/* -*-c-*-
*
- * $Id: mpx.h,v 1.6 1999/12/10 23:23:51 mdw Exp $
+ * $Id: mpx.h,v 1.18 2004/04/08 01:36:15 mdw Exp $
*
* Low level multiprecision arithmetic
*
* (c) 1999 Straylight/Edgeware
*/
-/*----- Licensing notice --------------------------------------------------*
+/*----- Licensing notice --------------------------------------------------*
*
* This file is part of Catacomb.
*
* 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
if (_v == _vl) \
(b) = 0; \
else { \
- unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \
+ unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \
mpw _w = _vl[-1]; \
- unsigned _k = MPW_BITS / 2; \
+ unsigned _k = MPW_P2; \
while (_k) { \
if (_w >> _k) { \
_w >>= _k; \
*/
#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; \
- } \
+ unsigned long _bb; \
+ MPX_BITS(_bb, (v), (vl)); \
+ (o) = (_bb + 7) >> 3; \
+} while (0)
+
+/* --- @MPX_OCTETS2C@ --- *
+ *
+ * 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, if
+ * you represent it as two's complement.
+ */
+
+#define MPX_OCTETS2C(o, v, vl) do { \
+ unsigned long _bb; \
+ MPX_BITS(_bb, (v), (vl)); \
+ (o) = (_bb >> 3) + 1; \
} while (0)
/* --- @MPX_COPY@ --- *
memset(_v, 0, MPWS(_vl - _v)); \
} while (0)
+/* --- @MPX_ONE@ --- *
+ *
+ * Arguments: @v, vl@ = base and limit of vector to clear
+ *
+ * Use: Fills the area between the two vector pointers with ones.
+ */
+
+#define MPX_ONE(v, vl) do { \
+ mpw * _v = (v); \
+ const mpw *_vl = (vl); \
+ while (_v < _vl) \
+ *_v++ = MPW_MAX; \
+} while (0)
+
/*----- Loading and storing -----------------------------------------------*/
/* --- @mpx_storel@ --- *
extern void mpx_loadb(mpw */*v*/, mpw */*vl*/,
const void */*p*/, size_t /*sz*/);
+/* --- @mpx_storel2cn@ --- *
+ *
+ * Arguments: @const mpw *v, *vl@ = base and limit of source vector
+ * @void *pp@ = pointer to octet array
+ * @size_t sz@ = size of octet array
+ *
+ * Returns: ---
+ *
+ * Use: Stores a negative MP in an octet array, least significant
+ * octet first, as two's complement. High-end octets are
+ * silently discarded if there isn't enough space for them.
+ * This obviously makes the output bad.
+ */
+
+extern void mpx_storel2cn(const mpw */*v*/, const mpw */*vl*/,
+ void */*p*/, size_t /*sz*/);
+
+/* --- @mpx_loadl2cn@ --- *
+ *
+ * Arguments: @mpw *v, *vl@ = base and limit of destination vector
+ * @const void *pp@ = pointer to octet array
+ * @size_t sz@ = size of octet array
+ *
+ * Returns: ---
+ *
+ * Use: Loads a negative MP in an octet array, least significant
+ * octet first, as two's complement. High-end octets are
+ * ignored if there isn't enough space for them. This probably
+ * means you made the wrong choice coming here.
+ */
+
+extern void mpx_loadl2cn(mpw */*v*/, mpw */*vl*/,
+ const void */*p*/, size_t /*sz*/);
+
+/* --- @mpx_storeb2cn@ --- *
+ *
+ * Arguments: @const mpw *v, *vl@ = base and limit of source vector
+ * @void *pp@ = pointer to octet array
+ * @size_t sz@ = size of octet array
+ *
+ * Returns: ---
+ *
+ * Use: Stores a negative MP in an octet array, most significant
+ * octet first, as two's complement. High-end octets are
+ * silently discarded if there isn't enough space for them,
+ * which probably isn't what you meant.
+ */
+
+extern void mpx_storeb2cn(const mpw */*v*/, const mpw */*vl*/,
+ void */*p*/, size_t /*sz*/);
+
+/* --- @mpx_loadb2cn@ --- *
+ *
+ * Arguments: @mpw *v, *vl@ = base and limit of destination vector
+ * @const void *pp@ = pointer to octet array
+ * @size_t sz@ = size of octet array
+ *
+ * Returns: ---
+ *
+ * Use: Loads a negative MP in an octet array, most significant octet
+ * first as two's complement. High-end octets are ignored if
+ * there isn't enough space for them. This probably means you
+ * chose this function wrongly.
+ */
+
+extern void mpx_loadb2cn(mpw */*v*/, mpw */*vl*/,
+ const void */*p*/, size_t /*sz*/);
+
+
/*----- Logical shifting --------------------------------------------------*/
/* --- @mpx_lsl@ --- *
const mpw */*av*/, const mpw */*avl*/,
size_t /*n*/);
+/* --- @mpx_lslc@ --- *
+ *
+ * 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, only
+ * it fills in the bits with ones instead of zeroes.
+ */
+
+extern void mpx_lslc(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*/, const mpw */*avl*/,
size_t /*n*/);
+/*----- Bitwise operations ------------------------------------------------*/
+
+/* --- @mpx_bitop@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination vector
+ * @const mpw *av, *avl@ = first source vector
+ * @const mpw *bv, *bvl@ = second source vector
+ *
+ * Returns: ---
+ *
+ * Use: Provide the dyadic boolean functions. The functions are
+ * named after the truth table they generate:
+ *
+ * a: 0011
+ * b: 0101
+ * @mpx_bitXXXX@
+ */
+
+#define MPX_DOBIN(what) \
+ what(0000) what(0001) what(0010) what(0011) \
+ what(0100) what(0101) what(0110) what(0111) \
+ what(1000) what(1001) what(1010) what(1011) \
+ what(1100) what(1101) what(1110) what(1111)
+
+#define MPX_BITDECL(string) \
+ extern void mpx_bit##string(mpw */*dv*/, mpw */*dvl*/, \
+ const mpw */*av*/, const mpw */*avl*/, \
+ const mpw */*bv*/, const mpw */*bvl*/);
+MPX_DOBIN(MPX_BITDECL)
+
+/* --- @mpx_[n]and@, @mpx_[n]or@, @mpx_xor@ --- *
+ *
+ * Synonyms for the commonly-used functions above.
+ */
+
+#define mpx_and mpx_bit0001
+#define mpx_or mpx_bit0111
+#define mpx_nand mpx_bit1110
+#define mpx_nor mpx_bit1000
+#define mpx_xor mpx_bit0110
+
+/* --- @mpx_not@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination vector
+ * @const mpw *av, *avl@ = first source vector
+ *
+ * Returns: ---
+ *
+ * Use; Bitwise NOT.
+ */
+
+extern void mpx_not(mpw */*dv*/, mpw */*dvl*/,
+ const mpw */*av*/, const mpw */*avl*/);
+
/*----- Unsigned arithmetic -----------------------------------------------*/
/* --- @mpx_2c@ --- *
extern void mpx_2c(mpw */*dv*/, mpw */*dvl*/,
const mpw */*v*/, const mpw */*vl*/);
+/* --- @mpx_ueq@ --- *
+ *
+ * Arguments: @const mpw *av, *avl@ = first argument vector base and limit
+ * @const mpw *bv, *bvl@ = second argument vector base and limit
+ *
+ * Returns: Nonzero if the two vectors are equal.
+ *
+ * Use: Performs an unsigned integer test for equality.
+ */
+
+extern int mpx_ueq(const mpw */*av*/, const mpw */*avl*/,
+ const mpw */*bv*/, const mpw */*bvl*/);
+
/* --- @mpx_ucmp@ --- *
*
* Arguments: @const mpw *av, *avl@ = first argument vector base and limit
extern void mpx_uaddn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/);
+/* --- @mpx_uaddnlsl@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination and first argument vector
+ * @mpw a@ = second argument
+ * @unsigned o@ = offset in bits
+ *
+ * Returns: ---
+ *
+ * Use: Computes %$d + 2^o a$%. If the result overflows then
+ * high-order bits are discarded, as usual. We must have
+ * @0 < o < MPW_BITS@.
+ */
+
+extern void mpx_uaddnlsl(mpw */*dv*/, mpw */*dvl*/,
+ mpw /*a*/, unsigned /*o*/);
+
/* --- @mpx_usub@ --- *
*
* Arguments: @mpw *dv, *dvl@ = destination vector base and limit
extern void mpx_usubn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/);
+/* --- @mpx_usubnlsl@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination and first argument vector
+ * @mpw a@ = second argument
+ * @unsigned o@ = offset in bits
+ *
+ * Returns: ---
+ *
+ * Use: Computes %$d - 2^o a$%. If the result overflows then
+ * high-order bits are discarded, as usual, so you get two's
+ * complement. Which might be what you wanted... We must have
+ * @0 < o < MPW_BITS@.
+ */
+
+extern void mpx_usubnlsl(mpw */*dv*/, mpw */*dvl*/,
+ mpw /*a*/, unsigned /*o*/);
+
/* --- @mpx_umul@ --- *
*
* Arguments: @mpw *dv, *dvl@ = destination vector base and limit
mpw _cc = 0; \
mpd _m = (m); \
\
- while (_av < _avl) { \
+ while (_dv < _dvl && _av < _avl) { \
mpd _x; \
- if (_dv >= _dvl) \
- break; \
_x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \
*_dv++ = MPW(_x); \
_cc = _x >> MPW_BITS; \
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*/);
+
+/* --- @mpx_udivn@ --- *
+ *
+ * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap
+ * dividend)
+ * @const mpw *rv, *rvl@ = dividend
+ * @mpw d@ = single-precision divisor
+ *
+ * Returns: Remainder after divison.
+ *
+ * Use: Performs a single-precision division operation.
+ */
+
+extern mpw mpx_udivn(mpw */*qv*/, mpw */*qvl*/,
+ const mpw */*rv*/, const mpw */*rvl*/, mpw /*d*/);
+
+/*----- Karatsuba multiplication algorithms -------------------------------*/
+
+/* --- @MPK_THRESH@ --- *
+ *
+ * This is the limiting length for using Karatsuba algorithms. It's best to
+ * use the simpler classical multiplication method on numbers smaller than
+ * this. It is unsafe to make this constant less than four (i.e., the
+ * algorithms will fail).
+ */
+
+#define MPK_THRESH 16
+
/* --- @mpx_kmul@ --- *
*
* Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
* 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 destination must be three times as large as the larger
+ * argument. The scratch space must be five times 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@ --- *
+/* --- @mpx_ksqr@ --- *
*
- * 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
+ * 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: 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.
+ * 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 three times as large as the larger
+ * argument. The scratch space must be five times as large as
+ * the larger argument.
*/
-extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/,
- const mpw */*dv*/, const mpw */*dvl*/,
+extern void mpx_ksqr(mpw */*dv*/, mpw */*dvl*/,
+ const mpw */*av*/, const mpw */*avl*/,
mpw */*sv*/, mpw */*svl*/);
/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff