193 lines
6.6 KiB
Common Lisp
193 lines
6.6 KiB
Common Lisp
/*
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* Copyright (c) 2014,2015 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 "tables.h"
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#include "../clcmacro.h"
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_CLC_OVERLOAD _CLC_DEF float cosh(float x) {
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// After dealing with special cases the computation is split into regions as follows.
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// abs(x) >= max_cosh_arg:
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// cosh(x) = sign(x)*Inf
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// abs(x) >= small_threshold:
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// cosh(x) = sign(x)*exp(abs(x))/2 computed using the
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// splitexp and scaleDouble functions as for exp_amd().
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// abs(x) < small_threshold:
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// compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
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// cosh(x) is then z.
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const float max_cosh_arg = 0x1.65a9fap+6f;
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const float small_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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float y = as_float(aux);
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// Find the integer part y0 of y and the increment dy = y - y0. We then compute
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// z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy)
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// z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy)
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// where sinh(y0) and cosh(y0) are tabulated above.
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int ind = (int)y;
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ind = (uint)ind > 36U ? 0 : ind;
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float dy = y - ind;
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float dy2 = dy * dy;
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float sdy = mad(dy2,
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mad(dy2,
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mad(dy2,
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mad(dy2,
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mad(dy2,
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mad(dy2, 0.7746188980094184251527126e-12f, 0.160576793121939886190847e-9f),
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0.250521176994133472333666e-7f),
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0.275573191913636406057211e-5f),
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0.198412698413242405162014e-3f),
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0.833333333333329931873097e-2f),
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0.166666666666666667013899e0f);
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sdy = mad(sdy, dy*dy2, dy);
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float cdy = mad(dy2,
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mad(dy2,
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mad(dy2,
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mad(dy2,
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mad(dy2,
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mad(dy2, 0.1163921388172173692062032e-10f, 0.208744349831471353536305e-8f),
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0.275573350756016588011357e-6f),
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0.248015872460622433115785e-4f),
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0.138888888889814854814536e-2f),
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0.416666666666660876512776e-1f),
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0.500000000000000005911074e0f);
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cdy = mad(cdy, dy2, 1.0f);
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float2 tv = USE_TABLE(sinhcosh_tbl, ind);
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float z = mad(tv.s0, sdy, tv.s1 * cdy);
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// When exp(-x) is insignificant compared to exp(x), return exp(x)/2
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float t = exp(y - 0x1.62e500p-1f);
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float zsmall = mad(0x1.a0210ep-18f, t, t);
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z = y >= small_threshold ? zsmall : z;
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// Corner cases
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z = y >= max_cosh_arg ? as_float(PINFBITPATT_SP32) : z;
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z = aux > PINFBITPATT_SP32 ? as_float(QNANBITPATT_SP32) : z;
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z = aux < 0x38800000 ? 1.0f : z;
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return z;
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cosh, 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 cosh(double x) {
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// After dealing with special cases the computation is split into
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// regions as follows:
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//
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// abs(x) >= max_cosh_arg:
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// cosh(x) = sign(x)*Inf
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//
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// abs(x) >= small_threshold:
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// cosh(x) = sign(x)*exp(abs(x))/2 computed using the
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// splitexp and scaleDouble functions as for exp_amd().
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//
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// abs(x) < small_threshold:
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// compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
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// cosh(x) is then sign(x)*z.
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// This is ln(2^1025)
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const double max_cosh_arg = 7.10475860073943977113e+02; // 0x408633ce8fb9f87e
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// This is where exp(-x) is insignificant compared to exp(x) = ln(2^27)
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const double small_threshold = 0x1.2b708872320e2p+4;
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double y = fabs(x);
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// In this range we find the integer part y0 of y
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// and the increment dy = y - y0. We then compute
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// z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy)
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// where sinh(y0) and cosh(y0) are tabulated above.
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int ind = min((int)y, 36);
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double dy = y - ind;
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double dy2 = dy * dy;
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double sdy = dy * dy2 *
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fma(dy2,
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fma(dy2,
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fma(dy2,
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fma(dy2,
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fma(dy2,
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fma(dy2, 0.7746188980094184251527126e-12, 0.160576793121939886190847e-9),
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0.250521176994133472333666e-7),
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0.275573191913636406057211e-5),
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0.198412698413242405162014e-3),
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0.833333333333329931873097e-2),
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0.166666666666666667013899e0);
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double cdy = dy2 * fma(dy2,
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fma(dy2,
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fma(dy2,
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fma(dy2,
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fma(dy2,
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fma(dy2, 0.1163921388172173692062032e-10, 0.208744349831471353536305e-8),
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0.275573350756016588011357e-6),
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0.248015872460622433115785e-4),
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0.138888888889814854814536e-2),
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0.416666666666660876512776e-1),
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0.500000000000000005911074e0);
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// At this point sinh(dy) is approximated by dy + sdy,
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// and cosh(dy) is approximated by 1 + cdy.
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double2 tv = USE_TABLE(cosh_tbl, ind);
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double cl = tv.s0;
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double ct = tv.s1;
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tv = USE_TABLE(sinh_tbl, ind);
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double sl = tv.s0;
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double st = tv.s1;
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double z = fma(sl, dy, fma(sl, sdy, fma(cl, cdy, fma(st, dy, fma(st, sdy, ct*cdy)) + ct))) + cl;
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// Other cases
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z = y < 0x1.0p-28 ? 1.0 : z;
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double t = exp(y - 0x1.62e42fefa3800p-1);
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t = fma(t, -0x1.ef35793c76641p-45, t);
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z = y >= small_threshold ? t : z;
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z = y >= max_cosh_arg ? as_double(PINFBITPATT_DP64) : z;
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z = isinf(x) | isnan(x) ? y : z;
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return z;
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cosh, double)
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#endif
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