3 * $Id: mp.h,v 1.14 2002/10/15 00:19:40 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 1.14 2002/10/15 00:19:40 mdw
34 * Bit setting and clearing functions.
36 * Revision 1.13 2002/10/06 22:52:50 mdw
37 * Pile of changes for supporting two's complement properly.
39 * Revision 1.12 2001/06/16 12:57:43 mdw
40 * Move the @mpmont_factor@ structure and rename it now that it's used for
41 * Barrett simultaneous exponentiation too.
43 * Revision 1.11 2001/04/03 19:36:05 mdw
44 * Add some simple bitwise operations so that Perl can use them.
46 * Revision 1.10 2000/10/08 12:03:16 mdw
47 * Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two
50 * Revision 1.9 2000/07/29 17:03:31 mdw
51 * Add support for left-to-right bitscanning, for use in modular
54 * Revision 1.8 2000/06/22 19:02:01 mdw
57 * Revision 1.7 2000/06/17 11:45:09 mdw
58 * Major memory management overhaul. Added arena support. Use the secure
59 * arena for secret integers. Replace and improve the MP management macros
60 * (e.g., replace MP_MODIFY by MP_DEST).
62 * Revision 1.6 1999/12/10 23:19:46 mdw
63 * Minor bugfixes. New interface for suggested destinations.
65 * Revision 1.5 1999/11/22 20:50:37 mdw
66 * Add support for computing Jacobi symbols.
68 * Revision 1.4 1999/11/21 22:13:02 mdw
69 * Add mp version of MPX_BITS.
71 * Revision 1.3 1999/11/19 13:19:14 mdw
72 * Fix const annotation.
74 * Revision 1.2 1999/11/17 18:02:16 mdw
75 * New multiprecision integer arithmetic suite.
86 /*----- Header files ------------------------------------------------------*/
93 #ifndef CATACOMB_MPW_H
97 #ifndef CATACOMB_ARENA_H
101 #ifndef CATACOMB_MPARENA_H
102 # include "mparena.h"
105 #ifndef CATACOMB_MPX_H
109 /*----- Data structures ---------------------------------------------------*/
111 /* --- A multiprecision integer --- */
114 mpw
*v
, *vl
; /* Vector of digits, current limit */
115 size_t sz
; /* Size of digit buffer in words */
116 mparena
*a
; /* Arena for buffer allocation */
117 unsigned f
; /* Flags (see below) */
118 unsigned ref
; /* Reference counter */
121 #define MP_NEG 1u /* Negative (signed magnitude) */
122 #define MP_BURN 2u /* Secret (viral flag) */
123 #define MP_CONST 4u /* Uses strange memory allocation */
124 #define MP_UNDEF 8u /* Contains nothing interesting */
125 #define MP_DESTROYED 16u /* Has been destroyed */
127 /* --- A factor for simultaneous exponentation --- *
129 * Used by the Montgomery and Barrett exponentiators.
132 typedef struct mp_expfactor
{
137 /*----- Useful constants --------------------------------------------------*/
139 extern mp mp_const
[];
141 #define MP_ZERO (&mp_const[0])
142 #define MP_ONE (&mp_const[1])
143 #define MP_TWO (&mp_const[2])
144 #define MP_THREE (&mp_const[3])
145 #define MP_FOUR (&mp_const[4])
146 #define MP_FIVE (&mp_const[5])
147 #define MP_TEN (&mp_const[6])
148 #define MP_256 (&mp_const[7])
149 #define MP_MONE (&mp_const[8])
151 #define MP_NEW ((mp *)0)
152 #define MP_NEWSEC (&mp_const[9])
154 /*----- Trivial macros ----------------------------------------------------*/
156 /* --- @MP_LEN@ --- *
158 * Arguments: @mp *m@ = pointer to a multiprecision integer
160 * Returns: Length of the integer, in words.
163 #define MP_LEN(m) ((m)->vl - ((m)->v))
165 /*----- Memory management and reference counting --------------------------*/
167 /* --- @mp_new@ --- *
169 * Arguments: @size_t sz@ = size of vector required
170 * @unsigned f@ = flags to set
172 * Returns: Pointer to a new MP structure.
174 * Use: Allocates a new multiprecision integer. The data space is
175 * allocated from either the standard global or secret arena,
176 * depending on the initial flags requested.
179 extern mp
*mp_new(size_t /*sz*/, unsigned /*f*/);
181 /* --- @mp_create@ --- *
183 * Arguments: @size_t sz@ = size of vector required
185 * Returns: Pointer to pristine new MP structure with enough memory
188 * Use: Creates a new multiprecision integer with indeterminate
189 * contents. The integer has a single reference.
192 extern mp
*mp_create(size_t /*sz*/);
194 /* --- @mp_createsecure@ --- *
196 * Arguments: @size_t sz@ = size of vector required
198 * Returns: Pointer to pristine new MP structure with enough memory
201 * Use: Creates a new multiprecision integer with indeterminate
202 * contents. The integer has a single reference. The integer's
203 * data space is allocated from the secure arena. Its burn flag
207 extern mp
*mp_createsecure(size_t /*sz*/);
209 /* --- @mp_build@ --- *
211 * Arguments: @mp *m@ = pointer to an MP block to fill in
212 * @mpw *v@ = pointer to a word array
213 * @mpw *vl@ = pointer just past end of array
217 * Use: Creates a multiprecision integer representing some smallish
218 * number. You must provide storage for the number and dispose
219 * of it when you've finished with it. The number is marked as
220 * constant while it exists.
223 extern void mp_build(mp */
*m*/
, mpw */
*v*/
, mpw */
*vl*/
);
225 /* --- @mp_destroy@ --- *
227 * Arguments: @mp *m@ = pointer to a multiprecision integer
231 * Use: Destroys a multiprecision integer. The reference count isn't
232 * checked. Don't use this function if you don't know what
233 * you're doing: use @mp_drop@ instead.
236 extern void mp_destroy(mp */
*m*/
);
238 /* --- @mp_copy@ --- *
240 * Arguments: @mp *m@ = pointer to a multiprecision integer
242 * Returns: A copy of the given multiprecision integer.
244 * Use: Copies the given integer. In fact you just get another
245 * reference to the same old one again.
248 extern mp
*mp_copy(mp */
*m*/
);
250 #define MP_COPY(m) ((m)->ref++, (m))
252 /* --- @mp_drop@ --- *
254 * Arguments: @mp *m@ = pointer to a multiprecision integer
258 * Use: Drops a reference to an integer which isn't wanted any more.
259 * If there are no more references, the integer is destroyed.
262 extern void mp_drop(mp */
*m*/
);
264 #define MP_DROP(m) do { \
267 if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \
271 /* --- @mp_split@ --- *
273 * Arguments: @mp *m@ = pointer to a multiprecision integer
275 * Returns: A reference to the same integer, possibly with a different
278 * Use: Splits off a modifiable version of the integer referred to.
281 extern mp
*mp_split(mp */
*m*/
);
283 #define MP_SPLIT(m) do { \
285 if ((_m->f & MP_CONST) || _m->ref > 1) { \
286 size_t _len = MP_LEN(_m); \
287 mp *_mm = mp_new(_len, _m->f); \
288 if (!(_m->f & MP_UNDEF)) \
289 memcpy(_mm->v, _m->v, MPWS(_len)); \
296 /* --- @mp_resize@ --- *
298 * Arguments: @mp *m@ = pointer to a multiprecision integer
299 * @size_t sz@ = new size
303 * Use: Resizes the vector containing the integer's digits. The new
304 * size must be at least as large as the current integer's
305 * length. This isn't really intended for client use.
308 extern void mp_resize(mp */
*m*/
, size_t /*sz*/);
310 #define MP_RESIZE(m, ssz) do { \
312 size_t _sz = (ssz); \
313 mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \
315 size_t _len = MP_LEN(_m); \
316 assert(((void)"can't make size less than length", _sz >= _len)); \
317 _v = mpalloc(_a, _sz); \
318 if (!(_m->f & MP_UNDEF)) \
319 memcpy(_v, _m->v, MPWS(_len)); \
320 if (_m->f & MP_BURN) \
321 memset(_m->v, 0, MPWS(_m->sz)); \
322 mpfree(_m->a, _m->v); \
325 _m->vl = _v + _len; \
328 /* --- @mp_ensure@ --- *
330 * Arguments: @mp *m@ = pointer to a multiprecision integer
331 * @size_t sz@ = required size
335 * Use: Ensures that the integer has enough space for @sz@ digits.
336 * The value is not changed.
339 extern void mp_ensure(mp */
*m*/
, size_t /*sz*/);
341 #define MP_ENSURE(m, ssz) do { \
343 size_t _ssz = (ssz); \
344 size_t _len = MP_LEN(_m); \
345 if (_ssz >= _len) { \
347 mp_resize(_m, _ssz); \
348 if (!(_m->f & MP_UNDEF) && _ssz > _len) \
349 memset(_m->vl, 0, MPWS(_ssz - _len)); \
350 _m->vl = _m->v + _ssz; \
354 /* --- @mp_dest@ --- *
356 * Arguments: @mp *m@ = a suggested destination integer
357 * @size_t sz@ = size required for result, in digits
358 * @unsigned f@ = various flags
360 * Returns: A pointer to an appropriate destination.
362 * Use: Converts a suggested destination into a real destination with
363 * the required properties. If the real destination is @d@,
364 * then the following properties will hold:
366 * * @d@ will have exactly one reference.
368 * * If @m@ is not @MP_NEW@, then the contents of @m@ will not
369 * change, unless @f@ has the @MP_UNDEF@ flag set.
371 * * If @m@ is not @MP_NEW@, then he reference count of @m@ on
372 * entry is equal to the sum of the counts of @d@ and @m@ on
375 * * The size of @d@ will be at least @sz@.
377 * * If @f@ has the @MP_BURN@ flag set, then @d@ will be
378 * allocated from @MPARENA_SECURE@.
380 * Understanding this function is crucial to using Catacomb's
381 * multiprecision integer library effectively.
384 extern mp
*mp_dest(mp */
*m*/
, size_t /*sz*/, unsigned /*f*/);
386 #define MP_DEST(m, ssz, f) do { \
388 size_t _ssz = (ssz); \
390 _m = mp_dest(_m, _ssz, _f); \
394 /*----- Size manipulation -------------------------------------------------*/
396 /* --- @mp_shrink@ --- *
398 * Arguments: @mp *m@ = pointer to a multiprecision integer
402 * Use: Reduces the recorded length of an integer. This doesn't
403 * reduce the amount of memory used, although it can improve
404 * performance a bit. To reduce memory, use @mp_minimize@
405 * instead. This can't change the value of an integer, and is
406 * therefore safe to use even when there are multiple
410 extern void mp_shrink(mp */
*m*/
);
412 #define MP_SHRINK(m) do { \
414 MPX_SHRINK(_mm->v, _mm->vl); \
419 /* --- @mp_minimize@ --- *
421 * Arguments: @mp *m@ = pointer to a multiprecision integer
425 * Use: Reduces the amount of memory an integer uses. It's best to
426 * do this to numbers which aren't going to change in the
430 extern void mp_minimize(mp */
*m*/
);
432 /*----- Bit scanning ------------------------------------------------------*/
434 #ifndef CATACOMB_MPSCAN_H
438 /* --- @mp_scan@ --- *
440 * Arguments: @mpscan *sc@ = pointer to bitscanner block
441 * @const mp *m@ = pointer to a multiprecision integer
445 * Use: Initializes a bitscanner on a multiprecision integer.
448 extern void mp_scan(mpscan */
*sc*/
, const mp */
*m*/
);
450 #define MP_SCAN(sc, m) do { \
451 const mp *_mm = (m); \
452 mpscan *_sc = (sc); \
453 MPSCAN_INITX(_sc, _mm->v, _mm->vl); \
456 /* --- @mp_rscan@ --- *
458 * Arguments: @mpscan *sc@ = pointer to bitscanner block
459 * @const mp *m@ = pointer to a multiprecision integer
463 * Use: Initializes a reverse bitscanner on a multiprecision
467 extern void mp_rscan(mpscan */
*sc*/
, const mp */
*m*/
);
469 #define MP_RSCAN(sc, m) do { \
470 const mp *_mm = (m); \
471 mpscan *_sc = (sc); \
472 MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \
475 /* --- Other bitscanning aliases --- */
477 #define mp_step mpscan_step
478 #define mp_bit mpscan_bit
479 #define mp_rstep mpscan_rstep
480 #define mp_rbit mpscan_rbit
482 #define MP_STEP MPSCAN_STEP
483 #define MP_BIT MPSCAN_BIT
484 #define MP_RSTEP MPSCAN_RSTEP
485 #define MP_RBIT MPSCAN_RBIT
487 /*----- Loading and storing -----------------------------------------------*/
489 /* --- @mp_octets@ --- *
491 * Arguments: @const mp *m@ = a multiprecision integer
493 * Returns: The number of octets required to represent @m@.
495 * Use: Calculates the external storage required for a multiprecision
499 extern size_t mp_octets(const mp */
*m*/
);
501 /* --- @mp_octets2c@ --- *
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
508 * integer represented as two's complement.
511 extern size_t mp_octets2c(const mp */
*m*/
);
513 /* --- @mp_bits@ --- *
515 * Arguments: @const mp *m@ = a multiprecision integer
517 * Returns: The number of bits required to represent @m@.
519 * Use: Calculates the external storage required for a multiprecision
523 extern unsigned long mp_bits(const mp */
*m*/
);
525 /* --- @mp_loadl@ --- *
527 * Arguments: @mp *d@ = destination
528 * @const void *pv@ = pointer to source data
529 * @size_t sz@ = size of the source data
531 * Returns: Resulting multiprecision number.
533 * Use: Loads a multiprecision number from an array of octets. The
534 * first byte in the array is the least significant. More
535 * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$%
536 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
539 extern mp
*mp_loadl(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
541 /* --- @mp_storel@ --- *
543 * Arguments: @const mp *m@ = source
544 * @void *pv@ = pointer to output array
545 * @size_t sz@ = size of the output array
549 * Use: Stores a multiprecision number in an array of octets. The
550 * first byte in the array is the least significant. If the
551 * array is too small to represent the number, high-order bits
552 * are truncated; if the array is too large, high order bytes
553 * are filled with zeros. More formally, if the number is
554 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
555 * then the array is %$b_0, b_1, \ldots, b_{n-1}$%.
558 extern void mp_storel(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
560 /* --- @mp_loadb@ --- *
562 * Arguments: @mp *d@ = destination
563 * @const void *pv@ = pointer to source data
564 * @size_t sz@ = size of the source data
566 * Returns: Resulting multiprecision number.
568 * Use: Loads a multiprecision number from an array of octets. The
569 * last byte in the array is the least significant. More
570 * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$%
571 * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%.
574 extern mp
*mp_loadb(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
576 /* --- @mp_storeb@ --- *
578 * Arguments: @const mp *m@ = source
579 * @void *pv@ = pointer to output array
580 * @size_t sz@ = size of the output array
584 * Use: Stores a multiprecision number in an array of octets. The
585 * last byte in the array is the least significant. If the
586 * array is too small to represent the number, high-order bits
587 * are truncated; if the array is too large, high order bytes
588 * are filled with zeros. More formally, if the number is
589 * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%,
590 * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%.
593 extern void mp_storeb(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
595 /* --- @mp_loadl2c@ --- *
597 * Arguments: @mp *d@ = destination
598 * @const void *pv@ = pointer to source data
599 * @size_t sz@ = size of the source data
601 * Returns: Resulting multiprecision number.
603 * Use: Loads a multiprecision number from an array of octets as
604 * two's complement. The first byte in the array is the least
608 extern mp
*mp_loadl2c(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
610 /* --- @mp_storel2c@ --- *
612 * Arguments: @const mp *m@ = source
613 * @void *pv@ = pointer to output array
614 * @size_t sz@ = size of the output array
618 * Use: Stores a multiprecision number in an array of octets as two's
619 * complement. The first byte in the array is the least
620 * significant. If the array is too small to represent the
621 * number, high-order bits are truncated; if the array is too
622 * large, high order bytes are sign-extended.
625 extern void mp_storel2c(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
627 /* --- @mp_loadb2c@ --- *
629 * Arguments: @mp *d@ = destination
630 * @const void *pv@ = pointer to source data
631 * @size_t sz@ = size of the source data
633 * Returns: Resulting multiprecision number.
635 * Use: Loads a multiprecision number from an array of octets as
636 * two's complement. The last byte in the array is the least
640 extern mp
*mp_loadb2c(mp */
*d*/
, const void */
*pv*/
, size_t /*sz*/);
642 /* --- @mp_storeb2c@ --- *
644 * Arguments: @const mp *m@ = source
645 * @void *pv@ = pointer to output array
646 * @size_t sz@ = size of the output array
650 * Use: Stores a multiprecision number in an array of octets, as
651 * two's complement. The last byte in the array is the least
652 * significant. If the array is too small to represent the
653 * number, high-order bits are truncated; if the array is too
654 * large, high order bytes are sign-extended.
657 extern void mp_storeb2c(const mp */
*m*/
, void */
*pv*/
, size_t /*sz*/);
659 /*----- Simple arithmetic -------------------------------------------------*/
661 /* --- @mp_lsl@, @mp_lsr@ --- *
663 * Arguments: @mp *d@ = destination
665 * @size_t n@ = number of bits to move
667 * Returns: Result, @a@ shifted left or right by @n@.
670 extern mp
*mp_lsl(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
671 extern mp
*mp_lsr(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
673 /* --- @mp_lsl2c@, @mp_lsr2c@ --- *
675 * Arguments: @mp *d@ = destination
677 * @size_t n@ = number of bits to move
679 * Returns: Result, @a@ shifted left or right by @n@. Handles the
680 * pretence of sign-extension for negative numbers.
683 extern mp
*mp_lsl2c(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
684 extern mp
*mp_lsr2c(mp */
*d*/
, mp */
*a*/
, size_t /*n*/);
686 /* --- @mp_testbit@ --- *
688 * Arguments: @mp *x@ = a large integer
689 * @unsigned long n@ = which bit to test
691 * Returns: Nonzero if the bit is set, zero if not.
694 extern int mp_testbit(mp */
*x*/
, unsigned long /*n*/);
696 /* --- @mp_testbit2c@ --- *
698 * Arguments: @mp *x@ = a large integer
699 * @unsigned long n@ = which bit to test
701 * Returns: Nonzero if the bit is set, zero if not. Fakes up two's
702 * complement representation.
705 extern int mp_testbit2c(mp */
*x*/
, unsigned long /*n*/);
709 * Arguments: @const mp *a, *b@ = two numbers
711 * Returns: Nonzero if the numbers are equal.
714 extern int mp_eq(const mp */
*a*/
, const mp */
*b*/
);
716 #define MP_EQ(a, b) \
717 ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \
718 mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl))
720 /* --- @mp_cmp@ --- *
722 * Arguments: @const mp *a, *b@ = two numbers
724 * Returns: Less than, equal to or greater than zero, according to
725 * whether @a@ is less than, equal to or greater than @b@.
728 extern int mp_cmp(const mp */
*a*/
, const mp */
*b*/
);
730 #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0)
732 /* --- @mp_setbit@, @mp_clearbit@ --- *
734 * Arguments: @mp *d@ = a destination
735 * @mp *x@ = a large integer
736 * @unsigned long n@ = which bit to modify
738 * Returns: The argument @x@, with the appropriate bit set or cleared.
741 extern mp
*mp_setbit(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
742 extern mp
*mp_clearbit(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
744 /* --- @mp_setbit2c@, @mp_clearbit2c@ --- *
746 * Arguments: @mp *d@ = a destination
747 * @mp *x@ = a large integer
748 * @unsigned long n@ = which bit to modify
750 * Returns: The argument @x@, with the appropriate bit set or cleared.
751 * Fakes up two's complement representation.
754 extern mp
*mp_setbit2c(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
755 extern mp
*mp_clearbit2c(mp */
*d*/
, mp */
*x*/
, unsigned long /*n*/);
757 /* --- @mp_bitop@ --- *
759 * Arguments: @mp *d@ = destination
760 * @mp *a, *b@ = sources
762 * Returns: The result of the given bitwise operation. These functions
763 * don't handle negative numbers at all sensibly. For that, use
764 * the @...2c@ variants. The functions are named after the
765 * truth tables they generate:
772 #define MP_BITDECL(string) \
773 extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/);
774 MPX_DOBIN(MP_BITDECL
)
776 /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- *
778 * Synonyms for the commonly-used functions.
781 #define mp_and mp_bit0001
782 #define mp_or mp_bit0111
783 #define mp_nand mp_bit1110
784 #define mp_nor mp_bit1000
785 #define mp_xor mp_bit0110
787 /* --- @mp_not@ --- *
789 * Arguments: @mp *d@ = destination
792 * Returns: The bitwise complement of the source.
795 extern mp
*mp_not(mp */
*d*/
, mp */
*a*/
);
797 /* --- @mp_bitop2c@ --- *
799 * Arguments: @mp *d@ = destination
800 * @mp *a, *b@ = sources
802 * Returns: The result of the given bitwise operation. Negative numbers
803 * are treated as two's complement, sign-extended infinitely to
804 * the left. The functions are named after the truth tables
812 #define MP_BIT2CDECL(string) \
813 extern mp *mp_bit##string##2c(mp */*d*/, mp */*a*/, mp */*b*/);
814 MPX_DOBIN(MP_BIT2CDECL
)
816 /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- *
818 * Synonyms for the commonly-used functions.
821 #define mp_and2c mp_bit00012c
822 #define mp_or2c mp_bit01112c
823 #define mp_nand2c mp_bit11102c
824 #define mp_nor2c mp_bit10002c
825 #define mp_xor2c mp_bit01102c
827 /* --- @mp_not2c@ --- *
829 * Arguments: @mp *d@ = destination
832 * Returns: The sign-extended complement of the argument.
835 extern mp
*mp_not2c(mp */
*d*/
, mp */
*a*/
);
837 /* --- @mp_add@ --- *
839 * Arguments: @mp *d@ = destination
840 * @mp *a, *b@ = sources
842 * Returns: Result, @a@ added to @b@.
845 extern mp
*mp_add(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
847 /* --- @mp_sub@ --- *
849 * Arguments: @mp *d@ = destination
850 * @mp *a, *b@ = sources
852 * Returns: Result, @b@ subtracted from @a@.
855 extern mp
*mp_sub(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
857 /* --- @mp_mul@ --- *
859 * Arguments: @mp *d@ = destination
860 * @mp *a, *b@ = sources
862 * Returns: Result, @a@ multiplied by @b@.
865 extern mp
*mp_mul(mp */
*d*/
, mp */
*a*/
, mp */
*b*/
);
867 /* --- @mp_sqr@ --- *
869 * Arguments: @mp *d@ = destination
872 * Returns: Result, @a@ squared.
875 extern mp
*mp_sqr(mp */
*d*/
, mp */
*a*/
);
877 /* --- @mp_div@ --- *
879 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
880 * @mp *a, *b@ = sources
882 * Use: Calculates the quotient and remainder when @a@ is divided by
886 extern void mp_div(mp
**/
*qq*/
, mp
**/
*rr*/
, mp */
*a*/
, mp */
*b*/
);
888 /* --- @mp_odd@ --- *
890 * Arguments: @mp *d@ = pointer to destination integer
891 * @mp *m@ = pointer to source integer
892 * @size_t *s@ = where to store the power of 2
894 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
896 * Use: Computes a power of two and an odd integer which, when
897 * multiplied, give a specified result. This sort of thing is
898 * useful in number theory quite often.
901 extern mp
*mp_odd(mp */
*d*/
, mp */
*m*/
, size_t */
*s*/
);
903 /*----- More advanced algorithms ------------------------------------------*/
905 /* --- @mp_sqrt@ --- *
907 * Arguments: @mp *d@ = pointer to destination integer
908 * @mp *a@ = (nonnegative) integer to take square root of
910 * Returns: The largest integer %$x$% such that %$x^2 \le a$%.
912 * Use: Computes integer square roots.
914 * The current implementation isn't very good: it uses the
915 * Newton-Raphson method to find an approximation to %$a$%. If
916 * there's any demand for a better version, I'll write one.
919 extern mp
*mp_sqrt(mp */
*d*/
, mp */
*a*/
);
921 /* --- @mp_gcd@ --- *
923 * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
924 * @mp *a, *b@ = sources (must be nonzero)
928 * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
929 * @ax + by = gcd(a, b)@. This is useful for computing modular
930 * inverses. Neither @a@ nor @b@ may be zero.
933 extern void mp_gcd(mp
**/
*gcd*/
, mp
**/
*xx*/
, mp
**/
*yy*/
,
934 mp */
*a*/
, mp */
*b*/
);
936 /* --- @mp_jacobi@ --- *
938 * Arguments: @mp *a@ = an integer less than @n@
939 * @mp *n@ = an odd integer
941 * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%.
943 * Use: Computes the Jacobi symbol. If @n@ is prime, this is the
944 * Legendre symbol and is equal to 1 if and only if @a@ is a
945 * quadratic residue mod @n@. The result is zero if and only if
946 * @a@ and @n@ have a common factor greater than one.
949 extern int mp_jacobi(mp */
*a*/
, mp */
*n*/
);
951 /* --- @mp_modsqrt@ --- *
953 * Arguments: @mp *d@ = destination integer
954 * @mp *a@ = source integer
955 * @mp *p@ = modulus (must be prime)
957 * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else
960 * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%,
961 * if one exists; else a null pointer. This function will not
962 * work if %$p$% is composite: you must factor the modulus, take
963 * a square root mod each factor, and recombine the results
964 * using the Chinese Remainder Theorem.
967 extern mp
*mp_modsqrt(mp */
*d*/
, mp */
*a*/
, mp */
*p*/
);
969 /*----- Test harness support ----------------------------------------------*/
971 #include <mLib/testrig.h>
973 #ifndef CATACOMB_MPTEXT_H
977 extern const test_type type_mp
;
979 /*----- That's all, folks -------------------------------------------------*/