/* hgcd2.c

   THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
   SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

Copyright 1996, 1998, 2000, 2001, 2002, 2003, 2004, 2008 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 3 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.  If not, see http://www.gnu.org/licenses/.  */

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

#if GMP_NAIL_BITS == 0

/* Copied from the old mpn/generic/gcdext.c, and modified slightly to return
   the remainder. */

/* Single-limb division optimized for small quotients. */
static inline mp_limb_t
div1 (mp_ptr rp,
      mp_limb_t n0,
      mp_limb_t d0)
{
  mp_limb_t q = 0;

  if ((mp_limb_signed_t) n0 < 0)
    {
      int cnt;
      for (cnt = 1; (mp_limb_signed_t) d0 >= 0; cnt++)
	{
	  d0 = d0 << 1;
	}

      q = 0;
      while (cnt)
	{
	  q <<= 1;
	  if (n0 >= d0)
	    {
	      n0 = n0 - d0;
	      q |= 1;
	    }
	  d0 = d0 >> 1;
	  cnt--;
	}
    }
  else
    {
      int cnt;
      for (cnt = 0; n0 >= d0; cnt++)
	{
	  d0 = d0 << 1;
	}

      q = 0;
      while (cnt)
	{
	  d0 = d0 >> 1;
	  q <<= 1;
	  if (n0 >= d0)
	    {
	      n0 = n0 - d0;
	      q |= 1;
	    }
	  cnt--;
	}
    }
  *rp = n0;
  return q;
}

/* Two-limb division optimized for small quotients.  */
static inline mp_limb_t
div2 (mp_ptr rp,
      mp_limb_t nh, mp_limb_t nl,
      mp_limb_t dh, mp_limb_t dl)
{
  mp_limb_t q = 0;

  if ((mp_limb_signed_t) nh < 0)
    {
      int cnt;
      for (cnt = 1; (mp_limb_signed_t) dh >= 0; cnt++)
	{
	  dh = (dh << 1) | (dl >> (GMP_LIMB_BITS - 1));
	  dl = dl << 1;
	}

      while (cnt)
	{
	  q <<= 1;
	  if (nh > dh || (nh == dh && nl >= dl))
	    {
	      sub_ddmmss (nh, nl, nh, nl, dh, dl);
	      q |= 1;
	    }
	  dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
	  dh = dh >> 1;
	  cnt--;
	}
    }
  else
    {
      int cnt;
      for (cnt = 0; nh > dh || (nh == dh && nl >= dl); cnt++)
	{
	  dh = (dh << 1) | (dl >> (GMP_LIMB_BITS - 1));
	  dl = dl << 1;
	}

      while (cnt)
	{
	  dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
	  dh = dh >> 1;
	  q <<= 1;
	  if (nh > dh || (nh == dh && nl >= dl))
	    {
	      sub_ddmmss (nh, nl, nh, nl, dh, dl);
	      q |= 1;
	    }
	  cnt--;
	}
    }

  rp[0] = nl;
  rp[1] = nh;

  return q;
}

#if 0
/* This div2 uses less branches, but it seems to nevertheless be
   slightly slower than the above code. */
static inline mp_limb_t
div2 (mp_ptr rp,
      mp_limb_t nh, mp_limb_t nl,
      mp_limb_t dh, mp_limb_t dl)
{
  mp_limb_t q = 0;
  int ncnt;
  int dcnt;

  count_leading_zeros (ncnt, nh);
  count_leading_zeros (dcnt, dh);
  dcnt -= ncnt;

  dh = (dh << dcnt) + (-(dcnt > 0) & (dl >> (GMP_LIMB_BITS - dcnt)));
  dl <<= dcnt;

  do
    {
      mp_limb_t bit;
      q <<= 1;
      if (UNLIKELY (nh == dh))
	bit = (nl >= dl);
      else
	bit = (nh > dh);

      q |= bit;

      sub_ddmmss (nh, nl, nh, nl, (-bit) & dh, (-bit) & dl);

      dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
      dh = dh >> 1;
    }
  while (dcnt--);

  rp[0] = nl;
  rp[1] = nh;

  return q;
}
#endif

#else /* GMP_NAIL_BITS != 0 */
/* Check all functions for nail support. */
/* hgcd2 should be defined to take inputs including nail bits, and
   produce a matrix with elements also including nail bits. This is
   necessary, for the matrix elements to be useful with mpn_mul_1,
   mpn_addmul_1 and friends. */
#error Not implemented
#endif /* GMP_NAIL_BITS != 0 */

/* Reduces a,b until |a-b| (almost) fits in one limb + 1 bit. Constructs
   matrix M. Returns 1 if we make progress, i.e. can perform at least
   one subtraction. Otherwise returns zero.. */

/* FIXME: Possible optimizations:

   The div2 function starts with checking the most significant bit of
   the numerator. We can maintained normalized operands here, call
   hgcd with normalized operands only, which should make the code
   simpler and possibly faster.

   Experiment with table lookups on the most significant bits.

   This function is also a candidate for assembler implementation.
*/
int
mpn_hgcd2 (mp_limb_t ah, mp_limb_t al, mp_limb_t bh, mp_limb_t bl,
	   struct hgcd_matrix1 *M)
{
  mp_limb_t u00, u01, u10, u11;

  if (ah < 2 || bh < 2)
    return 0;

  if (ah > bh || (ah == bh && al > bl))
    {
      sub_ddmmss (ah, al, ah, al, bh, bl);
      if (ah < 2)
	return 0;

      u00 = u01 = u11 = 1;
      u10 = 0;
    }
  else
    {
      sub_ddmmss (bh, bl, bh, bl, ah, al);
      if (bh < 2)
	return 0;

      u00 = u10 = u11 = 1;
      u01 = 0;
    }

  if (ah < bh)
    goto subtract_a;

  for (;;)
    {
      ASSERT (ah >= bh);
      if (ah == bh)
	goto done;

      if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
	{
	  ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
	  bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));

	  break;
	}

      /* Subtract a -= q b, and multiply M from the right by (1 q ; 0
	 1), affecting the second column of M. */
      ASSERT (ah > bh);
      sub_ddmmss (ah, al, ah, al, bh, bl);

      if (ah < 2)
	goto done;

      if (ah <= bh)
	{
	  /* Use q = 1 */
	  u01 += u00;
	  u11 += u10;
	}
      else
	{
	  mp_limb_t r[2];
	  mp_limb_t q = div2 (r, ah, al, bh, bl);
	  al = r[0]; ah = r[1];
	  if (ah < 2)
	    {
	      /* A is too small, but q is correct. */
	      u01 += q * u00;
	      u11 += q * u10;
	      goto done;
	    }
	  q++;
	  u01 += q * u00;
	  u11 += q * u10;
	}
    subtract_a:
      ASSERT (bh >= ah);
      if (ah == bh)
	goto done;

      if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
	{
	  ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
	  bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));

	  goto subtract_a1;
	}

      /* Subtract b -= q a, and multiply M from the right by (1 0 ; q
	 1), affecting the first column of M. */
      sub_ddmmss (bh, bl, bh, bl, ah, al);

      if (bh < 2)
	goto done;

      if (bh <= ah)
	{
	  /* Use q = 1 */
	  u00 += u01;
	  u10 += u11;
	}
      else
	{
	  mp_limb_t r[2];
	  mp_limb_t q = div2 (r, bh, bl, ah, al);
	  bl = r[0]; bh = r[1];
	  if (bh < 2)
	    {
	      /* B is too small, but q is correct. */
	      u00 += q * u01;
	      u10 += q * u11;
	      goto done;
	    }
	  q++;
	  u00 += q * u01;
	  u10 += q * u11;
	}
    }

  /* NOTE: Since we discard the least significant half limb, we don't
     get a truly maximal M (corresponding to |a - b| <
     2^{GMP_LIMB_BITS +1}). */
  /* Single precision loop */
  for (;;)
    {
      ASSERT (ah >= bh);
      if (ah == bh)
	break;

      ah -= bh;
      if (ah < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
	break;

      if (ah <= bh)
	{
	  /* Use q = 1 */
	  u01 += u00;
	  u11 += u10;
	}
      else
	{
	  mp_limb_t r;
	  mp_limb_t q = div1 (&r, ah, bh);
	  ah = r;
	  if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
	    {
	      /* A is too small, but q is correct. */
	      u01 += q * u00;
	      u11 += q * u10;
	      break;
	    }
	  q++;
	  u01 += q * u00;
	  u11 += q * u10;
	}
    subtract_a1:
      ASSERT (bh >= ah);
      if (ah == bh)
	break;

      bh -= ah;
      if (bh < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
	break;

      if (bh <= ah)
	{
	  /* Use q = 1 */
	  u00 += u01;
	  u10 += u11;
	}
      else
	{
	  mp_limb_t r;
	  mp_limb_t q = div1 (&r, bh, ah);
	  bh = r;
	  if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
	    {
	      /* B is too small, but q is correct. */
	      u00 += q * u01;
	      u10 += q * u11;
	      break;
	    }
	  q++;
	  u00 += q * u01;
	  u10 += q * u11;
	}
    }

 done:
  M->u[0][0] = u00; M->u[0][1] = u01;
  M->u[1][0] = u10; M->u[1][1] = u11;

  return 1;
}

/* Sets (r;b) = (a;b) M, with M = (u00, u01; u10, u11). Vector must
 * have space for n + 1 limbs. Uses three buffers to avoid a copy*/
mp_size_t
mpn_hgcd_mul_matrix1_vector (const struct hgcd_matrix1 *M,
			     mp_ptr rp, mp_srcptr ap, mp_ptr bp, mp_size_t n)
{
  mp_limb_t ah, bh;

  /* Compute (r,b) <-- (u00 a + u10 b, u01 a + u11 b) as

     r  = u00 * a
     r += u10 * b
     b *= u11
     b += u01 * a
  */

#if HAVE_NATIVE_mpn_addaddmul_1msb0
  ah = mpn_addaddmul_1msb0 (rp, ap, bp, n, M->u[0][0], M->u[1][0]);
  bh = mpn_addaddmul_1msb0 (bp, bp, ap, n, M->u[1][1], M->u[0][1]);
#else
  ah =     mpn_mul_1 (rp, ap, n, M->u[0][0]);
  ah += mpn_addmul_1 (rp, bp, n, M->u[1][0]);

  bh =     mpn_mul_1 (bp, bp, n, M->u[1][1]);
  bh += mpn_addmul_1 (bp, ap, n, M->u[0][1]);
#endif
  rp[n] = ah;
  bp[n] = bh;

  n += (ah | bh) > 0;
  return n;
}

/* Sets (r;b) = M^{-1}(a;b), with M^{-1} = (u11, -u01; -u10, u00) from
   the left. Uses three buffers, to avoid a copy. */
mp_size_t
mpn_hgcd_mul_matrix1_inverse_vector (const struct hgcd_matrix1 *M,
				     mp_ptr rp, mp_srcptr ap, mp_ptr bp, mp_size_t n)
{
  mp_limb_t h0, h1;

  /* Compute (r;b) <-- (u11 a - u01 b; -u10 a + u00 b) as

     r  = u11 * a
     r -= u01 * b
     b *= u00
     b -= u10 * a
  */

  h0 =    mpn_mul_1 (rp, ap, n, M->u[1][1]);
  h1 = mpn_submul_1 (rp, bp, n, M->u[0][1]);
  ASSERT (h0 == h1);

  h0 =    mpn_mul_1 (bp, bp, n, M->u[0][0]);
  h1 = mpn_submul_1 (bp, ap, n, M->u[1][0]);
  ASSERT (h0 == h1);

  n -= (rp[n-1] | bp[n-1]) == 0;
  return n;
}