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1 281 jeremybenn
------------------------------------------------------------------------------
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--                                                                          --
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--                         GNAT RUN-TIME COMPONENTS                         --
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--                                                                          --
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--                     G N A T . H E A P _ S O R T _ G                      --
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--                                                                          --
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--                                 B o d y                                  --
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--                                                                          --
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--                     Copyright (C) 1995-2008, AdaCore                     --
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--                                                                          --
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-- GNAT is free software;  you can  redistribute it  and/or modify it under --
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-- terms of the  GNU General Public License as published  by the Free Soft- --
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-- ware  Foundation;  either version 2,  or (at your option) any later ver- --
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-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
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-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
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-- or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License --
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-- for  more details.  You should have  received  a copy of the GNU General --
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-- Public License  distributed with GNAT;  see file COPYING.  If not, write --
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-- to  the  Free Software Foundation,  51  Franklin  Street,  Fifth  Floor, --
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-- Boston, MA 02110-1301, USA.                                              --
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--                                                                          --
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-- As a special exception,  if other files  instantiate  generics from this --
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-- unit, or you link  this unit with other files  to produce an executable, --
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-- this  unit  does not  by itself cause  the resulting  executable  to  be --
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-- covered  by the  GNU  General  Public  License.  This exception does not --
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-- however invalidate  any other reasons why  the executable file  might be --
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-- covered by the  GNU Public License.                                      --
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--                                                                          --
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-- GNAT was originally developed  by the GNAT team at  New York University. --
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-- Extensive contributions were provided by Ada Core Technologies Inc.      --
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--                                                                          --
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------------------------------------------------------------------------------
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package body GNAT.Heap_Sort_G is
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   ----------
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   -- Sort --
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   ----------
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   --  We are using the classical heapsort algorithm (i.e. Floyd's Treesort3)
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   --  as described by Knuth ("The Art of Programming", Volume III, first
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   --  edition, section 5.2.3, p. 145-147) with the modification that is
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   --  mentioned in exercise 18. For more details on this algorithm, see
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   --  Robert B. K. Dewar PhD thesis "The use of Computers in the X-ray
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   --  Phase Problem". University of Chicago, 1968, which was the first
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   --  publication of the modification, which reduces the number of compares
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   --  from 2NlogN to NlogN.
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   procedure Sort (N : Natural) is
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      Max : Natural := N;
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      --  Current Max index in tree being sifted
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      procedure Sift (S : Positive);
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      --  This procedure sifts up node S, i.e. converts the subtree rooted
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      --  at node S into a heap, given the precondition that any sons of
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      --  S are already heaps. On entry, the contents of node S is found
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      --  in the temporary (index 0), the actual contents of node S on
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      --  entry are irrelevant. This is just a minor optimization to avoid
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      --  what would otherwise be two junk moves in phase two of the sort.
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      ----------
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      -- Sift --
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      ----------
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      procedure Sift (S : Positive) is
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         C      : Positive := S;
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         Son    : Positive;
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         Father : Positive;
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         --  Note: by making the above all Positive, we ensure that a test
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         --  against zero for the temporary location can be resolved on the
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         --  basis of types when the routines are inlined.
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      begin
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         --  This is where the optimization is done, normally we would do a
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         --  comparison at each stage between the current node and the larger
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         --  of the two sons, and continue the sift only if the current node
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         --  was less than this maximum. In this modified optimized version,
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         --  we assume that the current node will be less than the larger
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         --  son, and unconditionally sift up. Then when we get to the bottom
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         --  of the tree, we check parents to make sure that we did not make
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         --  a mistake. This roughly cuts the number of comparisons in half,
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         --  since it is almost always the case that our assumption is correct.
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         --  Loop to pull up larger sons
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         loop
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            Son := 2 * C;
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            if Son < Max then
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               if Lt (Son, Son + 1) then
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                  Son := Son + 1;
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               end if;
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            elsif Son > Max then
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               exit;
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            end if;
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            Move (Son, C);
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            C := Son;
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         end loop;
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         --  Loop to check fathers
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         while C /= S loop
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            Father := C / 2;
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            if Lt (Father, 0) then
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               Move (Father, C);
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               C := Father;
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            else
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               exit;
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            end if;
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         end loop;
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         --  Last step is to pop the sifted node into place
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         Move (0, C);
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      end Sift;
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   --  Start of processing for Sort
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   begin
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      --  Phase one of heapsort is to build the heap. This is done by
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      --  sifting nodes N/2 .. 1 in sequence.
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      for J in reverse 1 .. N / 2 loop
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         Move (J, 0);
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         Sift (J);
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      end loop;
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      --  In phase 2, the largest node is moved to end, reducing the size
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      --  of the tree by one, and the displaced node is sifted down from
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      --  the top, so that the largest node is again at the top.
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      while Max > 1 loop
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         Move (Max, 0);
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         Move (1, Max);
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         Max := Max - 1;
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         Sift (1);
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      end loop;
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   end Sort;
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end GNAT.Heap_Sort_G;

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