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
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
| /*** bigint.c ***/
/* This is a very crude large integer package. The purpose is to teach, not to
be efficient. See freelip or miracl for very efficient code or check out the
commercial packages like Macsyma, Maple or the other similar products. The basis
of these routines come from J.W. Crenshaw and several articles in his "Programmers
Toolbox" in Embedded Systems Programming magazine from Dec. 1996 thru Sept. 1997
*/
#include <stdio.h>
#include "bigint.h"
/* clear all bits in a large integer storage block. */
void int_null( BIGINT *a)
{
INDEX i;
INTLOOP (i) a->hw[i] = 0;
}
/* copy one BIGINT block to another */
void int_copy(BIGINT *a, BIGINT *b)
{
INDEX i;
INTLOOP (i) b->hw[i] = a->hw[i];
}
/* for use in the far distant future, convert a packed field to a large
integer. Does a simple expansion. The large integer is 4 times bigger
to accomodate multiplication (once!).
*/
void field_to_int( FIELD2N *a, BIGINT *b)
{
INDEX i, j;
int_null( b);
for (i=NUMWORD; i>=0; i--)
{
j = INTMAX - ((NUMWORD - i)<<1);
b->hw[j] = a->e[i] & LOMASK;
j--;
b->hw[j] = (a->e[i] & HIMASK) >> HALFSIZE;
}
}
/* Pack a BIGINT variable back into a FIELD2N size one. */
void int_to_field( BIGINT *a, FIELD2N *b)
{
INDEX i, j;
SUMLOOP(i)
{
j = (i + MAXLONG) << 1;
b->e[i] = a->hw[j+1] | (a->hw[j] << HALFSIZE);
}
}
/* Negate a BIGINT in place. Each half word is complemented, then we add 1 */
void int_neg( BIGINT *a)
{
INDEX i;
INTLOOP(i) a->hw[i] = ~a->hw[i] & LOMASK;
INTLOOP(i)
{
a->hw[i]++;
if (a->hw[i] & LOMASK) break;
a->hw[i] &= LOMASK;
}
}
/* add two BIGINTS to get a third. c = a + b
Unlike the polynomial or ONB math, c can be one of a or b
*/
void int_add( BIGINT *a, BIGINT *b, BIGINT *c)
{
INDEX i;
ELEMENT ec;
ec = 0;
INTLOOP (i)
{
/* add previous carry bit to each term */
ec = a->hw[i] + b->hw[i] + (ec >> HALFSIZE);
c->hw[i] = ec & LOMASK;
}
}
/* subtract two BIGINTS, c = a - b == a + (-b).
as in addition, c can point to a or b and still works
*/
void int_sub( BIGINT *a, BIGINT *b, BIGINT *c)
{
BIGINT negb;
int_copy( b, &negb);
int_neg( &negb);
int_add( a, &negb, c);
}
/* multiply two BIGINTs to get a third.
Do NOT attempt to do 2 multiplies in a row without a division in between.
You may get an overflow and there is no provision in this code to return
an error condition for that. See more advanced packages for correct way
to do this. c can *not* be one of a or b, it must be a separate storage
location.
*/
void int_mul( BIGINT *a, BIGINT *b, BIGINT *c)
{
ELEMENT ea, eb, mul;
INDEX i, j, k;
BIGINT sum;
int_null(c);
for ( i = INTMAX; i > INTMAX/2; i--)
{
ea = a->hw[i];
int_null( &sum);
for ( j = INTMAX; j > INTMAX/2; j--)
{
eb = b->hw[j];
k = i + j - INTMAX;
mul = ea * eb + sum.hw[k];
sum.hw[k] = mul & LOMASK;
sum.hw[k-1] = mul >> HALFSIZE;
}
int_add( &sum, c, c);
}
}
/* unsigned divide. Input full sized numerator (top),
half sized denominator (bottom).
Output half sized quotient and half sized remainder.
Exceptionally crude but works ok for basics, error
conditions return zero results.
*/
void int_div( BIGINT *top, BIGINT *bottom, BIGINT *quotient, BIGINT *remainder)
{
BIGINT d, e;
ELEMENT mask;
INDEX l, m, n, i, j;
/* first step, initialize counters to most significant
bit position in top and bottom.
*/
int_copy( top, &d);
int_copy( bottom, &e);
l = (INTMAX + 1) * HALFSIZE;
for( i=0; i<=INTMAX; i++)
{
if (!d.hw[i]) l -= HALFSIZE;
else break;
}
mask = 1L << (HALFSIZE-1);
for ( j=0; j<HALFSIZE; j++)
{
if ( !(d.hw[i] & mask))
{
l--;
mask >>= 1;
}
else break;
}
/* same thing for bottom, compute msb position */
m = (INTMAX + 1) * HALFSIZE;
for( i=0; i<=INTMAX; i++)
{
if (!e.hw[i]) m -= HALFSIZE;
else break;
}
mask = 1L << (HALFSIZE-1);
for ( j=0; j<HALFSIZE; j++)
{
if ( !(e.hw[i] & mask))
{
m--;
mask >>= 1;
}
else break;
}
/* check for error inputs, does not check for zero, so is
actually incorrect.
*/
if (!m) /* x/1 = x */
{
int_copy( top, quotient);
int_null( remainder);
}
if (!l | (l<m)) /* 1/x = 0 */
{
int_null( quotient);
int_copy( bottom, remainder);
}
/* next step, shift bottom over to align msb with top msb */
n = l - m;
i = n;
while ( i > HALFSIZE )
{
for (j=0; j<INTMAX; j++) e.hw[j] = e.hw[j+1];
i -= HALFSIZE;
e.hw[INTMAX] = 0;
}
mask = 0;
while ( i > 0 )
{
INTLOOP (j)
{
e.hw[j] = (e.hw[j] << 1) | mask;
mask = e.hw[j] & CARRY ? 1 : 0;
e.hw[j] &= LOMASK;
}
i--;
}
/* main division loop. check to see if we can subtract shifted bottom
from what's left on top. If we can, set that bit in quotient and do
subtract. if we can't, just shift bottom right and repeat until only
remainder is left.
*/
int_null( quotient);
while ( n>=0)
{
i = INTMAX - l/HALFSIZE;
j = INTMAX - n/HALFSIZE;
while ( (d.hw[i] == e.hw[i]) && ( i<INTMAX) ) i++;
if ( d.hw[i] >= e.hw[i] )
{
int_sub( &d, &e, &d);
mask = 1L << ( n%HALFSIZE );
quotient->hw[j] |= mask;
}
INTLOOP(j)
{
if (j) mask = ( e.hw[j-1] & 1) ? CARRY : 0;
else mask = 0;
e.hw[j] = (e.hw[j] | mask) >> 1;
}
n--;
l--;
}
int_copy ( &d, remainder);
}
/* Convert ascii string of decimal digits into BIGINT binary.
Ignores out of range characters. This is very crude, 'a' = '1',
so watch out for input errors!
*/
void ascii_to_bigint( char *instring, BIGINT *outhex)
{
ELEMENT ch;
BIGINT ten, digit, temp;
INDEX i=0;
int_null( &ten); /* create decimal multiplier */
ten.hw[INTMAX] = 0xA;
int_null( &digit);
int_null( outhex);
while (ch = *instring++)
{
digit.hw[INTMAX] = ch & 0xF;
int_mul( outhex, &ten, &temp);
if (digit.hw[INTMAX] > 9) continue;
int_add( &temp, &digit, outhex);
}
}
/* Convert binary BIGINT to ascii string. Assumes destination has
enough characters to hold result. This is 4*HALFSIZE*MAXLONG bits
= Log(2)*4*HALFSIZE*MAXLONG = 1.20412*HALFSIZE*MAXLONG characters
or about 5/4*HALFSIZE*MAXLONG chars. Works backwards and blank
fills destination string.
*/
void bigint_to_ascii( BIGINT *inhex, char *outstring)
{
BIGINT top, ten, quotient, remainder;
ELEMENT check;
INDEX i;
int_copy( inhex, &top);
int_null( &ten); /* create constant 10 */
ten.hw[INTMAX] = 0xA;
for (i=0; i<MAXSTRING; i++) *outstring++ = ' '; /* blank fill and null string */
outstring--;
*outstring-- = 0;
check = 1;
while (check)
{
int_div( &top, &ten, "ient, &remainder);
*outstring-- = remainder.hw[INTMAX] | '0';
check = 0;
INTLOOP(i) check |= quotient.hw[i];
int_copy( "ient, &top);
}
} |
Opération sur de grands entiers
Répondre avec citation
Envoyé par tutu
:
Partager