| /* |
| * 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 asinpi(float x) { |
| // Computes arcsin(x). |
| // The argument is first reduced by noting that arcsin(x) |
| // is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x). |
| // For denormal and small arguments arcsin(x) = x to machine |
| // accuracy. Remaining argument ranges are handled as follows. |
| // For abs(x) <= 0.5 use |
| // arcsin(x) = x + x^3*R(x^2) |
| // where R(x^2) is a rational minimax approximation to |
| // (arcsin(x) - x)/x^3. |
| // For abs(x) > 0.5 exploit the identity: |
| // arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2) |
| // together with the above rational approximation, and |
| // reconstruct the terms carefully. |
| |
| |
| const float pi = 3.1415926535897933e+00f; |
| const float piby2_tail = 7.5497894159e-08F; /* 0x33a22168 */ |
| const float hpiby2_head = 7.8539812565e-01F; /* 0x3f490fda */ |
| |
| uint ux = as_uint(x); |
| uint aux = ux & EXSIGNBIT_SP32; |
| uint xs = ux ^ aux; |
| float shalf = as_float(xs | as_uint(0.5f)); |
| |
| int xexp = (int)(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; |
| |
| float y = as_float(aux); |
| |
| // abs(x) >= 0.5 |
| int transform = xexp >= -1; |
| |
| float y2 = y * y; |
| float rt = 0.5f * (1.0f - y); |
| float r = transform ? rt : y2; |
| |
| // Use a rational approximation for [0.0, 0.5] |
| float a = mad(r, |
| mad(r, |
| mad(r, -0.00396137437848476485201154797087F, -0.0133819288943925804214011424456F), |
| -0.0565298683201845211985026327361F), |
| 0.184161606965100694821398249421F); |
| float b = mad(r, -0.836411276854206731913362287293F, 1.10496961524520294485512696706F); |
| float u = r * MATH_DIVIDE(a, b); |
| |
| float s = MATH_SQRT(r); |
| float s1 = as_float(as_uint(s) & 0xffff0000); |
| float c = MATH_DIVIDE(mad(-s1, s1, r), s + s1); |
| float p = mad(2.0f*s, u, -mad(c, -2.0f, piby2_tail)); |
| float q = mad(s1, -2.0f, hpiby2_head); |
| float vt = hpiby2_head - (p - q); |
| float v = mad(y, u, y); |
| v = transform ? vt : v; |
| v = MATH_DIVIDE(v, pi); |
| float xbypi = MATH_DIVIDE(x, pi); |
| |
| float ret = as_float(xs | as_uint(v)); |
| ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret; |
| ret = aux == 0x3f800000U ? shalf : ret; |
| ret = xexp < -14 ? xbypi : ret; |
| |
| return ret; |
| } |
| |
| _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, asinpi, float) |
| |
| #ifdef cl_khr_fp64 |
| #pragma OPENCL EXTENSION cl_khr_fp64 : enable |
| |
| _CLC_OVERLOAD _CLC_DEF double asinpi(double x) { |
| // Computes arcsin(x). |
| // The argument is first reduced by noting that arcsin(x) |
| // is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x). |
| // For denormal and small arguments arcsin(x) = x to machine |
| // accuracy. Remaining argument ranges are handled as follows. |
| // For abs(x) <= 0.5 use |
| // arcsin(x) = x + x^3*R(x^2) |
| // where R(x^2) is a rational minimax approximation to |
| // (arcsin(x) - x)/x^3. |
| // For abs(x) > 0.5 exploit the identity: |
| // arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2) |
| // together with the above rational approximation, and |
| // reconstruct the terms carefully. |
| |
| const double pi = 0x1.921fb54442d18p+1; |
| const double piby2_tail = 6.1232339957367660e-17; /* 0x3c91a62633145c07 */ |
| const double hpiby2_head = 7.8539816339744831e-01; /* 0x3fe921fb54442d18 */ |
| |
| double y = fabs(x); |
| int xneg = as_int2(x).hi < 0; |
| int xexp = (as_int2(y).hi >> 20) - EXPBIAS_DP64; |
| |
| // abs(x) >= 0.5 |
| int transform = xexp >= -1; |
| |
| double rt = 0.5 * (1.0 - y); |
| double y2 = y * y; |
| double r = transform ? rt : y2; |
| |
| // Use a rational approximation for [0.0, 0.5] |
| double un = fma(r, |
| fma(r, |
| fma(r, |
| fma(r, |
| fma(r, 0.0000482901920344786991880522822991, |
| 0.00109242697235074662306043804220), |
| -0.0549989809235685841612020091328), |
| 0.275558175256937652532686256258), |
| -0.445017216867635649900123110649), |
| 0.227485835556935010735943483075); |
| |
| double ud = fma(r, |
| fma(r, |
| fma(r, |
| fma(r, 0.105869422087204370341222318533, |
| -0.943639137032492685763471240072), |
| 2.76568859157270989520376345954), |
| -3.28431505720958658909889444194), |
| 1.36491501334161032038194214209); |
| |
| double u = r * MATH_DIVIDE(un, ud); |
| |
| |
| // Reconstruct asin carefully in transformed region |
| double s = sqrt(r); |
| double sh = as_double(as_ulong(s) & 0xffffffff00000000UL); |
| double c = MATH_DIVIDE(fma(-sh, sh, r), s + sh); |
| double p = fma(2.0*s, u, -fma(-2.0, c, piby2_tail)); |
| double q = fma(-2.0, sh, hpiby2_head); |
| double vt = hpiby2_head - (p - q); |
| double v = fma(y, u, y); |
| v = transform ? vt : v; |
| |
| v = xexp < -28 ? y : v; |
| v = MATH_DIVIDE(v, pi); |
| v = xexp >= 0 ? as_double(QNANBITPATT_DP64) : v; |
| v = y == 1.0 ? 0.5 : v; |
| return xneg ? -v : v; |
| } |
| |
| _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, asinpi, double) |
| |
| #endif |