Math.IEEERemainder(Double, Double) Math.IEEERemainder(Double, Double) Math.IEEERemainder(Double, Double) Method

Definition

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

public:
 static double IEEERemainder(double x, double y);
public static double IEEERemainder (double x, double y);
Public Shared Function IEEERemainder (x As Double, y As Double) As Double
Parameters
x
Double Double Double

A dividend.

y
Double Double Double

A divisor.

Returns

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.

Examples

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
Module Example
   Public Sub 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)
   End Sub

   Private Sub ShowRemainders(number1 As Double, number2 As Double)
      Dim formula As String = String.Format("{0} / {1} = ", number1, number2)
      Console.WriteLine("{0,-16} {1,18} {2,20}", _
                       formula, _
                       Math.IEEERemainder(number1, number2), _
                       number1 Mod number2)  
   End Sub
End Module
' 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

Remarks

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)  

Applies to