mpih-mul.c

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/* mpihelp-mul.c  -  MPI helper functions
 * Copyright (C) 1994, 1996, 1998, 1999,
 *               2000 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 2 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, 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.
 *   The GNU MP Library itself is published under the LGPL;
 *   however I decided to publish this code under the plain GPL.
 */

#include <linux/string.h>
#include "mpi-internal.h"
#include "longlong.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)       \
            mpih_sqr_n_basecase(prodp, up, size);   \
        else                        \
            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 = mpihelp_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 = mpihelp_add_n(prodp, prodp, up, size);
        } else
            cy = mpihelp_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 = mpihelp_addmul_1(prodp + esize, up, esize, vp[esize]);
        prodp[esize + esize] = cy_limb;
        cy_limb = mpihelp_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 (mpihelp_cmp(up + hsize, up, hsize) >= 0) {
            mpihelp_sub_n(prodp, up + hsize, up, hsize);
            negflg = 0;
        } else {
            mpihelp_sub_n(prodp, up, up + hsize, hsize);
            negflg = 1;
        }
        if (mpihelp_cmp(vp + hsize, vp, hsize) >= 0) {
            mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize);
            negflg ^= 1;
        } else {
            mpihelp_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 = mpihelp_add_n(prodp + size, prodp + size,
                   prodp + size + hsize, hsize);

        /* Add product M (if NEGFLG M is a negative number) */
        if (negflg)
            cy -=
                mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace,
                      size);
        else
            cy +=
                mpihelp_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 += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
        if (cy)
            mpihelp_add_1(prodp + hsize + size,
                      prodp + hsize + size, hsize, cy);

        MPN_COPY(prodp, tspace, hsize);
        cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
                   hsize);
        if (cy)
            mpihelp_add_1(prodp + size, prodp + size, size, 1);
    }
}

void 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 = mpihelp_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 = mpihelp_add_n(prodp, prodp, up, size);
        } else
            cy_limb = mpihelp_addmul_1(prodp, up, size, v_limb);

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

void
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 = mpihelp_addmul_1(prodp + esize, up, esize, up[esize]);
        prodp[esize + esize] = cy_limb;
        cy_limb = mpihelp_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 (mpihelp_cmp(up + hsize, up, hsize) >= 0)
            mpihelp_sub_n(prodp, up + hsize, up, hsize);
        else
            mpihelp_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 = mpihelp_add_n(prodp + size, prodp + size,
                   prodp + size + hsize, hsize);

        /* Add product M (if NEGFLG M is a negative number).  */
        cy -= mpihelp_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 += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
        if (cy)
            mpihelp_add_1(prodp + hsize + size,
                      prodp + hsize + size, hsize, cy);

        MPN_COPY(prodp, tspace, hsize);
        cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
                   hsize);
        if (cy)
            mpihelp_add_1(prodp + size, prodp + size, size, 1);
    }
}

int
mpihelp_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)
            mpi_free_limb_space(ctx->tspace);
        ctx->tspace = mpi_alloc_limb_space(2 * vsize);
        if (!ctx->tspace)
            return -ENOMEM;
        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)
                mpi_free_limb_space(ctx->tp);
            ctx->tp = mpi_alloc_limb_space(2 * vsize);
            if (!ctx->tp) {
                if (ctx->tspace)
                    mpi_free_limb_space(ctx->tspace);
                ctx->tspace = NULL;
                return -ENOMEM;
            }
            ctx->tp_size = vsize;
        }

        do {
            MPN_MUL_N_RECURSE(ctx->tp, up, vp, vsize, ctx->tspace);
            cy = mpihelp_add_n(prodp, prodp, ctx->tp, vsize);
            mpihelp_add_1(prodp + vsize, ctx->tp + vsize, vsize,
                      cy);
            prodp += vsize;
            up += vsize;
            usize -= vsize;
        } while (usize >= vsize);
    }

    if (usize) {
        if (usize < KARATSUBA_THRESHOLD) {
            mpi_limb_t tmp;
            if (mpihelp_mul(ctx->tspace, vp, vsize, up, usize, &tmp)
                < 0)
                return -ENOMEM;
        } else {
            if (!ctx->next) {
                ctx->next = kzalloc(sizeof *ctx, GFP_KERNEL);
                if (!ctx->next)
                    return -ENOMEM;
            }
            if (mpihelp_mul_karatsuba_case(ctx->tspace,
                               vp, vsize,
                               up, usize,
                               ctx->next) < 0)
                return -ENOMEM;
        }

        cy = mpihelp_add_n(prodp, prodp, ctx->tspace, vsize);
        mpihelp_add_1(prodp + vsize, ctx->tspace + vsize, usize, cy);
    }

    return 0;
}

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

    if (ctx->tp)
        mpi_free_limb_space(ctx->tp);
    if (ctx->tspace)
        mpi_free_limb_space(ctx->tspace);
    for (ctx = ctx->next; ctx; ctx = ctx2) {
        ctx2 = ctx->next;
        if (ctx->tp)
            mpi_free_limb_space(ctx->tp);
        if (ctx->tspace)
            mpi_free_limb_space(ctx->tspace);
        kfree(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.
 */

int
mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
        mpi_ptr_t vp, mpi_size_t vsize, mpi_limb_t *_result)
{
    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) {
            *_result = 0;
            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 = mpihelp_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 = mpihelp_add_n(prodp, prodp, up,
                               usize);
            } else
                cy = mpihelp_addmul_1(prodp, up, usize, v_limb);

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

        *_result = cy;
        return 0;
    }

    memset(&ctx, 0, sizeof ctx);
    if (mpihelp_mul_karatsuba_case(prodp, up, usize, vp, vsize, &ctx) < 0)
        return -ENOMEM;
    mpihelp_release_karatsuba_ctx(&ctx);
    *_result = *prod_endp;
    return 0;
}