// SPDX-License-Identifier: GPL-2.0-or-later
/* mpihelp-div.c  -  MPI helper functions
 *      Copyright (C) 1994, 1996 Free Software Foundation, Inc.
 *      Copyright (C) 1998, 1999 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 "mpi-internal.h"
#include "longlong.h"

#ifndef UMUL_TIME
#define UMUL_TIME 1
#endif
#ifndef UDIV_TIME
#define UDIV_TIME UMUL_TIME
#endif


mpi_limb_t
mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
                        mpi_limb_t divisor_limb)
{
        mpi_size_t i;
        mpi_limb_t n1, n0, r;
        mpi_limb_t dummy __maybe_unused;

        /* Botch: Should this be handled at all?  Rely on callers?      */
        if (!dividend_size)
                return 0;

        /* If multiplication is much faster than division, and the
         * dividend is large, pre-invert the divisor, and use
         * only multiplications in the inner loop.
         *
         * This test should be read:
         *       Does it ever help to use udiv_qrnnd_preinv?
         *         && Does what we save compensate for the inversion overhead?
         */
        if (UDIV_TIME > (2 * UMUL_TIME + 6)
                        && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
                int normalization_steps;

                normalization_steps = count_leading_zeros(divisor_limb);
                if (normalization_steps) {
                        mpi_limb_t divisor_limb_inverted;

                        divisor_limb <<= normalization_steps;

                        /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
                         * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
                         * most significant bit (with weight 2**N) implicit.
                         *
                         * Special case for DIVISOR_LIMB == 100...000.
                         */
                        if (!(divisor_limb << 1))
                                divisor_limb_inverted = ~(mpi_limb_t)0;
                        else
                                udiv_qrnnd(divisor_limb_inverted, dummy,
                                                -divisor_limb, 0, divisor_limb);

                        n1 = dividend_ptr[dividend_size - 1];
                        r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

                        /* Possible optimization:
                         * if (r == 0
                         * && divisor_limb > ((n1 << normalization_steps)
                         *                     | (dividend_ptr[dividend_size - 2] >> ...)))
                         * ...one division less...
                         */
                        for (i = dividend_size - 2; i >= 0; i--) {
                                n0 = dividend_ptr[i];
                                UDIV_QRNND_PREINV(dummy, r, r,
                                                ((n1 << normalization_steps)
                                                 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
                                                divisor_limb, divisor_limb_inverted);
                                n1 = n0;
                        }
                        UDIV_QRNND_PREINV(dummy, r, r,
                                        n1 << normalization_steps,
                                        divisor_limb, divisor_limb_inverted);
                        return r >> normalization_steps;
                } else {
                        mpi_limb_t divisor_limb_inverted;

                        /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
                         * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
                         * most significant bit (with weight 2**N) implicit.
                         *
                         * Special case for DIVISOR_LIMB == 100...000.
                         */
                        if (!(divisor_limb << 1))
                                divisor_limb_inverted = ~(mpi_limb_t)0;
                        else
                                udiv_qrnnd(divisor_limb_inverted, dummy,
                                                -divisor_limb, 0, divisor_limb);

                        i = dividend_size - 1;
                        r = dividend_ptr[i];

                        if (r >= divisor_limb)
                                r = 0;
                        else
                                i--;

                        for ( ; i >= 0; i--) {
                                n0 = dividend_ptr[i];
                                UDIV_QRNND_PREINV(dummy, r, r,
                                                n0, divisor_limb, divisor_limb_inverted);
                        }
                        return r;
                }
        } else {
                if (UDIV_NEEDS_NORMALIZATION) {
                        int normalization_steps;

                        normalization_steps = count_leading_zeros(divisor_limb);
                        if (normalization_steps) {
                                divisor_limb <<= normalization_steps;

                                n1 = dividend_ptr[dividend_size - 1];
                                r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

                                /* Possible optimization:
                                 * if (r == 0
                                 * && divisor_limb > ((n1 << normalization_steps)
                                 *                 | (dividend_ptr[dividend_size - 2] >> ...)))
                                 * ...one division less...
                                 */
                                for (i = dividend_size - 2; i >= 0; i--) {
                                        n0 = dividend_ptr[i];
                                        udiv_qrnnd(dummy, r, r,
                                                ((n1 << normalization_steps)
                                                 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
                                                divisor_limb);
                                        n1 = n0;
                                }
                                udiv_qrnnd(dummy, r, r,
                                                n1 << normalization_steps,
                                                divisor_limb);
                                return r >> normalization_steps;
                        }
                }
                /* No normalization needed, either because udiv_qrnnd doesn't require
                 * it, or because DIVISOR_LIMB is already normalized.
                 */
                i = dividend_size - 1;
                r = dividend_ptr[i];

                if (r >= divisor_limb)
                        r = 0;
                else
                        i--;

                for (; i >= 0; i--) {
                        n0 = dividend_ptr[i];
                        udiv_qrnnd(dummy, r, r, n0, divisor_limb);
                }
                return r;
        }
}

/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
 * the NSIZE-DSIZE least significant quotient limbs at QP
 * and the DSIZE long remainder at NP.  If QEXTRA_LIMBS is
 * non-zero, generate that many fraction bits and append them after the
 * other quotient limbs.
 * Return the most significant limb of the quotient, this is always 0 or 1.
 *
 * Preconditions:
 * 0. NSIZE >= DSIZE.
 * 1. The most significant bit of the divisor must be set.
 * 2. QP must either not overlap with the input operands at all, or
 *    QP + DSIZE >= NP must hold true.  (This means that it's
 *    possible to put the quotient in the high part of NUM, right after the
 *    remainder in NUM.
 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
 */

mpi_limb_t
mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
               mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
{
        mpi_limb_t most_significant_q_limb = 0;

        switch (dsize) {
        case 0:
                /* We are asked to divide by zero, so go ahead and do it!  (To make
                   the compiler not remove this statement, return the value.)  */
                /*
                 * existing clients of this function have been modified
                 * not to call it with dsize == 0, so this should not happen
                 */
                return 1 / dsize;

        case 1:
                {
                        mpi_size_t i;
                        mpi_limb_t n1;
                        mpi_limb_t d;

                        d = dp[0];
                        n1 = np[nsize - 1];

                        if (n1 >= d) {
                                n1 -= d;
                                most_significant_q_limb = 1;
                        }

                        qp += qextra_limbs;
                        for (i = nsize - 2; i >= 0; i--)
                                udiv_qrnnd(qp[i], n1, n1, np[i], d);
                        qp -= qextra_limbs;

                        for (i = qextra_limbs - 1; i >= 0; i--)
                                udiv_qrnnd(qp[i], n1, n1, 0, d);

                        np[0] = n1;
                }
                break;

        case 2:
                {
                        mpi_size_t i;
                        mpi_limb_t n1, n0, n2;
                        mpi_limb_t d1, d0;

                        np += nsize - 2;
                        d1 = dp[1];
                        d0 = dp[0];
                        n1 = np[1];
                        n0 = np[0];

                        if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
                                sub_ddmmss(n1, n0, n1, n0, d1, d0);
                                most_significant_q_limb = 1;
                        }

                        for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
                                mpi_limb_t q;
                                mpi_limb_t r;

                                if (i >= qextra_limbs)
                                        np--;
                                else
                                        np[0] = 0;

                                if (n1 == d1) {
                                        /* Q should be either 111..111 or 111..110.  Need special
                                         * treatment of this rare case as normal division would
                                         * give overflow.  */
                                        q = ~(mpi_limb_t) 0;

                                        r = n0 + d1;
                                        if (r < d1) {   /* Carry in the addition? */
                                                add_ssaaaa(n1, n0, r - d0,
                                                           np[0], 0, d0);
                                                qp[i] = q;
                                                continue;
                                        }
                                        n1 = d0 - (d0 != 0 ? 1 : 0);
                                        n0 = -d0;
                                } else {
                                        udiv_qrnnd(q, r, n1, n0, d1);
                                        umul_ppmm(n1, n0, d0, q);
                                }

                                n2 = np[0];
q_test:
                                if (n1 > r || (n1 == r && n0 > n2)) {
                                        /* The estimated Q was too large.  */
                                        q--;
                                        sub_ddmmss(n1, n0, n1, n0, 0, d0);
                                        r += d1;
                                        if (r >= d1)    /* If not carry, test Q again.  */
                                                goto q_test;
                                }

                                qp[i] = q;
                                sub_ddmmss(n1, n0, r, n2, n1, n0);
                        }
                        np[1] = n1;
                        np[0] = n0;
                }
                break;

        default:
                {
                        mpi_size_t i;
                        mpi_limb_t dX, d1, n0;

                        np += nsize - dsize;
                        dX = dp[dsize - 1];
                        d1 = dp[dsize - 2];
                        n0 = np[dsize - 1];

                        if (n0 >= dX) {
                                if (n0 > dX
                                    || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
                                        mpihelp_sub_n(np, np, dp, dsize);
                                        n0 = np[dsize - 1];
                                        most_significant_q_limb = 1;
                                }
                        }

                        for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
                                mpi_limb_t q;
                                mpi_limb_t n1, n2;
                                mpi_limb_t cy_limb;

                                if (i >= qextra_limbs) {
                                        np--;
                                        n2 = np[dsize];
                                } else {
                                        n2 = np[dsize - 1];
                                        MPN_COPY_DECR(np + 1, np, dsize - 1);
                                        np[0] = 0;
                                }

                                if (n0 == dX) {
                                        /* This might over-estimate q, but it's probably not worth
                                         * the extra code here to find out.  */
                                        q = ~(mpi_limb_t) 0;
                                } else {
                                        mpi_limb_t r;

                                        udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
                                        umul_ppmm(n1, n0, d1, q);

                                        while (n1 > r
                                               || (n1 == r
                                                   && n0 > np[dsize - 2])) {
                                                q--;
                                                r += dX;
                                                if (r < dX)     /* I.e. "carry in previous addition?" */
                                                        break;
                                                n1 -= n0 < d1;
                                                n0 -= d1;
                                        }
                                }

                                /* Possible optimization: We already have (q * n0) and (1 * n1)
                                 * after the calculation of q.  Taking advantage of that, we
                                 * could make this loop make two iterations less.  */
                                cy_limb = mpihelp_submul_1(np, dp, dsize, q);

                                if (n2 != cy_limb) {
                                        mpihelp_add_n(np, np, dp, dsize);
                                        q--;
                                }

                                qp[i] = q;
                                n0 = np[dsize - 1];
                        }
                }
        }

        return most_significant_q_limb;
}

/****************
 * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
 * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
 * Return the single-limb remainder.
 * There are no constraints on the value of the divisor.
 *
 * QUOT_PTR and DIVIDEND_PTR might point to the same limb.
 */

mpi_limb_t
mpihelp_divmod_1(mpi_ptr_t quot_ptr,
                mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
                mpi_limb_t divisor_limb)
{
        mpi_size_t i;
        mpi_limb_t n1, n0, r;
        mpi_limb_t dummy __maybe_unused;

        if (!dividend_size)
                return 0;

        /* If multiplication is much faster than division, and the
         * dividend is large, pre-invert the divisor, and use
         * only multiplications in the inner loop.
         *
         * This test should be read:
         * Does it ever help to use udiv_qrnnd_preinv?
         * && Does what we save compensate for the inversion overhead?
         */
        if (UDIV_TIME > (2 * UMUL_TIME + 6)
                        && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
                int normalization_steps;

                normalization_steps = count_leading_zeros(divisor_limb);
                if (normalization_steps) {
                        mpi_limb_t divisor_limb_inverted;

                        divisor_limb <<= normalization_steps;

                        /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
                         * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
                         * most significant bit (with weight 2**N) implicit.
                         */
                        /* Special case for DIVISOR_LIMB == 100...000.  */
                        if (!(divisor_limb << 1))
                                divisor_limb_inverted = ~(mpi_limb_t)0;
                        else
                                udiv_qrnnd(divisor_limb_inverted, dummy,
                                                -divisor_limb, 0, divisor_limb);

                        n1 = dividend_ptr[dividend_size - 1];
                        r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

                        /* Possible optimization:
                         * if (r == 0
                         * && divisor_limb > ((n1 << normalization_steps)
                         *                     | (dividend_ptr[dividend_size - 2] >> ...)))
                         * ...one division less...
                         */
                        for (i = dividend_size - 2; i >= 0; i--) {
                                n0 = dividend_ptr[i];
                                UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r,
                                                ((n1 << normalization_steps)
                                                 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
                                                divisor_limb, divisor_limb_inverted);
                                n1 = n0;
                        }
                        UDIV_QRNND_PREINV(quot_ptr[0], r, r,
                                        n1 << normalization_steps,
                                        divisor_limb, divisor_limb_inverted);
                        return r >> normalization_steps;
                } else {
                        mpi_limb_t divisor_limb_inverted;

                        /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
                         * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
                         * most significant bit (with weight 2**N) implicit.
                         */
                        /* Special case for DIVISOR_LIMB == 100...000.  */
                        if (!(divisor_limb << 1))
                                divisor_limb_inverted = ~(mpi_limb_t) 0;
                        else
                                udiv_qrnnd(divisor_limb_inverted, dummy,
                                                -divisor_limb, 0, divisor_limb);

                        i = dividend_size - 1;
                        r = dividend_ptr[i];

                        if (r >= divisor_limb)
                                r = 0;
                        else
                                quot_ptr[i--] = 0;

                        for ( ; i >= 0; i--) {
                                n0 = dividend_ptr[i];
                                UDIV_QRNND_PREINV(quot_ptr[i], r, r,
                                                n0, divisor_limb, divisor_limb_inverted);
                        }
                        return r;
                }
        } else {
                if (UDIV_NEEDS_NORMALIZATION) {
                        int normalization_steps;

                        normalization_steps = count_leading_zeros(divisor_limb);
                        if (normalization_steps) {
                                divisor_limb <<= normalization_steps;

                                n1 = dividend_ptr[dividend_size - 1];
                                r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);

                                /* Possible optimization:
                                 * if (r == 0
                                 * && divisor_limb > ((n1 << normalization_steps)
                                 *                 | (dividend_ptr[dividend_size - 2] >> ...)))
                                 * ...one division less...
                                 */
                                for (i = dividend_size - 2; i >= 0; i--) {
                                        n0 = dividend_ptr[i];
                                        udiv_qrnnd(quot_ptr[i + 1], r, r,
                                                ((n1 << normalization_steps)
                                                 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
                                                divisor_limb);
                                        n1 = n0;
                                }
                                udiv_qrnnd(quot_ptr[0], r, r,
                                                n1 << normalization_steps,
                                                divisor_limb);
                                return r >> normalization_steps;
                        }
                }
                /* No normalization needed, either because udiv_qrnnd doesn't require
                 * it, or because DIVISOR_LIMB is already normalized.
                 */
                i = dividend_size - 1;
                r = dividend_ptr[i];

                if (r >= divisor_limb)
                        r = 0;
                else
                        quot_ptr[i--] = 0;

                for (; i >= 0; i--) {
                        n0 = dividend_ptr[i];
                        udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb);
                }
                return r;
        }
}