An answer of the exercise: Loops and Functions on a tour of Go

answer_exercise_gotour.go

package main

import (
	"fmt"
	"math"
)

const Delta = 0.0001

func isConverged(d float64) bool {
	if d < 0.0 {
		d = -d
	}
	if d < Delta {
		return true
	}
	return false
}

func Sqrt(x float64) float64 {
	z := 1.0
	tmp := 0.0
	for {
		tmp = z - (z * z - x) / 2 * z
		if d := tmp - z; isConverged(d) {
			return tmp
		}
		z = tmp
	}
	return z
}

func main() {
	attempt := Sqrt(2)
	expected := math.Sqrt(2)
	fmt.Printf("attempt = %g (expected = %g) error = %g\n",
		attempt, expected, attempt - expected)
}

Here's another take. Instead of fooling around with the delta and absolute values, let's convert the type to something more finite.

package main

import (
	"fmt"
	"math"
)

func Sqrt(start float64) float64 {
	for guess := 1.0; ; {
		state := guess
		guess -= (guess*guess - start) / (2 * guess)

		if float32(state) == float32(guess) {
			return guess
		}
	}
}

func main() {
	fmt.Println(Sqrt(6.0) == math.Sqrt(6.0)) // true
	fmt.Println(Sqrt(2) == math.Sqrt(2))     // true
	fmt.Println(Sqrt(866) == math.Sqrt(866)) // true
}

// SquareRoot x
func SquareRoot(x float64) float64 {
	z, count, thresh := float64(1), 10, float64(0.1)

	for index := 0; index < count; index++ {
		z = z - ((z*z - x) / (2 * z))

		fmt.Printf("Z Val [ %v ] , Predicted [ %v ], Actual [ %v ] \n", z, z*z, x)

		if guess := z * z; math.Abs(guess-x) < thresh {
			fmt.Printf("Fell within threshold of [ %v ] within [ %v ] counts \n", thresh, index)
			break
		}
	}

	return z
}

Sample output

Z Val [ 327 ] , Predicted [ 106929 ], Actual [ 653 ]
Z Val [ 164.49847094801223 ] , Predicted [ 27059.746944234023 ], Actual [ 653 ]
Z Val [ 84.23405635482261 ] , Predicted [ 7095.376249987432 ], Actual [ 653 ]
Z Val [ 45.99313261935662 ] , Predicted [ 2115.3682481417263 ], Actual [ 653 ]
Z Val [ 30.095452195580968 ] , Predicted [ 905.7362428564993 ], Actual [ 653 ]
Z Val [ 25.896541323366037 ] , Predicted [ 670.6308525128048 ], Actual [ 653 ]
Z Val [ 25.556131917093378 ] , Predicted [ 653.1158785638788 ], Actual [ 653 ]
Z Val [ 25.553864778931494 ] , Predicted [ 653.0000051399155 ], Actual [ 653 ]
Fell within threshold of [ 0.1 ] within [ 7 ] counts

package main

import (
	"fmt"
	"math"
)

func Sqrt(x float64) float64 {
	z := 1.0
	for x >= z {
		z -= (z*z - x) / (2 * z)
		fmt.Println(z)
		if z == math.Sqrt(x) {
			break
		}

	}
	return z

}

func main() {
	fmt.Println(Sqrt(9999800001))

	fmt.Println("printing")

	fmt.Println(math.Sqrt(9999800001))

}

import "fmt"

func Sqrt(x float64) float64{
	z := float64(1)
	mydict := make(map[float64]float64)
	for  {
		z -= (z*z - x) / (x * z)
		_, ok := mydict[z]
		if !ok{
			mydict[z] = z
		} else {
			break
		}
		fmt.Println(z)
	}
	return z
}

func main() {
	fmt.Println(Sqrt(3))
}

package main

import (
	"fmt"
)

func Sqrt(x float64) float64 {
	z := 1.0

	for {
		distance := z*z - x
		
		if distance > -.000000001 && distance < ..000000001 {
			break
		}
		
		z -= distance / (2*z)
		
		fmt.Println(z)
	}

	return z
}

func main() {
	fmt.Println(Sqrt(2))
}

package main

import (
	"fmt"
	"math"
)

const epison = 0.00001

func Sqrt(x float64) float64 {
	result := 1.
	for {
		result = result + (x / (2 * result) - result / 2)
		if math.Abs(result * result - x) < epison {
			break
		}
	}
	return result
}

func main() {
	fmt.Println(Sqrt(2))
}

package main
import (
"fmt"
"math"
)

func Sqrt(x float64) float64 {
z,t := 1.,0.

for math.Abs(t-z) >= 1e-8 {
    t,z = z, z - (z*z - x) / (2*z)
}
return z

}
func main() {
guess := Sqrt(2)
expected := math.Sqrt(2)
fmt.Printf("Guess: %v, Expected: %v, Error: %v", guess, expected, math.Abs(guess - expected))
}

Can anyone let me know the different of z -= (z*z - x) / (2 * x) and z -= (z * z - x)/(2 * z) in attached example?
The result is different between these expressions which make me very confuse

You can find the full code here https://go.dev/play/p/ff8LzDMIg8c

package main

import (
	"fmt"
	"math"
)

func Sqrt(x float64) float64 {
	z,p := 1.0, 0.0
	for math.Abs(p-z) >= 1e-8 {
		p,z = z, z - (z*z - x) / (2*z)
	}
	return z
}

func main() {
	fmt.Println(Sqrt(2))
}

package main

import (
	"fmt"
	"math"
)

func Sqrt(x float64) (z float64, iterations int) {
	z = 1.0
	iterations = 0
	for {
		iterations++
		temp := z - (z*z - x) / (2*z)
		if math.Round(temp * 100000) / 100000 == math.Round(z * 100000) / 100000 {
			break
		}
		z = temp
	}
	return
}

func main() {
	fmt.Println(Sqrt(2))
	fmt.Println(math.Sqrt(2))
}

As a total beginner I've done it with rounding

package main

import (
	"fmt"
)

func Sqrt(x float64) float64 {
	z := 1.0
	for i := 0; i <= 10; i++ {
		z -= (z*z - x) / (2 * z)
	}
	return z
}

func main() {
	fmt.Println(Sqrt(23123))
}

package main

import (
"fmt"
"math"
)

func Sqrt(x float64) float64 {
z:=1.0

for n:= 1;n < 10;n++ {
	z = z - ((z*z - x) / (2*z))
}
return z

}

func main() {
y := 169.
fmt.Println(Sqrt(y))
fmt.Println(math.Sqrt(y))
}

func Sqrt(x float64) float64 {
var z, tmp float64 = 1.0, 0.
for ; math.Abs(z - tmp) >= 1e-8 ; z, tmp = z - (zz-x)/(2z), z {}
return z
}

package main

import (
"fmt"
)

func Sqrt(x float64) float64 {
z := float64(1)
for i := 1; i <= 10; i++ {
nextZ := z - (zz-x)/(2z)
if nextZ == z {
return z
} else {
z = nextZ
fmt.Println(z, i)
}
}
return z
}

func main() {
p := 2.0
fmt.Println(Sqrt(p))
}