3 * $Id: mp.h,v 1.9 2000/07/29 17:03:31 mdw Exp $
5 * Simple multiprecision arithmetic
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 1.9 2000/07/29 17:03:31 mdw
34 * Add support for left-to-right bitscanning, for use in modular
37 * Revision 1.8 2000/06/22 19:02:01 mdw
40 * Revision 1.7 2000/06/17 11:45:09 mdw
41 * Major memory management overhaul. Added arena support. Use the secure
42 * arena for secret integers. Replace and improve the MP management macros
43 * (e.g., replace MP_MODIFY by MP_DEST).
45 * Revision 1.6 1999/12/10 23:19:46 mdw
46 * Minor bugfixes. New interface for suggested destinations.
48 * Revision 1.5 1999/11/22 20:50:37 mdw
49 * Add support for computing Jacobi symbols.
51 * Revision 1.4 1999/11/21 22:13:02 mdw
52 * Add mp version of MPX_BITS.
54 * Revision 1.3 1999/11/19 13:19:14 mdw
55 * Fix const annotation.
57 * Revision 1.2 1999/11/17 18:02:16 mdw
58 * New multiprecision integer arithmetic suite.
69 /*----- Header files ------------------------------------------------------*/
76 #ifndef CATACOMB_MPW_H
80 #ifndef CATACOMB_ARENA_H
84 #ifndef CATACOMB_MPARENA_H
88 #ifndef CATACOMB_MPX_H
92 /*----- Data structures ---------------------------------------------------*/
106 #define MP_DESTROYED 16u
108 /*----- Useful constants --------------------------------------------------*/
110 extern mp mp_const
[];
112 #define MP_ZERO (&mp_const[0])
113 #define MP_ONE (&mp_const[1])
114 #define MP_TWO (&mp_const[2])
115 #define MP_THREE (&mp_const[3])
116 #define MP_FOUR (&mp_const[4])
117 #define MP_FIVE (&mp_const[5])
118 #define MP_TEN (&mp_const[6])
119 #define MP_256 (&mp_const[7])
120 #define MP_MONE (&mp_const[8])
122 #define MP_NEW ((mp *)0)
123 #define MP_NEWSEC (&mp_const[9])
125 /*----- Trivial macros ----------------------------------------------------*/
127 /* --- @MP_LEN@ --- *
129 * Arguments: @mp *m@ = pointer to a multiprecision integer
131 * Returns: Length of the integer, in words.
134 #define MP_LEN(m) ((m)->vl - ((m)->v))
136 /*----- Memory management and reference counting --------------------------*/
138 /* --- @mp_new@ --- *
140 * Arguments: @size_t sz@ = size of vector required
141 * @unsigned f@ = flags to set
143 * Returns: Pointer to a new MP structure.
145 * Use: Allocates a new multiprecision integer. The data space is
146 * allocated from either the standard global or secret arena,
147 * depending on the initial flags requested.
150 extern mp
*mp_new(size_t /*sz*/, unsigned /*f*/);
152 /* --- @mp_create@ --- *
154 * Arguments: @size_t sz@ = size of vector required
156 * Returns: Pointer to pristine new MP structure with enough memory
159 * Use: Creates a new multiprecision integer with indeterminate
160 * contents. The integer has a single reference.
163 extern mp
*mp_create(size_t /*sz*/);
165 /* --- @mp_createsecure@ --- *
167 * Arguments: @size_t sz@ = size of vector required
169 * Returns: Pointer to pristine new MP structure with enough memory
172 * Use: Creates a new multiprecision integer with indeterminate
173 * contents. The integer has a single reference. The integer's
174 * data space is allocated from the secure arena. Its burn flag
178 extern mp
*mp_createsecure(size_t /*sz*/);
180 /* --- @mp_build@ --- *
182 * Arguments: @mp *m@ = pointer to an MP block to fill in
183 * @mpw *v@ = pointer to a word array
184 * @mpw *vl@ = pointer just past end of array
188 * Use: Creates a multiprecision integer representing some smallish
189 * number. You must provide storage for the number and dispose
190 * of it when you've finished with it. The number is marked as
191 * constant while it exists.
194 extern void mp_build(mp */
*m*/
, mpw */
*v*/
, mpw */
*vl*/
);
196 /* --- @mp_destroy@ --- *
198 * Arguments: @mp *m@ = pointer to a multiprecision integer
202 * Use: Destroys a multiprecision integer. The reference count isn't
203 * checked. Don't use this function if you don't know what
204 * you're doing: use @mp_drop@ instead.
207 extern void mp_destroy(mp */
*m*/
);
209 /* --- @mp_copy@ --- *
211 * Arguments: @mp *m@ = pointer to a multiprecision integer
213 * Returns: A copy of the given multiprecision integer.
215 * Use: Copies the given integer. In fact you just get another
216 * reference to the same old one again.
219 extern mp
*mp_copy(mp */
*m*/
);
221 #define MP_COPY(m) ((m)->ref++, (m))
223 /* --- @mp_drop@ --- *
225 * Arguments: @mp *m@ = pointer to a multiprecision integer
229 * Use: Drops a reference to an integer which isn't wanted any more.
230 * If there are no more references, the integer is destroyed.
233 extern void mp_drop(mp */
*m*/
);
235 #define MP_DROP(m) do { \
238 if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \
242 /* --- @mp_split@ --- *
244 * Arguments: @mp *m@ = pointer to a multiprecision integer
246 * Returns: A reference to the same integer, possibly with a different
249 * Use: Splits off a modifiable version of the integer referred to.
252 extern mp
*mp_split(mp */
*m*/
);
254 #define MP_SPLIT(m) do { \
256 if ((_m->f & MP_CONST) || _m->ref > 1) { \
257 size_t _len = MP_LEN(_m); \
258 mp *_mm = mp_new(_len, _m->f); \
259 if (!(_m->f & MP_UNDEF)) \
260 memcpy(_mm->v, _m->v, MPWS(_len)); \
267 /* --- @mp_resize@ --- *
269 * Arguments: @mp *m@ = pointer to a multiprecision integer
270 * @size_t sz@ = new size
274 * Use: Resizes the vector containing the integer's digits. The new
275 * size must be at least as large as the current integer's
276 * length. This isn't really intended for client use.
279 extern void mp_resize(mp */
*m*/
, size_t /*sz*/);
281 #define MP_RESIZE(m, ssz) do { \
283 size_t _sz = (ssz); \
284 mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \
286 size_t _len = MP_LEN(_m); \
287 assert(((void)"can't make size less than length", _sz >= _len)); \
288 _v = mpalloc(_a, _sz); \
289 if (!(_m->f & MP_UNDEF)) \
290 memcpy(_v, _m->v, MPWS(_len)); \
291 if (_m->f & MP_BURN) \
292 memset(_m->v, 0, MPWS(_m->sz)); \
293 mpfree(_m->a, _m->v); \
296 _m->vl = _v + _len; \
299 /* --- @mp_ensure@ --- *
301 * Arguments: @mp *m@ = pointer to a multiprecision integer
302 * @size_t sz@ = required size
306 * Use: Ensures that the integer has enough space for @sz@ digits.
307 * The value is not changed.
310 extern void mp_ensure(mp */
*m*/
, size_t /*sz*/);
312 #define MP_ENSURE(m, ssz) do { \
314 size_t _ssz = (ssz); \
315 size_t _len = MP_LEN(_m); \
316 if (_ssz >= _len) { \
318 mp_resize(_m, _ssz); \
319 if (!(_m->f & MP_UNDEF) && _ssz > _len) \
320 memset(_m->vl, 0, MPWS(_ssz - _len)); \
321 _m->vl = _m->v + _ssz; \
325 /* --- @mp_dest@ --- *
327 * Arguments: @mp *m@ = a suggested destination integer
328 * @size_t sz@ = size required for result, in digits
329 * @unsigned f@ = various flags
331 * Returns: A pointer to an appropriate destination.
333 * Use: Converts a suggested destination into a real destination with
334 * the required properties. If the real destination is @d@,
335 * then the following properties will hold:
337 * * @d@ will have exactly one reference.
339 * * If @m@ is not @MP_NEW@, then the contents of @m@ will not
340 * change, unless @f@ has the @MP_UNDEF@ flag set.
342 * * If @m@ is not @MP_NEW@, then he reference count of @m@ on
343 * entry is equal to the sum of the counts of @d@ and @m@ on
346 * * The size of @d@ will be at least @sz@.
348 * * If @f@ has the @MP_BURN@ flag set, then @d@ will be
349 * allocated from @MPARENA_SECURE@.
351 * Understanding this function is crucial to using Catacomb's
352 * multiprecision integer library effectively.
355 extern mp
*mp_dest(mp */
*m*/
, size_t /*sz*/, unsigned /*f*/);
357 #define MP_DEST(m, ssz, f) do { \
359 size_t _ssz = (ssz); \
361 _m = mp_dest(_m, _ssz, _f); \
365 /*----- Size manipulation -------------------------------------------------*/
367 /* --- @mp_shrink@ --- *
369 * Arguments: @mp *m@ = pointer to a multiprecision integer
373 * Use: Reduces the recorded length of an integer. This doesn't
374 * reduce the amount of memory used, although it can improve
375 * performance a bit. To reduce memory, use @mp_minimize@
376 * instead. This can't change the value of an integer, and is
377 * therefore safe to use even when there are multiple
381 extern void mp_shrink(mp */
*m*/
);
383 #define MP_SHRINK(m) do { \
385 MPX_SHRINK(_mm->v, _mm->vl); \
390 /* --- @mp_minimize@ --- *
392 * Arguments: @mp *m@ = pointer to a multiprecision integer
396 * Use: Reduces the amount of memory an integer uses. It's best to
397 * do this to numbers which aren't going to change in the
401 extern void mp_minimize(mp */
*m*/
);
403 /*----- Bit scanning ------------------------------------------------------*/
405 #ifndef CATACOMB_MPSCAN_H
409 /* --- @mp_scan@ --- *
411 * Arguments: @mpscan *sc@ = pointer to bitscanner block
412 * @const mp *m@ = pointer to a multiprecision integer
416 * Use: Initializes a bitscanner on a multiprecision integer.
419 extern void mp_scan(mpscan */
*sc*/
, const mp */
*m*/
);
421 #define MP_SCAN(sc, m) do { \
422 const mp *_mm = (m); \
423 mpscan *_sc = (sc); \
424 MPSCAN_INITX(_sc, _mm->v, _mm->vl); \
427 /* --- @mp_rscan@ --- *
429 * Arguments: @mpscan *sc@ = pointer to bitscanner block
430 * @const mp *m@ = pointer to a multiprecision integer
434 * Use: Initializes a reverse bitscanner on a multiprecision
438 extern void mp_rscan(mpscan */
*sc*/
, const mp */
*m*/
);
440 #define MP_RSCAN(sc, m) do { \
441 const mp *_mm = (m); \
442 mpscan *_sc = (sc); \
443 MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \
446 /* --- Other bitscanning aliases --- */
448 #define mp_step mpscan_step
449 #define mp_bit mpscan_bit
450 #define mp_rstep mpscan_rstep
451 #define mp_rbit mpscan_rbit
453 #define MP_STEP MPSCAN_STEP
454 #define MP_BIT MPSCAN_BIT
455 #define MP_RSTEP MPSCAN_RSTEP
456 #define MP_RBIT MPSCAN_RBIT
458 /*----- Loading and storing -----------------------------------------------*/
460 /* --- @mp_octets@ --- *
462 * Arguments: @const mp *m@ = a multiprecision integer
464 * Returns: The number of octets required to represent @m@.
466 * Use: Calculates the external storage required for a multiprecision
470 extern size_t mp_octets(const mp */
*m*/
);
472 /* --- @mp_bits@ --- *
474 * Arguments: @const mp *m@ = a multiprecision integer
476 * Returns: The number of bits required to represent @m@.
478 * Use: Calculates the external storage required for a multiprecision
482 extern unsigned long mp_bits(const mp */
*m*/
);
484 /* --- @mp_loadl@ --- *
486 * Arguments: @mp *d@ = destination
487 * @const void *pv@ = pointer to source data
488 * @size_t sz@ = size of the source data
490 * Returns: Resulting multiprecision number.
492 * Use: Loads a multiprecision number from an array of octets. The
493 * first byte in the array is the least significant. More
494 * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$%
495 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
498 extern mp
*mp_loadl(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
500 /* --- @mp_storel@ --- *
502 * Arguments: @const mp *m@ = source
503 * @void *pv@ = pointer to output array
504 * @size_t sz@ = size of the output array
508 * Use: Stores a multiprecision number in an array of octets. The
509 * first byte in the array is the least significant. If the
510 * array is too small to represent the number, high-order bits
511 * are truncated; if the array is too large, high order bytes
512 * are filled with zeros. More formally, if the number is
513 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
514 * then the array is %$b_0, b_1, \ldots, b_{n-1}$%.
517 extern void mp_storel(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
519 /* --- @mp_loadb@ --- *
521 * Arguments: @mp *d@ = destination
522 * @const void *pv@ = pointer to source data
523 * @size_t sz@ = size of the source data
525 * Returns: Resulting multiprecision number.
527 * Use: Loads a multiprecision number from an array of octets. The
528 * last byte in the array is the least significant. More
529 * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$%
530 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
533 extern mp
*mp_loadb(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
535 /* --- @mp_storeb@ --- *
537 * Arguments: @const mp *m@ = source
538 * @void *pv@ = pointer to output array
539 * @size_t sz@ = size of the output array
543 * Use: Stores a multiprecision number in an array of octets. The
544 * last byte in the array is the least significant. If the
545 * array is too small to represent the number, high-order bits
546 * are truncated; if the array is too large, high order bytes
547 * are filled with zeros. More formally, if the number is
548 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
549 * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%.
552 extern void mp_storeb(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
554 /*----- Simple arithmetic -------------------------------------------------*/
558 * Arguments: @mp *d@ = destination
561 * Returns: Result, @a@ converted to two's complement notation.
564 extern mp
*mp_2c(mp */
*d*/
, mp */
*a*/
);
568 * Arguments: @mp *d@ = destination
571 * Returns: Result, @a@ converted to the native signed-magnitude
575 extern mp
*mp_sm(mp */
*d*/
, mp */
*a*/
);
577 /* --- @mp_lsl@ --- *
579 * Arguments: @mp *d@ = destination
581 * @size_t n@ = number of bits to move
583 * Returns: Result, @a@ shifted left by @n@.
586 extern mp
*mp_lsl(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
588 /* --- @mp_lsr@ --- *
590 * Arguments: @mp *d@ = destination
592 * @size_t n@ = number of bits to move
594 * Returns: Result, @a@ shifted left by @n@.
597 extern mp
*mp_lsr(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
599 /* --- @mp_cmp@ --- *
601 * Arguments: @const mp *a, *b@ = two numbers
603 * Returns: Less than, equal to or greater than zero, according to
604 * whether @a@ is less than, equal to or greater than @b@.
607 extern int mp_cmp(const mp */
*a*/
, const mp */
*b*/
);
609 #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0)
611 /* --- @mp_add@ --- *
613 * Arguments: @mp *d@ = destination
614 * @mp *a, *b@ = sources
616 * Returns: Result, @a@ added to @b@.
619 extern mp
*mp_add(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
621 /* --- @mp_sub@ --- *
623 * Arguments: @mp *d@ = destination
624 * @mp *a, *b@ = sources
626 * Returns: Result, @b@ subtracted from @a@.
629 extern mp
*mp_sub(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
631 /* --- @mp_mul@ --- *
633 * Arguments: @mp *d@ = destination
634 * @mp *a, *b@ = sources
636 * Returns: Result, @a@ multiplied by @b@.
639 extern mp
*mp_mul(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
641 /* --- @mp_sqr@ --- *
643 * Arguments: @mp *d@ = destination
646 * Returns: Result, @a@ squared.
649 extern mp
*mp_sqr(mp */
*d*/
, mp */
*a*/
);
651 /* --- @mp_div@ --- *
653 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
654 * @mp *a, *b@ = sources
656 * Use: Calculates the quotient and remainder when @a@ is divided by
660 extern void mp_div(mp
**/
*qq*/
, mp
**/
*rr*/
, mp */
*a*/
, mp */
*b*/
);
662 /* --- @mp_odd@ --- *
664 * Arguments: @mp *d@ = pointer to destination integer
665 * @mp *m@ = pointer to source integer
666 * @size_t *s@ = where to store the power of 2
668 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
670 * Use: Computes a power of two and an odd integer which, when
671 * multiplied, give a specified result. This sort of thing is
672 * useful in number theory quite often.
675 extern mp
*mp_odd(mp */
*d*/
, mp */
*m*/
, size_t */
*s*/
);
677 /*----- More advanced algorithms ------------------------------------------*/
679 /* --- @mp_sqrt@ --- *
681 * Arguments: @mp *d@ = pointer to destination integer
682 * @mp *a@ = (nonnegative) integer to take square root of
684 * Returns: The largest integer %$x$% such that %$x^2 \le a$%.
686 * Use: Computes integer square roots.
688 * The current implementation isn't very good: it uses the
689 * Newton-Raphson method to find an approximation to %$a$%. If
690 * there's any demand for a better version, I'll write one.
693 extern mp
*mp_sqrt(mp */
*d*/
, mp */
*a*/
);
695 /* --- @mp_gcd@ --- *
697 * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
698 * @mp *a, *b@ = sources (must be nonzero)
702 * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
703 * @ax + by = gcd(a, b)@. This is useful for computing modular
704 * inverses. Neither @a@ nor @b@ may be zero.
707 extern void mp_gcd(mp
**/
*gcd*/
, mp
**/
*xx*/
, mp
**/
*yy*/
,
708 mp */
*a*/
, mp */
*b*/
);
710 /* --- @mp_jacobi@ --- *
712 * Arguments: @mp *a@ = an integer less than @n@
713 * @mp *n@ = an odd integer
715 * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%.
717 * Use: Computes the Jacobi symbol. If @n@ is prime, this is the
718 * Legendre symbol and is equal to 1 if and only if @a@ is a
719 * quadratic residue mod @n@. The result is zero if and only if
720 * @a@ and @n@ have a common factor greater than one.
723 extern int mp_jacobi(mp */
*a*/
, mp */
*n*/
);
725 /* --- @mp_modsqrt@ --- *
727 * Arguments: @mp *d@ = destination integer
728 * @mp *a@ = source integer
729 * @mp *p@ = modulus (must be prime)
731 * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else
734 * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%,
735 * if one exists; else a null pointer. This function will not
736 * work if %$p$% is composite: you must factor the modulus, take
737 * a square root mod each factor, and recombine the results
738 * using the Chinese Remainder Theorem.
741 extern mp
*mp_modsqrt(mp */
*d*/
, mp */
*a*/
, mp */
*p*/
);
743 /*----- Test harness support ----------------------------------------------*/
745 #include <mLib/testrig.h>
747 #ifndef CATACOMB_MPTEXT_H
751 extern const test_type type_mp
;
753 /*----- That's all, folks -------------------------------------------------*/