gistfile1.txt

val mc = new java.math.MathContext(300,java.math.RoundingMode.HALF_UP)

//Hack to work around poor bigdecimal support in Scala
def divide(a:BigDecimal, b:BigDecimal) =  {
  new BigDecimal(a.bigDecimal.divide(b.bigDecimal, mc))
}

def piSummands(n: BigDecimal): Stream[BigDecimal] = {
  Stream.cons(divide(BigDecimal(1), n), piSummands(n + BigDecimal(2)).map(_ * -1))
}

def scaleStream(stream:Stream[BigDecimal], factor:Int) = {
  stream.map( _ * factor)
}

def addStreams(s1:Stream[BigDecimal], s2:Stream[BigDecimal]) = {
  s1.zip(s2).map(z => z._1 + z._2)
}

def partialSums(s:Stream[BigDecimal]):Stream[BigDecimal] = {
  Stream.cons(s.head, addStreams(s.tail, partialSums(s)))
}

def piStream = scaleStream(partialSums(piSummands(1)), 4)

def square(s:BigDecimal) = s * s

def eulerTransform(s:Stream[BigDecimal]):Stream[BigDecimal] = {
  val s0 = s(0)
  val s1 = s(1)
  val s2 = s(2)
  val head = s2 - divide((square(s2 - s1)), ((s0 + (BigDecimal(-2) * s1) + s2)))
  Stream.cons(head, eulerTransform(s.tail))
}

type Transform = (Stream[BigDecimal]) => Stream[BigDecimal]

def makeTableau(transform: Transform, s:Stream[BigDecimal]):Stream[Stream[BigDecimal]] = {
  Stream.cons(s, makeTableau(transform, transform(s)))
}

def acceleratedSequence(transform:Transform, s:Stream[BigDecimal]) = {
  makeTableau(transform, s).map(_.head)
}

print(acceleratedSequence(eulerTransform, piStream).take(150).last)