3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
14 #include <sys/cdefs.h>
17 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
18 * 2. Reduce x to positive by (if x and y are unexceptional):
19 * ARG (x+iy) = arctan(y/x) ... if x > 0,
20 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
24 * ATAN2((anything), NaN ) is NaN;
25 * ATAN2(NAN , (anything) ) is NaN;
26 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
27 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
28 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
29 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
30 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
31 * ATAN2(+-INF,+INF ) is +-pi/4 ;
32 * ATAN2(+-INF,-INF ) is +-3pi/4;
33 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
36 * The hexadecimal values are the intended ones for the following
37 * constants. The decimal values may be used, provided that the
38 * compiler will convert from decimal to binary accurately enough
39 * to produce the hexadecimal values shown.
45 #include "math_private.h"
47 static volatile double
51 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
52 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
53 pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
54 static volatile double
55 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
58 atan2(double y, double x)
61 int32_t k,m,hx,hy,ix,iy;
64 EXTRACT_WORDS(hx,lx,x);
66 EXTRACT_WORDS(hy,ly,y);
68 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
69 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
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) */
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 */
84 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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)*/
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) */
105 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
109 if(k > 60) { /* |y/x| > 2**60 */
113 else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */
114 else z=atan(fabs(y/x)); /* safe to do y/x */
116 case 0: return z ; /* atan(+,+) */
117 case 1: return -z ; /* atan(-,+) */
118 case 2: return pi-(z-pi_lo);/* atan(+,-) */
119 default: /* case 3 */
120 return (z-pi_lo)-pi;/* atan(-,-) */
124 #if LDBL_MANT_DIG == 53
125 __weak_reference(atan2, atan2l);