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 /* @(#)e_atan2.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== * */ /* __ieee754_atan2(y,x) * Method : * 1. Reduce y to positive by ieee_atan2(y,x)=-ieee_atan2(-y,x). * 2. Reduce x to positive by (if x and y are unexceptional): * ARG (x+iy) = arctan(y/x) ... if x > 0, * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, * * Special cases: * * ATAN2((anything), NaN ) is NaN; * ATAN2(NAN , (anything) ) is NaN; * ATAN2(+-0, +(anything but NaN)) is +-0 ; * ATAN2(+-0, -(anything but NaN)) is +-pi ; * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; * ATAN2(+-INF,+INF ) is +-pi/4 ; * ATAN2(+-INF,-INF ) is +-3pi/4; * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; * * Constants: * The hexadecimal values are the intended ones for the following * constants. The decimal values may be used, provided that the * compiler will convert from decimal to binary accurately enough * to produce the hexadecimal values shown. */ #include "fdlibm.h" #ifdef __STDC__ static const double #else static double #endif tiny = 1.0e-300, zero = 0.0, pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ #ifdef __STDC__ double __ieee754_atan2(double y, double x) #else double __ieee754_atan2(y,x) double y,x; #endif { double z; int k,m,hx,hy,ix,iy; unsigned lx,ly; hx = __HI(x); ix = hx&0x7fffffff; lx = __LO(x); hy = __HI(y); iy = hy&0x7fffffff; ly = __LO(y); if(((ix|((lx|-lx)>>31))>0x7ff00000)|| ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ return x+y; if((hx-0x3ff00000|lx)==0) return ieee_atan(y); /* x=1.0 */ m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ /* when y = 0 */ if((iy|ly)==0) { switch(m) { case 0: case 1: return y; /* ieee_atan(+-0,+anything)=+-0 */ case 2: return pi+tiny;/* ieee_atan(+0,-anything) = pi */ case 3: return -pi-tiny;/* ieee_atan(-0,-anything) =-pi */ } } /* when x = 0 */ if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; /* when x is INF */ if(ix==0x7ff00000) { if(iy==0x7ff00000) { switch(m) { case 0: return pi_o_4+tiny;/* ieee_atan(+INF,+INF) */ case 1: return -pi_o_4-tiny;/* ieee_atan(-INF,+INF) */ case 2: return 3.0*pi_o_4+tiny;/*ieee_atan(+INF,-INF)*/ case 3: return -3.0*pi_o_4-tiny;/*ieee_atan(-INF,-INF)*/ } } else { switch(m) { case 0: return zero ; /* ieee_atan(+...,+INF) */ case 1: return -zero ; /* ieee_atan(-...,+INF) */ case 2: return pi+tiny ; /* ieee_atan(+...,-INF) */ case 3: return -pi-tiny ; /* ieee_atan(-...,-INF) */ } } } /* when y is INF */ if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; /* compute y/x */ k = (iy-ix)>>20; if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ else z=ieee_atan(ieee_fabs(y/x)); /* safe to do y/x */ switch (m) { case 0: return z ; /* ieee_atan(+,+) */ case 1: __HI(z) ^= 0x80000000; return z ; /* ieee_atan(-,+) */ case 2: return pi-(z-pi_lo);/* ieee_atan(+,-) */ default: /* case 3 */ return (z-pi_lo)-pi;/* ieee_atan(-,-) */ } }
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