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 #include <sys/cdefs.h>
16 __FBSDID("$FreeBSD$");
17 
18 /* __ieee754_atan2(y,x)
19  * Method :
20  *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
21  *	2. Reduce x to positive by (if x and y are unexceptional):
22  *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
23  *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
24  *
25  * Special cases:
26  *
27  *	ATAN2((anything), NaN ) is NaN;
28  *	ATAN2(NAN , (anything) ) is NaN;
29  *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
30  *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
31  *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
32  *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
33  *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
34  *	ATAN2(+-INF,+INF ) is +-pi/4 ;
35  *	ATAN2(+-INF,-INF ) is +-3pi/4;
36  *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
37  *
38  * Constants:
39  * The hexadecimal values are the intended ones for the following
40  * constants. The decimal values may be used, provided that the
41  * compiler will convert from decimal to binary accurately enough
42  * to produce the hexadecimal values shown.
43  */
44 
45 #include <float.h>
46 
47 #include "math.h"
48 #include "math_private.h"
49 
50 static volatile double
51 tiny  = 1.0e-300;
52 static const double
53 zero  = 0.0,
54 pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
55 pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
56 pi      = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
57 static volatile double
58 pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
59 
60 double
__ieee754_atan2(double y,double x)61 __ieee754_atan2(double y, double x)
62 {
63 	double z;
64 	int32_t k,m,hx,hy,ix,iy;
65 	u_int32_t lx,ly;
66 
67 	EXTRACT_WORDS(hx,lx,x);
68 	ix = hx&0x7fffffff;
69 	EXTRACT_WORDS(hy,ly,y);
70 	iy = hy&0x7fffffff;
71 	if(((ix|((lx|-lx)>>31))>0x7ff00000)||
72 	   ((iy|((ly|-ly)>>31))>0x7ff00000))	/* x or y is NaN */
73 	   return x+y;
74 	if((hx-0x3ff00000|lx)==0) return atan(y);   /* x=1.0 */
75 	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
76 
77     /* when y = 0 */
78 	if((iy|ly)==0) {
79 	    switch(m) {
80 		case 0:
81 		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
82 		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
83 		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
84 	    }
85 	}
86     /* when x = 0 */
87 	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
88 
89     /* when x is INF */
90 	if(ix==0x7ff00000) {
91 	    if(iy==0x7ff00000) {
92 		switch(m) {
93 		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
94 		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
95 		    case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
96 		    case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
97 		}
98 	    } else {
99 		switch(m) {
100 		    case 0: return  zero  ;	/* atan(+...,+INF) */
101 		    case 1: return -zero  ;	/* atan(-...,+INF) */
102 		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
103 		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
104 		}
105 	    }
106 	}
107     /* when y is INF */
108 	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
109 
110     /* compute y/x */
111 	k = (iy-ix)>>20;
112 	if(k > 60) {		 	/* |y/x| >  2**60 */
113 	    z=pi_o_2+0.5*pi_lo;
114 	    m&=1;
115 	}
116 	else if(hx<0&&k<-60) z=0.0; 	/* 0 > |y|/x > -2**-60 */
117 	else z=atan(fabs(y/x));		/* safe to do y/x */
118 	switch (m) {
119 	    case 0: return       z  ;	/* atan(+,+) */
120 	    case 1: return      -z  ;	/* atan(-,+) */
121 	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
122 	    default: /* case 3 */
123 	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
124 	}
125 }
126 
127 #if LDBL_MANT_DIG == 53
128 __weak_reference(atan2, atan2l);
129 #endif
130