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 /* @(#)e_hypot.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_hypot(x,y) * * Method : * If (assume round-to-nearest) z=x*x+y*y * has error less than ieee_sqrt(2)/2 ulp, than * sqrt(z) has error less than 1 ulp (exercise). * * So, compute ieee_sqrt(x*x+y*y) with some care as * follows to get the error below 1 ulp: * * Assume x>y>0; * (if possible, set rounding to round-to-nearest) * 1. if x > 2y use * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y * where x1 = x with lower 32 bits cleared, x2 = x-x1; else * 2. if x <= 2y use * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, * y1= y with lower 32 bits chopped, y2 = y-y1. * * NOTE: scaling may be necessary if some argument is too * large or too tiny * * Special cases: * hypot(x,y) is INF if x or y is +INF or -INF; else * hypot(x,y) is NAN if x or y is NAN. * * Accuracy: * hypot(x,y) returns ieee_sqrt(x^2+y^2) with error less * than 1 ulps (units in the last place) */ #include "fdlibm.h" #ifdef __STDC__ double __ieee754_hypot(double x, double y) #else double __ieee754_hypot(x,y) double x, y; #endif { double a=x,b=y,t1,t2,y1,y2,w; int j,k,ha,hb; ha = __HI(x)&0x7fffffff; /* high word of x */ hb = __HI(y)&0x7fffffff; /* high word of y */ if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} __HI(a) = ha; /* a <- |a| */ __HI(b) = hb; /* b <- |b| */ if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ k=0; if(ha > 0x5f300000) { /* a>2**500 */ if(ha >= 0x7ff00000) { /* Inf or NaN */ w = a+b; /* for sNaN */ if(((ha&0xfffff)|__LO(a))==0) w = a; if(((hb^0x7ff00000)|__LO(b))==0) w = b; return w; } /* scale a and b by 2**-600 */ ha -= 0x25800000; hb -= 0x25800000; k += 600; __HI(a) = ha; __HI(b) = hb; } if(hb < 0x20b00000) { /* b < 2**-500 */ if(hb <= 0x000fffff) { /* subnormal b or 0 */ if((hb|(__LO(b)))==0) return a; t1=0; __HI(t1) = 0x7fd00000; /* t1=2^1022 */ b *= t1; a *= t1; k -= 1022; } else { /* scale a and b by 2^600 */ ha += 0x25800000; /* a *= 2^600 */ hb += 0x25800000; /* b *= 2^600 */ k -= 600; __HI(a) = ha; __HI(b) = hb; } } /* medium size a and b */ w = a-b; if (w>b) { t1 = 0; __HI(t1) = ha; t2 = a-t1; w = ieee_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); } else { a = a+a; y1 = 0; __HI(y1) = hb; y2 = b - y1; t1 = 0; __HI(t1) = ha+0x00100000; t2 = a - t1; w = ieee_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); } if(k!=0) { t1 = 1.0; __HI(t1) += (k<<20); return t1*w; } else return w; }
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