TEST_VALUES
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.

Licensing:

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

Languages:

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.

Reference:

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,
    Verteilungsfunktionen,
    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,
    CRC Standard Mathematical Tables and Formulae,
    30th Edition,
    CRC Press, 1996,
    ISBN: 0-8493-2479-3,
    LC: QA47.M315.
14. Daniel Zwillinger, Steven Kokoska,
    Standard Probability and Statistical Tables,
    CRC Press, 2000,
    ISBN: 1-58488-059-7,
    LC: QA273.3.Z95.

Source Code:

• test_values.f, the source code.

Examples and Tests:

• test_values_test.f, a sample calling program.
• test_values_test.txt, the output file.

List of Routines:

• ABRAM0_VALUES returns some values of the Abramowitz0 function.
• ABRAM1_VALUES returns some values of the Abramowitz1 function.
• ABRAM2_VALUES returns some values of the Abramowitz2 function.
• AGM_VALUES returns some values of the arithmetic geometric mean.
• AIRY_AI_VALUES returns some values of the Airy Ai(x) function.
• AIRY_AI_INT_VALUES returns some values of the integral of the Airy function.
• AIRY_AI_PRIME_VALUES returns some values of the Airy function Ai'(x).
• AIRY_BI_VALUES returns some values of the Airy Bi(x) function.
• AIRY_BI_INT_VALUES returns some values of the integral of the Airy function.
• AIRY_BI_PRIME_VALUES returns some values of the Airy function Bi'(x).
• AIRY_CAI_VALUES returns some values of the Airy Ai(x) with complex argument.
• AIRY_CBI_VALUES returns some values of the Airy Bi(x) with complex argument.
• AIRY_GI_VALUES returns some values of the Airy Gi function.
• AIRY_HI_VALUES returns some values of the Airy Hi function.
• ARCCOS_VALUES returns some values of the arc cosine function.
• ARCCOSH_VALUES returns some values of the hyperbolic arc cosine function.
• ARCSIN_VALUES returns some values of the arc sine function.
• ARCSINH_VALUES returns some values of the hyperbolic arc sine function.
• ARCTAN_VALUES returns some values of the arc tangent function.
• ARCTAN2_VALUES: arc tangent function of two arguments.
• ARCTAN_INT_VALUES returns some values of the inverse tangent integral.
• ARCTANH_VALUES returns some values of the hyperbolic arc tangent function.
• BEI0_VALUES returns some values of the Kelvin BEI function of order NU = 0.
• BEI1_VALUES returns some values of the Kelvin BEI function of order NU = 1.
• BELL_VALUES returns some values of the Bell numbers for testing.
• BER0_VALUES returns some values of the Kelvin BER function of order NU = 0.
• BER1_VALUES returns some values of the Kelvin BER function of order NU = 1.
• BERNOULLI_NUMBER_VALUES returns some values of the Bernoulli numbers.
• BERNOULLI_POLY_VALUES returns some values of the Bernoulli polynomials.
• BERNSTEIN_POLY_01_VALUES returns some values of the Bernstein polynomials.
• BESSEL_I0_INT_VALUES returns some values of the Bessel I0 integral.
• BESSEL_I0_SPHERICAL_VALUES returns some values of the Spherical Bessel function i0.
• BESSEL_I0_VALUES returns some values of the I0 Bessel function.
• BESSEL_I1_SPHERICAL_VALUES returns some values of the Spherical Bessel function i1.
• BESSEL_I1_VALUES returns some values of the I1 Bessel function.
• BESSEL_IN_VALUES returns some values of the In Bessel function.
• BESSEL_IX_VALUES returns some values of the Ix Bessel function.
• BESSEL_J0_INT_VALUES returns some values of the Bessel J0 integral.
• BESSEL_J0_SPHERICAL_VALUES returns some values of the Spherical Bessel function j0.
• BESSEL_J0_VALUES returns some values of the J0 Bessel function.
• BESSEL_J1_SPHERICAL_VALUES returns some values of the Spherical Bessel function j1.
• BESSEL_J1_VALUES returns some values of the J1 Bessel function.
• BESSEL_JN_VALUES returns some values of the Jn Bessel function.
• BESSEL_JX_VALUES returns some values of the Jx Bessel function.
• BESSEL_K0_INT_VALUES returns some values of the Bessel K0 integral.
• BESSEL_K0_VALUES returns some values of the K0 Bessel function.
• BESSEL_K1_VALUES returns some values of the K1 Bessel function.
• BESSEL_KN_VALUES returns some values of the Kn Bessel function.
• BESSEL_KX_VALUES returns some values of the Kx Bessel function.
• BESSEL_Y0_INT_VALUES returns some values of the Bessel Y0 integral.
• BESSEL_Y0_SPHERICAL_VALUES returns some values of the Spherical Bessel function y0.
• BESSEL_Y0_VALUES returns some values of the Y0 Bessel function.
• BESSEL_Y1_SPHERICAL_VALUES returns some values of the Spherical Bessel function y1.
• BESSEL_Y1_VALUES returns some values of the Y1 Bessel function.
• BESSEL_YN_VALUES returns some values of the Yn Bessel function.
• BESSEL_YX_VALUES returns some values of the Yx Bessel function.
• BETA_CDF_VALUES returns some values of the Beta CDF.
• BETA_INC_VALUES returns some values of the incomplete Beta function.
• BETA_LOG_VALUES returns some values of the logarithm of the Beta function.
• BETA_NONCENTRAL_CDF_VALUES returns some values of the noncentral Beta CDF.
• BETA_VALUES returns some values of the Beta function.
• BINOMIAL_VALUES returns some values of the binomial coefficients.
• BINOMIAL_CDF_VALUES returns some values of the binomial CDF.
• BIVARIATE_NORMAL_CDF_VALUES returns some values of the bivariate normal CDF.
• CATALAN_VALUES returns some values of the Catalan numbers for testing.
• CAUCHY_CDF_VALUES returns some values of the Cauchy CDF.
• CBRT_VALUES returns some values of the cube root function.
• CHEBY_T_POLY_VALUES returns values of Chebyshev polynomials T(n,x).
• CHEBY_U_POLY_VALUES returns values of Chebyshev polynomials U(n,x).
• CHEBY_V_POLY_VALUES returns values of Chebyshev polynomials V(n,x).
• CHEBY_W_POLY_VALUES returns values of Chebyshev polynomials W(n,x).
• CHI_VALUES returns some values of the hyperbolic cosine integral function.
• CHI_SQUARE_CDF_VALUES returns some values of the Chi-Square CDF.
• CHI_SQUARE_NONCENTRAL_CDF_VALUES returns values of the noncentral chi CDF.
• CI_VALUES returns some values of the cosine integral function.
• CIN_VALUES returns some values of the alternate cosine integral function.
• CINH_VALUES returns some values of the alternate hyperbolic cosine integral.
• CLAUSEN_VALUES returns some values of the Clausen's integral.
• CLEBSCH_GORDAN_VALUES returns some values of the Clebsch-Gordan function.
• COLLATZ_COUNT_VALUES returns some values of the Collatz count function.
• COS_VALUES returns some values of the cosine function.
• COS_DEGREE_VALUES: the cosine function with argument in degrees.
• COS_POWER_INT_VALUES returns some values of the cosine power integral.
• COSH_VALUES returns some values of the hyperbolic cosine function.
• COT_VALUES returns some values of the cotangent function.
• CP_VALUES returns some values of the specific heat at constant pressure.
• DAWSON_VALUES returns some values of Dawson's integral.
• DEBYE1_VALUES returns some values of Debye's function of order 1.
• DEBYE2_VALUES returns some values of Debye's function of order 2.
• DEBYE3_VALUES returns some values of Debye's function of order 3.
• DEBYE4_VALUES returns some values of Debye's function of order 4.
• DEDEKIND_SUM_VALUES returns some values of the Dedekind sum.
• DIELECTRIC_VALUES returns some values of the static dielectric constant.
• DILOGARITHM_VALUES returns some values of the dilogarithm function.
• E1_VALUES returns some values of the exponential integral function E1(X).
• EI_VALUES returns some values of the exponential integral function EI(X).
• ELLIPTIC_EA_VALUES: values of the complete elliptic integral E(ALPHA).
• ELLIPTIC_EM_VALUES returns values of the complete elliptic integral E(M).
• ELLIPTIC_KA_VALUES: values of the complete elliptic integral K(ALPHA).
• ELLIPTIC_KM_VALUES returns values of the complete elliptic integral K(M).
• ERF_VALUES returns some values of the ERF or "error" function for testing.
• ERFC_VALUES returns some values of the ERFC or "complementary error" function for testing.
• EULER_NUMBER_VALUES returns some values of the Euler numbers.
• EULER_POLY_VALUES returns some values of the Euler polynomials.
• EXP_VALUES returns some values of the exponential function.
• EXP3_INT_VALUES returns some values of the EXP3 integral function.
• EXPONENTIAL_CDF_VALUES returns some values of the Exponential CDF.
• EXTREME_VALUES_CDF_VALUES returns some values of the Extreme Values CDF.
• F_CDF_VALUES returns some values of the F CDF test function.
• F_NONCENTRAL_CDF_VALUES returns some values of the F CDF test function.
• FACTORIAL_RISING_VALUES returns values of the rising factorial function.
• FACTORIAL_VALUES returns values of the factorial function.
• FACTORIAL2_VALUES returns values of the double factorial function.
• FRESNEL_COS_VALUES returns values of the Fresnel cosine integral function.
• FRESNEL_SIN_VALUES returns some values of the Fresnel sine integral function.
• FROBENIUS_NUMBER_DATA_VALUES returns data for the Frobenius problem.
• FROBENIUS_NUMBER_ORDER_VALUES returns orders of the Frobenius problem.
• FROBENIUS_NUMBER_ORDER2_VALUES returns values of the order 2 Frobenius number.
• GAMMA_VALUES returns some values of the Gamma function.
• GAMMA_CDF_VALUES returns some values of the Gamma CDF.
• GAMMA_INC_P_VALUES: values of normalized incomplete Gamma function P(A,X).
• GAMMA_INC_Q_VALUES: values of normalized incomplete Gamma function Q(A,X).
• GAMMA_INC_TRICOMI_VALUES: values of Tricomi's incomplete Gamma function.
• GAMMA_INC_VALUES: values of the incomplete Gamma function.
• GAMMA_LOG_VALUES returns some values of the Log Gamma function.
• GEGENBAUER_POLY_VALUES returns some values of the Gegenbauer polynomials.
• GEOMETRIC_CDF_VALUES returns values of the geometric CDF.
• GOODWIN_VALUES returns some values of the Goodwin and Staton function.
• GUD_VALUES returns some values of the Gudermannian function.
• HERMITE_FUNCTION_VALUES: values of the Hermite function.
• HERMITE_POLY_PHYS_VALUES: values of the physicist's Hermite polynomial.
• HERMITE_POLY_PROB_VALUES: values of the probabilist's Hermite polynomial.
• HYPER_1F1_VALUES returns some values of the hypergeometric function 1F1.
• HYPER_2F1_VALUES returns some values of the hypergeometric function 2F1.
• HYPERGEOMETRIC_CDF_VALUES returns some values of the hypergeometric CDF.
• HYPERGEOMETRIC_PDF_VALUES returns some values of the hypergeometric PDF.
• HYPERGEOMETRIC_U_VALUES: some values of the hypergeometric function U(a,b,x).
• I0ML0_VALUES returns some values of the I0ML0 function.
• I1ML1_VALUES returns some values of the I1ML1 function.
• INT_VALUES returns some values of the "integer part" function.
• JACOBI_CN_VALUES returns some values of the Jacobi elliptic function CN(A,X).
• JACOBI_DN_VALUES returns some values of the Jacobi elliptic function DN(A,X).
• JACOBI_POLY_VALUES returns some values of the Jacobi polynomial.
• JACOBI_SN_VALUES returns some values of the Jacobi elliptic function SN(A,X).
• JED_CE_VALUES returns the Common Era dates for Julian Ephemeris Dates.
• JED_MJD_VALUES returns the MJD for Julian Ephemeris Dates.
• JED_RD_VALUES returns the RD for Julian Ephemeris Dates.
• JED_WEEKDAY_VALUES returns the day of the week for Julian Ephemeris Dates.
• KEI0_VALUES returns some values of the Kelvin KEI function of order NU = 0.
• KEI1_VALUES returns some values of the Kelvin KEI function of order NU = 1.
• KER0_VALUES returns some values of the Kelvin KER function of order NU = 0.
• KER1_VALUES returns some values of the Kelvin KER function of order NU = 1.
• LAGUERRE_ASSOCIATED_VALUES returns values of associated Laguerre polynomials.
• LAGUERRE_GENERAL_VALUES returns values of the generalized Laguerre function.
• LAGUERRE_POLYNOMIAL_VALUES returns some values of the Laguerre polynomial.
• LAMBERT_W_VALUES returns some values of the Lambert W function.
• LAPLACE_CDF_VALUES returns some values of the Laplace CDF.
• LEGENDRE_ASSOCIATED_VALUES returns values of associated Legendre functions.
• LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES: normalized associated Legendre.
• LEGENDRE_ASSOCIATED_NORMALIZED_VALUES: normalized associated Legendre.
• LEGENDRE_FUNCTION_Q_VALUES returns values of the Legendre Q function.
• LEGENDRE_POLY_VALUES returns values of the Legendre polynomials.
• LERCH_VALUES returns some values of the Lerch transcendent function.
• LINEAR_SYSTEM_VALUES returns some linear systems.
• LOBACHEVSKY_VALUES returns some values of the Lobachevsky function.
• LOBATTO_POLYNOMIAL_VALUES returns values of the completed Lobatto polynomials.
• LOBATTO_POLYNOMIAL_DERIVATIVES: derivatives of completed Lobatto polynomials.
• LOG_VALUES returns some values of the natural logarithm function.
• LOG_NORMAL_CDF_VALUES returns some values of the Log Normal CDF.
• LOG_SERIES_CDF_VALUES returns some values of the log series CDF.
• LOG10_VALUES returns some values of the logarithm 10 function.
• LOGARITHMIC_INTEGRAL_VALUES returns values of the logarithmic integral LI(X).
• LOGISTIC_CDF_VALUES returns some values of the Logistic CDF.
• MATHIEU_EVEN_VALUES returns eigenvalues of even Mathieu solutions.
• MATHIEU_ODD_VALUES returns eigenvalues of odd Mathieu solutions.
• MERTENS_VALUES returns some values of the Mertens function.
• MOEBIUS_VALUES returns some values of the Moebius function.
• NEGATIVE_BINOMIAL_CDF_VALUES returns values of the negative binomial CDF.
• NINE_J_VALUES returns some values of the Wigner 9J function.
• NORMAL_CDF_VALUES returns some values of the Normal CDF.
• NORMAL_01_CDF_VALUES returns some values of the Normal 01 CDF.
• OMEGA_VALUES returns some values of the OMEGA function.
• OWEN_VALUES returns some values of Owen's T function.
• PARTITION_COUNT_VALUES returns some values of the integer partition count.
• PARTITION_DISTINCT_COUNT_VALUES returns some values of Q(N).
• PHI_VALUES returns some values of the PHI function.
• PI_VALUES returns values of the Pi function.
• POCHHAMMER_VALUES returns some values of the Pochhammer function.
• POISSON_CDF_VALUES returns some values of the Poisson CDF.
• POLYLOGARITHM_VALUES returns some values of the polylogarithm.
• PRANDTL_VALUES returns some values of the Prandtl number.
• PRIME_VALUES returns values of the prime function.
• PSAT_VALUES returns some values of the saturation pressure.
• PSI_VALUES returns some values of the Psi or Digamma function for testing.
• R8_FACTORIAL_VALUES returns values of the real factorial function.
• R8_FACTORIAL_LOG_VALUES returns values of log(n!).
• RAYLEIGH_CDF_VALUES returns some values of the Rayleigh CDF.
• SECVIR_VALUES returns some values of the second virial coefficient.
• SHI_VALUES returns some values of the hyperbolic sine integral function.
• SI_VALUES returns some values of the sine integral function.
• SIGMA_VALUES returns some values of the Sigma function.
• SIN_VALUES returns some values of the sine function.
• SIN_DEGREE_VALUES: the sine function with argument in degrees.
• SIN_POWER_INT_VALUES returns some values of the sine power integral.
• SINH_VALUES returns some values of the hyperbolic sine function.
• SIX_J_VALUES returns some values of the Wigner 6J function.
• SOUND_VALUES returns some values of the speed of sound.
• SPHERE_UNIT_AREA_VALUES returns some areas of the unit sphere in ND.
• SPHERE_UNIT_VOLUME_VALUES returns some volumes of the unit sphere in ND.
• SPHERICAL_HARMONIC_VALUES returns values of spherical harmonic functions.
• SQRT_VALUES returns some values of the square root function.
• STIRLING1_VALUES returns some values of the Stirling numbers, kind 1.
• STIRLING2_VALUES returns some values of the Stirling numbers, kind 2.
• STROMGEN_VALUES returns some values of the Stromgen function.
• STRUVE_H0_VALUES returns some values of the Struve H0 function.
• STRUVE_H1_VALUES returns some values of the Struve H1 function.
• STRUVE_L0_VALUES returns some values of the Struve L0 function.
• STRUVE_L1_VALUES returns some values of the Struve L1 function.
• STUDENT_CDF_VALUES returns some values of the Student CDF.
• STUDENT_NONCENTRAL_CDF_VALUES returns values of the noncentral Student CDF.
• SUBFACTORIAL_VALUES returns values of the subfactorial function.
• SURTEN_VALUES returns some values of the surface tension.
• SYNCH1_VALUES returns some values of the synchrotron radiation function.
• SYNCH2_VALUES returns some values of the synchrotron radiation function.
• TAN_VALUES returns some values of the tangent function.
• TANH_VALUES returns some values of the hyperbolic tangent function.
• TAU_VALUES returns some values of the Tau function.
• THERCON_VALUES returns some values of the thermal conductivity.
• THREE_J_VALUES returns some values of the Wigner 3J function.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• TRAN02_VALUES returns some values of the order 2 transportation function.
• TRAN03_VALUES returns some values of the order 3 transportation function.
• TRAN04_VALUES returns some values of the order 4 transportation function.
• TRAN05_VALUES returns some values of the order 5 transportation function.
• TRAN06_VALUES returns some values of the order 6 transportation function.
• TRAN07_VALUES returns some values of the order 7 transportation function.
• TRAN08_VALUES returns some values of the order 8 transportation function.
• TRAN09_VALUES returns some values of the order 9 transportation function.
• TRIGAMMA_VALUES returns some values of the TriGamma function.
• TRUNCATED_NORMAL_AB_CDF_VALUES: values of the Truncated Normal CDF.
• TRUNCATED_NORMAL_AB_PDF_VALUES: values of the Truncated Normal PDF.
• TRUNCATED_NORMAL_A_CDF_VALUES: values of the lower Truncated Normal CDF.
• TRUNCATED_NORMAL_A_PDF_VALUES: values of the lower Truncated Normal PDF.
• TRUNCATED_NORMAL_B_CDF_VALUES: values of the Upper Truncated Normal CDF.
• TRUNCATED_NORMAL_B_PDF_VALUES: values of the upper Truncated Normal PDF.
• TSAT_VALUES returns some values of the saturation temperature.
• VAN_DER_CORPUT_VALUES returns some values of the van der Corput sequence.
• VISCOSITY_VALUES returns some values of the viscosity function.
• VON_MISES_CDF_VALUES returns some values of the von Mises CDF.
• WEEKDAY_VALUES returns the day of the week for various dates.
• WEIBULL_CDF_VALUES returns some values of the Weibull CDF.
• ZETA_VALUES returns some values of the Riemann Zeta function.

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