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/* 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]);
}
}
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