use strict; use warnings; use feature 'say'; BEGIN { # Does not work on Windows unfortunately. die "Sorry, this script requires a UNIX based OS, exiting...\n" if $^O eq 'MSWin32'; } use PDL; use File::Map; # ensure that Perl has File::Map before loading FastRaw use PDL::IO::FastRaw; use MCE::Signal '$tmp_dir'; use MCE::Flow; use MCE::Candy; { no warnings 'once'; $PDL::BIGPDL = 1; eval q{ PDL::set_autopthread_targ(1) }; } use List::Util; BEGIN { *_min = \&List::Util::min; # collision *_max = \&List::Util::max } # with PDL use constant MAX => shift || 1e7; use constant TOP => _min( 20, MAX ); use constant CHUNK => _min( 40000, MAX ); # but keep it even use constant MAXLEN => MAX * 1; # ?? # x(1..2) use Time::HiRes 'time'; my $t = time; # create a raw file for lengths writefraw( ones( short, 3 + MAXLEN ), "$tmp_dir/lengths" ); # memory map the raw file my $lengths = mapfraw( "$tmp_dir/lengths" ); $lengths-> inplace-> setvaltobad( 1 ); $lengths-> set( 1, 1 ); $lengths-> set( 2, 2 ); $lengths-> set( 4, 3 ); my @top_seqs; MCE::Flow->init( max_workers => MCE::Util::get_ncpu(), chunk_size => CHUNK + 1, bounds_only => 1, init_relay => 1, gather => MCE::Candy::out_iter_array(\@top_seqs), user_end => sub { # wait for any remaining workers to complete processing MCE->sync; my $size = MAX / MCE->max_workers + 1; my $from = ( MCE->wid - 1 ) * $size + 1; my $to = $from + $size; $from++ if $from > 1; $to = MAX if $to > MAX; my $lengths_c = $lengths-> slice([ $from, $to ]); $lengths_c-> badflag( 0 ); my $sorted_i = $lengths_c-> qsorti; my $sorted = $lengths_c-> index( $sorted_i ); my $value = $sorted-> at( $to - $from - TOP ); my $pos = vsearch_insert_leftmost( $value, $sorted ); my $top_i = $sorted_i-> slice([ $to - $from, $pos ]); ( my $result = $lengths_c -> index( $top_i ) -> longlong -> bitnot -> cat( $top_i + $from ) -> transpose -> qsortvec -> slice([], [ 0, TOP - 1 ]) )-> slice([ 0 ], []) -> inplace -> bitnot; # From PDL to Perl: [ 0 1 ] becomes [ 1, 0 ], my $str = $result->string; $str =~ s/(\d+)\s+(\d+)(.*)/$2,$1$3,/g; my $ret = eval $str; MCE->gather( MCE->wid, @$ret ); }, ); mce_flow_s sub { my ( $mce, $chunk_ref, $chunk_id ) = @_; my ( $from, $to ) = @{ $chunk_ref }; my $seqs_c = $from + sequence( longlong, $to - $from + 1 ); if ( $chunk_id == 1 ) { $seqs_c-> setbadat( 0 ); $seqs_c-> setbadat( 1 ); $seqs_c-> badvalue( 2 ); } else { $seqs_c-> setbadat( $from % 2 ? 1 : 0 ); $seqs_c-> slice([ $from % 2 ? 1 : 0, $to - $from, 2 ]) .= 2; $seqs_c-> badvalue( 2 ); } my $lengths_c = $lengths-> slice([ $from, $to ]); my $current = zeroes( short, nelem( $seqs_c )); while ( any $seqs_c-> isgood ) { my ( $seqs_c_odd, $current_odd_masked ) = where( $seqs_c, $current, $seqs_c & 1 ); $current_odd_masked ++; $current ++; ( $seqs_c_odd *= 3 ) ++; $seqs_c >>= 1; my ( $seqs_cap, $lengths_cap, $current_cap ) = where( $seqs_c, $lengths_c, $current, $seqs_c <= MAXLEN ); my $lut = $lengths-> index( $seqs_cap ); # "_f" is for "finished" my ( $seqs_f, $lengths_f, $lut_f, $current_f ) = where( $seqs_cap, $lengths_cap, $lut, $current_cap, $lut-> isgood ); $lengths_f .= $lut_f + $current_f; $seqs_f .= 2; # i.e. BAD } # "_e" is for "at even positions, ahead" ## ## # my $from_e = _max( $from * 2, $to ) + 2; # bug ## my $from_e = $from == 0 ? $to + 2 : $from * 2; # fixed ## my $to_e = _min( $to * 2, MAXLEN ); ## ## MCE::relay { ## ( $lengths-> slice([ $from_e, $to_e, 2 ]) ## .= $lengths-> slice([ $from_e / 2, $to_e / 2 ])) ++ ## if $from_e <= MAXLEN; ## }; ## }, 0, MAX; MCE::Flow->finish; @top_seqs = ( sort { $b->[1] <=> $a->[1]} @top_seqs )[ 0..19 ]; printf "Collatz(%5d) has sequence length of %3d steps\n", @$_ for @top_seqs; say {*STDERR} time - $t;