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This commit bulk-updates the libclc license headers to the current Apache-2.0 WITH LLVM-exception license in situations where they were previously attributed to AMD - and occasionally under an additional single individual contributor - under an MIT license. AMD signed the LLVM relicensing agreement and so agreed for their past contributions under the new LLVM license. The LLVM project also has had a long-standing, unwritten, policy of not adding copyright notices to source code. This policy was recently written up [1]. This commit therefore also removes these copyright notices at the same time. Note that there are outstanding copyright notices attributed to others - and many files missing copyright headers - which will be dealt with in future work. [1] https://llvm.org/docs/DeveloperPolicy.html#embedded-copyright-or-contributed-by-statements
120 lines
4.5 KiB
C
120 lines
4.5 KiB
C
//===----------------------------------------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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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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_CLC_INLINE double2
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__clc_tan_piby4(double x, double xx)
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{
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const double piby4_lead = 7.85398163397448278999e-01; // 0x3fe921fb54442d18
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const double piby4_tail = 3.06161699786838240164e-17; // 0x3c81a62633145c06
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// In order to maintain relative precision transform using the identity:
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// tan(pi/4-x) = (1-tan(x))/(1+tan(x)) for arguments close to pi/4.
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// Similarly use tan(x-pi/4) = (tan(x)-1)/(tan(x)+1) close to -pi/4.
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int ca = x > 0.68;
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int cb = x < -0.68;
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double transform = ca ? 1.0 : 0.0;
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transform = cb ? -1.0 : transform;
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double tx = fma(-transform, x, piby4_lead) + fma(-transform, xx, piby4_tail);
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int c = ca | cb;
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x = c ? tx : x;
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xx = c ? 0.0 : xx;
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// Core Remez [2,3] approximation to tan(x+xx) on the interval [0,0.68].
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double t1 = x;
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double r = fma(2.0, x*xx, x*x);
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double a = fma(r,
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fma(r, 0.224044448537022097264602535574e-3, -0.229345080057565662883358588111e-1),
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0.372379159759792203640806338901e0);
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double b = fma(r,
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fma(r,
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fma(r, -0.232371494088563558304549252913e-3, 0.260656620398645407524064091208e-1),
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-0.515658515729031149329237816945e0),
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0.111713747927937668539901657944e1);
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double t2 = fma(MATH_DIVIDE(a, b), x*r, xx);
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double tp = t1 + t2;
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// Compute -1.0/(t1 + t2) accurately
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double z1 = as_double(as_long(tp) & 0xffffffff00000000L);
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double z2 = t2 - (z1 - t1);
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double trec = -MATH_RECIP(tp);
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double trec_top = as_double(as_long(trec) & 0xffffffff00000000L);
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double tpr = fma(fma(trec_top, z2, fma(trec_top, z1, 1.0)), trec, trec_top);
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double tpt = transform * (1.0 - MATH_DIVIDE(2.0*tp, 1.0 + tp));
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double tptr = transform * (MATH_DIVIDE(2.0*tp, tp - 1.0) - 1.0);
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double2 ret;
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ret.lo = c ? tpt : tp;
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ret.hi = c ? tptr : tpr;
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return ret;
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}
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