X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/b9b1c853917df1504dba8930834525f30b820076..02dfbd5b7af7816959dbd39c1fe628451204e35f:/mpx.h diff --git a/mpx.h b/mpx.h index 0f1a91d..f79cffd 100644 --- a/mpx.h +++ b/mpx.h @@ -1,6 +1,6 @@ /* -*-c-*- * - * $Id: mpx.h,v 1.2 1999/11/11 17:47:55 mdw Exp $ + * $Id: mpx.h,v 1.18 2004/04/08 01:36:15 mdw Exp $ * * Low level multiprecision arithmetic * @@ -27,19 +27,8 @@ * MA 02111-1307, USA. */ -/*----- Revision history --------------------------------------------------* - * - * $Log: mpx.h,v $ - * 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 MPX_H -#define MPX_H +#ifndef CATACOMB_MPX_H +#define CATACOMB_MPX_H #ifdef __cplusplus extern "C" { @@ -62,32 +51,10 @@ #include -#ifndef MPTYPES_H -# include "mptypes.h" +#ifndef CATACOMB_MPW_H +# include "mpw.h" #endif -/*----- Basic macros ------------------------------------------------------*/ - -/* --- @MPW@ --- * - * - * Arguments: @x@ = an unsigned value - * - * Use: Expands to the value of @x@ masked and typecast to a - * multiprecision integer word. - */ - -#define MPW(x) ((mpw)((x) & MPW_MAX)) - -/* --- @MPWS@ --- * - * - * Arguments: @n@ = number of words - * - * Use: Expands to the number of bytes occupied by a given number of - * words. - */ - -#define MPWS(n) ((n) * sizeof(mpw)) - /*----- General manipulation ----------------------------------------------*/ /* --- @MPX_SHRINK@ --- * @@ -99,10 +66,10 @@ */ #define MPX_SHRINK(v, vl) do { \ - const mpw *_v = (v), *_vl = (vl); \ - while (_vl > _v && *--_vl) \ - ; \ - (vl) = _vl; \ + const mpw *_vv = (v), *_vvl = (vl); \ + while (_vvl > _vv && !_vvl[-1]) \ + _vvl--; \ + (vl) = (mpw *)_vvl; \ } while (0) /* --- @MPX_BITS@ --- * @@ -116,6 +83,7 @@ #define MPX_BITS(b, v, vl) do { \ const mpw *_v = (v), *_vl = (vl); \ + MPX_SHRINK(_v, _vl); \ if (_v == _vl) \ (b) = 0; \ else { \ @@ -136,31 +104,30 @@ /* --- @MPX_OCTETS@ --- * * * Arguments: @size_t o@ = result variable - * @const mpw *v@ = pointer to array of words - * @size_t len@ = length of the array (from @MPX_LEN@) + * @const mpw *v, *vl@ = pointer to array of words * * Use: Calculates the number of octets in a multiprecision value. */ -#define MPX_OCTETS(o, v, len) do { \ - const mpw *_v = (v), *_vl = (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 > 3) { \ - if (_w >> _k) { \ - _w >>= _k; \ - _o += _k - 3; \ - } \ - _k >>= 1; \ - } \ - if (_w) \ - _o++; \ - (o) = _o; \ - } \ +#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@ --- * @@ -171,14 +138,14 @@ * Use: Copies a multiprecision integer. */ -#define MPX_COPY(dv, dvl, av, dvl) do { \ - mpw *_dv = (dv); \ - size_t _dn = (dvl) - _dv; \ - const mpw *_av = (av); \ - size_t _an = (avl) - _av; \ +#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(_avl, 0, MPWS(_dn - _an)); \ + memset(_dv, 0, MPWS(_dn - _an)); \ } else if (_an >= _dn) \ memmove(_dv, _av, MPWS(_dn)); \ else { \ @@ -194,9 +161,24 @@ * Use: Zeroes the area between the two vector pointers. */ -#define MPX_ZERO(v, vl) { \ +#define MPX_ZERO(v, vl) do { \ mpw *_v = (v), *_vl = (vl); \ - memset(_v, 0, MPWS(_vl - _v)); \ + 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 -----------------------------------------------*/ @@ -204,7 +186,7 @@ /* --- @mpx_storel@ --- * * * Arguments: @const mpw *v, *vl@ = base and limit of source vector - * @octet *p@ = pointer to octet array + * @void *p@ = pointer to octet array * @size_t sz@ = size of octet array * * Returns: --- @@ -215,12 +197,12 @@ */ extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, - octet */*p*/, size_t /*sz*/); + void */*p*/, size_t /*sz*/); /* --- @mpx_loadl@ --- * * * Arguments: @mpw *v, *vl@ = base and limit of destination vector - * @const octet *p@ = pointer to octet array + * @const void *p@ = pointer to octet array * @size_t sz@ = size of octet array * * Returns: --- @@ -231,12 +213,12 @@ extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, */ extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, - const octet */*p*/, size_t /*sz*/); + const void */*p*/, size_t /*sz*/); /* --- @mpx_storeb@ --- * * * Arguments: @const mpw *v, *vl@ = base and limit of source vector - * @octet *p@ = pointer to octet array + * @void *p@ = pointer to octet array * @size_t sz@ = size of octet array * * Returns: --- @@ -247,12 +229,12 @@ extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, */ extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, - octet */*p*/, size_t /*sz*/); + void */*p*/, size_t /*sz*/); /* --- @mpx_loadb@ --- * * * Arguments: @mpw *v, *vl@ = base and limit of destination vector - * @const octet *p@ = pointer to octet array + * @const void *p@ = pointer to octet array * @size_t sz@ = size of octet array * * Returns: --- @@ -263,7 +245,76 @@ extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, */ extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, - const octet */*p*/, size_t /*sz*/); + 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 --------------------------------------------------*/ @@ -282,6 +333,22 @@ 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 @@ -297,8 +364,88 @@ 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 @@ -337,6 +484,45 @@ 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 @@ -348,7 +534,7 @@ extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, * 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, althuogh that's more a side- + * 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. @@ -358,11 +544,74 @@ extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, const mpw */*av*/, const mpw */*avl*/, const mpw */*bv*/, const mpw */*bvl*/); -/* --- @MPX_UMULN@ --- * +/* --- @mpx_usubn@ --- * * - * Arguments: @dv, dvl@ = destination vector base and limit - * @av, avl@ = multiplicand vector base and limit - * @m@ = multiplier + * 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 @@ -379,7 +628,7 @@ extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, mpd _x; \ if (_dv >= _dvl) \ break; \ - _x = _m * *_av++ + c; \ + _x = (mpd)_m * (mpd)*_av++ + _c; \ *_dv++ = MPW(_x); \ _c = _x >> MPW_BITS; \ } \ @@ -389,11 +638,16 @@ extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, } \ } while (0) -/* --- @MPX_UMLAN@ --- * +extern void mpx_umuln(mpw */*dv*/, mpw */*dvl*/, + const mpw */*av*/, const mpw */*avl*/, mpw m); + +/* --- @mpx_umlan@ --- * * - * Arguments: @dv, dvl@ = destination/accumulator vector base and limit - * @av, avl@ = multiplicand vector base and limit - * @m@ = multiplier + * 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. @@ -402,46 +656,41 @@ extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ mpw *_dv = (dv), *_dvl = (dvl); \ const mpw *_av = (av), *_avl = (avl); \ - mpw _c = 0; \ + mpw _cc = 0; \ mpd _m = (m); \ \ - while (_av < _avl) { \ + while (_dv < _dvl && _av < _avl) { \ mpd _x; \ - if (_dv >= _dvl) \ - break; \ - _x = *_dv + _m * *_av++ + _c; \ + _x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \ *_dv++ = MPW(_x); \ - _c = _x >> MPW_BITS; \ - } \ - if (_dv < _dvl) { \ - *_dv++ = MPW(_c); \ - MPX_ZERO(_dv, _dvl); \ + _cc = _x >> MPW_BITS; \ } \ + MPX_UADDN(_dv, _dvl, _cc); \ } while (0) -/* --- @mpx_umul@ --- * +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, *avl@ = multiplicand vector base and limit - * @const mpw *bv, *bvl@ = multiplier vector base and limit + * @const mpw *av, *av@ = source 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. + * Use: Performs unsigned integer squaring. The result vector must + * not overlap the source vector in any way. */ -extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, - const mpw */*av*/, const mpw */*avl*/, - const mpw */*bv*/, const mpw */*bvl*/); +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: --- * @@ -450,11 +699,88 @@ extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, * 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. + * 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*/); + 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 -------------------------------------------------*/