use strict; use warnings; #use Math::Random qw(random_uniform random_set_seed_from_phrase random_binomial random_set_seed); #use Math::Random qw(random_binomial random_set_seed); #use Data::Dumper; use List::Util qw(sum); use Carp; #use Crypt::Random qw( makerandom ); #use File::Slurp; #for large list of real randoms #my @rands = read_file('rand.txt'); #print sum(@rands), "\n"; #croak; #my $r = makerandom ( Size => 10, Strength => 1 ); #print $r; #croak; #random_set_seed_from_phrase(2); #my @seed = (1 + int(rand(2147483562)), 1 + int(rand(2147483398))); #random_set_seed(@seed); #my @a = random_uniform($n); #my $runs = 1000; #my $counter = 1; # global: subroutine entry counter my $counter = 0; # global: subroutine entry counter #increment($runs, \@rands); start(); sub start { my $runs = 1000; my $n = 2**8; increment($runs, $n); } sub increment { # my ($runs, $randsref) = @_; my ($runs, $n) = @_; my (@axis, @data); # my @axis = 0; # my @data = 1; # my $start = 16655; # my $end = 16675; # my $start = 1; my $start = 0; my $end = 100; # for my $inc (16655..16675) { for my $inc ($start..$end) { # my @seed = (1 + int(rand(2147483562)), 1 + int(rand(2147483398))); # random_set_seed(@seed); # my $counter = 0; my $av = 0; my $p = $inc/100; for (1..$runs) { # my $p = $inc/100; # my $p = $inc/100000; # $counter = 1; $counter = 0; # my $p = 0.002374; # countit($p, $randsref); countit($p, $n); $av += $counter; # $counter = 0; # $counter = 1; } print $inc/100, ' ', sprintf("%.1f", $av/$runs), "\n"; # push @axis, $inc/100;# if $inc/10 == int($inc/10); push @axis, $p; push @data, sprintf("%.1f", $av/$runs); } dograph(\@axis, \@data, $start, $end); } sub countit { my ($p, $n) = @_; # my ($p, $randsref) = @_; # my $nt = 1; # my $n = 2**8; # my @seed = (1 + int(rand(2147483562)), 1 + int(rand(2147483398))); # random_set_seed(@seed); # my @a = random_binomial($n, $nt, $p); # my $bits = 10; # my $r = makerandom ( Size => $bits, Strength => 1 ); # my $divfactor = 2**$bits; # my $pmult = $p*$divfactor; # my @a = map {makerandom ( Size => $bits, Strength => 1 ) > $pmult ? 0 : 1} 1..$n; #print Dumper @a; #print "pmult $pmult\n"; #print makerandom ( Size => $bits, Strength => 1 ), "\n"; #croak; my @a = map {rand > $p ? 0 : 1} 1..$n; # my @a = map {(rand > $p)} 1..$n; # print $offset*$n, "\n"; # my $r = shift @rands; #print "$r, $p\n"; # my @a = map {shift(@rands) > $p ? 0 : 1} 1..$n; # my @a = makedist($n, $randsref, $p); # @a = (0, 1, 0, 0, 0, 0, 1, 0); my %h = map {$_ => 0} 0..$#a; # print Dumper @a; #croak; # print Dumper %h; # print "bs\n"; # if (sum(@a) > 0) { # my %temp = map {$h{$_} == 1} keys %h; # %h = %temp; # $counter++; # } else { # $counter++; binary_search(\@a, 0, \%h); my @misses = grep {$h{$_} != 1} keys %h; if (scalar @misses) { print join('', $_, ' ', $misses[$_], "\n") for @misses; croak "missed some\n"; } # } # my @misses = grep {$h{$_} != 1} keys %h; # croak "missed some\n/" if scalar @misses; # print "bs over $counter\n"; # print Dumper %h; # print Dumper @misses; } sub binary_search { my ($aref, $pos, $href) = @_; $counter++; #print scalar @$aref; #print " $pos \n"; #print Dumper $aref; # my $mid; # my @aref = @$aref; my $bigness = scalar(@$aref); if ($bigness == 1) { $href->{$pos}++; } else { my $mid = $bigness/2; if (sum(@$aref) > 0) { my @aref1 = @$aref[$mid..$#$aref]; binary_search(\@aref1, $mid+$pos, $href); my @aref2 = @$aref[0..--$mid]; binary_search(\@aref2, $pos, $href); } else { $href->{$_}++ for $pos..$pos+$bigness-1; } } } sub makedist { my ($n, $randsref, $p) = @_; my @a; for (1..$n) { my $thisone = shift @$randsref; my $bit = $thisone > $p ? 0 : 1; push @a, $bit; } return @a; } sub dograph { # my ($axisref, $dataref, $p, $n) = @_; my ($axisref, $dataref, $start, $end) = @_; # use GD::Graph::bars; use GD::Graph::points; use GD::Graph::Data; #use Carp; #my $data = GD::Graph::Data->new([ # ["1st","2nd","3rd","4th","5th","6th","7th", "8th", "9th"], # [ 1, 2, 5, 6, 3, 1.5, 1, 3, 4], #]) or croak GD::Graph::Data->error; # my $data = GD::Graph::Data->new([\@xaxis, \@data]) or croak GD::Graph::Data->error; my $data = GD::Graph::Data->new([$axisref, $dataref]) or croak GD::Graph::Data->error; # my $graph = GD::Graph::lines->new(800, 600); # my $graph = GD::Graph::bars->new(800, 600); my $graph = GD::Graph::points->new(800, 600); $graph->set( # x_label => 'X Label', # y_label => 'Y label', # title => $p, transparent => 0, t_margin => 10, b_margin => 10, l_margin => 10, r_margin => 10, # y_max_value => 520, y_max_value => 528, # y_max_value => 0.2, # y_min_value => -0.2, y_min_value => 0, # y_label_skip => 10 # x_label_skip => 10, x_label_skip => 4, # y_tick_number => 16, # y_tick_number => 8, y_tick_number => 33, # x_tick_number => 10, # x_tick_number => 26, markers => 8, marker_size => 2, long_ticks => 1, # x_max_value => 1, x_min_value => 0, ) or croak $graph->error; $graph->plot($data) or croak $graph->error; my $file = "bars$start-$end.png"; # my $file = $n."bars$p.png"; #my $file = "barssplicy$p.png"; open(my $out, '>', $file) or croak "Cannot open '$file' for write: $!"; binmode $out; print $out $graph->gd->png; close $out; # use GD::Graph::lines; use GD::Graph::points; }
download stats2.pl for a method using a closure instead of a global
download stats3.pl for an approach generating all the numbers (2, 10, 34, 94, 246, 606, 1422, 3262, 7454, 16766, 37182, 81662..)
download stats4.pl as above
download stats6.pl better guesses, splitting other than twice, equations for 2 and for 4
download stats7.pl guess best split
download file list
download zones.png splash picture
froggy come out of the pond again
all the little creatures are sent off to a big exam
badger gives all the little creatures a look as they leave
badger meets froggy
badger scowls
froggy senses that some of the creatures hide their work from other ones
froggy send all the little creatures all back to do the exam again
lucky for us there are enough badgers for this exam
froggy splashes into the pond to hide away from everyone