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/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* ***** BEGIN LICENSE BLOCK *****
* Version: MPL 1.1/GPL 2.0/LGPL 2.1
*
* The contents of this file are subject to the Mozilla Public License Version
* 1.1 (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* Software distributed under the License is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
* for the specific language governing rights and limitations under the
* License.
*
* The Original Code is Mozilla Communicator client code, released
* March 31, 1998.
*
* The Initial Developer of the Original Code is
* Sun Microsystems, Inc.
* Portions created by the Initial Developer are Copyright (C) 1998
* the Initial Developer. All Rights Reserved.
*
* Contributor(s):
*
* Alternatively, the contents of this file may be used under the terms of
* either of the GNU General Public License Version 2 or later (the "GPL"),
* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
* in which case the provisions of the GPL or the LGPL are applicable instead
* of those above. If you wish to allow use of your version of this file only
* under the terms of either the GPL or the LGPL, and not to allow others to
* use your version of this file under the terms of the MPL, indicate your
* decision by deleting the provisions above and replace them with the notice
* and other provisions required by the GPL or the LGPL. If you do not delete
* the provisions above, a recipient may use your version of this file under
* the terms of any one of the MPL, the GPL or the LGPL.
*
* ***** END LICENSE BLOCK ***** */
/* @(#)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 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 "fdlibm.h"
#ifdef __STDC__
double __ieee754_hypot(double x, double y)
#else
double __ieee754_hypot(x,y)
double x, y;
#endif
{
fd_twoints ux, uy;
double a=x,b=y,t1,t2,y1,y2,w;
int j,k,ha,hb;
ux.d = x; uy.d = y;
ha = __HI(ux)&0x7fffffff; /* high word of x */
hb = __HI(uy)&0x7fffffff; /* high word of y */
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
ux.d = a; uy.d = b;
__HI(ux) = ha; /* a <- |a| */
__HI(uy) = hb; /* b <- |b| */
a = ux.d; b = uy.d;
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 */
ux.d = a; uy.d = b;
if(((ha&0xfffff)|__LO(ux))==0) w = a;
if(((hb^0x7ff00000)|__LO(uy))==0) w = b;
return w;
}
/* scale a and b by 2**-600 */
ha -= 0x25800000; hb -= 0x25800000; k += 600;
ux.d = a; uy.d = b;
__HI(ux) = ha;
__HI(uy) = hb;
a = ux.d; b = uy.d;
}
if(hb < 0x20b00000) { /* b < 2**-500 */
if(hb <= 0x000fffff) { /* subnormal b or 0 */
uy.d = b;
if((hb|(__LO(uy)))==0) return a;
t1=0;
ux.d = t1;
__HI(ux) = 0x7fd00000; /* t1=2^1022 */
t1 = ux.d;
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;
ux.d = a; uy.d = b;
__HI(ux) = ha;
__HI(uy) = hb;
a = ux.d; b = uy.d;
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = 0;
ux.d = t1;
__HI(ux) = ha;
t1 = ux.d;
t2 = a-t1;
w = fd_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
ux.d = y1;
__HI(ux) = hb;
y1 = ux.d;
y2 = b - y1;
t1 = 0;
ux.d = t1;
__HI(ux) = ha+0x00100000;
t1 = ux.d;
t2 = a - t1;
w = fd_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
t1 = 1.0;
ux.d = t1;
__HI(ux) += (k<<20);
t1 = ux.d;
return t1*w;
} else return w;
}
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