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[libc][math] Refactor exp10f implementation to header-only in src/__support/math folder. (#148405)

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Part of #147386

in preparation for:
https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
This commit is contained in:
Muhammad Bassiouni
2025-07-17 20:25:00 +03:00
committed by GitHub
parent 46c059f925
commit b8bc3ff9be
15 changed files with 268 additions and 329 deletions
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1
libc/shared/math.h
View File

@@ -13,6 +13,7 @@
#include "math/exp.h"
#include "math/exp10.h"
#include "math/exp10f.h"
#include "math/expf.h"
#include "math/expf16.h"
#include "math/frexpf.h"

23
libc/shared/math/exp10f.h Normal file
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@@ -0,0 +1,23 @@
//===-- Shared exp10f function ----------------------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_LIBC_SHARED_MATH_EXP10F_H
#define LLVM_LIBC_SHARED_MATH_EXP10F_H
#include "shared/libc_common.h"
#include "src/__support/math/exp10f.h"
namespace LIBC_NAMESPACE_DECL {
namespace shared {
using math::exp10f;
} // namespace shared
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SHARED_MATH_EXP10F_H

28
libc/src/__support/math/CMakeLists.txt
View File

@@ -170,3 +170,31 @@ add_header_library(
libc.src.__support.integer_literals
libc.src.__support.macros.optimization
)
add_header_library(
exp10f_utils
HDRS
exp10f_utils.h
DEPENDS
libc.src.__support.FPUtil.basic_operations
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.nearest_integer
libc.src.__support.FPUtil.polyeval
libc.src.__support.common
libc.src.__support.math.exp_utils
)
add_header_library(
exp10f
HDRS
exp10f.h
DEPENDS
.exp10f_utils
libc.src.__support.macros.config
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
)

17
libc/src/math/generic/exp10f_impl.h → libc/src/__support/math/exp10f.h
View File

@@ -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

157
libc/src/__support/math/exp10f_utils.h Normal file
View File

@@ -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

37
libc/src/math/generic/CMakeLists.txt
View File

@@ -358,7 +358,6 @@ add_entrypoint_object(
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fma
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.macros.optimization
)
@@ -448,7 +447,6 @@ add_entrypoint_object(
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.fma
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
@@ -1461,21 +1459,6 @@ add_entrypoint_object(
libc.src.errno.errno
)
add_header_library(
exp10f_impl
HDRS
exp10f_impl.h
DEPENDS
.explogxf
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
libc.src.__support.common
libc.src.errno.errno
)
add_entrypoint_object(
exp10f
SRCS
@@ -1483,7 +1466,8 @@ add_entrypoint_object(
HDRS
../exp10f.h
DEPENDS
.exp10f_impl
libc.src.__support.math.exp10f
libc.src.errno.errno
)
add_entrypoint_object(
@@ -1620,17 +1604,15 @@ add_entrypoint_object(
../powf.h
DEPENDS
.common_constants
.exp10f_impl
.exp2f_impl
.explogxf
libc.src.__support.math.exp10f
libc.src.__support.CPP.bit
libc.src.__support.CPP.optional
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.nearest_integer
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.FPUtil.sqrt
libc.src.__support.FPUtil.triple_double
libc.src.__support.macros.optimization
@@ -3784,21 +3766,15 @@ 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.FPUtil.basic_operations
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.nearest_integer
libc.src.__support.FPUtil.polyeval
libc.src.__support.common
libc.src.__support.math.exp_utils
libc.src.__support.math.exp10f_utils
libc.src.__support.macros.properties.cpu_features
libc.src.errno.errno
)
@@ -3981,6 +3957,7 @@ add_entrypoint_object(
DEPENDS
.explogxf
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.macros.optimization
)

1
libc/src/math/generic/atanhf.cpp
View File

@@ -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

2
libc/src/math/generic/coshf.cpp
View File

@@ -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

7
libc/src/math/generic/exp10f.cpp
View File

@@ -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

75
libc/src/math/generic/explogxf.cpp
View File

@@ -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

182
libc/src/math/generic/explogxf.h
View File

@@ -10,166 +10,17 @@
#define LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H
#include "common_constants.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/properties/cpu_features.h"
#include "src/__support/common.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
@@ -269,33 +120,6 @@ template <bool is_sinh> LIBC_INLINE double exp_pm_eval(float x) {
return r;
}
// 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.

7
libc/src/math/generic/powf.cpp
View File

@@ -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
}

1
libc/src/math/generic/sinhf.cpp
View File

@@ -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"

5
libc/test/src/math/explogxf_test.cpp
View File

@@ -43,11 +43,6 @@ TEST_F(LlvmLibcExplogfTest, ExpInFloatRange) {
def_prec);
}
TEST_F(LlvmLibcExplogfTest, Log2InFloatRange) {
CHECK_DATA(0.0f, inf, mpfr::Operation::Log2, LIBC_NAMESPACE::log2_eval,
f_normal, def_count, def_prec);
}
TEST_F(LlvmLibcExplogfTest, LogInFloatRange) {
CHECK_DATA(0.0f, inf, mpfr::Operation::Log, LIBC_NAMESPACE::log_eval,
f_normal, def_count, def_prec);

54
utils/bazel/llvm-project-overlay/libc/BUILD.bazel
View File

@@ -1996,16 +1996,15 @@ libc_support_library(
libc_support_library(
name = "explogxf",
srcs = ["src/math/generic/explogxf.cpp"],
hdrs = ["src/math/generic/explogxf.h"],
deps = [
":__support_common",
":__support_fputil_fenv_impl",
":__support_fputil_fma",
":__support_fputil_multiply_add",
":__support_fputil_nearest_integer",
":__support_fputil_polyeval",
":__support_math_exp_utils",
":__support_math_exp10f_utils",
":__support_macros_properties_cpu_features",
":common_constants",
],
)
@@ -2050,19 +2049,6 @@ libc_support_library(
],
)
libc_support_library(
name = "exp10f_impl",
hdrs = ["src/math/generic/exp10f_impl.h"],
deps = [
":__support_fputil_fma",
":__support_fputil_multiply_add",
":__support_fputil_rounding_mode",
":__support_macros_optimization",
":common_constants",
":explogxf",
],
)
libc_support_library(
name = "exp2f_impl",
hdrs = ["src/math/generic/exp2f_impl.h"],
@@ -2263,6 +2249,33 @@ libc_support_library(
],
)
libc_support_library(
name = "__support_math_exp10f_utils",
hdrs = ["src/__support/math/exp10f_utils.h"],
deps = [
":__support_fputil_basic_operations",
":__support_fputil_fenv_impl",
":__support_fputil_multiply_add",
":__support_fputil_nearest_integer",
":__support_fputil_polyeval",
":__support_common",
":__support_math_exp_utils",
],
)
libc_support_library(
name = "__support_math_exp10f",
hdrs = ["src/__support/math/exp10f.h"],
deps = [
":__support_math_exp10f_utils",
":__support_fputil_fenv_impl",
":__support_fputil_fp_bits",
":__support_fputil_multiply_add",
":__support_fputil_rounding_mode",
":__support_macros_optimization",
],
)
############################### complex targets ################################
libc_function(
@@ -2726,10 +2739,10 @@ libc_math_function(
name = "cosf",
additional_deps = [
":__support_fputil_fma",
":__support_fputil_multiply_add",
":__support_macros_optimization",
":__support_macros_properties_cpu_features",
":sincosf_utils",
":errno",
],
)
@@ -2875,7 +2888,8 @@ libc_math_function(
libc_math_function(
name = "exp10f",
additional_deps = [
":exp10f_impl",
":__support_math_exp10f",
":errno",
],
)
@@ -3724,14 +3738,13 @@ libc_math_function(
":__support_fputil_multiply_add",
":__support_fputil_nearest_integer",
":__support_fputil_polyeval",
":__support_fputil_rounding_mode",
":__support_fputil_sqrt",
":__support_fputil_triple_double",
":__support_macros_optimization",
":__support_math_exp10f",
":common_constants",
":explogxf",
":exp2f_impl",
":exp10f_impl",
],
)
@@ -3840,7 +3853,6 @@ libc_math_function(
name = "sinf",
additional_deps = [
":__support_fputil_fma",
":__support_fputil_multiply_add",
":__support_fputil_polyeval",
":__support_fputil_rounding_mode",
":__support_macros_optimization",