/* mpn_mod_1s_4p (ap, n, b, cps)

   Divide (ap,,n) by b.  Return the single-limb remainder.

   Requires that d < B / 4.

   Contributed to the GNU project by Torbjorn Granlund.

   Based on a suggestion by Peter L. Montgomery.

   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 WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

Copyright 2008-2010 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 either:

  * 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.

or

  * the GNU General Public License as published by the Free Software

    Foundation; either version 2 of the License, or (at your option) any

    later version.

or both in parallel, as here.

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 General Public License

for more details.

You should have received copies of the GNU General Public License and the

GNU Lesser General Public License along with the GNU MP Library.  If not,

see https://www.gnu.org/licenses/.  */

#include "gmp.h"

#include "gmp-impl.h"

#include "longlong.h"

void

mpn_mod_1s_4p_cps (mp_limb_t cps[7], mp_limb_t b)

{

  mp_limb_t bi;

  mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb;

  int cnt;

  ASSERT (b <= (~(mp_limb_t) 0) / 4);

  count_leading_zeros (cnt, b);

  b <<= cnt;

  invert_limb (bi, b);

  cps[0] = bi;

  cps[1] = cnt;

  B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt));

  ASSERT (B1modb <= b);		/* NB: not fully reduced mod b */

  cps[2] = B1modb >> cnt;

  udiv_rnnd_preinv (B2modb, B1modb, CNST_LIMB(0), b, bi);

  cps[3] = B2modb >> cnt;

  udiv_rnnd_preinv (B3modb, B2modb, CNST_LIMB(0), b, bi);

  cps[4] = B3modb >> cnt;

  udiv_rnnd_preinv (B4modb, B3modb, CNST_LIMB(0), b, bi);

  cps[5] = B4modb >> cnt;

  udiv_rnnd_preinv (B5modb, B4modb, CNST_LIMB(0), b, bi);

  cps[6] = B5modb >> cnt;

#if WANT_ASSERT

  {

    int i;

    b = cps[2];

    for (i = 3; i <= 6; i++)

      {

	b += cps[i];

	ASSERT (b >= cps[i]);

      }

  }

#endif

}

mp_limb_t

mpn_mod_1s_4p (mp_srcptr ap, mp_size_t n, mp_limb_t b, const mp_limb_t cps[7])

{

  mp_limb_t rh, rl, bi, ph, pl, ch, cl, r;

  mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb;

  mp_size_t i;

  int cnt;

  ASSERT (n >= 1);

  B1modb = cps[2];

  B2modb = cps[3];

  B3modb = cps[4];

  B4modb = cps[5];

  B5modb = cps[6];

  switch (n & 3)

    {

    case 0:

      umul_ppmm (ph, pl, ap[n - 3], B1modb);

      add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 4]);

      umul_ppmm (ch, cl, ap[n - 2], B2modb);

      add_ssaaaa (ph, pl, ph, pl, ch, cl);

      umul_ppmm (rh, rl, ap[n - 1], B3modb);

      add_ssaaaa (rh, rl, rh, rl, ph, pl);

      n -= 4;

      break;

    case 1:

      rh = 0;

      rl = ap[n - 1];

      n -= 1;

      break;

    case 2:

      rh = ap[n - 1];

      rl = ap[n - 2];

      n -= 2;

      break;

    case 3:

      umul_ppmm (ph, pl, ap[n - 2], B1modb);

      add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 3]);

      umul_ppmm (rh, rl, ap[n - 1], B2modb);

      add_ssaaaa (rh, rl, rh, rl, ph, pl);

      n -= 3;

      break;

    }

  for (i = n - 4; i >= 0; i -= 4)

    {

      /* rr = ap[i]				< B

	    + ap[i+1] * (B mod b)		<= (B-1)(b-1)

	    + ap[i+2] * (B^2 mod b)		<= (B-1)(b-1)

	    + ap[i+3] * (B^3 mod b)		<= (B-1)(b-1)

	    + LO(rr)  * (B^4 mod b)		<= (B-1)(b-1)

	    + HI(rr)  * (B^5 mod b)		<= (B-1)(b-1)

      */

      umul_ppmm (ph, pl, ap[i + 1], B1modb);

      add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[i + 0]);

      umul_ppmm (ch, cl, ap[i + 2], B2modb);

      add_ssaaaa (ph, pl, ph, pl, ch, cl);

      umul_ppmm (ch, cl, ap[i + 3], B3modb);

      add_ssaaaa (ph, pl, ph, pl, ch, cl);

      umul_ppmm (ch, cl, rl, B4modb);

      add_ssaaaa (ph, pl, ph, pl, ch, cl);

      umul_ppmm (rh, rl, rh, B5modb);

      add_ssaaaa (rh, rl, rh, rl, ph, pl);

    }

  umul_ppmm (rh, cl, rh, B1modb);

  add_ssaaaa (rh, rl, rh, rl, CNST_LIMB(0), cl);

  cnt = cps[1];

  bi = cps[0];

  r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));

  udiv_rnnd_preinv (r, r, rl << cnt, b, bi);

  return r >> cnt;

}