source: trunk/libs/libmath/k_sin.c @ 620

Last change on this file since 620 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: 2.3 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/*
13 * Modified for ALMOS-MKH OS at UPMC, France, August 2018. (Alain Greiner)
14 */
15
16/* __kernel_sin( x, y, iy)
17 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
18 * Input x is assumed to be bounded by ~pi/4 in magnitude.
19 * Input y is the tail of x.
20 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
21 *
22 * Algorithm
23 *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
24 *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
25 *      3. sin(x) is approximated by a polynomial of degree 13 on
26 *         [0,pi/4]
27 *                               3            13
28 *              sin(x) ~ x + S1*x + ... + S6*x
29 *         where
30 *
31 *      |sin(x)         2     4     6     8     10     12  |     -58
32 *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
33 *      |  x                                               |
34 *
35 *      4. sin(x+y) = sin(x) + sin'(x')*y
36 *                  ~ sin(x) + (1-x*x/2)*y
37 *         For better accuracy, let
38 *                   3      2      2      2      2
39 *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
40 *         then                   3    2
41 *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
42 */
43
44#include "math.h"
45#include "math_private.h"
46
47static const double
48half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
49S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
50S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
51S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
52S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
53S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
54S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
55
56double __kernel_sin(double x, double y, int iy)
57{
58        double z,r,v;
59        int32_t ix;
60        GET_HIGH_WORD(ix,x);
61        ix &= 0x7fffffff;                       /* high word of x */
62        if(ix<0x3e400000)                       /* |x| < 2**-27 */
63           {if((int)x==0) return x;}            /* generate inexact */
64        z       =  x*x;
65        v       =  z*x;
66        r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
67        if(iy==0) return x+v*(S1+z*r);
68        else      return x-((z*(half*y-v*r)-y)-v*S1);
69}
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