logarithmic loop calculations

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  1. #1
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    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)
    do something

    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..

  2. #2
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    I'm having trouble understanding your problem. Please summarize the problem in one or two sentences while adhering to commonly accepted rules of English grammar.

    Greets,
    Philip
    All things begin as source code.
    Source code begins with an empty file.
    -- Tao Te Chip

  3. #3
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    Basically I trying to find an all purpose formula- derived from the following..

    A loop where the loop control body is multiplied or divided...

    for (i = m; i < n; i *= x)
    do something

    If the condition is < or > the formula is:

    num = ceiling (log x (n / m))

    If the condition is ≤ or ≥ the formula is:

    num = floor (log x (n / m)) + 1

    Where log x (log base x) is the multiple/divisor value


    Note with division we flip n and m in the formulas above.


    Based upon the following

    f(n) = ceil(log2 n) or where N is the iterations...

    Do the formulas I post look correct- they seem to hold up on paper...

  4. #4
    and the Hat of Guessing tabstop's Avatar
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    The num = are correct, so far as I can tell. I have no idea what you want f(n) to be, so who knows about that.

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