3 * $Id: mptext.c,v 1.8 2000/12/06 20:32:42 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 1.8 2000/12/06 20:32:42 mdw
34 * Reduce binary bytes (to allow marker bits to be ignored). Fix error
35 * message string a bit. Allow leading `+' signs.
37 * Revision 1.7 2000/07/15 10:01:08 mdw
38 * Bug fix in binary input.
40 * Revision 1.6 2000/06/25 12:58:23 mdw
41 * Fix the derivation of `depth' commentary.
43 * Revision 1.5 2000/06/17 11:46:19 mdw
44 * New and much faster stack-based algorithm for reading integers. Support
45 * reading and writing binary integers in bases between 2 and 256.
47 * Revision 1.4 1999/12/22 15:56:56 mdw
48 * Use clever recursive algorithm for writing numbers out.
50 * Revision 1.3 1999/12/10 23:23:26 mdw
51 * Allocate slightly less memory.
53 * Revision 1.2 1999/11/20 22:24:15 mdw
54 * Use function versions of MPX_UMULN and MPX_UADDN.
56 * Revision 1.1 1999/11/17 18:02:16 mdw
57 * New multiprecision integer arithmetic suite.
61 /*----- Header files ------------------------------------------------------*/
71 /*----- Magical numbers ---------------------------------------------------*/
73 /* --- Maximum recursion depth --- *
75 * This is the number of bits in a @size_t@ object. Why?
77 * To see this, let %$b = \mathit{MPW\_MAX} + 1$% and let %$Z$% be the
78 * largest @size_t@ value. Then the largest possible @mp@ is %$M - 1$% where
79 * %$M = b^Z$%. Let %$r$% be a radix to read or write. Since the recursion
80 * squares the radix at each step, the highest number reached by the
81 * recursion is %$d$%, where:
85 * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum,
86 * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%.
88 * Expressing %$\lg Z$% as @CHAR_BIT * sizeof(size_t)@ yields an
89 * overestimate, since a @size_t@ representation may contain `holes'.
90 * Choosing to represent %$\lg \lg b$% by 10 is almost certainly sufficient
91 * for `some time to come'.
94 #define DEPTH (CHAR_BIT * sizeof(size_t) + 10)
96 /*----- Main code ---------------------------------------------------------*/
98 /* --- @mp_read@ --- *
100 * Arguments: @mp *m@ = destination multiprecision number
101 * @int radix@ = base to assume for data (or zero to guess)
102 * @const mptext_ops *ops@ = pointer to operations block
103 * @void *p@ = data for the operations block
105 * Returns: The integer read, or zero if it didn't work.
107 * Use: Reads an integer from some source. If the @radix@ is
108 * specified, the number is assumed to be given in that radix,
109 * with the letters `a' (either upper- or lower-case) upwards
110 * standing for digits greater than 9. Otherwise, base 10 is
111 * assumed unless the number starts with `0' (octal), `0x' (hex)
112 * or `nnn_' (base `nnn'). An arbitrary amount of whitespace
113 * before the number is ignored.
116 /* --- About the algorithm --- *
118 * The algorithm here is rather aggressive. I maintain an array of
119 * successive squarings of the radix, and a stack of partial results, each
120 * with a counter attached indicating which radix square to multiply by.
121 * Once the item at the top of the stack reaches the same counter level as
122 * the next item down, they are combined together and the result is given a
123 * counter level one higher than either of the results.
125 * Gluing the results together at the end is slightly tricky. Pay attention
128 * This is more complicated because of the need to handle the slightly
132 mp
*mp_read(mp
*m
, int radix
, const mptext_ops
*ops
, void *p
)
134 int ch
; /* Current char being considered */
135 unsigned f
= 0; /* Flags about the current number */
136 int r
; /* Radix to switch over to */
137 mpw rd
; /* Radix as an @mp@ digit */
138 mp rr
; /* The @mp@ for the radix */
139 unsigned nf
= m ? m
->f
& MP_BURN
: 0; /* New @mp@ flags */
143 mp
*pow
[DEPTH
]; /* List of powers */
144 unsigned pows
; /* Next index to fill */
145 struct { unsigned i
; mp
*m
; } s
[DEPTH
]; /* Main stack */
146 unsigned sp
; /* Current stack pointer */
155 /* --- Initialize the stacks --- */
157 mp_build(&rr
, &rd
, &rd
+ 1);
163 /* --- Initialize the destination number --- */
168 /* --- Read an initial character --- */
174 /* --- Handle an initial sign --- */
176 if (radix
>= 0 && (ch
== '-' || ch
== '+')) {
179 do ch
= ops
->get(p
); while isspace(ch
);
182 /* --- If the radix is zero, look for leading zeros --- */
185 assert(((void)"ascii radix must be <= 36", radix
<= 36));
188 } else if (radix
< 0) {
190 assert(((void)"binary radix must fit in a byte", rd
< UCHAR_MAX
));
192 } else if (ch
!= '0') {
207 /* --- Time to start --- */
209 for (;; ch
= ops
->get(p
)) {
215 /* --- An underscore indicates a numbered base --- */
217 if (ch
== '_' && r
> 0 && r
<= 36) {
220 /* --- Clear out the stacks --- */
222 for (i
= 1; i
< pows
; i
++)
225 for (i
= 0; i
< sp
; i
++)
229 /* --- Restart the search --- */
237 /* --- Check that the character is a digit and in range --- */
244 if (ch
>= '0' && ch
<= '9')
248 if (ch
>= 'a' && ch
<= 'z') /* ASCII dependent! */
255 /* --- Sort out what to do with the character --- */
257 if (x
>= 10 && r
>= 0)
265 /* --- Stick the character on the end of my integer --- */
267 assert(((void)"Number is too unimaginably huge", sp
< DEPTH
));
268 s
[sp
].m
= m
= mp_new(1, nf
);
272 /* --- Now grind through the stack --- */
274 while (sp
> 0 && s
[sp
- 1].i
== s
[sp
].i
) {
276 /* --- Combine the top two items --- */
280 m
= mp_mul(m
, m
, pow
[s
[sp
].i
]);
281 m
= mp_add(m
, m
, s
[sp
+ 1].m
);
283 MP_DROP(s
[sp
+ 1].m
);
286 /* --- Make a new radix power if necessary --- */
288 if (s
[sp
].i
>= pows
) {
289 assert(((void)"Number is too unimaginably huge", pows
< DEPTH
));
290 pow
[pows
] = mp_sqr(MP_NEW
, pow
[pows
- 1]);
300 /* --- If we're done, compute the rest of the number --- */
311 /* --- Combine the top two items --- */
315 z
= mp_mul(z
, z
, pow
[s
[sp
+ 1].i
]);
317 m
= mp_add(m
, m
, s
[sp
+ 1].m
);
319 MP_DROP(s
[sp
+ 1].m
);
321 /* --- Make a new radix power if necessary --- */
323 if (s
[sp
].i
>= pows
) {
324 assert(((void)"Number is too unimaginably huge", pows
< DEPTH
));
325 pow
[pows
] = mp_sqr(MP_NEW
, pow
[pows
- 1]);
334 for (i
= 0; i
< sp
; i
++)
338 /* --- Clear the radix power list --- */
342 for (i
= 1; i
< pows
; i
++)
346 /* --- Bail out if the number was bad --- */
351 /* --- Set the sign and return --- */
358 /* --- @mp_write@ --- *
360 * Arguments: @mp *m@ = pointer to a multi-precision integer
361 * @int radix@ = radix to use when writing the number out
362 * @const mptext_ops *ops@ = pointer to an operations block
363 * @void *p@ = data for the operations block
365 * Returns: Zero if it worked, nonzero otherwise.
367 * Use: Writes a large integer in textual form.
370 /* --- Simple case --- *
372 * Use a fixed-sized buffer and the simple single-precision division
373 * algorithm to pick off low-order digits. Put each digit in a buffer,
374 * working backwards from the end. If the buffer becomes full, recurse to
375 * get another one. Ensure that there are at least @z@ digits by writing
376 * leading zeroes if there aren't enough real digits.
379 static int simple(mp
*m
, int radix
, unsigned z
,
380 const mptext_ops
*ops
, void *p
)
384 unsigned i
= sizeof(buf
);
385 int rd
= radix
> 0 ? radix
: -radix
;
391 x
= mpx_udivn(m
->v
, m
->vl
, m
->v
, m
->vl
, rd
);
404 } while (i
&& MP_LEN(m
));
407 rc
= simple(m
, radix
, z
, ops
, p
);
409 static const char zero
[32] = "00000000000000000000000000000000";
410 while (!rc
&& z
>= sizeof(zero
)) {
411 rc
= ops
->put(zero
, sizeof(zero
), p
);
415 rc
= ops
->put(zero
, z
, p
);
418 ops
->put(buf
+ i
, sizeof(buf
) - i
, p
);
424 /* --- Complicated case --- *
426 * If the number is small, fall back to the simple case above. Otherwise
427 * divide and take remainder by current large power of the radix, and emit
428 * each separately. Don't emit a zero quotient. Be very careful about
429 * leading zeroes on the remainder part, because they're deeply significant.
432 static int complicated(mp
*m
, int radix
, mp
**pr
, unsigned i
, unsigned z
,
433 const mptext_ops
*ops
, void *p
)
440 return (simple(m
, radix
, z
, ops
, p
));
442 mp_div(&q
, &m
, m
, pr
[i
]);
450 rc
= complicated(q
, radix
, pr
, i
- 1, z
, ops
, p
);
453 rc
= complicated(m
, radix
, pr
, i
- 1, d
, ops
, p
);
458 /* --- Main driver code --- */
460 int mp_write(mp
*m
, int radix
, const mptext_ops
*ops
, void *p
)
464 /* --- Set various things up --- */
469 /* --- Check the radix for sensibleness --- */
472 assert(((void)"ascii radix must be <= 36", radix
<= 36));
474 assert(((void)"binary radix must fit in a byte", -radix
< UCHAR_MAX
));
476 assert(((void)"radix can't be zero in mp_write", 0));
478 /* --- If the number is negative, sort that out --- */
481 if (ops
->put("-", 1, p
))
486 /* --- If the number is small, do it the easy way --- */
489 rc
= simple(m
, radix
, 0, ops
, p
);
491 /* --- Use a clever algorithm --- *
493 * Square the radix repeatedly, remembering old results, until I get
494 * something more than half the size of the number @m@. Use this to divide
495 * the number: the quotient and remainder will be approximately the same
496 * size, and I'll have split them on a digit boundary, so I can just emit
497 * the quotient and remainder recursively, in order.
502 size_t target
= MP_LEN(m
) / 2;
504 mp
*z
= mp_new(1, 0);
506 /* --- Set up the exponent table --- */
508 z
->v
[0] = (radix
> 0 ? radix
: -radix
);
511 assert(((void)"Number is too unimaginably huge", i
< DEPTH
));
513 if (MP_LEN(z
) > target
)
515 z
= mp_sqr(MP_NEW
, z
);
518 /* --- Write out the answer --- */
520 rc
= complicated(m
, radix
, pr
, i
- 1, 0, ops
, p
);
522 /* --- Tidy away the array --- */
528 /* --- Tidying up code --- */
534 /*----- Test rig ----------------------------------------------------------*/
538 #include <mLib/testrig.h>
540 static int verify(dstr
*v
)
543 int ib
= *(int *)v
[0].buf
, ob
= *(int *)v
[2].buf
;
545 mp
*m
= mp_readdstr(MP_NEW
, &v
[1], 0, ib
);
548 fprintf(stderr
, "*** unexpected successful parse\n"
549 "*** input [%i] = ", ib
);
551 type_hex
.dump(&v
[1], stderr
);
553 fputs(v
[1].buf
, stderr
);
554 mp_writedstr(m
, &d
, 10);
555 fprintf(stderr
, "\n*** (value = %s)\n", d
.buf
);
558 mp_writedstr(m
, &d
, ob
);
559 if (d
.len
!= v
[3].len
|| memcmp(d
.buf
, v
[3].buf
, d
.len
) != 0) {
560 fprintf(stderr
, "*** failed read or write\n"
561 "*** input [%i] = ", ib
);
563 type_hex
.dump(&v
[1], stderr
);
565 fputs(v
[1].buf
, stderr
);
566 fprintf(stderr
, "\n*** output [%i] = ", ob
);
568 type_hex
.dump(&d
, stderr
);
570 fputs(d
.buf
, stderr
);
571 fprintf(stderr
, "\n*** expected [%i] = ", ob
);
573 type_hex
.dump(&v
[3], stderr
);
575 fputs(v
[3].buf
, stderr
);
583 fprintf(stderr
, "*** unexpected parse failure\n"
584 "*** input [%i] = ", ib
);
586 type_hex
.dump(&v
[1], stderr
);
588 fputs(v
[1].buf
, stderr
);
589 fprintf(stderr
, "\n*** expected [%i] = ", ob
);
591 type_hex
.dump(&v
[3], stderr
);
593 fputs(v
[3].buf
, stderr
);
600 assert(mparena_count(MPARENA_GLOBAL
) == 0);
604 static test_chunk tests
[] = {
605 { "mptext-ascii", verify
,
606 { &type_int
, &type_string
, &type_int
, &type_string
, 0 } },
607 { "mptext-bin-in", verify
,
608 { &type_int
, &type_hex
, &type_int
, &type_string
, 0 } },
609 { "mptext-bin-out", verify
,
610 { &type_int
, &type_string
, &type_int
, &type_hex
, 0 } },
614 int main(int argc
, char *argv
[])
617 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mptext");
623 /*----- That's all, folks -------------------------------------------------*/