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("$FreeBSD$"); 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 <float.h> 46 47 #include "math.h" 48 #include "math_private.h" 49 50 static volatile double 51 tiny = 1.0e-300; 52 static const double 53 zero = 0.0, 54 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 55 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 56 pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ 57 static volatile double 58 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 59 60 double 61 __ieee754_atan2(double y, double x) 62 { 63 double z; 64 int32_t k,m,hx,hy,ix,iy; 65 u_int32_t lx,ly; 66 67 EXTRACT_WORDS(hx,lx,x); 68 ix = hx&0x7fffffff; 69 EXTRACT_WORDS(hy,ly,y); 70 iy = hy&0x7fffffff; 71 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 72 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 73 return x+y; 74 if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ 75 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 76 77 /* when y = 0 */ 78 if((iy|ly)==0) { 79 switch(m) { 80 case 0: 81 case 1: return y; /* atan(+-0,+anything)=+-0 */ 82 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 83 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 84 } 85 } 86 /* when x = 0 */ 87 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 88 89 /* when x is INF */ 90 if(ix==0x7ff00000) { 91 if(iy==0x7ff00000) { 92 switch(m) { 93 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 94 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 95 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 96 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 97 } 98 } else { 99 switch(m) { 100 case 0: return zero ; /* atan(+...,+INF) */ 101 case 1: return -zero ; /* atan(-...,+INF) */ 102 case 2: return pi+tiny ; /* atan(+...,-INF) */ 103 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 104 } 105 } 106 } 107 /* when y is INF */ 108 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 109 110 /* compute y/x */ 111 k = (iy-ix)>>20; 112 if(k > 60) { /* |y/x| > 2**60 */ 113 z=pi_o_2+0.5*pi_lo; 114 m&=1; 115 } 116 else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */ 117 else z=atan(fabs(y/x)); /* safe to do y/x */ 118 switch (m) { 119 case 0: return z ; /* atan(+,+) */ 120 case 1: 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 } 126 127 #if LDBL_MANT_DIG == 53 128 __weak_reference(atan2, atan2l); 129 #endif 130