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1//===----------------------------------------------------------------------===//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-exception6//7//===----------------------------------------------------------------------===//8 9#if __CLC_FPSIZE == 3210 11_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_tanh(__CLC_GENTYPE x) {12 // The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent13 // to the following three formulae:14 // 1. (exp(x) - exp(-x))/(exp(x) + exp(-x))15 // 2. (1 - (2/(exp(2*x) + 1 )))16 // 3. (exp(2*x) - 1)/(exp(2*x) + 1)17 // but computationally, some formulae are better on some ranges.18 19 const __CLC_GENTYPE large_threshold = 0x1.0a2b24p+3f;20 21 __CLC_UINTN ux = __CLC_AS_UINTN(x);22 __CLC_UINTN aux = ux & EXSIGNBIT_SP32;23 __CLC_UINTN xs = ux ^ aux;24 25 __CLC_GENTYPE y = __CLC_AS_GENTYPE(aux);26 __CLC_GENTYPE y2 = y * y;27 28 __CLC_GENTYPE a1 = __clc_mad(29 y2, __clc_mad(y2, 0.4891631088530669873e-4F, -0.14628356048797849e-2F),30 -0.28192806108402678e0F);31 __CLC_GENTYPE b1 =32 __clc_mad(y2, 0.3427017942262751343e0F, 0.845784192581041099e0F);33 34 __CLC_GENTYPE a2 = __clc_mad(35 y2, __clc_mad(y2, 0.3827534993599483396e-4F, -0.12325644183611929e-2F),36 -0.24069858695196524e0F);37 __CLC_GENTYPE b2 =38 __clc_mad(y2, 0.292529068698052819e0F, 0.72209738473684982e0F);39 40 __CLC_INTN c = y < 0.9f;41 __CLC_GENTYPE a = c ? a1 : a2;42 __CLC_GENTYPE b = c ? b1 : b2;43 __CLC_GENTYPE zlo = __clc_mad(MATH_DIVIDE(a, b), y * y2, y);44 45 __CLC_GENTYPE p = __clc_exp(2.0f * y) + 1.0f;46 __CLC_GENTYPE zhi = 1.0F - MATH_DIVIDE(2.0F, p);47 48 __CLC_GENTYPE z = y <= 1.0f ? zlo : zhi;49 z = __CLC_AS_GENTYPE(xs | __CLC_AS_UINTN(z));50 51 // Edge cases52 __CLC_GENTYPE sone = __CLC_AS_GENTYPE(0x3f800000U | xs);53 z = y > large_threshold ? sone : z;54 z = aux < 0x39000000 || aux > 0x7f800000 ? x : z;55 56 return z;57}58 59#elif __CLC_FPSIZE == 6460 61_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_tanh(__CLC_GENTYPE x) {62 // The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent63 // to the following three formulae:64 // 1. (exp(x) - exp(-x))/(exp(x) + exp(-x))65 // 2. (1 - (2/(exp(2*x) + 1 )))66 // 3. (exp(2*x) - 1)/(exp(2*x) + 1)67 // but computationally, some formulae are better on some ranges.68 69 // The point at which e^-x is insignificant compared to e^x = ln(2^27)70 const __CLC_GENTYPE large_threshold = 0x1.2b708872320e2p+4;71 72 __CLC_ULONGN ux = __CLC_AS_ULONGN(x);73 __CLC_ULONGN ax = ux & ~SIGNBIT_DP64;74 __CLC_ULONGN sx = ux ^ ax;75 __CLC_GENTYPE y = __CLC_AS_GENTYPE(ax);76 __CLC_GENTYPE y2 = y * y;77 78 // y < 0.979 __CLC_GENTYPE znl =80 __clc_fma(y2,81 __clc_fma(y2,82 __clc_fma(y2, -0.142077926378834722618091e-7,83 -0.200047621071909498730453e-3),84 -0.176016349003044679402273e-1),85 -0.274030424656179760118928e0);86 87 __CLC_GENTYPE zdl =88 __clc_fma(y2,89 __clc_fma(y2,90 __clc_fma(y2, 0.2091140262529164482568557e-3,91 0.201562166026937652780575e-1),92 0.381641414288328849317962e0),93 0.822091273968539282568011e0);94 95 // 0.9 <= y <= 196 __CLC_GENTYPE znm =97 __clc_fma(y2,98 __clc_fma(y2,99 __clc_fma(y2, -0.115475878996143396378318e-7,100 -0.165597043903549960486816e-3),101 -0.146173047288731678404066e-1),102 -0.227793870659088295252442e0);103 104 __CLC_GENTYPE zdm =105 __clc_fma(y2,106 __clc_fma(y2,107 __clc_fma(y2, 0.173076050126225961768710e-3,108 0.167358775461896562588695e-1),109 0.317204558977294374244770e0),110 0.683381611977295894959554e0);111 112 __CLC_LONGN c = y < 0.9;113 __CLC_GENTYPE zn = c ? znl : znm;114 __CLC_GENTYPE zd = c ? zdl : zdm;115 __CLC_GENTYPE z = y + y * y2 * MATH_DIVIDE(zn, zd);116 117 // y > 1118 __CLC_GENTYPE p = __clc_exp(2.0 * y) + 1.0;119 __CLC_GENTYPE zg = 1.0 - 2.0 / p;120 121 z = y > 1.0 ? zg : z;122 123 // Other cases124 z = y < 0x1.0p-28 || ax > PINFBITPATT_DP64 ? x : z;125 126 z = y > large_threshold ? 1.0 : z;127 128 return __CLC_AS_GENTYPE(sx | __CLC_AS_ULONGN(z));129}130 131#elif __CLC_FPSIZE == 16132 133_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_tanh(__CLC_GENTYPE x) {134 return __CLC_CONVERT_GENTYPE(__clc_tanh(__CLC_CONVERT_FLOATN(x)));135}136 137#endif138