------------------------------------------------------------------------------
-- --
-- GNAT COMPILER COMPONENTS --
-- --
-- S Y S T E M . 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) 2002-2023, AdaCore --
-- --
-- GNAT is free software; you can redistribute it and/or modify it under --
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-- GNAT was originally developed by the GNAT team at New York University. --
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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 System.Perfect_Hash_Generators is
type Optimization is (Memory_Space, CPU_Time);
-- Optimize either the memory space or the execution time. Note: in
-- practice, the optimization mode has little effect on speed. The tables
-- are somewhat smaller with Memory_Space.
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;
V : Positive;
Optim : Optimization;
Tries : Positive);
-- Initialize the generator and its internal structures. Set the number of
-- vertices in the random graphs. This value has to be greater than twice
-- the number of keys 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 this fails to find a perfect hash function,
-- invoke Initialize again with other configuration parameters (probably
-- with a greater number of vertices). Once successful, invoke Define and
-- Value, and then Finalize.
procedure Finalize;
-- Deallocate the internal structures and the words table
procedure Insert (Value : String);
-- Insert a new word into the table. ASCII.NUL characters are not allowed.
Too_Many_Tries : exception;
-- Raised after Tries unsuccessful runs
procedure Compute (Position : String);
-- Compute the hash function. Position allows the definition of selection
-- of character positions used in the word hash function. Positions can be
-- separated by commas and ranges 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 if the algorithm does not succeed within Tries
-- attempts (see Initialize).
-- 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. Together they can be used to retrieve the parameters of the
-- hash function which has been computed by a call to Compute.
-- 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 (J, K) of the table Name. When the
-- table has only one dimension, K is ignored.
end System.Perfect_Hash_Generators;