e_atan2.c revision 141296
1 2/* @(#)e_atan2.c 1.3 95/01/18 */ 3/* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 * 13 */ 14 15#ifndef lint 16static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_atan2.c 141296 2005-02-04 18:26:06Z das $"; 17#endif 18 19/* __ieee754_atan2(y,x) 20 * Method : 21 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 22 * 2. Reduce x to positive by (if x and y are unexceptional): 23 * ARG (x+iy) = arctan(y/x) ... if x > 0, 24 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 25 * 26 * Special cases: 27 * 28 * ATAN2((anything), NaN ) is NaN; 29 * ATAN2(NAN , (anything) ) is NaN; 30 * ATAN2(+-0, +(anything but NaN)) is +-0 ; 31 * ATAN2(+-0, -(anything but NaN)) is +-pi ; 32 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 33 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 34 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 35 * ATAN2(+-INF,+INF ) is +-pi/4 ; 36 * ATAN2(+-INF,-INF ) is +-3pi/4; 37 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 38 * 39 * Constants: 40 * The hexadecimal values are the intended ones for the following 41 * constants. The decimal values may be used, provided that the 42 * compiler will convert from decimal to binary accurately enough 43 * to produce the hexadecimal values shown. 44 */ 45 46#include "math.h" 47#include "math_private.h" 48 49static const double 50tiny = 1.0e-300, 51zero = 0.0, 52pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 53pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 54pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 55pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 56 57double 58__ieee754_atan2(double y, double x) 59{ 60 double z; 61 int32_t k,m,hx,hy,ix,iy; 62 u_int32_t lx,ly; 63 64 EXTRACT_WORDS(hx,lx,x); 65 ix = hx&0x7fffffff; 66 EXTRACT_WORDS(hy,ly,y); 67 iy = hy&0x7fffffff; 68 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 69 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 70 return x+y; 71 if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ 72 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 73 74 /* when y = 0 */ 75 if((iy|ly)==0) { 76 switch(m) { 77 case 0: 78 case 1: return y; /* atan(+-0,+anything)=+-0 */ 79 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 80 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 81 } 82 } 83 /* when x = 0 */ 84 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 85 86 /* when x is INF */ 87 if(ix==0x7ff00000) { 88 if(iy==0x7ff00000) { 89 switch(m) { 90 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 91 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 92 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 93 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 94 } 95 } else { 96 switch(m) { 97 case 0: return zero ; /* atan(+...,+INF) */ 98 case 1: return -zero ; /* atan(-...,+INF) */ 99 case 2: return pi+tiny ; /* atan(+...,-INF) */ 100 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 101 } 102 } 103 } 104 /* when y is INF */ 105 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 106 107 /* compute y/x */ 108 k = (iy-ix)>>20; 109 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 110 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 111 else z=atan(fabs(y/x)); /* safe to do y/x */ 112 switch (m) { 113 case 0: return z ; /* atan(+,+) */ 114 case 1: { 115 u_int32_t zh; 116 GET_HIGH_WORD(zh,z); 117 SET_HIGH_WORD(z,zh ^ 0x80000000); 118 } 119 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} 125