/*
* 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 "tables.h"
#include "../clcmacro.h"
_CLC_OVERLOAD _CLC_DEF float cosh(float x) {
// After dealing with special cases the computation is split into regions as follows.
// abs(x) >= max_cosh_arg:
// cosh(x) = sign(x)*Inf
// abs(x) >= small_threshold:
// cosh(x) = sign(x)*exp(abs(x))/2 computed using the
// splitexp and scaleDouble functions as for exp_amd().
// abs(x) < small_threshold:
// compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
// cosh(x) is then z.
const float max_cosh_arg = 0x1.65a9fap+6f;
const float small_threshold = 0x1.0a2b24p+3f;
uint ux = as_uint(x);
uint aux = ux & EXSIGNBIT_SP32;
float y = as_float(aux);
// Find the integer part y0 of y and the increment dy = y - y0. We then compute
// z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy)
// z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy)
// where sinh(y0) and cosh(y0) are tabulated above.
int ind = (int)y;
ind = (uint)ind > 36U ? 0 : ind;
float dy = y - ind;
float dy2 = dy * dy;
float sdy = mad(dy2,
mad(dy2,
mad(dy2,
mad(dy2,
mad(dy2,
mad(dy2, 0.7746188980094184251527126e-12f, 0.160576793121939886190847e-9f),
0.250521176994133472333666e-7f),
0.275573191913636406057211e-5f),
0.198412698413242405162014e-3f),
0.833333333333329931873097e-2f),
0.166666666666666667013899e0f);
sdy = mad(sdy, dy*dy2, dy);
float cdy = mad(dy2,
mad(dy2,
mad(dy2,
mad(dy2,
mad(dy2,
mad(dy2, 0.1163921388172173692062032e-10f, 0.208744349831471353536305e-8f),
0.275573350756016588011357e-6f),
0.248015872460622433115785e-4f),
0.138888888889814854814536e-2f),
0.416666666666660876512776e-1f),
0.500000000000000005911074e0f);
cdy = mad(cdy, dy2, 1.0f);
float2 tv = USE_TABLE(sinhcosh_tbl, ind);
float z = mad(tv.s0, sdy, tv.s1 * cdy);
// When exp(-x) is insignificant compared to exp(x), return exp(x)/2
float t = exp(y - 0x1.62e500p-1f);
float zsmall = mad(0x1.a0210ep-18f, t, t);
z = y >= small_threshold ? zsmall : z;
// Corner cases
z = y >= max_cosh_arg ? as_float(PINFBITPATT_SP32) : z;
z = aux > PINFBITPATT_SP32 ? as_float(QNANBITPATT_SP32) : z;
z = aux < 0x38800000 ? 1.0f : z;
return z;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cosh, float);
#ifdef cl_khr_fp64
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
_CLC_OVERLOAD _CLC_DEF double cosh(double x) {
// After dealing with special cases the computation is split into
// regions as follows:
//
// abs(x) >= max_cosh_arg:
// cosh(x) = sign(x)*Inf
//
// abs(x) >= small_threshold:
// cosh(x) = sign(x)*exp(abs(x))/2 computed using the
// splitexp and scaleDouble functions as for exp_amd().
//
// abs(x) < small_threshold:
// compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
// cosh(x) is then sign(x)*z.
// This is ln(2^1025)
const double max_cosh_arg = 7.10475860073943977113e+02; // 0x408633ce8fb9f87e
// This is where exp(-x) is insignificant compared to exp(x) = ln(2^27)
const double small_threshold = 0x1.2b708872320e2p+4;
double y = fabs(x);
// In this range we find the integer part y0 of y
// and the increment dy = y - y0. We then compute
// z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy)
// where sinh(y0) and cosh(y0) are tabulated above.
int ind = min((int)y, 36);
double dy = y - ind;
double dy2 = dy * dy;
double sdy = dy * dy2 *
fma(dy2,
fma(dy2,
fma(dy2,
fma(dy2,
fma(dy2,
fma(dy2, 0.7746188980094184251527126e-12, 0.160576793121939886190847e-9),
0.250521176994133472333666e-7),
0.275573191913636406057211e-5),
0.198412698413242405162014e-3),
0.833333333333329931873097e-2),
0.166666666666666667013899e0);
double cdy = dy2 * fma(dy2,
fma(dy2,
fma(dy2,
fma(dy2,
fma(dy2,
fma(dy2, 0.1163921388172173692062032e-10, 0.208744349831471353536305e-8),
0.275573350756016588011357e-6),
0.248015872460622433115785e-4),
0.138888888889814854814536e-2),
0.416666666666660876512776e-1),
0.500000000000000005911074e0);
// At this point sinh(dy) is approximated by dy + sdy,
// and cosh(dy) is approximated by 1 + cdy.
double2 tv = USE_TABLE(cosh_tbl, ind);
double cl = tv.s0;
double ct = tv.s1;
tv = USE_TABLE(sinh_tbl, ind);
double sl = tv.s0;
double st = tv.s1;
double z = fma(sl, dy, fma(sl, sdy, fma(cl, cdy, fma(st, dy, fma(st, sdy, ct*cdy)) + ct))) + cl;
// Other cases
z = y < 0x1.0p-28 ? 1.0 : z;
double t = exp(y - 0x1.62e42fefa3800p-1);
t = fma(t, -0x1.ef35793c76641p-45, t);
z = y >= small_threshold ? t : z;
z = y >= max_cosh_arg ? as_double(PINFBITPATT_DP64) : z;
z = isinf(x) | isnan(x) ? y : z;
return z;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cosh, double)
#endif
_CLC_DEFINE_UNARY_BUILTIN_FP16(cosh)
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