117 lines · c
1//===-- Implementation header for expf --------------------------*- C++ -*-===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8 9#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H11 12#include "exp_float_constants.h" // Lookup tables EXP_M1 and EXP_M2.13#include "src/__support/FPUtil/FEnvImpl.h"14#include "src/__support/FPUtil/FPBits.h"15#include "src/__support/FPUtil/PolyEval.h"16#include "src/__support/FPUtil/multiply_add.h"17#include "src/__support/FPUtil/nearest_integer.h"18#include "src/__support/FPUtil/rounding_mode.h"19#include "src/__support/common.h"20#include "src/__support/macros/config.h"21#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY22 23namespace LIBC_NAMESPACE_DECL {24 25namespace math {26 27LIBC_INLINE static constexpr float expf(float x) {28 using FPBits = typename fputil::FPBits<float>;29 FPBits xbits(x);30 31 uint32_t x_u = xbits.uintval();32 uint32_t x_abs = x_u & 0x7fff'ffffU;33 34#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS35 // Exceptional values36 if (LIBC_UNLIKELY(x_u == 0xc236'bd8cU)) { // x = -0x1.6d7b18p+5f37 return 0x1.108a58p-66f - x * 0x1.0p-95f;38 }39#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS40 41 // When |x| >= 89, |x| < 2^-25, or x is nan42 if (LIBC_UNLIKELY(x_abs >= 0x42b2'0000U || x_abs <= 0x3280'0000U)) {43 // |x| < 2^-2544 if (xbits.get_biased_exponent() <= 101) {45 return 1.0f + x;46 }47 48 // When x < log(2^-150) or nan49 if (xbits.uintval() >= 0xc2cf'f1b5U) {50 // exp(-Inf) = 051 if (xbits.is_inf())52 return 0.0f;53 // exp(nan) = nan54 if (xbits.is_nan())55 return x;56 if (fputil::fenv_is_round_up())57 return FPBits::min_subnormal().get_val();58 fputil::set_errno_if_required(ERANGE);59 fputil::raise_except_if_required(FE_UNDERFLOW);60 return 0.0f;61 }62 // x >= 89 or nan63 if (xbits.is_pos() && (xbits.uintval() >= 0x42b2'0000)) {64 // x is finite65 if (xbits.uintval() < 0x7f80'0000U) {66 int rounding = fputil::quick_get_round();67 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)68 return FPBits::max_normal().get_val();69 70 fputil::set_errno_if_required(ERANGE);71 fputil::raise_except_if_required(FE_OVERFLOW);72 }73 // x is +inf or nan74 return x + FPBits::inf().get_val();75 }76 }77 // For -104 < x < 89, to compute exp(x), we perform the following range78 // reduction: find hi, mid, lo such that:79 // x = hi + mid + lo, in which80 // hi is an integer,81 // mid * 2^7 is an integer82 // -2^(-8) <= lo < 2^-8.83 // In particular,84 // hi + mid = round(x * 2^7) * 2^(-7).85 // Then,86 // exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo).87 // We store exp(hi) and exp(mid) in the lookup tables EXP_M1 and EXP_M288 // respectively. exp(lo) is computed using a degree-4 minimax polynomial89 // generated by Sollya.90 91 // x_hi = (hi + mid) * 2^7 = round(x * 2^7).92 float kf = fputil::nearest_integer(x * 0x1.0p7f);93 // Subtract (hi + mid) from x to get lo.94 double xd = static_cast<double>(fputil::multiply_add(kf, -0x1.0p-7f, x));95 int x_hi = static_cast<int>(kf);96 x_hi += 104 << 7;97 // hi = x_hi >> 798 double exp_hi = EXP_M1[x_hi >> 7];99 // mid * 2^7 = x_hi & 0x0000'007fU;100 double exp_mid = EXP_M2[x_hi & 0x7f];101 // Degree-4 minimax polynomial generated by Sollya with the following102 // commands:103 // > display = hexadecimal;104 // > Q = fpminimax(expm1(x)/x, 3, [|D...|], [-2^-8, 2^-8]);105 // > Q;106 double exp_lo =107 fputil::polyeval(xd, 0x1p0, 0x1.ffffffffff777p-1, 0x1.000000000071cp-1,108 0x1.555566668e5e7p-3, 0x1.55555555ef243p-5);109 return static_cast<float>(exp_hi * exp_mid * exp_lo);110}111 112} // namespace math113 114} // namespace LIBC_NAMESPACE_DECL115 116#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H117