1 /* $OpenBSD: e_atan2l.c,v 1.1 2008/12/09 20:00:35 martynas 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
35 static volatile long double
36 tiny = 1.0e-300;
37 static const long double
38 zero = 0.0;
39
40 #if defined(__amd64__) || defined(__i386__)
41 /* XXX Work around the fact that gcc truncates long double constants on i386 */
42 static volatile double
43 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
44 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
45 #define pi ((long double)pi1 + pi2)
46 #else
47 static const long double
48 pi = 3.14159265358979323846264338327950280e+00L;
49 #endif
50
51 long double
atan2l(long double y,long double x)52 atan2l(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 }
164