e_atan2.c revision 181062
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#include <sys/cdefs.h> 16__FBSDID("$FreeBSD: head/lib/msun/src/e_atan2.c 181062 2008-07-31 19:57:50Z das $"); 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 48static volatile double 49tiny = 1.0e-300; 50static const double 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 */ 55static volatile double 56pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 57 58double 59__ieee754_atan2(double y, double x) 60{ 61 double z; 62 int32_t k,m,hx,hy,ix,iy; 63 u_int32_t lx,ly; 64 65 EXTRACT_WORDS(hx,lx,x); 66 ix = hx&0x7fffffff; 67 EXTRACT_WORDS(hy,ly,y); 68 iy = hy&0x7fffffff; 69 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 70 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 71 return x+y; 72 if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ 73 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 74 75 /* when y = 0 */ 76 if((iy|ly)==0) { 77 switch(m) { 78 case 0: 79 case 1: return y; /* atan(+-0,+anything)=+-0 */ 80 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 81 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 82 } 83 } 84 /* when x = 0 */ 85 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 86 87 /* when x is INF */ 88 if(ix==0x7ff00000) { 89 if(iy==0x7ff00000) { 90 switch(m) { 91 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 92 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 93 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 94 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 95 } 96 } else { 97 switch(m) { 98 case 0: return zero ; /* atan(+...,+INF) */ 99 case 1: return -zero ; /* atan(-...,+INF) */ 100 case 2: return pi+tiny ; /* atan(+...,-INF) */ 101 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 102 } 103 } 104 } 105 /* when y is INF */ 106 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 107 108 /* compute y/x */ 109 k = (iy-ix)>>20; 110 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 111 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 112 else z=atan(fabs(y/x)); /* safe to do y/x */ 113 switch (m) { 114 case 0: return z ; /* atan(+,+) */ 115 case 1: { 116 u_int32_t zh; 117 GET_HIGH_WORD(zh,z); 118 SET_HIGH_WORD(z,zh ^ 0x80000000); 119 } 120 return z ; /* atan(-,+) */ 121 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 122 default: /* case 3 */ 123 return (z-pi_lo)-pi;/* atan(-,-) */ 124 } 125} 126