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 13 /* atan2(y,x) 14 * Method : 15 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 16 * 2. Reduce x to positive by (if x and y are unexceptional): 17 * ARG (x+iy) = arctan(y/x) ... if x > 0, 18 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, 19 * 20 * Special cases: 21 * 22 * ATAN2((anything), NaN ) is NaN; 23 * ATAN2(NAN , (anything) ) is NaN; 24 * ATAN2(+-0, +(anything but NaN)) is +-0 ; 25 * ATAN2(+-0, -(anything but NaN)) is +-pi ; 26 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; 27 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; 28 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; 29 * ATAN2(+-INF,+INF ) is +-pi/4 ; 30 * ATAN2(+-INF,-INF ) is +-3pi/4; 31 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; 32 * 33 * Constants: 34 * The hexadecimal values are the intended ones for the following 35 * constants. The decimal values may be used, provided that the 36 * compiler will convert from decimal to binary accurately enough 37 * to produce the hexadecimal values shown. 38 */ 39 40 #include <float.h> 41 #include <math.h> 42 43 #include "math_private.h" 44 45 static const double 46 tiny = 1.0e-300, 47 zero = 0.0, 48 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ 49 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ 50 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 51 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 52 53 double 54 atan2(double y, double x) 55 { 56 double z; 57 int32_t k,m,hx,hy,ix,iy; 58 u_int32_t lx,ly; 59 60 EXTRACT_WORDS(hx,lx,x); 61 ix = hx&0x7fffffff; 62 EXTRACT_WORDS(hy,ly,y); 63 iy = hy&0x7fffffff; 64 if(((ix|((lx|-lx)>>31))>0x7ff00000)|| 65 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ 66 return x+y; 67 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ 68 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ 69 70 /* when y = 0 */ 71 if((iy|ly)==0) { 72 switch(m) { 73 case 0: 74 case 1: return y; /* atan(+-0,+anything)=+-0 */ 75 case 2: return pi+tiny;/* atan(+0,-anything) = pi */ 76 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ 77 } 78 } 79 /* when x = 0 */ 80 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 81 82 /* when x is INF */ 83 if(ix==0x7ff00000) { 84 if(iy==0x7ff00000) { 85 switch(m) { 86 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ 87 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ 88 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ 89 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ 90 } 91 } else { 92 switch(m) { 93 case 0: return zero ; /* atan(+...,+INF) */ 94 case 1: return -zero ; /* atan(-...,+INF) */ 95 case 2: return pi+tiny ; /* atan(+...,-INF) */ 96 case 3: return -pi-tiny ; /* atan(-...,-INF) */ 97 } 98 } 99 } 100 /* when y is INF */ 101 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; 102 103 /* compute y/x */ 104 k = (iy-ix)>>20; 105 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ 106 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ 107 else z=atan(fabs(y/x)); /* safe to do y/x */ 108 switch (m) { 109 case 0: return z ; /* atan(+,+) */ 110 case 1: { 111 u_int32_t zh; 112 GET_HIGH_WORD(zh,z); 113 SET_HIGH_WORD(z,zh ^ 0x80000000); 114 } 115 return z ; /* atan(-,+) */ 116 case 2: return pi-(z-pi_lo);/* atan(+,-) */ 117 default: /* case 3 */ 118 return (z-pi_lo)-pi;/* atan(-,-) */ 119 } 120 } 121 122 #if LDBL_MANT_DIG == DBL_MANT_DIG 123 __strong_alias(atan2l, atan2); 124 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 125