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Miller–Rabin primality test: Difference between revisions

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Miller–Rabin primality test (view source)

Revision as of 23:37, 5 October 2013

551 bytes removed ,  10 years ago
→‎{{header|Haskell}}
Line 1,183:
-- Miller-Rabin wrapped up as an (almost deterministic) pure function
isPrime :: Integer -> Bool
isPrime n = unsafePerformIO (isMillerRabinPrime 100 n)
 
 
isMillerRabinPrime :: Integer -> IO Bool▼
isMillerRabinPrime n:: Int -> Integer -> IO Bool
▲isMillerRabinPrime ::k Integer -> IO Booln
| even n = return (n==2)
| n < 100 = return (n `elem` primesTo100)
| otherwise = do ws <- witnesses 100k n
return $ and (map ([test n (pred n)) evens d a | a <- ws)]
where
(evens,odds) = span even (iterate (`div` 2) n_1(pred n))▼
d := n-1head odds▼
 
 
test :: Integral nat => nat -> nat -> [nat] -> nat -> nat -> Bool
test n n_1 wevens d a = n_1x `elem` powers[1,n_1] || lastn_1 `elem` powers == 1
where
x = powerMod n a d
▲ (evens,odds) = span even (iterate (`div` 2) n_1)
powers = map (powerMod n wa) (evens ++ take 1 odds)
 
witnesses :: (Num a, Ord a, Random a) => Int -> a -> IO [a]
Line 1,209 ⟶ 1,214:
primesTo100 :: [Integer]
primesTo100 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
 
 
-- powerMod m x n = x^n `mod` m
Line 1,218 ⟶ 1,224:
| otherwise = f (i-1) b (b*y `rem` m)
 
--------------------------------------
 
Testing in GHCi:
Line 1,228 ⟶ 1,235:
*~> dropWhile (<900) $ filter isPrime [2..1000]
[907,911,919,929,937,941,947,953,967,971,977,983,991,997]</pre>
 
=={{header|Icon}} and {{header|Unicon}}==
The following code works in both languages:
<lang unicon>procedure main()
every writes(primeTest(901 to 1000, 10)," ")
write()
end
 
procedure primeTest(n, k)
if n = 2 then return n
if n%2 = 0 then fail
s := 0
▲ d := n-1
while (d%2 ~= 0, s+:=1, d/:=2)
 
every (1 to k, x := ((1+?(n-2))^d)%n) do {
if x = (1 | (n-1)) then next
every (1 to s-1, x := (x^2)%n) do {
if x = 1 then fail
if x = n-1 then break next
}
fail
}
return n
end</lang>
{{out|Sample run}}
<pre>->mrpt
907 911 919 929 937 941 947 953 967 971 977 983 991 997
-></pre>
 
=={{header|J}}==
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