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147 lines
4.9 KiB
147 lines
4.9 KiB
/*
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* Copyright (c) 2014 Advanced Micro Devices, Inc.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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* THE SOFTWARE.
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*/
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#include <clc/clc.h>
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#include "math.h"
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#include "../clcmacro.h"
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_CLC_OVERLOAD _CLC_DEF float tanh(float x)
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{
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// The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent
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// to the following three formulae:
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// 1. (exp(x) - exp(-x))/(exp(x) + exp(-x))
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// 2. (1 - (2/(exp(2*x) + 1 )))
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// 3. (exp(2*x) - 1)/(exp(2*x) + 1)
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// but computationally, some formulae are better on some ranges.
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const float large_threshold = 0x1.0a2b24p+3f;
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uint ux = as_uint(x);
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uint aux = ux & EXSIGNBIT_SP32;
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uint xs = ux ^ aux;
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float y = as_float(aux);
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float y2 = y*y;
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float a1 = mad(y2,
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mad(y2, 0.4891631088530669873e-4F, -0.14628356048797849e-2F),
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-0.28192806108402678e0F);
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float b1 = mad(y2, 0.3427017942262751343e0F, 0.845784192581041099e0F);
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float a2 = mad(y2,
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mad(y2, 0.3827534993599483396e-4F, -0.12325644183611929e-2F),
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-0.24069858695196524e0F);
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float b2 = mad(y2, 0.292529068698052819e0F, 0.72209738473684982e0F);
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int c = y < 0.9f;
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float a = c ? a1 : a2;
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float b = c ? b1 : b2;
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float zlo = mad(MATH_DIVIDE(a, b), y*y2, y);
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float p = exp(2.0f * y) + 1.0f;
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float zhi = 1.0F - MATH_DIVIDE(2.0F, p);
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float z = y <= 1.0f ? zlo : zhi;
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z = as_float(xs | as_uint(z));
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// Edge cases
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float sone = as_float(0x3f800000U | xs);
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z = y > large_threshold ? sone : z;
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z = aux < 0x39000000 | aux > 0x7f800000 ? x : z;
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return z;
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, tanh, float);
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#ifdef cl_khr_fp64
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#pragma OPENCL EXTENSION cl_khr_fp64 : enable
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_CLC_OVERLOAD _CLC_DEF double tanh(double x)
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{
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// The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent
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// to the following three formulae:
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// 1. (exp(x) - exp(-x))/(exp(x) + exp(-x))
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// 2. (1 - (2/(exp(2*x) + 1 )))
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// 3. (exp(2*x) - 1)/(exp(2*x) + 1)
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// but computationally, some formulae are better on some ranges.
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// The point at which e^-x is insignificant compared to e^x = ln(2^27)
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const double large_threshold = 0x1.2b708872320e2p+4;
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ulong ux = as_ulong(x);
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ulong ax = ux & ~SIGNBIT_DP64;
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ulong sx = ux ^ ax;
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double y = as_double(ax);
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double y2 = y * y;
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// y < 0.9
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double znl = fma(y2,
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fma(y2,
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fma(y2, -0.142077926378834722618091e-7, -0.200047621071909498730453e-3),
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-0.176016349003044679402273e-1),
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-0.274030424656179760118928e0);
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double zdl = fma(y2,
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fma(y2,
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fma(y2, 0.2091140262529164482568557e-3, 0.201562166026937652780575e-1),
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0.381641414288328849317962e0),
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0.822091273968539282568011e0);
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// 0.9 <= y <= 1
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double znm = fma(y2,
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fma(y2,
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fma(y2, -0.115475878996143396378318e-7, -0.165597043903549960486816e-3),
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-0.146173047288731678404066e-1),
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-0.227793870659088295252442e0);
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double zdm = fma(y2,
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fma(y2,
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fma(y2, 0.173076050126225961768710e-3, 0.167358775461896562588695e-1),
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0.317204558977294374244770e0),
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0.683381611977295894959554e0);
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int c = y < 0.9;
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double zn = c ? znl : znm;
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double zd = c ? zdl : zdm;
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double z = y + y*y2 * MATH_DIVIDE(zn, zd);
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// y > 1
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double p = exp(2.0 * y) + 1.0;
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double zg = 1.0 - 2.0 / p;
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z = y > 1.0 ? zg : z;
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// Other cases
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z = y < 0x1.0p-28 | ax > PINFBITPATT_DP64 ? x : z;
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z = y > large_threshold ? 1.0 : z;
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return as_double(sx | as_ulong(z));
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, tanh, double);
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#endif // cl_khr_fp64
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