Fix handling of shared statistics with dropped databases

[pgsql.git] / src / tools / PerfectHash.pm

#----------------------------------------------------------------------
#
# PerfectHash.pm
#    Perl module that constructs minimal perfect hash functions
#
# This code constructs a minimal perfect hash function for the given
# set of keys, using an algorithm described in
# "An optimal algorithm for generating minimal perfect hash functions"
# by Czech, Havas and Majewski in Information Processing Letters,
# 43(5):256-264, October 1992.
# This implementation is loosely based on NetBSD's "nbperf",
# which was written by Joerg Sonnenberger.
#
# The resulting hash function is perfect in the sense that if the presented
# key is one of the original set, it will return the key's index in the set
# (in range 0..N-1).  However, the caller must still verify the match,
# as false positives are possible.  Also, the hash function may return
# values that are out of range (negative or >= N), due to summing unrelated
# hashtable entries.  This indicates that the presented key is definitely
# not in the set.
#
#
# Portions Copyright (c) 1996-2023, PostgreSQL Global Development Group
# Portions Copyright (c) 1994, Regents of the University of California
#
# src/tools/PerfectHash.pm
#
#----------------------------------------------------------------------

package PerfectHash;

use strict;
use warnings;


# At runtime, we'll compute two simple hash functions of the input key,
# and use them to index into a mapping table.  The hash functions are just
# multiply-and-add in uint32 arithmetic, with different multipliers and
# initial seeds.  All the complexity in this module is concerned with
# selecting hash parameters that will work and building the mapping table.

# We support making case-insensitive hash functions, though this only
# works for a strict-ASCII interpretation of case insensitivity,
# ie, A-Z maps onto a-z and nothing else.
my $case_fold = 0;


#
# Construct a C function implementing a perfect hash for the given keys.
# The C function definition is returned as a string.
#
# The keys should be passed as an array reference.  They can be any set
# of Perl strings; it is caller's responsibility that there not be any
# duplicates.  (Note that the "strings" can be binary data, but hashing
# e.g. OIDs has endianness hazards that callers must overcome.)
#
# The name to use for the function is specified as the second argument.
# It will be a global function by default, but the caller may prepend
# "static " to the result string if it wants a static function.
#
# Additional options can be specified as keyword-style arguments:
#
# case_fold => bool
# If specified as true, the hash function is case-insensitive, for the
# limited idea of case-insensitivity explained above.
#
# fixed_key_length => N
# If specified, all keys are assumed to have length N bytes, and the
# hash function signature will be just "int f(const void *key)"
# rather than "int f(const void *key, size_t keylen)".
#
sub generate_hash_function
{
        my ($keys_ref, $funcname, %options) = @_;

        # It's not worth passing this around as a parameter; just use a global.
        $case_fold = $options{case_fold} || 0;

        # Try different hash function parameters until we find a set that works
        # for these keys.  The multipliers are chosen to be primes that are cheap
        # to calculate via shift-and-add, so don't change them without care.
        # (Commonly, random seeds are tried, but we want reproducible results
        # from this program so we don't do that.)
        my $hash_mult1 = 257;
        my $hash_mult2;
        my $hash_seed1;
        my $hash_seed2;
        my @subresult;
  FIND_PARAMS:
        for ($hash_seed1 = 0; $hash_seed1 < 10; $hash_seed1++)
        {

                for ($hash_seed2 = 0; $hash_seed2 < 10; $hash_seed2++)
                {
                        foreach (17, 31, 127, 8191)
                        {
                                $hash_mult2 = $_;    # "foreach $hash_mult2" doesn't work
                                @subresult = _construct_hash_table(
                                        $keys_ref, $hash_mult1, $hash_mult2,
                                        $hash_seed1, $hash_seed2);
                                last FIND_PARAMS if @subresult;
                        }
                }
        }

        # Choke if we couldn't find a workable set of parameters.
        die "failed to generate perfect hash" if !@subresult;

        # Extract info from _construct_hash_table's result array.
        my $elemtype = $subresult[0];
        my @hashtab = @{ $subresult[1] };
        my $nhash = scalar(@hashtab);

        # OK, construct the hash function definition including the hash table.
        my $f = '';
        $f .= sprintf "int\n";
        if (defined $options{fixed_key_length})
        {
                $f .= sprintf "%s(const void *key)\n{\n", $funcname;
        }
        else
        {
                $f .= sprintf "%s(const void *key, size_t keylen)\n{\n", $funcname;
        }
        $f .= sprintf "\tstatic const %s h[%d] = {\n\t\t", $elemtype, $nhash;
        for (my $i = 0; $i < $nhash; $i++)
        {
                # Hash element.
                $f .= sprintf "%d", $hashtab[$i];
                next if ($i == $nhash - 1);

                # Optional indentation and newline, with eight items per line.
                $f .= sprintf ",%s",
                  ($i % 8 == 7 ? "\n\t\t" : ' ' x (6 - length($hashtab[$i])));
        }
        $f .= sprintf "\n" if ($nhash % 8 != 0);
        $f .= sprintf "\t};\n\n";
        $f .= sprintf "\tconst unsigned char *k = (const unsigned char *) key;\n";
        $f .= sprintf "\tsize_t\t\tkeylen = %d;\n", $options{fixed_key_length}
          if (defined $options{fixed_key_length});
        $f .= sprintf "\tuint32\t\ta = %d;\n", $hash_seed1;
        $f .= sprintf "\tuint32\t\tb = %d;\n\n", $hash_seed2;
        $f .= sprintf "\twhile (keylen--)\n\t{\n";
        $f .= sprintf "\t\tunsigned char c = *k++";
        $f .= sprintf " | 0x20" if $case_fold;                 # see comment below
        $f .= sprintf ";\n\n";
        $f .= sprintf "\t\ta = a * %d + c;\n", $hash_mult1;
        $f .= sprintf "\t\tb = b * %d + c;\n", $hash_mult2;
        $f .= sprintf "\t}\n";
        $f .= sprintf "\treturn h[a %% %d] + h[b %% %d];\n", $nhash, $nhash;
        $f .= sprintf "}\n";

        return $f;
}


# Calculate a hash function as the run-time code will do.
#
# If we are making a case-insensitive hash function, we implement that
# by OR'ing 0x20 into each byte of the key.  This correctly transforms
# upper-case ASCII into lower-case ASCII, while not changing digits or
# dollar signs.  (It does change '_', as well as other characters not
# likely to appear in keywords; this has little effect on the hash's
# ability to discriminate keywords.)
sub _calc_hash
{
        my ($key, $mult, $seed) = @_;

        my $result = $seed;
        for my $c (split //, $key)
        {
                my $cn = ord($c);
                $cn |= 0x20 if $case_fold;
                $result = ($result * $mult + $cn) % 4294967296;
        }
        return $result;
}


# Attempt to construct a mapping table for a minimal perfect hash function
# for the given keys, using the specified hash parameters.
#
# Returns an array containing the mapping table element type name as the
# first element, and a ref to an array of the table values as the second.
#
# Returns an empty array on failure; then caller should choose different
# hash parameter(s) and try again.
sub _construct_hash_table
{
        my ($keys_ref, $hash_mult1, $hash_mult2, $hash_seed1, $hash_seed2) = @_;
        my @keys = @{$keys_ref};

        # This algorithm is based on a graph whose edges correspond to the
        # keys and whose vertices correspond to entries of the mapping table.
        # A key's edge links the two vertices whose indexes are the outputs of
        # the two hash functions for that key.  For K keys, the mapping
        # table must have at least 2*K+1 entries, guaranteeing that there's at
        # least one unused entry.  (In principle, larger mapping tables make it
        # easier to find a workable hash and increase the number of inputs that
        # can be rejected due to touching unused hashtable entries.  In practice,
        # neither effect seems strong enough to justify using a larger table.)
        my $nedges = scalar @keys;       # number of edges
        my $nverts = 2 * $nedges + 1;    # number of vertices

        # However, it would be very bad if $nverts were exactly equal to either
        # $hash_mult1 or $hash_mult2: effectively, that hash function would be
        # sensitive to only the last byte of each key.  Cases where $nverts is a
        # multiple of either multiplier likewise lose information.  (But $nverts
        # can't actually divide them, if they've been intelligently chosen as
        # primes.)  We can avoid such problems by adjusting the table size.
        while ($nverts % $hash_mult1 == 0
                || $nverts % $hash_mult2 == 0)
        {
                $nverts++;
        }

        # Initialize the array of edges.
        my @E = ();
        foreach my $kw (@keys)
        {
                # Calculate hashes for this key.
                # The hashes are immediately reduced modulo the mapping table size.
                my $hash1 = _calc_hash($kw, $hash_mult1, $hash_seed1) % $nverts;
                my $hash2 = _calc_hash($kw, $hash_mult2, $hash_seed2) % $nverts;

                # If the two hashes are the same for any key, we have to fail
                # since this edge would itself form a cycle in the graph.
                return () if $hash1 == $hash2;

                # Add the edge for this key.
                push @E, { left => $hash1, right => $hash2 };
        }

        # Initialize the array of vertices, giving them all empty lists
        # of associated edges.  (The lists will be hashes of edge numbers.)
        my @V = ();
        for (my $v = 0; $v < $nverts; $v++)
        {
                push @V, { edges => {} };
        }

        # Insert each edge in the lists of edges connected to its vertices.
        for (my $e = 0; $e < $nedges; $e++)
        {
                my $v = $E[$e]{left};
                $V[$v]{edges}->{$e} = 1;

                $v = $E[$e]{right};
                $V[$v]{edges}->{$e} = 1;
        }

        # Now we attempt to prove the graph acyclic.
        # A cycle-free graph is either empty or has some vertex of degree 1.
        # Removing the edge attached to that vertex doesn't change this property,
        # so doing that repeatedly will reduce the size of the graph.
        # If the graph is empty at the end of the process, it was acyclic.
        # We track the order of edge removal so that the next phase can process
        # them in reverse order of removal.
        my @output_order = ();

        # Consider each vertex as a possible starting point for edge-removal.
        for (my $startv = 0; $startv < $nverts; $startv++)
        {
                my $v = $startv;

                # If vertex v is of degree 1 (i.e. exactly 1 edge connects to it),
                # remove that edge, and then consider the edge's other vertex to see
                # if it is now of degree 1.  The inner loop repeats until reaching a
                # vertex not of degree 1.
                while (scalar(keys(%{ $V[$v]{edges} })) == 1)
                {
                        # Unlink its only edge.
                        my $e = (keys(%{ $V[$v]{edges} }))[0];
                        delete($V[$v]{edges}->{$e});

                        # Unlink the edge from its other vertex, too.
                        my $v2 = $E[$e]{left};
                        $v2 = $E[$e]{right} if ($v2 == $v);
                        delete($V[$v2]{edges}->{$e});

                        # Push e onto the front of the output-order list.
                        unshift @output_order, $e;

                        # Consider v2 on next iteration of inner loop.
                        $v = $v2;
                }
        }

        # We succeeded only if all edges were removed from the graph.
        return () if (scalar(@output_order) != $nedges);

        # OK, build the hash table of size $nverts.
        my @hashtab = (0) x $nverts;
        # We need a "visited" flag array in this step, too.
        my @visited = (0) x $nverts;

        # The goal is that for any key, the sum of the hash table entries for
        # its first and second hash values is the desired output (i.e., the key
        # number).  By assigning hash table values in the selected edge order,
        # we can guarantee that that's true.  This works because the edge first
        # removed from the graph (and hence last to be visited here) must have
        # at least one vertex it shared with no other edge; hence it will have at
        # least one vertex (hashtable entry) still unvisited when we reach it here,
        # and we can assign that unvisited entry a value that makes the sum come
        # out as we wish.  By induction, the same holds for all the other edges.
        foreach my $e (@output_order)
        {
                my $l = $E[$e]{left};
                my $r = $E[$e]{right};
                if (!$visited[$l])
                {
                        # $hashtab[$r] might be zero, or some previously assigned value.
                        $hashtab[$l] = $e - $hashtab[$r];
                }
                else
                {
                        die "oops, doubly used hashtab entry" if $visited[$r];
                        # $hashtab[$l] might be zero, or some previously assigned value.
                        $hashtab[$r] = $e - $hashtab[$l];
                }
                # Now freeze both of these hashtab entries.
                $visited[$l] = 1;
                $visited[$r] = 1;
        }

        # Detect range of values needed in hash table.
        my $hmin = $nedges;
        my $hmax = 0;
        for (my $v = 0; $v < $nverts; $v++)
        {
                $hmin = $hashtab[$v] if $hashtab[$v] < $hmin;
                $hmax = $hashtab[$v] if $hashtab[$v] > $hmax;
        }

        # Choose width of hashtable entries.  In addition to the actual values,
        # we need to be able to store a flag for unused entries, and we wish to
        # have the property that adding any other entry value to the flag gives
        # an out-of-range result (>= $nedges).
        my $elemtype;
        my $unused_flag;

        if (   $hmin >= -0x7F
                && $hmax <= 0x7F
                && $hmin + 0x7F >= $nedges)
        {
                # int8 will work
                $elemtype = 'int8';
                $unused_flag = 0x7F;
        }
        elsif ($hmin >= -0x7FFF
                && $hmax <= 0x7FFF
                && $hmin + 0x7FFF >= $nedges)
        {
                # int16 will work
                $elemtype = 'int16';
                $unused_flag = 0x7FFF;
        }
        elsif ($hmin >= -0x7FFFFFFF
                && $hmax <= 0x7FFFFFFF
                && $hmin + 0x3FFFFFFF >= $nedges)
        {
                # int32 will work
                $elemtype = 'int32';
                $unused_flag = 0x3FFFFFFF;
        }
        else
        {
                die "hash table values too wide";
        }

        # Set any unvisited hashtable entries to $unused_flag.
        for (my $v = 0; $v < $nverts; $v++)
        {
                $hashtab[$v] = $unused_flag if !$visited[$v];
        }

        return ($elemtype, \@hashtab);
}

1;