3 * $Id: mp.h,v 1.17 2003/05/16 09:09:24 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 1.17 2003/05/16 09:09:24 mdw
34 * Fix @mp_lsl2c@. Turns out to be surprisingly tricky.
36 * Revision 1.16 2002/10/15 22:57:22 mdw
37 * Handy new comparison macros.
39 * Revision 1.15 2002/10/15 19:18:31 mdw
40 * New operation to negate numbers.
42 * Revision 1.14 2002/10/15 00:19:40 mdw
43 * Bit setting and clearing functions.
45 * Revision 1.13 2002/10/06 22:52:50 mdw
46 * Pile of changes for supporting two's complement properly.
48 * Revision 1.12 2001/06/16 12:57:43 mdw
49 * Move the @mpmont_factor@ structure and rename it now that it's used for
50 * Barrett simultaneous exponentiation too.
52 * Revision 1.11 2001/04/03 19:36:05 mdw
53 * Add some simple bitwise operations so that Perl can use them.
55 * Revision 1.10 2000/10/08 12:03:16 mdw
56 * Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two
59 * Revision 1.9 2000/07/29 17:03:31 mdw
60 * Add support for left-to-right bitscanning, for use in modular
63 * Revision 1.8 2000/06/22 19:02:01 mdw
66 * Revision 1.7 2000/06/17 11:45:09 mdw
67 * Major memory management overhaul. Added arena support. Use the secure
68 * arena for secret integers. Replace and improve the MP management macros
69 * (e.g., replace MP_MODIFY by MP_DEST).
71 * Revision 1.6 1999/12/10 23:19:46 mdw
72 * Minor bugfixes. New interface for suggested destinations.
74 * Revision 1.5 1999/11/22 20:50:37 mdw
75 * Add support for computing Jacobi symbols.
77 * Revision 1.4 1999/11/21 22:13:02 mdw
78 * Add mp version of MPX_BITS.
80 * Revision 1.3 1999/11/19 13:19:14 mdw
81 * Fix const annotation.
83 * Revision 1.2 1999/11/17 18:02:16 mdw
84 * New multiprecision integer arithmetic suite.
95 /*----- Header files ------------------------------------------------------*/
100 #include <mLib/sub.h>
102 #ifndef CATACOMB_MPW_H
106 #ifndef CATACOMB_ARENA_H
110 #ifndef CATACOMB_MPARENA_H
111 # include "mparena.h"
114 #ifndef CATACOMB_MPX_H
118 /*----- Data structures ---------------------------------------------------*/
120 /* --- A multiprecision integer --- */
123 mpw
*v
, *vl
; /* Vector of digits, current limit */
124 size_t sz
; /* Size of digit buffer in words */
125 mparena
*a
; /* Arena for buffer allocation */
126 unsigned f
; /* Flags (see below) */
127 unsigned ref
; /* Reference counter */
130 #define MP_NEG 1u /* Negative (signed magnitude) */
131 #define MP_BURN 2u /* Secret (viral flag) */
132 #define MP_CONST 4u /* Uses strange memory allocation */
133 #define MP_UNDEF 8u /* Contains nothing interesting */
134 #define MP_DESTROYED 16u /* Has been destroyed */
136 /* --- A factor for simultaneous exponentation --- *
138 * Used by the Montgomery and Barrett exponentiators.
141 typedef struct mp_expfactor
{
146 /*----- Useful constants --------------------------------------------------*/
148 extern mp mp_const
[];
150 #define MP_ZERO (&mp_const[0])
151 #define MP_ONE (&mp_const[1])
152 #define MP_TWO (&mp_const[2])
153 #define MP_THREE (&mp_const[3])
154 #define MP_FOUR (&mp_const[4])
155 #define MP_FIVE (&mp_const[5])
156 #define MP_TEN (&mp_const[6])
157 #define MP_256 (&mp_const[7])
158 #define MP_MONE (&mp_const[8])
160 #define MP_NEW ((mp *)0)
161 #define MP_NEWSEC (&mp_const[9])
163 /*----- Trivial macros ----------------------------------------------------*/
165 /* --- @MP_LEN@ --- *
167 * Arguments: @mp *m@ = pointer to a multiprecision integer
169 * Returns: Length of the integer, in words.
172 #define MP_LEN(m) ((m)->vl - ((m)->v))
174 /*----- Memory management and reference counting --------------------------*/
176 /* --- @mp_new@ --- *
178 * Arguments: @size_t sz@ = size of vector required
179 * @unsigned f@ = flags to set
181 * Returns: Pointer to a new MP structure.
183 * Use: Allocates a new multiprecision integer. The data space is
184 * allocated from either the standard global or secret arena,
185 * depending on the initial flags requested.
188 extern mp
*mp_new(size_t /*sz*/, unsigned /*f*/);
190 /* --- @mp_create@ --- *
192 * Arguments: @size_t sz@ = size of vector required
194 * Returns: Pointer to pristine new MP structure with enough memory
197 * Use: Creates a new multiprecision integer with indeterminate
198 * contents. The integer has a single reference.
201 extern mp
*mp_create(size_t /*sz*/);
203 /* --- @mp_createsecure@ --- *
205 * Arguments: @size_t sz@ = size of vector required
207 * Returns: Pointer to pristine new MP structure with enough memory
210 * Use: Creates a new multiprecision integer with indeterminate
211 * contents. The integer has a single reference. The integer's
212 * data space is allocated from the secure arena. Its burn flag
216 extern mp
*mp_createsecure(size_t /*sz*/);
218 /* --- @mp_build@ --- *
220 * Arguments: @mp *m@ = pointer to an MP block to fill in
221 * @mpw *v@ = pointer to a word array
222 * @mpw *vl@ = pointer just past end of array
226 * Use: Creates a multiprecision integer representing some smallish
227 * number. You must provide storage for the number and dispose
228 * of it when you've finished with it. The number is marked as
229 * constant while it exists.
232 extern void mp_build(mp */
*m*/
, mpw */
*v*/
, mpw */
*vl*/
);
234 /* --- @mp_destroy@ --- *
236 * Arguments: @mp *m@ = pointer to a multiprecision integer
240 * Use: Destroys a multiprecision integer. The reference count isn't
241 * checked. Don't use this function if you don't know what
242 * you're doing: use @mp_drop@ instead.
245 extern void mp_destroy(mp */
*m*/
);
247 /* --- @mp_copy@ --- *
249 * Arguments: @mp *m@ = pointer to a multiprecision integer
251 * Returns: A copy of the given multiprecision integer.
253 * Use: Copies the given integer. In fact you just get another
254 * reference to the same old one again.
257 extern mp
*mp_copy(mp */
*m*/
);
259 #define MP_COPY(m) ((m)->ref++, (m))
261 /* --- @mp_drop@ --- *
263 * Arguments: @mp *m@ = pointer to a multiprecision integer
267 * Use: Drops a reference to an integer which isn't wanted any more.
268 * If there are no more references, the integer is destroyed.
271 extern void mp_drop(mp */
*m*/
);
273 #define MP_DROP(m) do { \
276 if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \
280 /* --- @mp_split@ --- *
282 * Arguments: @mp *m@ = pointer to a multiprecision integer
284 * Returns: A reference to the same integer, possibly with a different
287 * Use: Splits off a modifiable version of the integer referred to.
290 extern mp
*mp_split(mp */
*m*/
);
292 #define MP_SPLIT(m) do { \
294 if ((_m->f & MP_CONST) || _m->ref > 1) { \
295 size_t _len = MP_LEN(_m); \
296 mp *_mm = mp_new(_len, _m->f); \
297 if (!(_m->f & MP_UNDEF)) \
298 memcpy(_mm->v, _m->v, MPWS(_len)); \
305 /* --- @mp_resize@ --- *
307 * Arguments: @mp *m@ = pointer to a multiprecision integer
308 * @size_t sz@ = new size
312 * Use: Resizes the vector containing the integer's digits. The new
313 * size must be at least as large as the current integer's
314 * length. This isn't really intended for client use.
317 extern void mp_resize(mp */
*m*/
, size_t /*sz*/);
319 #define MP_RESIZE(m, ssz) do { \
321 size_t _sz = (ssz); \
322 mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \
324 size_t _len = MP_LEN(_m); \
325 assert(((void)"can't make size less than length", _sz >= _len)); \
326 _v = mpalloc(_a, _sz); \
327 if (!(_m->f & MP_UNDEF)) \
328 memcpy(_v, _m->v, MPWS(_len)); \
329 if (_m->f & MP_BURN) \
330 memset(_m->v, 0, MPWS(_m->sz)); \
331 mpfree(_m->a, _m->v); \
334 _m->vl = _v + _len; \
337 /* --- @mp_ensure@ --- *
339 * Arguments: @mp *m@ = pointer to a multiprecision integer
340 * @size_t sz@ = required size
344 * Use: Ensures that the integer has enough space for @sz@ digits.
345 * The value is not changed.
348 extern void mp_ensure(mp */
*m*/
, size_t /*sz*/);
350 #define MP_ENSURE(m, ssz) do { \
352 size_t _ssz = (ssz); \
353 size_t _len = MP_LEN(_m); \
354 if (_ssz >= _len) { \
356 mp_resize(_m, _ssz); \
357 if (!(_m->f & MP_UNDEF) && _ssz > _len) \
358 memset(_m->vl, 0, MPWS(_ssz - _len)); \
359 _m->vl = _m->v + _ssz; \
363 /* --- @mp_dest@ --- *
365 * Arguments: @mp *m@ = a suggested destination integer
366 * @size_t sz@ = size required for result, in digits
367 * @unsigned f@ = various flags
369 * Returns: A pointer to an appropriate destination.
371 * Use: Converts a suggested destination into a real destination with
372 * the required properties. If the real destination is @d@,
373 * then the following properties will hold:
375 * * @d@ will have exactly one reference.
377 * * If @m@ is not @MP_NEW@, then the contents of @m@ will not
378 * change, unless @f@ has the @MP_UNDEF@ flag set.
380 * * If @m@ is not @MP_NEW@, then he reference count of @m@ on
381 * entry is equal to the sum of the counts of @d@ and @m@ on
384 * * The size of @d@ will be at least @sz@.
386 * * If @f@ has the @MP_BURN@ flag set, then @d@ will be
387 * allocated from @MPARENA_SECURE@.
389 * Understanding this function is crucial to using Catacomb's
390 * multiprecision integer library effectively.
393 extern mp
*mp_dest(mp */
*m*/
, size_t /*sz*/, unsigned /*f*/);
395 #define MP_DEST(m, ssz, f) do { \
397 size_t _ssz = (ssz); \
399 _m = mp_dest(_m, _ssz, _f); \
403 /*----- Size manipulation -------------------------------------------------*/
405 /* --- @mp_shrink@ --- *
407 * Arguments: @mp *m@ = pointer to a multiprecision integer
411 * Use: Reduces the recorded length of an integer. This doesn't
412 * reduce the amount of memory used, although it can improve
413 * performance a bit. To reduce memory, use @mp_minimize@
414 * instead. This can't change the value of an integer, and is
415 * therefore safe to use even when there are multiple
419 extern void mp_shrink(mp */
*m*/
);
421 #define MP_SHRINK(m) do { \
423 MPX_SHRINK(_mm->v, _mm->vl); \
428 /* --- @mp_minimize@ --- *
430 * Arguments: @mp *m@ = pointer to a multiprecision integer
434 * Use: Reduces the amount of memory an integer uses. It's best to
435 * do this to numbers which aren't going to change in the
439 extern void mp_minimize(mp */
*m*/
);
441 /*----- Bit scanning ------------------------------------------------------*/
443 #ifndef CATACOMB_MPSCAN_H
447 /* --- @mp_scan@ --- *
449 * Arguments: @mpscan *sc@ = pointer to bitscanner block
450 * @const mp *m@ = pointer to a multiprecision integer
454 * Use: Initializes a bitscanner on a multiprecision integer.
457 extern void mp_scan(mpscan */
*sc*/
, const mp */
*m*/
);
459 #define MP_SCAN(sc, m) do { \
460 const mp *_mm = (m); \
461 mpscan *_sc = (sc); \
462 MPSCAN_INITX(_sc, _mm->v, _mm->vl); \
465 /* --- @mp_rscan@ --- *
467 * Arguments: @mpscan *sc@ = pointer to bitscanner block
468 * @const mp *m@ = pointer to a multiprecision integer
472 * Use: Initializes a reverse bitscanner on a multiprecision
476 extern void mp_rscan(mpscan */
*sc*/
, const mp */
*m*/
);
478 #define MP_RSCAN(sc, m) do { \
479 const mp *_mm = (m); \
480 mpscan *_sc = (sc); \
481 MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \
484 /* --- Other bitscanning aliases --- */
486 #define mp_step mpscan_step
487 #define mp_bit mpscan_bit
488 #define mp_rstep mpscan_rstep
489 #define mp_rbit mpscan_rbit
491 #define MP_STEP MPSCAN_STEP
492 #define MP_BIT MPSCAN_BIT
493 #define MP_RSTEP MPSCAN_RSTEP
494 #define MP_RBIT MPSCAN_RBIT
496 /*----- Loading and storing -----------------------------------------------*/
498 /* --- @mp_octets@ --- *
500 * Arguments: @const mp *m@ = a multiprecision integer
502 * Returns: The number of octets required to represent @m@.
504 * Use: Calculates the external storage required for a multiprecision
508 extern size_t mp_octets(const mp */
*m*/
);
510 /* --- @mp_octets2c@ --- *
512 * Arguments: @const mp *m@ = a multiprecision integer
514 * Returns: The number of octets required to represent @m@.
516 * Use: Calculates the external storage required for a multiprecision
517 * integer represented as two's complement.
520 extern size_t mp_octets2c(const mp */
*m*/
);
522 /* --- @mp_bits@ --- *
524 * Arguments: @const mp *m@ = a multiprecision integer
526 * Returns: The number of bits required to represent @m@.
528 * Use: Calculates the external storage required for a multiprecision
532 extern unsigned long mp_bits(const mp */
*m*/
);
534 /* --- @mp_loadl@ --- *
536 * Arguments: @mp *d@ = destination
537 * @const void *pv@ = pointer to source data
538 * @size_t sz@ = size of the source data
540 * Returns: Resulting multiprecision number.
542 * Use: Loads a multiprecision number from an array of octets. The
543 * first byte in the array is the least significant. More
544 * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$%
545 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
548 extern mp
*mp_loadl(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
550 /* --- @mp_storel@ --- *
552 * Arguments: @const mp *m@ = source
553 * @void *pv@ = pointer to output array
554 * @size_t sz@ = size of the output array
558 * Use: Stores a multiprecision number in an array of octets. The
559 * first byte in the array is the least significant. If the
560 * array is too small to represent the number, high-order bits
561 * are truncated; if the array is too large, high order bytes
562 * are filled with zeros. More formally, if the number is
563 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
564 * then the array is %$b_0, b_1, \ldots, b_{n-1}$%.
567 extern void mp_storel(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
569 /* --- @mp_loadb@ --- *
571 * Arguments: @mp *d@ = destination
572 * @const void *pv@ = pointer to source data
573 * @size_t sz@ = size of the source data
575 * Returns: Resulting multiprecision number.
577 * Use: Loads a multiprecision number from an array of octets. The
578 * last byte in the array is the least significant. More
579 * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$%
580 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
583 extern mp
*mp_loadb(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
585 /* --- @mp_storeb@ --- *
587 * Arguments: @const mp *m@ = source
588 * @void *pv@ = pointer to output array
589 * @size_t sz@ = size of the output array
593 * Use: Stores a multiprecision number in an array of octets. The
594 * last byte in the array is the least significant. If the
595 * array is too small to represent the number, high-order bits
596 * are truncated; if the array is too large, high order bytes
597 * are filled with zeros. More formally, if the number is
598 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
599 * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%.
602 extern void mp_storeb(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
604 /* --- @mp_loadl2c@ --- *
606 * Arguments: @mp *d@ = destination
607 * @const void *pv@ = pointer to source data
608 * @size_t sz@ = size of the source data
610 * Returns: Resulting multiprecision number.
612 * Use: Loads a multiprecision number from an array of octets as
613 * two's complement. The first byte in the array is the least
617 extern mp
*mp_loadl2c(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
619 /* --- @mp_storel2c@ --- *
621 * Arguments: @const mp *m@ = source
622 * @void *pv@ = pointer to output array
623 * @size_t sz@ = size of the output array
627 * Use: Stores a multiprecision number in an array of octets as two's
628 * complement. The first byte in the array is the least
629 * significant. If the array is too small to represent the
630 * number, high-order bits are truncated; if the array is too
631 * large, high order bytes are sign-extended.
634 extern void mp_storel2c(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
636 /* --- @mp_loadb2c@ --- *
638 * Arguments: @mp *d@ = destination
639 * @const void *pv@ = pointer to source data
640 * @size_t sz@ = size of the source data
642 * Returns: Resulting multiprecision number.
644 * Use: Loads a multiprecision number from an array of octets as
645 * two's complement. The last byte in the array is the least
649 extern mp
*mp_loadb2c(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
651 /* --- @mp_storeb2c@ --- *
653 * Arguments: @const mp *m@ = source
654 * @void *pv@ = pointer to output array
655 * @size_t sz@ = size of the output array
659 * Use: Stores a multiprecision number in an array of octets, as
660 * two's complement. The last byte in the array is the least
661 * significant. If the array is too small to represent the
662 * number, high-order bits are truncated; if the array is too
663 * large, high order bytes are sign-extended.
666 extern void mp_storeb2c(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
668 /*----- Bit operations ----------------------------------------------------*/
670 /* --- @mp_not@ --- *
672 * Arguments: @mp *d@ = destination
675 * Returns: The bitwise complement of the source.
678 extern mp
*mp_not(mp */
*d*/
, mp */
*a*/
);
680 /* --- @mp_bitop@ --- *
682 * Arguments: @mp *d@ = destination
683 * @mp *a, *b@ = sources
685 * Returns: The result of the given bitwise operation. These functions
686 * don't handle negative numbers at all sensibly. For that, use
687 * the @...2c@ variants. The functions are named after the
688 * truth tables they generate:
695 #define MP_BITDECL(string) \
696 extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/);
697 MPX_DOBIN(MP_BITDECL
)
699 /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- *
701 * Synonyms for the commonly-used functions.
704 #define mp_and mp_bit0001
705 #define mp_or mp_bit0111
706 #define mp_nand mp_bit1110
707 #define mp_nor mp_bit1000
708 #define mp_xor mp_bit0110
710 /* --- @mp_testbit@ --- *
712 * Arguments: @mp *x@ = a large integer
713 * @unsigned long n@ = which bit to test
715 * Returns: Nonzero if the bit is set, zero if not.
718 extern int mp_testbit(mp */
*x*/
, unsigned long /*n*/);
720 /* --- @mp_setbit@, @mp_clearbit@ --- *
722 * Arguments: @mp *d@ = a destination
723 * @mp *x@ = a large integer
724 * @unsigned long n@ = which bit to modify
726 * Returns: The argument @x@, with the appropriate bit set or cleared.
729 extern mp
*mp_setbit(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
730 extern mp
*mp_clearbit(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
732 /* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- *
734 * Arguments: @mp *d@ = destination
736 * @size_t n@ = number of bits to move
738 * Returns: Result, @a@ shifted left or right by @n@.
740 * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced
741 * on the right with ones instead of zeroes: it's used
742 * internally by @mp_lsl2c@, though it may be useful on its
746 extern mp
*mp_lsl(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
747 extern mp
*mp_lslc(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
748 extern mp
*mp_lsr(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
750 /* --- @mp_not2c@ --- *
752 * Arguments: @mp *d@ = destination
755 * Returns: The sign-extended complement of the argument.
758 extern mp
*mp_not2c(mp */
*d*/
, mp */
*a*/
);
760 /* --- @mp_bitop2c@ --- *
762 * Arguments: @mp *d@ = destination
763 * @mp *a, *b@ = sources
765 * Returns: The result of the given bitwise operation. Negative numbers
766 * are treated as two's complement, sign-extended infinitely to
767 * the left. The functions are named after the truth tables
775 #define MP_BIT2CDECL(string) \
776 extern mp *mp_bit##string##2c(mp */*d*/, mp */*a*/, mp */*b*/);
777 MPX_DOBIN(MP_BIT2CDECL
)
779 /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- *
781 * Synonyms for the commonly-used functions.
784 #define mp_and2c mp_bit00012c
785 #define mp_or2c mp_bit01112c
786 #define mp_nand2c mp_bit11102c
787 #define mp_nor2c mp_bit10002c
788 #define mp_xor2c mp_bit01102c
790 /* --- @mp_lsl2c@, @mp_lsr2c@ --- *
792 * Arguments: @mp *d@ = destination
794 * @size_t n@ = number of bits to move
796 * Returns: Result, @a@ shifted left or right by @n@. Handles the
797 * pretence of sign-extension for negative numbers.
800 extern mp
*mp_lsl2c(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
801 extern mp
*mp_lsr2c(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
803 /* --- @mp_testbit2c@ --- *
805 * Arguments: @mp *x@ = a large integer
806 * @unsigned long n@ = which bit to test
808 * Returns: Nonzero if the bit is set, zero if not. Fakes up two's
809 * complement representation.
812 extern int mp_testbit2c(mp */
*x*/
, unsigned long /*n*/);
814 /* --- @mp_setbit2c@, @mp_clearbit2c@ --- *
816 * Arguments: @mp *d@ = a destination
817 * @mp *x@ = a large integer
818 * @unsigned long n@ = which bit to modify
820 * Returns: The argument @x@, with the appropriate bit set or cleared.
821 * Fakes up two's complement representation.
824 extern mp
*mp_setbit2c(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
825 extern mp
*mp_clearbit2c(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
827 /*----- Comparisons -------------------------------------------------------*/
831 * Arguments: @const mp *a, *b@ = two numbers
833 * Returns: Nonzero if the numbers are equal.
836 extern int mp_eq(const mp */
*a*/
, const mp */
*b*/
);
838 #define MP_EQ(a, b) \
839 ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \
840 mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl))
842 /* --- @mp_cmp@ --- *
844 * Arguments: @const mp *a, *b@ = two numbers
846 * Returns: Less than, equal to or greater than zero, according to
847 * whether @a@ is less than, equal to or greater than @b@.
850 extern int mp_cmp(const mp */
*a*/
, const mp */
*b*/
);
852 #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0)
854 /* --- Other handy macros --- */
856 #define MP_ISNEG(x) ((x)->f & MP_NEG)
857 #define MP_ISZERO(x) MP_EQ((x), MP_ZERO)
858 #define MP_ISPOS(x) (!MP_ISNEG(x) && !MP_ISZERO(x))
860 /*----- Arithmetic operations ---------------------------------------------*/
862 /* --- @mp_neg@ --- *
864 * Arguments: @mp *d@ = destination
867 * Returns: The negation of the argument.
869 * Use: Negates its argument.
872 extern mp
*mp_neg(mp */
*d*/
, mp */
*a*/
);
874 /* --- @mp_add@ --- *
876 * Arguments: @mp *d@ = destination
877 * @mp *a, *b@ = sources
879 * Returns: Result, @a@ added to @b@.
882 extern mp
*mp_add(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
884 /* --- @mp_sub@ --- *
886 * Arguments: @mp *d@ = destination
887 * @mp *a, *b@ = sources
889 * Returns: Result, @b@ subtracted from @a@.
892 extern mp
*mp_sub(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
894 /* --- @mp_mul@ --- *
896 * Arguments: @mp *d@ = destination
897 * @mp *a, *b@ = sources
899 * Returns: Result, @a@ multiplied by @b@.
902 extern mp
*mp_mul(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
904 /* --- @mp_sqr@ --- *
906 * Arguments: @mp *d@ = destination
909 * Returns: Result, @a@ squared.
912 extern mp
*mp_sqr(mp */
*d*/
, mp */
*a*/
);
914 /* --- @mp_div@ --- *
916 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
917 * @mp *a, *b@ = sources
919 * Use: Calculates the quotient and remainder when @a@ is divided by
923 extern void mp_div(mp
**/
*qq*/
, mp
**/
*rr*/
, mp */
*a*/
, mp */
*b*/
);
925 /* --- @mp_odd@ --- *
927 * Arguments: @mp *d@ = pointer to destination integer
928 * @mp *m@ = pointer to source integer
929 * @size_t *s@ = where to store the power of 2
931 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
933 * Use: Computes a power of two and an odd integer which, when
934 * multiplied, give a specified result. This sort of thing is
935 * useful in number theory quite often.
938 extern mp
*mp_odd(mp */
*d*/
, mp */
*m*/
, size_t */
*s*/
);
940 /*----- More advanced algorithms ------------------------------------------*/
942 /* --- @mp_sqrt@ --- *
944 * Arguments: @mp *d@ = pointer to destination integer
945 * @mp *a@ = (nonnegative) integer to take square root of
947 * Returns: The largest integer %$x$% such that %$x^2 \le a$%.
949 * Use: Computes integer square roots.
951 * The current implementation isn't very good: it uses the
952 * Newton-Raphson method to find an approximation to %$a$%. If
953 * there's any demand for a better version, I'll write one.
956 extern mp
*mp_sqrt(mp */
*d*/
, mp */
*a*/
);
958 /* --- @mp_gcd@ --- *
960 * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
961 * @mp *a, *b@ = sources (must be nonzero)
965 * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
966 * @ax + by = gcd(a, b)@. This is useful for computing modular
967 * inverses. Neither @a@ nor @b@ may be zero.
970 extern void mp_gcd(mp
**/
*gcd*/
, mp
**/
*xx*/
, mp
**/
*yy*/
,
971 mp */
*a*/
, mp */
*b*/
);
973 /* --- @mp_jacobi@ --- *
975 * Arguments: @mp *a@ = an integer less than @n@
976 * @mp *n@ = an odd integer
978 * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%.
980 * Use: Computes the Jacobi symbol. If @n@ is prime, this is the
981 * Legendre symbol and is equal to 1 if and only if @a@ is a
982 * quadratic residue mod @n@. The result is zero if and only if
983 * @a@ and @n@ have a common factor greater than one.
986 extern int mp_jacobi(mp */
*a*/
, mp */
*n*/
);
988 /* --- @mp_modsqrt@ --- *
990 * Arguments: @mp *d@ = destination integer
991 * @mp *a@ = source integer
992 * @mp *p@ = modulus (must be prime)
994 * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else
997 * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%,
998 * if one exists; else a null pointer. This function will not
999 * work if %$p$% is composite: you must factor the modulus, take
1000 * a square root mod each factor, and recombine the results
1001 * using the Chinese Remainder Theorem.
1004 extern mp
*mp_modsqrt(mp */
*d*/
, mp */
*a*/
, mp */
*p*/
);
1006 /*----- Test harness support ----------------------------------------------*/
1008 #include <mLib/testrig.h>
1010 #ifndef CATACOMB_MPTEXT_H
1011 # include "mptext.h"
1014 extern const test_type type_mp
;
1016 /*----- That's all, folks -------------------------------------------------*/