Hi vr,
Lots of PDL goodness. Wow! I do not know how this will perform unless taking a moment or two and give it a try. So here is a parallel version based on your 2nd example.
use strict;
use warnings;
use feature 'say';
use PDL;
use MCE::Flow;
use MCE::Candy;
use Time::HiRes 'time';
my $t = time;
# PDL Quick Reference
# https://www.perlmonks.org/?node_id=1214437
sub collatz_seq {
my ( $chunk_id, $seq_beg, $seq_end ) = @_;
my $max = $seq_end  $seq_beg + 2;
my $top = $max < 20 ? $max : 20;
my $seqs = pdl( longlong, 1, $seq_beg..$seq_end );
$seqs> setbadat( 0 );
$seqs> badvalue( 2 );
my $lengths = 1 + ones( short, $max );
$lengths> set( 0, 1 );
while ( any my $good_mask = $seqs> isgood ) {
my ( $seqs_odd, $lengths_odd_masked )
= where( $seqs, $lengths, $seqs & 1 );
$lengths_odd_masked ++;
$lengths> where( $good_mask ) ++;
( $seqs_odd *= 3 ) ++;
$seqs >>= 1;
}
my $sorted_i = $lengths> qsorti;
my $sorted = $lengths> index( $sorted_i );
my $value = $sorted> at( $max  $top );
my $pos = vsearch_insert_leftmost( $value, $sorted );
my $top_i = $sorted_i> slice([ $max  1 , $pos ]);
( my $result = $lengths
> index( $top_i )
> longlong
> bitnot
> cat( $top_i + 1 )
> 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;
$_>[0] = $_>[0] + $seq_beg  2 for @$ret;
MCE>gather( $chunk_id, @$ret );
}
my $size = shift  1e6;
$size = 1e6 if $size < 1e6; # minimum
$size = 1e9 if $size > 1e9; # maximum
my $chunk_size = $size >> 5;
my @seqs;
mce_flow_s {
max_workers => MCE::Util::get_ncpu(),
chunk_size => $chunk_size > 100000 ? 100000 : $chunk_size,
bounds_only => 1,
gather => MCE::Candy::out_iter_array(\@seqs),
}, sub {
my ( $mce, $chunk_ref, $chunk_id ) = @_;
collatz_seq( $chunk_id, @{ $chunk_ref } );
}, 2, $size;
MCE::Flow>finish;
@seqs = ( sort { $b>[1] <=> $a>[1]} @seqs )[ 0..19 ];
printf "Collatz(%5d) has sequence length of %3d steps\n", @$_
for @seqs;
say {*STDERR} time  $t;
Results:
I was expecting for mce_pdl2 using 1 core to be closer to vr_pdl2 than vr_pdl3. Maybe benefitting from CPU L2/L3 cache. Chunking seems to be the reason why mce_pdl2 (noncaching) ran nearly as fast as vr_pdl3 (caching). Below, includes 1 core testing for 1e7 with various chunk sizes.
1e7 testing
vr_pdl3: 46.328s cache
vr_pdl2: 1m16.058s noncache
mce_pdl2: 1m15.583s chunk_size => $size
mce_pdl2: 1m03.709s chunk_size => $size >> 1
mce_pdl2: 52.352s chunk_size => $size >> 2
mce_pdl2: 51.323s chunk_size => $size >> 3
mce_pdl2: 49.396s chunk_size => $size >> 4
mce_pdl2: 48.195s chunk_size => $size >> 5
mce_pdl2: 48.369s chunk_size => $size >> 6
mce_pdl2: 48.501s chunk_size => $size >> 7
chunk_size => 300000
mce_pdl2: 48.195s 1 core
mce_pdl2: 25.311s 2 cores
mce_pdl2: 14.085s 4 cores
mce_pdl2: 7.650s 8 cores
mce_pdl2: 4.517s 16 cores
mce_pdl2: 3.721s 32 cores
chunk_size => 100000
mce_pdl2: 48.395s 1 core
mce_pdl2: 25.402s 2 cores
mce_pdl2: 13.163s 4 cores
mce_pdl2: 6.860s 8 cores
mce_pdl2: 3.850s 16 cores
mce_pdl2: 2.347s 32 cores
Output
Collatz(8400511) has sequence length of 686 steps
Collatz(8865705) has sequence length of 668 steps
Collatz(6649279) has sequence length of 665 steps
Collatz(9973919) has sequence length of 663 steps
Collatz(6674175) has sequence length of 621 steps
Collatz(7332399) has sequence length of 616 steps
Collatz(7532665) has sequence length of 616 steps
Collatz(5649499) has sequence length of 613 steps
Collatz(8474249) has sequence length of 611 steps
Collatz(6355687) has sequence length of 608 steps
Collatz(8847225) has sequence length of 606 steps
Collatz(9533531) has sequence length of 606 steps
Collatz(6635419) has sequence length of 603 steps
Collatz(9953129) has sequence length of 601 steps
Collatz(7464846) has sequence length of 598 steps
Collatz(7464847) has sequence length of 598 steps
Collatz(3732423) has sequence length of 597 steps
Collatz(5598635) has sequence length of 595 steps
Collatz(8397953) has sequence length of 593 steps
Collatz(6298465) has sequence length of 590 steps
1e8 testing
vr_pdl3: 9m44.667s cache
vr_pdl2: 16m12.467s noncache
chunk_size => 300000
mce_pdl2: 9m06.078s 1 core
mce_pdl2: 4m43.529s 2 cores
mce_pdl2: 2m33.136s 4 cores
mce_pdl2: 1m21.434s 8 cores
mce_pdl2: 45.266s 16 cores
mce_pdl2: 36.925s 32 cores
chunk_size => 100000
mce_pdl2: 9m09.950s 1 core
mce_pdl2: 4m39.677s 2 cores
mce_pdl2: 2m24.230s 4 cores
mce_pdl2: 1m13.353s 8 cores
mce_pdl2: 37.923s 16 cores
mce_pdl2: 20.099s 32 cores
Output
Collatz(63728127) has sequence length of 950 steps
Collatz(95592191) has sequence length of 948 steps
Collatz(96883183) has sequence length of 811 steps
Collatz(86010015) has sequence length of 798 steps
Collatz(98110761) has sequence length of 749 steps
Collatz(73583070) has sequence length of 746 steps
Collatz(73583071) has sequence length of 746 steps
Collatz(36791535) has sequence length of 745 steps
Collatz(55187303) has sequence length of 743 steps
Collatz(56924955) has sequence length of 743 steps
Collatz(82780955) has sequence length of 741 steps
Collatz(85387433) has sequence length of 741 steps
Collatz(63101607) has sequence length of 738 steps
Collatz(64040575) has sequence length of 738 steps
Collatz(93128574) has sequence length of 736 steps
Collatz(93128575) has sequence length of 736 steps
Collatz(94652411) has sequence length of 736 steps
Collatz(96060863) has sequence length of 736 steps
Collatz(46564287) has sequence length of 735 steps
Collatz(69846431) has sequence length of 733 steps
Specifying 50000 for chunk size may run faster on 4/6/8 core machines.
8 cores
mce_pdl2 1e8 16.660s chunk_size => 300000
mce_pdl2 1e8 10.471s chunk_size => 100000
mce_pdl2 1e8 9.773s chunk_size => 50000
Regards, Mario
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