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: head/lib/msun/src/e_atan2.c 336362 2018-07-17 07:42:14Z bde $");
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.h"
48 #include "math_private.h"
49
50 static volatile double
51 tiny = 1.0e-300;
52 static const double
53 zero = 0.0,
54 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
55 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
56 pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
57 static volatile double
58 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
59
60 double
__ieee754_atan2(double y,double x)61 __ieee754_atan2(double y, double x)
62 {
63 double z;
64 int32_t k,m,hx,hy,ix,iy;
65 u_int32_t lx,ly;
66
67 EXTRACT_WORDS(hx,lx,x);
68 ix = hx&0x7fffffff;
69 EXTRACT_WORDS(hy,ly,y);
70 iy = hy&0x7fffffff;
71 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
72 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
73 return nan_mix(x, y);
74 if(hx==0x3ff00000&&lx==0) return atan(y); /* x=1.0 */
75 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
76
77 /* when y = 0 */
78 if((iy|ly)==0) {
79 switch(m) {
80 case 0:
81 case 1: return y; /* atan(+-0,+anything)=+-0 */
82 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
83 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
84 }
85 }
86 /* when x = 0 */
87 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
88
89 /* when x is INF */
90 if(ix==0x7ff00000) {
91 if(iy==0x7ff00000) {
92 switch(m) {
93 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
94 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
95 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
96 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
97 }
98 } else {
99 switch(m) {
100 case 0: return zero ; /* atan(+...,+INF) */
101 case 1: return -zero ; /* atan(-...,+INF) */
102 case 2: return pi+tiny ; /* atan(+...,-INF) */
103 case 3: return -pi-tiny ; /* atan(-...,-INF) */
104 }
105 }
106 }
107 /* when y is INF */
108 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
109
110 /* compute y/x */
111 k = (iy-ix)>>20;
112 if(k > 60) { /* |y/x| > 2**60 */
113 z=pi_o_2+0.5*pi_lo;
114 m&=1;
115 }
116 else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */
117 else z=atan(fabs(y/x)); /* safe to do y/x */
118 switch (m) {
119 case 0: return z ; /* atan(+,+) */
120 case 1: return -z ; /* atan(-,+) */
121 case 2: return pi-(z-pi_lo);/* atan(+,-) */
122 default: /* case 3 */
123 return (z-pi_lo)-pi;/* atan(-,-) */
124 }
125 }
126
127 #if LDBL_MANT_DIG == 53
128 __weak_reference(atan2, atan2l);
129 #endif
130