Math.IEEERemainder(Double, Double) Method
Definition
Important
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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);static member IEEERemainder : double * double -> doublePublic Shared Function IEEERemainder (x As Double, y As Double) As DoubleParameters
- x
- Double
A dividend.
- y
- 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 remainder operator.
using System;
public class Example
{
public static void Main()
{
Console.WriteLine($"{"IEEERemainder",35} {"Remainder operator",20}");
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)
{
var formula = $"{number1} / {number2} = ";
var ieeeRemainder = Math.IEEERemainder(number1, number2);
var remainder = number1 % number2;
Console.WriteLine($"{formula,-16} {ieeeRemainder,18} {remainder,20}");
}
}
// The example displays the following output:
//
//
// IEEERemainder Remainder operator
// 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
open System
let showRemainders number1 number2 =
let formula = $"{number1} / {number2} = "
let ieeeRemainder = Math.IEEERemainder(number1, number2)
let remainder = number1 % number2
printfn $"{formula,-16} {ieeeRemainder,18} {remainder,20}"
printfn " IEEERemainder Remainder operator"
showRemainders 3 2
showRemainders 4 2
showRemainders 10 3
showRemainders 11 3
showRemainders 27 4
showRemainders 28 5
showRemainders 17.8 4
showRemainders 17.8 4.1
showRemainders -16.3 4.1
showRemainders 17.8 -4.1
showRemainders -17.8 -4.1
// The example displays the following output:
//
//
// IEEERemainder Remainder operator
// 3 / 2 = -1 1
// 4 / 2 = 0 0
// 10 / 3 = 1 1
// 11 / 3 = -1 2
// 27 / 4 = -1 3
// 28 / 5 = -2 3
// 17.8 / 4 = 1.8 1.8
// 17.8 / 4.1 = 1.4 1.4
// -16.3 / 4.1 = 0.0999999999999979 -4
// 17.8 / -4.1 = 1.4 1.4
// -17.8 / -4.1 = -1.4 -1.4
Module Example
Public Sub Main()
Console.WriteLine($"{"IEEERemainder",35} {"Remainder operator",20}")
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 = $"{number1} / {number2} = "
Dim ieeeRemainder As Double = Math.IEEERemainder(number1, number2)
Dim remainder As Double = number1 Mod number2
Console.WriteLine($"{formula,-16} {ieeeRemainder,18} {remainder,20}")
End Sub
End Module
' The example displays the following output:
'
' IEEERemainder Remainder operator
' 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 remainder 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 remainder operator is:
Remainder = (Math.Abs(dividend) - (Math.Abs(divisor) *
(Math.Floor(Math.Abs(dividend) / Math.Abs(divisor))))) *
Math.Sign(dividend)
