-- Testcases for functions in math. -- -- Each line takes the form: -- -- -> -- -- where: -- -- is a short name identifying the test, -- -- is the function to be tested (exp, cos, asinh, ...), -- -- is a string representing a floating-point value -- -- is the expected (ideal) output value, again -- represented as a string. -- -- is a list of the floating-point flags required by C99 -- -- The possible flags are: -- -- divide-by-zero : raised when a finite input gives a -- mathematically infinite result. -- -- overflow : raised when a finite input gives a finite result that -- is too large to fit in the usual range of an IEEE 754 double. -- -- invalid : raised for invalid inputs (e.g., sqrt(-1)) -- -- ignore-sign : indicates that the sign of the result is -- unspecified; e.g., if the result is given as inf, -- then both -inf and inf should be accepted as correct. -- -- Flags may appear in any order. -- -- Lines beginning with '--' (like this one) start a comment, and are -- ignored. Blank lines, or lines containing only whitespace, are also -- ignored. -- Many of the values below were computed with the help of -- version 2.4 of the MPFR library for multiple-precision -- floating-point computations with correct rounding. All output -- values in this file are (modulo yet-to-be-discovered bugs) -- correctly rounded, provided that each input and output decimal -- floating-point value below is interpreted as a representation of -- the corresponding nearest IEEE 754 double-precision value. See the -- MPFR homepage at http://www.mpfr.org for more information about the -- MPFR project. --------------------------------------------------------- -- lgamma: log of absolute value of the gamma function -- --------------------------------------------------------- -- special values lgam0000 lgamma 0.0 -> inf divide-by-zero lgam0001 lgamma -0.0 -> inf divide-by-zero lgam0002 lgamma inf -> inf lgam0003 lgamma -inf -> inf lgam0004 lgamma nan -> nan -- negative integers lgam0010 lgamma -1 -> inf divide-by-zero lgam0011 lgamma -2 -> inf divide-by-zero lgam0012 lgamma -1e16 -> inf divide-by-zero lgam0013 lgamma -1e300 -> inf divide-by-zero lgam0014 lgamma -1.79e308 -> inf divide-by-zero -- small positive integers give factorials lgam0020 lgamma 1 -> 0.0 lgam0021 lgamma 2 -> 0.0 lgam0022 lgamma 3 -> 0.69314718055994529 lgam0023 lgamma 4 -> 1.791759469228055 lgam0024 lgamma 5 -> 3.1780538303479458 lgam0025 lgamma 6 -> 4.7874917427820458 -- half integers lgam0030 lgamma 0.5 -> 0.57236494292470008 lgam0031 lgamma 1.5 -> -0.12078223763524522 lgam0032 lgamma 2.5 -> 0.28468287047291918 lgam0033 lgamma 3.5 -> 1.2009736023470743 lgam0034 lgamma -0.5 -> 1.2655121234846454 lgam0035 lgamma -1.5 -> 0.86004701537648098 lgam0036 lgamma -2.5 -> -0.056243716497674054 lgam0037 lgamma -3.5 -> -1.309006684993042 -- values near 0 lgam0040 lgamma 0.1 -> 2.252712651734206 lgam0041 lgamma 0.01 -> 4.5994798780420219 lgam0042 lgamma 1e-8 -> 18.420680738180209 lgam0043 lgamma 1e-16 -> 36.841361487904734 lgam0044 lgamma 1e-30 -> 69.077552789821368 lgam0045 lgamma 1e-160 -> 368.41361487904732 lgam0046 lgamma 1e-308 -> 709.19620864216608 lgam0047 lgamma 5.6e-309 -> 709.77602713741896 lgam0048 lgamma 5.5e-309 -> 709.79404564292167 lgam0049 lgamma 1e-309 -> 711.49879373516012 lgam0050 lgamma 1e-323 -> 743.74692474082133 lgam0051 lgamma 5e-324 -> 744.44007192138122 lgam0060 lgamma -0.1 -> 2.3689613327287886 lgam0061 lgamma -0.01 -> 4.6110249927528013 lgam0062 lgamma -1e-8 -> 18.420680749724522 lgam0063 lgamma -1e-16 -> 36.841361487904734 lgam0064 lgamma -1e-30 -> 69.077552789821368 lgam0065 lgamma -1e-160 -> 368.41361487904732 lgam0066 lgamma -1e-308 -> 709.19620864216608 lgam0067 lgamma -5.6e-309 -> 709.77602713741896 lgam0068 lgamma -5.5e-309 -> 709.79404564292167 lgam0069 lgamma -1e-309 -> 711.49879373516012 lgam0070 lgamma -1e-323 -> 743.74692474082133 lgam0071 lgamma -5e-324 -> 744.44007192138122 -- values near negative integers lgam0080 lgamma -0.99999999999999989 -> 36.736800569677101 lgam0081 lgamma -1.0000000000000002 -> 36.043653389117154 lgam0082 lgamma -1.9999999999999998 -> 35.350506208557213 lgam0083 lgamma -2.0000000000000004 -> 34.657359027997266 lgam0084 lgamma -100.00000000000001 -> -331.85460524980607 lgam0085 lgamma -99.999999999999986 -> -331.85460524980596 -- large inputs lgam0100 lgamma 170 -> 701.43726380873704 lgam0101 lgamma 171 -> 706.57306224578736 lgam0102 lgamma 171.624 -> 709.78077443669895 lgam0103 lgamma 171.625 -> 709.78591682948365 lgam0104 lgamma 172 -> 711.71472580228999 lgam0105 lgamma 2000 -> 13198.923448054265 lgam0106 lgamma 2.55998332785163e305 -> 1.7976931348623099e+308 lgam0107 lgamma 2.55998332785164e305 -> inf overflow lgam0108 lgamma 1.7e308 -> inf overflow -- inputs for which gamma(x) is tiny lgam0120 lgamma -100.5 -> -364.90096830942736 lgam0121 lgamma -160.5 -> -656.88005261126432 lgam0122 lgamma -170.5 -> -707.99843314507882 lgam0123 lgamma -171.5 -> -713.14301641168481 lgam0124 lgamma -176.5 -> -738.95247590846486 lgam0125 lgamma -177.5 -> -744.13144651738037 lgam0126 lgamma -178.5 -> -749.3160351186001 lgam0130 lgamma -1000.5 -> -5914.4377011168517 lgam0131 lgamma -30000.5 -> -279278.6629959144 lgam0132 lgamma -4503599627370495.5 -> -1.5782258434492883e+17 -- results close to 0: positive argument ... lgam0150 lgamma 0.99999999999999989 -> 6.4083812134800075e-17 lgam0151 lgamma 1.0000000000000002 -> -1.2816762426960008e-16 lgam0152 lgamma 1.9999999999999998 -> -9.3876980655431170e-17 lgam0153 lgamma 2.0000000000000004 -> 1.8775396131086244e-16 -- ... and negative argument lgam0160 lgamma -2.7476826467 -> -5.2477408147689136e-11 lgam0161 lgamma -2.457024738 -> 3.3464637541912932e-10 --------------------------- -- gamma: Gamma function -- --------------------------- -- special values gam0000 gamma 0.0 -> inf divide-by-zero gam0001 gamma -0.0 -> -inf divide-by-zero gam0002 gamma inf -> inf gam0003 gamma -inf -> nan invalid gam0004 gamma nan -> nan -- negative integers inputs are invalid gam0010 gamma -1 -> nan invalid gam0011 gamma -2 -> nan invalid gam0012 gamma -1e16 -> nan invalid gam0013 gamma -1e300 -> nan invalid -- small positive integers give factorials gam0020 gamma 1 -> 1 gam0021 gamma 2 -> 1 gam0022 gamma 3 -> 2 gam0023 gamma 4 -> 6 gam0024 gamma 5 -> 24 gam0025 gamma 6 -> 120 -- half integers gam0030 gamma 0.5 -> 1.7724538509055161 gam0031 gamma 1.5 -> 0.88622692545275805 gam0032 gamma 2.5 -> 1.3293403881791370 gam0033 gamma 3.5 -> 3.3233509704478426 gam0034 gamma -0.5 -> -3.5449077018110322 gam0035 gamma -1.5 -> 2.3632718012073548 gam0036 gamma -2.5 -> -0.94530872048294190 gam0037 gamma -3.5 -> 0.27008820585226911 -- values near 0 gam0040 gamma 0.1 -> 9.5135076986687306 gam0041 gamma 0.01 -> 99.432585119150602 gam0042 gamma 1e-8 -> 99999999.422784343 gam0043 gamma 1e-16 -> 10000000000000000 gam0044 gamma 1e-30 -> 9.9999999999999988e+29 gam0045 gamma 1e-160 -> 1.0000000000000000e+160 gam0046 gamma 1e-308 -> 1.0000000000000000e+308 gam0047 gamma 5.6e-309 -> 1.7857142857142848e+308 gam0048 gamma 5.5e-309 -> inf overflow gam0049 gamma 1e-309 -> inf overflow gam0050 gamma 1e-323 -> inf overflow gam0051 gamma 5e-324 -> inf overflow gam0060 gamma -0.1 -> -10.686287021193193 gam0061 gamma -0.01 -> -100.58719796441078 gam0062 gamma -1e-8 -> -100000000.57721567 gam0063 gamma -1e-16 -> -10000000000000000 gam0064 gamma -1e-30 -> -9.9999999999999988e+29 gam0065 gamma -1e-160 -> -1.0000000000000000e+160 gam0066 gamma -1e-308 -> -1.0000000000000000e+308 gam0067 gamma -5.6e-309 -> -1.7857142857142848e+308 gam0068 gamma -5.5e-309 -> -inf overflow gam0069 gamma -1e-309 -> -inf overflow gam0070 gamma -1e-323 -> -inf overflow gam0071 gamma -5e-324 -> -inf overflow -- values near negative integers gam0080 gamma -0.99999999999999989 -> -9007199254740992.0 gam0081 gamma -1.0000000000000002 -> 4503599627370495.5 gam0082 gamma -1.9999999999999998 -> 2251799813685248.5 gam0083 gamma -2.0000000000000004 -> -1125899906842623.5 gam0084 gamma -100.00000000000001 -> -7.5400833348831090e-145 gam0085 gamma -99.999999999999986 -> 7.5400833348840962e-145 -- large inputs gam0100 gamma 170 -> 4.2690680090047051e+304 gam0101 gamma 171 -> 7.2574156153079990e+306 gam0102 gamma 171.624 -> 1.7942117599248104e+308 gam0103 gamma 171.625 -> inf overflow gam0104 gamma 172 -> inf overflow gam0105 gamma 2000 -> inf overflow gam0106 gamma 1.7e308 -> inf overflow -- inputs for which gamma(x) is tiny gam0120 gamma -100.5 -> -3.3536908198076787e-159 gam0121 gamma -160.5 -> -5.2555464470078293e-286 gam0122 gamma -170.5 -> -3.3127395215386074e-308 gam0123 gamma -171.5 -> 1.9316265431711902e-310 gam0124 gamma -176.5 -> -1.1956388629358166e-321 gam0125 gamma -177.5 -> 4.9406564584124654e-324 gam0126 gamma -178.5 -> -0.0 gam0127 gamma -179.5 -> 0.0 gam0128 gamma -201.0001 -> 0.0 gam0129 gamma -202.9999 -> -0.0 gam0130 gamma -1000.5 -> -0.0 gam0131 gamma -1000000000.3 -> -0.0 gam0132 gamma -4503599627370495.5 -> 0.0 -- inputs that cause problems for the standard reflection formula, -- thanks to loss of accuracy in 1-x gam0140 gamma -63.349078729022985 -> 4.1777971677761880e-88 gam0141 gamma -127.45117632943295 -> 1.1831110896236810e-214