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mpih-mul.c 14.91 KiB
/* 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);
}
}
/* This should be made into an inline function in gmp.h. */
int mpihelp_mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
{
if (up == vp) {
if (size < KARATSUBA_THRESHOLD)
mpih_sqr_n_basecase(prodp, up, size);
else {
mpi_ptr_t tspace;
tspace = mpi_alloc_limb_space(2 * size);
if (!tspace)
return -ENOMEM;
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;
tspace = mpi_alloc_limb_space(2 * size);
if (!tspace)
return -ENOMEM;
mul_n(prodp, up, vp, size, tspace);
mpi_free_limb_space(tspace);
}
}
return 0;
}
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;
}