1
2 /* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 *
13 */
14
15 /*
16 * See comments in e_atan2.c.
17 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
18 */
19
20 #include <float.h>
21
22 #include "invtrig.h"
23 #include "math.h"
24 #include "math_private.h"
25
26 static volatile long double
27 tiny = 1.0e-300;
28 static const long double
29 zero = 0.0;
30
31 #ifdef __i386__
32 /* XXX Work around the fact that gcc truncates long double constants on i386 */
33 static volatile double
34 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
35 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
36 #define pi ((long double)pi1 + pi2)
37 #else
38 static const long double
39 pi = 3.14159265358979323846264338327950280e+00L;
40 #endif
41
42 long double
atan2l(long double y,long double x)43 atan2l(long double y, long double x)
44 {
45 union IEEEl2bits ux, uy;
46 long double z;
47 int32_t k,m;
48 int16_t exptx, expsignx, expty, expsigny;
49
50 uy.e = y;
51 expsigny = uy.xbits.expsign;
52 expty = expsigny & 0x7fff;
53 ux.e = x;
54 expsignx = ux.xbits.expsign;
55 exptx = expsignx & 0x7fff;
56
57 if ((exptx==BIAS+LDBL_MAX_EXP &&
58 ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
59 (expty==BIAS+LDBL_MAX_EXP &&
60 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */
61 return nan_mix(x, y);
62 if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
63 return atanl(y); /* x=1.0 */
64 m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */
65
66 /* when y = 0 */
67 if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
68 switch(m) {
69 case 0:
70 case 1: return y; /* atan(+-0,+anything)=+-0 */
71 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
72 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
73 }
74 }
75 /* when x = 0 */
76 if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
77 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
78
79 /* when x is INF */
80 if(exptx==BIAS+LDBL_MAX_EXP) {
81 if(expty==BIAS+LDBL_MAX_EXP) {
82 switch(m) {
83 case 0: return pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
84 case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
85 case 2: return 1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
86 case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
87 }
88 } else {
89 switch(m) {
90 case 0: return zero ; /* atan(+...,+INF) */
91 case 1: return -zero ; /* atan(-...,+INF) */
92 case 2: return pi+tiny ; /* atan(+...,-INF) */
93 case 3: return -pi-tiny ; /* atan(-...,-INF) */
94 }
95 }
96 }
97 /* when y is INF */
98 if(expty==BIAS+LDBL_MAX_EXP)
99 return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
100
101 /* compute y/x */
102 k = expty-exptx;
103 if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
104 z=pio2_hi+pio2_lo;
105 m&=1;
106 }
107 else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; /* |y/x| tiny, x<0 */
108 else z=atanl(fabsl(y/x)); /* safe to do y/x */
109 switch (m) {
110 case 0: return z ; /* atan(+,+) */
111 case 1: return -z ; /* atan(-,+) */
112 case 2: return pi-(z-pi_lo);/* atan(+,-) */
113 default: /* case 3 */
114 return (z-pi_lo)-pi;/* atan(-,-) */
115 }
116 }
117