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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 <config.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <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);
+ }
+}
+
+
+/* This should be made into an inline function in gmp.h. */
+void
+mpihelp_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 )
+ mpih_sqr_n_basecase( prodp, up, size );
+ else {
+ mpi_ptr_t tspace;
+ secure = m_is_secure( up );
+ tspace = mpi_alloc_limb_space( 2 * size, secure );
+ mpih_sqr_n( prodp, up, size, tspace );
+ mpi_free_limb_space( tspace );
+ }
+ }
+ else {
+ if( size < KARATSUBA_THRESHOLD )
+ mul_n_basecase( prodp, up, vp, size );
+ else {
+ mpi_ptr_t tspace;
+ secure = m_is_secure( up ) || m_is_secure( vp );
+ tspace = mpi_alloc_limb_space( 2 * size, secure );
+ mul_n (prodp, up, vp, size, tspace);
+ mpi_free_limb_space( tspace );
+ }
+ }
+}
+
+
+
+void
+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,
+ m_is_secure( up ) || m_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 )
+ mpi_free_limb_space( ctx->tp );
+ ctx->tp = mpi_alloc_limb_space( 2 * vsize, m_is_secure( up )
+ || m_is_secure( vp ) );
+ 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 ) {
+ mpihelp_mul( ctx->tspace, vp, vsize, up, usize );
+ }
+ else {
+ if( !ctx->next ) {
+ ctx->next = m_alloc_clear( sizeof *ctx );
+ }
+ mpihelp_mul_karatsuba_case( ctx->tspace,
+ vp, vsize,
+ up, usize,
+ ctx->next );
+ }
+
+ cy = mpihelp_add_n( prodp, prodp, ctx->tspace, vsize);
+ mpihelp_add_1( prodp + vsize, ctx->tspace + vsize, usize, cy );
+ }
+}
+
+
+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 );
+ m_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
+mpihelp_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 = 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++;
+ }
+
+ return cy;
+ }
+
+ memset( &ctx, 0, sizeof ctx );
+ mpihelp_mul_karatsuba_case( prodp, up, usize, vp, vsize, &ctx );
+ mpihelp_release_karatsuba_ctx( &ctx );
+ return *prod_endp;
+}
+
+
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