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!-----------------------------------------------------------------------------------------------------
! This Fortran program finds the root of a function f(x) = x^3 + 2x^2 + x + 1 using the Secant Method
! where limits is the number of iteration steps can be no-convergent when the initial value a and b
! are not so close.
! it will also display the number o iteration used for finding the solution. 
!-----------------------------------------------------------------------------------------------------

PROGRAM SECANTMETHOD
    IMPLICIT NONE
    
    ! Declare variables
    REAL*8 ::a, b, eps, result
    INTEGER :: iter = 0, limit
    

    DO
        ! getting the value of a, b, eps, limits
        PRINT *, "----------------------------------------------------------------------------"
        PRINT *, "Please enter the value of a, b, eps and limit with spaces/commas"
        READ *, a, b, eps, limit
        
        IF (a .eq. 0 .and. b .eq. 0) THEN
            PRINT *, "PROGRAM EXIT!!!"
            EXIT
        ELSE
            ! the secant method will the find the approximate root uses
            ! two intial values a and b which are "close" to the solution.
            result = SECANT(a, b, eps, iter, limit)
            PRINT *, "RESULT: ", result
        END IF
        
    END DO

CONTAINS

    ! this secant function finds the approximate root uses two intial value of a and b
    ! and each itteration step an approximation x to the solution determine by the 
    ! secant line
    REAL*8 FUNCTION SECANT(a, b, eps, iter, limit)
        REAL*8 :: a, b, x
        INTEGER :: counter = 0
        REAL*8, INTENT (IN) :: eps
        INTEGER, INTENT(IN) :: limit, iter
    
        ! if the absoulate difference is less than eps # EXIT
        DO WHILE(abs(a - b) > eps)
            counter = counter + 1
            
            IF (limit .eq. counter) THEN
                PRINT *, "Result Not Found!! "
                PRINT *, "Number of tires: ", limit
                PRINT *, "Last Result is: "
                EXIT
            END IF

            IF ( f(b) .eq. f(a)) THEN
                b = b + 1
            END IF

            ! to find the x we have to draw a stright line betwen the a and b
            x = b - ((b - a) * f(b)) / (f(b) - f(a))
            a = b
            b = x
        END DO

        IF (iter .lt. limit) THEN
            PRINT *, "Number of tires: ", counter
        END IF

        SECANT = a
    END FUNCTION SECANT


    ! the testing function is f(x) = x^3 + 2x^2 + x + 1 
    REAL*8 FUNCTION f(x)
        REAL*8, INTENT(IN) :: x
        f = (x * x * x) - (2 * x * x) + x + 1
    END FUNCTION f


END PROGRAM SECANTMETHOD

PROGRAM expFunction1

IMPLICIT NONE
REAL :: x, y, z
! declare the value of the 2
x = -2.0

PRINT *, x, exp(x)
DO WHILE (x .lt. 6.25)
    y = exp(x)
    z = myexp(x)
    PRINT "(1X, F7.3, 2F12.6, 2(1PE13.5))", x, y, z, y, z
    x = x + 0.5
END DO


CONTAINS
REAL FUNCTION myexp(x)
    REAL, INTENT(IN) :: x
    REAL :: approx, sum, sum_prev, counter
    approx = x
    counter = 1.0
    sum_prev = 0.0
    sum = x

    DO WHILE (sum .ne. sum_prev)
        sum_prev = sum
        counter = counter + 1.0 
        approx = -(approx * (x / counter))
        sum = sum + approx
    END DO

    myexp = sum
END FUNCTION myexp


END PROGRAM expFunction1