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Re^3: Monte Carlo - Coin Toss

by roboticus (Canon)
on Mar 12, 2011 at 16:11 UTC ( #892833=note: print w/ replies, xml ) Need Help??


in reply to Re^2: Monte Carlo - Coin Toss
in thread Monte Carlo - Coin Toss

BrowserUk:

Heh, yep, that would be a good deal slower, all right! Of course, if speed gets to be an issue, you can always skip counting all the iterations, and directly compute the binomial expansion:

use strict; use warnings; use List::Util qw(reduce); my $numTosses = 20; #my $runs = (1<<$numTosses)-1; my @triangle = (0, 1, 0); for (1 .. $numTosses) { my @newTriangle=(0); push @newTriangle, $triangle[$_]+$triangle[$_+1] for 0 .. $#triang +le-1; push @newTriangle, 0; @triangle = @newTriangle; } print <<EOHDR; Tails Count % ----- ---------- ------ EOHDR my $runs = reduce { $a + $b } @triangle; for (my $i = 0; $i < $numTosses+1; $i++) { printf "% 4u % 10u %5.2f\n", $i, $triangle[$i+1], 100*$triangle[$i+1]/$runs; }

It runs a good bit faster:

$ time perl 892293.pl Name "main::a" used only once: possible typo at 892293.pl line 21. Name "main::b" used only once: possible typo at 892293.pl line 21. Tails Count % ----- ---------- ------ 0 1 0.00 1 20 0.00 2 190 0.02 3 1140 0.11 4 4845 0.46 5 15504 1.48 6 38760 3.70 7 77520 7.39 8 125970 12.01 9 167960 16.02 10 184756 17.62 11 167960 16.02 12 125970 12.01 13 77520 7.39 14 38760 3.70 15 15504 1.48 16 4845 0.46 17 1140 0.11 18 190 0.02 19 20 0.00 20 1 0.00 real 0m0.034s user 0m0.024s sys 0m0.012s

Even if you use 32 bits:

$ time perl 892293.pl Name "main::a" used only once: possible typo at 892293.pl line 21. Name "main::b" used only once: possible typo at 892293.pl line 21. Tails Count % ----- ---------- ------ 0 1 0.00 1 32 0.00 2 496 0.00 3 4960 0.00 4 35960 0.00 5 201376 0.00 6 906192 0.02 7 3365856 0.08 8 10518300 0.24 9 28048800 0.65 10 64512240 1.50 11 129024480 3.00 12 225792840 5.26 13 347373600 8.09 14 471435600 10.98 15 565722720 13.17 16 601080390 13.99 17 565722720 13.17 18 471435600 10.98 19 347373600 8.09 20 225792840 5.26 21 129024480 3.00 22 64512240 1.50 23 28048800 0.65 24 10518300 0.24 25 3365856 0.08 26 906192 0.02 27 201376 0.00 28 35960 0.00 29 4960 0.00 30 496 0.00 31 32 0.00 32 1 0.00 real 0m0.034s user 0m0.028s sys 0m0.004s

...roboticus

When your only tool is a hammer, all problems look like your thumb.

Update: When I use bignum;, it prints the PDF for 64 tosses per run in just over a second, but I haven't got it formatted nicely...

use strict; use warnings; use List::Util qw(reduce); use bignum; my $numTosses = 64; #my $runs = (1<<$numTosses)-1; my @triangle = (0, 1, 0); for (1 .. $numTosses) { my @newTriangle=(0); push @newTriangle, $triangle[$_]+$triangle[$_+1] for 0 .. $#triang +le-1; push @newTriangle, 0; @triangle = @newTriangle; } print <<EOHDR; Tails Count % ----- ---------- ------ EOHDR my $runs = reduce { $a + $b } @triangle; for (my $i = 0; $i < $numTosses+1; $i++) { print "$i\t$triangle[$i+1]\t",100*$triangle[$i+1]/$runs, "\n"; }

I guess I'll have to figure out how to make bugnum and printf cooperate better...


Comment on Re^3: Monte Carlo - Coin Toss
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Re^4: Monte Carlo - Coin Toss
by repellent (Priest) on Mar 13, 2011 at 04:31 UTC
    Here's a slightly speedier alternative to get Pascal's triangle row for the number of tosses:
    sub pascal_tri_row { my $r = shift; return () if $r < 0; my @row = (1) x ($r + 1); for my $i (1 .. $r - 1) { $row[$_] += $row[$_ - 1] for reverse 1 .. $i; } return @row; } sub triangle { my $numTosses = shift; my @triangle = (0, 1, 0); for (1 .. $numTosses) { my @newTriangle=(0); push @newTriangle, $triangle[$_]+$triangle[$_+1] for 0 .. $#tr +iangle-1; push @newTriangle, 0; @triangle = @newTriangle; } return @triangle; } use Benchmark qw(cmpthese); cmpthese -1, { robo_tri => sub { triangle(32) }, repel_tri => sub { 0, pascal_tri_row(32), 0 }, # 0's to match tria +ngle()'s return }; __END__ Rate robo_tri repel_tri robo_tri 1128/s -- -38% repel_tri 1811/s 60% --

      repellent:

      Sweet! So of course I had to take another look:

      sub pascal_tri_row { my $r = shift; return () if $r < 0; my @row = (1) x ($r + 1); for my $i (1 .. $r - 1) { $row[$_] += $row[$_ - 1] for reverse 1 .. $i; } return @row; } sub robo_2 { my $row = shift; my @cols = (1); ++$row; $cols[$_] = $cols[$_-1] * ($row-$_)/$_ for 1 .. $row-1; return @cols; } sub triangle { my $numTosses = shift; my @triangle = (0, 1, 0); for (1 .. $numTosses) { my @newTriangle=(0); push @newTriangle, $triangle[$_]+$triangle[$_+1] for 0 .. $#tr +iangle-1; push @newTriangle, 0; @triangle = @newTriangle; } return @triangle[1..$#triangle-1]; } use Benchmark qw(cmpthese); print "robo_1: ", join(" ",triangle(8)), "\n"; print "repel1: ", join(" ",pascal_tri_row(8)), "\n"; print "robo_2: ", join(" ",robo_2(8)), "\n"; cmpthese -1, { robo_tri => sub { triangle(32) }, repel_tri => sub { pascal_tri_row(32) }, robo_2 => sub { robo_2(32) }, };

      First I put in a trace so I could be sure I wasn't generating useless values. Next, I couldn't bear the zeroes you had to add to your function to match my original return value. They were just sentinel values to simplify the calculation, anyway. So I fixed the original to return only the values of interest. Finally, I had to squeeze a little more speed out of it:

      $ perl 892898.pl robo_1: 1 8 28 56 70 56 28 8 1 repel1: 1 8 28 56 70 56 28 8 1 robo_2: 1 8 28 56 70 56 28 8 1 Rate robo_tri repel_tri robo_2 robo_tri 2196/s -- -42% -93% repel_tri 3775/s 72% -- -88% robo_2 31946/s 1355% 746% --

      You should've read a bit further down in the wikipedia article you linked. It had a much better algorithm for calculating the coefficients of any row. It saved a nested loop.

      ;^)

      ...roboticus

      When your only tool is a hammer, all problems look like your thumb.

        Wonderful! That is the one. Thanks, roboticus.

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