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