C++ Boost

Mathematical Constants

Bibliography
  1. T. J. Dekker, Point Technique for Extending the Available Precision, Numer. Math. 18 (1971), pp. 224-242.
  2. S. Linnainmaa, Software for doubled-precision floating point computations ACM TOMS 7, 172-283 (1981).
  3. D. Priest, On properties of floating point arithmetics: numerical stability and the cost of accurate computations. Ph.D. Diss, Berkeley 1992. and more references in http: www.cs.wisc.edu/~shoup/ntl/quad_float.txt.
  4. M. Abramowitz & Irene A Stegun, Handbook of Mathematical Functions, Applied Math Series vol 55, National Bureau of Standards, US Gov Printing Off, Washington DC, 1965 p 948 – 972. Note that NIST project is in progress for a major revision of this.  See http://dlmf.nist.gov .
  5. Donald E. Knuth, The Art of Computer Programming, Volume 1 Fundamental algorithms, Appendix A, P 619 ISBN 0 201 89683 4.
  6. doubledouble implements doubled-double arithmetic (>30dp) on IEEE 754 floating-point hardware in (not Standard) C++. by Keith Briggs kmb28@cam.ac.uk. Definitive site for this code is: http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html is used in NTL which is used to verify some of these constants.
  7. Victor Shoup, NTL, www.shoup.net/ntl/ Numeric Template Library. Excellent arbitrary precision C++ function library. Used to calculate the constants in this collection of constants.
  8. LiDIA, Darmstadt University of Technology www.informatik.th-darmstadt.de/TI/LiDIA/
  9. Plouffe's Tables of Constants, Nov 20 1999, by S Plouffe, with rather more than ample decimal digits for this purpose! www.lacim.uqam.ca/pi/table.html
  10. P J Plauger, The Standard C Library, p 78 ISBN 0 13 131509 9 Prentice-Hall(1992).
  11. David Goldberg,"What Every Computer Scientist Should Know About Floating Point Arithmetic", March 91, Computing Surveys. http://www.acm.org/pubs/citations/journals/surveys/1991-23-1/p5-goldberg/ http://docs.sun.com/htmlcoll/coll.648.2/iso-8859-1/NUMCOMPGD/ncg_goldberg.html
  12. www.intel.com  27064004.pdf for 80C187 80-bit Math Coprocessor datasheet.
  13. AIX Version 4.3 General Programming Concepts, 128-bit long double float-point data type.
  14. http://www.opengroup.org/onlinepubs/007908799/xsh/math.h.html POSIX math.h provides some double(but NOT long double) precision constants.
  15. ftp://ftp.ccs.neu.edu/pub/people/will/howtoread.ps William D Clinger,  In Proceedings of the 1990 ACM Conference on Principles of Programming Languages, pages 92-101. How to read Floating-point accurately.
    Abstract: Consider the problem of converting decimal scientific notation for a number into the best binary floating-point approximation to that number, for some fixed precision. This problem cannot be solved using arithmetic of any fixed precision. Hence the IEEE Standard for Binary Floating-Point Arithmetic does not require the result of such a conversion to be the best approximation.
    This paper presents an efficient algorithm that always finds the best approximation. The algorithm uses a few extra bits of precision to compute an IEEE-conforming approximation while testing an intermediate result to determine whether the approximation could be other than the best. If the approximation might not be the best, then the best approximation is determined by a few simple operations on multiple-precision integers, where the precision is determined by the input. When using 64 bits of precision to compute IEEE double precision results, the algorithm avoids higher-precision arithmetic over 99% of the time.
  16. John F. Hart, Computer Approximations, Kreiger (1978) ISBN 0 88275 642 7, table of constants pages 334 - 335.
  17. Cephes Mathematical Library, Stephen L. B. Moshier,  www.netlib.org/cephes/ and http://people.ne.mediaone.net/moshier/index.html - in C. A perl interface and a DOS calculator also available.
  18. Methods and Programs for Mathematical Functions, Stephen L. B. Moshier, J Wiley, (1989) ISBN 0 7458-0289-3 & 0-470-21609 3 & 0 7458 0805 0.
  19. class constant based on a post by Michael Kenniston: http://groups.yahoo.com/group/boost/message/14867
  20. Software manual for the elementary functions. William J. Cody, Jr. and William Waite, Prentice-Hall series in computational mathematics, Englewood Cliffs, N.J., Prentice-Hall. 1980   ISBN:  0138220646.
  21. http://http.cs.berkeley.edu/~wkahan/ home page of William Kahan, pioneer of IEEE754 specification.
  22. http://http.cs.berkeley.edu/~wkahan/imporber.pdf, The Improbability of PROBABILISTIC ERROR ANALYSES for Numerical Computations.
  23. http://http.cs.berkeley.edu/~wkahan/names.pdf gives useful definitions and explanations of radix, exponent, etc.
  24. http://http.cs.berkley.edu/~wkahan/ieee754status/ieee754.ps page 4 gives significant digits for real formats.
  25. Alberto Squassabia, C++ Report Archives, March 2000 http://www.joopmag/html/from_pages/crarticle.asp?ID=396 & 397
  26. Programming Languages - C++, International Standard ISO/IEC 14882-1998,
  27. Programming Languages – C, ISO/IEC 9899:1990
  28. Programming Languages – C, ISO/IEC 9899: 1999
  29. Format of IBM S/390 processors, E. M. Schwarz & C. A. Krygowski, http://researchweb.watson.ibm.com/journal/rd/435/schwarz.html
  30. IEEE_754 Floating Point formats, Christopher Vickery http://babbage.cs.qc.edu/courses/cs341/IEEE-754references.html
  31. Physical constants and SI units http://physics.nist.gov/cuu/Units/bibliography.html
  32. W. E. Brown, http://home.fnal.gov/~wb/SItempl8.pdf
  33. Sun Numerical Computation Guide,  http://docs.sun.com/source/806-3568/ncg_lib.html
  34. Richard L. Burden, Numerical Analysis, BrooksCole, ISBN 0-534-38216-9 (2001)
  35. IHouse Bill No. 246, Indiana State Legislature, http://www.urbanlegends.com
  36. Armido R. Didinato and Alfred H. Morris, ACM TOMS Algorithm 708 (BRATIO), 18(3) 260-373 (1992).
  37. Barry W. Brown and Lawrence B Levy, Certification of algorithm 708, ACM TOMS 20(3) 393-397(1994).
  38. Gennadiy Rozental, Floating Point Comparison Algorithms, used in Boost test library.
  39. Pete Becker The Journeyman's Shop: Trap Handlers, Sticky Bits, and Floating-Point Comparisons C/C++ Users Journal December 2000.
  40. David H Bailey, MPFUN, Portable High Performance Multiprecision Package, http://www.nasa.gov/pubs/techreports/rnrreports/dbailey/RNR-090-022.html and
  41. David H Bailey, ACM TOMS, 19(3) sep 1993, 288 - 319, algorithm 719, Multiprecision FORTRAN programs.

http://www.hetp.u-net.com/public/bibliography.html, Revised 5 May 2005

© Copyright Paul A. Bristow 2002 -2005. All Rights Reserved.

Valid HTML 4.01!