1 /* @(#)e_atan2.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
12 * $NetBSD: e_atan2.c,v 1.12 2002/05/26 22:01:48 wiz Exp $
13 * $DragonFly: src/lib/libm/src/e_atan2.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
18 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
19 * 2. Reduce x to positive by (if x and y are unexceptional):
20 * ARG (x+iy) = arctan(y/x) ... if x > 0,
21 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
25 * ATAN2((anything), NaN ) is NaN;
26 * ATAN2(NAN , (anything) ) is NaN;
27 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
28 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
29 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
30 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
31 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
32 * ATAN2(+-INF,+INF ) is +-pi/4 ;
33 * ATAN2(+-INF,-INF ) is +-3pi/4;
34 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
37 * The hexadecimal values are the intended ones for the following
38 * constants. The decimal values may be used, provided that the
39 * compiler will convert from decimal to binary accurately enough
40 * to produce the hexadecimal values shown.
44 #include "math_private.h"
49 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
50 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
51 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
52 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
55 atan2(double y, double x)
58 int32_t k,m,hx,hy,ix,iy;
61 EXTRACT_WORDS(hx,lx,x);
63 EXTRACT_WORDS(hy,ly,y);
65 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
66 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
68 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
69 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
75 case 1: return y; /* atan(+-0,+anything)=+-0 */
76 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
77 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
81 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
87 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
88 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
89 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
90 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
94 case 0: return zero ; /* atan(+...,+INF) */
95 case 1: return -zero ; /* atan(-...,+INF) */
96 case 2: return pi+tiny ; /* atan(+...,-INF) */
97 case 3: return -pi-tiny ; /* atan(-...,-INF) */
102 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
106 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
107 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
108 else z=atan(fabs(y/x)); /* safe to do y/x */
110 case 0: return z ; /* atan(+,+) */
114 SET_HIGH_WORD(z,zh ^ 0x80000000);
116 return z ; /* atan(-,+) */
117 case 2: return pi-(z-pi_lo);/* atan(+,-) */
118 default: /* case 3 */
119 return (z-pi_lo)-pi;/* atan(-,-) */