--- /dev/null
+/* 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.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * 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
+
+/* FIXME: We should be using invert_limb (or invert_normalized_limb)
+ * here (not udiv_qrnnd).
+ */
+
+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;
+ int dummy;
+
+ /* 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;
+
+ count_leading_zeros( normalization_steps, 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;
+
+ count_leading_zeros(normalization_steps, 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.) */
+ 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;
+ int dummy;
+
+ 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;
+
+ count_leading_zeros( normalization_steps, 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;
+
+ count_leading_zeros (normalization_steps, 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;
+ }
+}
+
+
git://git.onelab.eu / linux-2.6.git / blobdiff