------------------------------------------------------------------------------ -- -- -- 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 -- -- -- -- S p e c -- -- -- -- Copyright (C) 2002-2005, AdaCore -- -- -- -- 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- -- -- ware Foundation; either version 2, or (at your option) any later ver- -- -- sion. GNAT is distributed in the hope that it will be useful, but WITH- -- -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -- -- or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License -- -- for more details. You should have received a copy of the GNU General -- -- Public License distributed with GNAT; see file COPYING. If not, write -- -- to the Free Software Foundation, 51 Franklin Street, Fifth Floor, -- -- Boston, MA 02110-1301, USA. -- -- -- -- As a special exception, if other files instantiate generics from this -- -- unit, or you link this unit with other files to produce an executable, -- -- this unit does not by itself cause the resulting executable to be -- -- covered by the GNU General Public License. This exception does not -- -- however invalidate any other reasons why the executable file might be -- -- covered by the GNU Public License. -- -- -- -- GNAT was originally developed by the GNAT team at New York University. -- -- Extensive contributions were provided by Ada Core Technologies Inc. -- -- -- ------------------------------------------------------------------------------ -- 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 of integers [0, k-1], where k is an -- integer, usually k >= m. h (w) where is a word 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 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 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 key set to be known in -- advance (they are "static" hash functions). The hash functions are also -- order preservering. If w2 is inserted after w1 in the generator, then (w1) -- < f (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 stricly 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 key 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 key set. procedure Finalize; -- Deallocate the internal structures and the key table procedure Insert (Value : String); -- Insert a new key in the table Too_Many_Tries : exception; -- Raised after Tries unsuccessfull runs procedure Compute (Position : String := Default_Position); -- Compute the hash function. Position allows to define selection of -- character positions used in the keywords hash function. Positions can be -- separated by commas and range like x-y may be used. Character '$' -- represents the final character of a key. 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 keys 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 key 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 key 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;