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| 22 | <title>Further Reading (GNU C Language Manual)</title>
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| 31 | <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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| 32 | <link href="Floating-Point-in-Depth.html" rel="up" title="Floating Point in Depth">
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| 33 | <link href="Compilation.html" rel="next" title="Compilation">
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| 57 | <body lang="en">
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| 58 | <span id="Further-Reading"></span><div class="header">
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| 59 | <p>
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| 60 | Previous: <a href="Round_002dTrip-Base-Conversion.html" accesskey="p" rel="prev">Round-Trip Base Conversion</a>, Up: <a href="Floating-Point-in-Depth.html" accesskey="u" rel="up">Floating Point in Depth</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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| 61 | </div>
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| 62 | <hr>
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| 63 | <span id="Further-Reading-1"></span><h3 class="section">28.21 Further Reading</h3>
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| 64 |
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| 65 | <p>The subject of floating-point arithmetic is much more complex
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| 66 | than many programmers seem to think, and few books on programming
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| 67 | languages spend much time in that area. In this chapter, we have
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| 68 | tried to expose the reader to some of the key ideas, and to warn
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| 69 | of easily overlooked pitfalls that can soon lead to nonsensical
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| 70 | results. There are a few good references that we recommend
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| 71 | for further reading, and for finding other important material
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| 72 | about computer arithmetic:
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| 73 | </p>
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| 74 |
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| 75 | <ul>
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| 76 | <li> Paul H. Abbott and 15 others, <cite>Architecture and software support
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| 77 | in IBM S/390 Parallel Enterprise Servers for IEEE Floating-Point
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| 78 | arithmetic</cite>, IBM Journal of Research and Development <b>43</b>(5/6)
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| 79 | 723–760 (1999),
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| 80 | <a href="https://doi.org/10.1147/rd.435.0723">https://doi.org/10.1147/rd.435.0723</a>. This article gives
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| 81 | a good description of IBM’s algorithm for exact decimal-to-binary
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| 82 | conversion, complementing earlier ones by Clinger and others.
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| 83 |
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| 84 | </li><li> Nelson H. F. Beebe, <cite>The Mathematical-Function Computation Handbook:
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| 85 | Programming Using the MathCW Portable Software Library</cite>,
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| 86 | Springer (2017), ISBN 3-319-64109-3 (hardcover), 3-319-64110-7 (e-book)
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| 87 | (xxxvi + 1114 pages),
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| 88 | <a href="https://doi.org/10.1007/978-3-319-64110-2">https://doi.org/10.1007/978-3-319-64110-2</a>.
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| 89 | This book describes portable implementations of a large superset
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| 90 | of the mathematical functions available in many programming
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| 91 | languages, extended to a future 256-bit format (70 decimal
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| 92 | digits), for both binary and decimal floating point. It includes
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| 93 | a substantial portion of the functions described in the famous
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| 94 | <cite>NIST Handbook of Mathematical Functions</cite>, Cambridge (2018),
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| 95 | ISBN 0-521-19225-0.
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| 96 | See
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| 97 | <a href="http://www.math.utah.edu/pub/mathcw">http://www.math.utah.edu/pub/mathcw</a>
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| 98 | for compilers and libraries.
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| 99 |
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| 100 | </li><li> William D. Clinger, <cite>How to Read Floating Point Numbers
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| 101 | Accurately</cite>, ACM SIGPLAN Notices <b>25</b>(6) 92–101 (June 1990),
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| 102 | <a href="https://doi.org/10.1145/93548.93557">https://doi.org/10.1145/93548.93557</a>.
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| 103 | See also the papers by Steele & White.
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| 104 |
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| 105 | </li><li> William D. Clinger, <cite>Retrospective: How to read floating
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| 106 | point numbers accurately</cite>, ACM SIGPLAN Notices <b>39</b>(4) 360–371 (April 2004),
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| 107 | <a href="http://doi.acm.org/10.1145/989393.989430">http://doi.acm.org/10.1145/989393.989430</a>. Reprint of 1990 paper,
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| 108 | with additional commentary.
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| 109 |
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| 110 | </li><li> I. Bennett Goldberg, <cite>27 Bits Are Not Enough For 8-Digit Accuracy</cite>,
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| 111 | Communications of the ACM <b>10</b>(2) 105–106 (February 1967),
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| 112 | <a href="http://doi.acm.org/10.1145/363067.363112">http://doi.acm.org/10.1145/363067.363112</a>. This paper,
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| 113 | and its companions by David Matula, address the base-conversion
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| 114 | problem, and show that the naive formulas are wrong by one or
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| 115 | two digits.
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| 116 |
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| 117 | </li><li> David Goldberg, <cite>What Every Computer Scientist Should Know
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| 118 | About Floating-Point Arithmetic</cite>, ACM Computing Surveys <b>23</b>(1)
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| 119 | 5–58 (March 1991), corrigendum <b>23</b>(3) 413 (September 1991),
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| 120 | <a href="https://doi.org/10.1145/103162.103163">https://doi.org/10.1145/103162.103163</a>.
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| 121 | This paper has been widely distributed, and reissued in vendor
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| 122 | programming-language documentation. It is well worth reading,
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| 123 | and then rereading from time to time.
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| 124 |
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| 125 | </li><li> Norbert Juffa and Nelson H. F. Beebe, <cite>A Bibliography of
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| 126 | Publications on Floating-Point Arithmetic</cite>,
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| 127 | <a href="http://www.math.utah.edu/pub/tex/bib/fparith.bib">http://www.math.utah.edu/pub/tex/bib/fparith.bib</a>.
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| 128 | This is the largest known bibliography of publications about
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| 129 | floating-point, and also integer, arithmetic. It is actively
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| 130 | maintained, and in mid 2019, contains more than 6400 references to
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| 131 | original research papers, reports, theses, books, and Web sites on the
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| 132 | subject matter. It can be used to locate the latest research in the
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| 133 | field, and the historical coverage dates back to a 1726 paper on
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| 134 | signed-digit arithmetic, and an 1837 paper by Charles Babbage, the
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| 135 | intellectual father of mechanical computers. The entries for the
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| 136 | Abbott, Clinger, and Steele & White papers cited earlier contain
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| 137 | pointers to several other important related papers on the
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| 138 | base-conversion problem.
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| 139 |
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| 140 | </li><li> William Kahan, <cite>Branch Cuts for Complex Elementary Functions, or
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| 141 | Much Ado About Nothing’s Sign Bit</cite>, (1987),
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| 142 | <a href="http://people.freebsd.org/~das/kahan86branch.pdf">http://people.freebsd.org/~das/kahan86branch.pdf</a>.
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| 143 | This Web document about the fine points of complex arithmetic
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| 144 | also appears in the volume edited by A. Iserles and
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| 145 | M. J. D. Powell, <cite>The State of the Art in Numerical
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| 146 | Analysis: Proceedings of the Joint IMA/SIAM Conference on the
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| 147 | State of the Art in Numerical Analysis held at the University of
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| 148 | Birmingham, 14–18 April 1986</cite>, Oxford University Press (1987),
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| 149 | ISBN 0-19-853614-3 (xiv + 719 pages). Its author is the famous
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| 150 | chief architect of the IEEE 754 arithmetic system, and one of the
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| 151 | world’s greatest experts in the field of floating-point
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| 152 | arithmetic. An entire generation of his students at the
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| 153 | University of California, Berkeley, have gone on to careers in
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| 154 | academic and industry, spreading the knowledge of how to do
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| 155 | floating-point arithmetic right.
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| 156 |
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| 157 | </li><li> Donald E. Knuth, <cite>A Simple Program Whose Proof Isn’t</cite>,
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| 158 | in <cite>Beauty is our business: a birthday salute to Edsger
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| 159 | W. Dijkstra</cite>, W. H. J. Feijen, A. J. M. van Gasteren,
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| 160 | D. Gries, and J. Misra (eds.), Springer (1990), ISBN
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| 161 | 1-4612-8792-8,
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| 162 | <a href="https://doi.org/10.1007/978-1-4612-4476-9">https://doi.org/10.1007/978-1-4612-4476-9</a>. This book
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| 163 | chapter supplies a correctness proof of the decimal to
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| 164 | binary, and binary to decimal, conversions in fixed-point
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| 165 | arithmetic in the TeX typesetting system. The proof evaded
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| 166 | its author for a dozen years.
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| 167 |
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| 168 | </li><li> David W. Matula, <cite>In-and-out conversions</cite>,
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| 169 | Communications of the ACM <b>11</b>(1) 57–50 (January 1968),
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| 170 | <a href="https://doi.org/10.1145/362851.362887">https://doi.org/10.1145/362851.362887</a>.
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| 171 |
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| 172 | </li><li> David W. Matula, <cite>The Base Conversion Theorem</cite>,
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| 173 | Proceedings of the American Mathematical Society <b>19</b>(3)
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| 174 | 716–723 (June 1968). See also other papers here by this author,
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| 175 | and by I. Bennett Goldberg.
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| 176 |
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| 177 | </li><li> David W. Matula, <cite>A Formalization of Floating-Point Numeric
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| 178 | Base Conversion</cite>, IEEE Transactions on Computers <b>C-19</b>(8)
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| 179 | 681–692 (August 1970),
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| 180 | <a href="https://doi.org/10.1109/T-C.1970.223017">https://doi.org/10.1109/T-C.1970.223017</a>.
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| 181 |
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| 182 | </li><li> Jean-Michel Muller and eight others, <cite>Handbook of
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| 183 | Floating-Point Arithmetic</cite>, Birkhäuser-Boston (2010), ISBN
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| 184 | 0-8176-4704-X (xxiii + 572 pages),
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| 185 | <a href="https://doi.org/10.1007/978-0-8176-4704-9">https://doi.org/10.1007/978-0-8176-4704-9</a>. This is a
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| 186 | comprehensive treatise from a French team who are among the
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| 187 | world’s greatest experts in floating-point arithmetic, and among
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| 188 | the most prolific writers of research papers in that field. They
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| 189 | have much to teach, and their book deserves a place on the
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| 190 | shelves of every serious numerical programmer.
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| 191 |
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| 192 | </li><li> Jean-Michel Muller and eight others, <cite>Handbook of
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| 193 | Floating-Point Arithmetic</cite>, Second edition, Birkhäuser-Boston (2018), ISBN
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| 194 | 3-319-76525-6 (xxv + 627 pages),
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| 195 | <a href="https://doi.org/10.1007/978-3-319-76526-6">https://doi.org/10.1007/978-3-319-76526-6</a>. This is a new
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| 196 | edition of the preceding entry.
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| 197 |
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| 198 | </li><li> Michael Overton, <cite>Numerical Computing with IEEE Floating
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| 199 | Point Arithmetic, Including One Theorem, One Rule of Thumb, and
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| 200 | One Hundred and One Exercises</cite>, SIAM (2001), ISBN 0-89871-482-6
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| 201 | (xiv + 104 pages),
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| 202 | <a href="http://www.ec-securehost.com/SIAM/ot76.html">http://www.ec-securehost.com/SIAM/ot76.html</a>.
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| 203 | This is a small volume that can be covered in a few hours.
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| 204 |
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| 205 | </li><li> Guy L. Steele Jr. and Jon L. White, <cite>How to Print
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| 206 | Floating-Point Numbers Accurately</cite>, ACM SIGPLAN Notices
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| 207 | <b>25</b>(6) 112–126 (June 1990),
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| 208 | <a href="https://doi.org/10.1145/93548.93559">https://doi.org/10.1145/93548.93559</a>.
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| 209 | See also the papers by Clinger.
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| 210 |
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| 211 | </li><li> Guy L. Steele Jr. and Jon L. White, <cite>Retrospective: How to
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| 212 | Print Floating-Point Numbers Accurately</cite>, ACM SIGPLAN Notices
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| 213 | <b>39</b>(4) 372–389 (April 2004),
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| 214 | <a href="http://doi.acm.org/10.1145/989393.989431">http://doi.acm.org/10.1145/989393.989431</a>. Reprint of 1990
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| 215 | paper, with additional commentary.
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| 216 |
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| 217 | </li><li> Pat H. Sterbenz, <cite>Floating Point Computation</cite>, Prentice-Hall
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| 218 | (1974), ISBN 0-13-322495-3 (xiv + 316 pages). This often-cited book
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| 219 | provides solid coverage of what floating-point arithmetic was like
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| 220 | <em>before</em> the introduction of IEEE 754 arithmetic.
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| 221 |
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| 222 | </li></ul>
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| 223 |
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| 224 | <hr>
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| 225 | <div class="header">
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| 226 | <p>
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| 227 | Previous: <a href="Round_002dTrip-Base-Conversion.html" accesskey="p" rel="prev">Round-Trip Base Conversion</a>, Up: <a href="Floating-Point-in-Depth.html" accesskey="u" rel="up">Floating Point in Depth</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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| 228 | </div>
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| 229 |
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| 230 |
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| 231 |
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| 233 | </html>
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