/* @(#)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. * ==================================================== */ //#include <sys/cdefs.h> //__FBSDID("$FreeBSD$"); /* __ieee754_hypot(x,y) * * Method : * If (assume round-to-nearest) z=x*x+y*y * has error less than sqrt(2)/2 ulp, than * sqrt(z) has error less than 1 ulp (exercise). * * So, compute 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 sqrt(x^2+y^2) with error less * than 1 ulps (units in the last place) */ #include <float.h> #include "math_private.h" double __ieee754_hypot(double x, double y) { double a,b,t1,t2,y1,y2,w; int32_t j,k,ha,hb; GET_HIGH_WORD(ha,x); ha &= 0x7fffffff; GET_HIGH_WORD(hb,y); hb &= 0x7fffffff; if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} a = fabs(a); b = fabs(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 */ u_int32_t low; /* Use original arg order iff result is NaN; quieten sNaNs. */ w = fabs(x+0.0)-fabs(y+0.0); GET_LOW_WORD(low,a); if(((ha&0xfffff)|low)==0) w = a; GET_LOW_WORD(low,b); if(((hb^0x7ff00000)|low)==0) w = b; return w; } /* scale a and b by 2**-600 */ ha -= 0x25800000; hb -= 0x25800000; k += 600; SET_HIGH_WORD(a,ha); SET_HIGH_WORD(b,hb); } if(hb < 0x20b00000) { /* b < 2**-500 */ if(hb <= 0x000fffff) { /* subnormal b or 0 */ u_int32_t low; GET_LOW_WORD(low,b); if((hb|low)==0) return a; t1=0; SET_HIGH_WORD(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; SET_HIGH_WORD(a,ha); SET_HIGH_WORD(b,hb); } } /* medium size a and b */ w = a-b; if (w>b) { t1 = 0; SET_HIGH_WORD(t1,ha); t2 = a-t1; w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); } else { a = a+a; y1 = 0; SET_HIGH_WORD(y1,hb); y2 = b - y1; t1 = 0; SET_HIGH_WORD(t1,ha+0x00100000); t2 = a - t1; w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); } if(k!=0) { u_int32_t high; t1 = 1.0; GET_HIGH_WORD(high,t1); SET_HIGH_WORD(t1,high+(k<<20)); return t1*w; } else return w; }