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 #ifndef lint 14 static char rcsid[] = "$FreeBSD$"; 15 #endif 16 17 /* __ieee754_atan2(y,x) 18 * Method : 19 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 20 * 2. Reduce x to positive by (if x and y are unexceptional): 21 * ARG (x+iy) = arctan(y/x) ... if x > 0, 22 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 23 * 24 * Special cases: 25 * 26 * ATAN2((anything), NaN ) is NaN; 27 * ATAN2(NAN , (anything) ) is NaN; 28 * ATAN2(+-0, +(anything but NaN)) is +-0 ; 29 * ATAN2(+-0, -(anything but NaN)) is +-pi ; 30 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 31 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 32 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 33 * ATAN2(+-INF,+INF ) is +-pi/4 ; 34 * ATAN2(+-INF,-INF ) is +-3pi/4; 35 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 36 * 37 * Constants: 38 * The hexadecimal values are the intended ones for the following 39 * constants. The decimal values may be used, provided that the 40 * compiler will convert from decimal to binary accurately enough 41 * to produce the hexadecimal values shown. 42 */ 43 44 #include "math.h" 45 #include "math_private.h" 46 47 static const double 48 tiny = 1.0e-300, 49 zero = 0.0, 50 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 51 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 52 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 53 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 54 55 double 56 __ieee754_atan2(double y, double x) 57 { 58 double z; 59 int32_t k,m,hx,hy,ix,iy; 60 u_int32_t lx,ly; 61 62 EXTRACT_WORDS(hx,lx,x); 63 ix = hx&0x7fffffff; 64 EXTRACT_WORDS(hy,ly,y); 65 iy = hy&0x7fffffff; 66 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 67 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 68 return x+y; 69 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ 70 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 71 72 /* when y = 0 */ 73 if((iy|ly)==0) { 74 switch(m) { 75 case 0: 76 case 1: return y; /* atan(+-0,+anything)=+-0 */ 77 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 78 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 79 } 80 } 81 /* when x = 0 */ 82 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 83 84 /* when x is INF */ 85 if(ix==0x7ff00000) { 86 if(iy==0x7ff00000) { 87 switch(m) { 88 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 89 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 90 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 91 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 92 } 93 } else { 94 switch(m) { 95 case 0: return zero ; /* atan(+...,+INF) */ 96 case 1: return -zero ; /* atan(-...,+INF) */ 97 case 2: return pi+tiny ; /* atan(+...,-INF) */ 98 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 99 } 100 } 101 } 102 /* when y is INF */ 103 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 104 105 /* compute y/x */ 106 k = (iy-ix)>>20; 107 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 108 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 109 else z=atan(fabs(y/x)); /* safe to do y/x */ 110 switch (m) { 111 case 0: return z ; /* atan(+,+) */ 112 case 1: { 113 u_int32_t zh; 114 GET_HIGH_WORD(zh,z); 115 SET_HIGH_WORD(z,zh ^ 0x80000000); 116 } 117 return z ; /* atan(-,+) */ 118 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 119 default: /* case 3 */ 120 return (z-pi_lo)-pi;/* atan(-,-) */ 121 } 122 } 123