Continued fraction: Difference between revisions

<lang Scala>object CF extends App {

import Stream._

val sqrt2 = 1 #:: from(2,0) zip from(1,0)

val napier = 2 #:: from(1) zip (1 #:: from(1))

val pi = 3 #:: from(6,0) zip (from(1,2) map {x=>x*x})

// reference values, source: wikipedia

val refPi = "3.14159265358979323846264338327950288419716939937510"

val refNapier = "2.71828182845904523536028747135266249775724709369995"

val refSQRT2 = "1.41421356237309504880168872420969807856967187537694"

def calc(cf: Stream[(Int, Int)], numberOfIters: Int=200): BigDecimal = {

(cf take numberOfIters toList).foldRight[BigDecimal](1)((a, z) => a._1+a._2/z)

}

def approx(cfV: BigDecimal, cfRefV: String): String = {

val p: Pair[Char,Char] => Boolean = pair =>(pair._1==pair._2)

((cfV.toString+" "*34).substring(0,34) zip cfRefV.toString.substring(0,34)).takeWhile(p).foldRight[String]("")((a:Pair[Char,Char],z)=>a._1+z)

}

List(("sqrt2",sqrt2,50,refSQRT2),("napier",napier,50,refNapier),("pi",pi,3000,refPi)) foreach {t=>

val (name,cf,iters,refV) = t

val cfV = calc(cf,iters)

println(name+":")

println("ref value: "+refV.substring(0,34))

println("cf value: "+(cfV.toString+" "*34).substring(0,34))

println("precision: "+approx(cfV,refV))

println()

}

}

<pre>sqrt2:

ref value: 1.41421356237309504880168872420969

cf value: 1.41421356237309504880168872420969

precision: 1.41421356237309504880168872420969

napier:

ref value: 2.71828182845904523536028747135266

cf value: 2.71828182845904523536028747135266

precision: 2.71828182845904523536028747135266

pi:

ref value: 3.14159265358979323846264338327950

cf value: 3.14159265358052780404906362935452

precision: 3.14159265358</pre>