------------------------------------------------------------------------------
--                                                                          --
--                         GNAT RUN-TIME COMPONENTS                         --
--                                                                          --
--                       G N A T . H E A P _ S O R T                        --
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--                                 B o d y                                  --
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--                     Copyright (C) 1995-2019, AdaCore                     --
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-- GNAT is free software;  you can  redistribute it  and/or modify it under --
-- terms of the  GNU General Public License as published  by the Free Soft- --
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-- GNAT was originally developed  by the GNAT team at  New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc.      --
--                                                                          --
------------------------------------------------------------------------------

package body GNAT.Heap_Sort is

   ----------
   -- Sort --
   ----------

   --  We are using the classical heapsort algorithm (i.e. Floyd's Treesort3)
   --  as described by Knuth ("The Art of Programming", Volume III, first
   --  edition, section 5.2.3, p. 145-147) with the modification that is
   --  mentioned in exercise 18. For more details on this algorithm, see
   --  Robert B. K. Dewar PhD thesis "The use of Computers in the X-ray
   --  Phase Problem". University of Chicago, 1968, which was the first
   --  publication of the modification, which reduces the number of compares
   --  from 2NlogN to NlogN.

   procedure Sort (N : Natural; Xchg : Xchg_Procedure; Lt : Lt_Function) is
      Max : Natural := N;
      --  Current Max index in tree being sifted. Note that we make Max
      --  Natural rather than Positive so that the case of sorting zero
      --  elements is correctly handled (i.e. does nothing at all).

      procedure Sift (S : Positive);
      --  This procedure sifts up node S, i.e. converts the subtree rooted
      --  at node S into a heap, given the precondition that any sons of
      --  S are already heaps.

      ----------
      -- Sift --
      ----------

      procedure Sift (S : Positive) is
         C      : Positive := S;
         Son    : Positive;
         Father : Positive;

      begin
         --  This is where the optimization is done, normally we would do a
         --  comparison at each stage between the current node and the larger
         --  of the two sons, and continue the sift only if the current node
         --  was less than this maximum. In this modified optimized version,
         --  we assume that the current node will be less than the larger
         --  son, and unconditionally sift up. Then when we get to the bottom
         --  of the tree, we check parents to make sure that we did not make
         --  a mistake. This roughly cuts the number of comparisons in half,
         --  since it is almost always the case that our assumption is correct.

         --  Loop to pull up larger sons

         loop
            Son := C + C;

            if Son < Max then
               if Lt (Son, Son + 1) then
                  Son := Son + 1;
               end if;
            elsif Son > Max then
               exit;
            end if;

            Xchg (Son, C);
            C := Son;
         end loop;

         --  Loop to check fathers

         while C /= S loop
            Father := C / 2;

            if Lt (Father, C) then
               Xchg (Father, C);
               C := Father;
            else
               exit;
            end if;
         end loop;
      end Sift;

   --  Start of processing for Sort

   begin
      --  Phase one of heapsort is to build the heap. This is done by
      --  sifting nodes N/2 .. 1 in sequence.

      for J in reverse 1 .. N / 2 loop
         Sift (J);
      end loop;

      --  In phase 2, the largest node is moved to end, reducing the size
      --  of the tree by one, and the displaced node is sifted down from
      --  the top, so that the largest node is again at the top.

      while Max > 1 loop
         Xchg (1, Max);
         Max := Max - 1;
         Sift (1);
      end loop;
   end Sort;

end GNAT.Heap_Sort;