diff --git a/libclc/generic/lib/math/acos.cl b/libclc/generic/lib/math/acos.cl --- a/libclc/generic/lib/math/acos.cl +++ b/libclc/generic/lib/math/acos.cl @@ -1,4 +1,173 @@ +/* + * 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 -#define __CLC_BODY -#include +#include "math.h" +#include "../clcmacro.h" + +_CLC_OVERLOAD _CLC_DEF float acos(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 piby2 = 1.5707963705e+00F; + const float pi = 3.1415926535897933e+00F; + const float piby2_head = 1.5707963267948965580e+00F; + const float piby2_tail = 6.12323399573676603587e-17F; + + 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(mad(s1, -s1, r), s + s1); + float rettn = mad(s + mad(y, u, -piby2_tail), -2.0f, pi); + float rettp = 2.0F * (s1 + mad(y, u, c)); + float rett = xneg ? rettn : rettp; + float ret = piby2_head - (x - mad(x, -u, piby2_tail)); + + ret = transform ? rett : ret; + ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret; + ret = ux == 0x3f800000U ? 0.0f : ret; + ret = ux == 0xbf800000U ? pi : ret; + ret = xexp < -26 ? piby2 : ret; + return ret; +} + +_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, acos, float); + +#ifdef cl_khr_fp64 + +#pragma OPENCL EXTENSION cl_khr_fp64 : enable + +_CLC_OVERLOAD _CLC_DEF double acos(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 = 3.1415926535897933e+00; /* 0x400921fb54442d18 */ + const double piby2 = 1.5707963267948965580e+00; /* 0x3ff921fb54442d18 */ + const double piby2_head = 1.5707963267948965580e+00; /* 0x3ff921fb54442d18 */ + 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; + + 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 acos carefully in transformed region + double s = sqrt(r); + double ztn = fma(-2.0, (s + fma(s, u, -piby2_tail)), pi); + + double s1 = as_double(as_ulong(s) & 0xffffffff00000000UL); + double c = MATH_DIVIDE(fma(-s1, s1, r), s + s1); + double ztp = 2.0 * (s1 + fma(s, u, c)); + double zt = xneg ? ztn : ztp; + double z = piby2_head - (x - fma(-x, u, piby2_tail)); + + z = transform ? zt : z; + + z = xexp < -56 ? piby2 : z; + z = isnan(x) ? as_double((as_ulong(x) | QNANBITPATT_DP64)) : z; + z = x == 1.0 ? 0.0 : z; + z = x == -1.0 ? pi : z; + + return z; +} + +_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, acos, double); + +#endif // cl_khr_fp64 diff --git a/libclc/generic/lib/math/acos.inc b/libclc/generic/lib/math/acos.inc deleted file mode 100644 --- a/libclc/generic/lib/math/acos.inc +++ /dev/null @@ -1,36 +0,0 @@ -/* - * There are multiple formulas for calculating arccosine of x: - * 1) acos(x) = (1/2*pi) + i * ln(i*x + sqrt(1-x^2)) (notice the 'i'...) - * 2) acos(x) = pi/2 + asin(-x) (asin isn't implemented yet) - * 3) acos(x) = pi/2 - asin(x) (ditto) - * 4) acos(x) = 2*atan2(sqrt(1-x), sqrt(1+x)) - * 5) acos(x) = pi/2 - atan2(x, ( sqrt(1-x^2) ) ) - * - * Options 1-3 are not currently usable, #5 generates more concise radeonsi - * bitcode and assembly than #4 (134 vs 132 instructions on radeonsi), but - * precision of #4 may be better. - */ - -// TODO: Enable half precision when atan2 is implemented -#if __CLC_FPSIZE > 16 - -#if __CLC_FPSIZE == 64 -#define __CLC_CONST(x) x -#elif __CLC_FPSIZE == 32 -#define __CLC_CONST(x) x ## f -#elif __CLC_FPSIZE == 16 -#define __CLC_CONST(x) x ## h -#endif - -_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE acos(__CLC_GENTYPE x) { - return ( - (__CLC_GENTYPE) __CLC_CONST(2.0) * atan2( - sqrt((__CLC_GENTYPE) __CLC_CONST(1.0) - x), - sqrt((__CLC_GENTYPE) __CLC_CONST(1.0) + x) - ) - ); -} - -#undef __CLC_CONST - -#endif