Arbitrary Precision Mathematics Framework in Java

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I am Subhomoy Haldar (ambigram_maker, on Stack Exchange sites), a "programmer" who wants to build an arbitrary-precision mathematics framework in Java. In simpler terms, I want to provide most of the functionality in the java.lang.Math class, plus more. The main features will be that BigInteger, BigDecimal and MathContext can be used harmoniously with this library. I plan to perform most calculations using rational arithmetic. I will also provide a seperate Rational class, capable of arbitrary precision arithmetic. Now, the problem is... there are a LOT of things that can be crammed into this library. I need help to narrow it down and actually find a starting point. Some people might say it is "Reinventing the Wheel", but I assure you... my approach will be slightly different from the existing ones.

What compulsory functionality should the framework contain? *

Other than square-root, cube-root, raising to a power, etc.

Trigonometric Functions (sin, asin, cos, acos, etc)

Rounding operations

Continued Fractions

Complex Numbers

Other:

Required

What should the behavior of the code be when supplied with invalid data? *

Suppose someone asks for the GCD of 32...

Scream with an Exception

Make sure such a situation never arises

Quietly accept it and return a default or error value

Other:

What are the possible things that you'll do with this library?

Specific answers like: "Build an arbitrary-precision scientific calculator" will be helpful.

What according to you, should NOT be done using this library?

Such as calculating π upto a billion digits...

What features according to you, will be cool if provided with this package?

Like Rational Approximation, or fast calculations of combinations and permutations...

Would you like to be associated with this project? *

This project will be open source and will be hosted on GitHub.

Yes

Can you suggest a cool name for this library?

The name of my organisation on GitHub is "Cristatus Solutions". A cool acronym (say, CrisMath) would be sweet. :-)

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