# source:trunk/libs/libmath/k_cos.c@610

Last change on this file since 610 was 469, checked in by alain, 4 years ago

1) Introduce the libsemaphore library.
2) Introduce a small libmath library, required by the "fft" application..
3) Introduce the multithreaded "fft" application.
4) Fix a bad synchronisation bug in the Copy-On-Write mechanism.

File size: 2.9 KB
Line
1/*
2 * ====================================================
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/*
13 * Modified for ALMOS-MKH OS at UPMC, France, August 2018. (Alain Greiner)
14 */
15
16/*
17 * __kernel_cos( x,  y )
18 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
19 * Input x is assumed to be bounded by ~pi/4 in magnitude.
20 * Input y is the tail of x.
21 *
22 * Algorithm
23 *      1. Since cos(-x) = cos(x), we need only to consider positive x.
24 *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
25 *      3. cos(x) is approximated by a polynomial of degree 14 on
26 *         [0,pi/4]
27 *                                       4            14
28 *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
29 *         where the remez error is
30 *
31 *      |              2     4     6     8     10    12     14 |     -58
32 *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
33 *      |                                                      |
34 *
35 *                     4     6     8     10    12     14
36 *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
37 *             cos(x) = 1 - x*x/2 + r
38 *         since cos(x+y) ~ cos(x) - sin(x)*y
39 *                        ~ cos(x) - x*y,
40 *         a correction term is necessary in cos(x) and hence
41 *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
42 *         For better accuracy when x > 0.3, let qx = |x|/4 with
43 *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
44 *         Then
45 *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
46 *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
47 *         magnitude of the latter is at least a quarter of x*x/2,
48 *         thus, reducing the rounding error in the subtraction.
49 */
50
51#include "math.h"
52#include "math_private.h"
53
54static const double
55one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
56C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
57C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
58C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
59C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
60C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
61C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
62
63double __kernel_cos(double x, double y)
64{
65        double a,hz,z,r,qx;
66        int32_t ix;
67        GET_HIGH_WORD(ix,x);
68        ix &= 0x7fffffff;                       /* ix = |x|'s high word*/
69        if(ix<0x3e400000) {                     /* if x < 2**27 */
70            if(((int)x)==0) return one;         /* generate inexact */
71        }
72        z  = x*x;
73        r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
74        if(ix < 0x3FD33333)                     /* if |x| < 0.3 */
75            return one - (0.5*z - (z*r - x*y));
76        else {
77            if(ix > 0x3fe90000) {               /* x > 0.78125 */
78                qx = 0.28125;
79            } else {
80                INSERT_WORDS(qx,ix-0x00200000,0);       /* x/4 */
81            }
82            hz = 0.5*z-qx;
83            a  = one-qx;
84            return a - (hz - (z*r-x*y));
85        }
86}
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