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-exception 6 // 7 //===----------------------------------------------------------------------===// 8 9 #include "src/math/logf16.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_LOGF16_EXCEPTS = 5; 28 #else 29 static constexpr size_t N_LOGF16_EXCEPTS = 11; 30 #endif 31 32 static constexpr fputil::ExceptValues<float16, N_LOGF16_EXCEPTS> 33 LOGF16_EXCEPTS = {{ 34 // (input, RZ output, RU offset, RD offset, RN offset) 35 #ifndef LIBC_TARGET_CPU_HAS_FMA 36 // x = 0x1.61cp-13, logf16(x) = -0x1.16p+3 (RZ) 37 {0x0987U, 0xc858U, 0U, 1U, 0U}, 38 // x = 0x1.f2p-12, logf16(x) = -0x1.e98p+2 (RZ) 39 {0x0fc8U, 0xc7a6U, 0U, 1U, 1U}, 40 #endif 41 // x = 0x1.4d4p-9, logf16(x) = -0x1.7e4p+2 (RZ) 42 {0x1935U, 0xc5f9U, 0U, 1U, 0U}, 43 // x = 0x1.5ep-8, logf16(x) = -0x1.4ecp+2 (RZ) 44 {0x1d78U, 0xc53bU, 0U, 1U, 0U}, 45 #ifndef LIBC_TARGET_CPU_HAS_FMA 46 // x = 0x1.fdp-1, logf16(x) = -0x1.81p-8 (RZ) 47 {0x3bf4U, 0x9e04U, 0U, 1U, 1U}, 48 // x = 0x1.fep-1, logf16(x) = -0x1.008p-8 (RZ) 49 {0x3bf8U, 0x9c02U, 0U, 1U, 0U}, 50 #endif 51 // x = 0x1.ffp-1, logf16(x) = -0x1.004p-9 (RZ) 52 {0x3bfcU, 0x9801U, 0U, 1U, 0U}, 53 // x = 0x1.ff8p-1, logf16(x) = -0x1p-10 (RZ) 54 {0x3bfeU, 0x9400U, 0U, 1U, 1U}, 55 #ifdef LIBC_TARGET_CPU_HAS_FMA 56 // x = 0x1.4c4p+1, logf16(x) = 0x1.e84p-1 (RZ) 57 {0x4131U, 0x3ba1U, 1U, 0U, 1U}, 58 #else 59 // x = 0x1.75p+2, logf16(x) = 0x1.c34p+0 (RZ) 60 {0x45d4U, 0x3f0dU, 1U, 0U, 0U}, 61 // x = 0x1.75p+2, logf16(x) = 0x1.c34p+0 (RZ) 62 {0x45d4U, 0x3f0dU, 1U, 0U, 0U}, 63 // x = 0x1.d5p+9, logf16(x) = 0x1.b5cp+2 (RZ) 64 {0x6354U, 0x46d7U, 1U, 0U, 1U}, 65 #endif 66 }}; 67 68 LLVM_LIBC_FUNCTION(float16, logf16, (float16 x)) { 69 using FPBits = fputil::FPBits<float16>; 70 FPBits x_bits(x); 71 72 uint16_t x_u = x_bits.uintval(); 73 74 // If x <= 0, or x is 1, or x is +inf, or x is NaN. 75 if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) { 76 // log(NaN) = NaN 77 if (x_bits.is_nan()) { 78 if (x_bits.is_signaling_nan()) { 79 fputil::raise_except_if_required(FE_INVALID); 80 return FPBits::quiet_nan().get_val(); 81 } 82 83 return x; 84 } 85 86 // log(+/-0) = −inf 87 if ((x_u & 0x7fffU) == 0U) { 88 fputil::raise_except_if_required(FE_DIVBYZERO); 89 return FPBits::inf(Sign::NEG).get_val(); 90 } 91 92 if (x_u == 0x3c00U) 93 return FPBits::zero().get_val(); 94 95 // When x < 0. 96 if (x_u > 0x8000U) { 97 fputil::set_errno_if_required(EDOM); 98 fputil::raise_except_if_required(FE_INVALID); 99 return FPBits::quiet_nan().get_val(); 100 } 101 102 // log(+inf) = +inf 103 return FPBits::inf().get_val(); 104 } 105 106 if (auto r = LOGF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) 107 return r.value(); 108 109 // To compute log(x), we perform the following range reduction: 110 // x = 2^m * 1.mant, 111 // log(x) = m * log(2) + log(1.mant). 112 // To compute log(1.mant), let f be the highest 6 bits including the hidden 113 // bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of 114 // the mantissa, then: 115 // log(1.mant) = log(f) + log(1.mant / f) 116 // = log(f) + log(1 + d/f) 117 // since d/f is sufficiently small. 118 // We store log(f) and 1/f in the lookup tables LOGF_F and ONE_OVER_F_F 119 // respectively. 120 121 int m = -FPBits::EXP_BIAS; 122 123 // When x is subnormal, normalize it. 124 if ((x_u & FPBits::EXP_MASK) == 0U) { 125 // Can't pass an integer to fputil::cast directly. 126 constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN; 127 x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP)); 128 x_u = x_bits.uintval(); 129 m -= FPBits::FRACTION_LEN; 130 } 131 132 uint16_t mant = x_bits.get_mantissa(); 133 // Leading 10 - 5 = 5 bits of the mantissa. 134 int f = mant >> 5; 135 // Unbiased exponent. 136 m += x_u >> FPBits::FRACTION_LEN; 137 138 // Set bits to 1.mant instead of 2^m * 1.mant. 139 x_bits.set_biased_exponent(FPBits::EXP_BIAS); 140 float mant_f = x_bits.get_val(); 141 // v = 1.mant * 1/f - 1 = d/f 142 float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f); 143 144 // Degree-3 minimax polynomial generated by Sollya with the following 145 // commands: 146 // > display = hexadecimal; 147 // > P = fpminimax(log(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]); 148 // > x * P; 149 float log1p_d_over_f = 150 v * fputil::polyeval(v, 0x1p+0f, -0x1.001804p-1f, 0x1.557ef6p-2f); 151 // log(1.mant) = log(f) + log(1 + d/f) 152 float log_1_mant = LOGF_F[f] + log1p_d_over_f; 153 return fputil::cast<float16>( 154 fputil::multiply_add(static_cast<float>(m), LOGF_2, log_1_mant)); 155 } 156 157 } // namespace LIBC_NAMESPACE_DECL 158