IEEE 754 floating point arithmetic rounding error in c# and javascript
I just read a book about javascript. The author mentioned a floating point arithmetic rounding error in the IEEE 754 standard.
For example adding 0.1 and 0.2 yields 0.30000000000000004 instead of 0.3.
so (0.1 + 0.2) == 0.3 returns false.
I also reproduced this error in c#.
So these are my question is:
How often this error occurs? What is the best practice workaround in c# and javascript? Which other languages have the same error?
It's not an error in the language. It's not an error in IEEE 754. It's an error in the expectation and usage of binary floating point numbers. Once you understand what binary floating point numbers really are, it makes perfect sense.
The best practice in C# is to use System.Decimal (aka decimal ) which is a decimal floating point type, whenever you're dealing with quantities which are naturally expressed in decimal - typically currency values.
See my articles on .NET binary floating point and decimal floating point for more information.
The error is NOT a rounding error, it's simply that some values cannot be exactly represented by the IEEE 754 standard. see Jon Skeet's article on binary floating point numbers in .net for further reading.
For dealing with numbers like your example (base-10) you should be using the decimal datatype in C# as it can represent these numbers exactly, so you get values you'd expect.
A typical way is to define some epsilon value, and check whether the result is within targetvalue +- epsilon:
double const epsilon = 0.000001; // or whatever
if(valueA >= valueB - epsilon && valueA <= valueB + epsilon)
{
// treat as valueA = valueB
}
The closest representations of those three numbers in double precision floating point are:
The next larger representable number beyond 0.29999999999999999 is:
The closest representation of
So you are comparing 0.29999999999999999 and 0.30000000000000004. Does this give you more insight as to what is happening?
As far as the use of decimal instead of binary representations, that doesn't work either. Take for example one third:
which has no exact representation even using decimal digits. Any computations should always take representation error into account.
链接地址: http://www.djcxy.com/p/27500.html上一篇: 处理浮点错误的最佳方法是什么？