1 /* derived from /netlib/fdlibm */ 2 3 /* @(#)e_atan2.c 1.3 95/01/18 */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunSoft, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 * 14 */ 15 16 /* __ieee754_atan2(y,x) 17 * Method : 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, 22 * 23 * Special cases: 24 * 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; 35 * 36 * Constants: 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. 41 */ 42 43 #include "fdlibm.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 __ieee754_atan2(double y, double x) 54 { 55 double z; 56 int k,m,hx,hy,ix,iy; 57 unsigned lx,ly; 58 59 hx = __HI(x); ix = hx&0x7fffffff; 60 lx = __LO(x); 61 hy = __HI(y); iy = hy&0x7fffffff; 62 ly = __LO(y); 63 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 64 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 65 return x+y; 66 if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ 67 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 68 69 /* when y = 0 */ 70 if((iy|ly)==0) { 71 switch(m) { 72 case 0: 73 case 1: return y; /* atan(+-0,+anything)=+-0 */ 74 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 75 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 76 } 77 } 78 /* when x = 0 */ 79 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 80 81 /* when x is INF */ 82 if(ix==0x7ff00000) { 83 if(iy==0x7ff00000) { 84 switch(m) { 85 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 86 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 87 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 88 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 89 } 90 } else { 91 switch(m) { 92 case 0: return zero ; /* atan(+...,+INF) */ 93 case 1: return -zero ; /* atan(-...,+INF) */ 94 case 2: return pi+tiny ; /* atan(+...,-INF) */ 95 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 96 } 97 } 98 } 99 /* when y is INF */ 100 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 101 102 /* compute y/x */ 103 k = (iy-ix)>>20; 104 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 105 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 106 else z=atan(fabs(y/x)); /* safe to do y/x */ 107 switch (m) { 108 case 0: return z ; /* atan(+,+) */ 109 case 1: __HI(z) ^= 0x80000000; 110 return z ; /* atan(-,+) */ 111 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 112 default: /* case 3 */ 113 return (z-pi_lo)-pi;/* atan(-,-) */ 114 } 115 } 116