add lucas-lehmer primality test

basis/math/primes/lucas-lehmer/authors.txt

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+Doug Coleman

basis/math/primes/lucas-lehmer/lucas-lehmer-docs.factor

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+! Copyright (C) 2009 Doug Coleman.
+! See http://factorcode.org/license.txt for BSD license.
+USING: help.markup help.syntax kernel ;
+IN: math.primes.lucas-lehmer
+
+HELP: lucas-lehmer
+{ $values
+    { "p" "a prime number" }
+    { "?" "a boolean" }
+}
+{ $description "Runs the Lucas-Lehmer test on the prime " { $snippet "p" } " and returns " { $link t } " if " { $snippet "(2 ^ p) - 1" } " is prime." }
+{ $examples
+    { $example "! Test that (2 ^ 61) - 1 is prime:"
+               "USING: math.primes.lucas-lehmer prettyprint ;"
+               "61 lucas-lehmer ."
+               "t"
+    }
+} ;
+
+ARTICLE: "math.primes.lucas-lehmer" "Lucas-Lehmer Mersenne Primality test"
+"The " { $vocab-link "math.primes.lucas-lehmer" } " vocabulary tests numbers of the form " { $snippet "(2 ^ p) - 1" } " for primality, where " { $snippet "p" } " is prime." $nl
+"Run the Lucas-Lehmer test:"
+{ $subsection lucas-lehmer } ;
+
+ABOUT: "math.primes.lucas-lehmer"

basis/math/primes/lucas-lehmer/lucas-lehmer-tests.factor

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+! Copyright (C) 2009 Doug Coleman.
+! See http://factorcode.org/license.txt for BSD license.
+USING: tools.test math.primes.lucas-lehmer ;
+IN: math.primes.lucas-lehmer.tests
+
+[ t ] [ 2 lucas-lehmer ] unit-test
+[ t ] [ 3 lucas-lehmer ] unit-test
+[ f ] [ 4 lucas-lehmer ] unit-test
+[ t ] [ 5 lucas-lehmer ] unit-test
+[ f ] [ 6 lucas-lehmer ] unit-test
+[ f ] [ 11 lucas-lehmer ] unit-test
+[ t ] [ 13 lucas-lehmer ] unit-test
+[ t ] [ 61 lucas-lehmer ] unit-test

basis/math/primes/lucas-lehmer/lucas-lehmer.factor

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+! Copyright (C) 2009 Doug Coleman.
+! See http://factorcode.org/license.txt for BSD license.
+USING: combinators fry kernel locals math
+math.primes combinators.short-circuit ;
+IN: math.primes.lucas-lehmer
+
+ERROR: invalid-lucas-lehmer-candidate obj ;
+
+<PRIVATE
+
+: do-lucas-lehmer ( p -- ? )
+    [ drop 4 ] [ 2 - ] [ 2^ 1 - ] tri
+    '[ sq 2 - _ mod ] times 0 = ;
+
+: lucas-lehmer-guard ( obj -- obj )
+    dup { [ integer? ] [ 0 > ] } 1&&
+    [ invalid-lucas-lehmer-candidate ] unless ;
+
+PRIVATE>
+
+: lucas-lehmer ( p -- ? )
+    lucas-lehmer-guard
+    {
+        { [ dup 2 = ] [ drop t ] }
+        { [ dup prime? ] [ do-lucas-lehmer ] }
+        [ drop f ]
+    } cond ;