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#!/usr/bin/perl -w
# Generate the spokes of a wheel, for wheel factorization.
# Copyright (C) 2001, 2005 Free Software Foundation, Inc.
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2, or (at your option)
# any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT 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
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
eval 'exec /usr/bin/perl -S $0 ${1+"$@"}'
if 0;
use strict;
(my $ME = $0) =~ s|.*/||;
# A global destructor to close standard output with error checking.
sub END
{
defined fileno STDOUT
or return;
close STDOUT
and return;
warn "$ME: closing standard output: $!\n";
$? ||= 1;
}
sub is_prime ($)
{
my ($n) = @_;
use integer;
$n == 2
and return 1;
my $d = 2;
my $w = 1;
while (1)
{
my $q = $n / $d;
$n == $q * $d
and return 0;
$d += $w;
$q < $d
and last;
$w = 2;
}
return 1;
}
{
@ARGV == 1
or die "$ME: missing argument\n";
my $wheel_size = $ARGV[0];
my @primes = (2);
my $product = $primes[0];
my $n_primes = 1;
for (my $i = 3; ; $i += 2)
{
if (is_prime $i)
{
push @primes, $i;
$product *= $i;
++$n_primes == $wheel_size
and last;
}
}
my $ws_m1 = $wheel_size - 1;
print <<EOF;
/* The first $ws_m1 elements correspond to the incremental offsets of the
first $wheel_size primes (@primes). The $wheel_size(th) element is the
difference between that last prime and the next largest integer
that is not a multiple of those primes. The remaining numbers
define the wheel. For more information, see
http://www.utm.edu/research/primes/glossary/WheelFactorization.html. */
EOF
my @increments;
my $prev = 2;
for (my $i = 3; ; $i += 2)
{
my $rel_prime = 1;
foreach my $divisor (@primes)
{
$i != $divisor && $i % $divisor == 0
and $rel_prime = 0;
}
if ($rel_prime)
{
#warn $i, ' ', $i - $prev, "\n";
push @increments, $i - $prev;
$prev = $i;
$product + 1 < $i
and last;
}
}
print join (",\n", @increments), "\n";
exit 0;
}
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