{"id":"https://openalex.org/W2069000895","doi":"https://doi.org/10.1109/tc.2014.2345391","title":"Parallel Reproducible Summation","display_name":"Parallel Reproducible Summation","publication_year":2014,"publication_date":"2014-08-11","ids":{"openalex":"https://openalex.org/W2069000895","doi":"https://doi.org/10.1109/tc.2014.2345391","mag":"2069000895"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2014.2345391","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2014.2345391","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076825233","display_name":"James Demmel","orcid":"https://orcid.org/0000-0003-1145-3745"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Demmel","raw_affiliation_strings":["Mathematics Department and CS Division, University of California at Berkeley, Berkeley, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department and CS Division, University of California at Berkeley, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004343262","display_name":"Hong Diep Nguyen","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hong Diep Nguyen","raw_affiliation_strings":["EECS Department, University of California at Berkeley, Berkeley, CA","EECS Department, University of California at Berkeley, Berkeley, CA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EECS Department, University of California at Berkeley, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"EECS Department, University of California at Berkeley, Berkeley, CA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.4444,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.98077241,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"64","issue":"7","first_page":"2060","last_page":"2070"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13650","display_name":"Computational Physics and Python Applications","score":0.9419000148773193,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7552208304405212},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.5757389664649963},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.5387588143348694},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5090562701225281},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5084460973739624},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.5054411888122559},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.47673237323760986},{"id":"https://openalex.org/keywords/loop-unrolling","display_name":"Loop unrolling","score":0.4556201100349426},{"id":"https://openalex.org/keywords/flops","display_name":"FLOPS","score":0.44958212971687317},{"id":"https://openalex.org/keywords/compiler","display_name":"Compiler","score":0.33356279134750366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26137787103652954}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7552208304405212},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.5757389664649963},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.5387588143348694},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5090562701225281},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5084460973739624},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.5054411888122559},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.47673237323760986},{"id":"https://openalex.org/C76970557","wikidata":"https://www.wikidata.org/wiki/Q1869750","display_name":"Loop unrolling","level":3,"score":0.4556201100349426},{"id":"https://openalex.org/C3826847","wikidata":"https://www.wikidata.org/wiki/Q188768","display_name":"FLOPS","level":2,"score":0.44958212971687317},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.33356279134750366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26137787103652954},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.2014.2345391","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2014.2345391","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G175367197","display_name":null,"funder_award_id":"HR0011-12-2-0016","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G1916933555","display_name":null,"funder_award_id":"DOE DE-SC0003959","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G2143835108","display_name":null,"funder_award_id":"DOE DE-SC0004938","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3789390052","display_name":null,"funder_award_id":"NSF ACI-1339676","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3840724586","display_name":null,"funder_award_id":"DOE DE-SC0008699","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5335406778","display_name":null,"funder_award_id":"DOE DE-SC0010200","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6735150843","display_name":null,"funder_award_id":"DOE AC02-05CH11231","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G693616945","display_name":null,"funder_award_id":"DOE DE-SC0008700","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7495676008","display_name":null,"funder_award_id":"NSF OCI-1032639","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8631934365","display_name":null,"funder_award_id":"DOE DE-SC0005136","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320307102","display_name":"Intel Corporation","ror":"https://ror.org/01ek73717"},{"id":"https://openalex.org/F4320307798","display_name":"Nokia","ror":"https://ror.org/04pkc8m17"},{"id":"https://openalex.org/F4320307904","display_name":"Oracle","ror":"https://ror.org/006c77m33"},{"id":"https://openalex.org/F4320309327","display_name":"Google","ror":"https://ror.org/00njsd438"},{"id":"https://openalex.org/F4320309480","display_name":"Nvidia","ror":"https://ror.org/03jdj4y14"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1977343658","https://openalex.org/W2006705329","https://openalex.org/W2012407419","https://openalex.org/W2020804487","https://openalex.org/W2030955243","https://openalex.org/W2041844083","https://openalex.org/W2048504605","https://openalex.org/W2052942864","https://openalex.org/W2098077956","https://openalex.org/W2168148904","https://openalex.org/W3022909171","https://openalex.org/W6684754296"],"related_works":["https://openalex.org/W2535419677","https://openalex.org/W2134876043","https://openalex.org/W2476214559","https://openalex.org/W3039927303","https://openalex.org/W4388911419","https://openalex.org/W4322008031","https://openalex.org/W2544512391","https://openalex.org/W2118569990","https://openalex.org/W2389154333","https://openalex.org/W1989068301"],"abstract_inverted_index":{"Reproducibility,":[0],"i.e.":[1,190],"getting":[2],"bitwise":[3],"identical":[4],"floating":[5,44,73,200],"point":[6,45,74,201],"results":[7,113,166],"from":[8],"multiple":[9],"runs":[10],"of":[11,36,39,61,64,80,83,119,131,139,152,188,193,196],"the":[12,34,59,81,150,169,185],"same":[13],"program,":[14],"is":[15,77,96,207],"a":[16,50,62,70,129,135],"property":[17],"that":[18,76],"many":[19,30],"users":[20],"depend":[21],"on":[22,177],"either":[23],"for":[24,53,72,90,174,210],"debugging":[25],"or":[26],"correctness":[27],"checking":[28],"in":[29,66,162],"codes":[31],"[10].":[32],"However,":[33],"combination":[35],"dynamic":[37],"scheduling":[38],"parallel":[40,212],"computing":[41,58],"resources,":[42],"and":[43,95,134,205],"nonassociativity,":[46],"makes":[47],"attaining":[48],"reproducibility":[49],"challenge":[51],"even":[52],"simple":[54],"reduction":[55,192],"operations":[56,159],"like":[57],"sum":[60],"vector":[63,92],"numbers":[65,202],"parallel.":[67],"We":[68],"propose":[69],"technique":[71,86],"summation":[75],"reproducible":[78,173],"independent":[79],"order":[82],"summation.":[84],"Our":[85,107],"uses":[87],"Rump's":[88],"algorithm":[89,108,183],"error-free":[91,153],"transformation":[93],"[7],":[94],"much":[97],"more":[98],"efficient":[99],"than":[100],"using":[101],"(possibly":[102],"very)":[103],"high":[104],"precision":[105,199],"arithmetic.":[106],"reproducibly":[109],"computes":[110],"highly":[111],"accurate":[112],"with":[114],"an":[115,194],"absolute":[116],"error":[117],"bound":[118],"n":[120],"\u00b7":[121],"2":[122],"<sup":[123],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[124],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-28</sup>":[125],"macheps":[126],"maxiIviI":[127],"at":[128],"cost":[130],"7n":[132],"FLOPs":[133],"small":[136],"constant":[137],"amount":[138],"extra":[140],"memory":[141],"usage.":[142],"Higher":[143],"accuracies":[144],"are":[145,160,172],"also":[146],"possible":[147],"by":[148,168],"increasing":[149],"number":[151,187],"transformations.":[154],"As":[155],"long":[156],"as":[157],"all":[158],"performed":[161],"to-nearest":[163],"rounding":[164],"mode,":[165],"computed":[167],"proposed":[170],"algorithms":[171],"any":[175,178],"run":[176],"platform.":[179],"In":[180],"particular,":[181],"our":[182],"requires":[184],"minimum":[186],"reductions,":[189],"one":[191],"array":[195],"six":[197],"double":[198],"per":[203],"sum,":[204],"hence":[206],"well":[208],"suited":[209],"massively":[211],"environments.":[213]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
