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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mptext.c,v 1.4 1999/12/22 15:56:56 mdw Exp $ |
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4 | * |
5 | * Textual representation of multiprecision numbers |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: mptext.c,v $ |
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33 | * Revision 1.4 1999/12/22 15:56:56 mdw |
34 | * Use clever recursive algorithm for writing numbers out. |
35 | * |
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36 | * Revision 1.3 1999/12/10 23:23:26 mdw |
37 | * Allocate slightly less memory. |
38 | * |
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39 | * Revision 1.2 1999/11/20 22:24:15 mdw |
40 | * Use function versions of MPX_UMULN and MPX_UADDN. |
41 | * |
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42 | * Revision 1.1 1999/11/17 18:02:16 mdw |
43 | * New multiprecision integer arithmetic suite. |
44 | * |
45 | */ |
46 | |
47 | /*----- Header files ------------------------------------------------------*/ |
48 | |
49 | #include <ctype.h> |
50 | #include <stdio.h> |
51 | |
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52 | #include "mp.h" |
53 | #include "mptext.h" |
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54 | #include "paranoia.h" |
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55 | |
56 | /*----- Main code ---------------------------------------------------------*/ |
57 | |
58 | /* --- @mp_read@ --- * |
59 | * |
60 | * Arguments: @mp *m@ = destination multiprecision number |
61 | * @int radix@ = base to assume for data (or zero to guess) |
62 | * @const mptext_ops *ops@ = pointer to operations block |
63 | * @void *p@ = data for the operations block |
64 | * |
65 | * Returns: The integer read, or zero if it didn't work. |
66 | * |
67 | * Use: Reads an integer from some source. If the @radix@ is |
68 | * specified, the number is assumed to be given in that radix, |
69 | * with the letters `a' (either upper- or lower-case) upwards |
70 | * standing for digits greater than 9. Otherwise, base 10 is |
71 | * assumed unless the number starts with `0' (octal), `0x' (hex) |
72 | * or `nnn_' (base `nnn'). An arbitrary amount of whitespace |
73 | * before the number is ignored. |
74 | */ |
75 | |
76 | mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p) |
77 | { |
78 | int r; |
79 | int ch; |
80 | unsigned f = 0; |
81 | |
82 | enum { |
83 | f_neg = 1u, |
84 | f_ok = 2u |
85 | }; |
86 | |
87 | /* --- Initialize the destination number --- */ |
88 | |
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89 | MP_MODIFY(m, 4); |
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90 | m->vl = m->v; |
91 | m->f &= ~MP_UNDEF; |
92 | |
93 | /* --- Read an initial character --- */ |
94 | |
95 | ch = ops->get(p); |
96 | while (isspace(ch)) |
97 | ch = ops->get(p); |
98 | |
99 | /* --- Handle an initial sign --- */ |
100 | |
101 | if (ch == '-') { |
102 | f |= f_neg; |
103 | ch = ops->get(p); |
104 | while (isspace(ch)) |
105 | ch = ops->get(p); |
106 | } |
107 | |
108 | /* --- If the radix is zero, look for leading zeros --- */ |
109 | |
110 | if (radix) |
111 | r = -1; |
112 | else if (ch != '0') { |
113 | radix = 10; |
114 | r = 0; |
115 | } else { |
116 | ch = ops->get(p); |
117 | if (ch == 'x') { |
118 | ch = ops->get(p); |
119 | radix = 16; |
120 | } else { |
121 | radix = 8; |
122 | f |= f_ok; |
123 | } |
124 | r = -1; |
125 | } |
126 | |
127 | /* --- Time to start --- */ |
128 | |
129 | for (;; ch = ops->get(p)) { |
130 | int x; |
131 | |
132 | /* --- An underscore indicates a numbered base --- */ |
133 | |
134 | if (ch == '_' && r > 0 && r <= 36) { |
135 | radix = r; |
136 | m->vl = m->v; |
137 | r = -1; |
138 | f &= ~f_ok; |
139 | continue; |
140 | } |
141 | |
142 | /* --- Check that the character is a digit and in range --- */ |
143 | |
144 | if (!isalnum(ch)) |
145 | break; |
146 | if (ch >= '0' && ch <= '9') |
147 | x = ch - '0'; |
148 | else { |
149 | ch = tolower(ch); |
150 | if (ch >= 'a' && ch <= 'z') /* ASCII dependent! */ |
151 | x = ch - 'a' + 10; |
152 | else |
153 | break; |
154 | } |
155 | |
156 | /* --- Sort out what to do with the character --- */ |
157 | |
158 | if (x >= 10 && r >= 0) |
159 | r = -1; |
160 | if (x >= radix) |
161 | break; |
162 | |
163 | if (r >= 0) |
164 | r = r * 10 + x; |
165 | |
166 | /* --- Stick the character on the end of my integer --- */ |
167 | |
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168 | mp_ensure(m, MP_LEN(m) + 1); |
169 | mpx_umuln(m->v, m->vl, m->v, m->vl - 1, radix); |
170 | mpx_uaddn(m->v, m->vl, x); |
171 | mp_shrink(m); |
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172 | f |= f_ok; |
173 | } |
174 | |
175 | ops->unget(ch, p); |
176 | |
177 | /* --- Bail out if the number was bad --- */ |
178 | |
179 | if (!(f & f_ok)) { |
180 | MP_DROP(m); |
181 | return (0); |
182 | } |
183 | |
184 | /* --- Set the sign and return --- */ |
185 | |
186 | m->f = 0; |
187 | if (f & f_neg) |
188 | m->f |= MP_NEG; |
189 | return (m); |
190 | } |
191 | |
192 | /* --- @mp_write@ --- * |
193 | * |
194 | * Arguments: @mp *m@ = pointer to a multi-precision integer |
195 | * @int radix@ = radix to use when writing the number out |
196 | * @const mptext_ops *ops@ = pointer to an operations block |
197 | * @void *p@ = data for the operations block |
198 | * |
199 | * Returns: Zero if it worked, nonzero otherwise. |
200 | * |
201 | * Use: Writes a large integer in textual form. |
202 | */ |
203 | |
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204 | /* --- Simple case --- * |
205 | * |
206 | * Use a fixed-sized buffer and the simple single-precision division |
207 | * algorithm to pick off low-order digits. Put each digit in a buffer, |
208 | * working backwards from the end. If the buffer becomes full, recurse to |
209 | * get another one. Ensure that there are at least @z@ digits by writing |
210 | * leading zeroes if there aren't enough real digits. |
211 | */ |
212 | |
213 | static int simple(mp *m, int radix, unsigned z, |
214 | const mptext_ops *ops, void *p) |
215 | { |
216 | int rc = 0; |
217 | char buf[64]; |
218 | unsigned i = sizeof(buf); |
219 | |
220 | do { |
221 | int ch; |
222 | mpw x; |
223 | |
224 | x = mpx_udivn(m->v, m->vl, m->v, m->vl, radix); |
225 | MP_SHRINK(m); |
226 | if (x < 10) |
227 | ch = '0' + x; |
228 | else |
229 | ch = 'a' + x - 10; |
230 | buf[--i] = ch; |
231 | if (z) |
232 | z--; |
233 | } while (i && MP_LEN(m)); |
234 | |
235 | if (MP_LEN(m)) |
236 | rc = simple(m, radix, z, ops, p); |
237 | else { |
238 | static const char zero[32] = "00000000000000000000000000000000"; |
239 | while (!rc && z >= sizeof(zero)) { |
240 | rc = ops->put(zero, sizeof(zero), p); |
241 | z -= sizeof(zero); |
242 | } |
243 | if (!rc && z) |
244 | rc = ops->put(zero, z, p); |
245 | } |
246 | if (!rc) |
247 | ops->put(buf + i, sizeof(buf) - i, p); |
248 | if (m->f & MP_BURN) |
249 | BURN(buf); |
250 | return (rc); |
251 | } |
252 | |
253 | /* --- Complicated case --- * |
254 | * |
255 | * If the number is small, fall back to the simple case above. Otherwise |
256 | * divide and take remainder by current large power of the radix, and emit |
257 | * each separately. Don't emit a zero quotient. Be very careful about |
258 | * leading zeroes on the remainder part, because they're deeply significant. |
259 | */ |
260 | |
261 | static int complicated(mp *m, int radix, mp **pr, unsigned i, unsigned z, |
262 | const mptext_ops *ops, void *p) |
263 | { |
264 | int rc = 0; |
265 | mp *q = MP_NEW; |
266 | unsigned d = 1 << i; |
267 | |
268 | if (MP_LEN(m) < 8) |
269 | return (simple(m, radix, z, ops, p)); |
270 | |
271 | mp_div(&q, &m, m, pr[i]); |
272 | if (!MP_LEN(q)) |
273 | d = z; |
274 | else { |
275 | if (z > d) |
276 | z -= d; |
277 | else |
278 | z = 0; |
279 | rc = complicated(q, radix, pr, i - 1, z, ops, p); |
280 | } |
281 | if (!rc) |
282 | rc = complicated(m, radix, pr, i - 1, d, ops, p); |
283 | mp_drop(q); |
284 | return (rc); |
285 | } |
286 | |
287 | /* --- Main driver code --- */ |
288 | |
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289 | int mp_write(mp *m, int radix, const mptext_ops *ops, void *p) |
290 | { |
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291 | int rc; |
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292 | |
293 | /* --- Set various things up --- */ |
294 | |
295 | m = MP_COPY(m); |
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296 | MP_SPLIT(m); |
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297 | |
298 | /* --- If the number is negative, sort that out --- */ |
299 | |
300 | if (m->f & MP_NEG) { |
301 | if (ops->put("-", 1, p)) |
302 | return (EOF); |
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303 | } |
304 | |
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305 | /* --- If the number is small, do it the easy way --- */ |
306 | |
307 | if (MP_LEN(m) < 8) |
308 | rc = simple(m, radix, 0, ops, p); |
309 | |
310 | /* --- Use a clever algorithm --- * |
311 | * |
312 | * Square the radix repeatedly, remembering old results, until I get |
313 | * something more than half the size of the number @m@. Use this to divide |
314 | * the number: the quotient and remainder will be approximately the same |
315 | * size, and I'll have split them on a digit boundary, so I can just emit |
316 | * the quotient and remainder recursively, in order. |
317 | * |
318 | * The array size copes with the largest number possibly representable on |
319 | * the host machine. Such a large number shouldn't ever arise in real use. |
320 | */ |
321 | |
322 | else { |
323 | mp *pr[CHAR_BIT * sizeof(size_t)]; |
324 | size_t target = MP_LEN(m) / 2; |
325 | unsigned i = 0; |
326 | mp *z = mp_create(1); |
327 | |
328 | /* --- Set up the exponent table --- */ |
329 | |
330 | z->v[0] = radix; |
331 | z->f = 0; |
332 | for (;;) { |
333 | assert(((void)"Number is too unimaginably huge", |
334 | i < sizeof(pr) / sizeof(pr[0]))); |
335 | pr[i++] = z; |
336 | if (MP_LEN(z) > target) |
337 | break; |
338 | z = mp_sqr(MP_NEW, z); |
339 | } |
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340 | |
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341 | /* --- Write out the answer --- */ |
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342 | |
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343 | rc = complicated(m, radix, pr, i - 1, 0, ops, p); |
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344 | |
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345 | /* --- Tidy away the array --- */ |
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346 | |
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347 | while (i > 0) |
348 | mp_drop(pr[--i]); |
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349 | } |
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350 | |
351 | /* --- Tidying up code --- */ |
352 | |
353 | MP_DROP(m); |
354 | return (rc); |
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355 | } |
356 | |
357 | /*----- Test rig ----------------------------------------------------------*/ |
358 | |
359 | #ifdef TEST_RIG |
360 | |
361 | #include <mLib/testrig.h> |
362 | |
363 | static int verify(dstr *v) |
364 | { |
365 | int ok = 1; |
366 | int ib = *(int *)v[0].buf, ob = *(int *)v[2].buf; |
367 | dstr d = DSTR_INIT; |
368 | mp *m = mp_readdstr(MP_NEW, &v[1], 0, ib); |
369 | if (m) { |
370 | if (!ob) { |
371 | fprintf(stderr, "*** unexpected successful parse\n" |
372 | "*** input [%i] = %s\n", |
373 | ib, v[1].buf); |
374 | mp_writedstr(m, &d, 10); |
375 | fprintf(stderr, "*** (value = %s)\n", d.buf); |
376 | ok = 0; |
377 | } else { |
378 | mp_writedstr(m, &d, ob); |
379 | if (d.len != v[3].len || memcmp(d.buf, v[3].buf, d.len) != 0) { |
380 | fprintf(stderr, "*** failed read or write\n" |
381 | "*** input [%i] = %s\n" |
382 | "*** output [%i] = %s\n" |
383 | "*** expected [%i] = %s\n", |
384 | ib, v[1].buf, ob, d.buf, ob, v[3].buf); |
385 | ok = 0; |
386 | } |
387 | } |
388 | mp_drop(m); |
389 | } else { |
390 | if (ob) { |
391 | fprintf(stderr, "*** unexpected parse failure\n" |
392 | "*** input [%i] = %s\n" |
393 | "*** expected [%i] = %s\n", |
394 | ib, v[1].buf, ob, v[3].buf); |
395 | ok = 0; |
396 | } |
397 | } |
398 | |
399 | dstr_destroy(&d); |
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400 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
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401 | return (ok); |
402 | } |
403 | |
404 | static test_chunk tests[] = { |
405 | { "mptext", verify, |
406 | { &type_int, &type_string, &type_int, &type_string, 0 } }, |
407 | { 0, 0, { 0 } } |
408 | }; |
409 | |
410 | int main(int argc, char *argv[]) |
411 | { |
412 | sub_init(); |
413 | test_run(argc, argv, tests, SRCDIR "/tests/mptext"); |
414 | return (0); |
415 | } |
416 | |
417 | #endif |
418 | |
419 | /*----- That's all, folks -------------------------------------------------*/ |