147 lines
5.2 KiB
Plaintext
147 lines
5.2 KiB
Plaintext
-- Testcases for functions in math.
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--
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-- Each line takes the form:
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--
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-- <testid> <function> <input_value> -> <output_value> <flags>
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--
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-- where:
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--
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-- <testid> is a short name identifying the test,
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--
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-- <function> is the function to be tested (exp, cos, asinh, ...),
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--
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-- <input_value> is a string representing a floating-point value
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--
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-- <output_value> is the expected (ideal) output value, again
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-- represented as a string.
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--
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-- <flags> is a list of the floating-point flags required by C99
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--
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-- The possible flags are:
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--
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-- divide-by-zero : raised when a finite input gives a
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-- mathematically infinite result.
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--
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-- overflow : raised when a finite input gives a finite result that
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-- is too large to fit in the usual range of an IEEE 754 double.
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--
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-- invalid : raised for invalid inputs (e.g., sqrt(-1))
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--
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-- ignore-sign : indicates that the sign of the result is
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-- unspecified; e.g., if the result is given as inf,
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-- then both -inf and inf should be accepted as correct.
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--
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-- Flags may appear in any order.
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--
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-- Lines beginning with '--' (like this one) start a comment, and are
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-- ignored. Blank lines, or lines containing only whitespace, are also
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-- ignored.
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-- Many of the values below were computed with the help of
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-- version 2.4 of the MPFR library for multiple-precision
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-- floating-point computations with correct rounding. All output
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-- values in this file are (modulo yet-to-be-discovered bugs)
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-- correctly rounded, provided that each input and output decimal
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-- floating-point value below is interpreted as a representation of
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-- the corresponding nearest IEEE 754 double-precision value. See the
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-- MPFR homepage at http://www.mpfr.org for more information about the
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-- MPFR project.
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---------------------------
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-- gamma: Gamma function --
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---------------------------
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-- special values
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gam0000 gamma 0.0 -> inf divide-by-zero
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gam0001 gamma -0.0 -> -inf divide-by-zero
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gam0002 gamma inf -> inf
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gam0003 gamma -inf -> nan invalid
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gam0004 gamma nan -> nan
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-- negative integers inputs are invalid
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gam0010 gamma -1 -> nan invalid
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gam0011 gamma -2 -> nan invalid
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gam0012 gamma -1e16 -> nan invalid
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gam0013 gamma -1e300 -> nan invalid
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-- small positive integers give factorials
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gam0020 gamma 1 -> 1
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gam0021 gamma 2 -> 1
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gam0022 gamma 3 -> 2
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gam0023 gamma 4 -> 6
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gam0024 gamma 5 -> 24
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gam0025 gamma 6 -> 120
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-- half integers
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gam0030 gamma 0.5 -> 1.7724538509055161
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gam0031 gamma 1.5 -> 0.88622692545275805
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gam0032 gamma 2.5 -> 1.3293403881791370
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gam0033 gamma 3.5 -> 3.3233509704478426
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gam0034 gamma -0.5 -> -3.5449077018110322
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gam0035 gamma -1.5 -> 2.3632718012073548
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gam0036 gamma -2.5 -> -0.94530872048294190
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gam0037 gamma -3.5 -> 0.27008820585226911
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-- values near 0
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gam0040 gamma 0.1 -> 9.5135076986687306
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gam0041 gamma 0.01 -> 99.432585119150602
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gam0042 gamma 1e-8 -> 99999999.422784343
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gam0043 gamma 1e-16 -> 10000000000000000
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gam0044 gamma 1e-30 -> 9.9999999999999988e+29
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gam0045 gamma 1e-160 -> 1.0000000000000000e+160
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gam0046 gamma 1e-308 -> 1.0000000000000000e+308
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gam0047 gamma 5.6e-309 -> 1.7857142857142848e+308
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gam0048 gamma 5.5e-309 -> inf overflow
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gam0049 gamma 1e-309 -> inf overflow
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gam0050 gamma 1e-323 -> inf overflow
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gam0051 gamma 5e-324 -> inf overflow
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gam0060 gamma -0.1 -> -10.686287021193193
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gam0061 gamma -0.01 -> -100.58719796441078
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gam0062 gamma -1e-8 -> -100000000.57721567
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gam0063 gamma -1e-16 -> -10000000000000000
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gam0064 gamma -1e-30 -> -9.9999999999999988e+29
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gam0065 gamma -1e-160 -> -1.0000000000000000e+160
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gam0066 gamma -1e-308 -> -1.0000000000000000e+308
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gam0067 gamma -5.6e-309 -> -1.7857142857142848e+308
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gam0068 gamma -5.5e-309 -> -inf overflow
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gam0069 gamma -1e-309 -> -inf overflow
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gam0070 gamma -1e-323 -> -inf overflow
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gam0071 gamma -5e-324 -> -inf overflow
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-- values near negative integers
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gam0080 gamma -0.99999999999999989 -> -9007199254740992.0
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gam0081 gamma -1.0000000000000002 -> 4503599627370495.5
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gam0082 gamma -1.9999999999999998 -> 2251799813685248.5
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gam0083 gamma -2.0000000000000004 -> -1125899906842623.5
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gam0084 gamma -100.00000000000001 -> -7.5400833348831090e-145
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gam0085 gamma -99.999999999999986 -> 7.5400833348840962e-145
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-- large inputs
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gam0100 gamma 170 -> 4.2690680090047051e+304
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gam0101 gamma 171 -> 7.2574156153079990e+306
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gam0102 gamma 171.624 -> 1.7942117599248104e+308
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gam0103 gamma 171.625 -> inf overflow
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gam0104 gamma 172 -> inf overflow
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gam0105 gamma 2000 -> inf overflow
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gam0106 gamma 1.7e308 -> inf overflow
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-- inputs for which gamma(x) is tiny
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gam0120 gamma -100.5 -> -3.3536908198076787e-159
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gam0121 gamma -160.5 -> -5.2555464470078293e-286
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gam0122 gamma -170.5 -> -3.3127395215386074e-308
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gam0123 gamma -171.5 -> 1.9316265431711902e-310
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gam0124 gamma -176.5 -> -1.1956388629358166e-321
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gam0125 gamma -177.5 -> 4.9406564584124654e-324
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gam0126 gamma -178.5 -> -0.0
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gam0127 gamma -179.5 -> 0.0
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gam0128 gamma -201.0001 -> 0.0
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gam0129 gamma -202.9999 -> -0.0
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gam0130 gamma -1000.5 -> -0.0
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gam0131 gamma -1000000000.3 -> -0.0
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gam0132 gamma -4503599627370495.5 -> 0.0
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-- inputs that cause problems for the standard reflection formula,
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-- thanks to loss of accuracy in 1-x
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gam0140 gamma -63.349078729022985 -> 4.1777971677761880e-88
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gam0141 gamma -127.45117632943295 -> 1.1831110896236810e-214
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