Sum of Factorials from a to b in scala - scala

Question

I'm trying to write a function in scala that finds the Sum of any (passed) function from a to b. Additionally , I'm trying to do it in a tail-wise recursive manner. I managed a tailwise recursive factorial function , so now i want to pass it to the "Summation" function and have it find the sum of all factorials from lower-bound a to upper-bound b . Here's what i have so far
object Sum {
def Summation( f : Double => Double , a: Double , b: Double):Double = {
def tailwiseSummation(accumulator:Double , count:Double):Double = {
if(count > b) accumulator
else tailwiseSummation(accumulator + f, a+1) // i dont know what to do here
}
}
def Factorial(num: Double): Double = { // i want to pass this function to `Summation`
def tailwise(accumulator: Double, deprecator: Double): Double = {
if (deprecator == 0) accumulator
else tailwise(accumulator * deprecator, deprecator - 1) // deprecator deprecating 1 unit at a time
}
tailwise(1, num)
}
}
can someone please help ?

Answer 1

You almost have it. Call f with count and add 1 to count in the recursive call tailwiseSummation. Also, you need the initialization function tailwiseSummation(f(a), a + 1) just like Factorial.
object Sum {
def Summation( f : Double => Double , a: Double , b: Double):Double = {
def tailwiseSummation(accumulator:Double , count:Double):Double = {
if(count > b) accumulator
else tailwiseSummation(accumulator + f(count), count+1)
}
// accumulator starts with f(a) , so count starts from a+1 to remove off-by-one error
tailwiseSummation(f(a), a + 1)
}
def Factorial(num: Double): Double = {
def tailwise(accumulator: Double, deprecator: Double): Double = {
if (deprecator == 0) accumulator
else tailwise(accumulator * deprecator, deprecator - 1) // deprecator deprecating 1 unit at a time
}
tailwise(1, num)
}
}
Run it:
scala> Sum.Summation(Sum.Factorial(_), 1, 5)
res0: Double = 153.0

Answer 2

Generic recursion over the range could be something like that :
def makeSum(f: Double => Double, a:Double, b:Double, step:Double = 1.0):Double = {
def makeSumAcc(f:Double =>Double, a:Double, b:Double, acc:Double) = {
if (a>=b) acc
else makeSumAcc(f, a+step, b, acc+f(a))
}
makeSum(f, a, b, 0)
}