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[libc][math] Refactor exp2m1f implementation to header-only in src/__support/math folder.
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9 files changed

+259
-188
lines changed

9 files changed

+259
-188
lines changed

‎libc/shared/math.h‎

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@@ -50,6 +50,7 @@
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#include "math/exp2.h"
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#include "math/exp2f.h"
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#include "math/exp2f16.h"
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#include "math/exp2m1f.h"
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#include "math/expf.h"
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#include "math/expf16.h"
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#include "math/frexpf.h"

‎libc/shared/math/exp2m1f.h‎

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//===-- Shared exp2m1f function ---------------------------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_SHARED_MATH_EXP2M1F_H
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#define LLVM_LIBC_SHARED_MATH_EXP2M1F_H
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#include "shared/libc_common.h"
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#include "src/__support/math/exp2m1f.h"
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namespace LIBC_NAMESPACE_DECL {
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namespace shared {
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using math::exp2m1f;
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} // namespace shared
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LLVM_LIBC_SHARED_MATH_EXP2M1F_H

‎libc/src/__support/math/CMakeLists.txt‎

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@@ -767,6 +767,24 @@ add_header_library(
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libc.src.__support.macros.optimization
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)
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add_header_library(
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exp2m1f
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HDRS
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exp2m1f.h
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DEPENDS
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.exp10f_utils
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libc.src.errno.errno
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libc.src.__support.common
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libc.src.__support.FPUtil.except_value_utils
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libc.src.__support.FPUtil.fenv_impl
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libc.src.__support.FPUtil.fp_bits
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libc.src.__support.FPUtil.multiply_add
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libc.src.__support.FPUtil.polyeval
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libc.src.__support.FPUtil.rounding_mode
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libc.src.__support.macros.optimization
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libc.src.__support.macros.properties.cpu_features
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)
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add_header_library(
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exp10
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HDRS

‎libc/src/__support/math/exp2m1f.h‎

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//===-- Implementation header for exp2m1f ------------------------*- C++-*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP2M1F_H
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#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP2M1F_H
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#include "exp10f_utils.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FPBits.h"
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#include "src/__support/FPUtil/PolyEval.h"
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#include "src/__support/FPUtil/except_value_utils.h"
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#include "src/__support/FPUtil/multiply_add.h"
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#include "src/__support/FPUtil/rounding_mode.h"
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#include "src/__support/common.h"
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#include "src/__support/libc_errno.h"
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#include "src/__support/macros/config.h"
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#include "src/__support/macros/optimization.h"
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#include "src/__support/macros/properties/cpu_features.h"
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namespace LIBC_NAMESPACE_DECL {
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namespace math {
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LIBC_INLINE static constexpr float exp2m1f(float x) {
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#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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constexpr size_t N_EXCEPTS_LO = 8;
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constexpr fputil::ExceptValues<float, N_EXCEPTS_LO> EXP2M1F_EXCEPTS_LO = {{
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// (input, RZ output, RU offset, RD offset, RN offset)
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// x = 0x1.36dc8ep-36, exp2m1f(x) = 0x1.aef212p-37 (RZ)
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{0x2d9b'6e47U, 0x2d57'7909U, 1U, 0U, 0U},
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// x = 0x1.224936p-19, exp2m1f(x) = 0x1.926c0ep-20 (RZ)
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{0x3611'249bU, 0x35c9'3607U, 1U, 0U, 1U},
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// x = 0x1.d16d2p-20, exp2m1f(x) = 0x1.429becp-20 (RZ)
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{0x35e8'b690U, 0x35a1'4df6U, 1U, 0U, 1U},
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// x = 0x1.17949ep-14, exp2m1f(x) = 0x1.8397p-15 (RZ)
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{0x388b'ca4fU, 0x3841'cb80U, 1U, 0U, 1U},
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// x = -0x1.9c3e1ep-38, exp2m1f(x) = -0x1.1dbeacp-38 (RZ)
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{0xacce'1f0fU, 0xac8e'df56U, 0U, 1U, 0U},
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// x = -0x1.4d89b4p-32, exp2m1f(x) = -0x1.ce61b6p-33 (RZ)
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{0xafa6'c4daU, 0xaf67'30dbU, 0U, 1U, 1U},
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// x = -0x1.a6eac4p-10, exp2m1f(x) = -0x1.24fadap-10 (RZ)
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{0xbad3'7562U, 0xba92'7d6dU, 0U, 1U, 1U},
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// x = -0x1.e7526ep-6, exp2m1f(x) = -0x1.4e53dep-6 (RZ)
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{0xbcf3'a937U, 0xbca7'29efU, 0U, 1U, 1U},
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}};
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constexpr size_t N_EXCEPTS_HI = 3;
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constexpr fputil::ExceptValues<float, N_EXCEPTS_HI> EXP2M1F_EXCEPTS_HI = {{
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// (input, RZ output, RU offset, RD offset, RN offset)
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// x = 0x1.16a972p-1, exp2m1f(x) = 0x1.d545b2p-2 (RZ)
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{0x3f0b'54b9U, 0x3eea'a2d9U, 1U, 0U, 0U},
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// x = -0x1.9f12acp-5, exp2m1f(x) = -0x1.1ab68cp-5 (RZ)
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{0xbd4f'8956U, 0xbd0d'5b46U, 0U, 1U, 0U},
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// x = -0x1.de7b9cp-5, exp2m1f(x) = -0x1.4508f4p-5 (RZ)
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{0xbd6f'3dceU, 0xbd22'847aU, 0U, 1U, 1U},
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}};
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#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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using FPBits = fputil::FPBits<float>;
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FPBits xbits(x);
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uint32_t x_u = xbits.uintval();
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uint32_t x_abs = x_u & 0x7fff'ffffU;
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// When |x| >= 128, or x is nan, or |x| <= 2^-5
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if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) {
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// |x| <= 2^-5
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if (x_abs <= 0x3d00'0000U) {
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#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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if (auto r = EXP2M1F_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
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return r.value();
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#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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// Minimax polynomial generated by Sollya with:
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// > display = hexadecimal;
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// > fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]);
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constexpr double COEFFS[] = {
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0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3, 0x1.c6b08d6f2d7aap-5,
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0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13};
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double xd = x;
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double xsq = xd * xd;
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double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
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double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
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double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
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double p = fputil::polyeval(xsq, c0, c1, c2);
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return static_cast<float>(p * xd);
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}
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// x >= 128, or x is nan
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if (xbits.is_pos()) {
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if (xbits.is_finite()) {
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int rounding = fputil::quick_get_round();
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if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
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return FPBits::max_normal().get_val();
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fputil::set_errno_if_required(ERANGE);
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fputil::raise_except_if_required(FE_OVERFLOW);
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}
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// x >= 128 and 2^x - 1 rounds to +inf, or x is +inf or nan
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return x + FPBits::inf().get_val();
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}
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}
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if (LIBC_UNLIKELY(x <= -25.0f)) {
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// 2^(-inf) - 1 = -1
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if (xbits.is_inf())
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return -1.0f;
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// 2^nan - 1 = nan
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if (xbits.is_nan())
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return x;
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int rounding = fputil::quick_get_round();
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if (rounding == FE_UPWARD || rounding == FE_TOWARDZERO)
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return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
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fputil::set_errno_if_required(ERANGE);
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fputil::raise_except_if_required(FE_UNDERFLOW);
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return -1.0f;
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}
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#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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if (auto r = EXP2M1F_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
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return r.value();
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#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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// For -25 < x < 128, to compute 2^x, we perform the following range
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// reduction: find hi, mid, lo such that:
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// x = hi + mid + lo, in which:
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// hi is an integer,
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// 0 <= mid * 2^5 < 32 is an integer,
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// -2^(-6) <= lo <= 2^(-6).
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// In particular,
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// hi + mid = round(x * 2^5) * 2^(-5).
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// Then,
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// 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
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// 2^mid is stored in the lookup table of 32 elements.
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// 2^lo is computed using a degree-4 minimax polynomial generated by Sollya.
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// We perform 2^hi * 2^mid by simply add hi to the exponent field of 2^mid.
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// kf = (hi + mid) * 2^5 = round(x * 2^5)
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float kf = 0;
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int k = 0;
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#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
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kf = fputil::nearest_integer(x * 32.0f);
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k = static_cast<int>(kf);
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#else
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constexpr float HALF[2] = {0.5f, -0.5f};
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k = static_cast<int>(fputil::multiply_add(x, 32.0f, HALF[x < 0.0f]));
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kf = static_cast<float>(k);
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#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
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// lo = x - (hi + mid) = x - kf * 2^(-5)
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double lo = fputil::multiply_add(-0x1.0p-5f, kf, x);
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// hi = floor(kf * 2^(-4))
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// exp2_hi = shift hi to the exponent field of double precision.
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int64_t exp2_hi =
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static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS)
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<< fputil::FPBits<double>::FRACTION_LEN);
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// mh = 2^hi * 2^mid
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// mh_bits = bit field of mh
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int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp2_hi;
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double mh = fputil::FPBits<double>(static_cast<uint64_t>(mh_bits)).get_val();
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// Degree-4 polynomial approximating (2^x - 1)/x generated by Sollya with:
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// > display = hexadecimal;
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// > fpminimax((2^x - 1)/x, 4, [|D...|], [-2^-6, 2^-6]);
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constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
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0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
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0x1.5d88091198529p-10};
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double lo_sq = lo * lo;
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double c1 = fputil::multiply_add(lo, COEFFS[0], 1.0);
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double c2 = fputil::multiply_add(lo, COEFFS[2], COEFFS[1]);
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double c3 = fputil::multiply_add(lo, COEFFS[4], COEFFS[3]);
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double exp2_lo = fputil::polyeval(lo_sq, c1, c2, c3);
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// 2^x - 1 = 2^(hi + mid + lo) - 1
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// = 2^(hi + mid) * 2^lo - 1
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// ~ mh * (1 + lo * P(lo)) - 1
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// = mh * exp2_lo - 1
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return static_cast<float>(fputil::multiply_add(exp2_lo, mh, -1.0));
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}
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} // namespace math
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP2M1F_H

‎libc/src/math/generic/CMakeLists.txt‎

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@@ -1478,17 +1478,7 @@ add_entrypoint_object(
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HDRS
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../exp2m1f.h
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DEPENDS
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libc.src.errno.errno
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libc.src.__support.common
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libc.src.__support.FPUtil.except_value_utils
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libc.src.__support.FPUtil.fenv_impl
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libc.src.__support.FPUtil.fp_bits
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libc.src.__support.FPUtil.multiply_add
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libc.src.__support.FPUtil.polyeval
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libc.src.__support.FPUtil.rounding_mode
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libc.src.__support.macros.optimization
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libc.src.__support.macros.properties.cpu_features
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libc.src.__support.math.exp10f_utils
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libc.src.__support.math.exp2m1f
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)
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add_entrypoint_object(

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