de336b0c5e
Bruce for putting lots of effort into these; getting them right isn't easy, and they went through many iterations. Submitted by: Steve Kargl <sgk@apl.washington.edu> with revisions from bde
63 lines
1.9 KiB
C
63 lines
1.9 KiB
C
/* From: @(#)k_sin.c 1.3 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/*
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* ld80 version of k_sin.c. See ../src/k_sin.c for most comments.
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*/
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#include "math_private.h"
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static const double
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half = 0.5;
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/*
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* Domain [-0.7854, 0.7854], range ~[-1.89e-22, 1.915e-22]
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* |sin(x)/x - s(x)| < 2**-72.1
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*
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* See ../ld80/k_cosl.c for more details about the polynomial.
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*/
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#if defined(__amd64__) || defined(__i386__)
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/* Long double constants are slow on these arches, and broken on i386. */
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static const volatile double
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S1hi = -0.16666666666666666, /* -0x15555555555555.0p-55 */
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S1lo = -9.2563760475949941e-18; /* -0x15580000000000.0p-109 */
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#define S1 ((long double)S1hi + S1lo)
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#else
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static const long double
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S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */
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#endif
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static const double
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S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */
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S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */
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S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */
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S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */
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S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */
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S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */
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S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */
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long double
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__kernel_sinl(long double x, long double y, int iy)
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{
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long double z,r,v;
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z = x*x;
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v = z*x;
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r = S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8)))));
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if(iy==0) return x+v*(S1+z*r);
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else return x-((z*(half*y-v*r)-y)-v*S1);
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}
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