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/* sqrt.c: bcmath library file. */
/*
Copyright (C) 1991, 1992, 1993, 1994, 1997 Free Software Foundation, Inc.
Copyright (C) 2000 Philip A. Nelson
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details. (COPYING.LIB)
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to:
The Free Software Foundation, Inc.
59 Temple Place, Suite 330
Boston, MA 02111-1307 USA.
You may contact the author by:
e-mail: philnelson@acm.org
us-mail: Philip A. Nelson
Computer Science Department, 9062
Western Washington University
Bellingham, WA 98226-9062
*************************************************************************/
#include <config.h>
#include <stdio.h>
#include <assert.h>
#include <stdlib.h>
#include <ctype.h>
#include <stdarg.h>
#include "bcmath.h"
#include "private.h"
/* Take the square root NUM and return it in NUM with SCALE digits
after the decimal place. */
int
bc_sqrt (bc_num *num, int scale TSRMLS_DC)
{
int rscale, cmp_res, done;
int cscale;
bc_num guess, guess1, point5, diff;
/* Initial checks. */
cmp_res = bc_compare (*num, BCG(_zero_));
if (cmp_res < 0)
return 0; /* error */
else
{
if (cmp_res == 0)
{
bc_free_num (num);
*num = bc_copy_num (BCG(_zero_));
return 1;
}
}
cmp_res = bc_compare (*num, BCG(_one_));
if (cmp_res == 0)
{
bc_free_num (num);
*num = bc_copy_num (BCG(_one_));
return 1;
}
/* Initialize the variables. */
rscale = MAX (scale, (*num)->n_scale);
bc_init_num(&guess TSRMLS_CC);
bc_init_num(&guess1 TSRMLS_CC);
bc_init_num(&diff TSRMLS_CC);
point5 = bc_new_num (1,1);
point5->n_value[1] = 5;
/* Calculate the initial guess. */
if (cmp_res < 0)
{
/* The number is between 0 and 1. Guess should start at 1. */
guess = bc_copy_num (BCG(_one_));
cscale = (*num)->n_scale;
}
else
{
/* The number is greater than 1. Guess should start at 10^(exp/2). */
bc_int2num (&guess,10);
bc_int2num (&guess1,(*num)->n_len);
bc_multiply (guess1, point5, &guess1, 0 TSRMLS_CC);
guess1->n_scale = 0;
bc_raise (guess, guess1, &guess, 0 TSRMLS_CC);
bc_free_num (&guess1);
cscale = 3;
}
/* Find the square root using Newton's algorithm. */
done = FALSE;
while (!done)
{
bc_free_num (&guess1);
guess1 = bc_copy_num (guess);
bc_divide (*num, guess, &guess, cscale TSRMLS_CC);
bc_add (guess, guess1, &guess, 0);
bc_multiply (guess, point5, &guess, cscale TSRMLS_CC);
bc_sub (guess, guess1, &diff, cscale+1);
if (bc_is_near_zero (diff, cscale))
{
if (cscale < rscale+1)
cscale = MIN (cscale*3, rscale+1);
else
done = TRUE;
}
}
/* Assign the number and clean up. */
bc_free_num (num);
bc_divide (guess,BCG(_one_),num,rscale TSRMLS_CC);
bc_free_num (&guess);
bc_free_num (&guess1);
bc_free_num (&point5);
bc_free_num (&diff);
return 1;
}