170 lines · cpp
1//===-- Half-precision log10(x) function ----------------------------------===//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#include "src/math/log10f16.h"10#include "hdr/errno_macros.h"11#include "hdr/fenv_macros.h"12#include "src/__support/FPUtil/FEnvImpl.h"13#include "src/__support/FPUtil/FPBits.h"14#include "src/__support/FPUtil/PolyEval.h"15#include "src/__support/FPUtil/cast.h"16#include "src/__support/FPUtil/except_value_utils.h"17#include "src/__support/FPUtil/multiply_add.h"18#include "src/__support/common.h"19#include "src/__support/macros/config.h"20#include "src/__support/macros/optimization.h"21#include "src/__support/macros/properties/cpu_features.h"22#include "src/__support/math/expxf16_utils.h"23 24namespace LIBC_NAMESPACE_DECL {25 26#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS27#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT28static constexpr size_t N_LOG10F16_EXCEPTS = 11;29#else30static constexpr size_t N_LOG10F16_EXCEPTS = 17;31#endif32 33static constexpr fputil::ExceptValues<float16, N_LOG10F16_EXCEPTS>34 LOG10F16_EXCEPTS = {{35 // (input, RZ output, RU offset, RD offset, RN offset)36 // x = 0x1.e3cp-3, log10f16(x) = -0x1.40cp-1 (RZ)37 {0x338fU, 0xb903U, 0U, 1U, 0U},38 // x = 0x1.fep-3, log10f16(x) = -0x1.35p-1 (RZ)39 {0x33f8U, 0xb8d4U, 0U, 1U, 1U},40#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT41 // x = 0x1.394p-1, log10f16(x) = -0x1.b4cp-3 (RZ)42 {0x38e5U, 0xb2d3U, 0U, 1U, 1U},43#endif44 // x = 0x1.ea8p-1, log10f16(x) = -0x1.31p-6 (RZ)45 {0x3baaU, 0xa4c4U, 0U, 1U, 1U},46 // x = 0x1.ebp-1, log10f16(x) = -0x1.29cp-6 (RZ)47 {0x3bacU, 0xa4a7U, 0U, 1U, 1U},48 // x = 0x1.f3p-1, log10f16(x) = -0x1.6dcp-7 (RZ)49 {0x3bccU, 0xa1b7U, 0U, 1U, 1U},50// x = 0x1.f38p-1, log10f16(x) = -0x1.5f8p-7 (RZ)51#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT52 {0x3bceU, 0xa17eU, 0U, 1U, 1U},53 // x = 0x1.fd8p-1, log10f16(x) = -0x1.168p-9 (RZ)54 {0x3bf6U, 0x985aU, 0U, 1U, 1U},55 // x = 0x1.ff8p-1, log10f16(x) = -0x1.bccp-12 (RZ)56 {0x3bfeU, 0x8ef3U, 0U, 1U, 1U},57 // x = 0x1.374p+0, log10f16(x) = 0x1.5b8p-4 (RZ)58 {0x3cddU, 0x2d6eU, 1U, 0U, 1U},59 // x = 0x1.3ecp+1, log10f16(x) = 0x1.958p-2 (RZ)60 {0x40fbU, 0x3656U, 1U, 0U, 1U},61#endif62 // x = 0x1.4p+3, log10f16(x) = 0x1p+0 (RZ)63 {0x4900U, 0x3c00U, 0U, 0U, 0U},64 // x = 0x1.9p+6, log10f16(x) = 0x1p+1 (RZ)65 {0x5640U, 0x4000U, 0U, 0U, 0U},66 // x = 0x1.f84p+6, log10f16(x) = 0x1.0ccp+1 (RZ)67 {0x57e1U, 0x4033U, 1U, 0U, 0U},68 // x = 0x1.f4p+9, log10f16(x) = 0x1.8p+1 (RZ)69 {0x63d0U, 0x4200U, 0U, 0U, 0U},70 // x = 0x1.388p+13, log10f16(x) = 0x1p+2 (RZ)71 {0x70e2U, 0x4400U, 0U, 0U, 0U},72 // x = 0x1.674p+13, log10f16(x) = 0x1.03cp+2 (RZ)73 {0x719dU, 0x440fU, 1U, 0U, 0U},74 }};75#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS76 77LLVM_LIBC_FUNCTION(float16, log10f16, (float16 x)) {78 using namespace math::expxf16_internal;79 using FPBits = fputil::FPBits<float16>;80 FPBits x_bits(x);81 82 uint16_t x_u = x_bits.uintval();83 84 // If x <= 0, or x is 1, or x is +inf, or x is NaN.85 if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) {86 // log10(NaN) = NaN87 if (x_bits.is_nan()) {88 if (x_bits.is_signaling_nan()) {89 fputil::raise_except_if_required(FE_INVALID);90 return FPBits::quiet_nan().get_val();91 }92 93 return x;94 }95 96 // log10(+/-0) = −inf97 if ((x_u & 0x7fffU) == 0U) {98 fputil::raise_except_if_required(FE_DIVBYZERO);99 return FPBits::inf(Sign::NEG).get_val();100 }101 102 if (x_u == 0x3c00U)103 return FPBits::zero().get_val();104 105 // When x < 0.106 if (x_u > 0x8000U) {107 fputil::set_errno_if_required(EDOM);108 fputil::raise_except_if_required(FE_INVALID);109 return FPBits::quiet_nan().get_val();110 }111 112 // log10(+inf) = +inf113 return FPBits::inf().get_val();114 }115 116#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS117 if (auto r = LOG10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))118 return r.value();119#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS120 121 // To compute log10(x), we perform the following range reduction:122 // x = 2^m * 1.mant,123 // log10(x) = m * log10(2) + log10(1.mant).124 // To compute log10(1.mant), let f be the highest 6 bits including the hidden125 // bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of126 // the mantissa, then:127 // log10(1.mant) = log10(f) + log10(1.mant / f)128 // = log10(f) + log10(1 + d/f)129 // since d/f is sufficiently small.130 // We store log10(f) and 1/f in the lookup tables LOG10F_F and ONE_OVER_F_F131 // respectively.132 133 int m = -FPBits::EXP_BIAS;134 135 // When x is subnormal, normalize it.136 if ((x_u & FPBits::EXP_MASK) == 0U) {137 // Can't pass an integer to fputil::cast directly.138 constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN;139 x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP));140 x_u = x_bits.uintval();141 m -= FPBits::FRACTION_LEN;142 }143 144 uint16_t mant = x_bits.get_mantissa();145 // Leading 10 - 5 = 5 bits of the mantissa.146 int f = mant >> 5;147 // Unbiased exponent.148 m += x_u >> FPBits::FRACTION_LEN;149 150 // Set bits to 1.mant instead of 2^m * 1.mant.151 x_bits.set_biased_exponent(FPBits::EXP_BIAS);152 float mant_f = x_bits.get_val();153 // v = 1.mant * 1/f - 1 = d/f154 float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f);155 156 // Degree-3 minimax polynomial generated by Sollya with the following157 // commands:158 // > display = hexadecimal;159 // > P = fpminimax(log10(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]);160 // > x * P;161 float log10p1_d_over_f =162 v * fputil::polyeval(v, 0x1.bcb7bp-2f, -0x1.bce168p-3f, 0x1.28acb8p-3f);163 // log10(1.mant) = log10(f) + log10(1 + d/f)164 float log10_1_mant = LOG10F_F[f] + log10p1_d_over_f;165 return fputil::cast<float16>(166 fputil::multiply_add(static_cast<float>(m), LOG10F_2, log10_1_mant));167}168 169} // namespace LIBC_NAMESPACE_DECL170