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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