source: trunk/sys/libm/k_sin.c @ 1

Last change on this file since 1 was 1, checked in by alain, 5 years ago

First import

File size: 2.4 KB
Line 
1
2/* @(#)k_sin.c 5.1 93/09/24 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, 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/* __kernel_sin( x, y, iy)
15 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
16 * Input x is assumed to be bounded by ~pi/4 in magnitude.
17 * Input y is the tail of x.
18 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
19 *
20 * Algorithm
21 *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
22 *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
23 *      3. sin(x) is approximated by a polynomial of degree 13 on
24 *         [0,pi/4]
25 *                               3            13
26 *              sin(x) ~ x + S1*x + ... + S6*x
27 *         where
28 *     
29 *      |sin(x)         2     4     6     8     10     12  |     -58
30 *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
31 *      |  x                                               |
32 *
33 *      4. sin(x+y) = sin(x) + sin'(x')*y
34 *                  ~ sin(x) + (1-x*x/2)*y
35 *         For better accuracy, let
36 *                   3      2      2      2      2
37 *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
38 *         then                   3    2
39 *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
40 */
41
42#include <libm/fdlibm.h>
43
44#ifdef __STDC__
45static const double 
46#else
47static double 
48#endif
49half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
50S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
51S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
52S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
53S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
54S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
55S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
56
57#ifdef __STDC__
58        double __kernel_sin(double x, double y, int iy)
59#else
60        double __kernel_sin(x, y, iy)
61        double x,y; int iy;             /* iy=0 if y is zero */
62#endif
63{
64        double z,r,v;
65        int n0, ix;
66        n0 = ((*(int*)&half)>>29)^1;            /* high word index */
67        ix = (*(n0+(int*)&x))&0x7fffffff;       /* high word of x */
68        if(ix<0x3e400000)                       /* |x| < 2**-27 */
69           {if((int)x==0) return x;}            /* generate inexact */
70        z       =  x*x;
71        v       =  z*x;
72        r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
73        if(iy==0) return x+v*(S1+z*r);
74        else      return x-((z*(half*y-v*r)-y)-v*S1);
75}
Note: See TracBrowser for help on using the repository browser.