2d067p-1,
+ 0x1.47ae147ae147bp-1, 0x1.460cbc7f5cf9ap-1, 0x1.446f86562d9fbp-1,
+ 0x1.42d6625d51f87p-1, 0x1.4141414141414p-1, 0x1.3fb013fb013fbp-1,
+ 0x1.3e22cbce4a902p-1, 0x1.3c995a47babe7p-1, 0x1.3b13b13b13b14p-1,
+ 0x1.3991c2c187f63p-1, 0x1.3813813813814p-1, 0x1.3698df3de0748p-1,
+ 0x1.3521cfb2b78c1p-1, 0x1.33ae45b57bcb2p-1, 0x1.323e34a2b10bfp-1,
+ 0x1.30d190130d190p-1, 0x1.2f684bda12f68p-1, 0x1.2e025c04b8097p-1,
+ 0x1.2c9fb4d812ca0p-1, 0x1.2b404ad012b40p-1, 0x1.29e4129e4129ep-1,
+ 0x1.288b01288b013p-1, 0x1.27350b8812735p-1, 0x1.25e22708092f1p-1,
+ 0x1.2492492492492p-1, 0x1.23456789abcdfp-1, 0x1.21fb78121fb78p-1,
+ 0x1.20b470c67c0d9p-1, 0x1.1f7047dc11f70p-1, 0x1.1e2ef3b3fb874p-1,
+ 0x1.1cf06ada2811dp-1, 0x1.1bb4a4046ed29p-1, 0x1.1a7b9611a7b96p-1,
+ 0x1.19453808ca29cp-1, 0x1.1811811811812p-1, 0x1.16e0689427379p-1,
+ 0x1.15b1e5f75270dp-1, 0x1.1485f0e0acd3bp-1, 0x1.135c81135c811p-1,
+ 0x1.12358e75d3033p-1, 0x1.1111111111111p-1, 0x1.0fef010fef011p-1,
+ 0x1.0ecf56be69c90p-1, 0x1.0db20a88f4696p-1, 0x1.0c9714fbcda3bp-1,
+ 0x1.0b7e6ec259dc8p-1, 0x1.0a6810a6810a7p-1, 0x1.0953f39010954p-1,
+ 0x1.0842108421084p-1, 0x1.073260a47f7c6p-1, 0x1.0624dd2f1a9fcp-1,
+ 0x1.05197f7d73404p-1, 0x1.0410410410410p-1, 0x1.03091b51f5e1ap-1,
+ 0x1.0204081020408p-1, 0x1.0101010101010p-1};
+
+// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127.
+static constexpr double LOG_F[128] = {
+ 0x0.0000000000000p+0, 0x1.fe02a6b106788p-8, 0x1.fc0a8b0fc03e3p-7,
+ 0x1.7b91b07d5b11ap-6, 0x1.f829b0e783300p-6, 0x1.39e87b9febd5fp-5,
+ 0x1.77458f632dcfcp-5, 0x1.b42dd711971bep-5, 0x1.f0a30c01162a6p-5,
+ 0x1.16536eea37ae0p-4, 0x1.341d7961bd1d0p-4, 0x1.51b073f06183fp-4,
+ 0x1.6f0d28ae56b4bp-4, 0x1.8c345d6319b20p-4, 0x1.a926d3a4ad563p-4,
+ 0x1.c5e548f5bc743p-4, 0x1.e27076e2af2e5p-4, 0x1.fec9131dbeabap-4,
+ 0x1.0d77e7cd08e59p-3, 0x1.1b72ad52f67a0p-3, 0x1.29552f81ff523p-3,
+ 0x1.371fc201e8f74p-3, 0x1.44d2b6ccb7d1ep-3, 0x1.526e5e3a1b437p-3,
+ 0x1.5ff3070a793d3p-3, 0x1.6d60fe719d21cp-3, 0x1.7ab890210d909p-3,
+ 0x1.87fa06520c910p-3, 0x1.9525a9cf456b4p-3, 0x1.a23bc1fe2b563p-3,
+ 0x1.af3c94e80bff2p-3, 0x1.bc286742d8cd6p-3, 0x1.c8ff7c79a9a21p-3,
+ 0x1.d5c216b4fbb91p-3, 0x1.e27076e2af2e5p-3, 0x1.ef0adcbdc5936p-3,
+ 0x1.fb9186d5e3e2ap-3, 0x1.0402594b4d040p-2, 0x1.0a324e27390e3p-2,
+ 0x1.1058bf9ae4ad5p-2, 0x1.1675cababa60ep-2, 0x1.1c898c16999fap-2,
+ 0x1.22941fbcf7965p-2, 0x1.2895a13de86a3p-2, 0x1.2e8e2bae11d30p-2,
+ 0x1.347dd9a987d54p-2, 0x1.3a64c556945e9p-2, 0x1.404308686a7e3p-2,
+ 0x1.4618bc21c5ec2p-2, 0x1.4be5f957778a0p-2, 0x1.51aad872df82dp-2,
+ 0x1.5767717455a6cp-2, 0x1.5d1bdbf5809cap-2, 0x1.62c82f2b9c795p-2,
+ 0x1.686c81e9b14aep-2, 0x1.6e08eaa2ba1e3p-2, 0x1.739d7f6bbd006p-2,
+ 0x1.792a55fdd47a2p-2, 0x1.7eaf83b82afc3p-2, 0x1.842d1da1e8b17p-2,
+ 0x1.89a3386c1425ap-2, 0x1.8f11e873662c7p-2, 0x1.947941c2116fap-2,
+ 0x1.99d958117e08ap-2, 0x1.9f323ecbf984bp-2, 0x1.a484090e5bb0ap-2,
+ 0x1.a9cec9a9a0849p-2, 0x1.af1293247786bp-2, 0x1.b44f77bcc8f62p-2,
+ 0x1.b9858969310fbp-2, 0x1.beb4d9da71b7bp-2, 0x1.c3dd7a7cdad4dp-2,
+ 0x1.c8ff7c79a9a21p-2, 0x1.ce1af0b85f3ebp-2, 0x1.d32fe7e00ebd5p-2,
+ 0x1.d83e7258a2f3ep-2, 0x1.dd46a04c1c4a0p-2, 0x1.e24881a7c6c26p-2,
+ 0x1.e744261d68787p-2, 0x1.ec399d2468cc0p-2, 0x1.f128f5faf06ecp-2,
+ 0x1.f6123fa7028acp-2, 0x1.faf588f78f31ep-2, 0x1.ffd2e0857f498p-2,
+ 0x1.02552a5a5d0fep-1, 0x1.04bdf9da926d2p-1, 0x1.0723e5c1cdf40p-1,
+ 0x1.0986f4f573520p-1, 0x1.0be72e4252a82p-1, 0x1.0e44985d1cc8bp-1,
+ 0x1.109f39e2d4c96p-1, 0x1.12f719593efbcp-1, 0x1.154c3d2f4d5e9p-1,
+ 0x1.179eabbd899a0p-1, 0x1.19ee6b467c96ep-1, 0x1.1c3b81f713c24p-1,
+ 0x1.1e85f5e7040d0p-1, 0x1.20cdcd192ab6dp-1, 0x1.23130d7bebf42p-1,
+ 0x1.2555bce98f7cbp-1, 0x1.2795e1289b11ap-1, 0x1.29d37fec2b08ap-1,
+ 0x1.2c0e9ed448e8bp-1, 0x1.2e47436e40268p-1, 0x1.307d7334f10bep-1,
+ 0x1.32b1339121d71p-1, 0x1.34e289d9ce1d3p-1, 0x1.37117b54747b5p-1,
+ 0x1.393e0d3562a19p-1, 0x1.3b68449fffc22p-1, 0x1.3d9026a7156fap-1,
+ 0x1.3fb5b84d16f42p-1, 0x1.41d8fe84672aep-1, 0x1.43f9fe2f9ce67p-1,
+ 0x1.4618bc21c5ec2p-1, 0x1.48353d1ea88dfp-1, 0x1.4a4f85db03ebbp-1,
+ 0x1.4c679afccee39p-1, 0x1.4e7d811b75bb0p-1, 0x1.50913cc01686bp-1,
+ 0x1.52a2d265bc5aap-1, 0x1.54b2467999497p-1, 0x1.56bf9d5b3f399p-1,
+ 0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1,
+ 0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1};
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSH_FLOAT_CONSTANTS_H
diff --git a/libc/src/__support/math/acoshf.h b/libc/src/__support/math/acoshf.h
new file mode 100644
index 0000000000000..658074486f8f5
--- /dev/null
+++ b/libc/src/__support/math/acoshf.h
@@ -0,0 +1,85 @@
+//===-- Implementation header for acoshf ------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_H
+
+#include "acoshf_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+static constexpr float acoshf(float x) {
+ using FPBits_t = typename fputil::FPBits<float>;
+ FPBits_t xbits(x);
+
+ if (LIBC_UNLIKELY(x <= 1.0f)) {
+ if (x == 1.0f)
+ return 0.0f;
+ // x < 1.
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits_t::quiet_nan().get_val();
+ }
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ uint32_t x_u = xbits.uintval();
+ if (LIBC_UNLIKELY(x_u >= 0x4f8ffb03)) {
+ if (LIBC_UNLIKELY(xbits.is_inf_or_nan()))
+ return x;
+
+ // Helper functions to set results for exceptional cases.
+ auto round_result_slightly_down = [](float r) -> float {
+ volatile float tmp = r;
+ tmp = tmp - 0x1.0p-25f;
+ return tmp;
+ };
+ auto round_result_slightly_up = [](float r) -> float {
+ volatile float tmp = r;
+ tmp = tmp + 0x1.0p-25f;
+ return tmp;
+ };
+
+ switch (x_u) {
+ case 0x4f8ffb03: // x = 0x1.1ff606p32f
+ return round_result_slightly_up(0x1.6fdd34p4f);
+ case 0x5c569e88: // x = 0x1.ad3d1p57f
+ return round_result_slightly_up(0x1.45c146p5f);
+ case 0x5e68984e: // x = 0x1.d1309cp61f
+ return round_result_slightly_up(0x1.5c9442p5f);
+ case 0x655890d3: // x = 0x1.b121a6p75f
+ return round_result_slightly_down(0x1.a9a3f2p5f);
+ case 0x6eb1a8ec: // x = 0x1.6351d8p94f
+ return round_result_slightly_down(0x1.08b512p6f);
+ case 0x7997f30a: // x = 0x1.2fe614p116f
+ return round_result_slightly_up(0x1.451436p6f);
+ }
+ }
+#else
+ if (LIBC_UNLIKELY(xbits.is_inf_or_nan()))
+ return x;
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+ double x_d = static_cast<double>(x);
+ // acosh(x) = log(x + sqrt(x^2 - 1))
+ return static_cast<float>(log_eval(
+ x_d + fputil::sqrt<double>(fputil::multiply_add(x_d, x_d, -1.0))));
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_H
diff --git a/libc/src/__support/math/acoshf_utils.h b/libc/src/__support/math/acoshf_utils.h
new file mode 100644
index 0000000000000..207913eb7a3f8
--- /dev/null
+++ b/libc/src/__support/math/acoshf_utils.h
@@ -0,0 +1,56 @@
+//===-- Collection of utils for acoshf --------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_UTILS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_UTILS_H
+
+#include "acosh_float_constants.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/multiply_add.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// x should be positive, normal finite value
+LIBC_INLINE static constexpr double log_eval(double x) {
+ // For x = 2^ex * (1 + mx)
+ // log(x) = ex * log(2) + log(1 + mx)
+ using FPB = fputil::FPBits<double>;
+ FPB bs(x);
+
+ double ex = static_cast<double>(bs.get_exponent());
+
+ // p1 is the leading 7 bits of mx, i.e.
+ // p1 * 2^(-7) <= m_x < (p1 + 1) * 2^(-7).
+ int p1 = static_cast<int>(bs.get_mantissa() >> (FPB::FRACTION_LEN - 7));
+
+ // Set bs to (1 + (mx - p1*2^(-7))
+ bs.set_uintval(bs.uintval() & (FPB::FRACTION_MASK >> 7));
+ bs.set_biased_exponent(FPB::EXP_BIAS);
+ // dx = (mx - p1*2^(-7)) / (1 + p1*2^(-7)).
+ double dx = (bs.get_val() - 1.0) * ONE_OVER_F[p1];
+
+ // Minimax polynomial of log(1 + dx) generated by Sollya with:
+ // > P = fpminimax(log(1 + x)/x, 6, [|D...|], [0, 2^-7]);
+ const double COEFFS[6] = {-0x1.ffffffffffffcp-2, 0x1.5555555552ddep-2,
+ -0x1.ffffffefe562dp-3, 0x1.9999817d3a50fp-3,
+ -0x1.554317b3f67a5p-3, 0x1.1dc5c45e09c18p-3};
+ double dx2 = dx * dx;
+ double c1 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]);
+ double c2 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]);
+ double c3 = fputil::multiply_add(dx, COEFFS[5], COEFFS[4]);
+
+ double p = fputil::polyeval(dx2, dx, c1, c2, c3);
+ double result =
+ fputil::multiply_add(ex, /*log(2)*/ 0x1.62e42fefa39efp-1, LOG_F[p1] + p);
+ return result;
+}
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_UTILS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 5fb82cd469451..d3b25aa6ba36a 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1894,6 +1894,7 @@ add_object_library(
common_constants.cpp
DEPENDS
libc.src.__support.math.exp_constants
+ libc.src.__support.math.acosh_float_constants
libc.src.__support.number_pair
)
@@ -3759,7 +3760,7 @@ add_object_library(
DEPENDS
.common_constants
libc.src.__support.math.exp_utils
- libc.src.__support.math.exp10f_utils
+ libc.src.__support.math.acoshf_utils
libc.src.__support.macros.properties.cpu_features
libc.src.errno.errno
)
@@ -3869,12 +3870,7 @@ add_entrypoint_object(
../acoshf.h
DEPENDS
.explogxf
- libc.src.__support.FPUtil.fenv_impl
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.FPUtil.sqrt
- libc.src.__support.macros.optimization
+ libc.src.__support.math.acoshf
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/acoshf.cpp b/libc/src/math/generic/acoshf.cpp
index c4927fa27a84b..5c04583650e62 100644
--- a/libc/src/math/generic/acoshf.cpp
+++ b/libc/src/math/generic/acoshf.cpp
@@ -7,73 +7,11 @@
//===----------------------------------------------------------------------===//
#include "src/math/acoshf.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/sqrt.h"
-#include "src/__support/macros/config.h"
-#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
-#include "src/math/generic/common_constants.h"
-#include "src/math/generic/explogxf.h"
-namespace LIBC_NAMESPACE_DECL {
-
-LLVM_LIBC_FUNCTION(float, acoshf, (float x)) {
- using FPBits_t = typename fputil::FPBits<float>;
- FPBits_t xbits(x);
-
- if (LIBC_UNLIKELY(x <= 1.0f)) {
- if (x == 1.0f)
- return 0.0f;
- // x < 1.
- fputil::set_errno_if_required(EDOM);
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits_t::quiet_nan().get_val();
- }
+#include "src/__support/math/acoshf.h"
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- uint32_t x_u = xbits.uintval();
- if (LIBC_UNLIKELY(x_u >= 0x4f8ffb03)) {
- if (LIBC_UNLIKELY(xbits.is_inf_or_nan()))
- return x;
-
- // Helper functions to set results for exceptional cases.
- auto round_result_slightly_down = [](float r) -> float {
- volatile float tmp = r;
- tmp = tmp - 0x1.0p-25f;
- return tmp;
- };
- auto round_result_slightly_up = [](float r) -> float {
- volatile float tmp = r;
- tmp = tmp + 0x1.0p-25f;
- return tmp;
- };
-
- switch (x_u) {
- case 0x4f8ffb03: // x = 0x1.1ff606p32f
- return round_result_slightly_up(0x1.6fdd34p4f);
- case 0x5c569e88: // x = 0x1.ad3d1p57f
- return round_result_slightly_up(0x1.45c146p5f);
- case 0x5e68984e: // x = 0x1.d1309cp61f
- return round_result_slightly_up(0x1.5c9442p5f);
- case 0x655890d3: // x = 0x1.b121a6p75f
- return round_result_slightly_down(0x1.a9a3f2p5f);
- case 0x6eb1a8ec: // x = 0x1.6351d8p94f
- return round_result_slightly_down(0x1.08b512p6f);
- case 0x7997f30a: // x = 0x1.2fe614p116f
- return round_result_slightly_up(0x1.451436p6f);
- }
- }
-#else
- if (LIBC_UNLIKELY(xbits.is_inf_or_nan()))
- return x;
-#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+namespace LIBC_NAMESPACE_DECL {
- double x_d = static_cast<double>(x);
- // acosh(x) = log(x + sqrt(x^2 - 1))
- return static_cast<float>(log_eval(
- x_d + fputil::sqrt<double>(fputil::multiply_add(x_d, x_d, -1.0))));
-}
+LLVM_LIBC_FUNCTION(float, acoshf, (float x)) { return math::acoshf(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp
index 4dcf84d00ad50..42e3ff0deb348 100644
--- a/libc/src/math/generic/common_constants.cpp
+++ b/libc/src/math/generic/common_constants.cpp
@@ -51,52 +51,6 @@ const float ONE_OVER_F_FLOAT[128] = {
0x1.08421p-1f, 0x1.07326p-1f, 0x1.0624dep-1f, 0x1.05198p-1f,
0x1.041042p-1f, 0x1.03091cp-1f, 0x1.020408p-1f, 0x1.010102p-1f};
-// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127.
-const double ONE_OVER_F[128] = {
- 0x1.0000000000000p+0, 0x1.fc07f01fc07f0p-1, 0x1.f81f81f81f820p-1,
- 0x1.f44659e4a4271p-1, 0x1.f07c1f07c1f08p-1, 0x1.ecc07b301ecc0p-1,
- 0x1.e9131abf0b767p-1, 0x1.e573ac901e574p-1, 0x1.e1e1e1e1e1e1ep-1,
- 0x1.de5d6e3f8868ap-1, 0x1.dae6076b981dbp-1, 0x1.d77b654b82c34p-1,
- 0x1.d41d41d41d41dp-1, 0x1.d0cb58f6ec074p-1, 0x1.cd85689039b0bp-1,
- 0x1.ca4b3055ee191p-1, 0x1.c71c71c71c71cp-1, 0x1.c3f8f01c3f8f0p-1,
- 0x1.c0e070381c0e0p-1, 0x1.bdd2b899406f7p-1, 0x1.bacf914c1bad0p-1,
- 0x1.b7d6c3dda338bp-1, 0x1.b4e81b4e81b4fp-1, 0x1.b2036406c80d9p-1,
- 0x1.af286bca1af28p-1, 0x1.ac5701ac5701bp-1, 0x1.a98ef606a63bep-1,
- 0x1.a6d01a6d01a6dp-1, 0x1.a41a41a41a41ap-1, 0x1.a16d3f97a4b02p-1,
- 0x1.9ec8e951033d9p-1, 0x1.9c2d14ee4a102p-1, 0x1.999999999999ap-1,
- 0x1.970e4f80cb872p-1, 0x1.948b0fcd6e9e0p-1, 0x1.920fb49d0e229p-1,
- 0x1.8f9c18f9c18fap-1, 0x1.8d3018d3018d3p-1, 0x1.8acb90f6bf3aap-1,
- 0x1.886e5f0abb04ap-1, 0x1.8618618618618p-1, 0x1.83c977ab2beddp-1,
- 0x1.8181818181818p-1, 0x1.7f405fd017f40p-1, 0x1.7d05f417d05f4p-1,
- 0x1.7ad2208e0ecc3p-1, 0x1.78a4c8178a4c8p-1, 0x1.767dce434a9b1p-1,
- 0x1.745d1745d1746p-1, 0x1.724287f46debcp-1, 0x1.702e05c0b8170p-1,
- 0x1.6e1f76b4337c7p-1, 0x1.6c16c16c16c17p-1, 0x1.6a13cd1537290p-1,
- 0x1.6816816816817p-1, 0x1.661ec6a5122f9p-1, 0x1.642c8590b2164p-1,
- 0x1.623fa77016240p-1, 0x1.6058160581606p-1, 0x1.5e75bb8d015e7p-1,
- 0x1.5c9882b931057p-1, 0x1.5ac056b015ac0p-1, 0x1.58ed2308158edp-1,
- 0x1.571ed3c506b3ap-1, 0x1.5555555555555p-1, 0x1.5390948f40febp-1,
- 0x1.51d07eae2f815p-1, 0x1.5015015015015p-1, 0x1.4e5e0a72f0539p-1,
- 0x1.4cab88725af6ep-1, 0x1.4afd6a052bf5bp-1, 0x1.49539e3b2d067p-1,
- 0x1.47ae147ae147bp-1, 0x1.460cbc7f5cf9ap-1, 0x1.446f86562d9fbp-1,
- 0x1.42d6625d51f87p-1, 0x1.4141414141414p-1, 0x1.3fb013fb013fbp-1,
- 0x1.3e22cbce4a902p-1, 0x1.3c995a47babe7p-1, 0x1.3b13b13b13b14p-1,
- 0x1.3991c2c187f63p-1, 0x1.3813813813814p-1, 0x1.3698df3de0748p-1,
- 0x1.3521cfb2b78c1p-1, 0x1.33ae45b57bcb2p-1, 0x1.323e34a2b10bfp-1,
- 0x1.30d190130d190p-1, 0x1.2f684bda12f68p-1, 0x1.2e025c04b8097p-1,
- 0x1.2c9fb4d812ca0p-1, 0x1.2b404ad012b40p-1, 0x1.29e4129e4129ep-1,
- 0x1.288b01288b013p-1, 0x1.27350b8812735p-1, 0x1.25e22708092f1p-1,
- 0x1.2492492492492p-1, 0x1.23456789abcdfp-1, 0x1.21fb78121fb78p-1,
- 0x1.20b470c67c0d9p-1, 0x1.1f7047dc11f70p-1, 0x1.1e2ef3b3fb874p-1,
- 0x1.1cf06ada2811dp-1, 0x1.1bb4a4046ed29p-1, 0x1.1a7b9611a7b96p-1,
- 0x1.19453808ca29cp-1, 0x1.1811811811812p-1, 0x1.16e0689427379p-1,
- 0x1.15b1e5f75270dp-1, 0x1.1485f0e0acd3bp-1, 0x1.135c81135c811p-1,
- 0x1.12358e75d3033p-1, 0x1.1111111111111p-1, 0x1.0fef010fef011p-1,
- 0x1.0ecf56be69c90p-1, 0x1.0db20a88f4696p-1, 0x1.0c9714fbcda3bp-1,
- 0x1.0b7e6ec259dc8p-1, 0x1.0a6810a6810a7p-1, 0x1.0953f39010954p-1,
- 0x1.0842108421084p-1, 0x1.073260a47f7c6p-1, 0x1.0624dd2f1a9fcp-1,
- 0x1.05197f7d73404p-1, 0x1.0410410410410p-1, 0x1.03091b51f5e1ap-1,
- 0x1.0204081020408p-1, 0x1.0101010101010p-1};
-
// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127,
// computed and stored as float precision constants.
// Generated by Sollya with the following commands:
@@ -136,52 +90,6 @@ const float LOG_F_FLOAT[128] = {
0x1.52a2d2p-1f, 0x1.54b246p-1f, 0x1.56bf9ep-1f, 0x1.58cadcp-1f,
0x1.5ad404p-1f, 0x1.5cdb1ep-1f, 0x1.5ee02ap-1f, 0x1.60e33p-1f};
-// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127.
-const double LOG_F[128] = {
- 0x0.0000000000000p+0, 0x1.fe02a6b106788p-8, 0x1.fc0a8b0fc03e3p-7,
- 0x1.7b91b07d5b11ap-6, 0x1.f829b0e783300p-6, 0x1.39e87b9febd5fp-5,
- 0x1.77458f632dcfcp-5, 0x1.b42dd711971bep-5, 0x1.f0a30c01162a6p-5,
- 0x1.16536eea37ae0p-4, 0x1.341d7961bd1d0p-4, 0x1.51b073f06183fp-4,
- 0x1.6f0d28ae56b4bp-4, 0x1.8c345d6319b20p-4, 0x1.a926d3a4ad563p-4,
- 0x1.c5e548f5bc743p-4, 0x1.e27076e2af2e5p-4, 0x1.fec9131dbeabap-4,
- 0x1.0d77e7cd08e59p-3, 0x1.1b72ad52f67a0p-3, 0x1.29552f81ff523p-3,
- 0x1.371fc201e8f74p-3, 0x1.44d2b6ccb7d1ep-3, 0x1.526e5e3a1b437p-3,
- 0x1.5ff3070a793d3p-3, 0x1.6d60fe719d21cp-3, 0x1.7ab890210d909p-3,
- 0x1.87fa06520c910p-3, 0x1.9525a9cf456b4p-3, 0x1.a23bc1fe2b563p-3,
- 0x1.af3c94e80bff2p-3, 0x1.bc286742d8cd6p-3, 0x1.c8ff7c79a9a21p-3,
- 0x1.d5c216b4fbb91p-3, 0x1.e27076e2af2e5p-3, 0x1.ef0adcbdc5936p-3,
- 0x1.fb9186d5e3e2ap-3, 0x1.0402594b4d040p-2, 0x1.0a324e27390e3p-2,
- 0x1.1058bf9ae4ad5p-2, 0x1.1675cababa60ep-2, 0x1.1c898c16999fap-2,
- 0x1.22941fbcf7965p-2, 0x1.2895a13de86a3p-2, 0x1.2e8e2bae11d30p-2,
- 0x1.347dd9a987d54p-2, 0x1.3a64c556945e9p-2, 0x1.404308686a7e3p-2,
- 0x1.4618bc21c5ec2p-2, 0x1.4be5f957778a0p-2, 0x1.51aad872df82dp-2,
- 0x1.5767717455a6cp-2, 0x1.5d1bdbf5809cap-2, 0x1.62c82f2b9c795p-2,
- 0x1.686c81e9b14aep-2, 0x1.6e08eaa2ba1e3p-2, 0x1.739d7f6bbd006p-2,
- 0x1.792a55fdd47a2p-2, 0x1.7eaf83b82afc3p-2, 0x1.842d1da1e8b17p-2,
- 0x1.89a3386c1425ap-2, 0x1.8f11e873662c7p-2, 0x1.947941c2116fap-2,
- 0x1.99d958117e08ap-2, 0x1.9f323ecbf984bp-2, 0x1.a484090e5bb0ap-2,
- 0x1.a9cec9a9a0849p-2, 0x1.af1293247786bp-2, 0x1.b44f77bcc8f62p-2,
- 0x1.b9858969310fbp-2, 0x1.beb4d9da71b7bp-2, 0x1.c3dd7a7cdad4dp-2,
- 0x1.c8ff7c79a9a21p-2, 0x1.ce1af0b85f3ebp-2, 0x1.d32fe7e00ebd5p-2,
- 0x1.d83e7258a2f3ep-2, 0x1.dd46a04c1c4a0p-2, 0x1.e24881a7c6c26p-2,
- 0x1.e744261d68787p-2, 0x1.ec399d2468cc0p-2, 0x1.f128f5faf06ecp-2,
- 0x1.f6123fa7028acp-2, 0x1.faf588f78f31ep-2, 0x1.ffd2e0857f498p-2,
- 0x1.02552a5a5d0fep-1, 0x1.04bdf9da926d2p-1, 0x1.0723e5c1cdf40p-1,
- 0x1.0986f4f573520p-1, 0x1.0be72e4252a82p-1, 0x1.0e44985d1cc8bp-1,
- 0x1.109f39e2d4c96p-1, 0x1.12f719593efbcp-1, 0x1.154c3d2f4d5e9p-1,
- 0x1.179eabbd899a0p-1, 0x1.19ee6b467c96ep-1, 0x1.1c3b81f713c24p-1,
- 0x1.1e85f5e7040d0p-1, 0x1.20cdcd192ab6dp-1, 0x1.23130d7bebf42p-1,
- 0x1.2555bce98f7cbp-1, 0x1.2795e1289b11ap-1, 0x1.29d37fec2b08ap-1,
- 0x1.2c0e9ed448e8bp-1, 0x1.2e47436e40268p-1, 0x1.307d7334f10bep-1,
- 0x1.32b1339121d71p-1, 0x1.34e289d9ce1d3p-1, 0x1.37117b54747b5p-1,
- 0x1.393e0d3562a19p-1, 0x1.3b68449fffc22p-1, 0x1.3d9026a7156fap-1,
- 0x1.3fb5b84d16f42p-1, 0x1.41d8fe84672aep-1, 0x1.43f9fe2f9ce67p-1,
- 0x1.4618bc21c5ec2p-1, 0x1.48353d1ea88dfp-1, 0x1.4a4f85db03ebbp-1,
- 0x1.4c679afccee39p-1, 0x1.4e7d811b75bb0p-1, 0x1.50913cc01686bp-1,
- 0x1.52a2d265bc5aap-1, 0x1.54b2467999497p-1, 0x1.56bf9d5b3f399p-1,
- 0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1,
- 0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1};
-
// Range reduction constants for logarithms.
// r(0) = 1, r(127) = 0.5
// r(k) = 2^-8 * ceil(2^8 * (1 - 2^-8) / (1 + k*2^-7))
diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h
index 291816a7889ad..72b1d564ca472 100644
--- a/libc/src/math/generic/common_constants.h
+++ b/libc/src/math/generic/common_constants.h
@@ -11,6 +11,7 @@
#include "src/__support/FPUtil/triple_double.h"
#include "src/__support/macros/config.h"
+#include "src/__support/math/acosh_float_constants.h"
#include "src/__support/math/exp_constants.h"
#include "src/__support/number_pair.h"
@@ -20,16 +21,10 @@ namespace LIBC_NAMESPACE_DECL {
// computed and stored as float precision constants.
extern const float ONE_OVER_F_FLOAT[128];
-// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127.
-extern const double ONE_OVER_F[128];
-
// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127,
// computed and stored as float precision constants.
extern const float LOG_F_FLOAT[128];
-// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127.
-extern const double LOG_F[128];
-
// Lookup table for range reduction constants r for logarithms.
extern const float R[128];
diff --git a/libc/src/math/generic/explogxf.h b/libc/src/math/generic/explogxf.h
index d9f39a0d6080f..94a977e2b98a5 100644
--- a/libc/src/math/generic/explogxf.h
+++ b/libc/src/math/generic/explogxf.h
@@ -13,6 +13,7 @@
#include "src/__support/common.h"
#include "src/__support/macros/properties/cpu_features.h"
+#include "src/__support/math/acoshf_utils.h"
#include "src/__support/math/exp10f_utils.h"
#include "src/__support/math/exp_utils.h"
@@ -187,41 +188,6 @@ LIBC_INLINE static float log_eval_f(float x) {
return result;
}
-// x should be positive, normal finite value
-LIBC_INLINE static double log_eval(double x) {
- // For x = 2^ex * (1 + mx)
- // log(x) = ex * log(2) + log(1 + mx)
- using FPB = fputil::FPBits<double>;
- FPB bs(x);
-
- double ex = static_cast<double>(bs.get_exponent());
-
- // p1 is the leading 7 bits of mx, i.e.
- // p1 * 2^(-7) <= m_x < (p1 + 1) * 2^(-7).
- int p1 = static_cast<int>(bs.get_mantissa() >> (FPB::FRACTION_LEN - 7));
-
- // Set bs to (1 + (mx - p1*2^(-7))
- bs.set_uintval(bs.uintval() & (FPB::FRACTION_MASK >> 7));
- bs.set_biased_exponent(FPB::EXP_BIAS);
- // dx = (mx - p1*2^(-7)) / (1 + p1*2^(-7)).
- double dx = (bs.get_val() - 1.0) * ONE_OVER_F[p1];
-
- // Minimax polynomial of log(1 + dx) generated by Sollya with:
- // > P = fpminimax(log(1 + x)/x, 6, [|D...|], [0, 2^-7]);
- const double COEFFS[6] = {-0x1.ffffffffffffcp-2, 0x1.5555555552ddep-2,
- -0x1.ffffffefe562dp-3, 0x1.9999817d3a50fp-3,
- -0x1.554317b3f67a5p-3, 0x1.1dc5c45e09c18p-3};
- double dx2 = dx * dx;
- double c1 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]);
- double c2 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]);
- double c3 = fputil::multiply_add(dx, COEFFS[5], COEFFS[4]);
-
- double p = fputil::polyeval(dx2, dx, c1, c2, c3);
- double result =
- fputil::multiply_add(ex, /*log(2)*/ 0x1.62e42fefa39efp-1, LOG_F[p1] + p);
- return result;
-}
-
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 74e331c0171e4..4df75c5b9ae5d 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -1920,6 +1920,7 @@ libc_support_library(
hdrs = ["src/math/generic/common_constants.h"],
deps = [
":__support_math_exp_constants",
+ ":__support_math_acosh_float_constants",
":__support_number_pair",
],
)
@@ -2005,6 +2006,7 @@ libc_support_library(
":__support_fputil_nearest_integer",
":__support_math_exp_utils",
":__support_math_exp10f_utils",
+ ":__support_math_acoshf_utils",
":__support_macros_properties_cpu_features",
":common_constants",
],
@@ -2108,6 +2110,38 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_acosh_float_constants",
+ hdrs = ["src/__support/math/acosh_float_constants.h"],
+ deps = [
+ ":__support_macros_config",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_acoshf_utils",
+ hdrs = ["src/__support/math/acoshf_utils.h"],
+ deps = [
+ ":__support_math_acosh_float_constants",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_polyeval",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_acoshf",
+ hdrs = ["src/__support/math/acoshf.h"],
+ deps = [
+ ":__support_math_acoshf_utils",
+ ":__support_fputil_fenv_impl",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_sqrt",
+ ":__support_macros_optimization",
+ ],
+)
+
libc_support_library(
name = "__support_math_asin_utils",
hdrs = ["src/__support/math/asin_utils.h"],
@@ -2644,13 +2678,7 @@ libc_math_function(
libc_math_function(
name = "acoshf",
additional_deps = [
- ":__support_fputil_fma",
- ":__support_fputil_multiply_add",
- ":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
- ":__support_fputil_sqrt",
- ":__support_macros_optimization",
- ":common_constants",
+ ":__support_math_acoshf",
":explogxf",
],
)
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