Exercise_08_d.f90

! Created by EverLookNeverSee@GitHub on 6/6/20
! For more information see FCS/img/Exercise_08_d.png

function fact(n) result(factorial)
    integer, intent(in) :: n
    integer :: i
    real :: factorial, temp
    if (n < 0) then
        factorial = -1.0    ! error
        else if(n == 0) then
        factorial = 1.0     ! factorial of zero
        else
        temp = 1.0
        do i = 2, n
            temp = temp * i
        end do
        factorial = temp
    end if
end function fact


program main
    implicit none
    ! x --> given value that we're gonna calculate its arcsin
    ! total --> sum of the elements in series
    ! previous --> sum of elements in previous step
    ! fact --> declaration of fact function
    ! Ea --> approximation error
    ! declaring and initializing variables
    integer :: k = 0
    real :: x = 0.5, total = 0.0, Ea, previous, fact
    do
        ! Adding up first element of series -> `x` itself
        if (k == 0) then
            total = total + x
            k = k + 1
        else ! Calculating and adding up rest of elements of series
            previous = total
            total = total + (fact(2 * k) * x ** (2 * k + 1) &
                    / (2 ** (2 * k) * fact(k) ** 2 * (2 * k + 1)))
            Ea = total - previous
            ! Exit whenever approximation error is less than 10e-10
            if (Ea < 10e-10) then
                exit
            else  ! keep going to calculate and add up next element of series
                k = k + 1
                cycle
            end if
        end if
    end do
    ! printing and comparing results
    print *, "Total(aka arcsin):", total
    print *, "Fortran intrinsic arcsin function:", ASIN(x)
end program main