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comparison src/libm/k_cos.c @ 2756:a98604b691c8

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Expanded the libm support and put it into a separate directory.
author Sam Lantinga <slouken@libsdl.org>
date Mon, 15 Sep 2008 06:33:23 +0000
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children dc1eb82ffdaa
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2755:2a3ec308d995 2756:a98604b691c8
1 /* @(#)k_cos.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 #if defined(LIBM_SCCS) && !defined(lint)
14 static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
15 #endif
16
17 /*
18 * __kernel_cos( x, y )
19 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
20 * Input x is assumed to be bounded by ~pi/4 in magnitude.
21 * Input y is the tail of x.
22 *
23 * Algorithm
24 * 1. Since cos(-x) = cos(x), we need only to consider positive x.
25 * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
26 * 3. cos(x) is approximated by a polynomial of degree 14 on
27 * [0,pi/4]
28 * 4 14
29 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
30 * where the remez error is
31 *
32 * | 2 4 6 8 10 12 14 | -58
33 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
34 * | |
35 *
36 * 4 6 8 10 12 14
37 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
38 * cos(x) = 1 - x*x/2 + r
39 * since cos(x+y) ~ cos(x) - sin(x)*y
40 * ~ cos(x) - x*y,
41 * a correction term is necessary in cos(x) and hence
42 * cos(x+y) = 1 - (x*x/2 - (r - x*y))
43 * For better accuracy when x > 0.3, let qx = |x|/4 with
44 * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
45 * Then
46 * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
47 * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
48 * magnitude of the latter is at least a quarter of x*x/2,
49 * thus, reducing the rounding error in the subtraction.
50 */
51
52 #include "math.h"
53 #include "math_private.h"
54
55 #ifdef __STDC__
56 static const double
57 #else
58 static double
59 #endif
60 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
61 C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
62 C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
63 C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
64 C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
65 C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
66 C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
67
68 #ifdef __STDC__
69 double attribute_hidden
70 __kernel_cos(double x, double y)
71 #else
72 double attribute_hidden
73 __kernel_cos(x, y)
74 double x, y;
75 #endif
76 {
77 double a, hz, z, r, qx;
78 int32_t ix;
79 GET_HIGH_WORD(ix, x);
80 ix &= 0x7fffffff; /* ix = |x|'s high word */
81 if (ix < 0x3e400000) { /* if x < 2**27 */
82 if (((int) x) == 0)
83 return one; /* generate inexact */
84 }
85 z = x * x;
86 r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
87 if (ix < 0x3FD33333) /* if |x| < 0.3 */
88 return one - (0.5 * z - (z * r - x * y));
89 else {
90 if (ix > 0x3fe90000) { /* x > 0.78125 */
91 qx = 0.28125;
92 } else {
93 INSERT_WORDS(qx, ix - 0x00200000, 0); /* x/4 */
94 }
95 hz = 0.5 * z - qx;
96 a = one - qx;
97 return a - (hz - (z * r - x * y));
98 }
99 }