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1//===-- Implementation header for exp10m1f16 --------------------*- 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_EXP10M1F16_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10M1F16_H11 12#include "include/llvm-libc-macros/float16-macros.h"13 14#ifdef LIBC_TYPES_HAS_FLOAT1615 16#include "exp10f16_utils.h"17#include "src/__support/FPUtil/FEnvImpl.h"18#include "src/__support/FPUtil/FPBits.h"19#include "src/__support/FPUtil/PolyEval.h"20#include "src/__support/FPUtil/cast.h"21#include "src/__support/FPUtil/except_value_utils.h"22#include "src/__support/FPUtil/multiply_add.h"23#include "src/__support/FPUtil/rounding_mode.h"24#include "src/__support/common.h"25#include "src/__support/macros/config.h"26#include "src/__support/macros/optimization.h"27#include "src/__support/macros/properties/cpu_features.h"28 29namespace LIBC_NAMESPACE_DECL {30 31namespace math {32 33LIBC_INLINE static constexpr float16 exp10m1f16(float16 x) {34 35#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS36 constexpr fputil::ExceptValues<float16, 3> EXP10M1F16_EXCEPTS_LO = {{37 // (input, RZ output, RU offset, RD offset, RN offset)38 // x = 0x1.5c4p-4, exp10m1f16(x) = 0x1.bacp-3 (RZ)39 {0x2d71U, 0x32ebU, 1U, 0U, 0U},40 // x = -0x1.5ep-13, exp10m1f16(x) = -0x1.92cp-12 (RZ)41 {0x8978U, 0x8e4bU, 0U, 1U, 0U},42 // x = -0x1.e2p-10, exp10m1f16(x) = -0x1.14cp-8 (RZ)43 {0x9788U, 0x9c53U, 0U, 1U, 0U},44 }};45 46#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT47 constexpr size_t N_EXP10M1F16_EXCEPTS_HI = 3;48#else49 constexpr size_t N_EXP10M1F16_EXCEPTS_HI = 6;50#endif51 52 constexpr fputil::ExceptValues<float16, N_EXP10M1F16_EXCEPTS_HI>53 EXP10M1F16_EXCEPTS_HI = {{54 // (input, RZ output, RU offset, RD offset, RN offset)55 // x = 0x1.8f4p-2, exp10m1f16(x) = 0x1.744p+0 (RZ)56 {0x363dU, 0x3dd1U, 1U, 0U, 0U},57 // x = 0x1.95cp-2, exp10m1f16(x) = 0x1.7d8p+0 (RZ)58 {0x3657U, 0x3df6U, 1U, 0U, 0U},59 // x = 0x1.d04p-2, exp10m1f16(x) = 0x1.d7p+0 (RZ)60 {0x3741U, 0x3f5cU, 1U, 0U, 1U},61#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT62 // x = 0x1.0cp+1, exp10m1f16(x) = 0x1.ec4p+6 (RZ)63 {0x4030U, 0x57b1U, 1U, 0U, 1U},64 // x = 0x1.1b8p+1, exp10m1f16(x) = 0x1.45cp+7 (RZ)65 {0x406eU, 0x5917U, 1U, 0U, 1U},66 // x = 0x1.2f4p+2, exp10m1f16(x) = 0x1.ab8p+15 (RZ)67 {0x44bdU, 0x7aaeU, 1U, 0U, 1U},68#endif69 }};70#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS71 72 using FPBits = fputil::FPBits<float16>;73 FPBits x_bits(x);74 75 uint16_t x_u = x_bits.uintval();76 uint16_t x_abs = x_u & 0x7fffU;77 78 // When |x| <= 2^(-3), or |x| >= 11 * log10(2), or x is NaN.79 if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x429fU)) {80 // exp10m1(NaN) = NaN81 if (x_bits.is_nan()) {82 if (x_bits.is_signaling_nan()) {83 fputil::raise_except_if_required(FE_INVALID);84 return FPBits::quiet_nan().get_val();85 }86 87 return x;88 }89 90 // When x >= 16 * log10(2).91 if (x_u >= 0x44d1U && x_bits.is_pos()) {92 // exp10m1(+inf) = +inf93 if (x_bits.is_inf())94 return FPBits::inf().get_val();95 96 switch (fputil::quick_get_round()) {97 case FE_TONEAREST:98 case FE_UPWARD:99 fputil::set_errno_if_required(ERANGE);100 fputil::raise_except_if_required(FE_OVERFLOW | FE_INEXACT);101 return FPBits::inf().get_val();102 default:103 return FPBits::max_normal().get_val();104 }105 }106 107 // When x < -11 * log10(2).108 if (x_u > 0xc29fU) {109 // exp10m1(-inf) = -1110 if (x_bits.is_inf())111 return FPBits::one(Sign::NEG).get_val();112 113 // When x >= -0x1.ce4p+1, round(10^x - 1, HP, RN) = -0x1.ffcp-1.114 if (x_u <= 0xc339U) {115 return fputil::round_result_slightly_down(116 fputil::cast<float16>(-0x1.ffcp-1));117 }118 119 // When x < -0x1.ce4p+1, round(10^x - 1, HP, RN) = -1.120 switch (fputil::quick_get_round()) {121 case FE_TONEAREST:122 case FE_DOWNWARD:123 return FPBits::one(Sign::NEG).get_val();124 default:125 return fputil::cast<float16>(-0x1.ffcp-1);126 }127 }128 129 // When |x| <= 2^(-3).130 if (x_abs <= 0x3000U) {131 if (LIBC_UNLIKELY(x_abs == 0))132 return x;133 134#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS135 if (auto r = EXP10M1F16_EXCEPTS_LO.lookup(x_u);136 LIBC_UNLIKELY(r.has_value()))137 return r.value();138#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS139 140 float xf = x;141 // Degree-5 minimax polynomial generated by Sollya with the following142 // commands:143 // > display = hexadecimal;144 // > P = fpminimax((10^x - 1)/x, 4, [|SG...|], [-2^-3, 2^-3]);145 // > x * P;146 return fputil::cast<float16>(147 xf * fputil::polyeval(xf, 0x1.26bb1cp+1f, 0x1.5351c8p+1f,148 0x1.04704p+1f, 0x1.2ce084p+0f, 0x1.14a6bep-1f));149 }150 }151 152 // When x is 1, 2, or 3. These are hard-to-round cases with exact results.153 // 10^4 - 1 = 9'999 is not exactly representable as a float16, but luckily the154 // polynomial approximation gives the correct result for x = 4 in all155 // rounding modes.156 if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) {157 switch (x_u) {158 case 0x3c00U: // x = 1.0f16159 return fputil::cast<float16>(9.0);160 case 0x4000U: // x = 2.0f16161 return fputil::cast<float16>(99.0);162 case 0x4200U: // x = 3.0f16163 return fputil::cast<float16>(999.0);164 }165 }166 167#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS168 if (auto r = EXP10M1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))169 return r.value();170#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS171 172 // exp10(x) = exp2((hi + mid) * log2(10)) * exp10(lo)173 auto [exp2_hi_mid, exp10_lo] = exp10_range_reduction(x);174 // exp10m1(x) = exp2((hi + mid) * log2(lo)) * exp10(lo) - 1175 return fputil::cast<float16>(176 fputil::multiply_add(exp2_hi_mid, exp10_lo, -1.0f));177}178 179} // namespace math180 181} // namespace LIBC_NAMESPACE_DECL182 183#endif // LIBC_TYPES_HAS_FLOAT16184 185#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10M1F16_H186