3 * $Id: mptext.c,v 1.6 2000/06/25 12:58:23 mdw Exp $
5 * Textual representation of multiprecision numbers
7 * (c) 1999 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Revision history --------------------------------------------------*
33 * Revision 1.6 2000/06/25 12:58:23 mdw
34 * Fix the derivation of `depth' commentary.
36 * Revision 1.5 2000/06/17 11:46:19 mdw
37 * New and much faster stack-based algorithm for reading integers. Support
38 * reading and writing binary integers in bases between 2 and 256.
40 * Revision 1.4 1999/12/22 15:56:56 mdw
41 * Use clever recursive algorithm for writing numbers out.
43 * Revision 1.3 1999/12/10 23:23:26 mdw
44 * Allocate slightly less memory.
46 * Revision 1.2 1999/11/20 22:24:15 mdw
47 * Use function versions of MPX_UMULN and MPX_UADDN.
49 * Revision 1.1 1999/11/17 18:02:16 mdw
50 * New multiprecision integer arithmetic suite.
54 /*----- Header files ------------------------------------------------------*/
64 /*----- Magical numbers ---------------------------------------------------*/
66 /* --- Maximum recursion depth --- *
68 * This is the number of bits in a @size_t@ object. Why?
70 * To see this, let %$b = \mathit{MPW\_MAX} + 1$% and let %$Z$% be the
71 * largest @size_t@ value. Then the largest possible @mp@ is %$M - 1$% where
72 * %$M = b^Z$%. Let %$r$% be a radix to read or write. Since the recursion
73 * squares the radix at each step, the highest number reached by the
74 * recursion is %$d$%, where:
78 * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum,
79 * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%.
81 * Expressing %$\lg Z$% as @CHAR_BIT * sizeof(size_t)@ yields an
82 * overestimate, since a @size_t@ representation may contain `holes'.
83 * Choosing to represent %$\lg \lg b$% by 10 is almost certainly sufficient
84 * for `some time to come'.
87 #define DEPTH (CHAR_BIT * sizeof(size_t) + 10)
89 /*----- Main code ---------------------------------------------------------*/
91 /* --- @mp_read@ --- *
93 * Arguments: @mp *m@ = destination multiprecision number
94 * @int radix@ = base to assume for data (or zero to guess)
95 * @const mptext_ops *ops@ = pointer to operations block
96 * @void *p@ = data for the operations block
98 * Returns: The integer read, or zero if it didn't work.
100 * Use: Reads an integer from some source. If the @radix@ is
101 * specified, the number is assumed to be given in that radix,
102 * with the letters `a' (either upper- or lower-case) upwards
103 * standing for digits greater than 9. Otherwise, base 10 is
104 * assumed unless the number starts with `0' (octal), `0x' (hex)
105 * or `nnn_' (base `nnn'). An arbitrary amount of whitespace
106 * before the number is ignored.
109 /* --- About the algorithm --- *
111 * The algorithm here is rather aggressive. I maintain an array of
112 * successive squarings of the radix, and a stack of partial results, each
113 * with a counter attached indicating which radix square to multiply by.
114 * Once the item at the top of the stack reaches the same counter level as
115 * the next item down, they are combined together and the result is given a
116 * counter level one higher than either of the results.
118 * Gluing the results together at the end is slightly tricky. Pay attention
121 * This is more complicated because of the need to handle the slightly
125 mp
*mp_read(mp
*m
, int radix
, const mptext_ops
*ops
, void *p
)
127 int ch
; /* Current char being considered */
128 unsigned f
= 0; /* Flags about the current number */
129 int r
; /* Radix to switch over to */
130 mpw rd
; /* Radix as an @mp@ digit */
131 mp rr
; /* The @mp@ for the radix */
132 unsigned nf
= m ? m
->f
& MP_BURN
: 0; /* New @mp@ flags */
136 mp
*pow
[DEPTH
]; /* List of powers */
137 unsigned pows
; /* Next index to fill */
138 struct { unsigned i
; mp
*m
; } s
[DEPTH
]; /* Main stack */
139 unsigned sp
; /* Current stack pointer */
148 /* --- Initialize the stacks --- */
150 mp_build(&rr
, &rd
, &rd
+ 1);
156 /* --- Initialize the destination number --- */
161 /* --- Read an initial character --- */
167 /* --- Handle an initial sign --- */
176 /* --- If the radix is zero, look for leading zeros --- */
179 assert(((void)"ascii radix must be <= 36", radix
<= 36));
182 } else if (radix
< 0) {
184 assert(((void)"binary radix must fit in a byte ", rd
< UCHAR_MAX
));
186 } else if (ch
!= '0') {
201 /* --- Time to start --- */
203 for (;; ch
= ops
->get(p
)) {
206 /* --- An underscore indicates a numbered base --- */
208 if (ch
== '_' && r
> 0 && r
<= 36) {
211 /* --- Clear out the stacks --- */
213 for (i
= 1; i
< pows
; i
++)
216 for (i
= 0; i
< sp
; i
++)
220 /* --- Restart the search --- */
228 /* --- Check that the character is a digit and in range --- */
235 if (ch
>= '0' && ch
<= '9')
239 if (ch
>= 'a' && ch
<= 'z') /* ASCII dependent! */
246 /* --- Sort out what to do with the character --- */
248 if (x
>= 10 && r
>= 0)
256 /* --- Stick the character on the end of my integer --- */
258 assert(((void)"Number is too unimaginably huge", sp
< DEPTH
));
259 s
[sp
].m
= m
= mp_new(1, nf
);
263 /* --- Now grind through the stack --- */
265 while (sp
> 0 && s
[sp
- 1].i
== s
[sp
].i
) {
267 /* --- Combine the top two items --- */
271 m
= mp_mul(m
, m
, pow
[s
[sp
].i
]);
272 m
= mp_add(m
, m
, s
[sp
+ 1].m
);
274 MP_DROP(s
[sp
+ 1].m
);
277 /* --- Make a new radix power if necessary --- */
279 if (s
[sp
].i
>= pows
) {
280 assert(((void)"Number is too unimaginably huge", pows
< DEPTH
));
281 pow
[pows
] = mp_sqr(MP_NEW
, pow
[pows
- 1]);
291 /* --- If we're done, compute the rest of the number --- */
302 /* --- Combine the top two items --- */
306 z
= mp_mul(z
, z
, pow
[s
[sp
+ 1].i
]);
308 m
= mp_add(m
, m
, s
[sp
+ 1].m
);
310 MP_DROP(s
[sp
+ 1].m
);
312 /* --- Make a new radix power if necessary --- */
314 if (s
[sp
].i
>= pows
) {
315 assert(((void)"Number is too unimaginably huge", pows
< DEPTH
));
316 pow
[pows
] = mp_sqr(MP_NEW
, pow
[pows
- 1]);
325 for (i
= 0; i
< sp
; i
++)
329 /* --- Clear the radix power list --- */
333 for (i
= 1; i
< pows
; i
++)
337 /* --- Bail out if the number was bad --- */
342 /* --- Set the sign and return --- */
349 /* --- @mp_write@ --- *
351 * Arguments: @mp *m@ = pointer to a multi-precision integer
352 * @int radix@ = radix to use when writing the number out
353 * @const mptext_ops *ops@ = pointer to an operations block
354 * @void *p@ = data for the operations block
356 * Returns: Zero if it worked, nonzero otherwise.
358 * Use: Writes a large integer in textual form.
361 /* --- Simple case --- *
363 * Use a fixed-sized buffer and the simple single-precision division
364 * algorithm to pick off low-order digits. Put each digit in a buffer,
365 * working backwards from the end. If the buffer becomes full, recurse to
366 * get another one. Ensure that there are at least @z@ digits by writing
367 * leading zeroes if there aren't enough real digits.
370 static int simple(mp
*m
, int radix
, unsigned z
,
371 const mptext_ops
*ops
, void *p
)
375 unsigned i
= sizeof(buf
);
376 int rd
= radix
> 0 ? radix
: -radix
;
382 x
= mpx_udivn(m
->v
, m
->vl
, m
->v
, m
->vl
, rd
);
395 } while (i
&& MP_LEN(m
));
398 rc
= simple(m
, radix
, z
, ops
, p
);
400 static const char zero
[32] = "00000000000000000000000000000000";
401 while (!rc
&& z
>= sizeof(zero
)) {
402 rc
= ops
->put(zero
, sizeof(zero
), p
);
406 rc
= ops
->put(zero
, z
, p
);
409 ops
->put(buf
+ i
, sizeof(buf
) - i
, p
);
415 /* --- Complicated case --- *
417 * If the number is small, fall back to the simple case above. Otherwise
418 * divide and take remainder by current large power of the radix, and emit
419 * each separately. Don't emit a zero quotient. Be very careful about
420 * leading zeroes on the remainder part, because they're deeply significant.
423 static int complicated(mp
*m
, int radix
, mp
**pr
, unsigned i
, unsigned z
,
424 const mptext_ops
*ops
, void *p
)
431 return (simple(m
, radix
, z
, ops
, p
));
433 mp_div(&q
, &m
, m
, pr
[i
]);
441 rc
= complicated(q
, radix
, pr
, i
- 1, z
, ops
, p
);
444 rc
= complicated(m
, radix
, pr
, i
- 1, d
, ops
, p
);
449 /* --- Main driver code --- */
451 int mp_write(mp
*m
, int radix
, const mptext_ops
*ops
, void *p
)
455 /* --- Set various things up --- */
460 /* --- Check the radix for sensibleness --- */
463 assert(((void)"ascii radix must be <= 36", radix
<= 36));
465 assert(((void)"binary radix must fit in a byte", -radix
< UCHAR_MAX
));
467 assert(((void)"radix can't be zero in mp_write", 0));
469 /* --- If the number is negative, sort that out --- */
472 if (ops
->put("-", 1, p
))
477 /* --- If the number is small, do it the easy way --- */
480 rc
= simple(m
, radix
, 0, ops
, p
);
482 /* --- Use a clever algorithm --- *
484 * Square the radix repeatedly, remembering old results, until I get
485 * something more than half the size of the number @m@. Use this to divide
486 * the number: the quotient and remainder will be approximately the same
487 * size, and I'll have split them on a digit boundary, so I can just emit
488 * the quotient and remainder recursively, in order.
493 size_t target
= MP_LEN(m
) / 2;
495 mp
*z
= mp_new(1, 0);
497 /* --- Set up the exponent table --- */
499 z
->v
[0] = (radix
> 0 ? radix
: -radix
);
502 assert(((void)"Number is too unimaginably huge", i
< DEPTH
));
504 if (MP_LEN(z
) > target
)
506 z
= mp_sqr(MP_NEW
, z
);
509 /* --- Write out the answer --- */
511 rc
= complicated(m
, radix
, pr
, i
- 1, 0, ops
, p
);
513 /* --- Tidy away the array --- */
519 /* --- Tidying up code --- */
525 /*----- Test rig ----------------------------------------------------------*/
529 #include <mLib/testrig.h>
531 static int verify(dstr
*v
)
534 int ib
= *(int *)v
[0].buf
, ob
= *(int *)v
[2].buf
;
536 mp
*m
= mp_readdstr(MP_NEW
, &v
[1], 0, ib
);
539 fprintf(stderr
, "*** unexpected successful parse\n"
540 "*** input [%i] = ", ib
);
542 type_hex
.dump(&v
[1], stderr
);
544 fputs(v
[1].buf
, stderr
);
545 mp_writedstr(m
, &d
, 10);
546 fprintf(stderr
, "\n*** (value = %s)\n", d
.buf
);
549 mp_writedstr(m
, &d
, ob
);
550 if (d
.len
!= v
[3].len
|| memcmp(d
.buf
, v
[3].buf
, d
.len
) != 0) {
551 fprintf(stderr
, "*** failed read or write\n"
552 "*** input [%i] = ", ib
);
554 type_hex
.dump(&v
[1], stderr
);
556 fputs(v
[1].buf
, stderr
);
557 fprintf(stderr
, "\n*** output [%i] = ", ob
);
559 type_hex
.dump(&d
, stderr
);
561 fputs(d
.buf
, stderr
);
562 fprintf(stderr
, "\n*** expected [%i] = ", ob
);
564 type_hex
.dump(&v
[3], stderr
);
566 fputs(v
[3].buf
, stderr
);
574 fprintf(stderr
, "*** unexpected parse failure\n"
575 "*** input [%i] = ", ib
);
577 type_hex
.dump(&v
[1], stderr
);
579 fputs(v
[1].buf
, stderr
);
580 fprintf(stderr
, "\n*** expected [%i] = ", ob
);
582 type_hex
.dump(&v
[3], stderr
);
584 fputs(v
[3].buf
, stderr
);
591 assert(mparena_count(MPARENA_GLOBAL
) == 0);
595 static test_chunk tests
[] = {
596 { "mptext-ascii", verify
,
597 { &type_int
, &type_string
, &type_int
, &type_string
, 0 } },
598 { "mptext-bin-in", verify
,
599 { &type_int
, &type_hex
, &type_int
, &type_string
, 0 } },
600 { "mptext-bin-out", verify
,
601 { &type_int
, &type_string
, &type_int
, &type_hex
, 0 } },
605 int main(int argc
, char *argv
[])
608 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mptext");
614 /*----- That's all, folks -------------------------------------------------*/