```
package Dumbbench;
use strict;
use warnings;
use Carp ();
use Time::HiRes ();
our $VERSION = '0.111';
require Dumbbench::Result;
require Dumbbench::Stats;
require Dumbbench::Instance;
use Params::Util '_INSTANCE';
use Class::XSAccessor {
getters => [qw(
target_rel_precision
target_abs_precision
initial_runs
max_iterations
variability_measure
started
outlier_rejection
subtract_dry_run
)],
accessors => [qw(verbosity)],
};
sub new {
my $proto = shift;
my $class = ref($proto)||$proto;
my $self;
if (not ref($proto)) {
$self = bless {
verbosity => 0,
target_rel_precision => 0.05,
target_abs_precision => 0,
initial_runs => 20,
max_iterations => 10000,
variability_measure => 'mad',
instances => [],
started => 0,
outlier_rejection => 3,
subtract_dry_run => 1,
@_,
} => $class;
}
else {
$self = bless {%$proto, @_} => $class;
my @inst = $self->instances;
$self->{instances} = [];
foreach my $instance (@inst) {
push @{$self->{instances}}, $instance->new;
}
}
if ($self->target_abs_precision <= 0 and $self->target_rel_precision <= 0) {
Carp::croak("Need either target_rel_precision or target_abs_precision > 0");
}
if ($self->initial_runs < 6) {
Carp::carp("Number of initial runs is very small (<6). Precision will be off.");
}
return $self;
}
sub add_instances {
my $self = shift;
if ($self->started) {
Carp::croak("Can't add instances after the benchmark has been started");
}
foreach my $instance (@_) {
if (not _INSTANCE($instance, 'Dumbbench::Instance')) {
Carp::croak("Argument to add_instances is not a Dumbbench::Instance");
}
}
push @{$self->{instances}}, @_;
}
sub instances {
my $self = shift;
return @{$self->{instances}};
}
sub run {
my $self = shift;
Carp::croak("Can't re-run same benchmark instance") if $self->started;
$self->dry_run_timings if $self->subtract_dry_run;
$self->run_timings;
}
sub run_timings {
my $self = shift;
$self->{started} = 1;
foreach my $instance ($self->instances) {
next if $instance->result;
$self->_run($instance);
}
}
sub dry_run_timings {
my $self = shift;
$self->{started} = 1;
foreach my $instance ($self->instances) {
next if $instance->dry_result;
$self->_run($instance, 'dry');
}
}
sub _run {
my $self = shift;
my $instance = shift;
my $dry = shift;
my $name = $instance->_name_prefix;
# for overriding in case of dry-run mode
my $V = $self->verbosity || 0;
my $initial_timings = $self->initial_runs;
my $abs_precision = $self->target_abs_precision;
my $rel_precision = $self->target_rel_precision;
my $max_iterations = $self->max_iterations;
if ($dry) {
$V--; $V = 0 if $V < 0;
$initial_timings *= 5;
$abs_precision = 0;
$rel_precision /= 2;
$max_iterations *= 10;
}
print "${name}Running initial timing for warming up the cache...\n" if $V;
if ($dry) {
# be generous, this is fast
$instance->single_dry_run() for 1..3;
}
else {
$instance->single_run();
}
my @timings;
print "${name}Running $initial_timings initial timings...\n" if $V;
foreach (1..$initial_timings) {
print "${name}Running timing $_...\n" if $V > 1;
push @timings, ($dry ? $instance->single_dry_run() : $instance->single_run());
}
print "${name}Iterating until target precision reached...\n" if $V;
my $stats = Dumbbench::Stats->new(data => \@timings);
my $sigma;
my $mean;
#My mental model for the distribution was Gauss+outliers.
#If my expectation is correct, the following algorithm should produce a reasonable EV +/- uncertainty:
#1) Calc. median of the whole distribution.
#2) Calculate the median-absolute deviation from the whole distribution (MAD, see wikipedia). It needs rescaling to become a measure of variability that is robust against outliers.
#(The MAD will be our initial guess for a "sigma")
#3) Reject the samples that are outside $median +/- $n*$MAD.
#I was expecting several high outliers but few lows. An ordinary truncated mean or the like would be unsuitable for removing the outliers in such a case since you'd get a significant upward bias of your EV.
#By using the median as the initial guess, we keep the initial bias to a minimum. The MAD will be similarly unaffected by outliers AND the asymmetry.
#Thus cutting the tails won't blow up the bias too strongly (hopefully).
#4) Calculate mean & MAD/sqrt($n) of the remaining distribution. These are our EV and uncertainty on the mean.
my $n_good = 0;
my $variability_measure = $self->variability_measure;
while (1) {
my ($good, $outliers) = $stats->filter_outliers(
variability_measure => $variability_measure,
nsigma_outliers => $self->outlier_rejection,
);
$n_good = @$good;
if (not $n_good and @timings >= $max_iterations) {
$mean = 0; $sigma = 0;
last;
}
if ($n_good) {
my $new_stats = Dumbbench::Stats->new(data => $good);
$sigma = $new_stats->$variability_measure() / sqrt($n_good);
$mean = $new_stats->mean();
# stop condition
my $need_iter = 0;
if ($rel_precision > 0) {
my $rel = $sigma/$mean;
print "${name}Reached relative precision $rel (neeed $rel_precision).\n" if $V > 1;
$need_iter++ if $rel > $rel_precision;
}
if ($abs_precision > 0) {
print "${name}Reached absolute precision $sigma (neeed $abs_precision).\n" if $V > 1;
$need_iter++ if $sigma > $abs_precision;
}
if ($n_good < $initial_timings) {
$need_iter++;
}
last if not $need_iter or @timings >= $max_iterations;
}
# progressively run more new timings in one go. Otherwise,
# we start to stall on the O(n*log(n)) complexity of the median.
my $n = List::Util::min( $max_iterations - @timings, List::Util::max(1, @timings*0.05) );
push @timings, ($dry ? $instance->single_dry_run() : $instance->single_run()) for 1..$n;
} # end while more data required
if (@timings >= $max_iterations and not $dry) {
print "${name}Reached maximum number of iterations. Stopping. Precision not reached.\n";
}
# rescale sigma
# This is necessary since by cutting everything outside of n-sigma,
# we artificially reduce the variability of the main distribution.
if ($self->outlier_rejection) {
# TODO implement
}
my $result = Dumbbench::Result->new(
timing => $mean,
uncertainty => $sigma,
nsamples => $n_good,
);
if ($dry) {
$instance->{dry_timings} = \@timings;
$instance->dry_result($result);
}
else {
$instance->{timings} = \@timings;
$result -= $instance->dry_result
if defined $instance->dry_result and $self->subtract_dry_run;
$instance->result($result);
}
}
sub report {
my ( $self, $raw, $options ) = @_;
$options ||= {};
Carp::carp( "The second option to report was not a hash ref" )
unless ref $options eq ref {};
foreach my $instance ($self->instances) {
my $result = $instance->result;
my $result_str = ($options->{float}) ? unscientific_notation($result) : "$result";
if (not $raw) {
my $mean = $result->raw_number;
my $sigma = $result->raw_error->[0];
my $name = $instance->_name_prefix;
printf(
"%sRan %u iterations (%u outliers).\n",
$name,
scalar(@{$instance->timings}),
scalar(@{$instance->timings})-$result->nsamples
);
printf(
"%sRounded run time per iteration: %s (%.1f%%)\n",
$name,
$result_str,
$sigma/$mean*100
);
if ($self->verbosity) {
printf("%sRaw: $mean +/- $sigma\n", $name);
}
}
else {
print $result_str, "\n";
}
}
}
sub box_plot {
my $self = shift;
eval "require Dumbbench::BoxPlot;";
return() if $@;
return Dumbbench::BoxPlot->new($self);
}
sub unscientific_notation {
sprintf( "%f %s %f", split( / /, $_[0] ) );
}
1;
__END__
=head1 NAME
Dumbbench - More reliable benchmarking with the least amount of thinking
=head1 SYNOPSIS
Command line interface: (See C<dumbbench --help>)
dumbbench -p 0.005 -- ./testprogram --testprogramoption
This will start churning for a while and then prints something like:
Ran 23 iterations of the command.
Rejected 3 samples as outliers.
Rounded run time per iteration: 9.519e-01 +/- 3.7e-03 (0.4%)
As a module:
use Dumbbench;
my $bench = Dumbbench->new(
target_rel_precision => 0.005, # seek ~0.5%
initial_runs => 20, # the higher the more reliable
);
$bench->add_instances(
Dumbbench::Instance::Cmd->new(command => [qw(perl -e 'something')]),
Dumbbench::Instance::PerlEval->new(code => 'for(1..1e7){something}'),
Dumbbench::Instance::PerlSub->new(code => sub {for(1..1e7){something}}),
);
# (Note: Comparing the run of externals commands with
# evals/subs probably isn't reliable)
$bench->run;
$bench->report;
=head1 DESCRIPTION
This module attempts to implement reasonably robust benchmarking with
little extra effort and expertise required from the user. That is to say,
benchmarking using this module is likely an improvement over
time some-command --to --benchmark
or
use Benchmark qw/timethis/;
timethis(1000, 'system("some-command", ...)');
The module currently works similar to the former command line, except (in layman terms)
it will run the command many times, estimate the uncertainty of the result and keep
iterating until a certain user-defined precision has been reached. Then, it calculates
the resulting uncertainty and goes through some pain to discard bad runs and subtract
overhead from the timings. The reported timing includes an uncertainty, so that multiple
benchmarks can more easily be compared.
Please note that C<Dumbbench> works entirely with wallclock time as reported by
C<Time::HiRes>' C<time()> function.
=head1 METHODS
In addition to the methods listed here, there are read-only
accessors for all named arguments of the constructor
(which are also object attributes).
=head2 new
Constructor that takes the following arguments (with defaults):
verbosity => 0, # 0, 1, or 2
target_rel_precision => 0.05, # 5% target precision
target_abs_precision => 0, # no target absolute precision (in s)
intial_runs => 20, # no. of guaranteed initial runs
max_iterations => 10000, # hard max. no of iterations
variability_measure => 'mad', # method for calculating uncertainty
outlier_rejection => 3, # no. of "sigma"s for the outlier rejection
C<variability_measure> and C<outlier_rejection> probably make sense
after reading C<HOW IT WORKS> below. Setting C<outlier_rejection> to 0
will turn it off entirely.
=head2 add_instances
Takes one ore more instances of subclasses of L<Dumbbench::Instance>
as argument. Each of those is one I<benchmark>, really.
They are run in sequence and reported separately.
Right now, there are the following C<Dumbbench::Instance> implementations:
L<Dumbbench::Instance::Cmd> for running/benchmarking external commands,
L<Dumbbench::Instance::PerlEval> for running/benchmarking
Perl code in this same process using C<eval>,
and
L<Dumbbench::Instance::PerlSub> for running/benchmarking
Perl code in this same process using a subroutine reference.
=head2 run
Runs the dry-run and benchmark run.
=head2 report
Prints a short report about the benchmark results.
=head2 instances
Returns a list of all instance objects in this benchmark set.
The instance objects each have a C<result()> and C<dry_result()>
method for accessing the numeric benchmark results.
=head2 box_plot
Returns a L<Dumbbench::BoxPlot> instance.
A L<Dumbbench::BoxPlot> is a nice an easy way to get a graphic chart if
you're in the mood instead of getting the same results from C<report>.
If you don't want to get into the details of L<Dumbbench::BoxPlot>, you can do:
# $bench is your Dumbbench instance
$bench->box_plot->show;
=head1 HOW IT WORKS AND WHY IT DOESN'T
=head2 Why it doesn't work and why we try regardless
Recall that the goal is to obtain a reliable estimate of the run-time of
a certain operation or command. Now, please realize that this is impossible
since the run-time of an operation may depend on many things that can change rapidly:
Modern CPUs change their frequency dynamically depending on load. CPU caches may be
invalidated at odd moments and page faults provide less fine-grained distration.
Naturally, OS kernels will do weird things just to spite you. It's almost hopeless.
Since people (you, I, everybody!) insist on benchmarking anyway, this is a best-effort
at estimating the run-time. Naturally, it includes estimating the uncertainty of the
run time. This is extremely important for comparing multiple benchmarks and that
is usually the ultimate goal. In order to get an estimate of the expectation value
and its uncertainty, we need a model of the underlying distribution:
=head2 A model for timing results
Let's take a step back and think about how the run-time of multiple
invocations of the same code will be distributed. Having a qualitative
idea what the distribution of many (B<MANY>) measurements looks like is
extremely important for estimating the expectation value and uncertainty
from a sample of few measurements.
In a perfect, deterministic, single-tasking computer, we will get N times the
exact same timing. In the real world, there are at least a million ways that
this assumption is broken on a small scale. For each run, the load of the
computer will be slightly different. The content of main memory and CPU
caches may differ. All of these small effects will make a given run a tiny
bit slower or faster than any other. Thankfully, this is a case where statistics (more precisely
the Central Limit Theorem) provides us with the I<qualitative> result: The
measurements will be normally distributed (i.e. following a Gaussian
distribution) around some expectation value (which happens to be the mean in this case).
Good. Unfortunately, benchmarks are more evil than that. In addition to the small-scale
effects that smear the result, there are things that (at the given run time of the benchmark)
may be large enough to cause a large jump in run time. Assuming these are
comparatively rare and typically cause extraordinarily long run-times (as opposed to
extraordinarily low run-times), we arrive at an overall model of
having a central, smooth-ish normal distribution with a few outliers towards
long run-times.
So in this model, if we perform C<N> measurements, almost all C<N> times
will be close to the expectation value and a fraction will be significantly higher.
This is troublesome because the outliers create a bias in the uncertainty
estimation and the asymmetry of the overall distribution will bias a simple
calculation of the mean.
What we would like to report to the user is the mean and uncertainty
of the main distribution while ignoring the outliers.
=head2 A robust estimation of the expectation value
Given the previously discussed model, we estimate the expectation value
with the following algorithm:
=over 2
=item 1)
Calculate the median of the whole distribution.
The median is a fairly robust estimator of the expectation value
with respect to outliers (assuming they're comparatively rare).
=item 2)
Calculate the median-absolute-deviation from the whole distribution
(MAD, see wikipedia). The MAD needs rescaling to become a measure
of variability. The MAD will be our initial guess for an uncertainty.
Like the median, it is quite robust against outliers.
=item 3)
We use the median and MAD to remove the tails of our distribution.
All timings that deviate from the median by more than C<$X> times the MAD
are rejected. This measure should cut outliers without introducing
much bias both in symmetric and asymmetric source distributions.
An alternative would be to use an ordinary truncated mean (that is
the mean of all timings while disregarding the C<$N> largest and C<$N>
smallest results). But the truncated mean can produce a biased result
in asymmetric source distributions. The resulting expectation value
would be artificially increased.
In summary: Using the median as the initial guess for the expectation value and the
MAD as the guess for the variability keeps the bias down in the general case.
=item 4)
Finally, the use the mean of the truncated distribution as the expectation
value and the MAD of the truncated distribution as a measure of variability.
To get the uncertainty on the expectation value, we take C<MAD / sqrt($N)> where
C<$N> is the number of remaining measurements.
=back
=head2 Conclusion
I hope I could convince you that interpreting less sophisticated benchmarks
is a dangerous if not futile exercise. The reason this module exists is
that not everybody is willing to go through such contortions to arrive
at a reliable conclusion, but everybody loves benchmarking. So let's at least
get the basics right. Do not compare raw timings of meaningless benchmarks but
robust estimates of the run time of meaningless benchmarks instead.
=head1 SEE ALSO
L<Dumbbench::Instance>,
L<Dumbbench::Instance::Cmd>,
L<Dumbbench::Instance::PerlEval>,
L<Dumbbench::Instance::PerlSub>,
L<Dumbbench::Result>
L<Benchmark>
L<Number::WithError> does the Gaussian error propagation.
L<http://en.wikipedia.org/wiki/Median_absolute_deviation>
=head1 AUTHOR
Steffen Mueller, E<lt>smueller@cpan.orgE<gt>
=head1 COPYRIGHT AND LICENSE
Copyright (C) 2010, 2011, 2012, 2013 by Steffen Mueller
This library is free software; you can redistribute it and/or modify
it under the same terms as Perl itself, either Perl version 5.8.1 or,
at your option, any later version of Perl 5 you may have available.
=cut
```