Computes the Jacobi Symbol for BigInteger - CSharp System

CSharp examples for System:Math Number

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Description

Computes the Jacobi Symbol for BigInteger

Demo Code

// All rights reserved.
using System;/* www.  j  a v  a 2 s . c  o m*/

public class Main{
        //***********************************************************************
    // Computes the Jacobi Symbol for a and b.
    // Algorithm adapted from [3] and [4] with some optimizations
    //***********************************************************************

    public static int Jacobi(BigInteger a, BigInteger b)
    {
        // Jacobi defined only for odd integers
        if ((b.data[0] & 0x1) == 0)
            throw (new ArgumentException("Jacobi defined only for odd integers."));

        if (a >= b) a %= b;
        if (a.dataLength == 1 && a.data[0] == 0) return 0;  // a == 0
        if (a.dataLength == 1 && a.data[0] == 1) return 1;  // a == 1

        if (a < 0)
        {
            if ((((b - 1).data[0]) & 0x2) == 0)       //if( (((b-1) >> 1).data[0] & 0x1) == 0)
                return Jacobi(-a, b);
            else
                return -Jacobi(-a, b);
        }

        int e = 0;
        for (int index = 0; index < a.dataLength; index++)
        {
            uint mask = 0x01;

            for (int i = 0; i < 32; i++)
            {
                if ((a.data[index] & mask) != 0)
                {
                    index = a.dataLength;      // to break the outer loop
                    break;
                }
                mask <<= 1;
                e++;
            }
        }

        BigInteger a1 = a >> e;

        int s = 1;
        if ((e & 0x1) != 0 && ((b.data[0] & 0x7) == 3 || (b.data[0] & 0x7) == 5))
            s = -1;

        if ((b.data[0] & 0x3) == 3 && (a1.data[0] & 0x3) == 3)
            s = -s;

        if (a1.dataLength == 1 && a1.data[0] == 1)
            return s;
        else
            return (s * Jacobi(b % a1, a1));
    }
}

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