1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT RUN-TIME COMPONENTS                         --
4--                                                                          --
5--                     G N A T . H E A P _ S O R T _ A                      --
6--                                                                          --
7--                                 B o d y                                  --
8--                                                                          --
9--                     Copyright (C) 1995-2010, AdaCore                     --
10--                                                                          --
11-- GNAT is free software;  you can  redistribute it  and/or modify it under --
12-- terms of the  GNU General Public License as published  by the Free Soft- --
13-- ware  Foundation;  either version 3,  or (at your option) any later ver- --
14-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
15-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
16-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
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19-- additional permissions described in the GCC Runtime Library Exception,   --
20-- version 3.1, as published by the Free Software Foundation.               --
21--                                                                          --
22-- You should have received a copy of the GNU General Public License and    --
23-- a copy of the GCC Runtime Library Exception along with this program;     --
24-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
25-- <http://www.gnu.org/licenses/>.                                          --
26--                                                                          --
27-- GNAT was originally developed  by the GNAT team at  New York University. --
28-- Extensive contributions were provided by Ada Core Technologies Inc.      --
29--                                                                          --
30------------------------------------------------------------------------------
31
32pragma Compiler_Unit;
33
34package body GNAT.Heap_Sort_A is
35
36   ----------
37   -- Sort --
38   ----------
39
40   --  We are using the classical heapsort algorithm (i.e. Floyd's Treesort3)
41   --  as described by Knuth ("The Art of Programming", Volume III, first
42   --  edition, section 5.2.3, p. 145-147) with the modification that is
43   --  mentioned in exercise 18. For more details on this algorithm, see
44   --  Robert B. K. Dewar PhD thesis "The use of Computers in the X-ray
45   --  Phase Problem". University of Chicago, 1968, which was the first
46   --  publication of the modification, which reduces the number of compares
47   --  from 2NlogN to NlogN.
48
49   procedure Sort (N : Natural; Move : Move_Procedure; Lt : Lt_Function) is
50
51      Max : Natural := N;
52      --  Current Max index in tree being sifted
53
54      procedure Sift (S : Positive);
55      --  This procedure sifts up node S, i.e. converts the subtree rooted
56      --  at node S into a heap, given the precondition that any sons of
57      --  S are already heaps. On entry, the contents of node S is found
58      --  in the temporary (index 0), the actual contents of node S on
59      --  entry are irrelevant. This is just a minor optimization to avoid
60      --  what would otherwise be two junk moves in phase two of the sort.
61
62      procedure Sift (S : Positive) is
63         C      : Positive := S;
64         Son    : Positive;
65         Father : Positive;
66
67      begin
68         --  This is where the optimization is done, normally we would do a
69         --  comparison at each stage between the current node and the larger
70         --  of the two sons, and continue the sift only if the current node
71         --  was less than this maximum. In this modified optimized version,
72         --  we assume that the current node will be less than the larger
73         --  son, and unconditionally sift up. Then when we get to the bottom
74         --  of the tree, we check parents to make sure that we did not make
75         --  a mistake. This roughly cuts the number of comparisons in half,
76         --  since it is almost always the case that our assumption is correct.
77
78         --  Loop to pull up larger sons
79
80         loop
81            Son := 2 * C;
82            exit when Son > Max;
83
84            if Son < Max and then Lt (Son, Son + 1) then
85               Son := Son + 1;
86            end if;
87
88            Move (Son, C);
89            C := Son;
90         end loop;
91
92         --  Loop to check fathers
93
94         while C /= S loop
95            Father := C / 2;
96
97            if Lt (Father, 0) then
98               Move (Father, C);
99               C := Father;
100            else
101               exit;
102            end if;
103         end loop;
104
105         --  Last step is to pop the sifted node into place
106
107         Move (0, C);
108      end Sift;
109
110   --  Start of processing for Sort
111
112   begin
113      --  Phase one of heapsort is to build the heap. This is done by
114      --  sifting nodes N/2 .. 1 in sequence.
115
116      for J in reverse 1 .. N / 2 loop
117         Move (J, 0);
118         Sift (J);
119      end loop;
120
121      --  In phase 2, the largest node is moved to end, reducing the size
122      --  of the tree by one, and the displaced node is sifted down from
123      --  the top, so that the largest node is again at the top.
124
125      while Max > 1 loop
126         Move (Max, 0);
127         Move (1, Max);
128         Max := Max - 1;
129         Sift (1);
130      end loop;
131
132   end Sort;
133
134end GNAT.Heap_Sort_A;
135