An answer of the advanced exercise: complex cube roots on a tour of Go

complex_cube_root.go

package main

import (
	"fmt"
	"math/cmplx"
	)

// FIXME:
// Currently calculate only real part of the input
// complex number.
func Cbrt(x complex128) complex128 {
	z := 1.0
	tmp := 0.0
	rx := real(x)
	for i := 0; i < 100000; i++ {
		tmp = z - (z * z * z - rx) / (3 * z * z)
		z = tmp
		// DEBUG
		// fmt.Printf("i = %d, %g\n", i, tmp)		
	}
	return complex(tmp, imag(x))
}

func main() {
	fmt.Println(Cbrt(2))
	fmt.Println(cmplx.Pow(2, 0.3333333))	
}

thansk for giving out these codes ~

thanks, now I know Go has the real function, oh...

func Cbrt(x complex128) complex128 {
    z := complex128(1)
    for i := 0; i < 10; i++ {
        z = z - (((z*z*z)-x)/(3*z*z))
    }
    return z
 }

func main() {
    fmt.Println(Cbrt(2))
    fmt.Println(cmplx.Pow(2,0.33333333333))
}

In order to take into account roots of negative and imaginary numbers, I did the following:

package main

import "fmt"
import "math/cmplx"

func Cbrt(x complex128) complex128 {
    z := complex128(1)
    if (imag(x) != 0.) || (real(x) < 0) {
        z += 1i
    }

    for i := 0; i < 30; i++ {
        z = z - (z*z*z - x)/(3*z*z)
    }

    return z
}

func main() {
    fmt.Println(Cbrt(2))
    fmt.Println(cmplx.Pow(2, 1./3.))
}

func Cbrt(x complex128) complex128 {
    z := complex128(1)
    for i := 0; i < 100; i++ {
        z = z - (cmplx.Pow(z,complex128(3)) - x) / (3 * cmplx.Pow(z, complex128(2)))
    }
    return z
}