annotate src/libm/k_sin.c @ 5067:61d53410eb41

Fixed bug #859 CREATE_SUBDIRS helps a lot if browsing HTML documentation in a file browser. ALWAYS_DETAILED_SEC makes sure everything has at least the automatic documentation like function prototype and source references. STRIP_FROM_PATH allows you to include only the relevant portions of the files' paths, cleaning up both the file list and directory tree, though you need to change the path listed here to match wherever you put SDL. ALIASES avoids some warnings generated by C:\source\svn.libsdl.org\trunk\SDL\src\joystick\darwin\10.3.9-FIX\IOHIDLib.h. It seems Apple uses a few commands which are not normally supported by Doxygen. BUILTIN_STL_SUPPORT adds support for parsing code which makes use of the standard template library. There isn't a lot of C++ in SDL (some in bwindow at least), but this still seems like a good idea. TYPEDEF_HIDES_STRUCT means that for code like this: typedef struct A {int B;} C; C is documented as a structure containing B instead of a typedef mapped to A. EXTRACT_ALL, EXTRACT_PRIVATE, EXTRACT_STATIC, EXTRACT_LOCAL_METHODS, EXTRACT_ANON_NSPACES and INTERNAL_DOCS make sure that _everything_ is documented. CASE_SENSE_NAMES = NO avoids potential conflicts when building documentation on case insensitive file systems like NTFS and FAT32. WARN_NO_PARAMDOC lets you know when you have documented some, but not all, of the parameters of a function. This is useful when you're working on adding such documentation since it makes partially documented functions easier to spot. WARN_LOGFILE writes warnings to a seperate file instead of mixing them in with stdout. When not running in quiet mode, these warnings can be hard to spot without this flag. I added *.h.in and *.h.default to FILE_PATTERNS to generate documentation for config.h.in and config.h.default. RECURSIVE tells doxygen to look not only in the input directory, but also in subfolders. EXCLUDE avoids documenting things like test programs, examples and templates which need to be documented separately. I've used EXCLUDE_PATTERNS to exclude non-source subdirectories that often find their way into source folders (such as obj or .svn). EXAMPLE_PATH lists directories doxygen will search to find included example code. So far, SDL doesn't really use this feature, but I've listed some likely locations. SOURCE_BROWSER adds syntax highlighted source code to the HTML output. USE_HTAGS is nice, but not available on Windows. INLINE_SOURCES adds the body of a function to it's documentation so you can quickly see exactly what it does. ALPHABETICAL_INDEX generates an alphabetical list of all structures, functions, etc., which makes it much easier to find what you're looking for. IGNORE_PREFIX skips the SDL_ prefix when deciding which index page to place an item on so you don't have everything show up under "S". HTML_DYNAMIC_SECTIONS hides the includes/included by diagrams by default and adds JavaScript to allow the user to show and hide them by clicking a link. ENUM_VALUES_PER_LINE = 1 makes enums easier to read by placing each value on it's own line. GENERATE_TREEVIEW produces a two frame index page with a navigation tree on the left. I have LaTeX and man pages turned off to speed up doxygen, you may want to turn them back on yourself. I added _WIN32=1 to PREDEFINED to cause SDL to output documentation related to Win32 builds of SDL. Normally, doxygen gets confused since there are multiple definitions for various structures and formats that vary by platform. Without this doxygen can produce broken documentation or, if you're lucky, output documentation only for the dummy drivers, which isn't very useful. You need to pick a platform. GENERATE_TAGFILE produces a file which can be used to link other doxygen documentation to the SDL documentation. CLASS_DIAGRAMS turns on class diagrams even when dot is not available. HAVE_DOT tells doxygen to try to use dot to generate diagrams. TEMPLATE_RELATIONS and INCLUDE_GRAPH add additional diagrams to the documentation. DOT_MULTI_TARGETS speeds up dot. OUTPUT_DIRECTORY, INPUT and other paths reflect the fact that this Doxyfile is intended to process src as well as include and is being run from a separate subdirectory. Doxygen produces several temporary files while it's running and if interrupted, can leave those files behind. It's easier to clean up if there aren't a hundred or so files in the same folder. I typically run doxygen in SDL/doxy and set the output directory to '.'. Since doxygen puts it's output in subfolders by type, this keeps things pretty well organised. You could use '../doc' instead and get the same results.
author Sam Lantinga <slouken@libsdl.org>
date Fri, 21 Jan 2011 12:57:01 -0800
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_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)
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_sin.c,v 1.8 1995/05/10 20:46:31 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 /* __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
19 * 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
20 * 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
21 * 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
22 * 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
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 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
26 * 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
27 * 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
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 * 3 13
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
30 * 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
31 * where
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 * |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
34 * |----- - (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
35 * | x |
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. 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
38 * ~ 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
39 * For better accuracy, let
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
40 * 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
41 * 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
42 * then 3 2
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
43 * 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
44 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
45
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
46 #include "math.h"
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
47 #include "math_private.h"
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
48
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
49 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
50 static const double
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
51 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
52 static double
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
53 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
54 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
55 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
56 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
57 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
58 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
59 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
60 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
61
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
62 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
63 double attribute_hidden
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
64 __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
65 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
66 double attribute_hidden
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
67 __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
68 double x, y;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
69 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
70 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
71 {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
72 double z, r, v;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
73 int32_t ix;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
74 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
75 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
76 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
77 if ((int) x == 0)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
78 return x;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
79 } /* generate inexact */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
80 z = x * x;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
81 v = z * x;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
82 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
83 if (iy == 0)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
84 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
85 else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
86 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
87 }