annotate src/libm/e_atan2.c @ 4974:1cd0a891b69a

Added info for building your code without optimizations on
author Sam Lantinga <slouken@libsdl.org>
date Wed, 12 Jan 2011 12:34:23 -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 }