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bassiounixbassiounix
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[libc][math] Refactor expm1f implementation to header-only in src/__support/math folder.
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9 files changed

+244
-178
lines changed

9 files changed

+244
-178
lines changed

‎libc/shared/math.h‎

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@@ -55,6 +55,7 @@
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#include "math/expf.h"
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#include "math/expf16.h"
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#include "math/expm1.h"
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#include "math/expm1f.h"
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#include "math/frexpf.h"
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#include "math/frexpf128.h"
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#include "math/frexpf16.h"

‎libc/shared/math/expm1f.h‎

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//===-- Shared expm1f 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_EXPM1F_H
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#define LLVM_LIBC_SHARED_MATH_EXPM1F_H
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#include "shared/libc_common.h"
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#include "src/__support/math/expm1f.h"
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namespace LIBC_NAMESPACE_DECL {
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namespace shared {
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using math::expm1f;
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} // namespace shared
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LLVM_LIBC_SHARED_MATH_EXPM1F_H

‎libc/src/__support/math/CMakeLists.txt‎

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@@ -906,6 +906,23 @@ add_header_library(
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libc.src.errno.errno
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)
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add_header_library(
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expm1f
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HDRS
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expm1f.h
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DEPENDS
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.common_constants
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libc.src.__support.FPUtil.basic_operations
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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.nearest_integer
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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.errno.errno
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)
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add_header_library(
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range_reduction_double
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HDRS

‎libc/src/__support/math/expm1f.h‎

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//===-- Implementation header for expm1f ------------------------*- 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_EXPM1F_H
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#define LLVM_LIBC_SRC___SUPPORT_MATH_EXPM1F_H
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#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
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#include "src/__support/FPUtil/BasicOperations.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FMA.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/multiply_add.h"
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#include "src/__support/FPUtil/nearest_integer.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/macros/config.h"
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#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
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#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
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namespace LIBC_NAMESPACE_DECL {
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namespace math {
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LIBC_INLINE static constexpr float expm1f(float x) {
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using namespace common_constants_internal;
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using FPBits = typename 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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#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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// Exceptional value
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if (LIBC_UNLIKELY(x_u == 0x3e35'bec5U)) { // x = 0x1.6b7d8ap-3f
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int round_mode = fputil::quick_get_round();
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if (round_mode == FE_TONEAREST || round_mode == FE_UPWARD)
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return 0x1.8dbe64p-3f;
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return 0x1.8dbe62p-3f;
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}
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#if !defined(LIBC_TARGET_CPU_HAS_FMA_DOUBLE)
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if (LIBC_UNLIKELY(x_u == 0xbdc1'c6cbU)) { // x = -0x1.838d96p-4f
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int round_mode = fputil::quick_get_round();
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if (round_mode == FE_TONEAREST || round_mode == FE_DOWNWARD)
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return -0x1.71c884p-4f;
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return -0x1.71c882p-4f;
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}
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#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
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#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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// When |x| > 25*log(2), or nan
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if (LIBC_UNLIKELY(x_abs >= 0x418a'a123U)) {
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// x < log(2^-25)
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if (xbits.is_neg()) {
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// exp(-Inf) = 0
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if (xbits.is_inf())
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return -1.0f;
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// exp(nan) = nan
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if (xbits.is_nan())
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return x;
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int round_mode = fputil::quick_get_round();
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if (round_mode == FE_UPWARD || round_mode == FE_TOWARDZERO)
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return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
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return -1.0f;
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} else {
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// x >= 89 or nan
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if (xbits.uintval() >= 0x42b2'0000) {
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if (xbits.uintval() < 0x7f80'0000U) {
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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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return x + FPBits::inf().get_val();
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}
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}
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}
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// |x| < 2^-4
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if (x_abs < 0x3d80'0000U) {
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// |x| < 2^-25
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if (x_abs < 0x3300'0000U) {
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// x = -0.0f
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if (LIBC_UNLIKELY(xbits.uintval() == 0x8000'0000U))
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return x;
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// When |x| < 2^-25, the relative error of the approximation e^x - 1 ~ x
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// is:
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// |(e^x - 1) - x| / |e^x - 1| < |x^2| / |x|
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// = |x|
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// < 2^-25
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// < epsilon(1)/2.
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// So the correctly rounded values of expm1(x) are:
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// = x + eps(x) if rounding mode = FE_UPWARD,
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// or (rounding mode = FE_TOWARDZERO and x is
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// negative),
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// = x otherwise.
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// To simplify the rounding decision and make it more efficient, we use
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// fma(x, x, x) ~ x + x^2 instead.
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// Note: to use the formula x + x^2 to decide the correct rounding, we
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// do need fma(x, x, x) to prevent underflow caused by x*x when |x| <
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// 2^-76. For targets without FMA instructions, we simply use double for
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// intermediate results as it is more efficient than using an emulated
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// version of FMA.
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#if defined(LIBC_TARGET_CPU_HAS_FMA_FLOAT)
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return fputil::multiply_add(x, x, x);
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#else
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double xd = x;
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return static_cast<float>(fputil::multiply_add(xd, xd, xd));
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#endif // LIBC_TARGET_CPU_HAS_FMA_FLOAT
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}
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constexpr double COEFFS[] = {0x1p-1,
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0x1.55555555557ddp-3,
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0x1.55555555552fap-5,
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0x1.111110fcd58b7p-7,
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0x1.6c16c1717660bp-10,
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0x1.a0241f0006d62p-13,
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0x1.a01e3f8d3c06p-16};
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// 2^-25 <= |x| < 2^-4
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double xd = static_cast<double>(x);
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double xsq = xd * xd;
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// Degree-8 minimax polynomial generated by Sollya with:
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// > display = hexadecimal;
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// > P = fpminimax((expm1(x) - x)/x^2, 6, [|D...|], [-2^-4, 2^-4]);
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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 r = fputil::polyeval(xsq, c0, c1, c2, COEFFS[6]);
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return static_cast<float>(fputil::multiply_add(r, xsq, xd));
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}
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// For -18 < x < 89, to compute expm1(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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// mid * 2^7 is an integer
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// -2^(-8) <= lo < 2^-8.
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// In particular,
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// hi + mid = round(x * 2^7) * 2^(-7).
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// Then,
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// expm1(x) = exp(hi + mid + lo) - 1 = exp(hi) * exp(mid) * exp(lo) - 1.
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// We store exp(hi) and exp(mid) in the lookup tables EXP_M1 and EXP_M2
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// respectively. exp(lo) is computed using a degree-4 minimax polynomial
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// generated by Sollya.
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// x_hi = hi + mid.
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float kf = fputil::nearest_integer(x * 0x1.0p7f);
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int x_hi = static_cast<int>(kf);
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// Subtract (hi + mid) from x to get lo.
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double xd = static_cast<double>(fputil::multiply_add(kf, -0x1.0p-7f, x));
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x_hi += 104 << 7;
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// hi = x_hi >> 7
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double exp_hi = EXP_M1[x_hi >> 7];
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// lo = x_hi & 0x0000'007fU;
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double exp_mid = EXP_M2[x_hi & 0x7f];
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double exp_hi_mid = exp_hi * exp_mid;
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// Degree-4 minimax polynomial generated by Sollya with the following
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// commands:
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// > display = hexadecimal;
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// > Q = fpminimax(expm1(x)/x, 3, [|D...|], [-2^-8, 2^-8]);
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// > Q;
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double exp_lo =
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fputil::polyeval(xd, 0x1.0p0, 0x1.ffffffffff777p-1, 0x1.000000000071cp-1,
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0x1.555566668e5e7p-3, 0x1.55555555ef243p-5);
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return static_cast<float>(fputil::multiply_add(exp_hi_mid, exp_lo, -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_EXPM1F_H

‎libc/src/math/generic/CMakeLists.txt‎

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@@ -1561,16 +1561,7 @@ add_entrypoint_object(
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HDRS
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../expm1f.h
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DEPENDS
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libc.src.__support.FPUtil.basic_operations
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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.nearest_integer
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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.math.common_constants
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libc.src.errno.errno
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libc.src.__support.math.expm1f
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)
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add_entrypoint_object(

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