/* * 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 #include "math.h" #include "tables.h" #include "../clcmacro.h" _CLC_OVERLOAD _CLC_DEF float sinh(float x) { // After dealing with special cases the computation is split into regions as follows. // abs(x) >= max_sinh_arg: // sinh(x) = sign(x)*Inf // abs(x) >= small_threshold: // sinh(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))) // sinh(x) is then sign(x)*z. const float max_sinh_arg = 0x1.65a9fap+6f; const float small_threshold = 0x1.0a2b24p+3f; uint ux = as_uint(x); uint aux = ux & EXSIGNBIT_SP32; uint xs = ux ^ aux; float y = as_float(aux); // We 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) // 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.s1, sdy, tv.s0 * cdy); z = as_float(xs | as_uint(z)); // When y is large enough so that the negative exponential is negligible, // so sinh(y) is approximated by sign(x)*exp(y)/2. float t = exp(y - 0x1.62e500p-1f); float zsmall = mad(0x1.a0210ep-18f, t, t); zsmall = as_float(xs | as_uint(zsmall)); z = y >= small_threshold ? zsmall : z; // Corner cases float zinf = as_float(PINFBITPATT_SP32 | xs); z = y >= max_sinh_arg ? zinf : z; z = aux > PINFBITPATT_SP32 | aux < 0x38800000U ? x : z; return z; } _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, sinh, float); #ifdef cl_khr_fp64 #pragma OPENCL EXTENSION cl_khr_fp64 : enable _CLC_OVERLOAD _CLC_DEF double sinh(double x) { // After dealing with special cases the computation is split into // regions as follows: // // abs(x) >= max_sinh_arg: // sinh(x) = sign(x)*Inf // // abs(x) >= small_threshold: // sinh(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))) // sinh(x) is then sign(x)*z. const double max_sinh_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 = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy) // where sinh(y0) and cosh(y0) are obtained from tables 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. // Shift some significant bits from dy to sdy. double sdy1 = as_double(as_ulong(dy) & 0xfffffffff8000000UL); double sdy2 = sdy + (dy - sdy1); 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(cl, sdy1, fma(sl, cdy, fma(cl, sdy2, fma(ct, sdy1, fma(st, cdy, ct*sdy2)) + st))) + sl; // Other cases z = (y < 0x1.0p-28) | isnan(x) | isinf(x) ? y : z; double t = exp(y - 0x1.62e42fefa3800p-1); t = fma(t, -0x1.ef35793c76641p-45, t); z = y >= small_threshold ? t : z; z = y >= max_sinh_arg ? as_double(PINFBITPATT_DP64) : z; return copysign(z, x); } _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, sinh, double) #endif