1
2/* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */
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/*
16 * See comments in e_atan2.c.
17 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
18 */
19
20#include <float.h>
21
22#include "invtrig.h"
23#include "math.h"
24#include "math_private.h"
25
26static volatile long double
27tiny  = 1.0e-300;
28static const long double
29zero  = 0.0;
30
31#ifdef __i386__
32/* XXX Work around the fact that gcc truncates long double constants on i386 */
33static volatile double
34pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
35pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
36#define	pi	((long double)pi1 + pi2)
37#else
38static const long double
39pi =  3.14159265358979323846264338327950280e+00L;
40#endif
41
42long double
43atan2l(long double y, long double x)
44{
45	union IEEEl2bits ux, uy;
46	long double z;
47	int32_t k,m;
48	int16_t exptx, expsignx, expty, expsigny;
49
50	uy.e = y;
51	expsigny = uy.xbits.expsign;
52	expty = expsigny & 0x7fff;
53	ux.e = x;
54	expsignx = ux.xbits.expsign;
55	exptx = expsignx & 0x7fff;
56
57	if ((exptx==BIAS+LDBL_MAX_EXP &&
58	     ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) ||	/* x is NaN */
59	    (expty==BIAS+LDBL_MAX_EXP &&
60	     ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0))	/* y is NaN */
61	    return nan_mix(x, y);
62	if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
63	    return atanl(y);					/* x=1.0 */
64	m = ((expsigny>>15)&1)|((expsignx>>14)&2);	/* 2*sign(x)+sign(y) */
65
66    /* when y = 0 */
67	if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==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(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
77	    return (expsigny<0)?  -pio2_hi-tiny: pio2_hi+tiny;
78
79    /* when x is INF */
80	if(exptx==BIAS+LDBL_MAX_EXP) {
81	    if(expty==BIAS+LDBL_MAX_EXP) {
82		switch(m) {
83		    case 0: return  pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
84		    case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
85		    case 2: return  1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
86		    case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
87		}
88	    } else {
89		switch(m) {
90		    case 0: return  zero  ;	/* atan(+...,+INF) */
91		    case 1: return -zero  ;	/* atan(-...,+INF) */
92		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
93		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
94		}
95	    }
96	}
97    /* when y is INF */
98	if(expty==BIAS+LDBL_MAX_EXP)
99	    return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
100
101    /* compute y/x */
102	k = expty-exptx;
103	if(k > LDBL_MANT_DIG+2) {			/* |y/x| huge */
104	    z=pio2_hi+pio2_lo;
105	    m&=1;
106	}
107	else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; 	/* |y/x| tiny, x<0 */
108	else z=atanl(fabsl(y/x));		/* safe to do y/x */
109	switch (m) {
110	    case 0: return       z  ;	/* atan(+,+) */
111	    case 1: 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}
117