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object m1 {
def average(x: Double, y: Double) = (x + y)/2;
def abs(x: Double): Double = if (x < 0) - x else x;
def isCloseEnough(x: Double, y: Double) = abs((x - y) / x) < 0.001;
def search(f: Double => Double, negPoint: Double, posPoint: Double): Double = {
val midPoint = average(negPoint, posPoint);
if (isCloseEnough(negPoint, posPoint))
midPoint
else {
val testVal = f(midPoint);
if (testVal > 0) search (f, negPoint, midPoint)
else if (testVal < 0) search (f, midPoint, posPoint)
else midPoint
}
}
def halfIntervalMethod(f: Double => Double, a: Double, b: Double): Double = {
val aval = f(a);
val bval = f(b);
if (aval < 0 && bval > 0) search(f, a, b)
else if (bval < 0 && aval > 0) search(f, b, a)
else error("Values are not of opposite sign")
}
}
object m2 {
def abs(x: Double): Double = if (x < 0) - x else x;
def isCloseEnough(x: Double, y: Double) = abs((x - y) / x) < 0.001;
def average(x: Double, y: Double) = (x + y)/2;
def fixedPoint(f: Double => Double, firstGuess: Double) = {
def try(guess: Double): Double = {
val next = f(guess);
if (isCloseEnough(guess, next)) next
else try(next)
}
try(firstGuess);
}
def sin(x: Double): Double = x;
def cos(x: Double): Double = x;
val result = fixedPoint((y => sin(y) + cos(y)), 1.0);
def averageDamp(f: Double => Double)(x: Double) =
average(x, f(x));
def sqrt(x: Double) =
fixedPoint(averageDamp(y => x/y), 1.0);
def cubeRoot(x: Double) =
fixedPoint(averageDamp(y => x/(y*y)), 1.0);
}
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