# Double.Equals Method

## Definition

Returns a value indicating whether two instances of Double represent the same value.

 Returns a value indicating whether this instance and a specified Double object represent the same value. Returns a value indicating whether this instance is equal to a specified object.

## Equals(Double)

Returns a value indicating whether this instance and a specified Double object represent the same value.

``````public:
virtual bool Equals(double obj);``````
``public bool Equals (double obj);``
``override this.Equals : double -> bool``
``Public Function Equals (obj As Double) As Boolean``

#### Parameters

obj
Double

A Double object to compare to this instance.

#### Returns

`true` if `obj` is equal to this instance; otherwise, `false`.

### Remarks

This method implements the System.IEquatable<T> interface, and performs slightly better than Equals because it does not have to convert the `obj` parameter to an object.

### Widening Conversions

Depending on your programming language, it might be possible to code a Equals method where the parameter type has fewer bits (is narrower) than the instance type. This is possible because some programming languages perform an implicit widening conversion that represents the parameter as a type with as many bits as the instance.

For example, suppose the instance type is Double and the parameter type is Int32. The Microsoft C# compiler generates instructions to represent the value of the parameter as a Double object, then generates a Double.Equals(Double) method that compares the values of the instance and the widened representation of the parameter.

Consult your programming language's documentation to determine if its compiler performs implicit widening conversions of numeric types. For more information, see the Type Conversion Tables topic.

### Precision in Comparisons

The Equals method should be used with caution, because two apparently equivalent values can be unequal due to the differing precision of the two values. The following example reports that the Double value .333333 and the Double value returned by dividing 1 by 3 are unequal.

``````// Initialize two doubles with apparently identical values
double double1 = .33333;
double double2 = 1/3;
// Compare them for equality
Console.WriteLine(double1.Equals(double2));    // displays false
``````
``````' Initialize two doubles with apparently identical values
Dim double1 As Double = .33333
Dim double2 As Double = 1/3
' Compare them for equality
Console.WriteLine(double1.Equals(double2))    ' displays False
``````

Rather than comparing for equality, one technique involves defining an acceptable relative margin of difference between two values (such as .001% of one of the values). If the absolute value of the difference between the two values is less than or equal to that margin, the difference is likely to be due to differences in precision and, therefore, the values are likely to be equal. The following example uses this technique to compare .33333 and 1/3, the two Double values that the previous code example found to be unequal. In this case, the values are equal.

``````// Initialize two doubles with apparently identical values
double double1 = .333333;
double double2 = (double) 1/3;
// Define the tolerance for variation in their values
double difference = Math.Abs(double1 * .00001);

// Compare the values
// The output to the console indicates that the two values are equal
if (Math.Abs(double1 - double2) <= difference)
Console.WriteLine("double1 and double2 are equal.");
else
Console.WriteLine("double1 and double2 are unequal.");
``````
``````' Initialize two doubles with apparently identical values
Dim double1 As Double = .33333
Dim double2 As Double = 1/3
' Define the tolerance for variation in their values
Dim difference As Double = Math.Abs(double1 * .00001)

' Compare the values
' The output to the console indicates that the two values are equal
If Math.Abs(double1 - double2) <= difference Then
Console.WriteLine("double1 and double2 are equal.")
Else
Console.WriteLine("double1 and double2 are unequal.")
End If
``````

Note

Because Epsilon defines the minimum expression of a positive value whose range is near zero, the margin of difference between two similar values must be greater than Epsilon. Typically, it is many times greater than Epsilon. Because of this, we recommend that you do not use Epsilon when comparing Double values for equality.

A second technique involves comparing the difference between two floating-point numbers with some absolute value. If the difference is less than or equal to that absolute value, the numbers are equal. If it is greater, the numbers are not equal. One alternative is to arbitrarily select an absolute value. This is problematic, however, because an acceptable margin of difference depends on the magnitude of the Double values. A second alternative takes advantage of a design feature of the floating-point format: The difference between the integer representation of two floating-point values indicates the number of possible floating-point values that separates them. For example, the difference between 0.0 and Epsilon is 1, because Epsilon is the smallest representable value when working with a Double whose value is zero. The following example uses this technique to compare .33333 and 1/3, which are the two Double values that the previous code example with the Equals(Double) method found to be unequal. Note that the example uses the BitConverter.DoubleToInt64Bits method to convert a double-precision floating-point value to its integer representation.

``````using System;

public class Example
{
public static void Main()
{
double value1 = .1 * 10;
double value2 = 0;
for (int ctr = 0; ctr < 10; ctr++)
value2 += .1;

Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2,
HasMinimalDifference(value1, value2, 1));
}

public static bool HasMinimalDifference(double value1, double value2, int units)
{
long lValue1 = BitConverter.DoubleToInt64Bits(value1);
long lValue2 = BitConverter.DoubleToInt64Bits(value2);

// If the signs are different, return false except for +0 and -0.
if ((lValue1 >> 63) != (lValue2 >> 63))
{
if (value1 == value2)
return true;

return false;
}

long diff = Math.Abs(lValue1 - lValue2);

if (diff <= (long) units)
return true;

return false;
}
}
// The example displays the following output:
//        01 = 0.99999999999999989: True
``````
``````Module Example
Public Sub Main()
Dim value1 As Double = .1 * 10
Dim value2 As Double = 0
For ctr As Integer =  0 To 9
value2 += .1
Next

Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2,
HasMinimalDifference(value1, value2, 1))
End Sub

Public Function HasMinimalDifference(value1 As Double, value2 As Double, units As Integer) As Boolean
Dim lValue1 As long =  BitConverter.DoubleToInt64Bits(value1)
Dim lValue2 As long =  BitConverter.DoubleToInt64Bits(value2)

' If the signs are different, Return False except for +0 and -0.
If ((lValue1 >> 63) <> (lValue2 >> 63)) Then
If value1 = value2 Then
Return True
End If
Return False
End If

Dim diff As Long =  Math.Abs(lValue1 - lValue2)

If diff <= units Then
Return True
End If

Return False
End Function
End Module
' The example displays the following output:
'       1 = 0.99999999999999989: True
``````

The precision of floating-point numbers beyond the documented precision is specific to the implementation and version of the .NET Framework. Consequently, a comparison of two particular numbers might change between versions of the .NET Framework because the precision of the numbers' internal representation might change.

If two Double.NaN values are tested for equality by calling the Equals method, the method returns `true`. However, if two NaN values are tested for equality by using the equality operator, the operator returns `false`. When you want to determine whether the value of a Double is not a number (NaN), an alternative is to call the IsNaN method.

### Notes to Callers

Compiler overload resolution may account for an apparent difference in the behavior of the two Equals(Object) method overloads. If an implicit conversion between the `obj` argument and a Double is defined and the argument is not typed as an Object, compilers may perform an implicit conversion and call the Equals(Double) method. Otherwise, they call the Equals(Object) method, which always returns `false` if its `obj` argument is not a Double value. The following example illustrates the difference in behavior between the two method overloads. In the case of all primitive numeric types except for Decimal and in C#, the first comparison returns `true` because the compiler automatically performs a widening conversion and calls the Equals(Double) method, whereas the second comparison returns `false` because the compiler calls the Equals(Object) method.

``````using System;

public class Example
{
static double value = 112;

public static void Main()
{
byte byte1= 112;
Console.WriteLine("value = byte1: {0,16}", value.Equals(byte1));
TestObjectForEquality(byte1);

short short1 = 112;
Console.WriteLine("value = short1: {0,16}", value.Equals(short1));
TestObjectForEquality(short1);

int int1 = 112;
Console.WriteLine("value = int1: {0,18}", value.Equals(int1));
TestObjectForEquality(int1);

long long1 = 112;
Console.WriteLine("value = long1: {0,17}", value.Equals(long1));
TestObjectForEquality(long1);

sbyte sbyte1 = 112;
Console.WriteLine("value = sbyte1: {0,16}", value.Equals(sbyte1));
TestObjectForEquality(sbyte1);

ushort ushort1 = 112;
Console.WriteLine("value = ushort1: {0,16}", value.Equals(ushort1));
TestObjectForEquality(ushort1);

uint uint1 = 112;
Console.WriteLine("value = uint1: {0,18}", value.Equals(uint1));
TestObjectForEquality(uint1);

ulong ulong1 = 112;
Console.WriteLine("value = ulong1: {0,17}", value.Equals(ulong1));
TestObjectForEquality(ulong1);

decimal dec1 = 112m;
Console.WriteLine("value = dec1: {0,21}", value.Equals(dec1));
TestObjectForEquality(dec1);

float sng1 = 112;
Console.WriteLine("value = sng1: {0,19}", value.Equals(sng1));
TestObjectForEquality(sng1);
}

private static void TestObjectForEquality(Object obj)
{
Console.WriteLine("{0} ({1}) = {2} ({3}): {4}\n",
value, value.GetType().Name,
obj, obj.GetType().Name,
value.Equals(obj));
}
}
// The example displays the following output:
//       value = byte1:             True
//       112 (Double) = 112 (Byte): False
//
//       value = short1:             True
//       112 (Double) = 112 (Int16): False
//
//       value = int1:               True
//       112 (Double) = 112 (Int32): False
//
//       value = long1:              True
//       112 (Double) = 112 (Int64): False
//
//       value = sbyte1:             True
//       112 (Double) = 112 (SByte): False
//
//       value = ushort1:             True
//       112 (Double) = 112 (UInt16): False
//
//       value = uint1:               True
//       112 (Double) = 112 (UInt32): False
//
//       value = ulong1:              True
//       112 (Double) = 112 (UInt64): False
//
//       value = dec1:                 False
//       112 (Double) = 112 (Decimal): False
//
//       value = sng1:                True
//       112 (Double) = 112 (Single): False
``````
``````Module Example
Dim value As Double = 112

Public Sub Main()
Dim byte1 As Byte = 112
Console.WriteLine("value = byte1: {0,16}", value.Equals(byte1))
TestObjectForEquality(byte1)

Dim short1 As Short = 112
Console.WriteLine("value = short1: {0,16}", value.Equals(short1))
TestObjectForEquality(short1)

Dim int1 As Integer = 112
Console.WriteLine("value = int1: {0,18}", value.Equals(int1))
TestObjectForEquality(int1)

Dim long1 As Long = 112
Console.WriteLine("value = long1: {0,17}", value.Equals(long1))
TestObjectForEquality(long1)

Dim sbyte1 As SByte = 112
Console.WriteLine("value = sbyte1: {0,16}", value.Equals(sbyte1))
TestObjectForEquality(sbyte1)

Dim ushort1 As UShort = 112
Console.WriteLine("value = ushort1: {0,16}", value.Equals(ushort1))
TestObjectForEquality(ushort1)

Dim uint1 As UInteger = 112
Console.WriteLine("value = uint1: {0,18}", value.Equals(uint1))
TestObjectForEquality(uint1)

Dim ulong1 As ULong = 112
Console.WriteLine("value = ulong1: {0,17}", value.Equals(ulong1))
TestObjectForEquality(ulong1)

Dim dec1 As Decimal = 112d
Console.WriteLine("value = dec1: {0,20}", value.Equals(dec1))
TestObjectForEquality(dec1)

Dim sng1 As Single = 112
Console.WriteLine("value = sng1: {0,19}", value.Equals(sng1))
TestObjectForEquality(sng1)
End Sub

Private Sub TestObjectForEquality(obj As Object)
Console.WriteLine("{0} ({1}) = {2} ({3}): {4}",
value, value.GetType().Name,
obj, obj.GetType().Name,
value.Equals(obj))
Console.WriteLine()
End Sub
End Module
' The example displays the following output:
'       value = byte1:             True
'       112 (Double) = 112 (Byte): False
'
'       value = short1:             True
'       112 (Double) = 112 (Int16): False
'
'       value = int1:               True
'       112 (Double) = 112 (Int32): False
'
'       value = long1:              True
'       112 (Double) = 112 (Int64): False
'
'       value = sbyte1:             True
'       112 (Double) = 112 (SByte): False
'
'       value = ushort1:             True
'       112 (Double) = 112 (UInt16): False
'
'       value = uint1:               True
'       112 (Double) = 112 (UInt32): False
'
'       value = ulong1:              True
'       112 (Double) = 112 (UInt64): False
'
'       value = dec1:                 True
'       112 (Double) = 112 (Decimal): False
'
'       value = sng1:                True
'       112 (Double) = 112 (Single): False
``````

## Equals(Object)

Returns a value indicating whether this instance is equal to a specified object.

``````public:
override bool Equals(System::Object ^ obj);``````
``public override bool Equals (object obj);``
``override this.Equals : obj -> bool``
``Public Overrides Function Equals (obj As Object) As Boolean``

#### Parameters

obj
Object

An object to compare with this instance.

#### Returns

`true` if `obj` is an instance of Double and equals the value of this instance; otherwise, `false`.

### Remarks

The Equals method should be used with caution, because two apparently equivalent values can be unequal due to the differing precision of the two values. The following example reports that the Double value .3333 and the Double returned by dividing 1 by 3 are unequal.

``````// Initialize two doubles with apparently identical values
double double1 = .33333;
object double2 = 1/3;
// Compare them for equality
Console.WriteLine(double1.Equals(double2));    // displays false
``````
``````' Initialize two doubles with apparently identical values
Dim double1 As Double = .33333
Dim double2 As Object = 1/3
' Compare them for equality
Console.WriteLine(double1.Equals(double2))    ' displays False
``````

For alternatives to calling the Equals method, see the documentation for the Equals(Double) overload.

Note

Because Epsilon defines the minimum expression of a positive value whose range is near zero, the margin of difference between two similar values must be greater than Epsilon. Typically, it is many times greater than Epsilon.

The precision of floating-point numbers beyond the documented precision is specific to the implementation and version of the .NET Framework. Consequently, a comparison of two particular numbers might change between versions of the .NET Framework because the precision of the numbers' internal representation might change.

If two Double.NaN values are tested for equality by calling the Equals method, the method returns `true`. However, if two NaN values are tested for equality by using the equality operator, the operator returns `false`. When you want to determine whether the value of a Double is not a number (NaN), an alternative is to call the IsNaN method.

### Notes to Callers

Compiler overload resolution may account for an apparent difference in the behavior of the two Equals(Object) method overloads. If an implicit conversion between the `obj` argument and a Double is defined and the argument is not typed as an Object, compilers may perform an implicit conversion and call the Equals(Double) method. Otherwise, they call the Equals(Object) method, which always returns `false` if its `obj` argument is not a Double value. The following example illustrates the difference in behavior between the two method overloads. In the case of all primitive numeric types except for Decimal and in C#, the first comparison returns `true` because the compiler automatically performs a widening conversion and calls the Equals(Double) method, whereas the second comparison returns `false` because the compiler calls the Equals(Object) method.

``````using System;

public class Example
{
static double value = 112;

public static void Main()
{
byte byte1= 112;
Console.WriteLine("value = byte1: {0,16}", value.Equals(byte1));
TestObjectForEquality(byte1);

short short1 = 112;
Console.WriteLine("value = short1: {0,16}", value.Equals(short1));
TestObjectForEquality(short1);

int int1 = 112;
Console.WriteLine("value = int1: {0,18}", value.Equals(int1));
TestObjectForEquality(int1);

long long1 = 112;
Console.WriteLine("value = long1: {0,17}", value.Equals(long1));
TestObjectForEquality(long1);

sbyte sbyte1 = 112;
Console.WriteLine("value = sbyte1: {0,16}", value.Equals(sbyte1));
TestObjectForEquality(sbyte1);

ushort ushort1 = 112;
Console.WriteLine("value = ushort1: {0,16}", value.Equals(ushort1));
TestObjectForEquality(ushort1);

uint uint1 = 112;
Console.WriteLine("value = uint1: {0,18}", value.Equals(uint1));
TestObjectForEquality(uint1);

ulong ulong1 = 112;
Console.WriteLine("value = ulong1: {0,17}", value.Equals(ulong1));
TestObjectForEquality(ulong1);

decimal dec1 = 112m;
Console.WriteLine("value = dec1: {0,21}", value.Equals(dec1));
TestObjectForEquality(dec1);

float sng1 = 112;
Console.WriteLine("value = sng1: {0,19}", value.Equals(sng1));
TestObjectForEquality(sng1);
}

private static void TestObjectForEquality(Object obj)
{
Console.WriteLine("{0} ({1}) = {2} ({3}): {4}\n",
value, value.GetType().Name,
obj, obj.GetType().Name,
value.Equals(obj));
}
}
// The example displays the following output:
//       value = byte1:             True
//       112 (Double) = 112 (Byte): False
//
//       value = short1:             True
//       112 (Double) = 112 (Int16): False
//
//       value = int1:               True
//       112 (Double) = 112 (Int32): False
//
//       value = long1:              True
//       112 (Double) = 112 (Int64): False
//
//       value = sbyte1:             True
//       112 (Double) = 112 (SByte): False
//
//       value = ushort1:             True
//       112 (Double) = 112 (UInt16): False
//
//       value = uint1:               True
//       112 (Double) = 112 (UInt32): False
//
//       value = ulong1:              True
//       112 (Double) = 112 (UInt64): False
//
//       value = dec1:                 False
//       112 (Double) = 112 (Decimal): False
//
//       value = sng1:                True
//       112 (Double) = 112 (Single): False
``````
``````Module Example
Dim value As Double = 112

Public Sub Main()
Dim byte1 As Byte = 112
Console.WriteLine("value = byte1: {0,16}", value.Equals(byte1))
TestObjectForEquality(byte1)

Dim short1 As Short = 112
Console.WriteLine("value = short1: {0,16}", value.Equals(short1))
TestObjectForEquality(short1)

Dim int1 As Integer = 112
Console.WriteLine("value = int1: {0,18}", value.Equals(int1))
TestObjectForEquality(int1)

Dim long1 As Long = 112
Console.WriteLine("value = long1: {0,17}", value.Equals(long1))
TestObjectForEquality(long1)

Dim sbyte1 As SByte = 112
Console.WriteLine("value = sbyte1: {0,16}", value.Equals(sbyte1))
TestObjectForEquality(sbyte1)

Dim ushort1 As UShort = 112
Console.WriteLine("value = ushort1: {0,16}", value.Equals(ushort1))
TestObjectForEquality(ushort1)

Dim uint1 As UInteger = 112
Console.WriteLine("value = uint1: {0,18}", value.Equals(uint1))
TestObjectForEquality(uint1)

Dim ulong1 As ULong = 112
Console.WriteLine("value = ulong1: {0,17}", value.Equals(ulong1))
TestObjectForEquality(ulong1)

Dim dec1 As Decimal = 112d
Console.WriteLine("value = dec1: {0,20}", value.Equals(dec1))
TestObjectForEquality(dec1)

Dim sng1 As Single = 112
Console.WriteLine("value = sng1: {0,19}", value.Equals(sng1))
TestObjectForEquality(sng1)
End Sub

Private Sub TestObjectForEquality(obj As Object)
Console.WriteLine("{0} ({1}) = {2} ({3}): {4}",
value, value.GetType().Name,
obj, obj.GetType().Name,
value.Equals(obj))
Console.WriteLine()
End Sub
End Module
' The example displays the following output:
'       value = byte1:             True
'       112 (Double) = 112 (Byte): False
'
'       value = short1:             True
'       112 (Double) = 112 (Int16): False
'
'       value = int1:               True
'       112 (Double) = 112 (Int32): False
'
'       value = long1:              True
'       112 (Double) = 112 (Int64): False
'
'       value = sbyte1:             True
'       112 (Double) = 112 (SByte): False
'
'       value = ushort1:             True
'       112 (Double) = 112 (UInt16): False
'
'       value = uint1:               True
'       112 (Double) = 112 (UInt32): False
'
'       value = ulong1:              True
'       112 (Double) = 112 (UInt64): False
'
'       value = dec1:                 True
'       112 (Double) = 112 (Decimal): False
'
'       value = sng1:                True
'       112 (Double) = 112 (Single): False
``````