d3409d5e |
1 | /* -*-c-*- |
2 | * |
50bea2af |
3 | * $Id: mptext.c,v 1.17 2002/10/19 11:59:04 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 $ |
50bea2af |
33 | * Revision 1.17 2002/10/19 11:59:04 mdw |
34 | * Fix leftovers bug in reading. |
35 | * |
9bca44cb |
36 | * Revision 1.16 2002/10/15 22:57:43 mdw |
37 | * Bug fix: prevent negative zero. |
38 | * |
afd054c1 |
39 | * Revision 1.15 2002/10/15 19:18:15 mdw |
40 | * Fix fencepost bugs in binary radix writing. |
41 | * |
3db58009 |
42 | * Revision 1.14 2002/10/09 00:33:44 mdw |
43 | * Allow `0o' and `0b' prefixes for octal and binary (from Haskell) |
44 | * |
6ea6fe51 |
45 | * Revision 1.13 2002/10/09 00:21:06 mdw |
46 | * Allow user-specified `r_xx' bases to be up to 62. |
47 | * |
631673a1 |
48 | * Revision 1.12 2002/01/13 19:51:18 mdw |
49 | * Extend the textual format to bases up to 62 by distinguishing case. |
50 | * |
eaa515d8 |
51 | * Revision 1.11 2001/06/16 23:42:17 mdw |
52 | * Typesetting fixes. |
53 | * |
a951033d |
54 | * Revision 1.10 2001/06/16 13:22:39 mdw |
55 | * Added fast-track code for binary output bases, and tests. |
56 | * |
3bc9cb53 |
57 | * Revision 1.9 2001/02/03 16:05:17 mdw |
58 | * Make flags be unsigned. Improve the write algorithm: recurse until the |
59 | * parts are one word long and use single-precision arithmetic from there. |
60 | * Fix off-by-one bug when breaking the number apart. |
61 | * |
9d3838a0 |
62 | * Revision 1.8 2000/12/06 20:32:42 mdw |
63 | * Reduce binary bytes (to allow marker bits to be ignored). Fix error |
64 | * message string a bit. Allow leading `+' signs. |
65 | * |
7d45ed6c |
66 | * Revision 1.7 2000/07/15 10:01:08 mdw |
67 | * Bug fix in binary input. |
68 | * |
dd9199f0 |
69 | * Revision 1.6 2000/06/25 12:58:23 mdw |
70 | * Fix the derivation of `depth' commentary. |
71 | * |
2b26f2d7 |
72 | * Revision 1.5 2000/06/17 11:46:19 mdw |
73 | * New and much faster stack-based algorithm for reading integers. Support |
74 | * reading and writing binary integers in bases between 2 and 256. |
75 | * |
e360a4f2 |
76 | * Revision 1.4 1999/12/22 15:56:56 mdw |
77 | * Use clever recursive algorithm for writing numbers out. |
78 | * |
9c3df6c0 |
79 | * Revision 1.3 1999/12/10 23:23:26 mdw |
80 | * Allocate slightly less memory. |
81 | * |
90b6f0be |
82 | * Revision 1.2 1999/11/20 22:24:15 mdw |
83 | * Use function versions of MPX_UMULN and MPX_UADDN. |
84 | * |
d3409d5e |
85 | * Revision 1.1 1999/11/17 18:02:16 mdw |
86 | * New multiprecision integer arithmetic suite. |
87 | * |
88 | */ |
89 | |
90 | /*----- Header files ------------------------------------------------------*/ |
91 | |
92 | #include <ctype.h> |
2b26f2d7 |
93 | #include <limits.h> |
d3409d5e |
94 | #include <stdio.h> |
95 | |
d3409d5e |
96 | #include "mp.h" |
97 | #include "mptext.h" |
e360a4f2 |
98 | #include "paranoia.h" |
d3409d5e |
99 | |
2b26f2d7 |
100 | /*----- Magical numbers ---------------------------------------------------*/ |
101 | |
102 | /* --- Maximum recursion depth --- * |
103 | * |
104 | * This is the number of bits in a @size_t@ object. Why? |
105 | * |
eaa515d8 |
106 | * To see this, let %$b = \textit{MPW\_MAX} + 1$% and let %$Z$% be the |
dd9199f0 |
107 | * largest @size_t@ value. Then the largest possible @mp@ is %$M - 1$% where |
108 | * %$M = b^Z$%. Let %$r$% be a radix to read or write. Since the recursion |
109 | * squares the radix at each step, the highest number reached by the |
110 | * recursion is %$d$%, where: |
2b26f2d7 |
111 | * |
dd9199f0 |
112 | * %$r^{2^d} = b^Z$%. |
2b26f2d7 |
113 | * |
114 | * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum, |
115 | * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%. |
116 | * |
117 | * Expressing %$\lg Z$% as @CHAR_BIT * sizeof(size_t)@ yields an |
118 | * overestimate, since a @size_t@ representation may contain `holes'. |
119 | * Choosing to represent %$\lg \lg b$% by 10 is almost certainly sufficient |
120 | * for `some time to come'. |
121 | */ |
122 | |
123 | #define DEPTH (CHAR_BIT * sizeof(size_t) + 10) |
124 | |
d3409d5e |
125 | /*----- Main code ---------------------------------------------------------*/ |
126 | |
127 | /* --- @mp_read@ --- * |
128 | * |
129 | * Arguments: @mp *m@ = destination multiprecision number |
130 | * @int radix@ = base to assume for data (or zero to guess) |
131 | * @const mptext_ops *ops@ = pointer to operations block |
132 | * @void *p@ = data for the operations block |
133 | * |
134 | * Returns: The integer read, or zero if it didn't work. |
135 | * |
136 | * Use: Reads an integer from some source. If the @radix@ is |
137 | * specified, the number is assumed to be given in that radix, |
138 | * with the letters `a' (either upper- or lower-case) upwards |
139 | * standing for digits greater than 9. Otherwise, base 10 is |
140 | * assumed unless the number starts with `0' (octal), `0x' (hex) |
141 | * or `nnn_' (base `nnn'). An arbitrary amount of whitespace |
142 | * before the number is ignored. |
143 | */ |
144 | |
2b26f2d7 |
145 | /* --- About the algorithm --- * |
146 | * |
147 | * The algorithm here is rather aggressive. I maintain an array of |
148 | * successive squarings of the radix, and a stack of partial results, each |
149 | * with a counter attached indicating which radix square to multiply by. |
150 | * Once the item at the top of the stack reaches the same counter level as |
151 | * the next item down, they are combined together and the result is given a |
152 | * counter level one higher than either of the results. |
153 | * |
154 | * Gluing the results together at the end is slightly tricky. Pay attention |
155 | * to the code. |
156 | * |
157 | * This is more complicated because of the need to handle the slightly |
158 | * bizarre syntax. |
159 | */ |
160 | |
d3409d5e |
161 | mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p) |
162 | { |
2b26f2d7 |
163 | int ch; /* Current char being considered */ |
164 | unsigned f = 0; /* Flags about the current number */ |
165 | int r; /* Radix to switch over to */ |
166 | mpw rd; /* Radix as an @mp@ digit */ |
167 | mp rr; /* The @mp@ for the radix */ |
168 | unsigned nf = m ? m->f & MP_BURN : 0; /* New @mp@ flags */ |
169 | |
170 | /* --- Stacks --- */ |
171 | |
172 | mp *pow[DEPTH]; /* List of powers */ |
173 | unsigned pows; /* Next index to fill */ |
174 | struct { unsigned i; mp *m; } s[DEPTH]; /* Main stack */ |
175 | unsigned sp; /* Current stack pointer */ |
176 | |
177 | /* --- Flags --- */ |
d3409d5e |
178 | |
3bc9cb53 |
179 | #define f_neg 1u |
180 | #define f_ok 2u |
a951033d |
181 | #define f_start 4u |
d3409d5e |
182 | |
2b26f2d7 |
183 | /* --- Initialize the stacks --- */ |
184 | |
185 | mp_build(&rr, &rd, &rd + 1); |
186 | pow[0] = &rr; |
187 | pows = 1; |
188 | |
189 | sp = 0; |
190 | |
d3409d5e |
191 | /* --- Initialize the destination number --- */ |
192 | |
2b26f2d7 |
193 | if (m) |
194 | MP_DROP(m); |
d3409d5e |
195 | |
196 | /* --- Read an initial character --- */ |
197 | |
198 | ch = ops->get(p); |
199 | while (isspace(ch)) |
200 | ch = ops->get(p); |
201 | |
202 | /* --- Handle an initial sign --- */ |
203 | |
9d3838a0 |
204 | if (radix >= 0 && (ch == '-' || ch == '+')) { |
205 | if (ch == '-') |
206 | f |= f_neg; |
207 | do ch = ops->get(p); while isspace(ch); |
d3409d5e |
208 | } |
209 | |
210 | /* --- If the radix is zero, look for leading zeros --- */ |
211 | |
2b26f2d7 |
212 | if (radix > 0) { |
631673a1 |
213 | assert(((void)"ascii radix must be <= 62", radix <= 62)); |
2b26f2d7 |
214 | rd = radix; |
215 | r = -1; |
216 | } else if (radix < 0) { |
217 | rd = -radix; |
9d3838a0 |
218 | assert(((void)"binary radix must fit in a byte", rd < UCHAR_MAX)); |
d3409d5e |
219 | r = -1; |
2b26f2d7 |
220 | } else if (ch != '0') { |
221 | rd = 10; |
d3409d5e |
222 | r = 0; |
223 | } else { |
224 | ch = ops->get(p); |
3db58009 |
225 | switch (ch) { |
226 | case 'x': |
227 | rd = 16; |
228 | goto prefix; |
229 | case 'o': |
230 | rd = 8; |
231 | goto prefix; |
232 | case 'b': |
233 | rd = 2; |
234 | goto prefix; |
235 | prefix: |
236 | ch = ops->get(p); |
237 | break; |
238 | default: |
239 | rd = 8; |
240 | f |= f_ok; |
d3409d5e |
241 | } |
242 | r = -1; |
243 | } |
244 | |
a951033d |
245 | /* --- Use fast algorithm for binary radix --- * |
246 | * |
247 | * This is the restart point after having parsed a radix number from the |
248 | * input. We check whether the radix is binary, and if so use a fast |
249 | * algorithm which just stacks the bits up in the right order. |
250 | */ |
251 | |
252 | restart: |
253 | switch (rd) { |
254 | unsigned bit; |
255 | |
256 | case 2: bit = 1; goto bin; |
257 | case 4: bit = 2; goto bin; |
258 | case 8: bit = 3; goto bin; |
259 | case 16: bit = 4; goto bin; |
260 | case 32: bit = 5; goto bin; |
261 | case 64: bit = 6; goto bin; |
262 | case 128: bit = 7; goto bin; |
263 | default: |
264 | break; |
265 | |
266 | /* --- The fast binary algorithm --- * |
267 | * |
268 | * We stack bits up starting at the top end of a word. When one word is |
269 | * full, we write it to the integer, and start another with the left-over |
270 | * bits. When the array in the integer is full, we resize using low-level |
271 | * calls and copy the current data to the top end. Finally, we do a single |
272 | * bit-shift when we know where the end of the number is. |
273 | */ |
274 | |
275 | bin: { |
276 | mpw a = 0; |
277 | unsigned b = MPW_BITS; |
278 | size_t len, n; |
279 | mpw *v; |
280 | |
281 | m = mp_dest(MP_NEW, 1, nf); |
282 | len = n = m->sz; |
283 | n = len; |
284 | v = m->v + n; |
285 | for (;; ch = ops->get(p)) { |
286 | unsigned x; |
287 | |
288 | if (ch < 0) |
289 | break; |
290 | |
291 | /* --- Check that the character is a digit and in range --- */ |
292 | |
293 | if (radix < 0) |
294 | x = ch % rd; |
295 | else { |
296 | if (!isalnum(ch)) |
297 | break; |
298 | if (ch >= '0' && ch <= '9') |
299 | x = ch - '0'; |
300 | else { |
631673a1 |
301 | if (rd <= 36) |
302 | ch = tolower(ch); |
a951033d |
303 | if (ch >= 'a' && ch <= 'z') /* ASCII dependent! */ |
304 | x = ch - 'a' + 10; |
631673a1 |
305 | else if (ch >= 'A' && ch <= 'Z') |
306 | x = ch - 'A' + 36; |
a951033d |
307 | else |
308 | break; |
309 | } |
310 | } |
311 | if (x >= rd) |
312 | break; |
313 | |
314 | /* --- Feed the digit into the accumulator --- */ |
315 | |
316 | f |= f_ok; |
317 | if (!x && !(f & f_start)) |
318 | continue; |
319 | f |= f_start; |
320 | if (b > bit) { |
321 | b -= bit; |
322 | a |= MPW(x) << b; |
323 | } else { |
324 | a |= MPW(x) >> (bit - b); |
325 | b += MPW_BITS - bit; |
326 | *--v = MPW(a); |
327 | n--; |
328 | if (!n) { |
329 | n = len; |
330 | len <<= 1; |
331 | v = mpalloc(m->a, len); |
332 | memcpy(v + n, m->v, MPWS(n)); |
333 | mpfree(m->a, m->v); |
334 | m->v = v; |
335 | v = m->v + n; |
336 | } |
337 | a = (b < MPW_BITS) ? MPW(x) << b : 0; |
338 | } |
339 | } |
340 | |
341 | /* --- Finish up --- */ |
342 | |
343 | if (!(f & f_ok)) { |
344 | mp_drop(m); |
345 | m = 0; |
346 | } else { |
347 | *--v = MPW(a); |
348 | n--; |
349 | m->sz = len; |
350 | m->vl = m->v + len; |
351 | m->f &= ~MP_UNDEF; |
352 | m = mp_lsr(m, m, (unsigned long)n * MPW_BITS + b); |
353 | } |
50bea2af |
354 | ops->unget(ch, p); |
a951033d |
355 | goto done; |
356 | }} |
357 | |
d3409d5e |
358 | /* --- Time to start --- */ |
359 | |
360 | for (;; ch = ops->get(p)) { |
a951033d |
361 | unsigned x; |
d3409d5e |
362 | |
7d45ed6c |
363 | if (ch < 0) |
364 | break; |
365 | |
d3409d5e |
366 | /* --- An underscore indicates a numbered base --- */ |
367 | |
6ea6fe51 |
368 | if (ch == '_' && r > 0 && r <= 62) { |
2b26f2d7 |
369 | unsigned i; |
370 | |
371 | /* --- Clear out the stacks --- */ |
372 | |
373 | for (i = 1; i < pows; i++) |
374 | MP_DROP(pow[i]); |
375 | pows = 1; |
376 | for (i = 0; i < sp; i++) |
377 | MP_DROP(s[i].m); |
378 | sp = 0; |
379 | |
380 | /* --- Restart the search --- */ |
381 | |
382 | rd = r; |
d3409d5e |
383 | r = -1; |
384 | f &= ~f_ok; |
a951033d |
385 | ch = ops->get(p); |
386 | goto restart; |
d3409d5e |
387 | } |
388 | |
389 | /* --- Check that the character is a digit and in range --- */ |
390 | |
2b26f2d7 |
391 | if (radix < 0) |
9d3838a0 |
392 | x = ch % rd; |
d3409d5e |
393 | else { |
2b26f2d7 |
394 | if (!isalnum(ch)) |
d3409d5e |
395 | break; |
2b26f2d7 |
396 | if (ch >= '0' && ch <= '9') |
397 | x = ch - '0'; |
398 | else { |
631673a1 |
399 | if (rd <= 36) |
400 | ch = tolower(ch); |
2b26f2d7 |
401 | if (ch >= 'a' && ch <= 'z') /* ASCII dependent! */ |
402 | x = ch - 'a' + 10; |
631673a1 |
403 | else if (ch >= 'A' && ch <= 'Z') |
404 | x = ch - 'A' + 36; |
2b26f2d7 |
405 | else |
406 | break; |
407 | } |
d3409d5e |
408 | } |
409 | |
410 | /* --- Sort out what to do with the character --- */ |
411 | |
412 | if (x >= 10 && r >= 0) |
413 | r = -1; |
2b26f2d7 |
414 | if (x >= rd) |
d3409d5e |
415 | break; |
416 | |
417 | if (r >= 0) |
418 | r = r * 10 + x; |
419 | |
420 | /* --- Stick the character on the end of my integer --- */ |
421 | |
2b26f2d7 |
422 | assert(((void)"Number is too unimaginably huge", sp < DEPTH)); |
423 | s[sp].m = m = mp_new(1, nf); |
424 | m->v[0] = x; |
425 | s[sp].i = 0; |
426 | |
427 | /* --- Now grind through the stack --- */ |
428 | |
429 | while (sp > 0 && s[sp - 1].i == s[sp].i) { |
430 | |
431 | /* --- Combine the top two items --- */ |
432 | |
433 | sp--; |
434 | m = s[sp].m; |
435 | m = mp_mul(m, m, pow[s[sp].i]); |
436 | m = mp_add(m, m, s[sp + 1].m); |
437 | s[sp].m = m; |
438 | MP_DROP(s[sp + 1].m); |
439 | s[sp].i++; |
440 | |
441 | /* --- Make a new radix power if necessary --- */ |
442 | |
443 | if (s[sp].i >= pows) { |
444 | assert(((void)"Number is too unimaginably huge", pows < DEPTH)); |
445 | pow[pows] = mp_sqr(MP_NEW, pow[pows - 1]); |
446 | pows++; |
447 | } |
448 | } |
d3409d5e |
449 | f |= f_ok; |
2b26f2d7 |
450 | sp++; |
d3409d5e |
451 | } |
452 | |
453 | ops->unget(ch, p); |
454 | |
2b26f2d7 |
455 | /* --- If we're done, compute the rest of the number --- */ |
456 | |
457 | if (f & f_ok) { |
458 | if (!sp) |
459 | return (MP_ZERO); |
460 | else { |
461 | mp *z = MP_ONE; |
462 | sp--; |
463 | |
464 | while (sp > 0) { |
465 | |
466 | /* --- Combine the top two items --- */ |
467 | |
468 | sp--; |
469 | m = s[sp].m; |
470 | z = mp_mul(z, z, pow[s[sp + 1].i]); |
471 | m = mp_mul(m, m, z); |
472 | m = mp_add(m, m, s[sp + 1].m); |
473 | s[sp].m = m; |
474 | MP_DROP(s[sp + 1].m); |
475 | |
476 | /* --- Make a new radix power if necessary --- */ |
477 | |
478 | if (s[sp].i >= pows) { |
479 | assert(((void)"Number is too unimaginably huge", pows < DEPTH)); |
480 | pow[pows] = mp_sqr(MP_NEW, pow[pows - 1]); |
481 | pows++; |
482 | } |
483 | } |
484 | MP_DROP(z); |
485 | m = s[0].m; |
486 | } |
487 | } else { |
488 | unsigned i; |
489 | for (i = 0; i < sp; i++) |
490 | MP_DROP(s[i].m); |
491 | } |
492 | |
493 | /* --- Clear the radix power list --- */ |
494 | |
495 | { |
496 | unsigned i; |
497 | for (i = 1; i < pows; i++) |
498 | MP_DROP(pow[i]); |
499 | } |
500 | |
d3409d5e |
501 | /* --- Bail out if the number was bad --- */ |
502 | |
a951033d |
503 | done: |
2b26f2d7 |
504 | if (!(f & f_ok)) |
d3409d5e |
505 | return (0); |
d3409d5e |
506 | |
507 | /* --- Set the sign and return --- */ |
508 | |
d3409d5e |
509 | if (f & f_neg) |
510 | m->f |= MP_NEG; |
9bca44cb |
511 | MP_SHRINK(m); |
d3409d5e |
512 | return (m); |
3bc9cb53 |
513 | |
a951033d |
514 | #undef f_start |
3bc9cb53 |
515 | #undef f_neg |
516 | #undef f_ok |
d3409d5e |
517 | } |
518 | |
519 | /* --- @mp_write@ --- * |
520 | * |
521 | * Arguments: @mp *m@ = pointer to a multi-precision integer |
522 | * @int radix@ = radix to use when writing the number out |
523 | * @const mptext_ops *ops@ = pointer to an operations block |
524 | * @void *p@ = data for the operations block |
525 | * |
526 | * Returns: Zero if it worked, nonzero otherwise. |
527 | * |
528 | * Use: Writes a large integer in textual form. |
529 | */ |
530 | |
e360a4f2 |
531 | /* --- Simple case --- * |
532 | * |
3bc9cb53 |
533 | * Use a fixed-sized buffer and single-precision arithmetic to pick off |
534 | * low-order digits. Put each digit in a buffer, working backwards from the |
535 | * end. If the buffer becomes full, recurse to get another one. Ensure that |
536 | * there are at least @z@ digits by writing leading zeroes if there aren't |
537 | * enough real digits. |
e360a4f2 |
538 | */ |
539 | |
3bc9cb53 |
540 | static int simple(mpw n, int radix, unsigned z, |
e360a4f2 |
541 | const mptext_ops *ops, void *p) |
542 | { |
543 | int rc = 0; |
544 | char buf[64]; |
545 | unsigned i = sizeof(buf); |
2b26f2d7 |
546 | int rd = radix > 0 ? radix : -radix; |
e360a4f2 |
547 | |
548 | do { |
549 | int ch; |
550 | mpw x; |
551 | |
3bc9cb53 |
552 | x = n % rd; |
553 | n /= rd; |
2b26f2d7 |
554 | if (radix < 0) |
555 | ch = x; |
3bc9cb53 |
556 | else if (x < 10) |
557 | ch = '0' + x; |
631673a1 |
558 | else if (x < 36) /* Ascii specific */ |
3bc9cb53 |
559 | ch = 'a' + x - 10; |
631673a1 |
560 | else |
561 | ch = 'A' + x - 36; |
e360a4f2 |
562 | buf[--i] = ch; |
563 | if (z) |
564 | z--; |
3bc9cb53 |
565 | } while (i && n); |
e360a4f2 |
566 | |
3bc9cb53 |
567 | if (n) |
568 | rc = simple(n, radix, z, ops, p); |
e360a4f2 |
569 | else { |
a951033d |
570 | char zbuf[32]; |
571 | memset(zbuf, (radix < 0) ? 0 : '0', sizeof(zbuf)); |
572 | while (!rc && z >= sizeof(zbuf)) { |
573 | rc = ops->put(zbuf, sizeof(zbuf), p); |
574 | z -= sizeof(zbuf); |
e360a4f2 |
575 | } |
576 | if (!rc && z) |
a951033d |
577 | rc = ops->put(zbuf, z, p); |
e360a4f2 |
578 | } |
579 | if (!rc) |
3bc9cb53 |
580 | rc = ops->put(buf + i, sizeof(buf) - i, p); |
581 | BURN(buf); |
e360a4f2 |
582 | return (rc); |
583 | } |
584 | |
585 | /* --- Complicated case --- * |
586 | * |
587 | * If the number is small, fall back to the simple case above. Otherwise |
588 | * divide and take remainder by current large power of the radix, and emit |
589 | * each separately. Don't emit a zero quotient. Be very careful about |
590 | * leading zeroes on the remainder part, because they're deeply significant. |
591 | */ |
592 | |
593 | static int complicated(mp *m, int radix, mp **pr, unsigned i, unsigned z, |
594 | const mptext_ops *ops, void *p) |
595 | { |
596 | int rc = 0; |
597 | mp *q = MP_NEW; |
598 | unsigned d = 1 << i; |
599 | |
3bc9cb53 |
600 | if (MP_LEN(m) < 2) |
601 | return (simple(MP_LEN(m) ? m->v[0] : 0, radix, z, ops, p)); |
e360a4f2 |
602 | |
3bc9cb53 |
603 | assert(i); |
e360a4f2 |
604 | mp_div(&q, &m, m, pr[i]); |
605 | if (!MP_LEN(q)) |
606 | d = z; |
607 | else { |
608 | if (z > d) |
609 | z -= d; |
610 | else |
611 | z = 0; |
612 | rc = complicated(q, radix, pr, i - 1, z, ops, p); |
613 | } |
614 | if (!rc) |
615 | rc = complicated(m, radix, pr, i - 1, d, ops, p); |
616 | mp_drop(q); |
617 | return (rc); |
618 | } |
619 | |
a951033d |
620 | /* --- Binary case --- * |
621 | * |
622 | * Special case for binary output. Goes much faster. |
623 | */ |
624 | |
625 | static int binary(mp *m, int bit, int radix, const mptext_ops *ops, void *p) |
626 | { |
627 | mpw *v; |
628 | mpw a; |
629 | int rc = 0; |
630 | unsigned b; |
631 | unsigned mask; |
632 | unsigned long n; |
633 | unsigned f = 0; |
634 | char buf[8], *q; |
635 | unsigned x; |
636 | int ch; |
637 | |
638 | #define f_out 1u |
639 | |
640 | /* --- Work out where to start --- */ |
641 | |
642 | n = mp_bits(m); |
afd054c1 |
643 | if (n % bit) |
644 | n += bit - (n % bit); |
a951033d |
645 | b = n % MPW_BITS; |
646 | n /= MPW_BITS; |
afd054c1 |
647 | |
648 | if (n >= MP_LEN(m)) { |
a951033d |
649 | n--; |
650 | b += MPW_BITS; |
651 | } |
652 | |
653 | v = m->v + n; |
654 | a = *v; |
655 | mask = (1 << bit) - 1; |
656 | q = buf; |
657 | |
658 | /* --- Main code --- */ |
659 | |
660 | for (;;) { |
661 | if (b > bit) { |
662 | b -= bit; |
663 | x = a >> b; |
664 | } else { |
665 | x = a << (bit - b); |
666 | b += MPW_BITS - bit; |
667 | if (v == m->v) |
668 | break; |
669 | a = *--v; |
670 | if (b < MPW_BITS) |
671 | x |= a >> b; |
672 | } |
673 | x &= mask; |
674 | if (!x && !(f & f_out)) |
675 | continue; |
676 | |
677 | if (radix < 0) |
678 | ch = x; |
679 | else if (x < 10) |
680 | ch = '0' + x; |
631673a1 |
681 | else if (x < 36) |
682 | ch = 'a' + x - 10; /* Ascii specific */ |
a951033d |
683 | else |
631673a1 |
684 | ch = 'A' + x - 36; |
a951033d |
685 | *q++ = ch; |
686 | if (q >= buf + sizeof(buf)) { |
687 | if ((rc = ops->put(buf, sizeof(buf), p)) != 0) |
688 | goto done; |
689 | q = buf; |
690 | } |
691 | f |= f_out; |
692 | } |
693 | |
694 | x &= mask; |
695 | if (radix < 0) |
696 | ch = x; |
697 | else if (x < 10) |
698 | ch = '0' + x; |
631673a1 |
699 | else if (x < 36) |
700 | ch = 'a' + x - 10; /* Ascii specific */ |
a951033d |
701 | else |
631673a1 |
702 | ch = 'A' + x - 36; |
a951033d |
703 | *q++ = ch; |
704 | rc = ops->put(buf, q - buf, p); |
705 | |
706 | done: |
707 | mp_drop(m); |
708 | return (rc); |
709 | |
710 | #undef f_out |
711 | } |
712 | |
e360a4f2 |
713 | /* --- Main driver code --- */ |
714 | |
d3409d5e |
715 | int mp_write(mp *m, int radix, const mptext_ops *ops, void *p) |
716 | { |
e360a4f2 |
717 | int rc; |
d3409d5e |
718 | |
afd054c1 |
719 | if (MP_EQ(m, MP_ZERO)) |
720 | return (ops->put("0", 1, p)); |
721 | |
d3409d5e |
722 | /* --- Set various things up --- */ |
723 | |
724 | m = MP_COPY(m); |
e360a4f2 |
725 | MP_SPLIT(m); |
d3409d5e |
726 | |
2b26f2d7 |
727 | /* --- Check the radix for sensibleness --- */ |
728 | |
729 | if (radix > 0) |
631673a1 |
730 | assert(((void)"ascii radix must be <= 62", radix <= 62)); |
2b26f2d7 |
731 | else if (radix < 0) |
732 | assert(((void)"binary radix must fit in a byte", -radix < UCHAR_MAX)); |
733 | else |
734 | assert(((void)"radix can't be zero in mp_write", 0)); |
735 | |
d3409d5e |
736 | /* --- If the number is negative, sort that out --- */ |
737 | |
738 | if (m->f & MP_NEG) { |
739 | if (ops->put("-", 1, p)) |
740 | return (EOF); |
2b26f2d7 |
741 | m->f &= ~MP_NEG; |
d3409d5e |
742 | } |
743 | |
a951033d |
744 | /* --- Handle binary radix --- */ |
745 | |
746 | switch (radix) { |
747 | case 2: case -2: return (binary(m, 1, radix, ops, p)); |
748 | case 4: case -4: return (binary(m, 2, radix, ops, p)); |
749 | case 8: case -8: return (binary(m, 3, radix, ops, p)); |
750 | case 16: case -16: return (binary(m, 4, radix, ops, p)); |
751 | case 32: case -32: return (binary(m, 5, radix, ops, p)); |
752 | case -64: return (binary(m, 6, radix, ops, p)); |
753 | case -128: return (binary(m, 7, radix, ops, p)); |
754 | } |
755 | |
e360a4f2 |
756 | /* --- If the number is small, do it the easy way --- */ |
757 | |
3bc9cb53 |
758 | if (MP_LEN(m) < 2) |
759 | rc = simple(MP_LEN(m) ? m->v[0] : 0, radix, 0, ops, p); |
e360a4f2 |
760 | |
761 | /* --- Use a clever algorithm --- * |
762 | * |
763 | * Square the radix repeatedly, remembering old results, until I get |
764 | * something more than half the size of the number @m@. Use this to divide |
765 | * the number: the quotient and remainder will be approximately the same |
766 | * size, and I'll have split them on a digit boundary, so I can just emit |
767 | * the quotient and remainder recursively, in order. |
e360a4f2 |
768 | */ |
769 | |
770 | else { |
2b26f2d7 |
771 | mp *pr[DEPTH]; |
3bc9cb53 |
772 | size_t target = (MP_LEN(m) + 1) / 2; |
e360a4f2 |
773 | unsigned i = 0; |
2b26f2d7 |
774 | mp *z = mp_new(1, 0); |
e360a4f2 |
775 | |
776 | /* --- Set up the exponent table --- */ |
777 | |
2b26f2d7 |
778 | z->v[0] = (radix > 0 ? radix : -radix); |
e360a4f2 |
779 | z->f = 0; |
780 | for (;;) { |
2b26f2d7 |
781 | assert(((void)"Number is too unimaginably huge", i < DEPTH)); |
e360a4f2 |
782 | pr[i++] = z; |
783 | if (MP_LEN(z) > target) |
784 | break; |
785 | z = mp_sqr(MP_NEW, z); |
786 | } |
d3409d5e |
787 | |
e360a4f2 |
788 | /* --- Write out the answer --- */ |
d3409d5e |
789 | |
e360a4f2 |
790 | rc = complicated(m, radix, pr, i - 1, 0, ops, p); |
d3409d5e |
791 | |
e360a4f2 |
792 | /* --- Tidy away the array --- */ |
d3409d5e |
793 | |
e360a4f2 |
794 | while (i > 0) |
795 | mp_drop(pr[--i]); |
d3409d5e |
796 | } |
e360a4f2 |
797 | |
798 | /* --- Tidying up code --- */ |
799 | |
800 | MP_DROP(m); |
801 | return (rc); |
d3409d5e |
802 | } |
803 | |
804 | /*----- Test rig ----------------------------------------------------------*/ |
805 | |
806 | #ifdef TEST_RIG |
807 | |
808 | #include <mLib/testrig.h> |
809 | |
810 | static int verify(dstr *v) |
811 | { |
812 | int ok = 1; |
813 | int ib = *(int *)v[0].buf, ob = *(int *)v[2].buf; |
814 | dstr d = DSTR_INIT; |
50bea2af |
815 | size_t off = 0; |
816 | mp *m = mp_readdstr(MP_NEW, &v[1], &off, ib); |
d3409d5e |
817 | if (m) { |
818 | if (!ob) { |
819 | fprintf(stderr, "*** unexpected successful parse\n" |
a951033d |
820 | "*** input [%2i] = ", ib); |
2b26f2d7 |
821 | if (ib < 0) |
822 | type_hex.dump(&v[1], stderr); |
823 | else |
824 | fputs(v[1].buf, stderr); |
d3409d5e |
825 | mp_writedstr(m, &d, 10); |
2b26f2d7 |
826 | fprintf(stderr, "\n*** (value = %s)\n", d.buf); |
d3409d5e |
827 | ok = 0; |
828 | } else { |
829 | mp_writedstr(m, &d, ob); |
830 | if (d.len != v[3].len || memcmp(d.buf, v[3].buf, d.len) != 0) { |
831 | fprintf(stderr, "*** failed read or write\n" |
a951033d |
832 | "*** input [%2i] = ", ib); |
2b26f2d7 |
833 | if (ib < 0) |
834 | type_hex.dump(&v[1], stderr); |
835 | else |
836 | fputs(v[1].buf, stderr); |
a951033d |
837 | fprintf(stderr, "\n*** output [%2i] = ", ob); |
2b26f2d7 |
838 | if (ob < 0) |
839 | type_hex.dump(&d, stderr); |
840 | else |
841 | fputs(d.buf, stderr); |
a951033d |
842 | fprintf(stderr, "\n*** expected [%2i] = ", ob); |
2b26f2d7 |
843 | if (ob < 0) |
844 | type_hex.dump(&v[3], stderr); |
845 | else |
846 | fputs(v[3].buf, stderr); |
847 | fputc('\n', stderr); |
d3409d5e |
848 | ok = 0; |
849 | } |
850 | } |
851 | mp_drop(m); |
852 | } else { |
853 | if (ob) { |
854 | fprintf(stderr, "*** unexpected parse failure\n" |
50bea2af |
855 | "*** input [%2i] = ", ib); |
2b26f2d7 |
856 | if (ib < 0) |
857 | type_hex.dump(&v[1], stderr); |
858 | else |
859 | fputs(v[1].buf, stderr); |
50bea2af |
860 | fprintf(stderr, "\n*** expected [%2i] = ", ob); |
2b26f2d7 |
861 | if (ob < 0) |
862 | type_hex.dump(&v[3], stderr); |
863 | else |
864 | fputs(v[3].buf, stderr); |
865 | fputc('\n', stderr); |
d3409d5e |
866 | ok = 0; |
867 | } |
868 | } |
869 | |
50bea2af |
870 | if (v[1].len - off != v[4].len || |
871 | memcmp(v[1].buf + off, v[4].buf, v[4].len) != 0) { |
872 | fprintf(stderr, "*** leftovers incorrect\n" |
873 | "*** input [%2i] = ", ib); |
874 | if (ib < 0) |
875 | type_hex.dump(&v[1], stderr); |
876 | else |
877 | fputs(v[1].buf, stderr); |
878 | fprintf(stderr, "\n*** expected `%s'\n" |
879 | "*** found `%s'\n", |
880 | v[4].buf, v[1].buf + off); |
881 | ok = 0; |
882 | } |
883 | |
d3409d5e |
884 | dstr_destroy(&d); |
9c3df6c0 |
885 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
886 | return (ok); |
887 | } |
888 | |
889 | static test_chunk tests[] = { |
2b26f2d7 |
890 | { "mptext-ascii", verify, |
50bea2af |
891 | { &type_int, &type_string, &type_int, &type_string, &type_string, 0 } }, |
2b26f2d7 |
892 | { "mptext-bin-in", verify, |
50bea2af |
893 | { &type_int, &type_hex, &type_int, &type_string, &type_string, 0 } }, |
2b26f2d7 |
894 | { "mptext-bin-out", verify, |
50bea2af |
895 | { &type_int, &type_string, &type_int, &type_hex, &type_string, 0 } }, |
d3409d5e |
896 | { 0, 0, { 0 } } |
897 | }; |
898 | |
899 | int main(int argc, char *argv[]) |
900 | { |
901 | sub_init(); |
902 | test_run(argc, argv, tests, SRCDIR "/tests/mptext"); |
903 | return (0); |
904 | } |
905 | |
906 | #endif |
907 | |
908 | /*----- That's all, folks -------------------------------------------------*/ |