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BibTeX entry
@Article{Steele:1990:HPF,
author = "Guy L. {Steele, Jr.} and Jon L. White",
title = "How to Print Floating-Point Numbers Accurately",
journal = j-SIGPLAN,
volume = "25",
number = "6",
pages = "112--126",
month = jun,
year = "1990",
CODEN = "SINODQ",
ISBN = "0-89791-364-7",
ISBN-13 = "978-0-89791-364-5",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160 (electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:53 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/93542/",
note = "See also input algorithm in
\cite{Clinger:1990:HRF,Clinger:2004:RHR}, and a faster
output algorithm in \cite{Burger:1996:PFP} and
\cite{Knuth:1990:SPW}, IBM S/360 algorithms in
\cite{Abbott:1999:ASS} for both IEEE 754 and S/360
formats, and a twenty-year retrospective in
\cite{Steele:2004:RHP}. In electronic mail dated Wed,
27 Jun 1990 11:55:36 EDT, Guy Steele reported that an
intrepid pre-SIGPLAN 90 conference implementation of
what is stated in the paper revealed 3 mistakes:
\begin{itemize} \item[1.] Table~5 (page 124):\par
\noindent insert {\tt k <-- 0} after assertion, and
also delete {\tt k <-- 0} from Table~6. \item[2.]
Table~9 (page 125):\par \noindent \begin{tabular} {ll}
for & {\tt -1:USER!({"}{"});} \\
substitute & {\tt -1:USER!({"}0{"});} \end{tabular}\par
\noindent and delete the comment. \item[3.] Table~10
(page 125):\par \noindent \begin{tabular}{ll} for &
{\tt fill(-k, {"}0{"})}\\
substitute & {\tt fill(-k-1, {"}0{"})} \end{tabular}
\end{itemize}
\def\EatBibTeXPeriod#1{\ifx#1.\else#1\fi}\EatBibTeXPeriod",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p112-steele/",
abstract = "Algorithms are presented for accurately converting
floating-point numbers to decimal representation. The
key idea is to carry along with the computation an
explicit representation of the required rounding
accuracy. The authors begin with the simpler problem of
converting fixed-point fractions. A modification of the
well-known algorithm for radix-conversion of
fixed-point fractions by multiplication explicitly
determines when to terminate the conversion process; a
variable number of digits are produced. They derive two
algorithms for free-format output of floating-point
numbers. Finally, they modify the free-format
conversion algorithm for use in fixed-format
applications. Information may be lost if the fixed
format provides too few digit positions, but the output
is always correctly rounded. On the other hand, no
`garbage digits' are ever produced, even if the fixed
format specifies too many digit positions (intuitively,
the `4/3 prints as 1.333333328366279602' problem does
not occur).",
acknowledgement = ack-nhfb,
affiliation = "Thinking Machines Corp",
affiliationaddress = "Cambridge, MA, USA",
classification = "722; 723; C5230 (Digital arithmetic methods); C7310
(Mathematics)",
confdate = "20-22 June 1990",
conference = "Proceedings of the ACM SIGPLAN '90 Conference on
Programming Language Design and Implementation",
conferenceyear = "1990",
conflocation = "White Plains, NY, USA",
confsponsor = "ACM",
journalabr = "SIGPLAN Not",
keywords = "algorithms; computer programming languages; computers,
digital --- computational methods; conversion process;
decimal representation; design; digit positions;
explicit representation; fixed-format applications;
fixed-point fractions; floating point numbers;
floating-point numbers; free-format conversion
algorithm; free-format output; garbage digits;
performance; radix-conversion; rounding accuracy;
verification",
remark = "Published as part of the Proceedings of PLDI'90.",
sponsor = "Assoc for Computing Machinery, Special Interest Group
on Programming Languages",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic.",
thesaurus = "Digital arithmetic; Mathematics computing",
xxabstract = "We present algorithms for accurately converting
floating-point numbers to decimal representation. The
key idea is to carry along with the computation an
explicit representation of the required rounding
accuracy. We begin with the simpler problem of
converting fixed-point fractions. A modification of the
well-known algorithm for radix-conversion of
fixed-point fractions by multiplication explicitly
determines when to terminate the conversion process; a
variable number of digits are produced. We then derive
two algorithms for free-format output of floating-point
numbers. Finally, we modify the free-format conversion
algorithm for use in fixed-format applications.",
}
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31(5)108,
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33(5)118
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30(3)83
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31(5)108
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31(5)108
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30(6)218
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26(4)303,
27(7)341,
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30(6)79-1,
30(8)39,
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32(10)301,
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25(6)92,
28(8)57,
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25(4)51,
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25(6)92,
25(6)197,
25(6)246,
27(7)200,
28(7)13,
29(3)33,
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29(9)91,
29(9)115,
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30(2)25,
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27(7)300
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25(6)92
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25(6)137,
25(6)189,
25(6)283,
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29(11)219,
29(11)252,
29(11)328,
30(3)13,
30(3)94,
30(3)119,
30(6)1,
30(6)67,
30(6)103,
30(6)291,
30(8)68,
30(8)134,
30(8)217,
30(11)20-1,
30(11)134,
33(7)19,
33(7)27
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25(6)85-1,
25(6)246,
27(7)32,
27(7)44,
27(7)55,
27(7)212,
27(7)235,
27(7)273,
27(7)322,
27(12)20,
27(12)28,
28(3)361,
28(6)1,
28(6)13,
28(7)23,
28(7)83,
29(6)1,
29(6)13,
29(6)36,
29(6)206,
29(6)266,
29(6)337,
29(6)337-1,
29(6)349,
29(6)349-1,
29(8)46,
29(8)59,
29(11)25,
29(11)183,
30(3)1,
30(3)62,
30(6)67,
30(6)246,
30(11)50,
30(11)79,
30(11)125,
30(11)134,
33(7)27,
34(4)17
- modification,
25(4)51,
25(5)117,
25(10)237,
26(4)86,
27(7)224,
28(6)56,
28(7)179,
29(6)49,
29(6)349,
29(6)349-1,
29(11)171,
30(4)29,
30(6)291,
33(10)144
- modify,
27(7)311,
30(6)291
- multiplication,
29(3)12,
29(6)61,
30(2)42,
30(8)58,
30(11)1,
31(11)33,
31(11)33-1,
33(11)252
- NUMERICAL,
25(6)92,
25(6)102,
25(6)322,
26(6)1,
26(6)15,
27(7)140,
29(6)61,
29(6)349-1,
30(6)139,
31(5)12,
32(5)122,
32(5)134,
32(5)146,
32(5)159,
32(5)183,
33(5)38,
33(5)118,
33(11)12,
33(11)228,
33(11)307
- numerical,
25(1)59,
25(3)109,
25(6)92,
25(6)102,
26(6)30,
27(7)140,
28(3)355,
28(6)13,
29(6)61,
29(6)121,
29(6)218,
29(6)349-1,
29(11)183,
30(6)139,
30(6)279,
30(8)48,
31(5)108,
31(9)60,
33(5)38
- occur,
27(7)1,
27(7)44,
27(7)273,
28(6)46,
29(6)1,
29(6)218,
29(6)230,
33(7)1
- output,
25(6)92,
27(7)200,
28(6)26,
28(6)100,
29(1)37,
29(8)59,
29(9)91,
29(12)58,
30(2)25,
30(3)35,
30(6)13,
30(6)32,
31(5)108
- page,
26(7)122,
29(6)196,
29(11)12,
29(11)86,
29(11)158,
29(11)171,
29(12)112,
31(9)244,
31(9)244-1,
32(11)49,
33(11)295,
34(12)37
- point,
25(1)59,
25(6)92,
25(10)312,
25(12)85,
26(4)28,
26(4)290,
26(6)219,
27(7)32,
27(7)224,
27(7)235,
27(9)223,
28(3)69,
28(6)68,
28(6)197,
29(6)1,
29(6)61,
29(6)121,
29(6)349,
29(6)349-1,
29(8)59,
29(10)85,
29(11)12,
29(11)98,
29(11)122,
29(11)208,
31(1)9,
31(1)9-1,
31(3)6,
31(3)6-1,
33(9)103
- Point, Floating-,
25(6)92,
26(4)28,
31(5)108,
32(3)57,
33(5)118
- point, floating-,
26(6)145,
27(5)z,
28(8)90,
29(6)186,
31(5)108,
33(11)252
- position,
25(6)16,
27(10)88,
28(3)69,
28(3)361,
29(6)230,
29(8)111,
32(1)59,
32(1)110
- presented,
24(3)34,
25(6)28,
25(6)102,
25(6)127-1,
27(7)12,
27(7)235,
27(7)341,
28(6)290,
28(7)23,
28(7)218,
28(7)229,
29(6)36,
29(6)147,
29(6)196,
29(8)94,
29(11)145,
30(8)134,
30(8)156,
30(11)41,
30(11)60,
30(11)88
- PROBLEM,
25(6)40,
25(6)66,
25(6)92,
25(6)102,
25(6)137,
25(6)150,
25(6)234,
25(6)272,
25(6)322,
25(6)337,
26(6)30,
26(6)130,
26(6)192,
26(6)204,
26(6)241,
26(6)256,
27(7)140,
27(9)98,
27(9)238,
28(3)363,
28(6)78-1,
28(6)268,
28(6)278,
28(6)290,
29(6)61,
29(6)85,
29(6)97,
29(6)121,
29(6)171,
29(6)218,
29(6)302,
30(6)32,
30(6)47,
30(6)56,
30(6)139,
30(6)186,
30(6)246,
30(6)279,
30(11)7,
30(11)60,
30(11)134,
31(5)108,
31(5)193,
31(9)60,
32(5)194,
32(5)334,
33(5)72,
33(5)85-1,
33(5)142,
33(11)24,
33(11)262,
33(11)272
- produced,
25(6)85-1,
25(6)165,
27(7)94,
27(7)273,
28(3)97,
28(3)177,
28(3)231,
28(3)299,
29(8)1,
29(11)61,
30(3)13,
30(3)119,
30(11)1
- reported,
25(4)59,
25(6)209,
28(7)179,
29(11)76-1,
29(11)242,
33(7)67
- required,
25(1)59,
25(6)102,
25(6)272,
25(6)337,
27(9)248,
28(3)299,
29(6)302,
29(11)76-1,
29(11)98,
29(11)171,
29(11)196,
29(11)319,
30(6)139,
30(11)20-1
- rounded,
31(5)108
- rounding,
31(5)108
- see,
17(9)18,
23(1)17,
25(6)92,
27(7)1,
27(12)13,
27(12)20,
27(12)61,
28(5)3,
28(9)25,
28(11)3,
29(6)49,
29(9)8,
30(4)13,
31(3)28,
31(5)108,
31(8)40,
32(9)39,
33(4)27,
33(12)44,
33(12)52,
33(12)72,
34(2)42,
34(2)46,
34(5)1,
34(5)13,
34(5)25-1,
34(5)37,
34(5)50,
34(5)64,
34(5)77,
34(5)91,
34(5)104,
34(5)118,
34(5)128,
34(5)139,
34(5)150,
34(5)155,
34(5)169,
34(5)181,
34(5)192,
34(5)204,
34(5)215,
34(5)229,
34(5)242,
34(5)247,
34(5)259,
34(5)270,
34(5)281,
34(5)293,
34(6)82,
34(12)35
- simpler,
25(6)102,
27(7)212,
27(9)248,
27(9)262,
29(11)171,
29(11)274,
30(6)246
- specify,
27(7)1,
27(7)249,
29(8)59,
29(11)263,
30(2)25,
30(6)47,
30(11)41
- Steele,
30(7)5,
32(1)14,
33(9)26-1
- Steele, Jr., Guy L.,
26(6)145,
26(6)145-1,
28(1)1,
28(3)231,
33(10)201,
34(5)z-1
- Steele:1990:HPF,
25(6)92,
31(5)108
- Steele:2004:RHP,
25(6)92,
31(5)108
- table,
17(9)18,
25(6)16,
27(7)68,
27(7)273,
27(7)331,
27(11)33,
28(3)359,
28(10)259,
29(6)49,
29(6)313,
29(9)68,
29(10)244,
29(10)244,
29(10)427,
30(10)141,
30(11)7,
32(10)108,
32(10)125,
32(10)162,
32(10)162-1,
32(10)206,
32(10)206-1,
32(10)345-1,
32(10)345-5,
33(11)295
- too,
25(6)102,
27(9)285,
29(11)25,
29(11)208,
30(6)279,
33(7)27,
34(9)8-1
- well-known,
25(6)223,
27(7)300
- what,
6(4)30,
25(6)311,
25(6)322,
27(7)1,
27(10)77,
27(10)91,
28(3)69,
28(7)187,
29(6)97,
29(8)1,
30(6)151,
30(9)33,
30(9)33,
31(6)92,
33(7)19,
33(10)341,
34(2)26,
34(2)26-1,
34(5)50,
34(11)73
- when,
24(3)34,
25(6)40,
25(6)66,
25(6)78,
25(6)92,
25(6)102,
25(6)137,
25(6)174,
25(6)223,
25(10)181,
27(7)1,
27(7)116,
27(7)188-1,
27(7)235,
27(7)311,
27(7)322,
27(9)285,
28(3)97,
28(3)361,
28(6)56,
28(6)100,
28(6)147,
28(6)187,
28(6)258,
28(6)278,
28(7)44,
28(7)83,
28(7)239,
28(8)90,
28(12)169,
29(6)1,
29(6)49,
29(6)85,
29(6)206,
29(11)2,
29(11)86,
29(11)145,
29(11)171,
29(11)242,
29(11)252,
30(3)23,
30(3)94,
30(6)1,
30(6)56,
30(6)93,
30(6)103,
30(6)151,
30(6)279,
30(8)123,
30(8)179,
30(8)189,
30(8)199,
31(5)108,
32(3)27,
32(3)27-1,
33(2)59,
33(7)19,
33(7)27,
33(7)67,
34(9)1