1/* 2 * Copyright (c) 2014,2015 Advanced Micro Devices, Inc. 3 * 4 * Permission is hereby granted, free of charge, to any person obtaining a copy 5 * of this software and associated documentation files (the "Software"), to deal 6 * in the Software without restriction, including without limitation the rights 7 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 8 * copies of the Software, and to permit persons to whom the Software is 9 * furnished to do so, subject to the following conditions: 10 * 11 * The above copyright notice and this permission notice shall be included in 12 * all copies or substantial portions of the Software. 13 * 14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 15 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 16 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 17 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 18 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 19 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 20 * THE SOFTWARE. 21 */ 22 23#include <clc/clc.h> 24#include <clc/clcmacro.h> 25#include <clc/math/math.h> 26 27_CLC_OVERLOAD _CLC_DEF float atanh(float x) { 28 uint ux = as_uint(x); 29 uint ax = ux & EXSIGNBIT_SP32; 30 uint xs = ux ^ ax; 31 32 // |x| > 1 or NaN 33 float z = as_float(QNANBITPATT_SP32); 34 35 // |x| == 1 36 float t = as_float(xs | PINFBITPATT_SP32); 37 z = ax == 0x3f800000U ? t : z; 38 39 // 1/2 <= |x| < 1 40 t = as_float(ax); 41 t = MATH_DIVIDE(2.0f*t, 1.0f - t); 42 t = 0.5f * log1p(t); 43 t = as_float(xs | as_uint(t)); 44 z = ax < 0x3f800000U ? t : z; 45 46 // |x| < 1/2 47 t = x * x; 48 float a = mad(mad(0.92834212715e-2f, t, -0.28120347286e0f), t, 0.39453629046e0f); 49 float b = mad(mad(0.45281890445e0f, t, -0.15537744551e1f), t, 0.11836088638e1f); 50 float p = MATH_DIVIDE(a, b); 51 t = mad(x*t, p, x); 52 z = ax < 0x3f000000 ? t : z; 53 54 // |x| < 2^-13 55 z = ax < 0x39000000U ? x : z; 56 57 return z; 58} 59 60_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atanh, float) 61 62#ifdef cl_khr_fp64 63#pragma OPENCL EXTENSION cl_khr_fp64 : enable 64 65_CLC_OVERLOAD _CLC_DEF double atanh(double x) { 66 double absx = fabs(x); 67 68 double ret = absx == 1.0 ? as_double(PINFBITPATT_DP64) : as_double(QNANBITPATT_DP64); 69 70 // |x| >= 0.5 71 // Note that atanh(x) = 0.5 * ln((1+x)/(1-x)) 72 // For greater accuracy we use 73 // ln((1+x)/(1-x)) = ln(1 + 2x/(1-x)) = log1p(2x/(1-x)). 74 double r = 0.5 * log1p(2.0 * absx / (1.0 - absx)); 75 ret = absx < 1.0 ? r : ret; 76 77 r = -ret; 78 ret = x < 0.0 ? r : ret; 79 80 // Arguments up to 0.5 in magnitude are 81 // approximated by a [5,5] minimax polynomial 82 double t = x * x; 83 84 double pn = fma(t, 85 fma(t, 86 fma(t, 87 fma(t, 88 fma(t, -0.10468158892753136958e-3, 0.28728638600548514553e-1), 89 -0.28180210961780814148e0), 90 0.88468142536501647470e0), 91 -0.11028356797846341457e1), 92 0.47482573589747356373e0); 93 94 double pd = fma(t, 95 fma(t, 96 fma(t, 97 fma(t, 98 fma(t, -0.35861554370169537512e-1, 0.49561196555503101989e0), 99 -0.22608883748988489342e1), 100 0.45414700626084508355e1), 101 -0.41631933639693546274e1), 102 0.14244772076924206909e1); 103 104 r = fma(x*t, pn/pd, x); 105 ret = absx < 0.5 ? r : ret; 106 107 return ret; 108} 109 110_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atanh, double) 111 112#endif 113 114#ifdef cl_khr_fp16 115 116#pragma OPENCL EXTENSION cl_khr_fp16 : enable 117 118_CLC_DEFINE_UNARY_BUILTIN_FP16(atanh) 119 120#endif 121