Add System.Half

[gewarren]

Fixes #23030. (Hide whitespace changes.)

See dotnet/runtime#37630 and dotnet/runtime#936.

Internal preview.

[adegeo]

It may be worth pointing out what is said in the API docs:

An IEEE 754 compliant float16 type.

[tannergooding]

The formal IEEE 754 name is binary16 for half, binary32 for single, and binary64 for double.

[adegeo]

@tannergooding we should probably update the API docs, as it says float16: https://docs.microsoft.com/en-us/dotnet/api/system.half?view=net-5.0

[tannergooding]

The exact range for Half is +/-65504.

The number of digits, mirroring what is used in the other columns is ~3-5 digits. However, that column is very misleading in my opinion and may give users a false sense that any value with 6 significant digits can be exactly represented.

In practice, the lower limit here is that if a string with at most n significant digits (3, 6, 15 for half, float, and double, respectively) is converted to a floating-point value and then back to a string with the same number of digits, the strings should match. That is, float.Parse(s).ToString("G6") == s should be true for any s that contains no more than 6 significant digits.

• This isn't guaranteed by the IEEE 754 spec and may depend on the formatting algorithm used

While the upper limit here is that if a floating-point value is converted to a string with that many digits (5, 9, 17 for half, float, and double, respectively), and then converted back to a floating-point value, the result should match the original floating-point value. That is, float.Parse(x.ToString("G9")).Equals(x) should be true for any float.

• This is guaranteed by the IEEE 754 spec, and we should be correctly implementing this in .NET Core 3.1 or higher

[gewarren]

I will plan to remove that column then. Thanks!

[pgovind]

Other reviews have called out everything I noticed too. Approving assuming the comments will be resolved! Overall LGTM!

[gewarren]

Thanks for the great reviews!