source: soft/giet_vm/giet_libs/math/k_cos.c

Last change on this file was 581, checked in by laurent, 9 years ago

Adding ocean application, some mathematics functions and distributed locks

File size: 2.9 KB
Line 
1/*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12/* Modified for GIET-VM static OS at UPMC, France 2015.
13 */
14
15/*
16 * __kernel_cos( x,  y )
17 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
18 * Input x is assumed to be bounded by ~pi/4 in magnitude.
19 * Input y is the tail of x.
20 *
21 * Algorithm
22 *      1. Since cos(-x) = cos(x), we need only to consider positive x.
23 *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
24 *      3. cos(x) is approximated by a polynomial of degree 14 on
25 *         [0,pi/4]
26 *                                       4            14
27 *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
28 *         where the remez error is
29 *
30 *      |              2     4     6     8     10    12     14 |     -58
31 *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
32 *      |                                                      |
33 *
34 *                     4     6     8     10    12     14
35 *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
36 *             cos(x) = 1 - x*x/2 + r
37 *         since cos(x+y) ~ cos(x) - sin(x)*y
38 *                        ~ cos(x) - x*y,
39 *         a correction term is necessary in cos(x) and hence
40 *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
41 *         For better accuracy when x > 0.3, let qx = |x|/4 with
42 *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
43 *         Then
44 *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
45 *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
46 *         magnitude of the latter is at least a quarter of x*x/2,
47 *         thus, reducing the rounding error in the subtraction.
48 */
49
50#include "math_private.h"
51
52static const double
53one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
54C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
55C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
56C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
57C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
58C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
59C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
60
61double __kernel_cos(double x, double y)
62{
63        double a,hz,z,r,qx;
64        int32_t ix;
65        GET_HIGH_WORD(ix,x);
66        ix &= 0x7fffffff;                       /* ix = |x|'s high word*/
67        if(ix<0x3e400000) {                     /* if x < 2**27 */
68            if(((int)x)==0) return one;         /* generate inexact */
69        }
70        z  = x*x;
71        r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
72        if(ix < 0x3FD33333)                     /* if |x| < 0.3 */
73            return one - (0.5*z - (z*r - x*y));
74        else {
75            if(ix > 0x3fe90000) {               /* x > 0.78125 */
76                qx = 0.28125;
77            } else {
78                INSERT_WORDS(qx,ix-0x00200000,0);       /* x/4 */
79            }
80            hz = 0.5*z-qx;
81            a  = one-qx;
82            return a - (hz - (z*r-x*y));
83        }
84}
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