Improve C# Math Base

[xqb-dpx]

Please update the Math Library and these issues:

• Factorial
• Integral
• Derivative or Hop
• Random ---> from clarck or etc.
• Fibonacci Series
• Complex Numbers
• Imaginary Numbers

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[tannergooding]

Math and MathF are effectively "soft deprecated" or "frozen". That is, they continue being valid for use and will always have correct up-to-date behavior, but we aren't planning on exposing any new APIs on these types moving forward. There are too many versioning problems with such static classes and it was inconsistent with how equivalent APIs were exposed for non-primitive types. We likewise must expose the APIs directly on the respective types in order to support the "Generic Math" feature, so all new APIs are only exposed on the respective T (such as T.DegreesToRadians(T value) for float, double, Half, etc).

As for the requests, any API suggestions need to follow the API review process and template detailed here: https://github.com/dotnet/runtime/blob/main/docs/project/api-review-process.md. That is to say, we need concrete signatures suggested, ideally with clarifications on intended behaviors where names can be ambiguous, types intended to be supported, etc. -- Meaning you'd need to open a new proposal, following the required template, and requesting the APIs be exposed on the relevant numeric types like float, double, Complex, int, long, BigInteger, and potentially the appropriate generic math interfaces such as INumber<T>

Some input based on the proposed APIs:

• Random ---> from clarck or etc.
  • .NET already provides System.Random and System.Security.Cryptography.RandomNumberGenerator. We aren't looking at adding another RNG type or set of APIs to the core libraries. Any requests for additional RNG APIs should be requested to be exposed on those types instead.
• Complex Numbers
  • This is already supported via System.Numerics.Complex for double. We may in the future expose some Complex<T> where T : IFloatingPointIeee754<T> type as well
• Imaginary Numbers
  • This is covered via Complex and we have no intention of exposing something purely for imaginary numbers.
• Factorial
  • This isn't a good general purpose API. Factorials are more a novelty in most scenarios and are trivial to roll your own support around. You can only handle up to 12! for 32-bit integers, 20! for 64-bit integers, and 34! for 128-bit integers. While for float/double, you have 10! and 17! before you start getting precision loss. These are all scenarios which are best handled by a small lookup table instead. BigInteger can theoretically handle up to the factorial of 500 million, but it's not something that's realistically needed in common code.
• Fibonacci Series
  • Similar to Factorial, this isn't really a good general purpose API and is more a novelty in practical use case scenarios, often better handled via a lookup table. fib(47) is the largest that fits in 32-bits while fib(93) is the largest that fits in 64-bits.
• Integral
  • You'll need to be more specific about which integral you're wanting here. I'd presume you want the definite rather than indefinite integral, but there is also the question of which definition to use (Reimann, Lebesgue, etc). This is not a common API in other languages.
• Derivative or Hop
  • Similar to Integral, you'll need to be a bit more specific due to the breadth of space this can cover. It is also not a common API in other languages.