Sample Function Values

TEST_VALUES is a FORTRAN77 library which stores a few selected values of various mathematical functions.

The intent of TEST_VALUES is to provide a means of making very simple tests for correctness of software designed to compute a variety of functions. The testing can be done automatically. The data provided is generally skimpy, and might not test the algorithm over a suitably wide range. It does, however, provide a small amount of reassurance that a given computation is (or is not) computing the appropriate quantity, and doing so reasonably accurately.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


TEST_VALUES is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATHEMATICA version and a MATLAB version and a Python version.

Related Programs:

CORDIC, a FORTRAN77 library which uses the CORDIC method to compute certain elementary functions.

FN, a FORTRAN77 library which contains routines by Wayne Fullerton for evaluating elementary and special functions.

POLPAK, a FORTRAN77 library which compute various mathematical functions; test values for many of these functions are available in TEST_VALUES.

PROB, a FORTRAN77 library which compute various statistical functions; test values for many of these functions are available in TEST_VALUES.

SPECFUN, a FORTRAN77 library which compute various special functions, particularly Bessel functions.

SPECIAL_FUNCTIONS, a FORTRAN77 library which computes special functions, by Shanjie Zhang, Jianming Jin;

STEAM, a FORTRAN90 library which computes various functions related to the physical properties of water; test values for many of these functions are available in TEST_VALUES.


  1. Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
  2. Robert Corless, Gaston Gonnet, David Hare, David Jeffrey, Donald Knuth,
    On the Lambert W Function,
    Advances in Computational Mathematics,
    Volume 5, 1996, pages 329-359.
  3. Lester Haar, John Gallagher, George Kell,
    NBS/NRC Steam Tables:
    Thermodynamic and Transport Properties and Computer Programs for Vapor and Liquid States of Water in SI Units,
    Hemisphere Publishing Corporation, Washington, 1984,
    ISBN: 0-89116-353-0,
    LC: TJ270.H3.
  4. Brian Hayes,
    "Why W?",
    The American Scientist,
    Volume 93, March-April 2005, pages 104-108.
  5. Kanti Mardia, Peter Jupp,
    Directional Statistics,
    Wiley, 2000,
    ISBN: 0471953334,
    LC: QA276.M335
  6. Allan McLeod,
    Algorithm 757: MISCFUN: A software package to compute uncommon special functions,
    ACM Transactions on Mathematical Software,
    Volume 22, Number 3, September 1996, pages 288-301.
  7. Karl Pearson,
    Tables of the Incomplete Beta Function,
    Cambridge University Press, 1968,
    LC: QA351.P38.
  8. Frank Powell,
    Statistical Tables for Sociology, Biology and Physical Sciences,
    Cambridge University Press, 1982,
    ISBN: 0521284732,
    LC: QA276.25.S73.
  9. Edward Reingold, Nachum Dershowitz,
    Calendrical Calculations: The Millennium Edition,
    Cambridge University Press, 2001,
    ISBN: 0-521-77752-6,
    LC: CE12.R45.
  10. Johannes van der Corput,
    Proc Akad Amsterdam,
    Volume 38, 1935,
    Volume 39, 1936.
  11. Eric Weisstein,
    CRC Concise Encyclopedia of Mathematics,
    CRC Press, 2002,
    Second edition,
    ISBN: 1584883472,
    LC: QA5.W45
  12. Stephen Wolfram,
    The Mathematica Book,
    Fourth Edition,
    Cambridge University Press, 1999,
    ISBN: 0-521-64314-7,
    LC: QA76.95.W65.
  13. Daniel Zwillinger, editor,
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    30th Edition,
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  14. Daniel Zwillinger, Steven Kokoska,
    Standard Probability and Statistical Tables,
    CRC Press, 2000,
    ISBN: 1-58488-059-7,
    LC: QA273.3.Z95.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN77 source codes.

Last revised on 18 November 2014.