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/*

 * ====================================================

 * 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.

 * ====================================================

 */

/* From e_hypotl.c -- long double version of e_hypot.c.

 * Conversion to long double by Jakub Jelinek, jakub@redhat.com.

 * Conversion to __float128 by FX Coudert, fxcoudert@gcc.gnu.org.

 */

/* hypotq(x,y)

 *

 * Method :

 *      If (assume round-to-nearest) z=x*x+y*y

 *      has error less than sqrtl(2)/2 ulp, than

 *      sqrtl(z) has error less than 1 ulp (exercise).

 *

 *      So, compute sqrtl(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:

 *      hypotq(x,y) is INF if x or y is +INF or -INF; else

 *      hypotq(x,y) is NAN if x or y is NAN.

 *

 * Accuracy:

 *      hypotq(x,y) returns sqrtl(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 */

         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;

      } 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 = 1.0Q;

      GET_FLT128_MSW64(high,t1);

      SET_FLT128_MSW64(t1,high+(k<<48));

      return t1*w;

  } else return w;

}