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e_atan2.c (3828B)
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1 /* @(#)e_atan2.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 #ifndef lint
14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_atan2.c,v 1.9 2003/07/23 04:53:46 peter Exp $";
15 #endif
16
17 /* __ieee754_atan2(y,x)
18 * Method :
19 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
20 * 2. Reduce x to positive by (if x and y are unexceptional):
21 * ARG (x+iy) = arctan(y/x) ... if x > 0,
22 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
23 *
24 * Special cases:
25 *
26 * ATAN2((anything), NaN ) is NaN;
27 * ATAN2(NAN , (anything) ) is NaN;
28 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
29 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
30 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
31 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
32 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
33 * ATAN2(+-INF,+INF ) is +-pi/4 ;
34 * ATAN2(+-INF,-INF ) is +-3pi/4;
35 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
36 *
37 * Constants:
38 * The hexadecimal values are the intended ones for the following
39 * constants. The decimal values may be used, provided that the
40 * compiler will convert from decimal to binary accurately enough
41 * to produce the hexadecimal values shown.
42 */
43
44 #include "math.h"
45 #include "math_private.h"
46
47 static const double
48 tiny = 1.0e-300,
49 zero = 0.0,
50 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
51 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
52 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
53 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
54
55 double
56 __ieee754_atan2(double y, double x)
57 {
58 double z;
59 int32_t k,m,hx,hy,ix,iy;
60 u_int32_t lx,ly;
61
62 EXTRACT_WORDS(hx,lx,x);
63 ix = hx&0x7fffffff;
64 EXTRACT_WORDS(hy,ly,y);
65 iy = hy&0x7fffffff;
66 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
67 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
68 return x+y;
69 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
70 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
71
72 /* when y = 0 */
73 if((iy|ly)==0) {
74 switch(m) {
75 case 0:
76 case 1: return y; /* atan(+-0,+anything)=+-0 */
77 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
78 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
79 }
80 }
81 /* when x = 0 */
82 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
83
84 /* when x is INF */
85 if(ix==0x7ff00000) {
86 if(iy==0x7ff00000) {
87 switch(m) {
88 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
89 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
90 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
91 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
92 }
93 } else {
94 switch(m) {
95 case 0: return zero ; /* atan(+...,+INF) */
96 case 1: return -zero ; /* atan(-...,+INF) */
97 case 2: return pi+tiny ; /* atan(+...,-INF) */
98 case 3: return -pi-tiny ; /* atan(-...,-INF) */
99 }
100 }
101 }
102 /* when y is INF */
103 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
104
105 /* compute y/x */
106 k = (iy-ix)>>20;
107 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
108 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
109 else z=atan(fabs(y/x)); /* safe to do y/x */
110 switch (m) {
111 case 0: return z ; /* atan(+,+) */
112 case 1: {
113 u_int32_t zh;
114 GET_HIGH_WORD(zh,z);
115 SET_HIGH_WORD(z,zh ^ 0x80000000);
116 }
117 return z ; /* atan(-,+) */
118 case 2: return pi-(z-pi_lo);/* atan(+,-) */
119 default: /* case 3 */
120 return (z-pi_lo)-pi;/* atan(-,-) */
121 }
122 }