forked from OSchip/llvm-project
79 lines
3.4 KiB
C
79 lines
3.4 KiB
C
/*
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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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#pragma OPENCL EXTENSION cl_khr_fp64 : enable
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_CLC_INLINE double2
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__libclc__sincos_piby4(double x, double xx)
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{
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// Taylor series for sin(x) is x - x^3/3! + x^5/5! - x^7/7! ...
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// = x * (1 - x^2/3! + x^4/5! - x^6/7! ...
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// = x * f(w)
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// where w = x*x and f(w) = (1 - w/3! + w^2/5! - w^3/7! ...
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// We use a minimax approximation of (f(w) - 1) / w
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// because this produces an expansion in even powers of x.
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// If xx (the tail of x) is non-zero, we add a correction
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// term g(x,xx) = (1-x*x/2)*xx to the result, where g(x,xx)
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// is an approximation to cos(x)*sin(xx) valid because
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// xx is tiny relative to x.
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// Taylor series for cos(x) is 1 - x^2/2! + x^4/4! - x^6/6! ...
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// = f(w)
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// where w = x*x and f(w) = (1 - w/2! + w^2/4! - w^3/6! ...
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// We use a minimax approximation of (f(w) - 1 + w/2) / (w*w)
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// because this produces an expansion in even powers of x.
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// If xx (the tail of x) is non-zero, we subtract a correction
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// term g(x,xx) = x*xx to the result, where g(x,xx)
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// is an approximation to sin(x)*sin(xx) valid because
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// xx is tiny relative to x.
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const double sc1 = -0.166666666666666646259241729;
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const double sc2 = 0.833333333333095043065222816e-2;
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const double sc3 = -0.19841269836761125688538679e-3;
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const double sc4 = 0.275573161037288022676895908448e-5;
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const double sc5 = -0.25051132068021699772257377197e-7;
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const double sc6 = 0.159181443044859136852668200e-9;
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const double cc1 = 0.41666666666666665390037e-1;
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const double cc2 = -0.13888888888887398280412e-2;
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const double cc3 = 0.248015872987670414957399e-4;
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const double cc4 = -0.275573172723441909470836e-6;
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const double cc5 = 0.208761463822329611076335e-8;
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const double cc6 = -0.113826398067944859590880e-10;
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double x2 = x * x;
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double x3 = x2 * x;
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double r = 0.5 * x2;
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double t = 1.0 - r;
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double sp = fma(fma(fma(fma(sc6, x2, sc5), x2, sc4), x2, sc3), x2, sc2);
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double cp = t + fma(fma(fma(fma(fma(fma(cc6, x2, cc5), x2, cc4), x2, cc3), x2, cc2), x2, cc1),
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x2*x2, fma(x, xx, (1.0 - t) - r));
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double2 ret;
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ret.lo = x - fma(-x3, sc1, fma(fma(-x3, sp, 0.5*xx), x2, -xx));
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ret.hi = cp;
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return ret;
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}
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