/* mpih-div.c  -  MPI helper functions

 * Copyright (C) 1994, 1996, 1998, 2000,

 *               2001, 2002 Free Software Foundation, Inc.

 *

 * This file is part of Libgcrypt.

 *

 * Libgcrypt 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.

 *

 * Libgcrypt 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 this program; if not, write to the Free Software

 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA

 *

 * Note: This code is heavily based on the GNU MP Library.

 *   Actually it's the same code with only minor changes in the

 *   way the data is stored; this is to support the abstraction

 *   of an optional secure memory allocation which may be used

 *   to avoid revealing of sensitive data due to paging etc.

 */

#include <config.h>

#include <stdio.h>

#include <stdlib.h>

#include "mpi-internal.h"

#include "longlong.h"

#ifndef UMUL_TIME

#define UMUL_TIME 1

#endif

#ifndef UDIV_TIME

#define UDIV_TIME UMUL_TIME

#endif

/* FIXME: We should be using invert_limb (or invert_normalized_limb)

 * here (not udiv_qrnnd).

 */

mpi_limb_t

_gcry_mpih_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,

              mpi_limb_t divisor_limb)

{

    mpi_size_t i;

    mpi_limb_t n1, n0, r;

    mpi_limb_t dummy GCC_ATTR_UNUSED;

    /* Botch: Should this be handled at all?  Rely on callers?  */

    if( !dividend_size )

  return 0;

    /* If multiplication is much faster than division, and the

     * dividend is large, pre-invert the divisor, and use

     * only multiplications in the inner loop.

     *

     * This test should be read:

     *   Does it ever help to use udiv_qrnnd_preinv?

     *     && Does what we save compensate for the inversion overhead?

     */

    if( UDIV_TIME > (2 * UMUL_TIME + 6)

  && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {

  int normalization_steps;

  count_leading_zeros( normalization_steps, divisor_limb );

  if( normalization_steps ) {

      mpi_limb_t divisor_limb_inverted;

      divisor_limb <<= normalization_steps;

      /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The

       * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the

       * most significant bit (with weight 2**N) implicit.

       *

       * Special case for DIVISOR_LIMB == 100...000.

       */

      if( !(divisor_limb << 1) )

    divisor_limb_inverted = ~(mpi_limb_t)0;

      else

    udiv_qrnnd(divisor_limb_inverted, dummy,

         -divisor_limb, 0, divisor_limb);

      n1 = dividend_ptr[dividend_size - 1];

      r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

      /* Possible optimization:

       * if (r == 0

       * && divisor_limb > ((n1 << normalization_steps)

       *           | (dividend_ptr[dividend_size - 2] >> ...)))

       * ...one division less...

       */

      for( i = dividend_size - 2; i >= 0; i--) {

    n0 = dividend_ptr[i];

    UDIV_QRNND_PREINV(dummy, r, r,

           ((n1 << normalization_steps)

        | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),

        divisor_limb, divisor_limb_inverted);

    n1 = n0;

      }

      UDIV_QRNND_PREINV(dummy, r, r,

            n1 << normalization_steps,

            divisor_limb, divisor_limb_inverted);

      return r >> normalization_steps;

  }

  else {

      mpi_limb_t divisor_limb_inverted;

      /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The

       * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the

       * most significant bit (with weight 2**N) implicit.

       *

       * Special case for DIVISOR_LIMB == 100...000.

       */

      if( !(divisor_limb << 1) )

    divisor_limb_inverted = ~(mpi_limb_t)0;

      else

    udiv_qrnnd(divisor_limb_inverted, dummy,

          -divisor_limb, 0, divisor_limb);

      i = dividend_size - 1;

      r = dividend_ptr[i];

      if( r >= divisor_limb )

    r = 0;

      else

    i--;

      for( ; i >= 0; i--) {

    n0 = dividend_ptr[i];

    UDIV_QRNND_PREINV(dummy, r, r,

          n0, divisor_limb, divisor_limb_inverted);

      }

      return r;

  }

    }

    else {

  if( UDIV_NEEDS_NORMALIZATION ) {

      int normalization_steps;

      count_leading_zeros(normalization_steps, divisor_limb);

      if( normalization_steps ) {

    divisor_limb <<= normalization_steps;

    n1 = dividend_ptr[dividend_size - 1];

    r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

    /* Possible optimization:

     * if (r == 0

     * && divisor_limb > ((n1 << normalization_steps)

     *       | (dividend_ptr[dividend_size - 2] >> ...)))

     * ...one division less...

     */

    for(i = dividend_size - 2; i >= 0; i--) {

        n0 = dividend_ptr[i];

        udiv_qrnnd (dummy, r, r,

        ((n1 << normalization_steps)

       | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),

       divisor_limb);

        n1 = n0;

    }

    udiv_qrnnd (dummy, r, r,

          n1 << normalization_steps,

          divisor_limb);

    return r >> normalization_steps;

      }

  }

  /* No normalization needed, either because udiv_qrnnd doesn't require

   * it, or because DIVISOR_LIMB is already normalized.  */

  i = dividend_size - 1;

  r = dividend_ptr[i];

  if(r >= divisor_limb)

      r = 0;

  else

      i--;

  for(; i >= 0; i--) {

      n0 = dividend_ptr[i];

      udiv_qrnnd (dummy, r, r, n0, divisor_limb);

  }

  return r;

    }

}

/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write

 * the NSIZE-DSIZE least significant quotient limbs at QP

 * and the DSIZE long remainder at NP.  If QEXTRA_LIMBS is

 * non-zero, generate that many fraction bits and append them after the

 * other quotient limbs.

 * Return the most significant limb of the quotient, this is always 0 or 1.

 *

 * Preconditions:

 * 0. NSIZE >= DSIZE.

 * 1. The most significant bit of the divisor must be set.

 * 2. QP must either not overlap with the input operands at all, or

 *    QP + DSIZE >= NP must hold true.  (This means that it's

 *    possible to put the quotient in the high part of NUM, right after the

 *    remainder in NUM.

 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.

 */

mpi_limb_t

_gcry_mpih_divrem( mpi_ptr_t qp, mpi_size_t qextra_limbs,

                      mpi_ptr_t np, mpi_size_t nsize,

                      mpi_ptr_t dp, mpi_size_t dsize)

{

    mpi_limb_t most_significant_q_limb = 0;

    switch(dsize) {

      case 0:

  _gcry_divide_by_zero();

  break;

      case 1:

  {

      mpi_size_t i;

      mpi_limb_t n1;

      mpi_limb_t d;

      d = dp[0];

      n1 = np[nsize - 1];

      if( n1 >= d ) {

    n1 -= d;

    most_significant_q_limb = 1;

      }

      qp += qextra_limbs;

      for( i = nsize - 2; i >= 0; i--)

    udiv_qrnnd( qp[i], n1, n1, np[i], d );

      qp -= qextra_limbs;

      for( i = qextra_limbs - 1; i >= 0; i-- )

    udiv_qrnnd (qp[i], n1, n1, 0, d);

      np[0] = n1;

  }

  break;

      case 2:

  {

      mpi_size_t i;

      mpi_limb_t n1, n0, n2;

      mpi_limb_t d1, d0;

      np += nsize - 2;

      d1 = dp[1];

      d0 = dp[0];

      n1 = np[1];

      n0 = np[0];

      if( n1 >= d1 && (n1 > d1 || n0 >= d0) ) {

    sub_ddmmss (n1, n0, n1, n0, d1, d0);

    most_significant_q_limb = 1;

      }

      for( i = qextra_limbs + nsize - 2 - 1; i >= 0; i-- ) {

    mpi_limb_t q;

    mpi_limb_t r;

    if( i >= qextra_limbs )

        np--;

    else

        np[0] = 0;

    if( n1 == d1 ) {

        /* Q should be either 111..111 or 111..110.  Need special

         * treatment of this rare case as normal division would

         * give overflow.  */

        q = ~(mpi_limb_t)0;

        r = n0 + d1;

        if( r < d1 ) {   /* Carry in the addition? */

      add_ssaaaa( n1, n0, r - d0, np[0], 0, d0 );

      qp[i] = q;

      continue;

        }

        n1 = d0 - (d0 != 0?1:0);

        n0 = -d0;

    }

    else {

        udiv_qrnnd (q, r, n1, n0, d1);

        umul_ppmm (n1, n0, d0, q);

    }

    n2 = np[0];

        q_test:

    if( n1 > r || (n1 == r && n0 > n2) ) {

        /* The estimated Q was too large.  */

        q--;

        sub_ddmmss (n1, n0, n1, n0, 0, d0);

        r += d1;

        if( r >= d1 )    /* If not carry, test Q again.  */

      goto q_test;

    }

    qp[i] = q;

    sub_ddmmss (n1, n0, r, n2, n1, n0);

      }

      np[1] = n1;

      np[0] = n0;

  }

  break;

      default:

  {

      mpi_size_t i;

      mpi_limb_t dX, d1, n0;

      np += nsize - dsize;

      dX = dp[dsize - 1];

      d1 = dp[dsize - 2];

      n0 = np[dsize - 1];

      if( n0 >= dX ) {

    if(n0 > dX || _gcry_mpih_cmp(np, dp, dsize - 1) >= 0 ) {

        _gcry_mpih_sub_n(np, np, dp, dsize);

        n0 = np[dsize - 1];

        most_significant_q_limb = 1;

    }

      }

      for( i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {

    mpi_limb_t q;

    mpi_limb_t n1, n2;

    mpi_limb_t cy_limb;

    if( i >= qextra_limbs ) {

        np--;

        n2 = np[dsize];

    }

    else {

        n2 = np[dsize - 1];

        MPN_COPY_DECR (np + 1, np, dsize - 1);

        np[0] = 0;

    }

    if( n0 == dX ) {

        /* This might over-estimate q, but it's probably not worth

         * the extra code here to find out.  */

        q = ~(mpi_limb_t)0;

    }

    else {

        mpi_limb_t r;

        udiv_qrnnd(q, r, n0, np[dsize - 1], dX);

        umul_ppmm(n1, n0, d1, q);

        while( n1 > r || (n1 == r && n0 > np[dsize - 2])) {

      q--;

      r += dX;

      if( r < dX ) /* I.e. "carry in previous addition?" */

          break;

      n1 -= n0 < d1;

      n0 -= d1;

        }

    }

    /* Possible optimization: We already have (q * n0) and (1 * n1)

     * after the calculation of q.  Taking advantage of that, we

     * could make this loop make two iterations less.  */

    cy_limb = _gcry_mpih_submul_1(np, dp, dsize, q);

    if( n2 != cy_limb ) {

        _gcry_mpih_add_n(np, np, dp, dsize);

        q--;

    }

    qp[i] = q;

    n0 = np[dsize - 1];

      }

  }

    }

    return most_significant_q_limb;

}

/****************

 * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.

 * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.

 * Return the single-limb remainder.

 * There are no constraints on the value of the divisor.

 *

 * QUOT_PTR and DIVIDEND_PTR might point to the same limb.

 */

mpi_limb_t

_gcry_mpih_divmod_1( mpi_ptr_t quot_ptr,

                        mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,

                        mpi_limb_t divisor_limb)

{

    mpi_size_t i;

    mpi_limb_t n1, n0, r;

    mpi_limb_t dummy GCC_ATTR_UNUSED;

    if( !dividend_size )

  return 0;

    /* If multiplication is much faster than division, and the

     * dividend is large, pre-invert the divisor, and use

     * only multiplications in the inner loop.

     *

     * This test should be read:

     * Does it ever help to use udiv_qrnnd_preinv?

     * && Does what we save compensate for the inversion overhead?

     */

    if( UDIV_TIME > (2 * UMUL_TIME + 6)

  && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {

  int normalization_steps;

  count_leading_zeros( normalization_steps, divisor_limb );

  if( normalization_steps ) {

      mpi_limb_t divisor_limb_inverted;

      divisor_limb <<= normalization_steps;

      /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The

       * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the

       * most significant bit (with weight 2**N) implicit.

       */

      /* Special case for DIVISOR_LIMB == 100...000.  */

      if( !(divisor_limb << 1) )

    divisor_limb_inverted = ~(mpi_limb_t)0;

      else

    udiv_qrnnd(divisor_limb_inverted, dummy,

         -divisor_limb, 0, divisor_limb);

      n1 = dividend_ptr[dividend_size - 1];

      r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

      /* Possible optimization:

       * if (r == 0

       * && divisor_limb > ((n1 << normalization_steps)

       *           | (dividend_ptr[dividend_size - 2] >> ...)))

       * ...one division less...

       */

      for( i = dividend_size - 2; i >= 0; i--) {

    n0 = dividend_ptr[i];

    UDIV_QRNND_PREINV( quot_ptr[i + 1], r, r,

           ((n1 << normalization_steps)

       | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),

            divisor_limb, divisor_limb_inverted);

    n1 = n0;

      }

      UDIV_QRNND_PREINV( quot_ptr[0], r, r,

             n1 << normalization_steps,

             divisor_limb, divisor_limb_inverted);

      return r >> normalization_steps;

  }

  else {

      mpi_limb_t divisor_limb_inverted;

      /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The

       * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the

       * most significant bit (with weight 2**N) implicit.

       */

      /* Special case for DIVISOR_LIMB == 100...000.  */

      if( !(divisor_limb << 1) )

    divisor_limb_inverted = ~(mpi_limb_t) 0;

      else

    udiv_qrnnd(divisor_limb_inverted, dummy,

         -divisor_limb, 0, divisor_limb);

      i = dividend_size - 1;

      r = dividend_ptr[i];

      if( r >= divisor_limb )

    r = 0;

      else

    quot_ptr[i--] = 0;

      for( ; i >= 0; i-- ) {

    n0 = dividend_ptr[i];

    UDIV_QRNND_PREINV( quot_ptr[i], r, r,

           n0, divisor_limb, divisor_limb_inverted);

      }

      return r;

  }

    }

    else {

  if(UDIV_NEEDS_NORMALIZATION) {

      int normalization_steps;

      count_leading_zeros (normalization_steps, divisor_limb);

      if( normalization_steps ) {

    divisor_limb <<= normalization_steps;

    n1 = dividend_ptr[dividend_size - 1];

    r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

    /* Possible optimization:

     * if (r == 0

     * && divisor_limb > ((n1 << normalization_steps)

     *       | (dividend_ptr[dividend_size - 2] >> ...)))

     * ...one division less...

     */

    for( i = dividend_size - 2; i >= 0; i--) {

        n0 = dividend_ptr[i];

        udiv_qrnnd (quot_ptr[i + 1], r, r,

           ((n1 << normalization_steps)

       | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),

        divisor_limb);

        n1 = n0;

    }

    udiv_qrnnd (quot_ptr[0], r, r,

          n1 << normalization_steps,

          divisor_limb);

    return r >> normalization_steps;

      }

  }

  /* No normalization needed, either because udiv_qrnnd doesn't require

   * it, or because DIVISOR_LIMB is already normalized.  */

  i = dividend_size - 1;

  r = dividend_ptr[i];

  if(r >= divisor_limb)

      r = 0;

  else

      quot_ptr[i--] = 0;

  for(; i >= 0; i--) {

      n0 = dividend_ptr[i];

      udiv_qrnnd( quot_ptr[i], r, r, n0, divisor_limb );

  }

  return r;

    }

}