1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
|
/* 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 (num, scale)
bc_num *num;
int scale;
{
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);
bc_init_num(&guess1);
bc_init_num(&diff);
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);
guess1->n_scale = 0;
bc_raise (guess, guess1, &guess, 0);
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);
bc_add (guess, guess1, &guess, 0);
bc_multiply (guess, point5, &guess, cscale);
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);
bc_free_num (&guess);
bc_free_num (&guess1);
bc_free_num (&point5);
bc_free_num (&diff);
return 1;
}
|