3 * $Id: mp.h,v 1.18 2004/04/03 03:32:05 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 1.18 2004/04/03 03:32:05 mdw
34 * General robustification.
36 * Revision 1.17 2003/05/16 09:09:24 mdw
37 * Fix @mp_lsl2c@. Turns out to be surprisingly tricky.
39 * Revision 1.16 2002/10/15 22:57:22 mdw
40 * Handy new comparison macros.
42 * Revision 1.15 2002/10/15 19:18:31 mdw
43 * New operation to negate numbers.
45 * Revision 1.14 2002/10/15 00:19:40 mdw
46 * Bit setting and clearing functions.
48 * Revision 1.13 2002/10/06 22:52:50 mdw
49 * Pile of changes for supporting two's complement properly.
51 * Revision 1.12 2001/06/16 12:57:43 mdw
52 * Move the @mpmont_factor@ structure and rename it now that it's used for
53 * Barrett simultaneous exponentiation too.
55 * Revision 1.11 2001/04/03 19:36:05 mdw
56 * Add some simple bitwise operations so that Perl can use them.
58 * Revision 1.10 2000/10/08 12:03:16 mdw
59 * Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two
62 * Revision 1.9 2000/07/29 17:03:31 mdw
63 * Add support for left-to-right bitscanning, for use in modular
66 * Revision 1.8 2000/06/22 19:02:01 mdw
69 * Revision 1.7 2000/06/17 11:45:09 mdw
70 * Major memory management overhaul. Added arena support. Use the secure
71 * arena for secret integers. Replace and improve the MP management macros
72 * (e.g., replace MP_MODIFY by MP_DEST).
74 * Revision 1.6 1999/12/10 23:19:46 mdw
75 * Minor bugfixes. New interface for suggested destinations.
77 * Revision 1.5 1999/11/22 20:50:37 mdw
78 * Add support for computing Jacobi symbols.
80 * Revision 1.4 1999/11/21 22:13:02 mdw
81 * Add mp version of MPX_BITS.
83 * Revision 1.3 1999/11/19 13:19:14 mdw
84 * Fix const annotation.
86 * Revision 1.2 1999/11/17 18:02:16 mdw
87 * New multiprecision integer arithmetic suite.
98 /*----- Header files ------------------------------------------------------*/
103 #include <mLib/sub.h>
105 #ifndef CATACOMB_MPW_H
109 #ifndef CATACOMB_ARENA_H
113 #ifndef CATACOMB_MPARENA_H
114 # include "mparena.h"
117 #ifndef CATACOMB_MPX_H
121 /*----- Data structures ---------------------------------------------------*/
123 /* --- A multiprecision integer --- */
126 mpw
*v
, *vl
; /* Vector of digits, current limit */
127 size_t sz
; /* Size of digit buffer in words */
128 mparena
*a
; /* Arena for buffer allocation */
129 unsigned f
; /* Flags (see below) */
130 unsigned ref
; /* Reference counter */
133 #define MP_NEG 1u /* Negative (signed magnitude) */
134 #define MP_BURN 2u /* Secret (viral flag) */
135 #define MP_CONST 4u /* Uses strange memory allocation */
136 #define MP_UNDEF 8u /* Contains nothing interesting */
137 #define MP_DESTROYED 16u /* Has been destroyed */
139 /* --- A factor for simultaneous exponentation --- *
141 * Used by the Montgomery and Barrett exponentiators.
144 typedef struct mp_expfactor
{
149 /*----- Useful constants --------------------------------------------------*/
151 extern mp mp_const
[];
153 #define MP_ZERO (&mp_const[0])
154 #define MP_ONE (&mp_const[1])
155 #define MP_TWO (&mp_const[2])
156 #define MP_THREE (&mp_const[3])
157 #define MP_FOUR (&mp_const[4])
158 #define MP_FIVE (&mp_const[5])
159 #define MP_TEN (&mp_const[6])
160 #define MP_256 (&mp_const[7])
161 #define MP_MONE (&mp_const[8])
163 #define MP_NEW ((mp *)0)
164 #define MP_NEWSEC (&mp_const[9])
166 /*----- Trivial macros ----------------------------------------------------*/
168 /* --- @MP_LEN@ --- *
170 * Arguments: @mp *m@ = pointer to a multiprecision integer
172 * Returns: Length of the integer, in words.
175 #define MP_LEN(m) ((m)->vl - ((m)->v))
177 /*----- Memory management and reference counting --------------------------*/
179 /* --- @mp_new@ --- *
181 * Arguments: @size_t sz@ = size of vector required
182 * @unsigned f@ = flags to set
184 * Returns: Pointer to a new MP structure.
186 * Use: Allocates a new multiprecision integer. The data space is
187 * allocated from either the standard global or secret arena,
188 * depending on the initial flags requested.
191 extern mp
*mp_new(size_t /*sz*/, unsigned /*f*/);
193 /* --- @mp_create@ --- *
195 * Arguments: @size_t sz@ = size of vector required
197 * Returns: Pointer to pristine new MP structure with enough memory
200 * Use: Creates a new multiprecision integer with indeterminate
201 * contents. The integer has a single reference.
204 extern mp
*mp_create(size_t /*sz*/);
206 /* --- @mp_createsecure@ --- *
208 * Arguments: @size_t sz@ = size of vector required
210 * Returns: Pointer to pristine new MP structure with enough memory
213 * Use: Creates a new multiprecision integer with indeterminate
214 * contents. The integer has a single reference. The integer's
215 * data space is allocated from the secure arena. Its burn flag
219 extern mp
*mp_createsecure(size_t /*sz*/);
221 /* --- @mp_build@ --- *
223 * Arguments: @mp *m@ = pointer to an MP block to fill in
224 * @mpw *v@ = pointer to a word array
225 * @mpw *vl@ = pointer just past end of array
229 * Use: Creates a multiprecision integer representing some smallish
230 * number. You must provide storage for the number and dispose
231 * of it when you've finished with it. The number is marked as
232 * constant while it exists.
235 extern void mp_build(mp */
*m*/
, mpw */
*v*/
, mpw */
*vl*/
);
237 /* --- @mp_destroy@ --- *
239 * Arguments: @mp *m@ = pointer to a multiprecision integer
243 * Use: Destroys a multiprecision integer. The reference count isn't
244 * checked. Don't use this function if you don't know what
245 * you're doing: use @mp_drop@ instead.
248 extern void mp_destroy(mp */
*m*/
);
250 /* --- @mp_copy@ --- *
252 * Arguments: @mp *m@ = pointer to a multiprecision integer
254 * Returns: A copy of the given multiprecision integer.
256 * Use: Copies the given integer. In fact you just get another
257 * reference to the same old one again.
260 extern mp
*mp_copy(mp */
*m*/
);
262 #define MP_COPY(m) ((m)->ref++, (m))
264 /* --- @mp_drop@ --- *
266 * Arguments: @mp *m@ = pointer to a multiprecision integer
270 * Use: Drops a reference to an integer which isn't wanted any more.
271 * If there are no more references, the integer is destroyed.
274 extern void mp_drop(mp */
*m*/
);
276 #define MP_DROP(m) do { \
279 if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \
283 /* --- @mp_split@ --- *
285 * Arguments: @mp *m@ = pointer to a multiprecision integer
287 * Returns: A reference to the same integer, possibly with a different
290 * Use: Splits off a modifiable version of the integer referred to.
293 extern mp
*mp_split(mp */
*m*/
);
295 #define MP_SPLIT(m) do { \
297 if ((_m->f & MP_CONST) || _m->ref > 1) { \
298 size_t _len = MP_LEN(_m); \
299 mp *_mm = mp_new(_len, _m->f); \
300 if (!(_m->f & MP_UNDEF)) \
301 memcpy(_mm->v, _m->v, MPWS(_len)); \
308 /* --- @mp_resize@ --- *
310 * Arguments: @mp *m@ = pointer to a multiprecision integer
311 * @size_t sz@ = new size
315 * Use: Resizes the vector containing the integer's digits. The new
316 * size must be at least as large as the current integer's
317 * length. This isn't really intended for client use.
320 extern void mp_resize(mp */
*m*/
, size_t /*sz*/);
322 #define MP_RESIZE(m, ssz) do { \
324 size_t _sz = (ssz); \
325 mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \
327 size_t _len = MP_LEN(_m); \
328 assert(((void)"can't make size less than length", _sz >= _len)); \
329 _v = mpalloc(_a, _sz); \
330 if (!(_m->f & MP_UNDEF)) \
331 memcpy(_v, _m->v, MPWS(_len)); \
332 if (_m->f & MP_BURN) \
333 memset(_m->v, 0, MPWS(_m->sz)); \
334 mpfree(_m->a, _m->v); \
337 _m->vl = _v + _len; \
340 /* --- @mp_ensure@ --- *
342 * Arguments: @mp *m@ = pointer to a multiprecision integer
343 * @size_t sz@ = required size
347 * Use: Ensures that the integer has enough space for @sz@ digits.
348 * The value is not changed.
351 extern void mp_ensure(mp */
*m*/
, size_t /*sz*/);
353 #define MP_ENSURE(m, ssz) do { \
355 size_t _ssz = (ssz); \
356 size_t _len = MP_LEN(_m); \
357 if (_ssz >= _len) { \
359 mp_resize(_m, _ssz); \
360 if (!(_m->f & MP_UNDEF) && _ssz > _len) \
361 memset(_m->vl, 0, MPWS(_ssz - _len)); \
362 _m->vl = _m->v + _ssz; \
366 /* --- @mp_dest@ --- *
368 * Arguments: @mp *m@ = a suggested destination integer
369 * @size_t sz@ = size required for result, in digits
370 * @unsigned f@ = various flags
372 * Returns: A pointer to an appropriate destination.
374 * Use: Converts a suggested destination into a real destination with
375 * the required properties. If the real destination is @d@,
376 * then the following properties will hold:
378 * * @d@ will have exactly one reference.
380 * * If @m@ is not @MP_NEW@, then the contents of @m@ will not
381 * change, unless @f@ has the @MP_UNDEF@ flag set.
383 * * If @m@ is not @MP_NEW@, then he reference count of @m@ on
384 * entry is equal to the sum of the counts of @d@ and @m@ on
387 * * The size of @d@ will be at least @sz@.
389 * * If @f@ has the @MP_BURN@ flag set, then @d@ will be
390 * allocated from @MPARENA_SECURE@.
392 * Understanding this function is crucial to using Catacomb's
393 * multiprecision integer library effectively.
396 extern mp
*mp_dest(mp */
*m*/
, size_t /*sz*/, unsigned /*f*/);
398 #define MP_DEST(m, ssz, f) do { \
400 size_t _ssz = (ssz); \
402 _m = mp_dest(_m, _ssz, _f); \
406 /*----- Size manipulation -------------------------------------------------*/
408 /* --- @mp_shrink@ --- *
410 * Arguments: @mp *m@ = pointer to a multiprecision integer
414 * Use: Reduces the recorded length of an integer. This doesn't
415 * reduce the amount of memory used, although it can improve
416 * performance a bit. To reduce memory, use @mp_minimize@
417 * instead. This can't change the value of an integer, and is
418 * therefore safe to use even when there are multiple
422 extern void mp_shrink(mp */
*m*/
);
424 #define MP_SHRINK(m) do { \
426 MPX_SHRINK(_mm->v, _mm->vl); \
431 /* --- @mp_minimize@ --- *
433 * Arguments: @mp *m@ = pointer to a multiprecision integer
437 * Use: Reduces the amount of memory an integer uses. It's best to
438 * do this to numbers which aren't going to change in the
442 extern void mp_minimize(mp */
*m*/
);
444 /*----- Bit scanning ------------------------------------------------------*/
446 #ifndef CATACOMB_MPSCAN_H
450 /* --- @mp_scan@ --- *
452 * Arguments: @mpscan *sc@ = pointer to bitscanner block
453 * @const mp *m@ = pointer to a multiprecision integer
457 * Use: Initializes a bitscanner on a multiprecision integer.
460 extern void mp_scan(mpscan */
*sc*/
, const mp */
*m*/
);
462 #define MP_SCAN(sc, m) do { \
463 const mp *_mm = (m); \
464 mpscan *_sc = (sc); \
465 MPSCAN_INITX(_sc, _mm->v, _mm->vl); \
468 /* --- @mp_rscan@ --- *
470 * Arguments: @mpscan *sc@ = pointer to bitscanner block
471 * @const mp *m@ = pointer to a multiprecision integer
475 * Use: Initializes a reverse bitscanner on a multiprecision
479 extern void mp_rscan(mpscan */
*sc*/
, const mp */
*m*/
);
481 #define MP_RSCAN(sc, m) do { \
482 const mp *_mm = (m); \
483 mpscan *_sc = (sc); \
484 MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \
487 /* --- Other bitscanning aliases --- */
489 #define mp_step mpscan_step
490 #define mp_bit mpscan_bit
491 #define mp_rstep mpscan_rstep
492 #define mp_rbit mpscan_rbit
494 #define MP_STEP MPSCAN_STEP
495 #define MP_BIT MPSCAN_BIT
496 #define MP_RSTEP MPSCAN_RSTEP
497 #define MP_RBIT MPSCAN_RBIT
499 /*----- Loading and storing -----------------------------------------------*/
501 /* --- @mp_octets@ --- *
503 * Arguments: @const mp *m@ = a multiprecision integer
505 * Returns: The number of octets required to represent @m@.
507 * Use: Calculates the external storage required for a multiprecision
511 extern size_t mp_octets(const mp */
*m*/
);
513 /* --- @mp_octets2c@ --- *
515 * Arguments: @const mp *m@ = a multiprecision integer
517 * Returns: The number of octets required to represent @m@.
519 * Use: Calculates the external storage required for a multiprecision
520 * integer represented as two's complement.
523 extern size_t mp_octets2c(const mp */
*m*/
);
525 /* --- @mp_bits@ --- *
527 * Arguments: @const mp *m@ = a multiprecision integer
529 * Returns: The number of bits required to represent @m@.
531 * Use: Calculates the external storage required for a multiprecision
535 extern unsigned long mp_bits(const mp */
*m*/
);
537 /* --- @mp_loadl@ --- *
539 * Arguments: @mp *d@ = destination
540 * @const void *pv@ = pointer to source data
541 * @size_t sz@ = size of the source data
543 * Returns: Resulting multiprecision number.
545 * Use: Loads a multiprecision number from an array of octets. The
546 * first byte in the array is the least significant. More
547 * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$%
548 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
551 extern mp
*mp_loadl(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
553 /* --- @mp_storel@ --- *
555 * Arguments: @const mp *m@ = source
556 * @void *pv@ = pointer to output array
557 * @size_t sz@ = size of the output array
561 * Use: Stores a multiprecision number in an array of octets. The
562 * first byte in the array is the least significant. If the
563 * array is too small to represent the number, high-order bits
564 * are truncated; if the array is too large, high order bytes
565 * are filled with zeros. More formally, if the number is
566 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
567 * then the array is %$b_0, b_1, \ldots, b_{n-1}$%.
570 extern void mp_storel(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
572 /* --- @mp_loadb@ --- *
574 * Arguments: @mp *d@ = destination
575 * @const void *pv@ = pointer to source data
576 * @size_t sz@ = size of the source data
578 * Returns: Resulting multiprecision number.
580 * Use: Loads a multiprecision number from an array of octets. The
581 * last byte in the array is the least significant. More
582 * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$%
583 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
586 extern mp
*mp_loadb(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
588 /* --- @mp_storeb@ --- *
590 * Arguments: @const mp *m@ = source
591 * @void *pv@ = pointer to output array
592 * @size_t sz@ = size of the output array
596 * Use: Stores a multiprecision number in an array of octets. The
597 * last byte in the array is the least significant. If the
598 * array is too small to represent the number, high-order bits
599 * are truncated; if the array is too large, high order bytes
600 * are filled with zeros. More formally, if the number is
601 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
602 * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%.
605 extern void mp_storeb(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
607 /* --- @mp_loadl2c@ --- *
609 * Arguments: @mp *d@ = destination
610 * @const void *pv@ = pointer to source data
611 * @size_t sz@ = size of the source data
613 * Returns: Resulting multiprecision number.
615 * Use: Loads a multiprecision number from an array of octets as
616 * two's complement. The first byte in the array is the least
620 extern mp
*mp_loadl2c(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
622 /* --- @mp_storel2c@ --- *
624 * Arguments: @const mp *m@ = source
625 * @void *pv@ = pointer to output array
626 * @size_t sz@ = size of the output array
630 * Use: Stores a multiprecision number in an array of octets as two's
631 * complement. The first byte in the array is the least
632 * significant. If the array is too small to represent the
633 * number, high-order bits are truncated; if the array is too
634 * large, high order bytes are sign-extended.
637 extern void mp_storel2c(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
639 /* --- @mp_loadb2c@ --- *
641 * Arguments: @mp *d@ = destination
642 * @const void *pv@ = pointer to source data
643 * @size_t sz@ = size of the source data
645 * Returns: Resulting multiprecision number.
647 * Use: Loads a multiprecision number from an array of octets as
648 * two's complement. The last byte in the array is the least
652 extern mp
*mp_loadb2c(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
654 /* --- @mp_storeb2c@ --- *
656 * Arguments: @const mp *m@ = source
657 * @void *pv@ = pointer to output array
658 * @size_t sz@ = size of the output array
662 * Use: Stores a multiprecision number in an array of octets, as
663 * two's complement. The last byte in the array is the least
664 * significant. If the array is too small to represent the
665 * number, high-order bits are truncated; if the array is too
666 * large, high order bytes are sign-extended.
669 extern void mp_storeb2c(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
671 /*----- Bit operations ----------------------------------------------------*/
673 /* --- @mp_not@ --- *
675 * Arguments: @mp *d@ = destination
678 * Returns: The bitwise complement of the source.
681 extern mp
*mp_not(mp */
*d*/
, mp */
*a*/
);
683 /* --- @mp_bitop@ --- *
685 * Arguments: @mp *d@ = destination
686 * @mp *a, *b@ = sources
688 * Returns: The result of the given bitwise operation. These functions
689 * don't handle negative numbers at all sensibly. For that, use
690 * the @...2c@ variants. The functions are named after the
691 * truth tables they generate:
698 #define MP_BITDECL(string) \
699 extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/);
700 MPX_DOBIN(MP_BITDECL
)
702 /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- *
704 * Synonyms for the commonly-used functions.
707 #define mp_and mp_bit0001
708 #define mp_or mp_bit0111
709 #define mp_nand mp_bit1110
710 #define mp_nor mp_bit1000
711 #define mp_xor mp_bit0110
713 /* --- @mp_testbit@ --- *
715 * Arguments: @mp *x@ = a large integer
716 * @unsigned long n@ = which bit to test
718 * Returns: Nonzero if the bit is set, zero if not.
721 extern int mp_testbit(mp */
*x*/
, unsigned long /*n*/);
723 /* --- @mp_setbit@, @mp_clearbit@ --- *
725 * Arguments: @mp *d@ = a destination
726 * @mp *x@ = a large integer
727 * @unsigned long n@ = which bit to modify
729 * Returns: The argument @x@, with the appropriate bit set or cleared.
732 extern mp
*mp_setbit(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
733 extern mp
*mp_clearbit(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
735 /* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- *
737 * Arguments: @mp *d@ = destination
739 * @size_t n@ = number of bits to move
741 * Returns: Result, @a@ shifted left or right by @n@.
743 * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced
744 * on the right with ones instead of zeroes: it's used
745 * internally by @mp_lsl2c@, though it may be useful on its
749 extern mp
*mp_lsl(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
750 extern mp
*mp_lslc(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
751 extern mp
*mp_lsr(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
753 /* --- @mp_not2c@ --- *
755 * Arguments: @mp *d@ = destination
758 * Returns: The sign-extended complement of the argument.
761 extern mp
*mp_not2c(mp */
*d*/
, mp */
*a*/
);
763 /* --- @mp_bitop2c@ --- *
765 * Arguments: @mp *d@ = destination
766 * @mp *a, *b@ = sources
768 * Returns: The result of the given bitwise operation. Negative numbers
769 * are treated as two's complement, sign-extended infinitely to
770 * the left. The functions are named after the truth tables
778 #define MP_BIT2CDECL(string) \
779 extern mp *mp_bit##string##2c(mp */*d*/, mp */*a*/, mp */*b*/);
780 MPX_DOBIN(MP_BIT2CDECL
)
782 /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- *
784 * Synonyms for the commonly-used functions.
787 #define mp_and2c mp_bit00012c
788 #define mp_or2c mp_bit01112c
789 #define mp_nand2c mp_bit11102c
790 #define mp_nor2c mp_bit10002c
791 #define mp_xor2c mp_bit01102c
793 /* --- @mp_lsl2c@, @mp_lsr2c@ --- *
795 * Arguments: @mp *d@ = destination
797 * @size_t n@ = number of bits to move
799 * Returns: Result, @a@ shifted left or right by @n@. Handles the
800 * pretence of sign-extension for negative numbers.
803 extern mp
*mp_lsl2c(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
804 extern mp
*mp_lsr2c(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
806 /* --- @mp_testbit2c@ --- *
808 * Arguments: @mp *x@ = a large integer
809 * @unsigned long n@ = which bit to test
811 * Returns: Nonzero if the bit is set, zero if not. Fakes up two's
812 * complement representation.
815 extern int mp_testbit2c(mp */
*x*/
, unsigned long /*n*/);
817 /* --- @mp_setbit2c@, @mp_clearbit2c@ --- *
819 * Arguments: @mp *d@ = a destination
820 * @mp *x@ = a large integer
821 * @unsigned long n@ = which bit to modify
823 * Returns: The argument @x@, with the appropriate bit set or cleared.
824 * Fakes up two's complement representation.
827 extern mp
*mp_setbit2c(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
828 extern mp
*mp_clearbit2c(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
830 /*----- Comparisons -------------------------------------------------------*/
834 * Arguments: @const mp *a, *b@ = two numbers
836 * Returns: Nonzero if the numbers are equal.
839 extern int mp_eq(const mp */
*a*/
, const mp */
*b*/
);
841 #define MP_EQ(a, b) \
842 ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \
843 mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl))
845 /* --- @mp_cmp@ --- *
847 * Arguments: @const mp *a, *b@ = two numbers
849 * Returns: Less than, equal to or greater than zero, according to
850 * whether @a@ is less than, equal to or greater than @b@.
853 extern int mp_cmp(const mp */
*a*/
, const mp */
*b*/
);
855 #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0)
857 /* --- Other handy macros --- */
859 #define MP_ISNEG(x) ((x)->f & MP_NEG)
860 #define MP_ISZERO(x) (!MP_LEN(x))
861 #define MP_ISPOS(x) (!MP_ISNEG(x) && !MP_ISZERO(x))
862 #define MP_ISODD(x) (!MP_ISZERO(x) && ((x)->v[0] & 1u))
863 #define MP_ISEVEN(x) (!MP_ISODD(x))
865 /*----- Arithmetic operations ---------------------------------------------*/
867 /* --- @mp_neg@ --- *
869 * Arguments: @mp *d@ = destination
872 * Returns: The negation of the argument.
874 * Use: Negates its argument.
877 extern mp
*mp_neg(mp */
*d*/
, mp */
*a*/
);
879 /* --- @mp_add@ --- *
881 * Arguments: @mp *d@ = destination
882 * @mp *a, *b@ = sources
884 * Returns: Result, @a@ added to @b@.
887 extern mp
*mp_add(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
889 /* --- @mp_sub@ --- *
891 * Arguments: @mp *d@ = destination
892 * @mp *a, *b@ = sources
894 * Returns: Result, @b@ subtracted from @a@.
897 extern mp
*mp_sub(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
899 /* --- @mp_mul@ --- *
901 * Arguments: @mp *d@ = destination
902 * @mp *a, *b@ = sources
904 * Returns: Result, @a@ multiplied by @b@.
907 extern mp
*mp_mul(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
909 /* --- @mp_sqr@ --- *
911 * Arguments: @mp *d@ = destination
914 * Returns: Result, @a@ squared.
917 extern mp
*mp_sqr(mp */
*d*/
, mp */
*a*/
);
919 /* --- @mp_div@ --- *
921 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
922 * @mp *a, *b@ = sources
924 * Use: Calculates the quotient and remainder when @a@ is divided by
928 extern void mp_div(mp
**/
*qq*/
, mp
**/
*rr*/
, mp */
*a*/
, mp */
*b*/
);
930 /* --- @mp_odd@ --- *
932 * Arguments: @mp *d@ = pointer to destination integer
933 * @mp *m@ = pointer to source integer
934 * @size_t *s@ = where to store the power of 2
936 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
938 * Use: Computes a power of two and an odd integer which, when
939 * multiplied, give a specified result. This sort of thing is
940 * useful in number theory quite often.
943 extern mp
*mp_odd(mp */
*d*/
, mp */
*m*/
, size_t */
*s*/
);
945 /*----- More advanced algorithms ------------------------------------------*/
947 /* --- @mp_sqrt@ --- *
949 * Arguments: @mp *d@ = pointer to destination integer
950 * @mp *a@ = (nonnegative) integer to take square root of
952 * Returns: The largest integer %$x$% such that %$x^2 \le a$%.
954 * Use: Computes integer square roots.
956 * The current implementation isn't very good: it uses the
957 * Newton-Raphson method to find an approximation to %$a$%. If
958 * there's any demand for a better version, I'll write one.
961 extern mp
*mp_sqrt(mp */
*d*/
, mp */
*a*/
);
963 /* --- @mp_gcd@ --- *
965 * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
966 * @mp *a, *b@ = sources (must be nonzero)
970 * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
971 * @ax + by = gcd(a, b)@. This is useful for computing modular
972 * inverses. Neither @a@ nor @b@ may be zero.
975 extern void mp_gcd(mp
**/
*gcd*/
, mp
**/
*xx*/
, mp
**/
*yy*/
,
976 mp */
*a*/
, mp */
*b*/
);
978 /* --- @mp_jacobi@ --- *
980 * Arguments: @mp *a@ = an integer less than @n@
981 * @mp *n@ = an odd integer
983 * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%.
985 * Use: Computes the Jacobi symbol. If @n@ is prime, this is the
986 * Legendre symbol and is equal to 1 if and only if @a@ is a
987 * quadratic residue mod @n@. The result is zero if and only if
988 * @a@ and @n@ have a common factor greater than one.
991 extern int mp_jacobi(mp */
*a*/
, mp */
*n*/
);
993 /* --- @mp_modsqrt@ --- *
995 * Arguments: @mp *d@ = destination integer
996 * @mp *a@ = source integer
997 * @mp *p@ = modulus (must be prime)
999 * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else
1002 * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%,
1003 * if one exists; else a null pointer. This function will not
1004 * work if %$p$% is composite: you must factor the modulus, take
1005 * a square root mod each factor, and recombine the results
1006 * using the Chinese Remainder Theorem.
1009 extern mp
*mp_modsqrt(mp */
*d*/
, mp */
*a*/
, mp */
*p*/
);
1011 /*----- Test harness support ----------------------------------------------*/
1013 #include <mLib/testrig.h>
1015 #ifndef CATACOMB_MPTEXT_H
1016 # include "mptext.h"
1019 extern const test_type type_mp
;
1021 /*----- That's all, folks -------------------------------------------------*/