1
2 /* @(#)e_atan2.c 1.3 95/01/18 */
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 #ifndef lint
16 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_atan2.c,v 1.10 2005/02/04 18:26:05 das Exp $";
17 #endif
18
19 /* __ieee754_atan2(y,x)
20 * Method :
21 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
22 * 2. Reduce x to positive by (if x and y are unexceptional):
23 * ARG (x+iy) = arctan(y/x) ... if x > 0,
24 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
25 *
26 * Special cases:
27 *
28 * ATAN2((anything), NaN ) is NaN;
29 * ATAN2(NAN , (anything) ) is NaN;
30 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
31 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
32 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
33 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
34 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
35 * ATAN2(+-INF,+INF ) is +-pi/4 ;
36 * ATAN2(+-INF,-INF ) is +-3pi/4;
37 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
38 *
39 * Constants:
40 * The hexadecimal values are the intended ones for the following
41 * constants. The decimal values may be used, provided that the
42 * compiler will convert from decimal to binary accurately enough
43 * to produce the hexadecimal values shown.
44 */
45
46 #include "math.h"
47 #include "math_private.h"
48
49 static const double
50 tiny = 1.0e-300,
51 zero = 0.0,
52 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
53 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
54 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
55 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
56
57 double
__ieee754_atan2(double y,double x)58 __ieee754_atan2(double y, double x)
59 {
60 double z;
61 int32_t k,m,hx,hy,ix,iy;
62 u_int32_t lx,ly;
63
64 EXTRACT_WORDS(hx,lx,x);
65 ix = hx&0x7fffffff;
66 EXTRACT_WORDS(hy,ly,y);
67 iy = hy&0x7fffffff;
68 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
69 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
70 return x+y;
71 if(((hx-0x3ff00000) | lx)==0) return atan(y); /* x=1.0 */
72 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
73
74 /* when y = 0 */
75 if((iy|ly)==0) {
76 switch(m) {
77 case 0:
78 case 1: return y; /* atan(+-0,+anything)=+-0 */
79 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
80 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
81 }
82 }
83 /* when x = 0 */
84 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
85
86 /* when x is INF */
87 if(ix==0x7ff00000) {
88 if(iy==0x7ff00000) {
89 switch(m) {
90 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
91 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
92 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
93 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
94 }
95 } else {
96 switch(m) {
97 case 0: return zero ; /* atan(+...,+INF) */
98 case 1: return -zero ; /* atan(-...,+INF) */
99 case 2: return pi+tiny ; /* atan(+...,-INF) */
100 case 3: return -pi-tiny ; /* atan(-...,-INF) */
101 }
102 }
103 }
104 /* when y is INF */
105 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
106
107 /* compute y/x */
108 k = (iy-ix)>>20;
109 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
110 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
111 else z=atan(fabs(y/x)); /* safe to do y/x */
112 switch (m) {
113 case 0: return z ; /* atan(+,+) */
114 case 1: {
115 u_int32_t zh;
116 GET_HIGH_WORD(zh,z);
117 SET_HIGH_WORD(z,zh ^ 0x80000000);
118 }
119 return z ; /* atan(-,+) */
120 case 2: return pi-(z-pi_lo);/* atan(+,-) */
121 default: /* case 3 */
122 return (z-pi_lo)-pi;/* atan(-,-) */
123 }
124 }
125