3 * Textual representation of multiprecision numbers
5 * (c) 1999 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
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.
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.
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,
28 /*----- Header files ------------------------------------------------------*/
38 /*----- Magical numbers ---------------------------------------------------*/
40 /* --- Maximum recursion depth --- *
42 * This is the number of bits in a @size_t@ object. Why?
44 * To see this, let %$b = \textit{MPW\_MAX} + 1$% and let %$Z$% be the
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:
52 * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum,
53 * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%.
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'.
61 #define DEPTH (CHAR_BIT * sizeof(size_t) + 10)
63 /*----- Input -------------------------------------------------------------*/
65 /* --- @mp_read@ --- *
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
72 * Returns: The integer read, or zero if it didn't work.
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.
83 /* --- About the algorithm --- *
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.
92 * Gluing the results together at the end is slightly tricky. Pay attention
95 * This is more complicated because of the need to handle the slightly
99 mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p)
101 int ch; /* Current char being considered */
102 unsigned f = 0; /* Flags about the current number */
103 int r; /* Radix to switch over to */
104 mpw rd; /* Radix as an @mp@ digit */
105 mp rr; /* The @mp@ for the radix */
106 unsigned nf = m ? m->f & MP_BURN : 0; /* New @mp@ flags */
110 mp *pow[DEPTH]; /* List of powers */
111 unsigned pows; /* Next index to fill */
112 struct { unsigned i; mp *m; } s[DEPTH]; /* Main stack */
113 unsigned sp; /* Current stack pointer */
121 /* --- Initialize the stacks --- */
123 mp_build(&rr, &rd, &rd + 1);
129 /* --- Initialize the destination number --- */
134 /* --- Read an initial character --- */
142 /* --- Handle an initial sign --- */
144 if (radix >= 0 && (ch == '-' || ch == '+')) {
147 do ch = ops->get(p); while isspace(ch);
150 /* --- If the radix is zero, look for leading zeros --- */
153 assert(((void)"ascii radix must be <= 62", radix <= 62));
156 } else if (radix < 0) {
158 assert(((void)"binary radix must fit in a byte", rd <= UCHAR_MAX));
160 } else if (ch != '0') {
185 /* --- Use fast algorithm for binary radix --- *
187 * This is the restart point after having parsed a radix number from the
188 * input. We check whether the radix is binary, and if so use a fast
189 * algorithm which just stacks the bits up in the right order.
196 case 2: bit = 1; goto bin;
197 case 4: bit = 2; goto bin;
198 case 8: bit = 3; goto bin;
199 case 16: bit = 4; goto bin;
200 case 32: bit = 5; goto bin;
201 case 64: bit = 6; goto bin;
202 case 128: bit = 7; goto bin;
206 /* --- The fast binary algorithm --- *
208 * We stack bits up starting at the top end of a word. When one word is
209 * full, we write it to the integer, and start another with the left-over
210 * bits. When the array in the integer is full, we resize using low-level
211 * calls and copy the current data to the top end. Finally, we do a single
212 * bit-shift when we know where the end of the number is.
217 unsigned b = MPW_BITS;
221 m = mp_dest(MP_NEW, 1, nf);
225 for (;; ch = ops->get(p)) {
231 /* --- Check that the character is a digit and in range --- */
238 if (ch >= '0' && ch <= '9')
243 if (ch >= 'a' && ch <= 'z') /* ASCII dependent! */
245 else if (ch >= 'A' && ch <= 'Z')
254 /* --- Feed the digit into the accumulator --- */
257 if (!x && !(f & f_start))
264 a |= MPW(x) >> (bit - b);
271 v = mpalloc(m->a, len);
272 memcpy(v + n, m->v, MPWS(n));
277 a = (b < MPW_BITS) ? MPW(x) << b : 0;
281 /* --- Finish up --- */
292 m = mp_lsr(m, m, (unsigned long)n * MPW_BITS + b);
298 /* --- Time to start --- */
300 for (;; ch = ops->get(p)) {
306 /* --- An underscore indicates a numbered base --- */
308 if (ch == '_' && r > 0 && r <= 62) {
311 /* --- Clear out the stacks --- */
313 for (i = 1; i < pows; i++)
316 for (i = 0; i < sp; i++)
320 /* --- Restart the search --- */
329 /* --- Check that the character is a digit and in range --- */
336 if (ch >= '0' && ch <= '9')
341 if (ch >= 'a' && ch <= 'z') /* ASCII dependent! */
343 else if (ch >= 'A' && ch <= 'Z')
350 /* --- Sort out what to do with the character --- */
352 if (x >= 10 && r >= 0)
360 /* --- Stick the character on the end of my integer --- */
362 assert(((void)"Number is too unimaginably huge", sp < DEPTH));
363 s[sp].m = m = mp_new(1, nf);
367 /* --- Now grind through the stack --- */
369 while (sp > 0 && s[sp - 1].i == s[sp].i) {
371 /* --- Combine the top two items --- */
375 m = mp_mul(m, m, pow[s[sp].i]);
376 m = mp_add(m, m, s[sp + 1].m);
378 MP_DROP(s[sp + 1].m);
381 /* --- Make a new radix power if necessary --- */
383 if (s[sp].i >= pows) {
384 assert(((void)"Number is too unimaginably huge", pows < DEPTH));
385 pow[pows] = mp_sqr(MP_NEW, pow[pows - 1]);
395 /* --- If we're done, compute the rest of the number --- */
406 /* --- Combine the top two items --- */
410 z = mp_mul(z, z, pow[s[sp + 1].i]);
412 m = mp_add(m, m, s[sp + 1].m);
414 MP_DROP(s[sp + 1].m);
416 /* --- Make a new radix power if necessary --- */
418 if (s[sp].i >= pows) {
419 assert(((void)"Number is too unimaginably huge", pows < DEPTH));
420 pow[pows] = mp_sqr(MP_NEW, pow[pows - 1]);
429 for (i = 0; i < sp; i++)
433 /* --- Clear the radix power list --- */
437 for (i = 1; i < pows; i++)
441 /* --- Bail out if the number was bad --- */
447 /* --- Set the sign and return --- */
459 /*----- Output ------------------------------------------------------------*/
461 /* --- @mp_write@ --- *
463 * Arguments: @mp *m@ = pointer to a multi-precision integer
464 * @int radix@ = radix to use when writing the number out
465 * @const mptext_ops *ops@ = pointer to an operations block
466 * @void *p@ = data for the operations block
468 * Returns: Zero if it worked, nonzero otherwise.
470 * Use: Writes a large integer in textual form.
473 static int digit_char(int d, int radix)
475 if (radix < 0) return (d);
476 else if (d < 10) return (d + '0');
477 else if (d < 26) return (d - 10 + 'a');
478 else return (d - 36 + 'A');
481 /* --- Simple case --- *
483 * Use a fixed-sized buffer and single-precision arithmetic to pick off
484 * low-order digits. Put each digit in a buffer, working backwards from the
485 * end. If the buffer becomes full, recurse to get another one. Ensure that
486 * there are at least @z@ digits by writing leading zeroes if there aren't
487 * enough real digits.
490 static int write_simple(mpw n, int radix, unsigned z,
491 const mptext_ops *ops, void *p)
495 unsigned i = sizeof(buf);
496 int rd = radix > 0 ? radix : -radix;
501 buf[--i] = digit_char(x, radix);
506 rc = write_simple(n, radix, z, ops, p);
509 memset(zbuf, (radix < 0) ? 0 : '0', sizeof(zbuf));
510 while (!rc && z >= sizeof(zbuf)) {
511 rc = ops->put(zbuf, sizeof(zbuf), p);
514 if (!rc && z) rc = ops->put(zbuf, z, p);
516 if (!rc) rc = ops->put(buf + i, sizeof(buf) - i, p);
521 /* --- Complicated case --- *
523 * If the number is small, fall back to the simple case above. Otherwise
524 * divide and take remainder by current large power of the radix, and emit
525 * each separately. Don't emit a zero quotient. Be very careful about
526 * leading zeroes on the remainder part, because they're deeply significant.
529 static int write_complicated(mp *m, int radix, mp **pr,
530 unsigned i, unsigned z,
531 const mptext_ops *ops, void *p)
538 return (write_simple(MP_LEN(m) ? m->v[0] : 0, radix, z, ops, p));
541 mp_div(&q, &m, m, pr[i]);
542 if (MP_ZEROP(q)) d = z;
546 rc = write_complicated(q, radix, pr, i - 1, z, ops, p);
548 if (!rc) rc = write_complicated(m, radix, pr, i - 1, d, ops, p);
553 /* --- Binary case --- *
555 * Special case for binary output. Goes much faster.
558 static int write_binary(mp *m, int bit, int radix,
559 const mptext_ops *ops, void *p)
573 /* --- Work out where to start --- */
576 if (n % bit) n += bit - (n % bit);
580 if (n >= MP_LEN(m)) {
587 mask = (1 << bit) - 1;
590 /* --- Main code --- */
599 if (v == m->v) break;
601 if (b < MPW_BITS) x |= a >> b;
604 if (!x && !(f & f_out)) continue;
606 *q++ = digit_char(x, radix);
607 if (q >= buf + sizeof(buf)) {
608 if ((rc = ops->put(buf, sizeof(buf), p)) != 0) goto done;
615 *q++ = digit_char(x, radix);
616 rc = ops->put(buf, q - buf, p);
625 /* --- Main driver code --- */
627 int mp_write(mp *m, int radix, const mptext_ops *ops, void *p)
635 if (MP_EQ(m, MP_ZERO))
636 return (ops->put(radix > 0 ? "0" : "\0", 1, p));
638 /* --- Set various things up --- */
643 /* --- Check the radix for sensibleness --- */
646 assert(((void)"ascii radix must be <= 62", radix <= 62));
648 assert(((void)"binary radix must fit in a byte", -radix <= UCHAR_MAX));
650 assert(((void)"radix can't be zero in mp_write", 0));
652 /* --- If the number is negative, sort that out --- */
656 if (ops->put("-", 1, p)) return (EOF);
660 /* --- Handle binary radix --- */
663 case 2: case -2: return (write_binary(m, 1, radix, ops, p));
664 case 4: case -4: return (write_binary(m, 2, radix, ops, p));
665 case 8: case -8: return (write_binary(m, 3, radix, ops, p));
666 case 16: case -16: return (write_binary(m, 4, radix, ops, p));
667 case 32: case -32: return (write_binary(m, 5, radix, ops, p));
668 case -64: return (write_binary(m, 6, radix, ops, p));
669 case -128: return (write_binary(m, 7, radix, ops, p));
672 /* --- If the number is small, do it the easy way --- */
675 rc = write_simple(MP_LEN(m) ? m->v[0] : 0, radix, 0, ops, p);
677 /* --- Use a clever algorithm --- *
679 * Square the radix repeatedly, remembering old results, until I get
680 * something more than half the size of the number @m@. Use this to divide
681 * the number: the quotient and remainder will be approximately the same
682 * size, and I'll have split them on a digit boundary, so I can just emit
683 * the quotient and remainder recursively, in order.
687 target = (MP_LEN(m) + 1) / 2;
690 /* --- Set up the exponent table --- */
692 z->v[0] = (radix > 0 ? radix : -radix);
695 assert(((void)"Number is too unimaginably huge", i < DEPTH));
697 if (MP_LEN(z) > target) break;
698 z = mp_sqr(MP_NEW, z);
701 /* --- Write out the answer --- */
703 rc = write_complicated(m, radix, pr, i - 1, 0, ops, p);
705 /* --- Tidy away the array --- */
707 while (i > 0) mp_drop(pr[--i]);
710 /* --- Tidying up code --- */
716 /*----- Test rig ----------------------------------------------------------*/
720 #include <mLib/testrig.h>
722 static int verify(dstr *v)
725 int ib = *(int *)v[0].buf, ob = *(int *)v[2].buf;
728 mp *m = mp_readdstr(MP_NEW, &v[1], &off, ib);
731 fprintf(stderr, "*** unexpected successful parse\n"
732 "*** input [%2i] = ", ib);
734 type_hex.dump(&v[1], stderr);
736 fputs(v[1].buf, stderr);
737 mp_writedstr(m, &d, 10);
738 fprintf(stderr, "\n*** (value = %s)\n", d.buf);
741 mp_writedstr(m, &d, ob);
742 if (d.len != v[3].len || memcmp(d.buf, v[3].buf, d.len) != 0) {
743 fprintf(stderr, "*** failed read or write\n"
744 "*** input [%2i] = ", ib);
746 type_hex.dump(&v[1], stderr);
748 fputs(v[1].buf, stderr);
749 fprintf(stderr, "\n*** output [%2i] = ", ob);
751 type_hex.dump(&d, stderr);
753 fputs(d.buf, stderr);
754 fprintf(stderr, "\n*** expected [%2i] = ", ob);
756 type_hex.dump(&v[3], stderr);
758 fputs(v[3].buf, stderr);
766 fprintf(stderr, "*** unexpected parse failure\n"
767 "*** input [%2i] = ", ib);
769 type_hex.dump(&v[1], stderr);
771 fputs(v[1].buf, stderr);
772 fprintf(stderr, "\n*** expected [%2i] = ", ob);
774 type_hex.dump(&v[3], stderr);
776 fputs(v[3].buf, stderr);
782 if (v[1].len - off != v[4].len ||
783 memcmp(v[1].buf + off, v[4].buf, v[4].len) != 0) {
784 fprintf(stderr, "*** leftovers incorrect\n"
785 "*** input [%2i] = ", ib);
787 type_hex.dump(&v[1], stderr);
789 fputs(v[1].buf, stderr);
790 fprintf(stderr, "\n*** expected `%s'\n"
792 v[4].buf, v[1].buf + off);
797 assert(mparena_count(MPARENA_GLOBAL) == 0);
801 static test_chunk tests[] = {
802 { "mptext-ascii", verify,
803 { &type_int, &type_string, &type_int, &type_string, &type_string, 0 } },
804 { "mptext-bin-in", verify,
805 { &type_int, &type_hex, &type_int, &type_string, &type_string, 0 } },
806 { "mptext-bin-out", verify,
807 { &type_int, &type_string, &type_int, &type_hex, &type_string, 0 } },
811 int main(int argc, char *argv[])
814 test_run(argc, argv, tests, SRCDIR "/t/mptext");
820 /*----- That's all, folks -------------------------------------------------*/