Well, I hate to post a complete solution to one of their problems, so I've changed it around. The question is, given the first 10 outputs of this pseudo-random number generator: 
for (1..10) {
   $s = ($s*0x5deece66d + 0xb) % 2**48;
   say(($s>>17)%1000);
}

[download]
Find the initial value of the seed $s, which is a randomly-chosen number less than 2**17. Here are the comparisons of a brute-force search using several different modules: 
          s/iter    BigInt BigIntGMP       GMP      Perl
BigInt      25.0        --      -42%      -94%     -100%
BigIntGMP   14.4       73%        --      -90%      -99%
GMP         1.47     1605%      885%        --      -93%
Perl       0.110    22701%    13070%     1238%        --

[download]
I'm running perl 5.24.1 on an aging MacBook. I could make the Perl faster, but it would require a 64-bit perl build. You could probably get good performance with Math::Int64, but I'll leave that as an exercise for the reader. Python is running in time comparable to the pure-Perl, and PyPy smokes them all at under a millisecond. Full code is below. You don't need to tell me that my benchmarking methodology is bad. 
use strict;
use warnings;
use Benchmark qw( cmpthese );
use Math::GMP ();
use Math::BigInt ();
use Math::BigInt::GMP ();

sub tryclass {
   my ($class, $nums) = @_;
   my $a = $class->new('0x5deece66d');
   my $b = $class->new('0xb');
   my $m = ($class->new(1)<<48)-1;
   SEED: for my $seed (0 .. (1<<17)-1) {
      my $s = $class->new($seed);
      for my $i (0 .. $#$nums) {
         $s = ($s * $a + $b) & $m;
         next SEED unless ($s >> 17) % 1000 == $nums->[$i];
      }
      print "$class $seed\n";
   }
}

sub tryperl {
   my ($nums) = @_;
   SEED: for my $seed (0 .. 2**17-1) {
      my $lo = $seed;
      my $hi = 0;
      for my $i (0 .. $#$nums) {
         $hi = $hi * 0xe66d + $lo * 0x2ef76
            + ($hi * 0x2ef76 % 2**14)*2**17;
         $lo = ($lo * 0xe66d + 0xb);
         $hi = ($hi + int($lo/2**17)) % 2**31;
         $lo %= 2**17;
         next SEED unless $hi % 1000 == $nums->[$i];
      }
      print "Perl $seed\n";
   }
}

my @nums;
{
   my $a = Math::GMP->new('0x5deece66d');
   my $b = Math::GMP->new('0xb');
   my $m = (Math::GMP->new(1)<<48)-1;
   my $s = Math::GMP->new(int rand 2**17);
   print "Seed $s\n";
   for my $i (1..10) {
      $s = ($s * $a + $b) & $m;
      push @nums, (($s>>17) % 1000) . '';
   }
   print "Nums @nums\n";
}

cmpthese(0, {
   GMP       => sub { tryclass('Math::GMP', \@nums) },
   BigInt    => sub { tryclass('Math::BigInt', \@nums) },
   BigIntGMP => sub { Math::BigInt->import(lib=>'GMP');
                      tryclass('Math::BigInt', \@nums) },
   Perl      => sub { tryperl(\@nums) },
});

[download]

In reply to Re^8: solve cubic equations (Java) by no_slogan
in thread solve cubic equations by no_slogan

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