langs a-z

Task/Miller-Rabin-primality-test/PARI-GP/miller-rabin-primality-test-1.pari

@@ -0,0 +1 @@
+MR(n,k)=ispseudoprime(n,k);

Task/Miller-Rabin-primality-test/PARI-GP/miller-rabin-primality-test-2.pari

@@ -0,0 +1,16 @@
+sprp(n,b)={
+	my(s = valuation(n-1, 2), d = Mod(b, n)^(n >> s));
+	if (d == 1, return(1));
+	for(i=1,s-1,
+		if (d == -1, return(1));
+		d = d^2;
+	);
+	d == -1
+};
+
+MR(n,k)={
+  for(i=1,k,
+    if(!sprp(n,random(n-2)+2), return(0))
+  );
+  1
+};

Task/Miller-Rabin-primality-test/PARI-GP/miller-rabin-primality-test-3.pari

@@ -0,0 +1,20 @@
+A006945=[9, 2047, 1373653, 25326001, 3215031751, 2152302898747, 3474749660383, 341550071728321, 341550071728321, 3825123056546413051];
+Miller(n)={
+  if (n%2 == 0, return(n == 2)); \\ Handle even numbers
+  if (n < 3, return(0)); \\ Handle 0, 1, and negative numbers
+
+  if (n < 1<<64,
+    \\ Feitsma
+    for(i=1,#A006945,
+      if (n < A006945[i], return(1));
+      if(!sprp(n, prime(i)), return(0));
+    );
+    sprp(n,31)&sprp(n,37)
+  ,
+    \\ Miller + Bach
+    for(b=2,2*log(n)^2,
+      if(!sprp(n, b), return(0))
+    );
+    1
+  )
+};

Task/Miller-Rabin-primality-test/Perl-6/miller-rabin-primality-test.pl6

@@ -0,0 +1,42 @@
+# the expmod-function from: http://rosettacode.org/wiki/Modular_exponentiation
+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 };
+
+my Bool multi sub is-prime(Int $n, Int $k)            { return False; }
+my Bool multi sub is-prime(2, Int $k)                 { return True; }
+my Bool multi sub is-prime(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);
+
+		# one could just write "next if $x == 1 | $n - 1"
+		# but this takes much more time in current rakudo/nom
+		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 !== $n - 1;
+	}
+
+	return True;
+}
+
+say (1..1000).grep({ is-prime($_, 10) }).join(", ");

Task/Miller-Rabin-primality-test/PureBasic/miller-rabin-primality-test.purebasic

@@ -0,0 +1,29 @@
+Enumeration
+  #Composite
+  #Probably_prime
+EndEnumeration
+
+Procedure Miller_Rabin(n, k)
+  Protected d=n-1, s, x, r
+  If n=2
+    ProcedureReturn #Probably_prime
+  ElseIf n%2=0 Or n<2
+    ProcedureReturn #Composite
+  EndIf
+  While d%2=0
+    d/2
+    s+1
+  Wend
+  While k>0
+    k-1
+    x=Int(Pow(2+Random(n-4),d))%n
+    If x=1 Or x=n-1: Continue: EndIf
+    For r=1 To s-1
+      x=(x*x)%n
+      If x=1: ProcedureReturn #Composite: EndIf
+      If x=n-1: Break: EndIf
+    Next
+    If x<>n-1: ProcedureReturn #Composite: EndIf
+  Wend
+  ProcedureReturn #Probably_prime
+EndProcedure

Task/Miller-Rabin-primality-test/Run-BASIC/miller-rabin-primality-test.run

@@ -0,0 +1,54 @@
+input "Input a number:";n
+input "Input test:";k
+
+test =  millerRabin(n,k)
+if test = 0 then
+  print "Probably Prime"
+ else
+  print "Composite"
+end if
+wait
+
+' ----------------------------------------
+' Returns
+'  Composite     = 1
+'  Probably Prime = 0
+' ----------------------------------------
+ FUNCTION millerRabin(n, k)
+  if n = 2 then
+    millerRabin = 0 'probablyPrime
+    goto [funEnd]
+  end if
+
+  if n mod 2 = 0 or n < 2 then
+    millerRabin = 1 'composite
+    goto [funEnd]
+  end if
+
+d = n - 1
+while d mod 2 = 0
+  d = d / 2
+  s = s + 1
+wend
+
+while k > 0
+  k = k - 1
+  x = (int(rnd(1) * (n-4))^d) mod n
+  if x = 1 or x = n-1 then
+    for r=1 To s-1
+      x =(x * x) mod n
+      if x=1 then
+       millerRabin = 1 ' composite
+       goto [funEnd]
+      end if
+      if x = n-1 then exit for
+    next r
+
+    if x<>n-1 then
+      millerRabin =  1 ' composite
+      goto [funEnd]
+    end if
+  end if
+wend
+[funEnd]
+END FUNCTION

Task/Miller-Rabin-primality-test/Standard-ML/miller-rabin-primality-test.ml

@@ -0,0 +1,49 @@
+open LargeInt;
+
+val mr_iterations = Int.toLarge 20;
+val rng = Random.rand (557216670, 13504100); (* arbitrary pair to seed RNG *)
+
+fun expmod base 0 m = 1
+  | expmod base exp m =
+      if exp mod 2 = 0
+      then let val rt = expmod base (exp div 2) m;
+               val sq = (rt*rt) mod m
+           in if sq = 1
+                 andalso rt <> 1     (* ignore the two *)
+                 andalso rt <> (m-1) (* 'trivial' roots *)
+              then 0
+              else sq
+           end
+      else (base*(expmod base (exp-1) m)) mod m;
+
+(* arbitrary precision random number [0,n) *)
+fun rand n =
+  let val base = Int.toLarge(valOf Int.maxInt)+1;
+      fun step r lim =
+        if lim < n then step (Int.toLarge(Random.randNat rng) + r*base) (lim*base)
+                   else r mod n
+  in step 0 1 end;
+
+fun miller_rabin n =
+  let fun trial n 0 = true
+        | trial n t = let val a = 1+rand(n-1)
+                      in (expmod a (n-1) n) = 1
+                         andalso trial n (t-1)
+                      end
+  in trial n mr_iterations end;
+
+fun trylist label lst = (label, ListPair.zip (lst, map miller_rabin lst));
+
+trylist "test the first six Carmichael numbers"
+        [561, 1105, 1729, 2465, 2821, 6601];
+
+trylist "test some known primes"
+        [7369, 7393, 7411, 27367, 27397, 27407];
+
+(* find ten random 30 digit primes (according to Miller-Rabin) *)
+let fun findPrime trials = let val t = trials+1;
+                               val n = 2*rand(500000000000000000000000000000)+1
+                           in if miller_rabin n
+                              then (n,t)
+                              else findPrime t end
+in List.tabulate (10, fn e => findPrime 0) end;