Tue Oct 19 11:36:04 2021 fn_test(): Python version: 2.7.17 Test fn(). airy_ai_values_test: Python version: 2.7.17 airy_ai_values stores values of the Airy function Ai(x). X Ai(X) 0.000000 0.3550280538878172 0.100000 0.3292031299435381 0.200000 0.3037031542863820 0.300000 0.2788064819550049 0.400000 0.2547423542956763 0.500000 0.2316936064808335 0.600000 0.2098000616663795 0.700000 0.1891624003981501 0.800000 0.1698463174443649 0.900000 0.1518868036405444 1.000000 0.1352924163128814 airy_ai_values_test: Normal end of execution. airy_ai_prime_values_test: Python version: 2.7.17 airy_ai_prime_values stores values of the derivative of the Airy Ai function. X FX 0.000000 -0.2588194037928068 0.100000 -0.2571304219075862 0.200000 -0.2524054702856195 0.300000 -0.2451463642190548 0.400000 -0.2358320344192082 0.500000 -0.2249105326646839 0.600000 -0.2127932593891585 0.700000 -0.1998511915822805 0.800000 -0.1864128638072717 0.900000 -0.1727638434616347 1.000000 -0.1591474412967932 airy_ai_prime_values_test: Normal end of execution. airy_bi_values_test: Python version: 2.7.17 airy_bi_values stores values of the Airy function Bi(x). X Bi(X) 0.000000 0.6149266274460007 0.100000 0.6598616901941892 0.200000 0.7054642029186612 0.300000 0.7524855850873156 0.400000 0.8017730000135972 0.500000 0.8542770431031556 0.600000 0.9110633416949405 0.700000 0.9733286558781659 0.800000 1.0424221712315609 0.900000 1.1198728131344471 1.000000 1.2074235949528711 airy_bi_values_test: Normal end of execution. airy_bi_prime_values_test: Python version: 2.7.17 airy_bi_prime_values stores values of the derivative of the Airy Bi function. X FX 0.000000 0.4482883573538264 0.100000 0.4515126311496465 0.200000 0.4617892843621509 0.300000 0.4800490287524480 0.400000 0.5072816760506224 0.500000 0.5445725641405923 0.600000 0.5931444786342857 0.700000 0.6544059191721400 0.800000 0.7300069016152518 0.900000 0.8219038903072090 1.000000 0.9324359333927756 airy_bi_prime_values_test: Normal end of execution. arccos_values_test: Python version: 2.7.17 arccos_values stores values of the arc cosine function. X F(X) -0.100000 1.670963747956457 0.000000 1.570796326794897 0.100000 1.470628905633337 0.200000 1.369438406004566 0.300000 1.266103672779499 0.400000 1.159279480727408 0.500000 1.047197551196598 0.600000 0.9272952180016122 0.700000 0.7953988301841436 0.800000 0.6435011087932844 0.900000 0.4510268117962624 1.000000 0 arccos_values_test: Normal end of execution. arccosh_values_test: Python version: 2.7.17 arccosh_values stores values of the hyperbolic arc cosine function. X F(X) 1.000000 0 1.010000 0.1413037694856486 1.100000 0.4435682543851152 1.200000 0.6223625037147786 1.300000 0.7564329108569596 1.400000 0.8670147264905651 1.500000 0.9624236501192069 2.000000 1.316957896924817 3.000000 1.762747174039086 3.141593 1.811526272460853 4.000000 2.06343706889556 5.000000 2.292431669561178 10.000000 2.993222846126381 100.000000 5.298292365610485 1000.000000 7.600902209541989 arccosh_values_test: Normal end of execution. arcsin_values_test: Python version: 2.7.17 arcsin_values stores values of the arc sine function. X F(X) -0.100000 -0.1001674211615598 0.000000 0 0.100000 0.1001674211615598 0.200000 0.2013579207903308 0.300000 0.3046926540153975 0.400000 0.411516846067488 0.500000 0.5235987755982989 0.600000 0.6435011087932844 0.700000 0.7753974966107531 0.800000 0.9272952180016122 0.900000 1.119769514998634 1.000000 1.570796326794897 arcsin_values_test: Normal end of execution. arcsinh_values_test: Python version: 2.7.17 arcsinh_values stores values of the hyperbolic arc sine function. X F(X) -5.000000 -2.312438341272752 -1.000000 -0.881373587019543 0.000000 0 0.100000 0.09983407889920756 0.200000 0.1986901103492414 0.300000 0.2956730475634224 0.400000 0.3900353197707153 0.500000 0.4812118250596035 0.600000 0.5688248987322475 0.700000 0.6526665660823557 0.800000 0.7326682560454109 0.900000 0.8088669356527824 1.000000 0.881373587019543 2.000000 1.44363547517881 3.000000 1.818446459232067 4.000000 2.094712547261101 5.000000 2.312438341272752 10.000000 2.99822295029797 100.000000 5.298342365610589 1000.000000 7.600902709541988 arcsinh_values_test: Normal end of execution. arctan_values_test: Python version: 2.7.17 arctan_values stores values of the arc tangent function. X F(X) 0.000000 0 0.250000 0.2449786631268641 0.333333 0.3217505543966422 0.500000 0.4636476090008061 1.000000 0.7853981633974483 2.000000 1.10714871779409 3.000000 1.249045772398254 4.000000 1.325817663668033 5.000000 1.373400766945016 10.000000 1.471127674303735 20.000000 1.520837931072954 arctan_values_test: Normal end of execution. arctan2_values_test: Python version: 2.7.17 arctan_values stores values of the arc tangent function. X Y F(X,Y) 0.000000 -1.000000 -1.570796326794897 0.500000 -0.866025 -1.047197551196598 0.866025 -0.500000 -0.5235987755982989 1.000000 0.000000 0 0.866025 0.500000 0.5235987755982989 0.500000 0.866025 1.047197551196598 0.000000 1.000000 1.570796326794897 -0.500000 0.866025 2.094395102393196 -0.866025 0.500000 2.617993877991494 -1.000000 0.000000 3.141592653589793 -0.866025 -0.500000 -2.617993877991494 -0.500000 -0.866025 -2.094395102393196 0.000000 -1.000000 -1.570796326794897 0.500000 -0.866025 -1.047197551196598 0.866025 -0.500000 -0.5235987755982989 1.000000 0.000000 0 0.866025 0.500000 0.5235987755982989 0.500000 0.866025 1.047197551196598 0.000000 1.000000 1.570796326794897 arctan2_values_test: Normal end of execution. arctanh_values_test: Python version: 2.7.17 arctanh_values stores values of the hyperbolic arc tangent function. X F(X) -0.500000 -0.5493061443340549 0.000000 0 0.001000 0.001000000333333533 0.100000 0.1003353477310756 0.200000 0.2027325540540822 0.300000 0.3095196042031117 0.400000 0.4236489301936018 0.500000 0.5493061443340549 0.600000 0.6931471805599453 0.700000 0.8673005276940532 0.800000 1.09861228866811 0.900000 1.47221948958322 0.990000 2.646652412362246 0.999000 3.8002011672502 0.999999 7.254328619262047 arctanh_values_test: Normal end of execution. bessel_i0_values_test: Python version: 2.7.17 bessel_i0_values stores values of the Bessel I function. of order 0. X I(0,X) 0.000000 1 0.200000 1.010025027795146 0.400000 1.040401782229341 0.600000 1.09204536431734 0.800000 1.166514922869803 1.000000 1.266065877752008 1.200000 1.393725584134064 1.400000 1.553395099731217 1.600000 1.749980639738909 1.800000 1.989559356618051 2.000000 2.279585302336067 2.500000 3.289839144050123 3.000000 4.880792585865024 3.500000 7.37820343222548 4.000000 11.30192195213633 4.500000 17.48117185560928 5.000000 27.23987182360445 6.000000 67.23440697647798 8.000000 427.5641157218048 10.000000 2815.716628466254 bessel_i0_values_test: Normal end of execution. bessel_i1_values_test: Python version: 2.7.17 bessel_i1_values stores values of the Bessel I function. of order 1. X I(1,X) 0.000000 0 0.200000 0.1005008340281251 0.400000 0.2040267557335706 0.600000 0.3137040256049221 0.800000 0.4328648026206398 1.000000 0.565159103992485 1.200000 0.7146779415526431 1.400000 0.8860919814143274 1.600000 1.08481063512988 1.800000 1.317167230391899 2.000000 1.590636854637329 2.500000 2.516716245288698 3.000000 3.953370217402609 3.500000 6.205834922258365 4.000000 9.759465153704451 4.500000 15.38922275373592 5.000000 24.33564214245053 6.000000 61.34193677764024 8.000000 399.8731367825601 10.000000 2670.988303701255 bessel_i1_values_test: Normal end of execution. bessel_j0_values_test: bessel_j0_values stores values of the Bessel J function. of order 0. X J(0,X) -5.000000 -0.1775967713143383 -4.000000 -0.3971498098638474 -3.000000 -0.2600519549019334 -2.000000 0.2238907791412357 -1.000000 0.7651976865579666 0.000000 1 1.000000 0.7651976865579666 2.000000 0.2238907791412357 3.000000 -0.2600519549019334 4.000000 -0.3971498098638474 5.000000 -0.1775967713143383 6.000000 0.1506452572509969 7.000000 0.3000792705195556 8.000000 0.1716508071375539 9.000000 -0.09033361118287613 10.000000 -0.2459357644513483 11.000000 -0.1711903004071961 12.000000 0.04768931079683354 13.000000 0.2069261023770678 14.000000 0.1710734761104587 15.000000 -0.01422447282678077 bessel_j0_values_test: Normal end of execution. bessel_j1_values_test: bessel_j1_values stores values of the Bessel J function. of order 1. X J(1,X) -5.000000 0.3275791375914652 -4.000000 0.06604332802354913 -3.000000 -0.3390589585259365 -2.000000 -0.5767248077568734 -1.000000 -0.4400505857449335 0.000000 0 1.000000 0.4400505857449335 2.000000 0.5767248077568734 3.000000 0.3390589585259365 4.000000 -0.06604332802354913 5.000000 -0.3275791375914652 6.000000 -0.2766838581275656 7.000000 -0.004682823482345833 8.000000 0.2346363468539146 9.000000 0.2453117865733253 10.000000 0.04347274616886144 11.000000 -0.1767852989567215 12.000000 -0.2234471044906276 13.000000 -0.07031805212177837 14.000000 0.1333751546987933 15.000000 0.2051040386135228 bessel_j1_values_test: Normal end of execution. bessel_k0_values_test: bessel_k0_values stores values of the Bessel K function. of order 0. X K(0,X) 0.100000 2.427069024702017 0.200000 1.752703855528146 0.400000 1.114529134524434 0.600000 0.7775220919047293 0.800000 0.5653471052658957 1.000000 0.4210244382407083 1.200000 0.3185082202865936 1.400000 0.2436550611815419 1.600000 0.1879547519693323 1.800000 0.145931400489828 2.000000 0.1138938727495334 2.500000 0.06234755320036619 3.000000 0.03473950438627925 3.500000 0.01959889717036849 4.000000 0.01115967608585302 4.500000 0.006399857243233975 5.000000 0.003691098334042594 6.000000 0.001243994328013123 8.000000 0.0001464707052228154 10.000000 1.778006231616765e-05 bessel_k0_values_test: Normal end of execution. bessel_k1_values_test: bessel_k1_values stores values of the Bessel K function. of order 1. X K(1,X) 0.100000 9.853844780870606 0.200000 4.775972543220472 0.400000 2.184354424732687 0.600000 1.302834939763502 0.800000 0.8617816344721803 1.000000 0.6019072301972346 1.200000 0.434592391060715 1.400000 0.3208359022298758 1.600000 0.2406339113576119 1.800000 0.182623099801747 2.000000 0.1398658818165224 2.500000 0.07389081634774707 3.000000 0.04015643112819418 3.500000 0.02223939292592383 4.000000 0.01248349888726843 4.500000 0.00707809490896809 5.000000 0.004044613445452164 6.000000 0.001343919717735509 8.000000 0.0001553692118050011 10.000000 1.864877345382558e-05 bessel_k1_values_test: Normal end of execution. bessel_kx_values_test: bessel_kx_values stores values of the Bessel K function. of real order NU. NU X K(NU,X) 0.500000 0.200000 2.294489339798475 0.500000 1.000000 0.4610685044478946 0.500000 2.000000 0.1199377719680614 0.500000 2.500000 0.06506594315400999 0.500000 3.000000 0.03602598513176459 0.500000 5.000000 0.003776613374642883 0.500000 10.000000 1.799347809370518e-05 0.500000 20.000000 5.776373974707445e-10 1.500000 1.000000 0.9221370088957891 1.500000 2.000000 0.1799066579520922 1.500000 5.000000 0.004531936049571459 1.500000 10.000000 1.97928259030757e-05 1.500000 50.000000 3.486992497366216e-23 2.500000 1.000000 3.227479531135262 2.500000 2.000000 0.3897977588961997 2.500000 5.000000 0.006495775004385758 2.500000 10.000000 2.393132586462789e-05 2.500000 50.000000 3.627839645299048e-23 1.250000 1.000000 0.7311451879202114 1.250000 2.000000 0.1567475478393932 1.250000 5.000000 0.004257389528177461 1.250000 10.000000 1.915541065869563e-05 1.250000 50.000000 3.463337593569306e-23 2.750000 1.000000 4.731184839919541 2.750000 2.000000 0.4976876225514758 2.750000 5.000000 0.007300864610941163 2.750000 10.000000 2.546421294106458e-05 2.750000 50.000000 3.675275677913656e-23 bessel_kx_values_test: Normal end of execution. bessel_y0_values_test: bessel_y0_values stores values of the Bessel Y function. of order 0. X Y(0,X) 0.100000 -1.534238651350367 1.000000 0.08825696421567696 2.000000 0.5103756726497451 3.000000 0.3768500100127904 4.000000 -0.01694073932506499 5.000000 -0.3085176252490338 6.000000 -0.2881946839815792 7.000000 -0.02594974396720926 8.000000 0.2235214893875662 9.000000 0.2499366982850247 10.000000 0.05567116728359939 11.000000 -0.1688473238920795 12.000000 -0.2252373126343614 13.000000 -0.07820786452787591 14.000000 0.1271925685821837 15.000000 0.2054642960389183 bessel_y0_values_test: Normal end of execution. bessel_y1_values_test: bessel_y1_values stores values of the Bessel Y function. of order 1. X Y(1,X) 0.100000 -6.458951094702027 1.000000 -0.7812128213002887 2.000000 -0.1070324315409375 3.000000 0.3246744247918 4.000000 0.3979257105571 5.000000 0.1478631433912268 6.000000 -0.1750103443003983 7.000000 -0.3026672370241849 8.000000 -0.1580604617312475 9.000000 0.1043145751967159 10.000000 0.2490154242069539 11.000000 0.1637055374149429 12.000000 -0.05709921826089652 13.000000 -0.2100814084206935 14.000000 -0.1666448418561723 15.000000 0.02107362803687351 bessel_y1_values_test: Normal end of execution. beta_values_test: Python version: 2.7.17 beta_values stores values of the BETA function. X Y BETA(X,Y) 0.200000 1.000000 5 0.400000 1.000000 2.5 0.600000 1.000000 1.666666666666667 0.800000 1.000000 1.25 1.000000 0.200000 5 1.000000 0.400000 2.5 1.000000 1.000000 1 2.000000 2.000000 0.1666666666666667 3.000000 3.000000 0.03333333333333333 4.000000 4.000000 0.007142857142857143 5.000000 5.000000 0.001587301587301587 6.000000 2.000000 0.02380952380952381 6.000000 3.000000 0.005952380952380952 6.000000 4.000000 0.001984126984126984 6.000000 5.000000 0.0007936507936507937 6.000000 6.000000 0.0003607503607503608 7.000000 7.000000 8.325008325008325e-05 beta_values_test: Normal end of execution. beta_inc_values_test: Python version: 2.7.17 beta_inc_values stores values of the BETA function. A B X beta_inc(A,B,X) 0.500000 0.500000 0.010000 0.06376856085851985 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1 1.000000 0.500000 0.000000 0 1.000000 0.500000 0.010000 0.005012562893380045 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5 2.000000 2.000000 0.100000 0.028 2.000000 2.000000 0.200000 0.104 2.000000 2.000000 0.300000 0.216 2.000000 2.000000 0.400000 0.352 2.000000 2.000000 0.500000 0.5 2.000000 2.000000 0.600000 0.648 2.000000 2.000000 0.700000 0.784 2.000000 2.000000 0.800000 0.896 2.000000 2.000000 0.900000 0.972 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.08978271484375 10.000000 5.000000 1.000000 1 10.000000 10.000000 0.500000 0.5 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.36 1.000000 3.000000 0.200000 0.488 1.000000 4.000000 0.200000 0.5904 1.000000 5.000000 0.200000 0.67232 2.000000 2.000000 0.300000 0.216 3.000000 2.000000 0.300000 0.0837 4.000000 2.000000 0.300000 0.03078 5.000000 2.000000 0.300000 0.010935 1.306250 11.756200 0.225609 0.918884684620518 1.306250 11.756200 0.033557 0.21052977489419 1.306250 11.756200 0.029522 0.1824130512500673 beta_inc_values_test: Normal end of execution. beta_log_values_test: beta_log_values stores values of the Log(BETA) function. X Y Log(BETA(X,Y)) 0.200000 1.000000 1.6094379124341 0.400000 1.000000 0.9162907318741551 0.600000 1.000000 0.5108256237659907 0.800000 1.000000 0.2231435513142098 1.000000 0.200000 1.6094379124341 1.000000 0.400000 0.9162907318741551 1.000000 1.000000 0 2.000000 2.000000 -1.791759469228055 3.000000 3.000000 -3.401197381662155 4.000000 4.000000 -4.941642422609304 5.000000 5.000000 -6.445719819385578 6.000000 2.000000 -3.737669618283368 6.000000 3.000000 -5.123963979403259 6.000000 4.000000 -6.222576268071369 6.000000 5.000000 -7.138866999945524 6.000000 6.000000 -7.927324360309794 7.000000 7.000000 -9.39366142910322 beta_log_values_test: Normal end of execution. binomial_values_test: binomial_values stores values of the BINOMIAL function. A B BINOMIAL(A,B) 1 0 1 6 1 6 6 3 20 6 5 6 15 1 15 15 3 455 15 5 3003 15 7 6435 15 9 5005 15 11 1365 15 13 105 25 1 25 25 3 2300 25 5 53130 25 7 480700 25 9 2042975 25 11 4457400 25 13 5200300 25 15 3268760 25 17 1081575 binomial_values_test: Normal end of execution. cbrt_values_test: Python version: 2.7.17 cbrt_values stores values of the cube root function. X CBRT(X) 0.000000 0.0000000000000000 -0.000000 -0.0020082988563383 0.090000 0.4481404746557165 -0.100000 -0.4641588833612779 0.400000 0.7368062997280773 -1.000000 -1.0000000000000000 2.000000 1.2599210498948732 -3.000000 -1.4422495703074083 3.141593 1.4645918875615234 -19.000000 -2.6684016487219449 29.000000 3.0723168256858471 -71.000000 -4.1408177494228529 97.000000 4.5947008922070394 -123456789.000000 -497.9338592181744616 cbrt_values_test: Normal end of execution. chi_values_test: Python version: 2.7.17 chi_values stores values of the hyperbolic cosine integral function. X CHI(X) 0.500000 -0.0527768449564936 0.600000 0.1577508933739787 0.700000 0.3455691756953907 0.800000 0.5183999848333914 0.900000 0.6813138871854340 1.000000 0.8378669409802082 1.200000 1.1418419241705950 1.400000 1.4454940757896440 1.600000 1.7595058076609651 1.800000 2.0925772140620320 2.000000 2.4526669226469151 2.500000 3.5244254883541650 3.000000 4.9603920947656102 3.500000 6.9591919276473932 4.000000 9.8135475588231866 4.500000 13.9658116485924300 chi_values_test: Normal end of execution. ci_values_test: Python version: 2.7.17 ci_values stores values of the cosine integral function. X CI(X) 0.500000 -0.1777840788066129 0.600000 -0.0222707069592798 0.700000 0.1005147070088978 0.800000 0.1982786159524672 0.900000 0.2760678304677729 1.000000 0.3374039229009681 1.200000 0.4204591828942405 1.400000 0.4620065850946773 1.600000 0.4717325169318778 1.800000 0.4568111294183369 2.000000 0.4229808287748650 2.500000 0.2858711963653835 3.000000 0.1196297860080003 3.500000 -0.0321285485124811 4.000000 -0.1409816978869304 4.500000 -0.1934911221017388 ci_values_test: Normal end of execution. cin_values_test: Python version: 2.7.17 cin_values stores values of the alternate cosine integral function. X CIN(X) 0.500000 0.0618525631482005 0.600000 0.0886607480948219 0.700000 0.1200260139539026 0.800000 0.1557934976348559 0.900000 0.1957873187759337 1.000000 0.2398117420005647 1.200000 0.3390780388012470 1.400000 0.4516813164280685 1.600000 0.5754867772153907 1.800000 0.7081912003853150 2.000000 0.8473820166866132 2.500000 1.2076352004103039 3.000000 1.5561981675616421 3.500000 1.8621071819093820 4.000000 2.1044917239083540 4.500000 2.2747841837795462 cin_values_test: Normal end of execution. cinh_values_test: Python version: 2.7.17 cinh_values: values of the alternate hyperbolic cosine integral function. X CINH(X) 0.000000 0.0000000000000000 0.500000 0.0631546707019188 0.600000 0.0913608522384365 0.700000 0.1250284547325902 0.800000 0.1643278712460683 0.900000 0.2094587379417273 1.000000 0.2606512760786754 1.200000 0.3823047024751071 1.400000 0.5318061742668980 1.600000 0.7122865135136963 1.800000 0.9275748842583805 2.000000 1.1823040771854361 2.500000 2.0309190915784781 3.000000 3.2845641411959670 3.500000 5.1292132942504933 4.000000 7.8500375328017622 4.500000 11.8845185869146306 cinh_values_test: Normal end of execution. cos_values_test: Python version: 2.7.17 cos_values stores values of the cosine function. X COS(X) 0.000000 1.0000000000000000 0.261799 0.9659258262890683 0.500000 0.8775825618903728 0.523599 0.8660254037844386 0.785398 0.7071067811865476 1.000000 0.5403023058681398 1.047198 0.5000000000000000 1.570796 0.0000000000000000 2.000000 -0.4161468365471424 3.000000 -0.9899924966004454 3.141593 -1.0000000000000000 4.000000 -0.6536436208636119 5.000000 0.2836621854632262 cos_values_test: Normal end of execution. cos_degree_values_test: Python version: 2.7.17 cos_degree_values stores values of the cosine function. X COS(X) -5.000000 0.9961946980917455 0.000000 1.0000000000000000 1.000000 0.9998476951563913 2.000000 0.9993908270190958 3.000000 0.9986295347545738 4.000000 0.9975640502598242 5.000000 0.9961946980917455 10.000000 0.9848077530122080 15.000000 0.9659258262890683 30.000000 0.8660254037844386 45.000000 0.7071067811865476 60.000000 0.5000000000000000 75.000000 0.2588190451025207 85.000000 0.0871557427476582 86.000000 0.0697564737441253 87.000000 0.0523359562429438 88.000000 0.0348994967025010 89.000000 0.0174524064372835 90.000000 0.0000000000000000 91.000000 -0.0174524064372835 105.000000 -0.2588190451025207 180.000000 -1.0000000000000000 cos_degree_values_test: Normal end of execution. cosh_values_test: Python version: 2.7.17 cosh_values stores values of the hyperbolic cosine function. X COSH(X) -5.000000 74.2099485247878476 -1.000000 1.5430806348152437 0.000000 1.0000000000000000 0.100000 1.0050041680558035 0.200000 1.0200667556190759 0.300000 1.0453385141288605 0.400000 1.0810723718384547 0.500000 1.1276259652063807 0.600000 1.1854652182422678 0.700000 1.2551690056309430 0.800000 1.3374349463048445 0.900000 1.4330863854487743 1.000000 1.5430806348152437 2.000000 3.7621956910836314 3.000000 10.0676619957777653 4.000000 27.3082328360164865 5.000000 74.2099485247878476 10.000000 11013.2329201033226127 cosh_values_test: Normal end of execution. cot_values_test: Python version: 2.7.17 cot_values stores values of the cotangent function. X COT(X) 0.083333 11.9722093536286618 0.261799 3.7320508075688772 0.500000 1.8304877217124520 0.523599 1.7320508075688772 0.785398 1.0000000000000000 1.000000 0.6420926159343308 1.047198 0.5773502691896257 1.308997 0.2679491924311227 1.570796 0.0000000000000000 1.439897 0.1316524975873959 1.505346 0.0655434628152382 2.000000 -0.4576575543602858 3.000000 -7.0152525514345339 4.000000 0.8636911544506166 5.000000 -0.2958129155327455 cot_values_test: Normal end of execution. dawson_values_test: Python version: 2.7.17 dawson_values stores values of the Dawson integral function. X F(X) 0.000000 0.0000000000000000 0.100000 0.0993359923978529 0.200000 0.1947510333680280 0.300000 0.2826316650213119 0.400000 0.3599434819348881 0.500000 0.4244363835020223 0.600000 0.4747632036629779 0.700000 0.5105040575592318 0.800000 0.5321017070563654 0.900000 0.5407243187262987 1.000000 0.5380795069127684 1.100000 0.5262066799705525 1.200000 0.5072734964077396 1.300000 0.4833975173848241 1.400000 0.4565072375268973 1.500000 0.4282490710853986 1.600000 0.3999398943230814 1.700000 0.3725593489740788 1.800000 0.3467727691148722 1.900000 0.3229743193228178 2.000000 0.3013403889237920 dawson_values_test: Normal end of execution. dilogarithm_values_test: Python version: 2.7.17 dilogarithm_values stores values of the dilogarithm function. X F(X) 0.000000 0.0000000000000000 0.050000 0.0506392924644960 0.100000 0.1026177910993911 0.150000 0.1560350339454831 0.200000 0.2110037754397048 0.250000 0.2676526390827326 0.300000 0.3261295100754761 0.350000 0.3866059411605865 0.400000 0.4492829744712817 0.450000 0.5143989891542119 0.500000 0.5822405264650125 0.550000 0.6531576315069018 0.600000 0.7275863077163334 0.650000 0.8060826895177240 0.700000 0.8893776242860387 0.750000 0.9784693929303061 0.800000 1.0747946000082480 0.850000 1.1805811238302550 0.900000 1.2997147230049590 0.950000 1.4406337969700389 1.000000 1.6449340668482260 dilogarithm_values_test: Normal end of execution. e1_values_test: Python version: 2.7.17 e1_values stores values of the exponential integral. X E1(X) 0.500000 0.5597735947761608 0.600000 0.4543795031894021 0.700000 0.3737688432335091 0.800000 0.3105965785455430 0.900000 0.2601839393259996 1.000000 0.2193839343955203 1.100000 0.1859909045360402 1.200000 0.1584084368514626 1.300000 0.1354509578491291 1.400000 0.1162193125713579 1.500000 0.1000195824066327 1.600000 0.0863083336975398 1.700000 0.0746546444012531 1.800000 0.0647131293638689 1.900000 0.0562043781745349 2.000000 0.0489005107080611 e1_values_test: Normal end of execution. ei_values_test: Python version: 2.7.17 ei_values stores values of the exponential integral. X EI(X) 0.500000 0.4542199048631736 0.600000 0.7698812899373594 0.700000 1.0649071946242910 0.800000 1.3473965482123260 0.900000 1.6228117136968669 1.000000 1.8951178163559370 1.100000 2.1673782795634029 1.200000 2.4420922851926519 1.300000 2.7213988802320239 1.400000 3.0072074641506461 1.500000 3.3012854491297978 1.600000 3.6053199490194690 1.700000 3.9209632013549038 1.800000 4.2498675574879341 1.900000 4.5937136869535848 2.000000 4.9542343560018898 ei_values_test: Normal end of execution. erf_values_test: Python version: 2.7.17 erf_values stores values of the error function. X ERF(X) 0.000000 0.0000000000000000 0.100000 0.1124629160182849 0.200000 0.2227025892104785 0.300000 0.3286267594591274 0.400000 0.4283923550466685 0.500000 0.5204998778130465 0.600000 0.6038560908479259 0.700000 0.6778011938374185 0.800000 0.7421009647076605 0.900000 0.7969082124228321 1.000000 0.8427007929497149 1.100000 0.8802050695740817 1.200000 0.9103139782296354 1.300000 0.9340079449406524 1.400000 0.9522851197626488 1.500000 0.9661051464753106 1.600000 0.9763483833446440 1.700000 0.9837904585907746 1.800000 0.9890905016357306 1.900000 0.9927904292352575 2.000000 0.9953222650189527 erf_values_test: Normal end of execution. erfc_values_test: Python version: 2.7.17 erfc_values stores values of the complementary error function. X ERFC(X) 0.000000 1.0000000000000000 0.200000 0.7772974107895215 0.400000 0.5716076449533315 0.600000 0.3961439091520741 0.800000 0.2578990352923395 1.000000 0.1572992070502851 1.200000 0.0896860217703646 1.400000 0.0477148802373512 1.600000 0.0236516166553560 1.800000 0.0109094983642693 2.000000 0.0046777349810473 2.200000 0.0018628462979819 2.400000 0.0006885138966451 2.600000 0.0002360344165293 2.800000 0.0000750131946655 3.000000 0.0000220904969986 3.200000 0.0000060257611518 3.400000 0.0000015219933629 3.600000 0.0000003558629930 3.800000 0.0000000770039275 4.000000 0.0000000154172579 erfc_values_test: Normal end of execution. exp_values_test: Python version: 2.7.17 exp_values stores values of the exponential function. X F(X) -10.000000 0.0000453999297625 -5.000000 0.0067379469990855 -1.000000 0.3678794411714423 0.000000 1.0000000000000000 0.000000 1.0000000099999999 0.000100 1.0001000050001667 0.001000 1.0010005001667084 0.010000 1.0100501670841679 0.100000 1.1051709180756477 0.200000 1.2214027581601699 0.300000 1.3498588075760032 0.400000 1.4918246976412703 0.500000 1.6487212707001282 0.600000 1.8221188003905089 0.700000 2.0137527074704766 0.800000 2.2255409284924674 0.900000 2.4596031111569499 1.000000 2.7182818284590451 2.000000 7.3890560989306504 3.141593 23.1406926327792704 5.000000 148.4131591025765999 10.000000 22026.4657948067178950 20.000000 485165195.4097902774810791 40.000000 235385266837020000.0000000000000000 exp_values_test: Normal end of execution. gamma_values_test(): Python version: 2.7.17 gamma_values stores values of the Gamma function. X GAMMA(X) -0.500000 -3.5449077018110322 -0.010000 -100.5871979644108052 0.010000 99.4325851191506018 0.100000 9.5135076986687324 0.200000 4.5908437119988026 0.400000 2.2181595437576882 0.500000 1.7724538509055161 0.600000 1.4891922488128171 0.800000 1.1642297137253030 1.000000 1.0000000000000000 1.100000 0.9513507698668732 1.200000 0.9181687423997607 1.300000 0.8974706963062772 1.400000 0.8872638175030753 1.500000 0.8862269254527581 1.600000 0.8935153492876903 1.700000 0.9086387328532904 1.800000 0.9313837709802427 1.900000 0.9617658319073874 2.000000 1.0000000000000000 3.000000 2.0000000000000000 4.000000 6.0000000000000000 10.000000 362880.0000000000000000 20.000000 121645100408832000.0000000000000000 30.000000 8841761993739701898620088352768.0000000000000000 gamma_values_test: Normal end of execution. gamma_inc_values_test: Python version: 2.7.17 gamma_inc_values stores values of the incomplete Gamma function. A X gamma_inc(A,X) 0.100000 0.030000 2.49030283630057 0.100000 0.300000 0.8718369702247978 0.100000 1.500000 0.1079213896175866 0.500000 0.075000 1.238121685818417 0.500000 0.750000 0.3911298052193973 0.500000 3.500000 0.01444722098952533 1.000000 0.100000 0.9048374180359596 1.000000 1.000000 0.3678794411714423 1.000000 5.000000 0.006737946999085467 1.100000 0.100000 0.8827966752611692 1.100000 1.000000 0.3908330082003269 1.100000 5.000000 0.008051456628620992 2.000000 0.150000 0.9898141728888165 2.000000 1.500000 0.5578254003710746 2.000000 7.000000 0.00729505572443613 6.000000 2.500000 114.9574754165633 6.000000 12.000000 2.440923530031405 11.000000 16.000000 280854.6620274718 26.000000 25.000000 8.576480283455533e+24 41.000000 45.000000 2.085031346403364e+47 gamma_inc_values_test: Normal end of execution. gamma_inc_tricomi_values_test: Python version: 2.7.17 gamma_inc_tricomi_values stores values of an incomplete Gamma function. A X F(A,X) 0.100000 0.030000 1.048292641463504 0.100000 0.300000 1.024577737369574 0.100000 1.500000 0.9493712443185374 0.500000 0.075000 1.100793230316492 0.500000 0.750000 0.8998911979655217 0.500000 3.500000 0.5301656062431039 1.000000 0.100000 0.9516258196404043 1.000000 1.000000 0.6321205588285577 1.000000 5.000000 0.1986524106001829 1.100000 0.100000 0.9071784510537487 1.100000 1.000000 0.5891809618706485 1.100000 5.000000 0.1688269752193589 2.000000 0.150000 0.4527034271637121 2.000000 1.500000 0.1965220442795224 2.000000 7.000000 0.02025928457705232 6.000000 2.500000 0.0001721181724479739 6.000000 12.000000 3.280858070850586e-07 11.000000 16.000000 5.24439647182159e-14 26.000000 25.000000 2.013462926183376e-37 41.000000 45.000000 1.230623887499875e-68 gamma_inc_tricomi_values_test: Normal end of execution. gamma_log_values_test(): Python version: 2.7.17 gamma_log_values stores values of the logarithm of the Gamma function. X gamma_log(X) 0.200000 1.5240638224307841 0.400000 0.7966778177017837 0.600000 0.3982338580692348 0.800000 0.1520596783998375 1.000000 0.0000000000000000 1.100000 -0.0498724412598397 1.200000 -0.0853740900033158 1.300000 -0.1081748095078604 1.400000 -0.1196129141723712 1.500000 -0.1207822376352452 1.600000 -0.1125917656967557 1.700000 -0.0958076974070659 1.800000 -0.0710838729143722 1.900000 -0.0389842759230833 2.000000 0.0000000000000000 3.000000 0.6931471805599453 4.000000 1.7917594692280550 10.000000 12.8018274800814691 20.000000 39.3398841871994946 30.000000 71.2570389671680147 gamma_log_values_test: Normal end of execution. hypergeometric_u_values_test: Python version: 2.7.17 hypergeometric_u_values stores values of the Hypergeometric U function. A B X F -2.500000 3.300000 0.250000 -68.69362872807861 -0.500000 1.100000 0.250000 -0.002971055137476107 0.500000 1.100000 0.250000 1.50086317421778 2.500000 3.300000 0.250000 20.6146882442006 -2.500000 3.300000 1.550000 7.456381546930555 -0.500000 1.100000 1.550000 1.015579376774929 0.500000 1.100000 1.550000 0.7344653893662267 2.500000 3.300000 1.550000 0.280464049418794 -2.500000 3.300000 2.850000 3.450815374144655 -0.500000 1.100000 2.850000 1.515663736875306 0.500000 1.100000 2.850000 0.56042118587935 2.500000 3.300000 2.850000 0.06489714773513422 0.825000 6.700000 0.250000 223432.0235697746 1.100000 6.700000 0.250000 263079.2598074081 1.650000 6.700000 0.250000 269802.9031935128 3.300000 6.700000 0.250000 82809.31133560656 0.825000 6.700000 1.550000 26.46568478313185 1.100000 6.700000 1.550000 28.09350617251606 1.650000 6.700000 1.550000 23.88916462451887 3.300000 6.700000 1.550000 4.533884785707039 0.825000 6.700000 2.850000 3.022446936269484 1.100000 6.700000 2.850000 2.804065091371336 1.650000 6.700000 2.850000 1.926257811148017 3.300000 6.700000 2.850000 0.2302051811586091 hypergeometric_u_values_test: Normal end of execution. int_values_test: Python version: 2.7.17 int_values stores values of the integer part function. X INT(X) -2.010000 -2.0000000000000000 -1.990000 -1.0000000000000000 -1.500000 -1.0000000000000000 -1.100000 -1.0000000000000000 -1.010000 -1.0000000000000000 -1.000000 -1.0000000000000000 -0.990000 0.0000000000000000 -0.900000 0.0000000000000000 -0.510000 0.0000000000000000 -0.500000 0.0000000000000000 -0.490000 0.0000000000000000 -0.010000 0.0000000000000000 0.000000 0.0000000000000000 0.010000 0.0000000000000000 0.490000 0.0000000000000000 0.500000 0.0000000000000000 0.510000 0.0000000000000000 0.900000 0.0000000000000000 0.990000 0.0000000000000000 1.000000 1.0000000000000000 1.010000 1.0000000000000000 1.100000 1.0000000000000000 1.500000 1.0000000000000000 1.990000 1.0000000000000000 2.010000 2.0000000000000000 int_values_test: Normal end of execution. log_values_test: Python version: 2.7.17 log_values stores values of the LOG function. X LOG(X) 0.000010 -11.5129254649702286 0.010000 -4.6051701859880918 0.100000 -2.3025850929940459 0.200000 -1.6094379124341003 0.300000 -1.2039728043259359 0.400000 -0.9162907318741551 0.500000 -0.6931471805599453 0.600000 -0.5108256237659907 0.700000 -0.3566749439387324 0.800000 -0.2231435513142098 0.900000 -0.1053605156578263 1.000000 0.0000000000000000 2.000000 0.6931471805599453 3.000000 1.0986122886681098 3.141593 1.1447298858494002 5.000000 1.6094379124341003 10.000000 2.3025850929940459 20.000000 2.9957322735539909 100.000000 4.6051701859880918 123456789.000000 18.6314017661680182 log_values_test: Normal end of execution. log10_values_test: Python version: 2.7.17 log10_values stores values of the LOG10 function. X LOG10(X) 0.000010 -5.0000000000000000 0.010000 -2.0000000000000000 0.100000 -1.0000000000000000 0.200000 -0.6989700043360189 0.300000 -0.5228787452803375 0.400000 -0.3979400086720376 0.500000 -0.3010299956639812 0.600000 -0.2218487496163564 0.700000 -0.1549019599857432 0.800000 -0.0969100130080564 0.900000 -0.0457574905606751 1.000000 0.0000000000000000 2.000000 0.3010299956639812 3.000000 0.4771212547196624 3.141593 0.4971498726941339 5.000000 0.6989700043360189 10.000000 1.0000000000000000 20.000000 1.3010299956639813 100.000000 2.0000000000000000 123456789.000000 8.0915149771692700 log10_values_test: Normal end of execution. logarithmic_integral_values_test: Python version: 2.7.17 logarithmic_integral_values stores values of the logarithmic_integral function. X logarithmic_integral(X) 0.000000 0.0000000000000000 0.100000 -0.0323897895932910 0.200000 -0.0851264867287941 0.300000 -0.1574149028946895 0.400000 -0.2529494192126213 0.500000 -0.3786710430610880 0.600000 -0.5468514142104171 0.700000 -0.7809468775455607 0.800000 -1.1340119573823271 0.900000 -1.7758006834235249 0.950000 -2.4436225538732250 0.975000 -3.1241900505072109 1.031250 -2.8729355103291199 1.062500 -2.1642825241382071 1.125000 -1.4403512962794081 1.250000 -0.6864884538258716 1.500000 0.1250649863152964 2.000000 1.0451637801174929 4.000000 2.9675850950390510 8.000000 5.2537182995589307 16.000000 8.5197164637110596 32.000000 13.6050921770917199 64.000000 21.9346683280510000 128.000000 36.0425483172294392 256.000000 60.5130653379173324 512.000000 103.7211171690372993 1024.000000 181.0780396816944915 2048.000000 321.1144156746836984 logarithmic_integral_values_test: Normal end of execution. psi_values_test: Python version: 2.7.17 psi_values stores values of the PSI function. X PSI(X) 0.100000 -10.4237549404110794 0.200000 -5.2890398965921879 0.300000 -3.5025242222001332 0.400000 -2.5613845445851160 0.500000 -1.9635100260214231 0.600000 -1.5406192138931900 0.700000 -1.2200235536979349 0.800000 -0.9650085667061385 0.900000 -0.7549269499470515 1.000000 -0.5772156649015329 1.100000 -0.4237549404110768 1.200000 -0.2890398965921883 1.300000 -0.1691908888667997 1.400000 -0.0613845445851161 1.500000 0.0364899739785765 1.600000 0.1260474527734763 1.700000 0.2085478748734940 1.800000 0.2849914332938615 1.900000 0.3561841611640597 2.000000 0.4227843350984671 psi_values_test: Normal end of execution. r8_factorial_values_test: Python version: 2.7.17 r8_factorial_values() returns values of the real factorial function. N r8_factorial(N) 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3.6288e+06 11 3.99168e+07 12 4.79002e+08 13 6.22702e+09 14 8.71783e+10 15 1.30767e+12 16 2.09228e+13 17 3.55687e+14 18 6.40237e+15 19 1.21645e+17 20 2.4329e+18 25 1.55112e+25 50 3.04141e+64 100 9.33262e+157 150 5.71338e+262 r8_factorial_values_test: Normal end of execution. r8_rise_values_test: Python version: 2.7.17 r8_rise_values() returns values of the rising factorial. X N r8_rise(X,N) 5.0000 4 1680 5.2500 4 1962.59765625 5.5000 4 2279.0625 5.7500 4 2631.97265625 6.0000 4 3024 7.5000 0 1 7.5000 1 7.5 7.5000 2 63.75 7.5000 3 605.625 7.5000 4 6359.0625 7.5000 5 73129.21875 7.5000 6 914115.234375 7.5000 7 12340555.6640625 7.5000 8 178938057.1289063 7.5000 9 2773539885.498047 r8_rise_values_test: Normal end of execution. shi_values_test: Python version: 2.7.17 shi_values stores values of the SHI function. X SHI(X) 0.500000 0.5069967498196672 0.600000 0.6121303965633808 0.700000 0.7193380189288998 0.800000 0.8289965633789345 0.900000 0.9414978265114335 1.000000 1.0572508753757290 1.200000 1.3002503610220570 1.400000 1.5617133883610019 1.600000 1.8458141413585041 1.800000 2.1572903434259012 2.000000 2.5015674333549760 2.500000 3.5493404062244349 3.000000 4.9734404758598068 3.500000 6.9661620675049418 4.000000 9.8173269112330335 4.500000 13.9678850493471494 shi_values_test: Normal end of execution. si_values_test: Python version: 2.7.17 si_values stores values of the SI function. X SI(X) 0.500000 0.4931074180430667 0.600000 0.5881288096080801 0.700000 0.6812222391166113 0.800000 0.7720957854819966 0.900000 0.8604707107452929 1.000000 0.9460830703671830 1.200000 1.1080471990137191 1.400000 1.2562267327792180 1.600000 1.3891804858704380 1.800000 1.5058167802555791 2.000000 1.6054129768026950 2.500000 1.7785201734438270 3.000000 1.8486525279994681 3.500000 1.8331253986659970 4.000000 1.7582031389490529 4.500000 1.6541404143792440 si_values_test: Normal end of execution. sin_values_test: Python version: 2.7.17 sin_values stores values of the SIN function. X SIN(X) 0.000000 0.0000000000000000 0.261799 0.2588190451025207 0.500000 0.4794255386042030 0.523599 0.5000000000000000 0.785398 0.7071067811865476 1.000000 0.8414709848078965 1.047198 0.8660254037844386 1.570796 1.0000000000000000 2.000000 0.9092974268256817 3.000000 0.1411200080598672 3.141593 0.0000000000000000 4.000000 -0.7568024953079282 5.000000 -0.9589242746631385 sin_values_test: Normal end of execution. sin_degree_values_test: Python version: 2.7.17 sin_degree_values stores values of the SIN function. X SIN(X) -5.000000 -0.0871557427476582 0.000000 0.0000000000000000 1.000000 0.0174524064372835 2.000000 0.0348994967025010 3.000000 0.0523359562429438 4.000000 0.0697564737441253 5.000000 0.0871557427476582 10.000000 0.1736481776669304 15.000000 0.2588190451025207 30.000000 0.5000000000000000 45.000000 0.7071067811865476 60.000000 0.8660254037844386 75.000000 0.9659258262890683 85.000000 0.9961946980917455 86.000000 0.9975640502598242 87.000000 0.9986295347545738 88.000000 0.9993908270190958 89.000000 0.9998476951563913 90.000000 1.0000000000000000 91.000000 0.9998476951563913 105.000000 0.9659258262890683 180.000000 0.0000000000000000 sin_degree_values_test: Normal end of execution. sinh_values_test: Python version: 2.7.17 sinh_values stores values of the SINH function. X SINH(X) -5.000000 -74.2032105777887523 -1.000000 -1.1752011936438014 0.000000 0.0000000000000000 0.100000 0.1001667500198440 0.200000 0.2013360025410940 0.300000 0.3045202934471426 0.400000 0.4107523258028155 0.500000 0.5210953054937474 0.600000 0.6366535821482413 0.700000 0.7585837018395335 0.800000 0.8881059821876230 0.900000 1.0265167257081753 1.000000 1.1752011936438014 2.000000 3.6268604078470186 3.000000 10.0178749274099026 4.000000 27.2899171971277532 5.000000 74.2032105777887523 10.000000 11013.2328747033934633 sinh_values_test: Normal end of execution. sqrt_values_test: Python version: 2.7.17 sqrt_values stores values of the SQRT function. X SQRT(X) 0.000000 0.0000000000000000 0.000000 0.0000900000004095 0.090000 0.3000000000000000 0.100000 0.3162277660168379 0.400000 0.6324555320336759 1.000000 1.0000000000000000 2.000000 1.4142135623730949 3.000000 1.7320508075688770 3.141593 1.7724538509055161 19.000000 4.3588989435406740 29.000000 5.3851648071345037 71.000000 8.4261497731763590 97.000000 9.8488578017961057 123456789.000000 11111.1110605555604707 sqrt_values_test: Normal end of execution. tan_values_test: Python version: 2.7.17 tan_values stores values of the TAN function. X TAN(X) 0 0 0.261799 0.2679491924311227 0.5 0.5463024898437905 0.523599 0.5773502691896257 0.785398 1 1 1.557407724654902 1.0472 1.732050807568877 1.309 3.732050807568877 1.4399 7.59575411272515 1.50535 15.25705168826554 2 -2.185039863261519 3 -0.1425465430742778 3.14159 0 4 1.157821282349577 5 -3.380515006246586 tan_values_test: Normal end of execution. tanh_values_test: Python version: 2.7.17 tanh_values stores values of the TANH function. X TANH(X) -5 -0.9999092042625951 -1 -0.7615941559557649 0 0 0.1 0.09966799462495582 0.2 0.197375320224904 0.3 0.2913126124515909 0.4 0.3799489622552249 0.5 0.4621171572600097 0.6 0.5370495669980353 0.7 0.6043677771171635 0.8 0.664036770267849 0.9 0.7162978701990245 1 0.7615941559557649 2 0.9640275800758169 3 0.9950547536867305 4 0.999329299739067 5 0.9999092042625951 10 0.9999999958776927 tanh_values_test: Normal end of execution. i4_mach_test Python version: 2.7.17 i4_mach reports the value of constants associated with integer computer arithmetic. Numbers associated with input/output units: i4_mach(1) = the standard input unit. 5 i4_mach(2) = the standard output unit. 6 i4_mach(3) = the standard punch unit. 7 i4_mach(4) = the standard error message unit. 6 Numbers associated with words: i4_mach(5) = the number of bits per integer. 32 i4_mach(6) = the number of characters per integer. 4 Numbers associated with integer values: Assume integers are represented in the S digit base A form: Sign * (X(S-1)*A^(S-1) + ... + X(1)*A + X(0)) where the digits X satisfy 0 <= X(1:S-1) < A. i4_mach(7) = A, the base. 2 i4_mach(8) = S, the number of base A digits. 31 i4_mach(9) = A^S-1, the largest integer. 2147483647 Numbers associated with floating point values: Assume floating point numbers are represented in the T digit base B form: Sign * (B^E) * ((X(1)/B) + ... + (X(T)/B^T) ) where 0 <= X(1:T) < B, 0 < X(1) (unless the value being represented is 0), EMIN <= E <= EMAX. i4_mach(10) = B, the base. 2 Numbers associated with single precision values: i4_mach(11) = T, the number of base B digits. 24 i4_mach(12) = EMIN, the smallest exponent E. -125 i4_mach(13) = EMAX, the largest exponent E. 128 Numbers associated with double precision values: i4_mach(14) = T, the number of base B digits. 53 i4_mach(15) = EMIN, the smallest exponent E. -1021 i4_mach(16) = EMAX, the largest exponent E. 1024 i4_mach_test Normal end of execution. r8_acos_test: Python version: 2.7.17 r8_acos evaluates the arc-cosine function X ARCCOS(X) r8_acos(X) Diff -0.1 1.67096 1.67096 2.22045e-16 0 1.5708 1.5708 0 0.1 1.47063 1.47063 0 0.2 1.36944 1.36944 2.22045e-16 0.3 1.2661 1.2661 2.22045e-16 0.4 1.15928 1.15928 0 0.5 1.0472 1.0472 0 0.6 0.927295 0.927295 0 0.7 0.795399 0.795399 0 0.8 0.643501 0.643501 1.11022e-16 0.9 0.451027 0.451027 5.55112e-17 1 0 0 0 r8_acos_test: Normal end of execution. r8_acosh_test: Python version: 2.7.17 r8_acosh evaluates the hyperbolic arccosine function X arccosh(X) r8_acosh(X) Diff 1 0 0 0 1.01 0.141304 0.141304 8.32667e-17 1.1 0.443568 0.443568 1.11022e-16 1.2 0.622363 0.622363 1.11022e-16 1.3 0.756433 0.756433 0 1.4 0.867015 0.867015 1.11022e-16 1.5 0.962424 0.962424 0 2 1.31696 1.31696 2.22045e-16 3 1.76275 1.76275 0 3.142 1.81153 1.81153 0 4 2.06344 2.06344 4.44089e-16 5 2.29243 2.29243 0 10 2.99322 2.99322 0 100 5.29829 5.29829 0 1000 7.6009 7.6009 0 r8_acosh_test: Normal end of execution. r8_ai_test: Python version: 2.7.17 r8_ai evaluates the Airy function Ai(X) X airy_ai(X) r8_ai(X) Diff 0 0.355028 0.355028 0 0.1 0.329203 0.329203 0 0.2 0.303703 0.303703 0 0.3 0.278806 0.278806 5.55112e-17 0.4 0.254742 0.254742 5.55112e-17 0.5 0.231694 0.231694 5.55112e-17 0.6 0.2098 0.2098 8.32667e-17 0.7 0.189162 0.189162 2.77556e-17 0.8 0.169846 0.169846 1.38778e-16 0.9 0.151887 0.151887 8.32667e-17 1 0.135292 0.135292 8.32667e-17 r8_ai_test: Normal end of execution. r8_aid_test: Python version: 2.7.17 r8_aid evaluates the derivative of the Airy function Ai(x) X airy_aid(X) r8_aid(X) Diff 0.0000 -0.258819 -0.258819 0 0.1000 -0.25713 -0.25713 1.11022e-16 0.2000 -0.252405 -0.252405 1.66533e-16 0.3000 -0.245146 -0.245146 3.88578e-16 0.4000 -0.235832 -0.235832 5.82867e-16 0.5000 -0.224911 -0.224911 6.66134e-16 0.6000 -0.212793 -0.212793 1.11022e-16 0.7000 -0.199851 -0.199851 1.41553e-15 0.8000 -0.186413 -0.186413 3.02536e-15 0.9000 -0.172764 -0.172764 9.4369e-16 1.0000 -0.159147 -0.159147 4.7462e-15 r8_aid_test: Normal end of execution. r8_aint_test: Python version: 2.7.17 r8_aint rounds an R8 towards 0. X AINT(X) r8_aint(X) Diff -2.0100 -2 -2 0 -1.9900 -1 -1 0 -1.5000 -1 -1 0 -1.1000 -1 -1 0 -1.0100 -1 -1 0 -1.0000 -1 -1 0 -0.9900 0 -0 0 -0.9000 0 -0 0 -0.5100 0 -0 0 -0.5000 0 -0 0 -0.4900 0 -0 0 -0.0100 0 -0 0 0.0000 0 0 0 0.0100 0 0 0 0.4900 0 0 0 0.5000 0 0 0 0.5100 0 0 0 0.9000 0 0 0 0.9900 0 0 0 1.0000 1 1 0 1.0100 1 1 0 1.1000 1 1 0 1.5000 1 1 0 1.9900 1 1 0 2.0100 2 2 0 r8_aint_test: Normal end of execution. r8_asin_test: Python version: 2.7.17 r8_asin evaluates the arc-sine function X arcsin(X) r8_asin(X) Diff -0.1000 -0.100167 -0.100167 0 0.0000 0 0 0 0.1000 0.100167 0.100167 0 0.2000 0.201358 0.201358 0 0.3000 0.304693 0.304693 0 0.4000 0.411517 0.411517 5.55112e-17 0.5000 0.523599 0.523599 1.11022e-16 0.6000 0.643501 0.643501 0 0.7000 0.775397 0.775397 1.11022e-16 0.8000 0.927295 0.927295 1.11022e-16 0.9000 1.11977 1.11977 0 1.0000 1.5708 1.5708 0 r8_asin_test: Normal end of execution. r8_asinh_test: Python version: 2.7.17 r8_asinh evaluates the arc hyperbolic sine function X arcsinH(X) r8_asinh(X) Diff -5.0000 -2.31244 -2.31244 0 -1.0000 -0.881374 -0.881374 0 0.0000 0 0 0 0.1000 0.0998341 0.0998341 1.38778e-17 0.2000 0.19869 0.19869 0 0.3000 0.295673 0.295673 0 0.4000 0.390035 0.390035 5.55112e-17 0.5000 0.481212 0.481212 5.55112e-17 0.6000 0.568825 0.568825 0 0.7000 0.652667 0.652667 0 0.8000 0.732668 0.732668 1.11022e-16 0.9000 0.808867 0.808867 0 1.0000 0.881374 0.881374 0 2.0000 1.44364 1.44364 0 3.0000 1.81845 1.81845 0 4.0000 2.09471 2.09471 0 5.0000 2.31244 2.31244 0 10.0000 2.99822 2.99822 0 100.0000 5.29834 5.29834 0 1000.0000 7.6009 7.6009 0 r8_asinh_test: Normal end of execution. r8_atan_test: Python version: 2.7.17 r8_atan evaluates the arc tangent function. X arctan(X) r8_atan(X) Diff 0 0 0 0 0.25 0.244979 0.244979 1.38778e-16 0.3333 0.321751 0.321751 5.55112e-17 0.5 0.463648 0.463648 0 1 0.785398 0.785398 0 2 1.10715 1.10715 2.22045e-16 3 1.24905 1.24905 0 4 1.32582 1.32582 2.22045e-16 5 1.3734 1.3734 2.22045e-16 10 1.47113 1.47113 0 20 1.52084 1.52084 0 r8_atan_test: Normal end of execution. r8_atan2_test: Python version: 2.7.17 r8_atan2 evaluates the arctangent function X Y arctan2(Y,X) r8_atan2(Y,X) Diff 0 -1.0000 -1.5708 -1.5708 0 0.5 -0.8660 -1.0472 -1.0472 2.22045e-16 0.866 -0.5000 -0.523599 -0.523599 1.11022e-16 1 0.0000 0 0 0 0.866 0.5000 0.523599 0.523599 1.11022e-16 0.5 0.8660 1.0472 1.0472 2.22045e-16 0 1.0000 1.5708 1.5708 0 -0.5 0.8660 2.0944 2.0944 0 -0.866 0.5000 2.61799 2.61799 4.44089e-16 -1 0.0000 3.14159 3.14159 0 -0.866 -0.5000 -2.61799 -2.61799 4.44089e-16 -0.5 -0.8660 -2.0944 -2.0944 0 0 -1.0000 -1.5708 -1.5708 0 0.5 -0.8660 -1.0472 -1.0472 2.22045e-16 0.866 -0.5000 -0.523599 -0.523599 1.11022e-16 1 0.0000 0 0 0 0.866 0.5000 0.523599 0.523599 1.11022e-16 0.5 0.8660 1.0472 1.0472 2.22045e-16 0 1.0000 1.5708 1.5708 0 r8_atan2_test: Normal end of execution. r8_atanh_test: Python version: 2.7.17 r8_atanh evaluates the hyperbolic arctangent function. X arctanH(X) r8_atanh(X) Diff -0.500000 -0.549306 -0.549306 1.11022e-16 0.000000 0 0 0 0.001000 0.001 0.001 2.1684e-19 0.100000 0.100335 0.100335 0 0.200000 0.202733 0.202733 0 0.300000 0.30952 0.30952 0 0.400000 0.423649 0.423649 5.55112e-17 0.500000 0.549306 0.549306 1.11022e-16 0.600000 0.693147 0.693147 0 0.700000 0.867301 0.867301 0 0.800000 1.09861 1.09861 0 0.900000 1.47222 1.47222 2.22045e-16 0.990000 2.64665 2.64665 4.44089e-16 0.999000 3.8002 3.8002 0 0.999999 7.25433 7.25433 1.43778e-11 r8_atanh_test: Normal end of execution. r8_besi0_test: Python version: 2.7.17 r8_besi0 evaluates the Bessel I0(x) function. X BESI0(X) r8_besi0(X) Diff 0.0000 1 1 0 0.2000 1.01003 1.01003 2.22045e-16 0.4000 1.0404 1.0404 8.88178e-16 0.6000 1.09205 1.09205 0 0.8000 1.16651 1.16651 6.66134e-16 1.0000 1.26607 1.26607 2.22045e-16 1.2000 1.39373 1.39373 8.88178e-16 1.4000 1.5534 1.5534 2.22045e-16 1.6000 1.74998 1.74998 2.22045e-16 1.8000 1.98956 1.98956 4.44089e-16 2.0000 2.27959 2.27959 4.44089e-16 2.5000 3.28984 3.28984 4.44089e-16 3.0000 4.88079 4.88079 0 3.5000 7.3782 7.3782 8.88178e-16 4.0000 11.3019 11.3019 1.77636e-15 4.5000 17.4812 17.4812 3.55271e-15 5.0000 27.2399 27.2399 7.10543e-15 6.0000 67.2344 67.2344 1.42109e-14 8.0000 427.564 427.564 5.68434e-14 10.0000 2815.72 2815.72 4.54747e-13 r8_besi0_test: Normal end of execution. r8_besi1_test: Python version: 2.7.17 r8_besi1 evaluates the Bessel I1(x) function X BESI1(X) r8_besi1(X) Diff 0.0000 0 0 0 0.2000 0.100501 0.100501 1.38778e-17 0.4000 0.204027 0.204027 2.77556e-17 0.6000 0.313704 0.313704 5.55112e-17 0.8000 0.432865 0.432865 5.55112e-17 1.0000 0.565159 0.565159 0 1.2000 0.714678 0.714678 0 1.4000 0.886092 0.886092 2.22045e-16 1.6000 1.08481 1.08481 4.44089e-16 1.8000 1.31717 1.31717 0 2.0000 1.59064 1.59064 0 2.5000 2.51672 2.51672 4.44089e-16 3.0000 3.95337 3.95337 4.44089e-16 3.5000 6.20583 6.20583 0 4.0000 9.75947 9.75947 1.77636e-15 4.5000 15.3892 15.3892 3.55271e-15 5.0000 24.3356 24.3356 3.55271e-15 6.0000 61.3419 61.3419 7.10543e-15 8.0000 399.873 399.873 0 10.0000 2670.99 2670.99 4.54747e-13 r8_besi1_test: Normal end of execution. r8_besj0_test: Python version: 2.7.17 r8_besj0 evaluates the Bessel J0(x) function X BESJ0(X) r8_besj0(X) Diff -5 -0.177597 -0.177597 1.38778e-16 -4 -0.39715 -0.39715 1.05471e-15 -3 -0.260052 -0.260052 1.05471e-15 -2 0.223891 0.223891 5.55112e-16 -1 0.765198 0.765198 8.88178e-16 0 1 1 0 1 0.765198 0.765198 8.88178e-16 2 0.223891 0.223891 5.55112e-16 3 -0.260052 -0.260052 1.05471e-15 4 -0.39715 -0.39715 1.05471e-15 5 -0.177597 -0.177597 1.38778e-16 6 0.150645 0.150645 5.55112e-17 7 0.300079 0.300079 0 8 0.171651 0.171651 2.77556e-17 9 -0.0903336 -0.0903336 2.91434e-16 10 -0.245936 -0.245936 5.55112e-17 11 -0.17119 -0.17119 5.55112e-17 12 0.0476893 0.0476893 2.70617e-16 13 0.206926 0.206926 8.32667e-17 14 0.171073 0.171073 0 15 -0.0142245 -0.0142245 1.30104e-16 r8_besj0_test: Normal end of execution. r8_besj1_test: Python version: 2.7.17 r8_besj1 evaluates the Bessel J1(x) function X BESJ1(X) r8_besj1(X) Diff -5.0000 0.327579 0.327579 1.11022e-16 -4.0000 0.0660433 0.0660433 6.93889e-17 -3.0000 -0.339059 -0.339059 1.11022e-16 -2.0000 -0.576725 -0.576725 1.11022e-16 -1.0000 -0.440051 -0.440051 0 0.0000 0 0 0 1.0000 0.440051 0.440051 0 2.0000 0.576725 0.576725 1.11022e-16 3.0000 0.339059 0.339059 1.11022e-16 4.0000 -0.0660433 -0.0660433 6.93889e-17 5.0000 -0.327579 -0.327579 1.11022e-16 6.0000 -0.276684 -0.276684 0 7.0000 -0.00468282 -0.00468282 9.28077e-17 8.0000 0.234636 0.234636 0 9.0000 0.245312 0.245312 2.77556e-17 10.0000 0.0434727 0.0434727 5.55112e-17 11.0000 -0.176785 -0.176785 2.77556e-16 12.0000 -0.223447 -0.223447 1.11022e-16 13.0000 -0.0703181 -0.0703181 2.08167e-16 14.0000 0.133375 0.133375 0 15.0000 0.205104 0.205104 5.55112e-17 r8_besj1_test: Normal end of execution. r8_besk0_test: Python version: 2.7.17 r8_besk0 evaluates Bessel functions K0(X) X BESK0(X) r8_besk0(X) Diff 0.1000 2.42707 2.42707 1.77636e-15 0.2000 1.7527 1.7527 6.66134e-16 0.4000 1.11453 1.11453 1.33227e-15 0.6000 0.777522 0.777522 6.66134e-16 0.8000 0.565347 0.565347 3.33067e-16 1.0000 0.421024 0.421024 4.996e-16 1.2000 0.318508 0.318508 4.996e-16 1.4000 0.243655 0.243655 3.60822e-16 1.6000 0.187955 0.187955 5.55112e-17 1.8000 0.145931 0.145931 2.77556e-17 2.0000 0.113894 0.113894 1.249e-16 2.5000 0.0623476 0.0623476 0 3.0000 0.0347395 0.0347395 6.93889e-18 3.5000 0.0195989 0.0195989 0 4.0000 0.0111597 0.0111597 3.46945e-18 4.5000 0.00639986 0.00639986 0 5.0000 0.0036911 0.0036911 4.33681e-19 6.0000 0.00124399 0.00124399 2.1684e-19 8.0000 0.000146471 0.000146471 0 10.0000 1.77801e-05 1.77801e-05 3.38813e-21 r8_besk0_test: Normal end of execution. r8_besk_test: Python version: 2.7.17 r8_besk evaluates Bessel K functtions K(NU,X). NU X BESK(X) r8_besk(X) Diff 0.5 0.2000 2.29449 2.29449 4.44089e-16 0.5 1.0000 0.461069 0.461069 1.66533e-16 0.5 2.0000 0.119938 0.119938 2.77556e-16 0.5 2.5000 0.0650659 0.0650659 1.38778e-17 0.5 3.0000 0.036026 0.036026 6.93889e-18 0.5 5.0000 0.00377661 0.00377661 4.33681e-19 0.5 10.0000 1.79935e-05 1.79935e-05 0 0.5 20.0000 5.77637e-10 5.77637e-10 0 1.5 1.0000 0.922137 0.922137 1.11022e-16 1.5 2.0000 0.179907 0.179907 1.38778e-16 1.5 5.0000 0.00453194 0.00453194 0 1.5 10.0000 1.97928e-05 1.97928e-05 0 1.5 50.0000 3.48699e-23 3.48699e-23 5.87747e-39 2.5 1.0000 3.22748 3.22748 4.44089e-16 2.5 2.0000 0.389798 0.389798 5.55112e-17 2.5 5.0000 0.00649578 0.00649578 0 2.5 10.0000 2.39313e-05 2.39313e-05 0 2.5 50.0000 3.62784e-23 3.62784e-23 0 1.25 1.0000 0.731145 0.731145 1.11022e-16 1.25 2.0000 0.156748 0.156748 1.94289e-16 1.25 5.0000 0.00425739 0.00425739 3.46945e-18 1.25 10.0000 1.91554e-05 1.91554e-05 0 1.25 50.0000 3.46334e-23 3.46334e-23 1.76324e-38 2.75 1.0000 4.73118 4.73118 0 2.75 2.0000 0.497688 0.497688 1.11022e-16 2.75 5.0000 0.00730086 0.00730086 1.73472e-18 2.75 10.0000 2.54642e-05 2.54642e-05 6.77626e-21 2.75 50.0000 3.67528e-23 3.67528e-23 1.17549e-38 r8_besk_test: Normal end of execution. r8_besk1_test: Python version: 2.7.17 r8_besk1 evaluates Bessel functions K1(x) X BESK1(X) r8_besk1(X) Diff 0.1000 9.85384 9.85384 1.59872e-14 0.2000 4.77597 4.77597 3.55271e-15 0.4000 2.18435 2.18435 5.77316e-15 0.6000 1.30283 1.30283 2.66454e-15 0.8000 0.861782 0.861782 1.11022e-15 1.0000 0.601907 0.601907 2.44249e-15 1.2000 0.434592 0.434592 1.11022e-15 1.4000 0.320836 0.320836 3.33067e-16 1.6000 0.240634 0.240634 8.04912e-16 1.8000 0.182623 0.182623 4.44089e-16 2.0000 0.139866 0.139866 1.249e-15 2.5000 0.0738908 0.0738908 0 3.0000 0.0401564 0.0401564 6.93889e-18 3.5000 0.0222394 0.0222394 3.46945e-18 4.0000 0.0124835 0.0124835 0 4.5000 0.00707809 0.00707809 0 5.0000 0.00404461 0.00404461 8.67362e-19 6.0000 0.00134392 0.00134392 2.1684e-19 8.0000 0.000155369 0.000155369 2.71051e-20 10.0000 1.86488e-05 1.86488e-05 3.38813e-21 r8_besk1_test: Normal end of execution. r8_besy0_test: Python version: 2.7.17 r8_besy0 evaluates the Bessel Y0(X) function. X BESY0(X) r8_besy0(X) Diff 0.1 -1.53424 -1.53424 1.9984e-15 1 0.088257 0.088257 3.747e-16 2 0.510376 0.510376 0 3 0.37685 0.37685 3.33067e-16 4 -0.0169407 -0.0169407 4.47559e-16 5 -0.308518 -0.308518 5.55112e-17 6 -0.288195 -0.288195 0 7 -0.0259497 -0.0259497 1.11022e-16 8 0.223521 0.223521 5.55112e-17 9 0.249937 0.249937 5.55112e-17 10 0.0556712 0.0556712 9.71445e-17 11 -0.168847 -0.168847 0 12 -0.225237 -0.225237 8.32667e-17 13 -0.0782079 -0.0782079 2.91434e-16 14 0.127193 0.127193 2.77556e-17 15 0.205464 0.205464 2.77556e-17 r8_besy0_test: Normal end of execution. r8_besy1_test: Python version: 2.7.17 r8_besy1 evaluates the Bessel Y1(x) function X BESY1(X) r8_besy1(X) Diff 0.1 -6.45895 -6.45895 8.88178e-16 1 -0.781213 -0.781213 3.33067e-16 2 -0.107032 -0.107032 2.22045e-16 3 0.324674 0.324674 0 4 0.397926 0.397926 5.55112e-17 5 0.147863 0.147863 2.77556e-17 6 -0.17501 -0.17501 2.77556e-17 7 -0.302667 -0.302667 1.11022e-16 8 -0.15806 -0.15806 5.55112e-17 9 0.104315 0.104315 1.38778e-17 10 0.249015 0.249015 5.55112e-17 11 0.163706 0.163706 3.05311e-16 12 -0.0570992 -0.0570992 4.09395e-16 13 -0.210081 -0.210081 8.32667e-17 14 -0.166645 -0.166645 5.55112e-17 15 0.0210736 0.0210736 4.85723e-17 r8_besy1_test: Normal end of execution. r8_beta_test: Python version: 2.7.17 r8_beta evaluates the Beta function. A B BETA(A,B) r8_beta(A,B) Diff 0.2 1 5 5 8.88178e-16 0.4 1 2.5 2.5 4.44089e-16 0.6 1 1.66667 1.66667 6.66134e-16 0.8 1 1.25 1.25 2.22045e-16 1 0.2 5 5 8.88178e-16 1 0.4 2.5 2.5 4.44089e-16 1 1 1 1 0 2 2 0.166667 0.166667 5.55112e-17 3 3 0.0333333 0.0333333 0 4 4 0.00714286 0.00714286 0 5 5 0.0015873 0.0015873 2.1684e-19 6 2 0.0238095 0.0238095 3.46945e-18 6 3 0.00595238 0.00595238 0 6 4 0.00198413 0.00198413 0 6 5 0.000793651 0.000793651 1.84314e-18 6 6 0.00036075 0.00036075 1.6263e-18 7 7 8.32501e-05 8.32501e-05 1.49078e-19 r8_beta_test: Normal end of execution. r8_betai_test: Python version: 2.7.17 r8_betai evaluates the incomplete Beta function. X A B BETAI(A,B) r8_betai(A,B) Diff 0.0100 0.5000 0.5 0.0637686 0.0637686 0 0.1000 0.5000 0.5 0.204833 0.204833 5.55112e-17 1.0000 0.5000 0.5 1 1 0 0.0000 1.0000 0.5 0 0 0 0.0100 1.0000 0.5 0.00501256 0.00501256 3.46945e-18 0.1000 1.0000 0.5 0.0513167 0.0513167 1.38778e-17 0.5000 1.0000 0.5 0.292893 0.292893 1.11022e-16 0.5000 1.0000 1 0.5 0.5 0 0.1000 2.0000 2 0.028 0.028 1.04083e-17 0.2000 2.0000 2 0.104 0.104 1.38778e-17 0.3000 2.0000 2 0.216 0.216 8.32667e-17 0.4000 2.0000 2 0.352 0.352 5.55112e-17 0.5000 2.0000 2 0.5 0.5 0 0.6000 2.0000 2 0.648 0.648 1.11022e-16 0.7000 2.0000 2 0.784 0.784 1.11022e-16 0.8000 2.0000 2 0.896 0.896 0 0.9000 2.0000 2 0.972 0.972 0 0.5000 5.5000 5 0.436191 0.436191 7.77156e-16 0.9000 10.0000 0.5 0.151641 0.151641 1.44329e-15 0.5000 10.0000 5 0.0897827 0.0897827 2.63678e-16 1.0000 10.0000 5 1 1 0 0.5000 10.0000 10 0.5 0.5 1.11022e-16 0.8000 20.0000 5 0.459877 0.459877 1.11022e-16 0.6000 20.0000 10 0.214682 0.214682 1.08247e-15 0.8000 20.0000 10 0.950736 0.950736 2.22045e-16 0.5000 20.0000 20 0.5 0.5 0 0.6000 20.0000 20 0.897941 0.897941 2.55351e-15 0.7000 30.0000 10 0.22413 0.22413 4.16334e-16 0.8000 30.0000 10 0.758641 0.758641 3.33067e-16 0.7000 40.0000 20 0.700178 0.700178 5.55112e-16 0.1000 1.0000 0.5 0.0513167 0.0513167 1.38778e-17 0.2000 1.0000 0.5 0.105573 0.105573 1.38778e-17 0.3000 1.0000 0.5 0.16334 0.16334 0 0.4000 1.0000 0.5 0.225403 0.225403 8.32667e-17 0.2000 1.0000 2 0.36 0.36 0 0.2000 1.0000 3 0.488 0.488 1.11022e-16 0.2000 1.0000 4 0.5904 0.5904 1.11022e-16 0.2000 1.0000 5 0.67232 0.67232 1.11022e-16 0.3000 2.0000 2 0.216 0.216 8.32667e-17 0.3000 3.0000 2 0.0837 0.0837 5.55112e-17 0.3000 4.0000 2 0.03078 0.03078 1.73472e-17 0.3000 5.0000 2 0.010935 0.010935 3.46945e-18 0.2256 1.3062 11.76 0.918885 0.918885 2.22045e-16 0.0336 1.3062 11.76 0.21053 0.21053 3.88578e-16 0.0295 1.3062 11.76 0.182413 0.182413 2.498e-16 r8_betai_test: Normal end of execution. r8_bi_test: Python version: 2.7.17 r8_bi evaluates the Airy Bi(X) function X airy_bi(X) r8_bi(X) Diff 0 0.614927 0.614927 0 0.1 0.659862 0.659862 1.11022e-16 0.2 0.705464 0.705464 0 0.3 0.752486 0.752486 1.11022e-16 0.4 0.801773 0.801773 2.22045e-16 0.5 0.854277 0.854277 1.11022e-16 0.6 0.911063 0.911063 2.22045e-16 0.7 0.973329 0.973329 1.11022e-16 0.8 1.04242 1.04242 2.22045e-16 0.9 1.11987 1.11987 0 1 1.20742 1.20742 2.22045e-16 r8_bi_test: Normal end of execution. r8_bid_test: Python version: 2.7.17 r8_bid evaluates the derivative of the Airy function Bi(X) X airy_bid(X) r8_bid(X) Diff 0.0000 0.448288 0.448288 5.55112e-17 0.1000 0.451513 0.451513 5.55112e-17 0.2000 0.461789 0.461789 4.44089e-16 0.3000 0.480049 0.480049 9.4369e-16 0.4000 0.507282 0.507282 1.66533e-15 0.5000 0.544573 0.544573 1.9984e-15 0.6000 0.593144 0.593144 1.44329e-15 0.7000 0.654406 0.654406 1.77636e-15 0.8000 0.730007 0.730007 5.88418e-15 0.9000 0.821904 0.821904 9.99201e-16 1.0000 0.932436 0.932436 9.32587e-15 r8_bid_test: Normal end of execution. r8_binom_test: Python version: 2.7.17 r8_binom evaluates the binomial coefficient. A B BINOM(A,B) r8_binom(A,B) Diff 1 0 1 1 0 6 1 6 6 0 6 3 20 20 0 6 5 6 6 0 15 1 15 15 0 15 3 455 455 0 15 5 3003 3003 0 15 7 6435 6435 0 15 9 5005 5005 0 15 11 1365 1365 0 15 13 105 105 0 25 1 25 25 0 25 3 2300 2300 0 25 5 53130 53130 0 25 7 480700 480700 0 25 9 2042975 2042975 0 25 11 4457400 4457400 0 25 13 5200300 5200300 0 25 15 3268760 3268760 0 25 17 1081575 1081575 0 r8_binom_test: Normal end of execution. r8_cbrt_test: Python version: 2.7.17 r8_cbrt evaluates the cube root function. X CBRT(X) r8_cbrt(X) Diff 0 0 0 0 -8.1e-09 -0.0020083 -0.0020083 4.33681e-19 0.09 0.44814 0.44814 0 -0.1 -0.464159 -0.464159 5.55112e-17 0.4 0.736806 0.736806 1.11022e-16 -1 -1 -1 0 2 1.25992 1.25992 0 -3 -1.44225 -1.44225 2.22045e-16 3.142 1.46459 1.46459 0 -19 -2.6684 -2.6684 4.44089e-16 29 3.07232 3.07232 4.44089e-16 -71 -4.14082 -4.14082 0 97 4.5947 4.5947 8.88178e-16 -1.235e+08 -497.934 -497.934 0 r8_cbrt_test: Normal end of execution. r8_chi_test: Python version: 2.7.17 r8_chi evaluates the hyperbolic cosine integral. X CHI(X) r8_chi(X) Diff 0.5000 -0.0527768 -0.0527768 7.63278e-17 0.6000 0.157751 0.157751 1.94289e-16 0.7000 0.345569 0.345569 1.11022e-16 0.8000 0.5184 0.5184 2.22045e-16 0.9000 0.681314 0.681314 2.22045e-16 1.0000 0.837867 0.837867 3.33067e-16 1.2000 1.14184 1.14184 2.22045e-16 1.4000 1.44549 1.44549 2.22045e-16 1.6000 1.75951 1.75951 0 1.8000 2.09258 2.09258 8.88178e-16 2.0000 2.45267 2.45267 4.44089e-16 2.5000 3.52443 3.52443 4.44089e-16 3.0000 4.96039 4.96039 8.88178e-16 3.5000 6.95919 6.95919 0 4.0000 9.81355 9.81355 1.77636e-15 4.5000 13.9658 13.9658 3.55271e-15 r8_chi_test: Normal end of execution. r8_chu_test: Python version: 2.7.17 r8_chu evaluates the hypergeometric U function. A B X CHU(A,B,X) r8_chu(A,B,X) Diff -2.5000 3.3000 0.25 -68.6936 -68.6936 5.68434e-14 -0.5000 1.1000 0.25 -0.00297106 -0.00297106 4.75748e-16 0.5000 1.1000 0.25 1.50086 1.50086 1.11022e-15 2.5000 3.3000 0.25 20.6147 20.6147 1.06581e-14 -2.5000 3.3000 1.55 7.45638 7.45638 1.77636e-15 -0.5000 1.1000 1.55 1.01558 1.01558 2.22045e-16 0.5000 1.1000 1.55 0.734465 0.734465 9.99201e-16 2.5000 3.3000 1.55 0.280464 0.280464 1.66533e-16 -2.5000 3.3000 2.85 3.45082 3.45082 5.77316e-15 -0.5000 1.1000 2.85 1.51566 1.51566 4.44089e-16 0.5000 1.1000 2.85 0.560421 0.560421 1.11022e-16 2.5000 3.3000 2.85 0.0648971 0.0648971 0 0.8250 6.7000 0.25 223432 223432 5.82077e-11 1.1000 6.7000 0.25 263079 263079 1.74623e-10 1.6500 6.7000 0.25 269803 269803 1.16415e-10 3.3000 6.7000 0.25 82809.3 82809.3 4.36557e-11 0.8250 6.7000 1.55 26.4657 26.4657 3.55271e-15 1.1000 6.7000 1.55 28.0935 28.0935 7.10543e-15 1.6500 6.7000 1.55 23.8892 23.8892 0 3.3000 6.7000 1.55 4.53388 4.53388 8.88178e-16 0.8250 6.7000 2.85 3.02245 3.02245 8.88178e-16 1.1000 6.7000 2.85 2.80407 2.80407 1.33227e-15 1.6500 6.7000 2.85 1.92626 1.92626 2.22045e-16 3.3000 6.7000 2.85 0.230205 0.230205 0 r8_chu_test: Normal end of execution. r8_ci_test: Python version: 2.7.17 r8_ci evaluates the cosine integral. X CI(X) r8_ci(X) Diff 0.5000 -0.177784 -0.177784 1.66533e-16 0.6000 -0.0222707 -0.0222707 4.09395e-16 0.7000 0.100515 0.100515 1.80411e-16 0.8000 0.198279 0.198279 1.11022e-16 0.9000 0.276068 0.276068 5.55112e-17 1.0000 0.337404 0.337404 1.11022e-16 1.2000 0.420459 0.420459 5.55112e-17 1.4000 0.462007 0.462007 5.55112e-17 1.6000 0.471733 0.471733 3.88578e-16 1.8000 0.456811 0.456811 2.22045e-16 2.0000 0.422981 0.422981 1.11022e-16 2.5000 0.285871 0.285871 2.22045e-16 3.0000 0.11963 0.11963 1.80411e-16 3.5000 -0.0321285 -0.0321285 1.94289e-16 4.0000 -0.140982 -0.140982 1.38778e-16 4.5000 -0.193491 -0.193491 5.55112e-17 r8_ci_test: Normal end of execution. r8_cin_test: Python version: 2.7.17 r8_cin evaluates the alternate hyperbolic cosine integral. X CIN(X) r8_cin(X) Diff 0.5000 0.0618526 0.0618526 1.38778e-17 0.6000 0.0886607 0.0886607 2.77556e-17 0.7000 0.120026 0.120026 6.93889e-17 0.8000 0.155793 0.155793 8.32667e-17 0.9000 0.195787 0.195787 2.77556e-17 1.0000 0.239812 0.239812 0 1.2000 0.339078 0.339078 1.11022e-16 1.4000 0.451681 0.451681 1.66533e-16 1.6000 0.575487 0.575487 1.11022e-16 1.8000 0.708191 0.708191 2.22045e-16 2.0000 0.847382 0.847382 1.11022e-16 2.5000 1.20764 1.20764 2.22045e-16 3.0000 1.5562 1.5562 6.66134e-16 3.5000 1.86211 1.86211 4.44089e-16 4.0000 2.10449 2.10449 1.33227e-15 4.5000 2.27478 2.27478 4.44089e-16 r8_cin_test: Normal end of execution. r8_cinh_test: Python version: 2.7.17 r8_cinh evaluates the alternate hyperbolic cosine integral. X CINH(X) r8_cinh(X) Diff 0.0000 0 0 0 0.5000 0.0631547 0.0631547 1.38778e-17 0.6000 0.0913609 0.0913609 2.77556e-17 0.7000 0.125028 0.125028 0 0.8000 0.164328 0.164328 1.11022e-16 0.9000 0.209459 0.209459 8.32667e-17 1.0000 0.260651 0.260651 5.55112e-17 1.2000 0.382305 0.382305 0 1.4000 0.531806 0.531806 2.22045e-16 1.6000 0.712287 0.712287 0 1.8000 0.927575 0.927575 2.22045e-16 2.0000 1.1823 1.1823 4.44089e-16 2.5000 2.03092 2.03092 0 3.0000 3.28456 3.28456 4.44089e-16 3.5000 5.12921 5.12921 8.88178e-16 4.0000 7.85004 7.85004 1.77636e-15 4.5000 11.8845 11.8845 5.32907e-15 r8_cinh_test: Normal end of execution. r8_cos_test: Python version: 2.7.17 r8_cos evaluates the cosine function. X COS(X) r8_cos(X) Diff 0.0000 1 1 0 0.2618 0.965926 0.965926 1.11022e-16 0.5000 0.877583 0.877583 2.22045e-16 0.5236 0.866025 0.866025 1.11022e-16 0.7854 0.707107 0.707107 0 1.0000 0.540302 0.540302 1.11022e-16 1.0472 0.5 0.5 1.11022e-16 1.5708 0 6.12574e-17 6.12574e-17 2.0000 -0.416147 -0.416147 0 3.0000 -0.989992 -0.989992 1.11022e-16 3.1416 -1 -1 2.22045e-16 4.0000 -0.653644 -0.653644 0 5.0000 0.283662 0.283662 5.55112e-17 r8_cos_test: Normal end of execution. r8_cos_deg_test: Python version: 2.7.17 r8_cos_deg evaluates the cosine of an argument in degrees. X cos_deg(X) r8_cos_deg(X) Diff -5.0000 0.996195 0.996195 2.22045e-16 0.0000 1 1 0 1.0000 0.999848 0.999848 0 2.0000 0.999391 0.999391 1.11022e-16 3.0000 0.99863 0.99863 0 4.0000 0.997564 0.997564 0 5.0000 0.996195 0.996195 2.22045e-16 10.0000 0.984808 0.984808 0 15.0000 0.965926 0.965926 1.11022e-16 30.0000 0.866025 0.866025 0 45.0000 0.707107 0.707107 0 60.0000 0.5 0.5 1.11022e-16 75.0000 0.258819 0.258819 0 85.0000 0.0871557 0.0871557 5.55112e-17 86.0000 0.0697565 0.0697565 8.32667e-17 87.0000 0.052336 0.052336 1.249e-16 88.0000 0.0348995 0.0348995 1.11022e-16 89.0000 0.0174524 0.0174524 8.67362e-17 90.0000 0 0 0 91.0000 -0.0174524 -0.0174524 3.81639e-17 105.0000 -0.258819 -0.258819 1.11022e-16 180.0000 -1 -1 0 r8_cos_deg_test: Normal end of execution. r8_cosh_test: Python version: 2.7.17 r8_cosh evaluates the hyperbolic cosine function. X COSH(X) r8_cosh(X) Diff -5.0000 74.2099 74.2099 4.26326e-14 -1.0000 1.54308 1.54308 2.22045e-16 0.0000 1 1 0 0.1000 1.005 1.005 0 0.2000 1.02007 1.02007 2.22045e-16 0.3000 1.04534 1.04534 4.44089e-16 0.4000 1.08107 1.08107 2.22045e-16 0.5000 1.12763 1.12763 4.44089e-16 0.6000 1.18547 1.18547 6.66134e-16 0.7000 1.25517 1.25517 0 0.8000 1.33743 1.33743 4.44089e-16 0.9000 1.43309 1.43309 8.88178e-16 1.0000 1.54308 1.54308 2.22045e-16 2.0000 3.7622 3.7622 4.44089e-16 3.0000 10.0677 10.0677 0 4.0000 27.3082 27.3082 7.10543e-15 5.0000 74.2099 74.2099 4.26326e-14 10.0000 11013.2 11013.2 1.63709e-11 r8_cosh_test: Normal end of execution. r8_cot_test: Python version: 2.7.17 r8_cot evaluates the cotangent function. X COT(X) r8_cot(X) Diff 0.0833 11.9722 11.9722 1.77636e-15 0.2618 3.73205 3.73205 0 0.5000 1.83049 1.83049 2.22045e-16 0.5236 1.73205 1.73205 0 0.7854 1 1 2.22045e-16 1.0000 0.642093 0.642093 1.11022e-16 1.0472 0.57735 0.57735 1.11022e-16 1.3090 0.267949 0.267949 5.55112e-17 1.5708 0 -2.22045e-16 2.22045e-16 1.4399 0.131652 0.131652 8.32667e-17 1.5053 0.0655435 0.0655435 1.38778e-16 2.0000 -0.457658 -0.457658 1.11022e-16 3.0000 -7.01525 -7.01525 8.88178e-16 4.0000 0.863691 0.863691 0 5.0000 -0.295813 -0.295813 5.55112e-17 r8_cot_test: Normal end of execution. r8_csevl_test: Python version: 2.7.17 r8_csevl evaluates a Chebyshev approximant of N terms at a point X. Here we use an approximant to the exponential function and average the absolute error at 21 points. N error 1 0.605859 2 0.172657 3 0.0290247 4 0.00362759 5 0.000367891 6 3.07777e-05 7 2.19352e-06 8 1.37199e-07 9 7.67356e-09 10 3.5653e-10 11 1.62784e-11 12 6.53432e-13 r8_csevl_test: Normal end of execution. r8_dawson_test: Python version: 2.7.17 r8_dawson evaluates Dawson's integral. X DAWSON(X) r8_dawson(X) Diff 0.0000 0 0 0 0.1000 0.099336 0.099336 1.38778e-17 0.2000 0.194751 0.194751 5.55112e-17 0.3000 0.282632 0.282632 5.55112e-17 0.4000 0.359943 0.359943 0 0.5000 0.424436 0.424436 0 0.6000 0.474763 0.474763 5.55112e-17 0.7000 0.510504 0.510504 0 0.8000 0.532102 0.532102 0 0.9000 0.540724 0.540724 0 1.0000 0.53808 0.53808 0 1.1000 0.526207 0.526207 1.11022e-16 1.2000 0.507273 0.507273 2.22045e-16 1.3000 0.483398 0.483398 1.11022e-16 1.4000 0.456507 0.456507 0 1.5000 0.428249 0.428249 1.11022e-16 1.6000 0.39994 0.39994 1.11022e-16 1.7000 0.372559 0.372559 5.55112e-17 1.8000 0.346773 0.346773 1.11022e-16 1.9000 0.322974 0.322974 2.22045e-16 2.0000 0.30134 0.30134 0 r8_dawson_test: Normal end of execution. r8_e1_test: Python version: 2.7.17 r8_e1 evaluates the E1(x) exponential function. X E1(X) r8_e1(X) Diff 0.5000 0.559774 0.559774 1.11022e-16 0.6000 0.45438 0.45438 1.11022e-16 0.7000 0.373769 0.373769 5.55112e-17 0.8000 0.310597 0.310597 5.55112e-17 0.9000 0.260184 0.260184 1.66533e-16 1.0000 0.219384 0.219384 8.32667e-17 1.1000 0.185991 0.185991 5.55112e-17 1.2000 0.158408 0.158408 0 1.3000 0.135451 0.135451 2.77556e-17 1.4000 0.116219 0.116219 1.38778e-17 1.5000 0.10002 0.10002 4.16334e-17 1.6000 0.0863083 0.0863083 2.77556e-17 1.7000 0.0746546 0.0746546 0 1.8000 0.0647131 0.0647131 1.38778e-17 1.9000 0.0562044 0.0562044 0 2.0000 0.0489005 0.0489005 6.93889e-18 r8_e1_test: Normal end of execution. r8_ei_test: Python version: 2.7.17 r8_ei evaluates the exponential integral Ei(X). X EI(X) r8_ei(X) Diff 0.5000 0.45422 0.45422 5.55112e-17 0.6000 0.769881 0.769881 1.11022e-16 0.7000 1.06491 1.06491 6.66134e-16 0.8000 1.3474 1.3474 2.22045e-16 0.9000 1.62281 1.62281 2.22045e-16 1.0000 1.89512 1.89512 4.44089e-16 1.1000 2.16738 2.16738 1.77636e-15 1.2000 2.44209 2.44209 4.44089e-16 1.3000 2.7214 2.7214 1.77636e-15 1.4000 3.00721 3.00721 0 1.5000 3.30129 3.30129 4.44089e-16 1.6000 3.60532 3.60532 8.88178e-16 1.7000 3.92096 3.92096 8.88178e-16 1.8000 4.24987 4.24987 8.88178e-16 1.9000 4.59371 4.59371 8.88178e-16 2.0000 4.95423 4.95423 8.88178e-16 r8_ei_test: Normal end of execution. r8_erf_test: r8_erf evaluates the error function. X ERF(X) r8_erf(X) Diff 0 0 0 0 0.1 0.112463 0.112463 1.38778e-17 0.2 0.222703 0.222703 2.77556e-17 0.3 0.328627 0.328627 5.55112e-17 0.4 0.428392 0.428392 1.11022e-16 0.5 0.5205 0.5205 1.11022e-16 0.6 0.603856 0.603856 0 0.7 0.677801 0.677801 0 0.8 0.742101 0.742101 0 0.9 0.796908 0.796908 2.22045e-16 1 0.842701 0.842701 3.33067e-16 1.1 0.880205 0.880205 0 1.2 0.910314 0.910314 1.11022e-16 1.3 0.934008 0.934008 0 1.4 0.952285 0.952285 0 1.5 0.966105 0.966105 1.11022e-16 1.6 0.976348 0.976348 0 1.7 0.98379 0.98379 1.11022e-16 1.8 0.989091 0.989091 1.11022e-16 1.9 0.99279 0.99279 0 2 0.995322 0.995322 0 r8_erf_test: Normal end of execution. r8_erfc_test: Python version: 2.7.17 r8_erfc evaluates the complementary error function. X ERFC(X) r8_erfc(X) Diff 0 1 1 0 0.2 0.777297 0.777297 0 0.4 0.571608 0.571608 1.11022e-16 0.6 0.396144 0.396144 0 0.8 0.257899 0.257899 0 1 0.157299 0.157299 3.33067e-16 1.2 0.089686 0.089686 0 1.4 0.0477149 0.0477149 1.38778e-17 1.6 0.0236516 0.0236516 6.93889e-18 1.8 0.0109095 0.0109095 8.67362e-18 2 0.00467773 0.00467773 8.67362e-19 2.2 0.00186285 0.00186285 1.0842e-18 2.4 0.000688514 0.000688514 3.25261e-19 2.6 0.000236034 0.000236034 1.6263e-19 2.8 7.50132e-05 7.50132e-05 6.77626e-20 3 2.20905e-05 2.20905e-05 6.77626e-21 3.2 6.02576e-06 6.02576e-06 1.35525e-20 3.4 1.52199e-06 1.52199e-06 2.11758e-21 3.6 3.55863e-07 3.55863e-07 3.70577e-22 3.8 7.70039e-08 7.70039e-08 5.29396e-23 4 1.54173e-08 1.54173e-08 3.30872e-24 r8_erfc_test: Normal end of execution. r8_exp_test: Python version: 2.7.17 r8_exp evaluates the exponential function. X EXP(X) r8_exp(X) Diff -10.0000 4.53999e-05 2.94382e-05 1.59617e-05 -5.0000 0.00673795 0.00383655 0.0029014 -1.0000 0.367879 0.249101 0.118778 0.0000 1 1 0 0.0000 1 1 0 0.0001 1.0001 1.0001 0 0.0010 1.001 1.001 0 0.0100 1.01005 1.01005 2.22045e-16 0.1000 1.10517 1.10517 2.22045e-16 0.2000 1.2214 1.2214 8.88178e-16 0.3000 1.34986 1.34986 1.33227e-15 0.4000 1.49182 1.49182 0 0.5000 1.64872 1.64872 1.55431e-15 0.6000 1.82212 1.82212 2.44249e-15 0.7000 2.01375 2.01375 0 0.8000 2.22554 2.22554 1.33227e-15 0.9000 2.4596 2.4596 1.77636e-15 1.0000 2.71828 2.71828 4.44089e-16 2.0000 7.38906 7.38906 8.88178e-16 3.1416 23.1407 23.1407 2.4869e-14 5.0000 148.413 148.413 8.52651e-14 10.0000 22026.5 22026.5 2.91038e-11 20.0000 4.85165e+08 4.85165e+08 2.38419e-07 40.0000 2.35385e+17 2.35385e+17 96 r8_exp_test: Normal end of execution. r8_fac_test: Python version: 2.7.17 r8_fac evaluates the factorial function. N FAC(N) r8_fac(N) Diff 0 1 1 0 1 1 1 0 2 2 2 0 3 6 6 0 4 24 24 0 5 120 120 0 6 720 720 0 7 5040 5040 0 8 40320 40320 0 9 362880 362880 0 10 3.6288e+06 3.6288e+06 0 11 3.99168e+07 3.99168e+07 0 12 4.79002e+08 4.79002e+08 0 13 6.22702e+09 6.22702e+09 0 14 8.71783e+10 8.71783e+10 0 15 1.30767e+12 1.30767e+12 0 16 2.09228e+13 2.09228e+13 0 17 3.55687e+14 3.55687e+14 0 18 6.40237e+15 6.40237e+15 0 19 1.21645e+17 1.21645e+17 0 20 2.4329e+18 2.4329e+18 0 25 1.55112e+25 1.55112e+25 4.29497e+09 50 3.04141e+64 3.04141e+64 3.62452e+50 100 9.33262e+157 9.33262e+157 1.90232e+144 150 5.71338e+262 5.71338e+262 4.99922e+249 r8_fac_test: Normal end of execution. r8_gamic_test: Python version: 2.7.17 r8_gamic evaluates the incomplete Gamma function. A X GAMIC(A,X) r8_gamic(A,X) Diff 0.1 0.0300 2.4903 2.4903 1.33227e-15 0.1 0.3000 0.871837 0.871837 0 0.1 1.5000 0.107921 0.107921 2.77556e-17 0.5 0.0750 1.23812 1.23812 4.44089e-16 0.5 0.7500 0.39113 0.39113 2.22045e-16 0.5 3.5000 0.0144472 0.0144472 0 1 0.1000 0.904837 0.904837 1.11022e-16 1 1.0000 0.367879 0.367879 5.55112e-17 1 5.0000 0.00673795 0.00673795 0 1.1 0.1000 0.882797 0.882797 0 1.1 1.0000 0.390833 0.390833 2.22045e-16 1.1 5.0000 0.00805146 0.00805146 3.46945e-18 2 0.1500 0.989814 0.989814 0 2 1.5000 0.557825 0.557825 1.11022e-16 2 7.0000 0.00729506 0.00729506 1.73472e-18 6 2.5000 114.957 114.957 9.9476e-14 6 12.0000 2.44092 2.44092 2.66454e-15 11 16.0000 280855 280855 5.82077e-11 26 25.0000 8.57648e+24 8.57648e+24 3.22123e+09 41 45.0000 2.08503e+47 2.08503e+47 2.83954e+32 r8_gamic_test: Normal end of execution. r8_gamit_test: Python version: 2.7.17 r8_gamit evaluates Tricomi's incomplete Gamma function A X GAMIT(A,X) r8_gamit(A,X) Diff 0.1 0.03 1.04829 1.04829 4.44089e-16 0.1 0.3 1.02458 1.02458 2.22045e-16 0.1 1.5 0.949371 0.949371 0 0.5 0.075 1.10079 1.10079 2.22045e-16 0.5 0.75 0.899891 0.899891 1.11022e-16 0.5 3.5 0.530166 0.530166 0 1 0.1 0.951626 0.951626 0 1 1 0.632121 0.632121 1.11022e-16 1 5 0.198652 0.198652 2.77556e-17 1.1 0.1 0.907178 0.907178 0 1.1 1 0.589181 0.589181 0 1.1 5 0.168827 0.168827 5.55112e-17 2 0.15 0.452703 0.452703 0 2 1.5 0.196522 0.196522 0 2 7 0.0202593 0.0202593 6.93889e-18 6 2.5 0.000172118 0.000172118 8.13152e-20 6 12 3.28086e-07 3.28086e-07 3.17637e-22 11 16 5.2444e-14 5.2444e-14 9.46633e-29 26 25 2.01346e-37 2.01346e-37 4.17619e-53 41 45 1.23062e-68 1.23062e-68 1.77076e-82 r8_gamit_test: Normal end of execution. r8_gaml_test: Python version: 2.7.17 r8_gaml returns bounds for the argument of the gamma function. Lower limit XMIN = -170.345 Upper limit XMAX = 171.345 r8_gaml_test: Normal end of execution. r8_gamma_test: Python version: 2.7.17 r8_gamma computes the Gamma function. X GAMMA(X) r8_gamma(X) Diff -0.5 -3.54491 -3.54491 0 -0.01 -100.587 -100.587 9.9476e-14 0.01 99.4326 99.4326 8.52651e-14 0.1 9.51351 9.51351 8.88178e-15 0.2 4.59084 4.59084 1.77636e-15 0.4 2.21816 2.21816 4.44089e-16 0.5 1.77245 1.77245 0 0.6 1.48919 1.48919 2.22045e-16 0.8 1.16423 1.16423 2.22045e-16 1 1 1 0 1.1 0.951351 0.951351 0 1.2 0.918169 0.918169 0 1.3 0.897471 0.897471 0 1.4 0.887264 0.887264 0 1.5 0.886227 0.886227 0 1.6 0.893515 0.893515 0 1.7 0.908639 0.908639 0 1.8 0.931384 0.931384 0 1.9 0.961766 0.961766 0 2 1 1 0 3 2 2 0 4 6 6 0 10 362880 362880 0 20 1.21645e+17 1.21645e+17 80 30 8.84176e+30 8.84176e+30 7.54353e+16 r8_gamma_test: Normal end of execution. r8_gamr_test: Python version: 2.7.17 r8_gamr computes the 1/Gamma(x). X 1/GAMMA(X) r8_gamr(X) Diff -0.5 -0.282095 -0.282095 0 -0.01 -0.00994162 -0.00994162 1.04083e-17 0.01 0.0100571 0.0100571 8.67362e-18 0.1 0.105114 0.105114 9.71445e-17 0.2 0.217825 0.217825 8.32667e-17 0.4 0.450824 0.450824 1.11022e-16 0.5 0.56419 0.56419 0 0.6 0.671505 0.671505 0 0.8 0.858937 0.858937 1.11022e-16 1 1 1 0 1.1 1.05114 1.05114 0 1.2 1.08912 1.08912 0 1.3 1.11424 1.11424 0 1.4 1.12706 1.12706 0 1.5 1.12838 1.12838 0 1.6 1.11917 1.11917 0 1.7 1.10055 1.10055 0 1.8 1.07367 1.07367 0 1.9 1.03975 1.03975 0 2 1 1 0 3 0.5 0.5 0 4 0.166667 0.166667 0 10 2.75573e-06 2.75573e-06 0 20 8.22064e-18 8.22064e-18 4.62223e-33 30 1.131e-31 1.131e-31 9.63393e-46 r8_gamr_test: Normal end of execution. r8_inits_test: Python version: 2.7.17 r8_inits determines the Chebyshev interpolant degree necessary to guarantee a desired accuracy level. Here, we use a 15 term Chebyshev expansion for the sine function. Accuracy Terms Needed 1 0 0.1 1 0.01 1 0.001 2 0.0001 2 1e-05 3 1e-06 3 1e-07 4 1e-08 4 1e-09 5 1e-10 5 1e-11 6 1e-12 6 1e-13 6 1e-14 7 1e-15 7 1e-16 8 1e-17 8 r8_inits_test: Normal end of execution. r8_int_test: Python version: 2.7.17 r8_int computes the integer part of an R8. X INT(X) r8_int(X) Diff -2.0100 -2 -2 0 -1.9900 -1 -1 0 -1.5000 -1 -1 0 -1.1000 -1 -1 0 -1.0100 -1 -1 0 -1.0000 -1 -1 0 -0.9900 0 -0 0 -0.9000 0 -0 0 -0.5100 0 -0 0 -0.5000 0 -0 0 -0.4900 0 -0 0 -0.0100 0 -0 0 0.0000 0 0 0 0.0100 0 0 0 0.4900 0 0 0 0.5000 0 0 0 0.5100 0 0 0 0.9000 0 0 0 0.9900 0 0 0 1.0000 1 1 0 1.0100 1 1 0 1.1000 1 1 0 1.5000 1 1 0 1.9900 1 1 0 2.0100 2 2 0 r8_int_test: Normal end of execution. r8_lbeta_test: Python version: 2.7.17 r8_lbeta evaluates the logarithm of the Beta function. A B LBETA(A,B) r8_lbeta(A,B) Diff 0.2000 1 1.60944 1.60944 4.44089e-16 0.4000 1 0.916291 0.916291 1.11022e-16 0.6000 1 0.510826 0.510826 1.11022e-16 0.8000 1 0.223144 0.223144 2.22045e-16 1.0000 0.2 1.60944 1.60944 4.44089e-16 1.0000 0.4 0.916291 0.916291 1.11022e-16 1.0000 1 0 0 0 2.0000 2 -1.79176 -1.79176 0 3.0000 3 -3.4012 -3.4012 4.44089e-16 4.0000 4 -4.94164 -4.94164 0 5.0000 5 -6.44572 -6.44572 8.88178e-16 6.0000 2 -3.73767 -3.73767 4.44089e-16 6.0000 3 -5.12396 -5.12396 0 6.0000 4 -6.22258 -6.22258 0 6.0000 5 -7.13887 -7.13887 2.66454e-15 6.0000 6 -7.92732 -7.92732 4.44089e-15 7.0000 7 -9.39366 -9.39366 1.77636e-15 r8_lbeta_test: Normal end of execution. r8_lgams_test: Python version: 2.7.17 r8_lgams evaluates the sign of Gamma(x) and the logarithm of the absolute value of Gamma(x). X LNGAM(X) Sign(Gamma(x)) Log(|Gamma(x)|) Diff 0.2 1.52406 1 1.52406 6.66134e-16 0.4 0.796678 1 0.796678 2.22045e-16 0.6 0.398234 1 0.398234 5.55112e-17 0.8 0.15206 1 0.15206 0 1 0 1 0 0 1.1 -0.0498724 1 -0.0498724 1.38778e-17 1.2 -0.0853741 1 -0.0853741 2.77556e-17 1.3 -0.108175 1 -0.108175 6.93889e-17 1.4 -0.119613 1 -0.119613 1.38778e-16 1.5 -0.120782 1 -0.120782 2.77556e-17 1.6 -0.112592 1 -0.112592 6.93889e-17 1.7 -0.0958077 1 -0.0958077 1.38778e-17 1.8 -0.0710839 1 -0.0710839 1.38778e-17 1.9 -0.0389843 1 -0.0389843 1.38778e-17 2 0 1 0 0 3 0.693147 1 0.693147 0 4 1.79176 1 1.79176 0 10 12.8018 1 12.8018 0 20 39.3399 1 39.3399 0 30 71.257 1 71.257 1.42109e-14 r8_lgams_test: Normal end of execution. r8_lgmc_test: Python version: 2.7.17 r8_lgmc evaluates the correction log gamma factor. r8_lgmc(x) = log ( gamma ( x ) ) - log ( sqrt ( 2 * pi ) - ( x - 0.5 ) * log ( x ) + x X LGMC(X) r8_lgmc(X) Diff 10.0000 0.00833056 0.00833056 1.65666e-15 20.0000 0.00416632 0.00416632 7.45931e-17 30.0000 0.00277767 0.00277767 7.4051e-15 r8_lgmc_test: Normal end of execution. r8_li_test: Python version: 2.7.17 r8_li evaluates the logarithmic integral. X LI(X) r8_li(X) Diff 0.0000 0 0 0 0.1000 -0.0323898 -0.0323898 6.93889e-18 0.2000 -0.0851265 -0.0851265 0 0.3000 -0.157415 -0.157415 5.55112e-17 0.4000 -0.252949 -0.252949 1.11022e-16 0.5000 -0.378671 -0.378671 0 0.6000 -0.546851 -0.546851 1.11022e-16 0.7000 -0.780947 -0.780947 2.22045e-16 0.8000 -1.13401 -1.13401 6.66134e-16 0.9000 -1.7758 -1.7758 6.66134e-16 0.9500 -2.44362 -2.44362 8.88178e-16 0.9750 -3.12419 -3.12419 3.10862e-15 1.0312 -2.87294 -2.87294 4.44089e-16 1.0625 -2.16428 -2.16428 4.44089e-16 1.1250 -1.44035 -1.44035 2.22045e-16 1.2500 -0.686488 -0.686488 1.11022e-16 1.5000 0.125065 0.125065 8.32667e-17 2.0000 1.04516 1.04516 2.22045e-16 4.0000 2.96759 2.96759 0 8.0000 5.25372 5.25372 8.88178e-16 16.0000 8.51972 8.51972 0 32.0000 13.6051 13.6051 3.55271e-15 64.0000 21.9347 21.9347 1.06581e-14 128.0000 36.0425 36.0425 7.10543e-15 256.0000 60.5131 60.5131 7.10543e-15 512.0000 103.721 103.721 2.84217e-14 1024.0000 181.078 181.078 2.84217e-14 2048.0000 321.114 321.114 0 r8_li_test: Normal end of execution. r8_lngam_test: Python version: 2.7.17 r8_lngam evaluates the logarithm of the Gamma function. X LNGAM(X) r8_lngam(X) Diff 0.2 1.52406 1.52406 6.66134e-16 0.4 0.796678 0.796678 2.22045e-16 0.6 0.398234 0.398234 5.55112e-17 0.8 0.15206 0.15206 0 1 0 0 0 1.1 -0.0498724 -0.0498724 1.38778e-17 1.2 -0.0853741 -0.0853741 2.77556e-17 1.3 -0.108175 -0.108175 6.93889e-17 1.4 -0.119613 -0.119613 1.38778e-16 1.5 -0.120782 -0.120782 2.77556e-17 1.6 -0.112592 -0.112592 6.93889e-17 1.7 -0.0958077 -0.0958077 1.38778e-17 1.8 -0.0710839 -0.0710839 1.38778e-17 1.9 -0.0389843 -0.0389843 1.38778e-17 2 0 0 0 3 0.693147 0.693147 0 4 1.79176 1.79176 0 10 12.8018 12.8018 0 20 39.3399 39.3399 0 30 71.257 71.257 1.42109e-14 r8_lngam_test: Normal end of execution. r8_lnrel_test: Python version: 2.7.17 r8_lnrel evaluates ln(1+X). X LN(1+X) r8_lnrel(X) Diff -0.99999 -11.5129 -11.5129 4.55103e-12 -0.99 -4.60517 -4.60517 8.88178e-16 -0.9 -2.30259 -2.30259 0 -0.8 -1.60944 -1.60944 2.22045e-16 -0.7 -1.20397 -1.20397 0 -0.6 -0.916291 -0.916291 1.11022e-16 -0.5 -0.693147 -0.693147 0 -0.4 -0.510826 -0.510826 0 -0.3 -0.356675 -0.356675 1.11022e-16 -0.2 -0.223144 -0.223144 5.55112e-17 -0.1 -0.105361 -0.105361 2.77556e-17 0 0 0 0 1 0.693147 0.693147 0 2 1.09861 1.09861 2.22045e-16 2.14159 1.14473 1.14473 0 4 1.60944 1.60944 2.22045e-16 9 2.30259 2.30259 0 19 2.99573 2.99573 0 99 4.60517 4.60517 0 1.23457e+08 18.6314 18.6314 0 r8_lnrel_test: Normal end of execution. r8_log_test: Python version: 2.7.17 r8_log evaluates the logarithm. X LOG(X) r8_log(X) Diff 1e-05 -11.5129 -11.5129 0 0.01 -4.60517 -4.60517 0 0.1 -2.30259 -2.30259 4.44089e-16 0.2 -1.60944 -1.60944 0 0.3 -1.20397 -1.20397 2.22045e-16 0.4 -0.916291 -0.916291 1.11022e-16 0.5 -0.693147 -0.693147 0 0.6 -0.510826 -0.510826 0 0.7 -0.356675 -0.356675 5.55112e-17 0.8 -0.223144 -0.223144 1.11022e-16 0.9 -0.105361 -0.105361 6.93889e-17 1 0 0 0 2 0.693147 0.693147 0 3 1.09861 1.09861 2.22045e-16 3.142 1.14473 1.14473 0 5 1.60944 1.60944 2.22045e-16 10 2.30259 2.30259 0 20 2.99573 2.99573 0 100 4.60517 4.60517 0 1.235e+08 18.6314 18.6314 0 r8_log_test: Normal end of execution. r8_log10_test: Python version: 2.7.17 r8_log10 evaluates the logarithm base 10. X LOG10(X) r8_log10(X) Diff 0.0000 -5 -5 0 0.0100 -2 -2 0 0.1000 -1 -1 1.11022e-16 0.2000 -0.69897 -0.69897 1.11022e-16 0.3000 -0.522879 -0.522879 1.11022e-16 0.4000 -0.39794 -0.39794 5.55112e-17 0.5000 -0.30103 -0.30103 0 0.6000 -0.221849 -0.221849 0 0.7000 -0.154902 -0.154902 2.77556e-17 0.8000 -0.09691 -0.09691 5.55112e-17 0.9000 -0.0457575 -0.0457575 2.77556e-17 1.0000 0 0 0 2.0000 0.30103 0.30103 0 3.0000 0.477121 0.477121 5.55112e-17 3.1416 0.49715 0.49715 0 5.0000 0.69897 0.69897 0 10.0000 1 1 0 20.0000 1.30103 1.30103 2.22045e-16 100.0000 2 2 0 123456789.0000 8.09151 8.09151 0 r8_log10_test: Normal end of execution. r8_mach_test Python version: 2.7.17 r8_mach reports the value of constants associated with real double precision computer arithmetic. Assume that double precision numbers are stored with a mantissa of T digits in base B, with an exponent whose value must lie between EMIN and EMAX. For input arguments of 1 <= I <= 5, r8_mach will return the following values: r8_mach(1) = B^(EMIN-1), the smallest positive magnitude. 1.1125369292536012e-308 r8_mach(2) = B^EMAX*(1-B^(-T)), the largest magnitude. 4.4942328371557888e+307 r8_mach(3) = B^(-T), the smallest relative spacing. 1.1102230246251570e-16 r8_mach(4) = B^(1-T), the largest relative spacing. 2.2204460492503131e-16 r8_mach(5) = log10(B). 3.0102999566398098e-01 r8_mach_test Normal end of execution. r8_mop_test(): r8_mop() evaluates (-1.0)^I4 as an R8. I4 r8_MOP(I4) -30 1.0 -88 1.0 69 -1.0 -94 1.0 56 1.0 -15 -1.0 9 -1.0 -2 1.0 6 1.0 92 1.0 r8_mop_test(): Normal end of execution. r8_pak_test: Python version: 2.7.17 r8_pak converts a mantissa and base 2 exponent to an R8. Mantissa Exponent R8 0.5 7 64 0.5 8 128 -0.5 7 -64 0.75 7 96 0.9375 4 15 0.5 0 0.5 0.5 -1 0.25 0.625 0 0.625 0.5048828125 7 64.625 0.7853981633974483 2 3.141592653589793 0 0 0 r8_pak_test: Normal end of execution. r8_poch_test: Python version: 2.7.17 r8_poch evaluates the Pochhammer symbol. A X POCH(A,X) r8_poch(A,X) Diff 5 4 1680 1680 0 5.25 4 1962.6 1962.6 0 5.5 4 2279.06 2279.06 0 5.75 4 2631.97 2631.97 0 6 4 3024 3024 0 7.5 0 1 1 0 7.5 1 7.5 7.5 0 7.5 2 63.75 63.75 0 7.5 3 605.625 605.625 0 7.5 4 6359.06 6359.06 0 7.5 5 73129.2 73129.2 0 7.5 6 914115 914115 0 7.5 7 1.23406e+07 1.23406e+07 0 7.5 8 1.78938e+08 1.78938e+08 5.96046e-08 7.5 9 2.77354e+09 2.77354e+09 0 r8_poch_test: Normal end of execution. r8_psi_test: Python version: 2.7.17 r8_psi evaluates the PSI function. X PSI(X) r8_psi(X) 0.1 -10.42375494041108 -10.42375494041108 0.2 -5.289039896592188 -5.289039896592188 0.3 -3.502524222200133 -3.502524222200133 0.4 -2.561384544585116 -2.561384544585116 0.5 -1.963510026021423 -1.963510026021424 0.6 -1.54061921389319 -1.540619213893191 0.7 -1.220023553697935 -1.220023553697935 0.8 -0.9650085667061385 -0.9650085667061382 0.9 -0.7549269499470515 -0.7549269499470511 1 -0.5772156649015329 -0.5772156649015329 1.1 -0.4237549404110768 -0.4237549404110768 1.2 -0.2890398965921883 -0.2890398965921884 1.3 -0.1691908888667997 -0.1691908888667995 1.4 -0.06138454458511615 -0.06138454458511624 1.5 0.03648997397857652 0.03648997397857652 1.6 0.1260474527734763 0.1260474527734763 1.7 0.208547874873494 0.208547874873494 1.8 0.2849914332938615 0.2849914332938615 1.9 0.3561841611640597 0.3561841611640596 2 0.4227843350984671 0.4227843350984672 r8_psi_test Normal end of execution. r8_rand_test: Python version: 2.7.17 r8_rand is a random number generator. I r8_rand Expected 1 0.000412703 0.000412703 2 0.675084 0.675084 3 0.161475 0.161475 4 0.90862 0.90862 10 0.552779 0.552779 100 0.360089 0.360089 1000 0.217699 0.217699 Average = 0.4999 0.5 Variance = 0.0832492 0.0833333 r8_rand_test: Normal end of execution. r8_randgs_test: Python version: 2.7.17 r8_randgs is a normal random number generator. Mean = 3 Standard Deviation = 2 I r8_randgs 0 4.40826 1 2.94895 2 2.13857 3 1.57902 4 8.76356 5 1.08396 6 3.87796 7 4.96727 8 0.673294 9 2.13816 10 3.28232 Sequence mean = 2.98999 Sequence standard deviation = 2.03537 r8_randgs_test: Normal end of execution. r8_random_test: Python version: 2.7.17 r8_random is a random number generator. I r8_random 1 0.0913844 2 0.161475 3 0.658159 4 0.272802 10 0.174952 100 0.820123 1000 0.640682 Average = 0.499899 0.5 Variance = 0.0832494 0.0833333 r8_random_test: Normal end of execution. r8_ren_test: Python version: 2.7.17 r8_ren is a random number generator. I r8_ren Expected 1 0.470393 0.470393 2 0.799066 0.799066 3 0.883261 0.883261 4 0.407667 0.407667 10 0.955566 0.955566 100 0.173576 0.173576 1000 0.0121733 0.0121733 Average = 0.49984 0.5 Variance = 0.0833074 0.0833333 r8_ren_test: Normal end of execution. r8_shi_test: Python version: 2.7.17 r8_shi evaluates the hyperbolic sine integral. X SHI(X) r8_shi(X) Diff 0.5000 0.506997 0.506997 0 0.6000 0.61213 0.61213 0 0.7000 0.719338 0.719338 1.11022e-16 0.8000 0.828997 0.828997 1.11022e-16 0.9000 0.941498 0.941498 1.11022e-16 1.0000 1.05725 1.05725 0 1.2000 1.30025 1.30025 4.44089e-16 1.4000 1.56171 1.56171 0 1.6000 1.84581 1.84581 6.66134e-16 1.8000 2.15729 2.15729 8.88178e-16 2.0000 2.50157 2.50157 0 2.5000 3.54934 3.54934 0 3.0000 4.97344 4.97344 0 3.5000 6.96616 6.96616 0 4.0000 9.81733 9.81733 1.77636e-15 4.5000 13.9679 13.9679 1.77636e-15 r8_shi_test: Normal end of execution. r8_si_test: Python version: 2.7.17 r8_si evaluates the sine integral. X SI(X) r8_si(X) Diff 0.5 0.493107 0.493107 0 0.6 0.588129 0.588129 1.11022e-16 0.7 0.681222 0.681222 0 0.8 0.772096 0.772096 0 0.9 0.860471 0.860471 0 1 0.946083 0.946083 0 1.2 1.10805 1.10805 4.44089e-16 1.4 1.25623 1.25623 2.22045e-16 1.6 1.38918 1.38918 6.66134e-16 1.8 1.50582 1.50582 4.44089e-16 2 1.60541 1.60541 2.22045e-16 2.5 1.77852 1.77852 2.22045e-16 3 1.84865 1.84865 2.22045e-16 3.5 1.83313 1.83313 0 4 1.7582 1.7582 0 4.5 1.65414 1.65414 0 r8_si_test: Normal end of execution. r8_sign_test Python version: 2.7.17 r8_sign returns the sign of an R8. R8 r8_sign(R8) -1.2500 -1 -0.2500 -1 0.0000 1 0.5000 1 9.0000 1 r8_sign_test Normal end of execution. r8_sin_test: Python version: 2.7.17 r8_sin evaluates the sine function. X SIN(X) r8_sin(X) Diff 0.0000 0 0 0 0.2618 0.258819 0.258819 5.55112e-17 0.5000 0.479426 0.479426 0 0.5236 0.5 0.5 0 0.7854 0.707107 0.707107 0 1.0000 0.841471 0.841471 0 1.0472 0.866025 0.866025 0 1.5708 1 1 2.22045e-16 2.0000 0.909297 0.909297 1.11022e-16 3.0000 0.14112 0.14112 0 3.1416 0 1.22515e-16 1.22515e-16 4.0000 -0.756802 -0.756802 2.22045e-16 5.0000 -0.958924 -0.958924 1.11022e-16 r8_sin_test: Normal end of execution. r8_sin_deg_test: Python version: 2.7.17 r8_sin_deg evaluates the sine of an argument in degrees. X sin_deg(X) r8_sin_deg(X) Diff -5.0000 -0.0871557 -0.0871557 1.38778e-17 0.0000 0 0 0 1.0000 0.0174524 0.0174524 0 2.0000 0.0348995 0.0348995 0 3.0000 0.052336 0.052336 0 4.0000 0.0697565 0.0697565 1.38778e-17 5.0000 0.0871557 0.0871557 1.38778e-17 10.0000 0.173648 0.173648 0 15.0000 0.258819 0.258819 0 30.0000 0.5 0.5 1.11022e-16 45.0000 0.707107 0.707107 0 60.0000 0.866025 0.866025 1.11022e-16 75.0000 0.965926 0.965926 1.11022e-16 85.0000 0.996195 0.996195 2.22045e-16 86.0000 0.997564 0.997564 0 87.0000 0.99863 0.99863 0 88.0000 0.999391 0.999391 1.11022e-16 89.0000 0.999848 0.999848 0 90.0000 1 1 0 91.0000 0.999848 0.999848 1.11022e-16 105.0000 0.965926 0.965926 1.11022e-16 180.0000 0 0 0 r8_sin_deg_test: Normal end of execution. r8_sinh_test: Python version: 2.7.17 r8_sinh evaluates the hyperbolic sine function. X SINH(X) r8_sinh(X) Diff -5.0000 -74.2032 -74.2032 0 -1.0000 -1.1752 -1.1752 0 0.0000 0 0 0 0.1000 0.100167 0.100167 1.38778e-17 0.2000 0.201336 0.201336 2.77556e-17 0.3000 0.30452 0.30452 0 0.4000 0.410752 0.410752 1.11022e-16 0.5000 0.521095 0.521095 0 0.6000 0.636654 0.636654 1.11022e-16 0.7000 0.758584 0.758584 1.11022e-16 0.8000 0.888106 0.888106 1.11022e-16 0.9000 1.02652 1.02652 0 1.0000 1.1752 1.1752 0 2.0000 3.62686 3.62686 4.44089e-16 3.0000 10.0179 10.0179 0 4.0000 27.2899 27.2899 3.55271e-15 5.0000 74.2032 74.2032 0 10.0000 11013.2 11013.2 0 r8_sinh_test: Normal end of execution. r8_spence_test: Python version: 2.7.17 r8_spence evaluates Spence's integral. X SPENCE(X) r8_spence(X) Diff 0.0000 0 0 0 0.0500 0.0506393 0.0506393 6.93889e-18 0.1000 0.102618 0.102618 2.77556e-17 0.1500 0.156035 0.156035 0 0.2000 0.211004 0.211004 2.77556e-17 0.2500 0.267653 0.267653 0 0.3000 0.32613 0.32613 5.55112e-17 0.3500 0.386606 0.386606 0 0.4000 0.449283 0.449283 5.55112e-17 0.4500 0.514399 0.514399 1.11022e-16 0.5000 0.582241 0.582241 0 0.5500 0.653158 0.653158 0 0.6000 0.727586 0.727586 0 0.6500 0.806083 0.806083 0 0.7000 0.889378 0.889378 2.22045e-16 0.7500 0.978469 0.978469 1.11022e-16 0.8000 1.07479 1.07479 4.44089e-16 0.8500 1.18058 1.18058 0 0.9000 1.29971 1.29971 2.22045e-16 0.9500 1.44063 1.44063 4.44089e-16 1.0000 1.64493 1.64493 4.44089e-16 r8_spence_test: Normal end of execution. r8_sqrt_test: Python version: 2.7.17 r8_sqrt evaluates the square root function. X SQRT(X) r8_sqrt(X) Diff 0.0000 0 0 0 0.0000 9e-05 9e-05 1.35525e-20 0.0900 0.3 0.3 5.55112e-17 0.1000 0.316228 0.316228 1.11022e-16 0.4000 0.632456 0.632456 1.11022e-16 1.0000 1 1 2.22045e-16 2.0000 1.41421 1.41421 2.22045e-16 3.0000 1.73205 1.73205 2.22045e-16 3.1416 1.77245 1.77245 2.22045e-16 19.0000 4.3589 4.3589 0 29.0000 5.38516 5.38516 0 71.0000 8.42615 8.42615 0 97.0000 9.84886 9.84886 0 123456789.0000 11111.1 11111.1 5.45697e-12 r8_sqrt_test: Normal end of execution. r8_tan_test: Python version: 2.7.17 r8_tan evaluates the tangent function. X TAN(X) r8_tan(X) Diff 0 0 0 0 0.2618 0.267949 0.267949 5.55112e-17 0.5 0.546302 0.546302 2.22045e-16 0.5236 0.57735 0.57735 2.22045e-16 0.7854 1 1 2.22045e-16 1 1.55741 1.55741 8.88178e-16 1.047 1.73205 1.73205 1.11022e-15 1.309 3.73205 3.73205 8.88178e-16 1.44 7.59575 7.59575 3.55271e-15 1.505 15.2571 15.2571 1.95399e-14 2 -2.18504 -2.18504 1.33227e-15 3 -0.142547 -0.142547 0 3.142 0 -1.11022e-16 1.11022e-16 4 1.15782 1.15782 0 5 -3.38052 -3.38052 0 r8_tan_test: Normal end of execution. r8_tanh_test: Python version: 2.7.17 r8_tanH evaluates the hyperbolic tangent function. tanh_values() returns some exact values. X TANH(X) r8_tanH(X) Diff -5 -0.999909 -0.999909 1.11022e-16 -1 -0.761594 -0.761594 2.22045e-16 0 0 0 0 0.1 0.099668 0.099668 1.38778e-17 0.2 0.197375 0.197375 0 0.3 0.291313 0.291313 5.55112e-17 0.4 0.379949 0.379949 5.55112e-17 0.5 0.462117 0.462117 5.55112e-17 0.6 0.53705 0.53705 1.11022e-16 0.7 0.604368 0.604368 0 0.8 0.664037 0.664037 1.11022e-16 0.9 0.716298 0.716298 0 1 0.761594 0.761594 2.22045e-16 2 0.964028 0.964028 1.11022e-16 3 0.995055 0.995055 1.11022e-16 4 0.999329 0.999329 1.11022e-16 5 0.999909 0.999909 1.11022e-16 10 1 1 1.11022e-16 r8_tanh_test: Normal end of execution. r8_upak_test: Python version: 2.7.17 r8_upak converts an R8 to a mantissa and base 2 exponent. X Mantissa Exponent 64 0.5 7 128 0.5 8 -64 -0.5 7 96 0.75 7 15 0.9375 4 0.5 0.5 0 0.25 0.5 -1 0.625 0.625 0 64.625 0.5048828125 7 3.141592653589793 0.7853981633974483 2 0 0 0 r8_upak_test: Normal end of execution. fn_test: Normal end of execution. Tue Oct 19 11:36:09 2021