[u/mdw/catacomb] / mpx.h

/* -*-c-*-
 *
 * $Id: mpx.h,v 1.8 1999/12/11 10:57:43 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 1.8  1999/12/11 10:57:43  mdw
 * Karatsuba squaring algorithm.
 *
 * Revision 1.7  1999/12/11 01:51:28  mdw
 * Change Karatsuba parameters slightly.
 *
 * 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 (_dv < _dvl && _av < _avl) {					\
    mpd _x;								\
    _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_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*/);

/*----- Karatsuba multiplication algorithms -------------------------------*/

/* --- @KARATSUBA_CUTOFF@ --- *
 *
 * This is the limiting length for using Karatsuba algorithms.  It's best to
 * use the simpler classical multiplication method on numbers smaller than
 * this.
 */

#define KARATSUBA_CUTOFF 16

/* --- @KARATSUBA_SLOP@ --- *
 *
 * The extra number of words required as scratch space by the Karatsuba
 * routines.  This is a (generous) guess, since the actual amount of space
 * required is proportional to the recursion depth.
 */

#define KARATSUBA_SLOP 32

/* --- @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.  The scratch space must be twice as
 *		large as the larger argument, plus the magic number
 *		@KARATSUBA_SLOP@.
 */

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_ksqr@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = pointer to destination buffer
 *		@const mpw *av, *avl@ = pointer to first argument
 *		@mpw *sv, *svl@ = pointer to scratch workspace
 *
 * Returns:	---
 *
 * Use:		Squares a multiprecision integers using something similar to
 *		Karatsuba's multiplication algorithm.  This is rather faster
 *		than traditional long multiplication (e.g., @mpx_umul@) on
 *		large numbers, although more expensive on small ones, and
 *		rather simpler than full-blown Karatsuba multiplication.
 *
 *		The destination must be twice as large as the argument.  The
 *		scratch space must be twice as large as the argument, plus
 *		the magic number @KARATSUBA_SLOP@.
 */

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

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

#ifdef __cplusplus
  }
#endif

#endif
Commit	Line	Data
d03ab969	1	/* --c--
d03ab969	2	*
5bf74dea	3	* $Id: mpx.h,v 1.8 1999/12/11 10:57:43 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 $
5bf74dea	33	* Revision 1.8 1999/12/11 10:57:43 mdw
	34	* Karatsuba squaring algorithm.
	35	*
652a6acf	36	* Revision 1.7 1999/12/11 01:51:28 mdw
	37	* Change Karatsuba parameters slightly.
	38	*
a86e33af	39	* Revision 1.6 1999/12/10 23:23:51 mdw
	40	* Karatsuba-Ofman multiplication algorithm.
	41	*
dd517851	42	* Revision 1.5 1999/11/20 22:23:27 mdw
	43	* Add function versions of some low-level macros with wider use.
	44	*
7c13f461	45	* Revision 1.4 1999/11/17 18:04:43 mdw
	46	* Add two's complement support. Fix a bug in MPX_UMLAN.
	47	*
3c9ede17	48	* Revision 1.3 1999/11/13 01:51:29 mdw
	49	* Minor interface changes. Should be stable now.
	50	*
b9b1c853	51	* Revision 1.2 1999/11/11 17:47:55 mdw
	52	* Minor changes for different `mptypes.h' format.
	53	*
d03ab969	54	* Revision 1.1 1999/09/03 08:41:12 mdw
	55	* Initial import.
	56	*
	57	*/
	58
a86e33af	59	#ifndef CATACOMB_MPX_H
a86e33af	60	#define CATACOMB_MPX_H
d03ab969	61
	62	#ifdef __cplusplus
	63	extern "C" {
	64	#endif
	65
	66	/----- The idea ----------------------------------------------------------
	67	*
	68	* This file provides functions and macros which work on vectors of words as
	69	* unsigned multiprecision integers. The interface works in terms of base
	70	* and limit pointers (i.e., a pointer to the start of a vector, and a
	71	* pointer just past its end) rather than base pointer and length, because
	72	* that requires more arithmetic and state to work on.
	73	*
	74	* The interfaces are slightly bizarre in other ways. Try to use the
	75	* higher-level functions where you can: they're rather better designed to
	76	* actually be friendly and useful.
	77	*/
	78
	79	/----- Header files ------------------------------------------------------/
	80
	81	#include <string.h>
	82
a86e33af	83	#ifndef CATACOMB_MPW_H
3c9ede17	84	# include "mpw.h"
d03ab969	85	#endif
	86
	87	/----- General manipulation ----------------------------------------------/
	88
	89	/* --- @MPX_SHRINK@ --- *
	90	*
	91	* Arguments: @const mpw *v@ = pointer to vector of words
	92	* @const mpw *vl@ = (updated) current limit of vector
	93	*
	94	* Use: Shrinks down the limit of a multiprecision integer vector.
	95	*/
	96
	97	#define MPX_SHRINK(v, vl) do { \
3c9ede17	98	const mpw _vv = (v), _vvl = (vl); \
	99	while (_vvl > _vv && !_vvl[-1]) \
	100	_vvl--; \
	101	(vl) = (mpw *)_vvl; \
d03ab969	102	} while (0)
	103
	104	/* --- @MPX_BITS@ --- *
	105	*
	106	* Arguments: @unsigned long b@ = result variable
	107	* @const mpw *v@ = pointer to array of words
	108	* @const mpw *vl@ = limit of vector (from @MPX_SHRINK@)
	109	*
	110	* Use: Calculates the number of bits in a multiprecision value.
	111	*/
	112
	113	#define MPX_BITS(b, v, vl) do { \
	114	const mpw _v = (v), _vl = (vl); \
3c9ede17	115	MPX_SHRINK(_v, _vl); \
d03ab969	116	if (_v == _vl) \
	117	(b) = 0; \
	118	else { \
	119	unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \
	120	mpw _w = _vl[-1]; \
	121	unsigned _k = MPW_BITS / 2; \
	122	while (_k) { \
	123	if (_w >> _k) { \
	124	_w >>= _k; \
	125	_b += _k; \
	126	} \
	127	_k >>= 1; \
	128	} \
	129	(b) = _b; \
	130	} \
	131	} while (0)
	132
	133	/* --- @MPX_OCTETS@ --- *
	134	*
	135	* Arguments: @size_t o@ = result variable
3c9ede17	136	* @const mpw v, vl@ = pointer to array of words
d03ab969	137	*
	138	* Use: Calculates the number of octets in a multiprecision value.
	139	*/
	140
3c9ede17	141	#define MPX_OCTETS(o, v, vl) do { \
d03ab969	142	const mpw _v = (v), _vl = (vl); \
3c9ede17	143	MPX_SHRINK(_v, _vl); \
d03ab969	144	if (_v == _vl) \
	145	(o) = 0; \
	146	else { \
3c9ede17	147	size_t _o = (MPW_BITS / 8) * (_vl - _v - 1); \
d03ab969	148	mpw _w = _vl[-1]; \
d03ab969	149	unsigned _k = MPW_BITS / 2; \
3c9ede17	150	while (_k >= 8) { \
d03ab969	151	if (_w >> _k) { \
d03ab969	152	_w >>= _k; \
3c9ede17	153	_o += _k >> 3; \
d03ab969	154	} \
	155	_k >>= 1; \
	156	} \
	157	if (_w) \
	158	_o++; \
	159	(o) = _o; \
	160	} \
	161	} while (0)
	162
	163	/* --- @MPX_COPY@ --- *
	164	*
	165	* Arguments: @dv, dvl@ = destination vector base and limit
	166	* @av, avl@ = source vector base and limit
	167	*
	168	* Use: Copies a multiprecision integer.
	169	*/
	170
3c9ede17	171	#define MPX_COPY(dv, dvl, av, avl) do { \
	172	mpw _dv = (dv), _dvl = (dvl); \
	173	size_t _dn = _dvl - _dv; \
	174	const mpw _av = (av), _avl = (avl); \
	175	size_t _an = _avl - _av; \
d03ab969	176	if (_av == _dv) { \
d03ab969	177	if (_dvl > _avl) \
3c9ede17	178	memset(_dv, 0, MPWS(_dn - _an)); \
d03ab969	179	} else if (_an >= _dn) \
	180	memmove(_dv, _av, MPWS(_dn)); \
	181	else { \
	182	memmove(_dv, _av, MPWS(_an)); \
	183	memset(_dv + _an, 0, MPWS(_dn - _an)); \
	184	} \
	185	} while (0)
	186
	187	/* --- @MPX_ZERO@ --- *
	188	*
	189	* Arguments: @v, vl@ = base and limit of vector to clear
	190	*
	191	* Use: Zeroes the area between the two vector pointers.
	192	*/
	193
3c9ede17	194	#define MPX_ZERO(v, vl) do { \
d03ab969	195	mpw _v = (v), _vl = (vl); \
3c9ede17	196	if (_v < _vl) \
3c9ede17	197	memset(_v, 0, MPWS(_vl - _v)); \
d03ab969	198	} while (0)
	199
	200	/----- Loading and storing -----------------------------------------------/
	201
	202	/* --- @mpx_storel@ --- *
	203	*
	204	* Arguments: @const mpw v, vl@ = base and limit of source vector
3c9ede17	205	* @void *p@ = pointer to octet array
d03ab969	206	* @size_t sz@ = size of octet array
	207	*
	208	* Returns: ---
	209	*
	210	* Use: Stores an MP in an octet array, least significant octet
	211	* first. High-end octets are silently discarded if there
	212	* isn't enough space for them.
	213	*/
	214
	215	extern void mpx_storel(const mpw /v/, const mpw /vl/,
3c9ede17	216	void /p/, size_t /sz*/);
d03ab969	217
	218	/* --- @mpx_loadl@ --- *
	219	*
	220	* Arguments: @mpw v, vl@ = base and limit of destination vector
3c9ede17	221	* @const void *p@ = pointer to octet array
d03ab969	222	* @size_t sz@ = size of octet array
	223	*
	224	* Returns: ---
	225	*
	226	* Use: Loads an MP in an octet array, least significant octet
	227	* first. High-end octets are ignored if there isn't enough
	228	* space for them.
	229	*/
	230
	231	extern void mpx_loadl(mpw /v/, mpw /vl/,
3c9ede17	232	const void /p/, size_t /sz*/);
d03ab969	233
	234	/* --- @mpx_storeb@ --- *
	235	*
	236	* Arguments: @const mpw v, vl@ = base and limit of source vector
3c9ede17	237	* @void *p@ = pointer to octet array
d03ab969	238	* @size_t sz@ = size of octet array
	239	*
	240	* Returns: ---
	241	*
	242	* Use: Stores an MP in an octet array, most significant octet
	243	* first. High-end octets are silently discarded if there
	244	* isn't enough space for them.
	245	*/
	246
	247	extern void mpx_storeb(const mpw /v/, const mpw /vl/,
3c9ede17	248	void /p/, size_t /sz*/);
d03ab969	249
	250	/* --- @mpx_loadb@ --- *
	251	*
	252	* Arguments: @mpw v, vl@ = base and limit of destination vector
3c9ede17	253	* @const void *p@ = pointer to octet array
d03ab969	254	* @size_t sz@ = size of octet array
	255	*
	256	* Returns: ---
	257	*
	258	* Use: Loads an MP in an octet array, most significant octet
	259	* first. High-end octets are ignored if there isn't enough
	260	* space for them.
	261	*/
	262
	263	extern void mpx_loadb(mpw /v/, mpw /vl/,
3c9ede17	264	const void /p/, size_t /sz*/);
d03ab969	265
	266	/----- Logical shifting --------------------------------------------------/
	267
	268	/* --- @mpx_lsl@ --- *
	269	*
	270	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	271	* @const mpw av, avl@ = source vector base and limit
	272	* @size_t n@ = number of bit positions to shift by
	273	*
	274	* Returns: ---
	275	*
	276	* Use: Performs a logical shift left operation on an integer.
	277	*/
	278
	279	extern void mpx_lsl(mpw /dv/, mpw /dvl/,
	280	const mpw /av/, const mpw /avl/,
	281	size_t /n/);
	282
	283	/* --- @mpx_lsr@ --- *
	284	*
	285	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	286	* @const mpw av, avl@ = source vector base and limit
	287	* @size_t n@ = number of bit positions to shift by
	288	*
	289	* Returns: ---
	290	*
	291	* Use: Performs a logical shift right operation on an integer.
	292	*/
	293
	294	extern void mpx_lsr(mpw /dv/, mpw /dvl/,
	295	const mpw /av/, const mpw /avl/,
	296	size_t /n/);
	297
	298	/----- Unsigned arithmetic -----------------------------------------------/
	299
7c13f461	300	/* --- @mpx_2c@ --- *
	301	*
	302	* Arguments: @mpw dv, dvl@ = destination vector
	303	* @const mpw v, vl@ = source vector
	304	*
	305	* Returns: ---
	306	*
	307	* Use: Calculates the two's complement of @v@.
	308	*/
	309
	310	extern void mpx_2c(mpw /dv/, mpw /dvl/,
	311	const mpw /v/, const mpw /vl/);
	312
d03ab969	313	/* --- @mpx_ucmp@ --- *
	314	*
	315	* Arguments: @const mpw av, avl@ = first argument vector base and limit
	316	* @const mpw bv, bvl@ = second argument vector base and limit
	317	*
	318	* Returns: Less than, equal to, or greater than zero depending on
	319	* whether @a@ is less than, equal to or greater than @b@,
	320	* respectively.
	321	*
	322	* Use: Performs an unsigned integer comparison.
	323	*/
	324
	325	#define MPX_UCMP(av, avl, op, dv, dvl) \
	326	(mpx_ucmp((av), (avl), (dv), (dvl)) op 0)
	327
	328	extern int mpx_ucmp(const mpw /av/, const mpw /avl/,
	329	const mpw /bv/, const mpw /bvl/);
	330
	331	/* --- @mpx_uadd@ --- *
	332	*
	333	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	334	* @const mpw av, avl@ = first addend vector base and limit
	335	* @const mpw bv, bvl@ = second addend vector base and limit
	336	*
	337	* Returns: ---
	338	*
	339	* Use: Performs unsigned integer addition. If the result overflows
	340	* the destination vector, high-order bits are discarded. This
	341	* means that two's complement addition happens more or less for
	342	* free, although that's more a side-effect than anything else.
	343	* The result vector may be equal to either or both source
	344	* vectors, but may not otherwise overlap them.
	345	*/
	346
	347	extern void mpx_uadd(mpw /dv/, mpw /dvl/,
	348	const mpw /av/, const mpw /avl/,
	349	const mpw /bv/, const mpw /bvl/);
	350
dd517851	351	/* --- @mpx_uaddn@ --- *
	352	*
	353	* Arguments: @mpw dv, dvl@ = source and destination base and limit
	354	* @mpw n@ = other addend
3c9ede17	355	*
dd517851	356	* Returns: ---
3c9ede17	357	*
	358	* Use: Adds a small integer to a multiprecision number.
	359	*/
	360
	361	#define MPX_UADDN(dv, dvl, n) do { \
	362	mpw _ddv = (dv), _ddvl = (dvl); \
	363	mpw _c = (n); \
	364	\
	365	while (_c && _ddv < _ddvl) { \
	366	mpd _x = (mpd)*_ddv + (mpd)_c; \
	367	*_ddv++ = MPW(_x); \
	368	_c = _x >> MPW_BITS; \
	369	} \
	370	} while (0)
	371
dd517851	372	extern void mpx_uaddn(mpw /dv/, mpw /dvl/, mpw /n/);
dd517851	373
d03ab969	374	/* --- @mpx_usub@ --- *
	375	*
	376	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	377	* @const mpw av, avl@ = first argument vector base and limit
	378	* @const mpw bv, bvl@ = second argument vector base and limit
	379	*
	380	* Returns: ---
	381	*
	382	* Use: Performs unsigned integer subtraction. If the result
	383	* overflows the destination vector, high-order bits are
	384	* discarded. This means that two's complement subtraction
3c9ede17	385	* happens more or less for free, although that's more a side-
d03ab969	386	* effect than anything else. The result vector may be equal to
	387	* either or both source vectors, but may not otherwise overlap
	388	* them.
	389	*/
	390
	391	extern void mpx_usub(mpw /dv/, mpw /dvl/,
	392	const mpw /av/, const mpw /avl/,
	393	const mpw /bv/, const mpw /bvl/);
	394
dd517851	395	/* --- @mpx_usubn@ --- *
3c9ede17	396	*
dd517851	397	* Arguments: @mpw dv, dvl@ = source and destination base and limit
	398	* @n@ = subtrahend
	399	*
	400	* Returns: ---
3c9ede17	401	*
	402	* Use: Subtracts a small integer from a multiprecision number.
	403	*/
	404
	405	#define MPX_USUBN(dv, dvl, n) do { \
	406	mpw _ddv = (dv), _ddvl = (dvl); \
	407	mpw _c = (n); \
	408	\
	409	while (_ddv < _ddvl) { \
	410	mpd _x = (mpd)*_ddv - (mpd)_c; \
	411	*_ddv++ = MPW(_x); \
	412	if (_x >> MPW_BITS) \
	413	_c = 1; \
	414	else \
	415	break; \
	416	} \
	417	} while (0)
	418
dd517851	419	extern void mpx_usubn(mpw /dv/, mpw /dvl/, mpw /n/);
dd517851	420
3c9ede17	421	/* --- @mpx_umul@ --- *
	422	*
	423	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	424	* @const mpw av, avl@ = multiplicand vector base and limit
	425	* @const mpw bv, bvl@ = multiplier vector base and limit
	426	*
	427	* Returns: ---
	428	*
	429	* Use: Performs unsigned integer multiplication. If the result
	430	* overflows the desination vector, high-order bits are
	431	* discarded. The result vector may not overlap the argument
	432	* vectors in any way.
	433	*/
	434
	435	extern void mpx_umul(mpw /dv/, mpw /dvl/,
	436	const mpw /av/, const mpw /avl/,
	437	const mpw /bv/, const mpw /bvl/);
	438
dd517851	439	/* --- @mpx_umuln@ --- *
d03ab969	440	*
dd517851	441	* Arguments: @mpw dv, dvl@ = destination vector base and limit
	442	* @const mpw av, avl@ = multiplicand vector base and limit
	443	* @mpw m@ = multiplier
	444	*
	445	* Returns: ---
d03ab969	446	*
	447	* Use: Multiplies a multiprecision integer by a single-word value.
	448	* The destination and source may be equal. The destination
	449	* is completely cleared after use.
	450	*/
	451
	452	#define MPX_UMULN(dv, dvl, av, avl, m) do { \
	453	mpw _dv = (dv), _dvl = (dvl); \
	454	const mpw _av = (av), _avl = (avl); \
	455	mpw _c = 0; \
	456	mpd _m = (m); \
	457	\
	458	while (_av < _avl) { \
	459	mpd _x; \
	460	if (_dv >= _dvl) \
	461	break; \
3c9ede17	462	_x = (mpd)_m * (mpd)*_av++ + _c; \
d03ab969	463	*_dv++ = MPW(_x); \
	464	_c = _x >> MPW_BITS; \
	465	} \
	466	if (_dv < _dvl) { \
	467	*_dv++ = MPW(_c); \
	468	MPX_ZERO(_dv, _dvl); \
	469	} \
	470	} while (0)
	471
dd517851	472	extern void mpx_umuln(mpw /dv/, mpw /dvl/,
	473	const mpw /av/, const mpw /avl/, mpw m);
	474
	475	/* --- @mpx_umlan@ --- *
d03ab969	476	*
dd517851	477	* Arguments: @mpw dv, dvl@ = destination/accumulator base and limit
	478	* @const mpw av, avl@ = multiplicand vector base and limit
	479	* @mpw m@ = multiplier
	480	*
	481	* Returns: ---
d03ab969	482	*
	483	* Use: Multiplies a multiprecision integer by a single-word value
	484	* and adds the result to an accumulator.
	485	*/
	486
	487	#define MPX_UMLAN(dv, dvl, av, avl, m) do { \
	488	mpw _dv = (dv), _dvl = (dvl); \
	489	const mpw _av = (av), _avl = (avl); \
7c13f461	490	mpw _cc = 0; \
d03ab969	491	mpd _m = (m); \
d03ab969	492	\
5bf74dea	493	while (_dv < _dvl && _av < _avl) { \
d03ab969	494	mpd _x; \
7c13f461	495	_x = (mpd)_dv + (mpd)_m (mpd)*_av++ + _cc; \
d03ab969	496	*_dv++ = MPW(_x); \
7c13f461	497	_cc = _x >> MPW_BITS; \
d03ab969	498	} \
7c13f461	499	MPX_UADDN(_dv, _dvl, _cc); \
d03ab969	500	} while (0)
d03ab969	501
dd517851	502	extern void mpx_umlan(mpw /dv/, mpw /dvl/,
	503	const mpw /av/, const mpw /avl/, mpw m);
	504
3c9ede17	505	/* --- @mpx_usqr@ --- *
d03ab969	506	*
d03ab969	507	* Arguments: @mpw dv, dvl@ = destination vector base and limit
3c9ede17	508	* @const mpw av, av@ = source vector base and limit
d03ab969	509	*
	510	* Returns: ---
	511	*
3c9ede17	512	* Use: Performs unsigned integer squaring. The result vector must
3c9ede17	513	* not overlap the source vector in any way.
d03ab969	514	*/
d03ab969	515
3c9ede17	516	extern void mpx_usqr(mpw /dv/, mpw /dvl/,
3c9ede17	517	const mpw /av/, const mpw /avl/);
d03ab969	518
5bf74dea	519	/* --- @mpx_udiv@ --- *
	520	*
	521	* Arguments: @mpw qv, qvl@ = quotient vector base and limit
	522	* @mpw rv, rvl@ = dividend/remainder vector base and limit
	523	* @const mpw dv, dvl@ = divisor vector base and limit
	524	* @mpw sv, svl@ = scratch workspace
	525	*
	526	* Returns: ---
	527	*
	528	* Use: Performs unsigned integer division. If the result overflows
	529	* the quotient vector, high-order bits are discarded. (Clearly
	530	* the remainder vector can't overflow.) The various vectors
	531	* may not overlap in any way. Yes, I know it's a bit odd
	532	* requiring the dividend to be in the result position but it
	533	* does make some sense really. The remainder must have
	534	* headroom for at least two extra words. The scratch space
	535	* must be at least one word larger than the divisor.
	536	*/
	537
	538	extern void mpx_udiv(mpw /qv/, mpw /qvl/, mpw /rv/, mpw /rvl/,
	539	const mpw /dv/, const mpw /dvl/,
	540	mpw /sv/, mpw /svl/);
	541
	542	/----- Karatsuba multiplication algorithms -------------------------------/
	543
	544	/* --- @KARATSUBA_CUTOFF@ --- *
	545	*
	546	* This is the limiting length for using Karatsuba algorithms. It's best to
	547	* use the simpler classical multiplication method on numbers smaller than
	548	* this.
	549	*/
	550
	551	#define KARATSUBA_CUTOFF 16
	552
	553	/* --- @KARATSUBA_SLOP@ --- *
	554	*
	555	* The extra number of words required as scratch space by the Karatsuba
	556	* routines. This is a (generous) guess, since the actual amount of space
	557	* required is proportional to the recursion depth.
	558	*/
	559
	560	#define KARATSUBA_SLOP 32
	561
a86e33af	562	/* --- @mpx_kmul@ --- *
	563	*
	564	* Arguments: @mpw dv, dvl@ = pointer to destination buffer
	565	* @const mpw av, avl@ = pointer to first argument
	566	* @const mpw bv, bvl@ = pointer to second argument
	567	* @mpw sv, svl@ = pointer to scratch workspace
	568	*
	569	* Returns: ---
	570	*
	571	* Use: Multiplies two multiprecision integers using Karatsuba's
	572	* algorithm. This is rather faster than traditional long
	573	* multiplication (e.g., @mpx_umul@) on large numbers, although
	574	* more expensive on small ones.
	575	*
	576	* The destination and scratch buffers must be twice as large as
5bf74dea	577	* the larger argument. The scratch space must be twice as
	578	* large as the larger argument, plus the magic number
	579	* @KARATSUBA_SLOP@.
a86e33af	580	*/
a86e33af	581
a86e33af	582	extern void mpx_kmul(mpw /dv/, mpw /dvl/,
	583	const mpw /av/, const mpw /avl/,
	584	const mpw /bv/, const mpw /bvl/,
	585	mpw /sv/, mpw /svl/);
	586
5bf74dea	587	/* --- @mpx_ksqr@ --- *
d03ab969	588	*
5bf74dea	589	* Arguments: @mpw dv, dvl@ = pointer to destination buffer
	590	* @const mpw av, avl@ = pointer to first argument
	591	* @mpw sv, svl@ = pointer to scratch workspace
d03ab969	592	*
	593	* Returns: ---
	594	*
5bf74dea	595	* Use: Squares a multiprecision integers using something similar to
	596	* Karatsuba's multiplication algorithm. This is rather faster
	597	* than traditional long multiplication (e.g., @mpx_umul@) on
	598	* large numbers, although more expensive on small ones, and
	599	* rather simpler than full-blown Karatsuba multiplication.
	600	*
	601	* The destination must be twice as large as the argument. The
	602	* scratch space must be twice as large as the argument, plus
	603	* the magic number @KARATSUBA_SLOP@.
d03ab969	604	*/
d03ab969	605
5bf74dea	606	extern void mpx_ksqr(mpw /dv/, mpw /dvl/,
5bf74dea	607	const mpw /av/, const mpw /avl/,
3c9ede17	608	mpw /sv/, mpw /svl/);
d03ab969	609
	610	/----- That's all, folks -------------------------------------------------/
	611
	612	#ifdef __cplusplus
	613	}
	614	#endif
	615
	616	#endif