Hi, I did some tests on pow(exponent) method. Unfortunately, my math skills are not strong enough to handle the following problem.

I'm using this code:

BigInteger.valueOf(2).pow(var);

Results:

• var | time in ms
• 2000000 | 11450
• 2500000 | 12471
• 3000000 | 22379
• 3500000 | 32147
• 4000000 | 46270
• 4500000 | 31459
• 5000000 | 49922

See? 2,500,000 exponent is calculated almost as fast as 2,000,000. 4,500,000 is calculated much faster then 4,000,000.

Why is that?

To give you some help, here's the original implementation of BigInteger.pow(exponent):

 public BigInteger pow(int exponent) {
    if (exponent < 0)
        throw new ArithmeticException("Negative exponent");
    if (signum==0)
        return (exponent==0 ? ONE : this);

    // Perform exponentiation using repeated squaring trick
        int newSign = (signum<0 && (exponent&1)==1 ? -1 : 1);
    int[] baseToPow2 = this.mag;
        int[] result = {1};

    while (exponent != 0) {
        if ((exponent & 1)==1) {
        result = multiplyToLen(result, result.length, 
                                       baseToPow2, baseToPow2.length, null);
        result = trustedStripLeadingZeroInts(result);
        }
        if ((exponent >>>= 1) != 0) {
                baseToPow2 = squareToLen(baseToPow2, baseToPow2.length, null);
        baseToPow2 = trustedStripLeadingZeroInts(baseToPow2);
        }
    }
    return new BigInteger(result, newSign);
    }