Double.Equals Method (Double)
July 28, 2014
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 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 .3333 and the Double returned by dividing 1 by 3 are unequal.
Rather than comparing for equality, one recommended technique 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 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 example found to be unequal.
// Initialize two doubles with apparently identical values double double1 = .33333; double double2 = (double)1 / 3; // Define the tolerance for variation in their values double difference = Math.Abs(double1 * .0001); // Compare the values // The output indicates that the two values are equal if (Math.Abs(double1 - double2) <= difference) outputBlock.Text += "double1 and double2 are equal." + "\n"; else outputBlock.Text += "double1 and double2 are unequal." + "\n";
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.
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.