3 * $Id: mp.h,v 1.8 2000/06/22 19:02:01 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 1.8 2000/06/22 19:02:01 mdw
36 * Revision 1.7 2000/06/17 11:45:09 mdw
37 * Major memory management overhaul. Added arena support. Use the secure
38 * arena for secret integers. Replace and improve the MP management macros
39 * (e.g., replace MP_MODIFY by MP_DEST).
41 * Revision 1.6 1999/12/10 23:19:46 mdw
42 * Minor bugfixes. New interface for suggested destinations.
44 * Revision 1.5 1999/11/22 20:50:37 mdw
45 * Add support for computing Jacobi symbols.
47 * Revision 1.4 1999/11/21 22:13:02 mdw
48 * Add mp version of MPX_BITS.
50 * Revision 1.3 1999/11/19 13:19:14 mdw
51 * Fix const annotation.
53 * Revision 1.2 1999/11/17 18:02:16 mdw
54 * New multiprecision integer arithmetic suite.
65 /*----- Header files ------------------------------------------------------*/
72 #ifndef CATACOMB_MPW_H
76 #ifndef CATACOMB_ARENA_H
80 #ifndef CATACOMB_MPARENA_H
84 #ifndef CATACOMB_MPX_H
88 /*----- Data structures ---------------------------------------------------*/
102 #define MP_DESTROYED 16u
104 /*----- Useful constants --------------------------------------------------*/
106 extern mp mp_const
[];
108 #define MP_ZERO (&mp_const[0])
109 #define MP_ONE (&mp_const[1])
110 #define MP_TWO (&mp_const[2])
111 #define MP_THREE (&mp_const[3])
112 #define MP_FOUR (&mp_const[4])
113 #define MP_FIVE (&mp_const[5])
114 #define MP_TEN (&mp_const[6])
115 #define MP_256 (&mp_const[7])
116 #define MP_MONE (&mp_const[8])
118 #define MP_NEW ((mp *)0)
119 #define MP_NEWSEC (&mp_const[9])
121 /*----- Trivial macros ----------------------------------------------------*/
123 /* --- @MP_LEN@ --- *
125 * Arguments: @mp *m@ = pointer to a multiprecision integer
127 * Returns: Length of the integer, in words.
130 #define MP_LEN(m) ((m)->vl - ((m)->v))
132 /*----- Memory management and reference counting --------------------------*/
134 /* --- @mp_new@ --- *
136 * Arguments: @size_t sz@ = size of vector required
137 * @unsigned f@ = flags to set
139 * Returns: Pointer to a new MP structure.
141 * Use: Allocates a new multiprecision integer. The data space is
142 * allocated from either the standard global or secret arena,
143 * depending on the initial flags requested.
146 extern mp
*mp_new(size_t /*sz*/, unsigned /*f*/);
148 /* --- @mp_create@ --- *
150 * Arguments: @size_t sz@ = size of vector required
152 * Returns: Pointer to pristine new MP structure with enough memory
155 * Use: Creates a new multiprecision integer with indeterminate
156 * contents. The integer has a single reference.
159 extern mp
*mp_create(size_t /*sz*/);
161 /* --- @mp_createsecure@ --- *
163 * Arguments: @size_t sz@ = size of vector required
165 * Returns: Pointer to pristine new MP structure with enough memory
168 * Use: Creates a new multiprecision integer with indeterminate
169 * contents. The integer has a single reference. The integer's
170 * data space is allocated from the secure arena. Its burn flag
174 extern mp
*mp_createsecure(size_t /*sz*/);
176 /* --- @mp_build@ --- *
178 * Arguments: @mp *m@ = pointer to an MP block to fill in
179 * @mpw *v@ = pointer to a word array
180 * @mpw *vl@ = pointer just past end of array
184 * Use: Creates a multiprecision integer representing some smallish
185 * number. You must provide storage for the number and dispose
186 * of it when you've finished with it. The number is marked as
187 * constant while it exists.
190 extern void mp_build(mp */
*m*/
, mpw */
*v*/
, mpw */
*vl*/
);
192 /* --- @mp_destroy@ --- *
194 * Arguments: @mp *m@ = pointer to a multiprecision integer
198 * Use: Destroys a multiprecision integer. The reference count isn't
199 * checked. Don't use this function if you don't know what
200 * you're doing: use @mp_drop@ instead.
203 extern void mp_destroy(mp */
*m*/
);
205 /* --- @mp_copy@ --- *
207 * Arguments: @mp *m@ = pointer to a multiprecision integer
209 * Returns: A copy of the given multiprecision integer.
211 * Use: Copies the given integer. In fact you just get another
212 * reference to the same old one again.
215 extern mp
*mp_copy(mp */
*m*/
);
217 #define MP_COPY(m) ((m)->ref++, (m))
219 /* --- @mp_drop@ --- *
221 * Arguments: @mp *m@ = pointer to a multiprecision integer
225 * Use: Drops a reference to an integer which isn't wanted any more.
226 * If there are no more references, the integer is destroyed.
229 extern void mp_drop(mp */
*m*/
);
231 #define MP_DROP(m) do { \
234 if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \
238 /* --- @mp_split@ --- *
240 * Arguments: @mp *m@ = pointer to a multiprecision integer
242 * Returns: A reference to the same integer, possibly with a different
245 * Use: Splits off a modifiable version of the integer referred to.
248 extern mp
*mp_split(mp */
*m*/
);
250 #define MP_SPLIT(m) do { \
252 if ((_m->f & MP_CONST) || _m->ref > 1) { \
253 size_t _len = MP_LEN(_m); \
254 mp *_mm = mp_new(_len, _m->f); \
255 if (!(_m->f & MP_UNDEF)) \
256 memcpy(_mm->v, _m->v, MPWS(_len)); \
263 /* --- @mp_resize@ --- *
265 * Arguments: @mp *m@ = pointer to a multiprecision integer
266 * @size_t sz@ = new size
270 * Use: Resizes the vector containing the integer's digits. The new
271 * size must be at least as large as the current integer's
272 * length. This isn't really intended for client use.
275 extern void mp_resize(mp */
*m*/
, size_t /*sz*/);
277 #define MP_RESIZE(m, ssz) do { \
279 size_t _sz = (ssz); \
280 mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \
282 size_t _len = MP_LEN(_m); \
283 assert(((void)"can't make size less than length", _sz >= _len)); \
284 _v = mpalloc(_a, _sz); \
285 if (!(_m->f & MP_UNDEF)) \
286 memcpy(_v, _m->v, MPWS(_len)); \
287 if (_m->f & MP_BURN) \
288 memset(_m->v, 0, MPWS(_m->sz)); \
289 mpfree(_m->a, _m->v); \
292 _m->vl = _v + _len; \
295 /* --- @mp_ensure@ --- *
297 * Arguments: @mp *m@ = pointer to a multiprecision integer
298 * @size_t sz@ = required size
302 * Use: Ensures that the integer has enough space for @sz@ digits.
303 * The value is not changed.
306 extern void mp_ensure(mp */
*m*/
, size_t /*sz*/);
308 #define MP_ENSURE(m, ssz) do { \
310 size_t _ssz = (ssz); \
311 size_t _len = MP_LEN(_m); \
312 if (_ssz >= _len) { \
314 mp_resize(_m, _ssz); \
315 if (!(_m->f & MP_UNDEF) && _ssz > _len) \
316 memset(_m->vl, 0, MPWS(_ssz - _len)); \
317 _m->vl = _m->v + _ssz; \
321 /* --- @mp_dest@ --- *
323 * Arguments: @mp *m@ = a suggested destination integer
324 * @size_t sz@ = size required for result, in digits
325 * @unsigned f@ = various flags
327 * Returns: A pointer to an appropriate destination.
329 * Use: Converts a suggested destination into a real destination with
330 * the required properties. If the real destination is @d@,
331 * then the following properties will hold:
333 * * @d@ will have exactly one reference.
335 * * If @m@ is not @MP_NEW@, then the contents of @m@ will not
336 * change, unless @f@ has the @MP_UNDEF@ flag set.
338 * * If @m@ is not @MP_NEW@, then he reference count of @m@ on
339 * entry is equal to the sum of the counts of @d@ and @m@ on
342 * * The size of @d@ will be at least @sz@.
344 * * If @f@ has the @MP_BURN@ flag set, then @d@ will be
345 * allocated from @MPARENA_SECURE@.
347 * Understanding this function is crucial to using Catacomb's
348 * multiprecision integer library effectively.
351 extern mp
*mp_dest(mp */
*m*/
, size_t /*sz*/, unsigned /*f*/);
353 #define MP_DEST(m, ssz, f) do { \
355 size_t _ssz = (ssz); \
357 _m = mp_dest(_m, _ssz, _f); \
361 /*----- Size manipulation -------------------------------------------------*/
363 /* --- @mp_shrink@ --- *
365 * Arguments: @mp *m@ = pointer to a multiprecision integer
369 * Use: Reduces the recorded length of an integer. This doesn't
370 * reduce the amount of memory used, although it can improve
371 * performance a bit. To reduce memory, use @mp_minimize@
372 * instead. This can't change the value of an integer, and is
373 * therefore safe to use even when there are multiple
377 extern void mp_shrink(mp */
*m*/
);
379 #define MP_SHRINK(m) do { \
381 MPX_SHRINK(_mm->v, _mm->vl); \
386 /* --- @mp_minimize@ --- *
388 * Arguments: @mp *m@ = pointer to a multiprecision integer
392 * Use: Reduces the amount of memory an integer uses. It's best to
393 * do this to numbers which aren't going to change in the
397 extern void mp_minimize(mp */
*m*/
);
399 /*----- Bit scanning ------------------------------------------------------*/
401 #ifndef CATACOMB_MPSCAN_H
405 /* --- @mp_scan@ --- *
407 * Arguments: @mpscan *sc@ = pointer to bitscanner block
408 * @const mp *m@ = pointer to a multiprecision integer
412 * Use: Initializes a bitscanner on a multiprecision integer.
415 extern void mp_scan(mpscan */
*sc*/
, const mp */
*m*/
);
417 #define MP_SCAN(sc, m) do { \
418 const mp *_mm = (m); \
419 mpscan *_sc = (sc); \
420 MPSCAN_INITX(_sc, _mm->v, _mm->vl); \
423 /* --- Other bitscanning aliases --- */
425 #define mp_step mpscan_step
426 #define mp_bit mpscan_bit
428 #define MP_STEP MPSCAN_STEP
429 #define MP_BIT MPSCAN_BIT
431 /*----- Loading and storing -----------------------------------------------*/
433 /* --- @mp_octets@ --- *
435 * Arguments: @const mp *m@ = a multiprecision integer
437 * Returns: The number of octets required to represent @m@.
439 * Use: Calculates the external storage required for a multiprecision
443 extern size_t mp_octets(const mp */
*m*/
);
445 /* --- @mp_bits@ --- *
447 * Arguments: @const mp *m@ = a multiprecision integer
449 * Returns: The number of bits required to represent @m@.
451 * Use: Calculates the external storage required for a multiprecision
455 extern unsigned long mp_bits(const mp */
*m*/
);
457 /* --- @mp_loadl@ --- *
459 * Arguments: @mp *d@ = destination
460 * @const void *pv@ = pointer to source data
461 * @size_t sz@ = size of the source data
463 * Returns: Resulting multiprecision number.
465 * Use: Loads a multiprecision number from an array of octets. The
466 * first byte in the array is the least significant. More
467 * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$%
468 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
471 extern mp
*mp_loadl(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
473 /* --- @mp_storel@ --- *
475 * Arguments: @const mp *m@ = source
476 * @void *pv@ = pointer to output array
477 * @size_t sz@ = size of the output array
481 * Use: Stores a multiprecision number in an array of octets. The
482 * first byte in the array is the least significant. If the
483 * array is too small to represent the number, high-order bits
484 * are truncated; if the array is too large, high order bytes
485 * are filled with zeros. More formally, if the number is
486 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
487 * then the array is %$b_0, b_1, \ldots, b_{n-1}$%.
490 extern void mp_storel(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
492 /* --- @mp_loadb@ --- *
494 * Arguments: @mp *d@ = destination
495 * @const void *pv@ = pointer to source data
496 * @size_t sz@ = size of the source data
498 * Returns: Resulting multiprecision number.
500 * Use: Loads a multiprecision number from an array of octets. The
501 * last byte in the array is the least significant. More
502 * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$%
503 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
506 extern mp
*mp_loadb(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
508 /* --- @mp_storeb@ --- *
510 * Arguments: @const mp *m@ = source
511 * @void *pv@ = pointer to output array
512 * @size_t sz@ = size of the output array
516 * Use: Stores a multiprecision number in an array of octets. The
517 * last byte in the array is the least significant. If the
518 * array is too small to represent the number, high-order bits
519 * are truncated; if the array is too large, high order bytes
520 * are filled with zeros. More formally, if the number is
521 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
522 * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%.
525 extern void mp_storeb(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
527 /*----- Simple arithmetic -------------------------------------------------*/
531 * Arguments: @mp *d@ = destination
534 * Returns: Result, @a@ converted to two's complement notation.
537 extern mp
*mp_2c(mp */
*d*/
, mp */
*a*/
);
541 * Arguments: @mp *d@ = destination
544 * Returns: Result, @a@ converted to the native signed-magnitude
548 extern mp
*mp_sm(mp */
*d*/
, mp */
*a*/
);
550 /* --- @mp_lsl@ --- *
552 * Arguments: @mp *d@ = destination
554 * @size_t n@ = number of bits to move
556 * Returns: Result, @a@ shifted left by @n@.
559 extern mp
*mp_lsl(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
561 /* --- @mp_lsr@ --- *
563 * Arguments: @mp *d@ = destination
565 * @size_t n@ = number of bits to move
567 * Returns: Result, @a@ shifted left by @n@.
570 extern mp
*mp_lsr(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
572 /* --- @mp_cmp@ --- *
574 * Arguments: @const mp *a, *b@ = two numbers
576 * Returns: Less than, equal to or greater than zero, according to
577 * whether @a@ is less than, equal to or greater than @b@.
580 extern int mp_cmp(const mp */
*a*/
, const mp */
*b*/
);
582 #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0)
584 /* --- @mp_add@ --- *
586 * Arguments: @mp *d@ = destination
587 * @mp *a, *b@ = sources
589 * Returns: Result, @a@ added to @b@.
592 extern mp
*mp_add(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
594 /* --- @mp_sub@ --- *
596 * Arguments: @mp *d@ = destination
597 * @mp *a, *b@ = sources
599 * Returns: Result, @b@ subtracted from @a@.
602 extern mp
*mp_sub(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
604 /* --- @mp_mul@ --- *
606 * Arguments: @mp *d@ = destination
607 * @mp *a, *b@ = sources
609 * Returns: Result, @a@ multiplied by @b@.
612 extern mp
*mp_mul(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
614 /* --- @mp_sqr@ --- *
616 * Arguments: @mp *d@ = destination
619 * Returns: Result, @a@ squared.
622 extern mp
*mp_sqr(mp */
*d*/
, mp */
*a*/
);
624 /* --- @mp_div@ --- *
626 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
627 * @mp *a, *b@ = sources
629 * Use: Calculates the quotient and remainder when @a@ is divided by
633 extern void mp_div(mp
**/
*qq*/
, mp
**/
*rr*/
, mp */
*a*/
, mp */
*b*/
);
635 /* --- @mp_odd@ --- *
637 * Arguments: @mp *d@ = pointer to destination integer
638 * @mp *m@ = pointer to source integer
639 * @size_t *s@ = where to store the power of 2
641 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
643 * Use: Computes a power of two and an odd integer which, when
644 * multiplied, give a specified result. This sort of thing is
645 * useful in number theory quite often.
648 extern mp
*mp_odd(mp */
*d*/
, mp */
*m*/
, size_t */
*s*/
);
650 /*----- More advanced algorithms ------------------------------------------*/
652 /* --- @mp_sqrt@ --- *
654 * Arguments: @mp *d@ = pointer to destination integer
655 * @mp *a@ = (nonnegative) integer to take square root of
657 * Returns: The largest integer %$x$% such that %$x^2 \le a$%.
659 * Use: Computes integer square roots.
661 * The current implementation isn't very good: it uses the
662 * Newton-Raphson method to find an approximation to %$a$%. If
663 * there's any demand for a better version, I'll write one.
666 extern mp
*mp_sqrt(mp */
*d*/
, mp */
*a*/
);
668 /* --- @mp_gcd@ --- *
670 * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
671 * @mp *a, *b@ = sources (must be nonzero)
675 * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
676 * @ax + by = gcd(a, b)@. This is useful for computing modular
677 * inverses. Neither @a@ nor @b@ may be zero.
680 extern void mp_gcd(mp
**/
*gcd*/
, mp
**/
*xx*/
, mp
**/
*yy*/
,
681 mp */
*a*/
, mp */
*b*/
);
683 /* --- @mp_jacobi@ --- *
685 * Arguments: @mp *a@ = an integer less than @n@
686 * @mp *n@ = an odd integer
688 * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%.
690 * Use: Computes the Jacobi symbol. If @n@ is prime, this is the
691 * Legendre symbol and is equal to 1 if and only if @a@ is a
692 * quadratic residue mod @n@. The result is zero if and only if
693 * @a@ and @n@ have a common factor greater than one.
696 extern int mp_jacobi(mp */
*a*/
, mp */
*n*/
);
698 /* --- @mp_modsqrt@ --- *
700 * Arguments: @mp *d@ = destination integer
701 * @mp *a@ = source integer
702 * @mp *p@ = modulus (must be prime)
704 * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else
707 * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%,
708 * if one exists; else a null pointer. This function will not
709 * work if %$p$% is composite: you must factor the modulus, take
710 * a square root mod each factor, and recombine the results
711 * using the Chinese Remainder Theorem.
714 extern mp
*mp_modsqrt(mp */
*d*/
, mp */
*a*/
, mp */
*p*/
);
716 /*----- Test harness support ----------------------------------------------*/
718 #include <mLib/testrig.h>
720 #ifndef CATACOMB_MPTEXT_H
724 extern const test_type type_mp
;
726 /*----- That's all, folks -------------------------------------------------*/