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On Ziv's Rounding Test
A very simple test, introduced by Ziv, allows one to determine if an approximation to the value f(x) of an elementary function at a given point x suffices to return the floating-point number nearest f(x) . The same test may be used when implementing floating-point operations with input and output op...
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| Published in: | ACM transactions on mathematical software 2013-07, Vol.39 (4), p.1-19 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c339t-70b88cef612c605a021a1840a4d9a72cf08ee3f2d6499297f3d22da469c9ef5c3 |
| container_end_page | 19 |
| container_issue | 4 |
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| container_title | ACM transactions on mathematical software |
| container_volume | 39 |
| creator | DE DINECHIN, Florent LAUTER, Christoph MULLER, Jean-Michel TORRES, Serge |
| description | A very simple test, introduced by Ziv, allows one to determine if an approximation to the value
f(x)
of an elementary function at a given point
x
suffices to return the floating-point number nearest
f(x)
. The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the same format. That test depends on a “magic constant”
e
. We show how to choose that constant
e
to make the test reliable and efficient. Various cases are considered, depending on the availability of an fma instruction, and on the range of
f(x)
. |
| doi_str_mv | 10.1145/2491491.2491495 |
| format | article |
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f(x)
of an elementary function at a given point
x
suffices to return the floating-point number nearest
f(x)
. The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the same format. That test depends on a “magic constant”
e
. We show how to choose that constant
e
to make the test reliable and efficient. Various cases are considered, depending on the availability of an fma instruction, and on the range of
f(x)
.</description><identifier>ISSN: 0098-3500</identifier><identifier>EISSN: 1557-7295</identifier><identifier>DOI: 10.1145/2491491.2491495</identifier><identifier>CODEN: ACMSCU</identifier><language>eng</language><publisher>New York, NY: Association for Computing Machinery</publisher><subject>Algorithmics. Computability. Computer arithmetics ; Applied sciences ; Approximation ; Computer Science ; Computer science; control theory; systems ; Electronics ; Exact sciences and technology ; Integrated circuits ; Integrated circuits by function (including memories and processors) ; Language processing and microprogramming ; Other ; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices ; Software ; Theoretical computing</subject><ispartof>ACM transactions on mathematical software, 2013-07, Vol.39 (4), p.1-19</ispartof><rights>2015 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c339t-70b88cef612c605a021a1840a4d9a72cf08ee3f2d6499297f3d22da469c9ef5c3</citedby><cites>FETCH-LOGICAL-c339t-70b88cef612c605a021a1840a4d9a72cf08ee3f2d6499297f3d22da469c9ef5c3</cites><orcidid>0000-0003-3588-0047 ; 0000-0001-7335-8220 ; 0000-0003-4927-3301</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=28010046$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://ens-lyon.hal.science/ensl-00693317$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>DE DINECHIN, Florent</creatorcontrib><creatorcontrib>LAUTER, Christoph</creatorcontrib><creatorcontrib>MULLER, Jean-Michel</creatorcontrib><creatorcontrib>TORRES, Serge</creatorcontrib><title>On Ziv's Rounding Test</title><title>ACM transactions on mathematical software</title><description>A very simple test, introduced by Ziv, allows one to determine if an approximation to the value
f(x)
of an elementary function at a given point
x
suffices to return the floating-point number nearest
f(x)
. The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the same format. That test depends on a “magic constant”
e
. We show how to choose that constant
e
to make the test reliable and efficient. Various cases are considered, depending on the availability of an fma instruction, and on the range of
f(x)
.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Approximation</subject><subject>Computer Science</subject><subject>Computer science; control theory; systems</subject><subject>Electronics</subject><subject>Exact sciences and technology</subject><subject>Integrated circuits</subject><subject>Integrated circuits by function (including memories and processors)</subject><subject>Language processing and microprogramming</subject><subject>Other</subject><subject>Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices</subject><subject>Software</subject><subject>Theoretical computing</subject><issn>0098-3500</issn><issn>1557-7295</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNo9kE1Lw0AQhhdRsFaveu1FFCHtzH5mj6WoFQIFqRcvy7rZ1Uia1Gxb8N-7klAYeC_PPDO8hNwgTBG5mFGuMc20T3FCRiiEyhTV4pSMAHSeMQFwTi5i_AYAigpH5HrVTN6rw12cvLb7pqyaz8nax90lOQu2jv5qyDF5e3pcL5ZZsXp-WcyLzDGmd5mCjzx3PkikToKwSWox52B5qa2iLkDuPQu0lFxrqlVgJaWl5VI77YNwbEweeu-Xrc22qza2-zWtrcxyXhjfxNoASM0YqgNN8H0Pb7v2Z5--NJsqOl_XtvHtPhoUIFm6RCGhsx51XRtj58NRjmD-6zJDXUOKtHE7yG10tg6dbVwVj2s0BwTgkv0B9x1lng</recordid><startdate>20130701</startdate><enddate>20130701</enddate><creator>DE DINECHIN, Florent</creator><creator>LAUTER, Christoph</creator><creator>MULLER, Jean-Michel</creator><creator>TORRES, Serge</creator><general>Association for Computing Machinery</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0003-3588-0047</orcidid><orcidid>https://orcid.org/0000-0001-7335-8220</orcidid><orcidid>https://orcid.org/0000-0003-4927-3301</orcidid></search><sort><creationdate>20130701</creationdate><title>On Ziv's Rounding Test</title><author>DE DINECHIN, Florent ; LAUTER, Christoph ; MULLER, Jean-Michel ; TORRES, Serge</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c339t-70b88cef612c605a021a1840a4d9a72cf08ee3f2d6499297f3d22da469c9ef5c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Applied sciences</topic><topic>Approximation</topic><topic>Computer Science</topic><topic>Computer science; control theory; systems</topic><topic>Electronics</topic><topic>Exact sciences and technology</topic><topic>Integrated circuits</topic><topic>Integrated circuits by function (including memories and processors)</topic><topic>Language processing and microprogramming</topic><topic>Other</topic><topic>Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices</topic><topic>Software</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>DE DINECHIN, Florent</creatorcontrib><creatorcontrib>LAUTER, Christoph</creatorcontrib><creatorcontrib>MULLER, Jean-Michel</creatorcontrib><creatorcontrib>TORRES, Serge</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>ACM transactions on mathematical software</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>DE DINECHIN, Florent</au><au>LAUTER, Christoph</au><au>MULLER, Jean-Michel</au><au>TORRES, Serge</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Ziv's Rounding Test</atitle><jtitle>ACM transactions on mathematical software</jtitle><date>2013-07-01</date><risdate>2013</risdate><volume>39</volume><issue>4</issue><spage>1</spage><epage>19</epage><pages>1-19</pages><issn>0098-3500</issn><eissn>1557-7295</eissn><coden>ACMSCU</coden><abstract>A very simple test, introduced by Ziv, allows one to determine if an approximation to the value
f(x)
of an elementary function at a given point
x
suffices to return the floating-point number nearest
f(x)
. The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the same format. That test depends on a “magic constant”
e
. We show how to choose that constant
e
to make the test reliable and efficient. Various cases are considered, depending on the availability of an fma instruction, and on the range of
f(x)
.</abstract><cop>New York, NY</cop><pub>Association for Computing Machinery</pub><doi>10.1145/2491491.2491495</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0003-3588-0047</orcidid><orcidid>https://orcid.org/0000-0001-7335-8220</orcidid><orcidid>https://orcid.org/0000-0003-4927-3301</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0098-3500 |
| ispartof | ACM transactions on mathematical software, 2013-07, Vol.39 (4), p.1-19 |
| issn | 0098-3500 1557-7295 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_ensl_00693317v2 |
| source | Association for Computing Machinery:Jisc Collections:ACM OPEN Journals 2023-2025 (reading list) |
| subjects | Algorithmics. Computability. Computer arithmetics Applied sciences Approximation Computer Science Computer science control theory systems Electronics Exact sciences and technology Integrated circuits Integrated circuits by function (including memories and processors) Language processing and microprogramming Other Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices Software Theoretical computing |
| title | On Ziv's Rounding Test |
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