Static analysis of arithmetical congruences

In this paper, a new kind of static (or semantic) analysis is defined: congruence analysis, which is conceived to discover the properties of the following type: "the integer valued variable X is congruent to c modulo m", where c and m are automatically determined integers. This analysis is...

Full description

Saved in:
Bibliographic Details
Published in:International journal of computer mathematics Vol. 30; no. 3-4; pp. 165 - 190
Main Author: Granger, Philippe
Format: Journal Article
Language:English
Published: Abingdon Gordon and Breach Science Publishers 01.01.1989
Taylor and Francis
Subjects:
Abstract interpretation
Applied sciences
automatic vectorization
Computer science; control theory; systems
D.1.2 [Programming Techniques]: Automatic Programming
D.3.4 [Processors]: Optimization
Exact sciences and technology
F.3.1 [Specifying and Verifying and Reasoning about Programs]: Invariants, Mechanical Verification
F.3.2. [Semantics of Programming Languages]: Operational Semantics
Programming theory
semantic analysis
Theoretical computing
ISSN:0020-7160, 1029-0265
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract In this paper, a new kind of static (or semantic) analysis is defined: congruence analysis, which is conceived to discover the properties of the following type: "the integer valued variable X is congruent to c modulo m", where c and m are automatically determined integers. This analysis is then related to an algebraic framework and wholly characterized. Moreover, we show an example how it can be useful for automatic vectorization. Finally, we present some extensions of it, namely its combination with the analysis of bounds, and also some analyses defined when the modulus of congruences is given a priori.
AbstractList In this paper, a new kind of static (or semantic) analysis is defined: congruence analysis, which is conceived to discover the properties of the following type: "the integer valued variable X is congruent to c modulo m", where c and m are automatically determined integers. This analysis is then related to an algebraic framework and wholly characterized. Moreover, we show an example how it can be useful for automatic vectorization. Finally, we present some extensions of it, namely its combination with the analysis of bounds, and also some analyses defined when the modulus of congruences is given a priori.
Author Granger, Philippe
Author_xml – sequence: 1
  givenname: Philippe
  surname: Granger
  fullname: Granger, Philippe
  organization: Laboratoire d'Informatique , Ecole Polytechnique
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=4985595$$DView record in Pascal Francis
BookMark eNp9kEtLAzEUhYNUsK3-AHezcCejN5kmk4AbKb6g4EJdhzw1Mk1KMiL9904Zu1F0deHe8x3OPTM0iSk6hE4xXGDgcAlAoMWMC-AcmrblB2iKgYgaCKMTNN3d60EAR2hWyjsAcNGyKTp_6lUfTKWi6rYllCr5SuXQv63dsFZdZVJ8zR8uGleO0aFXXXEn33OOXm5vnpf39erx7mF5vapNQ2hfO8eY0FRYazEjqvWaYQ6CCqMbohcL2jhsPDfcE2e91pYLTIn3rTFGA7PNHJ2NvhtVhgg-q2hCkZsc1ipv5UJwSgUdZO0oMzmVkp2XJuyeSbHPKnQSg9xVI39VM5D4B7n3_o-5GpkQfcpr9ZlyZ2Wvtl3K-4TN3_gXikV6Mw
CODEN IJCMAT
CitedBy_id crossref_primary_10_1145_3022670_2951937
crossref_primary_10_3390_computation9110113
crossref_primary_10_1016_0743_1066_92_90030_7
crossref_primary_10_1145_3689712
crossref_primary_10_1016_j_scico_2016_07_006
crossref_primary_10_1145_1159974_1134659
crossref_primary_10_1109_ACCESS_2022_3160729
crossref_primary_10_1145_3371082
crossref_primary_10_1016_j_cl_2017_09_001
crossref_primary_10_1016_j_sysarc_2010_06_009
crossref_primary_10_1145_3649837
crossref_primary_10_1145_2651360
crossref_primary_10_1145_2651361
crossref_primary_10_1145_773473_178263
crossref_primary_10_1007_s10009_003_0125_6
crossref_primary_10_1109_TR_2019_2925037
crossref_primary_10_1016_j_entcs_2012_10_003
crossref_primary_10_1007_s10703_009_0089_6
crossref_primary_10_1016_j_ic_2021_104791
crossref_primary_10_1145_3632897
crossref_primary_10_1145_1159974_1134666
crossref_primary_10_1145_2775051_2676987
crossref_primary_10_1016_S0167_6423_96_00041_X
crossref_primary_10_1145_3729298
crossref_primary_10_1007_s10703_025_00471_8
crossref_primary_10_1145_2395116_2395120
crossref_primary_10_1145_3591288
crossref_primary_10_1016_j_scico_2022_102906
crossref_primary_10_1016_j_scico_2012_06_001
crossref_primary_10_1145_1275497_1275501
crossref_primary_10_1145_982962_964016
Cites_doi 10.1145/29873.29875
10.1145/512950.512973
10.1145/512760.512770
ContentType Journal Article
Copyright Copyright Taylor & Francis Group, LLC 1989
1992 INIST-CNRS
Copyright_xml – notice: Copyright Taylor & Francis Group, LLC 1989
– notice: 1992 INIST-CNRS
DBID AAYXX
CITATION
IQODW
DOI 10.1080/00207168908803778
DatabaseName CrossRef
Pascal-Francis
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
Applied Sciences
EISSN 1029-0265
EndPage 190
ExternalDocumentID 4985595
10_1080_00207168908803778
8803778
GroupedDBID -~X
07G
0R~
1TA
4.4
5GY
5VS
AAIKQ
AAKBW
AAYJJ
ABEFU
ABJNI
ABUFD
ACGEE
ACGEJ
ACGFS
ACGOD
ACIWK
ACNCT
ADCVX
ADXPE
AENEX
AEPSL
AEUMN
AEYOC
AFFNX
AGLEN
AI.
ALMA_UNASSIGNED_HOLDINGS
AMVHM
AMXXU
AQTUD
AWYRJ
BCCOT
BPLKW
C06
CS3
DU5
DWIFK
EBS
EJD
H13
HZ~
IVXBP
NA5
NUSFT
NY~
O9-
P2P
PQQKQ
TAQ
TDBHL
TFL
TFMCV
TFW
TN5
TOXWX
UB9
UPT
UU8
V3K
V4Q
VH1
WH7
ZY4
.4S
.7F
.DC
.QJ
0BK
29J
30N
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
AAYXX
ABCCY
ABDBF
ABFIM
ABHAV
ABLIJ
ABPAQ
ABPEM
ABTAI
ABXUL
ABXYU
ACAGQ
ACTCW
ACTIO
ACUHS
ADGTB
AEISY
AEOZL
AFKVX
AFRVT
AGCQS
AGDLA
AGMYJ
AGROQ
AHDZW
AHMOU
AIJEM
AIYEW
AJWEG
AKBVH
AKOOK
ALCKM
ALQZU
AMEWO
AQRUH
ARCSS
AVBZW
BLEHA
CAG
CCCUG
CE4
CITATION
COF
CRFIH
DGEBU
DKSSO
DMQIW
EAP
EDO
EMK
EPL
EST
ESX
E~A
E~B
GTTXZ
HF~
H~9
H~P
IPNFZ
J.P
KYCEM
LJTGL
M4Z
MK~
QCRFL
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TASJS
TBQAZ
TEJ
TFT
TTHFI
TUROJ
TUS
TWF
UT5
UU3
ZGOLN
~S~
ABTAH
ADYSH
IQODW
ID FETCH-LOGICAL-c325t-ee669b59ddd162a7fb6180959cb32b4453e1cf8c8f2edfbbd89152ff7cccb06d3
IEDL.DBID TFW
ISICitedReferencesCount 84
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=10_1080_00207168908803778&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0020-7160
IngestDate Wed Apr 02 07:27:20 EDT 2025
Sat Nov 29 02:21:22 EST 2025
Tue Nov 18 20:59:42 EST 2025
Mon Oct 20 23:47:20 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 3-4
Language English
License CC BY 4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c325t-ee669b59ddd162a7fb6180959cb32b4453e1cf8c8f2edfbbd89152ff7cccb06d3
PageCount 26
ParticipantIDs pascalfrancis_primary_4985595
informaworld_taylorfrancis_310_1080_00207168908803778
crossref_citationtrail_10_1080_00207168908803778
crossref_primary_10_1080_00207168908803778
PublicationCentury 1900
PublicationDate 1/1/1989
1989-01-00
1989
PublicationDateYYYYMMDD 1989-01-01
PublicationDate_xml – month: 01
  year: 1989
  text: 1/1/1989
  day: 01
PublicationDecade 1980
PublicationPlace Abingdon
PublicationPlace_xml – name: Abingdon
PublicationTitle International journal of computer mathematics
PublicationYear 1989
Publisher Gordon and Breach Science Publishers
Taylor and Francis
Publisher_xml – name: Gordon and Breach Science Publishers
– name: Taylor and Francis
References Granger P. (CIT0006)
Cousot P. (CIT0002) 1981
CIT0001
Hardy G. H. (CIT0007) 1979
CIT0003
CIT0005
CIT0004
Lang S. (CIT0008) 1984
Stark H. M. (CIT0009) 1970
References_xml – ident: CIT0001
  doi: 10.1145/29873.29875
– volume-title: An Introduction to Number Theory
  year: 1970
  ident: CIT0009
– start-page: 303
  volume-title: Program Flow Analysis: Theory and Applications
  year: 1981
  ident: CIT0002
– ident: CIT0003
  doi: 10.1145/512950.512973
– ident: CIT0004
– volume-title: Rapport de recherche
  ident: CIT0006
– ident: CIT0005
  doi: 10.1145/512760.512770
– volume-title: Algebra
  year: 1984
  ident: CIT0008
– volume-title: An Introduction to the Theory of Numbers
  year: 1979
  ident: CIT0007
SSID ssj0008976
Score 1.475171
Snippet In this paper, a new kind of static (or semantic) analysis is defined: congruence analysis, which is conceived to discover the properties of the following...
SourceID pascalfrancis
crossref
informaworld
SourceType Index Database
Enrichment Source
Publisher
StartPage 165
SubjectTerms Abstract interpretation
Applied sciences
automatic vectorization
Computer science; control theory; systems
D.1.2 [Programming Techniques]: Automatic Programming
D.3.4 [Processors]: Optimization
Exact sciences and technology
F.3.1 [Specifying and Verifying and Reasoning about Programs]: Invariants, Mechanical Verification
F.3.2. [Semantics of Programming Languages]: Operational Semantics
Programming theory
semantic analysis
Theoretical computing
Title Static analysis of arithmetical congruences
URI https://www.tandfonline.com/doi/abs/10.1080/00207168908803778
Volume 30
WOSCitedRecordID wos10_1080_00207168908803778&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor & Francis Online Journals
  customDbUrl:
  eissn: 1029-0265
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0008976
  issn: 0020-7160
  databaseCode: TFW
  dateStart: 19640101
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LSwMxEA5SPHixPrFqJQdPQqC7eWxyFLF4kOKham_L5jFa0Fa6i7-_yW66tCI96D2PZWaSmcl-8w1C14JrRlmhiNapJSwBIMoZR3jiUmF8DA01kfbLYzYayclEPUVsThlhlSGHhoYoor6rw-EudLlCxIUKbu8YhQwQnQHNslDq66P6YN_j4Wt7D0tVt5YLo4kf3v7T_G2FDa-0wVkawJJF6eUFTaOLNe8z7P7zuw_Qfgw78W1jJ4dox82OUHfV0gHHE36M6uBzanARuUrwHLDPpqv3z6bYEfv0-W3RgK9P0PPwfnz3QGI_BWJoyivinBBKc2WtTURaZKBFYO_iymiaasY4dYkBaSSkzoLWVirv3QEyY4weCEtPUWc2n7kzhK30WgUf3GSFYj6x1VRyTZkA40CkUvfQYCXP3ESy8dDz4iNPWk7SH8LooZt2ylfDtLFtMF9XUl7VzxtRRTndMq-_oc12J6akz634-R_XvUB7DfgsvM1cok7lNdFHu-a7mpaLq9oul6wy3zM
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LSwMxEB60CnqxPrFqdQ-ehEB389jkKGJRrMVD1d6WzUsL2kq7-PtNdtOlFfGg90myzCSZx375BuCcUUkwyQWSMtGIxNYiYZRBNDYJUy6GtiWR9lMv7ff5cCgeQsFtFmCVPoe2FVFEeVf7w-2L0XNInH_C7Twj4x6j08FpyldhjTo_6yF9g-5zfRNzUTaX8-LIydd_NX-aYskvLbGWerhkPnMas1WriwX_023-98u3YStEntFltVV2YMWMd6E57-oQhUO-B2X8OVJRHuhKoomNXEJdvL5X7x0jl0G_TCv89T48dq8HVzcotFRACie0QMYwJiQVWuuYJXlqJfMEXlQoiRNJCMUmVpYrbhOjrZSaC-fgrU2VUrLDND6AxngyNocQae4Ma118k-aCuNxWYk4lJswqY1nCZQs6c4VmKvCN-7YXb1lc05J-U0YLLuohHxXZxm_CdNFKWVFWOIKNMvzLuPaSOeuViOAuvaJHf5z3DDZuBve9rHfbvzuGzQqL5ks1J9AonFXasK4-i9Fselpu0i_C0-NU
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT8MwDI5gIMSF8RQDBj1wQoq0Nk2aHBFQgZimHQbsVjUPwyTYpq3i95O0WbUhxAHuTlLZTmynXz4jdMmojEmcCyxlpHEcAmBhlME0NBFTNoeGkkj7uZv0enw4FH2PzZl7WKWroaEiiijPare5pxoWiDj3gtsGRsYdRKdDkoSvo42SGMu68yB9qQ9iLsreck4cW_n6p-ZPU6yEpRXSUoeWzOdWYVB1ulgKP2nznx--i3Z83hlcV46yh9bMeB81Fz0dAr_FD1CZfY5UkHuykmACgS2ni7eP6rVjYOvn11mFvj5ET-nd4OYe-4YKWJGIFtgYxoSkQmsdsihPQDJH30WFkiSScUyJCRVwxSEyGqTUXNjwDpAopWSHaXKEGuPJ2ByjQHNrVrDZTZKL2Fa2knAqScxAGWARly3UWegzU55t3DW9eM_CmpT0mzJa6KoeMq2oNn4TpstGyoryfsObKCO_jGuvWLNeKRbcFlf05I_zXqCt_m2adR96j6douwKiuXuaM9QorFHaaFN9FqP57Lx00S8FQuH4
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Static+analysis+of+arithmetical+congruences&rft.jtitle=International+journal+of+computer+mathematics&rft.au=GRANGER%2C+P&rft.date=1989&rft.pub=Taylor+and+Francis&rft.issn=0020-7160&rft.volume=30&rft.issue=3-4&rft.spage=165&rft.epage=190&rft_id=info:doi/10.1080%2F00207168908803778&rft.externalDBID=n%2Fa&rft.externalDocID=4985595
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-7160&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-7160&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-7160&client=summon