annotate src/libm/s_atan.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 67ad1c88dda0
children
rev   line source
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1 /*
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2 * ====================================================
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3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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4 *
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5 * Developed at SunPro, a Sun Microsystems, Inc. business.
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6 * Permission to use, copy, modify, and distribute this
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7 * software is freely granted, provided that this notice
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8 * is preserved.
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9 * ====================================================
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10 */
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11
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12 /* atan(x)
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13 * Method
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14 * 1. Reduce x to positive by atan(x) = -atan(-x).
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15 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
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16 * is further reduced to one of the following intervals and the
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17 * arctangent of t is evaluated by the corresponding formula:
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18 *
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19 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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20 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
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21 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
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22 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
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23 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
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24 *
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25 * Constants:
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26 * The hexadecimal values are the intended ones for the following
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27 * constants. The decimal values may be used, provided that the
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28 * compiler will convert from decimal to binary accurately enough
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29 * to produce the hexadecimal values shown.
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30 */
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31
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32 #include "math.h"
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33 #include "math_private.h"
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34
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35 static const double atanhi[] = {
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36 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
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37 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
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38 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
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39 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
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40 };
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41
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42 static const double atanlo[] = {
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43 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
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44 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
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45 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
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46 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
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47 };
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48
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49 static const double aT[] = {
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50 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
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51 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
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52 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
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53 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
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54 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
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55 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
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56 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
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57 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
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58 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
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59 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
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60 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
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61 };
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62
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63 static const double
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64 one = 1.0,
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65 huge = 1.0e300;
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66
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67 double atan(double x)
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68 {
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69 double w,s1,s2,z;
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70 int32_t ix,hx,id;
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71
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72 GET_HIGH_WORD(hx,x);
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73 ix = hx&0x7fffffff;
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74 if(ix>=0x44100000) { /* if |x| >= 2^66 */
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75 u_int32_t low;
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76 GET_LOW_WORD(low,x);
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77 if(ix>0x7ff00000||
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78 (ix==0x7ff00000&&(low!=0)))
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79 return x+x; /* NaN */
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80 if(hx>0) return atanhi[3]+atanlo[3];
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81 else return -atanhi[3]-atanlo[3];
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82 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
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83 if (ix < 0x3e200000) { /* |x| < 2^-29 */
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84 if(huge+x>one) return x; /* raise inexact */
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85 }
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86 id = -1;
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87 } else {
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88 x = fabs(x);
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89 if (ix < 0x3ff30000) { /* |x| < 1.1875 */
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90 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
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91 id = 0; x = (2.0*x-one)/(2.0+x);
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92 } else { /* 11/16<=|x|< 19/16 */
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93 id = 1; x = (x-one)/(x+one);
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94 }
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95 } else {
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96 if (ix < 0x40038000) { /* |x| < 2.4375 */
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97 id = 2; x = (x-1.5)/(one+1.5*x);
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98 } else { /* 2.4375 <= |x| < 2^66 */
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99 id = 3; x = -1.0/x;
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100 }
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101 }}
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102 /* end of argument reduction */
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103 z = x*x;
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104 w = z*z;
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105 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
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106 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
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107 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
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108 if (id<0) return x - x*(s1+s2);
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109 else {
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110 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
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111 return (hx<0)? -z:z;
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112 }
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113 }
67ad1c88dda0 Added atan implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
114 libm_hidden_def(atan)