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-exception 6 // 7 //===----------------------------------------------------------------------===// 8 9 #include "src/math/log10f16.h" 10 #include "expxf16.h" 11 #include "hdr/errno_macros.h" 12 #include "hdr/fenv_macros.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/cast.h" 17 #include "src/__support/FPUtil/except_value_utils.h" 18 #include "src/__support/FPUtil/multiply_add.h" 19 #include "src/__support/common.h" 20 #include "src/__support/macros/config.h" 21 #include "src/__support/macros/optimization.h" 22 #include "src/__support/macros/properties/cpu_features.h" 23 24 namespace LIBC_NAMESPACE_DECL { 25 26 #ifdef LIBC_TARGET_CPU_HAS_FMA 27 static constexpr size_t N_LOG10F16_EXCEPTS = 11; 28 #else 29 static constexpr size_t N_LOG10F16_EXCEPTS = 17; 30 #endif 31 32 static constexpr fputil::ExceptValues<float16, N_LOG10F16_EXCEPTS> 33 LOG10F16_EXCEPTS = {{ 34 // (input, RZ output, RU offset, RD offset, RN offset) 35 // x = 0x1.e3cp-3, log10f16(x) = -0x1.40cp-1 (RZ) 36 {0x338fU, 0xb903U, 0U, 1U, 0U}, 37 // x = 0x1.fep-3, log10f16(x) = -0x1.35p-1 (RZ) 38 {0x33f8U, 0xb8d4U, 0U, 1U, 1U}, 39 #ifndef LIBC_TARGET_CPU_HAS_FMA 40 // x = 0x1.394p-1, log10f16(x) = -0x1.b4cp-3 (RZ) 41 {0x38e5U, 0xb2d3U, 0U, 1U, 1U}, 42 #endif 43 // x = 0x1.ea8p-1, log10f16(x) = -0x1.31p-6 (RZ) 44 {0x3baaU, 0xa4c4U, 0U, 1U, 1U}, 45 // x = 0x1.ebp-1, log10f16(x) = -0x1.29cp-6 (RZ) 46 {0x3bacU, 0xa4a7U, 0U, 1U, 1U}, 47 // x = 0x1.f3p-1, log10f16(x) = -0x1.6dcp-7 (RZ) 48 {0x3bccU, 0xa1b7U, 0U, 1U, 1U}, 49 // x = 0x1.f38p-1, log10f16(x) = -0x1.5f8p-7 (RZ) 50 #ifndef LIBC_TARGET_CPU_HAS_FMA 51 {0x3bceU, 0xa17eU, 0U, 1U, 1U}, 52 // x = 0x1.fd8p-1, log10f16(x) = -0x1.168p-9 (RZ) 53 {0x3bf6U, 0x985aU, 0U, 1U, 1U}, 54 // x = 0x1.ff8p-1, log10f16(x) = -0x1.bccp-12 (RZ) 55 {0x3bfeU, 0x8ef3U, 0U, 1U, 1U}, 56 // x = 0x1.374p+0, log10f16(x) = 0x1.5b8p-4 (RZ) 57 {0x3cddU, 0x2d6eU, 1U, 0U, 1U}, 58 // x = 0x1.3ecp+1, log10f16(x) = 0x1.958p-2 (RZ) 59 {0x40fbU, 0x3656U, 1U, 0U, 1U}, 60 #endif 61 // x = 0x1.4p+3, log10f16(x) = 0x1p+0 (RZ) 62 {0x4900U, 0x3c00U, 0U, 0U, 0U}, 63 // x = 0x1.9p+6, log10f16(x) = 0x1p+1 (RZ) 64 {0x5640U, 0x4000U, 0U, 0U, 0U}, 65 // x = 0x1.f84p+6, log10f16(x) = 0x1.0ccp+1 (RZ) 66 {0x57e1U, 0x4033U, 1U, 0U, 0U}, 67 // x = 0x1.f4p+9, log10f16(x) = 0x1.8p+1 (RZ) 68 {0x63d0U, 0x4200U, 0U, 0U, 0U}, 69 // x = 0x1.388p+13, log10f16(x) = 0x1p+2 (RZ) 70 {0x70e2U, 0x4400U, 0U, 0U, 0U}, 71 // x = 0x1.674p+13, log10f16(x) = 0x1.03cp+2 (RZ) 72 {0x719dU, 0x440fU, 1U, 0U, 0U}, 73 }}; 74 75 LLVM_LIBC_FUNCTION(float16, log10f16, (float16 x)) { 76 using FPBits = fputil::FPBits<float16>; 77 FPBits x_bits(x); 78 79 uint16_t x_u = x_bits.uintval(); 80 81 // If x <= 0, or x is 1, or x is +inf, or x is NaN. 82 if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) { 83 // log10(NaN) = NaN 84 if (x_bits.is_nan()) { 85 if (x_bits.is_signaling_nan()) { 86 fputil::raise_except_if_required(FE_INVALID); 87 return FPBits::quiet_nan().get_val(); 88 } 89 90 return x; 91 } 92 93 // log10(+/-0) = −inf 94 if ((x_u & 0x7fffU) == 0U) { 95 fputil::raise_except_if_required(FE_DIVBYZERO); 96 return FPBits::inf(Sign::NEG).get_val(); 97 } 98 99 if (x_u == 0x3c00U) 100 return FPBits::zero().get_val(); 101 102 // When x < 0. 103 if (x_u > 0x8000U) { 104 fputil::set_errno_if_required(EDOM); 105 fputil::raise_except_if_required(FE_INVALID); 106 return FPBits::quiet_nan().get_val(); 107 } 108 109 // log10(+inf) = +inf 110 return FPBits::inf().get_val(); 111 } 112 113 if (auto r = LOG10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) 114 return r.value(); 115 116 // To compute log10(x), we perform the following range reduction: 117 // x = 2^m * 1.mant, 118 // log10(x) = m * log10(2) + log10(1.mant). 119 // To compute log10(1.mant), let f be the highest 6 bits including the hidden 120 // bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of 121 // the mantissa, then: 122 // log10(1.mant) = log10(f) + log10(1.mant / f) 123 // = log10(f) + log10(1 + d/f) 124 // since d/f is sufficiently small. 125 // We store log10(f) and 1/f in the lookup tables LOG10F_F and ONE_OVER_F_F 126 // respectively. 127 128 int m = -FPBits::EXP_BIAS; 129 130 // When x is subnormal, normalize it. 131 if ((x_u & FPBits::EXP_MASK) == 0U) { 132 // Can't pass an integer to fputil::cast directly. 133 constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN; 134 x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP)); 135 x_u = x_bits.uintval(); 136 m -= FPBits::FRACTION_LEN; 137 } 138 139 uint16_t mant = x_bits.get_mantissa(); 140 // Leading 10 - 5 = 5 bits of the mantissa. 141 int f = mant >> 5; 142 // Unbiased exponent. 143 m += x_u >> FPBits::FRACTION_LEN; 144 145 // Set bits to 1.mant instead of 2^m * 1.mant. 146 x_bits.set_biased_exponent(FPBits::EXP_BIAS); 147 float mant_f = x_bits.get_val(); 148 // v = 1.mant * 1/f - 1 = d/f 149 float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f); 150 151 // Degree-3 minimax polynomial generated by Sollya with the following 152 // commands: 153 // > display = hexadecimal; 154 // > P = fpminimax(log10(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]); 155 // > x * P; 156 float log10p1_d_over_f = 157 v * fputil::polyeval(v, 0x1.bcb7bp-2f, -0x1.bce168p-3f, 0x1.28acb8p-3f); 158 // log10(1.mant) = log10(f) + log10(1 + d/f) 159 float log10_1_mant = LOG10F_F[f] + log10p1_d_over_f; 160 return fputil::cast<float16>( 161 fputil::multiply_add(static_cast<float>(m), LOG10F_2, log10_1_mant)); 162 } 163 164 } // namespace LIBC_NAMESPACE_DECL 165