1 /* @(#)e_atan2.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 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 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: e_atan2.c,v 1.11 1999/07/02 15:37:38 simonb Exp $"); 16 #endif 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 "math.h" 46 #include "math_private.h" 47 48 #ifdef __STDC__ 49 static const double 50 #else 51 static double 52 #endif 53 tiny = 1.0e-300, 54 zero = 0.0, 55 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 56 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 57 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 58 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 59 60 #ifdef __STDC__ 61 double __ieee754_atan2(double y, double x) 62 #else 63 double __ieee754_atan2(y,x) 64 double y,x; 65 #endif 66 { 67 double z; 68 int32_t k,m,hx,hy,ix,iy; 69 u_int32_t lx,ly; 70 71 EXTRACT_WORDS(hx,lx,x); 72 ix = hx&0x7fffffff; 73 EXTRACT_WORDS(hy,ly,y); 74 iy = hy&0x7fffffff; 75 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 76 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 77 return x+y; 78 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ 79 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 80 81 /* when y = 0 */ 82 if((iy|ly)==0) { 83 switch(m) { 84 case 0: 85 case 1: return y; /* atan(+-0,+anything)=+-0 */ 86 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 87 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 88 } 89 } 90 /* when x = 0 */ 91 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 92 93 /* when x is INF */ 94 if(ix==0x7ff00000) { 95 if(iy==0x7ff00000) { 96 switch(m) { 97 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 98 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 99 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 100 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 101 } 102 } else { 103 switch(m) { 104 case 0: return zero ; /* atan(+...,+INF) */ 105 case 1: return -zero ; /* atan(-...,+INF) */ 106 case 2: return pi+tiny ; /* atan(+...,-INF) */ 107 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 108 } 109 } 110 } 111 /* when y is INF */ 112 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 113 114 /* compute y/x */ 115 k = (iy-ix)>>20; 116 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 117 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 118 else z=atan(fabs(y/x)); /* safe to do y/x */ 119 switch (m) { 120 case 0: return z ; /* atan(+,+) */ 121 case 1: { 122 u_int32_t zh; 123 GET_HIGH_WORD(zh,z); 124 SET_HIGH_WORD(z,zh ^ 0x80000000); 125 } 126 return z ; /* atan(-,+) */ 127 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 128 default: /* case 3 */ 129 return (z-pi_lo)-pi;/* atan(-,-) */ 130 } 131 } 132