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202 lines
4.2 KiB
C
202 lines
4.2 KiB
C
/* _sqrt.c
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*
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* Square root
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, _sqrt();
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*
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* y = _sqrt( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the square root of x.
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*
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* Range reduction involves isolating the power of two of the
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* argument and using a polynomial approximation to obtain
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* a rough value for the square root. Then Heron's iteration
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* is used three times to converge to an accurate value.
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*
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*
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*
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* ACCURACY:
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*
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC 0, 10 60000 2.1e-17 7.9e-18
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* IEEE 0,1.7e308 30000 1.7e-16 6.3e-17
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*
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* _sqrt domain x < 0 0.0
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*
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*/
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
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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 are met:
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1. Redistributions of source code must retain the above copyright notice,
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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. Neither the name of the <ORGANIZATION> nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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AND 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 COPYRIGHT OWNER OR CONTRIBUTORS BE
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LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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POSSIBILITY OF SUCH DAMAGE.
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*/
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#include "mconf.h"
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#ifdef ANSIPROT
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extern double frexp ( double, int * );
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extern double ldexp ( double, int );
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#else
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double frexp(), ldexp();
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#endif
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extern double SQRT2; /* _sqrt2 = 1.41421356237309504880 */
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double c_sqrt(x)
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double x;
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{
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int e;
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#ifndef UNK
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short *q;
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#endif
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double z, w;
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if( x <= 0.0 )
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{
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if( x < 0.0 )
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mtherr( "_sqrt", DOMAIN );
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return( 0.0 );
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}
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w = x;
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/* separate exponent and significand */
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#ifdef UNK
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z = frexp( x, &e );
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#endif
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#ifdef DEC
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q = (short *)&x;
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e = ((*q >> 7) & 0377) - 0200;
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*q &= 0177;
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*q |= 040000;
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z = x;
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#endif
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/* Note, frexp and ldexp are used in order to
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* handle denormal numbers properly.
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*/
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#ifdef IBMPC
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z = frexp( x, &e );
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q = (short *)&x;
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q += 3;
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/*
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e = ((*q >> 4) & 0x0fff) - 0x3fe;
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*q &= 0x000f;
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*q |= 0x3fe0;
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z = x;
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*/
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#endif
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#ifdef MIEEE
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z = frexp( x, &e );
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q = (short *)&x;
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/*
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e = ((*q >> 4) & 0x0fff) - 0x3fe;
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*q &= 0x000f;
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*q |= 0x3fe0;
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z = x;
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*/
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#endif
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/* approximate square root of number between 0.5 and 1
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* relative error of approximation = 7.47e-3
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*/
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x = 4.173075996388649989089E-1 + 5.9016206709064458299663E-1 * z;
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/* adjust for odd powers of 2 */
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if( (e & 1) != 0 )
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x *= SQRT2;
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/* re-insert exponent */
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#ifdef UNK
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x = ldexp( x, (e >> 1) );
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#endif
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#ifdef DEC
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*q += ((e >> 1) & 0377) << 7;
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*q &= 077777;
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#endif
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#ifdef IBMPC
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x = ldexp( x, (e >> 1) );
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/*
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*q += ((e >>1) & 0x7ff) << 4;
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*q &= 077777;
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*/
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#endif
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#ifdef MIEEE
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x = ldexp( x, (e >> 1) );
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/*
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*q += ((e >>1) & 0x7ff) << 4;
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*q &= 077777;
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*/
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#endif
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/* Newton iterations: */
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#ifdef UNK
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x = 0.5*(x + w/x);
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x = 0.5*(x + w/x);
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x = 0.5*(x + w/x);
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#endif
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/* Note, assume the square root cannot be denormal,
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* so it is safe to use integer exponent operations here.
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*/
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#ifdef DEC
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x += w/x;
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*q -= 0200;
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x += w/x;
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*q -= 0200;
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x += w/x;
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*q -= 0200;
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#endif
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#ifdef IBMPC
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x += w/x;
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*q -= 0x10;
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x += w/x;
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*q -= 0x10;
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x += w/x;
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*q -= 0x10;
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#endif
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#ifdef MIEEE
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x += w/x;
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*q -= 0x10;
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x += w/x;
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*q -= 0x10;
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x += w/x;
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*q -= 0x10;
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#endif
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return(x);
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}
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