math/ptab.in: Include the correct Oakley 2048 group!

[catacomb] / math / mpmont.c

/* -*-c-*-
 *
 * Montgomery reduction
 *
 * (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.
 */

/*----- Header files ------------------------------------------------------*/

#include "config.h"
#include "dispatch.h"
#include "mp.h"
#include "mpmont.h"

/*----- Tweakables --------------------------------------------------------*/

/* --- @MPMONT_DISABLE@ --- *
 *
 * Replace all the clever Montgomery reduction with good old-fashioned long
 * division.
 */

/* #define MPMONT_DISABLE */

/*----- Low-level implementation ------------------------------------------*/

#ifndef MPMONT_DISABLE

/* --- @redccore@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = base and limit of source/destination
 *		@const mpw *mv@ = base of modulus %$m$%
 *		@size_t n@ = length of modulus
 *		@const mpw *mi@ = base of REDC coefficient %$m'$%
 *
 * Returns:	---
 *
 * Use:		Let %$a$% be the input operand.  Store in %$d$% the value
 *		%$a + (m' a \bmod R) m$%.  The destination has space for at
 *		least %$2 n + 1$% words of result.
 */

CPU_DISPATCH(static, (void), void, redccore,
	     (mpw *dv, mpw *dvl, const mpw *mv, size_t n, const mpw *mi),
	     (dv, dvl, mv, n, mi), pick_redccore, simple_redccore);

static void simple_redccore(mpw *dv, mpw *dvl, const mpw *mv,
			    size_t n, const mpw *mi)
{
  mpw mi0 = *mi;
  size_t i;

  for (i = 0; i < n; i++) {
    MPX_UMLAN(dv, dvl, mv, mv + n, MPW(*dv*mi0));
    dv++;
  }
}

#define MAYBE_REDC4(impl)						\
  extern void mpxmont_redc4_##impl(mpw *dv, mpw *dvl, const mpw *mv,	\
				   size_t n, const mpw *mi);		\
  static void maybe_redc4_##impl(mpw *dv, mpw *dvl, const mpw *mv,	\
				 size_t n, const mpw *mi)		\
  {									\
    if (n%4) simple_redccore(dv, dvl, mv, n, mi);			\
    else mpxmont_redc4_##impl(dv, dvl, mv, n, mi);			\
  }

#if CPUFAM_X86
  MAYBE_REDC4(x86_sse2)
#endif

static redccore__functype *pick_redccore(void)
{
#if CPUFAM_X86
  DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_x86_sse2,
		     cpu_feature_p(CPUFEAT_X86_SSE2));
#endif
  DISPATCH_PICK_FALLBACK(mpmont_reduce, simple_redccore);
}

/* --- @redccore@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = base and limit of source/destination
 *		@const mpw *av, *avl@ = base and limit of first multiplicand
 *		@const mpw *bv, *bvl@ = base and limit of second multiplicand
 *		@const mpw *mv@ = base of modulus %$m$%
 *		@size_t n@ = length of modulus
 *		@const mpw *mi@ = base of REDC coefficient %$m'$%
 *
 * Returns:	---
 *
 * Use:		Let %$a$% and %$b$% be the multiplicands.  Let %$w = a b$%.
 *		Store in %$d$% the value %$a b + (m' a b \bmod R) m$%.
 */

CPU_DISPATCH(static, (void), void, mulcore,
	     (mpw *dv, mpw *dvl, const mpw *av, const mpw *avl,
	      const mpw *bv, const mpw *bvl, const mpw *mv,
	      size_t n, const mpw *mi),
	     (dv, dvl, av, avl, bv, bvl, mv, n, mi),
	     pick_mulcore, simple_mulcore);

static void simple_mulcore(mpw *dv, mpw *dvl,
			   const mpw *av, const mpw *avl,
			   const mpw *bv, const mpw *bvl,
			   const mpw *mv, size_t n, const mpw *mi)
{
  mpw ai, b0, y, mi0 = *mi;
  const mpw *tv, *tvl;
  const mpw *mvl = mv + n;
  size_t i = 0;

  /* --- Initial setup --- */

  MPX_ZERO(dv, dvl);
  if (avl - av > bvl - bv) {
    tv = av; av = bv; bv = tv;
    tvl = avl; avl = bvl; bvl = tvl;
  }
  b0 = *bv;

  /* --- Multiply, until we run out of multiplicand --- */

  while (i < n && av < avl) {
    ai = *av++;
    y = MPW((*dv + ai*b0)*mi0);
    MPX_UMLAN(dv, dvl, bv, bvl, ai);
    MPX_UMLAN(dv, dvl, mv, mvl, y);
    dv++; i++;
  }

  /* --- Continue reducing until we run out of modulus --- */

  while (i < n) {
    y = MPW(*dv*mi0);
    MPX_UMLAN(dv, dvl, mv, mvl, y);
    dv++; i++;
  }
}

#define MAYBE_MUL4(impl)						\
  extern void mpxmont_mul4_##impl(mpw *dv,				\
				  const mpw *av, const mpw *bv,		\
				  const mpw *mv,			\
				  size_t n, const mpw *mi);		\
  static void maybe_mul4_##impl(mpw *dv, mpw *dvl,			\
			   const mpw *av, const mpw *avl,		\
			   const mpw *bv, const mpw *bvl,		\
			   const mpw *mv, size_t n, const mpw *mi)	\
  {									\
    size_t an = avl - av, bn = bvl - bv;				\
    if (n%4 || an != n || bn != n)					\
      simple_mulcore(dv, dvl, av, avl, bv, bvl, mv, n, mi);		\
    else {								\
      mpxmont_mul4_##impl(dv, av, bv, mv, n, mi);			\
      MPX_ZERO(dv + 2*n + 1, dvl);					\
    }									\
  }

#if CPUFAM_X86
  MAYBE_MUL4(x86_sse2)
#endif

static mulcore__functype *pick_mulcore(void)
{
#if CPUFAM_X86
  DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_x86_sse2,
		     cpu_feature_p(CPUFEAT_X86_SSE2));
#endif
  DISPATCH_PICK_FALLBACK(mpmont_mul, simple_mulcore);
}

/* --- @finish@ --- *
 *
 * Arguments:	@mpmont *mm@ = pointer to a Montgomery reduction context
 *		*mp *d@ = pointer to mostly-reduced operand
 *
 * Returns:	---
 *
 * Use:		Applies the finishing touches to Montgomery reduction.  The
 *		operand @d@ is a multiple of %$R%$ at this point, so it needs
 *		to be shifted down; the result might need a further
 *		subtraction to get it into the right interval; and we may
 *		need to do an additional subtraction if %$d$% is negative.
 */

static void finish(mpmont *mm, mp *d)
{
  mpw *dv = d->v, *dvl = d->vl;
  size_t n = mm->n;

  memmove(dv, dv + n, MPWS(dvl - (dv + n)));
  dvl -= n;

  if (MPX_UCMP(dv, dvl, >=, mm->m->v, mm->m->vl))
    mpx_usub(dv, dvl, dv, dvl, mm->m->v, mm->m->vl);

  if (d->f & MP_NEG) {
    mpx_usub(dv, dvl, mm->m->v, mm->m->vl, dv, dvl);
    d->f &= ~MP_NEG;
  }

  d->vl = dvl;
  MP_SHRINK(d);
}

#endif

/*----- Reduction and multiplication --------------------------------------*/

/* --- @mpmont_create@ --- *
 *
 * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
 *		@mp *m@ = modulus to use
 *
 * Returns:	Zero on success, nonzero on error.
 *
 * Use:		Initializes a Montgomery reduction context ready for use.
 *		The argument @m@ must be a positive odd integer.
 */

#ifdef MPMONT_DISABLE

int mpmont_create(mpmont *mm, mp *m)
{
  mp_shrink(m);
  mm->m = MP_COPY(m);
  mm->r = MP_ONE;
  mm->r2 = MP_ONE;
  mm->mi = MP_ONE;
  return (0);
}

#else

int mpmont_create(mpmont *mm, mp *m)
{
  size_t n = MP_LEN(m);
  mp *r2 = mp_new(2 * n + 1, 0);
  mp r;

  /* --- Take a copy of the modulus --- */

 if (!MP_POSP(m) || !MP_ODDP(m))
   return (-1);
  mm->m = MP_COPY(m);

  /* --- Determine %$R^2$% --- */

  mm->n = n;
  MPX_ZERO(r2->v, r2->vl - 1);
  r2->vl[-1] = 1;

  /* --- Find the magic value @mi@ --- */

  mp_build(&r, r2->v + n, r2->vl);
  mm->mi = mp_modinv(MP_NEW, m, &r);
  mm->mi = mp_sub(mm->mi, &r, mm->mi);
  MP_ENSURE(mm->mi, n);

  /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */

  mm->r2 = MP_NEW;
  mp_div(0, &mm->r2, r2, m);
  mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
  MP_DROP(r2);
  return (0);
}

#endif

/* --- @mpmont_destroy@ --- *
 *
 * Arguments:	@mpmont *mm@ = pointer to a Montgomery reduction context
 *
 * Returns:	---
 *
 * Use:		Disposes of a context when it's no longer of any use to
 *		anyone.
 */

void mpmont_destroy(mpmont *mm)
{
  MP_DROP(mm->m);
  MP_DROP(mm->r);
  MP_DROP(mm->r2);
  MP_DROP(mm->mi);
}

/* --- @mpmont_reduce@ --- *
 *
 * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
 *		@mp *d@ = destination
 *		@mp *a@ = source, assumed positive
 *
 * Returns:	Result, %$a R^{-1} \bmod m$%.
 */

#ifdef MPMONT_DISABLE

mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
{
  mp_div(0, &d, a, mm->m);
  return (d);
}

#else

mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
{
  size_t n = mm->n;

  /* --- Check for serious Karatsuba reduction --- */

  if (n > MPK_THRESH * 3) {
    mp al;
    mpw *vl;
    mp *u;

    if (MP_LEN(a) >= n) vl = a->v + n;
    else vl = a->vl;
    mp_build(&al, a->v, vl);
    u = mp_mul(MP_NEW, &al, mm->mi);
    if (MP_LEN(u) > n) u->vl = u->v + n;
    u = mp_mul(u, u, mm->m);
    d = mp_add(d, a, u);
    MP_ENSURE(d, n);
    mp_drop(u);
  }

  /* --- Otherwise do it the hard way --- */

  else {
    a = MP_COPY(a);
    if (d) MP_DROP(d);
    d = a;
    MP_DEST(d, 2*mm->n + 1, a->f);
    redccore(d->v, d->vl, mm->m->v, mm->n, mm->mi->v);
  }

  /* --- Wrap everything up --- */

  finish(mm, d);
  return (d);
}

#endif

/* --- @mpmont_mul@ --- *
 *
 * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
 *		@mp *d@ = destination
 *		@mp *a, *b@ = sources, assumed positive
 *
 * Returns:	Result, %$a b R^{-1} \bmod m$%.
 */

#ifdef MPMONT_DISABLE

mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
{
  d = mp_mul(d, a, b);
  mp_div(0, &d, d, mm->m);
  return (d);
}

#else

mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
{
  size_t n = mm->n;

  if (n > MPK_THRESH * 3) {
    d = mp_mul(d, a, b);
    d = mpmont_reduce(mm, d, d);
  } else {
    a = MP_COPY(a); b = MP_COPY(b);
    MP_DEST(d, 2*n + 1, a->f | b->f | MP_UNDEF);
    mulcore(d->v, d->vl, a->v, a->vl, b->v, b->vl,
	    mm->m->v, mm->n, mm->mi->v);
    d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
    finish(mm, d);
    MP_DROP(a); MP_DROP(b);
  }

  return (d);
}

#endif

/*----- Test rig ----------------------------------------------------------*/

#ifdef TEST_RIG

static int tcreate(dstr *v)
{
  mp *m = *(mp **)v[0].buf;
  mp *mi = *(mp **)v[1].buf;
  mp *r = *(mp **)v[2].buf;
  mp *r2 = *(mp **)v[3].buf;

  mpmont mm;
  int ok = 1;

  mpmont_create(&mm, m);

  if (mm.mi->v[0] != mi->v[0]) {
    fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
	    (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
    fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
    fputc('\n', stderr);
    ok = 0;
  }

  if (!MP_EQ(mm.r, r)) {
    fputs("\n*** bad r", stderr);
    fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
    fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
    fputs("\n	found ", stderr); mp_writefile(mm.r, stderr, 10);
    fputc('\n', stderr);
    ok = 0;
  }

  if (!MP_EQ(mm.r2, r2)) {
    fputs("\n*** bad r2", stderr);
    fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
    fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
    fputs("\n	found ", stderr); mp_writefile(mm.r2, stderr, 10);
    fputc('\n', stderr);
    ok = 0;
  }

  MP_DROP(m);
  MP_DROP(mi);
  MP_DROP(r);
  MP_DROP(r2);
  mpmont_destroy(&mm);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  return (ok);
}

static int tmul(dstr *v)
{
  mp *m = *(mp **)v[0].buf;
  mp *a = *(mp **)v[1].buf;
  mp *b = *(mp **)v[2].buf;
  mp *r = *(mp **)v[3].buf;
  int ok = 1;

  mpmont mm;
  mpmont_create(&mm, m);

  {
    mp *qr = mp_mul(MP_NEW, a, b);
    mp_div(0, &qr, qr, m);

    if (!MP_EQ(qr, r)) {
      fputs("\n*** classical modmul failed", stderr);
      fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
      fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
      fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
      fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
      fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
      fputc('\n', stderr);
      ok = 0;
    }

    mp_drop(qr);
  }

  {
    mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
    mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
    mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
    mr = mpmont_reduce(&mm, mr, mr);
    if (!MP_EQ(mr, r)) {
      fputs("\n*** montgomery modmul failed", stderr);
      fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
      fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
      fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
      fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
      fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
      fputc('\n', stderr);
      ok = 0;
    }
    MP_DROP(ar); MP_DROP(br);
    mp_drop(mr);
  }


  MP_DROP(m);
  MP_DROP(a);
  MP_DROP(b);
  MP_DROP(r);
  mpmont_destroy(&mm);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  return ok;
}

static test_chunk tests[] = {
  { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
  { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
  { 0, 0, { 0 } },
};

int main(int argc, char *argv[])
{
  sub_init();
  test_run(argc, argv, tests, SRCDIR "/t/mpmont");
  return (0);
}

#endif

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