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#include <LibConfig.h> 13#include <sys/EfiCdefs.h> 14#if defined(LIBM_SCCS) && !defined(lint) 15__RCSID("$NetBSD: e_atan2.c,v 1.12 2002/05/26 22:01:48 wiz Exp $"); 16#endif 17 18#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */ 19 // unary minus operator applied to unsigned type, result still unsigned 20 #pragma warning ( disable : 4146 ) 21#endif 22 23/* __ieee754_atan2(y,x) 24 * Method : 25 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 26 * 2. Reduce x to positive by (if x and y are unexceptional): 27 * ARG (x+iy) = arctan(y/x) ... if x > 0, 28 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 29 * 30 * Special cases: 31 * 32 * ATAN2((anything), NaN ) is NaN; 33 * ATAN2(NAN , (anything) ) is NaN; 34 * ATAN2(+-0, +(anything but NaN)) is +-0 ; 35 * ATAN2(+-0, -(anything but NaN)) is +-pi ; 36 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 37 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 38 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 39 * ATAN2(+-INF,+INF ) is +-pi/4 ; 40 * ATAN2(+-INF,-INF ) is +-3pi/4; 41 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 42 * 43 * Constants: 44 * The hexadecimal values are the intended ones for the following 45 * constants. The decimal values may be used, provided that the 46 * compiler will convert from decimal to binary accurately enough 47 * to produce the hexadecimal values shown. 48 */ 49 50#include "math.h" 51#include "math_private.h" 52 53static const double 54tiny = 1.0e-300, 55zero = 0.0, 56pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 57pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 58pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 59pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 60 61double 62__ieee754_atan2(double y, double x) 63{ 64 double z; 65 int32_t k,m,hx,hy,ix,iy; 66 u_int32_t lx,ly; 67 68 EXTRACT_WORDS(hx,lx,x); 69 ix = hx&0x7fffffff; 70 EXTRACT_WORDS(hy,ly,y); 71 iy = hy&0x7fffffff; 72 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 73 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 74 return x+y; 75 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ 76 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 77 78 /* when y = 0 */ 79 if((iy|ly)==0) { 80 switch(m) { 81 case 0: 82 case 1: return y; /* atan(+-0,+anything)=+-0 */ 83 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 84 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 85 } 86 } 87 /* when x = 0 */ 88 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 89 90 /* when x is INF */ 91 if(ix==0x7ff00000) { 92 if(iy==0x7ff00000) { 93 switch(m) { 94 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 95 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 96 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 97 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 98 } 99 } else { 100 switch(m) { 101 case 0: return zero ; /* atan(+...,+INF) */ 102 case 1: return -zero ; /* atan(-...,+INF) */ 103 case 2: return pi+tiny ; /* atan(+...,-INF) */ 104 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 105 } 106 } 107 } 108 /* when y is INF */ 109 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 110 111 /* compute y/x */ 112 k = (iy-ix)>>20; 113 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 114 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 115 else z=atan(fabs(y/x)); /* safe to do y/x */ 116 switch (m) { 117 case 0: return z ; /* atan(+,+) */ 118 case 1: { 119 u_int32_t zh; 120 GET_HIGH_WORD(zh,z); 121 SET_HIGH_WORD(z,zh ^ 0x80000000); 122 } 123 return z ; /* atan(-,+) */ 124 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 125 default: /* case 3 */ 126 return (z-pi_lo)-pi;/* atan(-,-) */ 127 } 128} 129