1 //===-- Half-precision log2(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/log2f16.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_LOG2F16_EXCEPTS = 2; 28 #else 29 static constexpr size_t N_LOG2F16_EXCEPTS = 9; 30 #endif 31 32 static constexpr fputil::ExceptValues<float16, N_LOG2F16_EXCEPTS> 33 LOG2F16_EXCEPTS = {{ 34 // (input, RZ output, RU offset, RD offset, RN offset) 35 #ifndef LIBC_TARGET_CPU_HAS_FMA 36 // x = 0x1.224p-1, log2f16(x) = -0x1.a34p-1 (RZ) 37 {0x3889U, 0xba8dU, 0U, 1U, 0U}, 38 // x = 0x1.e34p-1, log2f16(x) = -0x1.558p-4 (RZ) 39 {0x3b8dU, 0xad56U, 0U, 1U, 0U}, 40 #endif 41 // x = 0x1.e8cp-1, log2f16(x) = -0x1.128p-4 (RZ) 42 {0x3ba3U, 0xac4aU, 0U, 1U, 0U}, 43 #ifndef LIBC_TARGET_CPU_HAS_FMA 44 // x = 0x1.f98p-1, log2f16(x) = -0x1.2ep-6 (RZ) 45 {0x3be6U, 0xa4b8U, 0U, 1U, 0U}, 46 // x = 0x1.facp-1, log2f16(x) = -0x1.e7p-7 (RZ) 47 {0x3bebU, 0xa39cU, 0U, 1U, 1U}, 48 #endif 49 // x = 0x1.fb4p-1, log2f16(x) = -0x1.b88p-7 (RZ) 50 {0x3bedU, 0xa2e2U, 0U, 1U, 1U}, 51 #ifndef LIBC_TARGET_CPU_HAS_FMA 52 // x = 0x1.fecp-1, log2f16(x) = -0x1.cep-9 (RZ) 53 {0x3bfbU, 0x9b38U, 0U, 1U, 1U}, 54 // x = 0x1.ffcp-1, log2f16(x) = -0x1.714p-11 (RZ) 55 {0x3bffU, 0x91c5U, 0U, 1U, 1U}, 56 // x = 0x1.224p+0, log2f16(x) = 0x1.72cp-3 (RZ) 57 {0x3c89U, 0x31cbU, 1U, 0U, 1U}, 58 #endif 59 }}; 60 61 LLVM_LIBC_FUNCTION(float16, log2f16, (float16 x)) { 62 using FPBits = fputil::FPBits<float16>; 63 FPBits x_bits(x); 64 65 uint16_t x_u = x_bits.uintval(); 66 67 // If x <= 0, or x is 1, or x is +inf, or x is NaN. 68 if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) { 69 // log2(NaN) = NaN 70 if (x_bits.is_nan()) { 71 if (x_bits.is_signaling_nan()) { 72 fputil::raise_except_if_required(FE_INVALID); 73 return FPBits::quiet_nan().get_val(); 74 } 75 76 return x; 77 } 78 79 // log2(+/-0) = −inf 80 if ((x_u & 0x7fffU) == 0U) { 81 fputil::raise_except_if_required(FE_DIVBYZERO); 82 return FPBits::inf(Sign::NEG).get_val(); 83 } 84 85 if (x_u == 0x3c00U) 86 return FPBits::zero().get_val(); 87 88 // When x < 0. 89 if (x_u > 0x8000U) { 90 fputil::set_errno_if_required(EDOM); 91 fputil::raise_except_if_required(FE_INVALID); 92 return FPBits::quiet_nan().get_val(); 93 } 94 95 // log2(+inf) = +inf 96 return FPBits::inf().get_val(); 97 } 98 99 if (auto r = LOG2F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) 100 return r.value(); 101 102 // To compute log2(x), we perform the following range reduction: 103 // x = 2^m * 1.mant, 104 // log2(x) = m + log2(1.mant). 105 // To compute log2(1.mant), let f be the highest 6 bits including the hidden 106 // bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of 107 // the mantissa, then: 108 // log2(1.mant) = log2(f) + log2(1.mant / f) 109 // = log2(f) + log2(1 + d/f) 110 // since d/f is sufficiently small. 111 // We store log2(f) and 1/f in the lookup tables LOG2F_F and ONE_OVER_F_F 112 // respectively. 113 114 int m = -FPBits::EXP_BIAS; 115 116 // When x is subnormal, normalize it. 117 if ((x_u & FPBits::EXP_MASK) == 0U) { 118 // Can't pass an integer to fputil::cast directly. 119 constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN; 120 x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP)); 121 x_u = x_bits.uintval(); 122 m -= FPBits::FRACTION_LEN; 123 } 124 125 uint16_t mant = x_bits.get_mantissa(); 126 // Leading 10 - 5 = 5 bits of the mantissa. 127 int f = mant >> 5; 128 // Unbiased exponent. 129 m += x_u >> FPBits::FRACTION_LEN; 130 131 // Set bits to 1.mant instead of 2^m * 1.mant. 132 x_bits.set_biased_exponent(FPBits::EXP_BIAS); 133 float mant_f = x_bits.get_val(); 134 // v = 1.mant * 1/f - 1 = d/f 135 float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f); 136 137 // Degree-3 minimax polynomial generated by Sollya with the following 138 // commands: 139 // > display = hexadecimal; 140 // > P = fpminimax(log2(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]); 141 // > x * P; 142 float log2p1_d_over_f = 143 v * fputil::polyeval(v, 0x1.715476p+0f, -0x1.71771ap-1f, 0x1.ecb38ep-2f); 144 // log2(1.mant) = log2(f) + log2(1 + d/f) 145 float log2_1_mant = LOG2F_F[f] + log2p1_d_over_f; 146 return fputil::cast<float16>(static_cast<float>(m) + log2_1_mant); 147 } 148 149 } // namespace LIBC_NAMESPACE_DECL 150