C# has three mathematical constants that look like constants in the C header file float.h. Two of these are not what you might expect.
The constant double.MaxValue in C# looks like the constant DBL_MAX in C, and indeed it is. Both give the maximum finite value of a double, which is on the order of 10^308. This might lead you to believe that double.MinValue in C# is the same as DBL_MIN in C or that double.Epsilon in C# is the same as DBL_EPSILON. If so, you’re in for a surprise.
The constants DBL_MAX and double.MaxValue are the same because there is no ambiguity over what “max” means: the largest finite value of a double. But DBL_MIN and double.MinValue are different because they minimize over different ranges. The constant DBL_MIN is the smallest positive value of a normalized double. The constant double.MinValue in C# is the smallest (i.e. most negative) value of a double and is the negative of double.MaxValue. The difference between DBL_MIN and double.MinValue is approximately the difference between 10^-308 and -10^308, between a very small positive number and a very large negative number.
C has a constant DBL_EPSILON for the smallest positive double precision number x such that 1 + x does not equal 1 in machine precision. Typically a double has about 15 figures of precision, and so DBL_EPSILON is on the order of 10^−16. (For a more precise description, see Anatomy of a floating point number.)
You might expect double.Epsilon in C# corresponds to DBL_EPSILON in C. I did, until a unit test failed on some numerical code I was porting from C++ to C#. But in C# double.Epsilon is the smallest positive value a (denormalized) double can take. It is similar to DBL_MIN, except that double.Epsilon is the possible smallest value of a double, not requiring normalization. The constant DBL_MIN is on the order of 10^−308 while double.Epsilon is on the order of 10^−324 because it allows denormalized values. (See Anatomy of a floating point number for details of denormalized numbers.)
Incidentally, the C constants DBL_MAX, DBL_MIN, and DBL_EPSILON equal the return values of max, min, and epsilon for the C++ class numeric_limits<double>.
To summarize,
double.MaxValue in C# equals DBL_MAX in C.double.MinValue in C# equals -DBL_MAX in C.double.Epsilon is similar to DBL_MIN in C, but orders of magnitude smaller.- C# has no analog of
DBL_EPSILON from C.
One could argue that the C# names are better than the C names. It makes sense for double.MinValue to be the negative of double.MaxValue. But the use of Epsilon was a mistake. The term “epsilon” in numeric computing has long been established and is not limited to C. It would have been better if Microsoft had used the name MinPositiveValue to be more explicit and not conflict with established terminology.
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