Commit | Line | Data |
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d3409d5e | 1 | /* -*-c-*- |
d3409d5e | 2 | * |
3 | * Textual representation of multiprecision numbers | |
4 | * | |
5 | * (c) 1999 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
d3409d5e | 9 | * |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
45c0fd36 | 16 | * |
d3409d5e | 17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
45c0fd36 | 21 | * |
d3409d5e | 22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
d3409d5e | 28 | /*----- Header files ------------------------------------------------------*/ |
29 | ||
30 | #include <ctype.h> | |
2b26f2d7 | 31 | #include <limits.h> |
d3409d5e | 32 | #include <stdio.h> |
33 | ||
d3409d5e | 34 | #include "mp.h" |
35 | #include "mptext.h" | |
e360a4f2 | 36 | #include "paranoia.h" |
d3409d5e | 37 | |
2b26f2d7 | 38 | /*----- Magical numbers ---------------------------------------------------*/ |
39 | ||
40 | /* --- Maximum recursion depth --- * | |
41 | * | |
45c0fd36 | 42 | * This is the number of bits in a @size_t@ object. Why? |
2b26f2d7 | 43 | * |
eaa515d8 | 44 | * To see this, let %$b = \textit{MPW\_MAX} + 1$% and let %$Z$% be the |
dd9199f0 | 45 | * largest @size_t@ value. Then the largest possible @mp@ is %$M - 1$% where |
46 | * %$M = b^Z$%. Let %$r$% be a radix to read or write. Since the recursion | |
47 | * squares the radix at each step, the highest number reached by the | |
48 | * recursion is %$d$%, where: | |
2b26f2d7 | 49 | * |
dd9199f0 | 50 | * %$r^{2^d} = b^Z$%. |
2b26f2d7 | 51 | * |
52 | * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum, | |
53 | * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%. | |
54 | * | |
55 | * Expressing %$\lg Z$% as @CHAR_BIT * sizeof(size_t)@ yields an | |
56 | * overestimate, since a @size_t@ representation may contain `holes'. | |
57 | * Choosing to represent %$\lg \lg b$% by 10 is almost certainly sufficient | |
58 | * for `some time to come'. | |
59 | */ | |
60 | ||
61 | #define DEPTH (CHAR_BIT * sizeof(size_t) + 10) | |
62 | ||
626cd971 | 63 | /*----- Input -------------------------------------------------------------*/ |
d3409d5e | 64 | |
65 | /* --- @mp_read@ --- * | |
66 | * | |
67 | * Arguments: @mp *m@ = destination multiprecision number | |
68 | * @int radix@ = base to assume for data (or zero to guess) | |
69 | * @const mptext_ops *ops@ = pointer to operations block | |
70 | * @void *p@ = data for the operations block | |
71 | * | |
72 | * Returns: The integer read, or zero if it didn't work. | |
73 | * | |
74 | * Use: Reads an integer from some source. If the @radix@ is | |
75 | * specified, the number is assumed to be given in that radix, | |
76 | * with the letters `a' (either upper- or lower-case) upwards | |
77 | * standing for digits greater than 9. Otherwise, base 10 is | |
78 | * assumed unless the number starts with `0' (octal), `0x' (hex) | |
79 | * or `nnn_' (base `nnn'). An arbitrary amount of whitespace | |
80 | * before the number is ignored. | |
81 | */ | |
82 | ||
2b26f2d7 | 83 | /* --- About the algorithm --- * |
84 | * | |
85 | * The algorithm here is rather aggressive. I maintain an array of | |
86 | * successive squarings of the radix, and a stack of partial results, each | |
87 | * with a counter attached indicating which radix square to multiply by. | |
88 | * Once the item at the top of the stack reaches the same counter level as | |
89 | * the next item down, they are combined together and the result is given a | |
90 | * counter level one higher than either of the results. | |
91 | * | |
92 | * Gluing the results together at the end is slightly tricky. Pay attention | |
93 | * to the code. | |
94 | * | |
95 | * This is more complicated because of the need to handle the slightly | |
96 | * bizarre syntax. | |
97 | */ | |
98 | ||
a6b6ae6b | 99 | static int char_digit(int ch, int radix) |
d3409d5e | 100 | { |
a6b6ae6b MW |
101 | int r = radix < 0 ? -radix : radix; |
102 | int d; | |
103 | ||
104 | if (ch < 0) return (-1); | |
105 | if (radix < 0) d = ch; | |
106 | else if ('0' <= ch && ch <= '9') d = ch - '0'; | |
107 | else if ('a' <= ch && ch <= 'z') d = ch - 'a' + 10; | |
108 | else if ('A' <= ch && ch <= 'Z') d = ch - 'A' + (radix > 36 ? 36 : 10); | |
109 | else return (-1); | |
110 | if (d >= r) return (-1); | |
111 | return (d); | |
112 | } | |
a951033d | 113 | |
a6b6ae6b MW |
114 | static mp *read_binary(int radix, unsigned bit, unsigned nf, |
115 | const mptext_ops *ops, void *p) | |
116 | { | |
117 | mpw a = 0; | |
118 | unsigned b = MPW_BITS; | |
119 | int any = 0, nz = 0; | |
120 | int ch, d; | |
121 | size_t len, n; | |
122 | mpw *v; | |
123 | mp *m; | |
a951033d | 124 | |
125 | /* --- The fast binary algorithm --- * | |
126 | * | |
127 | * We stack bits up starting at the top end of a word. When one word is | |
128 | * full, we write it to the integer, and start another with the left-over | |
129 | * bits. When the array in the integer is full, we resize using low-level | |
130 | * calls and copy the current data to the top end. Finally, we do a single | |
131 | * bit-shift when we know where the end of the number is. | |
132 | */ | |
133 | ||
a6b6ae6b MW |
134 | m = mp_dest(MP_NEW, 1, nf); |
135 | len = n = m->sz; | |
136 | n = len; | |
137 | v = m->v + n; | |
a951033d | 138 | |
a6b6ae6b MW |
139 | for (;;) { |
140 | ch = ops->get(p); | |
141 | if ((d = char_digit(ch, radix)) < 0) break; | |
a951033d | 142 | |
a6b6ae6b | 143 | /* --- Ignore leading zeroes, but notice that the number is valid --- */ |
a951033d | 144 | |
a6b6ae6b MW |
145 | any = 1; |
146 | if (!d && !nz) continue; | |
147 | nz = 1; | |
a951033d | 148 | |
a6b6ae6b | 149 | /* --- Feed the digit into the accumulator --- */ |
a951033d | 150 | |
a6b6ae6b MW |
151 | if (b > bit) { |
152 | b -= bit; | |
153 | a |= MPW(d) << b; | |
a951033d | 154 | } else { |
a6b6ae6b MW |
155 | a |= MPW(d) >> (bit - b); |
156 | b += MPW_BITS - bit; | |
157 | *--v = MPW(a); n--; | |
158 | if (!n) { | |
159 | n = len; len <<= 1; | |
160 | v = mpalloc(m->a, len); | |
161 | memcpy(v + n, m->v, MPWS(n)); | |
162 | mpfree(m->a, m->v); | |
163 | m->v = v; v = m->v + n; | |
164 | } | |
165 | a = (b < MPW_BITS) ? MPW(d) << b : 0; | |
a951033d | 166 | } |
a6b6ae6b | 167 | } |
a951033d | 168 | |
a6b6ae6b | 169 | /* --- Finish up --- */ |
d3409d5e | 170 | |
a6b6ae6b MW |
171 | ops->unget(ch, p); |
172 | if (!any) { mp_drop(m); return (0); } | |
d3409d5e | 173 | |
a6b6ae6b MW |
174 | *--v = MPW(a); n--; |
175 | m->sz = len; | |
176 | m->vl = m->v + len; | |
177 | m->f &= ~MP_UNDEF; | |
178 | m = mp_lsr(m, m, (unsigned long)n * MPW_BITS + b); | |
7d45ed6c | 179 | |
a6b6ae6b MW |
180 | return (m); |
181 | } | |
d3409d5e | 182 | |
a6b6ae6b | 183 | struct readstate { |
2b26f2d7 | 184 | |
a6b6ae6b MW |
185 | /* --- State for the general-base reader --- * |
186 | * | |
187 | * There are two arrays. The @pow@ array is set so that @pow[i]@ contains | |
188 | * %$R^{2^i}$% for @i < pows@. The stack @s@ contains partial results: | |
189 | * each entry contains a value @m@ corresponding to %$2^i$% digits. | |
190 | * Inductively, an empty stack represents zero; if a stack represents %$x$% | |
191 | * then pushing a new entry on the top causes the stack to represent | |
192 | * %$R^{2^i} x + m$%. | |
193 | * | |
194 | * It is an invariant that each entry has a strictly smaller @i@ than the | |
195 | * items beneath it. This is achieved by coaslescing entries at the top if | |
196 | * they have equal %$i$% values: if the top items are %$(m, i)$%, and | |
197 | * %$(M', i)$%, and the rest of the stack represents the integer %$x$%, | |
198 | * then %$R^{2^i} (R^{2^i} x + M) + m = R^{2^{i+1}} x + (R^{2^i} M + m)$%, | |
199 | * so we replace the top two items by %$((R^{2^i} M + m), i + 1)$%, and | |
200 | * repeat if necessary. | |
201 | */ | |
2b26f2d7 | 202 | |
a6b6ae6b MW |
203 | unsigned pows, sp; |
204 | struct { unsigned i; mp *m; } s[DEPTH]; | |
205 | mp *pow[DEPTH]; | |
206 | }; | |
2b26f2d7 | 207 | |
a6b6ae6b MW |
208 | static void ensure_power(struct readstate *rs) |
209 | { | |
210 | /* --- Make sure we have the necessary %$R^{2^i}$% computed --- */ | |
2b26f2d7 | 211 | |
a6b6ae6b MW |
212 | if (rs->s[rs->sp].i >= rs->pows) { |
213 | assert(rs->pows < DEPTH); | |
214 | rs->pow[rs->pows] = mp_sqr(MP_NEW, rs->pow[rs->pows - 1]); | |
215 | rs->pows++; | |
216 | } | |
217 | } | |
d3409d5e | 218 | |
a6b6ae6b MW |
219 | static void read_digit(struct readstate *rs, unsigned nf, int d) |
220 | { | |
221 | mp *m = mp_new(1, nf); | |
222 | m->v[0] = d; | |
d3409d5e | 223 | |
a6b6ae6b | 224 | /* --- Put the new digit on top --- */ |
d3409d5e | 225 | |
a6b6ae6b MW |
226 | assert(rs->sp < DEPTH); |
227 | rs->s[rs->sp].m = m; | |
228 | rs->s[rs->sp].i = 0; | |
d3409d5e | 229 | |
a6b6ae6b | 230 | /* --- Restore the stack invariant --- */ |
d3409d5e | 231 | |
a6b6ae6b MW |
232 | while (rs->sp && rs->s[rs->sp - 1].i <= rs->s[rs->sp].i) { |
233 | assert(rs->sp > 0); | |
234 | ensure_power(rs); | |
235 | rs->sp--; | |
d3409d5e | 236 | |
a6b6ae6b MW |
237 | m = rs->s[rs->sp].m; |
238 | m = mp_mul(m, m, rs->pow[rs->s[rs->sp + 1].i]); | |
239 | m = mp_add(m, m, rs->s[rs->sp + 1].m); | |
240 | MP_DROP(rs->s[rs->sp + 1].m); | |
241 | rs->s[rs->sp].m = m; | |
242 | rs->s[rs->sp].i++; | |
243 | } | |
d3409d5e | 244 | |
a6b6ae6b | 245 | /* --- Leave the stack pointer at an empty item --- */ |
2b26f2d7 | 246 | |
a6b6ae6b MW |
247 | rs->sp++; |
248 | } | |
2b26f2d7 | 249 | |
a6b6ae6b MW |
250 | static mp *read_general(int radix, unsigned t, unsigned nf, |
251 | const mptext_ops *ops, void *p) | |
252 | { | |
253 | struct readstate rs; | |
254 | unsigned char v[4]; | |
255 | unsigned i; | |
256 | mpw r; | |
257 | int any = 0; | |
258 | int ch, d; | |
259 | mp rr; | |
260 | mp *m, *z, *n; | |
261 | ||
262 | /* --- Prepare the stack --- */ | |
263 | ||
264 | r = radix < 0 ? -radix : radix; | |
265 | mp_build(&rr, &r, &r + 1); | |
266 | rs.pow[0] = &rr; | |
267 | rs.pows = 1; | |
268 | rs.sp = 0; | |
269 | ||
270 | /* --- If we've partially parsed some input then feed it in --- * | |
271 | * | |
272 | * Unfortunately, what we've got is backwards. Fortunately there's a | |
273 | * fairly tight upper bound on how many digits @t@ might be, since we | |
274 | * aborted that loop once it got too large. | |
275 | */ | |
276 | ||
277 | if (t) { | |
278 | i = 0; | |
279 | while (t) { assert(i < sizeof(v)); v[i++] = t%r; t /= r; } | |
280 | while (i) read_digit(&rs, nf, v[--i]); | |
281 | any = 1; | |
282 | } | |
2b26f2d7 | 283 | |
a6b6ae6b | 284 | /* --- Read more stuff --- */ |
2b26f2d7 | 285 | |
a6b6ae6b MW |
286 | for (;;) { |
287 | ch = ops->get(p); | |
288 | if ((d = char_digit(ch, radix)) < 0) break; | |
289 | read_digit(&rs, nf, d); any = 1; | |
290 | } | |
291 | ops->unget(ch, p); | |
2b26f2d7 | 292 | |
a6b6ae6b MW |
293 | /* --- Stitch all of the numbers together --- * |
294 | * | |
295 | * This is not the same code as @read_digit@. In particular, here we must | |
296 | * cope with the partial result being some inconvenient power of %$R$%, | |
297 | * rather than %$R^{2^i}$%. | |
298 | */ | |
2b26f2d7 | 299 | |
a6b6ae6b MW |
300 | if (!any) return (0); |
301 | m = MP_ZERO; z = MP_ONE; | |
302 | while (rs.sp) { | |
303 | rs.sp--; | |
304 | ensure_power(&rs); | |
305 | n = rs.s[rs.sp].m; | |
306 | n = mp_mul(n, n, z); | |
307 | m = mp_add(m, m, n); | |
308 | z = mp_mul(z, z, rs.pow[rs.s[rs.sp].i]); | |
309 | MP_DROP(n); | |
d3409d5e | 310 | } |
a6b6ae6b MW |
311 | for (i = 0; i < rs.pows; i++) MP_DROP(rs.pow[i]); |
312 | MP_DROP(z); | |
313 | return (m); | |
314 | } | |
d3409d5e | 315 | |
a6b6ae6b MW |
316 | mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p) |
317 | { | |
318 | unsigned t = 0; | |
319 | unsigned nf = 0; | |
320 | int ch, d, rd; | |
321 | ||
322 | unsigned f = 0; | |
323 | #define f_neg 1u | |
324 | #define f_ok 2u | |
d3409d5e | 325 | |
a6b6ae6b MW |
326 | /* --- We don't actually need a destination so throw it away --- * |
327 | * | |
328 | * But note the flags before we lose it entirely. | |
329 | */ | |
2b26f2d7 | 330 | |
a6b6ae6b MW |
331 | if (m) { |
332 | nf = m->f & MP_BURN; | |
333 | MP_DROP(m); | |
334 | } | |
2b26f2d7 | 335 | |
a6b6ae6b | 336 | /* --- Maintain a lookahead character --- */ |
2b26f2d7 | 337 | |
a6b6ae6b | 338 | ch = ops->get(p); |
2b26f2d7 | 339 | |
a6b6ae6b | 340 | /* --- If we're reading text, skip leading space, and maybe a sign --- */ |
2b26f2d7 | 341 | |
a6b6ae6b MW |
342 | if (radix >= 0) { |
343 | while (isspace(ch)) ch = ops->get(p); | |
344 | switch (ch) { | |
345 | case '-': f |= f_neg; /* and on */ | |
346 | case '+': do ch = ops->get(p); while (isspace(ch)); | |
347 | } | |
348 | } | |
349 | ||
350 | /* --- If we don't have a fixed radix, then parse one from the input --- * | |
351 | * | |
352 | * This is moderately easy if the input starts with `0x' or similar. If it | |
353 | * starts with `0' and something else, then it might be octal, or just a | |
354 | * plain old zero. Finally, it might start with a leading `NN_', in which | |
355 | * case we carefully collect the decimal number until we're sure it's | |
356 | * either a radix prefix (in which case we accept it and start over) or it | |
357 | * isn't (in which case it's actually the start of a large number we need | |
358 | * to read). | |
359 | */ | |
2b26f2d7 | 360 | |
a6b6ae6b MW |
361 | if (radix == 0) { |
362 | if (ch == '0') { | |
363 | ch = ops->get(p); | |
364 | switch (ch) { | |
365 | case 'x': case 'X': radix = 16; goto fetch; | |
366 | case 'o': case 'O': radix = 8; goto fetch; | |
367 | case 'b': case 'B': radix = 2; goto fetch; | |
368 | fetch: ch = ops->get(p); break; | |
369 | default: radix = 8; f |= f_ok; break; | |
370 | } | |
371 | } else { | |
372 | if ((d = char_digit(ch, 10)) < 0) { ops->unget(ch, p); return (0); } | |
373 | for (;;) { | |
374 | t = 10*t + d; | |
375 | ch = ops->get(p); | |
376 | if (t > 52) break; | |
377 | if ((d = char_digit(ch, 10)) < 0) break; | |
378 | } | |
379 | if (ch != '_' || t > 52) radix = 10; | |
380 | else { | |
381 | radix = t; t = 0; | |
382 | ch = ops->get(p); | |
2b26f2d7 | 383 | } |
2b26f2d7 | 384 | } |
2b26f2d7 | 385 | } |
386 | ||
a6b6ae6b MW |
387 | /* --- We're now ready to dispatch to the correct handler --- */ |
388 | ||
389 | rd = radix < 0 ? -radix : radix; | |
390 | ops->unget(ch, p); | |
391 | switch (rd) { | |
392 | case 2: m = read_binary(radix, 1, nf, ops, p); break; | |
393 | case 4: m = read_binary(radix, 2, nf, ops, p); break; | |
394 | case 8: m = read_binary(radix, 3, nf, ops, p); break; | |
395 | case 16: m = read_binary(radix, 4, nf, ops, p); break; | |
396 | case 32: m = read_binary(radix, 5, nf, ops, p); break; | |
397 | case 64: m = read_binary(radix, 6, nf, ops, p); break; | |
398 | case 128: m = read_binary(radix, 7, nf, ops, p); break; | |
399 | default: m = read_general(radix, t, nf, ops, p); break; | |
400 | } | |
401 | ||
402 | /* --- That didn't work --- * | |
403 | * | |
404 | * If we've already read something then return that. Otherwise it's an | |
405 | * error. | |
406 | */ | |
2b26f2d7 | 407 | |
a6b6ae6b MW |
408 | if (!m) { |
409 | if (f & f_ok) return (MP_ZERO); | |
410 | else return (0); | |
2b26f2d7 | 411 | } |
412 | ||
a6b6ae6b | 413 | /* --- Negate the result if we should do that --- */ |
d3409d5e | 414 | |
a6b6ae6b | 415 | if (f & f_neg) m = mp_neg(m, m); |
d3409d5e | 416 | |
a6b6ae6b | 417 | /* --- And we're all done --- */ |
d3409d5e | 418 | |
d3409d5e | 419 | return (m); |
3bc9cb53 | 420 | |
421 | #undef f_neg | |
422 | #undef f_ok | |
d3409d5e | 423 | } |
424 | ||
626cd971 MW |
425 | /*----- Output ------------------------------------------------------------*/ |
426 | ||
d3409d5e | 427 | /* --- @mp_write@ --- * |
428 | * | |
429 | * Arguments: @mp *m@ = pointer to a multi-precision integer | |
430 | * @int radix@ = radix to use when writing the number out | |
431 | * @const mptext_ops *ops@ = pointer to an operations block | |
432 | * @void *p@ = data for the operations block | |
433 | * | |
434 | * Returns: Zero if it worked, nonzero otherwise. | |
435 | * | |
436 | * Use: Writes a large integer in textual form. | |
437 | */ | |
438 | ||
626cd971 MW |
439 | static int digit_char(int d, int radix) |
440 | { | |
441 | if (radix < 0) return (d); | |
442 | else if (d < 10) return (d + '0'); | |
443 | else if (d < 26) return (d - 10 + 'a'); | |
444 | else return (d - 36 + 'A'); | |
445 | } | |
446 | ||
e360a4f2 | 447 | /* --- Simple case --- * |
448 | * | |
3bc9cb53 | 449 | * Use a fixed-sized buffer and single-precision arithmetic to pick off |
450 | * low-order digits. Put each digit in a buffer, working backwards from the | |
451 | * end. If the buffer becomes full, recurse to get another one. Ensure that | |
452 | * there are at least @z@ digits by writing leading zeroes if there aren't | |
453 | * enough real digits. | |
e360a4f2 | 454 | */ |
455 | ||
626cd971 MW |
456 | static int write_simple(mpw n, int radix, unsigned z, |
457 | const mptext_ops *ops, void *p) | |
e360a4f2 | 458 | { |
459 | int rc = 0; | |
460 | char buf[64]; | |
461 | unsigned i = sizeof(buf); | |
2b26f2d7 | 462 | int rd = radix > 0 ? radix : -radix; |
626cd971 | 463 | mpw x; |
e360a4f2 | 464 | |
465 | do { | |
626cd971 MW |
466 | x = n % rd; n /= rd; |
467 | buf[--i] = digit_char(x, radix); | |
468 | if (z) z--; | |
3bc9cb53 | 469 | } while (i && n); |
e360a4f2 | 470 | |
3bc9cb53 | 471 | if (n) |
626cd971 | 472 | rc = write_simple(n, radix, z, ops, p); |
e360a4f2 | 473 | else { |
a951033d | 474 | char zbuf[32]; |
475 | memset(zbuf, (radix < 0) ? 0 : '0', sizeof(zbuf)); | |
476 | while (!rc && z >= sizeof(zbuf)) { | |
477 | rc = ops->put(zbuf, sizeof(zbuf), p); | |
478 | z -= sizeof(zbuf); | |
e360a4f2 | 479 | } |
626cd971 | 480 | if (!rc && z) rc = ops->put(zbuf, z, p); |
e360a4f2 | 481 | } |
626cd971 | 482 | if (!rc) rc = ops->put(buf + i, sizeof(buf) - i, p); |
3bc9cb53 | 483 | BURN(buf); |
e360a4f2 | 484 | return (rc); |
485 | } | |
486 | ||
487 | /* --- Complicated case --- * | |
488 | * | |
489 | * If the number is small, fall back to the simple case above. Otherwise | |
490 | * divide and take remainder by current large power of the radix, and emit | |
491 | * each separately. Don't emit a zero quotient. Be very careful about | |
492 | * leading zeroes on the remainder part, because they're deeply significant. | |
493 | */ | |
494 | ||
626cd971 MW |
495 | static int write_complicated(mp *m, int radix, mp **pr, |
496 | unsigned i, unsigned z, | |
497 | const mptext_ops *ops, void *p) | |
e360a4f2 | 498 | { |
499 | int rc = 0; | |
500 | mp *q = MP_NEW; | |
501 | unsigned d = 1 << i; | |
502 | ||
3bc9cb53 | 503 | if (MP_LEN(m) < 2) |
626cd971 | 504 | return (write_simple(MP_LEN(m) ? m->v[0] : 0, radix, z, ops, p)); |
e360a4f2 | 505 | |
3bc9cb53 | 506 | assert(i); |
e360a4f2 | 507 | mp_div(&q, &m, m, pr[i]); |
626cd971 | 508 | if (MP_ZEROP(q)) d = z; |
e360a4f2 | 509 | else { |
626cd971 MW |
510 | if (z > d) z -= d; |
511 | else z = 0; | |
512 | rc = write_complicated(q, radix, pr, i - 1, z, ops, p); | |
e360a4f2 | 513 | } |
626cd971 | 514 | if (!rc) rc = write_complicated(m, radix, pr, i - 1, d, ops, p); |
e360a4f2 | 515 | mp_drop(q); |
516 | return (rc); | |
517 | } | |
518 | ||
a951033d | 519 | /* --- Binary case --- * |
520 | * | |
521 | * Special case for binary output. Goes much faster. | |
522 | */ | |
523 | ||
626cd971 MW |
524 | static int write_binary(mp *m, int bit, int radix, |
525 | const mptext_ops *ops, void *p) | |
a951033d | 526 | { |
527 | mpw *v; | |
528 | mpw a; | |
529 | int rc = 0; | |
530 | unsigned b; | |
531 | unsigned mask; | |
532 | unsigned long n; | |
533 | unsigned f = 0; | |
534 | char buf[8], *q; | |
535 | unsigned x; | |
a951033d | 536 | |
537 | #define f_out 1u | |
538 | ||
539 | /* --- Work out where to start --- */ | |
540 | ||
541 | n = mp_bits(m); | |
626cd971 | 542 | if (n % bit) n += bit - (n % bit); |
a951033d | 543 | b = n % MPW_BITS; |
544 | n /= MPW_BITS; | |
afd054c1 | 545 | |
546 | if (n >= MP_LEN(m)) { | |
a951033d | 547 | n--; |
548 | b += MPW_BITS; | |
549 | } | |
550 | ||
551 | v = m->v + n; | |
552 | a = *v; | |
553 | mask = (1 << bit) - 1; | |
554 | q = buf; | |
555 | ||
556 | /* --- Main code --- */ | |
557 | ||
558 | for (;;) { | |
559 | if (b > bit) { | |
560 | b -= bit; | |
561 | x = a >> b; | |
562 | } else { | |
563 | x = a << (bit - b); | |
564 | b += MPW_BITS - bit; | |
626cd971 | 565 | if (v == m->v) break; |
a951033d | 566 | a = *--v; |
626cd971 | 567 | if (b < MPW_BITS) x |= a >> b; |
a951033d | 568 | } |
569 | x &= mask; | |
626cd971 | 570 | if (!x && !(f & f_out)) continue; |
a951033d | 571 | |
626cd971 | 572 | *q++ = digit_char(x, radix); |
a951033d | 573 | if (q >= buf + sizeof(buf)) { |
626cd971 | 574 | if ((rc = ops->put(buf, sizeof(buf), p)) != 0) goto done; |
a951033d | 575 | q = buf; |
576 | } | |
577 | f |= f_out; | |
578 | } | |
579 | ||
580 | x &= mask; | |
626cd971 | 581 | *q++ = digit_char(x, radix); |
a951033d | 582 | rc = ops->put(buf, q - buf, p); |
583 | ||
584 | done: | |
585 | mp_drop(m); | |
586 | return (rc); | |
587 | ||
588 | #undef f_out | |
589 | } | |
590 | ||
e360a4f2 | 591 | /* --- Main driver code --- */ |
592 | ||
d3409d5e | 593 | int mp_write(mp *m, int radix, const mptext_ops *ops, void *p) |
594 | { | |
e360a4f2 | 595 | int rc; |
626cd971 MW |
596 | mp *pr[DEPTH]; |
597 | size_t target; | |
598 | unsigned i = 0; | |
599 | mp *z; | |
d3409d5e | 600 | |
afd054c1 | 601 | if (MP_EQ(m, MP_ZERO)) |
572b324a | 602 | return (ops->put(radix > 0 ? "0" : "\0", 1, p)); |
afd054c1 | 603 | |
d3409d5e | 604 | /* --- Set various things up --- */ |
605 | ||
606 | m = MP_COPY(m); | |
e360a4f2 | 607 | MP_SPLIT(m); |
d3409d5e | 608 | |
2b26f2d7 | 609 | /* --- Check the radix for sensibleness --- */ |
610 | ||
611 | if (radix > 0) | |
631673a1 | 612 | assert(((void)"ascii radix must be <= 62", radix <= 62)); |
2b26f2d7 | 613 | else if (radix < 0) |
25b5e686 | 614 | assert(((void)"binary radix must fit in a byte", -radix <= UCHAR_MAX)); |
2b26f2d7 | 615 | else |
616 | assert(((void)"radix can't be zero in mp_write", 0)); | |
617 | ||
d3409d5e | 618 | /* --- If the number is negative, sort that out --- */ |
619 | ||
a69a3efd | 620 | if (MP_NEGP(m)) { |
572b324a | 621 | assert(radix > 0); |
626cd971 | 622 | if (ops->put("-", 1, p)) return (EOF); |
2b26f2d7 | 623 | m->f &= ~MP_NEG; |
d3409d5e | 624 | } |
625 | ||
a951033d | 626 | /* --- Handle binary radix --- */ |
627 | ||
628 | switch (radix) { | |
626cd971 MW |
629 | case 2: case -2: return (write_binary(m, 1, radix, ops, p)); |
630 | case 4: case -4: return (write_binary(m, 2, radix, ops, p)); | |
631 | case 8: case -8: return (write_binary(m, 3, radix, ops, p)); | |
632 | case 16: case -16: return (write_binary(m, 4, radix, ops, p)); | |
633 | case 32: case -32: return (write_binary(m, 5, radix, ops, p)); | |
634 | case -64: return (write_binary(m, 6, radix, ops, p)); | |
635 | case -128: return (write_binary(m, 7, radix, ops, p)); | |
a951033d | 636 | } |
637 | ||
e360a4f2 | 638 | /* --- If the number is small, do it the easy way --- */ |
639 | ||
3bc9cb53 | 640 | if (MP_LEN(m) < 2) |
626cd971 | 641 | rc = write_simple(MP_LEN(m) ? m->v[0] : 0, radix, 0, ops, p); |
e360a4f2 | 642 | |
643 | /* --- Use a clever algorithm --- * | |
644 | * | |
645 | * Square the radix repeatedly, remembering old results, until I get | |
646 | * something more than half the size of the number @m@. Use this to divide | |
647 | * the number: the quotient and remainder will be approximately the same | |
648 | * size, and I'll have split them on a digit boundary, so I can just emit | |
649 | * the quotient and remainder recursively, in order. | |
e360a4f2 | 650 | */ |
651 | ||
652 | else { | |
626cd971 MW |
653 | target = (MP_LEN(m) + 1) / 2; |
654 | z = mp_new(1, 0); | |
e360a4f2 | 655 | |
656 | /* --- Set up the exponent table --- */ | |
657 | ||
2b26f2d7 | 658 | z->v[0] = (radix > 0 ? radix : -radix); |
e360a4f2 | 659 | z->f = 0; |
660 | for (;;) { | |
2b26f2d7 | 661 | assert(((void)"Number is too unimaginably huge", i < DEPTH)); |
e360a4f2 | 662 | pr[i++] = z; |
626cd971 | 663 | if (MP_LEN(z) > target) break; |
e360a4f2 | 664 | z = mp_sqr(MP_NEW, z); |
665 | } | |
d3409d5e | 666 | |
e360a4f2 | 667 | /* --- Write out the answer --- */ |
d3409d5e | 668 | |
626cd971 | 669 | rc = write_complicated(m, radix, pr, i - 1, 0, ops, p); |
d3409d5e | 670 | |
e360a4f2 | 671 | /* --- Tidy away the array --- */ |
d3409d5e | 672 | |
626cd971 | 673 | while (i > 0) mp_drop(pr[--i]); |
d3409d5e | 674 | } |
e360a4f2 | 675 | |
676 | /* --- Tidying up code --- */ | |
677 | ||
678 | MP_DROP(m); | |
679 | return (rc); | |
d3409d5e | 680 | } |
681 | ||
682 | /*----- Test rig ----------------------------------------------------------*/ | |
683 | ||
684 | #ifdef TEST_RIG | |
685 | ||
686 | #include <mLib/testrig.h> | |
687 | ||
688 | static int verify(dstr *v) | |
689 | { | |
690 | int ok = 1; | |
691 | int ib = *(int *)v[0].buf, ob = *(int *)v[2].buf; | |
692 | dstr d = DSTR_INIT; | |
50bea2af | 693 | size_t off = 0; |
694 | mp *m = mp_readdstr(MP_NEW, &v[1], &off, ib); | |
d3409d5e | 695 | if (m) { |
696 | if (!ob) { | |
697 | fprintf(stderr, "*** unexpected successful parse\n" | |
45c0fd36 | 698 | "*** input [%2i] = ", ib); |
2b26f2d7 | 699 | if (ib < 0) |
700 | type_hex.dump(&v[1], stderr); | |
701 | else | |
702 | fputs(v[1].buf, stderr); | |
d3409d5e | 703 | mp_writedstr(m, &d, 10); |
2b26f2d7 | 704 | fprintf(stderr, "\n*** (value = %s)\n", d.buf); |
d3409d5e | 705 | ok = 0; |
706 | } else { | |
707 | mp_writedstr(m, &d, ob); | |
708 | if (d.len != v[3].len || memcmp(d.buf, v[3].buf, d.len) != 0) { | |
709 | fprintf(stderr, "*** failed read or write\n" | |
45c0fd36 | 710 | "*** input [%2i] = ", ib); |
2b26f2d7 | 711 | if (ib < 0) |
712 | type_hex.dump(&v[1], stderr); | |
713 | else | |
714 | fputs(v[1].buf, stderr); | |
45c0fd36 | 715 | fprintf(stderr, "\n*** output [%2i] = ", ob); |
2b26f2d7 | 716 | if (ob < 0) |
717 | type_hex.dump(&d, stderr); | |
718 | else | |
719 | fputs(d.buf, stderr); | |
45c0fd36 | 720 | fprintf(stderr, "\n*** expected [%2i] = ", ob); |
2b26f2d7 | 721 | if (ob < 0) |
722 | type_hex.dump(&v[3], stderr); | |
723 | else | |
724 | fputs(v[3].buf, stderr); | |
725 | fputc('\n', stderr); | |
d3409d5e | 726 | ok = 0; |
727 | } | |
728 | } | |
729 | mp_drop(m); | |
730 | } else { | |
731 | if (ob) { | |
732 | fprintf(stderr, "*** unexpected parse failure\n" | |
45c0fd36 | 733 | "*** input [%2i] = ", ib); |
2b26f2d7 | 734 | if (ib < 0) |
735 | type_hex.dump(&v[1], stderr); | |
736 | else | |
737 | fputs(v[1].buf, stderr); | |
50bea2af | 738 | fprintf(stderr, "\n*** expected [%2i] = ", ob); |
2b26f2d7 | 739 | if (ob < 0) |
740 | type_hex.dump(&v[3], stderr); | |
741 | else | |
742 | fputs(v[3].buf, stderr); | |
743 | fputc('\n', stderr); | |
d3409d5e | 744 | ok = 0; |
745 | } | |
746 | } | |
747 | ||
50bea2af | 748 | if (v[1].len - off != v[4].len || |
749 | memcmp(v[1].buf + off, v[4].buf, v[4].len) != 0) { | |
750 | fprintf(stderr, "*** leftovers incorrect\n" | |
45c0fd36 | 751 | "*** input [%2i] = ", ib); |
50bea2af | 752 | if (ib < 0) |
753 | type_hex.dump(&v[1], stderr); | |
754 | else | |
755 | fputs(v[1].buf, stderr); | |
756 | fprintf(stderr, "\n*** expected `%s'\n" | |
45c0fd36 | 757 | "*** found `%s'\n", |
50bea2af | 758 | v[4].buf, v[1].buf + off); |
759 | ok = 0; | |
760 | } | |
45c0fd36 | 761 | |
d3409d5e | 762 | dstr_destroy(&d); |
9c3df6c0 | 763 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e | 764 | return (ok); |
765 | } | |
766 | ||
767 | static test_chunk tests[] = { | |
2b26f2d7 | 768 | { "mptext-ascii", verify, |
50bea2af | 769 | { &type_int, &type_string, &type_int, &type_string, &type_string, 0 } }, |
2b26f2d7 | 770 | { "mptext-bin-in", verify, |
50bea2af | 771 | { &type_int, &type_hex, &type_int, &type_string, &type_string, 0 } }, |
2b26f2d7 | 772 | { "mptext-bin-out", verify, |
50bea2af | 773 | { &type_int, &type_string, &type_int, &type_hex, &type_string, 0 } }, |
d3409d5e | 774 | { 0, 0, { 0 } } |
775 | }; | |
776 | ||
777 | int main(int argc, char *argv[]) | |
778 | { | |
779 | sub_init(); | |
0f00dc4c | 780 | test_run(argc, argv, tests, SRCDIR "/t/mptext"); |
d3409d5e | 781 | return (0); |
782 | } | |
783 | ||
784 | #endif | |
785 | ||
786 | /*----- That's all, folks -------------------------------------------------*/ |