+++ /dev/null
-// SPDX-License-Identifier: GPL-2.0-or-later
-/* mpihelp-mul.c - MPI helper functions
- * Copyright (C) 1994, 1996, 1998, 1999,
- * 2000 Free Software Foundation, Inc.
- *
- * This file is part of GnuPG.
- *
- * 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);
- }
-}
-
-
-void 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);
- 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);
- mul_n(prodp, up, vp, size, tspace);
- mpi_free_limb_space(tspace);
- }
- }
-}
-
-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;
-}
projects / linux-2.6-microblaze.git / blobdiff