Data commit

Task/Miller-Rabin-primality-test/Oz/miller-rabin-primality-test.oz

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+%--------------------------------------------------------------------------%
+% module: Primality
+% file: Primality.oz
+% version: 17 DEC 2014 @ 6:50AM
+%--------------------------------------------------------------------------%
+
+declare
+%--------------------------------------------------------------------------%
+
+fun {IsPrime N}			% main interface of module
+	if N < 2 then false
+	elseif N < 4 then true
+	elseif (N mod 2) == 0 then false
+	elseif N < 341330071728321 then {IsMRprime N {DetWit N}}
+	else {IsMRprime N {ProbWit N 20}}
+	end
+end
+%--------------------------------------------------------------------------%
+
+fun {DetWit N}			% deterministic witnesses
+	if N < 1373653 then [2 3]
+	elseif N < 9080191 then [31 73]
+	elseif N < 25326001 then [2 3 5]
+	elseif N < 3215031751 then [2 3 5 7]
+	elseif N < 4759123141 then [2 7 61]
+	elseif N < 1122004669633 then [2 13 23 1662803]
+	elseif N < 2152302898747 then [2 3 5 7 11]
+	elseif N < 3474749660383 then [2 3 5 7 11 13]
+	elseif N < 341550071728321 then [2 3 5 7 11 13 17]
+	else nil
+	end
+end
+%--------------------------------------------------------------------------%
+
+fun {ProbWit N K}		% probabilistic witnesses
+	local A B C in
+	A = 6364136223846793005
+	B = 1442695040888963407
+	C = N - 2
+	{RWloop N A B C K nil}
+	end
+end
+
+fun {RWloop N A B C K L}
+	local N1 in
+		N1 = (((N * A) + B) mod C) + 1
+		if K == 0 then L
+		else {RWloop N1 A B C (K - 1) N1|L}
+		end
+	end
+end
+%--------------------------------------------------------------------------%
+
+fun {IsMRprime N As}	% the Miller-Rabin algorithm	
+	local D S T Ts in
+	{FindDS N} = D|S
+	{OuterLoop N As D S}
+	end
+end
+
+fun {OuterLoop N As D S}
+	local A At Base C in
+	As = A|At
+	Base = {Powm A D N}
+	C = {InnerLoop Base N 0 S}
+	if {Not C} then false
+	elseif {And C (At == nil)} then true
+	else {OuterLoop N At D S}
+	end
+	end
+end
+							
+fun {InnerLoop Base N Loop S}
+	local NextBase NextLoop in
+	NextBase = (Base * Base) mod N
+	NextLoop = Loop + 1
+	   if {And (Loop == 0) (Base == 1)} then true
+	   elseif Base == (N - 1) then true
+	   elseif NextLoop == S then false
+	   else {InnerLoop NextBase N NextLoop S}
+	   end
+	end
+end
+%--------------------------------------------------------------------------%
+
+fun {FindDS N}
+	{FindDS1 (N - 1) 0}
+end
+
+fun {FindDS1 D S}
+	if (D mod 2 == 0) then {FindDS1 (D div 2) (S + 1)}
+	else D|S
+	end
+end
+%--------------------------------------------------------------------------%
+	
+fun {Powm A D N} 		% returns (A ^ D) mod N
+	if D == 0 then 1
+	elseif (D mod 2) == 0 then {Pow {Powm A (D div 2) N} 2} mod N
+	else (A * {Powm A (D - 1) N}) mod N
+	end
+end
+%--------------------------------------------------------------------------%	
+% end_module Primality