498 lines
14 KiB
C
498 lines
14 KiB
C
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/* mpihelp-mul.c - MPI helper functions
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* Copyright (C) 1994, 1996, 1998, 1999,
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* 2000 Free Software Foundation, Inc.
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*
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* This file is part of GnuPG.
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*
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* GnuPG is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* GnuPG is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
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*
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* Note: This code is heavily based on the GNU MP Library.
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* Actually it's the same code with only minor changes in the
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* way the data is stored; this is to support the abstraction
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* of an optional secure memory allocation which may be used
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* to avoid revealing of sensitive data due to paging etc.
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* The GNU MP Library itself is published under the LGPL;
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* however I decided to publish this code under the plain GPL.
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*/
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#include <linux/string.h>
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#include "mpi-internal.h"
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#include "longlong.h"
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#define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \
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do { \
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if ((size) < KARATSUBA_THRESHOLD) \
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mul_n_basecase(prodp, up, vp, size); \
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else \
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mul_n(prodp, up, vp, size, tspace); \
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} while (0);
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#define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \
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do { \
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if ((size) < KARATSUBA_THRESHOLD) \
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mpih_sqr_n_basecase(prodp, up, size); \
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else \
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mpih_sqr_n(prodp, up, size, tspace); \
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} while (0);
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/* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
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* both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are
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* always stored. Return the most significant limb.
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*
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* Argument constraints:
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* 1. PRODP != UP and PRODP != VP, i.e. the destination
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* must be distinct from the multiplier and the multiplicand.
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*
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*
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* Handle simple cases with traditional multiplication.
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*
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* This is the most critical code of multiplication. All multiplies rely
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* on this, both small and huge. Small ones arrive here immediately. Huge
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* ones arrive here as this is the base case for Karatsuba's recursive
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* algorithm below.
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*/
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static mpi_limb_t
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mul_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
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{
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mpi_size_t i;
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mpi_limb_t cy;
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mpi_limb_t v_limb;
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/* Multiply by the first limb in V separately, as the result can be
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* stored (not added) to PROD. We also avoid a loop for zeroing. */
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v_limb = vp[0];
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if (v_limb <= 1) {
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if (v_limb == 1)
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MPN_COPY(prodp, up, size);
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else
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MPN_ZERO(prodp, size);
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cy = 0;
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} else
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cy = mpihelp_mul_1(prodp, up, size, v_limb);
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prodp[size] = cy;
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prodp++;
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/* For each iteration in the outer loop, multiply one limb from
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* U with one limb from V, and add it to PROD. */
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for (i = 1; i < size; i++) {
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v_limb = vp[i];
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if (v_limb <= 1) {
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cy = 0;
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if (v_limb == 1)
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cy = mpihelp_add_n(prodp, prodp, up, size);
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} else
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cy = mpihelp_addmul_1(prodp, up, size, v_limb);
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prodp[size] = cy;
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prodp++;
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}
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return cy;
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}
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static void
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mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
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mpi_size_t size, mpi_ptr_t tspace)
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{
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if (size & 1) {
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/* The size is odd, and the code below doesn't handle that.
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* Multiply the least significant (size - 1) limbs with a recursive
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* call, and handle the most significant limb of S1 and S2
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* separately.
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* A slightly faster way to do this would be to make the Karatsuba
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* code below behave as if the size were even, and let it check for
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* odd size in the end. I.e., in essence move this code to the end.
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* Doing so would save us a recursive call, and potentially make the
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* stack grow a lot less.
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*/
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mpi_size_t esize = size - 1; /* even size */
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mpi_limb_t cy_limb;
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MPN_MUL_N_RECURSE(prodp, up, vp, esize, tspace);
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cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, vp[esize]);
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prodp[esize + esize] = cy_limb;
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cy_limb = mpihelp_addmul_1(prodp + esize, vp, size, up[esize]);
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prodp[esize + size] = cy_limb;
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} else {
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/* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
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*
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* Split U in two pieces, U1 and U0, such that
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* U = U0 + U1*(B**n),
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* and V in V1 and V0, such that
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* V = V0 + V1*(B**n).
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*
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* UV is then computed recursively using the identity
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*
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* 2n n n n
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* UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V
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* 1 1 1 0 0 1 0 0
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*
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* Where B = 2**BITS_PER_MP_LIMB.
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*/
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mpi_size_t hsize = size >> 1;
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mpi_limb_t cy;
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int negflg;
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/* Product H. ________________ ________________
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* |_____U1 x V1____||____U0 x V0_____|
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* Put result in upper part of PROD and pass low part of TSPACE
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* as new TSPACE.
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*/
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MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize,
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tspace);
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/* Product M. ________________
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* |_(U1-U0)(V0-V1)_|
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*/
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if (mpihelp_cmp(up + hsize, up, hsize) >= 0) {
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mpihelp_sub_n(prodp, up + hsize, up, hsize);
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negflg = 0;
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} else {
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mpihelp_sub_n(prodp, up, up + hsize, hsize);
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negflg = 1;
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}
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if (mpihelp_cmp(vp + hsize, vp, hsize) >= 0) {
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mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize);
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negflg ^= 1;
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} else {
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mpihelp_sub_n(prodp + hsize, vp, vp + hsize, hsize);
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/* No change of NEGFLG. */
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}
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/* Read temporary operands from low part of PROD.
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* Put result in low part of TSPACE using upper part of TSPACE
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* as new TSPACE.
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*/
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MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize,
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tspace + size);
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/* Add/copy product H. */
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MPN_COPY(prodp + hsize, prodp + size, hsize);
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cy = mpihelp_add_n(prodp + size, prodp + size,
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prodp + size + hsize, hsize);
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/* Add product M (if NEGFLG M is a negative number) */
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if (negflg)
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cy -=
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mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace,
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size);
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else
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cy +=
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mpihelp_add_n(prodp + hsize, prodp + hsize, tspace,
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size);
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/* Product L. ________________ ________________
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* |________________||____U0 x V0_____|
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* Read temporary operands from low part of PROD.
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* Put result in low part of TSPACE using upper part of TSPACE
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* as new TSPACE.
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*/
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MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size);
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/* Add/copy Product L (twice) */
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cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
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if (cy)
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mpihelp_add_1(prodp + hsize + size,
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prodp + hsize + size, hsize, cy);
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MPN_COPY(prodp, tspace, hsize);
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cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
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hsize);
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if (cy)
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mpihelp_add_1(prodp + size, prodp + size, size, 1);
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}
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}
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void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size)
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{
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mpi_size_t i;
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mpi_limb_t cy_limb;
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mpi_limb_t v_limb;
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/* Multiply by the first limb in V separately, as the result can be
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* stored (not added) to PROD. We also avoid a loop for zeroing. */
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v_limb = up[0];
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if (v_limb <= 1) {
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if (v_limb == 1)
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MPN_COPY(prodp, up, size);
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else
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MPN_ZERO(prodp, size);
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cy_limb = 0;
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} else
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cy_limb = mpihelp_mul_1(prodp, up, size, v_limb);
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prodp[size] = cy_limb;
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prodp++;
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/* For each iteration in the outer loop, multiply one limb from
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* U with one limb from V, and add it to PROD. */
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for (i = 1; i < size; i++) {
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v_limb = up[i];
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if (v_limb <= 1) {
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cy_limb = 0;
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if (v_limb == 1)
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cy_limb = mpihelp_add_n(prodp, prodp, up, size);
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} else
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cy_limb = mpihelp_addmul_1(prodp, up, size, v_limb);
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prodp[size] = cy_limb;
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prodp++;
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}
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}
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void
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mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace)
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{
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if (size & 1) {
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/* The size is odd, and the code below doesn't handle that.
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* Multiply the least significant (size - 1) limbs with a recursive
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* call, and handle the most significant limb of S1 and S2
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* separately.
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* A slightly faster way to do this would be to make the Karatsuba
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* code below behave as if the size were even, and let it check for
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* odd size in the end. I.e., in essence move this code to the end.
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* Doing so would save us a recursive call, and potentially make the
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* stack grow a lot less.
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*/
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mpi_size_t esize = size - 1; /* even size */
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mpi_limb_t cy_limb;
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MPN_SQR_N_RECURSE(prodp, up, esize, tspace);
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cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, up[esize]);
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prodp[esize + esize] = cy_limb;
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cy_limb = mpihelp_addmul_1(prodp + esize, up, size, up[esize]);
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prodp[esize + size] = cy_limb;
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} else {
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mpi_size_t hsize = size >> 1;
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mpi_limb_t cy;
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/* Product H. ________________ ________________
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* |_____U1 x U1____||____U0 x U0_____|
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* Put result in upper part of PROD and pass low part of TSPACE
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* as new TSPACE.
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*/
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MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace);
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/* Product M. ________________
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* |_(U1-U0)(U0-U1)_|
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*/
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if (mpihelp_cmp(up + hsize, up, hsize) >= 0)
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mpihelp_sub_n(prodp, up + hsize, up, hsize);
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else
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mpihelp_sub_n(prodp, up, up + hsize, hsize);
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/* Read temporary operands from low part of PROD.
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* Put result in low part of TSPACE using upper part of TSPACE
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* as new TSPACE. */
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MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size);
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/* Add/copy product H */
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MPN_COPY(prodp + hsize, prodp + size, hsize);
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cy = mpihelp_add_n(prodp + size, prodp + size,
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prodp + size + hsize, hsize);
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/* Add product M (if NEGFLG M is a negative number). */
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cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size);
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/* Product L. ________________ ________________
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* |________________||____U0 x U0_____|
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* Read temporary operands from low part of PROD.
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* Put result in low part of TSPACE using upper part of TSPACE
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* as new TSPACE. */
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MPN_SQR_N_RECURSE(tspace, up, hsize, tspace + size);
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/* Add/copy Product L (twice). */
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cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
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if (cy)
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mpihelp_add_1(prodp + hsize + size,
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prodp + hsize + size, hsize, cy);
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MPN_COPY(prodp, tspace, hsize);
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cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
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hsize);
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if (cy)
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mpihelp_add_1(prodp + size, prodp + size, size, 1);
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}
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}
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int
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mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,
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mpi_ptr_t up, mpi_size_t usize,
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mpi_ptr_t vp, mpi_size_t vsize,
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struct karatsuba_ctx *ctx)
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{
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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;
|
||
|
|
}
|