To overcome the limitations of conventional floatingpoint
number formats, an interval arithmetic and variablewidth
storage format called universal number (unum) has been
recently introduced . This paper presents the first (to the
best of our knowledge) silicon implementation measurements
of an application-specific integrated circuit (ASIC) for unum
floating-point arithmetic. The designed chip includes a 128-bit
wide unum arithmetic unit to execute additions and subtractions,
while also supporting lossless (for intermediate results) and lossy
(for external data movements) compression units to exploit the
memory usage reduction potential of the unum format. Our chip,
fabricated in a 65 nm CMOS process, achieves a maximum clock
frequency of 413 MHz at 1.2 V with an average measured power
of 210 uW/MHz.
An exclusive release of John Gustafson's active notebook onhis latest Type III Unums (posits) - October 2017.
An exclusive release of John Gustafson's active mathematical notebook on his latest Type III Unums (posits) - October 2017.
This work discusses the implementation of UNUM arithmetic and reports hardware implementation results of some of the UNUM operators.
A discussion on posit computing on 7 August 2017 with regards to John Gustafson's keynote at the HPC Advisory Council Australia Conference.
Supercomputing Asia magzine Issue 02, July 2017 featuring John Gustafson on "How posits revolutionaizing computing".
Dr. Gustafson was invited to Perth in July 2017 to give a keynote on unum. He shares in particular posit, the latest unum type, and how it beats floats.
This page contains a video where Yonemoto uses a "quire" Julia package, which is a data structure intended to be implemented on a binary hardware. He will demonstrate in the video on how he perform an exact solution to a system of linear equations.
A new data type called a "posit" is designed for direct drop-in replacement for IEEE Standard 754 floats. Unlike unum arithmetic, posits do not require interval-type mathematics or variable size operands, and they round if an answer is inexact, much the way floats do. However, they provide compelling advantages over floats, including simpler hardware implementation that scales from as few as two-bit operands to thousands of bits. For any bit width, they have a larger dynamic range, higher accuracy, better closure under arithmetic operations, and simpler exception-handling. For example, posits never overflow to infinity or underflow to zero, and there is no "Not-a-Number" (NaN) value. Posits should take up less space to implement in silicon than an IEEE float of the same size. With fewer gate delays per operation as well as lower silicon footprint, the posit operations per second (POPS) supported by a chip can be significantly higher than the FLOPs using similar hardware resources. GPU accelerators, in particular, could do more arithmetic per watt and per dollar yet deliver superior answer quality.
A series of comprehensive benchmarks compares how many decimals of accuracy can be produced for a set number of bits-per-value, using various number formats. Low-precision posits provide a better solution than "approximate computing" methods that try to tolerate decreases in answer quality. High-precision posits provide better answers (more correct decimals) than floats of the same size, suggesting that in some cases, a 32-bit posit may do a better job than a 64-bit float. In other words, posits beat floats at their own game.
A new data type called a posit is designed as a direct drop-in replacement for IEEE Standard 754 floating-point numbers (floats). Unlike earlier forms of universal number (unum) arithmetic, posits do not require interval arithmetic or variable size operands; like floats, they round if an answer is inexact. However, they provide compelling advantages over floats, including larger dynamic range, higher accuracy, better closure, bitwise identical results across systems, simpler hardware, and simpler exception handling. Posits never overflow to infinity or underflow to zero, and “Nota-Number”
(NaN) indicates an action instead of a bit pattern. A posit processing unit takes less circuitry than an IEEE float FPU. With lower power use and smaller silicon footprint, the posit operations per second (POPS) supported by a chip can be significantly higher than the FLOPS
using similar hardware resources. GPU accelerators and Deep Learning processors, in particular, can do more per watt and per dollar with posits, yet deliver superior answer quality.
A comprehensive series of benchmarks compares floats and posits for decimals of accuracy produced for a set precision. Low precision posits provide a better solution than “approximate computing” methods that try to tolerate decreased answer quality. High precision posits provide more correct decimals than floats of the same size; in some cases, a 32-bit posit may safely replace a 64-bit float. In other words, posits beat floats at their own game.
Gustafson slides: http://arith23.gforge.inria.fr/slides/Gustafson.pdf
Kahan slides: http://arith23.gforge.inria.fr/slides/Kahan.pdf
Full transcription of debate by John Gustafson: http://www.johngustafson.net/pdfs/DebateTranscription.pdf