I designed MOAT to be a math library which provides a common interface for operations used by TOAST and other projects. On the backend, MOAT can be linked against several vendor-optimized libraries. This allows other software to call a consistent API while still using the fastest implementation of a particular operation available on a given machine. MOAT contains modular "frameworks" which can be enabled at configure time. These provide tools for 1D FFTs, special functions, streamed random number generation, and spherical geometry operations.