xref: /freebsd/lib/msun/src/e_atan2.c (revision 1e413cf93298b5b97441a21d9a50fdcd0ee9945e)
1 
2 /* @(#)e_atan2.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  *
13  */
14 
15 #ifndef lint
16 static char rcsid[] = "$FreeBSD$";
17 #endif
18 
19 /* __ieee754_atan2(y,x)
20  * Method :
21  *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
22  *	2. Reduce x to positive by (if x and y are unexceptional):
23  *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
24  *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
25  *
26  * Special cases:
27  *
28  *	ATAN2((anything), NaN ) is NaN;
29  *	ATAN2(NAN , (anything) ) is NaN;
30  *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
31  *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
32  *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
33  *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
34  *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
35  *	ATAN2(+-INF,+INF ) is +-pi/4 ;
36  *	ATAN2(+-INF,-INF ) is +-3pi/4;
37  *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
38  *
39  * Constants:
40  * The hexadecimal values are the intended ones for the following
41  * constants. The decimal values may be used, provided that the
42  * compiler will convert from decimal to binary accurately enough
43  * to produce the hexadecimal values shown.
44  */
45 
46 #include "math.h"
47 #include "math_private.h"
48 
49 static const double
50 tiny  = 1.0e-300,
51 zero  = 0.0,
52 pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
53 pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
54 pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
55 pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
56 
57 double
58 __ieee754_atan2(double y, double x)
59 {
60 	double z;
61 	int32_t k,m,hx,hy,ix,iy;
62 	u_int32_t lx,ly;
63 
64 	EXTRACT_WORDS(hx,lx,x);
65 	ix = hx&0x7fffffff;
66 	EXTRACT_WORDS(hy,ly,y);
67 	iy = hy&0x7fffffff;
68 	if(((ix|((lx|-lx)>>31))>0x7ff00000)||
69 	   ((iy|((ly|-ly)>>31))>0x7ff00000))	/* x or y is NaN */
70 	   return x+y;
71 	if((hx-0x3ff00000|lx)==0) return atan(y);   /* x=1.0 */
72 	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
73 
74     /* when y = 0 */
75 	if((iy|ly)==0) {
76 	    switch(m) {
77 		case 0:
78 		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
79 		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
80 		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
81 	    }
82 	}
83     /* when x = 0 */
84 	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
85 
86     /* when x is INF */
87 	if(ix==0x7ff00000) {
88 	    if(iy==0x7ff00000) {
89 		switch(m) {
90 		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
91 		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
92 		    case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
93 		    case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
94 		}
95 	    } else {
96 		switch(m) {
97 		    case 0: return  zero  ;	/* atan(+...,+INF) */
98 		    case 1: return -zero  ;	/* atan(-...,+INF) */
99 		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
100 		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
101 		}
102 	    }
103 	}
104     /* when y is INF */
105 	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
106 
107     /* compute y/x */
108 	k = (iy-ix)>>20;
109 	if(k > 60) z=pi_o_2+0.5*pi_lo; 	/* |y/x| >  2**60 */
110 	else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
111 	else z=atan(fabs(y/x));		/* safe to do y/x */
112 	switch (m) {
113 	    case 0: return       z  ;	/* atan(+,+) */
114 	    case 1: {
115 	    	      u_int32_t zh;
116 		      GET_HIGH_WORD(zh,z);
117 		      SET_HIGH_WORD(z,zh ^ 0x80000000);
118 		    }
119 		    return       z  ;	/* atan(-,+) */
120 	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
121 	    default: /* case 3 */
122 	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
123 	}
124 }
125