/* mpn_sec_pi1_div_qr, mpn_sec_pi1_div_r -- Compute Q = floor(U / V), U = U

   mod V.  Side-channel silent under the assumption that the used instructions

   are side-channel silent.

   Contributed to the GNU project by Torbjörn Granlund.

   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 2011-2013 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-impl.h"

#include "longlong.h"

/* This side-channel silent division algorithm reduces the partial remainder by

   GMP_NUMB_BITS/2 bits at a time, compared to GMP_NUMB_BITS for the main

   division algorithm.  We actually do not insist on reducing by exactly

   GMP_NUMB_BITS/2, but may leave a partial remainder that is D*B^i to 3D*B^i

   too large (B is the limb base, D is the divisor, and i is the induction

   variable); the subsequent step will handle the extra partial remainder bits.

   With that partial remainder reduction, each step generates a quotient "half

   limb".  The outer loop generates two quotient half limbs, an upper (q1h) and

   a lower (q0h) which are stored sparsely in separate limb arrays.  These

   arrays are added at the end; using separate arrays avoids data-dependent

   carry propagation which could else pose a side-channel leakage problem.

   The quotient half limbs may be between -3 to 0 from the accurate value

   ("accurate" being the one which corresponds to a reduction to a principal

   partial remainder).  Too small quotient half limbs correspond to too large

   remainders, which we reduce later, as described above.

   In order to keep quotients from getting too big, corresponding to a negative

   partial remainder, we use an inverse which is slightly smaller than usually.

*/

#if OPERATION_sec_pi1_div_qr

/* Needs (dn + 1) + (nn - dn) + (nn - dn) = 2nn - dn + 1 limbs at tp. */

#define FNAME mpn_sec_pi1_div_qr

#define Q(q) q,

#define RETTYPE mp_limb_t

#endif

#if OPERATION_sec_pi1_div_r

/* Needs (dn + 1) limbs at tp.  */

#define FNAME mpn_sec_pi1_div_r

#define Q(q)

#define RETTYPE void

#endif

RETTYPE

FNAME (Q(mp_ptr qp)

       mp_ptr np, mp_size_t nn,

       mp_srcptr dp, mp_size_t dn,

       mp_limb_t dinv,

       mp_ptr tp)

{

  mp_limb_t nh, cy, q1h, q0h, dummy, cnd;

  mp_size_t i;

  mp_ptr hp;

#if OPERATION_sec_pi1_div_qr

  mp_limb_t qh;

  mp_ptr qlp, qhp;

#endif

  ASSERT (dn >= 1);

  ASSERT (nn >= dn);

  ASSERT ((dp[dn - 1] & GMP_NUMB_HIGHBIT) != 0);

  if (nn == dn)

    {

      cy = mpn_sub_n (np, np, dp, dn);

      mpn_cnd_add_n (cy, np, np, dp, dn);

#if OPERATION_sec_pi1_div_qr

      return 1 - cy;

#else

      return;

#endif

    }

  /* Create a divisor copy shifted half a limb.  */

  hp = tp;          /* (dn + 1) limbs */

  hp[dn] = mpn_lshift (hp, dp, dn, GMP_NUMB_BITS / 2);

#if OPERATION_sec_pi1_div_qr

  qlp = tp + (dn + 1);        /* (nn - dn) limbs */

  qhp = tp + (nn + 1);        /* (nn - dn) limbs */

#endif

  np += nn - dn;

  nh = 0;

  for (i = nn - dn - 1; i >= 0; i--)

    {

      np--;

      nh = (nh << GMP_NUMB_BITS/2) + (np[dn] >> GMP_NUMB_BITS/2);

      umul_ppmm (q1h, dummy, nh, dinv);

      q1h += nh;

#if OPERATION_sec_pi1_div_qr

      qhp[i] = q1h;

#endif

      mpn_submul_1 (np, hp, dn + 1, q1h);

      nh = np[dn];

      umul_ppmm (q0h, dummy, nh, dinv);

      q0h += nh;

#if OPERATION_sec_pi1_div_qr

      qlp[i] = q0h;

#endif

      nh -= mpn_submul_1 (np, dp, dn, q0h);

    }

  /* 1st adjustment depends on extra high remainder limb.  */

  cnd = nh != 0;        /* FIXME: cmp-to-int */

#if OPERATION_sec_pi1_div_qr

  qlp[0] += cnd;

#endif

  nh -= mpn_cnd_sub_n (cnd, np, np, dp, dn);

  /* 2nd adjustment depends on remainder/divisor comparison as well as whether

     extra remainder limb was nullified by previous subtract.  */

  cy = mpn_sub_n (np, np, dp, dn);

  cy = cy - nh;

#if OPERATION_sec_pi1_div_qr

  qlp[0] += 1 - cy;

#endif

  mpn_cnd_add_n (cy, np, np, dp, dn);

  /* 3rd adjustment depends on remainder/divisor comparison.  */

  cy = mpn_sub_n (np, np, dp, dn);

#if OPERATION_sec_pi1_div_qr

  qlp[0] += 1 - cy;

#endif

  mpn_cnd_add_n (cy, np, np, dp, dn);

#if OPERATION_sec_pi1_div_qr

  /* Combine quotient halves into final quotient.  */

  qh = mpn_lshift (qhp, qhp, nn - dn, GMP_NUMB_BITS/2);

  qh += mpn_add_n (qp, qhp, qlp, nn - dn);

  return qh;

#else

  return;

#endif

}