Do not agree. You should have ease of use _and_ efficiency. Modern C++ techniques allow for this.
I was trying to give myself wiggle room, but I pretty much agree with you. I don't expect anything as fast as GMP, but I imagine that a plain C++ library could still do very well.
It is not clear to me what you mean by "useful for number theory". You want the library to handle Z[sqrt(2)](log(2)) arbitrarily good? (this question is not rhetoric)
You would set the precision of your calculations with a function call. (Specify the number of digits of accuracy.) Example: set_precision(3); cout << arbitrary_sqrt(2) << endl; set_precision(10); cout << arbitrary_sqrt(2); Output: 1.414 1.4142135624
3) As well as arbitrary precision, it should provide error range math: 2.00 * 2.00 is not generally the same thing as 2.0 * 2.0
Do not fully understand, please expand this idea.
For example: 1.0 + 1.00 = 2.0 (plus or minus .05) 1.00 + 1.00 = 2.00 (plus or minus .005)
I do not fully like the idea of exceptions on the middle of my computations, I prefer to set the 'state' of the object to Nan. Even for big ints.
That would work too. Whatever the solution is though, I don't want it to attempt a normal int division by zero internally if asked to do a big int division by zero. There is no way to handle that sort of error at run time.
9) Precision for rational numbers may be set as a static member variable or it may not. In the second case, expressions involving rational numbers of different.
I see no point in using rational numbers, but maybe I am missing something.
By rational, I a type that is "more than just integers." (Mathematics is my field, not CS.) Built-in types like float and double hold rational numbers. So I am not talking about a struct that holds a numerator and a denominator, if that's what you were thinking. Joel Eidsath