# perl spectral-norm.pl 5500
# output: 1.274224153

# The Computer Language Benchmarks Game
# http://benchmarksgame.alioth.debian.org/
#
# Contributed by Andrew Rodland
# modified by R. Jelinek
# multicore by Mykola Zubach
# MCE::Map version by Mario Roy

use strict;
use MCE::Map;

my $n = shift || 500;
my $cpus = 4; ## MCE::Util->get_ncpu() || 4;

MCE::Map->init(
    max_workers => $cpus,
    chunk_size  => int(($n - 1) / $cpus) + 1,
);

my @v = multiplyAtAv(
    multiplyAtAv( multiplyAtAv((1) x $n) )
);

my @u = multiplyAtAv(@v);
my ($i, $vBv, $vv) = (0);

for my $v (@v) {
    $vBv += $u[$i++] * $v, $vv += $v ** 2;
}

printf "%0.9f\n", sqrt($vBv / $vv);

MCE::Map->finish();

sub multiplyAtAv {
    return multiplyAtv(multiplyAv(@_));
}

sub eval_A {
    use integer;
    my $div = (($_[0] + $_[1]) * ($_[0] + $_[1] + 1) >> 1) + $_[0] + 1;
    no integer;
    1 / $div;
}

sub multiplyAv {
    my @data = @_;
    return mce_map_s {
        my ($i, $sum) = ($_);
        $sum += eval_A($i, $_) * $data[$_] for (0 .. $#data);
        $sum;
    } 0, $#data;
}

sub multiplyAtv {
    my @data = @_;
    return mce_map_s {
        my ($i, $sum) = ($_);
        $sum += eval_A($_, $i) * $data[$_] for (0 .. $#data);
        $sum;
    } 0, $#data;
}