gnupg/mpi/mpih-div.c

/* mpihelp-div.c  -  MPI helper functions
 *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
 *	Copyright (C) 1998, 1999 Free Software Foundation, Inc.
 *
 * This file is part of GnuPG.
 *
 * GnuPG is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or
 * (at your option) any later version.
 *
 * GnuPG 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 a copy of the GNU General Public License
 * along with this program; if not, see <http://www.gnu.org/licenses/>.
 *
 * 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.
 *	 The GNU MP Library itself is published under the LGPL;
 *	 however I decided to publish this code under the plain GPL.
 */

#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
mpihelp_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;
    int dummy;

    /* 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
mpihelp_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:
	/* We are asked to divide by zero, so go ahead and do it!  (To make
	   the compiler not remove this statement, return the value.)  */
	return 1 / dsize;

      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 || mpihelp_cmp(np, dp, dsize - 1) >= 0 ) {
		    mpihelp_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 = mpihelp_submul_1(np, dp, dsize, q);

		if( n2 != cy_limb ) {
		    mpihelp_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
mpihelp_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;
    int dummy;

    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;
    }
}