From 93cb10d1d571c39a1f7b39b88d1fba745f2e31a9 Mon Sep 17 00:00:00 2001 From: Sam Moore Date: Tue, 22 Apr 2014 01:13:46 +0800 Subject: [PATCH] Today's battle with the Literature Despite a heroic effort I think I'd have to say I lost. --- .gitignore | 1 + LiteratureNotes.pdf | Bin 177727 -> 201185 bytes LiteratureNotes.tex | 137 ++++++++++++++++---- Makefile | 2 +- ProjectProposalDavid.pdf | Bin 131180 -> 131180 bytes ProjectProposalSam.pdf | Bin 116936 -> 116936 bytes figures/calculatepi.pdf | Bin 0 -> 8213 bytes papers.bib | 61 ++++++++- references/beebe2011round32.html | 177 ++++++++++++++++++++++++++ references/dekker1971afloating.pdf | Bin 0 -> 970552 bytes references/dodge_babbage.pdf | Bin 0 -> 204854 bytes references/hillesland2004paranoia.pdf | Bin 0 -> 32162 bytes references/ieee2008-754.pdf | Bin 0 -> 936360 bytes references/nature1871babbage.pdf | Bin 0 -> 340108 bytes 14 files changed, 352 insertions(+), 26 deletions(-) create mode 100644 figures/calculatepi.pdf create mode 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zcu^?W5C5Rk{|5|%(uYg2f6Bw4_5Yz4gX5Kv|4zp%aQ_{q`%f4i3l~-Yq{HD2;D|54 zI4lxeB4oj@-2u>r8Vwe2E4q&!T@Igw59tofVui1TpP6nJdLe3;8Ae(7pI5a yU}**0X0B&$fwr`=(j%B-%{SmIO#gQZZ{8aNHiyLG%mqka-vEVBRkd;;ApQ#wWb{7( literal 0 HcmV?d00001 diff --git a/papers.bib b/papers.bib index 0dec3ca..fa6ae7b 100644 --- a/papers.bib +++ b/papers.bib @@ -501,7 +501,7 @@ doi={10.1109/ARITH.1991.145549},} % On the design of IEEE floating point adders % Has algorithms! -@INPROCEEDINGS{seidal2001onthe, +@INPROCEEDINGS{seidel2001onthe, author={Seidel, P.-M. and Even, G.}, booktitle={Computer Arithmetic, 2001. Proceedings. 15th IEEE Symposium on}, title={On the design of fast IEEE floating-point adders}, @@ -527,4 +527,61 @@ ISSN={1063-6889},} howpublished = "\url{http://www.gaisler.com/doc/grfpu_dasia.pdf}" } - +% The best quote ever. +@misc{beebe2011round32, + title = "Re: round32 ( round64 ( X ) ) ?= round32 ( X )", + note = "IEEE 754 Working Group Mail Archives", + author = "Nelson H. F. Beebe", + howpublished = "\url{http://grouper.ieee.org/groups/754/email/msg04169.html}" +} + +% Biography of Charles Babbage because WHY NOT? + % I suspect this year is wrong?75 +@ARTICLE{dodge_babbage, +author={Dodge, N. S.}, +journal={Annals of the History of Computing, IEEE}, +title={Charles Babbage}, +year={2000}, +month={Oct}, +volume={22}, +number={4}, +pages={22-43}, +keywords={Accuracy;Art;Autobiographies;Biographies;Blood;Calculus;Educational institutions;History;Writing}, +doi={10.1109/MAHC.2000.887988}, +ISSN={1058-6180},} + +@article{nature1871babbage, + author = "Unknown Author", + journal = "Nature", + title = "Charles Babbage", + year = 1871, + volume = 5, + number = 106, + pages = "28-29" +} + +%IEEE 754 Really should have put this in earlier +@ARTICLE{ieee2008-754, +journal={IEEE Std 754-2008}, +title={IEEE Standard for Floating-Point Arithmetic}, +year={2008}, +month={Aug}, +pages={1-70}, +keywords={IEEE standards;floating point arithmetic;programming;IEEE standard;arithmetic formats;computer programming;decimal floating-point arithmetic;754-2008;NaN;arithmetic;binary;computer;decimal;exponent;floating-point;format;interchange;number;rounding;significand;subnormal}, +doi={10.1109/IEEESTD.2008.4610935},} + + +@article{dekker1971afloating +year={1971}, +issn={0029-599X}, +journal={Numerische Mathematik}, +volume={18}, +number={3}, +doi={10.1007/BF01397083}, +title={A floating-point technique for extending the available precision}, +url={http://dx.doi.org/10.1007/BF01397083}, +publisher={Springer-Verlag}, +author={Dekker, T.J.}, +pages={224-242}, +language={English} +} diff --git a/references/beebe2011round32.html b/references/beebe2011round32.html new file mode 100644 index 0000000..6ce6440 --- /dev/null +++ b/references/beebe2011round32.html @@ -0,0 +1,177 @@ + + + + + + + + + + + Re: round32 ( round64 ( X ) ) ?= round32 ( X ) + + + + + + +

+ + + + +
+[
Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index] + + + +

Re: round32 ( round64 ( X ) ) ?= round32 ( X )

+
+ + + + + +
+ + +
Peter Lawrence asks about the infamous problem of double rounding on
+systems with long internal registers (Honeywell mainframes of 1970s,
+Motorola 68K, and current Intel x86 and x86_64 families).
+
+Double rounding is indeed a nuisance, and there is a surprising recent
+discovery that it could have been prevented if there were an unusual
+rounding mode, round-to-odd (RO(x)).  The authors of the paper below
+show how to implement that rounding in software, and discuss how it
+can be used to fix the double-rounding problem.
+
+It is too late now to repair the mistakes of the past that are present
+in millions of installed systems, but it is good to know that careful
+research before designing hardware can be helpful.
+
+@String{j-IEEE-TRANS-COMPUT     = "IEEE Transactions on Computers"}
+
+@Article{Boldo:2008:EFC,
+  author =       "Sylvie Boldo and Guillaume Melquiond",
+  title =        "Emulation of a {FMA} and Correctly Rounded Sums:
+                 Proved Algorithms Using Rounding to Odd",
+  journal =      j-IEEE-TRANS-COMPUT,
+  volume =       "54",
+  number =       "4",
+  pages =        "462--471",
+  month =        apr,
+  year =         "2008",
+  CODEN =        "ITCOB4",
+  DOI =          "http://dx.doi.org/10.1109/TC.2007.70819";,
+  ISSN =         "0018-9340",
+  bibdate =      "Sat Feb 19 18:44:18 2011",
+  abstract =     "Rounding to odd is a nonstandard rounding on
+                 floating-point numbers. By using it for some
+                 intermediate values instead of rounding to nearest,
+                 correctly rounded results can be obtained at the end of
+                 computations. We present an algorithm for emulating the
+                 fused multiply-and-add operator. We also present an
+                 iterative algorithm for computing the correctly rounded
+                 sum of a set of floating-point numbers under mild
+                 assumptions. A variation on both previous algorithms is
+                 the correctly rounded sum of any three floating-point
+                 numbers. This leads to efficient implementations, even
+                 when this rounding is not available. In order to
+                 guarantee the correctness of these properties and
+                 algorithms, we formally proved them by using the Coq
+                 proof checker.",
+  acknowledgement = ack-nhfb,
+  fjournal =     "IEEE Transactions on Computers",
+  keyword =      "round-to-odd (RO(x))",
+}
+
+See also discussions of the double-rounding problem in this recent
+useful book:
+
+@String{pub-BIRKHAUSER-BOSTON   = "Birkh{\"a}user Boston Inc."}
+@String{pub-BIRKHAUSER-BOSTON:adr = "Cambridge, MA, USA"}
+
+@Book{Muller:2010:HFP,
+  author =       "Jean-Michel Muller and Nicolas Brisebarre and Florent
+                 de Dinechin and Claude-Pierre Jeannerod and Vincent
+                 Lef{\`e}vre and Guillaume Melquiond and Nathalie Revol
+                 and Damien Stehl{\'e} and Serge Torres",
+  title =        "Handbook of Floating-Point Arithmetic",
+  publisher =    pub-BIRKHAUSER-BOSTON,
+  address =      pub-BIRKHAUSER-BOSTON:adr,
+  pages =        "xxiii + 572",
+  year =         "2010",
+  DOI =          "http://dx.doi.org/10.1007/978-0-8176-4704-9";,
+  ISBN =         "0-8176-4704-X",
+  ISBN-13 =      "978-0-8176-4704-9",
+  LCCN =         "QA76.9.C62 H36 2010",
+  bibdate =      "Thu Jan 27 16:18:58 2011",
+  price =        "US\$90 (est.)",
+  acknowledgement = ack-nhfb,
+}
+
+-------------------------------------------------------------------------------
+- Nelson H. F. Beebe                    Tel: +1 801 581 5254                  -
+- University of Utah                    FAX: +1 801 581 4148                  -
+- Department of Mathematics, 110 LCB    Internet e-mail: beebe@xxxxxxxxxxxxx  -
+- 155 S 1400 E RM 233                       beebe@xxxxxxx  beebe@xxxxxxxxxxxx -
+- Salt Lake City, UT 84112-0090, USA    URL: http://www.math.utah.edu/~beebe/ -
+-------------------------------------------------------------------------------
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