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--                                                                          --

--                         GNAT COMPILER COMPONENTS                         --

--                                                                          --

--          G N A T . P E R F E C T _ H A S H _ G E N E R A T O R S         --

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--                                 S p e c                                  --

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--                     Copyright (C) 2002-2008, AdaCore                     --

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-- GNAT is free software;  you can  redistribute it  and/or modify it under --

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-- covered by the  GNU Public License.                                      --

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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.      --

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--  This package provides a generator of static minimal perfect hash functions.

--  To understand what a perfect hash function is, we define several notions.

--  These definitions are inspired from the following paper:

--    Zbigniew J. Czech, George Havas, and Bohdan S. Majewski ``An Optimal

--    Algorithm for Generating Minimal Perfect Hash Functions'', Information

--    Processing Letters, 43(1992) pp.257-264, Oct.1992

--  Let W be a set of m words. A hash function h is a function that maps the

--  set of words W into some given interval I of integers [0, k-1], where k is

--  an integer, usually k >= m. h (w) where w is a word in W computes an

--  address or an integer from I for the storage or the retrieval of that

--  item. The storage area used to store items is known as a hash table. Words

--  for which the same address is computed are called synonyms. Due to the

--  existence of synonyms a situation called collision may arise in which two

--  items w1 and w2 have the same address. Several schemes for resolving

--  collisions are known. A perfect hash function is an injection from the word

--  set W to the integer interval I with k >= m.  If k = m, then h is a minimal

--  perfect hash function. A hash function is order preserving if it puts

--  entries into the hash table in a prespecified order.

--  A minimal perfect hash function is defined by two properties:

--    Since no collisions occur each item can be retrieved from the table in

--    *one* probe. This represents the "perfect" property.

--    The hash table size corresponds to the exact size of W and *no larger*.

--    This represents the "minimal" property.

--  The functions generated by this package require the words to be known in

--  advance (they are "static" hash functions). The hash functions are also

--  order preserving. If w2 is inserted after w1 in the generator, then h (w1)

--  < h (w2). These hashing functions are convenient for use with realtime

--  applications.

package GNAT.Perfect_Hash_Generators is

   Default_K_To_V : constant Float  := 2.05;

   --  Default ratio for the algorithm. When K is the number of keys, V =

   --  (K_To_V) * K is the size of the main table of the hash function. To

   --  converge, the algorithm requires K_To_V to be strictly greater than 2.0.

   Default_Pkg_Name : constant String := "Perfect_Hash";

   --  Default package name in which the hash function is defined

   Default_Position : constant String := "";

   --  The generator allows selection of the character positions used in the

   --  hash function. By default, all positions are selected.

   Default_Tries : constant Positive := 20;

   --  This algorithm may not succeed to find a possible mapping on the first

   --  try and may have to iterate a number of times. This constant bounds the

   --  number of tries.

   type Optimization is (Memory_Space, CPU_Time);

   Default_Optimization : constant Optimization := CPU_Time;

   --  Optimize either the memory space or the execution time

   Verbose : Boolean := False;

   --  Output the status of the algorithm. For instance, the tables, the random

   --  graph (edges, vertices) and selected char positions are output between

   --  two iterations.

   procedure Initialize

     (Seed   : Natural;

      K_To_V : Float        := Default_K_To_V;

      Optim  : Optimization := CPU_Time;

      Tries  : Positive     := Default_Tries);

   --  Initialize the generator and its internal structures. Set the ratio of

   --  vertices over keys in the random graphs. This value has to be greater

   --  than 2.0 in order for the algorithm to succeed. The word set is not

   --  modified (in particular when it is already set). For instance, it is

   --  possible to run several times the generator with different settings on

   --  the same words.

   --

   --  A classical way of doing is to Insert all the words and then to invoke

   --  Initialize and Compute. If Compute fails to find a perfect hash

   --  function, invoke Initialize another time with other configuration

   --  parameters (probably with a greater K_To_V ratio). Once successful,

   --  invoke Produce and Finalize.

   procedure Finalize;

   --  Deallocate the internal structures and the words table

   procedure Insert (Value : String);

   --  Insert a new word in the table

   Too_Many_Tries : exception;

   --  Raised after Tries unsuccessful runs

   procedure Compute (Position : String := Default_Position);

   --  Compute the hash function. Position allows to define selection of

   --  character positions used in the word hash function. Positions can be

   --  separated by commas and range like x-y may be used. Character '$'

   --  represents the final character of a word. With an empty position, the

   --  generator automatically produces positions to reduce the memory usage.

   --  Raise Too_Many_Tries in case that the algorithm does not succeed in less

   --  than Tries attempts (see Initialize).

   procedure Produce (Pkg_Name  : String := Default_Pkg_Name);

   --  Generate the hash function package Pkg_Name. This package includes the

   --  minimal perfect Hash function.

   --  The routines and structures defined below allow producing the hash

   --  function using a different way from the procedure above. The procedure

   --  Define returns the lengths of an internal table and its item type size.

   --  The function Value returns the value of each item in the table.

   --  The hash function has the following form:

   --             h (w) = (g (f1 (w)) + g (f2 (w))) mod m

   --  G is a function based on a graph table [0,n-1] -> [0,m-1]. m is the

   --  number of keys. n is an internally computed value and it can be obtained

   --  as the length of vector G.

   --  F1 and F2 are two functions based on two function tables T1 and T2.

   --  Their definition depends on the chosen optimization mode.

   --  Only some character positions are used in the words because they are

   --  significant. They are listed in a character position table (P in the

   --  pseudo-code below). For instance, in {"jan", "feb", "mar", "apr", "jun",

   --  "jul", "aug", "sep", "oct", "nov", "dec"}, only positions 2 and 3 are

   --  significant (the first character can be ignored). In this example, P =

   --  {2, 3}

   --  When Optimization is CPU_Time, the first dimension of T1 and T2

   --  corresponds to the character position in the word and the second to the

   --  character set. As all the character set is not used, we define a used

   --  character table which associates a distinct index to each used character

   --  (unused characters are mapped to zero). In this case, the second

   --  dimension of T1 and T2 is reduced to the used character set (C in the

   --  pseudo-code below). Therefore, the hash function has the following:

   --    function Hash (S : String) return Natural is

   --       F      : constant Natural := S'First - 1;

   --       L      : constant Natural := S'Length;

   --       F1, F2 : Natural := 0;

   --       J      : <t>;

   --    begin

   --       for K in P'Range loop

   --          exit when L < P (K);

   --          J  := C (S (P (K) + F));

   --          F1 := (F1 + Natural (T1 (K, J))) mod <n>;

   --          F2 := (F2 + Natural (T2 (K, J))) mod <n>;

   --       end loop;

   --       return (Natural (G (F1)) + Natural (G (F2))) mod <m>;

   --    end Hash;

   --  When Optimization is Memory_Space, the first dimension of T1 and T2

   --  corresponds to the character position in the word and the second

   --  dimension is ignored. T1 and T2 are no longer matrices but vectors.

   --  Therefore, the used character table is not available. The hash function

   --  has the following form:

   --     function Hash (S : String) return Natural is

   --        F      : constant Natural := S'First - 1;

   --        L      : constant Natural := S'Length;

   --        F1, F2 : Natural := 0;

   --        J      : <t>;

   --     begin

   --        for K in P'Range loop

   --           exit when L < P (K);

   --           J  := Character'Pos (S (P (K) + F));

   --           F1 := (F1 + Natural (T1 (K) * J)) mod <n>;

   --           F2 := (F2 + Natural (T2 (K) * J)) mod <n>;

   --        end loop;

   --        return (Natural (G (F1)) + Natural (G (F2))) mod <m>;

   --     end Hash;

   type Table_Name is

     (Character_Position,

      Used_Character_Set,

      Function_Table_1,

      Function_Table_2,

      Graph_Table);

   procedure Define

     (Name      : Table_Name;

      Item_Size : out Natural;

      Length_1  : out Natural;

      Length_2  : out Natural);

   --  Return the definition of the table Name. This includes the length of

   --  dimensions 1 and 2 and the size of an unsigned integer item. When

   --  Length_2 is zero, the table has only one dimension. All the ranges

   --  start from zero.

   function Value

     (Name : Table_Name;

      J    : Natural;

      K    : Natural := 0) return Natural;

   --  Return the value of the component (I, J) of the table Name. When the

   --  table has only one dimension, J is ignored.

end GNAT.Perfect_Hash_Generators;