logarithmic loop calculations
Help with math calc
Calculating efficiency of loops from both
Gilberg and Hortsmann books...
Logarithmic Loops (multiplication and division):
Where log x (log base x) is the multiple/divisor value
Note with division we flip n and m in the formulas above.
Basically I trying to find an all purpose formula- derived from the following..
A loop where the loop control body is multiplied or divided...
f(n) = ceil(log2 n) or where N is the iterations...
what I came up with
Cases 1 and 2 are applicable to logarithmic loops as well.
3. Valid Execution:
Same test as above except:
for (i = m; i < n; i *= x)
o If the condition is < or > the formula is:
num = ceiling (log x (n / m))
o If the condition is ≤ or ≥ the formula is:
num = floor (log x (n / m)) + 1
Any additional insight for those math inclined with my quest of a general formula..