/* mpi-div.c  -  MPI functions
 * Copyright (C) 1994, 1996, 1998, 2001, 2002,
 *               2003 Free Software Foundation, Inc.
 *
 * This file is part of Libgcrypt.
 *
 * 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.
 */

#include "mpi-internal.h"
#include "longlong.h"

void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);

void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
{
        int divisor_sign = divisor->sign;
        MPI temp_divisor = NULL;

        /* We need the original value of the divisor after the remainder has been
         * preliminary calculated.      We have to copy it to temporary space if it's
         * the same variable as REM.
         */
        if (rem == divisor) {
                temp_divisor = mpi_copy(divisor);
                divisor = temp_divisor;
        }

        mpi_tdiv_r(rem, dividend, divisor);

        if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs)
                mpi_add(rem, rem, divisor);

        if (temp_divisor)
                mpi_free(temp_divisor);
}

void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
{
        MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
        mpi_fdiv_qr(quot, tmp, dividend, divisor);
        mpi_free(tmp);
}

void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
{
        int divisor_sign = divisor->sign;
        MPI temp_divisor = NULL;

        if (quot == divisor || rem == divisor) {
                temp_divisor = mpi_copy(divisor);
                divisor = temp_divisor;
        }

        mpi_tdiv_qr(quot, rem, dividend, divisor);

        if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
                mpi_sub_ui(quot, quot, 1);
                mpi_add(rem, rem, divisor);
        }

        if (temp_divisor)
                mpi_free(temp_divisor);
}

/* If den == quot, den needs temporary storage.
 * If den == rem, den needs temporary storage.
 * If num == quot, num needs temporary storage.
 * If den has temporary storage, it can be normalized while being copied,
 *   i.e no extra storage should be allocated.
 */

void mpi_tdiv_r(MPI rem, MPI num, MPI den)
{
        mpi_tdiv_qr(NULL, rem, num, den);
}

void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
{
        mpi_ptr_t np, dp;
        mpi_ptr_t qp, rp;
        mpi_size_t nsize = num->nlimbs;
        mpi_size_t dsize = den->nlimbs;
        mpi_size_t qsize, rsize;
        mpi_size_t sign_remainder = num->sign;
        mpi_size_t sign_quotient = num->sign ^ den->sign;
        unsigned int normalization_steps;
        mpi_limb_t q_limb;
        mpi_ptr_t marker[5];
        int markidx = 0;

        /* Ensure space is enough for quotient and remainder.
         * We need space for an extra limb in the remainder, because it's
         * up-shifted (normalized) below.
         */
        rsize = nsize + 1;
        mpi_resize(rem, rsize);

        qsize = rsize - dsize;    /* qsize cannot be bigger than this.  */
        if (qsize <= 0) {
                if (num != rem) {
                        rem->nlimbs = num->nlimbs;
                        rem->sign = num->sign;
                        MPN_COPY(rem->d, num->d, nsize);
                }
                if (quot) {
                        /* This needs to follow the assignment to rem, in case the
                         * numerator and quotient are the same.
                         */
                        quot->nlimbs = 0;
                        quot->sign = 0;
                }
                return;
        }

        if (quot)
                mpi_resize(quot, qsize);

        /* Read pointers here, when reallocation is finished.  */
        np = num->d;
        dp = den->d;
        rp = rem->d;

        /* Optimize division by a single-limb divisor.  */
        if (dsize == 1) {
                mpi_limb_t rlimb;
                if (quot) {
                        qp = quot->d;
                        rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
                        qsize -= qp[qsize - 1] == 0;
                        quot->nlimbs = qsize;
                        quot->sign = sign_quotient;
                } else
                        rlimb = mpihelp_mod_1(np, nsize, dp[0]);
                rp[0] = rlimb;
                rsize = rlimb != 0?1:0;
                rem->nlimbs = rsize;
                rem->sign = sign_remainder;
                return;
        }


        if (quot) {
                qp = quot->d;
                /* Make sure QP and NP point to different objects.  Otherwise the
                 * numerator would be gradually overwritten by the quotient limbs.
                 */
                if (qp == np) { /* Copy NP object to temporary space.  */
                        np = marker[markidx++] = mpi_alloc_limb_space(nsize);
                        MPN_COPY(np, qp, nsize);
                }
        } else /* Put quotient at top of remainder. */
                qp = rp + dsize;

        normalization_steps = count_leading_zeros(dp[dsize - 1]);

        /* Normalize the denominator, i.e. make its most significant bit set by
         * shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
         * numerator the same number of steps (to keep the quotient the same!).
         */
        if (normalization_steps) {
                mpi_ptr_t tp;
                mpi_limb_t nlimb;

                /* Shift up the denominator setting the most significant bit of
                 * the most significant word.  Use temporary storage not to clobber
                 * the original contents of the denominator.
                 */
                tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
                mpihelp_lshift(tp, dp, dsize, normalization_steps);
                dp = tp;

                /* Shift up the numerator, possibly introducing a new most
                 * significant word.  Move the shifted numerator in the remainder
                 * meanwhile.
                 */
                nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
                if (nlimb) {
                        rp[nsize] = nlimb;
                        rsize = nsize + 1;
                } else
                        rsize = nsize;
        } else {
                /* The denominator is already normalized, as required.  Copy it to
                 * temporary space if it overlaps with the quotient or remainder.
                 */
                if (dp == rp || (quot && (dp == qp))) {
                        mpi_ptr_t tp;

                        tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
                        MPN_COPY(tp, dp, dsize);
                        dp = tp;
                }

                /* Move the numerator to the remainder.  */
                if (rp != np)
                        MPN_COPY(rp, np, nsize);

                rsize = nsize;
        }

        q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);

        if (quot) {
                qsize = rsize - dsize;
                if (q_limb) {
                        qp[qsize] = q_limb;
                        qsize += 1;
                }

                quot->nlimbs = qsize;
                quot->sign = sign_quotient;
        }

        rsize = dsize;
        MPN_NORMALIZE(rp, rsize);

        if (normalization_steps && rsize) {
                mpihelp_rshift(rp, rp, rsize, normalization_steps);
                rsize -= rp[rsize - 1] == 0?1:0;
        }

        rem->nlimbs = rsize;
        rem->sign       = sign_remainder;
        while (markidx) {
                markidx--;
                mpi_free_limb_space(marker[markidx]);
        }
}