xref: /freebsd/lib/msun/ld80/k_sinl.c (revision 1c05a6ea6b849ff95e539c31adea887c644a6a01)
1 /* From: @(#)k_sin.c 1.3 95/01/18 */
2 /*
3  * ====================================================
4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5  * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
6  *
7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  */
13 
14 #include <sys/cdefs.h>
15 __FBSDID("$FreeBSD$");
16 
17 /*
18  * ld80 version of k_sin.c.  See ../src/k_sin.c for most comments.
19  */
20 
21 #include "math_private.h"
22 
23 static const double
24 half =  0.5;
25 
26 /*
27  * Domain [-0.7854, 0.7854], range ~[-1.89e-22, 1.915e-22]
28  * |sin(x)/x - s(x)| < 2**-72.1
29  *
30  * See ../ld80/k_cosl.c for more details about the polynomial.
31  */
32 #if defined(__amd64__) || defined(__i386__)
33 /* Long double constants are slow on these arches, and broken on i386. */
34 static const volatile double
35 S1hi = -0.16666666666666666,		/* -0x15555555555555.0p-55 */
36 S1lo = -9.2563760475949941e-18;		/* -0x15580000000000.0p-109 */
37 #define	S1	((long double)S1hi + S1lo)
38 #else
39 static const long double
40 S1 = -0.166666666666666666671L;		/* -0xaaaaaaaaaaaaaaab.0p-66 */
41 #endif
42 
43 static const double
44 S2 =  0.0083333333333333332,		/*  0x11111111111111.0p-59 */
45 S3 = -0.00019841269841269427,		/* -0x1a01a01a019f81.0p-65 */
46 S4 =  0.0000027557319223597490,		/*  0x171de3a55560f7.0p-71 */
47 S5 = -0.000000025052108218074604,	/* -0x1ae64564f16cad.0p-78 */
48 S6 =  1.6059006598854211e-10,		/*  0x161242b90243b5.0p-85 */
49 S7 = -7.6429779983024564e-13,		/* -0x1ae42ebd1b2e00.0p-93 */
50 S8 =  2.6174587166648325e-15;		/*  0x179372ea0b3f64.0p-101 */
51 
52 long double
53 __kernel_sinl(long double x, long double y, int iy)
54 {
55 	long double z,r,v;
56 
57 	z	=  x*x;
58 	v	=  z*x;
59 	r	=  S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8)))));
60 	if(iy==0) return x+v*(S1+z*r);
61 	else      return x-((z*(half*y-v*r)-y)-v*S1);
62 }
63