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[grub2.git] / grub-core / lib / libgcrypt-grub / mpi / mpih-mul.c

/* This file was automatically imported with 
   import_gcry.py. Please don't modify it */
/* mpih-mul.c  -  MPI helper functions
 * Copyright (C) 1994, 1996, 1998, 1999, 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 <string.h>
#include "mpi-internal.h"
#include "longlong.h"
#include "g10lib.h"

#define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \
    do {                                                \
        if( (size) < KARATSUBA_THRESHOLD )              \
            mul_n_basecase (prodp, up, vp, size);       \
        else                                            \
            mul_n (prodp, up, vp, size, tspace);        \
    } while (0);

#define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \
    do {                                            \
        if ((size) < KARATSUBA_THRESHOLD)           \
            _gcry_mpih_sqr_n_basecase (prodp, up, size);         \
        else                                        \
            _gcry_mpih_sqr_n (prodp, up, size, tspace);  \
    } while (0);




/* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
 * both with SIZE limbs, and store the result at PRODP.  2 * SIZE limbs are
 * always stored.  Return the most significant limb.
 *
 * Argument constraints:
 * 1. PRODP != UP and PRODP != VP, i.e. the destination
 *    must be distinct from the multiplier and the multiplicand.
 *
 *
 * Handle simple cases with traditional multiplication.
 *
 * This is the most critical code of multiplication.  All multiplies rely
 * on this, both small and huge.  Small ones arrive here immediately.  Huge
 * ones arrive here as this is the base case for Karatsuba's recursive
 * algorithm below.
 */

static mpi_limb_t
mul_n_basecase( mpi_ptr_t prodp, mpi_ptr_t up,
                                 mpi_ptr_t vp, mpi_size_t size)
{
    mpi_size_t i;
    mpi_limb_t cy;
    mpi_limb_t v_limb;

    /* Multiply by the first limb in V separately, as the result can be
     * stored (not added) to PROD.  We also avoid a loop for zeroing.  */
    v_limb = vp[0];
    if( v_limb <= 1 ) {
        if( v_limb == 1 )
            MPN_COPY( prodp, up, size );
        else
            MPN_ZERO( prodp, size );
        cy = 0;
    }
    else
        cy = _gcry_mpih_mul_1( prodp, up, size, v_limb );

    prodp[size] = cy;
    prodp++;

    /* For each iteration in the outer loop, multiply one limb from
     * U with one limb from V, and add it to PROD.  */
    for( i = 1; i < size; i++ ) {
        v_limb = vp[i];
        if( v_limb <= 1 ) {
            cy = 0;
            if( v_limb == 1 )
               cy = _gcry_mpih_add_n(prodp, prodp, up, size);
        }
        else
            cy = _gcry_mpih_addmul_1(prodp, up, size, v_limb);

        prodp[size] = cy;
        prodp++;
    }

    return cy;
}


static void
mul_n( mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
                        mpi_size_t size, mpi_ptr_t tspace )
{
    if( size & 1 ) {
      /* The size is odd, and the code below doesn't handle that.
       * Multiply the least significant (size - 1) limbs with a recursive
       * call, and handle the most significant limb of S1 and S2
       * separately.
       * A slightly faster way to do this would be to make the Karatsuba
       * code below behave as if the size were even, and let it check for
       * odd size in the end.  I.e., in essence move this code to the end.
       * Doing so would save us a recursive call, and potentially make the
       * stack grow a lot less.
       */
      mpi_size_t esize = size - 1;       /* even size */
      mpi_limb_t cy_limb;

      MPN_MUL_N_RECURSE( prodp, up, vp, esize, tspace );
      cy_limb = _gcry_mpih_addmul_1( prodp + esize, up, esize, vp[esize] );
      prodp[esize + esize] = cy_limb;
      cy_limb = _gcry_mpih_addmul_1( prodp + esize, vp, size, up[esize] );
      prodp[esize + size] = cy_limb;
    }
    else {
        /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
         *
         * Split U in two pieces, U1 and U0, such that
         * U = U0 + U1*(B**n),
         * and V in V1 and V0, such that
         * V = V0 + V1*(B**n).
         *
         * UV is then computed recursively using the identity
         *
         *        2n   n          n                     n
         * UV = (B  + B )U V  +  B (U -U )(V -V )  +  (B + 1)U V
         *                1 1        1  0   0  1              0 0
         *
         * Where B = 2**BITS_PER_MP_LIMB.
         */
        mpi_size_t hsize = size >> 1;
        mpi_limb_t cy;
        int negflg;

        /* Product H.      ________________  ________________
         *                |_____U1 x V1____||____U0 x V0_____|
         * Put result in upper part of PROD and pass low part of TSPACE
         * as new TSPACE.
         */
        MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize, tspace);

        /* Product M.      ________________
         *                |_(U1-U0)(V0-V1)_|
         */
        if( _gcry_mpih_cmp(up + hsize, up, hsize) >= 0 ) {
            _gcry_mpih_sub_n(prodp, up + hsize, up, hsize);
            negflg = 0;
        }
        else {
            _gcry_mpih_sub_n(prodp, up, up + hsize, hsize);
            negflg = 1;
        }
        if( _gcry_mpih_cmp(vp + hsize, vp, hsize) >= 0 ) {
            _gcry_mpih_sub_n(prodp + hsize, vp + hsize, vp, hsize);
            negflg ^= 1;
        }
        else {
            _gcry_mpih_sub_n(prodp + hsize, vp, vp + hsize, hsize);
            /* No change of NEGFLG.  */
        }
        /* Read temporary operands from low part of PROD.
         * Put result in low part of TSPACE using upper part of TSPACE
         * as new TSPACE.
         */
        MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize, tspace + size);

        /* Add/copy product H. */
        MPN_COPY (prodp + hsize, prodp + size, hsize);
        cy = _gcry_mpih_add_n( prodp + size, prodp + size,
                            prodp + size + hsize, hsize);

        /* Add product M (if NEGFLG M is a negative number) */
        if(negflg)
            cy -= _gcry_mpih_sub_n(prodp + hsize, prodp + hsize, tspace, size);
        else
            cy += _gcry_mpih_add_n(prodp + hsize, prodp + hsize, tspace, size);

        /* Product L.      ________________  ________________
         *                |________________||____U0 x V0_____|
         * Read temporary operands from low part of PROD.
         * Put result in low part of TSPACE using upper part of TSPACE
         * as new TSPACE.
         */
        MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size);

        /* Add/copy Product L (twice) */

        cy += _gcry_mpih_add_n(prodp + hsize, prodp + hsize, tspace, size);
        if( cy )
          _gcry_mpih_add_1(prodp + hsize + size, prodp + hsize + size, hsize, cy);

        MPN_COPY(prodp, tspace, hsize);
        cy = _gcry_mpih_add_n(prodp + hsize, prodp + hsize, tspace + hsize, hsize);
        if( cy )
            _gcry_mpih_add_1(prodp + size, prodp + size, size, 1);
    }
}


void
_gcry_mpih_sqr_n_basecase( mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size )
{
    mpi_size_t i;
    mpi_limb_t cy_limb;
    mpi_limb_t v_limb;

    /* Multiply by the first limb in V separately, as the result can be
     * stored (not added) to PROD.  We also avoid a loop for zeroing.  */
    v_limb = up[0];
    if( v_limb <= 1 ) {
        if( v_limb == 1 )
            MPN_COPY( prodp, up, size );
        else
            MPN_ZERO(prodp, size);
        cy_limb = 0;
    }
    else
        cy_limb = _gcry_mpih_mul_1( prodp, up, size, v_limb );

    prodp[size] = cy_limb;
    prodp++;

    /* For each iteration in the outer loop, multiply one limb from
     * U with one limb from V, and add it to PROD.  */
    for( i=1; i < size; i++) {
        v_limb = up[i];
        if( v_limb <= 1 ) {
            cy_limb = 0;
            if( v_limb == 1 )
                cy_limb = _gcry_mpih_add_n(prodp, prodp, up, size);
        }
        else
            cy_limb = _gcry_mpih_addmul_1(prodp, up, size, v_limb);

        prodp[size] = cy_limb;
        prodp++;
    }
}


void
_gcry_mpih_sqr_n( mpi_ptr_t prodp,
                  mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace)
{
    if( size & 1 ) {
        /* The size is odd, and the code below doesn't handle that.
         * Multiply the least significant (size - 1) limbs with a recursive
         * call, and handle the most significant limb of S1 and S2
         * separately.
         * A slightly faster way to do this would be to make the Karatsuba
         * code below behave as if the size were even, and let it check for
         * odd size in the end.  I.e., in essence move this code to the end.
         * Doing so would save us a recursive call, and potentially make the
         * stack grow a lot less.
         */
        mpi_size_t esize = size - 1;       /* even size */
        mpi_limb_t cy_limb;

        MPN_SQR_N_RECURSE( prodp, up, esize, tspace );
        cy_limb = _gcry_mpih_addmul_1( prodp + esize, up, esize, up[esize] );
        prodp[esize + esize] = cy_limb;
        cy_limb = _gcry_mpih_addmul_1( prodp + esize, up, size, up[esize] );

        prodp[esize + size] = cy_limb;
    }
    else {
        mpi_size_t hsize = size >> 1;
        mpi_limb_t cy;

        /* Product H.      ________________  ________________
         *                |_____U1 x U1____||____U0 x U0_____|
         * Put result in upper part of PROD and pass low part of TSPACE
         * as new TSPACE.
         */
        MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace);

        /* Product M.      ________________
         *                |_(U1-U0)(U0-U1)_|
         */
        if( _gcry_mpih_cmp( up + hsize, up, hsize) >= 0 )
            _gcry_mpih_sub_n( prodp, up + hsize, up, hsize);
        else
            _gcry_mpih_sub_n (prodp, up, up + hsize, hsize);

        /* Read temporary operands from low part of PROD.
         * Put result in low part of TSPACE using upper part of TSPACE
         * as new TSPACE.  */
        MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size);

        /* Add/copy product H  */
        MPN_COPY(prodp + hsize, prodp + size, hsize);
        cy = _gcry_mpih_add_n(prodp + size, prodp + size,
                           prodp + size + hsize, hsize);

        /* Add product M (if NEGFLG M is a negative number).  */
        cy -= _gcry_mpih_sub_n (prodp + hsize, prodp + hsize, tspace, size);

        /* Product L.      ________________  ________________
         *                |________________||____U0 x U0_____|
         * Read temporary operands from low part of PROD.
         * Put result in low part of TSPACE using upper part of TSPACE
         * as new TSPACE.  */
        MPN_SQR_N_RECURSE (tspace, up, hsize, tspace + size);

        /* Add/copy Product L (twice).  */
        cy += _gcry_mpih_add_n (prodp + hsize, prodp + hsize, tspace, size);
        if( cy )
            _gcry_mpih_add_1(prodp + hsize + size, prodp + hsize + size,
                                                            hsize, cy);

        MPN_COPY(prodp, tspace, hsize);
        cy = _gcry_mpih_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize);
        if( cy )
            _gcry_mpih_add_1 (prodp + size, prodp + size, size, 1);
    }
}


/* This should be made into an inline function in gmp.h.  */
void
_gcry_mpih_mul_n( mpi_ptr_t prodp,
                     mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
{
    int secure;

    if( up == vp ) {
        if( size < KARATSUBA_THRESHOLD )
            _gcry_mpih_sqr_n_basecase( prodp, up, size );
        else {
            mpi_ptr_t tspace;
            secure = gcry_is_secure( up );
            tspace = mpi_alloc_limb_space( 2 * size, secure );
            _gcry_mpih_sqr_n( prodp, up, size, tspace );
            _gcry_mpi_free_limb_space (tspace, 2 * size );
        }
    }
    else {
        if( size < KARATSUBA_THRESHOLD )
            mul_n_basecase( prodp, up, vp, size );
        else {
            mpi_ptr_t tspace;
            secure = gcry_is_secure( up ) || gcry_is_secure( vp );
            tspace = mpi_alloc_limb_space( 2 * size, secure );
            mul_n (prodp, up, vp, size, tspace);
            _gcry_mpi_free_limb_space (tspace, 2 * size );
        }
    }
}



void
_gcry_mpih_mul_karatsuba_case( mpi_ptr_t prodp,
                                  mpi_ptr_t up, mpi_size_t usize,
                                  mpi_ptr_t vp, mpi_size_t vsize,
                                  struct karatsuba_ctx *ctx )
{
    mpi_limb_t cy;

    if( !ctx->tspace || ctx->tspace_size < vsize ) {
        if( ctx->tspace )
            _gcry_mpi_free_limb_space( ctx->tspace, ctx->tspace_nlimbs );
        ctx->tspace_nlimbs = 2 * vsize;
        ctx->tspace = mpi_alloc_limb_space( 2 * vsize,
                                            (gcry_is_secure( up )
                                            || gcry_is_secure( vp )) );
        ctx->tspace_size = vsize;
    }

    MPN_MUL_N_RECURSE( prodp, up, vp, vsize, ctx->tspace );

    prodp += vsize;
    up += vsize;
    usize -= vsize;
    if( usize >= vsize ) {
        if( !ctx->tp || ctx->tp_size < vsize ) {
            if( ctx->tp )
                _gcry_mpi_free_limb_space( ctx->tp, ctx->tp_nlimbs );
            ctx->tp_nlimbs = 2 * vsize;
            ctx->tp = mpi_alloc_limb_space( 2 * vsize, gcry_is_secure( up )
                                                      || gcry_is_secure( vp ) );
            ctx->tp_size = vsize;
        }

        do {
            MPN_MUL_N_RECURSE( ctx->tp, up, vp, vsize, ctx->tspace );
            cy = _gcry_mpih_add_n( prodp, prodp, ctx->tp, vsize );
            _gcry_mpih_add_1( prodp + vsize, ctx->tp + vsize, vsize, cy );
            prodp += vsize;
            up += vsize;
            usize -= vsize;
        } while( usize >= vsize );
    }

    if( usize ) {
        if( usize < KARATSUBA_THRESHOLD ) {
            _gcry_mpih_mul( ctx->tspace, vp, vsize, up, usize );
        }
        else {
            if( !ctx->next ) {
                ctx->next = gcry_xcalloc( 1, sizeof *ctx );
            }
            _gcry_mpih_mul_karatsuba_case( ctx->tspace,
                                        vp, vsize,
                                        up, usize,
                                        ctx->next );
        }

        cy = _gcry_mpih_add_n( prodp, prodp, ctx->tspace, vsize);
        _gcry_mpih_add_1( prodp + vsize, ctx->tspace + vsize, usize, cy );
    }
}


void
_gcry_mpih_release_karatsuba_ctx( struct karatsuba_ctx *ctx )
{
    struct karatsuba_ctx *ctx2;

    if( ctx->tp )
        _gcry_mpi_free_limb_space( ctx->tp, ctx->tp_nlimbs );
    if( ctx->tspace )
        _gcry_mpi_free_limb_space( ctx->tspace, ctx->tspace_nlimbs );
    for( ctx=ctx->next; ctx; ctx = ctx2 ) {
        ctx2 = ctx->next;
        if( ctx->tp )
            _gcry_mpi_free_limb_space( ctx->tp, ctx->tp_nlimbs );
        if( ctx->tspace )
            _gcry_mpi_free_limb_space( ctx->tspace, ctx->tspace_nlimbs );
        gcry_free( ctx );
    }
}

/* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
 * and v (pointed to by VP, with VSIZE limbs), and store the result at
 * PRODP.  USIZE + VSIZE limbs are always stored, but if the input
 * operands are normalized.  Return the most significant limb of the
 * result.
 *
 * NOTE: The space pointed to by PRODP is overwritten before finished
 * with U and V, so overlap is an error.
 *
 * Argument constraints:
 * 1. USIZE >= VSIZE.
 * 2. PRODP != UP and PRODP != VP, i.e. the destination
 *    must be distinct from the multiplier and the multiplicand.
 */

mpi_limb_t
_gcry_mpih_mul( mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
                   mpi_ptr_t vp, mpi_size_t vsize)
{
    mpi_ptr_t prod_endp = prodp + usize + vsize - 1;
    mpi_limb_t cy;
    struct karatsuba_ctx ctx;

    if( vsize < KARATSUBA_THRESHOLD ) {
        mpi_size_t i;
        mpi_limb_t v_limb;

        if( !vsize )
            return 0;

        /* Multiply by the first limb in V separately, as the result can be
         * stored (not added) to PROD.  We also avoid a loop for zeroing.  */
        v_limb = vp[0];
        if( v_limb <= 1 ) {
            if( v_limb == 1 )
                MPN_COPY( prodp, up, usize );
            else
                MPN_ZERO( prodp, usize );
            cy = 0;
        }
        else
            cy = _gcry_mpih_mul_1( prodp, up, usize, v_limb );

        prodp[usize] = cy;
        prodp++;

        /* For each iteration in the outer loop, multiply one limb from
         * U with one limb from V, and add it to PROD.  */
        for( i = 1; i < vsize; i++ ) {
            v_limb = vp[i];
            if( v_limb <= 1 ) {
                cy = 0;
                if( v_limb == 1 )
                   cy = _gcry_mpih_add_n(prodp, prodp, up, usize);
            }
            else
                cy = _gcry_mpih_addmul_1(prodp, up, usize, v_limb);

            prodp[usize] = cy;
            prodp++;
        }

        return cy;
    }

    memset( &ctx, 0, sizeof ctx );
    _gcry_mpih_mul_karatsuba_case( prodp, up, usize, vp, vsize, &ctx );
    _gcry_mpih_release_karatsuba_ctx( &ctx );
    return *prod_endp;
}