Beefy Boxes and Bandwidth Generously Provided by pair Networks
Clear questions and runnable code
get the best and fastest answer
 
PerlMonks  

comment on

( [id://3333]=superdoc: print w/replies, xml ) Need Help??

Hi rjt,

Thank you for this challenge. This consumed so much of my time in a great way. The reason is partly due to, "What if possible for many CPU cores?" But first made attempts for fast using 1 core. Below are the 3 progressive solutions, each one running faster.

Update: Added results from two machines.

Laurent's demonstration plus updates:

#!/usr/bin/env perl use strict; use warnings; my $size = shift || 1e6; $size = 1e6 if $size < 1e6; # minimum $size = 1e9 if $size > 1e9; # maximum ## # Laurent's demonstration + updates # https://www.perlmonks.org/?node_id=11115520 # https://www.perlmonks.org/?node_id=11115540 # # Parallel solution # https://www.perlmonks.org/?node_id=11115544 ## my @cache = (0, 1, 2); my @seqs; sub collatz_seq { my $size = shift; my ($n, $steps); for my $input (2..$size) { $n = $input, $steps = 0; while ($n != 1) { $steps += $cache[$n], last if defined $cache[$n]; $n % 2 ? ( $steps += 2, $n = (3 * $n + 1) >> 1 ) : ( $steps += 1, $n = $n >> 1 ); } $cache[$input] = $steps if $input < $size; push @seqs, [ $input, $steps ] if $steps > 400; } } collatz_seq($size); @seqs = ( sort { $b->[1] <=> $a->[1]} @seqs )[ 0..19 ]; printf "Collatz(%5d) has sequence length of %3d steps\n", @$_ for @seqs;

iM71's C++ demonstration converted to Perl plus updates:

#!/usr/bin/env perl use strict; use warnings; my $size = shift || 1e6; $size = 1e6 if $size < 1e6; # minimum $size = 1e9 if $size > 1e9; # maximum ## # iM71's demonstration + applied T(x) notation and compression # https://stackoverflow.com/a/55361008 # https://www.youtube.com/watch?v=t1I9uHF9X5Y (1 min into video) # # Parallel solution # https://www.perlmonks.org/?node_id=11115780 ## my @cache = (0, 1, 2); my @seqs; sub collatz_seq { my $size = shift; my ($n, $steps); for my $input (2..$size) { $n = $input, $steps = 0; $n % 2 ? ( $steps += 2, $n = (3 * $n + 1) >> 1 ) : ( $steps += 1, $n = $n >> 1 ) while $n != 1 && $n >= $input; $cache[$input] = $steps += $cache[$n]; push @seqs, [ $input, $steps ] if $steps > 400; } } collatz_seq($size); @seqs = ( sort { $b->[1] <=> $a->[1]} @seqs )[ 0..19 ]; printf "Collatz(%5d) has sequence length of %3d steps\n", @$_ for @seqs;

Step counting using Inline C:

#!/usr/bin/env perl use strict; use warnings; use Inline C => Config => CCFLAGSEX => '-O2 -fomit-frame-pointer'; use Inline C => <<'END_OF_C_CODE'; #include <stdint.h> void num_steps_c( SV* _n, SV* _s ) { uint64_t n, input; int steps = 0; n = input = SvUV(_n); while ( n != 1 && n >= input ) { n % 2 ? ( steps += 2, n = (3 * n + 1) >> 1 ) : ( steps += 1, n = n >> 1 ); } sv_setuv(_n, n); sv_setiv(_s, steps); return; } END_OF_C_CODE my $size = shift || 1e6; $size = 1e6 if $size < 1e6; # minimum $size = 1e9 if $size > 1e9; # maximum ## # iM71's demonstration + applied T(x) notation and compression # https://stackoverflow.com/a/55361008 # https://www.youtube.com/watch?v=t1I9uHF9X5Y (1 min into video) # # Parallel solution # https://www.perlmonks.org/?node_id=11115780 ## my @cache = (0, 1, 2); my @seqs; sub collatz_seq { my $size = shift; my ($n, $steps); for my $input (2..$size) { num_steps_c($n = $input, $steps); $cache[$input] = $steps += $cache[$n]; push @seqs, [ $input, $steps ] if $steps > 400; } } collatz_seq($size); @seqs = ( sort { $b->[1] <=> $a->[1]} @seqs )[ 0..19 ]; printf "Collatz(%5d) has sequence length of %3d steps\n", @$_ for @seqs;

Results from two machines:

64-bit VM: rjt 0.903s Laurent + updates 0.696s iM71 + updates 0.602s Step counting in C 0.273s (1st time involves compiling) AMD 3970x: rjt 0.635s Laurent + updates 0.516s iM71 + updates 0.467s Step counting in C 0.191s (1st time involves compiling) Collatz(837799) has sequence length of 525 steps Collatz(626331) has sequence length of 509 steps Collatz(939497) has sequence length of 507 steps Collatz(704623) has sequence length of 504 steps Collatz(910107) has sequence length of 476 steps Collatz(927003) has sequence length of 476 steps Collatz(511935) has sequence length of 470 steps Collatz(767903) has sequence length of 468 steps Collatz(796095) has sequence length of 468 steps Collatz(970599) has sequence length of 458 steps Collatz(546681) has sequence length of 452 steps Collatz(818943) has sequence length of 450 steps Collatz(820022) has sequence length of 450 steps Collatz(820023) has sequence length of 450 steps Collatz(410011) has sequence length of 449 steps Collatz(615017) has sequence length of 447 steps Collatz(886953) has sequence length of 445 steps Collatz(906175) has sequence length of 445 steps Collatz(922524) has sequence length of 445 steps Collatz(922525) has sequence length of 445 steps

Regards, Mario


In reply to Re^2: Optimizing with Caching vs. Parallelizing (MCE::Map) by marioroy
in thread Optimizing with Caching vs. Parallelizing (MCE::Map) by 1nickt

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":



  • Are you posting in the right place? Check out Where do I post X? to know for sure.
  • Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
    <code> <a> <b> <big> <blockquote> <br /> <dd> <dl> <dt> <em> <font> <h1> <h2> <h3> <h4> <h5> <h6> <hr /> <i> <li> <nbsp> <ol> <p> <small> <strike> <strong> <sub> <sup> <table> <td> <th> <tr> <tt> <u> <ul>
  • Snippets of code should be wrapped in <code> tags not <pre> tags. In fact, <pre> tags should generally be avoided. If they must be used, extreme care should be taken to ensure that their contents do not have long lines (<70 chars), in order to prevent horizontal scrolling (and possible janitor intervention).
  • Want more info? How to link or How to display code and escape characters are good places to start.
Log In?
Username:
Password:

What's my password?
Create A New User
Domain Nodelet?
Chatterbox?
and the web crawler heard nothing...

How do I use this?Last hourOther CB clients
Other Users?
Others lurking in the Monastery: (5)
As of 2024-03-28 17:31 GMT
Sections?
Information?
Find Nodes?
Leftovers?
    Voting Booth?

    No recent polls found