[u/mdw/catacomb] / mpx.h

/* -*-c-*-
 *
 * $Id: mpx.h,v 1.6 1999/12/10 23:23:51 mdw Exp $
 *
 * Low level multiprecision arithmetic
 *
 * (c) 1999 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------* 
 *
 * This file is part of Catacomb.
 *
 * Catacomb is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 * 
 * Catacomb is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 * 
 * You should have received a copy of the GNU Library General Public
 * License along with Catacomb; if not, write to the Free
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

/*----- Revision history --------------------------------------------------* 
 *
 * $Log: mpx.h,v $
 * Revision 1.6  1999/12/10 23:23:51  mdw
 * Karatsuba-Ofman multiplication algorithm.
 *
 * Revision 1.5  1999/11/20 22:23:27  mdw
 * Add function versions of some low-level macros with wider use.
 *
 * Revision 1.4  1999/11/17 18:04:43  mdw
 * Add two's complement support.  Fix a bug in MPX_UMLAN.
 *
 * Revision 1.3  1999/11/13 01:51:29  mdw
 * Minor interface changes.  Should be stable now.
 *
 * Revision 1.2  1999/11/11 17:47:55  mdw
 * Minor changes for different `mptypes.h' format.
 *
 * Revision 1.1  1999/09/03 08:41:12  mdw
 * Initial import.
 *
 */

#ifndef CATACOMB_MPX_H
#define CATACOMB_MPX_H

#ifdef __cplusplus
  extern "C" {
#endif

/*----- The idea ----------------------------------------------------------*
 *
 * This file provides functions and macros which work on vectors of words as
 * unsigned multiprecision integers.  The interface works in terms of base
 * and limit pointers (i.e., a pointer to the start of a vector, and a
 * pointer just past its end) rather than base pointer and length, because
 * that requires more arithmetic and state to work on.
 *
 * The interfaces are slightly bizarre in other ways.  Try to use the
 * higher-level functions where you can: they're rather better designed to
 * actually be friendly and useful.
 */

/*----- Header files ------------------------------------------------------*/

#include <string.h>

#ifndef CATACOMB_MPW_H
#  include "mpw.h"
#endif

/*----- General manipulation ----------------------------------------------*/

/* --- @MPX_SHRINK@ --- *
 *
 * Arguments:	@const mpw *v@ = pointer to vector of words
 *		@const mpw *vl@ = (updated) current limit of vector
 *
 * Use:		Shrinks down the limit of a multiprecision integer vector.
 */

#define MPX_SHRINK(v, vl) do {						\
  const mpw *_vv = (v), *_vvl = (vl);					\
  while (_vvl > _vv && !_vvl[-1])					\
    _vvl--;								\
  (vl) = (mpw *)_vvl;							\
} while (0)

/* --- @MPX_BITS@ --- *
 *
 * Arguments:	@unsigned long b@ = result variable
 *		@const mpw *v@ = pointer to array of words
 *		@const mpw *vl@ = limit of vector (from @MPX_SHRINK@)
 *
 * Use:		Calculates the number of bits in a multiprecision value.
 */

#define MPX_BITS(b, v, vl) do {						\
  const mpw *_v = (v), *_vl = (vl);					\
  MPX_SHRINK(_v, _vl);							\
  if (_v == _vl)							\
    (b) = 0;								\
  else {								\
    unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1;	       		\
    mpw _w = _vl[-1];							\
    unsigned _k = MPW_BITS / 2;						\
    while (_k) {							\
      if (_w >> _k) {							\
	_w >>= _k;							\
	_b += _k;							\
      }									\
      _k >>= 1;								\
    }									\
    (b) = _b;								\
  }									\
} while (0)

/* --- @MPX_OCTETS@ --- *
 *
 * Arguments:	@size_t o@ = result variable
 *		@const mpw *v, *vl@ = pointer to array of words
 *
 * Use:		Calculates the number of octets in a multiprecision value.
 */

#define MPX_OCTETS(o, v, vl) do {					\
  const mpw *_v = (v), *_vl = (vl);					\
  MPX_SHRINK(_v, _vl);							\
  if (_v == _vl)							\
    (o) = 0;								\
  else {								\
    size_t _o = (MPW_BITS / 8) * (_vl - _v - 1);			\
    mpw _w = _vl[-1];							\
    unsigned _k = MPW_BITS / 2;						\
    while (_k >= 8) {							\
      if (_w >> _k) {							\
	_w >>= _k;							\
	_o += _k >> 3;							\
      }									\
      _k >>= 1;								\
    }									\
    if (_w)								\
      _o++;								\
    (o) = _o;								\
  }									\
} while (0)

/* --- @MPX_COPY@ --- *
 *
 * Arguments:	@dv, dvl@ = destination vector base and limit
 *		@av, avl@ = source vector base and limit
 *
 * Use:		Copies a multiprecision integer.
 */

#define MPX_COPY(dv, dvl, av, avl) do {					\
  mpw *_dv = (dv), *_dvl = (dvl);					\
  size_t _dn = _dvl - _dv;						\
  const mpw *_av = (av), *_avl = (avl);					\
  size_t _an = _avl - _av;						\
  if (_av == _dv) {							\
    if (_dvl > _avl)							\
      memset(_dv, 0, MPWS(_dn - _an));					\
  } else if (_an >= _dn)						\
    memmove(_dv, _av, MPWS(_dn));					\
  else {								\
    memmove(_dv, _av, MPWS(_an));					\
    memset(_dv + _an, 0, MPWS(_dn - _an));				\
  }									\
} while (0)

/* --- @MPX_ZERO@ --- *
 *
 * Arguments:	@v, vl@ = base and limit of vector to clear
 *
 * Use:		Zeroes the area between the two vector pointers.
 */

#define MPX_ZERO(v, vl) do {						\
  mpw *_v = (v), *_vl = (vl);						\
  if (_v < _vl)								\
    memset(_v, 0, MPWS(_vl - _v));					\
} while (0)

/*----- Loading and storing -----------------------------------------------*/

/* --- @mpx_storel@ --- *
 *
 * Arguments:	@const mpw *v, *vl@ = base and limit of source vector
 *		@void *p@ = pointer to octet array
 *		@size_t sz@ = size of octet array
 *
 * Returns:	---
 *
 * Use:		Stores an MP in an octet array, least significant octet
 *		first.  High-end octets are silently discarded if there
 *		isn't enough space for them.
 */

extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/,
		       void */*p*/, size_t /*sz*/);

/* --- @mpx_loadl@ --- *
 *
 * Arguments:	@mpw *v, *vl@ = base and limit of destination vector
 *		@const void *p@ = pointer to octet array
 *		@size_t sz@ = size of octet array
 *
 * Returns:	---
 *
 * Use:		Loads an MP in an octet array, least significant octet
 *		first.  High-end octets are ignored if there isn't enough
 *		space for them.
 */

extern void mpx_loadl(mpw */*v*/, mpw */*vl*/,
		      const void */*p*/, size_t /*sz*/);

/* --- @mpx_storeb@ --- *
 *
 * Arguments:	@const mpw *v, *vl@ = base and limit of source vector
 *		@void *p@ = pointer to octet array
 *		@size_t sz@ = size of octet array
 *
 * Returns:	---
 *
 * Use:		Stores an MP in an octet array, most significant octet
 *		first.  High-end octets are silently discarded if there
 *		isn't enough space for them.
 */

extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/,
		       void */*p*/, size_t /*sz*/);

/* --- @mpx_loadb@ --- *
 *
 * Arguments:	@mpw *v, *vl@ = base and limit of destination vector
 *		@const void *p@ = pointer to octet array
 *		@size_t sz@ = size of octet array
 *
 * Returns:	---
 *
 * Use:		Loads an MP in an octet array, most significant octet
 *		first.  High-end octets are ignored if there isn't enough
 *		space for them.
 */

extern void mpx_loadb(mpw */*v*/, mpw */*vl*/,
		      const void */*p*/, size_t /*sz*/);

/*----- Logical shifting --------------------------------------------------*/

/* --- @mpx_lsl@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = destination vector base and limit
 *		@const mpw *av, *avl@ = source vector base and limit
 *		@size_t n@ = number of bit positions to shift by
 *
 * Returns:	---
 *
 * Use:		Performs a logical shift left operation on an integer.
 */

extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/,
		    const mpw */*av*/, const mpw */*avl*/,
		    size_t /*n*/);

/* --- @mpx_lsr@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = destination vector base and limit
 *		@const mpw *av, *avl@ = source vector base and limit
 *		@size_t n@ = number of bit positions to shift by
 *
 * Returns:	---
 *
 * Use:		Performs a logical shift right operation on an integer.
 */

extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/,
		    const mpw */*av*/, const mpw */*avl*/,
		    size_t /*n*/);

/*----- Unsigned arithmetic -----------------------------------------------*/

/* --- @mpx_2c@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = destination vector
 *		@const mpw *v, *vl@ = source vector
 *
 * Returns:	---
 *
 * Use:		Calculates the two's complement of @v@.
 */

extern void mpx_2c(mpw */*dv*/, mpw */*dvl*/,
		   const mpw */*v*/, const mpw */*vl*/);

/* --- @mpx_ucmp@ --- *
 *
 * Arguments:	@const mpw *av, *avl@ = first argument vector base and limit
 *		@const mpw *bv, *bvl@ = second argument vector base and limit
 *
 * Returns:	Less than, equal to, or greater than zero depending on
 *		whether @a@ is less than, equal to or greater than @b@,
 *		respectively.
 *
 * Use:		Performs an unsigned integer comparison.
 */

#define MPX_UCMP(av, avl, op, dv, dvl)					\
  (mpx_ucmp((av), (avl), (dv), (dvl)) op 0)

extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/,
		    const mpw */*bv*/, const mpw */*bvl*/);

/* --- @mpx_uadd@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = destination vector base and limit
 *		@const mpw *av, *avl@ = first addend vector base and limit
 *		@const mpw *bv, *bvl@ = second addend vector base and limit
 *
 * Returns:	---
 *
 * Use:		Performs unsigned integer addition.  If the result overflows
 *		the destination vector, high-order bits are discarded.  This
 *		means that two's complement addition happens more or less for
 *		free, although that's more a side-effect than anything else.
 *		The result vector may be equal to either or both source
 *		vectors, but may not otherwise overlap them.
 */

extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/,
		     const mpw */*av*/, const mpw */*avl*/,
		     const mpw */*bv*/, const mpw */*bvl*/);

/* --- @mpx_uaddn@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = source and destination base and limit
 *		@mpw n@ = other addend
 *
 * Returns:	---
 *
 * Use:		Adds a small integer to a multiprecision number.
 */

#define MPX_UADDN(dv, dvl, n) do {					\
  mpw *_ddv = (dv), *_ddvl = (dvl);					\
  mpw _c = (n);								\
									\
  while (_c && _ddv < _ddvl) {						\
    mpd _x = (mpd)*_ddv + (mpd)_c;					\
    *_ddv++ = MPW(_x);							\
    _c = _x >> MPW_BITS;						\
  }									\
} while (0)

extern void mpx_uaddn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/);

/* --- @mpx_usub@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = destination vector base and limit
 *		@const mpw *av, *avl@ = first argument vector base and limit
 *		@const mpw *bv, *bvl@ = second argument vector base and limit
 *
 * Returns:	---
 *
 * Use:		Performs unsigned integer subtraction.  If the result
 *		overflows the destination vector, high-order bits are
 *		discarded.  This means that two's complement subtraction
 *		happens more or less for free, although that's more a side-
 *		effect than anything else.  The result vector may be equal to
 *		either or both source vectors, but may not otherwise overlap
 *		them.
 */

extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/,
		     const mpw */*av*/, const mpw */*avl*/,
		     const mpw */*bv*/, const mpw */*bvl*/);

/* --- @mpx_usubn@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = source and destination base and limit
 *		@n@ = subtrahend
 *
 * Returns:	---
 *
 * Use:		Subtracts a small integer from a multiprecision number.
 */

#define MPX_USUBN(dv, dvl, n) do {					\
  mpw *_ddv = (dv), *_ddvl = (dvl);					\
  mpw _c = (n);								\
									\
  while (_ddv < _ddvl) {						\
    mpd _x = (mpd)*_ddv - (mpd)_c;					\
    *_ddv++ = MPW(_x);							\
    if (_x >> MPW_BITS)							\
      _c = 1;								\
    else								\
      break;								\
  }									\
} while (0)

extern void mpx_usubn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/);

/* --- @mpx_umul@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = destination vector base and limit
 *		@const mpw *av, *avl@ = multiplicand vector base and limit
 *		@const mpw *bv, *bvl@ = multiplier vector base and limit
 *
 * Returns:	---
 *
 * Use:		Performs unsigned integer multiplication.  If the result
 *		overflows the desination vector, high-order bits are
 *		discarded.  The result vector may not overlap the argument
 *		vectors in any way.
 */

extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/,
		     const mpw */*av*/, const mpw */*avl*/,
		     const mpw */*bv*/, const mpw */*bvl*/);

/* --- @mpx_umuln@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = destination vector base and limit
 *		@const mpw *av, *avl@ = multiplicand vector base and limit
 *		@mpw m@ = multiplier
 *
 * Returns:	---
 *
 * Use:		Multiplies a multiprecision integer by a single-word value.
 *		The destination and source may be equal.  The destination
 *		is completely cleared after use.
 */

#define MPX_UMULN(dv, dvl, av, avl, m) do {				\
  mpw *_dv = (dv), *_dvl = (dvl);					\
  const mpw *_av = (av), *_avl = (avl);					\
  mpw _c = 0;								\
  mpd _m = (m);								\
									\
  while (_av < _avl) {							\
    mpd _x;								\
    if (_dv >= _dvl)							\
      break;								\
    _x = (mpd)_m * (mpd)*_av++ + _c;					\
    *_dv++ = MPW(_x);							\
    _c = _x >> MPW_BITS;						\
  }									\
  if (_dv < _dvl) {							\
    *_dv++ = MPW(_c);							\
    MPX_ZERO(_dv, _dvl);						\
  }									\
} while (0)

extern void mpx_umuln(mpw */*dv*/, mpw */*dvl*/,
		      const mpw */*av*/, const mpw */*avl*/, mpw m);

/* --- @mpx_umlan@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = destination/accumulator base and limit
 *		@const mpw *av, *avl@ = multiplicand vector base and limit
 *		@mpw m@ = multiplier
 *
 * Returns:	---
 *
 * Use:		Multiplies a multiprecision integer by a single-word value
 *		and adds the result to an accumulator.
 */

#define MPX_UMLAN(dv, dvl, av, avl, m) do {				\
  mpw *_dv = (dv), *_dvl = (dvl);					\
  const mpw *_av = (av), *_avl = (avl);					\
  mpw _cc = 0;								\
  mpd _m = (m);								\
									\
  while (_av < _avl) {							\
    mpd _x;								\
    if (_dv >= _dvl)							\
      break;								\
    _x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc;			\
    *_dv++ = MPW(_x);							\
    _cc = _x >> MPW_BITS;						\
  }									\
  MPX_UADDN(_dv, _dvl, _cc);						\
} while (0)

extern void mpx_umlan(mpw */*dv*/, mpw */*dvl*/,
		      const mpw */*av*/, const mpw */*avl*/, mpw m);

/* --- @mpx_usqr@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = destination vector base and limit
 *		@const mpw *av, *av@ = source vector base and limit
 *
 * Returns:	---
 *
 * Use:		Performs unsigned integer squaring.  The result vector must
 *		not overlap the source vector in any way.
 */

extern void mpx_usqr(mpw */*dv*/, mpw */*dvl*/,
		     const mpw */*av*/, const mpw */*avl*/);

/* --- @mpx_kmul@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = pointer to destination buffer
 *		@const mpw *av, *avl@ = pointer to first argument
 *		@const mpw *bv, *bvl@ = pointer to second argument
 *		@mpw *sv, *svl@ = pointer to scratch workspace
 *
 * Returns:	---
 *
 * Use:		Multiplies two multiprecision integers using Karatsuba's
 *		algorithm.  This is rather faster than traditional long
 *		multiplication (e.g., @mpx_umul@) on large numbers, although
 *		more expensive on small ones.
 *
 *		The destination and scratch buffers must be twice as large as
 *		the larger argument.
 */

#define KARATSUBA_CUTOFF 16
#define KARATSUBA_SLOP 32

extern void mpx_kmul(mpw */*dv*/, mpw */*dvl*/,
		     const mpw */*av*/, const mpw */*avl*/,
		     const mpw */*bv*/, const mpw */*bvl*/,
		     mpw */*sv*/, mpw */*svl*/);

/* --- @mpx_udiv@ --- *
 *
 * Arguments:	@mpw *qv, *qvl@ = quotient vector base and limit
 *		@mpw *rv, *rvl@ = dividend/remainder vector base and limit
 *		@const mpw *dv, *dvl@ = divisor vector base and limit
 *		@mpw *sv, *svl@ = scratch workspace 
 *
 * Returns:	---
 *
 * Use:		Performs unsigned integer division.  If the result overflows
 *		the quotient vector, high-order bits are discarded.  (Clearly
 *		the remainder vector can't overflow.)  The various vectors
 *		may not overlap in any way.  Yes, I know it's a bit odd
 *		requiring the dividend to be in the result position but it
 *		does make some sense really.  The remainder must have
 *		headroom for at least two extra words.  The scratch space
 *		must be at least one word larger than the divisor.
 */

extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/,
		     const mpw */*dv*/, const mpw */*dvl*/,
		     mpw */*sv*/, mpw */*svl*/);

/*----- That's all, folks -------------------------------------------------*/

#ifdef __cplusplus
  }
#endif

#endif
Commit	Line	Data
d03ab969	1	/* --c--
d03ab969	2	*
a86e33af	3	* $Id: mpx.h,v 1.6 1999/12/10 23:23:51 mdw Exp $
d03ab969	4	*
	5	* Low level multiprecision arithmetic
	6	*
	7	* (c) 1999 Straylight/Edgeware
	8	*/
	9
	10	/----- Licensing notice --------------------------------------------------
	11	*
	12	* This file is part of Catacomb.
	13	*
	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.
	18	*
	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.
	23	*
	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,
	27	* MA 02111-1307, USA.
	28	*/
	29
	30	/----- Revision history --------------------------------------------------
	31	*
	32	* $Log: mpx.h,v $
a86e33af	33	* Revision 1.6 1999/12/10 23:23:51 mdw
	34	* Karatsuba-Ofman multiplication algorithm.
	35	*
dd517851	36	* Revision 1.5 1999/11/20 22:23:27 mdw
	37	* Add function versions of some low-level macros with wider use.
	38	*
7c13f461	39	* Revision 1.4 1999/11/17 18:04:43 mdw
	40	* Add two's complement support. Fix a bug in MPX_UMLAN.
	41	*
3c9ede17	42	* Revision 1.3 1999/11/13 01:51:29 mdw
	43	* Minor interface changes. Should be stable now.
	44	*
b9b1c853	45	* Revision 1.2 1999/11/11 17:47:55 mdw
	46	* Minor changes for different `mptypes.h' format.
	47	*
d03ab969	48	* Revision 1.1 1999/09/03 08:41:12 mdw
	49	* Initial import.
	50	*
	51	*/
	52
a86e33af	53	#ifndef CATACOMB_MPX_H
a86e33af	54	#define CATACOMB_MPX_H
d03ab969	55
	56	#ifdef __cplusplus
	57	extern "C" {
	58	#endif
	59
	60	/----- The idea ----------------------------------------------------------
	61	*
	62	* This file provides functions and macros which work on vectors of words as
	63	* unsigned multiprecision integers. The interface works in terms of base
	64	* and limit pointers (i.e., a pointer to the start of a vector, and a
	65	* pointer just past its end) rather than base pointer and length, because
	66	* that requires more arithmetic and state to work on.
	67	*
	68	* The interfaces are slightly bizarre in other ways. Try to use the
	69	* higher-level functions where you can: they're rather better designed to
	70	* actually be friendly and useful.
	71	*/
	72
	73	/----- Header files ------------------------------------------------------/
	74
	75	#include <string.h>
	76
a86e33af	77	#ifndef CATACOMB_MPW_H
3c9ede17	78	# include "mpw.h"
d03ab969	79	#endif
	80
	81	/----- General manipulation ----------------------------------------------/
	82
	83	/* --- @MPX_SHRINK@ --- *
	84	*
	85	* Arguments: @const mpw *v@ = pointer to vector of words
	86	* @const mpw *vl@ = (updated) current limit of vector
	87	*
	88	* Use: Shrinks down the limit of a multiprecision integer vector.
	89	*/
	90
	91	#define MPX_SHRINK(v, vl) do { \
3c9ede17	92	const mpw _vv = (v), _vvl = (vl); \
	93	while (_vvl > _vv && !_vvl[-1]) \
	94	_vvl--; \
	95	(vl) = (mpw *)_vvl; \
d03ab969	96	} while (0)
	97
	98	/* --- @MPX_BITS@ --- *
	99	*
	100	* Arguments: @unsigned long b@ = result variable
	101	* @const mpw *v@ = pointer to array of words
	102	* @const mpw *vl@ = limit of vector (from @MPX_SHRINK@)
	103	*
	104	* Use: Calculates the number of bits in a multiprecision value.
	105	*/
	106
	107	#define MPX_BITS(b, v, vl) do { \
	108	const mpw _v = (v), _vl = (vl); \
3c9ede17	109	MPX_SHRINK(_v, _vl); \
d03ab969	110	if (_v == _vl) \
	111	(b) = 0; \
	112	else { \
	113	unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \
	114	mpw _w = _vl[-1]; \
	115	unsigned _k = MPW_BITS / 2; \
	116	while (_k) { \
	117	if (_w >> _k) { \
	118	_w >>= _k; \
	119	_b += _k; \
	120	} \
	121	_k >>= 1; \
	122	} \
	123	(b) = _b; \
	124	} \
	125	} while (0)
	126
	127	/* --- @MPX_OCTETS@ --- *
	128	*
	129	* Arguments: @size_t o@ = result variable
3c9ede17	130	* @const mpw v, vl@ = pointer to array of words
d03ab969	131	*
	132	* Use: Calculates the number of octets in a multiprecision value.
	133	*/
	134
3c9ede17	135	#define MPX_OCTETS(o, v, vl) do { \
d03ab969	136	const mpw _v = (v), _vl = (vl); \
3c9ede17	137	MPX_SHRINK(_v, _vl); \
d03ab969	138	if (_v == _vl) \
	139	(o) = 0; \
	140	else { \
3c9ede17	141	size_t _o = (MPW_BITS / 8) * (_vl - _v - 1); \
d03ab969	142	mpw _w = _vl[-1]; \
d03ab969	143	unsigned _k = MPW_BITS / 2; \
3c9ede17	144	while (_k >= 8) { \
d03ab969	145	if (_w >> _k) { \
d03ab969	146	_w >>= _k; \
3c9ede17	147	_o += _k >> 3; \
d03ab969	148	} \
	149	_k >>= 1; \
	150	} \
	151	if (_w) \
	152	_o++; \
	153	(o) = _o; \
	154	} \
	155	} while (0)
	156
	157	/* --- @MPX_COPY@ --- *
	158	*
	159	* Arguments: @dv, dvl@ = destination vector base and limit
	160	* @av, avl@ = source vector base and limit
	161	*
	162	* Use: Copies a multiprecision integer.
	163	*/
	164
3c9ede17	165	#define MPX_COPY(dv, dvl, av, avl) do { \
	166	mpw _dv = (dv), _dvl = (dvl); \
	167	size_t _dn = _dvl - _dv; \
	168	const mpw _av = (av), _avl = (avl); \
	169	size_t _an = _avl - _av; \
d03ab969	170	if (_av == _dv) { \
d03ab969	171	if (_dvl > _avl) \
3c9ede17	172	memset(_dv, 0, MPWS(_dn - _an)); \
d03ab969	173	} else if (_an >= _dn) \
	174	memmove(_dv, _av, MPWS(_dn)); \
	175	else { \
	176	memmove(_dv, _av, MPWS(_an)); \
	177	memset(_dv + _an, 0, MPWS(_dn - _an)); \
	178	} \
	179	} while (0)
	180
	181	/* --- @MPX_ZERO@ --- *
	182	*
	183	* Arguments: @v, vl@ = base and limit of vector to clear
	184	*
	185	* Use: Zeroes the area between the two vector pointers.
	186	*/
	187
3c9ede17	188	#define MPX_ZERO(v, vl) do { \
d03ab969	189	mpw _v = (v), _vl = (vl); \
3c9ede17	190	if (_v < _vl) \
3c9ede17	191	memset(_v, 0, MPWS(_vl - _v)); \
d03ab969	192	} while (0)
	193
	194	/----- Loading and storing -----------------------------------------------/
	195
	196	/* --- @mpx_storel@ --- *
	197	*
	198	* Arguments: @const mpw v, vl@ = base and limit of source vector
3c9ede17	199	* @void *p@ = pointer to octet array
d03ab969	200	* @size_t sz@ = size of octet array
	201	*
	202	* Returns: ---
	203	*
	204	* Use: Stores an MP in an octet array, least significant octet
	205	* first. High-end octets are silently discarded if there
	206	* isn't enough space for them.
	207	*/
	208
	209	extern void mpx_storel(const mpw /v/, const mpw /vl/,
3c9ede17	210	void /p/, size_t /sz*/);
d03ab969	211
	212	/* --- @mpx_loadl@ --- *
	213	*
	214	* Arguments: @mpw v, vl@ = base and limit of destination vector
3c9ede17	215	* @const void *p@ = pointer to octet array
d03ab969	216	* @size_t sz@ = size of octet array
	217	*
	218	* Returns: ---
	219	*
	220	* Use: Loads an MP in an octet array, least significant octet
	221	* first. High-end octets are ignored if there isn't enough
	222	* space for them.
	223	*/
	224
	225	extern void mpx_loadl(mpw /v/, mpw /vl/,
3c9ede17	226	const void /p/, size_t /sz*/);
d03ab969	227
	228	/* --- @mpx_storeb@ --- *
	229	*
	230	* Arguments: @const mpw v, vl@ = base and limit of source vector
3c9ede17	231	* @void *p@ = pointer to octet array
d03ab969	232	* @size_t sz@ = size of octet array
	233	*
	234	* Returns: ---
	235	*
	236	* Use: Stores an MP in an octet array, most significant octet
	237	* first. High-end octets are silently discarded if there
	238	* isn't enough space for them.
	239	*/
	240
	241	extern void mpx_storeb(const mpw /v/, const mpw /vl/,
3c9ede17	242	void /p/, size_t /sz*/);
d03ab969	243
	244	/* --- @mpx_loadb@ --- *
	245	*
	246	* Arguments: @mpw v, vl@ = base and limit of destination vector
3c9ede17	247	* @const void *p@ = pointer to octet array
d03ab969	248	* @size_t sz@ = size of octet array
	249	*
	250	* Returns: ---
	251	*
	252	* Use: Loads an MP in an octet array, most significant octet
	253	* first. High-end octets are ignored if there isn't enough
	254	* space for them.
	255	*/
	256
	257	extern void mpx_loadb(mpw /v/, mpw /vl/,
3c9ede17	258	const void /p/, size_t /sz*/);
d03ab969	259
	260	/----- Logical shifting --------------------------------------------------/
	261
	262	/* --- @mpx_lsl@ --- *
	263	*
	264	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	265	* @const mpw av, avl@ = source vector base and limit
	266	* @size_t n@ = number of bit positions to shift by
	267	*
	268	* Returns: ---
	269	*
	270	* Use: Performs a logical shift left operation on an integer.
	271	*/
	272
	273	extern void mpx_lsl(mpw /dv/, mpw /dvl/,
	274	const mpw /av/, const mpw /avl/,
	275	size_t /n/);
	276
	277	/* --- @mpx_lsr@ --- *
	278	*
	279	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	280	* @const mpw av, avl@ = source vector base and limit
	281	* @size_t n@ = number of bit positions to shift by
	282	*
	283	* Returns: ---
	284	*
	285	* Use: Performs a logical shift right operation on an integer.
	286	*/
	287
	288	extern void mpx_lsr(mpw /dv/, mpw /dvl/,
	289	const mpw /av/, const mpw /avl/,
	290	size_t /n/);
	291
	292	/----- Unsigned arithmetic -----------------------------------------------/
	293
7c13f461	294	/* --- @mpx_2c@ --- *
	295	*
	296	* Arguments: @mpw dv, dvl@ = destination vector
	297	* @const mpw v, vl@ = source vector
	298	*
	299	* Returns: ---
	300	*
	301	* Use: Calculates the two's complement of @v@.
	302	*/
	303
	304	extern void mpx_2c(mpw /dv/, mpw /dvl/,
	305	const mpw /v/, const mpw /vl/);
	306
d03ab969	307	/* --- @mpx_ucmp@ --- *
	308	*
	309	* Arguments: @const mpw av, avl@ = first argument vector base and limit
	310	* @const mpw bv, bvl@ = second argument vector base and limit
	311	*
	312	* Returns: Less than, equal to, or greater than zero depending on
	313	* whether @a@ is less than, equal to or greater than @b@,
	314	* respectively.
	315	*
	316	* Use: Performs an unsigned integer comparison.
	317	*/
	318
	319	#define MPX_UCMP(av, avl, op, dv, dvl) \
	320	(mpx_ucmp((av), (avl), (dv), (dvl)) op 0)
	321
	322	extern int mpx_ucmp(const mpw /av/, const mpw /avl/,
	323	const mpw /bv/, const mpw /bvl/);
	324
	325	/* --- @mpx_uadd@ --- *
	326	*
	327	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	328	* @const mpw av, avl@ = first addend vector base and limit
	329	* @const mpw bv, bvl@ = second addend vector base and limit
	330	*
	331	* Returns: ---
	332	*
	333	* Use: Performs unsigned integer addition. If the result overflows
	334	* the destination vector, high-order bits are discarded. This
	335	* means that two's complement addition happens more or less for
	336	* free, although that's more a side-effect than anything else.
	337	* The result vector may be equal to either or both source
	338	* vectors, but may not otherwise overlap them.
	339	*/
	340
	341	extern void mpx_uadd(mpw /dv/, mpw /dvl/,
	342	const mpw /av/, const mpw /avl/,
	343	const mpw /bv/, const mpw /bvl/);
	344
dd517851	345	/* --- @mpx_uaddn@ --- *
	346	*
	347	* Arguments: @mpw dv, dvl@ = source and destination base and limit
	348	* @mpw n@ = other addend
3c9ede17	349	*
dd517851	350	* Returns: ---
3c9ede17	351	*
	352	* Use: Adds a small integer to a multiprecision number.
	353	*/
	354
	355	#define MPX_UADDN(dv, dvl, n) do { \
	356	mpw _ddv = (dv), _ddvl = (dvl); \
	357	mpw _c = (n); \
	358	\
	359	while (_c && _ddv < _ddvl) { \
	360	mpd _x = (mpd)*_ddv + (mpd)_c; \
	361	*_ddv++ = MPW(_x); \
	362	_c = _x >> MPW_BITS; \
	363	} \
	364	} while (0)
	365
dd517851	366	extern void mpx_uaddn(mpw /dv/, mpw /dvl/, mpw /n/);
dd517851	367
d03ab969	368	/* --- @mpx_usub@ --- *
	369	*
	370	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	371	* @const mpw av, avl@ = first argument vector base and limit
	372	* @const mpw bv, bvl@ = second argument vector base and limit
	373	*
	374	* Returns: ---
	375	*
	376	* Use: Performs unsigned integer subtraction. If the result
	377	* overflows the destination vector, high-order bits are
	378	* discarded. This means that two's complement subtraction
3c9ede17	379	* happens more or less for free, although that's more a side-
d03ab969	380	* effect than anything else. The result vector may be equal to
	381	* either or both source vectors, but may not otherwise overlap
	382	* them.
	383	*/
	384
	385	extern void mpx_usub(mpw /dv/, mpw /dvl/,
	386	const mpw /av/, const mpw /avl/,
	387	const mpw /bv/, const mpw /bvl/);
	388
dd517851	389	/* --- @mpx_usubn@ --- *
3c9ede17	390	*
dd517851	391	* Arguments: @mpw dv, dvl@ = source and destination base and limit
	392	* @n@ = subtrahend
	393	*
	394	* Returns: ---
3c9ede17	395	*
	396	* Use: Subtracts a small integer from a multiprecision number.
	397	*/
	398
	399	#define MPX_USUBN(dv, dvl, n) do { \
	400	mpw _ddv = (dv), _ddvl = (dvl); \
	401	mpw _c = (n); \
	402	\
	403	while (_ddv < _ddvl) { \
	404	mpd _x = (mpd)*_ddv - (mpd)_c; \
	405	*_ddv++ = MPW(_x); \
	406	if (_x >> MPW_BITS) \
	407	_c = 1; \
	408	else \
	409	break; \
	410	} \
	411	} while (0)
	412
dd517851	413	extern void mpx_usubn(mpw /dv/, mpw /dvl/, mpw /n/);
dd517851	414
3c9ede17	415	/* --- @mpx_umul@ --- *
	416	*
	417	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	418	* @const mpw av, avl@ = multiplicand vector base and limit
	419	* @const mpw bv, bvl@ = multiplier vector base and limit
	420	*
	421	* Returns: ---
	422	*
	423	* Use: Performs unsigned integer multiplication. If the result
	424	* overflows the desination vector, high-order bits are
	425	* discarded. The result vector may not overlap the argument
	426	* vectors in any way.
	427	*/
	428
	429	extern void mpx_umul(mpw /dv/, mpw /dvl/,
	430	const mpw /av/, const mpw /avl/,
	431	const mpw /bv/, const mpw /bvl/);
	432
dd517851	433	/* --- @mpx_umuln@ --- *
d03ab969	434	*
dd517851	435	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	436	* @const mpw av, avl@ = multiplicand vector base and limit
	437	* @mpw m@ = multiplier
	438	*
	439	* Returns: ---
d03ab969	440	*
	441	* Use: Multiplies a multiprecision integer by a single-word value.
	442	* The destination and source may be equal. The destination
	443	* is completely cleared after use.
	444	*/
	445
	446	#define MPX_UMULN(dv, dvl, av, avl, m) do { \
	447	mpw _dv = (dv), _dvl = (dvl); \
	448	const mpw _av = (av), _avl = (avl); \
	449	mpw _c = 0; \
	450	mpd _m = (m); \
	451	\
	452	while (_av < _avl) { \
	453	mpd _x; \
	454	if (_dv >= _dvl) \
	455	break; \
3c9ede17	456	_x = (mpd)_m * (mpd)*_av++ + _c; \
d03ab969	457	*_dv++ = MPW(_x); \
	458	_c = _x >> MPW_BITS; \
	459	} \
	460	if (_dv < _dvl) { \
	461	*_dv++ = MPW(_c); \
	462	MPX_ZERO(_dv, _dvl); \
	463	} \
	464	} while (0)
	465
dd517851	466	extern void mpx_umuln(mpw /dv/, mpw /dvl/,
	467	const mpw /av/, const mpw /avl/, mpw m);
	468
	469	/* --- @mpx_umlan@ --- *
d03ab969	470	*
dd517851	471	* Arguments: @mpw dv, dvl@ = destination/accumulator base and limit
	472	* @const mpw av, avl@ = multiplicand vector base and limit
	473	* @mpw m@ = multiplier
	474	*
	475	* Returns: ---
d03ab969	476	*
	477	* Use: Multiplies a multiprecision integer by a single-word value
	478	* and adds the result to an accumulator.
	479	*/
	480
	481	#define MPX_UMLAN(dv, dvl, av, avl, m) do { \
	482	mpw _dv = (dv), _dvl = (dvl); \
	483	const mpw _av = (av), _avl = (avl); \
7c13f461	484	mpw _cc = 0; \
d03ab969	485	mpd _m = (m); \
	486	\
	487	while (_av < _avl) { \
	488	mpd _x; \
	489	if (_dv >= _dvl) \
	490	break; \
7c13f461	491	_x = (mpd)_dv + (mpd)_m (mpd)*_av++ + _cc; \
d03ab969	492	*_dv++ = MPW(_x); \
7c13f461	493	_cc = _x >> MPW_BITS; \
d03ab969	494	} \
7c13f461	495	MPX_UADDN(_dv, _dvl, _cc); \
d03ab969	496	} while (0)
d03ab969	497
dd517851	498	extern void mpx_umlan(mpw /dv/, mpw /dvl/,
	499	const mpw /av/, const mpw /avl/, mpw m);
	500
3c9ede17	501	/* --- @mpx_usqr@ --- *
d03ab969	502	*
d03ab969	503	* Arguments: @mpw dv, dvl@ = destination vector base and limit
3c9ede17	504	* @const mpw av, av@ = source vector base and limit
d03ab969	505	*
	506	* Returns: ---
	507	*
3c9ede17	508	* Use: Performs unsigned integer squaring. The result vector must
3c9ede17	509	* not overlap the source vector in any way.
d03ab969	510	*/
d03ab969	511
3c9ede17	512	extern void mpx_usqr(mpw /dv/, mpw /dvl/,
3c9ede17	513	const mpw /av/, const mpw /avl/);
d03ab969	514
a86e33af	515	/* --- @mpx_kmul@ --- *
	516	*
	517	* Arguments: @mpw dv, dvl@ = pointer to destination buffer
	518	* @const mpw av, avl@ = pointer to first argument
	519	* @const mpw bv, bvl@ = pointer to second argument
	520	* @mpw sv, svl@ = pointer to scratch workspace
	521	*
	522	* Returns: ---
	523	*
	524	* Use: Multiplies two multiprecision integers using Karatsuba's
	525	* algorithm. This is rather faster than traditional long
	526	* multiplication (e.g., @mpx_umul@) on large numbers, although
	527	* more expensive on small ones.
	528	*
	529	* The destination and scratch buffers must be twice as large as
	530	* the larger argument.
	531	*/
	532
	533	#define KARATSUBA_CUTOFF 16
	534	#define KARATSUBA_SLOP 32
	535
	536	extern void mpx_kmul(mpw /dv/, mpw /dvl/,
	537	const mpw /av/, const mpw /avl/,
	538	const mpw /bv/, const mpw /bvl/,
	539	mpw /sv/, mpw /svl/);
	540
d03ab969	541	/* --- @mpx_udiv@ --- *
	542	*
	543	* Arguments: @mpw qv, qvl@ = quotient vector base and limit
	544	* @mpw rv, rvl@ = dividend/remainder vector base and limit
	545	* @const mpw dv, dvl@ = divisor vector base and limit
3c9ede17	546	* @mpw sv, svl@ = scratch workspace
d03ab969	547	*
	548	* Returns: ---
	549	*
	550	* Use: Performs unsigned integer division. If the result overflows
	551	* the quotient vector, high-order bits are discarded. (Clearly
	552	* the remainder vector can't overflow.) The various vectors
	553	* may not overlap in any way. Yes, I know it's a bit odd
	554	* requiring the dividend to be in the result position but it
3c9ede17	555	* does make some sense really. The remainder must have
3c9ede17	556	* headroom for at least two extra words. The scratch space
7c13f461	557	* must be at least one word larger than the divisor.
d03ab969	558	*/
	559
	560	extern void mpx_udiv(mpw /qv/, mpw /qvl/, mpw /rv/, mpw /rvl/,
3c9ede17	561	const mpw /dv/, const mpw /dvl/,
3c9ede17	562	mpw /sv/, mpw /svl/);
d03ab969	563
	564	/----- That's all, folks -------------------------------------------------/
	565
	566	#ifdef __cplusplus
	567	}
	568	#endif
	569
	570	#endif