--- /dev/null
+/* -*-c-*-
+ *
+ * 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.
+ */
+
+#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_P2; \
+ 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 { \
+ 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@ --- *
+ *
+ * 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)
+
+/* --- @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@ --- *
+ *
+ * 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*/);
+
+/* --- @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@ --- *
+ *
+ * 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_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, *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*/);
+
+/*----- 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@ --- *
+ *
+ * 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_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
+ * @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_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
+ * @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_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
+ * @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*/);
+
+/* --- @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
+ * @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 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_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 three times as large as the larger
+ * argument. The scratch space must be five times as large as
+ * the larger argument.
+ */
+
+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
projects / u / mdw / catacomb / blobdiff