You are right. See the following benchmarks:
use strict;
use warnings;
use Benchmark 'cmpthese';
sub create { map {rand() < $_[1] ? 1 : 0} 1..$_[0] }
sub compare1 { # naive
my $x = shift;
my $n = shift;
return map { my $y=$_; scalar grep { $y->[$_] == 1 and $x->[$_] == 1
+ } 0..$n-1 } @_;
}
sub compare2 { # first find 1s in x, then check in ys
my $x = shift;
my $n = shift;
my @nxs = grep { $x->[$_] } 0..$n-1;
return map { my $y=$_; scalar grep { $y->[$_] == 1 } @nxs } @_ ;
}
sub compare3 { # stringify
my $x = shift;
$x = join '', @$x;
return map { my $j = $x & join'',@$_; $j =~ tr/1/1/ } @_;
}
my $n = 15000;
my $p = 0.005;
my $ny = 10;
my @x = create $n, $p;
my @ys = map { [ create $n, $p ] } 1..$ny;
my @r1 = compare1 \@x, $n, @ys;
my @r2 = compare2 \@x, $n, @ys;
my @r3 = compare3 \@x, @ys;
print "compare1: @r1\n";
print "compare2: @r2\n";
print "compare3: @r3\n";
cmpthese( -5, { compare1 => sub{ compare1 \@x, $n, @ys },
compare2 => sub{ compare2 \@x, $n, @ys },
compare3 => sub{ compare3 \@x, @ys },
}
);
Results:
Rate compare1 compare3 compare2
compare1 48.8/s -- -81% -91%
compare3 253/s 420% -- -53%
compare2 537/s 1002% 112% --