OpenCores
URL https://opencores.org/ocsvn/or1k/or1k/trunk

Subversion Repositories or1k

[/] [or1k/] [trunk/] [newlib-1.10.0/] [newlib/] [libm/] [math/] [k_sin.c] - Blame information for rev 1773

Go to most recent revision | Details | Compare with Previous | View Log

Line No. Rev Author Line
1 1010 ivang
 
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 "fdlibm.h"
43
 
44
#ifndef _DOUBLE_IS_32BITS
45
 
46
#ifdef __STDC__
47
static const double
48
#else
49
static double
50
#endif
51
half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
52
S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
53
S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
54
S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
55
S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
56
S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
57
S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
58
 
59
#ifdef __STDC__
60
        double __kernel_sin(double x, double y, int iy)
61
#else
62
        double __kernel_sin(x, y, iy)
63
        double x,y; int iy;             /* iy=0 if y is zero */
64
#endif
65
{
66
        double z,r,v;
67
        __int32_t ix;
68
        GET_HIGH_WORD(ix,x);
69
        ix &= 0x7fffffff;                       /* high word of x */
70
        if(ix<0x3e400000)                       /* |x| < 2**-27 */
71
           {if((int)x==0) return x;}             /* generate inexact */
72
        z       =  x*x;
73
        v       =  z*x;
74
        r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
75
        if(iy==0) return x+v*(S1+z*r);
76
        else      return x-((z*(half*y-v*r)-y)-v*S1);
77
}
78
 
79
#endif /* defined(_DOUBLE_IS_32BITS) */

powered by: WebSVN 2.1.0

© copyright 1999-2024 OpenCores.org, equivalent to Oliscience, all rights reserved. OpenCores®, registered trademark.