1 files changed, 545 insertions, 0 deletions

diff --git a/lib/mpi/mpih-div.c b/lib/mpi/mpih-div.c
new file mode 100644
index 000000000000..cde1aaec18da
--- /dev/null
+++ b/lib/mpi/mpih-div.c
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+/* 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.)  */
+                /*
+                 * 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;
+        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;
+        }
+}