3 * $Id: mptext.c,v 1.10 2001/06/16 13:22:39 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 1.10 2001/06/16 13:22:39 mdw
34 * Added fast-track code for binary output bases, and tests.
36 * Revision 1.9 2001/02/03 16:05:17 mdw
37 * Make flags be unsigned. Improve the write algorithm: recurse until the
38 * parts are one word long and use single-precision arithmetic from there.
39 * Fix off-by-one bug when breaking the number apart.
41 * Revision 1.8 2000/12/06 20:32:42 mdw
42 * Reduce binary bytes (to allow marker bits to be ignored). Fix error
43 * message string a bit. Allow leading `+' signs.
45 * Revision 1.7 2000/07/15 10:01:08 mdw
46 * Bug fix in binary input.
48 * Revision 1.6 2000/06/25 12:58:23 mdw
49 * Fix the derivation of `depth' commentary.
51 * Revision 1.5 2000/06/17 11:46:19 mdw
52 * New and much faster stack-based algorithm for reading integers. Support
53 * reading and writing binary integers in bases between 2 and 256.
55 * Revision 1.4 1999/12/22 15:56:56 mdw
56 * Use clever recursive algorithm for writing numbers out.
58 * Revision 1.3 1999/12/10 23:23:26 mdw
59 * Allocate slightly less memory.
61 * Revision 1.2 1999/11/20 22:24:15 mdw
62 * Use function versions of MPX_UMULN and MPX_UADDN.
64 * Revision 1.1 1999/11/17 18:02:16 mdw
65 * New multiprecision integer arithmetic suite.
69 /*----- Header files ------------------------------------------------------*/
79 /*----- Magical numbers ---------------------------------------------------*/
81 /* --- Maximum recursion depth --- *
83 * This is the number of bits in a @size_t@ object. Why?
85 * To see this, let %$b = \mathit{MPW\_MAX} + 1$% and let %$Z$% be the
86 * largest @size_t@ value. Then the largest possible @mp@ is %$M - 1$% where
87 * %$M = b^Z$%. Let %$r$% be a radix to read or write. Since the recursion
88 * squares the radix at each step, the highest number reached by the
89 * recursion is %$d$%, where:
93 * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum,
94 * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%.
96 * Expressing %$\lg Z$% as @CHAR_BIT * sizeof(size_t)@ yields an
97 * overestimate, since a @size_t@ representation may contain `holes'.
98 * Choosing to represent %$\lg \lg b$% by 10 is almost certainly sufficient
99 * for `some time to come'.
102 #define DEPTH (CHAR_BIT * sizeof(size_t) + 10)
104 /*----- Main code ---------------------------------------------------------*/
106 /* --- @mp_read@ --- *
108 * Arguments: @mp *m@ = destination multiprecision number
109 * @int radix@ = base to assume for data (or zero to guess)
110 * @const mptext_ops *ops@ = pointer to operations block
111 * @void *p@ = data for the operations block
113 * Returns: The integer read, or zero if it didn't work.
115 * Use: Reads an integer from some source. If the @radix@ is
116 * specified, the number is assumed to be given in that radix,
117 * with the letters `a' (either upper- or lower-case) upwards
118 * standing for digits greater than 9. Otherwise, base 10 is
119 * assumed unless the number starts with `0' (octal), `0x' (hex)
120 * or `nnn_' (base `nnn'). An arbitrary amount of whitespace
121 * before the number is ignored.
124 /* --- About the algorithm --- *
126 * The algorithm here is rather aggressive. I maintain an array of
127 * successive squarings of the radix, and a stack of partial results, each
128 * with a counter attached indicating which radix square to multiply by.
129 * Once the item at the top of the stack reaches the same counter level as
130 * the next item down, they are combined together and the result is given a
131 * counter level one higher than either of the results.
133 * Gluing the results together at the end is slightly tricky. Pay attention
136 * This is more complicated because of the need to handle the slightly
140 mp
*mp_read(mp
*m
, int radix
, const mptext_ops
*ops
, void *p
)
142 int ch
; /* Current char being considered */
143 unsigned f
= 0; /* Flags about the current number */
144 int r
; /* Radix to switch over to */
145 mpw rd
; /* Radix as an @mp@ digit */
146 mp rr
; /* The @mp@ for the radix */
147 unsigned nf
= m ? m
->f
& MP_BURN
: 0; /* New @mp@ flags */
151 mp
*pow
[DEPTH
]; /* List of powers */
152 unsigned pows
; /* Next index to fill */
153 struct { unsigned i
; mp
*m
; } s
[DEPTH
]; /* Main stack */
154 unsigned sp
; /* Current stack pointer */
162 /* --- Initialize the stacks --- */
164 mp_build(&rr
, &rd
, &rd
+ 1);
170 /* --- Initialize the destination number --- */
175 /* --- Read an initial character --- */
181 /* --- Handle an initial sign --- */
183 if (radix
>= 0 && (ch
== '-' || ch
== '+')) {
186 do ch
= ops
->get(p
); while isspace(ch
);
189 /* --- If the radix is zero, look for leading zeros --- */
192 assert(((void)"ascii radix must be <= 36", radix
<= 36));
195 } else if (radix
< 0) {
197 assert(((void)"binary radix must fit in a byte", rd
< UCHAR_MAX
));
199 } else if (ch
!= '0') {
214 /* --- Use fast algorithm for binary radix --- *
216 * This is the restart point after having parsed a radix number from the
217 * input. We check whether the radix is binary, and if so use a fast
218 * algorithm which just stacks the bits up in the right order.
225 case 2: bit
= 1; goto bin
;
226 case 4: bit
= 2; goto bin
;
227 case 8: bit
= 3; goto bin
;
228 case 16: bit
= 4; goto bin
;
229 case 32: bit
= 5; goto bin
;
230 case 64: bit
= 6; goto bin
;
231 case 128: bit
= 7; goto bin
;
235 /* --- The fast binary algorithm --- *
237 * We stack bits up starting at the top end of a word. When one word is
238 * full, we write it to the integer, and start another with the left-over
239 * bits. When the array in the integer is full, we resize using low-level
240 * calls and copy the current data to the top end. Finally, we do a single
241 * bit-shift when we know where the end of the number is.
246 unsigned b
= MPW_BITS
;
250 m
= mp_dest(MP_NEW
, 1, nf
);
254 for (;; ch
= ops
->get(p
)) {
260 /* --- Check that the character is a digit and in range --- */
267 if (ch
>= '0' && ch
<= '9')
271 if (ch
>= 'a' && ch
<= 'z') /* ASCII dependent! */
280 /* --- Feed the digit into the accumulator --- */
283 if (!x
&& !(f
& f_start
))
290 a
|= MPW(x
) >> (bit
- b
);
297 v
= mpalloc(m
->a
, len
);
298 memcpy(v
+ n
, m
->v
, MPWS(n
));
303 a
= (b
< MPW_BITS
) ?
MPW(x
) << b
: 0;
307 /* --- Finish up --- */
318 m
= mp_lsr(m
, m
, (unsigned long)n
* MPW_BITS
+ b
);
323 /* --- Time to start --- */
325 for (;; ch
= ops
->get(p
)) {
331 /* --- An underscore indicates a numbered base --- */
333 if (ch
== '_' && r
> 0 && r
<= 36) {
336 /* --- Clear out the stacks --- */
338 for (i
= 1; i
< pows
; i
++)
341 for (i
= 0; i
< sp
; i
++)
345 /* --- Restart the search --- */
354 /* --- Check that the character is a digit and in range --- */
361 if (ch
>= '0' && ch
<= '9')
365 if (ch
>= 'a' && ch
<= 'z') /* ASCII dependent! */
372 /* --- Sort out what to do with the character --- */
374 if (x
>= 10 && r
>= 0)
382 /* --- Stick the character on the end of my integer --- */
384 assert(((void)"Number is too unimaginably huge", sp
< DEPTH
));
385 s
[sp
].m
= m
= mp_new(1, nf
);
389 /* --- Now grind through the stack --- */
391 while (sp
> 0 && s
[sp
- 1].i
== s
[sp
].i
) {
393 /* --- Combine the top two items --- */
397 m
= mp_mul(m
, m
, pow
[s
[sp
].i
]);
398 m
= mp_add(m
, m
, s
[sp
+ 1].m
);
400 MP_DROP(s
[sp
+ 1].m
);
403 /* --- Make a new radix power if necessary --- */
405 if (s
[sp
].i
>= pows
) {
406 assert(((void)"Number is too unimaginably huge", pows
< DEPTH
));
407 pow
[pows
] = mp_sqr(MP_NEW
, pow
[pows
- 1]);
417 /* --- If we're done, compute the rest of the number --- */
428 /* --- Combine the top two items --- */
432 z
= mp_mul(z
, z
, pow
[s
[sp
+ 1].i
]);
434 m
= mp_add(m
, m
, s
[sp
+ 1].m
);
436 MP_DROP(s
[sp
+ 1].m
);
438 /* --- Make a new radix power if necessary --- */
440 if (s
[sp
].i
>= pows
) {
441 assert(((void)"Number is too unimaginably huge", pows
< DEPTH
));
442 pow
[pows
] = mp_sqr(MP_NEW
, pow
[pows
- 1]);
451 for (i
= 0; i
< sp
; i
++)
455 /* --- Clear the radix power list --- */
459 for (i
= 1; i
< pows
; i
++)
463 /* --- Bail out if the number was bad --- */
469 /* --- Set the sign and return --- */
480 /* --- @mp_write@ --- *
482 * Arguments: @mp *m@ = pointer to a multi-precision integer
483 * @int radix@ = radix to use when writing the number out
484 * @const mptext_ops *ops@ = pointer to an operations block
485 * @void *p@ = data for the operations block
487 * Returns: Zero if it worked, nonzero otherwise.
489 * Use: Writes a large integer in textual form.
492 /* --- Simple case --- *
494 * Use a fixed-sized buffer and single-precision arithmetic to pick off
495 * low-order digits. Put each digit in a buffer, working backwards from the
496 * end. If the buffer becomes full, recurse to get another one. Ensure that
497 * there are at least @z@ digits by writing leading zeroes if there aren't
498 * enough real digits.
501 static int simple(mpw n
, int radix
, unsigned z
,
502 const mptext_ops
*ops
, void *p
)
506 unsigned i
= sizeof(buf
);
507 int rd
= radix
> 0 ? radix
: -radix
;
527 rc
= simple(n
, radix
, z
, ops
, p
);
530 memset(zbuf
, (radix
< 0) ?
0 : '0', sizeof(zbuf
));
531 while (!rc
&& z
>= sizeof(zbuf
)) {
532 rc
= ops
->put(zbuf
, sizeof(zbuf
), p
);
536 rc
= ops
->put(zbuf
, z
, p
);
539 rc
= ops
->put(buf
+ i
, sizeof(buf
) - i
, p
);
544 /* --- Complicated case --- *
546 * If the number is small, fall back to the simple case above. Otherwise
547 * divide and take remainder by current large power of the radix, and emit
548 * each separately. Don't emit a zero quotient. Be very careful about
549 * leading zeroes on the remainder part, because they're deeply significant.
552 static int complicated(mp
*m
, int radix
, mp
**pr
, unsigned i
, unsigned z
,
553 const mptext_ops
*ops
, void *p
)
560 return (simple(MP_LEN(m
) ? m
->v
[0] : 0, radix
, z
, ops
, p
));
563 mp_div(&q
, &m
, m
, pr
[i
]);
571 rc
= complicated(q
, radix
, pr
, i
- 1, z
, ops
, p
);
574 rc
= complicated(m
, radix
, pr
, i
- 1, d
, ops
, p
);
579 /* --- Binary case --- *
581 * Special case for binary output. Goes much faster.
584 static int binary(mp
*m
, int bit
, int radix
, const mptext_ops
*ops
, void *p
)
599 /* --- Work out where to start --- */
602 n
+= bit
- (n
% bit
);
613 mask
= (1 << bit
) - 1;
616 /* --- Main code --- */
632 if (!x
&& !(f
& f_out
))
642 if (q
>= buf
+ sizeof(buf
)) {
643 if ((rc
= ops
->put(buf
, sizeof(buf
), p
)) != 0)
658 rc
= ops
->put(buf
, q
- buf
, p
);
667 /* --- Main driver code --- */
669 int mp_write(mp
*m
, int radix
, const mptext_ops
*ops
, void *p
)
673 /* --- Set various things up --- */
678 /* --- Check the radix for sensibleness --- */
681 assert(((void)"ascii radix must be <= 36", radix
<= 36));
683 assert(((void)"binary radix must fit in a byte", -radix
< UCHAR_MAX
));
685 assert(((void)"radix can't be zero in mp_write", 0));
687 /* --- If the number is negative, sort that out --- */
690 if (ops
->put("-", 1, p
))
695 /* --- Handle binary radix --- */
698 case 2: case -2: return (binary(m
, 1, radix
, ops
, p
));
699 case 4: case -4: return (binary(m
, 2, radix
, ops
, p
));
700 case 8: case -8: return (binary(m
, 3, radix
, ops
, p
));
701 case 16: case -16: return (binary(m
, 4, radix
, ops
, p
));
702 case 32: case -32: return (binary(m
, 5, radix
, ops
, p
));
703 case -64: return (binary(m
, 6, radix
, ops
, p
));
704 case -128: return (binary(m
, 7, radix
, ops
, p
));
707 /* --- If the number is small, do it the easy way --- */
710 rc
= simple(MP_LEN(m
) ? m
->v
[0] : 0, radix
, 0, ops
, p
);
712 /* --- Use a clever algorithm --- *
714 * Square the radix repeatedly, remembering old results, until I get
715 * something more than half the size of the number @m@. Use this to divide
716 * the number: the quotient and remainder will be approximately the same
717 * size, and I'll have split them on a digit boundary, so I can just emit
718 * the quotient and remainder recursively, in order.
723 size_t target
= (MP_LEN(m
) + 1) / 2;
725 mp
*z
= mp_new(1, 0);
727 /* --- Set up the exponent table --- */
729 z
->v
[0] = (radix
> 0 ? radix
: -radix
);
732 assert(((void)"Number is too unimaginably huge", i
< DEPTH
));
734 if (MP_LEN(z
) > target
)
736 z
= mp_sqr(MP_NEW
, z
);
739 /* --- Write out the answer --- */
741 rc
= complicated(m
, radix
, pr
, i
- 1, 0, ops
, p
);
743 /* --- Tidy away the array --- */
749 /* --- Tidying up code --- */
755 /*----- Test rig ----------------------------------------------------------*/
759 #include <mLib/testrig.h>
761 static int verify(dstr
*v
)
764 int ib
= *(int *)v
[0].buf
, ob
= *(int *)v
[2].buf
;
766 mp
*m
= mp_readdstr(MP_NEW
, &v
[1], 0, ib
);
769 fprintf(stderr
, "*** unexpected successful parse\n"
770 "*** input [%2i] = ", ib
);
772 type_hex
.dump(&v
[1], stderr
);
774 fputs(v
[1].buf
, stderr
);
775 mp_writedstr(m
, &d
, 10);
776 fprintf(stderr
, "\n*** (value = %s)\n", d
.buf
);
779 mp_writedstr(m
, &d
, ob
);
780 if (d
.len
!= v
[3].len
|| memcmp(d
.buf
, v
[3].buf
, d
.len
) != 0) {
781 fprintf(stderr
, "*** failed read or write\n"
782 "*** input [%2i] = ", ib
);
784 type_hex
.dump(&v
[1], stderr
);
786 fputs(v
[1].buf
, stderr
);
787 fprintf(stderr
, "\n*** output [%2i] = ", ob
);
789 type_hex
.dump(&d
, stderr
);
791 fputs(d
.buf
, stderr
);
792 fprintf(stderr
, "\n*** expected [%2i] = ", ob
);
794 type_hex
.dump(&v
[3], stderr
);
796 fputs(v
[3].buf
, stderr
);
804 fprintf(stderr
, "*** unexpected parse failure\n"
805 "*** input [%i] = ", ib
);
807 type_hex
.dump(&v
[1], stderr
);
809 fputs(v
[1].buf
, stderr
);
810 fprintf(stderr
, "\n*** expected [%i] = ", ob
);
812 type_hex
.dump(&v
[3], stderr
);
814 fputs(v
[3].buf
, stderr
);
821 assert(mparena_count(MPARENA_GLOBAL
) == 0);
825 static test_chunk tests
[] = {
826 { "mptext-ascii", verify
,
827 { &type_int
, &type_string
, &type_int
, &type_string
, 0 } },
828 { "mptext-bin-in", verify
,
829 { &type_int
, &type_hex
, &type_int
, &type_string
, 0 } },
830 { "mptext-bin-out", verify
,
831 { &type_int
, &type_string
, &type_int
, &type_hex
, 0 } },
835 int main(int argc
, char *argv
[])
838 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mptext");
844 /*----- That's all, folks -------------------------------------------------*/