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authorPeter Collingbourne <peter@pcc.me.uk>2025-07-18 13:26:00 -0700
committerPeter Collingbourne <peter@pcc.me.uk>2025-07-18 13:26:00 -0700
commit9bf3524731070cadc6175707314f3b6ca37190d5 (patch)
tree86dcab7604336b01ae938fe81062c29ff69efba8 /libc/src
parent3a84c15cc13b6daf8e812592898ab6c7f19091a9 (diff)
parent4f43f0606c3d7e1ce6d069583b5e59f036e112ce (diff)
Created using spr 1.3.6-beta.1
Diffstat (limited to 'libc/src')
-rw-r--r--libc/src/CMakeLists.txt1
-rw-r--r--libc/src/__support/CMakeLists.txt2
-rw-r--r--libc/src/__support/FPUtil/ManipulationFunctions.h2
-rw-r--r--libc/src/__support/FPUtil/PolyEval.h2
-rw-r--r--libc/src/__support/FPUtil/double_double.h4
-rw-r--r--libc/src/__support/FPUtil/multiply_add.h2
-rw-r--r--libc/src/__support/FPUtil/nearest_integer.h4
-rw-r--r--libc/src/__support/macros/properties/architectures.h2
-rw-r--r--libc/src/__support/math/CMakeLists.txt177
-rw-r--r--libc/src/__support/math/exp.h448
-rw-r--r--libc/src/__support/math/exp10.h501
-rw-r--r--libc/src/__support/math/exp10_float16_constants.h43
-rw-r--r--libc/src/__support/math/exp10f.h (renamed from libc/src/math/generic/exp10f_impl.h)17
-rw-r--r--libc/src/__support/math/exp10f16.h141
-rw-r--r--libc/src/__support/math/exp10f16_utils.h64
-rw-r--r--libc/src/__support/math/exp10f_utils.h157
-rw-r--r--libc/src/__support/math/exp_constants.h174
-rw-r--r--libc/src/__support/math/exp_utils.h72
-rw-r--r--libc/src/__support/math/expf16_utils.h2
-rw-r--r--libc/src/__support/math/frexpf.h28
-rw-r--r--libc/src/__support/math/frexpf128.h34
-rw-r--r--libc/src/__support/math/frexpf16.h34
-rw-r--r--libc/src/__support/math/ldexpf.h28
-rw-r--r--libc/src/__support/math/ldexpf128.h34
-rw-r--r--libc/src/__support/math/ldexpf16.h34
-rw-r--r--libc/src/__support/wchar/CMakeLists.txt14
-rw-r--r--libc/src/__support/wchar/character_converter.cpp11
-rw-r--r--libc/src/__support/wchar/character_converter.h4
-rw-r--r--libc/src/__support/wchar/string_converter.h116
-rw-r--r--libc/src/math/CMakeLists.txt2
-rw-r--r--libc/src/math/generic/CMakeLists.txt126
-rw-r--r--libc/src/math/generic/atanhf.cpp1
-rw-r--r--libc/src/math/generic/common_constants.cpp157
-rw-r--r--libc/src/math/generic/common_constants.h7
-rw-r--r--libc/src/math/generic/coshf.cpp2
-rw-r--r--libc/src/math/generic/exp.cpp429
-rw-r--r--libc/src/math/generic/exp10.cpp485
-rw-r--r--libc/src/math/generic/exp10f.cpp7
-rw-r--r--libc/src/math/generic/exp10f16.cpp122
-rw-r--r--libc/src/math/generic/exp10m1f16.cpp2
-rw-r--r--libc/src/math/generic/explogxf.cpp75
-rw-r--r--libc/src/math/generic/explogxf.h235
-rw-r--r--libc/src/math/generic/expxf16.h56
-rw-r--r--libc/src/math/generic/frexpf.cpp7
-rw-r--r--libc/src/math/generic/frexpf128.cpp7
-rw-r--r--libc/src/math/generic/frexpf16.cpp7
-rw-r--r--libc/src/math/generic/ldexpf.cpp6
-rw-r--r--libc/src/math/generic/ldexpf128.cpp7
-rw-r--r--libc/src/math/generic/ldexpf16.cpp7
-rw-r--r--libc/src/math/generic/powf.cpp7
-rw-r--r--libc/src/math/generic/sinhf.cpp1
-rw-r--r--libc/src/math/generic/tanpif.cpp106
-rw-r--r--libc/src/math/tanpif.h20
-rw-r--r--libc/src/string/memory_utils/CMakeLists.txt2
-rw-r--r--libc/src/string/memory_utils/arm/common.h55
-rw-r--r--libc/src/string/memory_utils/arm/inline_memcpy.h193
-rw-r--r--libc/src/string/memory_utils/arm/inline_memset.h156
-rw-r--r--libc/src/string/memory_utils/inline_memset.h6
-rw-r--r--libc/src/time/baremetal/CMakeLists.txt11
-rw-r--r--libc/src/time/baremetal/clock.cpp45
-rw-r--r--libc/src/wchar/CMakeLists.txt44
-rw-r--r--libc/src/wchar/wcstol.cpp30
-rw-r--r--libc/src/wchar/wcstol.h22
-rw-r--r--libc/src/wchar/wcstoll.cpp30
-rw-r--r--libc/src/wchar/wcstoll.h22
-rw-r--r--libc/src/wchar/wcstoul.cpp30
-rw-r--r--libc/src/wchar/wcstoul.h22
-rw-r--r--libc/src/wchar/wcstoull.cpp30
-rw-r--r--libc/src/wchar/wcstoull.h22
-rw-r--r--libc/src/wctype/CMakeLists.txt9
-rw-r--r--libc/src/wctype/iswalpha.cpp19
-rw-r--r--libc/src/wctype/iswalpha.h21
72 files changed, 3005 insertions, 1797 deletions
diff --git a/libc/src/CMakeLists.txt b/libc/src/CMakeLists.txt
index a665253c4cc0..d7a1e1f49e6f 100644
--- a/libc/src/CMakeLists.txt
+++ b/libc/src/CMakeLists.txt
@@ -17,6 +17,7 @@ add_subdirectory(strings)
add_subdirectory(time)
add_subdirectory(unistd)
add_subdirectory(wchar)
+add_subdirectory(wctype)
if(${LIBC_TARGET_OS} STREQUAL "linux")
add_subdirectory(dirent)
diff --git a/libc/src/__support/CMakeLists.txt b/libc/src/__support/CMakeLists.txt
index 294d68474bd5..37a27cc9b700 100644
--- a/libc/src/__support/CMakeLists.txt
+++ b/libc/src/__support/CMakeLists.txt
@@ -406,7 +406,7 @@ add_subdirectory(time)
# Requires access to uchar header which is not on macos
# Therefore, cannot currently build this on macos in overlay mode
-if(NOT(LIBC_TARGET_OS_IS_DARWIN))
+if(NOT (LIBC_TARGET_OS_IS_DARWIN))
add_subdirectory(wchar)
endif()
diff --git a/libc/src/__support/FPUtil/ManipulationFunctions.h b/libc/src/__support/FPUtil/ManipulationFunctions.h
index 9c10011ccd20..ea9ee5a57c36 100644
--- a/libc/src/__support/FPUtil/ManipulationFunctions.h
+++ b/libc/src/__support/FPUtil/ManipulationFunctions.h
@@ -29,7 +29,7 @@ namespace LIBC_NAMESPACE_DECL {
namespace fputil {
template <typename T, cpp::enable_if_t<cpp::is_floating_point_v<T>, int> = 0>
-LIBC_INLINE T frexp(T x, int &exp) {
+LIBC_INLINE constexpr T frexp(T x, int &exp) {
FPBits<T> bits(x);
if (bits.is_inf_or_nan()) {
#ifdef LIBC_FREXP_INF_NAN_EXPONENT
diff --git a/libc/src/__support/FPUtil/PolyEval.h b/libc/src/__support/FPUtil/PolyEval.h
index 41104620ed61..7bec4e30a996 100644
--- a/libc/src/__support/FPUtil/PolyEval.h
+++ b/libc/src/__support/FPUtil/PolyEval.h
@@ -37,7 +37,7 @@ LIBC_INLINE cpp::enable_if_t<(sizeof(T) <= sizeof(void *)), T> polyeval(T,
}
template <typename T, typename... Ts>
-LIBC_INLINE cpp::enable_if_t<(sizeof(T) > sizeof(void *)), T>
+LIBC_INLINE static constexpr cpp::enable_if_t<(sizeof(T) > sizeof(void *)), T>
polyeval(const T &x, const T &a0, const Ts &...a) {
return multiply_add(x, polyeval(x, a...), a0);
}
diff --git a/libc/src/__support/FPUtil/double_double.h b/libc/src/__support/FPUtil/double_double.h
index c27885aadc02..8e54e845de49 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/FPUtil/multiply_add.h b/libc/src/__support/FPUtil/multiply_add.h
index 8260702e2c9f..1469326c9ba3 100644
--- a/libc/src/__support/FPUtil/multiply_add.h
+++ b/libc/src/__support/FPUtil/multiply_add.h
@@ -29,7 +29,7 @@ multiply_add(const T &x, const T &y, const T &z) {
}
template <typename T>
-LIBC_INLINE cpp::enable_if_t<(sizeof(T) <= sizeof(void *)), T>
+LIBC_INLINE static constexpr cpp::enable_if_t<(sizeof(T) <= sizeof(void *)), T>
multiply_add(T x, T y, T z) {
return x * y + z;
}
diff --git a/libc/src/__support/FPUtil/nearest_integer.h b/libc/src/__support/FPUtil/nearest_integer.h
index 768f13414bd9..fabd309bd352 100644
--- a/libc/src/__support/FPUtil/nearest_integer.h
+++ b/libc/src/__support/FPUtil/nearest_integer.h
@@ -40,7 +40,7 @@ namespace fputil {
// Notice that for AARCH64 and x86-64 with SSE4.2 support, we will use their
// corresponding rounding instruction instead. And in those cases, the results
// are rounded to the nearest integer, tie-to-even.
-LIBC_INLINE float nearest_integer(float x) {
+LIBC_INLINE static constexpr float nearest_integer(float x) {
if (x < 0x1p24f && x > -0x1p24f) {
float r = x < 0 ? (x - 0x1.0p23f) + 0x1.0p23f : (x + 0x1.0p23f) - 0x1.0p23f;
float diff = x - r;
@@ -56,7 +56,7 @@ LIBC_INLINE float nearest_integer(float x) {
return x;
}
-LIBC_INLINE double nearest_integer(double x) {
+LIBC_INLINE static constexpr double nearest_integer(double x) {
if (x < 0x1p53 && x > -0x1p53) {
double r = x < 0 ? (x - 0x1.0p52) + 0x1.0p52 : (x + 0x1.0p52) - 0x1.0p52;
double diff = x - r;
diff --git a/libc/src/__support/macros/properties/architectures.h b/libc/src/__support/macros/properties/architectures.h
index c88956ff4114..ecc93196be28 100644
--- a/libc/src/__support/macros/properties/architectures.h
+++ b/libc/src/__support/macros/properties/architectures.h
@@ -21,7 +21,7 @@
#define LIBC_TARGET_ARCH_IS_GPU
#endif
-#if defined(__pnacl__) || defined(__CLR_VER) || defined(LIBC_TARGET_ARCH_IS_GPU)
+#if defined(__CLR_VER) || defined(LIBC_TARGET_ARCH_IS_GPU)
#define LIBC_TARGET_ARCH_IS_VM
#endif
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 4c73fba6613f..77a47c65489d 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -55,3 +55,180 @@ add_header_library(
libc.src.__support.macros.optimization
libc.include.llvm-libc-macros.float16_macros
)
+
+add_header_library(
+ frexpf128
+ HDRS
+ frexpf128.h
+ DEPENDS
+ libc.src.__support.macros.properties.types
+ libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_header_library(
+ frexpf16
+ HDRS
+ frexpf16.h
+ DEPENDS
+ libc.src.__support.macros.config
+ libc.src.__support.macros.properties.types
+ libc.src.__support.FPUtil.manipulation_functions
+)
+
+add_header_library(
+ frexpf
+ HDRS
+ frexpf.h
+ 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
+)
+
+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
+)
+
+add_header_library(
+ ldexpf
+ HDRS
+ ldexpf.h
+ 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
+)
+
+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
+)
+
+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
+)
+
+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/exp.h b/libc/src/__support/math/exp.h
new file mode 100644
index 000000000000..a538df1e825d
--- /dev/null
+++ b/libc/src/__support/math/exp.h
@@ -0,0 +1,448 @@
+//===-- 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 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 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 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 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 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 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 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/exp10.h b/libc/src/__support/math/exp10.h
new file mode 100644
index 000000000000..88748523deb3
--- /dev/null
+++ b/libc/src/__support/math/exp10.h
@@ -0,0 +1,501 @@
+//===-- 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)
+static 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
+static constexpr double MLOG10_2_EXP2_M12_HI = -0x1.3441350ap-14;
+static constexpr double MLOG10_2_EXP2_M12_MID = 0x1.0c0219dc1da99p-51;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr double MLOG10_2_EXP2_M12_MID_32 = 0x1.0c0219dcp-51;
+static 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.
+static constexpr double ERR_DD = 0x1.8p-99;
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+// 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 double exp10_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 exp10_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 exp10_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 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 = exp10_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 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 = exp10_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 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 = exp10_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 exp10_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 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 exp10_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 = exp10_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/__support/math/exp10_float16_constants.h b/libc/src/__support/math/exp10_float16_constants.h
new file mode 100644
index 000000000000..f5928db740ee
--- /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/math/generic/exp10f_impl.h b/libc/src/__support/math/exp10f.h
index 975fd01a0a25..807b4f0d6c10 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/exp10f16.h b/libc/src/__support/math/exp10f16.h
new file mode 100644
index 000000000000..0d8b12534884
--- /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 000000000000..bffb81ba606b
--- /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_EXP10F16_UTILS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_UTILS_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_UTILS_H
diff --git a/libc/src/__support/math/exp10f_utils.h b/libc/src/__support/math/exp10f_utils.h
new file mode 100644
index 000000000000..0493e1b993e0
--- /dev/null
+++ b/libc/src/__support/math/exp10f_utils.h
@@ -0,0 +1,157 @@
+//===-- 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);
+ }
+};
+
+// 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/__support/math/exp_constants.h b/libc/src/__support/math/exp_constants.h
new file mode 100644
index 000000000000..1abb4479e084
--- /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, "},");
+// };
+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, "},");
+// };
+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 000000000000..fc9ab10d76cc
--- /dev/null
+++ b/libc/src/__support/math/exp_utils.h
@@ -0,0 +1,72 @@
+//===-- 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/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
+// 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/__support/math/expf16_utils.h b/libc/src/__support/math/expf16_utils.h
index bebb72b09b88..8a2fc9415ab8 100644
--- a/libc/src/__support/math/expf16_utils.h
+++ b/libc/src/__support/math/expf16_utils.h
@@ -47,7 +47,7 @@ struct ExpRangeReduction {
float exp_lo;
};
-static constexpr ExpRangeReduction exp_range_reduction(float16 x) {
+[[maybe_unused]] static ExpRangeReduction exp_range_reduction(float16 x) {
// For -18 < x < 12, to compute exp(x), we perform the following range
// reduction: find hi, mid, lo, such that:
// x = hi + mid + lo, in which
diff --git a/libc/src/__support/math/frexpf.h b/libc/src/__support/math/frexpf.h
new file mode 100644
index 000000000000..4d2f4948f2af
--- /dev/null
+++ b/libc/src/__support/math/frexpf.h
@@ -0,0 +1,28 @@
+//===-- Implementation header for frexpf ------------------------*- 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_FREXPF_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_FREXPF_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 frexpf(float x, int *exp) {
+ return fputil::frexp(x, *exp);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_FREXPF_H
diff --git a/libc/src/__support/math/frexpf128.h b/libc/src/__support/math/frexpf128.h
new file mode 100644
index 000000000000..2fd5bc4318e2
--- /dev/null
+++ b/libc/src/__support/math/frexpf128.h
@@ -0,0 +1,34 @@
+//===-- Implementation header for expf --------------------------*- 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_FREXPF128_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_FREXPF128_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 frexpf128(float128 x, int *exp) {
+ return fputil::frexp(x, *exp);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT128
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_FREXPF128_H
diff --git a/libc/src/__support/math/frexpf16.h b/libc/src/__support/math/frexpf16.h
new file mode 100644
index 000000000000..8deeba0f43e3
--- /dev/null
+++ b/libc/src/__support/math/frexpf16.h
@@ -0,0 +1,34 @@
+//===-- Implementation header for frexpf16 ----------------------*- 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_FREXPF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_FREXPF16_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 frexpf16(float16 x, int *exp) {
+ return fputil::frexp(x, *exp);
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_FREXPF16_H
diff --git a/libc/src/__support/math/ldexpf.h b/libc/src/__support/math/ldexpf.h
new file mode 100644
index 000000000000..3a5ec1d47133
--- /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/__support/math/ldexpf128.h b/libc/src/__support/math/ldexpf128.h
new file mode 100644
index 000000000000..362583093b2f
--- /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/__support/math/ldexpf16.h b/libc/src/__support/math/ldexpf16.h
new file mode 100644
index 000000000000..fbead87d909a
--- /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/__support/wchar/CMakeLists.txt b/libc/src/__support/wchar/CMakeLists.txt
index d3fb58ed0c71..802441d37fe9 100644
--- a/libc/src/__support/wchar/CMakeLists.txt
+++ b/libc/src/__support/wchar/CMakeLists.txt
@@ -6,6 +6,19 @@ add_header_library(
libc.hdr.types.char32_t
)
+add_header_library(
+ string_converter
+ HDRS
+ string_converter.h
+ DEPENDS
+ libc.hdr.types.char8_t
+ libc.hdr.types.char32_t
+ libc.hdr.types.size_t
+ libc.src.__support.error_or
+ .mbstate
+ .character_converter
+)
+
add_object_library(
character_converter
HDRS
@@ -16,6 +29,7 @@ add_object_library(
libc.hdr.errno_macros
libc.hdr.types.char8_t
libc.hdr.types.char32_t
+ libc.hdr.types.size_t
libc.src.__support.error_or
libc.src.__support.math_extras
.mbstate
diff --git a/libc/src/__support/wchar/character_converter.cpp b/libc/src/__support/wchar/character_converter.cpp
index 3cacfa5689e4..15d0f478a18a 100644
--- a/libc/src/__support/wchar/character_converter.cpp
+++ b/libc/src/__support/wchar/character_converter.cpp
@@ -9,6 +9,7 @@
#include "hdr/errno_macros.h"
#include "hdr/types/char32_t.h"
#include "hdr/types/char8_t.h"
+#include "hdr/types/size_t.h"
#include "src/__support/CPP/bit.h"
#include "src/__support/common.h"
#include "src/__support/error_or.h"
@@ -92,6 +93,7 @@ int CharacterConverter::push(char8_t utf8_byte) {
state->bytes_stored++;
return 0;
}
+
// Invalid byte -> reset the state
clear();
return EILSEQ;
@@ -130,6 +132,12 @@ ErrorOr<char32_t> CharacterConverter::pop_utf32() {
return utf32;
}
+size_t CharacterConverter::sizeAsUTF32() {
+ return 1; // a single utf-32 value can fit an entire character
+}
+
+size_t CharacterConverter::sizeAsUTF8() { return state->total_bytes; }
+
ErrorOr<char8_t> CharacterConverter::pop_utf8() {
if (isEmpty())
return Error(-1);
@@ -156,6 +164,9 @@ ErrorOr<char8_t> CharacterConverter::pop_utf8() {
}
state->bytes_stored--;
+ if (state->bytes_stored == 0)
+ clear();
+
return static_cast<char8_t>(output);
}
diff --git a/libc/src/__support/wchar/character_converter.h b/libc/src/__support/wchar/character_converter.h
index d9a63fdc0522..b6d918f2d2ed 100644
--- a/libc/src/__support/wchar/character_converter.h
+++ b/libc/src/__support/wchar/character_converter.h
@@ -11,6 +11,7 @@
#include "hdr/types/char32_t.h"
#include "hdr/types/char8_t.h"
+#include "hdr/types/size_t.h"
#include "src/__support/common.h"
#include "src/__support/error_or.h"
#include "src/__support/wchar/mbstate.h"
@@ -30,6 +31,9 @@ public:
bool isEmpty();
bool isValidState();
+ size_t sizeAsUTF32();
+ size_t sizeAsUTF8();
+
int push(char8_t utf8_byte);
int push(char32_t utf32);
diff --git a/libc/src/__support/wchar/string_converter.h b/libc/src/__support/wchar/string_converter.h
new file mode 100644
index 000000000000..869ebdfc8b39
--- /dev/null
+++ b/libc/src/__support/wchar/string_converter.h
@@ -0,0 +1,116 @@
+//===-- Definition of a class for mbstate_t and conversion -----*-- 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_STRING_CONVERTER_H
+#define LLVM_LIBC_SRC___SUPPORT_STRING_CONVERTER_H
+
+#include "hdr/types/char32_t.h"
+#include "hdr/types/char8_t.h"
+#include "hdr/types/size_t.h"
+#include "src/__support/common.h"
+#include "src/__support/error_or.h"
+#include "src/__support/wchar/character_converter.h"
+#include "src/__support/wchar/mbstate.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace internal {
+
+template <typename T> class StringConverter {
+private:
+ CharacterConverter cr;
+ const T *src;
+ size_t src_len;
+ size_t src_idx;
+
+ // # of pops we are allowed to perform (essentially size of the dest buffer)
+ size_t num_to_write;
+
+ ErrorOr<size_t> pushFullCharacter() {
+ size_t num_pushed;
+ for (num_pushed = 0; !cr.isFull() && src_idx + num_pushed < src_len;
+ ++num_pushed) {
+ int err = cr.push(src[src_idx + num_pushed]);
+ if (err != 0)
+ return Error(err);
+ }
+
+ // if we aren't able to read a full character from the source string
+ if (src_idx + num_pushed == src_len && !cr.isFull()) {
+ src_idx += num_pushed;
+ return Error(-1);
+ }
+
+ return num_pushed;
+ }
+
+public:
+ StringConverter(const T *s, mbstate *ps, size_t dstlen,
+ size_t srclen = SIZE_MAX)
+ : cr(ps), src(s), src_len(srclen), src_idx(0), num_to_write(dstlen) {}
+
+ // TODO: following functions are almost identical
+ // look into templating CharacterConverter pop functions
+ ErrorOr<char32_t> popUTF32() {
+ if (num_to_write == 0)
+ return Error(-1);
+
+ if (cr.isEmpty() || src_idx == 0) {
+ auto src_elements_read = pushFullCharacter();
+ if (!src_elements_read.has_value())
+ return Error(src_elements_read.error());
+
+ if (cr.sizeAsUTF32() > num_to_write) {
+ cr.clear();
+ return Error(-1);
+ }
+
+ src_idx += src_elements_read.value();
+ }
+
+ auto out = cr.pop_utf32();
+ if (out.has_value() && out.value() == L'\0')
+ src_len = src_idx;
+
+ num_to_write--;
+
+ return out;
+ }
+
+ ErrorOr<char8_t> popUTF8() {
+ if (num_to_write == 0)
+ return Error(-1);
+
+ if (cr.isEmpty() || src_idx == 0) {
+ auto src_elements_read = pushFullCharacter();
+ if (!src_elements_read.has_value())
+ return Error(src_elements_read.error());
+
+ if (cr.sizeAsUTF8() > num_to_write) {
+ cr.clear();
+ return Error(-1);
+ }
+
+ src_idx += src_elements_read.value();
+ }
+
+ auto out = cr.pop_utf8();
+ if (out.has_value() && out.value() == '\0')
+ src_len = src_idx;
+
+ num_to_write--;
+
+ return out;
+ }
+
+ size_t getSourceIndex() { return src_idx; }
+};
+
+} // namespace internal
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_STRING_CONVERTER_H
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index b27b0d2b523f..455ad3456573 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -519,6 +519,8 @@ add_math_entrypoint_object(tanf16)
add_math_entrypoint_object(tanh)
add_math_entrypoint_object(tanhf)
add_math_entrypoint_object(tanhf16)
+
+add_math_entrypoint_object(tanpif)
add_math_entrypoint_object(tanpif16)
add_math_entrypoint_object(tgamma)
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 6c3f28f423c7..fb253a450270 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
@@ -607,6 +605,21 @@ add_entrypoint_object(
)
add_entrypoint_object(
+ tanpif
+ SRCS
+ tanpif.cpp
+ HDRS
+ ../tanpif.h
+ DEPENDS
+ .sincosf_utils
+ 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.macros.optimization
+)
+
+add_entrypoint_object(
tanpif16
SRCS
tanpif16.cpp
@@ -1297,20 +1310,7 @@ 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
)
@@ -1455,35 +1455,7 @@ 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.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.__support.math.exp10
libc.src.errno.errno
)
@@ -1494,7 +1466,8 @@ add_entrypoint_object(
HDRS
../exp10f.h
DEPENDS
- .exp10f_impl
+ libc.src.__support.math.exp10f
+ libc.src.errno.errno
)
add_entrypoint_object(
@@ -1504,20 +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(
@@ -1546,7 +1507,6 @@ add_entrypoint_object(
HDRS
../exp10m1f16.h
DEPENDS
- .expxf16
libc.hdr.errno_macros
libc.hdr.fenv_macros
libc.src.__support.FPUtil.cast
@@ -1558,6 +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(
@@ -1631,17 +1592,15 @@ 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
@@ -1744,7 +1703,7 @@ add_entrypoint_object(
HDRS
../frexpf.h
DEPENDS
- libc.src.__support.FPUtil.manipulation_functions
+ libc.src.__support.math.frexpf
)
add_entrypoint_object(
@@ -1764,8 +1723,7 @@ add_entrypoint_object(
HDRS
../frexpf16.h
DEPENDS
- libc.src.__support.macros.properties.types
- libc.src.__support.FPUtil.manipulation_functions
+ libc.src.__support.math.frexpf16
)
add_entrypoint_object(
@@ -1775,8 +1733,7 @@ add_entrypoint_object(
HDRS
../frexpf128.h
DEPENDS
- libc.src.__support.macros.properties.types
- libc.src.__support.FPUtil.manipulation_functions
+ libc.src.__support.math.frexpf128
)
add_entrypoint_object(
@@ -1900,7 +1857,7 @@ add_entrypoint_object(
HDRS
../ldexpf.h
DEPENDS
- libc.src.__support.FPUtil.manipulation_functions
+ libc.src.__support.math.ldexpf
)
add_entrypoint_object(
@@ -1920,8 +1877,7 @@ 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(
@@ -1931,8 +1887,7 @@ 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(
@@ -1942,8 +1897,8 @@ 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(
@@ -3799,24 +3754,15 @@ add_entrypoint_object(
)
#TODO: Add errno include to the hyperbolic functions.
-add_object_library(
+add_header_library(
explogxf
HDRS
explogxf.h
- SRCS
- 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.__support.math.exp10f_utils
+ libc.src.__support.macros.properties.cpu_features
libc.src.errno.errno
)
@@ -3999,6 +3945,7 @@ add_entrypoint_object(
DEPENDS
.explogxf
libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.fenv_impl
libc.src.__support.macros.optimization
)
@@ -5064,10 +5011,11 @@ 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/atanhf.cpp b/libc/src/math/generic/atanhf.cpp
index 2149314d2f67..f6fde766ef78 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/common_constants.cpp b/libc/src/math/generic/common_constants.cpp
index b2c1293c6326..4dcf84d00ad5 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 e65f00284595..291816a7889a 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/exp_constants.h"
#include "src/__support/number_pair.h"
namespace LIBC_NAMESPACE_DECL {
@@ -80,12 +81,6 @@ 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/coshf.cpp b/libc/src/math/generic/coshf.cpp
index c869f7d9dec5..9f87564d524a 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/exp.cpp b/libc/src/math/generic/exp.cpp
index 143800ca078a..dc4d2ca480cb 100644
--- a/libc/src/math/generic/exp.cpp
+++ b/libc/src/math/generic/exp.cpp
@@ -7,434 +7,9 @@
//===----------------------------------------------------------------------===//
#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
-}
+LLVM_LIBC_FUNCTION(double, exp, (double x)) { return math::exp(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/exp10.cpp b/libc/src/math/generic/exp10.cpp
index c464979b092c..5c36d28c166a 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/libc/src/math/generic/exp10f.cpp b/libc/src/math/generic/exp10f.cpp
index 5284c380f52e..b2d4f097bc7c 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/exp10f16.cpp b/libc/src/math/generic/exp10f16.cpp
index 31abf3b4f89b..cb3c8599c923 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 545c47969481..6c2fdbea418d 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/explogxf.cpp b/libc/src/math/generic/explogxf.cpp
deleted file mode 100644
index d38efa026969..000000000000
--- a/libc/src/math/generic/explogxf.cpp
+++ /dev/null
@@ -1,75 +0,0 @@
-//===-- Single-precision general exp/log functions ------------------------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-#include "explogxf.h"
-#include "src/__support/macros/config.h"
-
-namespace LIBC_NAMESPACE_DECL {
-
-// N[Table[Log[2, 1 + x], {x, 0/64, 63/64, 1/64}], 40]
-alignas(8) const double LOG_P1_LOG2[LOG_P1_SIZE] = {
- 0x0.0000000000000p+0, 0x1.6e79685c2d22ap-6, 0x1.6bad3758efd87p-5,
- 0x1.0eb389fa29f9bp-4, 0x1.663f6fac91316p-4, 0x1.bc84240adabbap-4,
- 0x1.08c588cda79e4p-3, 0x1.32ae9e278ae1ap-3, 0x1.5c01a39fbd688p-3,
- 0x1.84c2bd02f03b3p-3, 0x1.acf5e2db4ec94p-3, 0x1.d49ee4c325970p-3,
- 0x1.fbc16b902680ap-3, 0x1.11307dad30b76p-2, 0x1.24407ab0e073ap-2,
- 0x1.37124cea4cdedp-2, 0x1.49a784bcd1b8bp-2, 0x1.5c01a39fbd688p-2,
- 0x1.6e221cd9d0cdep-2, 0x1.800a563161c54p-2, 0x1.91bba891f1709p-2,
- 0x1.a33760a7f6051p-2, 0x1.b47ebf73882a1p-2, 0x1.c592fad295b56p-2,
- 0x1.d6753e032ea0fp-2, 0x1.e726aa1e754d2p-2, 0x1.f7a8568cb06cfp-2,
- 0x1.03fda8b97997fp-1, 0x1.0c10500d63aa6p-1, 0x1.140c9faa1e544p-1,
- 0x1.1bf311e95d00ep-1, 0x1.23c41d42727c8p-1, 0x1.2b803473f7ad1p-1,
- 0x1.3327c6ab49ca7p-1, 0x1.3abb3faa02167p-1, 0x1.423b07e986aa9p-1,
- 0x1.49a784bcd1b8bp-1, 0x1.510118708a8f9p-1, 0x1.5848226989d34p-1,
- 0x1.5f7cff41e09afp-1, 0x1.66a008e4788ccp-1, 0x1.6db196a76194ap-1,
- 0x1.74b1fd64e0754p-1, 0x1.7ba18f93502e4p-1, 0x1.82809d5be7073p-1,
- 0x1.894f74b06ef8bp-1, 0x1.900e6160002cdp-1, 0x1.96bdad2acb5f6p-1,
- 0x1.9d5d9fd5010b3p-1, 0x1.a3ee7f38e181fp-1, 0x1.aa708f58014d3p-1,
- 0x1.b0e4126bcc86cp-1, 0x1.b74948f5532dap-1, 0x1.bda071cc67e6ep-1,
- 0x1.c3e9ca2e1a055p-1, 0x1.ca258dca93316p-1, 0x1.d053f6d260896p-1,
- 0x1.d6753e032ea0fp-1, 0x1.dc899ab3ff56cp-1, 0x1.e29142e0e0140p-1,
- 0x1.e88c6b3626a73p-1, 0x1.ee7b471b3a950p-1, 0x1.f45e08bcf0655p-1,
- 0x1.fa34e1177c233p-1,
-};
-
-// N[Table[1/(1 + x), {x, 0/64, 63/64, 1/64}], 40]
-alignas(8) const double LOG_P1_1_OVER[LOG_P1_SIZE] = {
- 0x1.0000000000000p+0, 0x1.f81f81f81f820p-1, 0x1.f07c1f07c1f08p-1,
- 0x1.e9131abf0b767p-1, 0x1.e1e1e1e1e1e1ep-1, 0x1.dae6076b981dbp-1,
- 0x1.d41d41d41d41dp-1, 0x1.cd85689039b0bp-1, 0x1.c71c71c71c71cp-1,
- 0x1.c0e070381c0e0p-1, 0x1.bacf914c1bad0p-1, 0x1.b4e81b4e81b4fp-1,
- 0x1.af286bca1af28p-1, 0x1.a98ef606a63bep-1, 0x1.a41a41a41a41ap-1,
- 0x1.9ec8e951033d9p-1, 0x1.999999999999ap-1, 0x1.948b0fcd6e9e0p-1,
- 0x1.8f9c18f9c18fap-1, 0x1.8acb90f6bf3aap-1, 0x1.8618618618618p-1,
- 0x1.8181818181818p-1, 0x1.7d05f417d05f4p-1, 0x1.78a4c8178a4c8p-1,
- 0x1.745d1745d1746p-1, 0x1.702e05c0b8170p-1, 0x1.6c16c16c16c17p-1,
- 0x1.6816816816817p-1, 0x1.642c8590b2164p-1, 0x1.6058160581606p-1,
- 0x1.5c9882b931057p-1, 0x1.58ed2308158edp-1, 0x1.5555555555555p-1,
- 0x1.51d07eae2f815p-1, 0x1.4e5e0a72f0539p-1, 0x1.4afd6a052bf5bp-1,
- 0x1.47ae147ae147bp-1, 0x1.446f86562d9fbp-1, 0x1.4141414141414p-1,
- 0x1.3e22cbce4a902p-1, 0x1.3b13b13b13b14p-1, 0x1.3813813813814p-1,
- 0x1.3521cfb2b78c1p-1, 0x1.323e34a2b10bfp-1, 0x1.2f684bda12f68p-1,
- 0x1.2c9fb4d812ca0p-1, 0x1.29e4129e4129ep-1, 0x1.27350b8812735p-1,
- 0x1.2492492492492p-1, 0x1.21fb78121fb78p-1, 0x1.1f7047dc11f70p-1,
- 0x1.1cf06ada2811dp-1, 0x1.1a7b9611a7b96p-1, 0x1.1811811811812p-1,
- 0x1.15b1e5f75270dp-1, 0x1.135c81135c811p-1, 0x1.1111111111111p-1,
- 0x1.0ecf56be69c90p-1, 0x1.0c9714fbcda3bp-1, 0x1.0a6810a6810a7p-1,
- 0x1.0842108421084p-1, 0x1.0624dd2f1a9fcp-1, 0x1.0410410410410p-1,
- 0x1.0204081020408p-1};
-
-// Taylos series expansion for Log[2, 1 + x] splitted to EVEN AND ODD numbers
-// K_LOG2_ODD starts from x^3
-alignas(8) const
- double K_LOG2_ODD[4] = {0x1.ec709dc3a03fdp-2, 0x1.2776c50ef9bfep-2,
- 0x1.a61762a7aded9p-3, 0x1.484b13d7c02a9p-3};
-
-alignas(8) const
- double K_LOG2_EVEN[4] = {-0x1.71547652b82fep-1, -0x1.71547652b82fep-2,
- -0x1.ec709dc3a03fdp-3, -0x1.2776c50ef9bfep-3};
-
-} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/explogxf.h b/libc/src/math/generic/explogxf.h
index 212ede475854..be4328a4f48b 100644
--- a/libc/src/math/generic/explogxf.h
+++ b/libc/src/math/generic/explogxf.h
@@ -10,167 +10,17 @@
#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/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
@@ -271,33 +121,6 @@ template <bool is_sinh> LIBC_INLINE double exp_pm_eval(float x) {
}
// x should be positive, normal finite value
-LIBC_INLINE static double log2_eval(double x) {
- using FPB = fputil::FPBits<double>;
- FPB bs(x);
-
- double result = 0;
- result += bs.get_exponent();
-
- int p1 = (bs.get_mantissa() >> (FPB::FRACTION_LEN - LOG_P1_BITS)) &
- (LOG_P1_SIZE - 1);
-
- bs.set_uintval(bs.uintval() & (FPB::FRACTION_MASK >> LOG_P1_BITS));
- bs.set_biased_exponent(FPB::EXP_BIAS);
- double dx = (bs.get_val() - 1.0) * LOG_P1_1_OVER[p1];
-
- // Taylor series for log(2,1+x)
- double c1 = fputil::multiply_add(dx, K_LOG2_ODD[0], K_LOG2_EVEN[0]);
- double c2 = fputil::multiply_add(dx, K_LOG2_ODD[1], K_LOG2_EVEN[1]);
- double c3 = fputil::multiply_add(dx, K_LOG2_ODD[2], K_LOG2_EVEN[2]);
- double c4 = fputil::multiply_add(dx, K_LOG2_ODD[3], K_LOG2_EVEN[3]);
-
- // c0 = dx * (1.0 / ln(2)) + LOG_P1_LOG2[p1]
- double c0 = fputil::multiply_add(dx, 0x1.71547652b82fep+0, LOG_P1_LOG2[p1]);
- result += LIBC_NAMESPACE::fputil::polyeval(dx * dx, c0, c1, c2, c3, c4);
- return result;
-}
-
-// x should be positive, normal finite value
// TODO: Simplify range reduction and polynomial degree for float16.
// See issue #137190.
LIBC_INLINE static float log_eval_f(float x) {
@@ -375,58 +198,6 @@ 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/libc/src/math/generic/expxf16.h b/libc/src/math/generic/expxf16.h
index 05ac95d58682..b17b14fa2d75 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:
@@ -68,53 +61,6 @@ LIBC_INLINE ExpRangeReduction exp2_range_reduction(float16 x) {
// 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);
static constexpr float LOG2F_E = 0x1.715476p+0f;
diff --git a/libc/src/math/generic/frexpf.cpp b/libc/src/math/generic/frexpf.cpp
index 09227badc341..783880d44ce6 100644
--- a/libc/src/math/generic/frexpf.cpp
+++ b/libc/src/math/generic/frexpf.cpp
@@ -7,14 +7,13 @@
//===----------------------------------------------------------------------===//
#include "src/math/frexpf.h"
-#include "src/__support/FPUtil/ManipulationFunctions.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
+
+#include "src/__support/math/frexpf.h"
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float, frexpf, (float x, int *exp)) {
- return fputil::frexp(x, *exp);
+ return math::frexpf(x, exp);
}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/frexpf128.cpp b/libc/src/math/generic/frexpf128.cpp
index eb816c476970..55f7afcf4aea 100644
--- a/libc/src/math/generic/frexpf128.cpp
+++ b/libc/src/math/generic/frexpf128.cpp
@@ -7,14 +7,13 @@
//===----------------------------------------------------------------------===//
#include "src/math/frexpf128.h"
-#include "src/__support/FPUtil/ManipulationFunctions.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
+
+#include "src/__support/math/frexpf128.h"
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float128, frexpf128, (float128 x, int *exp)) {
- return fputil::frexp(x, *exp);
+ return math::frexpf128(x, exp);
}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/frexpf16.cpp b/libc/src/math/generic/frexpf16.cpp
index 4571b0d0ea38..fa918fd7ffc3 100644
--- a/libc/src/math/generic/frexpf16.cpp
+++ b/libc/src/math/generic/frexpf16.cpp
@@ -7,14 +7,13 @@
//===----------------------------------------------------------------------===//
#include "src/math/frexpf16.h"
-#include "src/__support/FPUtil/ManipulationFunctions.h"
-#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
+
+#include "src/__support/math/frexpf16.h"
namespace LIBC_NAMESPACE_DECL {
LLVM_LIBC_FUNCTION(float16, frexpf16, (float16 x, int *exp)) {
- return fputil::frexp(x, *exp);
+ return math::frexpf16(x, exp);
}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/ldexpf.cpp b/libc/src/math/generic/ldexpf.cpp
index 63c5d219f7a7..c5f30bb725e6 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/libc/src/math/generic/ldexpf128.cpp b/libc/src/math/generic/ldexpf128.cpp
index 03b1a2d2032e..40afa5b285bc 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/libc/src/math/generic/ldexpf16.cpp b/libc/src/math/generic/ldexpf16.cpp
index caa344b41476..ecf16337ee79 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/libc/src/math/generic/powf.cpp b/libc/src/math/generic/powf.cpp
index dfdfd5d6d576..a45ef511c9ba 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 d6158fd30253..63111f84de14 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/libc/src/math/generic/tanpif.cpp b/libc/src/math/generic/tanpif.cpp
new file mode 100644
index 000000000000..58d46c9481aa
--- /dev/null
+++ b/libc/src/math/generic/tanpif.cpp
@@ -0,0 +1,106 @@
+//===-- Single-precision tanpi function -----------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/tanpif.h"
+#include "sincosf_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/multiply_add.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+namespace LIBC_NAMESPACE_DECL {
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+constexpr size_t N_EXCEPTS = 3;
+
+constexpr fputil::ExceptValues<float, N_EXCEPTS> TANPIF_EXCEPTS{{
+ // (input, RZ output, RU offset, RD offset, RN offset)
+ {0x38F26685, 0x39BE6182, 1, 0, 0},
+ {0x3E933802, 0x3FA267DD, 1, 0, 0},
+ {0x3F3663FF, 0xBFA267DD, 0, 1, 0},
+}};
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+LLVM_LIBC_FUNCTION(float, tanpif, (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;
+ double xd = static_cast<double>(xbits.get_val());
+
+ // Handle exceptional values
+ if (LIBC_UNLIKELY(x_abs <= 0x3F3663FF)) {
+ if (LIBC_UNLIKELY(x_abs == 0U))
+ return x;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ bool x_sign = x_u >> 31;
+
+ if (auto r = TANPIF_EXCEPTS.lookup_odd(x_abs, x_sign);
+ LIBC_UNLIKELY(r.has_value()))
+ return r.value();
+#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ }
+
+ // Numbers greater or equal to 2^23 are always integers, or infinity, or NaN
+ if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {
+ // x is inf or NaN.
+ 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();
+ }
+
+ 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();
+ }
+
+ return FPBits::zero(xbits.sign()).get_val();
+ }
+
+ // Range reduction:
+ // For |x| > 1/32, we perform range reduction as follows:
+ // Find k and y such that:
+ // x = (k + y) * 1/32
+ // k is an integer
+ // |y| < 0.5
+ //
+ // This is done by performing:
+ // k = round(x * 32)
+ // y = x * 32 - k
+ //
+ // Once k and y are computed, we then deduce the answer by the formula:
+ // tan(x) = sin(x) / cos(x)
+ // = (sin_y * cos_k + cos_y * sin_k) / (cos_y * cos_k - sin_y * sin_k)
+ double sin_k, cos_k, sin_y, cosm1_y;
+ sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y);
+
+ if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) {
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_DIVBYZERO);
+
+ int32_t x_mp5_i = static_cast<int32_t>(xd - 0.5);
+ return FPBits::inf((x_mp5_i & 0x1) ? Sign::NEG : Sign::POS).get_val();
+ }
+
+ using fputil::multiply_add;
+ return fputil::cast<float>(
+ multiply_add(sin_y, cos_k, multiply_add(cosm1_y, sin_k, sin_k)) /
+ multiply_add(sin_y, -sin_k, multiply_add(cosm1_y, cos_k, cos_k)));
+}
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/tanpif.h b/libc/src/math/tanpif.h
new file mode 100644
index 000000000000..59e6dcfa9ff7
--- /dev/null
+++ b/libc/src/math/tanpif.h
@@ -0,0 +1,20 @@
+//===-- Implementation header for tanpif ------------------------*- 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_MATH_TANPIF_H
+#define LLVM_LIBC_SRC_MATH_TANPIF_H
+
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+float tanpif(float x);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_MATH_TANPIF_H
diff --git a/libc/src/string/memory_utils/CMakeLists.txt b/libc/src/string/memory_utils/CMakeLists.txt
index a967247db53f..8ab1c9ff98d2 100644
--- a/libc/src/string/memory_utils/CMakeLists.txt
+++ b/libc/src/string/memory_utils/CMakeLists.txt
@@ -7,7 +7,9 @@ add_header_library(
aarch64/inline_memcpy.h
aarch64/inline_memmove.h
aarch64/inline_memset.h
+ arm/common.h
arm/inline_memcpy.h
+ arm/inline_memset.h
generic/aligned_access.h
generic/byte_per_byte.h
inline_bcmp.h
diff --git a/libc/src/string/memory_utils/arm/common.h b/libc/src/string/memory_utils/arm/common.h
new file mode 100644
index 000000000000..b9f40b64fed9
--- /dev/null
+++ b/libc/src/string/memory_utils/arm/common.h
@@ -0,0 +1,55 @@
+//===-- Common constants and defines for arm --------------------*- 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_STRING_MEMORY_UTILS_ARM_COMMON_H
+#define LLVM_LIBC_SRC_STRING_MEMORY_UTILS_ARM_COMMON_H
+
+#include "src/__support/macros/attributes.h" // LIBC_INLINE_VAR
+#include "src/string/memory_utils/utils.h" // CPtr, Ptr, distance_to_align
+
+#include <stddef.h> // size_t
+
+// Our minimum supported compiler version does not recognize the standard
+// [[likely]] / [[unlikely]] attributes so we use the preprocessor.
+
+// https://libc.llvm.org/compiler_support.html
+// Support for [[likely]] / [[unlikely]]
+// [X] GCC 12.2
+// [X] Clang 12
+// [ ] Clang 11
+#define LIBC_ATTR_LIKELY [[likely]]
+#define LIBC_ATTR_UNLIKELY [[unlikely]]
+
+#if defined(LIBC_COMPILER_IS_CLANG)
+#if LIBC_COMPILER_CLANG_VER < 1200
+#undef LIBC_ATTR_LIKELY
+#undef LIBC_ATTR_UNLIKELY
+#define LIBC_ATTR_LIKELY
+#define LIBC_ATTR_UNLIKELY
+#endif
+#endif
+
+namespace LIBC_NAMESPACE_DECL {
+
+LIBC_INLINE_VAR constexpr size_t kWordSize = sizeof(uint32_t);
+
+enum class AssumeAccess { kUnknown, kAligned };
+enum class BlockOp { kFull, kByWord };
+
+LIBC_INLINE auto misaligned(CPtr ptr) {
+ return distance_to_align_down<kWordSize>(ptr);
+}
+
+LIBC_INLINE CPtr bitwise_or(CPtr a, CPtr b) {
+ return cpp::bit_cast<CPtr>(cpp::bit_cast<uintptr_t>(a) |
+ cpp::bit_cast<uintptr_t>(b));
+}
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_STRING_MEMORY_UTILS_ARM_COMMON_H
diff --git a/libc/src/string/memory_utils/arm/inline_memcpy.h b/libc/src/string/memory_utils/arm/inline_memcpy.h
index 61efebe29b48..c748048a3e58 100644
--- a/libc/src/string/memory_utils/arm/inline_memcpy.h
+++ b/libc/src/string/memory_utils/arm/inline_memcpy.h
@@ -5,63 +5,57 @@
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
+// The functions defined in this file give approximate code size. These sizes
+// assume the following configuration options:
+// - LIBC_CONF_KEEP_FRAME_POINTER = false
+// - LIBC_CONF_ENABLE_STRONG_STACK_PROTECTOR = false
+// - LIBC_ADD_NULL_CHECKS = false
#ifndef LLVM_LIBC_SRC_STRING_MEMORY_UTILS_ARM_INLINE_MEMCPY_H
#define LLVM_LIBC_SRC_STRING_MEMORY_UTILS_ARM_INLINE_MEMCPY_H
+#include "src/__support/CPP/type_traits.h" // always_false
#include "src/__support/macros/attributes.h" // LIBC_INLINE
#include "src/__support/macros/optimization.h" // LIBC_LOOP_NOUNROLL
+#include "src/string/memory_utils/arm/common.h" // LIBC_ATTR_LIKELY, LIBC_ATTR_UNLIKELY
#include "src/string/memory_utils/utils.h" // memcpy_inline, distance_to_align
#include <stddef.h> // size_t
-// https://libc.llvm.org/compiler_support.html
-// Support for [[likely]] / [[unlikely]]
-// [X] GCC 12.2
-// [X] Clang 12
-// [ ] Clang 11
-#define LIBC_ATTR_LIKELY [[likely]]
-#define LIBC_ATTR_UNLIKELY [[unlikely]]
-
-#if defined(LIBC_COMPILER_IS_CLANG)
-#if LIBC_COMPILER_CLANG_VER < 1200
-#undef LIBC_ATTR_LIKELY
-#undef LIBC_ATTR_UNLIKELY
-#define LIBC_ATTR_LIKELY
-#define LIBC_ATTR_UNLIKELY
-#endif
-#endif
-
namespace LIBC_NAMESPACE_DECL {
namespace {
-LIBC_INLINE_VAR constexpr size_t kWordSize = sizeof(uint32_t);
-
-enum Strategy {
- ForceWordLdStChain,
- AssumeWordAligned,
- AssumeUnaligned,
-};
+// Performs a copy of `bytes` byte from `src` to `dst`. This function has the
+// semantics of `memcpy` where `src` and `dst` are `__restrict`. The compiler is
+// free to use whatever instruction is best for the size and assumed access.
+template <size_t bytes, AssumeAccess access>
+LIBC_INLINE void copy(void *dst, const void *src) {
+ if constexpr (access == AssumeAccess::kAligned) {
+ constexpr size_t alignment = bytes > kWordSize ? kWordSize : bytes;
+ memcpy_inline<bytes>(assume_aligned<alignment>(dst),
+ assume_aligned<alignment>(src));
+ } else if constexpr (access == AssumeAccess::kUnknown) {
+ memcpy_inline<bytes>(dst, src);
+ } else {
+ static_assert(cpp::always_false<decltype(access)>, "Invalid AssumeAccess");
+ }
+}
-template <size_t bytes, Strategy strategy = AssumeUnaligned>
-LIBC_INLINE void copy_and_bump_pointers(Ptr &dst, CPtr &src) {
- if constexpr (strategy == AssumeUnaligned) {
- memcpy_inline<bytes>(assume_aligned<1>(dst), assume_aligned<1>(src));
- } else if constexpr (strategy == AssumeWordAligned) {
- static_assert(bytes >= kWordSize);
- memcpy_inline<bytes>(assume_aligned<kWordSize>(dst),
- assume_aligned<kWordSize>(src));
- } else if constexpr (strategy == ForceWordLdStChain) {
+template <size_t bytes, BlockOp block_op = BlockOp::kFull,
+ AssumeAccess access = AssumeAccess::kUnknown>
+LIBC_INLINE void copy_block_and_bump_pointers(Ptr &dst, CPtr &src) {
+ if constexpr (block_op == BlockOp::kFull) {
+ copy<bytes, access>(dst, src);
+ } else if constexpr (block_op == BlockOp::kByWord) {
// We restrict loads/stores to 4 byte to prevent the use of load/store
- // multiple (LDM, STM) and load/store double (LDRD, STRD). First, they may
- // fault (see notes below) and second, they use more registers which in turn
- // adds push/pop instructions in the hot path.
+ // multiple (LDM, STM) and load/store double (LDRD, STRD).
static_assert((bytes % kWordSize == 0) && (bytes >= kWordSize));
LIBC_LOOP_UNROLL
- for (size_t i = 0; i < bytes / kWordSize; ++i) {
- const size_t offset = i * kWordSize;
- memcpy_inline<kWordSize>(dst + offset, src + offset);
+ for (size_t offset = 0; offset < bytes; offset += kWordSize) {
+ copy<kWordSize, access>(dst + offset, src + offset);
}
+ } else {
+ static_assert(cpp::always_false<decltype(block_op)>, "Invalid BlockOp");
}
// In the 1, 2, 4 byte copy case, the compiler can fold pointer offsetting
// into the load/store instructions.
@@ -72,39 +66,27 @@ LIBC_INLINE void copy_and_bump_pointers(Ptr &dst, CPtr &src) {
src += bytes;
}
-LIBC_INLINE void copy_bytes_and_bump_pointers(Ptr &dst, CPtr &src,
- const size_t size) {
+template <size_t bytes, BlockOp block_op, AssumeAccess access>
+LIBC_INLINE void consume_by_block(Ptr &dst, CPtr &src, size_t &size) {
LIBC_LOOP_NOUNROLL
- for (size_t i = 0; i < size; ++i)
- *dst++ = *src++;
+ for (size_t i = 0; i < size / bytes; ++i)
+ copy_block_and_bump_pointers<bytes, block_op, access>(dst, src);
+ size %= bytes;
}
-template <size_t block_size, Strategy strategy>
-LIBC_INLINE void copy_blocks_and_update_args(Ptr &dst, CPtr &src,
- size_t &size) {
+[[maybe_unused]] LIBC_INLINE void
+copy_bytes_and_bump_pointers(Ptr &dst, CPtr &src, size_t size) {
LIBC_LOOP_NOUNROLL
- for (size_t i = 0; i < size / block_size; ++i)
- copy_and_bump_pointers<block_size, strategy>(dst, src);
- // Update `size` once at the end instead of once per iteration.
- size %= block_size;
-}
-
-LIBC_INLINE CPtr bitwise_or(CPtr a, CPtr b) {
- return cpp::bit_cast<CPtr>(cpp::bit_cast<uintptr_t>(a) |
- cpp::bit_cast<uintptr_t>(b));
-}
-
-LIBC_INLINE auto misaligned(CPtr a) {
- return distance_to_align_down<kWordSize>(a);
+ for (size_t i = 0; i < size; ++i)
+ *dst++ = *src++;
}
} // namespace
-// Implementation for Cortex-M0, M0+, M1.
-// Notes:
-// - It compiles down to 196 bytes, but 220 bytes when used through `memcpy`
-// that also needs to return the `dst` ptr.
-// - These cores do not allow for unaligned loads/stores.
+// Implementation for Cortex-M0, M0+, M1 cores that do not allow for unaligned
+// loads/stores. It compiles down to 208 bytes when used through `memcpy` that
+// also needs to return the `dst` ptr.
+// Note:
// - When `src` and `dst` are coaligned, we start by aligning them and perform
// bulk copies. We let the compiler know the pointers are aligned so it can
// use load/store multiple (LDM, STM). This significantly increase throughput
@@ -121,13 +103,20 @@ LIBC_INLINE auto misaligned(CPtr a) {
copy_bytes_and_bump_pointers(dst, src, offset);
size -= offset;
}
+ constexpr AssumeAccess kAligned = AssumeAccess::kAligned;
const auto src_alignment = distance_to_align_down<kWordSize>(src);
if (src_alignment == 0)
LIBC_ATTR_LIKELY {
// Both `src` and `dst` are now word-aligned.
- copy_blocks_and_update_args<64, AssumeWordAligned>(dst, src, size);
- copy_blocks_and_update_args<16, AssumeWordAligned>(dst, src, size);
- copy_blocks_and_update_args<4, AssumeWordAligned>(dst, src, size);
+ // We first copy by blocks of 64 bytes, the compiler will use 4
+ // load/store multiple (LDM, STM), each of 4 words. This requires more
+ // registers so additional push/pop are needed but the speedup is worth
+ // it.
+ consume_by_block<64, BlockOp::kFull, kAligned>(dst, src, size);
+ // Then we use blocks of 4 word load/store.
+ consume_by_block<16, BlockOp::kByWord, kAligned>(dst, src, size);
+ // Then we use word by word copy.
+ consume_by_block<4, BlockOp::kByWord, kAligned>(dst, src, size);
}
else {
// `dst` is aligned but `src` is not.
@@ -138,7 +127,7 @@ LIBC_INLINE auto misaligned(CPtr a) {
src_alignment == 2
? load_aligned<uint32_t, uint16_t, uint16_t>(src)
: load_aligned<uint32_t, uint8_t, uint16_t, uint8_t>(src);
- memcpy_inline<kWordSize>(assume_aligned<kWordSize>(dst), &value);
+ copy<kWordSize, kAligned>(dst, &value);
dst += kWordSize;
src += kWordSize;
size -= kWordSize;
@@ -151,17 +140,8 @@ LIBC_INLINE auto misaligned(CPtr a) {
}
// Implementation for Cortex-M3, M4, M7, M23, M33, M35P, M52 with hardware
-// support for unaligned loads and stores.
-// Notes:
-// - It compiles down to 266 bytes.
-// - `dst` and `src` are not `__restrict` to prevent the compiler from
-// reordering loads/stores.
-// - We keep state variables to a strict minimum to keep everything in the free
-// registers and prevent costly push / pop.
-// - If unaligned single loads/stores to normal memory are supported, unaligned
-// accesses for load/store multiple (LDM, STM) and load/store double (LDRD,
-// STRD) instructions are generally not supported and will still fault so we
-// make sure to restrict unrolling to word loads/stores.
+// support for unaligned loads and stores. It compiles down to 272 bytes when
+// used through `memcpy` that also needs to return the `dst` ptr.
[[maybe_unused]] LIBC_INLINE void inline_memcpy_arm_mid_end(Ptr dst, CPtr src,
size_t size) {
if (misaligned(bitwise_or(src, dst)))
@@ -169,38 +149,59 @@ LIBC_INLINE auto misaligned(CPtr a) {
if (size < 8)
LIBC_ATTR_UNLIKELY {
if (size & 1)
- copy_and_bump_pointers<1>(dst, src);
+ copy_block_and_bump_pointers<1>(dst, src);
if (size & 2)
- copy_and_bump_pointers<2>(dst, src);
+ copy_block_and_bump_pointers<2>(dst, src);
if (size & 4)
- copy_and_bump_pointers<4>(dst, src);
+ copy_block_and_bump_pointers<4>(dst, src);
return;
}
if (misaligned(src))
LIBC_ATTR_UNLIKELY {
const size_t offset = distance_to_align_up<kWordSize>(dst);
if (offset & 1)
- copy_and_bump_pointers<1>(dst, src);
+ copy_block_and_bump_pointers<1>(dst, src);
if (offset & 2)
- copy_and_bump_pointers<2>(dst, src);
+ copy_block_and_bump_pointers<2>(dst, src);
size -= offset;
}
}
- copy_blocks_and_update_args<64, ForceWordLdStChain>(dst, src, size);
- copy_blocks_and_update_args<16, ForceWordLdStChain>(dst, src, size);
- copy_blocks_and_update_args<4, AssumeUnaligned>(dst, src, size);
+ // `dst` and `src` are not necessarily both aligned at that point but this
+ // implementation assumes hardware support for unaligned loads and stores so
+ // it is still fast to perform unrolled word by word copy. Note that wider
+ // accesses through the use of load/store multiple (LDM, STM) and load/store
+ // double (LDRD, STRD) instructions are generally not supported and can fault.
+ // By forcing decomposition of 64 bytes copy into word by word copy, the
+ // compiler uses a load to prefetch the next cache line:
+ // ldr r3, [r1, #64]! <- prefetch next cache line
+ // str r3, [r0]
+ // ldr r3, [r1, #0x4]
+ // str r3, [r0, #0x4]
+ // ...
+ // ldr r3, [r1, #0x3c]
+ // str r3, [r0, #0x3c]
+ // This is a bit detrimental for sizes between 64 and 256 (less than 10%
+ // penalty) but the prefetch yields better throughput for larger copies.
+ constexpr AssumeAccess kUnknown = AssumeAccess::kUnknown;
+ consume_by_block<64, BlockOp::kByWord, kUnknown>(dst, src, size);
+ consume_by_block<16, BlockOp::kByWord, kUnknown>(dst, src, size);
+ consume_by_block<4, BlockOp::kByWord, kUnknown>(dst, src, size);
if (size & 1)
- copy_and_bump_pointers<1>(dst, src);
+ copy_block_and_bump_pointers<1>(dst, src);
if (size & 2)
- LIBC_ATTR_UNLIKELY
- copy_and_bump_pointers<2>(dst, src);
+ copy_block_and_bump_pointers<2>(dst, src);
}
-[[maybe_unused]] LIBC_INLINE void inline_memcpy_arm(void *__restrict dst_,
- const void *__restrict src_,
+[[maybe_unused]] LIBC_INLINE void inline_memcpy_arm(Ptr dst, CPtr src,
size_t size) {
- Ptr dst = cpp::bit_cast<Ptr>(dst_);
- CPtr src = cpp::bit_cast<CPtr>(src_);
+ // The compiler performs alias analysis and is able to prove that `dst` and
+ // `src` do not alias by propagating the `__restrict` keyword from the
+ // `memcpy` prototype. This allows the compiler to merge consecutive
+ // load/store (LDR, STR) instructions generated in
+ // `copy_block_and_bump_pointers` with `BlockOp::kByWord` into load/store
+ // double (LDRD, STRD) instructions, this is is undesirable so we prevent the
+ // compiler from inferring `__restrict` with the following line.
+ asm volatile("" : "+r"(dst), "+r"(src));
#ifdef __ARM_FEATURE_UNALIGNED
return inline_memcpy_arm_mid_end(dst, src, size);
#else
@@ -210,8 +211,4 @@ LIBC_INLINE auto misaligned(CPtr a) {
} // namespace LIBC_NAMESPACE_DECL
-// Cleanup local macros
-#undef LIBC_ATTR_LIKELY
-#undef LIBC_ATTR_UNLIKELY
-
#endif // LLVM_LIBC_SRC_STRING_MEMORY_UTILS_ARM_INLINE_MEMCPY_H
diff --git a/libc/src/string/memory_utils/arm/inline_memset.h b/libc/src/string/memory_utils/arm/inline_memset.h
new file mode 100644
index 000000000000..a7ef9cc7df91
--- /dev/null
+++ b/libc/src/string/memory_utils/arm/inline_memset.h
@@ -0,0 +1,156 @@
+//===-- Memset implementation for arm ---------------------------*- 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
+//
+//===----------------------------------------------------------------------===//
+// The functions defined in this file give approximate code size. These sizes
+// assume the following configuration options:
+// - LIBC_CONF_KEEP_FRAME_POINTER = false
+// - LIBC_CONF_ENABLE_STRONG_STACK_PROTECTOR = false
+// - LIBC_ADD_NULL_CHECKS = false
+#ifndef LLVM_LIBC_SRC_STRING_MEMORY_UTILS_ARM_INLINE_MEMSET_H
+#define LLVM_LIBC_SRC_STRING_MEMORY_UTILS_ARM_INLINE_MEMSET_H
+
+#include "src/__support/CPP/type_traits.h" // always_false
+#include "src/__support/macros/attributes.h" // LIBC_INLINE
+#include "src/__support/macros/optimization.h" // LIBC_LOOP_NOUNROLL
+#include "src/string/memory_utils/arm/common.h" // LIBC_ATTR_LIKELY, LIBC_ATTR_UNLIKELY
+#include "src/string/memory_utils/utils.h" // memcpy_inline, distance_to_align
+
+#include <stddef.h> // size_t
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace {
+
+template <size_t bytes, AssumeAccess access>
+LIBC_INLINE void set(void *dst, uint32_t value) {
+ static_assert(bytes == 1 || bytes == 2 || bytes == 4);
+ if constexpr (access == AssumeAccess::kAligned) {
+ constexpr size_t alignment = bytes > kWordSize ? kWordSize : bytes;
+ memcpy_inline<bytes>(assume_aligned<alignment>(dst), &value);
+ } else if constexpr (access == AssumeAccess::kUnknown) {
+ memcpy_inline<bytes>(dst, &value);
+ } else {
+ static_assert(cpp::always_false<decltype(access)>, "Invalid AssumeAccess");
+ }
+}
+
+template <size_t bytes, AssumeAccess access = AssumeAccess::kUnknown>
+LIBC_INLINE void set_block_and_bump_pointers(Ptr &dst, uint32_t value) {
+ if constexpr (bytes <= kWordSize) {
+ set<bytes, access>(dst, value);
+ } else {
+ static_assert(bytes % kWordSize == 0 && bytes >= kWordSize);
+ LIBC_LOOP_UNROLL
+ for (size_t offset = 0; offset < bytes; offset += kWordSize) {
+ set<kWordSize, access>(dst + offset, value);
+ }
+ }
+ // In the 1, 2, 4 byte set case, the compiler can fold pointer offsetting
+ // into the store instructions.
+ // e.g.,
+ // strb r3, [r0], #1
+ dst += bytes;
+}
+
+template <size_t bytes, AssumeAccess access>
+LIBC_INLINE void consume_by_block(Ptr &dst, uint32_t value, size_t &size) {
+ LIBC_LOOP_NOUNROLL
+ for (size_t i = 0; i < size / bytes; ++i)
+ set_block_and_bump_pointers<bytes, access>(dst, value);
+ size %= bytes;
+}
+
+[[maybe_unused]] LIBC_INLINE void
+set_bytes_and_bump_pointers(Ptr &dst, uint32_t value, size_t size) {
+ LIBC_LOOP_NOUNROLL
+ for (size_t i = 0; i < size; ++i) {
+ set<1, AssumeAccess::kUnknown>(dst++, value);
+ }
+}
+
+} // namespace
+
+// Implementation for Cortex-M0, M0+, M1. It compiles down to 140 bytes when
+// used through `memset` that also needs to return the `dst` ptr. These cores do
+// not allow unaligned stores so all accesses are aligned.
+[[maybe_unused]] LIBC_INLINE void
+inline_memset_arm_low_end(Ptr dst, uint8_t value, size_t size) {
+ if (size >= 8)
+ LIBC_ATTR_LIKELY {
+ // Align `dst` to word boundary.
+ if (const size_t offset = distance_to_align_up<kWordSize>(dst))
+ LIBC_ATTR_UNLIKELY {
+ set_bytes_and_bump_pointers(dst, value, offset);
+ size -= offset;
+ }
+ const uint32_t value32 = value * 0x01010101U; // splat value in each byte
+ consume_by_block<64, AssumeAccess::kAligned>(dst, value32, size);
+ consume_by_block<16, AssumeAccess::kAligned>(dst, value32, size);
+ consume_by_block<4, AssumeAccess::kAligned>(dst, value32, size);
+ }
+ set_bytes_and_bump_pointers(dst, value, size);
+}
+
+// Implementation for Cortex-M3, M4, M7, M23, M33, M35P, M52 with hardware
+// support for unaligned loads and stores. It compiles down to 186 bytes when
+// used through `memset` that also needs to return the `dst` ptr.
+[[maybe_unused]] LIBC_INLINE void
+inline_memset_arm_mid_end(Ptr dst, uint8_t value, size_t size) {
+ const uint32_t value32 = value * 0x01010101U; // splat value in each byte
+ if (misaligned(dst))
+ LIBC_ATTR_UNLIKELY {
+ if (size < 8)
+ LIBC_ATTR_UNLIKELY {
+ if (size & 1)
+ set_block_and_bump_pointers<1>(dst, value32);
+ if (size & 2)
+ set_block_and_bump_pointers<2>(dst, value32);
+ if (size & 4)
+ set_block_and_bump_pointers<4>(dst, value32);
+ return;
+ }
+ const size_t offset = distance_to_align_up<kWordSize>(dst);
+ if (offset & 1)
+ set_block_and_bump_pointers<1>(dst, value32);
+ if (offset & 2)
+ set_block_and_bump_pointers<2>(dst, value32);
+ size -= offset;
+ }
+ // If we tell the compiler that the stores are aligned it will generate 8 x
+ // STRD instructions. By not specifying alignment, the compiler conservatively
+ // uses 16 x STR.W and is able to use the first one to prefetch the
+ // destination in advance leading to better asymptotic performances.
+ // str r12, [r3, #64]! <- prefetch next cache line
+ // str.w r12, [r3, #0x4]
+ // str.w r12, [r3, #0x8]
+ // ...
+ // str.w r12, [r3, #0x38]
+ // str.w r12, [r3, #0x3c]
+ consume_by_block<64, AssumeAccess::kUnknown>(dst, value32, size);
+ // Prefetching does not matter anymore at this scale so using STRD yields
+ // better results.
+ consume_by_block<16, AssumeAccess::kAligned>(dst, value32, size);
+ consume_by_block<4, AssumeAccess::kAligned>(dst, value32, size);
+ if (size & 1)
+ set_block_and_bump_pointers<1>(dst, value32);
+ if (size & 2)
+ LIBC_ATTR_UNLIKELY
+ set_block_and_bump_pointers<2>(dst, value32);
+}
+
+[[maybe_unused]] LIBC_INLINE void
+inline_memset_arm_dispatch(Ptr dst, uint8_t value, size_t size) {
+#ifdef __ARM_FEATURE_UNALIGNED
+ return inline_memset_arm_mid_end(dst, value, size);
+#else
+ return inline_memset_arm_low_end(dst, value, size);
+#endif
+}
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_STRING_MEMORY_UTILS_ARM_INLINE_MEMCPY_H
diff --git a/libc/src/string/memory_utils/inline_memset.h b/libc/src/string/memory_utils/inline_memset.h
index fd9c29ea4410..e41bdb626d60 100644
--- a/libc/src/string/memory_utils/inline_memset.h
+++ b/libc/src/string/memory_utils/inline_memset.h
@@ -18,6 +18,9 @@
#if defined(LIBC_TARGET_ARCH_IS_X86)
#include "src/string/memory_utils/x86_64/inline_memset.h"
#define LIBC_SRC_STRING_MEMORY_UTILS_MEMSET inline_memset_x86
+#elif defined(LIBC_TARGET_ARCH_IS_ARM)
+#include "src/string/memory_utils/arm/inline_memset.h"
+#define LIBC_SRC_STRING_MEMORY_UTILS_MEMSET inline_memset_arm_dispatch
#elif defined(LIBC_TARGET_ARCH_IS_AARCH64)
#include "src/string/memory_utils/aarch64/inline_memset.h"
#define LIBC_SRC_STRING_MEMORY_UTILS_MEMSET inline_memset_aarch64_dispatch
@@ -34,7 +37,8 @@
namespace LIBC_NAMESPACE_DECL {
-LIBC_INLINE static void inline_memset(void *dst, uint8_t value, size_t count) {
+[[gnu::flatten]] LIBC_INLINE void inline_memset(void *dst, uint8_t value,
+ size_t count) {
LIBC_SRC_STRING_MEMORY_UTILS_MEMSET(reinterpret_cast<Ptr>(dst), value, count);
}
diff --git a/libc/src/time/baremetal/CMakeLists.txt b/libc/src/time/baremetal/CMakeLists.txt
index bf0d42e265d6..3072c8b14959 100644
--- a/libc/src/time/baremetal/CMakeLists.txt
+++ b/libc/src/time/baremetal/CMakeLists.txt
@@ -1,4 +1,15 @@
add_entrypoint_object(
+ clock
+ SRCS
+ clock.cpp
+ HDRS
+ ../clock.h
+ DEPENDS
+ libc.hdr.time_macros
+ libc.hdr.types.struct_timespec
+)
+
+add_entrypoint_object(
timespec_get
SRCS
timespec_get.cpp
diff --git a/libc/src/time/baremetal/clock.cpp b/libc/src/time/baremetal/clock.cpp
new file mode 100644
index 000000000000..26b75d782952
--- /dev/null
+++ b/libc/src/time/baremetal/clock.cpp
@@ -0,0 +1,45 @@
+//===-- Baremetal implementation of the clock function --------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/time/clock.h"
+#include "hdr/time_macros.h"
+#include "hdr/types/struct_timespec.h"
+#include "src/__support/CPP/limits.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/time/units.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+extern "C" bool __llvm_libc_timespec_get_active(struct timespec *ts);
+
+LLVM_LIBC_FUNCTION(clock_t, clock, ()) {
+ using namespace time_units;
+ struct timespec ts;
+ if (!__llvm_libc_timespec_get_active(&ts))
+ return clock_t(-1);
+
+ // The above call gets the CPU time in seconds plus nanoseconds.
+ // The standard requires that we return clock_t(-1) if we cannot represent
+ // clocks as a clock_t value.
+ constexpr clock_t CLOCK_SECS_MAX =
+ cpp::numeric_limits<clock_t>::max() / CLOCKS_PER_SEC;
+ if (ts.tv_sec > CLOCK_SECS_MAX)
+ return clock_t(-1);
+ if (ts.tv_nsec / 1_s_ns > CLOCK_SECS_MAX - ts.tv_sec)
+ return clock_t(-1);
+
+ // For the integer computation converting tv_nsec to clocks to work
+ // correctly, we want CLOCKS_PER_SEC to be less than 1000000000.
+ static_assert(1_s_ns > CLOCKS_PER_SEC,
+ "Expected CLOCKS_PER_SEC to be less than 1'000'000'000.");
+ return clock_t(ts.tv_sec * CLOCKS_PER_SEC +
+ ts.tv_nsec / (1_s_ns / CLOCKS_PER_SEC));
+}
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/wchar/CMakeLists.txt b/libc/src/wchar/CMakeLists.txt
index e3bd357a8fd1..7ace1a6ca66b 100644
--- a/libc/src/wchar/CMakeLists.txt
+++ b/libc/src/wchar/CMakeLists.txt
@@ -46,6 +46,50 @@ add_entrypoint_object(
)
add_entrypoint_object(
+ wcstol
+ SRCS
+ wcstol.cpp
+ HDRS
+ wcstol.h
+ DEPENDS
+ libc.src.errno.errno
+ libc.src.__support.wcs_to_integer
+)
+
+add_entrypoint_object(
+ wcstoll
+ SRCS
+ wcstoll.cpp
+ HDRS
+ wcstoll.h
+ DEPENDS
+ libc.src.errno.errno
+ libc.src.__support.wcs_to_integer
+)
+
+add_entrypoint_object(
+ wcstoul
+ SRCS
+ wcstoul.cpp
+ HDRS
+ wcstoul.h
+ DEPENDS
+ libc.src.errno.errno
+ libc.src.__support.wcs_to_integer
+)
+
+add_entrypoint_object(
+ wcstoull
+ SRCS
+ wcstoull.cpp
+ HDRS
+ wcstoull.h
+ DEPENDS
+ libc.src.errno.errno
+ libc.src.__support.wcs_to_integer
+)
+
+add_entrypoint_object(
wcstok
SRCS
wcstok.cpp
diff --git a/libc/src/wchar/wcstol.cpp b/libc/src/wchar/wcstol.cpp
new file mode 100644
index 000000000000..a05718f706df
--- /dev/null
+++ b/libc/src/wchar/wcstol.cpp
@@ -0,0 +1,30 @@
+//===-- Implementation of wcstol ------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/wchar/wcstol.h"
+#include "src/__support/common.h"
+#include "src/__support/libc_errno.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/wcs_to_integer.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+LLVM_LIBC_FUNCTION(long, wcstol,
+ (const wchar_t *__restrict str, wchar_t **__restrict str_end,
+ int base)) {
+ auto result = internal::wcstointeger<long>(str, base);
+ if (result.has_error())
+ libc_errno = result.error;
+
+ if (str_end != nullptr)
+ *str_end = const_cast<wchar_t *>(str + result.parsed_len);
+
+ return result;
+}
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/wchar/wcstol.h b/libc/src/wchar/wcstol.h
new file mode 100644
index 000000000000..08acd9717a23
--- /dev/null
+++ b/libc/src/wchar/wcstol.h
@@ -0,0 +1,22 @@
+//===-- Implementation header for wcstol ------------------------*- 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_WCHAR_WCSTOL_H
+#define LLVM_LIBC_SRC_WCHAR_WCSTOL_H
+
+#include "hdr/types/wint_t.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+long wcstol(const wchar_t *__restrict str, wchar_t **__restrict str_end,
+ int base);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_WCHAR_WCSTOL_H
diff --git a/libc/src/wchar/wcstoll.cpp b/libc/src/wchar/wcstoll.cpp
new file mode 100644
index 000000000000..de1299d681cd
--- /dev/null
+++ b/libc/src/wchar/wcstoll.cpp
@@ -0,0 +1,30 @@
+//===-- Implementation of wcstoll -----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/wchar/wcstoll.h"
+#include "src/__support/common.h"
+#include "src/__support/libc_errno.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/wcs_to_integer.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+LLVM_LIBC_FUNCTION(long long, wcstoll,
+ (const wchar_t *__restrict str, wchar_t **__restrict str_end,
+ int base)) {
+ auto result = internal::wcstointeger<long long>(str, base);
+ if (result.has_error())
+ libc_errno = result.error;
+
+ if (str_end != nullptr)
+ *str_end = const_cast<wchar_t *>(str + result.parsed_len);
+
+ return result;
+}
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/wchar/wcstoll.h b/libc/src/wchar/wcstoll.h
new file mode 100644
index 000000000000..627804356949
--- /dev/null
+++ b/libc/src/wchar/wcstoll.h
@@ -0,0 +1,22 @@
+//===-- Implementation header for wcstoll -----------------------*- 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_WCHAR_WCSTOLL_H
+#define LLVM_LIBC_SRC_WCHAR_WCSTOLL_H
+
+#include "hdr/types/wint_t.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+long long wcstoll(const wchar_t *__restrict str, wchar_t **__restrict str_end,
+ int base);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_WCHAR_WCSTOLL_H
diff --git a/libc/src/wchar/wcstoul.cpp b/libc/src/wchar/wcstoul.cpp
new file mode 100644
index 000000000000..79b8c9b5c9fa
--- /dev/null
+++ b/libc/src/wchar/wcstoul.cpp
@@ -0,0 +1,30 @@
+//===-- Implementation of wcstoul -----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/wchar/wcstoul.h"
+#include "src/__support/common.h"
+#include "src/__support/libc_errno.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/wcs_to_integer.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+LLVM_LIBC_FUNCTION(unsigned long, wcstoul,
+ (const wchar_t *__restrict str, wchar_t **__restrict str_end,
+ int base)) {
+ auto result = internal::wcstointeger<unsigned long>(str, base);
+ if (result.has_error())
+ libc_errno = result.error;
+
+ if (str_end != nullptr)
+ *str_end = const_cast<wchar_t *>(str + result.parsed_len);
+
+ return result;
+}
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/wchar/wcstoul.h b/libc/src/wchar/wcstoul.h
new file mode 100644
index 000000000000..81f530534e81
--- /dev/null
+++ b/libc/src/wchar/wcstoul.h
@@ -0,0 +1,22 @@
+//===-- Implementation header for wcstoul -----------------------*- 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_WCHAR_WCSTOUL_H
+#define LLVM_LIBC_SRC_WCHAR_WCSTOUL_H
+
+#include "hdr/types/wint_t.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+unsigned long wcstoul(const wchar_t *__restrict str,
+ wchar_t **__restrict str_end, int base);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_WCHAR_WCSTOUL_H
diff --git a/libc/src/wchar/wcstoull.cpp b/libc/src/wchar/wcstoull.cpp
new file mode 100644
index 000000000000..768e03c4bd18
--- /dev/null
+++ b/libc/src/wchar/wcstoull.cpp
@@ -0,0 +1,30 @@
+//===-- Implementation of wcstoull ----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/wchar/wcstoull.h"
+#include "src/__support/common.h"
+#include "src/__support/libc_errno.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/wcs_to_integer.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+LLVM_LIBC_FUNCTION(unsigned long long, wcstoull,
+ (const wchar_t *__restrict str, wchar_t **__restrict str_end,
+ int base)) {
+ auto result = internal::wcstointeger<unsigned long long>(str, base);
+ if (result.has_error())
+ libc_errno = result.error;
+
+ if (str_end != nullptr)
+ *str_end = const_cast<wchar_t *>(str + result.parsed_len);
+
+ return result;
+}
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/wchar/wcstoull.h b/libc/src/wchar/wcstoull.h
new file mode 100644
index 000000000000..e970a5792338
--- /dev/null
+++ b/libc/src/wchar/wcstoull.h
@@ -0,0 +1,22 @@
+//===-- Implementation header for wcstoull -----------------------*- 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_WCHAR_WCSTOULL_H
+#define LLVM_LIBC_SRC_WCHAR_WCSTOULL_H
+
+#include "hdr/types/wint_t.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+unsigned long long wcstoull(const wchar_t *__restrict str,
+ wchar_t **__restrict str_end, int base);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_WCHAR_WCSTOULL_H
diff --git a/libc/src/wctype/CMakeLists.txt b/libc/src/wctype/CMakeLists.txt
new file mode 100644
index 000000000000..3ac5eaef8ed8
--- /dev/null
+++ b/libc/src/wctype/CMakeLists.txt
@@ -0,0 +1,9 @@
+add_entrypoint_object(
+ iswalpha
+ SRCS
+ iswalpha.cpp
+ HDRS
+ iswalpha.h
+ DEPENDS
+ libc.src.__support.wctype_utils
+)
diff --git a/libc/src/wctype/iswalpha.cpp b/libc/src/wctype/iswalpha.cpp
new file mode 100644
index 000000000000..e18f29370fbd
--- /dev/null
+++ b/libc/src/wctype/iswalpha.cpp
@@ -0,0 +1,19 @@
+//===-- Implementation of iswalpha ----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/wctype/iswalpha.h"
+#include "src/__support/common.h"
+#include "src/__support/wctype_utils.h"
+
+#include "hdr/types/wint_t.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+LLVM_LIBC_FUNCTION(bool, iswalpha, (wint_t c)) { return internal::iswalpha(c); }
+
+} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/wctype/iswalpha.h b/libc/src/wctype/iswalpha.h
new file mode 100644
index 000000000000..681fc6ba79a5
--- /dev/null
+++ b/libc/src/wctype/iswalpha.h
@@ -0,0 +1,21 @@
+//===-- Implementation header for iswalpha ----------------------*- 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_WCTYPE_ISWALPHA_H
+#define LLVM_LIBC_SRC_WCTYPE_ISWALPHA_H
+
+#include "hdr/types/wint_t.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+bool iswalpha(wint_t c);
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC_WCTYPE_ISWALPHA_H