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A novel approach to generate correctly rounded math libraries for new floating point representations

Descriptive

TypeOfResource
Text
TitleInfo
Title
A novel approach to generate correctly rounded math libraries for new floating point representations
Name (type = personal)
NamePart (type = family)
Lim
NamePart (type = given)
Jay P.
Affiliation
Computer Science (New Brunswick), Rutgers University
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Aanjaneya
NamePart (type = given)
Mridul
Affiliation
Computer Science (New Brunswick), Rutgers University
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Gustafson
NamePart (type = given)
John
Affiliation
National University of Singapore
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Nagarakatte
NamePart (type = given)
Santosh
Affiliation
Computer Science (New Brunswick), Rutgers University
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (authority = RutgersOrg-Department); (type = corporate)
NamePart
Computer Science (New Brunswick)
Name (authority = RutgersOrg-School); (type = corporate)
NamePart
School of Arts and Sciences (SAS) (New Brunswick)
Genre (authority = RULIB-FS)
Other
Genre (authority = NISO JAV)
Unidentified version of a published work
Genre (authority = ExL-Esploro)
Technical documentation
Genre (authority = marcgt)
Technical report
Note (type = peerReview)
Peer reviewed
Note
Tecnical Report DCS-TR-753
OriginInfo
DateCreated (encoding = w3cdtf); (keyDate = yes); (qualifier = exact)
2020
Abstract (type = Abstract)
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded math libraries. Further, the use of existing FP libraries for these new representations can produce incorrect results. This paper proposes a novel methodology for generating polynomial approximations that can be used to implement correctly rounded math libraries. Existing methods produce polynomials that approximate the real value of an elementary function f(x) and experience wrong results due to errors in the approximation and due to rounding errors in the implementation. In contrast, our approach generates polynomials that approximate the correctly rounded value of f(x) (i.e., the value of f(x) rounded to the target representation). This methodology provides more margin to identify efficient polynomials that produce correctly rounded results for all inputs. We frame the problem of generating efficient polynomials that produce correctly rounded results as a linear programming problem. Our approach guarantees that we produce the correct result even with range reduction techniques. Using our approach, we have developed correctly rounded, yet faster, implementations of elementary functions for multiple target representations. Our Bfloat16 library is 2.3× faster than the corresponding state-of-the-art while producing correct results for all inputs.
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
PhysicalDescription
InternetMediaType
application/pdf
Extent
1 online resource (42 pages) : illustrations
Subject (authority = local)
Topic
Floating point
Subject (authority = local)
Topic
Math libraries
Subject (authority = local)
Topic
Correctly rounded result
Subject (authority = local)
Topic
Elementary functions
Extension
DescriptiveEvent
Type
Grant award
AssociatedEntity
Role
Funder
Name
National Science Foundation
AssociatedEntity
Role
Originator
Name
Santosh Nagarakatte
RelatedItem (type = host)
TitleInfo
Title
Nagarakatte, Santosh
Identifier (type = local)
rucore30274600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/t3-4er2-wh43
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Rights

RightsDeclaration (AUTHORITY = FS); (TYPE = [FS] statement #1); (ID = rulibRdec0004)
Copyright for scholarly resources published in RUcore is retained by the copyright holder. By virtue of its appearance in this open access medium, you are free to use this resource, with proper attribution, in educational and other non-commercial settings. Other uses, such as reproduction or republication, may require the permission of the copyright holder.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
RightsEvent
Type
Permission or license
AssociatedObject
Type
License
Name
Multiple author license v. 1
Detail
I hereby grant to Rutgers, The State University of New Jersey (Rutgers) the non-exclusive right to retain, reproduce, and distribute the deposited work (Work) in whole or in part, in and from its electronic format, without fee. This agreement does not represent a transfer of copyright to Rutgers.Rutgers may make and keep more than one copy of the Work for purposes of security, backup, preservation, and access and may migrate the Work to any medium or format for the purpose of preservation and access in the future. Rutgers will not make any alteration, other than as allowed by this agreement, to the Work.I represent and warrant to Rutgers that the Work is my original work. I also represent that the Work does not, to the best of my knowledge, infringe or violate any rights of others.I further represent and warrant that I have obtained all necessary rights to permit Rutgers to reproduce and distribute the Work and that any third-party owned content is clearly identified and acknowledged within the Work.By granting this license, I acknowledge that I have read and agreed to the terms of this agreement and all related RUcore and Rutgers policies.
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Technical

RULTechMD (ID = TECHNICAL1)
ContentModel
Document
CreatingApplication
Version
1.5
DateCreated (point = end); (encoding = w3cdtf); (qualifier = exact)
2020-07-09T17:43:14
DateCreated (point = end); (encoding = w3cdtf); (qualifier = exact)
2020-07-09T17:43:14
ApplicationName
pdfTeX-1.40.17
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