http://www.perlmonks.org?node_id=610253

in reply to ulam's spiral too slow

After seeing the difference in outputs between the OP code and liverpole's version, and then actually looking up the references at wikipedia, I realized that there were other problems besides execution speed: way too many spots were being drawn in black, which meant way too many numbers were being categorized as primes 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 !~ /^\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};
\$y += \$vector{\$direction};
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";
}