3 * $Id: mptext.c,v 1.7 2000/07/15 10:01:08 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 1.7 2000/07/15 10:01:08 mdw
34 * Bug fix in binary input.
36 * Revision 1.6 2000/06/25 12:58:23 mdw
37 * Fix the derivation of `depth' commentary.
39 * Revision 1.5 2000/06/17 11:46:19 mdw
40 * New and much faster stack-based algorithm for reading integers. Support
41 * reading and writing binary integers in bases between 2 and 256.
43 * Revision 1.4 1999/12/22 15:56:56 mdw
44 * Use clever recursive algorithm for writing numbers out.
46 * Revision 1.3 1999/12/10 23:23:26 mdw
47 * Allocate slightly less memory.
49 * Revision 1.2 1999/11/20 22:24:15 mdw
50 * Use function versions of MPX_UMULN and MPX_UADDN.
52 * Revision 1.1 1999/11/17 18:02:16 mdw
53 * New multiprecision integer arithmetic suite.
57 /*----- Header files ------------------------------------------------------*/
67 /*----- Magical numbers ---------------------------------------------------*/
69 /* --- Maximum recursion depth --- *
71 * This is the number of bits in a @size_t@ object. Why?
73 * To see this, let %$b = \mathit{MPW\_MAX} + 1$% and let %$Z$% be the
74 * largest @size_t@ value. Then the largest possible @mp@ is %$M - 1$% where
75 * %$M = b^Z$%. Let %$r$% be a radix to read or write. Since the recursion
76 * squares the radix at each step, the highest number reached by the
77 * recursion is %$d$%, where:
81 * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum,
82 * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%.
84 * Expressing %$\lg Z$% as @CHAR_BIT * sizeof(size_t)@ yields an
85 * overestimate, since a @size_t@ representation may contain `holes'.
86 * Choosing to represent %$\lg \lg b$% by 10 is almost certainly sufficient
87 * for `some time to come'.
90 #define DEPTH (CHAR_BIT * sizeof(size_t) + 10)
92 /*----- Main code ---------------------------------------------------------*/
94 /* --- @mp_read@ --- *
96 * Arguments: @mp *m@ = destination multiprecision number
97 * @int radix@ = base to assume for data (or zero to guess)
98 * @const mptext_ops *ops@ = pointer to operations block
99 * @void *p@ = data for the operations block
101 * Returns: The integer read, or zero if it didn't work.
103 * Use: Reads an integer from some source. If the @radix@ is
104 * specified, the number is assumed to be given in that radix,
105 * with the letters `a' (either upper- or lower-case) upwards
106 * standing for digits greater than 9. Otherwise, base 10 is
107 * assumed unless the number starts with `0' (octal), `0x' (hex)
108 * or `nnn_' (base `nnn'). An arbitrary amount of whitespace
109 * before the number is ignored.
112 /* --- About the algorithm --- *
114 * The algorithm here is rather aggressive. I maintain an array of
115 * successive squarings of the radix, and a stack of partial results, each
116 * with a counter attached indicating which radix square to multiply by.
117 * Once the item at the top of the stack reaches the same counter level as
118 * the next item down, they are combined together and the result is given a
119 * counter level one higher than either of the results.
121 * Gluing the results together at the end is slightly tricky. Pay attention
124 * This is more complicated because of the need to handle the slightly
128 mp
*mp_read(mp
*m
, int radix
, const mptext_ops
*ops
, void *p
)
130 int ch
; /* Current char being considered */
131 unsigned f
= 0; /* Flags about the current number */
132 int r
; /* Radix to switch over to */
133 mpw rd
; /* Radix as an @mp@ digit */
134 mp rr
; /* The @mp@ for the radix */
135 unsigned nf
= m ? m
->f
& MP_BURN
: 0; /* New @mp@ flags */
139 mp
*pow
[DEPTH
]; /* List of powers */
140 unsigned pows
; /* Next index to fill */
141 struct { unsigned i
; mp
*m
; } s
[DEPTH
]; /* Main stack */
142 unsigned sp
; /* Current stack pointer */
151 /* --- Initialize the stacks --- */
153 mp_build(&rr
, &rd
, &rd
+ 1);
159 /* --- Initialize the destination number --- */
164 /* --- Read an initial character --- */
170 /* --- Handle an initial sign --- */
172 if (radix
>= 0 && ch
== '-') {
179 /* --- If the radix is zero, look for leading zeros --- */
182 assert(((void)"ascii radix must be <= 36", radix
<= 36));
185 } else if (radix
< 0) {
187 assert(((void)"binary radix must fit in a byte ", rd
< UCHAR_MAX
));
189 } else if (ch
!= '0') {
204 /* --- Time to start --- */
206 for (;; ch
= ops
->get(p
)) {
212 /* --- An underscore indicates a numbered base --- */
214 if (ch
== '_' && r
> 0 && r
<= 36) {
217 /* --- Clear out the stacks --- */
219 for (i
= 1; i
< pows
; i
++)
222 for (i
= 0; i
< sp
; i
++)
226 /* --- Restart the search --- */
234 /* --- Check that the character is a digit and in range --- */
241 if (ch
>= '0' && ch
<= '9')
245 if (ch
>= 'a' && ch
<= 'z') /* ASCII dependent! */
252 /* --- Sort out what to do with the character --- */
254 if (x
>= 10 && r
>= 0)
262 /* --- Stick the character on the end of my integer --- */
264 assert(((void)"Number is too unimaginably huge", sp
< DEPTH
));
265 s
[sp
].m
= m
= mp_new(1, nf
);
269 /* --- Now grind through the stack --- */
271 while (sp
> 0 && s
[sp
- 1].i
== s
[sp
].i
) {
273 /* --- Combine the top two items --- */
277 m
= mp_mul(m
, m
, pow
[s
[sp
].i
]);
278 m
= mp_add(m
, m
, s
[sp
+ 1].m
);
280 MP_DROP(s
[sp
+ 1].m
);
283 /* --- Make a new radix power if necessary --- */
285 if (s
[sp
].i
>= pows
) {
286 assert(((void)"Number is too unimaginably huge", pows
< DEPTH
));
287 pow
[pows
] = mp_sqr(MP_NEW
, pow
[pows
- 1]);
297 /* --- If we're done, compute the rest of the number --- */
308 /* --- Combine the top two items --- */
312 z
= mp_mul(z
, z
, pow
[s
[sp
+ 1].i
]);
314 m
= mp_add(m
, m
, s
[sp
+ 1].m
);
316 MP_DROP(s
[sp
+ 1].m
);
318 /* --- Make a new radix power if necessary --- */
320 if (s
[sp
].i
>= pows
) {
321 assert(((void)"Number is too unimaginably huge", pows
< DEPTH
));
322 pow
[pows
] = mp_sqr(MP_NEW
, pow
[pows
- 1]);
331 for (i
= 0; i
< sp
; i
++)
335 /* --- Clear the radix power list --- */
339 for (i
= 1; i
< pows
; i
++)
343 /* --- Bail out if the number was bad --- */
348 /* --- Set the sign and return --- */
355 /* --- @mp_write@ --- *
357 * Arguments: @mp *m@ = pointer to a multi-precision integer
358 * @int radix@ = radix to use when writing the number out
359 * @const mptext_ops *ops@ = pointer to an operations block
360 * @void *p@ = data for the operations block
362 * Returns: Zero if it worked, nonzero otherwise.
364 * Use: Writes a large integer in textual form.
367 /* --- Simple case --- *
369 * Use a fixed-sized buffer and the simple single-precision division
370 * algorithm to pick off low-order digits. Put each digit in a buffer,
371 * working backwards from the end. If the buffer becomes full, recurse to
372 * get another one. Ensure that there are at least @z@ digits by writing
373 * leading zeroes if there aren't enough real digits.
376 static int simple(mp
*m
, int radix
, unsigned z
,
377 const mptext_ops
*ops
, void *p
)
381 unsigned i
= sizeof(buf
);
382 int rd
= radix
> 0 ? radix
: -radix
;
388 x
= mpx_udivn(m
->v
, m
->vl
, m
->v
, m
->vl
, rd
);
401 } while (i
&& MP_LEN(m
));
404 rc
= simple(m
, radix
, z
, ops
, p
);
406 static const char zero
[32] = "00000000000000000000000000000000";
407 while (!rc
&& z
>= sizeof(zero
)) {
408 rc
= ops
->put(zero
, sizeof(zero
), p
);
412 rc
= ops
->put(zero
, z
, p
);
415 ops
->put(buf
+ i
, sizeof(buf
) - i
, p
);
421 /* --- Complicated case --- *
423 * If the number is small, fall back to the simple case above. Otherwise
424 * divide and take remainder by current large power of the radix, and emit
425 * each separately. Don't emit a zero quotient. Be very careful about
426 * leading zeroes on the remainder part, because they're deeply significant.
429 static int complicated(mp
*m
, int radix
, mp
**pr
, unsigned i
, unsigned z
,
430 const mptext_ops
*ops
, void *p
)
437 return (simple(m
, radix
, z
, ops
, p
));
439 mp_div(&q
, &m
, m
, pr
[i
]);
447 rc
= complicated(q
, radix
, pr
, i
- 1, z
, ops
, p
);
450 rc
= complicated(m
, radix
, pr
, i
- 1, d
, ops
, p
);
455 /* --- Main driver code --- */
457 int mp_write(mp
*m
, int radix
, const mptext_ops
*ops
, void *p
)
461 /* --- Set various things up --- */
466 /* --- Check the radix for sensibleness --- */
469 assert(((void)"ascii radix must be <= 36", radix
<= 36));
471 assert(((void)"binary radix must fit in a byte", -radix
< UCHAR_MAX
));
473 assert(((void)"radix can't be zero in mp_write", 0));
475 /* --- If the number is negative, sort that out --- */
478 if (ops
->put("-", 1, p
))
483 /* --- If the number is small, do it the easy way --- */
486 rc
= simple(m
, radix
, 0, ops
, p
);
488 /* --- Use a clever algorithm --- *
490 * Square the radix repeatedly, remembering old results, until I get
491 * something more than half the size of the number @m@. Use this to divide
492 * the number: the quotient and remainder will be approximately the same
493 * size, and I'll have split them on a digit boundary, so I can just emit
494 * the quotient and remainder recursively, in order.
499 size_t target
= MP_LEN(m
) / 2;
501 mp
*z
= mp_new(1, 0);
503 /* --- Set up the exponent table --- */
505 z
->v
[0] = (radix
> 0 ? radix
: -radix
);
508 assert(((void)"Number is too unimaginably huge", i
< DEPTH
));
510 if (MP_LEN(z
) > target
)
512 z
= mp_sqr(MP_NEW
, z
);
515 /* --- Write out the answer --- */
517 rc
= complicated(m
, radix
, pr
, i
- 1, 0, ops
, p
);
519 /* --- Tidy away the array --- */
525 /* --- Tidying up code --- */
531 /*----- Test rig ----------------------------------------------------------*/
535 #include <mLib/testrig.h>
537 static int verify(dstr
*v
)
540 int ib
= *(int *)v
[0].buf
, ob
= *(int *)v
[2].buf
;
542 mp
*m
= mp_readdstr(MP_NEW
, &v
[1], 0, ib
);
545 fprintf(stderr
, "*** unexpected successful parse\n"
546 "*** input [%i] = ", ib
);
548 type_hex
.dump(&v
[1], stderr
);
550 fputs(v
[1].buf
, stderr
);
551 mp_writedstr(m
, &d
, 10);
552 fprintf(stderr
, "\n*** (value = %s)\n", d
.buf
);
555 mp_writedstr(m
, &d
, ob
);
556 if (d
.len
!= v
[3].len
|| memcmp(d
.buf
, v
[3].buf
, d
.len
) != 0) {
557 fprintf(stderr
, "*** failed read or write\n"
558 "*** input [%i] = ", ib
);
560 type_hex
.dump(&v
[1], stderr
);
562 fputs(v
[1].buf
, stderr
);
563 fprintf(stderr
, "\n*** output [%i] = ", ob
);
565 type_hex
.dump(&d
, stderr
);
567 fputs(d
.buf
, stderr
);
568 fprintf(stderr
, "\n*** expected [%i] = ", ob
);
570 type_hex
.dump(&v
[3], stderr
);
572 fputs(v
[3].buf
, stderr
);
580 fprintf(stderr
, "*** unexpected parse failure\n"
581 "*** input [%i] = ", ib
);
583 type_hex
.dump(&v
[1], stderr
);
585 fputs(v
[1].buf
, stderr
);
586 fprintf(stderr
, "\n*** expected [%i] = ", ob
);
588 type_hex
.dump(&v
[3], stderr
);
590 fputs(v
[3].buf
, stderr
);
597 assert(mparena_count(MPARENA_GLOBAL
) == 0);
601 static test_chunk tests
[] = {
602 { "mptext-ascii", verify
,
603 { &type_int
, &type_string
, &type_int
, &type_string
, 0 } },
604 { "mptext-bin-in", verify
,
605 { &type_int
, &type_hex
, &type_int
, &type_string
, 0 } },
606 { "mptext-bin-out", verify
,
607 { &type_int
, &type_string
, &type_int
, &type_hex
, 0 } },
611 int main(int argc
, char *argv
[])
614 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mptext");
620 /*----- That's all, folks -------------------------------------------------*/