Karatsuba乘法优化un Golang

时间:2015-01-20 08:19:10

标签: algorithm go biginteger

我已经和Go玩了几个星期了,我实现了Karatsuba的乘法版本(http://en.wikipedia.org/wiki/Karatsuba_algorithm#Pseudo_Code_Implementation):

package karatsuba

import (
    "math"
    "math/big"
)

func k_multiply(a, b *big.Int) *big.Int {
    if a.Cmp(big.NewInt(10)) < 1 || b.Cmp(big.NewInt(10)) < 1 {
        return mul(a, b)
    }

    m := _pivot(a, b)

    leftA, rightA := _split(a, uint(m))
    leftB, rightB := _split(b, uint(m))

    z0 := k_multiply(leftA, leftB)
    z1 := k_multiply(rightA, rightB)
    z2 := k_multiply(add(leftA, rightA), add(leftB, rightB))
    z2 = sub(z2, add(z0, z1))

    temp0 := mul(z0, big.NewInt(int64(math.Pow(10.0, 2.0*float64(m)))))
    temp1 := mul(z2, big.NewInt(int64(math.Pow(10.0, float64(m)))))
    temp2 := add(temp0, temp1)

    return add(temp2, z1)
}

func _split(a *big.Int, m uint) (left, right *big.Int) {
    denominator := big.NewInt(int64(math.Pow(10.0, float64(m))))

    left = big.NewInt(0).Div(a, denominator)
    right = sub(a, big.NewInt(0).Mul(left, denominator))

    return
}

func _pivot(a, b *big.Int) int {
    len_a := len(a.String())
    len_b := len(b.String())

    if len_a > len_b {
        return len_a/2 + len_a%2
    } else {
        return len_b/2 + len_b%2
    }
}

func add(a, b *big.Int) *big.Int {
    return big.NewInt(0).Add(a, b)
}

func mul(a, b *big.Int) *big.Int {
    return big.NewInt(0).Mul(a, b)
}

func sub(a, b *big.Int) *big.Int {
    return big.NewInt(0).Sub(a, b)
}

该算法工作正常,但我有几个问题: - 当我计算temp0和temp1时,我在欺骗,因为我正在使用mul将我的bigInt乘以十的幂。有没有更好的方法来做这个而不做额外的递归调用? - 我对k_multiply有基准big.Mul,结果非常令人费解:

BenchmarkMultiply    5000000           490 ns/op
BenchmarkKaratsubaMultiply      5000        485348 ns/op

这提出了两个问题:我的实施真的很糟糕,我能做些什么才能让它变得更好? big.Mul使用什么算法?

非常感谢您的帮助,非常感谢

0 个答案:

没有答案