163 lines · cpp
1//===-- Half-precision log(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/logf16.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_LOGF16_EXCEPTS = 5;29#else30static constexpr size_t N_LOGF16_EXCEPTS = 11;31#endif32 33static constexpr fputil::ExceptValues<float16, N_LOGF16_EXCEPTS>34 LOGF16_EXCEPTS = {{35// (input, RZ output, RU offset, RD offset, RN offset)36#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT37 // x = 0x1.61cp-13, logf16(x) = -0x1.16p+3 (RZ)38 {0x0987U, 0xc858U, 0U, 1U, 0U},39 // x = 0x1.f2p-12, logf16(x) = -0x1.e98p+2 (RZ)40 {0x0fc8U, 0xc7a6U, 0U, 1U, 1U},41#endif42 // x = 0x1.4d4p-9, logf16(x) = -0x1.7e4p+2 (RZ)43 {0x1935U, 0xc5f9U, 0U, 1U, 0U},44 // x = 0x1.5ep-8, logf16(x) = -0x1.4ecp+2 (RZ)45 {0x1d78U, 0xc53bU, 0U, 1U, 0U},46#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT47 // x = 0x1.fdp-1, logf16(x) = -0x1.81p-8 (RZ)48 {0x3bf4U, 0x9e04U, 0U, 1U, 1U},49 // x = 0x1.fep-1, logf16(x) = -0x1.008p-8 (RZ)50 {0x3bf8U, 0x9c02U, 0U, 1U, 0U},51#endif52 // x = 0x1.ffp-1, logf16(x) = -0x1.004p-9 (RZ)53 {0x3bfcU, 0x9801U, 0U, 1U, 0U},54 // x = 0x1.ff8p-1, logf16(x) = -0x1p-10 (RZ)55 {0x3bfeU, 0x9400U, 0U, 1U, 1U},56#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT57 // x = 0x1.4c4p+1, logf16(x) = 0x1.e84p-1 (RZ)58 {0x4131U, 0x3ba1U, 1U, 0U, 1U},59#else60 // x = 0x1.75p+2, logf16(x) = 0x1.c34p+0 (RZ)61 {0x45d4U, 0x3f0dU, 1U, 0U, 0U},62 // x = 0x1.75p+2, logf16(x) = 0x1.c34p+0 (RZ)63 {0x45d4U, 0x3f0dU, 1U, 0U, 0U},64 // x = 0x1.d5p+9, logf16(x) = 0x1.b5cp+2 (RZ)65 {0x6354U, 0x46d7U, 1U, 0U, 1U},66#endif67 }};68#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS69 70LLVM_LIBC_FUNCTION(float16, logf16, (float16 x)) {71 using namespace math::expxf16_internal;72 using FPBits = fputil::FPBits<float16>;73 FPBits x_bits(x);74 75 uint16_t x_u = x_bits.uintval();76 77 // If x <= 0, or x is 1, or x is +inf, or x is NaN.78 if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) {79 // log(NaN) = NaN80 if (x_bits.is_nan()) {81 if (x_bits.is_signaling_nan()) {82 fputil::raise_except_if_required(FE_INVALID);83 return FPBits::quiet_nan().get_val();84 }85 86 return x;87 }88 89 // log(+/-0) = −inf90 if ((x_u & 0x7fffU) == 0U) {91 fputil::raise_except_if_required(FE_DIVBYZERO);92 return FPBits::inf(Sign::NEG).get_val();93 }94 95 if (x_u == 0x3c00U)96 return FPBits::zero().get_val();97 98 // When x < 0.99 if (x_u > 0x8000U) {100 fputil::set_errno_if_required(EDOM);101 fputil::raise_except_if_required(FE_INVALID);102 return FPBits::quiet_nan().get_val();103 }104 105 // log(+inf) = +inf106 return FPBits::inf().get_val();107 }108 109#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS110 if (auto r = LOGF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))111 return r.value();112#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS113 114 // To compute log(x), we perform the following range reduction:115 // x = 2^m * 1.mant,116 // log(x) = m * log(2) + log(1.mant).117 // To compute log(1.mant), let f be the highest 6 bits including the hidden118 // bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of119 // the mantissa, then:120 // log(1.mant) = log(f) + log(1.mant / f)121 // = log(f) + log(1 + d/f)122 // since d/f is sufficiently small.123 // We store log(f) and 1/f in the lookup tables LOGF_F and ONE_OVER_F_F124 // respectively.125 126 int m = -FPBits::EXP_BIAS;127 128 // When x is subnormal, normalize it.129 if ((x_u & FPBits::EXP_MASK) == 0U) {130 // Can't pass an integer to fputil::cast directly.131 constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN;132 x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP));133 x_u = x_bits.uintval();134 m -= FPBits::FRACTION_LEN;135 }136 137 uint16_t mant = x_bits.get_mantissa();138 // Leading 10 - 5 = 5 bits of the mantissa.139 int f = mant >> 5;140 // Unbiased exponent.141 m += x_u >> FPBits::FRACTION_LEN;142 143 // Set bits to 1.mant instead of 2^m * 1.mant.144 x_bits.set_biased_exponent(FPBits::EXP_BIAS);145 float mant_f = x_bits.get_val();146 // v = 1.mant * 1/f - 1 = d/f147 float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f);148 149 // Degree-3 minimax polynomial generated by Sollya with the following150 // commands:151 // > display = hexadecimal;152 // > P = fpminimax(log(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]);153 // > x * P;154 float log1p_d_over_f =155 v * fputil::polyeval(v, 0x1p+0f, -0x1.001804p-1f, 0x1.557ef6p-2f);156 // log(1.mant) = log(f) + log(1 + d/f)157 float log_1_mant = LOGF_F[f] + log1p_d_over_f;158 return fputil::cast<float16>(159 fputil::multiply_add(static_cast<float>(m), LOGF_2, log_1_mant));160}161 162} // namespace LIBC_NAMESPACE_DECL163