1/*	$OpenBSD: e_atan2l.c,v 1.2 2016/09/12 19:47:02 guenther Exp $	*/
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/*
17 * See comments in e_atan2.c.
18 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
19 * Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>.
20 */
21
22#include <float.h>
23#include <math.h>
24
25#include "invtrig.h"
26#include "math.h"
27#include "math_private.h"
28
29#ifdef EXT_IMPLICIT_NBIT
30#define	LDBL_NBIT	0
31#else /* EXT_IMPLICIT_NBIT */
32#define	LDBL_NBIT	0x80000000
33#endif /* EXT_IMPLICIT_NBIT */
34
35static volatile long double
36tiny  = 1.0e-300;
37static const long double
38zero  = 0.0;
39
40#if defined(__amd64__) || defined(__i386__)
41/* XXX Work around the fact that gcc truncates long double constants on i386 */
42static volatile double
43pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
44pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
45#define	pi	((long double)pi1 + pi2)
46#else
47static const long double
48pi =  3.14159265358979323846264338327950280e+00L;
49#endif
50
51long double
52atan2l(long double y, long double x)
53{
54	union {
55		long double e;
56		struct ieee_ext bits;
57	} ux, uy;
58	long double z;
59	int32_t k,m;
60	int16_t exptx, expsignx, expty, expsigny;
61
62	uy.e = y;
63	expsigny = (uy.bits.ext_sign << 15) | uy.bits.ext_exp;
64	expty = expsigny & 0x7fff;
65	ux.e = x;
66	expsignx = (ux.bits.ext_sign << 15) | ux.bits.ext_exp;
67	exptx = expsignx & 0x7fff;
68
69	if ((exptx==BIAS+LDBL_MAX_EXP &&
70	     ((ux.bits.ext_frach&~LDBL_NBIT)
71#ifdef EXT_FRACHMBITS
72		| ux.bits.ext_frachm
73#endif /* EXT_FRACHMBITS */
74#ifdef EXT_FRACLMBITS
75		| ux.bits.ext_fraclm
76#endif /* EXT_FRACLMBITS */
77		| ux.bits.ext_fracl)!=0) ||	/* x is NaN */
78	    (expty==BIAS+LDBL_MAX_EXP &&
79	     ((uy.bits.ext_frach&~LDBL_NBIT)
80#ifdef EXT_FRACHMBITS
81		| uy.bits.ext_frachm
82#endif /* EXT_FRACHMBITS */
83#ifdef EXT_FRACLMBITS
84		| uy.bits.ext_fraclm
85#endif /* EXT_FRACLMBITS */
86		| uy.bits.ext_fracl)!=0))	/* y is NaN */
87	    return x+y;
88	if (expsignx==BIAS && ((ux.bits.ext_frach&~LDBL_NBIT)
89#ifdef EXT_FRACHMBITS
90		| ux.bits.ext_frachm
91#endif /* EXT_FRACHMBITS */
92#ifdef EXT_FRACLMBITS
93		| ux.bits.ext_fraclm
94#endif /* EXT_FRACLMBITS */
95		| ux.bits.ext_fracl)==0)
96	    return atanl(y);					/* x=1.0 */
97	m = ((expsigny>>15)&1)|((expsignx>>14)&2);	/* 2*sign(x)+sign(y) */
98
99    /* when y = 0 */
100	if(expty==0 && ((uy.bits.ext_frach&~LDBL_NBIT)
101#ifdef EXT_FRACHMBITS
102		| uy.bits.ext_frachm
103#endif /* EXT_FRACHMBITS */
104#ifdef EXT_FRACLMBITS
105		| uy.bits.ext_fraclm
106#endif /* EXT_FRACLMBITS */
107		| uy.bits.ext_fracl)==0) {
108	    switch(m) {
109		case 0:
110		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
111		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
112		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
113	    }
114	}
115    /* when x = 0 */
116	if(exptx==0 && ((ux.bits.ext_frach&~LDBL_NBIT)
117#ifdef EXT_FRACHMBITS
118		| ux.bits.ext_frachm
119#endif /* EXT_FRACHMBITS */
120#ifdef EXT_FRACLMBITS
121		| ux.bits.ext_fraclm
122#endif /* EXT_FRACLMBITS */
123		| ux.bits.ext_fracl)==0)
124	    return (expsigny<0)?  -pio2_hi-tiny: pio2_hi+tiny;
125
126    /* when x is INF */
127	if(exptx==BIAS+LDBL_MAX_EXP) {
128	    if(expty==BIAS+LDBL_MAX_EXP) {
129		switch(m) {
130		    case 0: return  pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
131		    case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
132		    case 2: return  1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
133		    case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
134		}
135	    } else {
136		switch(m) {
137		    case 0: return  zero  ;	/* atan(+...,+INF) */
138		    case 1: return -zero  ;	/* atan(-...,+INF) */
139		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
140		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
141		}
142	    }
143	}
144    /* when y is INF */
145	if(expty==BIAS+LDBL_MAX_EXP)
146	    return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
147
148    /* compute y/x */
149	k = expty-exptx;
150	if(k > LDBL_MANT_DIG+2) {			/* |y/x| huge */
151	    z=pio2_hi+pio2_lo;
152	    m&=1;
153	}
154	else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; 	/* |y/x| tiny, x<0 */
155	else z=atanl(fabsl(y/x));		/* safe to do y/x */
156	switch (m) {
157	    case 0: return       z  ;	/* atan(+,+) */
158	    case 1: return      -z  ;	/* atan(-,+) */
159	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
160	    default: /* case 3 */
161	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
162	}
163}
164DEF_STD(atan2l);
165