Re^10: High Performance Game of Life

[marioroy]

Hi eyepopslikeamosquito. Yes, I've been running tgol2.t found here and it's been running fine. I can comfirm that bit-manipulation is failing with the new tgot2.t. The initial test script did not test for negative $y. Thus, assumed that $y was always positive. The bit-manipulation code will no longer work.

Okay, will comment readers to your post and strike out the bit-manipulation sections. Thank you for posting Extra Test Program tgol.t.

Update: For closure, I tested mapping supporting negative $x and $y. Pack('i2') is faster unless running cperl.

use strict;
use warnings;
use Time::HiRes qw(time);

my ( $x , $y , $iters ) = ( -890394, 100, 5_000_000 );
my ( $xx, $yy, $n );

##
# sub _pack {
#    my ( $x, $y ) = @_;
#    return
#       $x < 0 ? -( abs($x) << 16 | $y ) : $x << 16 | $y;
# }
#
# sub _unpack {
#    my ( $n ) = @_;
#    return $n < 0
#       ? ( -( abs($n) >> 16 ), abs($n) & 0xFFFF )
#       : (        $n  >> 16  ,     $n  & 0xFFFF );
# }
##

bench( "bitops     ", sub {
   # map two integers $x and $y into $n
   # support negative $x only
   for ( 1 .. $iters ) {
      $n = $x < 0 ? -( abs($x) << 16 | $y ) : $x << 16 | $y;
      ( $xx, $yy ) = $n < 0
         ? ( -( abs($n) >> 16 ), abs($n) & 0xFFFF )
         : (        $n  >> 16  ,     $n  & 0xFFFF );
   }
});

##
# sub _pack {
#    my ( $x, $y ) = @_;
#    # bits 0,1 indicate neg flag for $x,$y respectively
#    return
#       ( abs($x) << 18 ) + ( $x < 0 ? 1 : 0 ) +
#       ( abs($y) << 2  ) + ( $y < 0 ? 2 : 0 );
# }
#
# sub _unpack {
#    my ( $n ) = @_;
#    # bits 0,1 indicate neg flag for $x,$y respectively
#    return (
#       $n & 0x1 ? -($n >> 18        ) : $n >> 18,
#       $n & 0x2 ? -($n >> 2 & 0xFFFF) : $n >> 2 & 0xFFFF
#    );
# }
##

bench( "bitops neg ", sub {
   # map two integers $x and $y into $n
   # support negative $x and $y
   for ( 1 .. $iters ) {
      $n = ( abs($x) << 18 ) + ( $x < 0 ? 1 : 0 ) +
           ( abs($y) << 2  ) + ( $y < 0 ? 2 : 0 );
      ( $xx, $yy ) = (
         $n & 0x1 ? -($n >> 18        ) : $n >> 18,
         $n & 0x2 ? -($n >> 2 & 0xFFFF) : $n >> 2 & 0xFFFF
      );
   }
});

bench( "(un)pack ii", sub {
   for ( 1 .. $iters ) {
      $n = pack 'ii', $x, $y;
      ( $xx, $yy ) = unpack 'ii', $n;
   }
});

bench( "(un)pack i2", sub {
   for ( 1 .. $iters ) {
      $n = pack 'i2', $x, $y;
      ( $xx, $yy ) = unpack 'i2', $n;
   }
});

exit;

sub bench {
   my ( $start, $desc, $fcn ) = ( scalar time, @_ );
   $fcn->();
   printf "duration $desc  %0.03f\n", time - $start;
}

Regards, Mario

[marioroy]

Update: Replaced bit-OR with addition to have $x and $y line up for better readability.

This post is a fun study, comparing pack 'i2' against the mapping of two integers into one via bit manipulation. A use case for doing this is wanting readable keys for storing into a database using one field. This laptop runs an i7 Haswell at 2.6 GHz. Unfortunately, I do not have anything slower to run on.

bin/perl v5.26.0

$ perl createblinker.pl 500000 -900000 100 >x.tmp 2>y.tmp

$ /opt/perl-5.26.0/bin/perl -I. tbench1.pl x.tmp 2      # pack i2
cell count at start = 1500000
run benchmark for 2 ticks
cell count at end = 1500000
time taken: 37 secs
time taken: 58 secs  <- 32-bit Windows VM

$ /opt/perl-5.26.0/bin/perl -I. tbench1.pl x.tmp 2      # mapping
cell count at start = 1500000
run benchmark for 2 ticks
cell count at end = 1500000
time taken: 39 secs
time taken: 64 secs  <- 32-bit Windows VM, applied 32-bit tip below

bin/cperl v5.24.3c

$ /opt/cperl-5.24.3c/bin/cperl -I. tbench1.pl x.tmp 2   # pack i2
cell count at start = 1500000
run benchmark for 2 ticks
cell count at end = 1500000
time taken: 37 secs

$ /opt/cperl-5.24.3c/bin/cperl -I. tbench1.pl x.tmp 2   # mapping
cell count at start = 1500000
run benchmark for 2 ticks
cell count at end = 1500000
time taken: 38 secs

I used tybalt89's update and applied the mapping logic. All tests pass, thanks to new test script by eyepopslikeamosquito. Please ensure Perl is compiled with 64-bit support. 16 bits hold the value for $y and 2 bits for whether $x,$y are less than 0. $x is stored in the remaining bits. This results in minimum key lenght as $y isn't big. Though, adjust accordingly the number of bits to shift and bitmask if necessary.

bits 63-18 contains the $x value
bits 17-2  contains the $y value
bit  1     set when $y < 0
bit  0     set when $x < 0

On 32-bit hardware, replace 18 and 0xFFFF with 10 and 0xFF throughout the module.

bits 31-10 contains the $x value
bits 9-2   contains the $y value
bit  1     set when $y < 0
bit  0     set when $x < 0

Both _unpack and _pack are inlined inside tick for maximum performance.

package Organism;

use strict;
# use warnings;

sub _pack {
   my ( $x, $y ) = @_;
   # bits 0,1 negative flag for $x,$y respectively
   return
      ( abs($x) << 18 ) + ( $x < 0 ? 1 : 0 ) +
      ( abs($y) << 2  ) + ( $y < 0 ? 2 : 0 );
}

sub _unpack {
   my ( $n ) = @_;
   # bits 0,1 negative flag for $x,$y respectively
   return (
      $n & 0x1 ? -($n >> 18        ) : $n >> 18,
      $n & 0x2 ? -($n >> 2 & 0xFFFF) : $n >> 2 & 0xFFFF
   );
}

sub count {
   return scalar keys %{ shift->{Cells} };
}

# Input a list of [ x, y ] coords
sub insert_cells {
   my $cells = shift->{Cells};
   for my $r (@_) { $cells->{ _pack @{$r} } = undef }
}

# Return sorted list of cells in the Organism.
# Used for verification and testing the state of the organism.
sub get_live_cells {
   sort { $a->[0] <=> $b->[0] || $a->[1] <=> $b->[1] }
      map { [ _unpack $_ ] }
      keys %{ shift->{Cells} };
}

sub tick {
   my $self  = shift;
   my $cells = $self->{Cells};
   my ( $k1, $k2, $k3, $k4, $k5, $k6, $k7, $k8,
        $x0, $x1, $x2, $y0, $y1, $y2, %new_cells, %dead_cells );

   for my $c (keys %{ $cells }) {
      # Get the (up to 8) dead cells surrounding the cell
      ( $x0, $y0 ) = (
         $c & 0x1 ? -($c >> 18        ) : $c >> 18,
         $c & 0x2 ? -($c >> 2 & 0xFFFF) : $c >> 2 & 0xFFFF
      );

      ( $x1, $x2, $y1, $y2 ) = ( $x0 - 1, $x0 + 1, $y0 - 1, $y0 + 1 );

      $dead_cells{$_}++ for my @zcells = (
         ( $k1 = ( abs($x1) << 18 ) + ( $x1 < 0 ? 1 : 0 ) +
                 ( abs($y1) << 2  ) + ( $y1 < 0 ? 2 : 0 )
         ) x !(exists $cells->{$k1}),

         ( $k2 = ( abs($x1) << 18 ) + ( $x1 < 0 ? 1 : 0 ) +
                 ( abs($y0) << 2  ) + ( $y0 < 0 ? 2 : 0 )
         ) x !(exists $cells->{$k2}),

         ( $k3 = ( abs($x1) << 18 ) + ( $x1 < 0 ? 1 : 0 ) +
                 ( abs($y2) << 2  ) + ( $y2 < 0 ? 2 : 0 )
         ) x !(exists $cells->{$k3}),

         ( $k4 = ( abs($x0) << 18 ) + ( $x0 < 0 ? 1 : 0 ) +
                 ( abs($y1) << 2  ) + ( $y1 < 0 ? 2 : 0 )
         ) x !(exists $cells->{$k4}),

         ( $k5 = ( abs($x0) << 18 ) + ( $x0 < 0 ? 1 : 0 ) +
                 ( abs($y2) << 2  ) + ( $y2 < 0 ? 2 : 0 )
         ) x !(exists $cells->{$k5}),

         ( $k6 = ( abs($x2) << 18 ) + ( $x2 < 0 ? 1 : 0 ) +
                 ( abs($y1) << 2  ) + ( $y1 < 0 ? 2 : 0 )
         ) x !(exists $cells->{$k6}),

         ( $k7 = ( abs($x2) << 18 ) + ( $x2 < 0 ? 1 : 0 ) +
                 ( abs($y0) << 2  ) + ( $y0 < 0 ? 2 : 0 )
         ) x !(exists $cells->{$k7}),

         ( $k8 = ( abs($x2) << 18 ) + ( $x2 < 0 ? 1 : 0 ) +
                 ( abs($y2) << 2  ) + ( $y2 < 0 ? 2 : 0 )
         ) x !(exists $cells->{$k8})
      );

      # Check the live cell
      # Note: next line equivalent to nlive == 2 || nlive == 3
      @zcells == 5 || @zcells == 6 and $new_cells{$c} = undef;
   }

   $dead_cells{$_} == 3 and $new_cells{$_} = undef for keys %dead_cell
+s;
   $self->{Cells} = \%new_cells;
}

sub new {
   my $class = shift;
   my %init_self = ( Cells => {} );
   bless \%init_self, $class;
}

1;

Pack is faster, of course. However, mapping two integers into one is not far behind.

Regards, Mario

[tybalt89]

I don't have access to a 64-bit perl. However, this is a 32-bit version of combining two 16 bit integers into a 32 bit number. While this runs as long as the coordinates are within range, I can't test it in the 64-bit version.

I like it because all offsets are found with a simple addition inside tick.
All the encode/decode mess is in the input and output routines.

In theory (completely untested), all that's needed is to change the line

my $half = 16; # make 32 for 64-bit perls

to

my $half = 32; # make 32 for 64-bit perls

to make it use the full range of two 32 bit numbers.

So here's the code

package Organism;

use strict;
use warnings;

sub count {
   return scalar keys %{ shift->{Cells} };
}

# Input a list of [ x, y ] coords
sub insert_cells {
   my $self = shift;
   my $cells = $self->{Cells};
   for my $r (@_) { $cells->{
    (($r->[0] + $self->{fudge}) << $self->{half}) |
    ($r->[1] + $self->{fudge})
    } = undef }
}

# Return sorted list of cells in the Organism.
# Used for verification and testing the state of the organism.
sub get_live_cells {
   my $self = shift;
   sort { $a->[0] <=> $b->[0] || $a->[1] <=> $b->[1] }
      map { [
      ($_ >> $self->{half}) - $self->{fudge},
      ($_ & (1 << $self->{half}) - 1) - $self->{fudge}
      ] } keys %{ $self->{Cells} };
}

sub tick {
   my $self  = shift;
   my $cells = $self->{Cells};
   my @deltas = @{ $self->{deltas} };
   my ( %new_cells, %dead_cells );

   for my $c (keys %{ $cells }) {
      # Get the (up to 8) dead cells surrounding the cell
      $dead_cells{$_}++ for my @zcells =
        grep !exists $cells->{$_}, map $c + $_, @deltas;

      # Check the live cell
      # Note: next line equivalent to nlive == 2 || nlive == 3
      @zcells == 5 || @zcells == 6 and $new_cells{$c} = undef;
   }
   $dead_cells{$_} == 3 and $new_cells{$_} = undef for keys %dead_cell
+s;
   $self->{Cells} = \%new_cells;
}

sub new {
   my $class = shift;
   my $half = 16; # make 32 for 64-bit perls
   my $base = 1 << $half;
   my $fudge = $base >> 1;
   my @deltas = ($base-1, $base, $base+1,
    -1, 1, -$base-1, -$base, -$base+1);
   my %init_self = ( Cells => {},
    fudge => $fudge, half => $half, deltas => \@deltas );
   bless \%init_self, $class;
}

1;

Preliminary testing with 16 bit numbers seemed to show it's about 10% slower than the pack version :(

[marioroy]

Hi tybalt89. The following was captured from a 64-bit laptop with $half = 32. Unfortunately, cperl is failing for some reason. I also tried $half = 16, same thing. The cell count at end isn't correct. To be sure, I pulled down the latest maint release and tried again.

$ perl createblinker.pl 500000 -900000 100 >x.tmp 2>y.tmp

bin/perl

$ /opt/perl-5.24.2/bin/perl -I. tbench1.pl x.tmp 2
cell count at start = 1500000
run benchmark for 2 ticks
cell count at end = 1500000
time taken: 42 secs

$ /opt/perl-5.26.0/bin/perl -I. tbench1.pl x.tmp 2
cell count at start = 1500000
run benchmark for 2 ticks
cell count at end = 1500000
time taken: 42 secs

bin/cperl

$ /opt/cperl-5.24.3c/bin/cperl -I. tbench1.pl x.tmp 2
cell count at start = 1500000
run benchmark for 2 ticks
cell count at end = 675003  <-- incorrect
time taken: 34 secs

$ /opt/cperl-5.26.1c/bin/cperl -I. tbench1.pl x.tmp 2
cell count at start = 1500000
run benchmark for 2 ticks
cell count at end = 675003  <-- incorrect
time taken: 34 secs

Regarding cperl, I built it using the following configure options. The source for cperl-maint-5.24c and cperl-maint-5.26c can be found on Github.

./Configure -Dprefix=/opt/cperl-5.24.3c -sder -Dusethreads -Dusecperl 
+-Accflags=-msse4.2

./Configure -Dprefix=/opt/cperl-5.26.1c -sder -Dusethreads -Dusecperl 
+-Accflags=-msse4.2

Regards, Mario