  With the proliferation of embedded systems requiring intelligent behavior,
custom number systems to optimize performance per Watt of the entire system
become essential components for successful commercial products. We present the
Universal Number Library, a high-performance number systems library that
includes arbitrary integer, decimal, fixed-point, floating-point, and
introduces two tapered floating-point types, posit and valid, that support
reproducible arithmetic computation in arbitrary concurrency environments. We
discuss the design of the Universal library as a run-time for application
development, and as a platform for application-driven hardware validation. The
library implementation is described, and examples are provided to show
educational examples to elucidate the number system properties, and how
specialization is used to yield very high-performance emulation on existing
x86, ARM, and POWER processors. We will highlight the integration of the
library in larger application environments in computational science and
engineering to enable multi-precision and adaptive precision algorithms to
improve performance and efficiency of large scale and real-time applications.
We will demonstrate the integration of the Universal library into a
high-performance reproducible linear algebra run-time. We will conclude with
the roadmap of additional functionality of the library as we are targeting new
application domains, such as Software Defined Radio, instrumentation, sensor
fusion, and model-predictive control.
