// 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;
}
}
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