e_atan2.cpp (3764B)
1 /* @(#)e_atan2.c 1.3 95/01/18 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 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 9 * is preserved. 10 * ==================================================== 11 * 12 */ 13 14 //#include <sys/cdefs.h> 15 //__FBSDID("$FreeBSD$"); 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 <float.h> 45 #include <math.h> 46 47 #include "math_private.h" 48 49 static volatile double 50 tiny = 1.0e-300; 51 static const double 52 zero = 0.0, 53 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 54 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 55 pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ 56 static volatile double 57 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 58 59 double 60 __ieee754_atan2(double y, double x) 61 { 62 double z; 63 int32_t k,m,hx,hy,ix,iy; 64 u_int32_t lx,ly; 65 66 EXTRACT_WORDS(hx,lx,x); 67 ix = hx&0x7fffffff; 68 EXTRACT_WORDS(hy,ly,y); 69 iy = hy&0x7fffffff; 70 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 71 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 72 return nan_mix(x, y); 73 if(hx==0x3ff00000&&lx==0) return atan(y); /* x=1.0 */ 74 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 75 76 /* when y = 0 */ 77 if((iy|ly)==0) { 78 switch(m) { 79 case 0: 80 case 1: return y; /* atan(+-0,+anything)=+-0 */ 81 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 82 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 83 } 84 } 85 /* when x = 0 */ 86 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 87 88 /* when x is INF */ 89 if(ix==0x7ff00000) { 90 if(iy==0x7ff00000) { 91 switch(m) { 92 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 93 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 94 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 95 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 96 } 97 } else { 98 switch(m) { 99 case 0: return zero ; /* atan(+...,+INF) */ 100 case 1: return -zero ; /* atan(-...,+INF) */ 101 case 2: return pi+tiny ; /* atan(+...,-INF) */ 102 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 103 } 104 } 105 } 106 /* when y is INF */ 107 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 108 109 /* compute y/x */ 110 k = (iy-ix)>>20; 111 if(k > 60) { /* |y/x| > 2**60 */ 112 z=pi_o_2+0.5*pi_lo; 113 m&=1; 114 } 115 else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */ 116 else z=atan(fabs(y/x)); /* safe to do y/x */ 117 switch (m) { 118 case 0: return z ; /* atan(+,+) */ 119 case 1: return -z ; /* atan(-,+) */ 120 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 121 default: /* case 3 */ 122 return (z-pi_lo)-pi;/* atan(-,-) */ 123 } 124 }