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Math.IEEERemainder Method

Updated: February 2009

Returns the remainder resulting from the division of a specified number by another specified number.

Namespace:  System
Assembly:  mscorlib (in mscorlib.dll)

public static double IEEERemainder(
	double x,
	double y
)

Parameters

x
Type: System.Double

A dividend.

y
Type: System.Double

A divisor.

Return Value

Type: System.Double
A number equal to x - (y Q), where Q is the quotient of x / y rounded to the nearest integer (if x / y falls halfway between two integers, the even integer is returned).
If x - (y Q) is zero, the value +0 is returned if x is positive, or -0 if x is negative.
If y = 0, NaN is returned.

This operation complies with the remainder operation defined in Section 5.1 of ANSI/IEEE Std 754-1985; IEEE Standard for Binary Floating-Point Arithmetic; Institute of Electrical and Electronics Engineers, Inc; 1985.

The IEEERemainder method is not the same as the modulus operator. Although both return the remainder after division, the formulas they use are different. The formula for the IEEERemainder method is:

IEEERemainder = dividend - (divisor * Math.Round(dividend / divisor))

In contrast, the formula for the modulus operator is:

Modulus = (Math.Abs(dividend) - (Math.Abs(divisor) * 
          (Math.Floor(Math.Abs(dividend) / Math.Abs(divisor))))) * 
          Math.Sign(dividend)

The following example contrasts the remainder returned by the IEEERemainder method with the remainder returned by the modulus division operator.

using System;

public class Example
{
   public static void Main()
   {
      Console.WriteLine("{0,35} {1,20}", "IEEERemainder", "Modulus");
      ShowRemainders(3, 2);
      ShowRemainders(4, 2);
      ShowRemainders(10, 3);
      ShowRemainders(11, 3);
      ShowRemainders(27, 4);
      ShowRemainders(28, 5);
      ShowRemainders(17.8, 4);
      ShowRemainders(17.8, 4.1);
      ShowRemainders(-16.3, 4.1);
      ShowRemainders(17.8, -4.1);
      ShowRemainders(-17.8, -4.1);
   }

   private static void ShowRemainders(double number1, double number2)
   {
      string formula = String.Format("{0} / {1} = ", number1, number2);
      Console.WriteLine("{0,-16} {1,18} {2,20}", 
                       formula, 
                       Math.IEEERemainder(number1, number2), 
                       number1 % number2);  
   }
}
// The example displays the following output: 
//        
//                             IEEERemainder              Modulus 
//       3 / 2 =                          -1                    1 
//       4 / 2 =                           0                    0 
//       10 / 3 =                          1                    1 
//       11 / 3 =                         -1                    2 
//       27 / 4 =                         -1                    3 
//       28 / 5 =                         -2                    3 
//       17.8 / 4 =                      1.8                  1.8 
//       17.8 / 4.1 =                    1.4                  1.4 
//       -16.3 / 4.1 =    0.0999999999999979                   -4 
//       17.8 / -4.1 =                   1.4                  1.4 
//       -17.8 / -4.1 =                 -1.4                 -1.4

Windows 7, Windows Vista, Windows XP SP2, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP Starter Edition, Windows Server 2008 R2, Windows Server 2008, Windows Server 2003, Windows Server 2000 SP4, Windows Millennium Edition, Windows 98, Windows CE, Windows Mobile for Smartphone, Windows Mobile for Pocket PC, Xbox 360, Zune

The .NET Framework and .NET Compact Framework do not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.

.NET Framework

Supported in: 3.5, 3.0, 2.0, 1.1, 1.0

.NET Compact Framework

Supported in: 3.5, 2.0, 1.0

XNA Framework

Supported in: 3.0, 2.0, 1.0

Date

History

Reason

February 2009

Expanded the Remarks section and replaced the example.

Customer feedback.

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