Mercurial > sdl-ios-xcode

annotate src/libm/e_atan2.c @ 5176:ebfedf3787b1

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Standardized on using the managed texture pool. Also experimented with dynamic textures, but didn't get any speed increase with them. More research and testing is needed.
author Sam Lantinga <slouken@libsdl.org>
date Fri, 04 Feb 2011 12:25:26 -0800
parents 8288636b861d
children
rev   line source
4870
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
1 /*
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
2 * ====================================================
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
4 *
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
6 * Permission to use, copy, modify, and distribute this
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
7 * software is freely granted, provided that this notice
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
8 * is preserved.
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
9 * ====================================================
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
10 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
11
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
12 /* __ieee754_atan2(y,x)
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
13 * Method :
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
14 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
15 * 2. Reduce x to positive by (if x and y are unexceptional):
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
16 * ARG (x+iy) = arctan(y/x) ... if x > 0,
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
17 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
18 *
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
19 * Special cases:
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
20 *
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
21 * ATAN2((anything), NaN ) is NaN;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
22 * ATAN2(NAN , (anything) ) is NaN;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
23 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
24 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
25 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
26 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
27 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
28 * ATAN2(+-INF,+INF ) is +-pi/4 ;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
29 * ATAN2(+-INF,-INF ) is +-3pi/4;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
30 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
31 *
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
32 * Constants:
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
33 * The hexadecimal values are the intended ones for the following
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
34 * constants. The decimal values may be used, provided that the
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
35 * compiler will convert from decimal to binary accurately enough
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
36 * to produce the hexadecimal values shown.
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
37 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
38
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
39 #include "math.h"
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
40 #include "math_private.h"
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
41
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
42 static const double
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
43 tiny = 1.0e-300,
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
44 zero = 0.0,
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
45 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
46 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
47 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
48 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
49
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
50 double attribute_hidden __ieee754_atan2(double y, double x)
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
51 {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
52 double z;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
53 int32_t k,m,hx,hy,ix,iy;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
54 u_int32_t lx,ly;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
55
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
56 EXTRACT_WORDS(hx,lx,x);
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
57 ix = hx&0x7fffffff;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
58 EXTRACT_WORDS(hy,ly,y);
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
59 iy = hy&0x7fffffff;
4874
8288636b861d Compiling in atan()/atan2() implementation on Visual Studio 2008.
Sam Lantinga <slouken@libsdl.org>
parents: 4870
diff changeset
60 if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)||
8288636b861d Compiling in atan()/atan2() implementation on Visual Studio 2008.
Sam Lantinga <slouken@libsdl.org>
parents: 4870
diff changeset
61 ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000)) /* x or y is NaN */
4870
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
62 return x+y;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
63 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
64 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
65
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
66 /* when y = 0 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
67 if((iy|ly)==0) {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
68 switch(m) {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
69 case 0:
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
70 case 1: return y; /* atan(+-0,+anything)=+-0 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
71 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
72 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
73 }
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
74 }
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
75 /* when x = 0 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
76 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
77
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
78 /* when x is INF */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
79 if(ix==0x7ff00000) {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
80 if(iy==0x7ff00000) {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
81 switch(m) {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
82 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
83 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
84 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
85 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
86 }
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
87 } else {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
88 switch(m) {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
89 case 0: return zero ; /* atan(+...,+INF) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
90 case 1: return -zero ; /* atan(-...,+INF) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
91 case 2: return pi+tiny ; /* atan(+...,-INF) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
92 case 3: return -pi-tiny ; /* atan(-...,-INF) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
93 }
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
94 }
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
95 }
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
96 /* when y is INF */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
97 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
98
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
99 /* compute y/x */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
100 k = (iy-ix)>>20;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
101 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
102 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
103 else z=atan(fabs(y/x)); /* safe to do y/x */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
104 switch (m) {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
105 case 0: return z ; /* atan(+,+) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
106 case 1: {
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
107 u_int32_t zh;
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
108 GET_HIGH_WORD(zh,z);
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
109 SET_HIGH_WORD(z,zh ^ 0x80000000);
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
110 }
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
111 return z ; /* atan(-,+) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
112 case 2: return pi-(z-pi_lo);/* atan(+,-) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
113 default: /* case 3 */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
114 return (z-pi_lo)-pi;/* atan(-,-) */
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
115 }
d275c95ddc05 Added atan2 implementation from uClibc
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
116 }