| /* |
| * 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 acospi(float x) { |
| // Computes arccos(x). |
| // The argument is first reduced by noting that arccos(x) |
| // is invalid for abs(x) > 1. For denormal and small |
| // arguments arccos(x) = pi/2 to machine accuracy. |
| // Remaining argument ranges are handled as follows. |
| // For abs(x) <= 0.5 use |
| // arccos(x) = pi/2 - arcsin(x) |
| // = pi/2 - (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: |
| // arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) |
| // together with the above rational approximation, and |
| // reconstruct the terms carefully. |
| |
| |
| // Some constants and split constants. |
| const float pi = 3.1415926535897933e+00f; |
| const float piby2_head = 1.5707963267948965580e+00f; /* 0x3ff921fb54442d18 */ |
| const float piby2_tail = 6.12323399573676603587e-17f; /* 0x3c91a62633145c07 */ |
| |
| uint ux = as_uint(x); |
| uint aux = ux & ~SIGNBIT_SP32; |
| int xneg = ux != aux; |
| int xexp = (int)(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; |
| |
| float y = as_float(aux); |
| |
| // transform if |x| >= 0.5 |
| int transform = xexp >= -1; |
| |
| float y2 = y * y; |
| float yt = 0.5f * (1.0f - y); |
| float r = transform ? yt : 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); |
| y = s; |
| float s1 = as_float(as_uint(s) & 0xffff0000); |
| float c = MATH_DIVIDE(r - s1 * s1, s + s1); |
| // float rettn = 1.0f - MATH_DIVIDE(2.0f * (s + (y * u - piby2_tail)), pi); |
| float rettn = 1.0f - MATH_DIVIDE(2.0f * (s + mad(y, u, -piby2_tail)), pi); |
| // float rettp = MATH_DIVIDE(2.0F * s1 + (2.0F * c + 2.0F * y * u), pi); |
| float rettp = MATH_DIVIDE(2.0f*(s1 + mad(y, u, c)), pi); |
| float rett = xneg ? rettn : rettp; |
| // float ret = MATH_DIVIDE(piby2_head - (x - (piby2_tail - x * u)), pi); |
| float ret = MATH_DIVIDE(piby2_head - (x - mad(x, -u, piby2_tail)), pi); |
| |
| ret = transform ? rett : ret; |
| ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret; |
| ret = ux == 0x3f800000U ? 0.0f : ret; |
| ret = ux == 0xbf800000U ? 1.0f : ret; |
| ret = xexp < -26 ? 0.5f : ret; |
| return ret; |
| } |
| |
| _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, acospi, float) |
| |
| #ifdef cl_khr_fp64 |
| #pragma OPENCL EXTENSION cl_khr_fp64 : enable |
| |
| _CLC_OVERLOAD _CLC_DEF double acospi(double x) { |
| // Computes arccos(x). |
| // The argument is first reduced by noting that arccos(x) |
| // is invalid for abs(x) > 1. For denormal and small |
| // arguments arccos(x) = pi/2 to machine accuracy. |
| // Remaining argument ranges are handled as follows. |
| // For abs(x) <= 0.5 use |
| // arccos(x) = pi/2 - arcsin(x) |
| // = pi/2 - (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: |
| // arccos(x) = pi - 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 = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */ |
| |
| 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; |
| |
| // Transform y into the range [0,0.5) |
| double r1 = 0.5 * (1.0 - y); |
| double s = sqrt(r1); |
| double r = y * y; |
| r = transform ? r1 : r; |
| y = transform ? s : y; |
| |
| // 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 acos carefully in transformed region |
| double res1 = fma(-2.0, MATH_DIVIDE(s + fma(y, u, -piby2_tail), pi), 1.0); |
| double s1 = as_double(as_ulong(s) & 0xffffffff00000000UL); |
| double c = MATH_DIVIDE(fma(-s1, s1, r), s + s1); |
| double res2 = MATH_DIVIDE(fma(2.0, s1, fma(2.0, c, 2.0 * y * u)), pi); |
| res1 = xneg ? res1 : res2; |
| res2 = 0.5 - fma(x, u, x) / pi; |
| res1 = transform ? res1 : res2; |
| |
| const double qnan = as_double(QNANBITPATT_DP64); |
| res2 = x == 1.0 ? 0.0 : qnan; |
| res2 = x == -1.0 ? 1.0 : res2; |
| res1 = xexp >= 0 ? res2 : res1; |
| res1 = xexp < -56 ? 0.5 : res1; |
| |
| return res1; |
| } |
| |
| _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, acospi, double) |
| |
| #endif |