Mercurial > sdl-ios-xcode

annotate src/libm/k_sin.c @ 2980:8789e4b0e0e7

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Bug 653 bugfix
author Szymon Wilczek <kazeuser@gmail.com>
date Sat, 03 Jan 2009 12:00:20 +0000
parents a98604b691c8
children dc1eb82ffdaa
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_sin.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)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
14 static char rcsid[] = "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
15 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
16
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
17 /* __kernel_sin( x, y, iy)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
18 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
19 * 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
20 * 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
21 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
22 *
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
23 * Algorithm
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
24 * 1. Since sin(-x) = -sin(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
25 * 2. if x < 2^-27 (hx<0x3e400000 0), return x 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
26 * 3. sin(x) is approximated by a polynomial of degree 13 on
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
27 * [0,pi/4]
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
28 * 3 13
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
29 * sin(x) ~ x + S1*x + ... + S6*x
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
30 * where
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
31 *
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
32 * |sin(x) 2 4 6 8 10 12 | -58
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
33 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
34 * | x |
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 * 4. sin(x+y) = sin(x) + sin'(x')*y
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
37 * ~ sin(x) + (1-x*x/2)*y
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
38 * For better accuracy, let
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
39 * 3 2 2 2 2
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
40 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
41 * then 3 2
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
42 * sin(x) = x + (S1*x + (x *(r-y/2)+y))
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
43 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
44
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
45 #include "math.h"
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
46 #include "math_private.h"
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
47
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
48 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
49 static const double
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
50 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
51 static double
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
52 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
53 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
54 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
55 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
56 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
57 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
58 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
59 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
60
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
61 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
62 double attribute_hidden
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
63 __kernel_sin(double x, double y, int iy)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
64 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
65 double attribute_hidden
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
66 __kernel_sin(x, y, iy)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
67 double x, y;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
68 int iy; /* iy=0 if y is zero */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
69 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
70 {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
71 double z, r, v;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
72 int32_t ix;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
73 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
74 ix &= 0x7fffffff; /* high word of x */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
75 if (ix < 0x3e400000) { /* |x| < 2**-27 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
76 if ((int) x == 0)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
77 return x;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
78 } /* generate inexact */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
79 z = x * x;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
80 v = z * x;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
81 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
82 if (iy == 0)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
83 return x + v * (S1 + z * r);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
84 else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
85 return x - ((z * (half * y - v * r) - y) - v * S1);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
86 }