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Single.Equals Method (Single)

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

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

public bool Equals(
	float obj


Type: System.Single

An object to compare with this instance.

Return Value

Type: System.Boolean
true if obj is equal to this instance; otherwise, false.



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 an 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 Single and the parameter type is Int32. The Microsoft C# compiler generates instructions to represent the value of the parameter as a Single object, and then generates a Single.Equals(Single) 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 in the .NET Framework topic.

Precision in Comparisons

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

// Initialize two floats with apparently identical values 
float float1 = .33333f;
float float2 = 1/3;
// Compare them for equality
Console.WriteLine(float1.Equals(float2));    // displays false

One comparison technique that avoids the problems associated with comparing for equality involves defining an acceptable margin of difference between two values (such as .01% 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 an outcome of differences in precision and, therefore, the values are likely to be equal. The following example uses this technique to compare .33333 and 1/3, which are the two Single values that the previous code example found to be unequal.

// Initialize two floats with apparently identical values 
float float1 = .33333f;
float float2 = (float) 1/3;
// Define the tolerance for variation in their values 
float difference = Math.Abs(float1 * .0001f);

// Compare the values 
// The output to the console indicates that the two values are equal 
if (Math.Abs(float1 - float2) <= difference)
   Console.WriteLine("float1 and float2 are equal.");
   Console.WriteLine("float1 and float2 are unequal.");

In this case, the values are equal.


Because Epsilon defines the minimum expression of a positive value whose range is near zero, the margin of difference 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 that avoids the problems associated with comparing for equality 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 way to do this is to arbitrarily select an absolute value. However, this is problematic, because an acceptable margin of difference depends on the magnitude of the Single values. A second way takes advantage of a design feature of the floating-point format: The difference between the mantissa components in the integer representations of two floating-point values indicates the number of possible floating-point values that separates the two values. For example, the difference between 0.0 and Epsilon is 1, because Epsilon is the smallest representable value when working with a Single 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(Single) method found to be unequal. Note that the example uses the BitConverter.GetBytes and BitConverter.ToInt32 methods to convert a single-precision floating-point value to its integer representation.

using System;

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

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

   public static bool HasMinimalDifference(float value1, float value2, int units)
      byte[] bytes = BitConverter.GetBytes(value1);
      int iValue1 = BitConverter.ToInt32(bytes, 0);

      bytes = BitConverter.GetBytes(value2);
      int iValue2 = BitConverter.ToInt32(bytes, 0);

      // If the signs are different, return false except for +0 and -0. 
      if ((iValue1 >> 31) != (iValue2 >> 31))
         if (value1 == value2)
            return true;

         return false;

      int diff = Math.Abs(iValue1 - iValue2);

      if (diff <= units)
         return true;

      return false;
// The example displays the following output: 
//        1 = 1.00000012: 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 numbers might produce different results depending on the version of the .NET Framework, because the precision of the numbers' internal representation might change.

.NET Framework

Supported in: 4.5, 4, 3.5, 3.0, 2.0

.NET Framework Client Profile

Supported in: 4, 3.5 SP1

Portable Class Library

Supported in: Portable Class Library

.NET for Windows Store apps

Supported in: Windows 8

.NET for Windows Phone apps

Supported in: Windows Phone 8.1, Windows Phone Silverlight 8.1, Windows Phone Silverlight 8

Windows Phone 8.1, Windows Phone 8, Windows 8.1, Windows Server 2012 R2, Windows 8, Windows Server 2012, Windows 7, Windows Vista SP2, Windows Server 2008 (Server Core Role not supported), Windows Server 2008 R2 (Server Core Role supported with SP1 or later; Itanium not supported)

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

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