in reply to Re: Optimizing with Caching vs. Parallelizing (MCE::Map) (PDL fun) in thread Optimizing with Caching vs. Parallelizing (MCE::Map)
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
Re^3: Optimizing with Caching vs. Parallelizing (MCE::Map) (PDL: faster)
by vr (Curate) on Apr 26, 2020 at 00:03 UTC

Sorry for delay with reply/update, first I got distracted with "let's try another optimization", then with other/unrelated things. I hope this topic is still warm :).
My "caching" PDL solution (I'd prefer "lookingup" to "caching" or "memoization" in this case) is slow because, if vector is processed as a whole, cache hits happen less frequently i.e. after quite a few more useless steps. To illustrate with sequence from original challenge:
23 → 70 → 35 → 106 → 53 → 160 → 80 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
Number 70 reaches 35 in only one step but 35 itself is yet very far from completion. Simplifying, if 1..70 range was divided into e.g. 2 chunks processed independently one after another, then it would alleviate the problem.
This "chunking" is very easy to add, just wrap the main loop into one external loop (labelled "CHUNKS"), which updates chunk boundaries and sets "views" into piddles, while internal loop (labelled "ITERATIONS") does exactly the same as in previous version. The $current piddle can now be of chunk size. The very first chunk includes dummy 0th element (size is CHUNK + 1), the final one can theoretically be as short as 1 single element.
For 1e7 numbers, the computation time drops by factor of 3, from ~65 to ~21 seconds, and doesn't change much (variations stay at "noise" level) for chunk sizes ~2e4 .. ~2e5.
Next, the idea was, that as soon as chunk is completed, e.g. chunk 11..20 with MAX = 100 and CHUNK = 10, it should be extremely cheap/easy to immediately get Collatz $lengths for even numbers in range 22..40, also marking these $seqs elements as BAD/completed. Though it would be almost as easily achieved "in due time", we don't need to consider/apply any masks at this early/immediate stage. Further, then it follows, we can simply set, in bulk and at the very beginning, each even $seqs element outside 1st chunk as BAD, even if CLs are unknown yet.
2 fragments marked with double '##' do exactly what previous paragraph says. They can be freely disabled for experiments; though the speedup is very modest, just ~0.5s.
Further "ideas"/considerations didn't result in palpable improvements (nor were pursued systematically).
If it's cheap to shiftleft indexes and increment CLs for each chunk as we go, what if we also populate and keep sparse (even only) CL LUT in range MAX..2MAX? Well, this range starts being populated relatively late, and if there was benefit of occasional additional cache hits, it seems to be cancelled out. No gain, no loss. The MAXLEN was introduced to check this.
I tried to add masks/slices/bads for $current, so that e.g. the line $current ++; applies to valid subset only, especially since now all elements at even positions are dead weight from the very start, in chunks 2+. Well, unconditional "en masse" cheap operation appears to be faster, regardless of uselessly tackling "dead weight".
I also considered variable chunk sizes (such as "begin with very short", etc.), but gave up.
use strict;
use warnings;
use feature 'say';
use PDL;
use List::Util;
BEGIN { *_min = \&List::Util::min; # collision
*_max = \&List::Util::max } # with PDL
use constant MAX => 1e7;
use constant TOP => _min( 20, MAX );
use constant CHUNK => _min( 8e4, MAX ); # but keep it even
use constant MAXLEN => MAX * 1; # ?? # x(1..2)
use Time::HiRes 'time';
my $t = time;
my $seqs = sequence( longlong, 1 + MAX );
$seqs> setbadat( 0 );
$seqs> setbadat( 1 );
$seqs> badvalue( 2 );
$seqs> slice([ CHUNK + 2, MAX, 2]) .= 2 ##
if CHUNK + 2 <= MAX; ##
my $lengths = ones( short, 1 + MAXLEN );
$lengths> inplace> setvaltobad( 1 );
$lengths> set( 1, 1 );
$lengths> set( 2, 2 );
$lengths> set( 4, 3 );
CHUNKS:
for ( my $from = my $to = 0; $to != MAX; $from = $to + 1 ) {
$to = _min( $from + CHUNK, MAX );
# "_c" is for "chunk"
my $seqs_c = $seqs> slice([ $from, $to ]);
my $lengths_c = $lengths> slice([ $from, $to ]);
my $current = zeroes( short, nelem( $seqs_c ));
ITERATIONS:
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 ); ##
##
( $lengths> slice([ $from_e, $to_e, 2 ]) ##
.= $lengths> slice([ $from_e / 2, $to_e / 2 ])) ++ ##
if $from_e <= MAXLEN ##
}
# same finale
$lengths> badflag( 0 );
$lengths = $lengths> slice([ 1, MAX ]);
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;
say $result;
say time  $t;
__END__
Edit (bug fix). :(( With "dummy 0th element prepended", my intention for chunks was e.g. "010,1120,2130, ..., i.e. 1st is one longer. Then I fooled with "better presentation", from "infinite" while loop, to while loop with explicit condition, to for loop, with slightly different formulas for from,to,from_e,to_e, and messed up. Some even lengths aren't calculated, as seen with MAX and CHUNK e.g. 10 and 4. Easiest fix now is to leave chunks all equal (CHUNK+1); one LOC fixed (see "fixed"), above. Sorry.
 [reply] [d/l] [select] 

Hi vr and all,
This is a parallel version for UNIX and Windows. The lengths piddle is shared using PDL::IO::FastRaw.
Update 1: Construct seqs_c from inside workers to consume lesser memory consumption.
Update 2: Applied vr's bug fix. Plus added 2nd example that runs parallel on Windows.
Update 3: Output not 100% consistent (1e7 diff). Not suited for parallelism due to cache miss. The nonPDL solutions here and here handle cache miss. But not yet here.
9,12c9,12
< [ 616 7532665] # correct
< [ 613 5649499]
< [ 611 8474249]
< [ 608 6355687]

> [ 615 7532665] # wrong
> [ 612 5649499]
> [ 610 8474249]
> [ 607 6355687]
14c14
< [ 606 9533531] # correct

> [ 605 9533531] # wrong
UNIX:
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;
{ no warnings 'once'; $PDL::BIGPDL = 1; }
use List::Util;
BEGIN { *_min = \&List::Util::min; # collision
*_max = \&List::Util::max } # with PDL
use constant MAX => shift  1e7;
use constant TOP => _min( 20, MAX );
use constant CHUNK => _min( 40000, MAX ); # but keep it even
use constant MAXLEN => MAX * 1; # ?? # x(1..2)
use Time::HiRes 'time';
# create a raw file for lengths
writefraw( ones( short, 3 + MAXLEN ), "$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 $t = time;
mce_flow_s {
max_workers => MCE::Util::get_ncpu(),
chunk_size => CHUNK + 1,
bounds_only => 1,
},
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 ); ##
##
( $lengths> slice([ $from_e, $to_e, 2 ]) ##
.= $lengths> slice([ $from_e / 2, $to_e / 2 ])) ++ ##
if $from_e <= MAXLEN; ##
}, 0, MAX;
MCE::Flow>finish;
say {*STDERR} "compute time: ", time  $t;
# same finale
$lengths> badflag( 0 );
$lengths = $lengths> slice([ 1, MAX ]);
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;
say $result;
say {*STDERR} "total time: ", time  $t;
Windows:
The following script works on Windows with up to 8 workers. Specifying higher than 8 workers causes PDL to emit, "PDL::Internal Error: data structure recursion limit exceeded (max 1000 levels)". I also tested on Linux. No problems there including 32 workers.
use strict;
use warnings;
use feature 'say';
use PDL;
use File::Map; # ensure that Perl has File::Map before loading FastRaw
use PDL::IO::FastRaw;
use MCE::Signal '$tmp_dir';
use MCE::Flow;
{ no warnings 'once'; $PDL::BIGPDL = 1; }
use List::Util;
BEGIN { *_min = \&List::Util::min; # collision
*_max = \&List::Util::max } # with PDL
use constant MAX => shift  1e7;
use constant TOP => _min( 20, MAX );
use constant CHUNK => _min( 40000, MAX ); # but keep it even
use constant MAXLEN => MAX * 1; # ?? # x(1..2)
use Time::HiRes 'time';
# create a raw file for lengths
writefraw( ones( short, 3 + MAXLEN ), "$tmp_dir/lengths" );
my $t = time;
my $lengths;
MCE::Flow>init(
max_workers => _min( 8, MCE::Util::get_ncpu() ),
chunk_size => CHUNK + 1,
bounds_only => 1,
init_relay => 1,
user_begin => sub {
$lengths = mapfraw( "$tmp_dir/lengths" );
if ( MCE>wid == 1 ) {
$lengths> inplace> setvaltobad( 1 );
$lengths> set( 1, 1 );
$lengths> set( 2, 2 );
$lengths> set( 4, 3 );
}
MCE>sync;
},
);
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;
say {*STDERR} "compute time: ", time  $t;
# same finale
$lengths = mapfraw( "$tmp_dir/lengths" );
$lengths> badflag( 0 );
$lengths = $lengths> slice([ 1, MAX ]);
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;
say $result;
say {*STDERR} "total time: ", time  $t;
Results:
Compute time excludes initial piddle creation and final sorting/output as these run serially. Total time is captured by running time perl script.pl.
1e7:
serial total 15.272s, compute 14.674s 1 core
parallel total 8.327s, compute 7.478s 2 cores
parallel total 4.726s, compute 3.912s 4 cores
parallel total 2.855s, compute 2.025s 8 cores
parallel total 1.911s, compute 1.085s 16 cores
parallel total 1.484s, compute 0.835s 32 cores
[
[ 686 8400511]
[ 668 8865705]
[ 665 6649279]
[ 663 9973919]
[ 621 6674175]
[ 616 7332399]
[ 616 7532665]
[ 613 5649499]
[ 611 8474249]
[ 608 6355687]
[ 606 8847225]
[ 606 9533531]
[ 603 6635419]
[ 601 9953129]
[ 598 7464846]
[ 598 7464847]
[ 597 3732423]
[ 595 5598635]
[ 593 8397953]
[ 590 6298465]
]
1e8:
parallel total 11.779s, compute 5.631s 32 cores
Regards, Mario
 [reply] [d/l] [select] 

Greetings,
The prior demonstration involves sorting (qsorti) using one core, taking ~ 5 extra seconds for 1e8. That led me to try parallel sorting inside user_end. Code for both UNIX and Windows are provided.
Update: Output not 100% consistent. Not suited for parallelism due to cache miss. The nonPDL solutions here and here handle cache miss. But not yet here.
UNIX:
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; }
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,
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 ); ##
##
( $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  $t;
Windows:
The following script works on Windows with up to 8 workers. Specifying higher than 8 workers causes PDL to emit, "PDL::Internal Error: data structure recursion limit exceeded (max 1000 levels)". I also tested on Linux. No problems there including 32 workers.
use strict;
use warnings;
use feature 'say';
use PDL;
use File::Map; # ensure that Perl has File::Map before loading FastRaw
use PDL::IO::FastRaw;
use MCE::Signal '$tmp_dir';
use MCE::Flow;
use MCE::Candy;
{ no warnings 'once'; $PDL::BIGPDL = 1; }
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" );
my @top_seqs;
my $lengths;
MCE::Flow>init(
max_workers => _min( 8, MCE::Util::get_ncpu() ),
chunk_size => CHUNK + 1,
bounds_only => 1,
init_relay => 1,
gather => MCE::Candy::out_iter_array(\@top_seqs),
user_begin => sub {
$lengths = mapfraw( "$tmp_dir/lengths" );
if ( MCE>wid == 1 ) {
$lengths> inplace> setvaltobad( 1 );
$lengths> set( 1, 1 );
$lengths> set( 2, 2 );
$lengths> set( 4, 3 );
}
MCE>sync;
},
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;
Results:
time perl script.pl
1e7:
serial 15.311s 1 core
parallel 7.898s 2 cores
parallel 4.229s 4 cores
parallel 2.244s 8 cores
parallel 1.265s 16 cores
parallel 0.815s 32 cores
1e8:
serial 2m38.645s 1 core
parallel 11.779s 32 cores before: serial qsorti
parallel 6.652s 32 cores after : parallel qsorti
parallel 2.656s 32 cores nonPDL solution
parallel 1.644s 32 cores nonPDL solution with Inline::C
https://perlmonks.org/?node_id=11115780
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
Regards, Mario
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