Mercurial > sdl-ios-xcode

annotate src/libm/k_cos.c @ 3690:e431b888ac6c

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Fixed compilation on iPhone
author Sam Lantinga <slouken@libsdl.org>
date Thu, 21 Jan 2010 16:12:24 +0000
parents dc1eb82ffdaa
children
rev   line source
2756
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
1 /* @(#)k_cos.c 5.1 93/09/24 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
2 /*
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
3 * ====================================================
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
5 *
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
7 * Permission to use, copy, modify, and distribute this
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
8 * software is freely granted, provided that this notice
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
9 * is preserved.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
10 * ====================================================
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
11 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
12
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
13 #if defined(LIBM_SCCS) && !defined(lint)
3162
dc1eb82ffdaa Von: Thomas Zimmermann
Sam Lantinga <slouken@libsdl.org>
parents: 2756
diff changeset
14 static const char rcsid[] =
dc1eb82ffdaa Von: Thomas Zimmermann
Sam Lantinga <slouken@libsdl.org>
parents: 2756
diff changeset
15 "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
2756
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
16 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
17
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
18 /*
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
19 * __kernel_cos( x, y )
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
20 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
21 * Input x is assumed to be bounded by ~pi/4 in magnitude.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
22 * Input y is the tail of x.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
23 *
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
24 * Algorithm
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
25 * 1. Since cos(-x) = cos(x), we need only to consider positive x.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
26 * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
27 * 3. cos(x) is approximated by a polynomial of degree 14 on
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
28 * [0,pi/4]
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
29 * 4 14
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
30 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
31 * where the remez error is
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
32 *
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
33 * | 2 4 6 8 10 12 14 | -58
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
34 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
35 * | |
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
36 *
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
37 * 4 6 8 10 12 14
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
38 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
39 * cos(x) = 1 - x*x/2 + r
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
40 * since cos(x+y) ~ cos(x) - sin(x)*y
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
41 * ~ cos(x) - x*y,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
42 * a correction term is necessary in cos(x) and hence
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
43 * cos(x+y) = 1 - (x*x/2 - (r - x*y))
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
44 * For better accuracy when x > 0.3, let qx = |x|/4 with
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
45 * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
46 * Then
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
47 * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
48 * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
49 * magnitude of the latter is at least a quarter of x*x/2,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
50 * thus, reducing the rounding error in the subtraction.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
51 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
52
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
53 #include "math.h"
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
54 #include "math_private.h"
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
55
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
56 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
57 static const double
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
58 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
59 static double
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
60 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
61 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
62 C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
63 C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
64 C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
65 C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
66 C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
67 C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
68
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
69 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
70 double attribute_hidden
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
71 __kernel_cos(double x, double y)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
72 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
73 double attribute_hidden
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
74 __kernel_cos(x, y)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
75 double x, y;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
76 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
77 {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
78 double a, hz, z, r, qx;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
79 int32_t ix;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
80 GET_HIGH_WORD(ix, x);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
81 ix &= 0x7fffffff; /* ix = |x|'s high word */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
82 if (ix < 0x3e400000) { /* if x < 2**27 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
83 if (((int) x) == 0)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
84 return one; /* generate inexact */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
85 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
86 z = x * x;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
87 r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
88 if (ix < 0x3FD33333) /* if |x| < 0.3 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
89 return one - (0.5 * z - (z * r - x * y));
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
90 else {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
91 if (ix > 0x3fe90000) { /* x > 0.78125 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
92 qx = 0.28125;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
93 } else {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
94 INSERT_WORDS(qx, ix - 0x00200000, 0); /* x/4 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
95 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
96 hz = 0.5 * z - qx;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
97 a = one - qx;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
98 return a - (hz - (z * r - x * y));
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
99 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
100 }