7e6a73959a
Increase fp16 support to allow clspv to continue to be OpenCL compliant following the update of the OpenCL-CTS adding more testing on math functions and conversions with half. Math functions are implemented by upscaling to fp32 and using the fp32 implementation. It garantees the accuracy required for half-precision float-point by the CTS.
176 lines
6.5 KiB
Common Lisp
176 lines
6.5 KiB
Common Lisp
/*
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* Copyright (c) 2014 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 "../clcmacro.h"
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_CLC_OVERLOAD _CLC_DEF float acos(float x) {
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// Computes arccos(x).
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// The argument is first reduced by noting that arccos(x)
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// is invalid for abs(x) > 1. For denormal and small
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// arguments arccos(x) = pi/2 to machine accuracy.
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// Remaining argument ranges are handled as follows.
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// For abs(x) <= 0.5 use
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// arccos(x) = pi/2 - arcsin(x)
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// = pi/2 - (x + x^3*R(x^2))
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// where R(x^2) is a rational minimax approximation to
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// (arcsin(x) - x)/x^3.
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// For abs(x) > 0.5 exploit the identity:
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// arccos(x) = pi - 2*arcsin(sqrt(1-x)/2)
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// together with the above rational approximation, and
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// reconstruct the terms carefully.
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// Some constants and split constants.
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const float piby2 = 1.5707963705e+00F;
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const float pi = 3.1415926535897933e+00F;
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const float piby2_head = 1.5707963267948965580e+00F;
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const float piby2_tail = 6.12323399573676603587e-17F;
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uint ux = as_uint(x);
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uint aux = ux & ~SIGNBIT_SP32;
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int xneg = ux != aux;
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int xexp = (int)(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
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float y = as_float(aux);
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// transform if |x| >= 0.5
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int transform = xexp >= -1;
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float y2 = y * y;
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float yt = 0.5f * (1.0f - y);
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float r = transform ? yt : y2;
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// Use a rational approximation for [0.0, 0.5]
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float a = mad(r,
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mad(r,
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mad(r, -0.00396137437848476485201154797087F, -0.0133819288943925804214011424456F),
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-0.0565298683201845211985026327361F),
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0.184161606965100694821398249421F);
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float b = mad(r, -0.836411276854206731913362287293F, 1.10496961524520294485512696706F);
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float u = r * MATH_DIVIDE(a, b);
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float s = MATH_SQRT(r);
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y = s;
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float s1 = as_float(as_uint(s) & 0xffff0000);
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float c = MATH_DIVIDE(mad(s1, -s1, r), s + s1);
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float rettn = mad(s + mad(y, u, -piby2_tail), -2.0f, pi);
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float rettp = 2.0F * (s1 + mad(y, u, c));
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float rett = xneg ? rettn : rettp;
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float ret = piby2_head - (x - mad(x, -u, piby2_tail));
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ret = transform ? rett : ret;
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ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret;
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ret = ux == 0x3f800000U ? 0.0f : ret;
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ret = ux == 0xbf800000U ? pi : ret;
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ret = xexp < -26 ? piby2 : ret;
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return ret;
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, acos, 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 acos(double x) {
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// Computes arccos(x).
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// The argument is first reduced by noting that arccos(x)
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// is invalid for abs(x) > 1. For denormal and small
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// arguments arccos(x) = pi/2 to machine accuracy.
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// Remaining argument ranges are handled as follows.
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// For abs(x) <= 0.5 use
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// arccos(x) = pi/2 - arcsin(x)
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// = pi/2 - (x + x^3*R(x^2))
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// where R(x^2) is a rational minimax approximation to
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// (arcsin(x) - x)/x^3.
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// For abs(x) > 0.5 exploit the identity:
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// arccos(x) = pi - 2*arcsin(sqrt(1-x)/2)
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// together with the above rational approximation, and
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// reconstruct the terms carefully.
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const double pi = 3.1415926535897933e+00; /* 0x400921fb54442d18 */
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const double piby2 = 1.5707963267948965580e+00; /* 0x3ff921fb54442d18 */
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const double piby2_head = 1.5707963267948965580e+00; /* 0x3ff921fb54442d18 */
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const double piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */
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double y = fabs(x);
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int xneg = as_int2(x).hi < 0;
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int xexp = (as_int2(y).hi >> 20) - EXPBIAS_DP64;
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// abs(x) >= 0.5
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int transform = xexp >= -1;
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double rt = 0.5 * (1.0 - y);
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double y2 = y * y;
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double r = transform ? rt : y2;
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// Use a rational approximation for [0.0, 0.5]
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double un = fma(r,
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fma(r,
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fma(r,
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fma(r,
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fma(r, 0.0000482901920344786991880522822991,
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0.00109242697235074662306043804220),
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-0.0549989809235685841612020091328),
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0.275558175256937652532686256258),
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-0.445017216867635649900123110649),
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0.227485835556935010735943483075);
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double ud = fma(r,
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fma(r,
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fma(r,
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fma(r, 0.105869422087204370341222318533,
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-0.943639137032492685763471240072),
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2.76568859157270989520376345954),
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-3.28431505720958658909889444194),
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1.36491501334161032038194214209);
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double u = r * MATH_DIVIDE(un, ud);
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// Reconstruct acos carefully in transformed region
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double s = sqrt(r);
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double ztn = fma(-2.0, (s + fma(s, u, -piby2_tail)), pi);
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double s1 = as_double(as_ulong(s) & 0xffffffff00000000UL);
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double c = MATH_DIVIDE(fma(-s1, s1, r), s + s1);
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double ztp = 2.0 * (s1 + fma(s, u, c));
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double zt = xneg ? ztn : ztp;
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double z = piby2_head - (x - fma(-x, u, piby2_tail));
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z = transform ? zt : z;
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z = xexp < -56 ? piby2 : z;
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z = isnan(x) ? as_double((as_ulong(x) | QNANBITPATT_DP64)) : z;
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z = x == 1.0 ? 0.0 : z;
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z = x == -1.0 ? pi : z;
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return z;
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, acos, double);
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#endif // cl_khr_fp64
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_CLC_DEFINE_UNARY_BUILTIN_FP16(acos)
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