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With the proliferation of embedded systems requiring intelligent behavior,custom number systems to optimize performance per Watt of the entire systembecome essential components for successful commercial products. We present theUniversal Number Library, a high-performance number systems library thatincludes arbitrary integer, decimal, fixed-point, floating-point, andintroduces two tapered floating-point types, posit and valid, that supportreproducible arithmetic computation in arbitrary concurrency environments. Wediscuss the design of the Universal library as a run-time for applicationdevelopment, and as a platform for application-driven hardware validation. Thelibrary implementation is described, and examples are provided to showeducational examples to elucidate the number system properties, and howspecialization is used to yield very high-performance emulation on existingx86, ARM, and POWER processors. We will highlight the integration of thelibrary in larger application environments in computational science andengineering to enable multi-precision and adaptive precision algorithms toimprove performance and efficiency of large scale and real-time applications.We will demonstrate the integration of the Universal library into ahigh-performance reproducible linear algebra run-time. We will conclude withthe roadmap of additional functionality of the library as we are targeting newapplication domains, such as Software Defined Radio, instrumentation, sensorfusion, and model-predictive control.

Universal Numbers Library: design and implementation of a high-performance reproducible number systems library