1 //===-- Implementation header for expf16 ------------------------*- C++ -*-===// 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 #ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H 10 #define LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H 11 12 #include "include/llvm-libc-macros/float16-macros.h" 13 14 #ifdef LIBC_TYPES_HAS_FLOAT16 15 16 #include "hdr/errno_macros.h" 17 #include "hdr/fenv_macros.h" 18 #include "src/__support/FPUtil/FEnvImpl.h" 19 #include "src/__support/FPUtil/FPBits.h" 20 #include "src/__support/FPUtil/PolyEval.h" 21 #include "src/__support/FPUtil/cast.h" 22 #include "src/__support/FPUtil/except_value_utils.h" 23 #include "src/__support/FPUtil/rounding_mode.h" 24 #include "src/__support/common.h" 25 #include "src/__support/macros/config.h" 26 #include "src/__support/macros/optimization.h" 27 28 #include "expf16_utils.h" 29 30 namespace LIBC_NAMESPACE_DECL { 31 32 namespace math { 33 34 static constexpr float16 expf16(float16 x) { 35 #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS 36 constexpr fputil::ExceptValues<float16, 2> EXPF16_EXCEPTS_LO = {{ 37 // (input, RZ output, RU offset, RD offset, RN offset) 38 // x = 0x1.de4p-8, expf16(x) = 0x1.01cp+0 (RZ) 39 {0x1f79U, 0x3c07U, 1U, 0U, 0U}, 40 // x = 0x1.73cp-6, expf16(x) = 0x1.05cp+0 (RZ) 41 {0x25cfU, 0x3c17U, 1U, 0U, 0U}, 42 }}; 43 44 constexpr fputil::ExceptValues<float16, 3> EXPF16_EXCEPTS_HI = {{ 45 // (input, RZ output, RU offset, RD offset, RN offset) 46 // x = 0x1.c34p+0, expf16(x) = 0x1.74cp+2 (RZ) 47 {0x3f0dU, 0x45d3U, 1U, 0U, 1U}, 48 // x = -0x1.488p-5, expf16(x) = 0x1.ebcp-1 (RZ) 49 {0xa922U, 0x3bafU, 1U, 0U, 0U}, 50 // x = -0x1.55p-5, expf16(x) = 0x1.ebp-1 (RZ) 51 {0xa954U, 0x3bacU, 1U, 0U, 0U}, 52 }}; 53 #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS 54 55 using FPBits = fputil::FPBits<float16>; 56 FPBits x_bits(x); 57 58 uint16_t x_u = x_bits.uintval(); 59 uint16_t x_abs = x_u & 0x7fffU; 60 61 // When 0 < |x| <= 2^(-5), or |x| >= 12, or x is NaN. 62 if (LIBC_UNLIKELY(x_abs <= 0x2800U || x_abs >= 0x4a00U)) { 63 // exp(NaN) = NaN 64 if (x_bits.is_nan()) { 65 if (x_bits.is_signaling_nan()) { 66 fputil::raise_except_if_required(FE_INVALID); 67 return FPBits::quiet_nan().get_val(); 68 } 69 70 return x; 71 } 72 73 // When x >= 12. 74 if (x_bits.is_pos() && x_abs >= 0x4a00U) { 75 // exp(+inf) = +inf 76 if (x_bits.is_inf()) 77 return FPBits::inf().get_val(); 78 79 switch (fputil::quick_get_round()) { 80 case FE_TONEAREST: 81 case FE_UPWARD: 82 fputil::set_errno_if_required(ERANGE); 83 fputil::raise_except_if_required(FE_OVERFLOW); 84 return FPBits::inf().get_val(); 85 default: 86 return FPBits::max_normal().get_val(); 87 } 88 } 89 90 // When x <= -18. 91 if (x_u >= 0xcc80U) { 92 // exp(-inf) = +0 93 if (x_bits.is_inf()) 94 return FPBits::zero().get_val(); 95 96 fputil::set_errno_if_required(ERANGE); 97 fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT); 98 99 switch (fputil::quick_get_round()) { 100 case FE_UPWARD: 101 return FPBits::min_subnormal().get_val(); 102 default: 103 return FPBits::zero().get_val(); 104 } 105 } 106 107 // When 0 < |x| <= 2^(-5). 108 if (x_abs <= 0x2800U && !x_bits.is_zero()) { 109 #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS 110 if (auto r = EXPF16_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value())) 111 return r.value(); 112 #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS 113 114 float xf = x; 115 // Degree-3 minimax polynomial generated by Sollya with the following 116 // commands: 117 // > display = hexadecimal; 118 // > P = fpminimax(expm1(x)/x, 2, [|SG...|], [-2^-5, 2^-5]); 119 // > 1 + x * P; 120 return fputil::cast<float16>( 121 fputil::polyeval(xf, 0x1p+0f, 0x1p+0f, 0x1.0004p-1f, 0x1.555778p-3f)); 122 } 123 } 124 125 #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS 126 if (auto r = EXPF16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) 127 return r.value(); 128 #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS 129 130 // exp(x) = exp(hi + mid) * exp(lo) 131 auto [exp_hi_mid, exp_lo] = exp_range_reduction(x); 132 return fputil::cast<float16>(exp_hi_mid * exp_lo); 133 } 134 135 } // namespace math 136 137 } // namespace LIBC_NAMESPACE_DECL 138 139 #endif // LIBC_TYPES_HAS_FLOAT16 140 141 #endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H 142