```
# Chi-square probability combining and related constants.
#
# <@LICENSE>
# Licensed to the Apache Software Foundation (ASF) under one or more
# contributor license agreements. See the NOTICE file distributed with
# this work for additional information regarding copyright ownership.
# The ASF licenses this file to you under the Apache License, Version 2.0
# (the "License"); you may not use this file except in compliance with
# the License. You may obtain a copy of the License at:
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# </@LICENSE>
use strict; # make Test::Perl::Critic happy
# this package is a no-op; the real impl code is in another pkg.
package Mail::SpamAssassin::Bayes::CombineChi; 1;
# Force into another package, so our symbols will appear in that namespace with
# no indirection, for speed. Other combiners must do the same, since Bayes.pm
# uses this namespace directly. This means only one combiner can be loaded at
# any time.
package Mail::SpamAssassin::Bayes::Combine;
use strict;
use warnings;
# use bytes;
use re 'taint';
use POSIX qw(frexp);
use constant LN2 => log(2);
# Value for 'x' in Gary Robinson's f(w) equation.
# "Let x = the number used when n [hits] is 0."
our $FW_X_CONSTANT = 0.538;
# Value for 's' in the f(w) equation. "We can see s as the "strength" (hence
# the use of "s") of an original assumed expectation ... relative to how
# strongly we want to consider our actual collected data." Low 's' means
# trust collected data more strongly.
our $FW_S_CONSTANT = 0.030;
# (s . x) for the f(w) equation.
our $FW_S_DOT_X = ($FW_X_CONSTANT * $FW_S_CONSTANT);
# Should we ignore tokens with probs very close to the middle ground (.5)?
# tokens need to be outside the [ .5-MPS, .5+MPS ] range to be used.
our $MIN_PROB_STRENGTH = 0.346;
###########################################################################
# Chi-Squared method. Produces mostly boolean $result,
# but with a grey area.
sub combine {
my ($ns, $nn, $sortedref) = @_;
# @$sortedref contains an array of the probabilities
my $wc = scalar @$sortedref;
return unless $wc;
my ($H, $S);
my ($Hexp, $Sexp);
$Hexp = $Sexp = 0;
# see bug 3118
my $totmsgs = ($ns + $nn);
if ($totmsgs == 0) { return; }
$S = ($ns / $totmsgs);
$H = ($nn / $totmsgs);
foreach my $prob (@$sortedref) {
$S *= 1.0 - $prob;
$H *= $prob;
if ($S < 1e-200) {
my $e;
($S, $e) = frexp($S);
$Sexp += $e;
}
if ($H < 1e-200) {
my $e;
($H, $e) = frexp($H);
$Hexp += $e;
}
}
$S = log($S) + $Sexp * LN2;
$H = log($H) + $Hexp * LN2;
# note: previous versions used (2 * $wc) as second arg ($v), but the chi2q()
# fn then just used ($v/2) internally! changed to simply supply $wc as
# ($halfv) directly instead to avoid redundant doubling and halving. The
# side-effect is that chi2q() uses a different API now, but it's only used
# here anyway.
$S = 1.0 - chi2q(-2.0 * $S, $wc);
$H = 1.0 - chi2q(-2.0 * $H, $wc);
return (($S - $H) + 1.0) / 2.0;
}
# Chi-squared function (API changed; see comment above)
sub chi2q {
my ($x2, $halfv) = @_;
my $m = $x2 / 2.0;
my ($sum, $term);
$sum = $term = exp(0 - $m);
# replace 'for my $i (1 .. (($v/2)-1))' idiom, which creates a temp
# array, with a plain C-style for loop
my $i;
for ($i = 1; $i < $halfv; $i++) {
$term *= $m / $i;
$sum += $term;
}
return $sum < 1.0 ? $sum : 1.0;
}
1;
```