121 lines
4.0 KiB
C
121 lines
4.0 KiB
C
/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)cbrt.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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#include <sys/cdefs.h>
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/* kahan's cube root (53 bits IEEE double precision)
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* for IEEE machines only
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* coded in C by K.C. Ng, 4/30/85
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*
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* Accuracy:
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* better than 0.667 ulps according to an error analysis. Maximum
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* error observed was 0.666 ulps in an 1,000,000 random arguments test.
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*
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* Warning: this code is semi machine dependent; the ordering of words in
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* a floating point number must be known in advance. I assume that the
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* long interger at the address of a floating point number will be the
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* leading 32 bits of that floating point number (i.e., sign, exponent,
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* and the 20 most significant bits).
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* On a National machine, it has different ordering; therefore, this code
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* must be compiled with flag -DNATIONAL.
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*/
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#if !defined(vax)&&!defined(tahoe)
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static const unsigned long
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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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static const double
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C= 19./35.,
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D= -864./1225.,
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E= 99./70.,
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F= 45./28.,
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G= 5./14.;
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double cbrt(x)
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double x;
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{
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double r,s,t=0.0,w;
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unsigned long *px = (unsigned long *) &x,
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*pt = (unsigned long *) &t,
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mexp,sign;
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#ifdef national /* ordering of words in a floating points number */
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const int n0=1,n1=0;
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#else /* national */
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const int n0=0,n1=1;
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#endif /* national */
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mexp=px[n0]&0x7ff00000;
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if(mexp==0x7ff00000) return(x); /* cbrt(NaN,INF) is itself */
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if(x==0.0) return(x); /* cbrt(0) is itself */
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sign=px[n0]&0x80000000; /* sign= sign(x) */
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px[n0] ^= sign; /* x=|x| */
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/* rough cbrt to 5 bits */
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if(mexp==0) /* subnormal number */
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{pt[n0]=0x43500000; /* set t= 2**54 */
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t*=x; pt[n0]=pt[n0]/3+B2;
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}
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else
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pt[n0]=px[n0]/3+B1;
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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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pt[n1]=0; pt[n0]+=0x00000001;
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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-t is exact */
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t=t+t*r;
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/* retore the sign bit */
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pt[n0] |= sign;
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return(t);
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}
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#endif
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