Problem with Mod() Funktion

[Jentec]

got problems on the funktion Mod() i got alltimes wrong output from this

mod("175367809538821201","1767842701") returns 421042353

but its wrong !?!

real output must be 421042338

why he tel me 421042353 and not 421042338 ?

what its wrong on this script ??

thx for help

[Jentec]

its ok i use a other way to got the right result

func Mod2($a, $b)
  $c = Int($a / $b)
  $b = $b * $c
  $c = $a - $b
  return $c
EndFunc

[Nutster]

This looks like a rounding problem. Mod is an integer function, but the numbers you gave are too big for integer (limited to just over 2 billion / 2 thousand-million). The fail-over is use floating-point numbers, but the storage for floating-point is limited and the least significant digits can be lost or scrambled during operations and storage, sort of like rounding off the decimals on a regular number.

Imagine that you are performing some calculations but you can only store 2 digits after the decimal point. This is an example of limited storage that I was talking about earlier.

Determine 500 / 17 * 17 = ?

500 / 17 = 29.41176470588235294118...

Rounding to the nearest 2 digits yields 29.41.

29.41 * 17 = 499.97

So under these circumstances, 500 / 17 * 17 = 499.97, due to rounding error.

The effect gets more noticeable with larger denominators and you are using a pretty big denominator.

The reason the second method, using int and subtraction, worked is that the Int function reset that precision back to 0 as it were. Much easier to work with.

One way to mitigate rounding errors is to see if you can simplify things before asking the computer to perform the calculations. The calculations can be faster and more accurate that way.

Edited December 8, 2009 by Nutster

[martin]

got problems on the funktion Mod() i got alltimes wrong output from this

mod("175367809538821201","1767842701") returns 421042353

but its wrong !?!

real output must be 421042338

why he tel me 421042353 and not 421042338 ?

what its wrong on this script ??

thx for help

For the same reason that

mod(175367809538821201,175367809538821200)

gives 32 when you think it should be 1.

The internal precision of numbers is not great enough when dividing and multiplying.

This will work, and could be speeded up I expect

$a = 175367809538821201
$b=1767842701
while $a > $b
    $a -= $b
WEnd
ConsoleWrite($a & @CRLF);mod result

EDIT:

The BigNum udf in example scripts does a much better job.

EDIT AGAIN: I didn't see post #2 until now. That's a much better idea

Edited December 7, 2009 by martin

[PsaltyDS]

Try this:

ConsoleWrite(15 / 175367809538821201 & @LF)

; Result = 8.55345119463298e-017

The floating point format used hits rounding limits at about 15 significant digits. The difference in your answer is below that limit by two digits. You can reduce the introduced error by reducing the scale of the numbers below that limit, too:

Global $iX = 175367809538821201, $iY = 1767842701

ConsoleWrite("Plain Mod():  " & Mod($iX, $iY) & @LF) ; returns 421042353

ConsoleWrite("_MyMod():  " & _MyMod($iX, $iY) & @LF) ; returns 421042338

Func _MyMod($A, $B)
    Local $iScale

    While $B * 2 < $A
        $iScale = $B
        While $iScale * 2 < $A
            $iScale *= 2
        WEnd
        $A -= $iScale
    WEnd

    Return Mod($A, $B)
EndFunc   ;==>_MyMod

Edit: Didn't see Martin's post while testing mine, but this should be faster at reducing the scale.

Edit2: Hmm... I thought that Int() trick in Mod2() above would fail too because of the non-integer parts of the method. But it works just as well as using all integer maths until the last operation.

Edited December 7, 2009 by PsaltyDS