{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T05:54:07Z","timestamp":1675749247666},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2016,3]]},"abstract":"<jats:p> This paper presents a three-integers multiplication algorithm R = A * X * Y for Reconfigurable Mesh (RM). It is based on a three-integer multiplication algorithm for faster FPGA implementations. We show that multiplying three integers of n bits can be performed on a 3D RM of size <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\" altimg=\"eq-00001.gif\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>3<\/mml:mn><mml:mi>n<\/mml:mi><mml:mtext>\u00a0<\/mml:mtext><mml:mo>+<\/mml:mo><mml:mtext>\u00a0<\/mml:mtext><mml:mi>log<\/mml:mi><mml:mo>\u2061<\/mml:mo><mml:mtext>\u00a0<\/mml:mtext><mml:mi>n<\/mml:mi><mml:mtext>\u00a0<\/mml:mtext><mml:mo>+<\/mml:mo><mml:mtext>\u00a0<\/mml:mtext><mml:mn>1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mtext>\u00a0<\/mml:mtext><mml:mo>\u00d7<\/mml:mo><mml:mtext>\u00a0<\/mml:mtext><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>2<\/mml:mn><mml:msqrt><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msqrt><mml:mtext>\u2009<\/mml:mtext><mml:mtext>\u2009<\/mml:mtext><mml:mo>+<\/mml:mo><mml:mn>3<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mtext>\u2009<\/mml:mtext><mml:mtext>\u2009<\/mml:mtext><mml:mo>\u00d7<\/mml:mo><mml:mtext>\u2009<\/mml:mtext><mml:msqrt><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msqrt><\/mml:math> using 44 + 18 \u00b7 log log MNO steps, where MNO is a bound which is related to the number of sequences of \u20181\u2019s in the multiplied numbers. The value of MNO is bounded by n but experimentally we show that on the average it is <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\" altimg=\"eq-00002.gif\"><mml:msqrt><mml:mi>n<\/mml:mi><\/mml:msqrt><\/mml:math>. Two algorithms for solving multiplication on a RM exists and their techniques are asymptotically better time wise, O(1) and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\" altimg=\"eq-00003.gif\"><mml:mi>O<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>log<\/mml:mi><mml:mo>\u2061<\/mml:mo><mml:mo>*<\/mml:mo><mml:mtext>\u00a0<\/mml:mtext><mml:mi>n<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, but they suffer from large hidden constants and slow data insertion time <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\" altimg=\"eq-00004.gif\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>O<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msqrt><mml:mi>n<\/mml:mi><\/mml:msqrt><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> respectively. The proposed algorithm is relatively simple and faster on the average (via sampling input values) then the previous two algorithms thus contributes in making the RM a practical and feasible model. Our experiments show a significant improvement in the expected number of elementary operations for the proposed algorithm. <\/jats:p>","DOI":"10.1142\/s0219265915500097","type":"journal-article","created":{"date-parts":[[2016,9,21]],"date-time":"2016-09-21T02:27:42Z","timestamp":1474424862000},"page":"1550009","source":"Crossref","is-referenced-by-count":2,"title":["Adaptive Booth Algorithm for Three-integers Multiplication for Reconfigurable Mesh"],"prefix":"10.1142","volume":"16","author":[{"given":"YOSI BEN","family":"ASHER","sequence":"first","affiliation":[{"name":"CS, University of Haifa, Haifa Israel, 31905, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ESTI","family":"STEIN","sequence":"additional","affiliation":[{"name":"CS, The Academic College of Tel-Aviv Yaffo, Tel Aviv, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,9,20]]},"reference":[{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(90)90158-T"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2013.174"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1109\/12.277290"},{"issue":"11","key":"p_13","first-page":"3894","volume":"74","author":"Nakano K.","year":"1991","journal-title":"IEICE Transactions, E"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(97)00007-8"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(93)90138-Y"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265915500097","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:15:26Z","timestamp":1565111726000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265915500097"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3]]},"references-count":6,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2016,9,20]]},"published-print":{"date-parts":[[2016,3]]}},"alternative-id":["10.1142\/S0219265915500097"],"URL":"https:\/\/doi.org\/10.1142\/s0219265915500097","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3]]}}}