138 lines · cpp
1//===-- BFloat16 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/log_bf16.h"10#include "src/__support/FPUtil/FPBits.h"11#include "src/__support/FPUtil/bfloat16.h"12#include "src/__support/FPUtil/cast.h"13#include "src/__support/FPUtil/multiply_add.h"14#include "src/__support/common.h"15#include "src/__support/macros/config.h"16#include "src/__support/macros/optimization.h"17#include "src/__support/macros/properties/cpu_features.h"18 19namespace LIBC_NAMESPACE_DECL {20 21// Generated by Sollya with the following commands:22// > display = hexadecimal;23// > round(log(2), SG, RN);24static constexpr float LOGF_2 = 0x1.62e43p-1f;25 26// Generated by Sollya with the following commands:27// > display = hexadecimal;28// > for i from 0 to 127 do print(round(log(1 + i * 2^-7), SG, RN));29static constexpr float LOG_1_PLUS_M[128] = {30 0x0.0p0f, 0x1.fe02a6p-8f, 0x1.fc0a8cp-7f, 0x1.7b91bp-6f,31 0x1.f829bp-6f, 0x1.39e87cp-5f, 0x1.77459p-5f, 0x1.b42dd8p-5f,32 0x1.f0a30cp-5f, 0x1.16536ep-4f, 0x1.341d7ap-4f, 0x1.51b074p-4f,33 0x1.6f0d28p-4f, 0x1.8c345ep-4f, 0x1.a926d4p-4f, 0x1.c5e548p-4f,34 0x1.e27076p-4f, 0x1.fec914p-4f, 0x1.0d77e8p-3f, 0x1.1b72aep-3f,35 0x1.29553p-3f, 0x1.371fc2p-3f, 0x1.44d2b6p-3f, 0x1.526e5ep-3f,36 0x1.5ff308p-3f, 0x1.6d60fep-3f, 0x1.7ab89p-3f, 0x1.87fa06p-3f,37 0x1.9525aap-3f, 0x1.a23bc2p-3f, 0x1.af3c94p-3f, 0x1.bc2868p-3f,38 0x1.c8ff7cp-3f, 0x1.d5c216p-3f, 0x1.e27076p-3f, 0x1.ef0adcp-3f,39 0x1.fb9186p-3f, 0x1.04025ap-2f, 0x1.0a324ep-2f, 0x1.1058cp-2f,40 0x1.1675cap-2f, 0x1.1c898cp-2f, 0x1.22942p-2f, 0x1.2895a2p-2f,41 0x1.2e8e2cp-2f, 0x1.347ddap-2f, 0x1.3a64c6p-2f, 0x1.404308p-2f,42 0x1.4618bcp-2f, 0x1.4be5fap-2f, 0x1.51aad8p-2f, 0x1.576772p-2f,43 0x1.5d1bdcp-2f, 0x1.62c83p-2f, 0x1.686c82p-2f, 0x1.6e08eap-2f,44 0x1.739d8p-2f, 0x1.792a56p-2f, 0x1.7eaf84p-2f, 0x1.842d1ep-2f,45 0x1.89a338p-2f, 0x1.8f11e8p-2f, 0x1.947942p-2f, 0x1.99d958p-2f,46 0x1.9f323ep-2f, 0x1.a4840ap-2f, 0x1.a9cecap-2f, 0x1.af1294p-2f,47 0x1.b44f78p-2f, 0x1.b9858ap-2f, 0x1.beb4dap-2f, 0x1.c3dd7ap-2f,48 0x1.c8ff7cp-2f, 0x1.ce1afp-2f, 0x1.d32fe8p-2f, 0x1.d83e72p-2f,49 0x1.dd46ap-2f, 0x1.e24882p-2f, 0x1.e74426p-2f, 0x1.ec399ep-2f,50 0x1.f128f6p-2f, 0x1.f6124p-2f, 0x1.faf588p-2f, 0x1.ffd2ep-2f,51 0x1.02552ap-1f, 0x1.04bdfap-1f, 0x1.0723e6p-1f, 0x1.0986f4p-1f,52 0x1.0be72ep-1f, 0x1.0e4498p-1f, 0x1.109f3ap-1f, 0x1.12f71ap-1f,53 0x1.154c3ep-1f, 0x1.179eacp-1f, 0x1.19ee6cp-1f, 0x1.1c3b82p-1f,54 0x1.1e85f6p-1f, 0x1.20cdcep-1f, 0x1.23130ep-1f, 0x1.2555bcp-1f,55 0x1.2795e2p-1f, 0x1.29d38p-1f, 0x1.2c0e9ep-1f, 0x1.2e4744p-1f,56 0x1.307d74p-1f, 0x1.32b134p-1f, 0x1.34e28ap-1f, 0x1.37117cp-1f,57 0x1.393e0ep-1f, 0x1.3b6844p-1f, 0x1.3d9026p-1f, 0x1.3fb5b8p-1f,58 0x1.41d8fep-1f, 0x1.43f9fep-1f, 0x1.4618bcp-1f, 0x1.48353ep-1f,59 0x1.4a4f86p-1f, 0x1.4c679ap-1f, 0x1.4e7d82p-1f, 0x1.50913cp-1f,60 0x1.52a2d2p-1f, 0x1.54b246p-1f, 0x1.56bf9ep-1f, 0x1.58cadcp-1f,61 0x1.5ad404p-1f, 0x1.5cdb1ep-1f, 0x1.5ee02ap-1f, 0x1.60e33p-1f,62};63 64LLVM_LIBC_FUNCTION(bfloat16, log_bf16, (bfloat16 x)) {65 using FPBits = fputil::FPBits<bfloat16>;66 FPBits x_bits(x);67 68 uint16_t x_u = x_bits.uintval();69 70 // If x <= 0, or x is 1, or x is +inf, or x is NaN.71 if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3f80U || x_u >= 0x7f80U)) {72 // log(NaN) = NaN73 if (x_bits.is_nan()) {74 if (x_bits.is_signaling_nan()) {75 fputil::raise_except_if_required(FE_INVALID);76 return FPBits::quiet_nan().get_val();77 }78 79 return x;80 }81 82 // log(+/-0) = −inf83 if ((x_u & 0x7fffU) == 0U) {84 fputil::raise_except_if_required(FE_DIVBYZERO);85 return FPBits::inf(Sign::NEG).get_val();86 }87 88 // log(1) = 089 if (x_u == 0x3f80U)90 return FPBits::zero().get_val();91 92 // x < 093 if (x_u > 0x8000U) {94 fputil::set_errno_if_required(EDOM);95 fputil::raise_except_if_required(FE_INVALID);96 return FPBits::quiet_nan().get_val();97 }98 99 // log(+inf) = +inf100 return FPBits::inf().get_val();101 }102 103#ifndef LIBC_TARGET_CPU_HAS_FMA104 // log(0.00000000000000171390679426508540927898138761520386)105 // ~= -34.00000095106 if (LIBC_UNLIKELY(x_u == 0x26F7U))107 return bfloat16(-34.0000009);108#endif // LIBC_TARGET_CPU_HAS_FMA109 110 int e = -FPBits::EXP_BIAS;111 112 // When x is subnormal, normalize it.113 if ((x_u & FPBits::EXP_MASK) == 0U) {114 // Can't pass an integer to fputil::cast directly.115 constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN;116 x_bits = FPBits(x_bits.get_val() * fputil::cast<bfloat16>(NORMALIZE_EXP));117 x_u = x_bits.uintval();118 e -= FPBits::FRACTION_LEN;119 }120 121 // To compute log(x), we perform the following range reduction:122 // x = 2^e * (1 + m),123 // log(x) = e * log(2) + log(1 + m).124 // for BFloat16, mantissa is at most 7 explicit bits, so we lookup125 // log(1 + m) in LOG_1_PLUS_M table using `m` as key.126 127 // Get the 7-bit mantissa directly as the table index128 uint16_t m = x_bits.get_mantissa();129 130 // Get unbiased exponent131 e += x_u >> FPBits::FRACTION_LEN;132 133 return fputil::cast<bfloat16>(134 fputil::multiply_add(static_cast<float>(e), LOGF_2, LOG_1_PLUS_M[m]));135}136 137} // namespace LIBC_NAMESPACE_DECL138