gcc/libquadmath/math/hypotq.c

/*
 * ====================================================
 * 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 = 1.0L;
      GET_FLT128_MSW64(high,t1);
      SET_FLT128_MSW64(t1,high+(k<<48));
      return t1*w;
  } else return w;
}