1
2/* @(#)e_atan2.c 1.3 95/01/18 */
3/* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */
4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 *
14 */
15
16#include <sys/cdefs.h>
17__FBSDID("$FreeBSD$");
18
19/*
20 * See comments in e_atan2.c.
21 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
22 */
23
24#include <float.h>
25
26#include "invtrig.h"
27#include "math.h"
28#include "math_private.h"
29
30static volatile long double
31tiny  = 1.0e-300;
32static const long double
33zero  = 0.0;
34
35#ifdef __i386__
36/* XXX Work around the fact that gcc truncates long double constants on i386 */
37static volatile double
38pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
39pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
40#define	pi	((long double)pi1 + pi2)
41#else
42static const long double
43pi =  3.14159265358979323846264338327950280e+00L;
44#endif
45
46long double
47atan2l(long double y, long double x)
48{
49	union IEEEl2bits ux, uy;
50	long double z;
51	int32_t k,m;
52	int16_t exptx, expsignx, expty, expsigny;
53
54	uy.e = y;
55	expsigny = uy.xbits.expsign;
56	expty = expsigny & 0x7fff;
57	ux.e = x;
58	expsignx = ux.xbits.expsign;
59	exptx = expsignx & 0x7fff;
60
61	if ((exptx==BIAS+LDBL_MAX_EXP &&
62	     ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) ||	/* x is NaN */
63	    (expty==BIAS+LDBL_MAX_EXP &&
64	     ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0))	/* y is NaN */
65	    return x+y;
66	if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
67	    return atanl(y);					/* x=1.0 */
68	m = ((expsigny>>15)&1)|((expsignx>>14)&2);	/* 2*sign(x)+sign(y) */
69
70    /* when y = 0 */
71	if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
72	    switch(m) {
73		case 0:
74		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
75		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
76		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
77	    }
78	}
79    /* when x = 0 */
80	if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
81	    return (expsigny<0)?  -pio2_hi-tiny: pio2_hi+tiny;
82
83    /* when x is INF */
84	if(exptx==BIAS+LDBL_MAX_EXP) {
85	    if(expty==BIAS+LDBL_MAX_EXP) {
86		switch(m) {
87		    case 0: return  pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
88		    case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
89		    case 2: return  1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
90		    case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
91		}
92	    } else {
93		switch(m) {
94		    case 0: return  zero  ;	/* atan(+...,+INF) */
95		    case 1: return -zero  ;	/* atan(-...,+INF) */
96		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
97		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
98		}
99	    }
100	}
101    /* when y is INF */
102	if(expty==BIAS+LDBL_MAX_EXP)
103	    return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
104
105    /* compute y/x */
106	k = expty-exptx;
107	if(k > LDBL_MANT_DIG+2) {			/* |y/x| huge */
108	    z=pio2_hi+pio2_lo;
109	    m&=1;
110	}
111	else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; 	/* |y/x| tiny, x<0 */
112	else z=atanl(fabsl(y/x));		/* safe to do y/x */
113	switch (m) {
114	    case 0: return       z  ;	/* atan(+,+) */
115	    case 1: return      -z  ;	/* atan(-,+) */
116	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
117	    default: /* case 3 */
118	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
119	}
120}
121