xref: /netbsd-src/lib/libm/src/e_atan2l.c (revision 3f3b0ded092b378b433be0bc7541910db5a04ce4)
1 /*	$NetBSD: e_atan2l.c,v 1.2 2024/01/23 15:45:07 christos 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 #include <sys/cdefs.h>
17 __RCSID("$NetBSD: e_atan2l.c,v 1.2 2024/01/23 15:45:07 christos Exp $");
18 
19 /*
20  * See comments in e_atan2.c.
21  * Converted to long double by David Schultz <das@FreeBSD.ORG>.
22  */
23 
24 #include "namespace.h"
25 
26 #ifdef __weak_alias
27 __weak_alias(atan2l, _atan2l)
28 #endif
29 
30 #include <float.h>
31 #include <machine/ieee.h>
32 
33 #include "math.h"
34 #include "math_private.h"
35 
36 #ifdef __HAVE_LONG_DOUBLE
37 
38 #if LDBL_MANT_DIG == 64
39 #include "../ld80/invtrig.h"
40 #elif LDBL_MANT_DIG == 113
41 #include "../ld128/invtrig.h"
42 #else
43 #error "Unsupported long double format"
44 #endif
45 
46 #ifdef LDBL_IMPLICIT_NBIT
47 #define	LDBL_NBIT	0
48 #endif
49 
50 static volatile long double
51 tiny  = 1.0e-300;
52 static const long double
53 zero  = 0.0;
54 
55 #ifdef __i386__
56 /* XXX Work around the fact that gcc truncates long double constants on i386 */
57 static volatile double
58 pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
59 pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
60 #define	pi	((long double)pi1 + pi2)
61 #else
62 static const long double
63 pi =  3.14159265358979323846264338327950280e+00L;
64 #endif
65 
66 long double
atan2l(long double y,long double x)67 atan2l(long double y, long double x)
68 {
69 	union ieee_ext_u ux, uy;
70 	long double z;
71 	int32_t k,m;
72 	int16_t exptx, expsignx, expty, expsigny;
73 
74 	uy.extu_ld = y;
75 	expsigny = GET_EXPSIGN(&uy);
76 	expty = expsigny & 0x7fff;
77 	ux.extu_ld = x;
78 	expsignx = GET_EXPSIGN(&ux);
79 	exptx = expsignx & 0x7fff;
80 
81 	if ((exptx==BIAS+LDBL_MAX_EXP &&
82 	     ((ux.extu_frach&~LDBL_NBIT)|ux.extu_fracl)!=0) ||	/* x is NaN */
83 	    (expty==BIAS+LDBL_MAX_EXP &&
84 	     ((uy.extu_frach&~LDBL_NBIT)|uy.extu_fracl)!=0))	/* y is NaN */
85 	    return nan_mix(x, y);
86 	if (expsignx==BIAS && ((ux.extu_frach&~LDBL_NBIT)|ux.extu_fracl)==0)
87 	    return atanl(y);					/* x=1.0 */
88 	m = ((expsigny>>15)&1)|((expsignx>>14)&2);	/* 2*sign(x)+sign(y) */
89 
90     /* when y = 0 */
91 	if(expty==0 && ((uy.extu_frach&~LDBL_NBIT)|uy.extu_fracl)==0) {
92 	    switch(m) {
93 		case 0:
94 		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
95 		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
96 		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
97 	    }
98 	}
99     /* when x = 0 */
100 	if(exptx==0 && ((ux.extu_frach&~LDBL_NBIT)|ux.extu_fracl)==0)
101 	    return (expsigny<0)?  -pio2_hi-tiny: pio2_hi+tiny;
102 
103     /* when x is INF */
104 	if(exptx==BIAS+LDBL_MAX_EXP) {
105 	    if(expty==BIAS+LDBL_MAX_EXP) {
106 		switch(m) {
107 		    case 0: return  pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
108 		    case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
109 		    case 2: return  1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
110 		    case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
111 		}
112 	    } else {
113 		switch(m) {
114 		    case 0: return  zero  ;	/* atan(+...,+INF) */
115 		    case 1: return -zero  ;	/* atan(-...,+INF) */
116 		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
117 		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
118 		}
119 	    }
120 	}
121     /* when y is INF */
122 	if(expty==BIAS+LDBL_MAX_EXP)
123 	    return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
124 
125     /* compute y/x */
126 	k = expty-exptx;
127 	if(k > LDBL_MANT_DIG+2) {			/* |y/x| huge */
128 	    z=pio2_hi+pio2_lo;
129 	    m&=1;
130 	}
131 	else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; 	/* |y/x| tiny, x<0 */
132 	else z=atanl(fabsl(y/x));		/* safe to do y/x */
133 	switch (m) {
134 	    case 0: return       z  ;	/* atan(+,+) */
135 	    case 1: return      -z  ;	/* atan(-,+) */
136 	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
137 	    default: /* case 3 */
138 	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
139 	}
140 }
141 
142 #else
143 
144 long double
145 atan2l(long double y, long double x)
146 {
147 	return atan2(y, x);
148 }
149 
150 #endif
151