generic/lib/math/cosh.cl - llvm-project/libclc - Git at Google

 /*
  * 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
	/*
	* 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