/*
* Copyright (c) 2014 Advanced Micro Devices, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#include <clc/clc.h>
#include "math.h"
#include "../clcmacro.h"
_CLC_OVERLOAD _CLC_DEF float tanh(float x)
{
// The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent
// to the following three formulae:
// 1. (exp(x) - exp(-x))/(exp(x) + exp(-x))
// 2. (1 - (2/(exp(2*x) + 1 )))
// 3. (exp(2*x) - 1)/(exp(2*x) + 1)
// but computationally, some formulae are better on some ranges.
const float large_threshold = 0x1.0a2b24p+3f;
uint ux = as_uint(x);
uint aux = ux & EXSIGNBIT_SP32;
uint xs = ux ^ aux;
float y = as_float(aux);
float y2 = y*y;
float a1 = mad(y2,
mad(y2, 0.4891631088530669873e-4F, -0.14628356048797849e-2F),
-0.28192806108402678e0F);
float b1 = mad(y2, 0.3427017942262751343e0F, 0.845784192581041099e0F);
float a2 = mad(y2,
mad(y2, 0.3827534993599483396e-4F, -0.12325644183611929e-2F),
-0.24069858695196524e0F);
float b2 = mad(y2, 0.292529068698052819e0F, 0.72209738473684982e0F);
int c = y < 0.9f;
float a = c ? a1 : a2;
float b = c ? b1 : b2;
float zlo = mad(MATH_DIVIDE(a, b), y*y2, y);
float p = exp(2.0f * y) + 1.0f;
float zhi = 1.0F - MATH_DIVIDE(2.0F, p);
float z = y <= 1.0f ? zlo : zhi;
z = as_float(xs | as_uint(z));
// Edge cases
float sone = as_float(0x3f800000U | xs);
z = y > large_threshold ? sone : z;
z = aux < 0x39000000 | aux > 0x7f800000 ? x : z;
return z;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, tanh, float);
#ifdef cl_khr_fp64
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
_CLC_OVERLOAD _CLC_DEF double tanh(double x)
{
// The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent
// to the following three formulae:
// 1. (exp(x) - exp(-x))/(exp(x) + exp(-x))
// 2. (1 - (2/(exp(2*x) + 1 )))
// 3. (exp(2*x) - 1)/(exp(2*x) + 1)
// but computationally, some formulae are better on some ranges.
// The point at which e^-x is insignificant compared to e^x = ln(2^27)
const double large_threshold = 0x1.2b708872320e2p+4;
ulong ux = as_ulong(x);
ulong ax = ux & ~SIGNBIT_DP64;
ulong sx = ux ^ ax;
double y = as_double(ax);
double y2 = y * y;
// y < 0.9
double znl = fma(y2,
fma(y2,
fma(y2, -0.142077926378834722618091e-7, -0.200047621071909498730453e-3),
-0.176016349003044679402273e-1),
-0.274030424656179760118928e0);
double zdl = fma(y2,
fma(y2,
fma(y2, 0.2091140262529164482568557e-3, 0.201562166026937652780575e-1),
0.381641414288328849317962e0),
0.822091273968539282568011e0);
// 0.9 <= y <= 1
double znm = fma(y2,
fma(y2,
fma(y2, -0.115475878996143396378318e-7, -0.165597043903549960486816e-3),
-0.146173047288731678404066e-1),
-0.227793870659088295252442e0);
double zdm = fma(y2,
fma(y2,
fma(y2, 0.173076050126225961768710e-3, 0.167358775461896562588695e-1),
0.317204558977294374244770e0),
0.683381611977295894959554e0);
int c = y < 0.9;
double zn = c ? znl : znm;
double zd = c ? zdl : zdm;
double z = y + y*y2 * MATH_DIVIDE(zn, zd);
// y > 1
double p = exp(2.0 * y) + 1.0;
double zg = 1.0 - 2.0 / p;
z = y > 1.0 ? zg : z;
// Other cases
z = y < 0x1.0p-28 | ax > PINFBITPATT_DP64 ? x : z;
z = y > large_threshold ? 1.0 : z;
return as_double(sx | as_ulong(z));
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, tanh, double);
#endif // cl_khr_fp64
_CLC_DEFINE_UNARY_BUILTIN_FP16(tanh)
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