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authorAaron Spike <aaron@ekips.org>2006-04-12 13:20:54 +0000
committeracspike <acspike@users.sourceforge.net>2006-04-12 13:20:54 +0000
commitddfaffe08d23e4663fe759d67ae33fd67fc9ce5b (patch)
tree234f5425a7ef7058e69dc2ab77f89810e4f3ed91 /src/dom/js/fdlibm/e_hypot.c
parentfix 1466070 (diff)
downloadinkscape-ddfaffe08d23e4663fe759d67ae33fd67fc9ce5b.tar.gz
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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;
-}