1 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 /* atan2(y,x) 15 * Method : 16 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 17 * 2. Reduce x to positive by (if x and y are unexceptional): 18 * ARG (x+iy) = arctan(y/x) ... if x > 0, 19 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 20 * 21 * Special cases: 22 * 23 * ATAN2((anything), NaN ) is NaN; 24 * ATAN2(NAN , (anything) ) is NaN; 25 * ATAN2(+-0, +(anything but NaN)) is +-0 ; 26 * ATAN2(+-0, -(anything but NaN)) is +-pi ; 27 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 28 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 29 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 30 * ATAN2(+-INF,+INF ) is +-pi/4 ; 31 * ATAN2(+-INF,-INF ) is +-3pi/4; 32 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 33 * 34 * Constants: 35 * The hexadecimal values are the intended ones for the following 36 * constants. The decimal values may be used, provided that the 37 * compiler will convert from decimal to binary accurately enough 38 * to produce the hexadecimal values shown. 39 */ 40 41 #include <float.h> 42 43 #include "math.h" 44 #include "math_private.h" 45 46 static volatile double 47 tiny = 1.0e-300; 48 static const double 49 zero = 0.0, 50 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 51 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 52 pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ 53 static volatile double 54 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 55 56 double 57 atan2(double y, double x) 58 { 59 double z; 60 int32_t k,m,hx,hy,ix,iy; 61 u_int32_t lx,ly; 62 63 EXTRACT_WORDS(hx,lx,x); 64 ix = hx&0x7fffffff; 65 EXTRACT_WORDS(hy,ly,y); 66 iy = hy&0x7fffffff; 67 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 68 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 69 return nan_mix(x, y); 70 if(hx==0x3ff00000&&lx==0) return atan(y); /* x=1.0 */ 71 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 72 73 /* when y = 0 */ 74 if((iy|ly)==0) { 75 switch(m) { 76 case 0: 77 case 1: return y; /* atan(+-0,+anything)=+-0 */ 78 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 79 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 80 } 81 } 82 /* when x = 0 */ 83 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 84 85 /* when x is INF */ 86 if(ix==0x7ff00000) { 87 if(iy==0x7ff00000) { 88 switch(m) { 89 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 90 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 91 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 92 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 93 } 94 } else { 95 switch(m) { 96 case 0: return zero ; /* atan(+...,+INF) */ 97 case 1: return -zero ; /* atan(-...,+INF) */ 98 case 2: return pi+tiny ; /* atan(+...,-INF) */ 99 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 100 } 101 } 102 } 103 /* when y is INF */ 104 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 105 106 /* compute y/x */ 107 k = (iy-ix)>>20; 108 if(k > 60) { /* |y/x| > 2**60 */ 109 z=pi_o_2+0.5*pi_lo; 110 m&=1; 111 } 112 else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */ 113 else z=atan(fabs(y/x)); /* safe to do y/x */ 114 switch (m) { 115 case 0: return z ; /* atan(+,+) */ 116 case 1: return -z ; /* atan(-,+) */ 117 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 118 default: /* case 3 */ 119 return (z-pi_lo)-pi;/* atan(-,-) */ 120 } 121 } 122 123 #if LDBL_MANT_DIG == 53 124 __weak_reference(atan2, atan2l); 125 #endif 126