# Subversion RepositoriesKolibri OS

Rev
1. /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */
2. /* @(#)k_cos.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_cos.c,v 1.6 1994/08/18 23:06:08 jtc Exp \$";
16. #endif
17.
18. /*
19.  * __kernel_cos( x,  y )
20.  * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
21.  * Input x is assumed to be bounded by ~pi/4 in magnitude.
22.  * Input y is the tail of x.
23.  *
24.  * Algorithm
25.  *      1. Since cos(-x) = cos(x), we need only to consider positive x.
26.  *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
27.  *      3. cos(x) is approximated by a polynomial of degree 14 on
28.  *         [0,pi/4]
29.  *                                       4            14
30.  *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
31.  *         where the remez error is
32.  *
33.  *      |              2     4     6     8     10    12     14 |     -58
34.  *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
35.  *      |                                                      |
36.  *
37.  *                     4     6     8     10    12     14
38.  *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
39.  *             cos(x) = 1 - x*x/2 + r
40.  *         since cos(x+y) ~ cos(x) - sin(x)*y
41.  *                        ~ cos(x) - x*y,
42.  *         a correction term is necessary in cos(x) and hence
43.  *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
44.  *         For better accuracy when x > 0.3, let qx = |x|/4 with
45.  *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
46.  *         Then
47.  *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
48.  *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
49.  *         magnitude of the latter is at least a quarter of x*x/2,
50.  *         thus, reducing the rounding error in the subtraction.
51.  */
52.
53. #include "math.h"
54. #include "math_private.h"
55.
56. #ifdef __STDC__
57. static const double
58. #else
59. static double
60. #endif
61. one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
62. C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
63. C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
64. C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
65. C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
66. C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
67. C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
68.
69. #ifdef __STDC__
70.         double __kernel_cos(double x, double y)
71. #else
72.         double __kernel_cos(x, y)
73.         double x,y;
74. #endif
75. {
76.         double a,hz,z,r,qx;
77.         int32_t ix;
78.         GET_HIGH_WORD(ix,x);
79.         ix &= 0x7fffffff;                       /* ix = |x|'s high word*/
80.         if(ix<0x3e400000) {                     /* if x < 2**27 */
81.             if(((int)x)==0) return one;         /* generate inexact */
82.         }
83.         z  = x*x;
84.         r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
85.         if(ix < 0x3FD33333)                     /* if |x| < 0.3 */
86.             return one - (0.5*z - (z*r - x*y));
87.         else {
88.             if(ix > 0x3fe90000) {               /* x > 0.78125 */
89.                 qx = 0.28125;
90.             } else {
91.                 INSERT_WORDS(qx,ix-0x00200000,0);       /* x/4 */
92.             }
93.             hz = 0.5*z-qx;
94.             a  = one-qx;
95.             return a - (hz - (z*r-x*y));
96.         }
97. }
98.