/*
* Copyright (c) 2014,2015 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 atanh(float x) {
uint ux = as_uint(x);
uint ax = ux & EXSIGNBIT_SP32;
uint xs = ux ^ ax;
// |x| > 1 or NaN
float z = as_float(QNANBITPATT_SP32);
// |x| == 1
float t = as_float(xs | PINFBITPATT_SP32);
z = ax == 0x3f800000U ? t : z;
// 1/2 <= |x| < 1
t = as_float(ax);
t = MATH_DIVIDE(2.0f*t, 1.0f - t);
t = 0.5f * log1p(t);
t = as_float(xs | as_uint(t));
z = ax < 0x3f800000U ? t : z;
// |x| < 1/2
t = x * x;
float a = mad(mad(0.92834212715e-2f, t, -0.28120347286e0f), t, 0.39453629046e0f);
float b = mad(mad(0.45281890445e0f, t, -0.15537744551e1f), t, 0.11836088638e1f);
float p = MATH_DIVIDE(a, b);
t = mad(x*t, p, x);
z = ax < 0x3f000000 ? t : z;
// |x| < 2^-13
z = ax < 0x39000000U ? x : z;
return z;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atanh, float)
#ifdef cl_khr_fp64
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
_CLC_OVERLOAD _CLC_DEF double atanh(double x) {
double absx = fabs(x);
double ret = absx == 1.0 ? as_double(PINFBITPATT_DP64) : as_double(QNANBITPATT_DP64);
// |x| >= 0.5
// Note that atanh(x) = 0.5 * ln((1+x)/(1-x))
// For greater accuracy we use
// ln((1+x)/(1-x)) = ln(1 + 2x/(1-x)) = log1p(2x/(1-x)).
double r = 0.5 * log1p(2.0 * absx / (1.0 - absx));
ret = absx < 1.0 ? r : ret;
r = -ret;
ret = x < 0.0 ? r : ret;
// Arguments up to 0.5 in magnitude are
// approximated by a [5,5] minimax polynomial
double t = x * x;
double pn = fma(t,
fma(t,
fma(t,
fma(t,
fma(t, -0.10468158892753136958e-3, 0.28728638600548514553e-1),
-0.28180210961780814148e0),
0.88468142536501647470e0),
-0.11028356797846341457e1),
0.47482573589747356373e0);
double pd = fma(t,
fma(t,
fma(t,
fma(t,
fma(t, -0.35861554370169537512e-1, 0.49561196555503101989e0),
-0.22608883748988489342e1),
0.45414700626084508355e1),
-0.41631933639693546274e1),
0.14244772076924206909e1);
r = fma(x*t, pn/pd, x);
ret = absx < 0.5 ? r : ret;
return ret;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atanh, double)
#endif
_CLC_DEFINE_UNARY_BUILTIN_FP16(atanh)
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