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

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

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1
2/* @(#)k_cos.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/*
15 * __kernel_cos( x,  y )
16 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
17 * Input x is assumed to be bounded by ~pi/4 in magnitude.
18 * Input y is the tail of x.
19 *
20 * Algorithm
21 *      1. Since cos(-x) = cos(x), we need only to consider positive x.
22 *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
23 *      3. cos(x) is approximated by a polynomial of degree 14 on
24 *         [0,pi/4]
25 *                                       4            14
26 *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
27 *         where the remez error is
28 *     
29 *      |              2     4     6     8     10    12     14 |     -58
30 *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
31 *      |                                                      |
32 *
33 *                     4     6     8     10    12     14
34 *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
35 *             cos(x) = 1 - x*x/2 + r
36 *         since cos(x+y) ~ cos(x) - sin(x)*y
37 *                        ~ cos(x) - x*y,
38 *         a correction term is necessary in cos(x) and hence
39 *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
40 *         For better accuracy when x > 0.3, let qx = |x|/4 with
41 *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
42 *         Then
43 *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
44 *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
45 *         magnitude of the latter is at least a quarter of x*x/2,
46 *         thus, reducing the rounding error in the subtraction.
47 */
48
49#include <libm/fdlibm.h>
50
51#ifdef __STDC__
52static const double 
53#else
54static double 
55#endif
56one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
57C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
58C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
59C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
60C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
61C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
62C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
63
64#ifdef __STDC__
65        double __kernel_cos(double x, double y)
66#else
67        double __kernel_cos(x, y)
68        double x,y;
69#endif
70{
71        double a,hz,z,r,qx;
72        int n0, ix;
73        n0 = ((*(int*)&one)>>29)^1;             /* high word index */
74        ix = (*(n0+(int*)&x))&0x7fffffff;       /* ix = |x|'s high word*/
75        if(ix<0x3e400000) {                     /* if x < 2**27 */
76            if(((int)x)==0) return one;         /* generate inexact */
77        }
78        z  = x*x;
79        r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
80        if(ix < 0x3FD33333)                     /* if |x| < 0.3 */ 
81            return one - (0.5*z - (z*r - x*y));
82        else {
83            if(ix > 0x3fe90000) {               /* x > 0.78125 */
84                qx = 0.28125;
85            } else {
86                *(n0+(int*)&qx) = ix-0x00200000;        /* x/4 */
87                *(1-n0+(int*)&qx) = 0;
88            }
89            hz = 0.5*z-qx;
90            a  = one-qx;
91            return a - (hz - (z*r-x*y));
92        }
93}
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