gen_expand

#!/usr/bin/perl
# Copyright 2015 Google Inc. All Rights Reserved.
# Licensed 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.

use warnings;
use strict;

defined(my $n = shift)
        or die "usage: $0 n\n";

# special cases i can't be bothered to handle otherwise
print "#define x1(x) x\n";
print "#define x2(x) x x\n";
print "#define x3(x) x2(x) x\n";

sub find_largest_factors($) {
        my ($x) = @_;
        for (my $y = int(sqrt($x)); $y >= 2; --$y) {
                if ($x % $y == 0) {
                        my $z = $x/$y;
                        return "x$y(x$z(x))";
                }
        }
        return undef;
}

foreach my $i (4..$n) {
        if (my $factors = find_largest_factors($i)) {
                print "#define x$i(x) $factors\n";
        }
        else {
                my $factors = find_largest_factors($i-1);
                print "#define x$i(x) $factors x\n";
        }
}