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 /* e_hypotl.c -- long double version of e_hypot.c. * Conversion to long double by Jakub Jelinek, jakub@redhat.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* hypotq(x,y) * * Method : * If (assume round-to-nearest) z=x*x+y*y * has error less than sqrtq(2)/2 ulp, than * sqrtq(z) has error less than 1 ulp (exercise). * * So, compute sqrtq(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 64 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 64 bits cleared, t2 = 2x-t1, * y1= y with lower 64 bits chopped, y2 = y-y1. * * NOTE: scaling may be necessary if some argument is too * large or too tiny * * Special cases: * hypotl(x,y) is INF if x or y is +INF or -INF; else * hypotl(x,y) is NAN if x or y is NAN. * * Accuracy: * hypotl(x,y) returns sqrtq(x^2+y^2) with error less * than 1 ulps (units in the last place) */ #include "quadmath-imp.h" __float128 hypotq(__float128 x, __float128 y) { __float128 a,b,t1,t2,y1,y2,w; int64_t j,k,ha,hb; GET_FLT128_MSW64(ha,x); ha &= 0x7fffffffffffffffLL; GET_FLT128_MSW64(hb,y); hb &= 0x7fffffffffffffffLL; if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} SET_FLT128_MSW64(a,ha); /* a <- |a| */ SET_FLT128_MSW64(b,hb); /* b <- |b| */ if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */ k=0; if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */ if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */ uint64_t low; w = a+b; /* for sNaN */ if (issignalingq (a) || issignalingq (b)) return w; GET_FLT128_LSW64(low,a); if(((ha&0xffffffffffffLL)|low)==0) w = a; GET_FLT128_LSW64(low,b); if(((hb^0x7fff000000000000LL)|low)==0) w = b; return w; } /* scale a and b by 2**-9600 */ ha -= 0x2580000000000000LL; hb -= 0x2580000000000000LL; k += 9600; SET_FLT128_MSW64(a,ha); SET_FLT128_MSW64(b,hb); } if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */ if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */ uint64_t low; GET_FLT128_LSW64(low,b); if((hb|low)==0) return a; t1=0; SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */ b *= t1; a *= t1; k -= 16382; GET_FLT128_MSW64 (ha, a); GET_FLT128_MSW64 (hb, b); if (hb > ha) { t1 = a; a = b; b = t1; j = ha; ha = hb; hb = j; } } else { /* scale a and b by 2^9600 */ ha += 0x2580000000000000LL; /* a *= 2^9600 */ hb += 0x2580000000000000LL; /* b *= 2^9600 */ k -= 9600; SET_FLT128_MSW64(a,ha); SET_FLT128_MSW64(b,hb); } } /* medium size a and b */ w = a-b; if (w>b) { t1 = 0; SET_FLT128_MSW64(t1,ha); t2 = a-t1; w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1))); } else { a = a+a; y1 = 0; SET_FLT128_MSW64(y1,hb); y2 = b - y1; t1 = 0; SET_FLT128_MSW64(t1,ha+0x0001000000000000LL); t2 = a - t1; w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b))); } if(k!=0) { uint64_t high; t1 = 1; GET_FLT128_MSW64(high,t1); SET_FLT128_MSW64(t1,high+(k<<48)); w *= t1; math_check_force_underflow_nonneg (w); return w; } else return w; }