And an Inline::C implementation of the algorithm is 20x faster still:

#! perl -slw
use strict;
use Inline C => Config => BUILD_NOISY => 1;
use Inline C => <<'END_C',  NAME => '_luhn', CLEAN_AFTER_BUILD =>0;

int c_luhn( char *s ) {
    int i, total = 0;

    for( i=0; i < 15; ++i ) {
        int d = s[ i ] - '0';
        if( !( i  & 1 ) ) {
            d *= 2;
            if( d > 9 ) d -= 9;
        }
        total += d;
    }
    total *= 9;
    return total % 10;
}

END_C
use Time::HiRes qw[ time ];

my @samples = qw[
    4011350000000008
    4011350000000016
    4011350000000024
    4011350000000032
    4011350000000040
    4011350000000057
    4011350000000065
    4011350000000073
    4011350000000081
    4011350000000099
];

sub luhn {
    use integer;
    my $s = $_[ 0 ];
    my $total = 0;
    for my $i ( 0 .. 14 ) {
        my $d = substr( $s, $i, 1 );
        unless( $i & 1 ) {
            $d *= 2;
            $d -= 9 if $d > 9;
        }
        $total += $d;
    }
    $total *= 9;
    return chop $total;
}

for ( @samples ) {
    print "$_: ", luhn( substr $_, 0, 15 );
}

my $start = time;
for ( 401135000000000..401135000999999 ) {
    my $chk = luhn( $_ );
}
printf "Took %.9f seconds.\n", time() - $start;

for ( @samples ) {
    print "$_: ", c_luhn( $_ );
}

my $start = time;
for ( 401135000000000..401135000999999 ) {
    my $chk = c_luhn( $_ );
}
printf "Took %.9f seconds.\n", time() - $start;
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