{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:09:00Z","timestamp":1760202540318},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540040293"},{"type":"electronic","value":"9783540357674"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/3-540-35767-x_17","type":"book-chapter","created":{"date-parts":[[2007,8,16]],"date-time":"2007-08-16T07:19:15Z","timestamp":1187248755000},"page":"254-273","source":"Crossref","is-referenced-by-count":3,"title":["Strength Reduction of Integer Division and Modulo Operations"],"prefix":"10.1007","author":[{"given":"Jeffrey","family":"Sheldon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Walter","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ben","family":"Greenwald","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saman","family":"Amarasinghe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2003,5,13]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"R. Alverson. Integer Division Using Reciprocals. In Proceedings of the Tenth Symposium on Computer Arithmetic, Grenoble, France, June 1991.","key":"17_CR1","DOI":"10.1109\/ARITH.1991.145558"},{"unstructured":"S. Amarasinghe. Parallelizing Compiler Techniques Based on Linear Inequalities. In Ph.D Thesis, Stanford University. Also appears as Techical Report CSL-TR-97-714, Jan 1997.","key":"17_CR2"},{"doi-asserted-by":"crossref","unstructured":"C. Ancourt and F. Irigoin. Scanning Polyhedra with Do Loops. In Proceedings of the Third ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, pages 39\u201350, Williamsburg, VA, Apr. 1991.","key":"17_CR3","DOI":"10.1145\/109625.109631"},{"unstructured":"M. Ancourt. G\u00e9n\u00e9ration Automatique de Codes de Transfert pour Multiprocesseurs \u00e0 M\u00e9moires Locales. PhD thesis, Universit\u00e9 Paris VI, Mar. 1991.","key":"17_CR4"},{"doi-asserted-by":"crossref","unstructured":"J. M. Anderson, S. P. Amarasinghe, and M. S. Lam. Data and Computation Transformations for Multiprocessors. In Proceedings of the Fifth ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, pages 166\u2013178, Santa Barbara, CA, July 1995.","key":"17_CR5","DOI":"10.1145\/209936.209954"},{"doi-asserted-by":"crossref","unstructured":"R. Barua, W. Lee, S. Amarasinghe, and A. Agarwal. Maps: A Compiler-Managed Memory System for Raw Machines. In Proceedings of the 26th International Symposium on Computer Architecture, Atlanta, GA, May 1999.","key":"17_CR6","DOI":"10.1109\/ISCA.1999.765935"},{"issue":"6","key":"17_CR7","doi-asserted-by":"publisher","first-page":"692","DOI":"10.1147\/rd.246.0692","volume":"24","author":"J. Cocke","year":"1980","unstructured":"J. Cocke and P. Markstein. Strength Reduction for Division and Modulo with Application to Accessing a Multilevel Store. IBM Journal of Research and Development, 24(6):692\u2013694, November 1980.","journal-title":"IBM Journal of Research and Development"},{"key":"17_CR8","volume-title":"Linear Programming and Extensions","author":"G. Dantzig","year":"1963","unstructured":"G. Dantzig. Linear Programming and Extensions. Princeton University Press, Princeton, NJ, 1963."},{"key":"17_CR9","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1016\/0097-3165(73)90004-6","volume":"14","author":"G. Dantzig","year":"1973","unstructured":"G. Dantzig and B. Eaves. Fourier-Motzkin Elimination and its Dual. Journal of Combinatorial Theory (A), 14:288\u2013297, 1973.","journal-title":"Journal of Combinatorial Theory (A)"},{"key":"17_CR10","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/BFb0121242","volume":"1","author":"R. Duffin","year":"1974","unstructured":"R. Duffin. On Fourier\u2019s Analysis of Linear Inequality Systems. In Mathematical Programming Study 1, pages 71\u201395. North-Holland, 1974.","journal-title":"Mathematical Programming Study"},{"key":"17_CR11","volume-title":"Concrete Mathematics","author":"R. L. Graham","year":"1989","unstructured":"R. L. Graham, D. E. Knuth, and O. Patashnik. Concrete Mathematics. Addison-Wesley, Reading, MA, 1989."},{"doi-asserted-by":"crossref","unstructured":"T. Granlund and P. Montgomery. Division by Invariant Integers using Multiplication. In Proceedings of the SIGPLAN\u2019 94 Conference on Programming Language Design and Implementation, Orlando, FL, June 1994.","key":"17_CR12","DOI":"10.1145\/178243.178249"},{"unstructured":"B. Greenwald. A Technique for Compilation to Exposed Memory Hierarchy. Master\u2019s thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, September 1999.","key":"17_CR13"},{"key":"17_CR14","doi-asserted-by":"publisher","first-page":"980","DOI":"10.1109\/12.2248","volume":"37","author":"D. Magenheimer","year":"1988","unstructured":"D. Magenheimer, L. Peters, K. Peters, and D. Zuras. Integer Multiplication and Division On the HP Precision Architecture. IEEE Transactions on Computers, 37:980\u2013990, Aug. 1988.","journal-title":"IEEE Transactions on Computers"},{"unstructured":"C. A. Moritz, M. Frank, W. Lee, and S. Amarasinghe. Hot Pages: Software Caching for Raw Microprocessors. Technical Memo LCS-TM-599, Laboratory for Computer Science, Massachusetts Institute of Technology, Sept 1999.","key":"17_CR15"},{"unstructured":"S. Oberman. Design Issues in High Performance Floating Point Arithmetic Units. PhD thesis, Stanford University, December 1996.","key":"17_CR16"},{"doi-asserted-by":"crossref","unstructured":"W. Pugh. The Omega test: A fast and practical integer programming algorithm for dependence analysis. In Proceedings of Supercomputing\u2019 91, Albuquerque, NM, Nov. 1991.","key":"17_CR17","DOI":"10.1145\/125826.125848"},{"key":"17_CR18","volume-title":"Theory of Linear and Integer Programming","author":"A. Schrijver","year":"1986","unstructured":"A. Schrijver. Theory of Linear and Integer Programming. John Wiley and Sons, Chichester, Great Britain, 1986."},{"unstructured":"M. B. Taylor. Design Decisions in the Implementation of a Raw Architecture Workstation. Master\u2019s thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, September 1999.","key":"17_CR19"},{"key":"17_CR20","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1016\/0097-3165(76)90055-8","volume":"21","author":"H. Williams","year":"1976","unstructured":"H. Williams. Fourier-Motzkin Elimination Extension to Integer Programming Problems. Journal of Combinatorial Theory, 21:118\u2013123, 1976.","journal-title":"Journal of Combinatorial Theory"},{"doi-asserted-by":"crossref","unstructured":"R. Wilson, R. French, C. Wilson, S. Amarasinghe, J. Anderson, S. Tjiang, S.-W. Liao, C.-W. Tseng, M. Hall, M. Lam, and J. Hennessy. SUIF: An Infrastructure for Research on Parallelizing and Optimizing Compilers. ACM SIGPLAN Notices, 29(12), Dec. 1996.","key":"17_CR21","DOI":"10.1145\/193209.193217"},{"unstructured":"M. E. Wolf. Improving Locality and Parallelism in Nested Loops. PhD thesis, Dept. of Computer Science, Stanford University, Aug. 1992.","key":"17_CR22"}],"container-title":["Lecture Notes in Computer Science","Languages and Compilers for Parallel Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-35767-X_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,21]],"date-time":"2019-02-21T22:12:14Z","timestamp":1550787134000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-35767-X_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540040293","9783540357674"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/3-540-35767-x_17","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2003]]}}}