Let a, b, and m be positive whole numbers. Required is a fast algorithm for evaluating Σ_k=0..m floor(ka/b), floor(x) being the greatest integer that does not exceed the real number x.

 Let a=5, b=17, m=23. Then

 

Sum_{0<=k<=23}floor(5*k/17) + Sum_{0<=l<=6}ceiling(17*l/5)=6*(23+1)=144,

 

where ceiling(x) is the least integer not less than x (so that ceiling is like floor, but it rounds non-integers up instead of down).

 

 

 

Edited on December 29, 2005, 9:27 pm

Posted by Richard on 2005-12-29 21:16:02