randlc2x.c

/* Linear Congruential pseudo-random number generator functions.

Copyright 1999, 2000, 2001, 2002, 2003, 2005 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The GNU MP Library 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */

#include "mpir.h"
#include "gmp-impl.h"


/* State structure for LC, the RNG_STATE() pointer in a gmp_randstate_t.

   _mp_seed holds the current seed value, in the range 0 to 2^m2exp-1.
   SIZ(_mp_seed) is fixed at BITS_TO_LIMBS(_mp_m2exp) and the value is
   padded with high zero limbs if necessary.  ALLOC(_mp_seed) is the current
   size of PTR(_mp_seed) in the usual way.  There only needs to be
   BITS_TO_LIMBS(_mp_m2exp) allocated, but the mpz functions in the
   initialization and seeding end up making it a bit more than this.

   _mp_a is the "a" multiplier, in the range 0 to 2^m2exp-1.  SIZ(_mp_a) is
   the size of the value in the normal way for an mpz_t, except that a value
   of zero is held with SIZ(_mp_a)==1 and PTR(_mp_a)[0]==0.  This makes it
   easy to call mpn_mul, and the case of a==0 is highly un-random and not
   worth any trouble to optimize.

   {_cp,_cn} is the "c" addend.  Normally _cn is 1, but when nails are in
   use a ulong can be bigger than one limb, and in this case _cn is 2 if
   necessary.  c==0 is stored as _cp[0]==0 and _cn==1, which makes it easy
   to call __GMPN_ADD.  c==0 is fairly un-random so isn't worth optimizing.

   _mp_m2exp gives the modulus, namely 2^m2exp.  We demand m2exp>=1, since
   m2exp==0 would mean no bits at all out of each iteration, which makes no
   sense.  */

typedef struct {
  mpz_t          _mp_seed;
  mpz_t          _mp_a;
  mp_size_t      _cn;
  mp_limb_t      _cp[LIMBS_PER_UI];
  mpir_ui  _mp_m2exp;
} gmp_rand_lc_struct;


/* lc (rp, state) -- Generate next number in LC sequence.  Return the
   number of valid bits in the result.  Discards the lower half of the
   result.  */

static mpir_ui
lc (mp_ptr rp, gmp_randstate_t rstate)
{
  mp_ptr tp, seedp, ap;
  mp_size_t ta;
  mp_size_t tn, seedn, an;
  mpir_ui m2exp;
  mpir_ui bits;
  int cy;
  mp_size_t xn;
  gmp_rand_lc_struct *p;
  TMP_DECL;

  p = (gmp_rand_lc_struct *) RNG_STATE (rstate);

  m2exp = p->_mp_m2exp;

  seedp = PTR (p->_mp_seed);
  seedn = SIZ (p->_mp_seed);

  ap = PTR (p->_mp_a);
  an = SIZ (p->_mp_a);

  /* Allocate temporary storage.  Let there be room for calculation of
     (A * seed + C) % M, or M if bigger than that.  */

  TMP_MARK;

  ta = an + seedn + 1;
  tn = BITS_TO_LIMBS (m2exp);
  if (ta <= tn) /* that is, if (ta < tn + 1) */
    {
      mp_size_t tmp = an + seedn;
      ta = tn + 1;
      tp = (mp_ptr) TMP_ALLOC (ta * BYTES_PER_MP_LIMB);
      MPN_ZERO (&tp[tmp], ta - tmp); /* mpn_mul won't zero it out.  */
    }
  else
    tp = (mp_ptr) TMP_ALLOC (ta * BYTES_PER_MP_LIMB);

  /* t = a * seed.  NOTE: an is always > 0; see initialization.  */
  ASSERT (seedn >= an && an > 0);
  mpn_mul (tp, seedp, seedn, ap, an);

  /* t = t + c.  NOTE: tn is always >= p->_cn (precondition for __GMPN_ADD);
     see initialization.  */
  ASSERT (tn >= p->_cn);
  __GMPN_ADD (cy, tp, tp, tn, p->_cp, p->_cn);

  /* t = t % m */
  tp[m2exp / GMP_NUMB_BITS] &= (CNST_LIMB (1) << m2exp % GMP_NUMB_BITS) - 1;

  /* Save result as next seed.  */
  MPN_COPY (PTR (p->_mp_seed), tp, tn);

  /* Discard the lower m2exp/2 of the result.  */
  bits = m2exp / 2;
  xn = bits / GMP_NUMB_BITS;

  tn -= xn;
  if (tn > 0)
    {
      unsigned int cnt = bits % GMP_NUMB_BITS;
      if (cnt != 0)
	{
	  mpn_rshift (tp, tp + xn, tn, cnt);
	  MPN_COPY_INCR (rp, tp, xn + 1);
	}
      else			/* Even limb boundary.  */
	MPN_COPY_INCR (rp, tp + xn, tn);
    }

  TMP_FREE;

  /* Return number of valid bits in the result.  */
  return (m2exp + 1) / 2;
}


/* Obtain a sequence of random numbers.  */
static void
randget_lc (gmp_randstate_t rstate, mp_ptr rp, mpir_ui nbits)
{
  mpir_ui rbitpos;
  int chunk_nbits;
  mp_ptr tp;
  mp_size_t tn;
  gmp_rand_lc_struct *p;
  TMP_DECL;

  p = (gmp_rand_lc_struct *) RNG_STATE (rstate);

  TMP_MARK;

  chunk_nbits = p->_mp_m2exp / 2;
  tn = BITS_TO_LIMBS (chunk_nbits);

  tp = (mp_ptr) TMP_ALLOC (tn * BYTES_PER_MP_LIMB);

  rbitpos = 0;
  while (rbitpos + chunk_nbits <= nbits)
    {
      mp_ptr r2p = rp + rbitpos / GMP_NUMB_BITS;

      if (rbitpos % GMP_NUMB_BITS != 0)
	{
	  mp_limb_t savelimb, rcy;
	  /* Target of new chunk is not bit aligned.  Use temp space
	     and align things by shifting it up.  */
	  lc (tp, rstate);
	  savelimb = r2p[0];
	  rcy = mpn_lshift (r2p, tp, tn, rbitpos % GMP_NUMB_BITS);
	  r2p[0] |= savelimb;
	  /* bogus */
	  if ((chunk_nbits % GMP_NUMB_BITS + rbitpos % GMP_NUMB_BITS)
	      > GMP_NUMB_BITS)
	    r2p[tn] = rcy;
	}
      else
	{
	  /* Target of new chunk is bit aligned.  Let `lc' put bits
	     directly into our target variable.  */
	  lc (r2p, rstate);
	}
      rbitpos += chunk_nbits;
    }

  /* Handle last [0..chunk_nbits) bits.  */
  if (rbitpos != nbits)
    {
      mp_ptr r2p = rp + rbitpos / GMP_NUMB_BITS;
      int last_nbits = nbits - rbitpos;
      tn = BITS_TO_LIMBS (last_nbits);
      lc (tp, rstate);
      if (rbitpos % GMP_NUMB_BITS != 0)
	{
	  mp_limb_t savelimb, rcy;
	  /* Target of new chunk is not bit aligned.  Use temp space
	     and align things by shifting it up.  */
	  savelimb = r2p[0];
	  rcy = mpn_lshift (r2p, tp, tn, rbitpos % GMP_NUMB_BITS);
	  r2p[0] |= savelimb;
	  if (rbitpos + tn * GMP_NUMB_BITS - rbitpos % GMP_NUMB_BITS < nbits)
	    r2p[tn] = rcy;
	}
      else
	{
	  MPN_COPY (r2p, tp, tn);
	}
      /* Mask off top bits if needed.  */
      if (nbits % GMP_NUMB_BITS != 0)
	rp[nbits / GMP_NUMB_BITS]
	  &= ~(~CNST_LIMB (0) << nbits % GMP_NUMB_BITS);
    }

  TMP_FREE;
}


static void
randseed_lc (gmp_randstate_t rstate, mpz_srcptr seed)
{
  gmp_rand_lc_struct *p = (gmp_rand_lc_struct *) RNG_STATE (rstate);
  mpz_ptr seedz = p->_mp_seed;
  mp_size_t seedn = BITS_TO_LIMBS (p->_mp_m2exp);

  /* Store p->_mp_seed as an unnormalized integer with size enough
     for numbers up to 2^m2exp-1.  That size can't be zero.  */
  mpz_fdiv_r_2exp (seedz, seed, p->_mp_m2exp);
  MPN_ZERO (&PTR (seedz)[SIZ (seedz)], seedn - SIZ (seedz));
  SIZ (seedz) = seedn;
}


static void
randclear_lc (gmp_randstate_t rstate)
{
  gmp_rand_lc_struct *p = (gmp_rand_lc_struct *) RNG_STATE (rstate);

  mpz_clear (p->_mp_seed);
  mpz_clear (p->_mp_a);
  (*__gmp_free_func) (p, sizeof (gmp_rand_lc_struct));
}

static void randiset_lc(gmp_randstate_ptr dst, gmp_randstate_srcptr src);

static const gmp_randfnptr_t Linear_Congruential_Generator = {
  randseed_lc,
  randget_lc,
  randclear_lc,
  randiset_lc
};

static void
randiset_lc (gmp_randstate_ptr dst, gmp_randstate_srcptr src)
{
  gmp_rand_lc_struct *dstp, *srcp;

  srcp = (gmp_rand_lc_struct *) RNG_STATE (src);
  dstp = (*__gmp_allocate_func) (sizeof (gmp_rand_lc_struct));

  RNG_STATE (dst) = (void *) dstp;
  RNG_FNPTR (dst) = (void *) &Linear_Congruential_Generator;

  /* _mp_seed and _mp_a might be unnormalized (high zero limbs), but
     mpz_init_set won't worry about that */
  mpz_init_set (dstp->_mp_seed, srcp->_mp_seed);
  mpz_init_set (dstp->_mp_a,    srcp->_mp_a);

  dstp->_cn = srcp->_cn;

  dstp->_cp[0] = srcp->_cp[0];
  if (LIMBS_PER_UI > 1)
    dstp->_cp[1] = srcp->_cp[1];
  if (LIMBS_PER_UI > 2)  /* usually there's only 1 or 2 */
    MPN_COPY (dstp->_cp + 2, srcp->_cp + 2, LIMBS_PER_UI - 2);

  dstp->_mp_m2exp = srcp->_mp_m2exp;
}


void
gmp_randinit_lc_2exp (gmp_randstate_t rstate,
		      mpz_srcptr a,
		      mpir_ui c,
		      mp_bitcnt_t m2exp)
{
  gmp_rand_lc_struct *p;
  mp_size_t seedn = BITS_TO_LIMBS (m2exp);

  ASSERT_ALWAYS (m2exp != 0);

  p = __GMP_ALLOCATE_FUNC_TYPE (1, gmp_rand_lc_struct);
  RNG_STATE (rstate) = (void *) p;
  RNG_FNPTR (rstate) = (void *) &Linear_Congruential_Generator;

  /* allocate m2exp bits of space for p->_mp_seed, and initial seed "1" */
  mpz_init2 (p->_mp_seed, m2exp);
  MPN_ZERO (PTR (p->_mp_seed), seedn);
  SIZ (p->_mp_seed) = seedn;
  PTR (p->_mp_seed)[0] = 1;

  /* "a", forced to 0 to 2^m2exp-1 */
  mpz_init (p->_mp_a);
  mpz_fdiv_r_2exp (p->_mp_a, a, m2exp);

  /* Avoid SIZ(a) == 0 to avoid checking for special case in lc().  */
  if (SIZ (p->_mp_a) == 0)
    {
      SIZ (p->_mp_a) = 1;
      PTR (p->_mp_a)[0] = CNST_LIMB (0);
    }

  MPN_SET_UI (p->_cp, p->_cn, c);

  /* Internally we may discard any bits of c above m2exp.  The following
     code ensures that __GMPN_ADD in lc() will always work.  */
  if (seedn < p->_cn)
    p->_cn = (p->_cp[0] != 0);

  p->_mp_m2exp = m2exp;
}