The most compact algorithm for Simpson's rule??

[Namir]

Here is a (corrected, based on feedback from site members) pseudo code for what I hope to be the most compact way to implement Simpson's rule:

Code:


Given function f(x), integration interval [A, B] and N divisions, where N is even.
To calculate the integral of f(x) for X=A to x=B using Simpson's Rule

h=(B-A)/N
Sum=f(A)-f(B)
CHS=1
A=A+h
Do
  Sum = Sum + (3+CHS)*f(A)
  CHS=-CHS
  A=A+h
  N=N-1
Loop Until N=0
Area=h/3*Sum

Many implementations use two summations--one for odd terms and one for even terms. In addition these implementations use two loops with slightly different ranges. The above pseudo-coode implements a simple version that uses one loop and a few simple computational tricks.

Namir