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
132
133
134
135
136
|
#include <stdio.h>
#include <stdlib.h>
#include "boolector.h"
#include "utils/btorutil.h"
int
main (int argc, char **argv)
{
int num_bits, num_bits_index, num_elements, i, num_iterations;
Btor *btor;
BoolectorNode **indices, *array, *eq, *ult, *ulte, *ugt, *temp, *read1;
BoolectorNode *read2, *formula, *val, *index, *found, *sorted, *low, *high;
BoolectorNode *two, *one, *mid, *sub, *udiv, *inc, *dec;
BoolectorSort sort_index, sort_elem, sort_array;
if (argc != 3)
{
printf ("Usage: ./binarysearch <num-bits> <num-elements>\n");
return 1;
}
num_bits = atoi (argv[1]);
if (num_bits <= 0)
{
printf ("Number of bits must be greater than zero\n");
return 1;
}
num_elements = atoi (argv[2]);
if (num_elements < 4)
{
printf ("Number of elements must be at least four\n");
return 1;
}
if (!btor_util_is_power_of_2 (num_elements))
{
printf ("Number of elements must be a power of two\n");
return 1;
}
num_bits_index = btor_util_log_2 (num_elements);
/* binary search needs log2(size(array)) + 1 iterations in the worst case */
num_iterations = num_bits_index + 1;
btor = boolector_new ();
sort_elem = boolector_bitvec_sort (btor, num_bits);
sort_index = boolector_bitvec_sort (btor, num_bits_index);
sort_array = boolector_array_sort (btor, sort_index, sort_elem);
boolector_set_opt (btor, BTOR_OPT_REWRITE_LEVEL, 0);
indices = (BoolectorNode **) malloc (sizeof (BtorNode *) * num_elements);
for (i = 0; i < num_elements; i++)
indices[i] = boolector_int (btor, i, sort_index);
array = boolector_array (btor, sort_array, "array");
/* we write arbitrary search value into array at an arbitrary index */
val = boolector_var (btor, sort_elem, "search_val");
index = boolector_var (btor, sort_index, "search_index");
temp = boolector_write (btor, array, index, val);
boolector_release (btor, array);
array = temp;
/* we assume that array is sorted */
sorted = boolector_const (btor, "1");
for (i = 0; i < num_elements - 1; i++)
{
read1 = boolector_read (btor, array, indices[i]);
read2 = boolector_read (btor, array, indices[i + 1]);
ulte = boolector_ulte (btor, read1, read2);
temp = boolector_and (btor, sorted, ulte);
boolector_release (btor, sorted);
sorted = temp;
boolector_release (btor, read1);
boolector_release (btor, read2);
boolector_release (btor, ulte);
}
/* binary search algorithm */
low = boolector_int (btor, 0, sort_index);
high = boolector_int (btor, num_elements - 1, sort_index);
two = boolector_int (btor, 2, sort_index);
one = boolector_int (btor, 1, sort_index);
found = boolector_const (btor, "0");
for (i = 0; i < num_iterations; i++)
{
/* compute mid */
sub = boolector_sub (btor, high, low);
udiv = boolector_udiv (btor, sub, two);
mid = boolector_add (btor, low, udiv);
/* read mid element */
read1 = boolector_read (btor, array, mid);
/* compare element with search val */
eq = boolector_eq (btor, val, read1);
ult = boolector_ult (btor, val, read1);
ugt = boolector_ugt (btor, val, read1);
/* found element ? */
temp = boolector_or (btor, found, eq);
boolector_release (btor, found);
found = temp;
/* adapt high (if necessary) */
dec = boolector_sub (btor, mid, one);
temp = boolector_cond (btor, ult, dec, high);
boolector_release (btor, high);
high = temp;
/* adapt low (if necessary) */
inc = boolector_add (btor, mid, one);
temp = boolector_cond (btor, ugt, inc, low);
boolector_release (btor, low);
low = temp;
boolector_release (btor, sub);
boolector_release (btor, udiv);
boolector_release (btor, mid);
boolector_release (btor, eq);
boolector_release (btor, ult);
boolector_release (btor, ugt);
boolector_release (btor, read1);
boolector_release (btor, inc);
boolector_release (btor, dec);
}
/* the array is sorted implies that we have found the element */
formula = boolector_implies (btor, sorted, found);
/* we negate the formula and show that it is unsatisfiable */
temp = boolector_not (btor, formula);
boolector_release (btor, formula);
formula = temp;
boolector_dump_btor_node (btor, stdout, formula);
/* clean up */
for (i = 0; i < num_elements; i++) boolector_release (btor, indices[i]);
boolector_release (btor, formula);
boolector_release (btor, index);
boolector_release (btor, val);
boolector_release (btor, found);
boolector_release (btor, array);
boolector_release (btor, sorted);
boolector_release (btor, low);
boolector_release (btor, high);
boolector_release (btor, two);
boolector_release (btor, one);
boolector_release_sort (btor, sort_index);
boolector_release_sort (btor, sort_elem);
boolector_release_sort (btor, sort_array);
boolector_delete (btor);
free (indices);
return 0;
}
|
