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
17 /*
18 * See comments in e_atan2.c.
19 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
20 */
21
22
23 #include "invtrig.h"
24
25 static const long double tiny = 1.0e-300l;
26 static const long double zero = 0.0l;
27 static const long double pi = _M_PI_L;
28
29 long double
atan2l(long double y,long double x)30 atan2l(long double y, long double x)
31 {
32 union IEEEl2bits ux, uy;
33 long double z;
34 int32_t k,m;
35 int16_t exptx, expsignx, expty, expsigny;
36
37 uy.e = y;
38 expsigny = uy.xbits.expsign;
39 expty = expsigny & 0x7fff;
40 ux.e = x;
41 expsignx = ux.xbits.expsign;
42 exptx = expsignx & 0x7fff;
43
44 if ((exptx==BIAS+LDBL_MAX_EXP &&
45 ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
46 (expty==BIAS+LDBL_MAX_EXP &&
47 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */
48 return x+y;
49 if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
50 return atanl(y); /* x=1.0 */
51 m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */
52
53 /* when y = 0 */
54 if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
55 switch(m) {
56 case 0:
57 case 1: return y; /* atan(+-0,+anything)=+-0 */
58 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
59 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
60 }
61 }
62 /* when x = 0 */
63 if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
64 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
65
66 /* when x is INF */
67 if(exptx==BIAS+LDBL_MAX_EXP) {
68 if(expty==BIAS+LDBL_MAX_EXP) {
69 switch(m) {
70 case 0: return pio2_hi*0.5l+tiny;/* atan(+INF,+INF) */
71 case 1: return -pio2_hi*0.5l-tiny;/* atan(-INF,+INF) */
72 case 2: return 1.5l*pio2_hi+tiny;/*atan(+INF,-INF)*/
73 case 3: return -1.5l*pio2_hi-tiny;/*atan(-INF,-INF)*/
74 }
75 } else {
76 switch(m) {
77 case 0: return zero ; /* atan(+...,+INF) */
78 case 1: return -zero ; /* atan(-...,+INF) */
79 case 2: return pi+tiny ; /* atan(+...,-INF) */
80 case 3: return -pi-tiny ; /* atan(-...,-INF) */
81 }
82 }
83 }
84 /* when y is INF */
85 if(expty==BIAS+LDBL_MAX_EXP)
86 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
87
88 /* compute y/x */
89 k = expty-exptx;
90 if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
91 z=pio2_hi+pio2_lo;
92 m&=1;
93 }
94 else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0l; /* |y/x| tiny, x<0 */
95 else z=atanl(check_uflowl(fabsl(y/x))); /* safe to do y/x */
96 switch (m) {
97 case 0: return z ; /* atan(+,+) */
98 case 1: return -z ; /* atan(-,+) */
99 case 2: return pi-(z-pi_lo);/* atan(+,-) */
100 default: /* case 3 */
101 return (z-pi_lo)-pi;/* atan(-,-) */
102 }
103 }
104
105 #if __LDBL_MANT_DIG__ == 113
106 #if defined(_HAVE_ALIAS_ATTRIBUTE)
107 #ifndef __clang__
108 #pragma GCC diagnostic ignored "-Wmissing-attributes"
109 #endif
110 __strong_reference(atan2l, __atan2ieee128);
111 #endif
112 #endif
113
