src/libm/e_atan2.c
 author Philipp Wiesemann Sun, 28 Dec 2014 22:00:24 +0100 changeset 9301 7377a9a3aed6 parent 7678 286c42d7c5ed child 11683 48bcba563d9c permissions -rw-r--r--
1 /*
2  * ====================================================
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
12 /* __ieee754_atan2(y,x)
13  * Method :
14  *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
15  *	2. Reduce x to positive by (if x and y are unexceptional):
16  *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
17  *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
18  *
19  * Special cases:
20  *
21  *	ATAN2((anything), NaN ) is NaN;
22  *	ATAN2(NAN , (anything) ) is NaN;
23  *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
24  *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
25  *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
26  *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
27  *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
28  *	ATAN2(+-INF,+INF ) is +-pi/4 ;
29  *	ATAN2(+-INF,-INF ) is +-3pi/4;
30  *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
31  *
32  * Constants:
33  * The hexadecimal values are the intended ones for the following
34  * constants. The decimal values may be used, provided that the
35  * compiler will convert from decimal to binary accurately enough
36  * to produce the hexadecimal values shown.
37  */
39 #include "math_libm.h"
40 #include "math_private.h"
42 static const double
43 tiny  = 1.0e-300,
44 zero  = 0.0,
45 pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
46 pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
47 pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
48 pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
50 double attribute_hidden __ieee754_atan2(double y, double x)
51 {
52 	double z;
53 	int32_t k,m,hx,hy,ix,iy;
54 	u_int32_t lx,ly;
56 	EXTRACT_WORDS(hx,lx,x);
57 	ix = hx&0x7fffffff;
58 	EXTRACT_WORDS(hy,ly,y);
59 	iy = hy&0x7fffffff;
60 	if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)||
61 	   ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000))	/* x or y is NaN */
62 	   return x+y;
63 	if(((hx-0x3ff00000)|lx)==0) return atan(y);   /* x=1.0 */
64 	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
66     /* when y = 0 */
67 	if((iy|ly)==0) {
68 	    switch(m) {
69 		case 0:
70 		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
71 		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
72 		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
73 	    }
74 	}
75     /* when x = 0 */
76 	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
78     /* when x is INF */
79 	if(ix==0x7ff00000) {
80 	    if(iy==0x7ff00000) {
81 		switch(m) {
82 		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
83 		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
84 		    case 2: return  3.0*pi_o_4+tiny;/* atan(+INF,-INF) */
85 		    case 3: return -3.0*pi_o_4-tiny;/* atan(-INF,-INF) */
86 		}
87 	    } else {
88 		switch(m) {
89 		    case 0: return  zero  ;	/* atan(+...,+INF) */
90 		    case 1: return -zero  ;	/* atan(-...,+INF) */
91 		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
92 		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
93 		}
94 	    }
95 	}
96     /* when y is INF */
97 	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
99     /* compute y/x */
100 	k = (iy-ix)>>20;
101 	if(k > 60) z=pi_o_2+0.5*pi_lo; 	/* |y/x| >  2**60 */
102 	else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
103 	else z=atan(fabs(y/x));		/* safe to do y/x */
104 	switch (m) {
105 	    case 0: return       z  ;	/* atan(+,+) */
106 	    case 1: {
107 	    	      u_int32_t zh;
108 		      GET_HIGH_WORD(zh,z);
109 		      SET_HIGH_WORD(z,zh ^ 0x80000000);
110 		    }
111 		    return       z  ;	/* atan(-,+) */
112 	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
113 	    default: /* case 3 */
114 	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
115 	}
116 }