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c++/Others/Fig10_62.cpp - Randomized primality testing algorithm, with a test program.cpp

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+Fig10_62.cpp - Randomized primality testing algorithm, with a test program
+	
+	#include <iostream.h>
+        #include "Random.h"
+
+        typedef int HugeInt;
+
+/* START: Fig10_62.txt */
+        /**
+         * Method that implements the basic primality test.
+         * If witness does not return 1, n is definitely composite.
+         * Do this by computing a^i (mod n) and looking for
+         * non-trivial square roots of 1 along the way.
+         */
+        HugeInt witness( const HugeInt & a, const HugeInt & i, const HugeInt & n )
+        {
+            if( i == 0 )
+                return 1;
+
+            HugeInt x = witness( a, i / 2, n );
+            if( x == 0 )    // If n is recursively composite, stop
+                return 0;
+
+            // n is not prime if we find a non-trivial square root of 1
+            HugeInt y = ( x * x ) % n;
+            if( y == 1 && x != 1 && x != n - 1 )
+                return 0;
+
+            if( i % 2 != 0 )
+                y = ( a * y ) % n;
+
+            return y;
+        }
+
+        /**
+         * The number of witnesses queried in randomized primality test.
+         */
+        const int TRIALS = 5;
+
+        /**
+         * Randomized primality test.
+         * Adjust TRIALS to increase confidence level.
+         * n is the number to test.
+         * If return value is false, n is definitely not prime.
+         * If return value is true,  n is probably prime.
+         */
+        bool isPrime( const HugeInt & n )
+        {
+            Random r;
+
+            for( int counter = 0; counter < TRIALS; counter++ )
+                if( witness( r.randomInt( 2, (int) n - 2 ), n - 1, n ) != 1 )
+                    return false;
+
+            return true;
+        }
+
+        int main( )
+        {
+            for( int i = 101; i < 200; i += 2 )
+                if( isPrime( i ) )
+                    cout << i << " is prime" << endl;
+
+            return 0;
+        }