// 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);
        }
}

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_obj(*ctx);
                                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;
}