Double.Equals Method (Double)
Returns a value indicating whether this instance and a specified Double object represent the same value.
Assembly: mscorlib (in mscorlib.dll)
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 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 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.
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.
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 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.
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.
Compiler overload resolution may account for an apparent difference in the behavior of the two Equals 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 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 method, whereas the second comparison returns false because the compiler calls the Equals(Object) method.