Path: csiph.com!weretis.net!feeder9.news.weretis.net!news.misty.com!news.iecc.com!.POSTED.news.iecc.com!nerds-end From: anton@mips.complang.tuwien.ac.at Newsgroups: comp.compilers Subject: Re: Paper: dividing by seven Date: Sun, 19 Apr 2026 14:30:03 +0000 Organization: Compilers Central Sender: johnl%iecc.com Approved: comp.compilers@iecc.com Message-ID: <26-04-005@comp.compilers> References: <26-04-002@comp.compilers> <26-04-004@comp.compilers> MIME-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Injection-Info: gal.iecc.com; posting-host="news.iecc.com:2001:470:1f07:1126:0:676f:7373:6970"; logging-data="55688"; mail-complaints-to="abuse@iecc.com" Keywords: books, optimize Posted-Date: 22 Apr 2026 10:38:57 EDT X-submission-address: compilers@iecc.com X-moderator-address: compilers-request@iecc.com X-FAQ-and-archives: http://compilers.iecc.com Xref: csiph.com comp.compilers:3729 robin51@dodo.com.au writes: >Might be useful to look at Hacker's Delight (H. S. Warren, Jr). I looked at the first edition of this book for my paper , but its Chapter 10 only got an honourable mention at the end of my Related-Work section; there is a second edition of this book, however. In any case, I wrote at the start of my related-work section: |If you read only one paper about the topic, my recommendation is |Robison���s [Rob05]. @InProceedings{robison05, author = "Arch D. Robison", title = "{$N$}-Bit Unsigned Division Via {$N$}-Bit Multiply-Add", OPTeditor = "Paolo Montuschi and Eric (Eric Mark) Schwarz", booktitle = "{Proceedings of the 17th IEEE Symposium on Computer Arithmetic (ARITH-17)}", publisher = "IEEE Computer Society Press", ISBN = "0-7695-2366-8", ISBN-13 = "978-0-7695-2366-8", year = "2005", bibdate = "Wed Jun 22 07:02:55 2005", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.acsel-lab.com/arithmetic/arith17/papers/ARITH17_Robison.pdf", abstract = "Integer division on modern processors is expensive compared to multiplication. Previous algorithms for performing unsigned division by an invariant divisor, via reciprocal approximation, suffer in the worst case from a common requirement for $ n + 1 $ bit multiplication, which typically must be synthesized from $n$-bit multiplication and extra arithmetic operations. This paper presents, and proves, a hybrid of previous algorithms that replaces $ n + 1 $ bit multiplication with a single fused multiply-add operation on $n$-bit operands, thus reducing any $n$-bit unsigned division to the upper $n$ bits of a multiply-add, followed by a single right shift. An additional benefit is that the prerequisite calculations are simple and fast. On the Itanium 2 processor, the technique is advantageous for as few as two quotients that share a common run-time divisor.", acknowledgement = "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|", keywords = "ARITH-17", pagecount = "9", } - anton -- M. Anton Ertl anton@mips.complang.tuwien.ac.at http://www.complang.tuwien.ac.at/anton/