program Askisi_2
	implicit none

	real :: a,b,c,F,Ftonos,xk,xkplinena
	integer :: i

	!Input
	write(*,*)'Eisagete A,B kai akriveia'
	read(*,*)a,b,c

	!Checking if root exists
	if ((F(a) * F(b)) < 0) then
		
		!initialising
		xkplinena = (a + b) / 2 
		xk = xkplinena - F(xkplinena) / Ftonos(xkplinena)
		i = 1

		!Methodos newton raphson
		do while (abs(xk - xkplinena) > c)
			xkplinena = xk
			xk = xkplinena - F(xkplinena) / Ftonos(xkplinena)
			i = i + 1 !counting loops
		enddo
		
		!printing results
		write(*,*)'Riza : ',xk 
		write(*,*)'Found after:',i, ' loops'
		write(*,*)c

	else !no root in space [a,b]
		write(*,*)'Den yparxei riza'
	end if
end program

!------------------------------------------
real function F(x)
	real :: x
	F = exp(x)-2*x-1
end function

real function Ftonos(x)
	real :: x
	Ftonos = exp(x)-2
end function