# bibtab

bibtype: article
filename: fparith.bib
label: Zou:2020:DFP
author: Daming Zou and Muhan Zeng and Yingfei Xiong and Zhoulai Fu and Lu Zhang and Zhendong Su
title: Detecting floating-point errors via atomic conditions
journal: j-PACMPL
volume: 4
number: POPL
pages: 60:1--60:27
month: jan
monthnumber: 1
year: 2020
DOI: https://doi.org/10.1145/3371128
ISSN: 2475-1421 OR 24751421
bibdate: Fri Aug 7 18:46:52 MDT 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/pacmpl.bib
bibtimestamp: 2020.08.07 18:46:52 MDT
URL: https://dl.acm.org/doi/abs/10.1145/3371128
fjournal: Proceedings of the ACM on Programming Languages
acknowledgement: ack-nhfb
articleno: 60
journalURL: https://pacmpl.acm.org/
rawauthor: Daming Zou and Muhan Zeng and Yingfei Xiong and Zhoulai Fu and Lu Zhang and Zhendong Su
rawtitle: Detecting floating-point errors via atomic conditions
abstract:
This paper tackles the important, difficult problem of detecting program inputs that trigger large floating-point errors in numerical code. It introduces a novel, principled em dynamic analysis that leverages the mathematically rigorously analyzed em condition numbers for atomic numerical operations, which we call em atomic conditions, to effectively guide the search for large floating-point errors. Compared with existing approaches, our work based on atomic conditions has several distinctive benefits: (1) it does not rely on high-precision implementations to act as approximate oracles, which are difficult to obtain in general and computationally costly; and (2) atomic conditions provide accurate, modular search guidance. These benefits in combination lead to a highly effective approach that detects more significant errors in real-world code (e.g., widely-used numerical library functions) and achieves several orders of speedups over the state-of-the-art, thus making error analysis significantly more practical. We expect the methodology and principles behind our approach to benefit other floating-point program analysis tasks such as debugging, repair and synthesis. To facilitate the reproduction of our work, we have made our implementation, evaluation data and results publicly available on GitHub at url https://github.com/FP-Analysis/atomic-condition

rawabstract:
This paper tackles the important, difficult problem of detecting program inputs that trigger large floating-point errors in numerical code. It introduces a novel, principled {\em dynamic analysis\/} that leverages the mathematically rigorously analyzed {\em condition numbers\/} for atomic numerical operations, which we call {\em atomic conditions}, to effectively guide the search for large floating-point errors. Compared with existing approaches, our work based on atomic conditions has several distinctive benefits: (1) it does not rely on high-precision implementations to act as approximate oracles, which are difficult to obtain in general and computationally costly; and (2) atomic conditions provide accurate, modular search guidance. These benefits in combination lead to a highly effective approach that detects more significant errors in real-world code (e.g., widely-used numerical library functions) and achieves several orders of speedups over the state-of-the-art, thus making error analysis significantly more practical. We expect the methodology and principles behind our approach to benefit other floating-point program analysis tasks such as debugging, repair and synthesis. To facilitate the reproduction of our work, we have made our implementation, evaluation data and results publicly available on GitHub at \url{https://github.com/FP-Analysis/atomic-condition}

entry:
@Article{Zou:2020:DFP,
  author =       "Daming Zou and Muhan Zeng and Yingfei Xiong and
                 Zhoulai Fu and Lu Zhang and Zhendong Su",
  title =        "Detecting floating-point errors via atomic
                 conditions",
  journal =      j-PACMPL,
  volume =       "4",
  number =       "POPL",
  pages =        "60:1--60:27",
  month =        jan,
  year =         "2020",
  DOI =          "https://doi.org/10.1145/3371128",
  ISSN =         "2475-1421",
  bibdate =      "Fri Aug 7 18:46:52 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3371128",
  abstract =     "This paper tackles the important, difficult problem of
                 detecting program inputs that trigger large
                 floating-point errors in numerical code. It introduces
                 a novel, principled {\em dynamic analysis\/} that
                 leverages the mathematically rigorously analyzed {\em
                 condition numbers\/} for atomic numerical operations,
                 which we call {\em atomic conditions}, to effectively
                 guide the search for large floating-point errors.
                 Compared with existing approaches, our work based on
                 atomic conditions has several distinctive benefits: (1)
                 it does not rely on high-precision implementations to
                 act as approximate oracles, which are difficult to
                 obtain in general and computationally costly; and (2)
                 atomic conditions provide accurate, modular search
                 guidance. These benefits in combination lead to a
                 highly effective approach that detects more significant
                 errors in real-world code (e.g., widely-used numerical
                 library functions) and achieves several orders of
                 speedups over the state-of-the-art, thus making error
                 analysis significantly more practical. We expect the
                 methodology and principles behind our approach to
                 benefit other floating-point program analysis tasks
                 such as debugging, repair and synthesis. To facilitate
                 the reproduction of our work, we have made our
                 implementation, evaluation data and results publicly
                 available on GitHub at
                 \url{https://github.com/FP-Analysis/atomic-condition}",
  acknowledgement = ack-nhfb,
  articleno =    "60",
  fjournal =     "Proceedings of the ACM on Programming Languages",
  journal-URL =  "https://pacmpl.acm.org/",
}


bibtype: article
filename: fparith.bib
label: Ahn:2021:KSK
title: Keeping science on keel when software moves
journal: j-CACM
volume: 64
number: 2
pages: 66--74
month: feb
monthnumber: 2
year: 2021
CODEN: CACMA2
DOI: https://doi.org/10.1145/3382037
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Jan 26 14:34:25 MST 2021
bibtimestamp: 2021.01.26 14:34:25 MST
URL: https://dl.acm.org/doi/10.1145/3382037
abstract: An approach to reproducibility problems related to porting software across machines and compilers.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
ajournal: Commun. ACM
journalURL: https://dl.acm.org/loi/cacm
rawabstract: An approach to reproducibility problems related to porting software across machines and compilers.
rawtitle: Keeping science on keel when software moves
author:
Dong H. Ahn and Allison H. Baker and Michael Bentley and Ian Briggs and Ganesh Gopalakrishnan and Dorit M. Hammerling and Ignacio Laguna and Gregory L. Lee and Daniel J. Milroy and Mariana Vertenstein

bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm2020.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawauthor:
Dong H. Ahn and Allison H. Baker and Michael Bentley and Ian Briggs and Ganesh Gopalakrishnan and Dorit M. Hammerling and Ignacio Laguna and Gregory L. Lee and Daniel J. Milroy and Mariana Vertenstein

entry:
@Article{Ahn:2021:KSK,
  author =       "Dong H. Ahn and Allison H. Baker and Michael Bentley
                 and Ian Briggs and Ganesh Gopalakrishnan and Dorit M.
                 Hammerling and Ignacio Laguna and Gregory L. Lee and
                 Daniel J. Milroy and Mariana Vertenstein",
  title =        "Keeping science on keel when software moves",
  journal =      j-CACM,
  volume =       "64",
  number =       "2",
  pages =        "66--74",
  month =        feb,
  year =         "2021",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/3382037",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Jan 26 14:34:25 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3382037",
  abstract =     "An approach to reproducibility problems related to
                 porting software across machines and compilers.",
  acknowledgement = ack-nhfb,
  ajournal =     "Commun. ACM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: inproceedings
filename: fparith.bib
label: Alouani:2021:IIR
author: Ihsen Alouani and Anouar Ben Khalifa and Farhad Merchant and Rainer Leupers
editor: IEEE
title: An Investigation on Inherent Robustness of Posit Data Representation
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 276--281
year: 2021
DOI: https://doi.org/10.1109/VLSID51830.2021.00052
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Ihsen Alouani and Anouar {Ben Khalifa} and Farhad Merchant and Rainer Leupers
raweditor: {IEEE}
rawtitle: An Investigation on Inherent Robustness of Posit Data Representation
booktitle:
2021 34th International Conference on VLSI Design and 2021 20th International Conference on Embedded Systems (VLSID)

rawbooktitle:
{2021 34th International Conference on VLSI Design and 2021 20th International Conference on Embedded Systems (VLSID)}

entry:
@InProceedings{Alouani:2021:IIR,
  author =       "Ihsen Alouani and Anouar {Ben Khalifa} and Farhad
                 Merchant and Rainer Leupers",
  editor =       "{IEEE}",
  booktitle =    "{2021 34th International Conference on VLSI Design and
                 2021 20th International Conference on Embedded Systems
                 (VLSID)}",
  title =        "An Investigation on Inherent Robustness of Posit Data
                 Representation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "276--281",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/VLSID51830.2021.00052",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2021:AI
author: Anonymous
title: Author Index
crossref: IEEE:2021:ISC
pages: 141--141
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00037
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Author Index
entry:
@InProceedings{Anonymous:2021:AI,
  author =       "Anonymous",
  title =        "Author Index",
  crossref =     "IEEE:2021:ISC",
  pages =        "141--141",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00037",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2021:CN
author: Anonymous
title: [Copyright notice]
crossref: IEEE:2021:ISC
pages: 1--1
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00003
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: [{Copyright} notice]
entry:
@InProceedings{Anonymous:2021:CN,
  author =       "Anonymous",
  title =        "[{Copyright} notice]",
  crossref =     "IEEE:2021:ISC",
  pages =        "1--1",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00003",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2021:FC
author: Anonymous
title: [Front cover]
crossref: IEEE:2021:ISC
pages: 1--1
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00002
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: [{Front} cover]
entry:
@InProceedings{Anonymous:2021:FC,
  author =       "Anonymous",
  title =        "[{Front} cover]",
  crossref =     "IEEE:2021:ISC",
  pages =        "1--1",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00002",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2021:IPA
author: Anonymous
title: Industry Panel ARITH 2021: Processors for the Computing of the 2020s
crossref: IEEE:2021:ISC
pages: xv--xv
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00010
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Industry Panel {ARITH 2021}: Processors for the Computing of the 2020s
entry:
@InProceedings{Anonymous:2021:IPA,
  author =       "Anonymous",
  title =        "Industry Panel {ARITH 2021}: Processors for the
                 Computing of the 2020s",
  crossref =     "IEEE:2021:ISC",
  pages =        "xv--xv",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00010",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2021:PCA
author: Anonymous
title: Program Committee ARITH 2021
crossref: IEEE:2021:ISC
pages: xii--xii
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00007
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Program Committee {ARITH 2021}
entry:
@InProceedings{Anonymous:2021:PCA,
  author =       "Anonymous",
  title =        "Program Committee {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xii--xii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00007",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2021:SA
author: Anonymous
title: Sponsors ARITH 2021
crossref: IEEE:2021:ISC
pages: xviii--xviii
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00012
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Sponsors {ARITH 2021}
entry:
@InProceedings{Anonymous:2021:SA,
  author =       "Anonymous",
  title =        "Sponsors {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xviii--xviii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00012",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2021:SCA
author: Anonymous
title: Steering Committee ARITH 2021
crossref: IEEE:2021:ISC
pages: xiii--xiii
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00008
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Steering Committee {ARITH 2021}
entry:
@InProceedings{Anonymous:2021:SCA,
  author =       "Anonymous",
  title =        "Steering Committee {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xiii--xiii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00008",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2021:TC
author: Anonymous
title: Table of Contents
crossref: IEEE:2021:ISC
pages: v--viii
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00004
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Table of Contents
entry:
@InProceedings{Anonymous:2021:TC,
  author =       "Anonymous",
  title =        "Table of Contents",
  crossref =     "IEEE:2021:ISC",
  pages =        "v--viii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00004",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2021:TP
author: Anonymous
title: [Title page]
crossref: IEEE:2021:ISC
pages: 1--1
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00001
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: [{Title} page]
entry:
@InProceedings{Anonymous:2021:TP,
  author =       "Anonymous",
  title =        "[{Title} page]",
  crossref =     "IEEE:2021:ISC",
  pages =        "1--1",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00001",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Ashmawy:2021:FHI
author: Doaa Ashmawy and Arash Reyhani-Masoleh
title: A Faster Hardware Implementation of the AES S-box
crossref: IEEE:2021:ISC
pages: 123--130
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00034
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Doaa Ashmawy and Arash Reyhani-Masoleh
rawtitle: A Faster Hardware Implementation of the {AES} {S}-box
entry:
@InProceedings{Ashmawy:2021:FHI,
  author =       "Doaa Ashmawy and Arash Reyhani-Masoleh",
  title =        "A Faster Hardware Implementation of the {AES}
                 {S}-box",
  crossref =     "IEEE:2021:ISC",
  pages =        "123--130",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00034",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Bagnara:2021:PAV
author: Roberto Bagnara and Michele Chiari and Roberta Gori and Abramo Bagnara
journal: j-TOSEM
volume: 30
number: 1
pages: 9:1--9:53
month: jan
monthnumber: 1
year: 2021
CODEN: ATSMER
DOI: https://doi.org/10.1145/3410875
ISSN: 1049-331X (print), 1557-7392 (electronic) OR 1049331X (print), 15577392 (electronic)
ISSNL: 1049-331X OR 1049331X
bibdate: Fri Jan 22 07:02:14 MST 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/tosem.bib
bibtimestamp: 2021.01.22 07:02:14 MST
URL: https://dl.acm.org/doi/10.1145/3410875
fjournal: ACM Transactions on Software Engineering and Methodology
acknowledgement: ack-nhfb
articleno: 9
journalURL: https://dl.acm.org/loi/tosem
rawauthor: Roberto Bagnara and Michele Chiari and Roberta Gori and Abramo Bagnara
title:
A Practical Approach to Verification of Floating-Point C / C++ Programs with tt math.h / tt cmath Functions

abstract:
Verification of C/C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the computed results. This would seem to prevent any attempt at formal verification of programs that use them: without a specification for the functions, no conclusion can be drawn statically about the behavior of the program. We propose an alternative to surrender. We introduce a pragmatic approach that leverages the fact that most tt math.h / tt cmath functions are almost piecewise monotonic: as we discovered through exhaustive testing, they may have glitches, often of very small size and in small numbers. We develop interval refinement techniques for such functions based on a modified dichotomic search, which enable verification via symbolic execution based model checking, abstract interpretation, and test data generation. To the best of our knowledge, our refinement algorithms are the first in the literature to be able to handle non-correctly rounded function implementations, enabling verification in the presence of the most common implementations. We experimentally evaluate our approach on real-world code, showing its ability to detect or rule out anomalous behaviors.

rawabstract:
Verification of C/C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the computed results. This would seem to prevent any attempt at formal verification of programs that use them: without a specification for the functions, no conclusion can be drawn statically about the behavior of the program. We propose an alternative to surrender. We introduce a pragmatic approach that leverages the fact that most {\tt math.h}\slash {\tt cmath} functions are almost piecewise monotonic: as we discovered through exhaustive testing, they may have glitches, often of very small size and in small numbers. We develop interval refinement techniques for such functions based on a modified dichotomic search, which enable verification via symbolic execution based model checking, abstract interpretation, and test data generation. To the best of our knowledge, our refinement algorithms are the first in the literature to be able to handle non-correctly rounded function implementations, enabling verification in the presence of the most common implementations. We experimentally evaluate our approach on real-world code, showing its ability to detect or rule out anomalous behaviors.

rawtitle:
A Practical Approach to Verification of Floating-Point {C\slash C++} Programs with {\tt math.h}\slash {\tt cmath} Functions

entry:
@Article{Bagnara:2021:PAV,
  author =       "Roberto Bagnara and Michele Chiari and Roberta Gori
                 and Abramo Bagnara",
  title =        "A Practical Approach to Verification of Floating-Point
                 {C\slash C++} Programs with {\tt math.h}\slash {\tt
                 cmath} Functions",
  journal =      j-TOSEM,
  volume =       "30",
  number =       "1",
  pages =        "9:1--9:53",
  month =        jan,
  year =         "2021",
  CODEN =        "ATSMER",
  DOI =          "https://doi.org/10.1145/3410875",
  ISSN =         "1049-331X (print), 1557-7392 (electronic)",
  ISSN-L =       "1049-331X",
  bibdate =      "Fri Jan 22 07:02:14 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tosem.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3410875",
  abstract =     "Verification of C/C++ programs has seen considerable
                 progress in several areas, but not for programs that
                 use these languages' mathematical libraries. The reason
                 is that all libraries in widespread use come with no
                 guarantees about the computed results. This would seem
                 to prevent any attempt at formal verification of
                 programs that use them: without a specification for the
                 functions, no conclusion can be drawn statically about
                 the behavior of the program. We propose an alternative
                 to surrender. We introduce a pragmatic approach that
                 leverages the fact that most {\tt math.h}\slash {\tt
                 cmath} functions are almost piecewise monotonic: as we
                 discovered through exhaustive testing, they may have
                 glitches, often of very small size and in small
                 numbers. We develop interval refinement techniques for
                 such functions based on a modified dichotomic search,
                 which enable verification via symbolic execution based
                 model checking, abstract interpretation, and test data
                 generation. To the best of our knowledge, our
                 refinement algorithms are the first in the literature
                 to be able to handle non-correctly rounded function
                 implementations, enabling verification in the presence
                 of the most common implementations. We experimentally
                 evaluate our approach on real-world code, showing its
                 ability to detect or rule out anomalous behaviors.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Software Engineering and
                 Methodology",
  journal-URL =  "https://dl.acm.org/loi/tosem",
}


bibtype: misc
filename: fparith.bib
label: Bailey:2021:PMN
author: David H. Bailey
title: pkg MPFUN2020: A new thread-safe arbitrary precision package
pages: 54
day: 18
month: may
monthnumber: 5
year: 2021
bibdate: Mon Dec 05 07:32:16 2022
bibtimestamp: 2022.12.05 07:32:16 ???
URL: https://www.davidhbailey.com/dhbpapers/mpfun2020.pdf
acknowledgement: ack-nhfb
howpublished: Web document
rawauthor: David H. Bailey
rawtitle: \pkg{MPFUN2020}: A new thread-safe arbitrary precision package
abstract:
Numerous research studies have arisen, particularly in mathematical physics and experimental mathematics, that require extremely high numeric precision. Such precision greatly magnifies computer run times, so software packages to support high-precision computing must be designed for thread-based parallel processing. This paper describes a new arbitrary precision software package (``MPFUN2020'') that features several significant improvements over an earlier package. It comes in two versions: a self-contained all-Fortran version, and a version based on the MPFR package, which is even faster. Both versions feature: (a) a completely thread-safe design, so user codes can be converted for parallel execution at the application level; (b) a full-featured high-level Fortran interface, so that most applications can be converted to multiprecision with relatively minor changes to source code; (c) full support for both real and complex datatypes; (d) a wide variety of transcendental functions and special functions; (e) run-time checking and other facilities to overcome problems with converting double precision constants and data; (f) a medium precision datatype, which improves performance and reduces memory cost on large variable precision applications; and (g) interoperability --- with a simple restriction, application codes written for one version can be run with the other without change.

rawabstract:
Numerous research studies have arisen, particularly in mathematical physics and experimental mathematics, that require extremely high numeric precision. Such precision greatly magnifies computer run times, so software packages to support high-precision computing must be designed for thread-based parallel processing. This paper describes a new arbitrary precision software package (``MPFUN2020'') that features several significant improvements over an earlier package. It comes in two versions: a self-contained all-Fortran version, and a version based on the MPFR package, which is even faster. Both versions feature: (a) a completely thread-safe design, so user codes can be converted for parallel execution at the application level; (b) a full-featured high-level Fortran interface, so that most applications can be converted to multiprecision with relatively minor changes to source code; (c) full support for both real and complex datatypes; (d) a wide variety of transcendental functions and special functions; (e) run-time checking and other facilities to overcome problems with converting double precision constants and data; (f) a medium precision datatype, which improves performance and reduces memory cost on large variable precision applications; and (g) interoperability --- with a simple restriction, application codes written for one version can be run with the other without change.

entry:
@Misc{Bailey:2021:PMN,
  author =       "David H. Bailey",
  title =        "\pkg{MPFUN2020}: A new thread-safe arbitrary precision
                 package",
  howpublished = "Web document",
  pages =        "54",
  day =          "18",
  month =        may,
  year =         "2021",
  bibdate =      "Mon Dec 05 07:32:16 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.davidhbailey.com/dhbpapers/mpfun2020.pdf",
  abstract =     "Numerous research studies have arisen, particularly in
                 mathematical physics and experimental mathematics, that
                 require extremely high numeric precision. Such
                 precision greatly magnifies computer run times, so
                 software packages to support high-precision computing
                 must be designed for thread-based parallel
                 processing.

                 This paper describes a new arbitrary precision software
                 package (``MPFUN2020'') that features several
                 significant improvements over an earlier package. It
                 comes in two versions: a self-contained all-Fortran
                 version, and a version based on the MPFR package, which
                 is even faster. Both versions feature: (a) a completely
                 thread-safe design, so user codes can be converted for
                 parallel execution at the application level; (b) a
                 full-featured high-level Fortran interface, so that
                 most applications can be converted to multiprecision
                 with relatively minor changes to source code; (c) full
                 support for both real and complex datatypes; (d) a wide
                 variety of transcendental functions and special
                 functions; (e) run-time checking and other facilities
                 to overcome problems with converting double precision
                 constants and data; (f) a medium precision datatype,
                 which improves performance and reduces memory cost on
                 large variable precision applications; and (g)
                 interoperability --- with a simple restriction,
                 application codes written for one version can be run
                 with the other without change.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Bajard:2021:GRN
title: Generating Residue Number System Bases
crossref: IEEE:2021:ISC
pages: 86--93
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00027
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawtitle: Generating Residue Number System Bases
author:
Jean-Claude Bajard and Kazuhide Fukushima and Shinsaku Kiyomoto and Thomas Plantard and Arnaud Sipasseuth and Willy Susilo

rawauthor:
Jean-Claude Bajard and Kazuhide Fukushima and Shinsaku Kiyomoto and Thomas Plantard and Arnaud Sipasseuth and Willy Susilo

entry:
@InProceedings{Bajard:2021:GRN,
  author =       "Jean-Claude Bajard and Kazuhide Fukushima and Shinsaku
                 Kiyomoto and Thomas Plantard and Arnaud Sipasseuth and
                 Willy Susilo",
  title =        "Generating Residue Number System Bases",
  crossref =     "IEEE:2021:ISC",
  pages =        "86--93",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00027",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Bertaccini:2021:TFL
editor: IEEE
booktitle: 2021 IEEE International Symposium on Circuits and Systems (ISCAS)
title: Tiny-FPU: Low-Cost Floating-Point Support for Small RISC-V MCU Cores
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--5
year: 2021
DOI: https://doi.org/10.1109/ISCAS51556.2021.9401149
bibdate: Sat Dec 16 15:51:40 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.12.16 15:51:40 ???
acknowledgement: ack-nhfb
rawbooktitle: {2021 IEEE International Symposium on Circuits and Systems (ISCAS)}
raweditor: {IEEE}
rawtitle: {Tiny-FPU}: Low-Cost Floating-Point Support for Small {RISC-V MCU} Cores
author:
Luca Bertaccini and Matteo Perotti and Stefan Mach and Pasquale Davide Schiavone and Florian Zaruba and Luca Benini

rawauthor:
Luca Bertaccini and Matteo Perotti and Stefan Mach and Pasquale Davide Schiavone and Florian Zaruba and Luca Benini

entry:
@InProceedings{Bertaccini:2021:TFL,
  author =       "Luca Bertaccini and Matteo Perotti and Stefan Mach and
                 Pasquale Davide Schiavone and Florian Zaruba and Luca
                 Benini",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "{Tiny-FPU}: Low-Cost Floating-Point Support for Small
                 {RISC-V MCU} Cores",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISCAS51556.2021.9401149",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Bigou:2021:ERA
author: Karim Bigou and Mojtaba Bisheh Niasar and Luis Fiolhais and Rogerio Paludo and Hwajeong Seo
title: External Reviewers ARITH 2021
crossref: IEEE:2021:ISC
pages: xiv--xiv
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00009
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Karim Bigou and Mojtaba Bisheh Niasar and Lu{\'\i}s Fiolhais and Rogerio Paludo and Hwajeong Seo
rawtitle: External Reviewers {ARITH 2021}
entry:
@InProceedings{Bigou:2021:ERA,
  author =       "Karim Bigou and Mojtaba Bisheh Niasar and Lu{\'\i}s
                 Fiolhais and Rogerio Paludo and Hwajeong Seo",
  title =        "External Reviewers {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xiv--xiv",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00009",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Bisheh-Niasar:2021:HSN
author: Mojtaba Bisheh-Niasar and Reza Azarderakhsh and Mehran Mozaffari-Kermani
title: High-Speed NTT-based Polynomial Multiplication Accelerator for Post-Quantum Cryptography
crossref: IEEE:2021:ISC
pages: 94--101
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00028
bibdate: Thu Sep 21 10:36:08 2023
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Mojtaba Bisheh-Niasar and Reza Azarderakhsh and Mehran Mozaffari-Kermani
rawtitle: High-Speed {NTT}-based Polynomial Multiplication Accelerator for Post-Quantum Cryptography
bibsource:
https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@InProceedings{Bisheh-Niasar:2021:HSN,
  author =       "Mojtaba Bisheh-Niasar and Reza Azarderakhsh and Mehran
                 Mozaffari-Kermani",
  title =        "High-Speed {NTT}-based Polynomial Multiplication
                 Accelerator for Post-Quantum Cryptography",
  crossref =     "IEEE:2021:ISC",
  pages =        "94--101",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00028",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Boldo:2021:ERN
author: Sylvie Boldo and Christoph Quirin Lauter and Jean-Michel Muller
journal: j-IEEE-TRANS-COMPUT
volume: 70
number: 7
pages: 1046--1058
month: jul
monthnumber: 7
year: 2021
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2020.3002702
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jun 10 15:51:57 2021
bibtimestamp: 2021.06.10 15:51:57 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Sylvie Boldo and Christoph Quirin Lauter and Jean-Michel Muller
title:
Emulating Round-to-Nearest-Ties-to-Zero ``augmented'' Floating-Point Operations Using Round-to-Nearest-Ties-to-Even Arithmetic

rawtitle:
Emulating Round-to-Nearest-Ties-to-Zero ``augmented'' Floating-Point Operations Using Round-to-Nearest-Ties-to-Even Arithmetic

entry:
@Article{Boldo:2021:ERN,
  author =       "Sylvie Boldo and Christoph Quirin Lauter and
                 Jean-Michel Muller",
  title =        "Emulating Round-to-Nearest-Ties-to-Zero ``augmented''
                 Floating-Point Operations Using
                 Round-to-Nearest-Ties-to-Even Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "7",
  pages =        "1046--1058",
  month =        jul,
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.3002702",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jun 10 15:51:57 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Boldo:2021:SFT
author: Sylvie Boldo and Guillaume Melquiond
title: Some Formal Tools for Computer Arithmetic: Flocq and Gappa
crossref: IEEE:2021:ISC
pages: 111--114
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00031
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Sylvie Boldo and Guillaume Melquiond
rawtitle: Some Formal Tools for Computer Arithmetic: {Flocq} and {Gappa}
entry:
@InProceedings{Boldo:2021:SFT,
  author =       "Sylvie Boldo and Guillaume Melquiond",
  title =        "Some Formal Tools for Computer Arithmetic: {Flocq} and
                 {Gappa}",
  crossref =     "IEEE:2021:ISC",
  pages =        "111--114",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00031",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Borges:2021:AIA
author: Carlos F. Borges
title: Algorithm 1014: an Improved Algorithm for tt hypot(x,y)
journal: j-TOMS
volume: 47
number: 1
pages: 9:1--9:12
month: jan
monthnumber: 1
year: 2021
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3428446
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Jan 7 10:31:04 MST 2021
bibtimestamp: 2021.01.07 10:31:04 MST
URL: https://dl.acm.org/doi/10.1145/3428446
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 9
journalURL: https://dl.acm.org/loi/toms
rawauthor: Carlos F. Borges
rawtitle: {Algorithm 1014}: an Improved Algorithm for {\tt hypot(x,y)}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/julia.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
We develop fast and accurate algorithms for evaluating $ sqrt x^2 + y^2 $ for two floating-point numbers $x$ and $y$. Library functions that perform this computation are generally named tt hypot(x,y). We compare five approaches that we will develop in this article to the current resident library function that is delivered with Julia 1.1 and to the code that has been distributed with the C math library for decades. We will investigate the accuracy of our algorithms by simulation.

rawabstract:
We develop fast and accurate algorithms for evaluating $ \sqrt {x^2 + y^2} $ for two floating-point numbers $x$ and $y$. Library functions that perform this computation are generally named {\tt hypot(x,y)}. We compare five approaches that we will develop in this article to the current resident library function that is delivered with Julia 1.1 and to the code that has been distributed with the C math library for decades. We will investigate the accuracy of our algorithms by simulation.

entry:
@Article{Borges:2021:AIA,
  author =       "Carlos F. Borges",
  title =        "{Algorithm 1014}: an Improved Algorithm for {\tt
                 hypot(x,y)}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "9:1--9:12",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3428446",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3428446",
  abstract =     "We develop fast and accurate algorithms for evaluating
                 $ \sqrt {x^2 + y^2} $ for two floating-point numbers
                 $x$ and $y$. Library functions that perform this
                 computation are generally named {\tt hypot(x,y)}. We
                 compare five approaches that we will develop in this
                 article to the current resident library function that
                 is delivered with Julia 1.1 and to the code that has
                 been distributed with the C math library for decades.
                 We will investigate the accuracy of our algorithms by
                 simulation.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Borges:2021:CRN
author: Carlos F. Borges
title: A Correctly Rounded Newton Step for the Reciprocal Square Root
journal: arXiv.org
pages: 1--8
day: 28
month: dec
monthnumber: 12
year: 2021
bibdate: Fri Sep 22 16:08:53 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.22 16:08:53 ???
URL: https://arxiv.org/abs/2112.14321
acknowledgement: ack-nhfb
rawauthor: Carlos F. Borges
rawtitle: A Correctly Rounded {Newton} Step for the Reciprocal Square Root
abstract:
The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example cite Moroz,863046,863031 and the references therein). A common theme is the use of Newton's method to refine the estimates. In this paper we develop a correctly rounded Newton step that can be used to improve the accuracy of a naive calculation (using methods similar to those developed in cite borges) The approach relies on the use of the fused multiply-add (FMA) which is widely available in hardware on a variety of modern computer architectures. We then introduce the notion of em weak rounding and prove that our proposed algorithm meets this standard. We then show how to leverage the exact Newton step to get a Halley's method compensation which requires one additional FMA and one additional multiplication. This method appears to give correctly rounded results experimentally and we show that it can be combined with a square root free method for estimating the reciprocal square root to get a method that is both very fast (in computing environments with a slow square root) and, experimentally, highly accurate.

rawabstract:
The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example \cite{Moroz,863046,863031} and the references therein). A common theme is the use of Newton's method to refine the estimates. In this paper we develop a correctly rounded Newton step that can be used to improve the accuracy of a naive calculation (using methods similar to those developed in \cite{borges}) The approach relies on the use of the fused multiply-add (FMA) which is widely available in hardware on a variety of modern computer architectures. We then introduce the notion of {\em weak rounding} and prove that our proposed algorithm meets this standard. We then show how to leverage the exact Newton step to get a Halley's method compensation which requires one additional FMA and one additional multiplication. This method appears to give correctly rounded results experimentally and we show that it can be combined with a square root free method for estimating the reciprocal square root to get a method that is both very fast (in computing environments with a slow square root) and, experimentally, highly accurate.

entry:
@Article{Borges:2021:CRN,
  author =       "Carlos F. Borges",
  title =        "A Correctly Rounded {Newton} Step for the Reciprocal
                 Square Root",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--8",
  day =          "28",
  month =        dec,
  year =         "2021",
  bibdate =      "Fri Sep 22 16:08:53 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2112.14321",
  abstract =     "The reciprocal square root is an important computation
                 for which many sophisticated algorithms exist (see for
                 example \cite{Moroz,863046,863031} and the references
                 therein). A common theme is the use of Newton's method
                 to refine the estimates. In this paper we develop a
                 correctly rounded Newton step that can be used to
                 improve the accuracy of a naive calculation (using
                 methods similar to those developed in \cite{borges})
                 The approach relies on the use of the fused
                 multiply-add (FMA) which is widely available in
                 hardware on a variety of modern computer architectures.
                 We then introduce the notion of {\em weak rounding} and
                 prove that our proposed algorithm meets this standard.
                 We then show how to leverage the exact Newton step to
                 get a Halley's method compensation which requires one
                 additional FMA and one additional multiplication. This
                 method appears to give correctly rounded results
                 experimentally and we show that it can be combined with
                 a square root free method for estimating the reciprocal
                 square root to get a method that is both very fast (in
                 computing environments with a slow square root) and,
                 experimentally, highly accurate.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Borges:2021:FCA
author: Carlos F. Borges
journal: arXiv.org
pages: 1--11
day: 23
month: feb
monthnumber: 2
year: 2021
bibdate: Fri Sep 22 16:05:47 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.22 16:05:47 ???
URL: https://arxiv.org/abs/2103.08694
acknowledgement: ack-nhfb
rawauthor: Carlos F. Borges
title:
Fast compensated algorithms for the reciprocal square root, the reciprocal hypotenuse, and Givens rotations

abstract:
The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example cite 863046,863031 and the references therein). In this paper we develop a simple differential compensation (much like those developed in cite borges) that can be used to improve the accuracy of a naive calculation. The approach relies on the use of the fused multiply-add (FMA) which is widely available in hardware on a variety of modern computer architectures. We then demonstrate how to combine this approach with a somewhat inaccurate but fast square root free method for estimating the reciprocal square root to get a method that is both fast (in computing environments with a slow square root) and, experimentally, highly accurate. Finally, we show how this same approach can be extended to the reciprocal hypotenuse calculation and, most importantly, to the construction of Givens rotations.

rawabstract:
The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example \cite{863046,863031} and the references therein). In this paper we develop a simple differential compensation (much like those developed in \cite{borges}) that can be used to improve the accuracy of a naive calculation. The approach relies on the use of the fused multiply-add (FMA) which is widely available in hardware on a variety of modern computer architectures. We then demonstrate how to combine this approach with a somewhat inaccurate but fast square root free method for estimating the reciprocal square root to get a method that is both fast (in computing environments with a slow square root) and, experimentally, highly accurate. Finally, we show how this same approach can be extended to the reciprocal hypotenuse calculation and, most importantly, to the construction of Givens rotations.

rawtitle:
Fast compensated algorithms for the reciprocal square root, the reciprocal hypotenuse, and {Givens} rotations

entry:
@Article{Borges:2021:FCA,
  author =       "Carlos F. Borges",
  title =        "Fast compensated algorithms for the reciprocal square
                 root, the reciprocal hypotenuse, and {Givens}
                 rotations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--11",
  day =          "23",
  month =        feb,
  year =         "2021",
  bibdate =      "Fri Sep 22 16:05:47 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2103.08694",
  abstract =     "The reciprocal square root is an important computation
                 for which many very sophisticated algorithms exist (see
                 for example \cite{863046,863031} and the references
                 therein). In this paper we develop a simple
                 differential compensation (much like those developed in
                 \cite{borges}) that can be used to improve the accuracy
                 of a naive calculation. The approach relies on the use
                 of the fused multiply-add (FMA) which is widely
                 available in hardware on a variety of modern computer
                 architectures. We then demonstrate how to combine this
                 approach with a somewhat inaccurate but fast square
                 root free method for estimating the reciprocal square
                 root to get a method that is both fast (in computing
                 environments with a slow square root) and,
                 experimentally, highly accurate. Finally, we show how
                 this same approach can be extended to the reciprocal
                 hypotenuse calculation and, most importantly, to the
                 construction of Givens rotations.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Bos:2021:MPM
author: Joppe W. Bos and Kristin E. Lauter
title: In Memoriam: Peter L. Montgomery (1947--2020)
journal: j-NAMS
volume: 68
number: 4
pages: 538--545
month: apr
monthnumber: 4
year: 2021
CODEN: AMNOAN
DOI: https://doi.org/10.1090/noti2258
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
bibdate: Sat May 29 18:37:36 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2021.05.29 18:37:36 ???
fjournal: Notices of the American Mathematical Society
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/notices/
rawauthor: Joppe W. Bos and Kristin E. Lauter
rawtitle: In Memoriam: {Peter L. Montgomery} (1947--2020)
entry:
@Article{Bos:2021:MPM,
  author =       "Joppe W. Bos and Kristin E. Lauter",
  title =        "In Memoriam: {Peter L. Montgomery} (1947--2020)",
  journal =      j-NAMS,
  volume =       "68",
  number =       "4",
  pages =        "538--545",
  month =        apr,
  year =         "2021",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti2258",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Sat May 29 18:37:36 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
}


bibtype: inproceedings
filename: fparith.bib
label: Bottcher:2021:ROT
author: Andreas Bottcher and Martin Kumm and Florent de Dinechin
title: Resource Optimal Truncated Multipliers for FPGAs
crossref: IEEE:2021:ISC
pages: 102--109
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00029
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Andreas B{\"o}ttcher and Martin Kumm and Florent de Dinechin
rawtitle: Resource Optimal Truncated Multipliers for {FPGAs}
entry:
@InProceedings{Bottcher:2021:ROT,
  author =       "Andreas B{\"o}ttcher and Martin Kumm and Florent de
                 Dinechin",
  title =        "Resource Optimal Truncated Multipliers for {FPGAs}",
  crossref =     "IEEE:2021:ISC",
  pages =        "102--109",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00029",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Brun:2021:SEBa
title: A Study of the Effects and Benefits of Custom-Precision Mathematical Libraries for HPC Codes
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 9
number: 3
pages: 1467--1478
month: jul
monthnumber: 7
year: 2021
DOI: https://doi.org/10.1109/TETC.2021.3070422
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
note: See cite Brun:2021:SEBb.
fjournal: IEEE Transactions on Emerging Topics in Computing
keywords: ARITH-28
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawnote: See \cite{Brun:2021:SEBb}.
rawtitle: A Study of the Effects and Benefits of Custom-Precision Mathematical Libraries for {HPC} Codes
author:
Emeric Brun and David Defour and Pablo de Oliveira Castro and Matei Istoan and Davide Mancusi and Eric Petit and Alan Vaquet

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib

rawauthor:
Emeric Brun and David Defour and Pablo {de Oliveira Castro} and Matei I{\c{s}}toan and Davide Mancusi and Eric Petit and Alan Vaquet

entry:
@Article{Brun:2021:SEBa,
  author =       "Emeric Brun and David Defour and Pablo {de Oliveira
                 Castro} and Matei I{\c{s}}toan and Davide Mancusi and
                 Eric Petit and Alan Vaquet",
  title =        "A Study of the Effects and Benefits of
                 Custom-Precision Mathematical Libraries for {HPC}
                 Codes",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1467--1478",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3070422",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  note =         "See \cite{Brun:2021:SEBb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Brun:2021:SEBb
title: A Study of the Effects and Benefits of Custom-Precision Mathematical Libraries for HPC Codes
crossref: IEEE:2021:ISC
pages: 62--62
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00022
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
note: See cite Brun:2021:SEBa.
keywords: ARITH-28
acknowledgement: ack-nhfb
rawnote: See \cite{Brun:2021:SEBa}.
rawtitle: A Study of the Effects and Benefits of Custom-Precision Mathematical Libraries for {HPC} Codes
author:
Emeric Brun and David Defour and Pablo De Oliveira Castro and Matei Istoan and Davide Mancusi and Eric Petit and Alan Vaquet

remark:
Published in IEEE Transactions on Emerging Topics in Computing, Volume: 9, Issue: 3, July--September 2021, and orally presented at ARITH 2021.

rawauthor:
Emeric Brun and David Defour and Pablo {De Oliveira Castro} and Matei Istoan and Davide Mancusi and Eric Petit and Alan Vaquet

entry:
@InProceedings{Brun:2021:SEBb,
  author =       "Emeric Brun and David Defour and Pablo {De Oliveira
                 Castro} and Matei Istoan and Davide Mancusi and Eric
                 Petit and Alan Vaquet",
  title =        "A Study of the Effects and Benefits of
                 Custom-Precision Mathematical Libraries for {HPC}
                 Codes",
  crossref =     "IEEE:2021:ISC",
  pages =        "62--62",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00022",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Brun:2021:SEBa}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
  remark =       "Published in IEEE Transactions on Emerging Topics in
                 Computing, Volume: 9, Issue: 3, July--September 2021,
                 and orally presented at ARITH 2021.",
}


bibtype: inproceedings
filename: fparith.bib
label: Brunie:2021:MAE
author: Nicolas Brunie
title: Manifest for an Approximation Exchange Format
crossref: IEEE:2021:ISC
pages: 63--68
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00023
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Nicolas Brunie
rawtitle: Manifest for an Approximation Exchange Format
abstract:
We introduce AXF, Approximation eXchange Format, a file format dedicated to the description of basic constructs for function approximation, such as numerical description of piecewise polynomial approximations. AXF is designed as a numerical intermediate representation between approximation generation and approximation implementation tools.

rawabstract:
We introduce AXF, Approximation eXchange Format, a file format dedicated to the description of basic constructs for function approximation, such as numerical description of piecewise polynomial approximations. AXF is designed as a numerical intermediate representation between approximation generation and approximation implementation tools.

entry:
@InProceedings{Brunie:2021:MAE,
  author =       "Nicolas Brunie",
  title =        "Manifest for an Approximation Exchange Format",
  crossref =     "IEEE:2021:ISC",
  pages =        "63--68",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00023",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We introduce AXF, Approximation eXchange Format, a
                 file format dedicated to the description of basic
                 constructs for function approximation, such as
                 numerical description of piecewise polynomial
                 approximations. AXF is designed as a numerical
                 intermediate representation between approximation
                 generation and approximation implementation tools.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Ciocirlan:2021:AEPa
title: The Accuracy and Efficiency of Posit Arithmetic
journal: arXiv.org
pages: 63--68
day: 16
month: sep
monthnumber: 9
year: 2021
bibdate: Sat Dec 16 15:13:00 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.12.16 15:13:00 ???
acknowledgement: ack-nhfb
rawtitle: The Accuracy and Efficiency of Posit Arithmetic
author:
Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya Ramapantulu and Nicolae Tapus and Yong Meng Teo

abstract:
Motivated by the increasing interest in the posit numeric format, in this paper we evaluate the accuracy and efficiency of posit arithmetic in contrast to the traditional IEEE 754 32-bit floating-point (FP32) arithmetic. We first design and implement a Posit Arithmetic Unit (PAU), called POSAR, with flexible bit-sized arithmetic suitable for applications that can trade accuracy for savings in chip area. Next, we analyze the accuracy and efficiency of POSAR with a series of benchmarks including mathematical computations, ML kernels, NAS Parallel Benchmarks (NPB), and Cifar-10 CNN. This analysis is done on our implementation of POSAR integrated into a RISC-V Rocket Chip core in comparison with the IEEE 754-based Floating Point Unit (FPU) of Rocket Chip. Our analysis shows that POSAR can outperform the FPU, but the results are not spectacular. For NPB, 32-bit posit achieves better accuracy than FP32 and improves the execution by up to 2%. However, POSAR with 32-bit posit needs 30% more FPGA resources compared to the FPU. For classic ML algorithms, we find that 8-bit posits are not suitable to replace FP32 because they exhibit low accuracy leading to wrong results. Instead, 16-bit posit offers the best option in terms of accuracy and efficiency. For example, 16-bit posit achieves the same Top-1 accuracy as FP32 on a Cifar-10 CNN with a speedup of 18%.

rawabstract:
Motivated by the increasing interest in the posit numeric format, in this paper we evaluate the accuracy and efficiency of posit arithmetic in contrast to the traditional IEEE 754 32-bit floating-point (FP32) arithmetic. We first design and implement a Posit Arithmetic Unit (PAU), called POSAR, with flexible bit-sized arithmetic suitable for applications that can trade accuracy for savings in chip area. Next, we analyze the accuracy and efficiency of POSAR with a series of benchmarks including mathematical computations, ML kernels, NAS Parallel Benchmarks (NPB), and Cifar-10 CNN. This analysis is done on our implementation of POSAR integrated into a RISC-V Rocket Chip core in comparison with the IEEE 754-based Floating Point Unit (FPU) of Rocket Chip. Our analysis shows that POSAR can outperform the FPU, but the results are not spectacular. For NPB, 32-bit posit achieves better accuracy than FP32 and improves the execution by up to 2\%. However, POSAR with 32-bit posit needs 30\% more FPGA resources compared to the FPU. For classic ML algorithms, we find that 8-bit posits are not suitable to replace FP32 because they exhibit low accuracy leading to wrong results. Instead, 16-bit posit offers the best option in terms of accuracy and efficiency. For example, 16-bit posit achieves the same Top-1 accuracy as FP32 on a Cifar-10 CNN with a speedup of 18\%.

rawauthor:
Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya Ramapantulu and Nicolae Tapus and Yong Meng Teo

entry:
@Article{Ciocirlan:2021:AEPa,
  author =       "Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya
                 Ramapantulu and Nicolae Tapus and Yong Meng Teo",
  title =        "The Accuracy and Efficiency of Posit Arithmetic",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  day =          "16",
  month =        sep,
  year =         "2021",
  bibdate =      "Sat Dec 16 15:13:00 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  abstract =     "Motivated by the increasing interest in the posit
                 numeric format, in this paper we evaluate the accuracy
                 and efficiency of posit arithmetic in contrast to the
                 traditional IEEE 754 32-bit floating-point (FP32)
                 arithmetic. We first design and implement a Posit
                 Arithmetic Unit (PAU), called POSAR, with flexible
                 bit-sized arithmetic suitable for applications that can
                 trade accuracy for savings in chip area. Next, we
                 analyze the accuracy and efficiency of POSAR with a
                 series of benchmarks including mathematical
                 computations, ML kernels, NAS Parallel Benchmarks
                 (NPB), and Cifar-10 CNN. This analysis is done on our
                 implementation of POSAR integrated into a RISC-V Rocket
                 Chip core in comparison with the IEEE 754-based
                 Floating Point Unit (FPU) of Rocket Chip. Our analysis
                 shows that POSAR can outperform the FPU, but the
                 results are not spectacular. For NPB, 32-bit posit
                 achieves better accuracy than FP32 and improves the
                 execution by up to 2\%. However, POSAR with 32-bit
                 posit needs 30\% more FPGA resources compared to the
                 FPU. For classic ML algorithms, we find that 8-bit
                 posits are not suitable to replace FP32 because they
                 exhibit low accuracy leading to wrong results. Instead,
                 16-bit posit offers the best option in terms of
                 accuracy and efficiency. For example, 16-bit posit
                 achieves the same Top-1 accuracy as FP32 on a Cifar-10
                 CNN with a speedup of 18\%.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "2109.08225",
  primaryclass = "cs.AR",
}


bibtype: inproceedings
filename: fparith.bib
label: Ciocirlan:2021:AEPb
author: Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya Ramapantulu and Nicolae pu and Yong Meng Teo
editor: IEEE
booktitle: 2021 IEEE 39th International Conference on Computer Design (ICCD)
title: The Accuracy and Efficiency of Posit Arithmetic
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 83--87
year: 2021
DOI: https://doi.org/10.1109/ICCD53106.2021.00024
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.12.15 09:21:55 ???
keywords: posit arithmetic; RISC-V
acknowledgement: ack-nhfb
rawbooktitle: {2021 IEEE 39th International Conference on Computer Design (ICCD)}
raweditor: {IEEE}
rawtitle: The Accuracy and Efficiency of Posit Arithmetic
rawauthor:
Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya Ramapantulu and Nicolae {pu } and Yong Meng Teo

entry:
@InProceedings{Ciocirlan:2021:AEPb,
  author =       "Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya
                 Ramapantulu and Nicolae {pu } and Yong Meng Teo",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE 39th International Conference on Computer
                 Design (ICCD)}",
  title =        "The Accuracy and Efficiency of Posit Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "83--87",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ICCD53106.2021.00024",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic; RISC-V",
}


bibtype: article
filename: fparith.bib
label: Cococcioni:2021:VPO
author: Marco Cococcioni and Federico Rossi and Emanuele Ruffaldi and Sergio Saponara
journal: Neural Computing and Applications
volume: 33
number: 16
publisher: pub-SV
address: pub-SV:adr
pages: 10575--10585
month: feb
monthnumber: 2
year: 2021
DOI: https://doi.org/10.1007/s00521-021-05814-0
ISSN: 1433-3058 OR 14333058
ISSNL: 0941-0643 OR 09410643
bibdate: Fri Dec 15 11:31:31 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.12.15 11:31:31 ???
keywords: posit arithmetic
acknowledgement: ack-nhfb
rawauthor: Marco Cococcioni and Federico Rossi and Emanuele Ruffaldi and Sergio Saponara
title:
Vectorizing posit operations on RISC-V for faster deep neural networks: experiments and comparison with ARM SVE

rawtitle:
Vectorizing posit operations on {RISC-V} for faster deep neural networks: experiments and comparison with {ARM SVE}

entry:
@Article{Cococcioni:2021:VPO,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  title =        "Vectorizing posit operations on {RISC-V} for faster
                 deep neural networks: experiments and comparison with
                 {ARM SVE}",
  journal =      "Neural Computing and Applications",
  volume =       "33",
  number =       "16",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "10575--10585",
  month =        feb,
  year =         "2021",
  DOI =          "https://doi.org/10.1007/s00521-021-05814-0",
  ISSN =         "1433-3058",
  ISSN-L =       "0941-0643",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Coladon:2021:MFR
author: Titouan Coladon and Philippe Elbaz-Vincent and Cyril Hugounenq
crossref: IEEE:2021:ISC
pages: 78--85
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00026
bibdate: Thu Sep 21 10:36:08 2023
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Titouan Coladon and Philippe Elbaz-Vincent and Cyril Hugounenq
title:
MPHELL: a fast and robust library with unified and versatile arithmetics for elliptic curves cryptography

bibsource:
https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
{MPHELL}: a fast and robust library with unified and versatile arithmetics for elliptic curves cryptography

entry:
@InProceedings{Coladon:2021:MFR,
  author =       "Titouan Coladon and Philippe Elbaz-Vincent and Cyril
                 Hugounenq",
  title =        "{MPHELL}: a fast and robust library with unified and
                 versatile arithmetics for elliptic curves
                 cryptography",
  crossref =     "IEEE:2021:ISC",
  pages =        "78--85",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00026",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Connolly:2021:SRP
author: Michael P. Connolly and Nicholas J. Higham and Theo Mary
title: Stochastic Rounding and Its Probabilistic Backward Error Analysis
journal: j-SIAM-J-SCI-COMP
volume: 43
number: 1
pages: A566--A585
year: 2021
CODEN: SJOCE3
DOI: https://doi.org/10.1137/20M1334796
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
bibdate: Fri Mar 12 11:40:06 MST 2021
bibtimestamp: 2021.03.12 11:40:06 MST
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
onlinedate: January 2021
rawauthor: Michael P. Connolly and Nicholas J. Higham and Theo Mary
rawtitle: Stochastic Rounding and Its Probabilistic Backward Error Analysis
bibsource:
http://epubs.siam.org/toc/sjoce3/43/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib

entry:
@Article{Connolly:2021:SRP,
  author =       "Michael P. Connolly and Nicholas J. Higham and Theo
                 Mary",
  title =        "Stochastic Rounding and Its Probabilistic Backward
                 Error Analysis",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "43",
  number =       "1",
  pages =        "A566--A585",
  month =        "????",
  year =         "2021",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/20M1334796",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Mar 12 11:40:06 MST 2021",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/43/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2021",
}


bibtype: article
filename: fparith.bib
label: Czachor:2021:NNM
author: Marek Czachor
journal: j-FOUND-SCI
volume: 26
number: 1
pages: 75--95
month: mar
monthnumber: 3
year: 2021
CODEN: FOSCFI
DOI: https://doi.org/10.1007/s10699-020-09687-9
ISSN: 1233-1821 (print), 1572-8471 (electronic) OR 12331821 (print), 15728471 (electronic)
ISSNL: 1233-1821 OR 12331821
bibdate: Mon Apr 19 10:16:53 MDT 2021
bibtimestamp: 2021.04.19 10:16:53 MDT
URL: https://link.springer.com/article/10.1007/s10699-020-09687-9
fjournal: Foundations of Science
acknowledgement: ack-nhfb
ajournal: Found. Sci.
journalURL: http://link.springer.com/journal/10699
rawauthor: Marek Czachor
title:
Non-Newtonian Mathematics Instead of Non-Newtonian Physics: Dark Matter and Dark Energy from a Mismatch of Arithmetics

bibsource:
https://www.math.utah.edu/pub/tex/bib/foundsci.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
Non-{Newtonian} Mathematics Instead of Non-{Newtonian} Physics: Dark Matter and Dark Energy from a Mismatch of Arithmetics

entry:
@Article{Czachor:2021:NNM,
  author =       "Marek Czachor",
  title =        "Non-{Newtonian} Mathematics Instead of Non-{Newtonian}
                 Physics: Dark Matter and Dark Energy from a Mismatch of
                 Arithmetics",
  journal =      j-FOUND-SCI,
  volume =       "26",
  number =       "1",
  pages =        "75--95",
  month =        mar,
  year =         "2021",
  CODEN =        "FOSCFI",
  DOI =          "https://doi.org/10.1007/s10699-020-09687-9",
  ISSN =         "1233-1821 (print), 1572-8471 (electronic)",
  ISSN-L =       "1233-1821",
  bibdate =      "Mon Apr 19 10:16:53 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/foundsci.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://link.springer.com/article/10.1007/s10699-020-09687-9",
  acknowledgement = ack-nhfb,
  ajournal =     "Found. Sci.",
  fjournal =     "Foundations of Science",
  journal-URL =  "http://link.springer.com/journal/10699",
  online-date =  "Published: 28 July 2020 Pages: 75 - 95",
}


bibtype: misc
filename: fparith.bib
label: Darcy:2021:FPA
author: Joseph D. Darcy
title: Floating-Point Arithmetic: What Every Java Programmer Should Know!
pages: 75--95
year: 2021
bibdate: Tue Feb 27 11:53:09 2024
bibtimestamp: 2024.02.27 11:53:09 ???
URL: https://youtu.be/ajaHQ9S4uTA
acknowledgement: ack-nhfb
howpublished: Web site 29m37s video.
rawauthor: Joseph D. Darcy
rawtitle: Floating-Point Arithmetic: What Every {Java} Programmer Should Know!
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/java2020.bib

entry:
@Misc{Darcy:2021:FPA,
  author =       "Joseph D. Darcy",
  title =        "Floating-Point Arithmetic: What Every {Java}
                 Programmer Should Know!",
  howpublished = "Web site 29m37s video.",
  year =         "2021",
  bibdate =      "Tue Feb 27 11:53:09 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2020.bib",
  URL =          "https://youtu.be/ajaHQ9S4uTA",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: deDinechin:2021:TAC
author: Florent de Dinechin and Silviu-Ioan Filip and Martin Kumm and Anastasia Volkova
title: Towards Arithmetic-Centered Filter Design
crossref: IEEE:2021:ISC
pages: 115--118
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00032
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Florent de Dinechin and Silviu-Ioan Filip and Martin Kumm and Anastasia Volkova
rawtitle: Towards Arithmetic-Centered Filter Design
entry:
@InProceedings{deDinechin:2021:TAC,
  author =       "Florent de Dinechin and Silviu-Ioan Filip and Martin
                 Kumm and Anastasia Volkova",
  title =        "Towards Arithmetic-Centered Filter Design",
  crossref =     "IEEE:2021:ISC",
  pages =        "115--118",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00032",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Defour:2021:SCB
author: David Defour and Pablo de Oliveira Castro and Matei Istoan and Eric Petit
title: Shadow computation with BFloat16 to estimate the numerical accuracy of summations
crossref: IEEE:2021:ISC
pages: 33--36
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00017
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: David Defour and Pablo de Oliveira Castro and Matei I{\c{s}}toan and Eric Petit
rawtitle: Shadow computation with {BFloat16} to estimate the numerical accuracy of summations
entry:
@InProceedings{Defour:2021:SCB,
  author =       "David Defour and Pablo de Oliveira Castro and Matei
                 I{\c{s}}toan and Eric Petit",
  title =        "Shadow computation with {BFloat16} to estimate the
                 numerical accuracy of summations",
  crossref =     "IEEE:2021:ISC",
  pages =        "33--36",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00017",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: delaFraga:2021:DEU
author: Luis Gerardo de la Fraga
title: Differential Evolution under Fixed Point Arithmetic and FP16 Numbers
journal: j-MATH-COMPUT-APPL
volume: 26
number: 1
pages: 13--??
month: mar
monthnumber: 3
year: 2021
DOI: https://doi.org/10.3390/mca26010013
ISSN: 2297-8747 OR 22978747
ISSNL: 2297-8747 OR 22978747
bibdate: Sun Feb 18 06:28:40 MST 2024
bibtimestamp: 2024.02.18 06:28:40 MST
URL: https://www.mdpi.com/2297-8747/26/1/13
fjournal: Mathematical and Computational Applications
acknowledgement: ack-nhfb
journalURL: https://www.mdpi.com/journal/mca
rawauthor: Luis Gerardo de la Fraga
rawtitle: Differential Evolution under Fixed Point Arithmetic and {FP16} Numbers
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib

entry:
@Article{delaFraga:2021:DEU,
  author =       "Luis Gerardo de la Fraga",
  title =        "Differential Evolution under Fixed Point Arithmetic
                 and {FP16} Numbers",
  journal =      j-MATH-COMPUT-APPL,
  volume =       "26",
  number =       "1",
  pages =        "13--??",
  month =        mar,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.3390/mca26010013",
  ISSN =         "2297-8747",
  ISSN-L =       "2297-8747",
  bibdate =      "Sun Feb 18 06:28:40 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
  URL =          "https://www.mdpi.com/2297-8747/26/1/13",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical and Computational Applications",
  journal-URL =  "https://www.mdpi.com/journal/mca",
}


bibtype: inproceedings
filename: fparith.bib
label: Demeure:2021:TET
author: Nestor Demeure and Cedric Chevalier and Christophe Denis and Pierre Dossantos-Uzarralde
title: Tagged error: tracing numerical error through computations
crossref: IEEE:2021:ISC
pages: 9--16
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00014
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Nestor Demeure and C{\'e}dric Chevalier and Christophe Denis and Pierre Dossantos-Uzarralde
rawtitle: Tagged error: tracing numerical error through computations
entry:
@InProceedings{Demeure:2021:TET,
  author =       "Nestor Demeure and C{\'e}dric Chevalier and Christophe
                 Denis and Pierre Dossantos-Uzarralde",
  title =        "Tagged error: tracing numerical error through
                 computations",
  crossref =     "IEEE:2021:ISC",
  pages =        "9--16",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00014",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Demmel:2021:NIS
author: James Demmel and Jason Riedy
title: A New IEEE 754 Standard for Floating-Point Arithmetic in an Ever-Changing World
journal: j-SIAM-NEWS
volume: 54
number: 6
pages: ??--??
month: jul
monthnumber: 7
year: 2021
ISSN: 0036-1437 OR 00361437
bibdate: Tue Nov 16 08:21:39 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2021.11.16 08:21:39 ???
fjournal: SIAM News
acknowledgement: ack-nhfb
journalURL: http://www.siam.org/news/
rawauthor: James Demmel and Jason Riedy
rawtitle: A New {IEEE 754} Standard for Floating-Point Arithmetic in an Ever-Changing World
URL:
https://sinews.siam.org/Details-Page/a-new-ieee-754-standard-for-floating-point-arithmetic-in-an-ever-changing-world

entry:
@Article{Demmel:2021:NIS,
  author =       "James Demmel and Jason Riedy",
  title =        "A New {IEEE 754} Standard for Floating-Point
                 Arithmetic in an Ever-Changing World",
  journal =      j-SIAM-NEWS,
  volume =       "54",
  number =       "6",
  pages =        "??--??",
  month =        jul # "\slash " # aug,
  year =         "2021",
  ISSN =         "0036-1437",
  bibdate =      "Tue Nov 16 08:21:39 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sinews.siam.org/Details-Page/a-new-ieee-754-standard-for-floating-point-arithmetic-in-an-ever-changing-world",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}


bibtype: article
filename: fparith.bib
label: Dimitrakopoulos:2021:SPAa
author: Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos and Vassilis Paliouras
title: Sum Propagate Adders
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 9
number: 3
pages: 1479--1488
month: jul
monthnumber: 7
year: 2021
DOI: https://doi.org/10.1109/TETC.2021.3068729
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
note: See cite Dimitrakopoulos:2021:SPAb.
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos and Vassilis Paliouras
rawnote: See \cite{Dimitrakopoulos:2021:SPAb}.
rawtitle: Sum Propagate Adders
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib

entry:
@Article{Dimitrakopoulos:2021:SPAa,
  author =       "Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos
                 and Vassilis Paliouras",
  title =        "Sum Propagate Adders",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1479--1488",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3068729",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  note =         "See \cite{Dimitrakopoulos:2021:SPAb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: inproceedings
filename: fparith.bib
label: Dimitrakopoulos:2021:SPAb
author: Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos and Vassilis Paliouras
title: Sum Propagate Adders
crossref: IEEE:2021:ISC
pages: 110--110
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00030
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
note: See cite Dimitrakopoulos:2021:SPAa.
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos and Vassilis Paliouras
rawnote: See \cite{Dimitrakopoulos:2021:SPAa}.
rawtitle: Sum Propagate Adders
remark:
Published in IEEE Transactions on Emerging Topics in Computing, Volume: 9, Issue: 3, July--September 2021, and orally presented at ARITH 2021.

entry:
@InProceedings{Dimitrakopoulos:2021:SPAb,
  author =       "Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos
                 and Vassilis Paliouras",
  title =        "Sum Propagate Adders",
  crossref =     "IEEE:2021:ISC",
  pages =        "110--110",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00030",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Dimitrakopoulos:2021:SPAa}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
  remark =       "Published in IEEE Transactions on Emerging Topics in
                 Computing, Volume: 9, Issue: 3, July--September 2021,
                 and orally presented at ARITH 2021.",
}


bibtype: misc
filename: fparith.bib
label: Druck:2021:NSB
author: Philip Druck
title: A Novel Set of Base-Prime Floating Point Numbers
pages: 110--110
day: 16
month: feb
monthnumber: 2
year: 2021
DOI: https://doi.org/10.36227/techrxiv.13960829.v1
bibdate: Fri Sep 29 14:28:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.29 14:28:55 ???
acknowledgement: ack-nhfb
howpublished: TechRxiv preprint.
rawauthor: Philip Druck
rawtitle: A Novel Set of Base-Prime Floating Point Numbers
abstract:
A novel set is presented that generalizes the usual base representations of floating point real numbers. It uses base-prime numbers instead of the usual base 2 (binary), base 3 (for the Cantor set), base 10 (decimal), base 16 (hexadecimal) and the like. This base-prime set, denoted DS, is essentially an experimental finding, identified in unrelated patented research on nonuniform signal data sampling [1] and self-stabilizing computer arithmetic [2].

rawabstract:
A novel set is presented that generalizes the usual base representations of floating point real numbers. It uses base-prime numbers instead of the usual base 2 (binary), base 3 (for the Cantor set), base 10 (decimal), base 16 (hexadecimal) and the like. This base-prime set, denoted DS, is essentially an experimental finding, identified in unrelated patented research on nonuniform signal data sampling [1] and self-stabilizing computer arithmetic [2].

entry:
@Misc{Druck:2021:NSB,
  author =       "Philip Druck",
  title =        "A Novel Set of Base-Prime Floating Point Numbers",
  howpublished = "TechRxiv preprint.",
  day =          "16",
  month =        feb,
  year =         "2021",
  DOI =          "https://doi.org/10.36227/techrxiv.13960829.v1",
  bibdate =      "Fri Sep 29 14:28:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A novel set is presented that generalizes the usual
                 base representations of floating point real numbers. It
                 uses base-prime numbers instead of the usual base 2
                 (binary), base 3 (for the Cantor set), base 10
                 (decimal), base 16 (hexadecimal) and the like. This
                 base-prime set, denoted DS, is essentially an
                 experimental finding, identified in unrelated patented
                 research on nonuniform signal data sampling [1] and
                 self-stabilizing computer arithmetic [2].",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Eliahu:2021:MME
author: Adi Eliahu and Ronny Ronen and Pierre-Emmanuel Gaillardon and Shahar Kvatinsky
journal: j-JETC
volume: 17
number: 2
pages: 24:1--24:27
month: apr
monthnumber: 4
year: 2021
DOI: https://doi.org/10.1145/3432815
ISSN: 1550-4832 (print), 1550-4840 (electronic) OR 15504832 (print), 15504840 (electronic)
ISSNL: 1550-4832 OR 15504832
bibdate: Fri Apr 30 06:39:29 MDT 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jetc.bib
bibtimestamp: 2021.04.30 06:39:29 MDT
URL: https://dl.acm.org/doi/10.1145/3432815
fjournal: ACM Journal on Emerging Technologies in Computing Systems (JETC)
acknowledgement: ack-nhfb
articleno: 24
journalURL: https://dl.acm.org/loi/jetc
rawauthor: Adi Eliahu and Ronny Ronen and Pierre-Emmanuel Gaillardon and Shahar Kvatinsky
title:
multiPULPly: a Multiplication Engine for Accelerating Neural Networks on Ultra-low-power Architectures

abstract:
Computationally intensive neural network applications often need to run on resource-limited low-power devices. Numerous hardware accelerators have been developed to speed up the performance of neural network applications and reduce power consumption; however, most focus on data centers and full-fledged systems. Acceleration in ultra-low-power systems has been only partially addressed. In this article, we present multiPULPly, an accelerator that integrates memristive technologies within standard low-power CMOS technology, to accelerate multiplication in neural network inference on ultra-low-power systems. This accelerator was designated for PULP, an open-source microcontroller system that uses low-power RISC-V processors. Memristors were integrated into the accelerator to enable power consumption only when the memory is active, to continue the task with no context-restoring overhead, and to enable highly parallel analog multiplication. To reduce the energy consumption, we propose novel dataflows that handle common multiplication scenarios and are tailored for our architecture. The accelerator was tested on FPGA and achieved a peak energy efficiency of 19.5 TOPS/W, outperforming state-of-the-art accelerators by $ 1.5 times $ to $ 4.5 times $.

rawabstract:
Computationally intensive neural network applications often need to run on resource-limited low-power devices. Numerous hardware accelerators have been developed to speed up the performance of neural network applications and reduce power consumption; however, most focus on data centers and full-fledged systems. Acceleration in ultra-low-power systems has been only partially addressed. In this article, we present multiPULPly, an accelerator that integrates memristive technologies within standard low-power CMOS technology, to accelerate multiplication in neural network inference on ultra-low-power systems. This accelerator was designated for PULP, an open-source microcontroller system that uses low-power RISC-V processors. Memristors were integrated into the accelerator to enable power consumption only when the memory is active, to continue the task with no context-restoring overhead, and to enable highly parallel analog multiplication. To reduce the energy consumption, we propose novel dataflows that handle common multiplication scenarios and are tailored for our architecture. The accelerator was tested on FPGA and achieved a peak energy efficiency of 19.5 TOPS/W, outperforming state-of-the-art accelerators by $ 1.5 \times $ to $ 4.5 \times $.

rawtitle:
{multiPULPly}: a Multiplication Engine for Accelerating Neural Networks on Ultra-low-power Architectures

entry:
@Article{Eliahu:2021:MME,
  author =       "Adi Eliahu and Ronny Ronen and Pierre-Emmanuel
                 Gaillardon and Shahar Kvatinsky",
  title =        "{multiPULPly}: a Multiplication Engine for
                 Accelerating Neural Networks on Ultra-low-power
                 Architectures",
  journal =      j-JETC,
  volume =       "17",
  number =       "2",
  pages =        "24:1--24:27",
  month =        apr,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3432815",
  ISSN =         "1550-4832 (print), 1550-4840 (electronic)",
  ISSN-L =       "1550-4832",
  bibdate =      "Fri Apr 30 06:39:29 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jetc.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3432815",
  abstract =     "Computationally intensive neural network applications
                 often need to run on resource-limited low-power
                 devices. Numerous hardware accelerators have been
                 developed to speed up the performance of neural network
                 applications and reduce power consumption; however,
                 most focus on data centers and full-fledged systems.
                 Acceleration in ultra-low-power systems has been only
                 partially addressed. In this article, we present
                 multiPULPly, an accelerator that integrates memristive
                 technologies within standard low-power CMOS technology,
                 to accelerate multiplication in neural network
                 inference on ultra-low-power systems. This accelerator
                 was designated for PULP, an open-source microcontroller
                 system that uses low-power RISC-V processors.
                 Memristors were integrated into the accelerator to
                 enable power consumption only when the memory is
                 active, to continue the task with no context-restoring
                 overhead, and to enable highly parallel analog
                 multiplication. To reduce the energy consumption, we
                 propose novel dataflows that handle common
                 multiplication scenarios and are tailored for our
                 architecture. The accelerator was tested on FPGA and
                 achieved a peak energy efficiency of 19.5 TOPS/W,
                 outperforming state-of-the-art accelerators by $ 1.5
                 \times $ to $ 4.5 \times $.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "https://dl.acm.org/loi/jetc",
}


bibtype: inproceedings
filename: fparith.bib
label: Elkhatib:2021:ARV
author: Rami Elkhatib and Reza Azarderakhsh and Mehran Mozaffari-Kermani
title: Accelerated RISC-V for SIKE
crossref: IEEE:2021:ISC
pages: 131--138
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00035
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Rami Elkhatib and Reza Azarderakhsh and Mehran Mozaffari-Kermani
rawtitle: Accelerated {RISC-V} for {SIKE}
entry:
@InProceedings{Elkhatib:2021:ARV,
  author =       "Rami Elkhatib and Reza Azarderakhsh and Mehran
                 Mozaffari-Kermani",
  title =        "Accelerated {RISC-V} for {SIKE}",
  crossref =     "IEEE:2021:ISC",
  pages =        "131--138",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00035",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Fasi:2021:ASRa
author: Massimiliano Fasi and Mantas Mikaitis
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 9
number: 3
pages: 1451--1466
month: jul
monthnumber: 7
year: 2021
DOI: https://doi.org/10.1109/TETC.2021.3069165
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
note: See cite Fasi:2021:ASRb.
fjournal: IEEE Transactions on Emerging Topics in Computing
keywords: ARITH-28
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Massimiliano Fasi and Mantas Mikaitis
rawnote: See \cite{Fasi:2021:ASRb}.
title:
Algorithms for Stochastically Rounded Elementary Arithmetic Operations in IEEE 754 Floating-Point Arithmetic

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib

rawtitle:
Algorithms for Stochastically Rounded Elementary Arithmetic Operations in {IEEE 754} Floating-Point Arithmetic

entry:
@Article{Fasi:2021:ASRa,
  author =       "Massimiliano Fasi and Mantas Mikaitis",
  title =        "Algorithms for Stochastically Rounded Elementary
                 Arithmetic Operations in {IEEE 754} Floating-Point
                 Arithmetic",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1451--1466",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3069165",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  note =         "See \cite{Fasi:2021:ASRb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Fasi:2021:ASRb
author: Massimiliano Fasi and Mantas Mikaitis
crossref: IEEE:2021:ISC
pages: 69--69
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00024
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
note: See cite Fasi:2021:ASRa.
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Massimiliano Fasi and Mantas Mikaitis
rawnote: See \cite{Fasi:2021:ASRa}.
title:
Algorithms for Stochastically Rounded Elementary Arithmetic Operations in IEEE 754 Floating-Point Arithmetic

remark:
Published in IEEE Transactions on Emerging Topics in Computing, Volume: 9, Issue: 3, July--September 2021, and orally presented at ARITH 2021.

rawtitle:
Algorithms for Stochastically Rounded Elementary Arithmetic Operations in {IEEE 754} Floating-Point Arithmetic

entry:
@InProceedings{Fasi:2021:ASRb,
  author =       "Massimiliano Fasi and Mantas Mikaitis",
  title =        "Algorithms for Stochastically Rounded Elementary
                 Arithmetic Operations in {IEEE 754} Floating-Point
                 Arithmetic",
  crossref =     "IEEE:2021:ISC",
  pages =        "69--69",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00024",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fasi:2021:ASRa}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
  remark =       "Published in IEEE Transactions on Emerging Topics in
                 Computing, Volume: 9, Issue: 3, July--September 2021,
                 and orally presented at ARITH 2021.",
}


bibtype: article
filename: fparith.bib
label: Fortin:2021:HPS
author: Pierre Fortin and Ambroise Fleury and Francois Lemaire and Michael Monagan
title: High-performance SIMD modular arithmetic for polynomial evaluation
journal: j-CCPE
volume: 33
number: 16
pages: e6270:1--e6270:??
day: 25
month: aug
monthnumber: 8
year: 2021
CODEN: CCPEBO
DOI: https://doi.org/10.1002/cpe.6270
ISSN: 1532-0626 (print), 1532-0634 (electronic) OR 15320626 (print), 15320634 (electronic)
ISSNL: 1532-0626 OR 15320626
bibdate: Tue Feb 22 09:49:56 MST 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/ccpe.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.02.22 09:49:56 MST
fjournal: Concurrency and Computation: Practice and Experience
acknowledgement: ack-nhfb
ajournal: Concurr. Comput.
journalURL: http://www.interscience.wiley.com/jpages/1532-0626
onlinedate: 25 May 2021
rawauthor: Pierre Fortin and Ambroise Fleury and Fran{\c{c}}ois Lemaire and Michael Monagan
rawtitle: High-performance {SIMD} modular arithmetic for polynomial evaluation
entry:
@Article{Fortin:2021:HPS,
  author =       "Pierre Fortin and Ambroise Fleury and Fran{\c{c}}ois
                 Lemaire and Michael Monagan",
  title =        "High-performance {SIMD} modular arithmetic for
                 polynomial evaluation",
  journal =      j-CCPE,
  volume =       "33",
  number =       "16",
  pages =        "e6270:1--e6270:??",
  day =          "25",
  month =        aug,
  year =         "2021",
  CODEN =        "CCPEBO",
  DOI =          "https://doi.org/10.1002/cpe.6270",
  ISSN =         "1532-0626 (print), 1532-0634 (electronic)",
  ISSN-L =       "1532-0626",
  bibdate =      "Tue Feb 22 09:49:56 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Concurr. Comput.",
  fjournal =     "Concurrency and Computation: Practice and Experience",
  journal-URL =  "http://www.interscience.wiley.com/jpages/1532-0626",
  onlinedate =   "25 May 2021",
}


bibtype: article
filename: fparith.bib
label: Garofalo:2021:XEEa
author: Angelo Garofalo and Giuseppe Tagliavini and Francesco Conti and Luca Benini and Davide Rossi
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 9
number: 3
pages: 1489--1505
month: jul
monthnumber: 7
year: 2021
DOI: https://doi.org/10.1109/TETC.2021.3072337
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
note: See cite Garofalo:2021:XEEb.
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Angelo Garofalo and Giuseppe Tagliavini and Francesco Conti and Luca Benini and Davide Rossi
rawnote: See \cite{Garofalo:2021:XEEb}.
title:
XpulpNN: Enabling Energy Efficient and Flexible Inference of Quantized Neural Networks on RISC-V Based IoT End Nodes

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib

rawtitle:
{XpulpNN}: Enabling Energy Efficient and Flexible Inference of Quantized Neural Networks on {RISC-V} Based {IoT} End Nodes

entry:
@Article{Garofalo:2021:XEEa,
  author =       "Angelo Garofalo and Giuseppe Tagliavini and Francesco
                 Conti and Luca Benini and Davide Rossi",
  title =        "{XpulpNN}: Enabling Energy Efficient and Flexible
                 Inference of Quantized Neural Networks on {RISC-V}
                 Based {IoT} End Nodes",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1489--1505",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3072337",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  note =         "See \cite{Garofalo:2021:XEEb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: inproceedings
filename: fparith.bib
label: Garofalo:2021:XEEb
author: Angelo Garofalo and Giuseppe Tagliavini and Francesco Conti and Luca Benini and Davide Rossi
crossref: IEEE:2021:ISC
pages: 53--53
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00020
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
note: See cite Garofalo:2021:XEEa.
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Angelo Garofalo and Giuseppe Tagliavini and Francesco Conti and Luca Benini and Davide Rossi
rawnote: See \cite{Garofalo:2021:XEEa}.
title:
XpulpNN: Enabling Energy Efficient and Flexible Inference of Quantized Neural Networks on RISC-V based IoT End Nodes

rawtitle:
{XpulpNN}: Enabling Energy Efficient and Flexible Inference of Quantized Neural Networks on {RISC-V} based {IoT} End Nodes

entry:
@InProceedings{Garofalo:2021:XEEb,
  author =       "Angelo Garofalo and Giuseppe Tagliavini and Francesco
                 Conti and Luca Benini and Davide Rossi",
  title =        "{XpulpNN}: Enabling Energy Efficient and Flexible
                 Inference of Quantized Neural Networks on {RISC-V}
                 based {IoT} End Nodes",
  crossref =     "IEEE:2021:ISC",
  pages =        "53--53",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00020",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Garofalo:2021:XEEa}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
  remark =       "Published in IEEE Transactions on Emerging Topics in
                 Computing, Volume: 9, Issue: 3, July--September 2021,
                 and orally presented at ARITH 2021.",
}


bibtype: article
filename: fparith.bib
label: Gohil:2021:FPF
author: Varun Gohil and Sumit Walia and Joycee Mekie and Manu Awasthi
title: Fixed-Posit: a Floating-Point Representation for Error-Resilient Applications
journal: j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS
volume: 68
number: 10
pages: 3341--3345
year: 2021
DOI: https://doi.org/10.1109/TCSII.2021.3072217
ISSN: 1549-7747 (print), 1558-3791 (electronic) OR 15497747 (print), 15583791 (electronic)
ISSNL: 1549-7747 OR 15497747
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
fjournal: IEEE Transactions on Circuits and Systems II: Express Briefs
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/issues?punumber=8920
rawauthor: Varun Gohil and Sumit Walia and Joycee Mekie and Manu Awasthi
rawtitle: Fixed-Posit: a Floating-Point Representation for Error-Resilient Applications
entry:
@Article{Gohil:2021:FPF,
  author =       "Varun Gohil and Sumit Walia and Joycee Mekie and Manu
                 Awasthi",
  title =        "Fixed-Posit: a Floating-Point Representation for
                 Error-Resilient Applications",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "68",
  number =       "10",
  pages =        "3341--3345",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TCSII.2021.3072217",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}


bibtype: inproceedings
filename: fparith.bib
label: Gopalakrishnan:2021:GNA
title: Guarding Numerics Amidst Rising Heterogeneity
publisher: pub-IEEE
address: pub-IEEE:adr
year: 2021
bibdate: Mon Sep 11 06:54:23 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.11 06:54:23 ???
URL: https://correctness-workshop.github.io/2021/
acknowledgement: ack-nhfb
rawtitle: Guarding Numerics Amidst Rising Heterogeneity
author:
Ganesh Gopalakrishnan and Ignacio Laguna and Ang Li and Pavel Panchekha and Cindy Rubio-Gonzalez and Zachary Tatlock

booktitle:
Correctness 2021: Fifth International Workshop on Software Correctness for HPC Applications, November 19, 2021, America's Center Convention Complex St. Louis, MO, USA

rawauthor:
Ganesh Gopalakrishnan and Ignacio Laguna and Ang Li and Pavel Panchekha and Cindy Rubio-Gonz{\'a}lez and Zachary Tatlock

rawbooktitle:
{Correctness 2021: Fifth International Workshop on Software Correctness for HPC Applications, November 19, 2021, America's Center Convention Complex St. Louis, MO, USA}

entry:
@InProceedings{Gopalakrishnan:2021:GNA,
  author =       "Ganesh Gopalakrishnan and Ignacio Laguna and Ang Li
                 and Pavel Panchekha and Cindy Rubio-Gonz{\'a}lez and
                 Zachary Tatlock",
  editor =       "????",
  booktitle =    "{Correctness 2021: Fifth International Workshop on
                 Software Correctness for HPC Applications, November 19,
                 2021, America's Center Convention Complex St. Louis,
                 MO, USA}",
  title =        "Guarding Numerics Amidst Rising Heterogeneity",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2021",
  bibdate =      "Mon Sep 11 06:54:23 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://correctness-workshop.github.io/2021/",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Gustafsson:2021:AFP
author: Oscar Gustafsson and Noah Hellman
title: Approximate Floating-Point Operations with Integer Units by Processing in the Logarithmic Domain
crossref: IEEE:2021:ISC
pages: 45--52
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00019
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Oscar Gustafsson and Noah Hellman
rawtitle: Approximate Floating-Point Operations with Integer Units by Processing in the Logarithmic Domain
entry:
@InProceedings{Gustafsson:2021:AFP,
  author =       "Oscar Gustafsson and Noah Hellman",
  title =        "Approximate Floating-Point Operations with Integer
                 Units by Processing in the Logarithmic Domain",
  crossref =     "IEEE:2021:ISC",
  pages =        "45--52",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00019",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Held:2021:KRP
author: James P. Held and Theo Mary
title: Keynote 1: Realizing the Promise of Quantum Computing
crossref: IEEE:2021:ISC
pages: xvi--xvi
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00011
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: James P. Held and Th{\'e}o Mary
rawtitle: Keynote 1: Realizing the Promise of Quantum Computing
entry:
@InProceedings{Held:2021:KRP,
  author =       "James P. Held and Th{\'e}o Mary",
  title =        "Keynote 1: Realizing the Promise of Quantum
                 Computing",
  crossref =     "IEEE:2021:ISC",
  pages =        "xvi--xvi",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00011",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: mastersthesis
filename: fparith.bib
label: Hellman:2021:MBA
author: Noah Hellman
title: Mitchell-Based Approximate Operations on Floating-Point Numbers
type: Master of Science Thesis in Electrical Engineering
school: Department of Electrical Engineering, Linkoping University
address: Linkoping, Sweden
pages: 56
day: 19
month: jun
monthnumber: 6
year: 2021
bibdate: Wed Dec 20 07:05:10 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.20 07:05:10 ???
remark: See cite Mitchell:1962:CMD.
acknowledgement: ack-nhfb
advisor: Oscar Gustafsson
rawauthor: Noah Hellman
rawtitle: {Mitchell}-Based Approximate Operations on Floating-Point Numbers
URL:
http://liu.diva-portal.org/smash/get/diva2:1590166/FULLTEXT01.pdf; http://liu.diva-portal.org/smash/record.jsf?pid=diva2%3A1590166&dswid=5128

abstract:
By adapting Mitchell's algorithm for floating-point numbers, one can efficiently perform arithmetic floating-point operations in an approximate logarithmic domain in order to perform approximate computations of functions such as multiplication, division, square root and others. This work examines how this algorithm can be improved in terms of accuracy and hardware complexity by applying a set of various methods that are parametrized and offer a large design space. Optimal coefficients for a large portion of this space is determined and used to synthesize circuits for both ASIC and FPGA circuits using the bfloat16 format. Optimal configurations are then extracted to create an optimal curve where one can select an acceptable error range and obtain a circuit with a minimal hardware cost.

rawabstract:
By adapting Mitchell's algorithm for floating-point numbers, one can efficiently perform arithmetic floating-point operations in an approximate logarithmic domain in order to perform approximate computations of functions such as multiplication, division, square root and others. This work examines how this algorithm can be improved in terms of accuracy and hardware complexity by applying a set of various methods that are parametrized and offer a large design space. Optimal coefficients for a large portion of this space is determined and used to synthesize circuits for both ASIC and FPGA circuits using the bfloat16 format. Optimal configurations are then extracted to create an optimal curve where one can select an acceptable error range and obtain a circuit with a minimal hardware cost.

entry:
@MastersThesis{Hellman:2021:MBA,
  author =       "Noah Hellman",
  title =        "{Mitchell}-Based Approximate Operations on
                 Floating-Point Numbers",
  type =         "{Master of Science Thesis in Electrical Engineering}",
  school =       "Department of Electrical Engineering, Link{\"o}ping
                 University",
  address =      "Link{\"o}ping, Sweden",
  pages =        "56",
  day =          "19",
  month =        jun,
  year =         "2021",
  bibdate =      "Wed Dec 20 07:05:10 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://liu.diva-portal.org/smash/get/diva2:1590166/FULLTEXT01.pdf;
                 http://liu.diva-portal.org/smash/record.jsf?pid=diva2%3A1590166&dswid=5128",
  abstract =     "By adapting Mitchell's algorithm for floating-point
                 numbers, one can efficiently perform arithmetic
                 floating-point operations in an approximate logarithmic
                 domain in order to perform approximate computations of
                 functions such as multiplication, division, square root
                 and others. This work examines how this algorithm can
                 be improved in terms of accuracy and hardware
                 complexity by applying a set of various methods that
                 are parametrized and offer a large design space.
                 Optimal coefficients for a large portion of this space
                 is determined and used to synthesize circuits for both
                 ASIC and FPGA circuits using the bfloat16 format.
                 Optimal configurations are then extracted to create an
                 optimal curve where one can select an acceptable error
                 range and obtain a circuit with a minimal hardware
                 cost.",
  acknowledgement = ack-nhfb,
  advisor =      "Oscar Gustafsson",
  remark =       "See \cite{Mitchell:1962:CMD}.",
}


bibtype: article
filename: fparith.bib
label: Ho:2021:GFD
author: Nhut-Minh Ho and Himeshi De Silva and Weng-Fai Wong
title: GRAM: a Framework for Dynamically Mixing Precisions in GPU Applications
journal: j-TACO
volume: 18
number: 2
pages: 19:1--19:24
month: mar
monthnumber: 3
year: 2021
DOI: https://doi.org/10.1145/3441830
ISSN: 1544-3566 (print), 1544-3973 (electronic) OR 15443566 (print), 15443973 (electronic)
ISSNL: 1544-3566 OR 15443566
bibdate: Sat Mar 20 17:25:10 MDT 2021
bibtimestamp: 2021.03.20 17:25:10 MDT
URL: https://dl.acm.org/doi/10.1145/3441830
fjournal: ACM Transactions on Architecture and Code Optimization (TACO)
acknowledgement: ack-nhfb
articleno: 19
journalURL: https://dl.acm.org/loi/taco
rawauthor: Nhut-Minh Ho and Himeshi {De Silva} and Weng-Fai Wong
rawtitle: {GRAM}: a Framework for Dynamically Mixing Precisions in {GPU} Applications
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib; https://www.math.utah.edu/pub/tex/bib/taco.bib

abstract:
This article presents GRAM (GPU-based Runtime Adaption for Mixed-precision) a framework for the effective use of mixed precision arithmetic for CUDA programs. Our method provides a fine-grain tradeoff between output error and performance. It can create many variants that satisfy different accuracy requirements by assigning different groups of threads to different precision levels adaptively at runtime. To widen the range of applications that can benefit from its approximation, GRAM comes with an optional half-precision approximate math library. Using GRAM, we can trade off precision for any performance improvement of up to 540%, depending on the application and accuracy requirement.

rawabstract:
This article presents GRAM (GPU-based Runtime Adaption for Mixed-precision) a framework for the effective use of mixed precision arithmetic for CUDA programs. Our method provides a fine-grain tradeoff between output error and performance. It can create many variants that satisfy different accuracy requirements by assigning different groups of threads to different precision levels adaptively at runtime. To widen the range of applications that can benefit from its approximation, GRAM comes with an optional half-precision approximate math library. Using GRAM, we can trade off precision for any performance improvement of up to 540\%, depending on the application and accuracy requirement.

entry:
@Article{Ho:2021:GFD,
  author =       "Nhut-Minh Ho and Himeshi {De Silva} and Weng-Fai
                 Wong",
  title =        "{GRAM}: a Framework for Dynamically Mixing Precisions
                 in {GPU} Applications",
  journal =      j-TACO,
  volume =       "18",
  number =       "2",
  pages =        "19:1--19:24",
  month =        mar,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3441830",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Sat Mar 20 17:25:10 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3441830",
  abstract =     "This article presents GRAM (GPU-based Runtime Adaption
                 for Mixed-precision) a framework for the effective use
                 of mixed precision arithmetic for CUDA programs. Our
                 method provides a fine-grain tradeoff between output
                 error and performance. It can create many variants that
                 satisfy different accuracy requirements by assigning
                 different groups of threads to different precision
                 levels adaptively at runtime. To widen the range of
                 applications that can benefit from its approximation,
                 GRAM comes with an optional half-precision approximate
                 math library. Using GRAM, we can trade off precision
                 for any performance improvement of up to 540\%,
                 depending on the application and accuracy
                 requirement.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "https://dl.acm.org/loi/taco",
}


bibtype: inproceedings
filename: fparith.bib
label: Ho:2021:PAT
editor: IEEE
booktitle: 2021 Design, Automation & Test in Europe Conference & Exhibition (DATE)
title: Posit Arithmetic for the Training and Deployment of Generative Adversarial Networks
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1350--1355
year: 2021
DOI: https://doi.org/10.23919/DATE51398.2021.9473933
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawbooktitle: {2021 Design, Automation \& Test in Europe Conference \& Exhibition (DATE)}
raweditor: {IEEE}
rawtitle: Posit Arithmetic for the Training and Deployment of Generative Adversarial Networks
author:
Nhut-Minh Ho and Duy-Thanh Nguyen and Himeshi De Silva and John L. Gustafson and Weng-Fai Wong and Ik Joon Chang

rawauthor:
Nhut-Minh Ho and Duy-Thanh Nguyen and Himeshi {De Silva} and John L. Gustafson and Weng-Fai Wong and Ik Joon Chang

entry:
@InProceedings{Ho:2021:PAT,
  author =       "Nhut-Minh Ho and Duy-Thanh Nguyen and Himeshi {De
                 Silva} and John L. Gustafson and Weng-Fai Wong and Ik
                 Joon Chang",
  editor =       "{IEEE}",
  booktitle =    "{2021 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "Posit Arithmetic for the Training and Deployment of
                 Generative Adversarial Networks",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1350--1355",
  year =         "2021",
  DOI =          "https://doi.org/10.23919/DATE51398.2021.9473933",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Hormigo:2021:FAB
author: Javier Hormigo and Gabriel Caffarena
title: FPGA acceleration of bit-true simulations for word-length optimization
crossref: IEEE:2021:ISC
pages: 119--122
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00033
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Javier Hormigo and Gabriel Caffarena
rawtitle: {FPGA} acceleration of bit-true simulations for word-length optimization
entry:
@InProceedings{Hormigo:2021:FAB,
  author =       "Javier Hormigo and Gabriel Caffarena",
  title =        "{FPGA} acceleration of bit-true simulations for
                 word-length optimization",
  crossref =     "IEEE:2021:ISC",
  pages =        "119--122",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00033",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Hough:2021:ISO
author: David G. Hough
title: The IEEE Standard 754: One for the History Books
journal: j-COMPUT-EDGE
number: 4
pages: 42--46
month: aug
monthnumber: 8
year: 2021
DOI: https://doi.org/10.1109/MC.2019.2926614
ISSN: 2469-7087 OR 24697087
bibdate: Thu Aug 19 14:23:25 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2021.08.19 14:23:25 ???
fjournal: Computing Edge
keywords: Floating-point arithmetic; Hardware; History; IEEE Standards; Microprocessors; Software
remark: Reprint of cite Hough:2019:ISO.
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/web/computingedge
rawauthor: David G. Hough
rawtitle: The {IEEE Standard 754}: One for the History Books
URL:
http://grouper.ieee.org/groups/msc/ANSI_IEEE-Std-754-2019/background/ieee-computer.pdf; https://www.computer.org/csdl/magazine/co/2019/12/08909942/1f8KFWxbTCU

entry:
@Article{Hough:2021:ISO,
  author =       "David G. Hough",
  title =        "The {IEEE Standard 754}: One for the History Books",
  journal =      j-COMPUT-EDGE,
  volume =       "??",
  number =       "4",
  pages =        "42--46",
  month =        aug,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/MC.2019.2926614",
  ISSN =         "2469-7087",
  bibdate =      "Thu Aug 19 14:23:25 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://grouper.ieee.org/groups/msc/ANSI_IEEE-Std-754-2019/background/ieee-computer.pdf;
                 https://www.computer.org/csdl/magazine/co/2019/12/08909942/1f8KFWxbTCU",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing Edge",
  journal-URL =  "http://www.computer.org/web/computingedge",
  keywords =     "Floating-point arithmetic; Hardware; History; IEEE
                 Standards; Microprocessors; Software",
  remark =       "Reprint of \cite{Hough:2019:ISO}.",
  xxISSN =       "2376-113X",
}


bibtype: misc
filename: fparith.bib
label: Jain:2021:M
author: Riya Jain and Niraj Nayan Sharma
title: Melodica
pages: 42--46
year: 2021
bibdate: Sat Dec 16 15:21:57 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.16 15:21:57 ???
URL: https://github.com/HPC-Lab-IITB/Melodica
keywords: posit arithmetic
acknowledgement: ack-nhfb
howpublished: Web software.
rawauthor: Riya Jain and Niraj Nayan Sharma
rawtitle: {Melodica}
entry:
@Misc{Jain:2021:M,
  author =       "Riya Jain and Niraj Nayan Sharma",
  title =        "{Melodica}",
  howpublished = "Web software.",
  year =         "2021",
  bibdate =      "Sat Dec 16 15:21:57 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/HPC-Lab-IITB/Melodica",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Jean:2021:PFN
editor: IEEE
title: P-FMA: a Novel Parameterized Posit Fused Multiply-Accumulate Arithmetic Processor
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 282--287
year: 2021
DOI: https://doi.org/10.1109/VLSID51830.2021.00053
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
raweditor: {IEEE}
rawtitle: {P-FMA}: a Novel Parameterized Posit Fused Multiply-Accumulate Arithmetic Processor
author:
Sandra Jean and Aneesh Raveendran and A. David Selvakumar and Gagandeep Kaur and Shankar G Dharani and Shashikala Gunderao Pattanshetty and Vivian Desalphine

booktitle:
2021 34th International Conference on VLSI Design and 2021 20th International Conference on Embedded Systems (VLSID)

rawauthor:
Sandra Jean and Aneesh Raveendran and A. David Selvakumar and Gagandeep Kaur and Shankar G Dharani and Shashikala Gunderao Pattanshetty and Vivian Desalphine

rawbooktitle:
{2021 34th International Conference on VLSI Design and 2021 20th International Conference on Embedded Systems (VLSID)}

entry:
@InProceedings{Jean:2021:PFN,
  author =       "Sandra Jean and Aneesh Raveendran and A. David
                 Selvakumar and Gagandeep Kaur and Shankar G Dharani and
                 Shashikala Gunderao Pattanshetty and Vivian
                 Desalphine",
  editor =       "{IEEE}",
  booktitle =    "{2021 34th International Conference on VLSI Design and
                 2021 20th International Conference on Embedded Systems
                 (VLSID)}",
  title =        "{P-FMA}: a Novel Parameterized Posit Fused
                 Multiply-Accumulate Arithmetic Processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "282--287",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/VLSID51830.2021.00053",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Joldes:2021:FA
author: Mioara Joldes and Fabrizio Lambert
title: Foreword ARITH 2021
crossref: IEEE:2021:ISC
pages: ix--x
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00005
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Mioara Joldes and Fabrizio Lambert
rawtitle: Foreword {ARITH 2021}
entry:
@InProceedings{Joldes:2021:FA,
  author =       "Mioara Joldes and Fabrizio Lambert",
  title =        "Foreword {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "ix--x",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00005",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Joldes:2021:SSE
author: Mioara Joldes and Fabrizio Lamberti and Alberto Nannarelli
title: Special Section on Emerging and Impacting Trends on Computer Arithmetic
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 9
number: 3
pages: 1449--1450
month: jul
monthnumber: 7
year: 2021
DOI: https://doi.org/10.1109/TETC.2021.3096698
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Mioara Joldes and Fabrizio Lamberti and Alberto Nannarelli
rawtitle: Special Section on Emerging and Impacting Trends on Computer Arithmetic
entry:
@Article{Joldes:2021:SSE,
  author =       "Mioara Joldes and Fabrizio Lamberti and Alberto
                 Nannarelli",
  title =        "Special Section on Emerging and Impacting Trends on
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1449--1450",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3096698",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: inproceedings
filename: fparith.bib
label: Kant:2021:IPI
author: Manash Kant and Rajeev Thakur
editor: IEEE
booktitle: 2021 Fifth International Conference on I-SMAC (IoT in Social, Mobile, Analytics and Cloud) (I-SMAC)
title: Implementation and Performance Improvement of POSIT Multiplier for Advance DSP Applications
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1730--1736
year: 2021
DOI: https://doi.org/10.1109/I-SMAC52330.2021.9640999
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Manash Kant and Rajeev Thakur
raweditor: {IEEE}
rawtitle: Implementation and Performance Improvement of {POSIT} Multiplier for Advance {DSP} Applications
rawbooktitle:
{2021 Fifth International Conference on I-SMAC (IoT in Social, Mobile, Analytics and Cloud) (I-SMAC)}

entry:
@InProceedings{Kant:2021:IPI,
  author =       "Manash Kant and Rajeev Thakur",
  editor =       "{IEEE}",
  booktitle =    "{2021 Fifth International Conference on I-SMAC (IoT in
                 Social, Mobile, Analytics and Cloud) (I-SMAC)}",
  title =        "Implementation and Performance Improvement of {POSIT}
                 Multiplier for Advance {DSP} Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1730--1736",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/I-SMAC52330.2021.9640999",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kouya:2021:ALD
author: Tomonori Kouya
crossref: IEEE:2021:ISC
pages: 54--61
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00021
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Tomonori Kouya
title:
Acceleration of $ L U $ decomposition supporting double--double, triple--double, and quadruple--double precision floating-point arithmetic with AVX2

rawtitle:
Acceleration of {$ L U $} decomposition supporting double--double, triple--double, and quadruple--double precision floating-point arithmetic with {AVX2}

entry:
@InProceedings{Kouya:2021:ALD,
  author =       "Tomonori Kouya",
  title =        "Acceleration of {$ L U $} decomposition supporting
                 double--double, triple--double, and quadruple--double
                 precision floating-point arithmetic with {AVX2}",
  crossref =     "IEEE:2021:ISC",
  pages =        "54--61",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00021",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Kulkarni:2021:PVS
editor: IEEE
title: PositGen --- a Verification Suite for Posit Arithmetic
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 204--209
year: 2021
DOI: https://doi.org/10.1109/VLSID51830.2021.00040
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
raweditor: {IEEE}
rawtitle: {PositGen} --- a Verification Suite for Posit Arithmetic
author:
Annarao Kulkarni and Shashikala Pattanshetty and Aneesh Raveendran and David Selvakumar and Sandra Jean and Vivian Desalphine

booktitle:
2021 34th International Conference on VLSI Design and 2021 20th International Conference on Embedded Systems (VLSID)

rawauthor:
Annarao Kulkarni and Shashikala Pattanshetty and Aneesh Raveendran and David Selvakumar and Sandra Jean and Vivian Desalphine

rawbooktitle:
{2021 34th International Conference on VLSI Design and 2021 20th International Conference on Embedded Systems (VLSID)}

entry:
@InProceedings{Kulkarni:2021:PVS,
  author =       "Annarao Kulkarni and Shashikala Pattanshetty and
                 Aneesh Raveendran and David Selvakumar and Sandra Jean
                 and Vivian Desalphine",
  editor =       "{IEEE}",
  booktitle =    "{2021 34th International Conference on VLSI Design and
                 2021 20th International Conference on Embedded Systems
                 (VLSID)}",
  title =        "{PositGen} --- a Verification Suite for Posit
                 Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "204--209",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/VLSID51830.2021.00040",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Lange:2021:CND
author: Marko Lange and Shin'ichi Oishi
title: Correction to: A note on Dekker's FastTwoSum algorithm
journal: j-NUM-MATH
volume: 149
number: 1
pages: 227--228
month: sep
monthnumber: 9
year: 2021
CODEN: NUMMA7
DOI: https://doi.org/10.1007/s00211-021-01213-8
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Wed Sep 15 05:50:42 MDT 2021
bibtimestamp: 2021.09.15 05:50:42 MDT
note: See cite Lange:2020:NDF.
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Marko Lange and Shin'ichi Oishi
rawnote: See \cite{Lange:2020:NDF}.
rawtitle: Correction to: {A note on Dekker's FastTwoSum algorithm}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/nummath2020.bib

URL:
http://link.springer.com/article/10.1007/s00211-021-01213-8; https://link.springer.com/content/pdf/10.1007/s00211-021-01213-8.pdf

entry:
@Article{Lange:2021:CND,
  author =       "Marko Lange and Shin'ichi Oishi",
  title =        "Correction to: {A note on Dekker's FastTwoSum
                 algorithm}",
  journal =      j-NUM-MATH,
  volume =       "149",
  number =       "1",
  pages =        "227--228",
  month =        sep,
  year =         "2021",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-021-01213-8",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Wed Sep 15 05:50:42 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
  note =         "See \cite{Lange:2020:NDF}.",
  URL =          "http://link.springer.com/article/10.1007/s00211-021-01213-8;
                 https://link.springer.com/content/pdf/10.1007/s00211-021-01213-8.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: inproceedings
filename: fparith.bib
label: Langroudi:2021:AAQ
editor: IEEE
booktitle: 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)
title: Alps: Adaptive Quantization of Deep Neural Networks with GeneraLized PositS
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 3094--3103
year: 2021
DOI: https://doi.org/10.1109/CVPRW53098.2021.00346
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawbooktitle: {2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)}
raweditor: {IEEE}
rawtitle: Alps: Adaptive Quantization of Deep Neural Networks with {GeneraLized} {PositS}
author:
Hamed F. Langroudi and Vedant Karia and Zachariah Carmichael and Abdullah Zyarah and Tej Pandit and John L. Gustafson and Dhireesha Kudithipudi

rawauthor:
Hamed F. Langroudi and Vedant Karia and Zachariah Carmichael and Abdullah Zyarah and Tej Pandit and John L. Gustafson and Dhireesha Kudithipudi

entry:
@InProceedings{Langroudi:2021:AAQ,
  author =       "Hamed F. Langroudi and Vedant Karia and Zachariah
                 Carmichael and Abdullah Zyarah and Tej Pandit and John
                 L. Gustafson and Dhireesha Kudithipudi",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE/CVF Conference on Computer Vision and
                 Pattern Recognition Workshops (CVPRW)}",
  title =        "Alps: Adaptive Quantization of Deep Neural Networks
                 with {GeneraLized} {PositS}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3094--3103",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/CVPRW53098.2021.00346",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Lemire:2021:NPG
author: Daniel Lemire
title: Number parsing at a gigabyte per second
journal: j-SPE
volume: 51
number: 8
pages: 1700--1727
month: aug
monthnumber: 8
year: 2021
CODEN: SPEXBL
DOI: https://doi.org/10.1002/spe.2984
ISSN: 0038-0644 (print), 1097-024X (electronic) OR 00380644 (print), 1097024X (electronic)
ISSNL: 0038-0644 OR 00380644
bibdate: Fri Jul 23 09:04:36 MDT 2021
bibtimestamp: 2021.07.23 09:04:36 MDT
note: See improvement cite Mushtak:2023:FNP.
fjournal: Software --- Practice and Experience
acknowledgement: ack-nhfb
ajournal: Softw. Pract. Exp.
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X
onlinedate: 11 May 2021
rawauthor: Daniel Lemire
rawnote: See improvement \cite{Mushtak:2023:FNP}.
rawtitle: Number parsing at a gigabyte per second
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/go.bib; https://www.math.utah.edu/pub/tex/bib/spe.bib

abstract:
With disks and networks providing gigabytes per second, parsing decimal numbers from strings becomes a bottleneck. We consider the problem of parsing decimal numbers to the nearest binary floating-point value. The general problem requires variable-precision arithmetic. However, we need at most 17 digits to represent 64-bit standard floating-point numbers (IEEE 754). Thus, we can represent the decimal significand with a single 64-bit word. By combining the significand and precomputed tables, we can compute the nearest floating-point number using as few as one or two 64-bit multiplications. Our implementation can be several times faster than conventional functions present in standard C libraries on modern 64-bit systems (Intel, AMD, ARM, and POWER9). Our work is available as open source software used by major systems such as Apache Arrow and Yandex ClickHouse. The Go standard library has adopted a version of our approach.

rawabstract:
With disks and networks providing gigabytes per second, parsing decimal numbers from strings becomes a bottleneck. We consider the problem of parsing decimal numbers to the nearest binary floating-point value. The general problem requires variable-precision arithmetic. However, we need at most 17 digits to represent 64-bit standard floating-point numbers (IEEE 754). Thus, we can represent the decimal significand with a single 64-bit word. By combining the significand and precomputed tables, we can compute the nearest floating-point number using as few as one or two 64-bit multiplications. Our implementation can be several times faster than conventional functions present in standard C libraries on modern 64-bit systems (Intel, AMD, ARM, and POWER9). Our work is available as open source software used by major systems such as Apache Arrow and Yandex ClickHouse. The Go standard library has adopted a version of our approach.

entry:
@Article{Lemire:2021:NPG,
  author =       "Daniel Lemire",
  title =        "Number parsing at a gigabyte per second",
  journal =      j-SPE,
  volume =       "51",
  number =       "8",
  pages =        "1700--1727",
  month =        aug,
  year =         "2021",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.2984",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Fri Jul 23 09:04:36 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/go.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  note =         "See improvement \cite{Mushtak:2023:FNP}.",
  abstract =     "With disks and networks providing gigabytes per
                 second, parsing decimal numbers from strings becomes a
                 bottleneck. We consider the problem of parsing decimal
                 numbers to the nearest binary floating-point value. The
                 general problem requires variable-precision arithmetic.
                 However, we need at most 17 digits to represent 64-bit
                 standard floating-point numbers (IEEE 754). Thus, we
                 can represent the decimal significand with a single
                 64-bit word. By combining the significand and
                 precomputed tables, we can compute the nearest
                 floating-point number using as few as one or two 64-bit
                 multiplications. Our implementation can be several
                 times faster than conventional functions present in
                 standard C libraries on modern 64-bit systems (Intel,
                 AMD, ARM, and POWER9). Our work is available as open
                 source software used by major systems such as Apache
                 Arrow and Yandex ClickHouse. The Go standard library
                 has adopted a version of our approach.",
  acknowledgement = ack-nhfb,
  ajournal =     "Softw. Pract. Exp.",
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "11 May 2021",
}


bibtype: article
filename: fparith.bib
label: Leon:2021:IPD
title: Improving Power of DSP and CNN Hardware Accelerators Using Approximate Floating-point Multipliers
journal: j-TECS
volume: 20
number: 5
pages: 39:1--39:21
month: jul
monthnumber: 7
year: 2021
DOI: https://doi.org/10.1145/3448980
ISSN: 1539-9087 (print), 1558-3465 (electronic) OR 15399087 (print), 15583465 (electronic)
ISSNL: 1539-9087 OR 15399087
bibdate: Tue Aug 10 13:35:00 MDT 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/tecs.bib
bibtimestamp: 2021.08.10 13:35:00 MDT
URL: https://dl.acm.org/doi/10.1145/3448980
fjournal: ACM Transactions on Embedded Computing Systems
acknowledgement: ack-nhfb
articleno: 39
journalURL: https://dl.acm.org/loi/tecs
author:
Vasileios Leon and Theodora Paparouni and Evangelos Petrongonas and Dimitrios Soudris and Kiamal Pekmestzi

abstract:
Approximate computing has emerged as a promising design alternative for delivering power-efficient systems and circuits by exploiting the inherent error resiliency of numerous applications. The current article aims to tackle the increased hardware cost of floating-point multiplication units, which prohibits their usage in embedded computing. We introduce AFMU (Approximate Floating-point MUltiplier), an area/power-efficient family of multipliers, which apply two approximation techniques in the resource-hungry mantissa multiplication and can be seamlessly extended to support dynamic configuration of the approximation levels via gating signals. AFMU offers large accuracy configuration margins, provides negligible logic overhead for dynamic configuration, and detects unexpected results that may arise due to the approximations. Our evaluation shows that AFMU delivers energy gains in the range 3.6%--53.5% for half-precision and 37.2%--82.4% for single-precision, in exchange for mean relative error around 0.05%--3.33% and 0.01%--2.20%, respectively. In comparison with state-of-the-art multipliers, AFMU exhibits up to 4--6 $ times $ smaller error on average while delivering more energy-efficient computing. The evaluation in image processing shows that AFMU provides sufficient quality of service, i.e., more than 50db PSNR and near 1 SSIM values, and up to 57.4% power reduction. When used in floating-point CNNs, the accuracy loss is small (or zero), i.e., up to 5.4% for MNIST and CIFAR-10, in exchange for up to 63.8% power gain.

rawabstract:
Approximate computing has emerged as a promising design alternative for delivering power-efficient systems and circuits by exploiting the inherent error resiliency of numerous applications. The current article aims to tackle the increased hardware cost of floating-point multiplication units, which prohibits their usage in embedded computing. We introduce AFMU (Approximate Floating-point MUltiplier), an area/power-efficient family of multipliers, which apply two approximation techniques in the resource-hungry mantissa multiplication and can be seamlessly extended to support dynamic configuration of the approximation levels via gating signals. AFMU offers large accuracy configuration margins, provides negligible logic overhead for dynamic configuration, and detects unexpected results that may arise due to the approximations. Our evaluation shows that AFMU delivers energy gains in the range 3.6\%--53.5\% for half-precision and 37.2\%--82.4\% for single-precision, in exchange for mean relative error around 0.05\%--3.33\% and 0.01\%--2.20\%, respectively. In comparison with state-of-the-art multipliers, AFMU exhibits up to 4--6 $ \times $ smaller error on average while delivering more energy-efficient computing. The evaluation in image processing shows that AFMU provides sufficient quality of service, i.e., more than 50db PSNR and near 1 SSIM values, and up to 57.4\% power reduction. When used in floating-point CNNs, the accuracy loss is small (or zero), i.e., up to 5.4\% for MNIST and CIFAR-10, in exchange for up to 63.8\% power gain.

rawauthor:
Vasileios Leon and Theodora Paparouni and Evangelos Petrongonas and Dimitrios Soudris and Kiamal Pekmestzi

rawtitle:
Improving Power of {DSP} and {CNN} Hardware Accelerators Using Approximate Floating-point Multipliers

entry:
@Article{Leon:2021:IPD,
  author =       "Vasileios Leon and Theodora Paparouni and Evangelos
                 Petrongonas and Dimitrios Soudris and Kiamal
                 Pekmestzi",
  title =        "Improving Power of {DSP} and {CNN} Hardware
                 Accelerators Using Approximate Floating-point
                 Multipliers",
  journal =      j-TECS,
  volume =       "20",
  number =       "5",
  pages =        "39:1--39:21",
  month =        jul,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3448980",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Tue Aug 10 13:35:00 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3448980",
  abstract =     "Approximate computing has emerged as a promising
                 design alternative for delivering power-efficient
                 systems and circuits by exploiting the inherent error
                 resiliency of numerous applications. The current
                 article aims to tackle the increased hardware cost of
                 floating-point multiplication units, which prohibits
                 their usage in embedded computing. We introduce AFMU
                 (Approximate Floating-point MUltiplier), an
                 area/power-efficient family of multipliers, which apply
                 two approximation techniques in the resource-hungry
                 mantissa multiplication and can be seamlessly extended
                 to support dynamic configuration of the approximation
                 levels via gating signals. AFMU offers large accuracy
                 configuration margins, provides negligible logic
                 overhead for dynamic configuration, and detects
                 unexpected results that may arise due to the
                 approximations. Our evaluation shows that AFMU delivers
                 energy gains in the range 3.6\%--53.5\% for
                 half-precision and 37.2\%--82.4\% for single-precision,
                 in exchange for mean relative error around
                 0.05\%--3.33\% and 0.01\%--2.20\%, respectively. In
                 comparison with state-of-the-art multipliers, AFMU
                 exhibits up to 4--6 $ \times $ smaller error on average
                 while delivering more energy-efficient computing. The
                 evaluation in image processing shows that AFMU provides
                 sufficient quality of service, i.e., more than 50db
                 PSNR and near 1 SSIM values, and up to 57.4\% power
                 reduction. When used in floating-point CNNs, the
                 accuracy loss is small (or zero), i.e., up to 5.4\% for
                 MNIST and CIFAR-10, in exchange for up to 63.8\% power
                 gain.",
  acknowledgement = ack-nhfb,
  articleno =    "39",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}


bibtype: article
filename: fparith.bib
label: Liu:2021:DAM
title: Design and Analysis of Majority Logic-Based Approximate Adders and Multipliers
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 9
number: 3
pages: 1609--1624
month: jul
monthnumber: 7
year: 2021
DOI: https://doi.org/10.1109/TETC.2019.2929100
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawtitle: Design and Analysis of Majority Logic-Based Approximate Adders and Multipliers
author:
Weiqiang Liu and Tingting Zhang and Emma McLarnon and Maire O'Neill and Paolo Montuschi and Fabrizio Lombardi

rawauthor:
Weiqiang Liu and Tingting Zhang and Emma McLarnon and Maire O'Neill and Paolo Montuschi and Fabrizio Lombardi

entry:
@Article{Liu:2021:DAM,
  author =       "Weiqiang Liu and Tingting Zhang and Emma McLarnon and
                 Maire O'Neill and Paolo Montuschi and Fabrizio
                 Lombardi",
  title =        "Design and Analysis of Majority Logic-Based
                 Approximate Adders and Multipliers",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1609--1624",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2019.2929100",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: article
filename: fparith.bib
label: Lu:2021:EDN
author: Jinming Lu and Chao Fang and Mingyang Xu and Jun Lin and Zhongfeng Wang
title: Evaluations on Deep Neural Networks Training Using Posit Number System
journal: j-IEEE-TRANS-COMPUT
volume: 70
number: 2
pages: 174--187
year: 2021
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2020.2985971
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jinming Lu and Chao Fang and Mingyang Xu and Jun Lin and Zhongfeng Wang
rawtitle: Evaluations on Deep Neural Networks Training Using Posit Number System
entry:
@Article{Lu:2021:EDN,
  author =       "Jinming Lu and Chao Fang and Mingyang Xu and Jun Lin
                 and Zhongfeng Wang",
  title =        "Evaluations on Deep Neural Networks Training Using
                 Posit Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "2",
  pages =        "174--187",
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.2985971",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Mary:2021:KOM
author: Theo Mary
title: Keynote 2: Opportunities for Mixed Precision Arithmetic in Numerical Linear Algebra
crossref: IEEE:2021:ISC
pages: xvii--xvii
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00011
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Th{\'e}o Mary
rawtitle: Keynote 2: Opportunities for Mixed Precision Arithmetic in Numerical Linear Algebra
entry:
@InProceedings{Mary:2021:KOM,
  author =       "Th{\'e}o Mary",
  title =        "Keynote 2: Opportunities for Mixed Precision
                 Arithmetic in Numerical Linear Algebra",
  crossref =     "IEEE:2021:ISC",
  pages =        "xvii--xvii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00011",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Matos:2021:EFP
author: Jose A. O. Matos and Paulo B. Vasconcelos
title: Effectiveness of Floating-Point Precision on the Numerical Approximation by Spectral Methods
journal: j-MATH-COMPUT-APPL
volume: 26
number: 2
pages: 42--??
month: jun
monthnumber: 6
year: 2021
DOI: https://doi.org/10.3390/mca26020042
ISSN: 2297-8747 OR 22978747
ISSNL: 2297-8747 OR 22978747
bibdate: Sun Feb 18 06:28:40 MST 2024
bibtimestamp: 2024.02.18 06:28:40 MST
URL: https://www.mdpi.com/2297-8747/26/2/42
fjournal: Mathematical and Computational Applications
acknowledgement: ack-nhfb
journalURL: https://www.mdpi.com/journal/mca
rawauthor: Jos{\'e} A. O. Matos and Paulo B. Vasconcelos
rawtitle: Effectiveness of Floating-Point Precision on the Numerical Approximation by Spectral Methods
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib

entry:
@Article{Matos:2021:EFP,
  author =       "Jos{\'e} A. O. Matos and Paulo B. Vasconcelos",
  title =        "Effectiveness of Floating-Point Precision on the
                 Numerical Approximation by Spectral Methods",
  journal =      j-MATH-COMPUT-APPL,
  volume =       "26",
  number =       "2",
  pages =        "42--??",
  month =        jun,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.3390/mca26020042",
  ISSN =         "2297-8747",
  ISSN-L =       "2297-8747",
  bibdate =      "Sun Feb 18 06:28:40 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
  URL =          "https://www.mdpi.com/2297-8747/26/2/42",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical and Computational Applications",
  journal-URL =  "https://www.mdpi.com/journal/mca",
}


bibtype: techreport
filename: fparith.bib
label: MPFR:2021:MLA
author: The MPFR Team
title: The MPFR Library: Algorithms and Proofs
type: Report
pages: 69
day: 5
month: nov
monthnumber: 11
year: 2021
bibdate: Tue Mar 14 13:13:13 2023
bibtimestamp: 2023.03.14 13:13:13 ???
URL: https://www.mpfr.org/algorithms.pdf
acknowledgement: ack-nhfb
rawauthor: {The MPFR Team}
rawtitle: The {MPFR} Library: Algorithms and Proofs
entry:
@TechReport{MPFR:2021:MLA,
  author =       "{The MPFR Team}",
  title =        "The {MPFR} Library: Algorithms and Proofs",
  type =         "Report",
  institution =  "????",
  address =      "????",
  pages =        "69",
  day =          "5",
  month =        nov,
  year =         "2021",
  bibdate =      "Tue Mar 14 13:13:13 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.mpfr.org/algorithms.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Muller:2021:X
author: Jean-Michel Muller
title: $ a cdot (x cdot x) $ or $ (a cdot x) cdot x? $
crossref: IEEE:2021:ISC
pages: 17--24
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00015
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Jean-Michel Muller
rawtitle: $ a \cdot (x \cdot \ x) $ or $ (a \cdot x) \cdot x? $
abstract:
Expressions such as $ a x^2 $, $ a x y $, or $ a x^3 $, where $a$ is a constant, are not infrequent in computing. There are several ways of parenthesizing them (and therefore, choosing the order of evaluation). Depending on the value of $a$, is there a more accurate evaluation order? We discuss this point (with a small digression on spurious underflows and overflows).

rawabstract:
Expressions such as $ a x^2 $, $ a x y $, or $ a x^3 $, where $a$ is a constant, are not infrequent in computing. There are several ways of parenthesizing them (and therefore, choosing the order of evaluation). Depending on the value of $a$, is there a more accurate evaluation order? We discuss this point (with a small digression on spurious underflows and overflows).

entry:
@InProceedings{Muller:2021:X,
  author =       "Jean-Michel Muller",
  title =        "$ a \cdot (x \cdot \ x) $ or $ (a \cdot x) \cdot x?
                 $",
  crossref =     "IEEE:2021:ISC",
  pages =        "17--24",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00015",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Expressions such as $ a x^2 $, $ a x y $, or $ a x^3
                 $, where $a$ is a constant, are not infrequent in
                 computing. There are several ways of parenthesizing
                 them (and therefore, choosing the order of evaluation).
                 Depending on the value of $a$, is there a more accurate
                 evaluation order? We discuss this point (with a small
                 digression on spurious underflows and overflows).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Muntean:2021:IIR
author: Paul Muntean and Martin Monperrus and Hao Sun and Jens Grossklags and Claudia Eckert
title: IntRepair: Informed Repairing of Integer Overflows
journal: j-IEEE-TRANS-SOFTW-ENG
volume: 47
number: 10
pages: 2225--2241
month: oct
monthnumber: 10
year: 2021
CODEN: IESEDJ
DOI: https://doi.org/10.1109/TSE.2019.2946148
ISSN: 0098-5589 (print), 1939-3520 (electronic) OR 00985589 (print), 19393520 (electronic)
ISSNL: 0098-5589 OR 00985589
bibdate: Thu Oct 21 10:49:15 2021
bibtimestamp: 2021.10.21 10:49:15 ???
fjournal: IEEE Transactions on Software Engineering
keywords: integer overflow detection and repair
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32
rawauthor: Paul Muntean and Martin Monperrus and Hao Sun and Jens Grossklags and Claudia Eckert
rawtitle: {IntRepair}: Informed Repairing of Integer Overflows
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranssoftweng2020.bib

abstract:
Integer overflows have threatened software applications for decades. Thus, in this paper, we propose a novel technique to provide automatic repairs of integer overflows in C source code. Our technique, based on static symbolic execution, fuses detection , repair generation and validation. This technique is implemented in a prototype named IntRepair. We applied IntRepair to 2,052 C programs (approx. 1 million lines of code) contained in SAMATE's Juliet test suite and 50 synthesized programs that range up to 20 KLOC. Our experimental results show that IntRepair is able to effectively detect integer overflows and successfully repair them, while only increasing the source code (LOC) and binary (Kb) size by around 1 percent, respectively. Further, we present the results of a user study with 30 participants which shows that IntRepair repairs are more than 10x efficient as compared to manually generated code repairs.

rawabstract:
Integer overflows have threatened software applications for decades. Thus, in this paper, we propose a novel technique to provide automatic repairs of integer overflows in C source code. Our technique, based on static symbolic execution, fuses detection , repair generation and validation. This technique is implemented in a prototype named IntRepair. We applied IntRepair to 2,052 C programs (approx. 1 million lines of code) contained in SAMATE's Juliet test suite and 50 synthesized programs that range up to 20 KLOC. Our experimental results show that IntRepair is able to effectively detect integer overflows and successfully repair them, while only increasing the source code (LOC) and binary (Kb) size by around 1 percent, respectively. Further, we present the results of a user study with 30 participants which shows that IntRepair repairs are more than 10x efficient as compared to manually generated code repairs.

entry:
@Article{Muntean:2021:IIR,
  author =       "Paul Muntean and Martin Monperrus and Hao Sun and Jens
                 Grossklags and Claudia Eckert",
  title =        "{IntRepair}: Informed Repairing of Integer Overflows",
  journal =      j-IEEE-TRANS-SOFTW-ENG,
  volume =       "47",
  number =       "10",
  pages =        "2225--2241",
  month =        oct,
  year =         "2021",
  CODEN =        "IESEDJ",
  DOI =          "https://doi.org/10.1109/TSE.2019.2946148",
  ISSN =         "0098-5589 (print), 1939-3520 (electronic)",
  ISSN-L =       "0098-5589",
  bibdate =      "Thu Oct 21 10:49:15 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranssoftweng2020.bib",
  abstract =     "Integer overflows have threatened software
                 applications for decades. Thus, in this paper, we
                 propose a novel technique to provide automatic repairs
                 of integer overflows in C source code. Our technique,
                 based on static symbolic execution, fuses detection ,
                 repair generation and validation. This technique is
                 implemented in a prototype named IntRepair. We applied
                 IntRepair to 2,052 C programs (approx. 1 million lines
                 of code) contained in SAMATE's Juliet test suite and 50
                 synthesized programs that range up to 20 KLOC. Our
                 experimental results show that IntRepair is able to
                 effectively detect integer overflows and successfully
                 repair them, while only increasing the source code
                 (LOC) and binary (Kb) size by around 1 percent,
                 respectively. Further, we present the results of a user
                 study with 30 participants which shows that IntRepair
                 repairs are more than 10x efficient as compared to
                 manually generated code repairs.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Software Engineering",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
  keywords =     "integer overflow detection and repair",
}


bibtype: inproceedings
filename: fparith.bib
label: Murillo:2021:EEM
author: Raul Murillo and David Mallasen and Alberto A. Del Barrio and Guillermo Botella
editor: IEEE
title: Energy-Efficient MAC Units for Fused Posit Arithmetic
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 138--145
month: oct
monthnumber: 10
year: 2021
DOI: https://doi.org/10.1109/iccd53106.2021.00032
bibdate: Thu Dec 14 18:10:59 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.14 18:10:59 ???
acknowledgement: ack-nhfb
rawauthor: Raul Murillo and David Mallasen and Alberto A. {Del Barrio} and Guillermo Botella
raweditor: {IEEE}
rawtitle: Energy-Efficient {MAC} Units for Fused Posit Arithmetic
booktitle:
2021 IEEE 39th International Conference on Computer Design (ICCD): 24--27 October 2021, Storrs, CT, USA

rawbooktitle:
{2021 IEEE 39th International Conference on Computer Design (ICCD): 24--27 October 2021, Storrs, CT, USA}

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  author =       "Raul Murillo and David Mallasen and Alberto A. {Del
                 Barrio} and Guillermo Botella",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE 39th International Conference on Computer
                 Design (ICCD): 24--27 October 2021, Storrs, CT, USA}",
  title =        "Energy-Efficient {MAC} Units for Fused Posit
                 Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "138--145",
  month =        oct,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/iccd53106.2021.00032",
  bibdate =      "Thu Dec 14 18:10:59 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
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bibtype: article
filename: fparith.bib
label: Nambi:2021:EDE
title: ExPAN(N)D: Exploring Posits for Efficient Artificial Neural Network Design in FPGA-Based Systems
journal: j-IEEE-ACCESS
volume: 9
pages: 103691--103708
year: 2021
DOI: https://doi.org/10.1109/ACCESS.2021.3098730
ISSN: 2169-3536 OR 21693536
ISSNL: 2169-3536 OR 21693536
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
fjournal: IEEE Access
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639
author:
Suresh Nambi and Salim Ullah and Siva Satyendra Sahoo and Aditya Lohana and Farhad Merchant and Akash Kumar

rawauthor:
Suresh Nambi and Salim Ullah and Siva Satyendra Sahoo and Aditya Lohana and Farhad Merchant and Akash Kumar

rawtitle:
{ExPAN(N)D}: Exploring Posits for Efficient Artificial Neural Network Design in {FPGA}-Based Systems

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@Article{Nambi:2021:EDE,
  author =       "Suresh Nambi and Salim Ullah and Siva Satyendra Sahoo
                 and Aditya Lohana and Farhad Merchant and Akash Kumar",
  title =        "{ExPAN(N)D}: Exploring Posits for Efficient Artificial
                 Neural Network Design in {FPGA}-Based Systems",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "103691--103708",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3098730",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}


bibtype: inproceedings
filename: fparith.bib
label: Nannarelli:2021:OCA
title: Organizing Committee ARITH 2021
crossref: IEEE:2021:ISC
pages: xi--xi
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00006
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawtitle: Organizing Committee {ARITH 2021}
author:
Alberto Nannarelli and Mioara Joldes and Fabrizio Lamberti and Flemming Stassen and Daniele Jahier Pagliari and Alberto Cannavo

rawauthor:
Alberto Nannarelli and Mioara Joldes and Fabrizio Lamberti and Flemming Stassen and Daniele Jahier Pagliari and Alberto Cannav{\`o}

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@InProceedings{Nannarelli:2021:OCA,
  author =       "Alberto Nannarelli and Mioara Joldes and Fabrizio
                 Lamberti and Flemming Stassen and Daniele Jahier
                 Pagliari and Alberto Cannav{\`o}",
  title =        "Organizing Committee {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xi--xi",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00006",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Norris:2021:AIP
author: Cameron James Norris and Sunwoong Kim
editor: IEEE
booktitle: 2021 IEEE International Symposium on Circuits and Systems (ISCAS)
title: An Approximate and Iterative Posit Multiplier Architecture for FPGAs
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--5
year: 2021
DOI: https://doi.org/10.1109/ISCAS51556.2021.9401158
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Cameron James Norris and Sunwoong Kim
rawbooktitle: {2021 IEEE International Symposium on Circuits and Systems (ISCAS)}
raweditor: {IEEE}
rawtitle: An Approximate and Iterative Posit Multiplier Architecture for {FPGAs}
entry:
@InProceedings{Norris:2021:AIP,
  author =       "Cameron James Norris and Sunwoong Kim",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "An Approximate and Iterative Posit Multiplier
                 Architecture for {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISCAS51556.2021.9401158",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
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bibtype: inproceedings
filename: fparith.bib
label: Parrot:2021:POU
author: Remi Parrot and Mikael Briday and Olivier H. Roux
title: Pipeline Optimization using a Cost Extension of Timed Petri Nets
crossref: IEEE:2021:ISC
pages: 37--44
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00018
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: R{\'e}mi Parrot and Mika{\"e}l Briday and Olivier H. Roux
rawtitle: Pipeline Optimization using a Cost Extension of Timed Petri Nets
entry:
@InProceedings{Parrot:2021:POU,
  author =       "R{\'e}mi Parrot and Mika{\"e}l Briday and Olivier H.
                 Roux",
  title =        "Pipeline Optimization using a Cost Extension of Timed
                 Petri Nets",
  crossref =     "IEEE:2021:ISC",
  pages =        "37--44",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00018",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Plantard:2021:EWSa
author: Thomas Plantard
title: Efficient Word Size Modular Arithmetic
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 9
number: 3
pages: 1506--1518
month: jul
monthnumber: 7
year: 2021
DOI: https://doi.org/10.1109/TETC.2021.3073475
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
note: See cite Plantard:2021:EWSb.
fjournal: IEEE Transactions on Emerging Topics in Computing
keywords: ARITH-28
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Thomas Plantard
rawnote: See \cite{Plantard:2021:EWSb}.
rawtitle: Efficient Word Size Modular Arithmetic
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@Article{Plantard:2021:EWSa,
  author =       "Thomas Plantard",
  title =        "Efficient Word Size Modular Arithmetic",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1506--1518",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3073475",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  note =         "See \cite{Plantard:2021:EWSb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
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bibtype: inproceedings
filename: fparith.bib
label: Plantard:2021:EWSb
author: Thomas Plantard
title: Efficient Word Size Modular Arithmetic
crossref: IEEE:2021:ISC
pages: 139--139
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00036
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
note: See cite Plantard:2021:EWSa.
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Thomas Plantard
rawnote: See \cite{Plantard:2021:EWSa}.
rawtitle: Efficient Word Size Modular Arithmetic
entry:
@InProceedings{Plantard:2021:EWSb,
  author =       "Thomas Plantard",
  title =        "Efficient Word Size Modular Arithmetic",
  crossref =     "IEEE:2021:ISC",
  pages =        "139--139",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00036",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Plantard:2021:EWSa}.",
  acknowledgement = ack-nhfb,
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  remark =       "Published in IEEE Transactions on Emerging Topics in
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}


bibtype: inproceedings
filename: fparith.bib
label: Rao:2021:PND
author: Dhage Navaneet Rao and Ganne Sai Charan and Degala Veera Venkata Sairam and Kamatchi S.
title: Posit Number Division using Newton--Raphson method
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--6
month: feb
monthnumber: 2
year: 2021
DOI: https://doi.org/10.1109/icaect49130.2021.9392582
bibdate: Fri Dec 15 06:57:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 06:57:08 ???
acknowledgement: ack-nhfb
rawauthor: Dhage Navaneet Rao and Ganne Sai Charan and Degala Veera Venkata Sairam and Kamatchi S.
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2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT)

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{2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT)}

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@InProceedings{Rao:2021:PND,
  author =       "Dhage Navaneet Rao and Ganne Sai Charan and Degala
                 Veera Venkata Sairam and Kamatchi S.",
  booktitle =    "{2021 International Conference on Advances in
                 Electrical, Computing, Communication and Sustainable
                 Technologies (ICAECT)}",
  title =        "Posit Number Division using {Newton--Raphson} method",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  month =        feb,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/icaect49130.2021.9392582",
  bibdate =      "Fri Dec 15 06:57:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
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bibtype: inproceedings
filename: fparith.bib
label: Raposo:2021:PTD
author: Goncalo Raposo and Pedro Tomas and Nuno Roma
editor: IEEE
title: Positnn: Training Deep Neural Networks with Mixed Low-Precision Posit
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 7908--7912
year: 2021
DOI: https://doi.org/10.1109/ICASSP39728.2021.9413919
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Gon{\c{c}}alo Raposo and Pedro Tom{\'a}s and Nuno Roma
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rawtitle: Positnn: Training Deep Neural Networks with Mixed Low-Precision Posit
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ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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{ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}

entry:
@InProceedings{Raposo:2021:PTD,
  author =       "Gon{\c{c}}alo Raposo and Pedro Tom{\'a}s and Nuno
                 Roma",
  editor =       "{IEEE}",
  booktitle =    "{ICASSP 2021 - 2021 IEEE International Conference on
                 Acoustics, Speech and Signal Processing (ICASSP)}",
  title =        "Positnn: Training Deep Neural Networks with Mixed
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  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "7908--7912",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ICASSP39728.2021.9413919",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
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bibtype: article
filename: fparith.bib
label: Reichenbach:2021:RVR
author: Marc Reichenbach and Johannes Knodtel and Sebastian Rachuj and Dietmar Fey
title: RISC-V3: a RISC-V Compatible CPU With a Data Path Based on Redundant Number Systems
journal: j-IEEE-ACCESS
volume: 9
pages: 43684--43700
year: 2021
DOI: https://doi.org/10.1109/ACCESS.2021.3063238
ISSN: 2169-3536 OR 21693536
bibdate: Sat Dec 16 15:51:40 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.12.16 15:51:40 ???
fjournal: IEEE Access
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639
rawauthor: Marc Reichenbach and Johannes Kn{\"o}dtel and Sebastian Rachuj and Dietmar Fey
rawtitle: {RISC-V3}: a {RISC-V} Compatible {CPU} With a Data Path Based on Redundant Number Systems
entry:
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  author =       "Marc Reichenbach and Johannes Kn{\"o}dtel and
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  journal =      j-IEEE-ACCESS,
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  pages =        "43684--43700",
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  DOI =          "https://doi.org/10.1109/ACCESS.2021.3063238",
  ISSN =         "2169-3536",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
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bibtype: inproceedings
filename: fparith.bib
label: Revy:2021:AIF
author: Guillaume Revy
title: Analyzing the impact of floating-point precision adaptation in iterative programs
crossref: IEEE:2021:ISC
pages: 25--32
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00016
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Guillaume Revy
rawtitle: Analyzing the impact of floating-point precision adaptation in iterative programs
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@InProceedings{Revy:2021:AIF,
  author =       "Guillaume Revy",
  title =        "Analyzing the impact of floating-point precision
                 adaptation in iterative programs",
  crossref =     "IEEE:2021:ISC",
  pages =        "25--32",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00016",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
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bibtype: book
filename: fparith.bib
label: Rodriguez:2021:DLS
author: Andres Rodriguez
title: Deep Learning Systems: Algorithms, Compilers, and Processors for Large-Scale Production
publisher: pub-SV
address: pub-SV:adr
pages: 25--32
year: 2021
DOI: https://doi.org/10.1007/978-3-031-01769-8
ISBN: 3-031-01769-2 OR 3031017692
ISBN13: 978-3-031-01769-8 OR 9783031017698
ISSN: 1935-3243 OR 19353243
ISSNL: 1935-3235 OR 19353235
bibdate: Fri Dec 15 11:31:31 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 11:31:31 ???
series: Synthesis Lectures on Computer Architecture
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acknowledgement: ack-nhfb
rawauthor: Andres Rodriguez
rawtitle: Deep Learning Systems: Algorithms, Compilers, and Processors for Large-Scale Production
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@Book{Rodriguez:2021:DLS,
  author =       "Andres Rodriguez",
  title =        "Deep Learning Systems: Algorithms, Compilers, and
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  publisher =    pub-SV,
  address =      pub-SV:adr,
  year =         "2021",
  DOI =          "https://doi.org/10.1007/978-3-031-01769-8",
  ISBN =         "3-031-01769-2",
  ISBN-13 =      "978-3-031-01769-8",
  ISSN =         "1935-3243",
  ISSN-L =       "1935-3235",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Synthesis Lectures on Computer Architecture",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}


bibtype: article
filename: fparith.bib
label: Romanov:2021:APB
title: Analysis of Posit and Bfloat Arithmetic of Real Numbers for Machine Learning
journal: j-IEEE-ACCESS
volume: 9
pages: 82318--82324
year: 2021
DOI: https://doi.org/10.1109/ACCESS.2021.3086669
ISSN: 2169-3536 OR 21693536
ISSNL: 2169-3536 OR 21693536
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
fjournal: IEEE Access
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639
rawtitle: Analysis of Posit and {Bfloat} Arithmetic of Real Numbers for Machine Learning
author:
Aleksandr Yu. Romanov and Alexander L. Stempkovsky and Ilia V. Lariushkin and Georgy E. Novoselov and Roman A. Solovyev and Vladimir A. Starykh and Irina I. Romanova and Dmitry V. Telpukhov and Ilya A. Mkrtchan

rawauthor:
Aleksandr Yu. Romanov and Alexander L. Stempkovsky and Ilia V. Lariushkin and Georgy E. Novoselov and Roman A. Solovyev and Vladimir A. Starykh and Irina I. Romanova and Dmitry V. Telpukhov and Ilya A. Mkrtchan

entry:
@Article{Romanov:2021:APB,
  author =       "Aleksandr Yu. Romanov and Alexander L. Stempkovsky and
                 Ilia V. Lariushkin and Georgy E. Novoselov and Roman A.
                 Solovyev and Vladimir A. Starykh and Irina I. Romanova
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  journal =      j-IEEE-ACCESS,
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  DOI =          "https://doi.org/10.1109/ACCESS.2021.3086669",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}


bibtype: inproceedings
filename: fparith.bib
label: Saiki:2021:CPT
author: Brett Saiki and Oliver Flatt and Chandrakana Nandi and Pavel Panchekha and Zachary Tatlock
title: Combining Precision Tuning and Rewriting
crossref: IEEE:2021:ISC
pages: 1--8
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00013
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Brett Saiki and Oliver Flatt and Chandrakana Nandi and Pavel Panchekha and Zachary Tatlock
rawtitle: Combining Precision Tuning and Rewriting
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@InProceedings{Saiki:2021:CPT,
  author =       "Brett Saiki and Oliver Flatt and Chandrakana Nandi and
                 Pavel Panchekha and Zachary Tatlock",
  title =        "Combining Precision Tuning and Rewriting",
  crossref =     "IEEE:2021:ISC",
  pages =        "1--8",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00013",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: inproceedings
filename: fparith.bib
label: Saxena:2021:BOF
editor: IEEE
booktitle: 2021 22nd International Symposium on Quality Electronic Design (ISQED)
title: Brightening the Optical Flow through Posit Arithmetic
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 463--468
year: 2021
DOI: https://doi.org/10.1109/ISQED51717.2021.9424360
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawbooktitle: {2021 22nd International Symposium on Quality Electronic Design (ISQED)}
raweditor: {IEEE}
rawtitle: Brightening the Optical Flow through Posit Arithmetic
author:
Vinay Saxena and Ankitha Reddy and Jonathan Neudorfer and John Gustafson and Sangeeth Nambiar and Rainer Leupers and Farhad Merchant

rawauthor:
Vinay Saxena and Ankitha Reddy and Jonathan Neudorfer and John Gustafson and Sangeeth Nambiar and Rainer Leupers and Farhad Merchant

entry:
@InProceedings{Saxena:2021:BOF,
  author =       "Vinay Saxena and Ankitha Reddy and Jonathan Neudorfer
                 and John Gustafson and Sangeeth Nambiar and Rainer
                 Leupers and Farhad Merchant",
  editor =       "{IEEE}",
  booktitle =    "{2021 22nd International Symposium on Quality
                 Electronic Design (ISQED)}",
  title =        "Brightening the Optical Flow through Posit
                 Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "463--468",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISQED51717.2021.9424360",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Shah:2021:PWS
editor: IEEE
booktitle: 2021 IEEE International Solid-State Circuits Conference (ISSCC)
volume: 64
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 150--152
year: 2021
DOI: https://doi.org/10.1109/ISSCC42613.2021.9366061
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawbooktitle: {2021 IEEE International Solid-State Circuits Conference (ISSCC)}
raweditor: {IEEE}
author:
Nimish Shah and Laura Isabel Galindez Olascoaga and Shirui Zhao and Wannes Meert and Marian Verhelst

title:
9.4 PIU: a 248GOPS/W Stream-Based Processor for Irregular Probabilistic Inference Networks Using Precision-Scalable Posit Arithmetic in 28nm

rawauthor:
Nimish Shah and Laura Isabel Galindez Olascoaga and Shirui Zhao and Wannes Meert and Marian Verhelst

rawtitle:
{9.4 PIU}: a {248GOPS/W} Stream-Based Processor for Irregular Probabilistic Inference Networks Using Precision-Scalable Posit Arithmetic in 28nm

entry:
@InProceedings{Shah:2021:PWS,
  author =       "Nimish Shah and Laura Isabel Galindez Olascoaga and
                 Shirui Zhao and Wannes Meert and Marian Verhelst",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE International Solid-State Circuits
                 Conference (ISSCC)}",
  title =        "{9.4 PIU}: a {248GOPS/W} Stream-Based Processor for
                 Irregular Probabilistic Inference Networks Using
                 Precision-Scalable Posit Arithmetic in 28nm",
  volume =       "64",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "150--152",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISSCC42613.2021.9366061",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Shekhawat:2021:HGP
author: Diksha Shekhawat and Apoorva Jangir and Jai Gopal Pandey
editor: IEEE
booktitle: 2021 25th International Symposium on VLSI Design and Test (VDAT)
title: A Hardware Generator for Posit Arithmetic and its FPGA Prototyping
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--6
year: 2021
DOI: https://doi.org/10.1109/VDAT53777.2021.9601025
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Diksha Shekhawat and Apoorva Jangir and Jai Gopal Pandey
rawbooktitle: {2021 25th International Symposium on VLSI Design and Test (VDAT)}
raweditor: {IEEE}
rawtitle: A Hardware Generator for Posit Arithmetic and its {FPGA} Prototyping
entry:
@InProceedings{Shekhawat:2021:HGP,
  author =       "Diksha Shekhawat and Apoorva Jangir and Jai Gopal
                 Pandey",
  editor =       "{IEEE}",
  booktitle =    "{2021 25th International Symposium on VLSI Design and
                 Test (VDAT)}",
  title =        "A Hardware Generator for Posit Arithmetic and its
                 {FPGA} Prototyping",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/VDAT53777.2021.9601025",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: SmallPositHDL:2021:CBS
author: SmallPositHDL
title: Chisel-based SmallPositHDL
pages: 1--6
year: 2021
bibdate: Sat Dec 16 15:23:17 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.16 15:23:17 ???
URL: https://github.com/starbrilliance/SmallPositHDL
keywords: posit arithmetic
acknowledgement: ack-nhfb
howpublished: Web software
rawauthor: {SmallPositHDL}
rawtitle: Chisel-based {SmallPositHDL}
entry:
@Misc{SmallPositHDL:2021:CBS,
  author =       "{SmallPositHDL}",
  title =        "Chisel-based {SmallPositHDL}",
  howpublished = "Web software",
  year =         "2021",
  bibdate =      "Sat Dec 16 15:23:17 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/starbrilliance/SmallPositHDL",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}


bibtype: article
filename: fparith.bib
label: Sohier:2021:CIS
title: Confidence Intervals for Stochastic Arithmetic
journal: j-TOMS
volume: 47
number: 2
pages: 10:1--10:33
month: apr
monthnumber: 4
year: 2021
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3432184
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Apr 27 08:23:28 MDT 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2021.04.27 08:23:28 MDT
URL: https://dl.acm.org/doi/10.1145/3432184
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 10
journalURL: https://dl.acm.org/loi/toms
rawtitle: Confidence Intervals for Stochastic Arithmetic
author:
Devan Sohier and Pablo De Oliveira Castro and Francois Fevotte and Bruno Lathuiliere and Eric Petit and Olivier Jamond

abstract:
Quantifying errors and losses due to the use of Floating-point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation, and Uncertainty Quantification process. Stochastic Arithmetic is one way to model and estimate FP losses of accuracy, which scales well to large, industrial codes. It exists in different flavors, such as CESTAC or MCA, implemented in various tools such as CADNA, Verificarlo, or Verrou. These methodologies and tools are based on the idea that FP losses of accuracy can be modeled via randomness. Therefore, they share the same need to perform a statistical analysis of programs results to estimate the significance of the results.par In this article, we propose a framework to perform a solid statistical analysis of Stochastic Arithmetic. This framework unifies all existing definitions of the number of significant digits (CESTAC and MCA), and also proposes a new quantity of interest: the number of digits contributing to the accuracy of the results. Sound confidence intervals are provided for all estimators, both in the case of normally distributed results, and in the general case. The use of this framework is demonstrated by two case studies of industrial codes: Europlexus and codeaster .

rawabstract:
Quantifying errors and losses due to the use of Floating-point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation, and Uncertainty Quantification process. Stochastic Arithmetic is one way to model and estimate FP losses of accuracy, which scales well to large, industrial codes. It exists in different flavors, such as CESTAC or MCA, implemented in various tools such as CADNA, Verificarlo, or Verrou. These methodologies and tools are based on the idea that FP losses of accuracy can be modeled via randomness. Therefore, they share the same need to perform a statistical analysis of programs results to estimate the significance of the results.\par In this article, we propose a framework to perform a solid statistical analysis of Stochastic Arithmetic. This framework unifies all existing definitions of the number of significant digits (CESTAC and MCA), and also proposes a new quantity of interest: the number of digits contributing to the accuracy of the results. Sound confidence intervals are provided for all estimators, both in the case of normally distributed results, and in the general case. The use of this framework is demonstrated by two case studies of industrial codes: Europlexus and code\aster.

rawauthor:
Devan Sohier and Pablo {De Oliveira Castro} and Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re and Eric Petit and Olivier Jamond

entry:
@Article{Sohier:2021:CIS,
  author =       "Devan Sohier and Pablo {De Oliveira Castro} and
                 Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re
                 and Eric Petit and Olivier Jamond",
  title =        "Confidence Intervals for Stochastic Arithmetic",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "10:1--10:33",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3432184",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3432184",
  abstract =     "Quantifying errors and losses due to the use of
                 Floating-point (FP) calculations in industrial
                 scientific computing codes is an important part of the
                 Verification, Validation, and Uncertainty
                 Quantification process. Stochastic Arithmetic is one
                 way to model and estimate FP losses of accuracy, which
                 scales well to large, industrial codes. It exists in
                 different flavors, such as CESTAC or MCA, implemented
                 in various tools such as CADNA, Verificarlo, or Verrou.
                 These methodologies and tools are based on the idea
                 that FP losses of accuracy can be modeled via
                 randomness. Therefore, they share the same need to
                 perform a statistical analysis of programs results to
                 estimate the significance of the results.\par

                 In this article, we propose a framework to perform a
                 solid statistical analysis of Stochastic Arithmetic.
                 This framework unifies all existing definitions of the
                 number of significant digits (CESTAC and MCA), and also
                 proposes a new quantity of interest: the number of
                 digits contributing to the accuracy of the results.
                 Sound confidence intervals are provided for all
                 estimators, both in the case of normally distributed
                 results, and in the general case. The use of this
                 framework is demonstrated by two case studies of
                 industrial codes: Europlexus and code\aster.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Soylu:2021:IAC
author: Gultekin Soylu
title: Improved Arithmetic of Complex Fans
journal: j-TOMS
volume: 47
number: 2
pages: 11:1--11:10
month: apr
monthnumber: 4
year: 2021
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3434400
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Apr 27 08:23:28 MDT 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2021.04.27 08:23:28 MDT
URL: https://dl.acm.org/doi/10.1145/3434400
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 11
journalURL: https://dl.acm.org/loi/toms
rawauthor: G{\"u}ltekin Soylu
rawtitle: Improved Arithmetic of Complex Fans
abstract:
Complex fans are sets of complex numbers whose magnitudes and angles range in closed intervals. The fact that the sum of two fans is a disordered shape gives rise to the need for computational methods to find the minimal enclosing fan. Cases where the sum of two fans contains the origin of the complex plane as a boundary point are of special interest. The result of the addition is then enclosed by circles in current methods, but under certain circumstances this turns out to be an overestimate. The focus of this article is the diagnosis and treatment of such cases.

rawabstract:
Complex fans are sets of complex numbers whose magnitudes and angles range in closed intervals. The fact that the sum of two fans is a disordered shape gives rise to the need for computational methods to find the minimal enclosing fan. Cases where the sum of two fans contains the origin of the complex plane as a boundary point are of special interest. The result of the addition is then enclosed by circles in current methods, but under certain circumstances this turns out to be an overestimate. The focus of this article is the diagnosis and treatment of such cases.

entry:
@Article{Soylu:2021:IAC,
  author =       "G{\"u}ltekin Soylu",
  title =        "Improved Arithmetic of Complex Fans",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "11:1--11:10",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3434400",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3434400",
  abstract =     "Complex fans are sets of complex numbers whose
                 magnitudes and angles range in closed intervals. The
                 fact that the sum of two fans is a disordered shape
                 gives rise to the need for computational methods to
                 find the minimal enclosing fan. Cases where the sum of
                 two fans contains the origin of the complex plane as a
                 boundary point are of special interest. The result of
                 the addition is then enclosed by circles in current
                 methods, but under certain circumstances this turns out
                 to be an overestimate. The focus of this article is the
                 diagnosis and treatment of such cases.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Thapliyal:2021:QCD
author: Himanshu Thapliyal and Edgard Munoz-Coreas and T. S. S. Varun and Travis S. Humble
title: Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 9
number: 2
pages: 1045--1056
month: apr
monthnumber: 4
year: 2021
DOI: https://doi.org/10.1109/TETC.2019.2910870
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Himanshu Thapliyal and Edgard Mu{\~n}oz-Coreas and T. S. S. Varun and Travis S. Humble
rawtitle: Quantum Circuit Designs of Integer Division Optimizing {T}-count and {T}-depth
entry:
@Article{Thapliyal:2021:QCD,
  author =       "Himanshu Thapliyal and Edgard Mu{\~n}oz-Coreas and T.
                 S. S. Varun and Travis S. Humble",
  title =        "Quantum Circuit Designs of Integer Division Optimizing
                 {T}-count and {T}-depth",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "2",
  pages =        "1045--1056",
  month =        apr # "\slash " # jun,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2019.2910870",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: article
filename: fparith.bib
label: Tiwari:2021:PCP
author: Sugandha Tiwari and Neel Gala and Chester Rebeiro and V. Kamakoti
title: PERI: a Configurable Posit Enabled RISC-V Core
journal: j-TACO
volume: 18
number: 3
pages: 25:1--25:26
month: jun
monthnumber: 6
year: 2021
DOI: https://doi.org/10.1145/3446210
ISSN: 1544-3566 (print), 1544-3973 (electronic) OR 15443566 (print), 15443973 (electronic)
ISSNL: 1544-3566 OR 15443566
bibdate: Tue Jun 29 08:21:11 MDT 2021
bibtimestamp: 2021.06.29 08:21:11 MDT
URL: https://dl.acm.org/doi/10.1145/3446210
fjournal: ACM Transactions on Architecture and Code Optimization (TACO)
acknowledgement: ack-nhfb
articleno: 25
journalURL: https://dl.acm.org/loi/taco
rawauthor: Sugandha Tiwari and Neel Gala and Chester Rebeiro and V. Kamakoti
rawtitle: {PERI}: a Configurable Posit Enabled {RISC-V} Core
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib; https://www.math.utah.edu/pub/tex/bib/taco.bib

abstract:
Owing to the failure of Dennard's scaling, the past decade has seen a steep growth of prominent new paradigms leveraging opportunities in computer architecture. Two technologies of interest are Posit and RISC-V. Posit was introduced in mid-2017 as a ldots 

rawabstract:
Owing to the failure of Dennard's scaling, the past decade has seen a steep growth of prominent new paradigms leveraging opportunities in computer architecture. Two technologies of interest are Posit and RISC-V. Posit was introduced in mid-2017 as a \ldots{}

entry:
@Article{Tiwari:2021:PCP,
  author =       "Sugandha Tiwari and Neel Gala and Chester Rebeiro and
                 V. Kamakoti",
  title =        "{PERI}: a Configurable Posit Enabled {RISC-V} Core",
  journal =      j-TACO,
  volume =       "18",
  number =       "3",
  pages =        "25:1--25:26",
  month =        jun,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3446210",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Tue Jun 29 08:21:11 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3446210",
  abstract =     "Owing to the failure of Dennard's scaling, the past
                 decade has seen a steep growth of prominent new
                 paradigms leveraging opportunities in computer
                 architecture. Two technologies of interest are Posit
                 and RISC-V. Posit was introduced in mid-2017 as a
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "https://dl.acm.org/loi/taco",
}


bibtype: article
filename: fparith.bib
label: Ullah:2021:AOA
author: S. Ullah and H. Schmidl and S. S. Sahoo and S. Rehman and A. Kumar
title: Area-Optimized Accurate and Approximate Softcore Signed Multiplier Architectures
journal: j-IEEE-TRANS-COMPUT
volume: 70
number: 3
pages: 384--392
year: 2021
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2020.2988404
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Tue Feb 23 12:51:19 2021
bibtimestamp: 2021.02.23 12:51:19 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Ullah and H. Schmidl and S. S. Sahoo and S. Rehman and A. Kumar
rawtitle: Area-Optimized Accurate and Approximate Softcore Signed Multiplier Architectures
entry:
@Article{Ullah:2021:AOA,
  author =       "S. Ullah and H. Schmidl and S. S. Sahoo and S. Rehman
                 and A. Kumar",
  title =        "Area-Optimized Accurate and Approximate Softcore
                 Signed Multiplier Architectures",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "3",
  pages =        "384--392",
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.2988404",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Feb 23 12:51:19 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: VanZee:2021:SMD
author: Field G. Van Zee and Devangi N. Parikh and Robert A. Van De Geijn
title: Supporting Mixed-domain Mixed-precision Matrix Multiplication within the BLIS Framework
journal: j-TOMS
volume: 47
number: 2
pages: 12:1--12:26
month: apr
monthnumber: 4
year: 2021
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3402225
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Apr 27 08:23:28 MDT 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2021.04.27 08:23:28 MDT
URL: https://dl.acm.org/doi/10.1145/3402225
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 12
journalURL: https://dl.acm.org/loi/toms
rawauthor: Field G. {Van Zee} and Devangi N. Parikh and Robert A. {Van De Geijn}
rawtitle: Supporting Mixed-domain Mixed-precision Matrix Multiplication within the {BLIS} Framework
abstract:
We approach the problem of implementing mixed-datatype support within the general matrix multiplication (gemm) operation of the BLAS-like Library Instantiation Software framework, whereby each matrix operand A, B, and C may be stored as single- or double-precision real or complex values. Another factor of complexity, whereby the matrix product and accumulation are allowed to take place in a precision different from the storage precisions of either A or B, is also discussed. We first break the problem into orthogonal dimensions, considering the mixing of domains separately from mixing precisions. Support for all combinations of matrix operands stored in either the real or complex domain is mapped out by enumerating the cases and describing an implementation approach for each. Supporting all combinations of storage and computation precisions is handled by typecasting the matrices at key stages of the computation --- during packing and/or accumulation, as needed. Several optional optimizations are also documented. Performance results gathered on a 56-core Marvell ThunderX2 and a 52-core Intel Xeon Platinum demonstrate that high performance is mostly preserved, with modest slowdowns incurred from unavoidable typecast instructions. The mixed-datatype implementation confirms that combinatorial intractability is avoided, with the framework relying on only two assembly microkernels to implement 128 datatype combinations.

rawabstract:
We approach the problem of implementing mixed-datatype support within the general matrix multiplication (gemm) operation of the BLAS-like Library Instantiation Software framework, whereby each matrix operand A, B, and C may be stored as single- or double-precision real or complex values. Another factor of complexity, whereby the matrix product and accumulation are allowed to take place in a precision different from the storage precisions of either A or B, is also discussed. We first break the problem into orthogonal dimensions, considering the mixing of domains separately from mixing precisions. Support for all combinations of matrix operands stored in either the real or complex domain is mapped out by enumerating the cases and describing an implementation approach for each. Supporting all combinations of storage and computation precisions is handled by typecasting the matrices at key stages of the computation --- during packing and/or accumulation, as needed. Several optional optimizations are also documented. Performance results gathered on a 56-core Marvell ThunderX2 and a 52-core Intel Xeon Platinum demonstrate that high performance is mostly preserved, with modest slowdowns incurred from unavoidable typecast instructions. The mixed-datatype implementation confirms that combinatorial intractability is avoided, with the framework relying on only two assembly microkernels to implement 128 datatype combinations.

entry:
@Article{VanZee:2021:SMD,
  author =       "Field G. {Van Zee} and Devangi N. Parikh and Robert A.
                 {Van De Geijn}",
  title =        "Supporting Mixed-domain Mixed-precision Matrix
                 Multiplication within the {BLIS} Framework",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "12:1--12:26",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3402225",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3402225",
  abstract =     "We approach the problem of implementing mixed-datatype
                 support within the general matrix multiplication (gemm)
                 operation of the BLAS-like Library Instantiation
                 Software framework, whereby each matrix operand A, B,
                 and C may be stored as single- or double-precision real
                 or complex values. Another factor of complexity,
                 whereby the matrix product and accumulation are allowed
                 to take place in a precision different from the storage
                 precisions of either A or B, is also discussed. We
                 first break the problem into orthogonal dimensions,
                 considering the mixing of domains separately from
                 mixing precisions. Support for all combinations of
                 matrix operands stored in either the real or complex
                 domain is mapped out by enumerating the cases and
                 describing an implementation approach for each.
                 Supporting all combinations of storage and computation
                 precisions is handled by typecasting the matrices at
                 key stages of the computation --- during packing and/or
                 accumulation, as needed. Several optional optimizations
                 are also documented. Performance results gathered on a
                 56-core Marvell ThunderX2 and a 52-core Intel Xeon
                 Platinum demonstrate that high performance is mostly
                 preserved, with modest slowdowns incurred from
                 unavoidable typecast instructions. The mixed-datatype
                 implementation confirms that combinatorial
                 intractability is avoided, with the framework relying
                 on only two assembly microkernels to implement 128
                 datatype combinations.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: fparith.bib
label: Vestias:2021:DMF
author: Mario P. Vestias and Horacio C. Neto
title: Decimal Multiplication in FPGA with a Novel Decimal Adder / Subtractor
journal: j-ALGORITHMS-BASEL
volume: 14
number: 7
pages: 12:1--12:26
month: jul
monthnumber: 7
year: 2021
CODEN: ALGOCH
DOI: https://doi.org/10.3390/a14070198
ISSN: 1999-4893 (electronic) OR 19994893 (electronic)
ISSNL: 1999-4893 OR 19994893
bibdate: Fri Jul 23 15:05:28 MDT 2021
bibtimestamp: 2021.07.23 15:05:28 MDT
URL: https://www.mdpi.com/1999-4893/14/7/198
fjournal: Algorithms (Basel)
acknowledgement: ack-nhfb
articleno: 198
journalURL: https://www.mdpi.com/journal/algorithms
rawauthor: M{\'a}rio P. V{\'e}stias and Hor{\'a}cio C. Neto
rawtitle: Decimal Multiplication in {FPGA} with a Novel Decimal Adder\slash Subtractor
bibsource:
https://www.math.utah.edu/pub/tex/bib/algorithms.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Vestias:2021:DMF,
  author =       "M{\'a}rio P. V{\'e}stias and Hor{\'a}cio C. Neto",
  title =        "Decimal Multiplication in {FPGA} with a Novel Decimal
                 Adder\slash Subtractor",
  journal =      j-ALGORITHMS-BASEL,
  volume =       "14",
  number =       "7",
  month =        jul,
  year =         "2021",
  CODEN =        "ALGOCH",
  DOI =          "https://doi.org/10.3390/a14070198",
  ISSN =         "1999-4893 (electronic)",
  ISSN-L =       "1999-4893",
  bibdate =      "Fri Jul 23 15:05:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.mdpi.com/1999-4893/14/7/198",
  acknowledgement = ack-nhfb,
  articleno =    "198",
  fjournal =     "Algorithms (Basel)",
  journal-URL =  "https://www.mdpi.com/journal/algorithms",
  pagecount =    "??",
}


bibtype: article
filename: fparith.bib
label: Walczyk:2021:IAF
author: Cezary J. Walczyk and Leonid V. Moroz and Jan L. Cieslinski
title: Improving the Accuracy of the Fast Inverse Square Root by Modifying Newton--Raphson Corrections
journal: j-ENTROPY
volume: 23
number: 1
pages: 86:1--86:20
month: jan
monthnumber: 1
year: 2021
CODEN: ENTRFG
DOI: https://doi.org/10.3390/e23010086
ISSN: 1099-4300 OR 10994300
ISSNL: 1099-4300 OR 10994300
bibdate: Wed Dec 20 07:52:39 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.20 07:52:39 ???
fjournal: Entropy
acknowledgement: ack-nhfb
journalURL: https://www.mdpi.com/journal/entropy/
rawauthor: Cezary J. Walczyk and Leonid V. Moroz and Jan L. Cie{\'s}li{\'n}ski
rawtitle: Improving the Accuracy of the Fast Inverse Square Root by Modifying {Newton--Raphson} Corrections
entry:
@Article{Walczyk:2021:IAF,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Improving the Accuracy of the Fast Inverse Square Root
                 by Modifying {Newton--Raphson} Corrections",
  journal =      j-ENTROPY,
  volume =       "23",
  number =       "1",
  pages =        "86:1--86:20",
  month =        jan,
  year =         "2021",
  CODEN =        "ENTRFG",
  DOI =          "https://doi.org/10.3390/e23010086",
  ISSN =         "1099-4300",
  ISSN-L =       "1099-4300",
  bibdate =      "Wed Dec 20 07:52:39 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Entropy",
  journal-URL =  "https://www.mdpi.com/journal/entropy/",
}


bibtype: inproceedings
filename: fparith.bib
label: Wang:2021:LLP
author: Yang Wang and Dazheng Deng and Leibo Liu and Shaojun Wei and Shouyi Yin
editor: IEEE
booktitle: 2021 IEEE 3rd International Conference on Artificial Intelligence Circuits and Systems (AICAS)
title: LPE: Logarithm Posit Processing Element for Energy-Efficient Edge-Device Training
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--4
year: 2021
DOI: https://doi.org/10.1109/AICAS51828.2021.9458421
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Yang Wang and Dazheng Deng and Leibo Liu and Shaojun Wei and Shouyi Yin
rawbooktitle: {2021 IEEE 3rd International Conference on Artificial Intelligence Circuits and Systems (AICAS)}
raweditor: {IEEE}
rawtitle: {LPE}: Logarithm Posit Processing Element for Energy-Efficient Edge-Device Training
entry:
@InProceedings{Wang:2021:LLP,
  author =       "Yang Wang and Dazheng Deng and Leibo Liu and Shaojun
                 Wei and Shouyi Yin",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE 3rd International Conference on Artificial
                 Intelligence Circuits and Systems (AICAS)}",
  title =        "{LPE}: Logarithm Posit Processing Element for
                 Energy-Efficient Edge-Device Training",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/AICAS51828.2021.9458421",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Ward-Foxton:2021:BBT
author: Sally Ward-Foxton
title: Bringing 8-Bit Training Breakthroughs to AI Hardware
pages: 1--4
day: 2
month: mar
monthnumber: 3
year: 2021
bibdate: Wed May 19 12:05:25 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2021.05.19 12:05:25 ???
URL: https://www.eetasia.com/bringing-8-bit-training-breakthroughs-to-ai-hardware/
keywords: FP8
acknowledgement: ack-nhfb
howpublished: EET Asia Web site
rawauthor: Sally Ward-Foxton
rawtitle: Bringing 8-Bit Training Breakthroughs to {AI} Hardware
entry:
@Misc{Ward-Foxton:2021:BBT,
  author =       "Sally Ward-Foxton",
  title =        "Bringing 8-Bit Training Breakthroughs to {AI}
                 Hardware",
  howpublished = "EET Asia Web site",
  day =          "2",
  month =        mar,
  year =         "2021",
  bibdate =      "Wed May 19 12:05:25 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.eetasia.com/bringing-8-bit-training-breakthroughs-to-ai-hardware/",
  acknowledgement = ack-nhfb,
  keywords =     "FP8",
}


bibtype: inproceedings
filename: fparith.bib
label: Wu:2021:DCH
author: Chai Wah Wu
title: Dither computing: a hybrid deterministic-stochastic computing framework
crossref: IEEE:2021:ISC
pages: 70--77
year: 2021
DOI: https://doi.org/10.1109/ARITH51176.2021.00025
bibdate: Thu Sep 21 10:36:08 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:36:08 ???
keywords: ARITH-28
acknowledgement: ack-nhfb
rawauthor: Chai Wah Wu
rawtitle: Dither computing: a hybrid deterministic-stochastic computing framework
entry:
@InProceedings{Wu:2021:DCH,
  author =       "Chai Wah Wu",
  title =        "Dither computing: a hybrid deterministic-stochastic
                 computing framework",
  crossref =     "IEEE:2021:ISC",
  pages =        "70--77",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00025",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
}


bibtype: article
filename: fparith.bib
label: Zaruba:2021:MCR
author: Florian Zaruba and Fabian Schuiki and Luca Benini
title: Manticore: A 4096-Core RISC-V Chiplet Architecture for Ultraefficient Floating-Point Computing
journal: j-IEEE-MICRO
volume: 41
number: 2
pages: 36--42
month: mar
monthnumber: 3
year: 2021
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/MM.2020.3045564
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Sat Dec 16 15:51:40 2023
bibtimestamp: 2023.12.16 15:51:40 ???
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40
rawauthor: Florian Zaruba and Fabian Schuiki and Luca Benini
rawtitle: {Manticore}: A 4096-Core {RISC-V} Chiplet Architecture for Ultraefficient Floating-Point Computing
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/hot-chips.bib; https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib

entry:
@Article{Zaruba:2021:MCR,
  author =       "Florian Zaruba and Fabian Schuiki and Luca Benini",
  title =        "{Manticore}: A 4096-Core {RISC-V} Chiplet Architecture
                 for Ultraefficient Floating-Point Computing",
  journal =      j-IEEE-MICRO,
  volume =       "41",
  number =       "2",
  pages =        "36--42",
  month =        mar # "\slash " # apr,
  year =         "2021",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2020.3045564",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hot-chips.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
}


bibtype: article
filename: fparith.bib
label: Zaruba:2021:STP
author: Florian Zaruba and Fabian Schuiki and Torsten Hoefler and Luca Benini
journal: j-IEEE-TRANS-COMPUT
volume: 70
number: 11
pages: 1845--1860
month: nov
monthnumber: 11
year: 2021
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2020.3027900
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Oct 14 10:04:00 2021
bibtimestamp: 2021.10.14 10:04:00 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Florian Zaruba and Fabian Schuiki and Torsten Hoefler and Luca Benini
title:
Snitch: A Tiny Pseudo Dual-Issue Processor for Area and Energy Efficient Execution of Floating-Point Intensive Workloads

rawtitle:
{Snitch}: A Tiny Pseudo Dual-Issue Processor for Area and Energy Efficient Execution of Floating-Point Intensive Workloads

entry:
@Article{Zaruba:2021:STP,
  author =       "Florian Zaruba and Fabian Schuiki and Torsten Hoefler
                 and Luca Benini",
  title =        "{Snitch}: A Tiny Pseudo Dual-Issue Processor for Area
                 and Energy Efficient Execution of Floating-Point
                 Intensive Workloads",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "11",
  pages =        "1845--1860",
  month =        nov,
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.3027900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Oct 14 10:04:00 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Zhang:2021:EMP
author: Hao Zhang and Seok-Bum Ko
editor: IEEE
booktitle: 2021 IEEE International Symposium on Circuits and Systems (ISCAS)
title: Efficient Multiple-Precision Posit Multiplier
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--5
year: 2021
DOI: https://doi.org/10.1109/ISCAS51556.2021.9401213
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Hao Zhang and Seok-Bum Ko
rawbooktitle: {2021 IEEE International Symposium on Circuits and Systems (ISCAS)}
raweditor: {IEEE}
rawtitle: Efficient Multiple-Precision Posit Multiplier
entry:
@InProceedings{Zhang:2021:EMP,
  author =       "Hao Zhang and Seok-Bum Ko",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Efficient Multiple-Precision Posit Multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISCAS51556.2021.9401213",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Ziols:2021:HPB
author: Ryan Ziols and Kathryn L. Kirchgasler
title: Health and pathology: a brief history of the biopolitics of US mathematics education
journal: j-EDUC-STUD-MATH
volume: 108
number: 1--2
publisher: pub-SV
address: pub-SV:adr
pages: 123--142
month: oct
monthnumber: 10
year: 2021
CODEN: EDSMAN
DOI: https://doi.org/10.1007/s10649-021-10110-8
ISSN: 1573-0816 OR 15730816
ISSNL: 0013-1954 OR 00131954
bibdate: Fri Dec 15 11:31:31 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 11:31:31 ???
fjournal: Educational Studies in Mathematics
keywords: posit arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10649
rawauthor: Ryan Ziols and Kathryn L. Kirchgasler
rawtitle: Health and pathology: a brief history of the biopolitics of {US} mathematics education
entry:
@Article{Ziols:2021:HPB,
  author =       "Ryan Ziols and Kathryn L. Kirchgasler",
  title =        "Health and pathology: a brief history of the
                 biopolitics of {US} mathematics education",
  journal =      j-EDUC-STUD-MATH,
  volume =       "108",
  number =       "1--2",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "123--142",
  month =        oct,
  year =         "2021",
  CODEN =        "EDSMAN",
  DOI =          "https://doi.org/10.1007/s10649-021-10110-8",
  ISSN =         "1573-0816",
  ISSN-L =       "0013-1954",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Educational Studies in Mathematics",
  journal-URL =  "http://link.springer.com/journal/10649",
  keywords =     "posit arithmetic",
}


bibtype: article
filename: fparith.bib
label: Zlatopolski:2021:MES
author: Dmitry M. Zlatopolski
title: Method for extracting square and cubic roots in the binary number system. (Russian)
journal: Inform. School
volume: 1
pages: 42--45
year: 2021
DOI: https://doi.org/10.32517/2221-1993-2021-1-42-45
bibdate: Fri Mar 17 09:03:18 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.03.17 09:03:18 ???
language: Russian
remark: DOI does not resolve; cited as final reference in cite Zlatopolski:2023:PAV.
acknowledgement: ack-nhfb
rawauthor: Dmitry M. Zlatopolski
rawtitle: Method for extracting square and cubic roots in the binary number system. ({Russian})
entry:
@Article{Zlatopolski:2021:MES,
  author =       "Dmitry M. Zlatopolski",
  title =        "Method for extracting square and cubic roots in the
                 binary number system. ({Russian})",
  journal =      "Inform. School",
  volume =       "1",
  number =       "??",
  pages =        "42--45",
  month =        "????",
  year =         "2021",
  DOI =          "https://doi.org/10.32517/2221-1993-2021-1-42-45",
  bibdate =      "Fri Mar 17 09:03:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
  remark =       "DOI does not resolve; cited as final reference in
                 \cite{Zlatopolski:2023:PAV}.",
}


bibtype: article
filename: fparith.bib
label: Ahmadinejad:2022:EQE
author: Mohammad Ahmadinejad and Mohammad Hossein Moaiyeri
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 10
number: 2
pages: 1105--1116
month: apr
monthnumber: 4
year: 2022
DOI: https://doi.org/10.1109/TETC.2021.3072666
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Mohammad Ahmadinejad and Mohammad Hossein Moaiyeri
title:
Energy- and Quality-Efficient Approximate Multipliers for Neural Network and Image Processing Applications

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib; https://www.math.utah.edu/pub/tex/bib/matlab.bib

abstract:
Approximate computing is a new trend that trades off computational accuracy for lower energy dissipation and design complexity in various applications, where high precision is not a critical need. In this paper, energy- and quality- efficient approximate multipliers based on new approximate compressors are proposed. We use NAND gates for generating the complemented partial products, which reduces the number of transistors. Furthermore, new approximate compressors with different accuracy and performance characteristics are designed. Accordingly, three hybrid approximate multipliers offering different trade-offs between accuracy and hardware efficiency are proposed. The proposed designs are simulated using HSPICE with the 7nm FinFET model as a modern technology. Furthermore, the efficacies of the approximate multipliers in the neural network and image processing applications are evaluated using MATLAB. According to the results, the proposed designs provide far better compromises between the quality and energy metrics in comparison with the previous designs and can be considered as efficient alternatives for the exact multipliers in neural network and image processing applications.

rawabstract:
Approximate computing is a new trend that trades off computational accuracy for lower energy dissipation and design complexity in various applications, where high precision is not a critical need. In this paper, energy- and quality- efficient approximate multipliers based on new approximate compressors are proposed. We use NAND gates for generating the complemented partial products, which reduces the number of transistors. Furthermore, new approximate compressors with different accuracy and performance characteristics are designed. Accordingly, three hybrid approximate multipliers offering different trade-offs between accuracy and hardware efficiency are proposed. The proposed designs are simulated using HSPICE with the 7nm FinFET model as a modern technology. Furthermore, the efficacies of the approximate multipliers in the neural network and image processing applications are evaluated using MATLAB. According to the results, the proposed designs provide far better compromises between the quality and energy metrics in comparison with the previous designs and can be considered as efficient alternatives for the exact multipliers in neural network and image processing applications.

rawtitle:
Energy- and Quality-Efficient Approximate Multipliers for Neural Network and Image Processing Applications

entry:
@Article{Ahmadinejad:2022:EQE,
  author =       "Mohammad Ahmadinejad and Mohammad Hossein Moaiyeri",
  title =        "Energy- and Quality-Efficient Approximate Multipliers
                 for Neural Network and Image Processing Applications",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "2",
  pages =        "1105--1116",
  month =        apr # "\slash " # jun,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3072666",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  abstract =     "Approximate computing is a new trend that trades off
                 computational accuracy for lower energy dissipation and
                 design complexity in various applications, where high
                 precision is not a critical need. In this paper,
                 energy- and quality- efficient approximate multipliers
                 based on new approximate compressors are proposed. We
                 use NAND gates for generating the complemented partial
                 products, which reduces the number of transistors.
                 Furthermore, new approximate compressors with different
                 accuracy and performance characteristics are designed.
                 Accordingly, three hybrid approximate multipliers
                 offering different trade-offs between accuracy and
                 hardware efficiency are proposed. The proposed designs
                 are simulated using HSPICE with the 7nm FinFET model as
                 a modern technology. Furthermore, the efficacies of the
                 approximate multipliers in the neural network and image
                 processing applications are evaluated using MATLAB.
                 According to the results, the proposed designs provide
                 far better compromises between the quality and energy
                 metrics in comparison with the previous designs and can
                 be considered as efficient alternatives for the exact
                 multipliers in neural network and image processing
                 applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: article
filename: fparith.bib
label: Ahmadpour:2022:BMM
author: Zabihollah Ahmadpour and Ghassem Jaberipur
journal: j-IEEE-TRANS-COMPUT
volume: 71
number: 6
pages: 1399--1410
month: jun
monthnumber: 6
year: 2022
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2021.3086071
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed May 25 09:41:19 2022
bibtimestamp: 2022.05.25 09:41:19 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Zabihollah Ahmadpour and Ghassem Jaberipur
title:
Up to $ 8 k $-bit Modular Montgomery Multiplication in Residue Number Systems With Fast 16-bit Residue Channels

rawtitle:
Up to $ 8 k $-bit Modular {Montgomery} Multiplication in Residue Number Systems With Fast 16-bit Residue Channels

entry:
@Article{Ahmadpour:2022:BMM,
  author =       "Zabihollah Ahmadpour and Ghassem Jaberipur",
  title =        "Up to $ 8 k $-bit Modular {Montgomery} Multiplication
                 in Residue Number Systems With Fast 16-bit Residue
                 Channels",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "71",
  number =       "6",
  pages =        "1399--1410",
  month =        jun,
  year =         "2022",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2021.3086071",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed May 25 09:41:19 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Alder:2022:FPU
author: Fritz Alder and Jo Van Bulck and Jesse Spielman and David Oswald and Frank Piessens
title: Faulty Point Unit: ABI Poisoning Attacks on Trusted Execution Environments
journal: j-DTRAP
volume: 3
number: 2
pages: 13:1--13:26
month: jun
monthnumber: 6
year: 2022
DOI: https://doi.org/10.1145/3491264
ISSN: 2692-1626 (print), 2576-5337 (electronic) OR 26921626 (print), 25765337 (electronic)
ISSNL: 2576-5337 OR 25765337
bibdate: Sat Jul 30 07:34:14 MDT 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/dtrap.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.07.30 07:34:14 MDT
URL: https://dl.acm.org/doi/10.1145/3491264
fjournal: Digital Threats: Research and Practice (DTRAP)
acknowledgement: ack-nhfb
articleno: 13
journalURL: https://dl.acm.org/loi/dtrap
rawauthor: Fritz Alder and Jo {Van Bulck} and Jesse Spielman and David Oswald and Frank Piessens
rawtitle: Faulty Point Unit: {ABI} Poisoning Attacks on Trusted Execution Environments
abstract:
This article analyzes a previously overlooked attack surface that allows unprivileged adversaries to impact floating-point computations in enclaves through the Application Binary Interface (ABI). In a comprehensive study across 7 industry-standard and esearch enclave shielding runtimes for Intel Software Guard Extensions (SGX), we show that control and state registers of the x87 Floating-Point Unit (FPU) and Intel Streaming SIMD Extensions are not always properly sanitized on enclave entry. We furthermore show that this attack goes beyond the x86 architecture and can also affect RISC-V enclaves. Focusing on SGX, we abuse the adversary's control over precision and rounding modes as an ABI fault injection primitive to corrupt enclaved floating-point operations. Our analysis reveals that this is especially relevant for applications that use the older x87 FPU, which is still under certain conditions used by modern compilers. We exemplify the potential impact of ABI quality-degradation attacks for enclaved machine learning and for the SPEC benchmarks. We then explore the impact on confidentiality, showing that control over exception masks can be abused as a controlled channel to recover enclaved multiplication operands. Our findings, affecting 5 of 7 studied SGX runtimes and one RISC-V runtime, demonstrate the challenges of implementing high-assurance trusted execution across computing architectures.

rawabstract:
This article analyzes a previously overlooked attack surface that allows unprivileged adversaries to impact floating-point computations in enclaves through the Application Binary Interface (ABI). In a comprehensive study across 7 industry-standard and esearch enclave shielding runtimes for Intel Software Guard Extensions (SGX), we show that control and state registers of the x87 Floating-Point Unit (FPU) and Intel Streaming SIMD Extensions are not always properly sanitized on enclave entry. We furthermore show that this attack goes beyond the x86 architecture and can also affect RISC-V enclaves. Focusing on SGX, we abuse the adversary's control over precision and rounding modes as an ABI fault injection primitive to corrupt enclaved floating-point operations. Our analysis reveals that this is especially relevant for applications that use the older x87 FPU, which is still under certain conditions used by modern compilers. We exemplify the potential impact of ABI quality-degradation attacks for enclaved machine learning and for the SPEC benchmarks. We then explore the impact on confidentiality, showing that control over exception masks can be abused as a controlled channel to recover enclaved multiplication operands. Our findings, affecting 5 of 7 studied SGX runtimes and one RISC-V runtime, demonstrate the challenges of implementing high-assurance trusted execution across computing architectures.

entry:
@Article{Alder:2022:FPU,
  author =       "Fritz Alder and Jo {Van Bulck} and Jesse Spielman and
                 David Oswald and Frank Piessens",
  title =        "Faulty Point Unit: {ABI} Poisoning Attacks on Trusted
                 Execution Environments",
  journal =      j-DTRAP,
  volume =       "3",
  number =       "2",
  pages =        "13:1--13:26",
  month =        jun,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3491264",
  ISSN =         "2692-1626 (print), 2576-5337 (electronic)",
  ISSN-L =       "2576-5337",
  bibdate =      "Sat Jul 30 07:34:14 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/dtrap.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3491264",
  abstract =     "This article analyzes a previously overlooked attack
                 surface that allows unprivileged adversaries to impact
                 floating-point computations in enclaves through the
                 Application Binary Interface (ABI). In a comprehensive
                 study across 7 industry-standard and esearch enclave
                 shielding runtimes for Intel Software Guard Extensions
                 (SGX), we show that control and state registers of the
                 x87 Floating-Point Unit (FPU) and Intel Streaming SIMD
                 Extensions are not always properly sanitized on enclave
                 entry. We furthermore show that this attack goes beyond
                 the x86 architecture and can also affect RISC-V
                 enclaves. Focusing on SGX, we abuse the adversary's
                 control over precision and rounding modes as an ABI
                 fault injection primitive to corrupt enclaved
                 floating-point operations. Our analysis reveals that
                 this is especially relevant for applications that use
                 the older x87 FPU, which is still under certain
                 conditions used by modern compilers. We exemplify the
                 potential impact of ABI quality-degradation attacks for
                 enclaved machine learning and for the SPEC benchmarks.
                 We then explore the impact on confidentiality, showing
                 that control over exception masks can be abused as a
                 controlled channel to recover enclaved multiplication
                 operands. Our findings, affecting 5 of 7 studied SGX
                 runtimes and one RISC-V runtime, demonstrate the
                 challenges of implementing high-assurance trusted
                 execution across computing architectures.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "Digital Threats: Research and Practice (DTRAP)",
  journal-URL =  "https://dl.acm.org/loi/dtrap",
}


bibtype: misc
filename: fparith.bib
label: AMD:2022:AIM
author: AMD Corporation
title: ``AMD Instinct MI200'' Instruction Set Architecture Reference Guide
pages: viii + 267
day: 4
month: feb
monthnumber: 2
year: 2022
bibdate: Fri Dec 01 14:05:58 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.01 14:05:58 ???
acknowledgement: ack-nhfb
howpublished: Web document
rawauthor: {AMD Corporation}
rawtitle: {``AMD Instinct MI200''} Instruction Set Architecture Reference Guide
URL:
https://www.amd.com/content/dam/amd/en/documents/instinct-tech-docs/instruction-set-architectures/instinct-mi200-cdna2-instruction-set-architecture.pdf

remark:
This document describes the AMD GPUs in the ``Instinct'' product line, which replaces the earlier FirePro and Radeon products. The new CPUs support 8-, 16-, 32-, and 64-bit signed and unsigned integers, the binary32 and binary64 IEEE 754 floating-point formats, and the BF16 (Bfloat16) 16-bit floating-point values. However, it appears that fused multiply-add is only supported in the vector instruction set.

entry:
@Misc{AMD:2022:AIM,
  author =       "{AMD Corporation}",
  title =        "{``AMD Instinct MI200''} Instruction Set Architecture
                 Reference Guide",
  howpublished = "Web document",
  pages =        "viii + 267",
  day =          "4",
  month =        feb,
  year =         "2022",
  bibdate =      "Fri Dec 01 14:05:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.amd.com/content/dam/amd/en/documents/instinct-tech-docs/instruction-set-architectures/instinct-mi200-cdna2-instruction-set-architecture.pdf",
  acknowledgement = ack-nhfb,
  remark =       "This document describes the AMD GPUs in the
                 ``Instinct'' product line, which replaces the earlier
                 FirePro and Radeon products. The new CPUs support 8-,
                 16-, 32-, and 64-bit signed and unsigned integers, the
                 binary32 and binary64 IEEE 754 floating-point formats,
                 and the BF16 (Bfloat16) 16-bit floating-point values.
                 However, it appears that fused multiply-add is only
                 supported in the vector instruction set.",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2022:AI
author: Anonymous
title: Author Index
crossref: IEEE:2022:ISC
pages: 133--134
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00033
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Author Index
entry:
@InProceedings{Anonymous:2022:AI,
  author =       "Anonymous",
  title =        "Author Index",
  crossref =     "IEEE:2022:ISC",
  pages =        "133--134",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00033",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2022:C
author: Anonymous
title: Copyright
crossref: IEEE:2022:ISC
pages: 1--1
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00003
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Copyright
entry:
@InProceedings{Anonymous:2022:C,
  author =       "Anonymous",
  title =        "Copyright",
  crossref =     "IEEE:2022:ISC",
  pages =        "1--1",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00003",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2022:PCA
author: Anonymous
title: Program Committee: ARITH 2022
crossref: IEEE:2022:ISC
pages: ix--ix
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00007
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Program Committee: {ARITH 2022}
entry:
@InProceedings{Anonymous:2022:PCA,
  author =       "Anonymous",
  title =        "Program Committee: {ARITH 2022}",
  crossref =     "IEEE:2022:ISC",
  pages =        "ix--ix",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00007",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2022:SA
author: Anonymous
title: Sponsors: ARITH 2022
crossref: IEEE:2022:ISC
pages: xi--xi
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00009
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Sponsors: {ARITH 2022}
entry:
@InProceedings{Anonymous:2022:SA,
  author =       "Anonymous",
  title =        "Sponsors: {ARITH 2022}",
  crossref =     "IEEE:2022:ISC",
  pages =        "xi--xi",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00009",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2022:SCA
author: Anonymous
title: Steering Committee: ARITH 2022
crossref: IEEE:2022:ISC
pages: x--x
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00008
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Steering Committee: {ARITH 2022}
entry:
@InProceedings{Anonymous:2022:SCA,
  author =       "Anonymous",
  title =        "Steering Committee: {ARITH 2022}",
  crossref =     "IEEE:2022:ISC",
  pages =        "x--x",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00008",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2022:TC
author: Anonymous
title: Table of Contents
crossref: IEEE:2022:ISC
pages: iv--vi
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00004
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Table of Contents
entry:
@InProceedings{Anonymous:2022:TC,
  author =       "Anonymous",
  title =        "Table of Contents",
  crossref =     "IEEE:2022:ISC",
  pages =        "iv--vi",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00004",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2022:TP
author: Anonymous
title: Title Page I
crossref: IEEE:2022:ISC
pages: 1--1
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00001
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Title Page {I}
entry:
@InProceedings{Anonymous:2022:TP,
  author =       "Anonymous",
  title =        "Title Page {I}",
  crossref =     "IEEE:2022:ISC",
  pages =        "1--1",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00001",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Anonymous:2022:TPI
author: Anonymous
title: Title Page III
crossref: IEEE:2022:ISC
pages: 1--1
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00002
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Title Page {III}
entry:
@InProceedings{Anonymous:2022:TPI,
  author =       "Anonymous",
  title =        "Title Page {III}",
  crossref =     "IEEE:2022:ISC",
  pages =        "1--1",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00002",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Aoki:2022:EWS
author: Daichi Aoki and Kazuhiko Minematsu and Toshihiko Okamura and Tsuyoshi Takagi
title: Efficient Word Size Modular Multiplication over Signed Integers
crossref: IEEE:2022:ISC
pages: 94--101
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00026
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Daichi Aoki and Kazuhiko Minematsu and Toshihiko Okamura and Tsuyoshi Takagi
rawtitle: Efficient Word Size Modular Multiplication over Signed Integers
entry:
@InProceedings{Aoki:2022:EWS,
  author =       "Daichi Aoki and Kazuhiko Minematsu and Toshihiko
                 Okamura and Tsuyoshi Takagi",
  title =        "Efficient Word Size Modular Multiplication over Signed
                 Integers",
  crossref =     "IEEE:2022:ISC",
  pages =        "94--101",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00026",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Arnold:2022:TQL
author: Mark G. Arnold
title: Towards Quantum Logarithm Number Systems
crossref: IEEE:2022:ISC
pages: 76--83
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00022
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Mark G. Arnold
rawtitle: Towards Quantum Logarithm Number Systems
entry:
@InProceedings{Arnold:2022:TQL,
  author =       "Mark G. Arnold",
  title =        "Towards Quantum Logarithm Number Systems",
  crossref =     "IEEE:2022:ISC",
  pages =        "76--83",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00022",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Bajard:2022:GVL
author: Jean-Claude Bajard and Kazuhide Fukushima and Thomas Plantard and Arnaud Sipasseuth
title: Generating Very Large RNS Bases
crossref: IEEE:2022:ISC
pages: 102--102
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00027
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29; Residue Number System (RNS)
acknowledgement: ack-nhfb
rawauthor: Jean-Claude Bajard and Kazuhide Fukushima and Thomas Plantard and Arnaud Sipasseuth
rawtitle: Generating Very Large {RNS} Bases
entry:
@InProceedings{Bajard:2022:GVL,
  author =       "Jean-Claude Bajard and Kazuhide Fukushima and Thomas
                 Plantard and Arnaud Sipasseuth",
  title =        "Generating Very Large {RNS} Bases",
  crossref =     "IEEE:2022:ISC",
  pages =        "102--102",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00027",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29; Residue Number System (RNS)",
}


bibtype: inproceedings
filename: fparith.bib
label: Barthel:2022:TIO
author: Moritz Barthel and Nils Hulsmeier and Jochen Rust and Steffen Paul
title: On the Implementation of Edge Detection Algorithms with SORN Arithmetic
crossref: Gustafson:2022:NGA
pages: 1--13
year: 2022
DOI: https://doi.org/10.1007/978-3-031-09779-9_1
bibdate: Fri Dec 15 07:04:06 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 07:04:06 ???
keywords: posit arithmetic; Sets-Of-Real-Numbers (SORN) arithmetic
acknowledgement: ack-nhfb
rawauthor: Moritz B{\"a}rthel and Nils H{\"u}lsmeier and Jochen Rust and Steffen Paul
rawtitle: On the Implementation of Edge Detection Algorithms with {SORN} Arithmetic
entry:
@InProceedings{Barthel:2022:TIO,
  author =       "Moritz B{\"a}rthel and Nils H{\"u}lsmeier and Jochen
                 Rust and Steffen Paul",
  title =        "On the Implementation of Edge Detection Algorithms
                 with {SORN} Arithmetic",
  crossref =     "Gustafson:2022:NGA",
  pages =        "1--13",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_1",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic; Sets-Of-Real-Numbers (SORN)
                 arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Benmouhoub:2022:ESA
author: Farah Benmouhoub and Pierre-Loic Garoche and Matthieu Martel
publisher: pub-SV
address: pub-SV:adr
pages: 165--181
year: 2022
DOI: https://doi.org/10.1007/978-3-030-95561-8_10
ISBN: 3-030-95561-3 OR 3030955613
ISBN13: 978-3-030-95561-8 OR 9783030955618
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Dec 9 08:51:02 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.09 08:51:02 ???
keywords: accurate floating-point summation; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Farah Benmouhoub and Pierre-Loic Garoche and Matthieu Martel
booktitle:
Software Verification: 13th International Conference, VSTTE 2021, New Haven, CT, USA, October 18--19, 2021, and 14th International Workshop, NSV 2021, Los Angeles, CA, USA, July 18--19, 2021

title:
An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods

abstract:
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE 754 Standard. In this context, an elementary brick of computation, used everywhere, is the sum of a sequence of numbers. This sum is subject to many numerical errors in floating-point arithmetic. To alleviate this issue, we have introduced a new parallel algorithm for summing a sequence of floating-point numbers. This algorithm which scales up easily with the number of processors, adds numbers of the same exponents first. In this article, our main contribution is an extensive analysis of its efficiency with respect to several properties: accuracy, convergence and reproducibility. In order to show the usefulness of our algorithm, we have chosen a set of representative numerical methods which are Simpson, Jacobi, LU factorization and the Iterated power method.

rawabstract:
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE 754 Standard. In this context, an elementary brick of computation, used everywhere, is the sum of a sequence of numbers. This sum is subject to many numerical errors in floating-point arithmetic. To alleviate this issue, we have introduced a new parallel algorithm for summing a sequence of floating-point numbers. This algorithm which scales up easily with the number of processors, adds numbers of the same exponents first. In this article, our main contribution is an extensive analysis of its efficiency with respect to several properties: accuracy, convergence and reproducibility. In order to show the usefulness of our algorithm, we have chosen a set of representative numerical methods which are Simpson, Jacobi, LU factorization and the Iterated power method.

rawbooktitle:
Software Verification: {13th International Conference, VSTTE 2021, New Haven, CT, USA, October 18--19, 2021, and 14th International Workshop, NSV 2021, Los Angeles, CA, USA, July 18--19, 2021}

rawtitle:
An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods

entry:
@InProceedings{Benmouhoub:2022:ESA,
  author =       "Farah Benmouhoub and Pierre-Loic Garoche and Matthieu
                 Martel",
  booktitle =    "Software Verification: {13th International Conference,
                 VSTTE 2021, New Haven, CT, USA, October 18--19, 2021,
                 and 14th International Workshop, NSV 2021, Los Angeles,
                 CA, USA, July 18--19, 2021}",
  title =        "An Efficient Summation Algorithm for the Accuracy,
                 Convergence and Reproducibility of Parallel Numerical
                 Methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "165--181",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-030-95561-8_10",
  ISBN =         "3-030-95561-3",
  ISBN-13 =      "978-3-030-95561-8",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Dec 9 08:51:02 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Nowadays, parallel computing is ubiquitous in several
                 application fields, both in engineering and science.
                 The computations rely on the floating-point arithmetic
                 specified by the IEEE 754 Standard. In this context, an
                 elementary brick of computation, used everywhere, is
                 the sum of a sequence of numbers. This sum is subject
                 to many numerical errors in floating-point arithmetic.
                 To alleviate this issue, we have introduced a new
                 parallel algorithm for summing a sequence of
                 floating-point numbers. This algorithm which scales up
                 easily with the number of processors, adds numbers of
                 the same exponents first. In this article, our main
                 contribution is an extensive analysis of its efficiency
                 with respect to several properties: accuracy,
                 convergence and reproducibility. In order to show the
                 usefulness of our algorithm, we have chosen a set of
                 representative numerical methods which are Simpson,
                 Jacobi, LU factorization and the Iterated power
                 method.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: BenSalem-Knapp:2022:BRE
author: Louise Ben Salem-Knapp and Sylvie Boldo and William Weens
title: Bounding the Round-Off Error of the Upwind Scheme for Advection
crossref: IEEE:2022:ISC
pages: 127--127
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00031
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Louise {Ben Salem-Knapp} and Sylvie Boldo and William Weens
rawtitle: Bounding the Round-Off Error of the Upwind Scheme for Advection
entry:
@InProceedings{BenSalem-Knapp:2022:BRE,
  author =       "Louise {Ben Salem-Knapp} and Sylvie Boldo and William
                 Weens",
  title =        "Bounding the Round-Off Error of the Upwind Scheme for
                 Advection",
  crossref =     "IEEE:2022:ISC",
  pages =        "127--127",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00031",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Bertaccini:2022:MNE
author: Luca Bertaccini and Gianna Paulin and Tim Fischer and Stefan Mach and Luca Benini
crossref: IEEE:2022:ISC
pages: 1--8
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00010
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Luca Bertaccini and Gianna Paulin and Tim Fischer and Stefan Mach and Luca Benini
title:
MiniFloat-NN and ExSdotp: an ISA Extension and a Modular Open Hardware Unit for Low-Precision Training on RISC-V Cores

rawtitle:
{MiniFloat-NN} and {ExSdotp}: an {ISA} Extension and a Modular Open Hardware Unit for Low-Precision Training on {RISC-V} Cores

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@InProceedings{Bertaccini:2022:MNE,
  author =       "Luca Bertaccini and Gianna Paulin and Tim Fischer and
                 Stefan Mach and Luca Benini",
  title =        "{MiniFloat-NN} and {ExSdotp}: an {ISA} Extension and a
                 Modular Open Hardware Unit for Low-Precision Training
                 on {RISC-V} Cores",
  crossref =     "IEEE:2022:ISC",
  pages =        "1--8",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00010",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Borges:2022:HLA
author: Carlos F. Borges and Claude-Pierre Jeannerod and Jean-Michel Muller
title: High-level algorithms for correctly-rounded reciprocal square roots
crossref: IEEE:2022:ISC
pages: 18--25
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00013
bibdate: Thu Sep 21 10:14:25 2023
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29; correct rounding; floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Carlos F. Borges and Claude-Pierre Jeannerod and Jean-Michel Muller
rawtitle: High-level algorithms for correctly-rounded reciprocal square roots
entry:
@InProceedings{Borges:2022:HLA,
  author =       "Carlos F. Borges and Claude-Pierre Jeannerod and
                 Jean-Michel Muller",
  title =        "High-level algorithms for correctly-rounded reciprocal
                 square roots",
  crossref =     "IEEE:2022:ISC",
  pages =        "18--25",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00013",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29; correct rounding; floating-point
                 arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Bruguera:2022:LLH
author: Javier D. Bruguera
title: Low-Latency and High-Bandwidth Pipelined Radix-64 Division and Square Root Unit
crossref: IEEE:2022:ISC
pages: 10--17
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00012
bibdate: Thu Sep 21 10:14:25 2023
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Javier D. Bruguera
rawtitle: Low-Latency and High-Bandwidth Pipelined Radix-64 Division and Square Root Unit
entry:
@InProceedings{Bruguera:2022:LLH,
  author =       "Javier D. Bruguera",
  title =        "Low-Latency and High-Bandwidth Pipelined Radix-64
                 Division and Square Root Unit",
  crossref =     "IEEE:2022:ISC",
  pages =        "10--17",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00012",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: article
filename: fparith.bib
label: Buhrow:2022:PMM
author: Benjamin Buhrow and Barry Gilbert and Clifton Haider
title: Parallel modular multiplication using 512-bit advanced vector instructions
journal: j-J-CRYPTO-ENG
volume: 12
number: 1
pages: 95--105
month: apr
monthnumber: 4
year: 2022
DOI: https://doi.org/10.1007/s13389-021-00256-9
ISSN: 2190-8508 (print), 2190-8516 (electronic) OR 21908508 (print), 21908516 (electronic)
ISSNL: 2190-8508 OR 21908508
bibdate: Sat Apr 16 13:18:32 MDT 2022
bibtimestamp: 2022.04.16 13:18:32 MDT
URL: https://link.springer.com/article/10.1007/s13389-021-00256-9
fjournal: Journal of Cryptographic Engineering
acknowledgement: ack-nhfb
ajournal: J. Crypto. Eng.
journalURL: http://link.springer.com/journal/13389
rawauthor: Benjamin Buhrow and Barry Gilbert and Clifton Haider
rawtitle: Parallel modular multiplication using 512-bit advanced vector instructions
entry:
@Article{Buhrow:2022:PMM,
  author =       "Benjamin Buhrow and Barry Gilbert and Clifton Haider",
  title =        "Parallel modular multiplication using 512-bit advanced
                 vector instructions",
  journal =      j-J-CRYPTO-ENG,
  volume =       "12",
  number =       "1",
  pages =        "95--105",
  month =        apr,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-021-00256-9",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Sat Apr 16 13:18:32 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "https://link.springer.com/article/10.1007/s13389-021-00256-9",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Crypto. Eng.",
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}


bibtype: article
filename: fparith.bib
label: Cardarilli:2022:DSE
title: Design Space Exploration Based Methodology for Residue Number System Digital Filters Implementation
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 10
number: 1
pages: 186--198
month: jan
monthnumber: 1
year: 2022
DOI: https://doi.org/10.1109/TETC.2020.2997067
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawtitle: Design Space Exploration Based Methodology for Residue Number System Digital Filters Implementation
author:
Gian Carlo Cardarilli and Luca Di Nunzio and Rocco Fazzolari and Alberto Nannarelli and Massimo Petricca and Marco Re

rawauthor:
Gian Carlo Cardarilli and Luca {Di Nunzio} and Rocco Fazzolari and Alberto Nannarelli and Massimo Petricca and Marco Re

entry:
@Article{Cardarilli:2022:DSE,
  author =       "Gian Carlo Cardarilli and Luca {Di Nunzio} and Rocco
                 Fazzolari and Alberto Nannarelli and Massimo Petricca
                 and Marco Re",
  title =        "Design Space Exploration Based Methodology for Residue
                 Number System Digital Filters Implementation",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "1",
  pages =        "186--198",
  month =        jan # "\slash " # mar,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2020.2997067",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: article
filename: fparith.bib
label: Chen:2022:PPL
author: Chuangtao Chen and Weikang Qian and Mohsen Imani and Xunzhao Yin and Cheng Zhuo
journal: j-IEEE-TRANS-COMPUT
volume: 71
number: 10
pages: 2473--2486
month: oct
monthnumber: 10
year: 2022
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2021.3131850
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 8 07:59:47 2022
bibtimestamp: 2022.09.08 07:59:47 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Chuangtao Chen and Weikang Qian and Mohsen Imani and Xunzhao Yin and Cheng Zhuo
title:
PAM: a Piecewise-Linearly-Approximated Floating-Point Multiplier With Unbiasedness and Configurability

rawtitle:
{PAM}: a Piecewise-Linearly-Approximated Floating-Point Multiplier With Unbiasedness and Configurability

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@Article{Chen:2022:PPL,
  author =       "Chuangtao Chen and Weikang Qian and Mohsen Imani and
                 Xunzhao Yin and Cheng Zhuo",
  title =        "{PAM}: a Piecewise-Linearly-Approximated
                 Floating-Point Multiplier With Unbiasedness and
                 Configurability",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "71",
  number =       "10",
  pages =        "2473--2486",
  month =        oct,
  year =         "2022",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2021.3131850",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 8 07:59:47 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Cococcioni:2022:ERO
author: Marco Cococcioni and Federico Rossi and Emanuele Ruffaldi and Sergio Saponara
booktitle: Applications in Electronics Pervading Industry, Environment and Society
publisher: pub-SV
address: pub-SV:adr
pages: 61--68
year: 2022
DOI: https://doi.org/10.1007/978-3-030-95498-7_9
ISBN: 3-030-95498-6 OR 3030954986
ISBN13: 978-3-030-95498-7 OR 9783030954987
ISSN: 1876-1119 OR 18761119
ISSNL: 1876-1100 OR 18761100
bibdate: Fri Dec 15 11:31:31 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 11:31:31 ???
keywords: posit arithmetic
acknowledgement: ack-nhfb
rawauthor: Marco Cococcioni and Federico Rossi and Emanuele Ruffaldi and Sergio Saponara
rawbooktitle: Applications in Electronics Pervading Industry, Environment and Society
title:
Experimental Results of Vectorized Posit-Based DNNs on a Real ARM SVE High Performance Computing Machine

rawtitle:
Experimental Results of Vectorized Posit-Based {DNNs} on a Real {ARM SVE} High Performance Computing Machine

entry:
@InProceedings{Cococcioni:2022:ERO,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  booktitle =    "Applications in Electronics Pervading Industry,
                 Environment and Society",
  title =        "Experimental Results of Vectorized Posit-Based {DNNs}
                 on a Real {ARM SVE} High Performance Computing
                 Machine",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "61--68",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-030-95498-7_9",
  ISBN =         "3-030-95498-6",
  ISBN-13 =      "978-3-030-95498-7",
  ISSN =         "1876-1119",
  ISSN-L =       "1876-1100",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}


bibtype: article
filename: fparith.bib
label: Cococcioni:2022:LPP
author: Marco Cococcioni and Federico Rossi and Emanuele Ruffaldi and Sergio Saponara
title: A Lightweight Posit Processing Unit for RISC-V Processors in Deep Neural Network Applications
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 10
number: 4
pages: 1898--1908
month: oct
monthnumber: 10
year: 2022
DOI: https://doi.org/10.1109/TETC.2021.3120538
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Marco Cococcioni and Federico Rossi and Emanuele Ruffaldi and Sergio Saponara
rawtitle: A Lightweight Posit Processing Unit for {RISC-V} Processors in Deep Neural Network Applications
bibsource:
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entry:
@Article{Cococcioni:2022:LPP,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  title =        "A Lightweight Posit Processing Unit for {RISC-V}
                 Processors in Deep Neural Network Applications",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "4",
  pages =        "1898--1908",
  month =        oct # "\slash " # dec,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3120538",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
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bibtype: inproceedings
filename: fparith.bib
label: Cococcioni:2022:SRR
author: Marco Cococcioni and Federico Rossi and Emanuele Ruffaldi and Sergio Saponara
title: Small Reals Representations for Deep Learning at the Edge: a Comparison
crossref: Gustafson:2022:NGA
pages: 117--133
year: 2022
DOI: https://doi.org/10.1007/978-3-031-09779-9_8
bibdate: Fri Dec 15 07:04:06 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 07:04:06 ???
keywords: posit arithmetic
acknowledgement: ack-nhfb
rawauthor: Marco Cococcioni and Federico Rossi and Emanuele Ruffaldi and Sergio Saponara
rawtitle: Small Reals Representations for Deep Learning at the Edge: a Comparison
entry:
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  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  title =        "Small Reals Representations for Deep Learning at the
                 Edge: a Comparison",
  crossref =     "Gustafson:2022:NGA",
  pages =        "117--133",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_8",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Coward:2022:ADO
author: Samuel Coward and George A. Constantinides and Theo Drane
title: Automatic Datapath Optimization using E-Graphs
crossref: IEEE:2022:ISC
pages: 43--50
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00016
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Samuel Coward and George A. Constantinides and Theo Drane
rawtitle: Automatic Datapath Optimization using E-Graphs
entry:
@InProceedings{Coward:2022:ADO,
  author =       "Samuel Coward and George A. Constantinides and Theo
                 Drane",
  title =        "Automatic Datapath Optimization using E-Graphs",
  crossref =     "IEEE:2022:ISC",
  pages =        "43--50",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00016",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: misc
filename: fparith.bib
label: Cowlishaw:2022:DAFa
author: Mike Cowlishaw
title: Decimal Arithmetic FAQ: Part 1 --- General Questions
pages: 43--50
day: 21
month: apr
monthnumber: 4
year: 2022
bibdate: Mon Apr 25 17:12:00 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.04.25 17:12:00 ???
URL: http://speleotrove.com/decimal/decifaq1.html
remark: Previous versions 2000, 2007.
acknowledgement: ack-nhfb
howpublished: Web site.
rawauthor: Mike Cowlishaw
rawtitle: Decimal Arithmetic {FAQ}: {Part} 1 --- General Questions
entry:
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  author =       "Mike Cowlishaw",
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  howpublished = "Web site.",
  day =          "21",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq1.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}


bibtype: misc
filename: fparith.bib
label: Cowlishaw:2022:DAFb
author: Mike Cowlishaw
title: Decimal Arithmetic FAQ: Part 2 --- Definitions
pages: 43--50
day: 25
month: apr
monthnumber: 4
year: 2022
bibdate: Mon Apr 25 17:12:00 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.04.25 17:12:00 ???
URL: http://speleotrove.com/decimal/decifaq2.html
remark: Previous versions 2000, 2007.
acknowledgement: ack-nhfb
howpublished: Web site.
rawauthor: Mike Cowlishaw
rawtitle: Decimal Arithmetic {FAQ}: {Part} 2 --- Definitions
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  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq2.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}


bibtype: misc
filename: fparith.bib
label: Cowlishaw:2022:DAFc
author: Mike Cowlishaw
title: Decimal Arithmetic FAQ: Part 3 --- Hardware Questions
pages: 43--50
day: 25
month: apr
monthnumber: 4
year: 2022
bibdate: Mon Apr 25 17:12:00 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.04.25 17:12:00 ???
URL: http://speleotrove.com/decimal/decifaq3.html
remark: Previous versions 2000, 2007.
acknowledgement: ack-nhfb
howpublished: Web site.
rawauthor: Mike Cowlishaw
rawtitle: Decimal Arithmetic {FAQ}: {Part} 3 --- Hardware Questions
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  howpublished = "Web site.",
  day =          "25",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq3.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}


bibtype: misc
filename: fparith.bib
label: Cowlishaw:2022:DAFd
author: Mike Cowlishaw
title: Decimal Arithmetic FAQ: Part 4 --- Arithmetic Specification Questions
pages: 43--50
day: 25
month: apr
monthnumber: 4
year: 2022
bibdate: Mon Apr 25 17:12:00 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.04.25 17:12:00 ???
URL: http://speleotrove.com/decimal/decifaq4.html
remark: Previous versions 2000, 2007.
acknowledgement: ack-nhfb
howpublished: Web site.
rawauthor: Mike Cowlishaw
rawtitle: Decimal Arithmetic {FAQ}: {Part} 4 --- Arithmetic Specification Questions
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  title =        "Decimal Arithmetic {FAQ}: {Part} 4 --- Arithmetic
                 Specification Questions",
  howpublished = "Web site.",
  day =          "25",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq4.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}


bibtype: misc
filename: fparith.bib
label: Cowlishaw:2022:DAFe
author: Mike Cowlishaw
title: Decimal Arithmetic FAQ: Part 5 --- Encoding Questions
pages: 43--50
day: 25
month: apr
monthnumber: 4
year: 2022
bibdate: Mon Apr 25 17:12:00 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.04.25 17:12:00 ???
URL: http://speleotrove.com/decimal/decifaq1.html
remark: Previous versions 2000, 2007.
acknowledgement: ack-nhfb
howpublished: Web site.
rawauthor: Mike Cowlishaw
rawtitle: Decimal Arithmetic {FAQ}: {Part} 5 --- Encoding Questions
entry:
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  author =       "Mike Cowlishaw",
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                 Questions",
  howpublished = "Web site.",
  day =          "25",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq1.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}


bibtype: misc
filename: fparith.bib
label: Cowlishaw:2022:DAFf
author: Mike Cowlishaw
title: Decimal Arithmetic FAQ: Part 5 --- Miscellaneous Questions
pages: 43--50
day: 25
month: apr
monthnumber: 4
year: 2022
bibdate: Mon Apr 25 17:12:00 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.04.25 17:12:00 ???
URL: http://speleotrove.com/decimal/decifaq6.html
remark: Previous versions 2000, 2007.
acknowledgement: ack-nhfb
howpublished: Web site.
rawauthor: Mike Cowlishaw
rawtitle: Decimal Arithmetic {FAQ}: {Part} 5 --- Miscellaneous Questions
entry:
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  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic {FAQ}: {Part} 5 --- Miscellaneous
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  howpublished = "Web site.",
  day =          "25",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq6.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}


bibtype: article
filename: fparith.bib
label: Crespo:2022:UPI
author: Luis Crespo and Pedro Tomas and Nuno Roma and Nuno Neves
title: Unified Posit / IEEE-754 Vector MAC Unit for Transprecision Computing
journal: j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS
volume: 69
number: 5
pages: 2478--2482
year: 2022
DOI: https://doi.org/10.1109/TCSII.2022.3160191
ISSN: 1549-7747 (print), 1558-3791 (electronic) OR 15497747 (print), 15583791 (electronic)
ISSNL: 1549-7747 OR 15497747
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
fjournal: IEEE Transactions on Circuits and Systems II: Express Briefs
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/issues?punumber=8920
rawauthor: Lu{\'\i}s Crespo and Pedro Tom{\'a}s and Nuno Roma and Nuno Neves
rawtitle: Unified Posit\slash {IEEE-754} Vector {MAC} Unit for Transprecision Computing
entry:
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  author =       "Lu{\'\i}s Crespo and Pedro Tom{\'a}s and Nuno Roma and
                 Nuno Neves",
  title =        "Unified Posit\slash {IEEE-754} Vector {MAC} Unit for
                 Transprecision Computing",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "69",
  number =       "5",
  pages =        "2478--2482",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TCSII.2022.3160191",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
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bibtype: inproceedings
filename: fparith.bib
label: deDinechin:2022:FA
author: Florent de Dinechin and Stuart Oberman and Bogdan Pasca and Leonel Sousa
title: Foreword: ARITH 2022
crossref: IEEE:2022:ISC
pages: vii--vii
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00005
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Florent de Dinechin and Stuart Oberman and Bogdan Pasca and Leonel Sousa
rawtitle: Foreword: {ARITH 2022}
entry:
@InProceedings{deDinechin:2022:FA,
  author =       "Florent de Dinechin and Stuart Oberman and Bogdan
                 Pasca and Leonel Sousa",
  title =        "Foreword: {ARITH 2022}",
  crossref =     "IEEE:2022:ISC",
  pages =        "vii--vii",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00005",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: deDinechin:2022:OCA
title: Organizing Committee: ARITH 2022
crossref: IEEE:2022:ISC
pages: viii--viii
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00006
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawtitle: Organizing Committee: {ARITH 2022}
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Florent de Dinechin and Stuart Oberman and Bogdan Pasca and Leonel Sousa and Guillaume Melquiond and Marc Mezzarobba and Vojin G. Oklobdzija

rawauthor:
Florent de Dinechin and Stuart Oberman and Bogdan Pasca and Leonel Sousa and Guillaume Melquiond and Marc Mezzarobba and Vojin G. Oklobdzija

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  author =       "Florent de Dinechin and Stuart Oberman and Bogdan
                 Pasca and Leonel Sousa and Guillaume Melquiond and Marc
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  crossref =     "IEEE:2022:ISC",
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  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00006",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
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bibtype: article
filename: fparith.bib
label: Demmel:2022:PCE
title: Proposed Consistent Exception Handling for the BLAS and LAPACK
journal: arXiv.org
pages: 92
day: 19
month: jul
monthnumber: 7
year: 2022
bibdate: Mon Sep 11 06:47:01 2023
bibtimestamp: 2023.09.11 06:47:01 ???
URL: https://arxiv.org/abs/2207.09281
acknowledgement: ack-nhfb
rawtitle: Proposed Consistent Exception Handling for the {BLAS} and {LAPACK}
author:
James Demmel and Jack Dongarra and Mark Gates and Greg Henry and Julien Langou and Xiaoye Li and Piotr Luszczek and Weslley Pereira and Jason Riedy and Cindy Rubio-Gonzalez

abstract:
Numerical exceptions, which may be caused by overflow, operations like division by 0 or sqrt(-1), or convergence failures, are unavoidable in many cases, in particular when software is used on unforeseen and difficult inputs. As more aspects of society become automated, e.g., self-driving cars, health monitors, and cyber-physical systems more generally, it is becoming increasingly important to design software that is resilient to exceptions, and that responds to them in a consistent way. Consistency is needed to allow users to build higher-level software that is also resilient and consistent (and so on recursively). In this paper we explore the design space of consistent exception handling for the widely used BLAS and LAPACK linear algebra libraries, pointing out a variety of instances of inconsistent exception handling in the current versions, and propose a new design that balances consistency, complexity, ease of use, and performance. Some compromises are needed, because there are preexisting inconsistencies that are outside our control, including in or between existing vendor BLAS implementations, different programming languages, and even compilers for the same programming language. And user requests from our surveys are quite diverse. We also propose our design as a possible model for other numerical software, and welcome comments on our design choices

rawabstract:
Numerical exceptions, which may be caused by overflow, operations like division by 0 or sqrt(-1), or convergence failures, are unavoidable in many cases, in particular when software is used on unforeseen and difficult inputs. As more aspects of society become automated, e.g., self-driving cars, health monitors, and cyber-physical systems more generally, it is becoming increasingly important to design software that is resilient to exceptions, and that responds to them in a consistent way. Consistency is needed to allow users to build higher-level software that is also resilient and consistent (and so on recursively). In this paper we explore the design space of consistent exception handling for the widely used BLAS and LAPACK linear algebra libraries, pointing out a variety of instances of inconsistent exception handling in the current versions, and propose a new design that balances consistency, complexity, ease of use, and performance. Some compromises are needed, because there are preexisting inconsistencies that are outside our control, including in or between existing vendor BLAS implementations, different programming languages, and even compilers for the same programming language. And user requests from our surveys are quite diverse. We also propose our design as a possible model for other numerical software, and welcome comments on our design choices

rawauthor:
James Demmel and Jack Dongarra and Mark Gates and Greg Henry and Julien Langou and Xiaoye Li and Piotr Luszczek and Weslley Pereira and Jason Riedy and Cindy Rubio-Gonz{\'a}lez

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  author =       "James Demmel and Jack Dongarra and Mark Gates and Greg
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bibtype: inproceedings
filename: fparith.bib
label: Desrentes:2022:PDO
author: Oregane Desrentes and Diana Resmerita and Benoit Dupont de Dinechin
title: A Posit8 Decompression Operator for Deep Neural Network Inference
crossref: Gustafson:2022:NGA
pages: 14--30
year: 2022
DOI: https://doi.org/10.1007/978-3-031-09779-9_2
bibdate: Fri Dec 15 07:04:06 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 07:04:06 ???
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acknowledgement: ack-nhfb
rawauthor: Or{\'e}gane Desrentes and Diana Resmerita and Beno{\^\i}t Dupont de Dinechin
rawtitle: A {Posit8} Decompression Operator for Deep Neural Network Inference
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  author =       "Or{\'e}gane Desrentes and Diana Resmerita and
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  title =        "A {Posit8} Decompression Operator for Deep Neural
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  crossref =     "Gustafson:2022:NGA",
  pages =        "14--30",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_2",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
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bibtype: inproceedings
filename: fparith.bib
label: Didier:2022:SCR
author: Laurent-Stephane Didier and Jean-Marc Robert and Fangan Yssouf Dosso and Nadia El Mrabet
title: A software comparison of RNS and PMNS
crossref: IEEE:2022:ISC
pages: 86--93
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00025
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
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rawtitle: A software comparison of {RNS} and {PMNS}
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  author =       "Laurent-St{\'e}phane Didier and Jean-Marc Robert and
                 Fangan Yssouf Dosso and Nadia {El Mrabet}",
  title =        "A software comparison of {RNS} and {PMNS}",
  crossref =     "IEEE:2022:ISC",
  pages =        "86--93",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00025",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29; Polynomial Modular Number System (PMNS);
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bibtype: article
filename: fparith.bib
label: DiMeo:2022:AFP
author: Gennaro Di Meo and Gerardo Saggese and Antonio G. M. Strollo and Davide De Caro and Nicola Petra
title: Approximate Floating-Point Multiplier based on Static Segmentation
journal: j-ELECTRONICS
volume: 11
number: 11
pages: 3005:1--3005:23
year: 2022
DOI: https://doi.org/10.3390/electronics1119
ISSN: 2079-9292 OR 20799292
ISSNL: 2079-9292 OR 20799292
bibdate: Wed Dec 20 07:43:28 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.20 07:43:28 ???
fjournal: Electronics
acknowledgement: ack-nhfb
journalURL: https://www.mdpi.com/journal/electronics
rawtitle: Approximate Floating-Point Multiplier based on Static Segmentation
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https://mdpi-res.com/d_attachment/electronics/electronics-11-03005/article_deploy/electronics-11-03005.pdf

rawauthor:
Gennaro {Di Meo} and Gerardo Saggese and Antonio G. M. Strollo and Davide {De Caro} and Nicola Petra

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  author =       "Gennaro {Di Meo} and Gerardo Saggese and Antonio G. M.
                 Strollo and Davide {De Caro} and Nicola Petra",
  title =        "Approximate Floating-Point Multiplier based on Static
                 Segmentation",
  journal =      j-ELECTRONICS,
  volume =       "11",
  number =       "11",
  pages =        "3005:1--3005:23",
  year =         "2022",
  DOI =          "https://doi.org/10.3390/electronics1119",
  ISSN =         "2079-9292",
  ISSN-L =       "2079-9292",
  bibdate =      "Wed Dec 20 07:43:28 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://mdpi-res.com/d_attachment/electronics/electronics-11-03005/article_deploy/electronics-11-03005.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}


bibtype: inproceedings
filename: fparith.bib
label: Dosso:2022:PEA
author: Fangan Yssouf Dosso and Jean-Marc Robert and Pascal Veron
title: PMNS for efficient arithmetic and small memory cost
crossref: IEEE:2022:ISC
pages: 84--84
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00023
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Fangan Yssouf Dosso and Jean-Marc Robert and Pascal V{\'e}ron
rawtitle: {PMNS} for efficient arithmetic and small memory cost
entry:
@InProceedings{Dosso:2022:PEA,
  author =       "Fangan Yssouf Dosso and Jean-Marc Robert and Pascal
                 V{\'e}ron",
  title =        "{PMNS} for efficient arithmetic and small memory
                 cost",
  crossref =     "IEEE:2022:ISC",
  pages =        "84--84",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00023",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Durand:2022:AVC
title: Accelerating Variants of the Conjugate Gradient with the Variable Precision Processor
crossref: IEEE:2022:ISC
pages: 51--57
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00017
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawtitle: Accelerating Variants of the Conjugate Gradient with the Variable Precision Processor
author:
Yves Durand and Eric Guthmuller and Cesar Fuguet and Jerome Fereyre and Andrea Bocco and Riccardo Alidori

rawauthor:
Yves Durand and Eric Guthmuller and Cesar Fuguet and J{\'e}r{\^o}me Fereyre and Andrea Bocco and Riccardo Alidori

entry:
@InProceedings{Durand:2022:AVC,
  author =       "Yves Durand and Eric Guthmuller and Cesar Fuguet and
                 J{\'e}r{\^o}me Fereyre and Andrea Bocco and Riccardo
                 Alidori",
  title =        "Accelerating Variants of the Conjugate Gradient with
                 the Variable Precision Processor",
  crossref =     "IEEE:2022:ISC",
  pages =        "51--57",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00017",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: ElArar:2022:PES
author: El-Mehdi El Arar and Devan Sohier and Pablo de Oliveira Castro and Eric Petit
title: The Positive Effects of Stochastic Rounding in Numerical Algorithms
crossref: IEEE:2022:ISC
pages: 58--65
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00018
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: El-Mehdi {El Arar} and Devan Sohier and Pablo {de Oliveira Castro} and Eric Petit
rawtitle: The Positive Effects of Stochastic Rounding in Numerical Algorithms
abstract:
Recently, stochastic rounding (SR) has been implemented in specialized hardware but most current computing nodes do not yet support this rounding mode. Several works empirically illustrate the benefit of stochastic rounding in various fields such as neural networks and ordinary differential equations. For some algorithms, such as summation, inner product or matrix-vector multiplication, it has been proved that SR provides probabilistic error bounds better than the traditional deterministic bounds.par In this paper, we extend this theoretical ground for a wider adoption of SR in computer architecture. First, we analyze the biases of the two SR modes: SR-nearness and SR-up-or-down. We demonstrate on a case-study of Euler's forward method that IEEE-754 default rounding modes and SR-up-or-down accumulate rounding errors across iterations and that SR-nearness, being unbiased, does not. Second, we prove a $ O(sqrt n) $ probabilistic bound on the forward error of Horner's polynomial evaluation method with SR, improving on the known deterministic $ O(n) $ bound.

rawabstract:
Recently, stochastic rounding (SR) has been implemented in specialized hardware but most current computing nodes do not yet support this rounding mode. Several works empirically illustrate the benefit of stochastic rounding in various fields such as neural networks and ordinary differential equations. For some algorithms, such as summation, inner product or matrix-vector multiplication, it has been proved that SR provides probabilistic error bounds better than the traditional deterministic bounds.\par In this paper, we extend this theoretical ground for a wider adoption of SR in computer architecture. First, we analyze the biases of the two SR modes: SR-nearness and SR-up-or-down. We demonstrate on a case-study of Euler's forward method that IEEE-754 default rounding modes and SR-up-or-down accumulate rounding errors across iterations and that SR-nearness, being unbiased, does not. Second, we prove a $ O(\sqrt {n}) $ probabilistic bound on the forward error of Horner's polynomial evaluation method with SR, improving on the known deterministic $ O(n) $ bound.

entry:
@InProceedings{ElArar:2022:PES,
  author =       "El-Mehdi {El Arar} and Devan Sohier and Pablo {de
                 Oliveira Castro} and Eric Petit",
  title =        "The Positive Effects of Stochastic Rounding in
                 Numerical Algorithms",
  crossref =     "IEEE:2022:ISC",
  pages =        "58--65",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00018",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recently, stochastic rounding (SR) has been
                 implemented in specialized hardware but most current
                 computing nodes do not yet support this rounding mode.
                 Several works empirically illustrate the benefit of
                 stochastic rounding in various fields such as neural
                 networks and ordinary differential equations. For some
                 algorithms, such as summation, inner product or
                 matrix-vector multiplication, it has been proved that
                 SR provides probabilistic error bounds better than the
                 traditional deterministic bounds.\par

                 In this paper, we extend this theoretical ground for a
                 wider adoption of SR in computer architecture. First,
                 we analyze the biases of the two SR modes: SR-nearness
                 and SR-up-or-down. We demonstrate on a case-study of
                 Euler's forward method that IEEE-754 default rounding
                 modes and SR-up-or-down accumulate rounding errors
                 across iterations and that SR-nearness, being unbiased,
                 does not. Second, we prove a $ O(\sqrt {n}) $
                 probabilistic bound on the forward error of Horner's
                 polynomial evaluation method with SR, improving on the
                 known deterministic $ O(n) $ bound.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Elsaid:2022:OFA
author: Kareem Elsaid and Mona Safar and M. Watheq El-Kharashi
editor: IEEE
booktitle: 2022 International Conference on Microelectronics (ICM)
title: Optimized FPGA Architecture for Machine Learning Applications using Posit Multipliers
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 50--53
year: 2022
DOI: https://doi.org/10.1109/ICM56065.2022.10005431
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Kareem Elsaid and Mona Safar and M. Watheq El-Kharashi
rawbooktitle: {2022 International Conference on Microelectronics (ICM)}
raweditor: {IEEE}
rawtitle: Optimized {FPGA} Architecture for Machine Learning Applications using Posit Multipliers
entry:
@InProceedings{Elsaid:2022:OFA,
  author =       "Kareem Elsaid and Mona Safar and M. Watheq
                 El-Kharashi",
  editor =       "{IEEE}",
  booktitle =    "{2022 International Conference on Microelectronics
                 (ICM)}",
  title =        "Optimized {FPGA} Architecture for Machine Learning
                 Applications using Posit Multipliers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "50--53",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ICM56065.2022.10005431",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Ene:2022:PTS
author: Teodor Dumitru Ene and James E. Stine
title: Point-Targeted Sparseness and Ling Transforms on Parallel Prefix Adder Trees
crossref: IEEE:2022:ISC
pages: 68--75
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00021
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Teodor Dumitru Ene and James E. Stine
rawtitle: Point-Targeted Sparseness and {Ling} Transforms on Parallel Prefix Adder Trees
entry:
@InProceedings{Ene:2022:PTS,
  author =       "Teodor Dumitru Ene and James E. Stine",
  title =        "Point-Targeted Sparseness and {Ling} Transforms on
                 Parallel Prefix Adder Trees",
  crossref =     "IEEE:2022:ISC",
  pages =        "68--75",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00021",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Essam:2022:DIL
author: Mohammed Essam and Ahmed Shalaby and Mohamed Taher
editor: IEEE
title: Design and Implementation of Low Power Posit Arithmetic Unit for Efficient Hardware Accelerators
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 68--71
year: 2022
DOI: https://doi.org/10.1109/JAC-ECC56395.2022.10043893
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Mohammed Essam and Ahmed Shalaby and Mohamed Taher
raweditor: {IEEE}
rawtitle: Design and Implementation of Low Power Posit Arithmetic Unit for Efficient Hardware Accelerators
booktitle:
2022 10th International Japan-Africa Conference on Electronics, Communications, and Computations (JAC-ECC)

rawbooktitle:
{2022 10th International Japan-Africa Conference on Electronics, Communications, and Computations (JAC-ECC)}

entry:
@InProceedings{Essam:2022:DIL,
  author =       "Mohammed Essam and Ahmed Shalaby and Mohamed Taher",
  editor =       "{IEEE}",
  booktitle =    "{2022 10th International Japan-Africa Conference on
                 Electronics, Communications, and Computations
                 (JAC-ECC)}",
  title =        "Design and Implementation of Low Power Posit
                 Arithmetic Unit for Efficient Hardware Accelerators",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "68--71",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/JAC-ECC56395.2022.10043893",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Evstigneev:2022:CSD
author: N. M. Evstigneev and O. I. Ryabkov and A. N. Bocharov and V. P. Petrovskiy and I. O. Teplyakov
journal: j-J-COMPUT-APPL-MATH
volume: 414
pages: ??--??
month: nov
monthnumber: 11
year: 2022
CODEN: JCAMDI
DOI: https://doi.org/10.1016/j.cam.2022.114434
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Tue Jun 14 16:20:17 MDT 2022
bibtimestamp: 2022.06.14 16:20:17 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0377042722002047
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
articleno: 114434
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: N. M. Evstigneev and O. I. Ryabkov and A. N. Bocharov and V. P. Petrovskiy and I. O. Teplyakov
title:
Compensated summation and dot product algorithms for floating-point vectors on parallel architectures: Error bounds, implementation and application in the Krylov subspace methods

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib

rawtitle:
Compensated summation and dot product algorithms for floating-point vectors on parallel architectures: Error bounds, implementation and application in the {Krylov} subspace methods

entry:
@Article{Evstigneev:2022:CSD,
  author =       "N. M. Evstigneev and O. I. Ryabkov and A. N. Bocharov
                 and V. P. Petrovskiy and I. O. Teplyakov",
  title =        "Compensated summation and dot product algorithms for
                 floating-point vectors on parallel architectures: Error
                 bounds, implementation and application in the {Krylov}
                 subspace methods",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "414",
  number =       "??",
  pages =        "??--??",
  month =        nov,
  year =         "2022",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2022.114434",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Tue Jun 14 16:20:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042722002047",
  acknowledgement = ack-nhfb,
  articleno =    "114434",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: fparith.bib
label: Gao:2022:TFI
author: Zhanyuan Gao and Laiping Zhao and Haonan Chen
editor: IEEE
booktitle: 2022 IEEE / ACIS 22nd International Conference on Computer and Information Science (ICIS)
title: A Trigonometric Function Instruction Set Extension Method Based on RISC-V
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 119--126
year: 2022
DOI: https://doi.org/10.1109/ICIS54925.2022.9882453
bibdate: Sat Dec 16 15:51:40 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.12.16 15:51:40 ???
acknowledgement: ack-nhfb
rawauthor: Zhanyuan Gao and Laiping Zhao and Haonan Chen
rawbooktitle: {2022 IEEE\slash ACIS 22nd International Conference on Computer and Information Science (ICIS)}
raweditor: {IEEE}
rawtitle: A Trigonometric Function Instruction Set Extension Method Based on {RISC-V}
entry:
@InProceedings{Gao:2022:TFI,
  author =       "Zhanyuan Gao and Laiping Zhao and Haonan Chen",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE\slash ACIS 22nd International Conference on
                 Computer and Information Science (ICIS)}",
  title =        "A Trigonometric Function Instruction Set Extension
                 Method Based on {RISC-V}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "119--126",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ICIS54925.2022.9882453",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Genkina:2022:PNK
author: Dina Genkina
pages: 119--126
day: 26
month: sep
monthnumber: 9
year: 2022
bibdate: Wed Sep 28 10:46:38 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2022.09.28 10:46:38 ???
URL: https://spectrum.ieee.org/floating-point-numbers-posits-processor
acknowledgement: ack-nhfb
howpublished: IEEE Spectrum Web site
rawauthor: Dina Genkina
title:
Posits, a New Kind of Number, Improves the Math of AI: The first posit-based processor core gave a ten-thousandfold accuracy boost

rawtitle:
Posits, a New Kind of Number, Improves the Math of {AI}: The first posit-based processor core gave a ten-thousandfold accuracy boost

entry:
@Misc{Genkina:2022:PNK,
  author =       "Dina Genkina",
  title =        "Posits, a New Kind of Number, Improves the Math of
                 {AI}: The first posit-based processor core gave a
                 ten-thousandfold accuracy boost",
  howpublished = "IEEE Spectrum Web site",
  day =          "26",
  month =        sep,
  year =         "2022",
  bibdate =      "Wed Sep 28 10:46:38 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://spectrum.ieee.org/floating-point-numbers-posits-processor",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Greuet:2022:QAM
author: Aurelien Greuet and Simon Montoya and Clemence Vermeersch
title: Quotient Approximation Modular Reduction
crossref: IEEE:2022:ISC
pages: 103--110
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00028
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Aur{\'e}lien Greuet and Simon Montoya and Cl{\'e}mence Vermeersch
rawtitle: Quotient Approximation Modular Reduction
entry:
@InProceedings{Greuet:2022:QAM,
  author =       "Aur{\'e}lien Greuet and Simon Montoya and Cl{\'e}mence
                 Vermeersch",
  title =        "Quotient Approximation Modular Reduction",
  crossref =     "IEEE:2022:ISC",
  pages =        "103--110",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00028",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Ho:2022:QNG
author: Nhut-Minh Ho and Himeshi De Silva and John L. Gustafson and Weng-Fai Wong
title: Qtorch+: Next Generation Arithmetic for Pytorch Machine Learning
crossref: Gustafson:2022:NGA
pages: 31--49
year: 2022
DOI: https://doi.org/10.1007/978-3-031-09779-9_3
bibdate: Fri Dec 15 07:04:06 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 07:04:06 ???
keywords: posit arithmetic
acknowledgement: ack-nhfb
rawauthor: Nhut-Minh Ho and Himeshi De Silva and John L. Gustafson and Weng-Fai Wong
rawtitle: {Qtorch+}: Next Generation Arithmetic for {Pytorch} Machine Learning
entry:
@InProceedings{Ho:2022:QNG,
  author =       "Nhut-Minh Ho and Himeshi De Silva and John L.
                 Gustafson and Weng-Fai Wong",
  title =        "{Qtorch+}: Next Generation Arithmetic for {Pytorch}
                 Machine Learning",
  crossref =     "Gustafson:2022:NGA",
  pages =        "31--49",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_3",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Immaneni:2022:PEO
author: Amritha Immaneni and Salim Ullah and Suresh Nambi and Siva Satyendra Sahoo and Akash Kumar
editor: IEEE
booktitle: 2022 25th Euromicro Conference on Digital System Design (DSD)
title: PosAx-O: Exploring Operator-level Approximations for Posit Arithmetic in Embedded AI / ML
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 214--223
year: 2022
DOI: https://doi.org/10.1109/DSD57027.2022.00037
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Amritha Immaneni and Salim Ullah and Suresh Nambi and Siva Satyendra Sahoo and Akash Kumar
rawbooktitle: {2022 25th Euromicro Conference on Digital System Design (DSD)}
raweditor: {IEEE}
rawtitle: {PosAx-O}: Exploring Operator-level Approximations for Posit Arithmetic in Embedded {AI\slash ML}
entry:
@InProceedings{Immaneni:2022:PEO,
  author =       "Amritha Immaneni and Salim Ullah and Suresh Nambi and
                 Siva Satyendra Sahoo and Akash Kumar",
  editor =       "{IEEE}",
  booktitle =    "{2022 25th Euromicro Conference on Digital System
                 Design (DSD)}",
  title =        "{PosAx-O}: Exploring Operator-level Approximations for
                 Posit Arithmetic in Embedded {AI\slash ML}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "214--223",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/DSD57027.2022.00037",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Isupov:2022:MPS
author: Konstantin Isupov
title: Multiple-precision sparse matrix--vector multiplication on GPUs
journal: j-J-COMPUT-SCI
volume: 61
pages: ??--??
month: may
monthnumber: 5
year: 2022
DOI: https://doi.org/10.1016/j.jocs.2022.101609
ISSN: 1877-7503 (print), 1877-7511 (electronic) OR 18777503 (print), 18777511 (electronic)
ISSNL: 1877-7503 OR 18777503
bibdate: Tue Sep 19 13:56:09 MDT 2023
bibtimestamp: 2023.09.19 13:56:09 MDT
URL: https://www.sciencedirect.com/science/article/pii/S1877750322000382
fjournal: Journal of Computational Science
acknowledgement: ack-nhfb
ajournal: J. Comput. Sci.
articleno: 101609
journalURL: https://www.sciencedirect.com/journal/journal-of-computational-science
rawauthor: Konstantin Isupov
rawtitle: Multiple-precision sparse matrix--vector multiplication on {GPUs}
entry:
@Article{Isupov:2022:MPS,
  author =       "Konstantin Isupov",
  title =        "Multiple-precision sparse matrix--vector
                 multiplication on {GPUs}",
  journal =      j-J-COMPUT-SCI,
  volume =       "61",
  pages =        "??--??",
  month =        may,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jocs.2022.101609",
  ISSN =         "1877-7503 (print), 1877-7511 (electronic)",
  ISSN-L =       "1877-7503",
  bibdate =      "Tue Sep 19 13:56:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputsci.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S1877750322000382",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Comput. Sci.",
  articleno =    "101609",
  fjournal =     "Journal of Computational Science",
  journal-URL =  "https://www.sciencedirect.com/journal/journal-of-computational-science",
}


bibtype: inproceedings
filename: fparith.bib
label: Keerthi:2022:DIM
author: T Keerthi and Yashu Swami
editor: IEEE
title: Design and Implementation of MAC by Using Efficient Posit Multiplier
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--4
year: 2022
DOI: https://doi.org/10.1109/VLSISATA54927.2022.10046599
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: T Keerthi and Yashu Swami
raweditor: {IEEE}
rawtitle: Design and Implementation of {MAC} by Using Efficient Posit Multiplier
booktitle:
2022 IEEE 3rd International Conference on VLSI Systems, Architecture, Technology and Applications (VLSI SATA)

rawbooktitle:
{2022 IEEE 3rd International Conference on VLSI Systems, Architecture, Technology and Applications (VLSI SATA)}

entry:
@InProceedings{Keerthi:2022:DIM,
  author =       "T Keerthi and Yashu Swami",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE 3rd International Conference on VLSI
                 Systems, Architecture, Technology and Applications
                 (VLSI SATA)}",
  title =        "Design and Implementation of {MAC} by Using Efficient
                 Posit Multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/VLSISATA54927.2022.10046599",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Kim:2022:EAM
author: Min Soo Kim and Alberto A. Del Barrio and HyunJin Kim and Nader Bagherzadeh
title: The Effects of Approximate Multiplication on Convolutional Neural Networks
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 10
number: 2
pages: 904--916
month: apr
monthnumber: 4
year: 2022
DOI: https://doi.org/10.1109/TETC.2021.3050989
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Min Soo Kim and Alberto A. {Del Barrio} and HyunJin Kim and Nader Bagherzadeh
rawtitle: The Effects of Approximate Multiplication on Convolutional Neural Networks
abstract:
This article analyzes the effects of approximate multiplication when performing inferences on deep convolutional neural networks (CNNs). The approximate multiplication can reduce the cost of the underlying circuits so that CNN inferences can be performed more efficiently in hardware accelerators. The study identifies the critical factors in the convolution, fully-connected, and batch normalization layers that allow more accurate CNN predictions despite the errors from approximate multiplication. The same factors also provide an arithmetic explanation of why bfloat16 multiplication performs well on CNNs. The experiments are performed with recognized network architectures to show that the approximate multipliers can produce predictions that are nearly as accurate as the FP32 references, without additional training. For example, the ResNet and Inception-v4 models with Mitch-$w$ 6 multiplication produces Top-5 errors that are within 0.2 percent compared to the FP32 references. A brief cost comparison of Mitch-$w$ 6 against bfloat16 is presented where a MAC operation saves up to 80 percent of energy compared to the bfloat16 arithmetic. The most far-reaching contribution of this article is the analytical justification that multiplications can be approximated while additions need to be exact in CNN MAC operations.

rawabstract:
This article analyzes the effects of approximate multiplication when performing inferences on deep convolutional neural networks (CNNs). The approximate multiplication can reduce the cost of the underlying circuits so that CNN inferences can be performed more efficiently in hardware accelerators. The study identifies the critical factors in the convolution, fully-connected, and batch normalization layers that allow more accurate CNN predictions despite the errors from approximate multiplication. The same factors also provide an arithmetic explanation of why bfloat16 multiplication performs well on CNNs. The experiments are performed with recognized network architectures to show that the approximate multipliers can produce predictions that are nearly as accurate as the FP32 references, without additional training. For example, the ResNet and Inception-v4 models with Mitch-$w$ 6 multiplication produces Top-5 errors that are within 0.2 percent compared to the FP32 references. A brief cost comparison of Mitch-$w$ 6 against bfloat16 is presented where a MAC operation saves up to 80 percent of energy compared to the bfloat16 arithmetic. The most far-reaching contribution of this article is the analytical justification that multiplications can be approximated while additions need to be exact in CNN MAC operations.

entry:
@Article{Kim:2022:EAM,
  author =       "Min Soo Kim and Alberto A. {Del Barrio} and HyunJin
                 Kim and Nader Bagherzadeh",
  title =        "The Effects of Approximate Multiplication on
                 Convolutional Neural Networks",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "2",
  pages =        "904--916",
  month =        apr # "\slash " # jun,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3050989",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "This article analyzes the effects of approximate
                 multiplication when performing inferences on deep
                 convolutional neural networks (CNNs). The approximate
                 multiplication can reduce the cost of the underlying
                 circuits so that CNN inferences can be performed more
                 efficiently in hardware accelerators. The study
                 identifies the critical factors in the convolution,
                 fully-connected, and batch normalization layers that
                 allow more accurate CNN predictions despite the errors
                 from approximate multiplication. The same factors also
                 provide an arithmetic explanation of why bfloat16
                 multiplication performs well on CNNs. The experiments
                 are performed with recognized network architectures to
                 show that the approximate multipliers can produce
                 predictions that are nearly as accurate as the FP32
                 references, without additional training. For example,
                 the ResNet and Inception-v4 models with Mitch-$w$ 6
                 multiplication produces Top-5 errors that are within
                 0.2 percent compared to the FP32 references. A brief
                 cost comparison of Mitch-$w$ 6 against bfloat16 is
                 presented where a MAC operation saves up to 80 percent
                 of energy compared to the bfloat16 arithmetic. The most
                 far-reaching contribution of this article is the
                 analytical justification that multiplications can be
                 approximated while additions need to be exact in CNN
                 MAC operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: inproceedings
filename: fparith.bib
label: Knodtel:2022:SID
author: Johannes Knodtel and Sebastian Rachuj and Marc Reichenbach
editor: IEEE
booktitle: 2022 25th Euromicro Conference on Digital System Design (DSD)
title: Suitability of ISAs for Data Paths Based on Redundant Number Systems: Is RISC-V the best?
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 247--253
year: 2022
DOI: https://doi.org/10.1109/DSD57027.2022.00041
bibdate: Sat Dec 16 15:51:40 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.12.16 15:51:40 ???
acknowledgement: ack-nhfb
rawauthor: Johannes Kn{\"o}dtel and Sebastian Rachuj and Marc Reichenbach
rawbooktitle: {2022 25th Euromicro Conference on Digital System Design (DSD)}
raweditor: {IEEE}
rawtitle: Suitability of {ISAs} for Data Paths Based on Redundant Number Systems: Is {RISC-V} the best?
entry:
@InProceedings{Knodtel:2022:SID,
  author =       "Johannes Kn{\"o}dtel and Sebastian Rachuj and Marc
                 Reichenbach",
  editor =       "{IEEE}",
  booktitle =    "{2022 25th Euromicro Conference on Digital System
                 Design (DSD)}",
  title =        "Suitability of {ISAs} for Data Paths Based on
                 Redundant Number Systems: Is {RISC-V} the best?",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "247--253",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/DSD57027.2022.00041",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kuang:2022:HSN
author: Honglin Kuang and Yifan Zhao and Jun Han
editor: IEEE
booktitle: 2022 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 592--595
year: 2022
DOI: https://doi.org/10.1109/APCCAS55924.2022.10090293
bibdate: Sat Dec 16 15:51:40 2023
bibtimestamp: 2023.12.16 15:51:40 ???
acknowledgement: ack-nhfb
rawauthor: Honglin Kuang and Yifan Zhao and Jun Han
rawbooktitle: {2022 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)}
raweditor: {IEEE}
title:
A High-Speed NTT-Based Polynomial Multiplication Accelerator with Vector Extension of RISC-V for Saber Algorithm

bibsource:
https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib

rawtitle:
A High-Speed {NTT}-Based Polynomial Multiplication Accelerator with Vector Extension of {RISC-V} for {Saber} Algorithm

entry:
@InProceedings{Kuang:2022:HSN,
  author =       "Honglin Kuang and Yifan Zhao and Jun Han",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE Asia Pacific Conference on Circuits and
                 Systems (APCCAS)}",
  title =        "A High-Speed {NTT}-Based Polynomial Multiplication
                 Accelerator with Vector Extension of {RISC-V} for
                 {Saber} Algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "592--595",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/APCCAS55924.2022.10090293",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Laguna:2022:BAF
author: Ignacio Laguna and Xinyi Li and Ganesh Gopalakrishnan
title: BinFPE: Accurate Floating-Point Exception Detection for GPU Applications
publisher: pub-ACM
address: pub-ACM:adr
pages: 1--8
year: 2022
DOI: https://doi.org/10.1145/3520313.3534655
ISBN: 1-4503-9274-1 OR 1450392741
ISBN13: 978-1-4503-9274-7 OR 9781450392747
bibdate: Mon Sep 11 07:11:11 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.11 07:11:11 ???
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1145/3520313
bookpages: 50
rawauthor: Ignacio Laguna and Xinyi Li and Ganesh Gopalakrishnan
rawtitle: {BinFPE}: Accurate Floating-Point Exception Detection for {GPU} Applications
booktitle:
SOAP 2022: Proceedings of the 11th ACM SIGPLAN International Workshop on the State Of the Art in Program Analysis, San Diego, CA, USA, 14 June 2022

abstract:
When modern heterogeneous HPC systems perform numerical computations, floating-point exceptional quantities such as NaN and infinity in the GPU context, remain insufficiently handled. This is because commonly used GPUs and the CUDA language have no inherent exception detection capabilities. Existing compiler-based approaches for this problem are tied to a given compiler and cannot detect exceptions generated by binaries and precompiled libraries. This paper contributes BinFPE, a unique tool that addresses these challenges. BinFPE uses the NVBit dynamic binary instrumentation framework to check the machine registers after each calculation to recognize exceptions, and conveys this information to the CPU for final reporting. We demonstrate the effectiveness of BinFPE on 42 CUDA programs, reporting previously unreported exceptions. We also present the limitations of BinFPE and our perspective on building GPU tools via binary instrumentation.

rawabstract:
When modern heterogeneous HPC systems perform numerical computations, floating-point exceptional quantities such as NaN and infinity in the GPU context, remain insufficiently handled. This is because commonly used GPUs and the CUDA language have no inherent exception detection capabilities. Existing compiler-based approaches for this problem are tied to a given compiler and cannot detect exceptions generated by binaries and precompiled libraries. This paper contributes BinFPE, a unique tool that addresses these challenges. BinFPE uses the NVBit dynamic binary instrumentation framework to check the machine registers after each calculation to recognize exceptions, and conveys this information to the CPU for final reporting. We demonstrate the effectiveness of BinFPE on 42 CUDA programs, reporting previously unreported exceptions. We also present the limitations of BinFPE and our perspective on building GPU tools via binary instrumentation.

rawbooktitle:
{SOAP 2022: Proceedings of the 11th ACM SIGPLAN International Workshop on the State Of the Art in Program Analysis, San Diego, CA, USA, 14 June 2022}

entry:
@InProceedings{Laguna:2022:BAF,
  author =       "Ignacio Laguna and Xinyi Li and Ganesh
                 Gopalakrishnan",
  editor =       "????",
  booktitle =    "{SOAP 2022: Proceedings of the 11th ACM SIGPLAN
                 International Workshop on the State Of the Art in
                 Program Analysis, San Diego, CA, USA, 14 June 2022}",
  title =        "{BinFPE}: Accurate Floating-Point Exception Detection
                 for {GPU} Applications",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "50",
  pages =        "1--8",
  year =         "2022",
  DOI =          "https://doi.org/10.1145/3520313.3534655",
  ISBN =         "1-4503-9274-1",
  ISBN-13 =      "978-1-4503-9274-7",
  bibdate =      "Mon Sep 11 07:11:11 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When modern heterogeneous HPC systems perform
                 numerical computations, floating-point exceptional
                 quantities such as NaN and infinity in the GPU context,
                 remain insufficiently handled. This is because commonly
                 used GPUs and the CUDA language have no inherent
                 exception detection capabilities. Existing
                 compiler-based approaches for this problem are tied to
                 a given compiler and cannot detect exceptions generated
                 by binaries and precompiled libraries. This paper
                 contributes BinFPE, a unique tool that addresses these
                 challenges. BinFPE uses the NVBit dynamic binary
                 instrumentation framework to check the machine
                 registers after each calculation to recognize
                 exceptions, and conveys this information to the CPU for
                 final reporting. We demonstrate the effectiveness of
                 BinFPE on 42 CUDA programs, reporting previously
                 unreported exceptions. We also present the limitations
                 of BinFPE and our perspective on building GPU tools via
                 binary instrumentation.",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1145/3520313",
}


bibtype: inproceedings
filename: fparith.bib
label: Laguna:2022:FIT
author: Ignacio Laguna and Ganesh Gopalakrishnan
editor: ACM
title: Finding Inputs that Trigger Floating-Point Exceptions in GPUs via Bayesian Optimization
publisher: pub-ACM
address: pub-ACM:adr
pages: 464--475
year: 2022
ISBN: 1-66545-444-X OR 166545444X
ISBN13: 978-1-66545-444-5 OR 9781665454445
ISSN: 2167-4329 (print), 2167-4337 (electronic) OR 21674329 (print), 21674337 (electronic)
ISSNL: 2167-4337 OR 21674337
bibdate: Mon Sep 11 07:09:51 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.11 07:09:51 ???
acknowledgement: ack-nhfb
rawauthor: Ignacio Laguna and Ganesh Gopalakrishnan
raweditor: {ACM}
rawtitle: Finding Inputs that Trigger Floating-Point Exceptions in {GPUs} via {Bayesian} Optimization
booktitle:
SC '22: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, Dallas, Texas, November 13--18, 2022

abstract:
Testing code for floating-point exceptions is crucial as exceptions can quickly propagate and produce unreliable numerical answers. The state-of-the-art to test for floating-point exceptions in GPUs is quite limited and solutions require the application's source code, which precludes their use in accelerated libraries where the source is not publicly available. We present an approach to find inputs that trigger floating-point exceptions in black-box GPU functions, i.e., functions where the source code and information about input bounds are unavailable. Our approach is the first to use Bayesian optimization (BO) to identify such inputs and uses novel strategies to overcome the challenges that arise in applying BO to this problem. We implement our approach in the Xscope framework and demonstrate it on 58 functions from the CUDA Math Library and functions from ten HPC programs. Xscope is able to identify inputs that trigger exceptions in about 72% of the tested functions.

rawabstract:
Testing code for floating-point exceptions is crucial as exceptions can quickly propagate and produce unreliable numerical answers. The state-of-the-art to test for floating-point exceptions in GPUs is quite limited and solutions require the application's source code, which precludes their use in accelerated libraries where the source is not publicly available. We present an approach to find inputs that trigger floating-point exceptions in black-box GPU functions, i.e., functions where the source code and information about input bounds are unavailable. Our approach is the first to use Bayesian optimization (BO) to identify such inputs and uses novel strategies to overcome the challenges that arise in applying BO to this problem. We implement our approach in the Xscope framework and demonstrate it on 58 functions from the CUDA Math Library and functions from ten HPC programs. Xscope is able to identify inputs that trigger exceptions in about 72\% of the tested functions.

rawbooktitle:
{SC '22: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, Dallas, Texas, November 13--18, 2022}

entry:
@InProceedings{Laguna:2022:FIT,
  author =       "Ignacio Laguna and Ganesh Gopalakrishnan",
  editor =       "{ACM}",
  booktitle =    "{SC '22: Proceedings of the International Conference
                 on High Performance Computing, Networking, Storage and
                 Analysis, Dallas, Texas, November 13--18, 2022}",
  title =        "Finding Inputs that Trigger Floating-Point Exceptions
                 in {GPUs} via {Bayesian} Optimization",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "464--475",
  year =         "2022",
  ISBN =         "1-66545-444-X",
  ISBN-13 =      "978-1-66545-444-5",
  ISSN =         "2167-4329 (print), 2167-4337 (electronic)",
  ISSN-L =       "2167-4337",
  bibdate =      "Mon Sep 11 07:09:51 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Testing code for floating-point exceptions is crucial
                 as exceptions can quickly propagate and produce
                 unreliable numerical answers. The state-of-the-art to
                 test for floating-point exceptions in GPUs is quite
                 limited and solutions require the application's source
                 code, which precludes their use in accelerated
                 libraries where the source is not publicly available.
                 We present an approach to find inputs that trigger
                 floating-point exceptions in black-box GPU functions,
                 i.e., functions where the source code and information
                 about input bounds are unavailable. Our approach is the
                 first to use Bayesian optimization (BO) to identify
                 such inputs and uses novel strategies to overcome the
                 challenges that arise in applying BO to this problem.
                 We implement our approach in the Xscope framework and
                 demonstrate it on 58 functions from the CUDA Math
                 Library and functions from ten HPC programs. Xscope is
                 able to identify inputs that trigger exceptions in
                 about 72\% of the tested functions.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Langroudi:2022:AAH
author: Hamed F. Langroudi and Vedant Karia and Tej Pandit and Becky Mashaido and Dhireesha Kudithipudi
crossref: Gustafson:2022:NGA
pages: 50--65
year: 2022
DOI: https://doi.org/10.1007/978-3-031-09779-9_4
bibdate: Fri Dec 15 07:04:06 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 07:04:06 ???
keywords: posit arithmetic
acknowledgement: ack-nhfb
rawauthor: Hamed F. Langroudi and Vedant Karia and Tej Pandit and Becky Mashaido and Dhireesha Kudithipudi
title:
ACTION: Automated Hardware--Software Codesign Framework for Low-precision Numerical Format SelecTION in TinyML

rawtitle:
{ACTION}: {Automated Hardware--Software Codesign Framework for Low-precision Numerical Format SelecTION} in {TinyML}

entry:
@InProceedings{Langroudi:2022:AAH,
  author =       "Hamed F. Langroudi and Vedant Karia and Tej Pandit and
                 Becky Mashaido and Dhireesha Kudithipudi",
  title =        "{ACTION}: {Automated Hardware--Software Codesign
                 Framework for Low-precision Numerical Format SelecTION}
                 in {TinyML}",
  crossref =     "Gustafson:2022:NGA",
  pages =        "50--65",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_4",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}


bibtype: article
filename: fparith.bib
label: Lim:2022:OPA
author: Jay P. Lim and Santosh Nagarakatte
journal: j-PACMPL
volume: 6
number: POPL
pages: 3:1--3:28
month: jan
monthnumber: 1
year: 2022
DOI: https://doi.org/10.1145/3498664
ISSN: 2475-1421 (electronic) OR 24751421 (electronic)
ISSNL: 2475-1421 OR 24751421
bibdate: Thu May 26 06:32:48 MDT 2022
bibtimestamp: 2022.05.26 06:32:48 MDT
URL: https://dl.acm.org/doi/10.1145/3498664
fjournal: Proceedings of the ACM on Programming Languages (PACMPL)
keywords: correct rounding; elementary functions
acknowledgement: ack-nhfb
articleno: 3
journalURL: https://dl.acm.org/loi/pacmpl
rawauthor: Jay P. Lim and Santosh Nagarakatte
title:
One polynomial approximation to produce correctly rounded results of an elementary function for multiple representations and rounding modes

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/pacmpl.bib

abstract:
Mainstream math libraries for floating point (FP) do not produce correctly rounded results for all inputs. In contrast, CR-LIBM and RLIBM provide correctly rounded implementations for a specific FP representation with one rounding mode. Using such libraries for a representation with a new rounding mode or with different precision will result in wrong results due to double rounding. This paper proposes a novel method to generate a single polynomial approximation that produces correctly rounded results for all inputs for multiple rounding modes and multiple precision configurations. To generate a correctly rounded library for n-bits, our key idea is to generate a polynomial approximation for a representation with n+2-bits using the round-to-odd mode. We prove that the resulting polynomial approximation will produce correctly rounded results for all five rounding modes in the standard and for multiple representations with k-bits such that $ |E| + 1 < k leq n $, where $ |E| $ is the number of exponent bits in the representation. Similar to our prior work in the RLIBM project, we approximate the correctly rounded result when we generate the library with n+2-bits using the round-to-odd mode. We also generate polynomial approximations by structuring it as a linear programming problem but propose enhancements to polynomial generation to handle the round-to-odd mode. Our prototype is the first 32-bit float library that produces correctly rounded results with all rounding modes in the IEEE standard for all inputs with a single polynomial approximation. It also produces correctly rounded results for any FP configuration ranging from 10-bits to 32-bits while also being faster than mainstream libraries.

rawabstract:
Mainstream math libraries for floating point (FP) do not produce correctly rounded results for all inputs. In contrast, CR-LIBM and RLIBM provide correctly rounded implementations for a specific FP representation with one rounding mode. Using such libraries for a representation with a new rounding mode or with different precision will result in wrong results due to double rounding. This paper proposes a novel method to generate a single polynomial approximation that produces correctly rounded results for all inputs for multiple rounding modes and multiple precision configurations. To generate a correctly rounded library for n-bits, our key idea is to generate a polynomial approximation for a representation with n+2-bits using the round-to-odd mode. We prove that the resulting polynomial approximation will produce correctly rounded results for all five rounding modes in the standard and for multiple representations with k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $ is the number of exponent bits in the representation. Similar to our prior work in the RLIBM project, we approximate the correctly rounded result when we generate the library with n+2-bits using the round-to-odd mode. We also generate polynomial approximations by structuring it as a linear programming problem but propose enhancements to polynomial generation to handle the round-to-odd mode. Our prototype is the first 32-bit float library that produces correctly rounded results with all rounding modes in the IEEE standard for all inputs with a single polynomial approximation. It also produces correctly rounded results for any FP configuration ranging from 10-bits to 32-bits while also being faster than mainstream libraries.

rawtitle:
One polynomial approximation to produce correctly rounded results of an elementary function for multiple representations and rounding modes

entry:
@Article{Lim:2022:OPA,
  author =       "Jay P. Lim and Santosh Nagarakatte",
  title =        "One polynomial approximation to produce correctly
                 rounded results of an elementary function for multiple
                 representations and rounding modes",
  journal =      j-PACMPL,
  volume =       "6",
  number =       "POPL",
  pages =        "3:1--3:28",
  month =        jan,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3498664",
  ISSN =         "2475-1421 (electronic)",
  ISSN-L =       "2475-1421",
  bibdate =      "Thu May 26 06:32:48 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3498664",
  abstract =     "Mainstream math libraries for floating point (FP) do
                 not produce correctly rounded results for all inputs.
                 In contrast, CR-LIBM and RLIBM provide correctly
                 rounded implementations for a specific FP
                 representation with one rounding mode. Using such
                 libraries for a representation with a new rounding mode
                 or with different precision will result in wrong
                 results due to double rounding. This paper proposes a
                 novel method to generate a single polynomial
                 approximation that produces correctly rounded results
                 for all inputs for multiple rounding modes and multiple
                 precision configurations. To generate a correctly
                 rounded library for n-bits, our key idea is to generate
                 a polynomial approximation for a representation with
                 n+2-bits using the round-to-odd mode. We prove that the
                 resulting polynomial approximation will produce
                 correctly rounded results for all five rounding modes
                 in the standard and for multiple representations with
                 k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $
                 is the number of exponent bits in the representation.
                 Similar to our prior work in the RLIBM project, we
                 approximate the correctly rounded result when we
                 generate the library with n+2-bits using the
                 round-to-odd mode. We also generate polynomial
                 approximations by structuring it as a linear
                 programming problem but propose enhancements to
                 polynomial generation to handle the round-to-odd mode.
                 Our prototype is the first 32-bit float library that
                 produces correctly rounded results with all rounding
                 modes in the IEEE standard for all inputs with a single
                 polynomial approximation. It also produces correctly
                 rounded results for any FP configuration ranging from
                 10-bits to 32-bits while also being faster than
                 mainstream libraries.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "https://dl.acm.org/loi/pacmpl",
  keywords =     "correct rounding; elementary functions",
}


bibtype: inproceedings
filename: fparith.bib
label: Lindstrom:2022:MUC
author: Peter Lindstrom
title: MultiPosits: Universal Coding of $ mathbb R^n $
crossref: Gustafson:2022:NGA
pages: 66--83
year: 2022
DOI: https://doi.org/10.1007/978-3-031-09779-9_5
bibdate: Fri Dec 15 07:04:06 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 07:04:06 ???
keywords: posit arithmetic
acknowledgement: ack-nhfb
rawauthor: Peter Lindstrom
rawtitle: {MultiPosits}: Universal Coding of $ \mathbb {R}^n $
entry:
@InProceedings{Lindstrom:2022:MUC,
  author =       "Peter Lindstrom",
  title =        "{MultiPosits}: Universal Coding of $ \mathbb {R}^n $",
  crossref =     "Gustafson:2022:NGA",
  pages =        "66--83",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_5",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}


bibtype: article
filename: fparith.bib
label: Liu:2022:DUA
author: Weiqiang Liu and Tao Xu and Jing Li and Chenghua Wang and Paolo Montuschi and Fabrizio Lombardi
title: Design of Unsigned Approximate Hybrid Dividers Based on Restoring Array and Logarithmic Dividers
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 10
number: 1
pages: 339--350
month: jan
monthnumber: 1
year: 2022
DOI: https://doi.org/10.1109/TETC.2020.3022290
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Thu Sep 21 14:02:06 2023
bibtimestamp: 2023.09.21 14:02:06 ???
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawauthor: Weiqiang Liu and Tao Xu and Jing Li and Chenghua Wang and Paolo Montuschi and Fabrizio Lombardi
rawtitle: Design of Unsigned Approximate Hybrid Dividers Based on Restoring Array and Logarithmic Dividers
abstract:
Approximate computer arithmetic has been extensively studied due to its advantages to further reduce power consumption and increase performance at reduced accuracy. Although a number of approximate adders and multipliers have been studied, only a few approximate dividers have been proposed. A logarithmic divider (LD) has low complexity and accuracy, while an exact array divider (EXD) has a high complexity. Therefore, in this article, an approximate hybrid divider (AXHD) is proposed. It takes advantage of both LD and EXD to achieve a tradeoff between hardware performance and accuracy. Exact restoring divider cells are used to generate the most significant bits (MSBs) of the quotient for attaining a high accuracy while the other quotient digits are generated by using a LD as an approximate scheme to improve figures of merit such as power consumption, area and delay. To further save hardware resources, a so-called eliminated approximate hybrid divider (E-AXHD) based on AXHD is also proposed. In this improved design, a reduced width divider is used to replace the EXD in AXHD. Specifically, for a 16-by-8 design, $ n / (n + 1) $ array division is used to replace the $ n / 8 $ array division ($ n < 8$). The proposed AXHD and E-AXHD are evaluated and analyzed using error and hardware metrics. The proposed designs are also compared with EXD, LD and previous approximate dividers. The results show that the proposed designs outperform previous approximate dividers by considering both energy and error. The proposed hybrid dividers are of particular interest for error tolerant applications such as image processing and machine learning.

rawabstract:
Approximate computer arithmetic has been extensively studied due to its advantages to further reduce power consumption and increase performance at reduced accuracy. Although a number of approximate adders and multipliers have been studied, only a few approximate dividers have been proposed. A logarithmic divider (LD) has low complexity and accuracy, while an exact array divider (EXD) has a high complexity. Therefore, in this article, an approximate hybrid divider (AXHD) is proposed. It takes advantage of both LD and EXD to achieve a tradeoff between hardware performance and accuracy. Exact restoring divider cells are used to generate the most significant bits (MSBs) of the quotient for attaining a high accuracy while the other quotient digits are generated by using a LD as an approximate scheme to improve figures of merit such as power consumption, area and delay. To further save hardware resources, a so-called eliminated approximate hybrid divider (E-AXHD) based on AXHD is also proposed. In this improved design, a reduced width divider is used to replace the EXD in AXHD. Specifically, for a 16-by-8 design, $ n / (n + 1) $ array division is used to replace the $ n / 8 $ array division ($ n < 8$). The proposed AXHD and E-AXHD are evaluated and analyzed using error and hardware metrics. The proposed designs are also compared with EXD, LD and previous approximate dividers. The results show that the proposed designs outperform previous approximate dividers by considering both energy and error. The proposed hybrid dividers are of particular interest for error tolerant applications such as image processing and machine learning.

entry:
@Article{Liu:2022:DUA,
  author =       "Weiqiang Liu and Tao Xu and Jing Li and Chenghua Wang
                 and Paolo Montuschi and Fabrizio Lombardi",
  title =        "Design of Unsigned Approximate Hybrid Dividers Based
                 on Restoring Array and Logarithmic Dividers",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "1",
  pages =        "339--350",
  month =        jan # "\slash " # mar,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2020.3022290",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "Approximate computer arithmetic has been extensively
                 studied due to its advantages to further reduce power
                 consumption and increase performance at reduced
                 accuracy. Although a number of approximate adders and
                 multipliers have been studied, only a few approximate
                 dividers have been proposed. A logarithmic divider (LD)
                 has low complexity and accuracy, while an exact array
                 divider (EXD) has a high complexity. Therefore, in this
                 article, an approximate hybrid divider (AXHD) is
                 proposed. It takes advantage of both LD and EXD to
                 achieve a tradeoff between hardware performance and
                 accuracy. Exact restoring divider cells are used to
                 generate the most significant bits (MSBs) of the
                 quotient for attaining a high accuracy while the other
                 quotient digits are generated by using a LD as an
                 approximate scheme to improve figures of merit such as
                 power consumption, area and delay. To further save
                 hardware resources, a so-called eliminated approximate
                 hybrid divider (E-AXHD) based on AXHD is also proposed.
                 In this improved design, a reduced width divider is
                 used to replace the EXD in AXHD. Specifically, for a
                 16-by-8 design, $ n / (n + 1) $ array division is used
                 to replace the $ n / 8 $ array division ($ n < 8$). The
                 proposed AXHD and E-AXHD are evaluated and analyzed
                 using error and hardware metrics. The proposed designs
                 are also compared with EXD, LD and previous approximate
                 dividers. The results show that the proposed designs
                 outperform previous approximate dividers by considering
                 both energy and error. The proposed hybrid dividers are
                 of particular interest for error tolerant applications
                 such as image processing and machine learning.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: inproceedings
filename: fparith.bib
label: Mallasen:2022:CCR
editor: IEEE
booktitle: 2022 37th Conference on Design of Circuits and Integrated Circuits (DCIS)
title: Customizing the CVA6 RISC-V Core to Integrate Posit and Quire Instructions
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 01--06
year: 2022
DOI: https://doi.org/10.1109/DCIS55711.2022.9970026
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawbooktitle: {2022 37th Conference on Design of Circuits and Integrated Circuits (DCIS)}
raweditor: {IEEE}
rawtitle: Customizing the {CVA6 RISC-V} Core to Integrate Posit and Quire Instructions
author:
David Mallasen and Raul Murillo and Alberto A. Del Barrio and Guillermo Botella and Luis Pinuel and Manuel Prieto Matias

rawauthor:
David Mallas{\'e}n and Raul Murillo and Alberto A. {Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel and Manuel Prieto Matias

entry:
@InProceedings{Mallasen:2022:CCR,
  author =       "David Mallas{\'e}n and Raul Murillo and Alberto A.
                 {Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel
                 and Manuel Prieto Matias",
  editor =       "{IEEE}",
  booktitle =    "{2022 37th Conference on Design of Circuits and
                 Integrated Circuits (DCIS)}",
  title =        "Customizing the {CVA6 RISC-V} Core to Integrate Posit
                 and Quire Instructions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "01--06",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/DCIS55711.2022.9970026",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Mallasen:2022:POSa
title: PERCIVAL: Open-Source Posit RISC-V Core With Quire Capability
journal: j-IEEE-TRANS-EMERG-TOP-COMPUT
volume: 10
number: 3
pages: 1241--1252
year: 2022
DOI: https://doi.org/10.1109/TETC.2022.3187199
ISSN: 2168-6750 (print), 2376-4562 (electronic) OR 21686750 (print), 23764562 (electronic)
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.12.15 09:21:55 ???
fjournal: IEEE Transactions on Emerging Topics in Computing
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516
rawtitle: {PERCIVAL}: Open-Source Posit {RISC-V} Core With Quire Capability
author:
David Mallasen and Raul Murillo and Alberto A. Del Barrio and Guillermo Botella and Luis Pinuel and Manuel Prieto-Matias

rawauthor:
David Mallas{\'e}n and Raul Murillo and Alberto A. {Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel and Manuel Prieto-Matias

entry:
@Article{Mallasen:2022:POSa,
  author =       "David Mallas{\'e}n and Raul Murillo and Alberto A.
                 {Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel
                 and Manuel Prieto-Matias",
  title =        "{PERCIVAL}: Open-Source Posit {RISC-V} Core With Quire
                 Capability",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "3",
  pages =        "1241--1252",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2022.3187199",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}


bibtype: inproceedings
filename: fparith.bib
label: Mallasen:2022:POSb
title: PERCIVAL: Open-Source Posit RISC-V Core With Quire Capability
crossref: IEEE:2022:ISC
pages: 66--66
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00019
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib
bibtimestamp: 2023.09.21 10:14:25 ???
note: Authors and title only.
keywords: ARITH-29
acknowledgement: ack-nhfb
rawnote: Authors and title only.
rawtitle: {PERCIVAL}: Open-Source Posit {RISC-V} Core With Quire Capability
author:
David Mallasen and Raul Murillo and Alberto A. Del Barrio and Guillermo Botella and Luis Pinuel and Manuel Prieto-Matias

rawauthor:
David Mallas{\'e}n and Raul Murillo and Alberto A. {Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel and Manuel Prieto-Matias

entry:
@InProceedings{Mallasen:2022:POSb,
  author =       "David Mallas{\'e}n and Raul Murillo and Alberto A.
                 {Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel
                 and Manuel Prieto-Matias",
  title =        "{PERCIVAL}: Open-Source Posit {RISC-V} Core With Quire
                 Capability",
  crossref =     "IEEE:2022:ISC",
  pages =        "66--66",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00019",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  note =         "Authors and title only.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Mathis:2022:IHP
author: Brett Mathis and James E. Stine
editor: IEEE
booktitle: 2022 IEEE International Symposium on Circuits and Systems (ISCAS)
title: Implementation of High Performance IEEE 754-Posit Conversion Hardware
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 934--937
year: 2022
DOI: https://doi.org/10.1109/ISCAS48785.2022.9937426
bibdate: Fri Dec 15 09:21:55 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Brett Mathis and James E. Stine
rawbooktitle: {2022 IEEE International Symposium on Circuits and Systems (ISCAS)}
raweditor: {IEEE}
rawtitle: Implementation of High Performance {IEEE 754}-Posit Conversion Hardware
entry:
@InProceedings{Mathis:2022:IHP,
  author =       "Brett Mathis and James E. Stine",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Implementation of High Performance {IEEE 754}-Posit
                 Conversion Hardware",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "934--937",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISCAS48785.2022.9937426",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Mccoid:2022:PRA
author: Conor Mccoid and Martin J. Gander
title: A Provably Robust Algorithm for Triangle--triangle Intersections in Floating-point Arithmetic
journal: j-TOMS
volume: 48
number: 2
pages: 17:1--17:30
month: jun
monthnumber: 6
year: 2022
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3513264
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Jul 20 07:04:17 MDT 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2022.07.20 07:04:17 MDT
URL: https://dl.acm.org/doi/10.1145/3513264
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 17
journalURL: https://dl.acm.org/loi/toms
rawauthor: Conor Mccoid and Martin J. Gander
rawtitle: A Provably Robust Algorithm for Triangle--triangle Intersections in Floating-point Arithmetic
abstract:
Motivated by the unexpected failure of the triangle intersection component of the Projection Algorithm for Nonmatching Grids (PANG), this article provides a robust version with proof of backward stability. The new triangle intersection algorithm ensures consistency and parsimony across three types of calculations. The set of intersections produced by the algorithm, called representations, is shown to match the set of geometric intersections, called models. The article concludes with a comparison between the old and new intersection algorithms for PANG using an example found to reliably generate failures in the former.

rawabstract:
Motivated by the unexpected failure of the triangle intersection component of the Projection Algorithm for Nonmatching Grids (PANG), this article provides a robust version with proof of backward stability. The new triangle intersection algorithm ensures consistency and parsimony across three types of calculations. The set of intersections produced by the algorithm, called representations, is shown to match the set of geometric intersections, called models. The article concludes with a comparison between the old and new intersection algorithms for PANG using an example found to reliably generate failures in the former.

entry:
@Article{Mccoid:2022:PRA,
  author =       "Conor Mccoid and Martin J. Gander",
  title =        "A Provably Robust Algorithm for Triangle--triangle
                 Intersections in Floating-point Arithmetic",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "17:1--17:30",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3513264",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3513264",
  abstract =     "Motivated by the unexpected failure of the triangle
                 intersection component of the Projection Algorithm for
                 Nonmatching Grids (PANG), this article provides a
                 robust version with proof of backward stability. The
                 new triangle intersection algorithm ensures consistency
                 and parsimony across three types of calculations. The
                 set of intersections produced by the algorithm, called
                 representations, is shown to match the set of geometric
                 intersections, called models. The article concludes
                 with a comparison between the old and new intersection
                 algorithms for PANG using an example found to reliably
                 generate failures in the former.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: fparith.bib
label: Meloni:2022:AAP
author: Nicolas Meloni
title: An Alternative Approach to Polynomial Modular Number System Internal Reduction
crossref: IEEE:2022:ISC
pages: 85--85
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00024
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Nicolas Meloni
rawtitle: An Alternative Approach to Polynomial Modular Number System Internal Reduction
entry:
@InProceedings{Meloni:2022:AAP,
  author =       "Nicolas Meloni",
  title =        "An Alternative Approach to Polynomial Modular Number
                 System Internal Reduction",
  crossref =     "IEEE:2022:ISC",
  pages =        "85--85",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00024",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: fparith.bib
label: Monniaux:2022:FVB
author: David Monniaux and Alice Pain
title: Formally verified 32- and 64-bit integer division using double-precision floating-point arithmetic
crossref: IEEE:2022:ISC
pages: 128--132
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00032
bibdate: Thu Sep 21 10:14:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.21 10:14:25 ???
URL: https://hal.science/hal-03722203/
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: David Monniaux and Alice Pain
rawtitle: Formally verified 32- and 64-bit integer division using double-precision floating-point arithmetic
abstract:
Some recent processors are not equipped with an integer division unit. Compilers then implement division by a call to a special function supplied by the processor designers, which implements division by a loop producing one bit of quotient per iteration. This hinders compiler optimizations and results in non-constant time computation, which is a problem in some applications. We advocate instead using the processor's floating-point unit, and propose code that the compiler can easily interleave with other computations. We fully proved the correctness of our algorithm, which mixes floating-point and fixed-bitwidth integer computations, using the Coq proof assistant and successfully integrated it into the CompCert formally verified compiler.

rawabstract:
Some recent processors are not equipped with an integer division unit. Compilers then implement division by a call to a special function supplied by the processor designers, which implements division by a loop producing one bit of quotient per iteration. This hinders compiler optimizations and results in non-constant time computation, which is a problem in some applications. We advocate instead using the processor's floating-point unit, and propose code that the compiler can easily interleave with other computations. We fully proved the correctness of our algorithm, which mixes floating-point and fixed-bitwidth integer computations, using the Coq proof assistant and successfully integrated it into the CompCert formally verified compiler.

entry:
@InProceedings{Monniaux:2022:FVB,
  author =       "David Monniaux and Alice Pain",
  title =        "Formally verified 32- and 64-bit integer division
                 using double-precision floating-point arithmetic",
  crossref =     "IEEE:2022:ISC",
  pages =        "128--132",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00032",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-03722203/",
  abstract =     "Some recent processors are not equipped with an
                 integer division unit. Compilers then implement
                 division by a call to a special function supplied by
                 the processor designers, which implements division by a
                 loop producing one bit of quotient per iteration. This
                 hinders compiler optimizations and results in
                 non-constant time computation, which is a problem in
                 some applications. We advocate instead using the
                 processor's floating-point unit, and propose code that
                 the compiler can easily interleave with other
                 computations. We fully proved the correctness of our
                 algorithm, which mixes floating-point and
                 fixed-bitwidth integer computations, using the Coq
                 proof assistant and successfully integrated it into the
                 CompCert formally verified compiler.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: article
filename: fparith.bib
label: Montuschi:2022:CAC
author: Paolo Montuschi and Jean-Michel Muller and Florent de Dinechin
title: Computer Arithmetic: Continuing a Long and Steady Emergence
journal: j-COMPUTER
volume: 55
number: 10
pages: 4--6
month: oct
monthnumber: 10
year: 2022
CODEN: CPTRB4
DOI: https://doi.org/10.1109/MC.2022.3193206
ISSN: 0018-9162 (print), 1558-0814 (electronic) OR 00189162 (print), 15580814 (electronic)
ISSNL: 0018-9162 OR 00189162
bibdate: Thu Oct 27 08:20:29 2022
bibtimestamp: 2022.10.27 08:20:29 ???
fjournal: Computer
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2
rawauthor: Paolo Montuschi and Jean-Michel Muller and Florent de Dinechin
rawtitle: Computer Arithmetic: Continuing a Long and Steady Emergence
bibsource:
https://www.math.utah.edu/pub/tex/bib/computer2020.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Montuschi:2022:CAC,
  author =       "Paolo Montuschi and Jean-Michel Muller and Florent de
                 Dinechin",
  title =        "Computer Arithmetic: Continuing a Long and Steady
                 Emergence",
  journal =      j-COMPUTER,
  volume =       "55",
  number =       "10",
  pages =        "4--6",
  month =        oct,
  year =         "2022",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/MC.2022.3193206",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Oct 27 08:20:29 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}


bibtype: article
filename: fparith.bib
label: Muller:2022:FDW
author: Jean-Michel Muller and Laurence Rideau
journal: j-TOMS
volume: 48
number: 1
pages: 9:1--9:24
month: mar
monthnumber: 3
year: 2022
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3484514
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Feb 17 08:00:57 MST 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2022.02.17 08:00:57 MST
URL: https://dl.acm.org/doi/10.1145/3484514
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 9
journalURL: https://dl.acm.org/loi/toms
rawauthor: Jean-Michel Muller and Laurence Rideau
title:
Formalization of Double-Word Arithmetic, and Comments on ``Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic''

abstract:
Recently, a complete set of algorithms for manipulating double-word numbers (some classical, some new) was analyzed [16]. We have formally proven all the theorems given in that article, using the Coq proof assistant. The formal proof work led us to: (i) locate mistakes in some of the original paper proofs (mistakes that, however, do not hinder the validity of the algorithms), (ii) significantly improve some error bounds, and (iii) generalize some results by showing that they are still valid if we slightly change the rounding mode. The consequence is that the algorithms presented in [16] can be used with high confidence, and that some of them are even more accurate than what was believed before. This illustrates what formal proof can bring to computer arithmetic: beyond mere (yet extremely useful) verification, correction, and consolidation of already known results, it can help to find new properties. All our formal proofs are freely available.

rawabstract:
Recently, a complete set of algorithms for manipulating double-word numbers (some classical, some new) was analyzed [16]. We have formally proven all the theorems given in that article, using the Coq proof assistant. The formal proof work led us to: (i) locate mistakes in some of the original paper proofs (mistakes that, however, do not hinder the validity of the algorithms), (ii) significantly improve some error bounds, and (iii) generalize some results by showing that they are still valid if we slightly change the rounding mode. The consequence is that the algorithms presented in [16] can be used with high confidence, and that some of them are even more accurate than what was believed before. This illustrates what formal proof can bring to computer arithmetic: beyond mere (yet extremely useful) verification, correction, and consolidation of already known results, it can help to find new properties. All our formal proofs are freely available.

rawtitle:
Formalization of Double-Word Arithmetic, and Comments on {``Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic''}

entry:
@Article{Muller:2022:FDW,
  author =       "Jean-Michel Muller and Laurence Rideau",
  title =        "Formalization of Double-Word Arithmetic, and Comments
                 on {``Tight and Rigorous Error Bounds for Basic
                 Building Blocks of Double-Word Arithmetic''}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "9:1--9:24",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3484514",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3484514",
  abstract =     "Recently, a complete set of algorithms for
                 manipulating double-word numbers (some classical, some
                 new) was analyzed [16]. We have formally proven all the
                 theorems given in that article, using the Coq proof
                 assistant. The formal proof work led us to: (i) locate
                 mistakes in some of the original paper proofs (mistakes
                 that, however, do not hinder the validity of the
                 algorithms), (ii) significantly improve some error
                 bounds, and (iii) generalize some results by showing
                 that they are still valid if we slightly change the
                 rounding mode. The consequence is that the algorithms
                 presented in [16] can be used with high confidence, and
                 that some of them are even more accurate than what was
                 believed before. This illustrates what formal proof can
                 bring to computer arithmetic: beyond mere (yet
                 extremely useful) verification, correction, and
                 consolidation of already known results, it can help to
                 find new properties. All our formal proofs are freely
                 available.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


