1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT RUN-TIME COMPONENTS                         --
4--                                                                          --
5--                     G N A T . H E A P _ S O R T _ G                      --
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.                                     --
17--                                                                          --
18-- As a special exception under Section 7 of GPL version 3, you are granted --
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
32package body GNAT.Heap_Sort_G is
33
34   ----------
35   -- Sort --
36   ----------
37
38   --  We are using the classical heapsort algorithm (i.e. Floyd's Treesort3)
39   --  as described by Knuth ("The Art of Programming", Volume III, first
40   --  edition, section 5.2.3, p. 145-147) with the modification that is
41   --  mentioned in exercise 18. For more details on this algorithm, see
42   --  Robert B. K. Dewar PhD thesis "The use of Computers in the X-ray
43   --  Phase Problem". University of Chicago, 1968, which was the first
44   --  publication of the modification, which reduces the number of compares
45   --  from 2NlogN to NlogN.
46
47   procedure Sort (N : Natural) is
48
49      Max : Natural := N;
50      --  Current Max index in tree being sifted
51
52      procedure Sift (S : Positive);
53      --  This procedure sifts up node S, i.e. converts the subtree rooted
54      --  at node S into a heap, given the precondition that any sons of
55      --  S are already heaps. On entry, the contents of node S is found
56      --  in the temporary (index 0), the actual contents of node S on
57      --  entry are irrelevant. This is just a minor optimization to avoid
58      --  what would otherwise be two junk moves in phase two of the sort.
59
60      ----------
61      -- Sift --
62      ----------
63
64      procedure Sift (S : Positive) is
65         C      : Positive := S;
66         Son    : Positive;
67         Father : Positive;
68         --  Note: by making the above all Positive, we ensure that a test
69         --  against zero for the temporary location can be resolved on the
70         --  basis of types when the routines are inlined.
71
72      begin
73         --  This is where the optimization is done, normally we would do a
74         --  comparison at each stage between the current node and the larger
75         --  of the two sons, and continue the sift only if the current node
76         --  was less than this maximum. In this modified optimized version,
77         --  we assume that the current node will be less than the larger
78         --  son, and unconditionally sift up. Then when we get to the bottom
79         --  of the tree, we check parents to make sure that we did not make
80         --  a mistake. This roughly cuts the number of comparisons in half,
81         --  since it is almost always the case that our assumption is correct.
82
83         --  Loop to pull up larger sons
84
85         loop
86            Son := 2 * C;
87
88            if Son < Max then
89               if Lt (Son, Son + 1) then
90                  Son := Son + 1;
91               end if;
92            elsif Son > Max then
93               exit;
94            end if;
95
96            Move (Son, C);
97            C := Son;
98         end loop;
99
100         --  Loop to check fathers
101
102         while C /= S loop
103            Father := C / 2;
104
105            if Lt (Father, 0) then
106               Move (Father, C);
107               C := Father;
108            else
109               exit;
110            end if;
111         end loop;
112
113         --  Last step is to pop the sifted node into place
114
115         Move (0, C);
116      end Sift;
117
118   --  Start of processing for Sort
119
120   begin
121      --  Phase one of heapsort is to build the heap. This is done by
122      --  sifting nodes N/2 .. 1 in sequence.
123
124      for J in reverse 1 .. N / 2 loop
125         Move (J, 0);
126         Sift (J);
127      end loop;
128
129      --  In phase 2, the largest node is moved to end, reducing the size
130      --  of the tree by one, and the displaced node is sifted down from
131      --  the top, so that the largest node is again at the top.
132
133      while Max > 1 loop
134         Move (Max, 0);
135         Move (1, Max);
136         Max := Max - 1;
137         Sift (1);
138      end loop;
139
140   end Sort;
141
142end GNAT.Heap_Sort_G;
143