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
50static volatile double
51tiny  = 1.0e-300;
52static const double
53zero  = 0.0,
54pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
55pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
56pi      = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
57static volatile double
58pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
59
60double
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