shakespear / static_math

Compile time mathematic functions for C++14.

static_math is a C++ library dedicated to compile time mathematics.

Compatibility

static_math heavily relies on C++ features from the latest standard (C++14 at the time of writing), therefore only recent compilers will be able to compile it. The latest g++ and clang++ should be able to compile it, but the constexpr support in Microsoft Visual Studio may not be sufficient yet.

Principle

static_math makes a heavy use of the C++11 keyword constexpr to reimplement a number of existing mathematical functions and some new ones. It also provides a range of classes (rational, complex, etc...) whose functions can be used at compile time too. The library also contains some common mathematical constants.

The library also offers compile-time mathematics at the template parameter level thanks to it constant class, which is a bit like std::integral_constant but with an an explicit math support: for example constant<int, 5>{} + constant<int, 3>{} will return an instance of constant<int, 8>. One could also write 5_c + 3_c thanks to the provided user-defined literals.

Design choices

Compile time library

static_math has only been made to be usable at compile time and shall not be used at runtime. It's still possible to use it at runtime though, but it's not well advised.

Since the library is only meant to be used at compile time, some design choices have been made to improve usability, convenience or safety over performance. For example, the rational numbers are simplified after each operation, which could badly alter the performance in a runtime context, but which greatly lessens the risk of overflow in rational operations.

Intuitive feel

One of static_math's aims is to be easy to use. The functions are implemented so that they can be used in a straightforward way. This implies that the user will not have to deal with complex metaprogramming tricks - even though some are used in the implementation.

This intuitive feel is the one reason why static_math needs a recent compiler since the library will need a heavy support for constexpr, std::initializer_list and variadic templates in order to work fine.

Some classes (e.g. rational and complex) use public member variables instead of getters. This simplifies the access to the internals and also ensures that they cannot be modified after construction.

Flexibility

Some classes such as rational or complex make a heavy use of some type traits facilities such as std::common_type in order to offer some flexibility. Many functions accept different number types and return and instance of the common type of the arguments::

// Two different types used to represent numbers
int a = 5;
long int b = 100000;

// The bigger of them is used as the output type
auto c = gcd(a, b); // type is long int

Documentation

You can find some documentation in the associated wiki. You can also generate some anemic documentation thanks to the Doxygen comments in the code. If you want to know more about the details, reading the source code might still be an interesting solution: the code should be pretty straightforward and readable enough. Never hesiste to open a documentation issue if you ever feel that some parts of the documentation are not complete enough or need more examples.