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Re^8: solve cubic equations (Java)

by no_slogan (Deacon)
on May 05, 2017 at 16:03 UTC ( #1189584=note: print w/replies, xml ) Need Help??


in reply to Re^7: solve cubic equations (Java)
in thread solve cubic equations

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); }
Find the initial value of the seed $s, which is a randomly-chosen number less than 2**17. Here are the comparisons of a brute-force search using several different modules:
s/iter BigInt BigIntGMP GMP Perl BigInt 25.0 -- -42% -94% -100% BigIntGMP 14.4 73% -- -90% -99% GMP 1.47 1605% 885% -- -93% Perl 0.110 22701% 13070% 1238% --
I'm running perl 5.24.1 on an aging MacBook. I could make the Perl faster, but it would require a 64-bit perl build. You could probably get good performance with Math::Int64, but I'll leave that as an exercise for the reader. Python is running in time comparable to the pure-Perl, and PyPy smokes them all at under a millisecond. Full code is below. You don't need to tell me that my benchmarking methodology is bad.
use strict; use warnings; use Benchmark qw( cmpthese ); use Math::GMP (); use Math::BigInt (); use Math::BigInt::GMP (); sub tryclass { my ($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) }, });

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