LCOV - code coverage report
Current view: top level - mpi - mpih-div.c (source / functions) Hit Total Coverage
Test: coverage.info Lines: 91 110 82.7 %
Date: 2016-12-01 18:32:04 Functions: 3 3 100.0 %

          Line data    Source code
       1             : /* mpih-div.c  -  MPI helper functions
       2             :  * Copyright (C) 1994, 1996, 1998, 2000,
       3             :  *               2001, 2002 Free Software Foundation, Inc.
       4             :  *
       5             :  * This file is part of Libgcrypt.
       6             :  *
       7             :  * Libgcrypt is free software; you can redistribute it and/or modify
       8             :  * it under the terms of the GNU Lesser General Public License as
       9             :  * published by the Free Software Foundation; either version 2.1 of
      10             :  * the License, or (at your option) any later version.
      11             :  *
      12             :  * Libgcrypt is distributed in the hope that it will be useful,
      13             :  * but WITHOUT ANY WARRANTY; without even the implied warranty of
      14             :  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
      15             :  * GNU Lesser General Public License for more details.
      16             :  *
      17             :  * You should have received a copy of the GNU Lesser General Public
      18             :  * License along with this program; if not, write to the Free Software
      19             :  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
      20             :  *
      21             :  * Note: This code is heavily based on the GNU MP Library.
      22             :  *       Actually it's the same code with only minor changes in the
      23             :  *       way the data is stored; this is to support the abstraction
      24             :  *       of an optional secure memory allocation which may be used
      25             :  *       to avoid revealing of sensitive data due to paging etc.
      26             :  */
      27             : 
      28             : #include <config.h>
      29             : #include <stdio.h>
      30             : #include <stdlib.h>
      31             : #include "mpi-internal.h"
      32             : #include "longlong.h"
      33             : 
      34             : #ifndef UMUL_TIME
      35             : #define UMUL_TIME 1
      36             : #endif
      37             : #ifndef UDIV_TIME
      38             : #define UDIV_TIME UMUL_TIME
      39             : #endif
      40             : 
      41             : /* FIXME: We should be using invert_limb (or invert_normalized_limb)
      42             :  * here (not udiv_qrnnd).
      43             :  */
      44             : 
      45             : mpi_limb_t
      46     3265089 : _gcry_mpih_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
      47             :                                       mpi_limb_t divisor_limb)
      48             : {
      49             :     mpi_size_t i;
      50             :     mpi_limb_t n1, n0, r;
      51             :     mpi_limb_t dummy GCC_ATTR_UNUSED;
      52             : 
      53             :     /* Botch: Should this be handled at all?  Rely on callers?  */
      54     3265089 :     if( !dividend_size )
      55           0 :         return 0;
      56             : 
      57             :     /* If multiplication is much faster than division, and the
      58             :      * dividend is large, pre-invert the divisor, and use
      59             :      * only multiplications in the inner loop.
      60             :      *
      61             :      * This test should be read:
      62             :      *   Does it ever help to use udiv_qrnnd_preinv?
      63             :      *     && Does what we save compensate for the inversion overhead?
      64             :      */
      65             :     if( UDIV_TIME > (2 * UMUL_TIME + 6)
      66             :         && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
      67             :         int normalization_steps;
      68             : 
      69             :         count_leading_zeros( normalization_steps, divisor_limb );
      70             :         if( normalization_steps ) {
      71             :             mpi_limb_t divisor_limb_inverted;
      72             : 
      73             :             divisor_limb <<= normalization_steps;
      74             : 
      75             :             /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
      76             :              * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
      77             :              * most significant bit (with weight 2**N) implicit.
      78             :              *
      79             :              * Special case for DIVISOR_LIMB == 100...000.
      80             :              */
      81             :             if( !(divisor_limb << 1) )
      82             :                 divisor_limb_inverted = ~(mpi_limb_t)0;
      83             :             else
      84             :                 udiv_qrnnd(divisor_limb_inverted, dummy,
      85             :                            -divisor_limb, 0, divisor_limb);
      86             : 
      87             :             n1 = dividend_ptr[dividend_size - 1];
      88             :             r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
      89             : 
      90             :             /* Possible optimization:
      91             :              * if (r == 0
      92             :              * && divisor_limb > ((n1 << normalization_steps)
      93             :              *                 | (dividend_ptr[dividend_size - 2] >> ...)))
      94             :              * ...one division less...
      95             :              */
      96             :             for( i = dividend_size - 2; i >= 0; i--) {
      97             :                 n0 = dividend_ptr[i];
      98             :                 UDIV_QRNND_PREINV(dummy, r, r,
      99             :                                    ((n1 << normalization_steps)
     100             :                           | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
     101             :                           divisor_limb, divisor_limb_inverted);
     102             :                 n1 = n0;
     103             :             }
     104             :             UDIV_QRNND_PREINV(dummy, r, r,
     105             :                               n1 << normalization_steps,
     106             :                               divisor_limb, divisor_limb_inverted);
     107             :             return r >> normalization_steps;
     108             :         }
     109             :         else {
     110             :             mpi_limb_t divisor_limb_inverted;
     111             : 
     112             :             /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
     113             :              * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
     114             :              * most significant bit (with weight 2**N) implicit.
     115             :              *
     116             :              * Special case for DIVISOR_LIMB == 100...000.
     117             :              */
     118             :             if( !(divisor_limb << 1) )
     119             :                 divisor_limb_inverted = ~(mpi_limb_t)0;
     120             :             else
     121             :                 udiv_qrnnd(divisor_limb_inverted, dummy,
     122             :                             -divisor_limb, 0, divisor_limb);
     123             : 
     124             :             i = dividend_size - 1;
     125             :             r = dividend_ptr[i];
     126             : 
     127             :             if( r >= divisor_limb )
     128             :                 r = 0;
     129             :             else
     130             :                 i--;
     131             : 
     132             :             for( ; i >= 0; i--) {
     133             :                 n0 = dividend_ptr[i];
     134             :                 UDIV_QRNND_PREINV(dummy, r, r,
     135             :                                   n0, divisor_limb, divisor_limb_inverted);
     136             :             }
     137             :             return r;
     138             :         }
     139             :     }
     140             :     else {
     141             :         if( UDIV_NEEDS_NORMALIZATION ) {
     142             :             int normalization_steps;
     143             : 
     144             :             count_leading_zeros(normalization_steps, divisor_limb);
     145             :             if( normalization_steps ) {
     146             :                 divisor_limb <<= normalization_steps;
     147             : 
     148             :                 n1 = dividend_ptr[dividend_size - 1];
     149             :                 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
     150             : 
     151             :                 /* Possible optimization:
     152             :                  * if (r == 0
     153             :                  * && divisor_limb > ((n1 << normalization_steps)
     154             :                  *                 | (dividend_ptr[dividend_size - 2] >> ...)))
     155             :                  * ...one division less...
     156             :                  */
     157             :                 for(i = dividend_size - 2; i >= 0; i--) {
     158             :                     n0 = dividend_ptr[i];
     159             :                     udiv_qrnnd (dummy, r, r,
     160             :                                 ((n1 << normalization_steps)
     161             :                          | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
     162             :                          divisor_limb);
     163             :                     n1 = n0;
     164             :                 }
     165             :                 udiv_qrnnd (dummy, r, r,
     166             :                             n1 << normalization_steps,
     167             :                             divisor_limb);
     168             :                 return r >> normalization_steps;
     169             :             }
     170             :         }
     171             :         /* No normalization needed, either because udiv_qrnnd doesn't require
     172             :          * it, or because DIVISOR_LIMB is already normalized.  */
     173     3265089 :         i = dividend_size - 1;
     174     3265089 :         r = dividend_ptr[i];
     175             : 
     176     3265089 :         if(r >= divisor_limb)
     177     3231309 :             r = 0;
     178             :         else
     179       33780 :             i--;
     180             : 
     181    68263703 :         for(; i >= 0; i--) {
     182    64998614 :             n0 = dividend_ptr[i];
     183    64998614 :             udiv_qrnnd (dummy, r, r, n0, divisor_limb);
     184             :         }
     185     3265089 :         return r;
     186             :     }
     187             : }
     188             : 
     189             : /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
     190             :  * the NSIZE-DSIZE least significant quotient limbs at QP
     191             :  * and the DSIZE long remainder at NP.  If QEXTRA_LIMBS is
     192             :  * non-zero, generate that many fraction bits and append them after the
     193             :  * other quotient limbs.
     194             :  * Return the most significant limb of the quotient, this is always 0 or 1.
     195             :  *
     196             :  * Preconditions:
     197             :  * 0. NSIZE >= DSIZE.
     198             :  * 1. The most significant bit of the divisor must be set.
     199             :  * 2. QP must either not overlap with the input operands at all, or
     200             :  *    QP + DSIZE >= NP must hold true.       (This means that it's
     201             :  *    possible to put the quotient in the high part of NUM, right after the
     202             :  *    remainder in NUM.
     203             :  * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
     204             :  */
     205             : 
     206             : mpi_limb_t
     207    52804823 : _gcry_mpih_divrem( mpi_ptr_t qp, mpi_size_t qextra_limbs,
     208             :                       mpi_ptr_t np, mpi_size_t nsize,
     209             :                       mpi_ptr_t dp, mpi_size_t dsize)
     210             : {
     211    52804823 :     mpi_limb_t most_significant_q_limb = 0;
     212             : 
     213    52804823 :     switch(dsize) {
     214             :       case 0:
     215           0 :         _gcry_divide_by_zero();
     216             :         break;
     217             : 
     218             :       case 1:
     219             :         {
     220             :             mpi_size_t i;
     221             :             mpi_limb_t n1;
     222             :             mpi_limb_t d;
     223             : 
     224       12767 :             d = dp[0];
     225       12767 :             n1 = np[nsize - 1];
     226             : 
     227       12767 :             if( n1 >= d ) {
     228           0 :                 n1 -= d;
     229           0 :                 most_significant_q_limb = 1;
     230             :             }
     231             : 
     232       12767 :             qp += qextra_limbs;
     233       25534 :             for( i = nsize - 2; i >= 0; i--)
     234       12767 :                 udiv_qrnnd( qp[i], n1, n1, np[i], d );
     235       12767 :             qp -= qextra_limbs;
     236             : 
     237       12767 :             for( i = qextra_limbs - 1; i >= 0; i-- )
     238           0 :                 udiv_qrnnd (qp[i], n1, n1, 0, d);
     239             : 
     240       12767 :             np[0] = n1;
     241             :         }
     242       12767 :         break;
     243             : 
     244             :       case 2:
     245             :         {
     246             :             mpi_size_t i;
     247             :             mpi_limb_t n1, n0, n2;
     248             :             mpi_limb_t d1, d0;
     249             : 
     250      304844 :             np += nsize - 2;
     251      304844 :             d1 = dp[1];
     252      304844 :             d0 = dp[0];
     253      304844 :             n1 = np[1];
     254      304844 :             n0 = np[0];
     255             : 
     256      304844 :             if( n1 >= d1 && (n1 > d1 || n0 >= d0) ) {
     257         970 :                 sub_ddmmss (n1, n0, n1, n0, d1, d0);
     258         970 :                 most_significant_q_limb = 1;
     259             :             }
     260             : 
     261      899053 :             for( i = qextra_limbs + nsize - 2 - 1; i >= 0; i-- ) {
     262             :                 mpi_limb_t q;
     263             :                 mpi_limb_t r;
     264             : 
     265      594209 :                 if( i >= qextra_limbs )
     266      594209 :                     np--;
     267             :                 else
     268           0 :                     np[0] = 0;
     269             : 
     270      594209 :                 if( n1 == d1 ) {
     271             :                     /* Q should be either 111..111 or 111..110.  Need special
     272             :                      * treatment of this rare case as normal division would
     273             :                      * give overflow.  */
     274           0 :                     q = ~(mpi_limb_t)0;
     275             : 
     276           0 :                     r = n0 + d1;
     277           0 :                     if( r < d1 ) {   /* Carry in the addition? */
     278           0 :                         add_ssaaaa( n1, n0, r - d0, np[0], 0, d0 );
     279           0 :                         qp[i] = q;
     280           0 :                         continue;
     281             :                     }
     282           0 :                     n1 = d0 - (d0 != 0?1:0);
     283           0 :                     n0 = -d0;
     284             :                 }
     285             :                 else {
     286      594209 :                     udiv_qrnnd (q, r, n1, n0, d1);
     287      594209 :                     umul_ppmm (n1, n0, d0, q);
     288             :                 }
     289             : 
     290      594209 :                 n2 = np[0];
     291             :               q_test:
     292      663547 :                 if( n1 > r || (n1 == r && n0 > n2) ) {
     293             :                     /* The estimated Q was too large.  */
     294      113738 :                     q--;
     295      113738 :                     sub_ddmmss (n1, n0, n1, n0, 0, d0);
     296      113738 :                     r += d1;
     297      113738 :                     if( r >= d1 )    /* If not carry, test Q again.  */
     298       69338 :                         goto q_test;
     299             :                 }
     300             : 
     301      594209 :                 qp[i] = q;
     302      594209 :                 sub_ddmmss (n1, n0, r, n2, n1, n0);
     303             :             }
     304      304844 :             np[1] = n1;
     305      304844 :             np[0] = n0;
     306             :         }
     307      304844 :         break;
     308             : 
     309             :       default:
     310             :         {
     311             :             mpi_size_t i;
     312             :             mpi_limb_t dX, d1, n0;
     313             : 
     314    52487212 :             np += nsize - dsize;
     315    52487212 :             dX = dp[dsize - 1];
     316    52487212 :             d1 = dp[dsize - 2];
     317    52487212 :             n0 = np[dsize - 1];
     318             : 
     319    52487212 :             if( n0 >= dX ) {
     320      136613 :                 if(n0 > dX || _gcry_mpih_cmp(np, dp, dsize - 1) >= 0 ) {
     321      118451 :                     _gcry_mpih_sub_n(np, np, dp, dsize);
     322      118451 :                     n0 = np[dsize - 1];
     323      118451 :                     most_significant_q_limb = 1;
     324             :                 }
     325             :             }
     326             : 
     327   439743959 :             for( i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
     328             :                 mpi_limb_t q;
     329             :                 mpi_limb_t n1, n2;
     330             :                 mpi_limb_t cy_limb;
     331             : 
     332   387256747 :                 if( i >= qextra_limbs ) {
     333   387256747 :                     np--;
     334   387256747 :                     n2 = np[dsize];
     335             :                 }
     336             :                 else {
     337           0 :                     n2 = np[dsize - 1];
     338           0 :                     MPN_COPY_DECR (np + 1, np, dsize - 1);
     339           0 :                     np[0] = 0;
     340             :                 }
     341             : 
     342   387256747 :                 if( n0 == dX ) {
     343             :                     /* This might over-estimate q, but it's probably not worth
     344             :                      * the extra code here to find out.  */
     345       10638 :                     q = ~(mpi_limb_t)0;
     346             :                 }
     347             :                 else {
     348             :                     mpi_limb_t r;
     349             : 
     350   387246109 :                     udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
     351   387246109 :                     umul_ppmm(n1, n0, d1, q);
     352             : 
     353   823371583 :                     while( n1 > r || (n1 == r && n0 > np[dsize - 2])) {
     354   125156920 :                         q--;
     355   125156920 :                         r += dX;
     356   125156920 :                         if( r < dX ) /* I.e. "carry in previous addition?" */
     357    76277555 :                             break;
     358    48879365 :                         n1 -= n0 < d1;
     359    48879365 :                         n0 -= d1;
     360             :                     }
     361             :                 }
     362             : 
     363             :                 /* Possible optimization: We already have (q * n0) and (1 * n1)
     364             :                  * after the calculation of q.  Taking advantage of that, we
     365             :                  * could make this loop make two iterations less.  */
     366   387256747 :                 cy_limb = _gcry_mpih_submul_1(np, dp, dsize, q);
     367             : 
     368   387256747 :                 if( n2 != cy_limb ) {
     369        8799 :                     _gcry_mpih_add_n(np, np, dp, dsize);
     370        8799 :                     q--;
     371             :                 }
     372             : 
     373   387256747 :                 qp[i] = q;
     374   387256747 :                 n0 = np[dsize - 1];
     375             :             }
     376             :         }
     377             :     }
     378             : 
     379    52804823 :     return most_significant_q_limb;
     380             : }
     381             : 
     382             : 
     383             : /****************
     384             :  * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
     385             :  * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
     386             :  * Return the single-limb remainder.
     387             :  * There are no constraints on the value of the divisor.
     388             :  *
     389             :  * QUOT_PTR and DIVIDEND_PTR might point to the same limb.
     390             :  */
     391             : 
     392             : mpi_limb_t
     393          63 : _gcry_mpih_divmod_1( mpi_ptr_t quot_ptr,
     394             :                         mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
     395             :                         mpi_limb_t divisor_limb)
     396             : {
     397             :     mpi_size_t i;
     398             :     mpi_limb_t n1, n0, r;
     399             :     mpi_limb_t dummy GCC_ATTR_UNUSED;
     400             : 
     401          63 :     if( !dividend_size )
     402           0 :         return 0;
     403             : 
     404             :     /* If multiplication is much faster than division, and the
     405             :      * dividend is large, pre-invert the divisor, and use
     406             :      * only multiplications in the inner loop.
     407             :      *
     408             :      * This test should be read:
     409             :      * Does it ever help to use udiv_qrnnd_preinv?
     410             :      * && Does what we save compensate for the inversion overhead?
     411             :      */
     412             :     if( UDIV_TIME > (2 * UMUL_TIME + 6)
     413             :         && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
     414             :         int normalization_steps;
     415             : 
     416             :         count_leading_zeros( normalization_steps, divisor_limb );
     417             :         if( normalization_steps ) {
     418             :             mpi_limb_t divisor_limb_inverted;
     419             : 
     420             :             divisor_limb <<= normalization_steps;
     421             : 
     422             :             /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
     423             :              * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
     424             :              * most significant bit (with weight 2**N) implicit.
     425             :              */
     426             :             /* Special case for DIVISOR_LIMB == 100...000.  */
     427             :             if( !(divisor_limb << 1) )
     428             :                 divisor_limb_inverted = ~(mpi_limb_t)0;
     429             :             else
     430             :                 udiv_qrnnd(divisor_limb_inverted, dummy,
     431             :                            -divisor_limb, 0, divisor_limb);
     432             : 
     433             :             n1 = dividend_ptr[dividend_size - 1];
     434             :             r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
     435             : 
     436             :             /* Possible optimization:
     437             :              * if (r == 0
     438             :              * && divisor_limb > ((n1 << normalization_steps)
     439             :              *                 | (dividend_ptr[dividend_size - 2] >> ...)))
     440             :              * ...one division less...
     441             :              */
     442             :             for( i = dividend_size - 2; i >= 0; i--) {
     443             :                 n0 = dividend_ptr[i];
     444             :                 UDIV_QRNND_PREINV( quot_ptr[i + 1], r, r,
     445             :                                    ((n1 << normalization_steps)
     446             :                          | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
     447             :                               divisor_limb, divisor_limb_inverted);
     448             :                 n1 = n0;
     449             :             }
     450             :             UDIV_QRNND_PREINV( quot_ptr[0], r, r,
     451             :                                n1 << normalization_steps,
     452             :                                divisor_limb, divisor_limb_inverted);
     453             :             return r >> normalization_steps;
     454             :         }
     455             :         else {
     456             :             mpi_limb_t divisor_limb_inverted;
     457             : 
     458             :             /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
     459             :              * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
     460             :              * most significant bit (with weight 2**N) implicit.
     461             :              */
     462             :             /* Special case for DIVISOR_LIMB == 100...000.  */
     463             :             if( !(divisor_limb << 1) )
     464             :                 divisor_limb_inverted = ~(mpi_limb_t) 0;
     465             :             else
     466             :                 udiv_qrnnd(divisor_limb_inverted, dummy,
     467             :                            -divisor_limb, 0, divisor_limb);
     468             : 
     469             :             i = dividend_size - 1;
     470             :             r = dividend_ptr[i];
     471             : 
     472             :             if( r >= divisor_limb )
     473             :                 r = 0;
     474             :             else
     475             :                 quot_ptr[i--] = 0;
     476             : 
     477             :             for( ; i >= 0; i-- ) {
     478             :                 n0 = dividend_ptr[i];
     479             :                 UDIV_QRNND_PREINV( quot_ptr[i], r, r,
     480             :                                    n0, divisor_limb, divisor_limb_inverted);
     481             :             }
     482             :             return r;
     483             :         }
     484             :     }
     485             :     else {
     486             :         if(UDIV_NEEDS_NORMALIZATION) {
     487             :             int normalization_steps;
     488             : 
     489             :             count_leading_zeros (normalization_steps, divisor_limb);
     490             :             if( normalization_steps ) {
     491             :                 divisor_limb <<= normalization_steps;
     492             : 
     493             :                 n1 = dividend_ptr[dividend_size - 1];
     494             :                 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
     495             : 
     496             :                 /* Possible optimization:
     497             :                  * if (r == 0
     498             :                  * && divisor_limb > ((n1 << normalization_steps)
     499             :                  *                 | (dividend_ptr[dividend_size - 2] >> ...)))
     500             :                  * ...one division less...
     501             :                  */
     502             :                 for( i = dividend_size - 2; i >= 0; i--) {
     503             :                     n0 = dividend_ptr[i];
     504             :                     udiv_qrnnd (quot_ptr[i + 1], r, r,
     505             :                              ((n1 << normalization_steps)
     506             :                          | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
     507             :                                 divisor_limb);
     508             :                     n1 = n0;
     509             :                 }
     510             :                 udiv_qrnnd (quot_ptr[0], r, r,
     511             :                             n1 << normalization_steps,
     512             :                             divisor_limb);
     513             :                 return r >> normalization_steps;
     514             :             }
     515             :         }
     516             :         /* No normalization needed, either because udiv_qrnnd doesn't require
     517             :          * it, or because DIVISOR_LIMB is already normalized.  */
     518          63 :         i = dividend_size - 1;
     519          63 :         r = dividend_ptr[i];
     520             : 
     521          63 :         if(r >= divisor_limb)
     522          63 :             r = 0;
     523             :         else
     524           0 :             quot_ptr[i--] = 0;
     525             : 
     526        1099 :         for(; i >= 0; i--) {
     527        1036 :             n0 = dividend_ptr[i];
     528        1036 :             udiv_qrnnd( quot_ptr[i], r, r, n0, divisor_limb );
     529             :         }
     530          63 :         return r;
     531             :     }
     532             : }

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