Parameterized Posit Arithmetic Hardware Generator

Chaurasiya, Rohit B.; Gustafson, John L.; Shrestha, Rahul; Neudorfer, Jonathan; Nambiar, Sangeeth; Niyogi, Kaustav; Merchant, Farhad; Leupers, Rainer

doi:10.1109/iccd.2018.00057

Cited by 88 publications

(86 citation statements)

References 8 publications

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“…Although an exact accumulator has been shown to be a cost-effective way of implementing an IEEE-compliant FP16 format [3], for larger formats hardware quire support is not expected to be cheap, as section 6 will show. Indeed, at the time of writing, none of the leading posit hardware developments supports the quire [4,27].…”

Section: The Good: Summations Rounding Properties and Doubled Precismentioning

confidence: 99%

“…This section complements exisiting work comparing hardware implementations of floats and posits [4,27] with a high-level point of view that focuses on architectural parameters and includes a discussion of the quire. range quire parameters custom FP Posits are a form of floating-point numbers whose significand fraction can take a maximum size w f and whose exponent value can fit on w e bits (whatever the encoding of these fractions and significand, e.g.…”

Section: Hardware Considerationsmentioning

confidence: 99%

“…With these simplifications, this three-block implementation embodies the unavoidable amount of work in a posit operation, and leading hardware posit implementations [4,27] follow it. Compared to IEEE floats, it trades the overhead of subnormal and other special cases for the overhead of the LDCs (Leading Digit Counters) and shifts in the conversion units.…”

Section: Hardware Considerationsmentioning

confidence: 99%

“…See https://en.wikipedia.org/wiki/International_System_of_Units and the references therein4 It seems the arithmetic community missed an opportunity to push for binaryrepresentable values... Constants defining the standard international units…”

mentioning

confidence: 99%

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Posits

Dinechin

Forget

Muller

et al. 2019

Proceedings of the Conference for Next Generation Arithmetic 2019

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Many properties of the IEEE-754 floating-point number system are taken for granted in modern computers and are deeply embedded in compilers and low-level software routines such as elementary functions or BLAS. This article reviews such properties on the posit number system. Some are still true. Some are no longer true, but sensible work-arounds are possible, and even represent exciting challenges for the community. Some represent a danger if posits are to replace floating point completely. This study helps framing where posits are better than floating-point, where they are worse, what is the cost of posit hardware, and what tools are missing in the posit landscape. For general-purpose computing, using posits as a storage format could be a way to reap their benefits without losing those of classical floating-point.

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Section: The Good: Summations Rounding Properties and Doubled Precismentioning

confidence: 99%

Section: Hardware Considerationsmentioning

confidence: 99%

Section: Hardware Considerationsmentioning

confidence: 99%

mentioning

confidence: 99%

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Posits

Dinechin

Forget

Muller

et al. 2019

Proceedings of the Conference for Next Generation Arithmetic 2019

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“…We use a Julia-based emulator on a conventional CPU, as posit hardware is not yet available. Posit research currently focuses on hardware implementations [6,7,12,32].…”

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confidence: 99%

Posits as an alternative to floats for weather and climate models

Klöwer

Dueben

Palmer

2019

Proceedings of the Conference for Next Generation Arithmetic 2019

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Posit numbers, a recently proposed alternative to floating-point numbers, claim to have smaller arithmetic rounding errors in many applications. By studying weather and climate models of low and medium complexity (the Lorenz system and a shallow water model) we present benefits of posits compared to floats at 16 bit. As a standardised posit processor does not exist yet, we emulate posit arithmetic on a conventional CPU. Using a shallow water model, forecasts based on 16-bit posits with 1 or 2 exponent bits are clearly more accurate than half precision floats. We therefore propose 16 bit with 2 exponent bits as a standard posit format, as its wide dynamic range of 32 orders of magnitude provides a great potential for many weather and climate models. Although the focus is on geophysical fluid simulations, the results are also meaningful and promising for reduced precision posit arithmetic in the wider field of computational fluid dynamics.

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Computational Techniques

2023

Design for Embedded Image Processing on FPGAs

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Parameterized Posit Arithmetic Hardware Generator

Cited by 88 publications

References 8 publications

Posits

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Posits as an alternative to floats for weather and climate models

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