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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;
