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//############################################################################
// Programmation IV - 2002 - Week 10
//############################################################################
import math.{Pi, log}
object M0 {
def addStream (s1: Stream[Int], s2: Stream[Int]): Stream[Int] =
Stream.cons(s1.head + s2.head, addStream(s1.tail, s2.tail));
val fib: Stream[Int] =
Stream.cons(0, Stream.cons(1, addStream(this.fib, this.fib.tail)));
def test = {
var i = 0;
fib.take(20).foreach(n => {Console.println("fib("+i+") = "+n); i=i+1});
Console.println;
}
}
//############################################################################
object M1 {
def scale(x: Double, s: Stream[Double]): Stream[Double] =
s map { e: Double => e*x }
def partialSums(s: Stream[Double]): Stream[Double] =
Stream.cons(s.head, partialSums(s.tail) map (x => x + s.head));
def euler(s: Stream[Double]): Stream[Double] = {
val nm1 = s apply 0;
val n = s apply 1;
val np1 = s apply 2;
Stream.cons(np1 - ((np1 - n)*(np1 - n) / (nm1 - 2*n + np1)),euler(s.tail))
};
def better(s: Stream[Double], transform: Stream[Double] => Stream[Double])
: Stream[Stream[Double]] =
Stream.cons(s, better(transform(s), transform));
def veryGood(s: Stream[Double], transform: Stream[Double] => Stream[Double])
: Stream[Double] =
better(s, transform) map (x => x.head);
def lnSummands(n: Double): Stream[Double] =
Stream.cons(1.0 / n, lnSummands(n + 1.0) map { x: Double => -x })
var ln0 = partialSums(lnSummands(1.0));
var ln1 = euler(ln0);
var ln2 = veryGood(ln0, euler);
def piSummands(n: Double): Stream[Double] =
Stream.cons(1.0 / n, piSummands(n + 2.0) map { x: Double => -x })
var pi0 = scale(4.0, partialSums(piSummands(1.0)));
var pi1 = euler(pi0);
var pi2 = veryGood(pi0, euler);
def pad(s: String, n: Int): String =
if (n <= 0) s.substring(0, s.length() + n)
else pad(s + " ", n - 1);
def str(d: Double) = { val s = d.toString(); pad(s, 18 - s.length()) };
def test = {
var i = 0;
while (i < 10) {
Console.print("pi("+i+") = ");
Console.print(str(pi0.apply(i)) + ", ");
Console.print(str(pi1.apply(i)) + ", ");
Console.print(str(pi2.apply(i)) + "\n");
i = i + 1;
}
Console.print("pi = ");
Console.print(str(Pi) + ", ");
Console.print(str(Pi) + ", ");
Console.print(str(Pi) + "\n");
Console.println;
i = 0;
while (i < 10) {
Console.print("ln("+i+") = ");
Console.print(str(ln0.apply(i)) + ", ");
Console.print(str(ln1.apply(i)) + ", ");
Console.print(str(ln2.apply(i)) + "\n");
i = i + 1;
}
Console.print("ln = ");
Console.print(str(log(2)) + ", ");
Console.print(str(log(2)) + ", ");
Console.print(str(log(2)) + "\n");
Console.println;
}
}
//############################################################################
object M2 {
class IntIterator(start: Int) extends Iterator[Int] {
var current: Int = start;
def hasNext = true;
def next = { current = current + 1; current - 1 };
}
class PrimeIterator() extends Iterator[Int] {
var current: Iterator[Int] = new IntIterator(2);
def hasNext = true;
def next = {
val p = current.next;
current = current filter { x => !((x % p) == 0) };
p
}
}
def test = {
val i = (new PrimeIterator()).take(30);
Console.print("prime numbers:");
while (i.hasNext) { Console.print(" " + i.next); }
Console.println;
}
}
//############################################################################
object Test {
def main(args: Array[String]): Unit = {
M0.test;
M1.test;
M2.test;
()
}
}
//############################################################################
|
