d3409d5e |
1 | /* -*-c-*- |
2 | * |
9bca44cb |
3 | * $Id: mptext.c,v 1.16 2002/10/15 22:57:43 mdw Exp $ |
d3409d5e |
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 $ |
9bca44cb |
33 | * Revision 1.16 2002/10/15 22:57:43 mdw |
34 | * Bug fix: prevent negative zero. |
35 | * |
afd054c1 |
36 | * Revision 1.15 2002/10/15 19:18:15 mdw |
37 | * Fix fencepost bugs in binary radix writing. |
38 | * |
3db58009 |
39 | * Revision 1.14 2002/10/09 00:33:44 mdw |
40 | * Allow `0o' and `0b' prefixes for octal and binary (from Haskell) |
41 | * |
6ea6fe51 |
42 | * Revision 1.13 2002/10/09 00:21:06 mdw |
43 | * Allow user-specified `r_xx' bases to be up to 62. |
44 | * |
631673a1 |
45 | * Revision 1.12 2002/01/13 19:51:18 mdw |
46 | * Extend the textual format to bases up to 62 by distinguishing case. |
47 | * |
eaa515d8 |
48 | * Revision 1.11 2001/06/16 23:42:17 mdw |
49 | * Typesetting fixes. |
50 | * |
a951033d |
51 | * Revision 1.10 2001/06/16 13:22:39 mdw |
52 | * Added fast-track code for binary output bases, and tests. |
53 | * |
3bc9cb53 |
54 | * Revision 1.9 2001/02/03 16:05:17 mdw |
55 | * Make flags be unsigned. Improve the write algorithm: recurse until the |
56 | * parts are one word long and use single-precision arithmetic from there. |
57 | * Fix off-by-one bug when breaking the number apart. |
58 | * |
9d3838a0 |
59 | * Revision 1.8 2000/12/06 20:32:42 mdw |
60 | * Reduce binary bytes (to allow marker bits to be ignored). Fix error |
61 | * message string a bit. Allow leading `+' signs. |
62 | * |
7d45ed6c |
63 | * Revision 1.7 2000/07/15 10:01:08 mdw |
64 | * Bug fix in binary input. |
65 | * |
dd9199f0 |
66 | * Revision 1.6 2000/06/25 12:58:23 mdw |
67 | * Fix the derivation of `depth' commentary. |
68 | * |
2b26f2d7 |
69 | * Revision 1.5 2000/06/17 11:46:19 mdw |
70 | * New and much faster stack-based algorithm for reading integers. Support |
71 | * reading and writing binary integers in bases between 2 and 256. |
72 | * |
e360a4f2 |
73 | * Revision 1.4 1999/12/22 15:56:56 mdw |
74 | * Use clever recursive algorithm for writing numbers out. |
75 | * |
9c3df6c0 |
76 | * Revision 1.3 1999/12/10 23:23:26 mdw |
77 | * Allocate slightly less memory. |
78 | * |
90b6f0be |
79 | * Revision 1.2 1999/11/20 22:24:15 mdw |
80 | * Use function versions of MPX_UMULN and MPX_UADDN. |
81 | * |
d3409d5e |
82 | * Revision 1.1 1999/11/17 18:02:16 mdw |
83 | * New multiprecision integer arithmetic suite. |
84 | * |
85 | */ |
86 | |
87 | /*----- Header files ------------------------------------------------------*/ |
88 | |
89 | #include <ctype.h> |
2b26f2d7 |
90 | #include <limits.h> |
d3409d5e |
91 | #include <stdio.h> |
92 | |
d3409d5e |
93 | #include "mp.h" |
94 | #include "mptext.h" |
e360a4f2 |
95 | #include "paranoia.h" |
d3409d5e |
96 | |
2b26f2d7 |
97 | /*----- Magical numbers ---------------------------------------------------*/ |
98 | |
99 | /* --- Maximum recursion depth --- * |
100 | * |
101 | * This is the number of bits in a @size_t@ object. Why? |
102 | * |
eaa515d8 |
103 | * To see this, let %$b = \textit{MPW\_MAX} + 1$% and let %$Z$% be the |
dd9199f0 |
104 | * largest @size_t@ value. Then the largest possible @mp@ is %$M - 1$% where |
105 | * %$M = b^Z$%. Let %$r$% be a radix to read or write. Since the recursion |
106 | * squares the radix at each step, the highest number reached by the |
107 | * recursion is %$d$%, where: |
2b26f2d7 |
108 | * |
dd9199f0 |
109 | * %$r^{2^d} = b^Z$%. |
2b26f2d7 |
110 | * |
111 | * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum, |
112 | * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%. |
113 | * |
114 | * Expressing %$\lg Z$% as @CHAR_BIT * sizeof(size_t)@ yields an |
115 | * overestimate, since a @size_t@ representation may contain `holes'. |
116 | * Choosing to represent %$\lg \lg b$% by 10 is almost certainly sufficient |
117 | * for `some time to come'. |
118 | */ |
119 | |
120 | #define DEPTH (CHAR_BIT * sizeof(size_t) + 10) |
121 | |
d3409d5e |
122 | /*----- Main code ---------------------------------------------------------*/ |
123 | |
124 | /* --- @mp_read@ --- * |
125 | * |
126 | * Arguments: @mp *m@ = destination multiprecision number |
127 | * @int radix@ = base to assume for data (or zero to guess) |
128 | * @const mptext_ops *ops@ = pointer to operations block |
129 | * @void *p@ = data for the operations block |
130 | * |
131 | * Returns: The integer read, or zero if it didn't work. |
132 | * |
133 | * Use: Reads an integer from some source. If the @radix@ is |
134 | * specified, the number is assumed to be given in that radix, |
135 | * with the letters `a' (either upper- or lower-case) upwards |
136 | * standing for digits greater than 9. Otherwise, base 10 is |
137 | * assumed unless the number starts with `0' (octal), `0x' (hex) |
138 | * or `nnn_' (base `nnn'). An arbitrary amount of whitespace |
139 | * before the number is ignored. |
140 | */ |
141 | |
2b26f2d7 |
142 | /* --- About the algorithm --- * |
143 | * |
144 | * The algorithm here is rather aggressive. I maintain an array of |
145 | * successive squarings of the radix, and a stack of partial results, each |
146 | * with a counter attached indicating which radix square to multiply by. |
147 | * Once the item at the top of the stack reaches the same counter level as |
148 | * the next item down, they are combined together and the result is given a |
149 | * counter level one higher than either of the results. |
150 | * |
151 | * Gluing the results together at the end is slightly tricky. Pay attention |
152 | * to the code. |
153 | * |
154 | * This is more complicated because of the need to handle the slightly |
155 | * bizarre syntax. |
156 | */ |
157 | |
d3409d5e |
158 | mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p) |
159 | { |
2b26f2d7 |
160 | int ch; /* Current char being considered */ |
161 | unsigned f = 0; /* Flags about the current number */ |
162 | int r; /* Radix to switch over to */ |
163 | mpw rd; /* Radix as an @mp@ digit */ |
164 | mp rr; /* The @mp@ for the radix */ |
165 | unsigned nf = m ? m->f & MP_BURN : 0; /* New @mp@ flags */ |
166 | |
167 | /* --- Stacks --- */ |
168 | |
169 | mp *pow[DEPTH]; /* List of powers */ |
170 | unsigned pows; /* Next index to fill */ |
171 | struct { unsigned i; mp *m; } s[DEPTH]; /* Main stack */ |
172 | unsigned sp; /* Current stack pointer */ |
173 | |
174 | /* --- Flags --- */ |
d3409d5e |
175 | |
3bc9cb53 |
176 | #define f_neg 1u |
177 | #define f_ok 2u |
a951033d |
178 | #define f_start 4u |
d3409d5e |
179 | |
2b26f2d7 |
180 | /* --- Initialize the stacks --- */ |
181 | |
182 | mp_build(&rr, &rd, &rd + 1); |
183 | pow[0] = &rr; |
184 | pows = 1; |
185 | |
186 | sp = 0; |
187 | |
d3409d5e |
188 | /* --- Initialize the destination number --- */ |
189 | |
2b26f2d7 |
190 | if (m) |
191 | MP_DROP(m); |
d3409d5e |
192 | |
193 | /* --- Read an initial character --- */ |
194 | |
195 | ch = ops->get(p); |
196 | while (isspace(ch)) |
197 | ch = ops->get(p); |
198 | |
199 | /* --- Handle an initial sign --- */ |
200 | |
9d3838a0 |
201 | if (radix >= 0 && (ch == '-' || ch == '+')) { |
202 | if (ch == '-') |
203 | f |= f_neg; |
204 | do ch = ops->get(p); while isspace(ch); |
d3409d5e |
205 | } |
206 | |
207 | /* --- If the radix is zero, look for leading zeros --- */ |
208 | |
2b26f2d7 |
209 | if (radix > 0) { |
631673a1 |
210 | assert(((void)"ascii radix must be <= 62", radix <= 62)); |
2b26f2d7 |
211 | rd = radix; |
212 | r = -1; |
213 | } else if (radix < 0) { |
214 | rd = -radix; |
9d3838a0 |
215 | assert(((void)"binary radix must fit in a byte", rd < UCHAR_MAX)); |
d3409d5e |
216 | r = -1; |
2b26f2d7 |
217 | } else if (ch != '0') { |
218 | rd = 10; |
d3409d5e |
219 | r = 0; |
220 | } else { |
221 | ch = ops->get(p); |
3db58009 |
222 | switch (ch) { |
223 | case 'x': |
224 | rd = 16; |
225 | goto prefix; |
226 | case 'o': |
227 | rd = 8; |
228 | goto prefix; |
229 | case 'b': |
230 | rd = 2; |
231 | goto prefix; |
232 | prefix: |
233 | ch = ops->get(p); |
234 | break; |
235 | default: |
236 | rd = 8; |
237 | f |= f_ok; |
d3409d5e |
238 | } |
239 | r = -1; |
240 | } |
241 | |
a951033d |
242 | /* --- Use fast algorithm for binary radix --- * |
243 | * |
244 | * This is the restart point after having parsed a radix number from the |
245 | * input. We check whether the radix is binary, and if so use a fast |
246 | * algorithm which just stacks the bits up in the right order. |
247 | */ |
248 | |
249 | restart: |
250 | switch (rd) { |
251 | unsigned bit; |
252 | |
253 | case 2: bit = 1; goto bin; |
254 | case 4: bit = 2; goto bin; |
255 | case 8: bit = 3; goto bin; |
256 | case 16: bit = 4; goto bin; |
257 | case 32: bit = 5; goto bin; |
258 | case 64: bit = 6; goto bin; |
259 | case 128: bit = 7; goto bin; |
260 | default: |
261 | break; |
262 | |
263 | /* --- The fast binary algorithm --- * |
264 | * |
265 | * We stack bits up starting at the top end of a word. When one word is |
266 | * full, we write it to the integer, and start another with the left-over |
267 | * bits. When the array in the integer is full, we resize using low-level |
268 | * calls and copy the current data to the top end. Finally, we do a single |
269 | * bit-shift when we know where the end of the number is. |
270 | */ |
271 | |
272 | bin: { |
273 | mpw a = 0; |
274 | unsigned b = MPW_BITS; |
275 | size_t len, n; |
276 | mpw *v; |
277 | |
278 | m = mp_dest(MP_NEW, 1, nf); |
279 | len = n = m->sz; |
280 | n = len; |
281 | v = m->v + n; |
282 | for (;; ch = ops->get(p)) { |
283 | unsigned x; |
284 | |
285 | if (ch < 0) |
286 | break; |
287 | |
288 | /* --- Check that the character is a digit and in range --- */ |
289 | |
290 | if (radix < 0) |
291 | x = ch % rd; |
292 | else { |
293 | if (!isalnum(ch)) |
294 | break; |
295 | if (ch >= '0' && ch <= '9') |
296 | x = ch - '0'; |
297 | else { |
631673a1 |
298 | if (rd <= 36) |
299 | ch = tolower(ch); |
a951033d |
300 | if (ch >= 'a' && ch <= 'z') /* ASCII dependent! */ |
301 | x = ch - 'a' + 10; |
631673a1 |
302 | else if (ch >= 'A' && ch <= 'Z') |
303 | x = ch - 'A' + 36; |
a951033d |
304 | else |
305 | break; |
306 | } |
307 | } |
308 | if (x >= rd) |
309 | break; |
310 | |
311 | /* --- Feed the digit into the accumulator --- */ |
312 | |
313 | f |= f_ok; |
314 | if (!x && !(f & f_start)) |
315 | continue; |
316 | f |= f_start; |
317 | if (b > bit) { |
318 | b -= bit; |
319 | a |= MPW(x) << b; |
320 | } else { |
321 | a |= MPW(x) >> (bit - b); |
322 | b += MPW_BITS - bit; |
323 | *--v = MPW(a); |
324 | n--; |
325 | if (!n) { |
326 | n = len; |
327 | len <<= 1; |
328 | v = mpalloc(m->a, len); |
329 | memcpy(v + n, m->v, MPWS(n)); |
330 | mpfree(m->a, m->v); |
331 | m->v = v; |
332 | v = m->v + n; |
333 | } |
334 | a = (b < MPW_BITS) ? MPW(x) << b : 0; |
335 | } |
336 | } |
337 | |
338 | /* --- Finish up --- */ |
339 | |
340 | if (!(f & f_ok)) { |
341 | mp_drop(m); |
342 | m = 0; |
343 | } else { |
344 | *--v = MPW(a); |
345 | n--; |
346 | m->sz = len; |
347 | m->vl = m->v + len; |
348 | m->f &= ~MP_UNDEF; |
349 | m = mp_lsr(m, m, (unsigned long)n * MPW_BITS + b); |
350 | } |
351 | goto done; |
352 | }} |
353 | |
d3409d5e |
354 | /* --- Time to start --- */ |
355 | |
356 | for (;; ch = ops->get(p)) { |
a951033d |
357 | unsigned x; |
d3409d5e |
358 | |
7d45ed6c |
359 | if (ch < 0) |
360 | break; |
361 | |
d3409d5e |
362 | /* --- An underscore indicates a numbered base --- */ |
363 | |
6ea6fe51 |
364 | if (ch == '_' && r > 0 && r <= 62) { |
2b26f2d7 |
365 | unsigned i; |
366 | |
367 | /* --- Clear out the stacks --- */ |
368 | |
369 | for (i = 1; i < pows; i++) |
370 | MP_DROP(pow[i]); |
371 | pows = 1; |
372 | for (i = 0; i < sp; i++) |
373 | MP_DROP(s[i].m); |
374 | sp = 0; |
375 | |
376 | /* --- Restart the search --- */ |
377 | |
378 | rd = r; |
d3409d5e |
379 | r = -1; |
380 | f &= ~f_ok; |
a951033d |
381 | ch = ops->get(p); |
382 | goto restart; |
d3409d5e |
383 | } |
384 | |
385 | /* --- Check that the character is a digit and in range --- */ |
386 | |
2b26f2d7 |
387 | if (radix < 0) |
9d3838a0 |
388 | x = ch % rd; |
d3409d5e |
389 | else { |
2b26f2d7 |
390 | if (!isalnum(ch)) |
d3409d5e |
391 | break; |
2b26f2d7 |
392 | if (ch >= '0' && ch <= '9') |
393 | x = ch - '0'; |
394 | else { |
631673a1 |
395 | if (rd <= 36) |
396 | ch = tolower(ch); |
2b26f2d7 |
397 | if (ch >= 'a' && ch <= 'z') /* ASCII dependent! */ |
398 | x = ch - 'a' + 10; |
631673a1 |
399 | else if (ch >= 'A' && ch <= 'Z') |
400 | x = ch - 'A' + 36; |
2b26f2d7 |
401 | else |
402 | break; |
403 | } |
d3409d5e |
404 | } |
405 | |
406 | /* --- Sort out what to do with the character --- */ |
407 | |
408 | if (x >= 10 && r >= 0) |
409 | r = -1; |
2b26f2d7 |
410 | if (x >= rd) |
d3409d5e |
411 | break; |
412 | |
413 | if (r >= 0) |
414 | r = r * 10 + x; |
415 | |
416 | /* --- Stick the character on the end of my integer --- */ |
417 | |
2b26f2d7 |
418 | assert(((void)"Number is too unimaginably huge", sp < DEPTH)); |
419 | s[sp].m = m = mp_new(1, nf); |
420 | m->v[0] = x; |
421 | s[sp].i = 0; |
422 | |
423 | /* --- Now grind through the stack --- */ |
424 | |
425 | while (sp > 0 && s[sp - 1].i == s[sp].i) { |
426 | |
427 | /* --- Combine the top two items --- */ |
428 | |
429 | sp--; |
430 | m = s[sp].m; |
431 | m = mp_mul(m, m, pow[s[sp].i]); |
432 | m = mp_add(m, m, s[sp + 1].m); |
433 | s[sp].m = m; |
434 | MP_DROP(s[sp + 1].m); |
435 | s[sp].i++; |
436 | |
437 | /* --- Make a new radix power if necessary --- */ |
438 | |
439 | if (s[sp].i >= pows) { |
440 | assert(((void)"Number is too unimaginably huge", pows < DEPTH)); |
441 | pow[pows] = mp_sqr(MP_NEW, pow[pows - 1]); |
442 | pows++; |
443 | } |
444 | } |
d3409d5e |
445 | f |= f_ok; |
2b26f2d7 |
446 | sp++; |
d3409d5e |
447 | } |
448 | |
449 | ops->unget(ch, p); |
450 | |
2b26f2d7 |
451 | /* --- If we're done, compute the rest of the number --- */ |
452 | |
453 | if (f & f_ok) { |
454 | if (!sp) |
455 | return (MP_ZERO); |
456 | else { |
457 | mp *z = MP_ONE; |
458 | sp--; |
459 | |
460 | while (sp > 0) { |
461 | |
462 | /* --- Combine the top two items --- */ |
463 | |
464 | sp--; |
465 | m = s[sp].m; |
466 | z = mp_mul(z, z, pow[s[sp + 1].i]); |
467 | m = mp_mul(m, m, z); |
468 | m = mp_add(m, m, s[sp + 1].m); |
469 | s[sp].m = m; |
470 | MP_DROP(s[sp + 1].m); |
471 | |
472 | /* --- Make a new radix power if necessary --- */ |
473 | |
474 | if (s[sp].i >= pows) { |
475 | assert(((void)"Number is too unimaginably huge", pows < DEPTH)); |
476 | pow[pows] = mp_sqr(MP_NEW, pow[pows - 1]); |
477 | pows++; |
478 | } |
479 | } |
480 | MP_DROP(z); |
481 | m = s[0].m; |
482 | } |
483 | } else { |
484 | unsigned i; |
485 | for (i = 0; i < sp; i++) |
486 | MP_DROP(s[i].m); |
487 | } |
488 | |
489 | /* --- Clear the radix power list --- */ |
490 | |
491 | { |
492 | unsigned i; |
493 | for (i = 1; i < pows; i++) |
494 | MP_DROP(pow[i]); |
495 | } |
496 | |
d3409d5e |
497 | /* --- Bail out if the number was bad --- */ |
498 | |
a951033d |
499 | done: |
2b26f2d7 |
500 | if (!(f & f_ok)) |
d3409d5e |
501 | return (0); |
d3409d5e |
502 | |
503 | /* --- Set the sign and return --- */ |
504 | |
d3409d5e |
505 | if (f & f_neg) |
506 | m->f |= MP_NEG; |
9bca44cb |
507 | MP_SHRINK(m); |
d3409d5e |
508 | return (m); |
3bc9cb53 |
509 | |
a951033d |
510 | #undef f_start |
3bc9cb53 |
511 | #undef f_neg |
512 | #undef f_ok |
d3409d5e |
513 | } |
514 | |
515 | /* --- @mp_write@ --- * |
516 | * |
517 | * Arguments: @mp *m@ = pointer to a multi-precision integer |
518 | * @int radix@ = radix to use when writing the number out |
519 | * @const mptext_ops *ops@ = pointer to an operations block |
520 | * @void *p@ = data for the operations block |
521 | * |
522 | * Returns: Zero if it worked, nonzero otherwise. |
523 | * |
524 | * Use: Writes a large integer in textual form. |
525 | */ |
526 | |
e360a4f2 |
527 | /* --- Simple case --- * |
528 | * |
3bc9cb53 |
529 | * Use a fixed-sized buffer and single-precision arithmetic to pick off |
530 | * low-order digits. Put each digit in a buffer, working backwards from the |
531 | * end. If the buffer becomes full, recurse to get another one. Ensure that |
532 | * there are at least @z@ digits by writing leading zeroes if there aren't |
533 | * enough real digits. |
e360a4f2 |
534 | */ |
535 | |
3bc9cb53 |
536 | static int simple(mpw n, int radix, unsigned z, |
e360a4f2 |
537 | const mptext_ops *ops, void *p) |
538 | { |
539 | int rc = 0; |
540 | char buf[64]; |
541 | unsigned i = sizeof(buf); |
2b26f2d7 |
542 | int rd = radix > 0 ? radix : -radix; |
e360a4f2 |
543 | |
544 | do { |
545 | int ch; |
546 | mpw x; |
547 | |
3bc9cb53 |
548 | x = n % rd; |
549 | n /= rd; |
2b26f2d7 |
550 | if (radix < 0) |
551 | ch = x; |
3bc9cb53 |
552 | else if (x < 10) |
553 | ch = '0' + x; |
631673a1 |
554 | else if (x < 36) /* Ascii specific */ |
3bc9cb53 |
555 | ch = 'a' + x - 10; |
631673a1 |
556 | else |
557 | ch = 'A' + x - 36; |
e360a4f2 |
558 | buf[--i] = ch; |
559 | if (z) |
560 | z--; |
3bc9cb53 |
561 | } while (i && n); |
e360a4f2 |
562 | |
3bc9cb53 |
563 | if (n) |
564 | rc = simple(n, radix, z, ops, p); |
e360a4f2 |
565 | else { |
a951033d |
566 | char zbuf[32]; |
567 | memset(zbuf, (radix < 0) ? 0 : '0', sizeof(zbuf)); |
568 | while (!rc && z >= sizeof(zbuf)) { |
569 | rc = ops->put(zbuf, sizeof(zbuf), p); |
570 | z -= sizeof(zbuf); |
e360a4f2 |
571 | } |
572 | if (!rc && z) |
a951033d |
573 | rc = ops->put(zbuf, z, p); |
e360a4f2 |
574 | } |
575 | if (!rc) |
3bc9cb53 |
576 | rc = ops->put(buf + i, sizeof(buf) - i, p); |
577 | BURN(buf); |
e360a4f2 |
578 | return (rc); |
579 | } |
580 | |
581 | /* --- Complicated case --- * |
582 | * |
583 | * If the number is small, fall back to the simple case above. Otherwise |
584 | * divide and take remainder by current large power of the radix, and emit |
585 | * each separately. Don't emit a zero quotient. Be very careful about |
586 | * leading zeroes on the remainder part, because they're deeply significant. |
587 | */ |
588 | |
589 | static int complicated(mp *m, int radix, mp **pr, unsigned i, unsigned z, |
590 | const mptext_ops *ops, void *p) |
591 | { |
592 | int rc = 0; |
593 | mp *q = MP_NEW; |
594 | unsigned d = 1 << i; |
595 | |
3bc9cb53 |
596 | if (MP_LEN(m) < 2) |
597 | return (simple(MP_LEN(m) ? m->v[0] : 0, radix, z, ops, p)); |
e360a4f2 |
598 | |
3bc9cb53 |
599 | assert(i); |
e360a4f2 |
600 | mp_div(&q, &m, m, pr[i]); |
601 | if (!MP_LEN(q)) |
602 | d = z; |
603 | else { |
604 | if (z > d) |
605 | z -= d; |
606 | else |
607 | z = 0; |
608 | rc = complicated(q, radix, pr, i - 1, z, ops, p); |
609 | } |
610 | if (!rc) |
611 | rc = complicated(m, radix, pr, i - 1, d, ops, p); |
612 | mp_drop(q); |
613 | return (rc); |
614 | } |
615 | |
a951033d |
616 | /* --- Binary case --- * |
617 | * |
618 | * Special case for binary output. Goes much faster. |
619 | */ |
620 | |
621 | static int binary(mp *m, int bit, int radix, const mptext_ops *ops, void *p) |
622 | { |
623 | mpw *v; |
624 | mpw a; |
625 | int rc = 0; |
626 | unsigned b; |
627 | unsigned mask; |
628 | unsigned long n; |
629 | unsigned f = 0; |
630 | char buf[8], *q; |
631 | unsigned x; |
632 | int ch; |
633 | |
634 | #define f_out 1u |
635 | |
636 | /* --- Work out where to start --- */ |
637 | |
638 | n = mp_bits(m); |
afd054c1 |
639 | if (n % bit) |
640 | n += bit - (n % bit); |
a951033d |
641 | b = n % MPW_BITS; |
642 | n /= MPW_BITS; |
afd054c1 |
643 | |
644 | if (n >= MP_LEN(m)) { |
a951033d |
645 | n--; |
646 | b += MPW_BITS; |
647 | } |
648 | |
649 | v = m->v + n; |
650 | a = *v; |
651 | mask = (1 << bit) - 1; |
652 | q = buf; |
653 | |
654 | /* --- Main code --- */ |
655 | |
656 | for (;;) { |
657 | if (b > bit) { |
658 | b -= bit; |
659 | x = a >> b; |
660 | } else { |
661 | x = a << (bit - b); |
662 | b += MPW_BITS - bit; |
663 | if (v == m->v) |
664 | break; |
665 | a = *--v; |
666 | if (b < MPW_BITS) |
667 | x |= a >> b; |
668 | } |
669 | x &= mask; |
670 | if (!x && !(f & f_out)) |
671 | continue; |
672 | |
673 | if (radix < 0) |
674 | ch = x; |
675 | else if (x < 10) |
676 | ch = '0' + x; |
631673a1 |
677 | else if (x < 36) |
678 | ch = 'a' + x - 10; /* Ascii specific */ |
a951033d |
679 | else |
631673a1 |
680 | ch = 'A' + x - 36; |
a951033d |
681 | *q++ = ch; |
682 | if (q >= buf + sizeof(buf)) { |
683 | if ((rc = ops->put(buf, sizeof(buf), p)) != 0) |
684 | goto done; |
685 | q = buf; |
686 | } |
687 | f |= f_out; |
688 | } |
689 | |
690 | x &= mask; |
691 | if (radix < 0) |
692 | ch = x; |
693 | else if (x < 10) |
694 | ch = '0' + x; |
631673a1 |
695 | else if (x < 36) |
696 | ch = 'a' + x - 10; /* Ascii specific */ |
a951033d |
697 | else |
631673a1 |
698 | ch = 'A' + x - 36; |
a951033d |
699 | *q++ = ch; |
700 | rc = ops->put(buf, q - buf, p); |
701 | |
702 | done: |
703 | mp_drop(m); |
704 | return (rc); |
705 | |
706 | #undef f_out |
707 | } |
708 | |
e360a4f2 |
709 | /* --- Main driver code --- */ |
710 | |
d3409d5e |
711 | int mp_write(mp *m, int radix, const mptext_ops *ops, void *p) |
712 | { |
e360a4f2 |
713 | int rc; |
d3409d5e |
714 | |
afd054c1 |
715 | if (MP_EQ(m, MP_ZERO)) |
716 | return (ops->put("0", 1, p)); |
717 | |
d3409d5e |
718 | /* --- Set various things up --- */ |
719 | |
720 | m = MP_COPY(m); |
e360a4f2 |
721 | MP_SPLIT(m); |
d3409d5e |
722 | |
2b26f2d7 |
723 | /* --- Check the radix for sensibleness --- */ |
724 | |
725 | if (radix > 0) |
631673a1 |
726 | assert(((void)"ascii radix must be <= 62", radix <= 62)); |
2b26f2d7 |
727 | else if (radix < 0) |
728 | assert(((void)"binary radix must fit in a byte", -radix < UCHAR_MAX)); |
729 | else |
730 | assert(((void)"radix can't be zero in mp_write", 0)); |
731 | |
d3409d5e |
732 | /* --- If the number is negative, sort that out --- */ |
733 | |
734 | if (m->f & MP_NEG) { |
735 | if (ops->put("-", 1, p)) |
736 | return (EOF); |
2b26f2d7 |
737 | m->f &= ~MP_NEG; |
d3409d5e |
738 | } |
739 | |
a951033d |
740 | /* --- Handle binary radix --- */ |
741 | |
742 | switch (radix) { |
743 | case 2: case -2: return (binary(m, 1, radix, ops, p)); |
744 | case 4: case -4: return (binary(m, 2, radix, ops, p)); |
745 | case 8: case -8: return (binary(m, 3, radix, ops, p)); |
746 | case 16: case -16: return (binary(m, 4, radix, ops, p)); |
747 | case 32: case -32: return (binary(m, 5, radix, ops, p)); |
748 | case -64: return (binary(m, 6, radix, ops, p)); |
749 | case -128: return (binary(m, 7, radix, ops, p)); |
750 | } |
751 | |
e360a4f2 |
752 | /* --- If the number is small, do it the easy way --- */ |
753 | |
3bc9cb53 |
754 | if (MP_LEN(m) < 2) |
755 | rc = simple(MP_LEN(m) ? m->v[0] : 0, radix, 0, ops, p); |
e360a4f2 |
756 | |
757 | /* --- Use a clever algorithm --- * |
758 | * |
759 | * Square the radix repeatedly, remembering old results, until I get |
760 | * something more than half the size of the number @m@. Use this to divide |
761 | * the number: the quotient and remainder will be approximately the same |
762 | * size, and I'll have split them on a digit boundary, so I can just emit |
763 | * the quotient and remainder recursively, in order. |
e360a4f2 |
764 | */ |
765 | |
766 | else { |
2b26f2d7 |
767 | mp *pr[DEPTH]; |
3bc9cb53 |
768 | size_t target = (MP_LEN(m) + 1) / 2; |
e360a4f2 |
769 | unsigned i = 0; |
2b26f2d7 |
770 | mp *z = mp_new(1, 0); |
e360a4f2 |
771 | |
772 | /* --- Set up the exponent table --- */ |
773 | |
2b26f2d7 |
774 | z->v[0] = (radix > 0 ? radix : -radix); |
e360a4f2 |
775 | z->f = 0; |
776 | for (;;) { |
2b26f2d7 |
777 | assert(((void)"Number is too unimaginably huge", i < DEPTH)); |
e360a4f2 |
778 | pr[i++] = z; |
779 | if (MP_LEN(z) > target) |
780 | break; |
781 | z = mp_sqr(MP_NEW, z); |
782 | } |
d3409d5e |
783 | |
e360a4f2 |
784 | /* --- Write out the answer --- */ |
d3409d5e |
785 | |
e360a4f2 |
786 | rc = complicated(m, radix, pr, i - 1, 0, ops, p); |
d3409d5e |
787 | |
e360a4f2 |
788 | /* --- Tidy away the array --- */ |
d3409d5e |
789 | |
e360a4f2 |
790 | while (i > 0) |
791 | mp_drop(pr[--i]); |
d3409d5e |
792 | } |
e360a4f2 |
793 | |
794 | /* --- Tidying up code --- */ |
795 | |
796 | MP_DROP(m); |
797 | return (rc); |
d3409d5e |
798 | } |
799 | |
800 | /*----- Test rig ----------------------------------------------------------*/ |
801 | |
802 | #ifdef TEST_RIG |
803 | |
804 | #include <mLib/testrig.h> |
805 | |
806 | static int verify(dstr *v) |
807 | { |
808 | int ok = 1; |
809 | int ib = *(int *)v[0].buf, ob = *(int *)v[2].buf; |
810 | dstr d = DSTR_INIT; |
811 | mp *m = mp_readdstr(MP_NEW, &v[1], 0, ib); |
812 | if (m) { |
813 | if (!ob) { |
814 | fprintf(stderr, "*** unexpected successful parse\n" |
a951033d |
815 | "*** input [%2i] = ", ib); |
2b26f2d7 |
816 | if (ib < 0) |
817 | type_hex.dump(&v[1], stderr); |
818 | else |
819 | fputs(v[1].buf, stderr); |
d3409d5e |
820 | mp_writedstr(m, &d, 10); |
2b26f2d7 |
821 | fprintf(stderr, "\n*** (value = %s)\n", d.buf); |
d3409d5e |
822 | ok = 0; |
823 | } else { |
824 | mp_writedstr(m, &d, ob); |
825 | if (d.len != v[3].len || memcmp(d.buf, v[3].buf, d.len) != 0) { |
826 | fprintf(stderr, "*** failed read or write\n" |
a951033d |
827 | "*** input [%2i] = ", ib); |
2b26f2d7 |
828 | if (ib < 0) |
829 | type_hex.dump(&v[1], stderr); |
830 | else |
831 | fputs(v[1].buf, stderr); |
a951033d |
832 | fprintf(stderr, "\n*** output [%2i] = ", ob); |
2b26f2d7 |
833 | if (ob < 0) |
834 | type_hex.dump(&d, stderr); |
835 | else |
836 | fputs(d.buf, stderr); |
a951033d |
837 | fprintf(stderr, "\n*** expected [%2i] = ", ob); |
2b26f2d7 |
838 | if (ob < 0) |
839 | type_hex.dump(&v[3], stderr); |
840 | else |
841 | fputs(v[3].buf, stderr); |
842 | fputc('\n', stderr); |
d3409d5e |
843 | ok = 0; |
844 | } |
845 | } |
846 | mp_drop(m); |
847 | } else { |
848 | if (ob) { |
849 | fprintf(stderr, "*** unexpected parse failure\n" |
2b26f2d7 |
850 | "*** input [%i] = ", ib); |
851 | if (ib < 0) |
852 | type_hex.dump(&v[1], stderr); |
853 | else |
854 | fputs(v[1].buf, stderr); |
855 | fprintf(stderr, "\n*** expected [%i] = ", ob); |
856 | if (ob < 0) |
857 | type_hex.dump(&v[3], stderr); |
858 | else |
859 | fputs(v[3].buf, stderr); |
860 | fputc('\n', stderr); |
d3409d5e |
861 | ok = 0; |
862 | } |
863 | } |
864 | |
865 | dstr_destroy(&d); |
9c3df6c0 |
866 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
867 | return (ok); |
868 | } |
869 | |
870 | static test_chunk tests[] = { |
2b26f2d7 |
871 | { "mptext-ascii", verify, |
d3409d5e |
872 | { &type_int, &type_string, &type_int, &type_string, 0 } }, |
2b26f2d7 |
873 | { "mptext-bin-in", verify, |
874 | { &type_int, &type_hex, &type_int, &type_string, 0 } }, |
875 | { "mptext-bin-out", verify, |
876 | { &type_int, &type_string, &type_int, &type_hex, 0 } }, |
d3409d5e |
877 | { 0, 0, { 0 } } |
878 | }; |
879 | |
880 | int main(int argc, char *argv[]) |
881 | { |
882 | sub_init(); |
883 | test_run(argc, argv, tests, SRCDIR "/tests/mptext"); |
884 | return (0); |
885 | } |
886 | |
887 | #endif |
888 | |
889 | /*----- That's all, folks -------------------------------------------------*/ |