e_atan2.c revision 97407 
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
14static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_atan2.c 97407 2002-05-28 17:03:12Z alfred $";
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
47static const double
48tiny  = 1.0e-300,
49zero  = 0.0,
50pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
51pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
52pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
53pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
54
55double
56__generic___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}
123