# Subversion RepositoriesKolibri OS

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1. /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */
2. /* @(#)k_sin.c 5.1 93/09/24 */
3. /*
4.  * ====================================================
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. #if defined(LIBM_SCCS) && !defined(lint)
15. static char rcsid[] = "\$Id: k_sin.c,v 1.6 1994/08/18 23:06:14 jtc Exp \$";
16. #endif
17.
18. /* __kernel_sin( x, y, iy)
19.  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
20.  * Input x is assumed to be bounded by ~pi/4 in magnitude.
21.  * Input y is the tail of x.
22.  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
23.  *
24.  * Algorithm
25.  *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
26.  *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
27.  *      3. sin(x) is approximated by a polynomial of degree 13 on
28.  *         [0,pi/4]
29.  *                               3            13
30.  *              sin(x) ~ x + S1*x + ... + S6*x
31.  *         where
32.  *
33.  *      |sin(x)         2     4     6     8     10     12  |     -58
34.  *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
35.  *      |  x                                               |
36.  *
37.  *      4. sin(x+y) = sin(x) + sin'(x')*y
38.  *                  ~ sin(x) + (1-x*x/2)*y
39.  *         For better accuracy, let
40.  *                   3      2      2      2      2
41.  *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
42.  *         then                   3    2
43.  *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
44.  */
45.
46. #include "math.h"
47. #include "math_private.h"
48.
49. #ifdef __STDC__
50. static const double
51. #else
52. static double
53. #endif
54. half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
55. S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
56. S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
57. S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
58. S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
59. S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
60. S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
61.
62. #ifdef __STDC__
63.         double __kernel_sin(double x, double y, int iy)
64. #else
65.         double __kernel_sin(x, y, iy)
66.         double x,y; int iy;             /* iy=0 if y is zero */
67. #endif
68. {
69.         double z,r,v;
70.         int32_t ix;
71.         GET_HIGH_WORD(ix,x);
72.         ix &= 0x7fffffff;                       /* high word of x */
73.         if(ix<0x3e400000)                       /* |x| < 2**-27 */
74.            {if((int)x==0) return x;}            /* generate inexact */
75.         z       =  x*x;
76.         v       =  z*x;
77.         r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
78.         if(iy==0) return x+v*(S1+z*r);
79.         else      return x-((z*(half*y-v*r)-y)-v*S1);
80. }
81.