in reply to ulam's spiral too slow

*I felt compelled to figure out who was wrong; I have updated my earlier reply accordingly.*

I also noticed that the OP code actually draws all the points (from 1 to $max), both the supposed primes and the supposed non-primes. But you really only need to draw one set, and just leave the other set as "background color".

Then, I thought it would be helpful to get a sense of what took longest -- computing or drawing -- so I decided to refactor the code as follows:

- run through all the desired numeric range before doing any drawning, keeping track of the x/y coords as we go;
- each time we find a prime number, store that as both a hash key and as an item in an ascending array; use the hash value to store the x/y coords where the dot should be drawn for that prime;
- once all the primes have been found, set up the Tk::Canvas, then run through the sorted list of prime values (which are hash keys), and draw a dot for each one.

As it turns out, the computing takes about twice as long as the drawing (4 sec vs. 2 sec for a max number of 150,000, which pretty well fills the given grid); but bear in mind the compute step loops over all integers in the given range, while the drawing step only loops over the primes.

And luckily, the resulting canvas looks a lot more like the pictures I saw over at wikipedia (it still might not be entirely correct -- but you could try dumping a portion of the %primecoord hash structure to make sure the values are as intended).

#!/usr/local/bin/perl use strict; use Tk; die "Usage: $0 max_number\n" # use the command-line, Luke! if ( @ARGV != 1 or $ARGV[0] !~ /^\d+/ ); my $lastnumber = shift; my ( $mincoord, $midcoord, $maxcoord ) = ( 50, 250, 450 ); plot_grid( compute_primes( $lastnumber )); MainLoop; { # closure for building prime number hash structure my @sorted_primes = ( 1 ); # primes in ascending order my %primecoord = ( 1 => [$midcoord, $midcoord] ); # HoA: keys are primes, values are x/y coords in grid sub ck_prime { my ( $num, $x, $y ) = @_; my $end = int( sqrt( $num )); my $keep = 1; for my $prime ( @sorted_primes ) { if ( 0 == $num % $prime ) { $keep = 0; last; } elsif ( $prime > $end ) { last; } } if ( $keep ) { $primecoord{$num} = [ $x, $y ]; push @sorted_primes, $num; } } sub compute_primes { # list of directions for incrementing x, y coordinates: my %vector = ( 0 => [ 1, 0 ], # rightward 1 => [ 0, 1 ], # downward 2 => [ -1, 0 ], # leftward 3 => [ 0, -1 ], # upward ); my $x = my $y = 250; # starting position my $direction = 0; # changes when we've gone $pathlen steps my $traveled = 0; # no. of points drawn in current direction my $pathlen = 1; # increments on every second direction chang +e my $changes = 0; # no. of dir. changes since last $pathlen in +crement my $number = 1; my $bgn = time; while ( ++$number <= $lastnumber ) { $x += $vector{$direction}[0]; $y += $vector{$direction}[1]; last if ( $x < $mincoord or $x > $maxcoord ); if ( ++$traveled == $pathlen ) { $direction = ++$direction % 4; $traveled = 0; if ( ++$changes % 2 == 0 ) { $changes = 0; $pathlen++; } } ck_prime( $number, $x, $y ); } my $end = time; warn "Checked $lastnumber integers in ", $end - $bgn, " sec\n" +; return( \@sorted_primes, \%primecoord ); } } sub plot_grid { my ( $primes, $coords ) = @_; my $mw = MainWindow->new; my $c = $mw->Canvas(-width => $maxcoord+50, -height => $maxcoord+5 +0, -background => 'white' )->pack; $c->createLine( $mincoord, $midcoord, $maxcoord, $midcoord ); $c->createText( $mincoord-30, $midcoord, -fill => 'blue', -text => + 'X'); $c->createLine( $midcoord, $mincoord, $midcoord, $maxcoord ); $c->createText( $midcoord, $mincoord-30, -fill => 'blue', -text => + 'Y'); my $bgn = time; for my $prime ( @$primes ) { my ( $x, $y ) = @{$$coords{$prime}}; $c->createText( $x, $y, -fill => 'black', -text => "\xb7" ); } my $end = time; warn "Plotted ", scalar @$primes, " primes in ", $end - $bgn, " se +c\n"; }

(updated to correct the comments about the "%vector" hash, to reflect the fact that coords in Tk::Canvas put 0,0 at the upper left corner)