Find n-th root of a big number

[Hau Phan]

i can't find get n-th root in document of go big package so i decided to do it myself using newton's method. i found a solution at https://www.geeksforgeeks.org/n-th-root-number/ and start to implement in go. but my code only work fine for base 2. other base result gone too far from correct.

Anyone could show me where am i wrong.

Here's my code

```go

package main

import (

"fmt"

"math/big"

"math/rand"

)

// PowFloat return x^n

func PowFloat(x *big.Float, n int64) *big.Float {

result := new(big.Float).SetInt64(1)

for i := 0; i < int(n); i++ {

result.Mul(result, x)

}

return result

}

// GetNthRoothFloat get nth root of a using newton's method

func GetNthRoothFloat(a *big.Float, n int64) *big.Float {

N := new(big.Float).SetInt64(n)

xPre := new(big.Float).SetInt64(int64(rand.Intn(10) + 1))

eps := new(big.Float).SetFloat64(0.00000000001)

delX := new(big.Float).SetInt64(2147483647)

xK := new(big.Float).SetInt64(0)

for delX.Cmp(eps) > 0 {

t1 := new(big.Float).Sub(N, new(big.Float).SetFloat64(1.0)) // t1 = n-1

t1 = t1.Mul(t1, xPre)                                       // t1 = (N-1) * xPre

t2 := new(big.Float).Quo(a, PowFloat(xPre, n-1))            // t2 = a/( xPre^(n-1) )

t3 := new(big.Float).Add(t1, t2)                            // t3 = t1 + t2

xK.Quo(t3, N)

delX = new(big.Float).Sub(xK, xPre)

delX.Abs(delX)

xPre = xK.Copy(xK)

}

return xK

}

func main() {

t := new(big.Float).SetInt64(64)

fmt.Println(GetNthRoothFloat(t, 3))

}

```

[Rob Pike]

I'm not going to debug you program for you - you'll learn more doing it yourself, but I glanced at it and saw immediately that you're missing an easy optimization. Raising a number to an integer power can be done much faster by repeated squaring according to the bit pattern of the exponent. I'll leave that cryptic comment alone to let you puzzle it out yourself. (Don't look it up; it's much more fun to figure out.)

-rob

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[Nasir Hussain]

The Amazing Rob Pike :D

To view this discussion on the web visit https://groups.google.com/d/msgid/golang-nuts/CAOXNBZQrjBjT-dDEK1Atu7R32aT1mgTsSAYhXAF7hXmj35BjuQ%40mail.gmail.com.

[roger peppe]

Relevant issue: https://golang.org/issue/14102

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