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IEEERemainder  
Method  
Remainder from the division of 2 floating point numbers to IEEE standards
Math Class
System NameSpace
CF1.  Procedure IEEERemainder ( X : Double; Y : Double ) ; Static;
CF : Methods with this mark are Compact Framework Compatible
Description
IEEERemainder gives the remainder when dividing two floating point numbers. The mechanics of the process adhere to IEEE standards, but are not intuitive.
 
The algorithm used is as follows:
 
Quotient        = X / Y
 
RoundedQuotient = Round(Quotient)
 
Remainder       = X - (Y * RoundedQuotient)
 
Note : The Round function uses so-called Bankers rules : rounding is to the nearest whole integer except that a value of exactly *.5 always gets to the nearest even integer.
Notes
Static methods are not methods of an object - they are simply class functions or procedures available at any time.
References
Round
Microsoft MSDN Links
System
System.Math
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Illustrating the peculiarities of IEEERemainder
program Project1;
{$APPTYPE CONSOLE}

var
  float : Double;
begin
  // 10/5 gives quotient of 2.0 which gets rounded to 2
  // The returned remainder = 10 - (5 * 2) = 0
  float := System.Math.IEEERemainder(10, 5);
  Console.WriteLine('Remainder of 10  /5 = {0}', float.ToString);

  // 12/5 gives quotient of 2.4 which gets rounded to 2
  // The returned remainder = 12 - (5 * 2) = 2
  float := System.Math.IEEERemainder(12, 5);
  Console.WriteLine('Remainder of 12  /5 = {0}', float.ToString);

  // 12.5/5 gives quotient of 2.5 which gets rounded to 2
  // The returned remainder = 12.5 - (5 * 2) = 2.5
  float := System.Math.IEEERemainder(12.5, 5);
  Console.WriteLine('Remainder of 12.5/5 = {0}', float.ToString);

  // 13/5 gives quotient of 2.6 which gets rounded to 3
  // The returned remainder = 13 - (5 * 3) = -2
  float := System.Math.IEEERemainder(13, 5);
  Console.WriteLine('Remainder of 13  /5 = {0}', float.ToString);

  // This illustrates Banker's rounding to the nearest even integer
  // 17.5/5 gives quotient of 3.5 which gets rounded to 4
  // The returned remainder = 17.5 - (5 * 4) = -2.5
  float := System.Math.IEEERemainder(17.5, 5);
  Console.WriteLine('Remainder of 17.5/5 = {0}', float.ToString);

  // Divide by zero returns NaN - Not a Number
  float := System.Math.IEEERemainder(1, 0);
  Console.WriteLine('Remainder of  1  /0 = {0}', float.ToString);

  Console.ReadLine;
end.
   Remainder of 10  /5 = 0
   Remainder of 12  /5 = 2
   Remainder of 12.5/5 = 2.5
   Remainder of 13  /5 = -2
   Remainder of 17.5/5 = -2.5
   Remainder of  1  /0 = NaN
 
 
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