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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;
+}
+