adding 2012 advent day 14

integration/advent2012-day14.t

@@ -0,0 +1,72 @@
+# http://perl6advent.wordpress.com/2012/12/14/primal-needs/
+use v6;
+use Test;
+
+plan 6;
+
+sub is-prime-alpha($n) { $n %% none 2..sqrt $n }
+
+my @primes := 2, 3, 5, -> $p { ($p+2, $p+4 ... &is-prime-beta)[*-1] } ... *;
+sub is-prime-beta($n) { $n %% none @primes ...^  * > sqrt $n }
+
+sub expmod(Int $a is copy, Int $b is copy, $n) {
+    my $c = 1;
+    repeat while $b div= 2 {
+    	   ($c *= $a) %= $n if $b % 2;
+	       ($a *= $a) %= $n;
+	       }
+	       $c;
+}
+
+subset PrimeCandidate of Int where { $_ > 2 and $_ % 2 };
+subset Two of Int where { $_ == 2 };
+
+my Bool multi sub is-prime-rm(Int $n, Int $k) is default { return False; }
+my Bool multi sub is-prime-rm(2, Int $k)                 { return True; }
+my Bool multi sub is-prime-rm(PrimeCandidate $n, Int $k) {
+   my Int $d = $n - 1;
+   my Int $s = 0;
+
+   while $d %% 2 {
+       $d div= 2;
+       $s++;
+   }
+
+   for (2 ..^ $n).pick($k) -> $a {
+       my $x = expmod($a, $d, $n);
+
+       next if $x == 1 or $x == $n - 1;
+
+       for 1 ..^ $s {
+	   $x = $x ** 2 mod $n;
+	   return False if $x == 1;
+	   last if $x == $n - 1;
+       }
+       return False if $x !== $n - 1;
+   }
+
+   return True;
+}
+
+my @primes_lt_20 = 2, 3, 5, 7, 11, 13, 17, 19;
+
+# don't check  1. errouneously considered a prime by is-prime-alpha() and
+# is-prime-beta()
+is_deeply [(2 .. 20).grep({is-prime-alpha($_)})], @primes_lt_20, 'prime (alpha)';
+is_deeply [(2 .. 20).grep({is-prime-beta($_)})], @primes_lt_20, 'prime (beta)';
+is_deeply [(2 .. 20).grep({is-prime-rm($_, $_)})], @primes_lt_20, 'prime (rabin-miller)';
+
+my $primes_lt_200 = set (@primes_lt_20, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199);
+my $primes-beta = set (2 .. 200).grep({is-prime-beta($_)});
+
+is_deeply $primes-beta, $primes_lt_200, 'primes under 200 (beta)';
+
+my $primes-rm = set (2 .. 200).grep({is-prime-rm($_, 3)});
+my $is-superset = ($primes-rm (>=) $primes_lt_200);
+ok $is-superset, 'primes under 200 (rabin-miller)';
+
+# ... "there is a chance that it will tell you that a number
+#     is prime when it actually isn’t"
+my $false-positives = ($primes-rm (-) $primes_lt_200);
+ok $false-positives <= 4, 'accuracy (rabin-miller)';
+