BigInteger的大部分时间优化的乘法 [英] BigInteger most time optimized multiplication

问题描述

您好我想乘2个大整数，一个最及时的优化的方式。我目前使用Karatsuba的算法。任何人都可以提出来做到这一点更优化的方式或算法中。

Hi I want to multiply 2 big integer in a most timely optimized way. I am currently using karatsuba algorithm. Can anyone suggest more optimized way or algo to do it.

感谢

public static BigInteger karatsuba(BigInteger x, BigInteger y) {

        // cutoff to brute force
        int N = Math.max(x.bitLength(), y.bitLength());
        System.out.println(N);
        if (N <= 2000) return x.multiply(y);                // optimize this parameter

        // number of bits divided by 2, rounded up
        N = (N / 2) + (N % 2);

        // x = a + 2^N b,   y = c + 2^N d
        BigInteger b = x.shiftRight(N);
        BigInteger a = x.subtract(b.shiftLeft(N));
        BigInteger d = y.shiftRight(N);
        BigInteger c = y.subtract(d.shiftLeft(N));

        // compute sub-expressions
        BigInteger ac    = karatsuba(a, c);
        BigInteger bd    = karatsuba(b, d);
        BigInteger abcd  = karatsuba(a.add(b), c.add(d));

        return ac.add(abcd.subtract(ac).subtract(bd).shiftLeft(N)).add(bd.shiftLeft(2*N));
    }

推荐答案

BigInteger的在幼稚算法之间jdk8开关的版本中，该TOOM-库克算法，和Karatsuba的根据输入的大小，以获得优异的性能。

The version of BigInteger in jdk8 switches between the naive algorithm, The Toom-Cook algorithm, and Karatsuba depending on the size of the input to get excellent performance.

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