1 //===-- Half-precision e^x - 1 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/expm1f16.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/FPUtil/rounding_mode.h" 20 #include "src/__support/common.h" 21 #include "src/__support/macros/config.h" 22 #include "src/__support/macros/optimization.h" 23 24 namespace LIBC_NAMESPACE_DECL { 25 26 static constexpr fputil::ExceptValues<float16, 1> EXPM1F16_EXCEPTS_LO = {{ 27 // (input, RZ output, RU offset, RD offset, RN offset) 28 // x = 0x1.564p-5, expm1f16(x) = 0x1.5d4p-5 (RZ) 29 {0x2959U, 0x2975U, 1U, 0U, 1U}, 30 }}; 31 32 #ifdef LIBC_TARGET_CPU_HAS_FMA 33 static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 2; 34 #else 35 static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 3; 36 #endif 37 38 static constexpr fputil::ExceptValues<float16, N_EXPM1F16_EXCEPTS_HI> 39 EXPM1F16_EXCEPTS_HI = {{ 40 // (input, RZ output, RU offset, RD offset, RN offset) 41 // x = 0x1.c34p+0, expm1f16(x) = 0x1.34cp+2 (RZ) 42 {0x3f0dU, 0x44d3U, 1U, 0U, 1U}, 43 // x = -0x1.e28p-3, expm1f16(x) = -0x1.adcp-3 (RZ) 44 {0xb38aU, 0xb2b7U, 0U, 1U, 1U}, 45 #ifndef LIBC_TARGET_CPU_HAS_FMA 46 // x = 0x1.a08p-3, exp10m1f(x) = 0x1.cdcp-3 (RZ) 47 {0x3282U, 0x3337U, 1U, 0U, 0U}, 48 #endif 49 }}; 50 51 LLVM_LIBC_FUNCTION(float16, expm1f16, (float16 x)) { 52 using FPBits = fputil::FPBits<float16>; 53 FPBits x_bits(x); 54 55 uint16_t x_u = x_bits.uintval(); 56 uint16_t x_abs = x_u & 0x7fffU; 57 58 // When |x| <= 2^(-3), or |x| >= -11 * log(2), or x is NaN. 59 if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x47a0U)) { 60 // expm1(NaN) = NaN 61 if (x_bits.is_nan()) { 62 if (x_bits.is_signaling_nan()) { 63 fputil::raise_except_if_required(FE_INVALID); 64 return FPBits::quiet_nan().get_val(); 65 } 66 67 return x; 68 } 69 70 // expm1(+/-0) = +/-0 71 if (x_abs == 0) 72 return x; 73 74 // When x >= 16 * log(2). 75 if (x_bits.is_pos() && x_abs >= 0x498cU) { 76 // expm1(+inf) = +inf 77 if (x_bits.is_inf()) 78 return FPBits::inf().get_val(); 79 80 switch (fputil::quick_get_round()) { 81 case FE_TONEAREST: 82 case FE_UPWARD: 83 fputil::set_errno_if_required(ERANGE); 84 fputil::raise_except_if_required(FE_OVERFLOW | FE_INEXACT); 85 return FPBits::inf().get_val(); 86 default: 87 return FPBits::max_normal().get_val(); 88 } 89 } 90 91 // When x <= -11 * log(2). 92 if (x_u >= 0xc7a0U) { 93 // expm1(-inf) = -1 94 if (x_bits.is_inf()) 95 return FPBits::one(Sign::NEG).get_val(); 96 97 // When x > -0x1.0ap+3, round(expm1(x), HP, RN) = -1. 98 if (x_u > 0xc828U) 99 return fputil::round_result_slightly_up( 100 FPBits::one(Sign::NEG).get_val()); 101 // When x <= -0x1.0ap+3, round(expm1(x), HP, RN) = -0x1.ffcp-1. 102 return fputil::round_result_slightly_down( 103 fputil::cast<float16>(-0x1.ffcp-1)); 104 } 105 106 // When 0 < |x| <= 2^(-3). 107 if (x_abs <= 0x3000U && !x_bits.is_zero()) { 108 if (auto r = EXPM1F16_EXCEPTS_LO.lookup(x_u); 109 LIBC_UNLIKELY(r.has_value())) 110 return r.value(); 111 112 float xf = x; 113 // Degree-5 minimax polynomial generated by Sollya with the following 114 // commands: 115 // > display = hexadecimal; 116 // > P = fpminimax(expm1(x)/x, 4, [|SG...|], [-2^-3, 2^-3]); 117 // > x * P; 118 return fputil::cast<float16>( 119 xf * fputil::polyeval(xf, 0x1p+0f, 0x1.fffff8p-2f, 0x1.555556p-3f, 120 0x1.55905ep-5f, 0x1.1124c2p-7f)); 121 } 122 } 123 124 if (auto r = EXPM1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) 125 return r.value(); 126 127 // exp(x) = exp(hi + mid) * exp(lo) 128 auto [exp_hi_mid, exp_lo] = exp_range_reduction(x); 129 // expm1(x) = exp(hi + mid) * exp(lo) - 1 130 return fputil::cast<float16>(fputil::multiply_add(exp_hi_mid, exp_lo, -1.0f)); 131 } 132 133 } // namespace LIBC_NAMESPACE_DECL 134