1 /* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */ 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 /* 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 "libm.h" 41 42 static const double 43 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 44 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ 45 46 double atan2(double y, double x) 47 { 48 double z; 49 uint32_t m,lx,ly,ix,iy; 50 51 if (isnan(x) || isnan(y)) 52 return x+y; 53 EXTRACT_WORDS(ix, lx, x); 54 EXTRACT_WORDS(iy, ly, y); 55 if ((ix-0x3ff00000 | lx) == 0) /* x = 1.0 */ 56 return atan(y); 57 m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */ 58 ix = ix & 0x7fffffff; 59 iy = iy & 0x7fffffff; 60 61 /* when y = 0 */ 62 if ((iy|ly) == 0) { 63 switch(m) { 64 case 0: 65 case 1: return y; /* atan(+-0,+anything)=+-0 */ 66 case 2: return pi; /* atan(+0,-anything) = pi */ 67 case 3: return -pi; /* atan(-0,-anything) =-pi */ 68 } 69 } 70 /* when x = 0 */ 71 if ((ix|lx) == 0) 72 return m&1 ? -pi/2 : pi/2; 73 /* when x is INF */ 74 if (ix == 0x7ff00000) { 75 if (iy == 0x7ff00000) { 76 switch(m) { 77 case 0: return pi/4; /* atan(+INF,+INF) */ 78 case 1: return -pi/4; /* atan(-INF,+INF) */ 79 case 2: return 3*pi/4; /* atan(+INF,-INF) */ 80 case 3: return -3*pi/4; /* atan(-INF,-INF) */ 81 } 82 } else { 83 switch(m) { 84 case 0: return 0.0; /* atan(+...,+INF) */ 85 case 1: return -0.0; /* atan(-...,+INF) */ 86 case 2: return pi; /* atan(+...,-INF) */ 87 case 3: return -pi; /* atan(-...,-INF) */ 88 } 89 } 90 } 91 /* |y/x| > 0x1p64 */ 92 if (ix+(64<<20) < iy || iy == 0x7ff00000) 93 return m&1 ? -pi/2 : pi/2; 94 95 /* z = atan(|y/x|) without spurious underflow */ 96 if ((m&2) && iy+(64<<20) < ix) /* |y/x| < 0x1p-64, x<0 */ 97 z = 0; 98 else 99 z = atan(fabs(y/x)); 100 switch (m) { 101 case 0: return z; /* atan(+,+) */ 102 case 1: return -z; /* atan(-,+) */ 103 case 2: return pi - (z-pi_lo); /* atan(+,-) */ 104 default: /* case 3 */ 105 return (z-pi_lo) - pi; /* atan(-,-) */ 106 } 107 } 108