X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/d03ab969116fe715d569304c1c474749b2f64529..d3409d5ecf2492cff862616de72a580d1a8e8dc0:/mp.h diff --git a/mp.h b/mp.h index fcccee2..72aa675 100644 --- a/mp.h +++ b/mp.h @@ -1,8 +1,8 @@ /* -*-c-*- * - * $Id: mp.h,v 1.1 1999/09/03 08:41:12 mdw Exp $ + * $Id: mp.h,v 1.2 1999/11/17 18:02:16 mdw Exp $ * - * Multiprecision arithmetic + * Simple multiprecision arithmetic * * (c) 1999 Straylight/Edgeware */ @@ -30,8 +30,8 @@ /*----- Revision history --------------------------------------------------* * * $Log: mp.h,v $ - * Revision 1.1 1999/09/03 08:41:12 mdw - * Initial import. + * Revision 1.2 1999/11/17 18:02:16 mdw + * New multiprecision integer arithmetic suite. * */ @@ -44,401 +44,592 @@ /*----- Header files ------------------------------------------------------*/ -#include +#include #include -#ifndef MPTYPES_H -# include "mptypes.h" +#include + +#ifndef MPW_H +# include "mpw.h" #endif #ifndef MPX_H # include "mpx.h" #endif -#ifndef MPSCAN_H -# include "mpscan.h" -#endif - /*----- Data structures ---------------------------------------------------*/ typedef struct mp { - mpw *v; /* Vector of words */ - unsigned f; /* Various flags */ - size_t sz; /* Size allocated to word vector */ - size_t len; /* Length of current word vector */ + mpw *v, *vl; + size_t sz; + unsigned f; + unsigned ref; } mp; -enum { - MPF_SIGN = 1, /* Sign bit */ - MPF_BURN = 2 /* Burn word vector after use */ -}; +#define MP_NEG 1u +#define MP_BURN 2u +#define MP_CONST 4u +#define MP_UNDEF 8u -typedef struct mp_bitscan { - const mp *x; /* Pointer to target MP */ - size_t i; /* Index into MP vector */ - mpw w; /* Current value being examined */ - unsigned bits; /* Number of bits left in @w@ */ -} mp_bitscan; +/*----- Useful constants --------------------------------------------------*/ -/*----- External variables ------------------------------------------------*/ +extern mp mp_const[]; -extern mp mp_std; +#define MP_ZERO (&mp_const[0]) +#define MP_ONE (&mp_const[1]) +#define MP_TWO (&mp_const[2]) +#define MP_THREE (&mp_const[3]) +#define MP_FOUR (&mp_const[4]) +#define MP_FIVE (&mp_const[5]) +#define MP_TEN (&mp_const[6]) +#define MP_MONE (&mp_const[7]) -#define MP_ZERO (mp_std + 0) -#define MP_ONE (mp_std + 1) -#define MP_TWO (mp_std + 2) -#define MP_THREE (mp_std + 3) -#define MP_FOUR (mp_std + 4) -#define MP_FIVE (mp_std + 5) -#define MP_TEN (mp_std + 6) -#define MP_MONE (mp_std + 7) +#define MP_NEW ((mp *)0) -/*----- Memory allocation and low-level fiddling --------------------------*/ +/*----- Memory allocation hooks -------------------------------------------*/ -/* --- @mp_create@ --- * +#ifndef MPARENA_H +# include "mparena.h" +#endif + +/* --- @MP_ARENA@ --- * * - * Arguments @mp *x@ = pointer to MP head + * This selects where memory is allocated from. Tweak to use more fancy + * things like custom arenas. + */ + +#ifndef MP_ARENA +# define MP_ARENA MPARENA_GLOBAL +#endif + +/* --- @MP_ALLOC@ --- * * - * Returns: --- + * Arguments: @size_t sz@ = size required + * + * Returns: Pointer to an allocated vector of the requested size. * - * Use: Initializes an MP ready for use. The initial value is zero. + * Use: Hook for vector allocation. */ -#define MP_INIT { 0, 0, 0, 0 } - -extern void mp_create(mp */*x*/); +#ifndef MP_ALLOC +# define MP_ALLOC(sz) mpalloc(MP_ARENA, (sz)) +#endif -/* --- @MP_BURN@ --- * +/* --- @MP_FREE@ --- * + * + * Arguments: @mpw *v@ = pointer to vector * - * Arguments: @x@ = pointer to MP head + * Returns: --- * - * Use: Burns the contents of the MP, if it contains sensitive data. + * Use: Hook for vector deallocation. */ -#define MP_BURN(x) do { \ - mp *_y = (x) \ - if (_y->v && _y->f & mpf_burn) { \ - memset(_y->v, 0, _y->sz * sizeof(mpw)); \ - _y->f &= ~MPF_BURN; \ - } \ -} while (0) +#ifndef MP_FREE +# define MP_FREE(v) mpfree(MP_ARENA, (v)) +#endif -/* --- @mp_free@ --- * +/*----- Paranoia management -----------------------------------------------*/ + +/* --- @mp_burn@ --- * * - * Arguments: @mp *x@ = pointer to MP head + * Arguments: @mp *m@ = pointer to a multiprecision integer * * Returns: --- * - * Use: Releases the memory used by an MP. + * Use: Marks the integer as `burn-after-use'. When the integer's + * memory is deallocated, it is deleted so that traces can't + * remain in the swap file. In theory. */ -#define MP_DESTROY(x) do { \ - mp *_x = (x); \ - MP_BURN(_x); \ - if (_x->v) \ - free(_x->v); \ - _x->v = 0; \ - _x->f = 0; \ - _x->sz = 0; \ - _x->len = 0; \ -} while (0) - -extern void mp_free(mp */*x*/); +extern void mp_burn(mp */*m*/); -/* --- @MP_ENSURE@ --- * +/*----- Trivial macros ----------------------------------------------------*/ + +/* --- @MP_LEN@ --- * * - * Arguments: @x@ = pointer to MP head - * @len@ = length required (in words) + * Arguments: @mp *m@ = pointer to a multiprecision integer * - * Use: Ensures that the MP has enough memory to store a @len@-word - * value. + * Returns: Length of the integer, in words. */ -#define MP_ENSURE(x, len) do { \ - mp *_x = (x); \ - size_t _len = (len); \ - if (_x->sz < _len) \ - mp_resize(_x, _len); \ -} while (0) +#define MP_LEN(m) ((m)->vl - ((m)->v)) -/* --- @mp_resize@ --- * +/*----- Memory management and reference counting --------------------------*/ + +/* --- @mp_create@ --- * * - * Arguments: @mp *x@ = pointer to MP head - * @size_t sz@ = size required (in words) + * Arguments: @size_t sz@ = size of vector required * - * Returns: --- + * Returns: Pointer to pristine new MP structure with enough memory + * bolted onto it. * - * Use: Resizes the MP so that its word vector has space for - * exactly @sz@ words. + * Use: Creates a new multiprecision integer with indeterminate + * contents. The integer has a single reference. */ -extern void mp_resize(mp */*x*/, size_t /*sz*/); +extern mp *mp_create(size_t /*sz*/); -/* --- @mp_norm@ --- * +/* --- @mp_build@ --- * * - * Arguments: @mp *x@ = pointer to MP head + * Arguments: @mp *m@ = pointer to an MP block to fill in + * @mpw *v@ = pointer to a word array + * @mpw *vl@ = pointer just past end of array * * Returns: --- * - * Use: `Normalizes' an MP. Fixes the @len@ field so that it's - * correct. Assumes that @len@ is either already correct or - * too large. + * Use: Creates a multiprecision integer representing some smallish + * number. You must provide storage for the number and dispose + * of it when you've finished with it. The number is marked as + * constant while it exists. */ -#define MP_NORM(x) do { \ - mp *_y = (x); \ - MPX_LEN(_y->len, _y->v, _y->len); \ -} while (0) +extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); -extern void mp_norm(mp */*x*/); - -/* --- @mp_dump@ --- * +/* --- @mp_destroy@ --- * * - * Arguments: @mp *x@ = pointer to MP head - * @FILE *fp@ = pointer to stream to write on + * Arguments: @mp *m@ = pointer to a multiprecision integer * * Returns: --- * - * Use: Dumps an MP to a stream. + * Use: Destroys a multiprecision integer. The reference count isn't + * checked. Don't use this function if you don't know what + * you're doing: use @mp_drop@ instead. */ -extern void mp_dump(mp */*x*/, FILE */*fp*/); +extern void mp_destroy(mp */*m*/); -/* --- @MP_PARANOID@ --- * +/* --- @mp_copy@ --- * * - * Arguments: @x@ = pointer to MP head + * Arguments: @mp *m@ = pointer to a multiprecision integer * - * Use: Marks the MP as containing sensitive data which should be - * burnt when no longer required. + * Returns: A copy of the given multiprecision integer. + * + * Use: Copies the given integer. In fact you just get another + * reference to the same old one again. */ -#define MP_PARANOID(x) ((x)->f |= MPF_BURN) +extern mp *mp_copy(mp */*m*/); -/* --- @mp_copy@ --- * +#define MP_COPY(m) ((m)->ref++, (m)) + +/* --- @mp_drop@ --- * * - * Arguments: @mp *d@ = pointer to MP head for destination - * @const mp *s@ = pointer to MP head for source + * Arguments: @mp *m@ = pointer to a multiprecision integer * * Returns: --- * - * Use: Copies an MP. + * Use: Drops a reference to an integer which isn't wanted any more. + * If there are no more references, the integer is destroyed. */ -extern void mp_copy(mp */*d*/, const mp */*s*/); +extern void mp_drop(mp */*m*/); -/* --- @mp_bits@ --- * +#define MP_DROP(m) do { \ + mp *_mm = (m); \ + if (_mm->ref > 1) \ + _mm->ref--; \ + else if (!(_mm->f & MP_CONST)) \ + mp_destroy(_mm); \ +} while (0) + +/* --- @mp_split@ --- * * - * Arguments: @mp *x@ = pointer to MP head + * Arguments: @mp *m@ = pointer to a multiprecision integer * - * Returns: Length of the number in bits. + * Returns: A reference to the same integer, possibly with a different + * address. * - * Use: Calculates the number of bits required to represent a number. - * The number must be normalized. + * Use: Splits off a modifiable version of the integer referred to. */ -unsigned long mp_bits(mp */*x*/); +extern mp *mp_split(mp */*m*/); + +#define MP_SPLIT(m) do { \ + mp *_mm = (m); \ + if ((_mm->f & MP_CONST) || _mm->ref != 1) { \ + mp *_dd = mp_create(_mm->sz); \ + _dd->vl = _dd->v + MP_LEN(_mm); \ + _dd->f = _mm->f & (MP_NEG | MP_BURN); \ + memcpy(_dd->v, _mm->v, MPWS(MP_LEN(_mm))); \ + _dd->ref = 1; \ + _mm->ref--; \ + (m) = _dd; \ + } \ +} while (0) -/* --- @mp_octets@ --- * +/* --- @mp_resize@ --- * * - * Arguments: @mp *x@ = pointer to MP head + * Arguments: @mp *m@ = pointer to a multiprecision integer + * @size_t sz@ = new size * - * Returns: Length of number in octets. + * Returns: --- * - * Use: Calculates the number of octets required to represent a - * number. The number must be normalized. + * Use: Resizes the vector containing the integer's digits. The new + * size must be at least as large as the current integer's + * length. The integer's length is increased and new digits are + * filled with zeroes. This isn't really intended for client + * use. */ -extern size_t mp_octets(mp */*x*/); - -/*----- Loading and storing as binary data --------------------------------*/ +extern void mp_resize(mp */*m*/, size_t /*sz*/); + +#define MP_RESIZE(m, ssz) do { \ + mp *_m = (m); \ + size_t _sz = (ssz); \ + size_t _len = MP_LEN(_m); \ + mpw *_v = MP_ALLOC(_sz); \ + memcpy(_v, _m->v, MPWS(_len)); \ + if (_m->f & MP_BURN) \ + memset(_m->v, 0, MPWS(_m->sz)); \ + MP_FREE(_m->v); \ + _m->v = _v; \ + _m->vl = _v + _len; \ + _m->sz = _sz; \ +} while (0) -/* --- @mp_storel@ --- * +/* --- @mp_ensure@ --- * * - * Arguments: @mp *x@ = pointer to MP head - * @octet *p@ = pointer to octet array - * @size_t sz@ = size of octet array + * Arguments: @mp *m@ = pointer to a multiprecision integer + * @size_t sz@ = required size * * 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. + * Use: Ensures that the integer has enough space for @sz@ digits. + * The value is not changed. */ -extern void mp_storel(mp */*x*/, octet */*p*/, size_t /*sz*/); +extern void mp_ensure(mp */*m*/, size_t /*sz*/); + +#define MP_ENSURE(m, ssz) do { \ + mp *_mm = (m); \ + size_t _ssz = (ssz); \ + size_t _len = MP_LEN(_mm); \ + if (_ssz > _mm->sz) \ + MP_RESIZE(_mm, _ssz); \ + if (!(_mm->f & MP_UNDEF) && _ssz > _len) { \ + memset(_mm->vl, 0, MPWS(_ssz - _len)); \ + _mm->vl = _mm->v + _ssz; \ + } \ +} while (0) -/* --- @mp_loadl@ --- * +/* --- @mp_modify@ --- * * - * Arguments: @mp *x@ = pointer to MP head - * @const octet *p@ = pointer to octet array - * @size_t sz@ = size of octet array + * Arguments: @mp *m@ = pointer to a multiprecision integer + * @size_t sz@ = size required * - * Returns: --- + * Returns: Pointer to the integer (possibly different). * - * Use: Loads an MP in an octet array, least significant octet - * first. + * Use: Prepares an integer to be overwritten. It's split off from + * other references to the same integer, and sufficient space is + * allocated. */ -extern void mp_loadl(mp */*x*/, const octet */*p*/, size_t /*sz*/); +extern mp *mp_modify(mp */*m*/, size_t /*sz*/); -/* --- @mp_storeb@ --- * +#define MP_MODIFY(m, sz) do { \ + size_t _rq = (sz); \ + mp *_m = (m); \ + if (_m == MP_NEW) \ + _m = mp_create(_rq); \ + else { \ + MP_SPLIT(_m); \ + MP_ENSURE(_m, _rq); \ + } \ + _m->vl = _m->v + _rq; \ + (m) = _m; \ +} while (0) + +/*----- Size manipulation -------------------------------------------------*/ + +/* --- @mp_shrink@ --- * * - * Arguments: @mp *x@ = pointer to MP head - * @octet *p@ = pointer to octet array - * @size_t sz@ = size of octet array + * Arguments: @mp *m@ = pointer to a multiprecision integer * * 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. + * Use: Reduces the recorded length of an integer. This doesn't + * reduce the amount of memory used, although it can improve + * performance a bit. To reduce memory, use @mp_minimize@ + * instead. This can't change the value of an integer, and is + * therefore safe to use even when there are multiple + * references. */ -extern void mp_storeb(mp */*x*/, octet */*p*/, size_t /*sz*/); +extern void mp_shrink(mp */*m*/); -/* --- @mp_loadb@ --- * +#define MP_SHRINK(m) do { \ + mp *_mm = (m); \ + MPX_SHRINK(_mm->v, _mm->vl); \ + if (!MP_LEN(_mm)) \ + _mm->f &= ~MP_NEG; \ +} while (0) + +/* --- @mp_minimize@ --- * * - * Arguments: @mp *x@ = pointer to MP head - * @const octet *p@ = pointer to octet array - * @size_t sz@ = size of octet array + * Arguments: @mp *m@ = pointer to a multiprecision integer * * Returns: --- * - * Use: Loads an MP in an octet array, most significant octet - * first. + * Use: Reduces the amount of memory an integer uses. It's best to + * do this to numbers which aren't going to change in the + * future. */ -extern void mp_loadb(mp */*x*/, const octet */*p*/, size_t /*sz*/); +extern void mp_minimize(mp */*m*/); -/*----- Iterating through bits --------------------------------------------*/ +/*----- Bit scanning ------------------------------------------------------*/ -/* --- @mp_mkbitscan@ --- * +#ifndef MPSCAN_H +# include "mpscan.h" +#endif + +/* --- @mp_scan@ --- * * - * Arguments: @mp_bitscan *sc@ = pointer to bitscan object - * @const mp *x@ = pointer to MP head + * Arguments: @mpscan *sc@ = pointer to bitscanner block + * @const mp *m@ = pointer to a multiprecision integer * * Returns: --- * - * Use: Initializes a bitscan object. + * Use: Initializes a bitscanner on a multiprecision integer. */ -extern void mp_mkbitscan(mp_bitscan */*sc*/, const mp */*x*/); +extern void mp_scan(mpscan */*sc*/, const mp */*m*/); + +#define MP_SCAN(sc, m) do { \ + mp *_mm = (m); \ + mpscan *_sc = (sc); \ + MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ +} while (0) + +/* --- Other bitscanning aliases --- */ + +#define mp_step mpscan_step +#define mp_bit mpscan_bit + +#define MP_STEP MPSCAN_STEP +#define MP_BIT MPSCAN_BIT + +/*----- Loading and storing -----------------------------------------------*/ -/* --- @mp_bstep@ --- * +/* --- @mp_octets@ --- * * - * Arguments: @mp_bitscan *sc@ = pointer to bitscanner object + * Arguments: @const mp *m@ = a multiprecision integer * - * Returns: Nonzero if there is another bit to read. + * Returns: The number of octets required to represent @m@. * - * Use: Steps on to the next bit, and tells the caller whether one - * exists. + * Use: Calculates the external storage required for a multiprecision + * integer. */ -extern int mp_bstep(mp_bitscan */*sc*/); +extern size_t mp_octets(const mp *m); -/* --- @mp_bit@ --- * +/* --- @mp_loadl@ --- * * - * Arguments: @const mp_bitscan *sc@ = pointer to bitscanner + * Arguments: @mp *d@ = destination + * @const void *pv@ = pointer to source data + * @size_t sz@ = size of the source data * - * Returns: Current bit value. + * Returns: Resulting multiprecision number. * - * Use: Returns the value of the current bit. + * Use: Loads a multiprecision number from an array of octets. The + * first byte in the array is the least significant. More + * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% + * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. */ -#define MP_BIT(sc) ((sc)->w & 1) +extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); -extern int mp_bit(const mp_bitscan */*sc*/); +/* --- @mp_storel@ --- * + * + * Arguments: @const mp *m@ = source + * @void *pv@ = pointer to output array + * @size_t sz@ = size of the output array + * + * Returns: --- + * + * Use: Stores a multiprecision number in an array of octets. The + * first byte in the array is the least significant. If the + * array is too small to represent the number, high-order bits + * are truncated; if the array is too large, high order bytes + * are filled with zeros. More formally, if the number is + * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, + * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. + */ -/*----- Shifting ----------------------------------------------------------*/ +extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); -/* --- @mp_lsl@ --- * +/* --- @mp_loadb@ --- * * - * Arguments: @mp *d@ = pointer to MP head of destination - * @const mp *x@ = pointer to MP head of source - * @size_t n@ = number of bits to shift + * Arguments: @mp *d@ = destination + * @const void *pv@ = pointer to source data + * @size_t sz@ = size of the source data * - * Returns: --- + * Returns: Resulting multiprecision number. * - * Use: Shifts a number left by a given number of bit positions. + * Use: Loads a multiprecision number from an array of octets. The + * last byte in the array is the least significant. More + * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% + * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. */ -extern void mp_lsl(mp */*d*/, const mp */*x*/, size_t /*n*/); +extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); -/* --- @mp_lsr@ --- * +/* --- @mp_storeb@ --- * * - * Arguments: @mp *d@ = pointer to MP head of destination - * @const mp *x@ = pointer to MP head of source - * @size_t n@ = number of bits to shift + * Arguments: @const mp *m@ = source + * @void *pv@ = pointer to output array + * @size_t sz@ = size of the output array * * Returns: --- * - * Use: Shifts a number right by a given number of bit positions. + * Use: Stores a multiprecision number in an array of octets. The + * last byte in the array is the least significant. If the + * array is too small to represent the number, high-order bits + * are truncated; if the array is too large, high order bytes + * are filled with zeros. More formally, if the number is + * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, + * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. */ -extern void mp_lsr(mp */*d*/, const mp */*x*/, size_t /*n*/); +extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); -/*----- Unsigned arithmetic -----------------------------------------------*/ +/*----- Simple arithmetic -------------------------------------------------*/ -/* --- @mp_uadd@ --- * +/* --- @mp_2c@ --- * * - * Arguments: @const mp *d@ = pointers to MP head of destination - * @const mp *x, *y@ = pointers to MP heads of operands + * Arguments: @mp *d@ = destination + * @mp *a@ = source * - * Returns: --- + * Returns: Result, @a@ converted to two's complement notation. + */ + +extern mp *mp_2c(mp */*d*/, mp */*a*/); + +/* --- @mp_sm@ --- * + * + * Arguments: @mp *d@ = destination + * @mp *a@ = source * - * Use: Performs unsigned MP addition. + * Returns: Result, @a@ converted to the native signed-magnitude + * notation. */ -extern void mp_uadd(mp */*d*/, const mp */*x*/, const mp */*y*/); +extern mp *mp_sm(mp */*d*/, mp */*a*/); -/* --- @mp_usub@ --- * +/* --- @mp_lsl@ --- * * - * Arguments: @const mp *d@ = pointers to MP head of destination - * @const mp *x, *y@ = pointers to MP heads of operands + * Arguments: @mp *d@ = destination + * @const mp *a@ = source + * @size_t n@ = number of bits to move * - * Returns: --- + * Returns: Result, @a@ shifted left by @n@. + */ + +extern mp *mp_lsl(mp */*d*/, const mp */*a*/, size_t /*n*/); + +/* --- @mp_lsr@ --- * + * + * Arguments: @mp *d@ = destination + * @const mp *a@ = source + * @size_t n@ = number of bits to move * - * Use: Performs unsigned MP subtraction. + * Returns: Result, @a@ shifted left by @n@. */ -extern void mp_usub(mp */*d*/, const mp */*x*/, const mp */*y*/); +extern mp *mp_lsr(mp */*d*/, const mp */*a*/, size_t /*n*/); -/* --- @mp_ucmp@ --- * +/* --- @mp_cmp@ --- * * - * Arguments: @const mp *x, *y@ = pointers to MP heads of operands + * Arguments: @const mp *a, *b@ = two numbers * - * Returns: Less than, equal to, or greater than zero. + * Returns: Less than, equal to or greater than zero, according to + * whether @a@ is less than, equal to or greater than @b@. + */ + +extern int mp_cmp(const mp */*a*/, const mp */*b*/); + +#define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) + +/* --- @mp_add@ --- * * - * Use: Performs unsigned MP comparison. + * Arguments: @mp *d@ = destination + * @const mp *a, *b@ = sources + * + * Returns: Result, @a@ added to @b@. */ -#define MP_UCMP(x, op, y) (mp_ucmp((x), (y)) op 0) +extern mp *mp_add(mp */*d*/, const mp */*a*/, const mp */*b*/); -extern int mp_ucmp(const mp */*x*/, const mp */*y*/); +/* --- @mp_sub@ --- * + * + * Arguments: @mp *d@ = destination + * @const mp *a, *b@ = sources + * + * Returns: Result, @b@ subtracted from @a@. + */ -/* --- @mp_umul@ --- * +extern mp *mp_sub(mp */*d*/, const mp */*a*/, const mp */*b*/); + +/* --- @mp_mul@ --- * * - * Arguments: @mp *d@ = pointer to MP head of destination - * @const mp *x, *y@ = pointes to MP heads of operands + * Arguments: @mp *d@ = destination + * @const mp *a, *b@ = sources * - * Returns: --- + * Returns: Result, @a@ multiplied by @b@. + */ + +extern mp *mp_mul(mp */*d*/, const mp */*a*/, const mp */*b*/); + +/* --- @mp_sqr@ --- * + * + * Arguments: @mp *d@ = destination + * @const mp *a@ = source + * + * Returns: Result, @a@ squared. + */ + +extern mp *mp_sqr(mp */*d*/, const mp */*a*/); + +/* --- @mp_div@ --- * * - * Use: Performs unsigned MP multiplication. + * Arguments: @mp **qq, **rr@ = destination, quotient and remainder + * @const mp *a, *b@ = sources + * + * Use: Calculates the quotient and remainder when @a@ is divided by + * @b@. */ -extern void mp_umul(mp */*d*/, const mp */*x*/, const mp */*y*/); +extern void mp_div(mp **/*qq*/, mp **/*rr*/, + const mp */*a*/, const mp */*b*/); + +/*----- More advanced algorithms ------------------------------------------*/ -/* --- @mp_udiv@ --- * +/* --- @mp_gcd@ --- * * - * Arguments: @mp *q, *r@ = pointers to MP heads for quotient, remainder - * @const mp *x, *y@ = pointers to MP heads for operands + * Arguments: @mp **gcd, **xx, **yy@ = where to write the results + * @mp *a, *b@ = sources (must be nonzero) * * Returns: --- * - * Use: Performs unsigned MP division. + * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that + * @ax + by = gcd(a, b)@. This is useful for computing modular + * inverses. Neither @a@ nor @b@ may be zero. Note that, + * unlike @mp_div@ for example, it is not possible to specify + * explicit destinations -- new MPs are always allocated. */ -extern void mp_udiv(mp */*q*/, mp */*r*/, const mp */*x*/, const mp */*y*/); +extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, + mp */*a*/, mp */*b*/); + +/*----- Test harness support ----------------------------------------------*/ + +#include + +#ifndef MPTEXT_H +# include "mptext.h" +#endif + +extern const test_type type_mp; /*----- That's all, folks -------------------------------------------------*/