1  /* mpn_divexact_1 -- mpn by limb exact division.
       2  
       3     THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY.  THEY'RE ALMOST
       4     CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
       5     FUTURE GNU MP RELEASES.
       6  
       7  Copyright 2000-2003, 2005, 2013 Free Software Foundation, Inc.
       8  
       9  This file is part of the GNU MP Library.
      10  
      11  The GNU MP Library is free software; you can redistribute it and/or modify
      12  it under the terms of either:
      13  
      14    * the GNU Lesser General Public License as published by the Free
      15      Software Foundation; either version 3 of the License, or (at your
      16      option) any later version.
      17  
      18  or
      19  
      20    * the GNU General Public License as published by the Free Software
      21      Foundation; either version 2 of the License, or (at your option) any
      22      later version.
      23  
      24  or both in parallel, as here.
      25  
      26  The GNU MP Library is distributed in the hope that it will be useful, but
      27  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
      28  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
      29  for more details.
      30  
      31  You should have received copies of the GNU General Public License and the
      32  GNU Lesser General Public License along with the GNU MP Library.  If not,
      33  see https://www.gnu.org/licenses/.  */
      34  
      35  #include "gmp-impl.h"
      36  #include "longlong.h"
      37  
      38  
      39  
      40  /* Divide a={src,size} by d=divisor and store the quotient in q={dst,size}.
      41     q will only be correct if d divides a exactly.
      42  
      43     A separate loop is used for shift==0 because n<<GMP_LIMB_BITS doesn't
      44     give zero on all CPUs (for instance it doesn't on the x86s).  This
      45     separate loop might run faster too, helping odd divisors.
      46  
      47     Possibilities:
      48  
      49     mpn_divexact_1c could be created, accepting and returning c.  This would
      50     let a long calculation be done piece by piece.  Currently there's no
      51     particular need for that, and not returning c means that a final umul can
      52     be skipped.
      53  
      54     Another use for returning c would be letting the caller know whether the
      55     division was in fact exact.  It would work just to return the carry bit
      56     "c=(l>s)" and let the caller do a final umul if interested.
      57  
      58     When the divisor is even, the factors of two could be handled with a
      59     separate mpn_rshift, instead of shifting on the fly.  That might be
      60     faster on some CPUs and would mean just the shift==0 style loop would be
      61     needed.
      62  
      63     If n<<GMP_LIMB_BITS gives zero on a particular CPU then the separate
      64     shift==0 loop is unnecessary, and could be eliminated if there's no great
      65     speed difference.
      66  
      67     It's not clear whether "/" is the best way to handle size==1.  Alpha gcc
      68     2.95 for instance has a poor "/" and might prefer the modular method.
      69     Perhaps a tuned parameter should control this.
      70  
      71     If src[size-1] < divisor then dst[size-1] will be zero, and one divide
      72     step could be skipped.  A test at last step for s<divisor (or ls in the
      73     even case) might be a good way to do that.  But if this code is often
      74     used with small divisors then it might not be worth bothering  */
      75  
      76  void
      77  mpn_divexact_1 (mp_ptr dst, mp_srcptr src, mp_size_t size, mp_limb_t divisor)
      78  {
      79    mp_size_t  i;
      80    mp_limb_t  c, h, l, ls, s, s_next, inverse, dummy;
      81    unsigned   shift;
      82  
      83    ASSERT (size >= 1);
      84    ASSERT (divisor != 0);
      85    ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, size));
      86    ASSERT_MPN (src, size);
      87    ASSERT_LIMB (divisor);
      88  
      89    if ((divisor & 1) == 0)
      90      {
      91        count_trailing_zeros (shift, divisor);
      92        divisor >>= shift;
      93      }
      94    else
      95      shift = 0;
      96  
      97    binvert_limb (inverse, divisor);
      98    divisor <<= GMP_NAIL_BITS;
      99  
     100    if (shift != 0)
     101      {
     102        c = 0;
     103  
     104        s = src[0];
     105  
     106        for (i = 1; i < size; i++)
     107  	{
     108  	  s_next = src[i];
     109  	  ls = ((s >> shift) | (s_next << (GMP_NUMB_BITS-shift))) & GMP_NUMB_MASK;
     110  	  s = s_next;
     111  
     112  	  SUBC_LIMB (c, l, ls, c);
     113  
     114  	  l = (l * inverse) & GMP_NUMB_MASK;
     115  	  dst[i - 1] = l;
     116  
     117  	  umul_ppmm (h, dummy, l, divisor);
     118  	  c += h;
     119  	}
     120  
     121        ls = s >> shift;
     122        l = ls - c;
     123        l = (l * inverse) & GMP_NUMB_MASK;
     124        dst[size - 1] = l;
     125      }
     126    else
     127      {
     128        s = src[0];
     129  
     130        l = (s * inverse) & GMP_NUMB_MASK;
     131        dst[0] = l;
     132        c = 0;
     133  
     134        for (i = 1; i < size; i++)
     135  	{
     136  	  umul_ppmm (h, dummy, l, divisor);
     137  	  c += h;
     138  
     139  	  s = src[i];
     140  	  SUBC_LIMB (c, l, s, c);
     141  
     142  	  l = (l * inverse) & GMP_NUMB_MASK;
     143  	  dst[i] = l;
     144  	}
     145      }
     146  }