2001-09-20 04:02:59 +04:00
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/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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1998-11-05 03:08:43 +03:00
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*
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2003-11-15 03:11:16 +03:00
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* ***** BEGIN LICENSE BLOCK *****
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* Version: MPL 1.1/GPL 2.0/LGPL 2.1
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1998-11-05 03:08:43 +03:00
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*
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2003-11-15 03:11:16 +03:00
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* The contents of this file are subject to the Mozilla Public License Version
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* 1.1 (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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*
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* Software distributed under the License is distributed on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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* for the specific language governing rights and limitations under the
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* License.
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1998-11-05 03:08:43 +03:00
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*
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2001-09-20 04:02:59 +04:00
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* The Original Code is Mozilla Communicator client code, released
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* March 31, 1998.
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1999-09-29 03:12:09 +04:00
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*
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2003-11-15 03:11:16 +03:00
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* The Initial Developer of the Original Code is
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* Sun Microsystems, Inc.
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* Portions created by the Initial Developer are Copyright (C) 1998
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* the Initial Developer. All Rights Reserved.
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*
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* Contributor(s):
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*
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* Alternatively, the contents of this file may be used under the terms of
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* either of the GNU General Public License Version 2 or later (the "GPL"),
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* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
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* in which case the provisions of the GPL or the LGPL are applicable instead
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* of those above. If you wish to allow use of your version of this file only
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* under the terms of either the GPL or the LGPL, and not to allow others to
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* use your version of this file under the terms of the MPL, indicate your
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* decision by deleting the provisions above and replace them with the notice
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* and other provisions required by the GPL or the LGPL. If you do not delete
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* the provisions above, a recipient may use your version of this file under
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* the terms of any one of the MPL, the GPL or the LGPL.
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*
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* ***** END LICENSE BLOCK ***** */
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1998-11-05 03:08:43 +03:00
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/* @(#)s_cbrt.c 1.3 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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*/
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#include "fdlibm.h"
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/* cbrt(x)
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* Return cube root of x
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*/
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#ifdef __STDC__
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static const unsigned
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#else
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static unsigned
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#endif
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B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
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B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
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D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
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E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
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F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
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G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
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#ifdef __STDC__
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double fd_cbrt(double x)
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#else
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double fd_cbrt(x)
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double x;
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#endif
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{
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fd_twoints u;
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int hx;
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double r,s,t=0.0,w;
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unsigned sign;
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u.d = x;
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hx = __HI(u); /* high word of x */
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sign=hx&0x80000000; /* sign= sign(x) */
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hx ^=sign;
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if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
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if((hx|__LO(u))==0) {
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x = u.d;
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return(x); /* cbrt(0) is itself */
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}
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u.d = x;
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__HI(u) = hx; /* x <- |x| */
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x = u.d;
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/* rough cbrt to 5 bits */
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if(hx<0x00100000) /* subnormal number */
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{u.d = t; __HI(u)=0x43500000; t=u.d; /* set t= 2**54 */
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t*=x; __HI(u)=__HI(u)/3+B2;
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}
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else {
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u.d = t; __HI(u)=hx/3+B1; t = u.d;
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}
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/* new cbrt to 23 bits, may be implemented in single precision */
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r=t*t/x;
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s=C+r*t;
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t*=G+F/(s+E+D/s);
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/* chopped to 20 bits and make it larger than cbrt(x) */
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u.d = t;
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__LO(u)=0; __HI(u)+=0x00000001;
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t = u.d;
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/* one step newton iteration to 53 bits with error less than 0.667 ulps */
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s=t*t; /* t*t is exact */
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r=x/s;
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w=t+t;
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r=(r-t)/(w+r); /* r-s is exact */
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t=t+t*r;
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/* retore the sign bit */
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u.d = t;
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__HI(u) |= sign;
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t = u.d;
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return(t);
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}
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