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1//===-- Implementation header for exp10f ------------------------*- 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_EXP10F_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_H11 12#include "exp10f_utils.h"13#include "src/__support/FPUtil/FEnvImpl.h"14#include "src/__support/FPUtil/FPBits.h"15#include "src/__support/FPUtil/multiply_add.h"16#include "src/__support/FPUtil/rounding_mode.h"17#include "src/__support/macros/config.h"18#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY19 20namespace LIBC_NAMESPACE_DECL {21namespace math {22 23LIBC_INLINE static constexpr float exp10f(float x) {24 using FPBits = typename fputil::FPBits<float>;25 FPBits xbits(x);26 27 uint32_t x_u = xbits.uintval();28 uint32_t x_abs = x_u & 0x7fff'ffffU;29 30 // When |x| >= log10(2^128), or x is nan31 if (LIBC_UNLIKELY(x_abs >= 0x421a'209bU)) {32 // When x < log10(2^-150) or nan33 if (x_u > 0xc234'9e35U) {34 // exp(-Inf) = 035 if (xbits.is_inf())36 return 0.0f;37 // exp(nan) = nan38 if (xbits.is_nan())39 return x;40 if (fputil::fenv_is_round_up())41 return FPBits::min_subnormal().get_val();42 fputil::set_errno_if_required(ERANGE);43 fputil::raise_except_if_required(FE_UNDERFLOW);44 return 0.0f;45 }46 // x >= log10(2^128) or nan47 if (xbits.is_pos() && (x_u >= 0x421a'209bU)) {48 // x is finite49 if (x_u < 0x7f80'0000U) {50 int rounding = fputil::quick_get_round();51 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)52 return FPBits::max_normal().get_val();53 54 fputil::set_errno_if_required(ERANGE);55 fputil::raise_except_if_required(FE_OVERFLOW);56 }57 // x is +inf or nan58 return x + FPBits::inf().get_val();59 }60 }61 62 // When |x| <= log10(2)*2^-663 if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) {64 if (LIBC_UNLIKELY(x_u == 0xb25e'5bd9U)) { // x = -0x1.bcb7b2p-27f65 if (fputil::fenv_is_round_to_nearest())66 return 0x1.fffffep-1f;67 }68 // |x| < 2^-2569 // 10^x ~ 1 + log(10) * x70 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {71 return fputil::multiply_add(x, 0x1.26bb1cp+1f, 1.0f);72 }73 74 return static_cast<float>(Exp10Base::powb_lo(x));75 }76 77 // Exceptional value.78 if (LIBC_UNLIKELY(x_u == 0x3d14'd956U)) { // x = 0x1.29b2acp-5f79 if (fputil::fenv_is_round_up())80 return 0x1.1657c4p+0f;81 }82 83 // Exact outputs when x = 1, 2, ..., 10.84 // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)85 if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) {86 switch (x_u) {87 case 0x3f800000U: // x = 1.0f88 return 10.0f;89 case 0x40000000U: // x = 2.0f90 return 100.0f;91 case 0x40400000U: // x = 3.0f92 return 1'000.0f;93 case 0x40800000U: // x = 4.0f94 return 10'000.0f;95 case 0x40a00000U: // x = 5.0f96 return 100'000.0f;97 case 0x40c00000U: // x = 6.0f98 return 1'000'000.0f;99 case 0x40e00000U: // x = 7.0f100 return 10'000'000.0f;101 case 0x41000000U: // x = 8.0f102 return 100'000'000.0f;103 case 0x41100000U: // x = 9.0f104 return 1'000'000'000.0f;105 case 0x41200000U: // x = 10.0f106 return 10'000'000'000.0f;107 }108 }109 110 // Range reduction: 10^x = 2^(mid + hi) * 10^lo111 // rr = (2^(mid + hi), lo)112 auto rr = exp_b_range_reduc<Exp10Base>(x);113 114 // The low part is approximated by a degree-5 minimax polynomial.115 // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5116 using fputil::multiply_add;117 double lo2 = rr.lo * rr.lo;118 // c0 = 1 + COEFFS[0] * lo119 double c0 = multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0);120 // c1 = COEFFS[1] + COEFFS[2] * lo121 double c1 = multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);122 // c2 = COEFFS[3] + COEFFS[4] * lo123 double c2 = multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);124 // p = c1 + c2 * lo^2125 // = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3126 double p = multiply_add(lo2, c2, c1);127 // 10^lo ~ c0 + p * lo^2128 // 10^x = 2^(mid + hi) * 10^lo129 // ~ mh * (c0 + p * lo^2)130 // = (mh * c0) + p * (mh * lo^2)131 return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh));132}133 134} // namespace math135} // namespace LIBC_NAMESPACE_DECL136 137#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_H138