solution to exercise 1
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package main
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import (
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"fmt"
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"math"
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)
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const min_threshold = 1e-200
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func Sqrt(x float64, threshold float64) (z float64, iterations int) {
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z = x
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old_z := z
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for {
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z = z - (z*z-x)/(2*x)
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if math.Abs(z-old_z) < threshold {
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break
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}
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old_z = z
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iterations++
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}
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return
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}
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func main() {
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threshold := 1.0
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right_answer := math.Sqrt(2)
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for threshold > min_threshold {
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answer, iterations := Sqrt(2, threshold)
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fmt.Printf("%0.4g %0.4g %0.20f %0.20f %0.2d\n",
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threshold, right_answer-answer, right_answer, answer,
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iterations)
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threshold = threshold / 10.0
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}
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}
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