Search the Community

_LongProduct - Multiply two large integers using 'old school' long multiplication. I wanted to have a go at this for a while. It's not breaking any new ground but it has been a useful exercise for me. I haven't looked at BigNum UDF functions in any detail - I really wanted to try this out for myself. ; ; #FUNCTION# ==================================================================================================================== ; Name...........: _LongProduct ; Description ...: Multiplies two large positive integers together using old school long multiplication method ; Syntax.........: _LongProduct($vInt1, $vInt2) ; Parameters ....: $vInt1 - First integer - can be a number or a string of digits ; $vInt2 - Second integer - as above ; Return values .: Success - Returns the product of the two numbers ; Failure - Sets @error to 1 if either parameter contains non digit characters ; Author ........: czardas ; Comments ......; A separate function must be created if you want to preprocess floating point numbers ; =============================================================================================================================== Func _LongProduct($vInt1, $vInt2) If Not (StringIsDigit($vInt1) And StringIsDigit($vInt2)) Then Return SetError(1) Local $vTemp ; Reuseable placeholder If StringLen($vInt2) > StringLen($vInt1) Then ; Set $vInt2 to be the shortest numeric string to reduce array size later $vTemp = $vInt1 $vInt1 = $vInt2 $vInt2 = $vTemp EndIf Local $iBound = StringLen($vInt2), $sZeros = "0" ; Zero padding for the method of long multiplication While StringLen($sZeros) < $iBound $sZeros &= $sZeros ; Tens, hundreds, thousands etc... WEnd $sZeros = StringRight($sZeros, $iBound -1) ; Highest order of magnitude needed Local $aPartProduct[$iBound], $iCarryForward ; Placeholder for tens of units, hundreds, thousands etc... For $i = 1 To $iBound ; Starting with the most significant digit in $vInt2 $aPartProduct[$i -1] = "" $iCarryForward = 0 ; Maximum possible value in this code section is 8 ==> 89 = 9*9+8 For $j = StringLen($vInt1) To 1 Step -1 ; Multiply every digit in $vInt2 by every digit in $vInt1 $vTemp = StringMid($vInt2, $i, 1) * StringMid($vInt1, $j, 1) ; Add the tens of units left over from the previous calculation $vTemp += $iCarryForward $iCarryForward = Number(StringTrimRight($vTemp, 1)) ; This will be added on the next run ; Append the units $aPartProduct[$i -1] &= StringRight($vTemp, 1) ; Digits appear in reverse sequence Next $aPartProduct[$i -1] &= $iCarryForward ; Pad with the correct number of zeros $aPartProduct[$i -1] = StringRight($sZeros, $iBound - $i) & $aPartProduct[$i -1] & StringTrimRight($sZeros, $iBound - $i) Next $iCarryForward = 0 ; Reset this variable for the following process ; Take the sum of all the part products in the array Local $sProduct = "" For $i = 1 To StringLen($aPartProduct[0]) ; Starting with the least significant digit $vTemp = 0 ; Sum value For $j = 0 To UBound($aPartProduct) -1 ; Add the digits from the units, tens of units, hundreds, thousands etc... $vTemp += StringMid($aPartProduct[$j], $i, 1) Next ; Add the value left over from the previous calculation $vTemp += $iCarryForward $iCarryForward = Number(StringTrimRight($vTemp, 1)) ; This will be added on the next run $sProduct = StringRight($vTemp, 1) & $sProduct ; Returns the digits in the correct order Next If $iCarryForward Then $sProduct = $iCarryForward & $sProduct If StringLeft($sProduct, 1) = "0" Then $sProduct = StringTrimLeft($sProduct, 1) Return $sProduct EndFunc ;==> _LongProduct ; Example Local $i1 = "192801867453620948267810191872736619839409271" Local $i2 = "99999999999999999999999999999999999999999989" ConsoleWrite(_LongProduct($i1, $i2) & @LF)