Archive
Posts Tagged ‘approximation’
The square root function using Newton’s method
February 3, 2014
1 comment
Newton’s method approximates Sqrt(x) by picking a starting point z (e.g. 1.0) and then repeating:
Let’s see an implementation in Go. We repeat until the value only changes a very small delta. The number of steps is also displayed.
package main
import (
"fmt"
"math"
)
func Sqrt(x float64) float64 {
prev, z := 1.0, 1.0
const delta = 0.000000000001
steps := 0
for {
z -= (z*z-x) / (2*z)
if math.Abs(prev-z) < delta {
break
}
prev = z
steps++
}
fmt.Println("# steps:", steps)
return z
}
func main() {
n := float64(7)
fmt.Println(Sqrt(n))
fmt.Println(math.Sqrt(n))
}
Hmm, it seems WordPress.com doesn’t support Go syntax highlighting :(
Output for Sqrt(7):
# steps: 6 2.6457513110645907 2.6457513110645907
Idea from here: http://tour.golang.org/#25
Categories: golang, math
approximation, Newton, sqrt
Seconds in one year
October 24, 2011
Leave a comment
In 1 year there are about seconds.
Exact value:
365 * 24 * 60 * 60 = 31536000
Approximation:
>>> math.pi * 10**7 31415926
Difference:
120074 seconds, i.e. 33.35 hours.
Categories: Uncategorized
approximation, pi, seconds, year
The Ubuntu Incident
You must be logged in to post a comment.