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I needed this library to continue working on one or two of my projects. Hopefully it will be of use to someone else too. These functions attempt to perform accurate calculations for the largest Int-64 values, testing for integer overflow and resorting to floats when results go out of range. This library is primarily intended to be used with Int-32 or Int-64 values and it offers no advantage whatsoever to pass floats as parameters. It only makes sense if you intend to perform accurate calculations on large Int-64 values. I know this can be done using strings too, but I prefer not to speculate as to the difference in time penalties. ; #INDEX# ====================================================================================================================== ; Title .........: operator64 ; AutoIt Version : 3.3.14.0 ; Language ......: English ; Description ...: Helper functions for basic maths operations to be used with Int-32 and Int-64 numeric data types. ; Notes .........: Tests for integer overflow and attempts to correct for small inaccuracies affecting certain calculations. ; Return values are cast as Int-32 or Int-64 when possible, otherwise the result will be returned as a double. ; If it is not possible to return an Int-64 data type, the @extended flag is always set to non zero. ; Extended return values indicate that 100% accuracy cannot be guaranteed or that the result is ambiguous. ; The following values are valid for all functions in this library ; |@error = 1 The input or first operand is not an integer. ; |@error = 2 The second operand is not an integer. ; |@error = 3 Internal function error (ignore). ; |@extended = 1 The result is limited to double precision. ; |@extended = 2 The result is not an integer. ; |@extended = 3 The result is out of range for Int-64. ; |@extended = 4 The result is infinity. ; |@extended = 5 The result is an imaginary number. ; When an error occurs, the @extended flag is always set to non zero and a value returned regardless. ; Author(s) .....: czardas ; ============================================================================================================================== ; #CURRENT# ==================================================================================================================== ; _Abs64 ; _Add64 ; _Divide64 ; _Multiply64 ; _Power64 ; _Root64 ; _Subtract64 ; ============================================================================================================================== ; #INTERNAL_USE_ONLY#=========================================================================================================== ; __DoubleTo64 ; __Integer64 ; __OverflowDetect ; __Product64 ; __WholeNumberDivision ; ============================================================================================================================== ; #FUNCTION# =================================================================================================================== ; Name...........: _Abs64 ; Description ...: Returns the absolute value of an integer. ; Syntax.........: _Abs64($iInteger) ; Parameters.....; $iInteger - The integer to operate on. ; Return values .: Returns an Int-32, or Int-64, value. ; Failure returns the executed expression and sets the following flags: ; |@error = 1 The input parameter is not an integer. ; |@extended = 2 The result is not an integer. ; |@extended = 3 The absolute value (2^63) is out of range for Int-64. ; Author.........: czardas ; ============================================================================================================================== Func _Abs64($iInteger) $iInteger = __Integer64($iInteger) If @error Then Return SetError(1, 2, Abs($iInteger)) If $iInteger = 0x8000000000000000 Then Return SetExtended(3, Abs($iInteger)) Return $iInteger < 0 ? $iInteger *-1 : $iInteger EndFunc ;==> _Abs64 ; #FUNCTION# =================================================================================================================== ; Name...........: _Add64 ; Description ...: Adds two integers together. ; Syntax.........: _Add64($iOperand_1, $iOperand_2) ; Parameters.....; $iOperand_1 - The first operand. ; $iOperand_2 - The second operand. ; Return values .: Returns an Int-32, or Int-64, value. ; Failure returns the executed expression and sets the following flags: ; |@error = 1 The first parameter is not an integer. ; |@error = 2 The second parameter is not an integer. ; |@extended = 1 The result is limited to double precision. ; |@extended = 3 The result is out of range for Int-64. ; Author.........: czardas ; ============================================================================================================================== Func _Add64($iOperand_1, $iOperand_2) $iOperand_1 = __Integer64($iOperand_1) If @error Then Return SetError(1, 1, __DoubleTo64($iOperand_1 + $iOperand_2)) ; may still return an integer $iOperand_2 = __Integer64($iOperand_2) If @error Then Return SetError(2, 1, __DoubleTo64($iOperand_1 + $iOperand_2)) ; ditto Local $bOverflow, $nResult $bOverflow = __OverflowDetect('+', $iOperand_1, $iOperand_2, $nResult) Return SetExtended($bOverflow *3, $nResult) EndFunc ;==> _Add64 ; #FUNCTION# =================================================================================================================== ; Name...........: _Divide64 ; Description ...: Divides two integers. ; Syntax.........: _Divide64($iOperand_1, $iOperand_2) ; Parameters.....; $iOperand_1 - The first operand. ; $iOperand_2 - The second operand. ; Failure returns the executed expression and sets the following flags: ; |@error = 1 The first parameter is not an integer. ; |@error = 2 The second parameter is not an integer. ; |@extended = 1 The result is limited to double precision. ; |@extended = 2 The result is not an integer. ; |@extended = 4 The result is infinity. ; Author.........: czardas ; Comments ......; Due to internal rounding, errors may return an integer with the extended flag set to 2. This is not a bug! ; ============================================================================================================================== Func _Divide64($iOperand_1, $iOperand_2) $iOperand_1 = __Integer64($iOperand_1) If @error Then Return SetError(1, 1, __DoubleTo64($iOperand_1 / $iOperand_2)) ; may still return an integer $iOperand_2 = __Integer64($iOperand_2) If @error Then Return SetError(2, 1, __DoubleTo64($iOperand_1 / $iOperand_2)) ; as above If $iOperand_1 = 0x8000000000000000 Then ; this is not dealt with by the internal function If $iOperand_2 = 0x8000000000000000 Then Return 1 ; $iOperand_1 is divided by itself ; divide both values by 2 to remain within the specified range of the function __WholeNumberDivision() $iOperand_1 = 0xC000000000000000 ; -4611686018427387904 $iOperand_2 = __WholeNumberDivision($iOperand_2, 2) If @extended Then Return SetExtended(@extended, $iOperand_1 / $iOperand_2) EndIf Local $nResult = __WholeNumberDivision($iOperand_1, $iOperand_2) Return SetExtended(@extended, $nResult) EndFunc ;==> _Divide64 ; #FUNCTION# =================================================================================================================== ; Name...........: _Multiply64 ; Description ...: Multiplies two integers together. ; Syntax.........: _Multiply64($iOperand_1, $iOperand_2) ; Parameters.....; $iOperand_1 - The first operand. ; $iOperand_2 - The second operand. ; Return values .: Returns an Int-32, or Int-64, value. ; Failure returns the executed expression and sets the following flags: ; |@error = 1 The first parameter is not an integer. ; |@error = 2 The second parameter is not an integer. ; |@extended = 2 The result is not an integer. ; |@extended = 3 The result is out of range for Int-64. ; Author.........: czardas ; Comments ......; Due to internal rounding, errors may return an integer with the extended flag set to 2. This is not a bug! ; ============================================================================================================================== Func _Multiply64($iOperand_1, $iOperand_2) $iOperand_1 = __Integer64($iOperand_1) If @error Then Return SetError(1, 2, $iOperand_1 * $iOperand_2) $iOperand_2 = __Integer64($iOperand_2) If @error Then Return SetError(2, 2, $iOperand_1 * $iOperand_2) Local $iProduct = __Product64($iOperand_1, $iOperand_2) Return SetExtended(@extended, $iProduct) EndFunc ;==> _Multiply64 ; #FUNCTION# =================================================================================================================== ; Name...........: _Power64 ; Description ...: Raises an integer to the power of a second integer. ; Syntax.........: _Power64($iInteger, $iPower) ; Parameters.....; $iInteger - The integer to operate on. ; $iPower - The power to raise the integer to. ; Return values .: Returns an Int-32, or Int-64, value. ; Failure returns the executed expression and sets the following flags: ; |@error = 1 The first parameter is not an integer. ; |@error = 2 The second parameter is not an integer. ; |@extended = 1 The result is limited to double precision. ; |@extended = 3 The result is out of range for Int-64. ; Author.........: czardas ; ============================================================================================================================== Func _Power64($iInteger, $iPower) $iInteger = __Integer64($iInteger) If @error Then Return SetError(1, 1, $iInteger ^ $iPower) $iPower = __Integer64($iPower) If @error Then Return SetError(2, 1, $iInteger ^ $iPower) If $iInteger = 1 Or $iPower = 0 Then Return 1 If $iPower < 0 Or $iPower > 63 Then Return SetExtended(1, $iInteger ^ $iPower) Local $iTriggers = 0, $iCount = 0, $iPow = $iPower While $iPow > 1 If Mod($iPow, 2) Then $iPow -= 1 Else ; to reduce calls to __Product64() ; triggers indicate the product should be squared (see next loop) $iTriggers += 2 ^ $iCount ; set trigger $iPow /= 2 EndIf $iCount += 1 WEnd Local $iOperand, $iResult = $iInteger For $i = $iCount -1 To 0 Step -1 ; multiply the product either by itself or the original value $iOperand = BitAND($iTriggers, 2^$i) ? $iResult : $iInteger $iResult = __Product64($iResult, $iOperand) If @extended Then Return SetExtended(3, $iInteger ^ $iPower) Next Return $iResult EndFunc ;==> _Power64 ; #FUNCTION# =================================================================================================================== ; Name...........: _Root64 ; Description ...: Calculates the nth root of an integer. ; Syntax.........: _Root64($iInteger, $iRoot) ; Parameters.....; $iInteger - The integer to operate on. ; $iRoot - The root of the integer to calculate. ; Return values .: Returns an Int-32, or Int-64, value. ; Failure returns the executed expression and sets the following flags: ; |@error = 1 The first parameter is not an integer. ; |@error = 2 The second parameter is not an integer. ; |@extended = 1 The result is limited to double precision. ; |@extended = 2 The result is not an integer. ; |@extended = 5 The result is an imaginary number. ; Author.........: czardas ; Comments ......; _Root64() has limited application beyond forcing an integer return value whenever possible. ; Roots of negative integers return a defined value if one exists, otherwise the result is always undefined. ; ============================================================================================================================== Func _Root64($iInteger, $iRoot) $iInteger = __Integer64($iInteger) If @error Then Return SetError(1, 1, $iInteger ^ (1 / $iRoot)) $iRoot = __Integer64($iRoot) If @error Then Return SetError(2, 1, $iInteger ^ (1 / $iRoot)) If $iRoot > 63 Or $iRoot < 1 Then Return SetExtended(1, $iInteger ^ (1 / $iRoot)) ; out of range If $iRoot = 1 Then Return $iInteger Local $iSign = $iInteger < 0 ? -1 : 1 If $iSign = -1 And Not Mod($iRoot, 2) Then Return SetExtended(5, $iInteger ^ (1 / $iRoot)) ; undefined If $iInteger = 0x8000000000000000 Then ; here the absolute value cannot be represented by Int-64 ; a small set of defined return values are simply hard coded Local $aMaxRoot = [[3,-2097152],[7,-512],[9,-128],[21,-8],[63,-2]] ; there are only five cases For $i = 0 To 4 If $iRoot = $aMaxRoot[$i][0] Then Return $aMaxRoot[$i][1] Next Return SetExtended(2, $iInteger ^ (1 / $iRoot)) ; the return value is not an integer EndIf ; positive values are used to calculate the odd roots of negative integers Local $iOperand = $iSign = 1 ? $iInteger : $iInteger *-1 ; here the margin of error with Int() is probably too small to necessitate further processing Local $iReturn = Int($iOperand ^ (1 / $iRoot)) ; check the result Local $iCompare = $iReturn For $i = 2 To $iRoot $iCompare *= $iReturn Next ; the chances that this comparison will fail seem negligible - see comments above If $iCompare <> $iOperand Then Return SetExtended(2, $iInteger ^ (1 / $iRoot)) ; the return value is not an integer Return $iReturn * $iSign EndFunc ;==> _Root64 ; #FUNCTION# =================================================================================================================== ; Name...........: _Subtract64 ; Description ...: Subtracts one integer from another. ; Syntax.........: _Subtract64($iOperand_1, $iOperand_2) ; Parameters.....; $iOperand_1 - The first operand. ; $iOperand_2 - The second operand. ; Return values .: Returns an Int-32, or Int-64, value. ; Failure returns the executed expression and sets the following flags: ; |@error = 1 The first parameter is not an integer. ; |@error = 2 The second parameter is not an integer. ; |@extended = 1 The result is limited to double precision. ; |@extended = 3 The result is out of range for Int-64. ; Author.........: czardas ; ============================================================================================================================== Func _Subtract64($iOperand_1, $iOperand_2) $iOperand_1 = __Integer64($iOperand_1) If @error Then Return SetError(1, 1, __DoubleTo64($iOperand_1 - $iOperand_2)) ; may still return an integer $iOperand_2 = __Integer64($iOperand_2) If @error Then Return SetError(2, 1, __DoubleTo64($iOperand_1 - $iOperand_2)) ; ditto Local $bOverflow, $nResult $bOverflow = __OverflowDetect('-', $iOperand_1, $iOperand_2, $nResult) Return SetExtended($bOverflow *3, $nResult) EndFunc ;==> _Subtract64 #Region - Internal Functions ; #INTERNAL_USE_ONLY# ========================================================================================================== ; Name...........: __DoubleTo64 ; Description ...: Helper function - converts an integer value double to Int-32 or Int-64. ; Syntax.........: __DoubleTo64($nValue) ; Parameters.....; $nValue - The double to convert ; Return values .: Success returns Int-32 or Int-64 when the interpreter evaluates the converted double equal to the input. ; Failure returns the input parameter without any modification and sets the following flags: ; |@error = 3 Internal error (x2) ==> see comments in the code. ; |@extended = 2 Conversion failed ==> the return value is not an integer. ; Author ........: czardas ; Comments ......; Doubles representing integer values greater than 15 digits cannot be relied on for accuracy. ; ============================================================================================================================== Func __DoubleTo64($nValue) If Not IsNumber($nValue) Then Return SetError(3, 2, $nValue) ; the input is not a number. If $nValue > -1.0e+015 And $nValue < 1.0e+015 Then Local $iVal64 = Number($nValue, 2) ; convert to Int-64 If $iVal64 = $nValue Then ; check to see if conversion was a success [expected range +/- 5.62949953421311e+014] Return ($iVal64 > 2147483647 Or $iVal64 < -2147483648) ? $iVal64 : Number($iVal64, 1) ; Int-64 or Int-32 ElseIf $iVal64 -1 = $nValue Then ; attempt to adjust for inaccuracies [subject to possible change] Return $iVal64 -1 ElseIf $iVal64 +1 = $nValue Then ; as above Return $iVal64 +1 EndIf EndIf Return SetError(3, 2, $nValue) ; conversion failed EndFunc ;==> __DoubleTo64 ; #INTERNAL_USE_ONLY# ========================================================================================================== ; Name...........: __Integer64 ; Description ...: Checks if a number is an integer and converts doubles to Int-32 or Int-64 if the result appears unambiguous. ; Syntax.........: __Integer64($nParam) ; Parameters.....; $nParam - The number to test ; Return values .: Success returns Int-32 or Int-64 when the interpreter evaluates the returned integer equal to the input. ; Failure returns the input parameter without any modification and sets the following flags: ; |@error = 1 The input is not an integer. ; |@extended = 2 The return value is not an integer. ; Author ........: czardas ; Comments ......; Doubles representing integer values greater than 15 digits cannot be relied on for accuracy. ; ============================================================================================================================== Func __Integer64($nParam) If Not StringInStr(VarGetType($nParam), 'Int') Then Local $iInt64 = __DoubleTo64($nParam) ; attempt conversion If @error Then Return SetError(1, 2, $nParam) ; $fParam <> $iInt64 $nParam = $iInt64 ; float was compared as being equal to an integer EndIf Return $nParam EndFunc ;==> __Integer64 ; #INTERNAL_USE_ONLY# ========================================================================================================== ; Name...........: __OverflowDetect ; Description ...: Checks for integer overflow on execution of the expression. ; Syntax.........: __OverflowDetect($sOperator, $iOperand_1, $iOperand_2, $nResult) ; Parameters.....; $sOperator - May be +, - or *. ; $iOperand_1 - The first operand. ; $iOperand_2 - The second operand. ; $nResult - [ByRef] Result of executed expression. ; Return values .: Returns True if integer overflow occurs - otherwise returns False. Returns $nResult ByRef. ; Author ........: czardas ; Comments ......; Int-32 or Int-64 only. No error checks! ; ============================================================================================================================== Func __OverflowDetect($sOperator, $iOperand_1, $iOperand_2, ByRef $nResult) Local $iExecute, $fCompare Switch $sOperator Case '+' ; execute the expression $iExecute = $iOperand_1 + $iOperand_2 ; execute the expression with the operands converted to doubles $fCompare = Number($iOperand_1, 3) + Number($iOperand_2, 3) Case '-' ; as above $iExecute = $iOperand_1 - $iOperand_2 $fCompare = Number($iOperand_1, 3) - Number($iOperand_2, 3) Case '*' ; as above $iExecute = $iOperand_1 * $iOperand_2 $fCompare = Number($iOperand_1, 3) * Number($iOperand_2, 3) EndSwitch ; the results should be approximately equal Local $bReturn = StringFormat('%.14e', $iExecute) <> StringFormat('%.14e', $fCompare) ; %.15e is too sensitive $nResult = $bReturn ? $fCompare : $iExecute Return $bReturn EndFunc ;==> __OverflowDetect ; #INTERNAL_USE_ONLY# ========================================================================================================== ; Name...........: __Product64($iOperand_1, $iOperand_2) ; Description ...: Helper function - multiplies two Int-32 or Int-64 values together. ; Syntax.........: __Product64($iOperand_1, $iOperand_2) ; Parameters.....; $iOperand_1 - The first integer. ; $iOperand_2 - The second integer. ; Return values .: Returns an Int-32, or Int-64, value. ; Failure returns the executed expression and sets the following flags: ; |@extended = 3 The result is out of range for Int-64. ; Author.........: czardas ; Comments ......; Int-32 or Int-64 only. No error checks! ; ============================================================================================================================== Func __Product64($iOperand_1, $iOperand_2) Local $bOverflow, $nResult $bOverflow = __OverflowDetect('*', $iOperand_1, $iOperand_2, $nResult) Return SetExtended($bOverflow *3, $nResult) EndFunc ;==> __Product64 ; #INTERNAL_USE_ONLY# ========================================================================================================== ; Name...........: __WholeNumberDivision ; Description ...: Divides two integers. ; Syntax.........: __WholeNumberDivision($iDividend, $iDivisor) ; Parameters.....; $iDividend - The first operand. ; $iDivisor - The second operand. ; Return values .: Returns an Int-32, or Int-64, value. ; Failure returns the executed expression and sets the following flags: ; |@extended = 1 The result is limited to double precision. ; |@extended = 2 The result is not an integer. ; |@extended = 4 The result is infinity. ; Author ........: czardas ; Comments ......; Input is limited to +/- 9223372036854775807 for both consitency and compatibility with future libraries. ; May return an integer with the extended flag set to 2 due to internal rounding. This is not a bug! ; ============================================================================================================================== Func __WholeNumberDivision($iDividend, $iDivisor) ; Input ranges -9223372036854775807 To 9223372036854775807 If $iDivisor = 0 Then Return SetExtended(4, $iDividend / $iDivisor) ; division by zero Local $aDiv = [$iDividend, $iDivisor], _ $iSign = 1 For $i = 0 To 1 If $aDiv[$i] > 0x7FFFFFFFFFFFFFFF Or $aDiv[$i] < 0x8000000000000001 Then Return SetExtended(1, $iDividend / $iDivisor) ; input range exceeded If $aDiv[$i] < 0 Then ; force positive integers $aDiv[$i] *= -1 $iSign *= -1 ; to add back later EndIf Next If Mod($aDiv[0], $aDiv[1]) Then Return SetExtended(2, $iDividend / $iDivisor) ; not divisible If $aDiv[0] = 0 Then Return 0 If $aDiv[1] = 1 Then Return $aDiv[0] * $iSign Local $iDivision = Floor($aDiv[0] / $aDiv[1]), $iDifference, $iIntegral While $iDivision * $aDiv[1] > $aDiv[0] ; division is overstated $iDifference = ($aDiv[1] * $iDivision) - $aDiv[0] $iIntegral = Floor($iDifference / $aDiv[1]) ; avoid shooting beyond the target If $iIntegral = 0 Then $iIntegral = 1 ; prevents hanging in an infinite loop $iDivision -= $iIntegral WEnd While $iDivision * $aDiv[1] < $aDiv[0] ; division is understated $iDifference = $aDiv[0] - ($aDiv[1] * $iDivision) $iIntegral = Floor($iDifference / $aDiv[1]) ; as above If $iIntegral = 0 Then $iIntegral = 1 ; prevents hanging $iDivision += $iIntegral WEnd Return $iDivision * $iSign EndFunc ;==> __WholeNumberDivision #EndRegion The following tests need updating because values for @error and @extended have changed. #include 'operator64.au3' ConsoleWrite("Testing _Abs64()" & @LF) ; ==> Err Ext Result $test = _Abs64(0xC000000000000000) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 4611686018427387904 $test = _Abs64(0x8000000000000000) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 2 1 9.22337203685478e+018 $test = _Abs64(0x8000000000000001) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 9223372036854775807 $test = _Abs64(-0.123) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 1 1 0.123 ;=========================================================== ConsoleWrite(@LF & "Testing _Add64()" & @LF) $test = _Add64(0x7FFFFFFFFFFFFFFF, 1) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 1 9.22337203685478e+018 $test = _Add64(0x7FFFFFFFFFFFFFFF, 0) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 9223372036854775807 $test = _Add64(0x7FFFFFFFFFFFFFFF, -1) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 9223372036854775806 $test = _Add64(33, 15) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 48 ;=========================================================== ConsoleWrite(@LF & "Testing _Divide64()" & @LF) $test = _Divide64(0x7FFFFFFFFFFFFFFF, -1) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 -9223372036854775807 $test = _Divide64(0x8000000000000000, -2) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 4611686018427387904 $test = _Divide64(10.0, 2) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 5 $test = _Divide64(9223372036854775552, -2) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 -4611686018427387776 $test = _Divide64(9223372036854775552, 0) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 2 1 1.#INF $test = _Divide64(675432.0097, -987) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 1 1 -684.328277304965 $test = _Divide64(6922337, 15) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 4 1 461489.133333333 ;=========================================================== ConsoleWrite(@LF & "Testing _Multiply64()" & @LF) $test = _Multiply64(9223372036854775552, -2) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 1 -1.84467440737096e+019 $test = _Multiply64(223372036854775552, 9) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 2010348331692979968 $test = _Multiply64(1.01, -1) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 1 1 -1.01 ;=========================================================== ConsoleWrite(@LF & "Testing _Power64()" & @LF) $test = _Power64(-2.0, 63) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 -9223372036854775808 $test = _Power64(37, 12.0) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 6582952005840035281 $test = _Power64(17, 19) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 1 2.39072435685151e+023 ;=========================================================== ConsoleWrite(@LF & "Testing _Subtract64()" & @LF) $test = _Subtract64(1.0, 1) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 0 $test = _Subtract64(0x8000000000000000, -1) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 -9223372036854775807 $test = _Subtract64(0x8000000000000000, 0) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 0 -9223372036854775808 $test = _Subtract64(0x8000000000000000, 1) ConsoleWrite(@Error & @TAB & @Extended & @TAB & $test & @LF) ; ==> 0 1 -9.22337203685478e+018It's nice to try and figure out something like this for yourself, but it would be quite impossible without the hints and advice I receive from others when I take a wrong turn sometimes. So thanks to those people.