OpenEuphoria

simpson.ex: The Simpson Rule

• Posted by Alan Tu <ATU5713 at COMPUSERVE.COM> Dec 17, 1998
• 463 views

For all you calculists or whatever, the Simpson Rule for finding integrals
in Euphoria!  SIMPSON.EX will ask for A, B, and N (N must be even).  There
is one catch: the function f(atom x).  This must be a global function in
function.e.  And it must be, well, euphoric.  For example, BASIC recognizes
the standard way of doing exponents on computer x^2 is x squared.  But
Euphoria does not.  To write x squared, you must do power(x,2).  x cubed
would be power(x,3).  Order of operations are consistent with standard
algebraic practice.  sin, cos, and tan are self-explanatory; Euphoria has
these functions.  All those who are interested in RAM programs (LRAM, MRAM,
and RRAM), I've written those too.  So, without further waiting, this is
simpson.ex

Last thing, speed does matter, so suggestions to improve speed and all
other suggestions are welcome!

Alan

include get.e
include function.e
type even(integer x)
    return integer(0.5*x)
end type
atom delta, coeff, solution, real, answer
object a, b, n
even subd
real = 0
clear_screen()
puts(1,"Enter A: ")
a = get(0)
a = a[2]
puts(1,"\nEnter B: ")
b = get(0)
b = b[2]
puts(1,"\nEnter N: ")
n = get(0)
subd = n[2]
delta = (b-a)/subd
coeff = (1/3)*delta
puts(1,"\n")
for i = 0 to subd do
    solution = f(a+i*delta)
    if i = 0 or i = subd then
        real = real+solution
    elsif 0.5*i != floor(0.5*i) then
        real = real+4*solution
    elsif 0.5*i = floor(0.5*i) then
        real = real+2*solution
    end if
end for
answer = coeff*real
puts(1,"The estimated integral is: ")
print(1,answer)
puts(1,"\nNote: Simpson's Rule often provides exact answers.")

--begin sample function.e
global function f(atom x)
    return 1/x
end function