Help With Math Accuracy.

[Bokkie]

Guys,

I'm putting a library of permutation routines together and I've stumbled on a problem that only occurs at the 'higher' end of the numeric values. For example, I'm converting a number from decimal to factoradic format. Not wanting to bore you too much but 533 can be converted to 4(5!) + 2(4!) + 0(3!) + 2(2!) + 1(1!). You'll have to accept that in AutoIT the highest factorial you can calculate is 20! before it exceeds the maximum precision the data type can accomodate. This is all well.

My problem occurs when I try to do the same conversion but using 20! - 1. Using .Net as my 'gold' standard where the same routine works 20! - 1 would convert to 1(19!) + 2(18!) + 3(17!) ... + 19(1!).

My first two numbers in the sequence would be 243290200817663999 / 121645100408832000.

Multiply 121645100408832000 * 20 and you get 243290200817664000 so the division should be 19.9999 or something like it. In my .Net I truncate the division to get 19 but in AutoIT the truncation yields 20 and that renders the rest of the sequence invalid. I know that AutoIT uses variants but I'd really like to ask if there is a coding solution that would give me the result I'm after?

TIA.

Edited April 15, 2006 by Peter Hamilton-Scott

[RazerM]

use Int() it lowers any number to an integer thus 19.9999 becomes 19

[Bokkie]

use Int() it lowers any number to an integer thus 19.9999 becomes 19

I have tried that. Here's a code sample you could try for me.

local $a = 2432902008176639999; 20! - 1
local $b = 121645100408832000; 19!
local $c = Int($a / $b)
MsgBox(0, "Calculated.", $a & " / " & $b & " = " & $c)

I still get the result 20 with or without the Int. Perhaps there is some precision creepage that either yields 20 on the dot or it transitions from 19.9999 to 20.0001 or something like that?

Edit #1: I changed the code to factor some precision into the calculation. If I use this:

local $a = 2432902008176639999; 20! - 1
local $b = 121645100408832000; 19!
local $c = Int($a / $b - 0.0000000000001)
MsgBox(0, "Calculated.", $a & " / " & $b & " = " & $c)

I get the result I'm after. I'll have to see if this artificial nudge affects the other calculations.

Edit #2: Attached screenshot shows the code I'm using and the result of the calculation I'm getting.

Edited April 15, 2006 by Peter Hamilton-Scott

[Bokkie]

I found a workaround. I just need to subtract 1 from the count by checking if the count * factorial exceeds the value I'm using. This works and I now get consistent results (so far).

local $upper = UBound($result) - 1, $count
for $i = 0 to $upper
    $factorial = Factorial(UBound($result) - $i)
    $count = Int($p_n / $factorial)
    if $count * $factorial > $p_n then
        $count -= 1
    endif
    $p_n -= $count * $factorial
    $result[$i] = $count
    if $p_n = 0 then
        exitLoop
    endif
next

Apologies for hijacking my own thread. I just thought you'd like to know how it progressed.

Edited April 15, 2006 by Peter Hamilton-Scott

[Valik]

AutoIt has some auto-correction built-in to fix floating point numbers that are within a certain representational distance from the nearest whole number when using Int(). There were some circumstances where using Int() on a "whole" floating point number would produce an integer that was one below the expected value. The obvious side effect to the auto-correction is that sometimes, the value really does need truncated to that value.