1 /* @(#)e_atan2.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 /* atan2(y,x)
14 * Method :
15 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
16 * 2. Reduce x to positive by (if x and y are unexceptional):
17 * ARG (x+iy) = arctan(y/x) ... if x > 0,
18 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
19 *
20 * Special cases:
21 *
22 * ATAN2((anything), NaN ) is NaN;
23 * ATAN2(NAN , (anything) ) is NaN;
24 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
25 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
26 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
27 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
28 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
29 * ATAN2(+-INF,+INF ) is +-pi/4 ;
30 * ATAN2(+-INF,-INF ) is +-3pi/4;
31 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
32 *
33 * Constants:
34 * The hexadecimal values are the intended ones for the following
35 * constants. The decimal values may be used, provided that the
36 * compiler will convert from decimal to binary accurately enough
37 * to produce the hexadecimal values shown.
38 */
39
40 #include <float.h>
41 #include <math.h>
42
43 #include "math_private.h"
44
45 static const double
46 tiny = 1.0e-300,
47 zero = 0.0,
48 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
49 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
50 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
51 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
52
53 double
atan2(double y,double x)54 atan2(double y, double x)
55 {
56 double z;
57 int32_t k,m,hx,hy,ix,iy;
58 u_int32_t lx,ly;
59
60 EXTRACT_WORDS(hx,lx,x);
61 ix = hx&0x7fffffff;
62 EXTRACT_WORDS(hy,ly,y);
63 iy = hy&0x7fffffff;
64 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
65 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
66 return x+y;
67 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
68 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
69
70 /* when y = 0 */
71 if((iy|ly)==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((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
81
82 /* when x is INF */
83 if(ix==0x7ff00000) {
84 if(iy==0x7ff00000) {
85 switch(m) {
86 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
87 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
88 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
89 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
90 }
91 } else {
92 switch(m) {
93 case 0: return zero ; /* atan(+...,+INF) */
94 case 1: return -zero ; /* atan(-...,+INF) */
95 case 2: return pi+tiny ; /* atan(+...,-INF) */
96 case 3: return -pi-tiny ; /* atan(-...,-INF) */
97 }
98 }
99 }
100 /* when y is INF */
101 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
102
103 /* compute y/x */
104 k = (iy-ix)>>20;
105 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
106 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
107 else z=atan(fabs(y/x)); /* safe to do y/x */
108 switch (m) {
109 case 0: return z ; /* atan(+,+) */
110 case 1: {
111 u_int32_t zh;
112 GET_HIGH_WORD(zh,z);
113 SET_HIGH_WORD(z,zh ^ 0x80000000);
114 }
115 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 DEF_STD(atan2);
122 LDBL_MAYBE_CLONE(atan2);
123