package main

import (
	"fmt"
	"math"
)

const min_threshold = 1e-200

type ErrNegativeSqrt float64

func (e ErrNegativeSqrt) Error() string {
	return fmt.Sprintf("cannot Sqrt negative number: %v", float64(e))
}

func Sqrt(x float64, threshold float64) (z float64, iterations int, err error) {
	if x < 0 {
		err = ErrNegativeSqrt(x)
		return
	}
	z = x
	old_z := z
	for {
		z = z - (z*z-x)/(2*x)
		if math.Abs(z-old_z) < threshold {
			break
		}
		old_z = z
		iterations++
	}
	return
}

func main() {
	threshold := 1.0
	right_answer := math.Sqrt(2)
	for threshold > min_threshold {
		answer, iterations, err := Sqrt(2, threshold)
		if err != nil {
			panic(err)
		}
		fmt.Printf("%0.4g %0.4g %0.20f %0.20f %0.2d\n",
			threshold, right_answer-answer, right_answer, answer,
			iterations)
		threshold = threshold / 10.0
	}
}