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