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Posit is a recently proposed alternative to the floating point representation (FP). It provides tapered accuracy. Given a fixed number of bits, the posit representation can provide better precision for some numbers compared to FP, which has generated significant interest in numerous domains. Being a representation with tapered accuracy, it can introduce high rounding errors for numbers outside the above golden zone. Programmers currently lack tools to detect and debug errors while programming with posits. This paper presents PositDebug, a compile-time instrumentation that performs shadow execution with high pre- cision values to detect various errors in computation using posits. To assist the programmer in debugging the reported error, PositDebug also provides directed acyclic graphs of instructions, which are likely responsible for the error. A contribution of this paper is the design of the metadata per memory location for shadow execution that enables productive debugging of errors with long-running programs. We have used PositDebug to detect and debug errors in various numerical applications written using posits. To demonstrate that these ideas are applicable even for FP programs, we have built a shadow execution framework for FP programs that is an order of magnitude faster than Herbgrind.
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Posits and the state of numerical representations in the age of exascale and edge computing
Abstract Growing constraints on memory utilization, power consumption, and I/O throughput have increasingly become limiting factors to the advancement of high performance computing (HPC) and edge computing applications. IEEE‐754 floating‐point types have been the de facto standard for floating‐point number systems for decades, but the drawbacks of this numerical representation leave much to be desired. Alternative representations are gaining traction, both in HPC and machine learning environments. Posits have recently been proposed as a drop‐in replacement for the IEEE‐754 floating‐point representation. We survey the state‐of‐the‐art and state‐of‐the‐practice in the development and use of posits in edge computing and HPC. The current literature supports posits as a promising alternative to traditional floating‐point systems, both as a stand‐alone replacement and in a mixed‐precision environment. Development and standardization of the posit type is ongoing, and much research remains to explore the application of posits in different domains, how to best implement them in hardware, and where they fit with other numerical representations.
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- PAR ID:
- 10367705
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Software: Practice and Experience
- Volume:
- 52
- Issue:
- 2
- ISSN:
- 0038-0644
- Page Range / eLocation ID:
- p. 619-635
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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