// 
    // This High Precision Calculator is (c) 2003 by Edward Martin III
    // All rights reserved.  Please contact me for permission to use any or
    // all of this source in a commercial product.
    // Eventually, it'll have all sorts of neat functions, but for now, its 
    // primary function is to not crash a browser.  And whatever's below:
    // 
    // MODIFICATION HISTORY
    //
    // wishlist:   
    //             How can I get some kind of real progress indicator?!
    //             Euler's Totient function
    //             export to an HTML file
    //             improve browser-related routine in Multiply
    //
    // 01-27-2004: Fixed a bug in the IsPrime function, which meant that the 
    //             calculator can now handle the nontrivial assertions that 
    //             asking if "0" or "1" is a prime is just a goofy question. 
    //             Thanks to Etienne Dumortier for finding it!
    // 06-27-2003: Added a couple of checks in the Power function, such that
    //             if the argument = 0 or 1, then the thing immediately makes 
    //             the shortcut answer.  It was just taking too long to 
    //             compute 1^5000000. 
    // 03-28-2003: Fixed a damn bug in the Multiplication function.  
    //             Eduard Martos Parejo found it for me (thank you, Eduard!) 
    //             and not only did I blast it away, but I was able to 
    //             finally clean up a bit of code that came close to being 
    //             a browser-sniffer.  I'm much happier with what it is 
    //             this time!
    // 01-28-2003: Fixed a damn bug in the DIV_MOD function
    // 01-27-2003: Added Floor(Sqrt(x)) function.  Also added an
    //             IsThisAPerfectSquare function, because the coding is 
    //             pretty trivial, once I have some form of sqrt function.  
    //             It's still a memory-gobbler, though.  I'm open to 
    //             algorithms to reduce this time/computation chunking...
    // 01-14-2003: Added IsPrime function.
    // 01-10-2003: Added Floor and Ceiling, as well as a couple of supporting
    //             rounding functions.  Added GCD and LCM and cleaned up a bit
    //             of code in various places.  Time for a deployment!
    // 01-09-2003: Finished Division.  Yay!  It seems to work pretty
    //             well, including using signs and decimals, but I expect I'll 
    //             have more than a few people point out errors to me.  I hope 
    //             not -- it seems pretty tough.
    //             Also fixed BuildString so that it can handle strings of 
    //             characters of pretty much any length (previously, it had 
    //             been limited to a count no higher than the limit of integers, 
    //             but now it uses the Calculator's own tools for manipulating 
    //             large numbers.)
    // 01-08-2003: Modified the Addition routine to behave better independent of 
    //             browser.  There's still a chunk of code in Multiply that has 
    //             to do result-checks because of browser incompatibilities, but 
    //             eventually, I might nail it, too.  Just not fond of even 
    //             coming CLOSE to results that vary browser-to-browser...
    // 12-19-2002: Added a Help button and associated window.  Much better!
    // 12-03-2002: Added a Status window.  This allows people to know something's 
    //             "going on" during long calculations.  I can't decide if I want 
    //             to disable buttons during long calculations, but this is a 
    //             good interim solution.  It's certainly better than an alert 
    //             window!
    // 11-21-2002: Completed Factorials and Powers.  My sympathies to anyone 
    //             feeding a big number into it -- it takes a bit of time.
    // 11-20-2002: Completed all the trivial cases for DIV and MOD, meaning cases
    //             where one of the numbers = 0, where the Divisor = 1, where 
    //             the Divisor is greater than the Dividend, and where the Divisor 
    //             equals the Dividend.
    // 11-14-2002: Wrangled the last bits of the page to XHTML standards.  Yay!
    //             Also added a ^2 function.  I added a memory bank, such that 
    //             you can "store" results into ten "accumulators".  I'm 
    //             picking ten for the heck of it.  If you really think you need
    //             more, I guess you could just ask.
    // 09-11-2002: Fixed a bug in the IsEqual routine.  Perhaps I should hire
    //             Matthew to find bugs -- he's nailed me twice so far!  Updated
    //             the IsLessThan and IsGreaterThan functions to account for sign
    //             and reinstated those on the client page.  I've changed the 
    //             graphic image of buttons to real buttons, which I HOPE will be 
    //             XHTML transitional acceptable.  For a while, it looked like 
    //             I'd have crazy-shaped buttons, but then I found I can specify 
    //             button width in the stylesheet.  So I did and it works quite 
    //             attractively.  At this moment, I haven't tested the changes 
    //             under Netscape, but I will before deployment.
    // 09-10-2002: Fixed a bug in the Subtraction routine.  Now, the Minuend and
    //             Subtrahend are padded with decimals before any comparisons are
    //             made.  Much smarter that way.  Thanks to Matthew Mastracci for
    //             pointing it out!  I also converted the page to my best attempt
    //             at XHTML and to use a stylesheet.  Always on the bleeding edge, 
    //             we are.  Alas, I miss the transitional mark because href can't 
    //             take an onClick event, but that's the only way to make it work 
    //             (as far as I can tell at the moment) in Netscape.  Grumble...  
    //             I'll bang on it more later.
    // 07-09-2002: Added Multiplication.  I also fixed a bug in the ZeroTrim function.   
    //             It wasn't producing incorrect answers until I implemented the  
    //             Multiplication function, so any valuable scientific research based  
    //             on my JavaScript calculator hasn't been subjected to trouble.
    // 10-04-2001: Added Sign switching functions to buttons and updated addition to 
    //             include negatives.  Added a "No Function Yet" reporter to functions 
    //             that, well, don't work yet.
    // 10-03-2001: Added subtraction.
    // 09-27-2001: Added graphic buttons for interface and changed code to be more 
    //             universal for browsers.  Only trouble with graphical buttons is 
    //             that they're not obviously "disabled" like they were in Explorer.  
    //             I guess I could do "disabled" looking buttons, but later...
    // 09-19-2001: Finished coding the basic addition block.  Looking in dread at 
    //             the future.
    // 

    function SleepButtons()
      {
        document.APCalculator.Status.value="Calculating...";
      }

    function WakeButtons()
      {
        document.APCalculator.Status.value="Done!";
      }

    function NilFunction()
      {
        var reporter="No Function Yet."
        return reporter;
      }

    function BuildString (Symbol, Multiple)
      // returns a string that consists of the a Multiple number of Symbols.
      // for example, BuildString(x,5) returns "xxxxx"
    {
    var CompoundString="";
      while (IsEqualTo(Multiple,"0") == "FALSE")
        {
          CompoundString = CompoundString + Symbol;
          Multiple = Subtraction(Multiple,"1");
        }
      return CompoundString;
    }

    function RoundBigNumberUp (BigPositiveNumber)
      // Rounds a 'big' number up.  The assumption is that the number is Positive
      {
        var Answer = "";
        BigPositiveNumber = ZeroTrim(BigPositiveNumber); // in case it has lotsa zeroes at the end
        if (BigPositiveNumber.search(/\./) != (-1)) // if the number contains a decimal...
          {
            Answer = CalculatorAdd(RegExp.leftContext,"1");
          }
        else // there is no decimal in the number, therefore, it is already rounded
          {
            Answer = BigPositiveNumber;
          }
        return Answer;
      }

    function RoundBigNumberDown (BigPositiveNumber)
      // Rounds a 'big' number down.  The assumption is that the number is Positive
      {
        var Answer = "";
        BigPositiveNumber = ZeroTrim(BigPositiveNumber); // in case it has lotsa zeroes at the end
        if (BigPositiveNumber.search(/\./) != (-1)) // if the number contains a decimal...
          {
            Answer = RegExp.leftContext;
          }
        else // there is no decimal in the number, therefore, it is already rounded
          {
            Answer = BigPositiveNumber;
          }
        return Answer;
      }

    function BigNumberCeiling (BigRealNumber)
      // Finds the ceiling of BigRealNumber.
      {
        var Answer = "";
        if (BigRealNumber.charAt(0) == "-") // then it is a negative number
          {Answer = "-" + RoundBigNumberDown(BigRealNumber.substring(1,BigRealNumber.length));}
        else
          {Answer = RoundBigNumberUp(BigRealNumber);}
        return Answer;
      }

    function BigNumberFloor (BigRealNumber)
      // Finds the floor of BigRealNumber.
      {
        var Answer = "";
        if (BigRealNumber.charAt(0) == "-") // then it is a negative number
          {Answer = "-" + RoundBigNumberUp(BigRealNumber.substring(1,BigRealNumber.length));}
        else
          {Answer = RoundBigNumberDown(BigRealNumber);}
        return Answer;
      }

    function SubProduct (Multiplicand, SingleDigitMultiplier)
      // Multiplies Multiplicand (any number of digits) by a single digit Multiplier
      {
        var Carry = "0";
        var SubProduct = "";
        var TempProd = "0";
        for (var counter = Multiplicand.length-1; counter > (-1); counter--)
        {
          var TempProd = (Multiplicand.charAt(counter) * SingleDigitMultiplier) + parseInt(Carry);
          if (TempProd < 10) {TempProd = "0" + TempProd} // Now all small products are 2-digit numbers
          Carry = (TempProd + "").charAt(0);
          SubProduct = (TempProd + "").charAt(1) + SubProduct;
        }
        if (Carry != "0") {SubProduct = (Carry + SubProduct)}
        return SubProduct;
      }

    function ZeroTrim(BloatyAnswer) // trim trailing zeroes after the decimal and leading zeroes before
    {
      if (BloatyAnswer.search(/\./i) == -1)
        {
        BloatyAnswer = BloatyAnswer + ".0";
        }
      if (BloatyAnswer.charAt(0) == ".")
        {
        BloatyAnswer = "0" + BloatyAnswer;
        }
      while (BloatyAnswer.charAt(BloatyAnswer.length - 1) == "0")
        {
          BloatyAnswer = BloatyAnswer.substring(0,BloatyAnswer.length - 1);
          // trim that last character off if it's a zero
        }
        if (BloatyAnswer.charAt(BloatyAnswer.length - 1) == ".")
          // trim off that last decimal point, if it's there
          {
            BloatyAnswer = BloatyAnswer.substring(0,BloatyAnswer.length - 1);
          }
      // trim leading zeroes, but if the answer is simply "0", then stop.
         while ((BloatyAnswer.length>1) && (BloatyAnswer.charAt(0)=="0") && (BloatyAnswer.charAt(1)!="."))
           {
             BloatyAnswer = BloatyAnswer.substring(1,BloatyAnswer.length);
           }
      return BloatyAnswer;
    }

    function SwitchSign(Arg)
    {
      if (Arg.charAt(0)=="-")
        Arg = Arg.substring(1,Arg.length);
      else
        {
          Arg="-"+Arg;
        }
      return Arg;
    }

    function IsLessThan(Arg1,Arg2) // Is Arg1 less than Arg2?
    {
      var Result = "";
      // If Arg1 is negative and Arg2 is positive, then the answer is automatically true
        if (Arg1.charAt(0) == "-" && Arg2.charAt(0) !="-") {Result = "TRUE"}
      // If Arg1 is positive and Arg2 is negative, then the answer is automatically false
        if (Arg1.charAt(0) != "-" && Arg2.charAt(0) =="-") {Result = "FALSE"}
      // If Arg1 = Arg2, then the answer is automatically false
        if (IsEqualTo(Arg1,Arg2) == "TRUE") {Result = "FALSE"}
      // If Arg1 and Arg2 are both negative, then we swap them, switch signs, and try again.
        if (Arg1.charAt(0) == "-" && Arg2.charAt(0) =="-") {Result = IsLessThan(SwitchSign(Arg2),SwitchSign(Arg1))}
      // If Arg1 and Arg2 are both positive
        if (Result == "")
          {
            // Pad them with zeroes to line up the decimal (if it exists)
               var type = "";
               var AnswerArray1 = Arg1.split("."); // Split into an array
               var AnswerArray2 = Arg2.split("."); // Split into an array
               // make sure arrays have '0' instead of 'undefined' or '' as elements
               // split produces a mixed response, an empty string on the left of the split
               // and undefined on the right of the split.  This is further complicated by
               // the fact that Navigator understands "undefined" in comparisions, but
               // IE doesn't, so I have to create a variable and assign it to a typeof.
                  if (AnswerArray1[0] == "") {AnswerArray1[0] = "0"}
                  type = typeof AnswerArray1[1];
                  if (type == "undefined") {AnswerArray1[1] = "0"}
                  if (AnswerArray2[0] == "") {AnswerArray2[0] = "0"}
                  type = typeof AnswerArray2[1];
                  if (type == "undefined") {AnswerArray2[1] = "0"}

               // Rebuild operands as strings with decimals.
                  Arg1 = AnswerArray1[0] + "." + AnswerArray1[1];
                  Arg2 = AnswerArray2[0] + "." + AnswerArray2[1];
               // if decimal split !=, then equalize by adding trailing zeroes to the short decimal
                  if (AnswerArray1[1].length > AnswerArray2[1].length)
                    {
                      Arg2 += BuildString("0",AnswerArray1[1].length-AnswerArray2[1].length+"");
                    }
                  if (AnswerArray2[1].length > AnswerArray1[1].length)
                    {
                      Arg1 += BuildString("0",AnswerArray2[1].length-AnswerArray1[1].length+"");
                    }

               // if integer split != then equalize by adding leading zeroes to the short integer
                  if (AnswerArray1[0].length > AnswerArray2[0].length)
                    {
                      Arg2 = BuildString("0",AnswerArray1[0].length-AnswerArray2[0].length+"") + Arg2;
                    }
                  if (AnswerArray2[0].length > AnswerArray1[0].length)
                    {
                      Arg1 = BuildString("0",AnswerArray2[0].length-AnswerArray1[0].length+"") + Arg1;
                    }
            var counter = 0;
            while ((Result=="") && (counter < Arg1.length))
            {
              if (Arg2.charAt(counter) < Arg1.charAt(counter)) {Result = "FALSE"}
              if (Arg2.charAt(counter) > Arg1.charAt(counter)) {Result = "TRUE"}
              counter++;
            }
          }
      // Return Result
        return Result;
    }

    function IsGreaterThan(Arg1,Arg2) // Is Arg1 greater than Arg2?
    {
      var Result = "";
      // If Arg1 is negative and Arg2 is positive, then the answer is automatically false
        if (Arg1.charAt(0) == "-" && Arg2.charAt(0) !="-") {Result = "FALSE"}
      // If Arg1 is positive and Arg2 is negative, then the answer is automatically true
        if (Arg1.charAt(0) != "-" && Arg2.charAt(0) =="-") {Result = "TRUE"}
      // If Arg1 = Arg2, then the answer is automatically false
        if (IsEqualTo(Arg1,Arg2) == "TRUE") {Result = "FALSE"}
      // If Arg1 and Arg2 are both negative, then we swap them, switch signs, and try again.
        if (Arg1.charAt(0) == "-" && Arg2.charAt(0) =="-") {Result = IsGreaterThan(SwitchSign(Arg2),SwitchSign(Arg1))}
      // If Arg1 and Arg2 are both positive
        if (Result == "")
          {
            // Pad them with zeroes to line up the decimal (if it exists)
               var type = "";
               var AnswerArray1 = Arg1.split("."); // Split into an array
               var AnswerArray2 = Arg2.split("."); // Split into an array
               // make sure arrays have '0' instead of 'undefined' or '' as elements
               // split produces a mixed response, an empty string on the left of the split
               // and undefined on the right of the split.  This is further complicated by
               // the fact that Navigator understands "undefined" in comparisions, but
               // IE doesn't, so I have to create a variable and assign it to a typeof.
                  if (AnswerArray1[0] == "") {AnswerArray1[0] = "0"}
                  type = typeof AnswerArray1[1];
                  if (type == "undefined") {AnswerArray1[1] = "0"}
                  if (AnswerArray2[0] == "") {AnswerArray2[0] = "0"}
                  type = typeof AnswerArray2[1];
                  if (type == "undefined") {AnswerArray2[1] = "0"}

               // Rebuild operands as strings with decimals.
                  Arg1 = AnswerArray1[0] + "." + AnswerArray1[1];
                  Arg2 = AnswerArray2[0] + "." + AnswerArray2[1];
               // if decimal split !=, then equalize by adding trailing zeroes to the short decimal
                  if (AnswerArray1[1].length > AnswerArray2[1].length)
                    {
                      Arg2 += BuildString("0",AnswerArray1[1].length-AnswerArray2[1].length+"");
                    }
                  if (AnswerArray2[1].length > AnswerArray1[1].length)
                    {
                      Arg1 += BuildString("0",AnswerArray2[1].length-AnswerArray1[1].length+"");
                    }

               // if integer split != then equalize by adding leading zeroes to the short integer
                  if (AnswerArray1[0].length > AnswerArray2[0].length)
                    {
                      Arg2 = BuildString("0",AnswerArray1[0].length-AnswerArray2[0].length+"") + Arg2;
                    }
                  if (AnswerArray2[0].length > AnswerArray1[0].length)
                    {
                      Arg1 = BuildString("0",AnswerArray2[0].length-AnswerArray1[0].length+"") + Arg1;
                    }
            var counter = 0;
            while ((Result=="") && (counter < Arg1.length))
            {
              if (Arg2.charAt(counter) < Arg1.charAt(counter)) {Result = "TRUE"}
              if (Arg2.charAt(counter) > Arg1.charAt(counter)) {Result = "FALSE"}
              counter++;
            }
          }
      // Return Result
        return Result;
    }

    function IsEqualTo(Arg1,Arg2)
    {
      var Result = "FALSE";
      if (Arg1.length == Arg2.length)
        {
          Result = "TRUE";
          for (counter = 0; counter < Arg1.length; counter++)
            {
              if (Arg1.charAt(counter) != Arg2.charAt(counter)) {Result = "FALSE"}
            }
        }

      // Return Result
        return Result;
    }

    function Subtraction(Minuend,Subtrahend) // Minuend - Subtrahend = Difference
    {
      var Difference = "";
      // Pad them with zeroes to line up the decimal (if it exists)
         var type="";
         var AnswerArray1 = Minuend.split("."); // Split into an array
         var AnswerArray2 = Subtrahend.split("."); // Split into an array
         // make sure arrays have '0' instead of 'undefined' or '' as elements
         // split produces a mixed response, an empty string on the left of the split
         // and undefined on the right of the split.  This is further complicated by
         // the fact that Navigator understands "undefined" in comparisions, but
         // IE doesn't, so I have to create a variable and assign it to a typeof.
            if (AnswerArray1[0] == "") {AnswerArray1[0] = "0"}
            type = typeof AnswerArray1[1];
            if (type == "undefined") {AnswerArray1[1] = "0"}
            if (AnswerArray2[0] == "") {AnswerArray2[0] = "0"}
            type = typeof AnswerArray2[1];
            if (type == "undefined") {AnswerArray2[1] = "0"}

         // Rebuild operands as strings with decimals.
            Minuend = AnswerArray1[0] + "." + AnswerArray1[1];
            Subtrahend = AnswerArray2[0] + "." + AnswerArray2[1];
         // if decimal split !=, then equalize by adding trailing zeroes to the short decimal
            if (AnswerArray1[1].length > AnswerArray2[1].length)
              {
                Subtrahend += BuildString("0",AnswerArray1[1].length-AnswerArray2[1].length+"");
              }
            if (AnswerArray2[1].length > AnswerArray1[1].length)
              {
                Minuend += BuildString("0",AnswerArray2[1].length-AnswerArray1[1].length+"");
              }
         // if integer split != then equalize by adding leading zeroes to the short integer
            if (AnswerArray1[0].length > AnswerArray2[0].length)
              {
                Subtrahend = BuildString("0",AnswerArray1[0].length-AnswerArray2[0].length+"") + Subtrahend;
              }
            if (AnswerArray2[0].length > AnswerArray1[0].length)
              {
                Minuend = BuildString("0",AnswerArray2[0].length-AnswerArray1[0].length+"") + Minuend;
              }
      // If Minuend == Subtrahend, then the answer is simply 0
         if (!Difference && (IsEqualTo(Minuend,Subtrahend)=="TRUE")) {Difference= "0"}
      // If Minuend is positive and Subtrahend is negative,
      // then this is an addition problem
         if (!Difference && Minuend.charAt(0)!="-" && Subtrahend.charAt(0)=="-")
           {
             Subtrahend=Subtrahend.substring(1,Subtrahend.length);
             Difference = CalculatorAdd(Minuend,Subtrahend);
           }
      // If Minuend and Subtrahend are negative, invert both
      //  signs and reverse operands -- continue
         if (!Difference && Minuend.charAt(0)=="-" && Subtrahend.charAt(0)=="-")
           {
             Subtrahend=Subtrahend.substring(1,Subtrahend.length);
             Minuend=Minuend.substring(1,Minuend.length);
             var TemporaryVariable = Subtrahend;
             Subtrahend = Minuend;
             Minuend = TemporaryVariable;
           }
      // If Minuend is negative and Subtrahend is positive, then
      // remove Minuend sign, process as an addition, and then
      // append negative sign.
         if (!Difference && Minuend.charAt(0) == "-" && Subtrahend.charAt(0) !="-")
           {
             Minuend=Minuend.substring(1,Minuend.length);
             Difference = "-" + CalculatorAdd(Minuend,Subtrahend);
           }
      // Minuend and Subtrahend are both positive numbers,
      // either because they started out that way, or they started
      // out as both negative numbers and were converted by an
      // earlier process.  For all other cases, Difference has
      // already been assigned a value
         if (!Difference)
           {
             // If the Minuend is smaller than the Subtrahend, then the
             // result will be a negative number, so set a "negative"
             // tag (NegativeTag = "-" instead of ""), reverse the
             // operands, and continue.
                var NegativeTag = "";
                if (IsLessThan(Minuend,Subtrahend)=="TRUE")
                {
                  var TempVariable = Minuend;
                  Minuend = Subtrahend;
                  Subtrahend = TempVariable;
                  NegativeTag="-";
                }
             // Perform the digit-by-digit subtraction
                var BorrowFlag="0";
                for (counter = Minuend.length-1; counter > -1; counter--)
                {
                  if (Minuend.charAt(counter) ==".") // then it's a decimal point
                    Difference = "." + Difference
                  else // it's a genuine number
                    {
                      // because it's a number, perform the subtraction and append it to Difference
                      var MinuendPiece = parseInt(Minuend.charAt(counter));
                      var SubtrahendPiece = parseInt(Subtrahend.charAt(counter));
                      if (BorrowFlag == 1) {BorrowFlag = 0; MinuendPiece = MinuendPiece -1}
                      if (MinuendPiece < 0) {MinuendPiece = 9; BorrowFlag = 1}
                      if (MinuendPiece < SubtrahendPiece)
                        {
                          MinuendPiece = MinuendPiece + 10;
                          BorrowFlag = 1;
                        }
                      Difference = (MinuendPiece - SubtrahendPiece) + Difference;
                    }
                }
             // Remove trailing and leading zeroes
                Difference = ZeroTrim(Difference);
             // Append to the NegativeTag
                Difference = NegativeTag + Difference;
           }
        // Return Difference
      return Difference;
    }

    function CalculatorAdd(operand1,operand2)
    {
      var answer = "";

      if (operand1.charAt(0)!="-" && operand2.charAt(0)=="-") {answer = Subtraction(operand1,SwitchSign(operand2))}
      if (operand1.charAt(0)=="-" && operand2.charAt(0)!="-") {answer = Subtraction(operand2,SwitchSign(operand1))}
      if (operand1.charAt(0)=="-" && operand2.charAt(0)=="-") {answer = Subtraction(operand1,SwitchSign(operand2))}
      if (answer=="")
      {
        // Equalize both sides of the decimals
           var Operand1LeftPad = "";
           var Operand2LeftPad = "";
           var Operand1RightPad = "";
           var Operand2RightPad = "";
           var Operand1RightSide = "";
           var Operand2RightSide = "";
           var Operand1LeftSide = "";
           var Operand2LeftSide = "";

           if (operand1.search(/\./) == -1) // then there is no decimal in operand1
             {
               Operand1RightSide = "0";
               Operand1LeftSide = operand1;
             }
             else // there is a decimal and we must determine the values of the sides
               {
                 Operand1RightSide=RegExp.rightContext;
                 Operand1LeftSide=RegExp.leftContext;
               }
           if (operand2.search(/\./) == -1) // then there is no decimal in operand2
             {
               Operand2RightSide = "0";
               Operand2LeftSide = operand2;
             }
             else // there is a decimal and we must determine the values of the sides
               {
                 Operand2RightSide=RegExp.rightContext;
                 Operand2LeftSide=RegExp.leftContext;
               }
           if (Operand1LeftSide.length > Operand2LeftSide.length)
             { Operand2LeftPad = BuildString("0",(Operand1LeftSide.length - Operand2LeftSide.length+"")+""); }
           if (Operand1LeftSide.length < Operand2LeftSide.length)
             { Operand1LeftPad = BuildString("0",(Operand2LeftSide.length - Operand1LeftSide.length)+""); }

           if (Operand1RightSide.length > Operand2RightSide.length)
             { Operand2RightPad = BuildString("0",(Operand1RightSide.length - Operand2RightSide.length)+""); }
           if (Operand1RightSide.length < Operand2RightSide.length)
             { Operand1RightPad = BuildString("0",(Operand2RightSide.length - Operand1RightSide.length)+""); }

           operand1 = Operand1LeftPad + Operand1LeftSide + "." + Operand1RightSide + Operand1RightPad;
           operand2 = Operand2LeftPad + Operand2LeftSide + "." + Operand2RightSide + Operand2RightPad;

      // perform digit-by-digit addition
         var CarryFlag = 0;
             answer = "";
         for (counter=operand1.length-1; counter > (-1); counter--)
           {
             var temp = parseInt(operand1.charAt(counter)) + parseInt(operand2.charAt(counter)) + parseInt(CarryFlag);
             if ((temp > (-1)) && (temp < 20))
               {
               if (temp > 9)
                 {
                   CarryFlag = 1;
                   answer = temp-10 + answer;
                 }
               else
                 {
                   CarryFlag = 0;
                   answer = temp + answer;
                 }
               }
             else
               {
                 answer = "." + answer;
                 // unless the answer is an actual number, it's going 
                 // to be NaN or undefined, or perhaps something else.  
                 // I just force the conversion to a decimal, but I 
                 // should consider adding some kind of error catching 
                 // routine here.
               }
           }
         // and just in case the CarryFlag is carrying something after all the digits are done...
         if (CarryFlag == 1) {answer = "1" + answer}

      //  In order to make things smoother earlier, I just converted both numbers to
      //  decimals, even if they weren't.  So now that the addition's over, there are
      //  two possibilities that would leave a number unattractive.  One, if I added
      //  two whole numbers such as 5 & 7, the result looks like 12.0, in which case
      //  I want to trim off the trailing zero AND the decimal point.  Another
      //  possibility is if trailing digits totaled out to 0, in which case they would
      //  still be there.  For example, 1.05 and 1.05 should be 2.1, but reports as
      //  2.10 so time to clean that up.
          answer = ZeroTrim(answer);
      }
      return answer;
    }

    function Multiply(Multiplicand,Multiplier)
      {
        var Product = "";
        var DecimalShift = "0";
        var ProductSign = "";
        // Determine the Product Sign and render both numbers positive
          if (Multiplicand.charAt(0) == "-" && Multiplier.charAt(0) != "-") {ProductSign = "-"}
          if (Multiplicand.charAt(0) != "-" && Multiplier.charAt(0) == "-") {ProductSign = "-"}
          if (Multiplicand.charAt(0) == "-") {Multiplicand = Multiplicand.substring(1,Multiplicand.length)}
          if (Multiplier.charAt(0) == "-") {Multiplier = Multiplier.substring(1,Multiplier.length)}

        // Handle the easy cases (when either the Muliplicand or the Multiplier is "1" or "0")
          if (ZeroTrim(Multiplicand) == "0")
            {
              Product = "0";
              ProductSign="";
            }
          if (ZeroTrim(Multiplier) == "0")
            {
              Product = "0";
              ProductSign="";
            }
          if (ZeroTrim(Multiplicand) == "1")
            {
              Product = Multiplier;
            }
          if (ZeroTrim(Multiplier) == "1")
            {
              Product = Multiplicand;
            }
        // If the Product ISN'T a no-brainer...
          if (Product == "")
            {
             // Determine the Product Decimal Shift
               // If there is a decimal in either factor, then the answer will include a 
               // decimal (unless it zeroes out), so we must determine where in the final 
               // Product the new decimal will appear.
               var DecimalShift = 0;
               var DecimalShiftMultiplicand = Multiplicand.length-(Multiplicand.indexOf(".")+1);
               var DecimalShiftMultiplier = Multiplier.length-(Multiplier.indexOf(".")+1);
               if(DecimalShiftMultiplicand == Multiplicand.length) { DecimalShiftMultiplicand = 0; }
               if(DecimalShiftMultiplier == Multiplier.length) { DecimalShiftMultiplier = 0; }
               DecimalShift = DecimalShiftMultiplier + DecimalShiftMultiplicand;
             // Remove the decimals from the numbers
               Multiplicand=ZeroTrim(Multiplicand.replace(".",""));
               Multiplier=ZeroTrim(Multiplier.replace(".",""));
               
             // Multiply the Multiplicand by the Multiplier
               Product = "0";
               for (var counter = Multiplier.length-1; counter > -1; counter--)
                 {
                   NumberOfZeroes = BuildString("0",Multiplier.length - counter - 1+"");
                   Product = CalculatorAdd(Product,(SubProduct(Multiplicand,Multiplier.charAt(counter)) + NumberOfZeroes));
                 }

             // Split the Product and re-insert the Decimal
                if (DecimalShift > Product.length)
                  { Product = "0." + BuildString("0",DecimalShift - Product.length + "") + Product; }
                else if (DecimalShift == Product.length)
                  { Product = "0." + Product; }
                else if (DecimalShift < Product.length)
                  { Product = Product.substr(0,Product.length - DecimalShift) + "." + Product.substr(Product.length - DecimalShift,DecimalShift); }
            }

        // Sign the Product
          Product = ZeroTrim(ProductSign + Product);

        // Return the Result
           return Product;
      }

    function DIV_MOD(Divisor,Dividend,Operation)
      {
	      	      
        // Declare variables
           var Quotient = "";
           var Remainder = "";
           var Answer = "";
           var QuotientSign = "";
           var counterDiv = 0;
           var DivHashTable = new Array(10);
           var OldDivisor;
           var OldDividend;
           var temp = "";

        

        // Determine the sign of the quotient and strip sign from the Divisor and Dividend
           // If Divisor is positive, but Dividend is negative, then the Quotient is Negative
              if (!Quotient && Divisor.charAt(0)!="-" && Dividend.charAt(0)=="-")
                {
                  QuotientSign = "-"
                  Dividend = Dividend.substring(1,Dividend.length)
                }
           // If Dividend is positive, but Divisor is negative, then the Quotient is Negative
              if (!Quotient && Divisor.charAt(0)=="-" && Dividend.charAt(0)!="-")
                {
                  QuotientSign = "-"
                  Divisor = Divisor.substring(1,Divisor.length)
                }
           // If Divisor AND Dividend are negative, then the Quotient is Positive
              if (!Quotient && Divisor.charAt(0)=="-" && Dividend.charAt(0)=="-")
                {
                  Dividend = Dividend.substring(1,Dividend.length)
                  Divisor = Divisor.substring(1,Divisor.length)
                }

        // Handle the situation if the Divisor is greater than the Dividend
           if (IsLessThan(Dividend,Divisor) == "TRUE" && !Quotient) // Is Arg1 less than Arg2?
           {
             Quotient = "0";
             Remainder = Dividend;
           }

        // Handle the situation if the Divisor and the Dividend are equal
           if (IsEqualTo(Divisor,Dividend) == "TRUE" && !Quotient)
           {
             Quotient = "1";
             Remainder = "0";
           }

        // Handle the situation if the Divisor == 1
           if (Divisor == "1" && !Quotient)
           {
             Quotient = Dividend;
             Remainder = "0";
           }


        // At this point, we probably have a normal, well-behaved division
           if (Quotient == "")
           {
             OldDivisor = Divisor;
             OldDividend = Dividend;
             if ((Divisor.search(/\./) == -1) && (Dividend.search(/\./) == -1)) // if each number contains no decimal, do nothing
             ;
             else // but if either one contains a decimal, then they must both be multiplied until they are Whole numbers.

               {
                 // Multiply by a power of 10 to remove the decimals.
                    var Throwaway = "";
                    var DivisorMultiplier = "";
                    var DividendMultiplier = "";
                    if (Divisor.search(/\./) == (-1)) DivisorMultiplier = ""; else {DivisorMultiplier = RegExp.rightContext};
                    if (Dividend.search(/\./) == (-1)) DividendMultiplier = ""; else {DividendMultiplier = RegExp.rightContext};
                    var TempMultiplier = Math.max(DivisorMultiplier.length,DividendMultiplier.length)+"";
                    TempMultiplier = "1" + BuildString("0",TempMultiplier+""); // Build the Multiplier
                    Divisor=Multiply(Divisor,TempMultiplier); // Perform the Big Multiplication
                    Dividend=Multiply(Dividend,TempMultiplier); // Perform the Big Multiplication
               }

             // Create a searchable hash table of Divisor values
                for (counterDiv = 0; counterDiv < 10; counterDiv++)
                  {
                    DivHashTable[counterDiv] = Multiply(Divisor,(counterDiv + '')); // the "+''" converts counterDiv to a string
                    // DivHashTable[0] = 0 * Divisor and so on...
                  }

             // Perform an ordinary division
                   
                // Set up variables
                   var CurrentAnswer = "";
                   var NewDividend = Dividend;
                   var Pointer = "";
                   var DividendMultiplierSubstring = "";
                   var TempMultiplier = "";
                   var HashCounter;
                // Start Looping through Dividend
                   while ((IsGreaterThan(NewDividend,Divisor) == "TRUE") || (IsEqualTo(NewDividend,Divisor) == "TRUE"))
                     {
                       // Set pointer at beginning of NewDividend
                          Pointer = 1;
                       // Increment the Pointer until DividendMultiplierString >= Divisor
                          while (IsLessThan(NewDividend.substring(0,Pointer),Divisor) == "TRUE")
                            {
                              Pointer++ ;
                            }
                          DividendMultiplierSubstring = NewDividend.substring(0,Pointer);
                       // Find the largest result in the hash table still less than DividendMultiplierSubstring
                          HashCounter = 9;
                          while (IsGreaterThan(DivHashTable[HashCounter]+"",DividendMultiplierSubstring) == "TRUE")
                            {
                              HashCounter-- ;
                            }
                       // HashCounter is its key in the Hash Table

                       // Append the same number of zeroes to the key as decimals to the right of pointer, making TempMultiplier
                          TempMultiplier = HashCounter+"" + BuildString("0",NewDividend.length-DividendMultiplierSubstring.length+"");

                       // Add TempMultiplier to CurrentAnswer
                          CurrentAnswer = CalculatorAdd(CurrentAnswer,TempMultiplier);
                       // Subtract the product of Divisor and TempMultiplier from NewDividend to get a NEW NewDividend
                          NewDividend = Subtraction(NewDividend,Multiply(Divisor,TempMultiplier));
                     } // while ((IsGreaterThan(NewDividend,Divisor) == "TRUE") ||...

             // Nail the calculated values down
                Quotient = CurrentAnswer;
                Remainder = Subtraction(OldDividend,Multiply(OldDivisor,Quotient));

             } // if (Quotient == "")

        // Return Answer to main program
           if (Operation == "DIV") {Answer = QuotientSign + Quotient}
           if (Operation == "MOD") {Answer = Remainder}
           return Answer;
      }

    function Factorial(StartNumber) // Look, Mom -- no recursion!
      {
        // Declare variables
           var Answer = "";
           var BigCounter = "";
           var RangeCheck = "";
           var Warning = "NOTE:"
                         + "\n"
                         + "The Factorial operator is designed to function only"
                         + "\n"
                         + "for the non-negative integers: {0, 1, 2, 3,...}."
                         + "\n\n"
                         + "Negative or Decimal arguments are not valid.";

        // If StartNumber = 0 or 1 then Answer = 1
           if (StartNumber == "0") {Answer = "1"}

        // Check and invalidate for Decimals
           if (!Answer && (StartNumber.indexOf(".") != "-1"))
             {
               Answer = "Undefined";
               alert(Warning);
             }

        // Check and invalidate for negative numbers
           if (!Answer && (StartNumber.charAt(0) == "-"))
             {
               Answer = "Undefined";
               alert(Warning);
             }

        // If the answer is nontrivial, then perform the calculation
           if (!Answer)
             {
               Answer = "1";
               BigCounter = "1";
               RangeCheck = CalculatorAdd(StartNumber,"1");
               while (BigCounter != RangeCheck)
                 {
                   Answer = Multiply(Answer,BigCounter);
                   BigCounter = CalculatorAdd(BigCounter,"1");
                 }
             }

        // Return the Answer
           return Answer;
      }

    function Power(StartNumber,Exponent)
      {
        // Declare variables
           var Answer = "";
           var BigCounter = "";
           var RangeCheck = "";
           var Warning = "NOTE:"
                         + "\n"
                         + "The Power operator is designed to function only with exponents"
                         + "\n"
                         + "that are non-negative integers {0, 1, 2, 3,...}."
                         + "\n\n"
                         + "Negative or Decimal exponents are not valid at this time.";

        // If Exponent = 0 then Answer = 1
           if (Exponent == "0") {Answer = "1"}

        // If Exponent = 1 then Answer = StartNumber
           if (Exponent == "1") {Answer = StartNumber}

        // If StartNumber = 0 then Answer = 0
           if (StartNumber == "0") {Answer = "0"}

        // If StartNumber = 1 then Answer = 1
           if (StartNumber == "1") {Answer = "1"}

        // Check and invalidate for Decimals
           if (!Answer && (Exponent.indexOf(".") != "-1"))
             {
               Answer = "Not valid at this time.";
               alert(Warning);
             }

        // Check and invalidate for negative numbers
           if (!Answer && (Exponent.charAt(0) == "-"))
             {
               Answer = "Not valid at this time.";
               alert(Warning);
             }

        // If the answer is nontrivial, then perform the calculation
           if (!Answer)
             {
               Answer = "1";
               BigCounter = "1";
               RangeCheck = CalculatorAdd(Exponent,"1");
               while (BigCounter != RangeCheck)
                 {
                   Answer = Multiply(Answer,StartNumber);
                   BigCounter = CalculatorAdd(BigCounter,"1");
                 }
             }

        // Return the Answer
           return Answer;
      }

    function GCD(XValue,YValue)
      {
        // Declare variables
           var Answer = "";
           var ZValue = "";
           var TempNumber = "";
           var Warning = "NOTE:"
                         + "\n"
                         + "The GCD operator is designed to function only"
                         + "\n"
                         + "for the non-negative integers: {0, 1, 2, 3,...}."
                         + "\n\n"
                         + "Negative or Decimal arguments are not valid.";
        // Error Checking
          if ((XValue.charAt(0) == "-") || (YValue.charAt(0) == "-") || ZeroTrim(XValue).search(/\./) != (-1) || ZeroTrim(YValue).search(/\./) != (-1))
            {
              Answer = "";
              alert(Warning);
            }
          else // We can do the calculation
            {
              while (IsEqualTo(XValue,YValue) == "FALSE")
                {
                  if (IsLessThan(XValue,YValue) == "TRUE") // then swap 'em
                    {
                      TempNumber = XValue;
                      XValue = YValue;
                      YValue = TempNumber;
                    }
                  ZValue = Subtraction(XValue,YValue);
                  XValue = YValue;
                  YValue = ZValue;
                }
              Answer = XValue; // The revised XValue from above
            }
        // Return Answer
           return Answer;
      }

    function LCM(XValue,YValue)
      {
        // Declare variables
           var Answer = "";
           var Warning = "NOTE:"
                         + "\n"
                         + "The LCM operator is designed to function only"
                         + "\n"
                         + "for the non-negative integers: {0, 1, 2, 3,...}."
                         + "\n\n"
                         + "Negative or Decimal arguments are not valid.";
        // Error Checking
          if ((XValue.charAt(0) == "-") || (YValue.charAt(0) == "-") || ZeroTrim(XValue).search(/\./) != (-1) || ZeroTrim(YValue).search(/\./) != (-1))
            {
              Answer = "";
              alert(Warning);
            }
          else // We can do the calculation
            {
              Answer = DIV_MOD(GCD(XValue,YValue),Multiply(XValue,YValue),"DIV");
            }
        // Return Answer
           return Answer;
      }

    function IsPrime(Argument) // Returns FALSE if Argument is Composite, TRUE if Argument is Prime
      {
        // Declare variables
           var Answer = "TRUE";
           var RollingNumber = "";
           var Counter;
           var DigitSum;
           var Warning = "NOTE:"
                         + "\n"
                         + "The Is Prime function is designed to function only"
                         + "\n"
                         + "for non-negative integers greater than 1: {2, 3, 4,...}."
                         + "\n\n"
                         + "0, 1, Negative or Decimal arguments are not valid.";
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        // Error Checking
          if ((Argument.charAt(0) == "-") || ZeroTrim(Argument).search(/\./) != (-1) || Argument == "0" || Argument == "1")
            {
              Answer = "";
              alert(Warning);
            }
          else
            {
              // Check for easy divisions
                 if (((parseInt(Argument.charAt(Argument.length-1))) % 2 == 0) && (Argument != "2")) // is divisible by 2
                   { Answer = "FALSE"; }
                 if ((Argument.charAt(Argument.length-1) == "5") && (Argument != "5")) // is divisible by 5
                   { Answer = "FALSE"; }
                 DigitSum = 0;
                 for (Counter = 0; Counter < Argument.length; Counter++)
                   {
                     DigitSum = DigitSum + parseInt(Argument.charAt(Counter));
                   }
                 if ((DigitSum % 3 == 0) && (Argument != "3")) // is divisible by 3
                   { Answer = "FALSE"; }
                 if (Answer == "TRUE")
                    {
                      // Now we check a big array of primes
                         for(var PrimeCounter=0; PrimeCounter < (PrimeArray.length + 1); PrimeCounter++) // Is a divisor of the Argument in the array?
                           {
                             if (PrimeArray[PrimeCounter] == Argument) // if it's one of the primes in the list...
                               { return "TRUE"; }
                           }
                         for(var PrimeCounter=0; PrimeCounter < (PrimeArray.length + 1); PrimeCounter++) // Is a divisor of the Argument in the array?
                           {
                             if (DIV_MOD(PrimeArray[PrimeCounter],Argument,"MOD") == "0") // then a divisor has been found in the list
                               { return "FALSE"; }
                           }
                    }
              // If no easy shortcuts, then do it the hard way...
                 if (Answer == "TRUE")
                    // then the number is not divisible by any prime from the list, meaning
                    // it must be greater than the square of the highest prime on the list. 
                    // (a number is either a prime or divisible by primes and we just 
                    // finished checking a crapload of primes...)
                   {
                     // RollingNumber is the square of the highest prime on the list.
                     RollingNumber = Multiply(PrimeArray[PrimeArray.length-1],PrimeArray[PrimeArray.length-1]);
                     while ((IsLessThan(Multiply(RollingNumber,RollingNumber),Argument) == "TRUE") && (Answer == "TRUE"))
                       {
                         RollingNumber = CalculatorAdd(RollingNumber,"2"); // only odd numbers
                         if ((DIV_MOD(RollingNumber,Argument,"MOD") == "0") && (IsEqualTo(RollingNumber,Argument) == "FALSE"))
                           {
                             Answer = "FALSE";
                             // alert(Argument + " is evenly divided by " + RollingNumber); // uncomment this if you want to know the first divisor of Argument.
                           }
                       }
                   }
            }
        // Return Answer
           return Answer;
      }

    function SqrtFloor(Argument) // Returns the FLOOR of the Square Root of Argument
      {
        // Declare variables
           var Estimate = "";
           var ContinueLoop = "TRUE";
           var Warning = "NOTE:"
                         + "\n"
                         + "The Square Root function is designed"
                         + "\n"
                         + "only for non-negative numbers."
                         + "\n\n"
                         + "Negative arguments are not valid.";
        // If it's a non-negative number...
           if (Argument.charAt(0) == "-")
             {
               alert(Warning);
             }
           else
             {
               Estimate = "2";
               while (ContinueLoop == "TRUE")
                 {
                   Estimate = DIV_MOD("2",(CalculatorAdd(Estimate,DIV_MOD(Estimate,Argument,"DIV"))),"DIV");
                   if (IsEqualTo(Argument,Multiply(Estimate,Estimate)) == "TRUE")
                     { ContinueLoop = "FALSE"; }
                   if ((IsLessThan(Multiply(Estimate,Estimate),Argument) == "TRUE") && (IsGreaterThan(Multiply(CalculatorAdd(Estimate,"1"),CalculatorAdd(Estimate,"1")),Argument) == "TRUE"))
                     { ContinueLoop = "FALSE"; }
                 }
             }

        // Return Answer
           return Estimate;
      }

    function PerfectSquare(Argument) // Returns TRUE if the argument is a perfect square, otherwise FALSE
      {
        // Declare variables
           var Answer = "";
           var Warning = "NOTE:"
                         + "\n"
                         + "The IsPerfectSquare function is designed"
                         + "\n"
                         + "only for non-negative numbers."
                         + "\n\n"
                         + "Negative arguments are not valid.";
        // If it's a non-negative number...
           if (Argument.charAt(0) == "-")
             {
               alert(Warning);
             }
           else
             {
               Answer = IsEqualTo(Multiply(SqrtFloor(Argument),SqrtFloor(Argument)),Argument);
             }

        // Return Answer
           return Answer;
      }