Some Math Utility Functions (on GitHub) to help out with Project Euler

I've been working through the problems on the Project Euler website recently, and as there were some maths functions that I needed over and over I decided to put them into a (C++) utility namespace, MathUtils, which I've put up on GitHub. This post is a short overview of what MathsUtils currently provides. The code should (hopefully) be self explanatory so I'll not provide much more detail here.

(I've also got a class up there called embiguint, which is an unsigned integer that can be arbitrarily large. It has proved useful in its current state but I intend to add a lot more functionality and make it behave more like a built in type at which point I'll do a blog post on it too.)

The functions currently included in MathsUtils are:
template <typename T> std::string
                     ToAlternateBaseRepresentation(
                     const T& value, const T& base);
template <typename T> std::vector<T>
                     GetDivisors(const T& number);
template <typename T> emu64 GetSumOfDivisors(const T& number);
template <typename T> emu64 Factorial(const T& x);
template <typename T> T
                     PowerOf(const T& base, const T& power);
template <typename T> std::vector<bool>
                     GetPrimesBoolArrayToN(const T& n);
template <typename T> std::vector<T> GetPrimesToN(const T& n);

I had originally developed the functions in a class with static members but I changed this to a namespace as it seemed more more natural. After all, classes are intended to define how to build objects whereas namespaces are used to group related functionality. In Effective C++, in an item entitled Perfer non-member non-friend functions to member functions, Scott Meyers argues that this approach helps to increase extensiblity and (counter-intuitively) encapsulation.

All the functions are templated as I want to make them as easy to use as possible. There's still lots more I could add to these functions, for example the PowerOf functions only works with non-negative exponents, however each function was written or extended with a particular problem in mind. I'll add more functionality as I need it and in the mean time the functions should throw a useful exception if you ask them to do something they can't do.

There's also lots more I can do with regard to optimisation, and this should give me an opportunity to try out (and learn) some new C++11 features. For example PowerOf and Factorial could benefit from constexpr, although I've just been looking at the release of Visual Studio 2013 and I don't think this feature has made it in.  I guess I can achieve the same result with template metaprogramming if I really want quicker run-time code.

Anyway, my MathUtils are in place and poised to help out on more Project Euler problems.