MCE 1.831 and MCE::Shared 1.832 have been released containing the fix. What follows is the parallel demonstration for danaj's example. For sequence of numbers, the MCE bounds_only option is handy. Workers receive the begin and end values only.

use strict;
use warnings;

use ntheory 0.67 ":all";
use MCE::Flow 1.831;

my ( $name, $rng );

my %rand = (
  "drand48" => sub { int(rand(1 << 32)) },
  "ChaCha20" => sub { irand64() },
  "/dev/urandom" => sub { unpack("Q", random_bytes(8)) }
);

# Workers receive [ begin, end ] values.

MCE::Flow::init(
  max_workers => MCE::Util::get_ncpu(),
  chunk_size  => 10000,
  bounds_only => 1,
  user_begin  => sub {
    $name = MCE->user_args()->[0];
    $rng  = $rand{ $name };
  }
);

sub func {
  my ( $beg_seq, $end_seq ) = @{ $_ };
  my ( $t ) = ( 0 );

  for ( $beg_seq .. $end_seq ) {
    $t++ if gcd( $rng->(), $rng->() ) == 1;
  }

  MCE->gather($t);
}

# The user_args option is how to pass arguments.
# Workers persist between each run.

sub cesaro {
  my ( $name ) = @_;
  print "Usage $name:\n";

  for my $e ( 1..7 ) {
    my $n   = 10 ** $e;
    my @ret = mce_flow_s { user_args => [$name] }, \&func, 0, $n - 1;
    my $t   = 0;   $t += $_ for @ret;

    printf "%8d  %0.8f\n", $n, sqrt(6 * $n / $t);
  }

  printf "%9s %s\n\n", "Pi", Pi();
}

for ( "drand48", "ChaCha20", "/dev/urandom" ) {
  cesaro($_);
}

[download]

Output.

Usage drand48:
      10  3.46410162
     100  3.11085508
    1000  3.12347524
   10000  3.15335577
  100000  3.14122349
 1000000  3.14092649
10000000  3.14209456
       Pi 3.14159265358979

Usage ChaCha20:
      10  3.46410162
     100  3.08606700
    1000  3.11588476
   10000  3.14606477
  100000  3.14461263
 1000000  3.14453748
10000000  3.14269499
       Pi 3.14159265358979

Usage /dev/urandom:
      10  3.16227766
     100  3.13625024
    1000  3.24727816
   10000  3.13959750
  100000  3.14238646
 1000000  3.14247180
10000000  3.14023908
       Pi 3.14159265358979

[download]

The parallel code scales linearly. It runs about 4x faster on a machine with 4 "real" cores. A little faster with extra hyper-threads.

Regards, Mario

In reply to Re^3: PRNG/TRNG Cesaro's theorem by marioroy
in thread PRNG/TRNG Cesaro's theorem by CDCozy

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