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1//===-- Implementation header for exp10m1f ----------------------*- 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_EXP10M1F_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10M1F_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/PolyEval.h"16#include "src/__support/FPUtil/except_value_utils.h"17#include "src/__support/FPUtil/multiply_add.h"18#include "src/__support/FPUtil/rounding_mode.h"19#include "src/__support/common.h"20#include "src/__support/libc_errno.h"21#include "src/__support/macros/config.h"22#include "src/__support/macros/optimization.h"23 24namespace LIBC_NAMESPACE_DECL {25 26namespace math {27 28namespace exp10m1f_internal {29 30#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS31static constexpr size_t N_EXCEPTS_LO = 11;32 33static constexpr fputil::ExceptValues<float, N_EXCEPTS_LO> EXP10M1F_EXCEPTS_LO =34 {{35 // x = 0x1.0fe54ep-11, exp10m1f(x) = 0x1.3937eep-10 (RZ)36 {0x3a07'f2a7U, 0x3a9c'9bf7U, 1U, 0U, 1U},37 // x = 0x1.80e6eap-11, exp10m1f(x) = 0x1.bb8272p-10 (RZ)38 {0x3a40'7375U, 0x3add'c139U, 1U, 0U, 1U},39 // x = -0x1.2a33bcp-51, exp10m1f(x) = -0x1.57515ep-50 (RZ)40 {0xa615'19deU, 0xa6ab'a8afU, 0U, 1U, 0U},41 // x = -0x0p+0, exp10m1f(x) = -0x0p+0 (RZ)42 {0x8000'0000U, 0x8000'0000U, 0U, 0U, 0U},43 // x = -0x1.b59e08p-31, exp10m1f(x) = -0x1.f7d356p-30 (RZ)44 {0xb05a'cf04U, 0xb0fb'e9abU, 0U, 1U, 1U},45 // x = -0x1.bf342p-12, exp10m1f(x) = -0x1.014e02p-10 (RZ)46 {0xb9df'9a10U, 0xba80'a701U, 0U, 1U, 0U},47 // x = -0x1.6207fp-11, exp10m1f(x) = -0x1.9746cap-10 (RZ)48 {0xba31'03f8U, 0xbacb'a365U, 0U, 1U, 1U},49 // x = -0x1.bd0c66p-11, exp10m1f(x) = -0x1.ffe168p-10 (RZ)50 {0xba5e'8633U, 0xbaff'f0b4U, 0U, 1U, 1U},51 // x = -0x1.ffd84cp-10, exp10m1f(x) = -0x1.25faf2p-8 (RZ)52 {0xbaff'ec26U, 0xbb92'fd79U, 0U, 1U, 0U},53 // x = -0x1.a74172p-9, exp10m1f(x) = -0x1.e57be2p-8 (RZ)54 {0xbb53'a0b9U, 0xbbf2'bdf1U, 0U, 1U, 1U},55 // x = -0x1.cb694cp-9, exp10m1f(x) = -0x1.0764e4p-7 (RZ)56 {0xbb65'b4a6U, 0xbc03'b272U, 0U, 1U, 0U},57 }};58 59static constexpr size_t N_EXCEPTS_HI = 19;60 61static constexpr fputil::ExceptValues<float, N_EXCEPTS_HI> EXP10M1F_EXCEPTS_HI =62 {{63 // (input, RZ output, RU offset, RD offset, RN offset)64 // x = 0x1.8d31eep-8, exp10m1f(x) = 0x1.cc7e4cp-7 (RZ)65 {0x3bc6'98f7U, 0x3c66'3f26U, 1U, 0U, 1U},66 // x = 0x1.915fcep-8, exp10m1f(x) = 0x1.d15f72p-7 (RZ)67 {0x3bc8'afe7U, 0x3c68'afb9U, 1U, 0U, 0U},68 // x = 0x1.bcf982p-8, exp10m1f(x) = 0x1.022928p-6 (RZ)69 {0x3bde'7cc1U, 0x3c81'1494U, 1U, 0U, 1U},70 // x = 0x1.99ff0ap-7, exp10m1f(x) = 0x1.dee416p-6 (RZ)71 {0x3c4c'ff85U, 0x3cef'720bU, 1U, 0U, 0U},72 // x = 0x1.75ea14p-6, exp10m1f(x) = 0x1.b9ff16p-5 (RZ)73 {0x3cba'f50aU, 0x3d5c'ff8bU, 1U, 0U, 0U},74 // x = 0x1.f81b64p-6, exp10m1f(x) = 0x1.2cb6bcp-4 (RZ)75 {0x3cfc'0db2U, 0x3d96'5b5eU, 1U, 0U, 0U},76 // x = 0x1.fafecp+3, exp10m1f(x) = 0x1.8c880ap+52 (RZ)77 {0x417d'7f60U, 0x59c6'4405U, 1U, 0U, 0U},78 // x = -0x1.3bf094p-8, exp10m1f(x) = -0x1.69ba4ap-7 (RZ)79 {0xbb9d'f84aU, 0xbc34'dd25U, 0U, 1U, 0U},80 // x = -0x1.4558bcp-8, exp10m1f(x) = -0x1.746fb8p-7 (RZ)81 {0xbba2'ac5eU, 0xbc3a'37dcU, 0U, 1U, 1U},82 // x = -0x1.4bb43p-8, exp10m1f(x) = -0x1.7babe4p-7 (RZ)83 {0xbba5'da18U, 0xbc3d'd5f2U, 0U, 1U, 1U},84 // x = -0x1.776cc8p-8, exp10m1f(x) = -0x1.ad62c4p-7 (RZ)85 {0xbbbb'b664U, 0xbc56'b162U, 0U, 1U, 0U},86 // x = -0x1.f024cp-8, exp10m1f(x) = -0x1.1b20d6p-6 (RZ)87 {0xbbf8'1260U, 0xbc8d'906bU, 0U, 1U, 1U},88 // x = -0x1.f510eep-8, exp10m1f(x) = -0x1.1de9aap-6 (RZ)89 {0xbbfa'8877U, 0xbc8e'f4d5U, 0U, 1U, 0U},90 // x = -0x1.0b43c4p-7, exp10m1f(x) = -0x1.30d418p-6 (RZ)91 {0xbc05'a1e2U, 0xbc98'6a0cU, 0U, 1U, 0U},92 // x = -0x1.245ee4p-7, exp10m1f(x) = -0x1.4d2b86p-6 (RZ)93 {0xbc12'2f72U, 0xbca6'95c3U, 0U, 1U, 0U},94 // x = -0x1.f9f2dap-7, exp10m1f(x) = -0x1.1e2186p-5 (RZ)95 {0xbc7c'f96dU, 0xbd0f'10c3U, 0U, 1U, 0U},96 // x = -0x1.08e42p-6, exp10m1f(x) = -0x1.2b5c4p-5 (RZ)97 {0xbc84'7210U, 0xbd15'ae20U, 0U, 1U, 1U},98 // x = -0x1.0cdc44p-5, exp10m1f(x) = -0x1.2a2152p-4 (RZ)99 {0xbd06'6e22U, 0xbd95'10a9U, 0U, 1U, 1U},100 // x = -0x1.ca4322p-5, exp10m1f(x) = -0x1.ef073p-4 (RZ)101 {0xbd65'2191U, 0xbdf7'8398U, 0U, 1U, 1U},102 }};103#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS104 105} // namespace exp10m1f_internal106 107LIBC_INLINE static constexpr float exp10m1f(float x) {108 using namespace exp10m1f_internal;109 using FPBits = fputil::FPBits<float>;110 FPBits xbits(x);111 112 uint32_t x_u = xbits.uintval();113 uint32_t x_abs = x_u & 0x7fff'ffffU;114 115 // When x >= log10(2^128), or x is nan116 if (LIBC_UNLIKELY(xbits.is_pos() && x_u >= 0x421a'209bU)) {117 if (xbits.is_finite()) {118 int rounding = fputil::quick_get_round();119 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)120 return FPBits::max_normal().get_val();121 122 fputil::set_errno_if_required(ERANGE);123 fputil::raise_except_if_required(FE_OVERFLOW);124 }125 126 // x >= log10(2^128) and 10^x - 1 rounds to +inf, or x is +inf or nan127 return x + FPBits::inf().get_val();128 }129 130 // When |x| <= log10(2) * 2^(-6)131 if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) {132#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS133 if (auto r = EXP10M1F_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))134 return r.value();135#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS136 137 double dx = x;138 double dx_sq = dx * dx;139 double c0 = dx * Exp10Base::COEFFS[0];140 double c1 =141 fputil::multiply_add(dx, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);142 double c2 =143 fputil::multiply_add(dx, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);144 // 10^dx - 1 ~ (1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5) - 1145 // = COEFFS[0] * dx + ... + COEFFS[4] * dx^5146 return static_cast<float>(fputil::polyeval(dx_sq, c0, c1, c2));147 }148 149 // When x <= log10(2^-25), or x is nan150 if (LIBC_UNLIKELY(x_u >= 0xc0f0d2f1)) {151 // exp10m1(-inf) = -1152 if (xbits.is_inf())153 return -1.0f;154 // exp10m1(nan) = nan155 if (xbits.is_nan())156 return x;157 158 int rounding = fputil::quick_get_round();159 if (rounding == FE_UPWARD || rounding == FE_TOWARDZERO ||160 (rounding == FE_TONEAREST && x_u == 0xc0f0d2f1))161 return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f162 163 fputil::set_errno_if_required(ERANGE);164 fputil::raise_except_if_required(FE_UNDERFLOW);165 return -1.0f;166 }167 168 // Exact outputs when x = 1, 2, ..., 10.169 // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)170 if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) {171 switch (x_u) {172 case 0x3f800000U: // x = 1.0f173 return 9.0f;174 case 0x40000000U: // x = 2.0f175 return 99.0f;176 case 0x40400000U: // x = 3.0f177 return 999.0f;178 case 0x40800000U: // x = 4.0f179 return 9'999.0f;180 case 0x40a00000U: // x = 5.0f181 return 99'999.0f;182 case 0x40c00000U: // x = 6.0f183 return 999'999.0f;184 case 0x40e00000U: // x = 7.0f185 return 9'999'999.0f;186 case 0x41000000U: { // x = 8.0f187 int rounding = fputil::quick_get_round();188 if (rounding == FE_UPWARD || rounding == FE_TONEAREST)189 return 100'000'000.0f;190 return 99'999'992.0f;191 }192 case 0x41100000U: { // x = 9.0f193 int rounding = fputil::quick_get_round();194 if (rounding == FE_UPWARD || rounding == FE_TONEAREST)195 return 1'000'000'000.0f;196 return 999'999'936.0f;197 }198 case 0x41200000U: { // x = 10.0f199 int rounding = fputil::quick_get_round();200 if (rounding == FE_UPWARD || rounding == FE_TONEAREST)201 return 10'000'000'000.0f;202 return 9'999'998'976.0f;203 }204 }205 }206 207#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS208 if (auto r = EXP10M1F_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))209 return r.value();210#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS211 212 // Range reduction: 10^x = 2^(mid + hi) * 10^lo213 // rr = (2^(mid + hi), lo)214 auto rr = exp_b_range_reduc<Exp10Base>(x);215 216 // The low part is approximated by a degree-5 minimax polynomial.217 // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5218 double lo_sq = rr.lo * rr.lo;219 double c0 = fputil::multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0);220 double c1 =221 fputil::multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);222 double c2 =223 fputil::multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);224 double exp10_lo = fputil::polyeval(lo_sq, c0, c1, c2);225 // 10^x - 1 = 2^(mid + hi) * 10^lo - 1226 // ~ mh * exp10_lo - 1227 return static_cast<float>(fputil::multiply_add(exp10_lo, rr.mh, -1.0));228}229 230} // namespace math231 232} // namespace LIBC_NAMESPACE_DECL233 234#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10M1F_H235