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 #include <sys/cdefs.h>
17 __FBSDID("$FreeBSD$");
18
19 /*
20 * See comments in e_atan2.c.
21 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
22 */
23
24 #include <float.h>
25
26 #include "invtrig.h"
27 #include "math.h"
28 #include "math_private.h"
29
30 static volatile long double
31 tiny = 1.0e-300;
32 static const long double
33 zero = 0.0;
34
35 #ifdef __i386__
36 /* XXX Work around the fact that gcc truncates long double constants on i386 */
37 static volatile double
38 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
39 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
40 #define pi ((long double)pi1 + pi2)
41 #else
42 static const long double
43 pi = 3.14159265358979323846264338327950280e+00L;
44 #endif
45
46 long double
atan2l(long double y,long double x)47 atan2l(long double y, long double x)
48 {
49 union IEEEl2bits ux, uy;
50 long double z;
51 int32_t k,m;
52 int16_t exptx, expsignx, expty, expsigny;
53
54 uy.e = y;
55 expsigny = uy.xbits.expsign;
56 expty = expsigny & 0x7fff;
57 ux.e = x;
58 expsignx = ux.xbits.expsign;
59 exptx = expsignx & 0x7fff;
60
61 if ((exptx==BIAS+LDBL_MAX_EXP &&
62 ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
63 (expty==BIAS+LDBL_MAX_EXP &&
64 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */
65 return nan_mix(x, y);
66 if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
67 return atanl(y); /* x=1.0 */
68 m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */
69
70 /* when y = 0 */
71 if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
72 switch(m) {
73 case 0:
74 case 1: return y; /* atan(+-0,+anything)=+-0 */
75 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
76 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
77 }
78 }
79 /* when x = 0 */
80 if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
81 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
82
83 /* when x is INF */
84 if(exptx==BIAS+LDBL_MAX_EXP) {
85 if(expty==BIAS+LDBL_MAX_EXP) {
86 switch(m) {
87 case 0: return pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
88 case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
89 case 2: return 1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
90 case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
91 }
92 } else {
93 switch(m) {
94 case 0: return zero ; /* atan(+...,+INF) */
95 case 1: return -zero ; /* atan(-...,+INF) */
96 case 2: return pi+tiny ; /* atan(+...,-INF) */
97 case 3: return -pi-tiny ; /* atan(-...,-INF) */
98 }
99 }
100 }
101 /* when y is INF */
102 if(expty==BIAS+LDBL_MAX_EXP)
103 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
104
105 /* compute y/x */
106 k = expty-exptx;
107 if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
108 z=pio2_hi+pio2_lo;
109 m&=1;
110 }
111 else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; /* |y/x| tiny, x<0 */
112 else z=atanl(fabsl(y/x)); /* safe to do y/x */
113 switch (m) {
114 case 0: return z ; /* atan(+,+) */
115 case 1: return -z ; /* atan(-,+) */
116 case 2: return pi-(z-pi_lo);/* atan(+,-) */
117 default: /* case 3 */
118 return (z-pi_lo)-pi;/* atan(-,-) */
119 }
120 }
121