26-Jul-2022 16:00:22 toms577_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 toms577() evaluates Carlson's elliptic functions. rc_test(): rc() evaluates the elementary integral RC(X,Y) X Y RC(X,Y) 1.51e-78 1.51e-78 8.137884587711593e+38 3.01e-78 5.5e-79 9.524521540989471e+38 0 3.01e-78 9.053919509295885e+38 9.9e+74 5.5e-79 5.629713505821428e-36 0 9.9e+74 4.992318443077758e-38 9.9e+74 9.9e+74 3.178208630818641e-38 RC - Error! Invalid input arguments. X = 0 Y = 2e-78 0 2e-78 **Error*** 0 0.25 3.141592653589793 0.0625 0.125 3.141592653589793 2.25 2 0.6931471805599454 0.01 1 1.478037662374775 0.02 1 1.443406235712271 0.05 1 1.380231154269966 0.1 1 1.316609847527586 0.2 1 1.237829897094659 0.4 1 1.143920647968054 0.6 1 1.082636119571208 0.8 1 1.036747571331046 1 1 1 1.2 1 0.9693519329631458 1.5 1 0.9312298594527122 2 1 0.8813735870195432 3 1 0.8104969894767539 4 1 0.7603459963009465 5 1 0.7218177375894052 10 1 0.6061488197440222 20 1 0.4997299176960261 50 1 0.3777315372940898 100 1 0.3008302149854818 1000 1 0.131198146266784 10000 1 0.05298557300099017 100000 1 0.02039555141711115 1000000 1 0.007600906009995943 10000000 1 0.002767687204982141 100000000 1 0.0009903487599553565 1000000000 1 0.0003495828416193509 10000000000 1 0.0001220607264611548 1000000000000 1 1.450865773853122e-05 1000000000000000 1 5.680252434588194e-07 1e+20 1 2.37189981105004e-09 1e+30 1 3.523192357547063e-14 1e+40 1 4.674484904044085e-19 1e+50 1 5.825777450541109e-24 rc_test2(): Compare LOG(X)/(X-1) and ARCTAN(X) with values based on rc(). X From LOG From RC 0.2 2.011797390542625 2.011797390542625 0.4 1.527151219790258 1.527151219790258 0.6 1.277064059414976 1.277064059414977 0.8 1.115717756571049 1.115717756571049 1 ***** ZERO DIVIDE ***** 1 1 0.9116077839697732 0.911607783969773 1 0.8411805915530323 0.8411805915530324 2 0.7833393820762259 0.7833393820762258 2 0.7347333311276488 0.7347333311276486 2 0.6931471805599453 0.6931471805599454 Extreme values of X X From LOG From RC 1e-75 172.6938819745534 172.6938819745534 1e-65 149.668031044613 149.668031044613 1e-55 126.6421801146725 126.6421801146725 1e-45 103.6163291847321 103.616329184732 1e-35 80.59047825479161 80.59047825479161 1e-25 57.56462732485114 57.56462732485113 1e-15 34.53877639491072 34.53877639491072 1e-05 11.51304059537618 11.51304059537618 1e+05 0.0001151304059537618 0.0001151304059537618 1e+15 3.453877639491072e-14 3.453877639491072e-14 1e+25 5.756462732485114e-24 5.756462732485114e-24 1e+35 8.059047825479162e-34 8.059047825479158e-34 1e+45 1.036163291847321e-43 1.036163291847321e-43 1e+55 1.266421801146725e-53 1.266421801146725e-53 1e+65 1.49668031044613e-63 1.49668031044613e-63 1e+75 1.726938819745534e-73 1.726938819745534e-73 X From ARCTAN From RC RC - Error! Invalid input arguments. X = 1e+75 Y = 1e+75 1e-75 1e-75 0 1e-15 1e-15 9.999999999999999e-16 0.001 0.0009999996666668668 0.0009999996666668666 0.1 0.09966865249116204 0.09966865249116202 0.2 0.1973955598498808 0.1973955598498808 0.5 0.4636476090008061 0.4636476090008061 1 0.7853981633974483 0.7853981633974482 2 1.10714871779409 1.107148717794091 5 1.373400766945016 1.373400766945016 1e+01 1.471127674303735 1.471127674303734 1e+03 1.56979632712823 1.56979632712823 1e+15 1.570796326794896 1.570796326794896 1e+75 1.570796326794897 1.570796326794897 rd_test(): rd() evaluates the Carlson elliptic integral of the second kind, RD(X,Y,Z) X Y Z RD(X,Y,Z) 0 6.010000000000001e-51 6.010000000000001e-51 5.057075390167092e+75 5.5e-79 6.010000000000001e-51 6.010000000000001e-51 5.057075390167032e+75 0 6.010000000000001e-51 9.9e+47 3.455579458524223e-70 5.5e-79 6.010000000000001e-51 9.9e+47 3.455579458524223e-70 0 9.9e+47 6.010000000000001e-51 5.016827696801392e+26 5.5e-79 9.9e+47 6.010000000000001e-51 5.016827696801343e+26 0 9.9e+47 9.9e+47 2.391984406816877e-72 5.5e-79 9.9e+47 9.9e+47 2.391984406816877e-72 3.01e-51 3.01e-51 6.010000000000001e-51 3.170935022408316e+75 3.01e-51 3.01e-51 9.9e+47 3.444999003763636e-70 9.9e+47 9.9e+47 6.010000000000001e-51 3.908848372573853e-23 9.9e+47 9.9e+47 9.9e+47 1.015189712383042e-72 RD - Error! Invalid input arguments. X = 0 Y = 3.01e-51 Z = 1 0 3.01e-51 1 ***Error*** 0 2 1 1.797210352103389 0.5 1 1e-10 424255.9649759194 0.5 1 1e-05 1333.576985789446 0.5 1 0.01 35.43137955816859 0.5 1 0.1 8.049184457709792 0.5 1 0.2 4.795496764410121 0.5 1 0.5 2.260648559158617 0.5 1 1 1.210841860059132 0.5 1 2 0.617673967507255 0.5 1 5 0.2361769958541499 0.5 1 10 0.108671998114634 0.5 1 100 0.006540379849123936 0.5 1 100000 5.320236560151541e-07 0.5 1 10000000000 3.409325949193374e-14 rf_test(): rf() evaluates the Carlson elliptic integral of the first kind, RF(X,Y,Z) X Y Z RF(X,Y,Z) 1.51e-78 1.51e-78 1.51e-78 8.137884587711593e+38 1.51e-78 1.51e-78 9.9e+74 5.613664399997798e-36 0 3.01e-78 3.01e-78 9.053919509295885e+38 0 3.01e-78 9.9e+74 5.624731938415326e-36 0 9.9e+74 9.9e+74 4.992318443077759e-38 9.9e+74 9.9e+74 9.9e+74 3.178208630818641e-38 5.5e-79 3.01e-78 3.01e-78 7.198956468812792e+38 5.5e-79 3.01e-78 9.9e+74 5.613420743331975e-36 5.5e-79 9.9e+74 9.9e+74 4.992318443077759e-38 RF - Error! Invalid input arguments. X = 0 Y = 2e-78 Z = 1 0 2e-78 1 ***Error*** 0 1 2 1.31102877714606 0.5 1 1 1.110720734539592 0.5 1 1.1 1.091430716268119 0.5 1 1.2 1.073732561377385 0.5 1 1.3 1.057389655801202 0.5 1 1.4 1.042214695930046 0.5 1 1.5 1.028056801052127 0.5 1 1.6 1.014792597551546 0.5 1 1.7 1.002319885847406 0.5 1 1.8 0.9905530382414446 0.5 1 1.9 0.9794195874708435 0.5 1 2 0.9688576532724523 0.5 1 2.2 0.9492423586314841 0.5 1 2.4 0.931359056602438 0.5 1 2.6 0.9149398964447096 0.5 1 2.8 0.8997743463505848 0.5 1 3 0.8856939232035483 0.5 1 3.5 0.8543997654075564 0.5 1 4 0.8275182379903345 0.5 1 4.5 0.8040168167992912 0.5 1 5 0.7831840398091505 0.5 1 6 0.7476135036481746 0.5 1 7 0.7180694683312081 0.5 1 8 0.6929108826625124 0.5 1 9 0.6710782484938838 0.5 1 10 0.6518490214136576 0.5 1 20 0.5331872892861481 0.5 1 30 0.4706527717638377 0.5 1 40 0.4295233682160168 0.5 1 50 0.3994861473220863 0.5 1 100 0.3163981445460594 0.5 1 200 0.2479287246742144 0.5 1 500 0.1771580322263678 0.5 1 1000 0.1361926299714245 0.5 1 10000 0.05456849363690315 0.5 1 100000 0.02089626719954944 0.5 1 1000000 0.007759252354859355 0.5 1 100000000 0.001006183477210615 0.5 1 10000000000 0.0001236441982979439 0.5 1 1000000000000 1.46670049223499e-05 0.5 1 1000000000000000 5.73032621078277e-07 0.5 1 1e+20 2.387734529432078e-09 0.5 1 1e+30 3.539027075929101e-14 0.5 1 1e+40 4.690319622426123e-19 0.5 1 1e+50 5.841612168923146e-24 rj_test(): rj() evaluates the Carlson elliptic integral of the third kind, RJ(X,Y,Z,P) X Y Z P RJ(X,Y,Z,P) 1.01e-26 1.01e-26 1.01e-26 2.01e-26 6.363797977910284e+38 1.01e-26 1.01e-26 2.99e+24 2.01e-26 59698096408103.98 0 2.01e-26 2.01e-26 2.01e-26 8.268315690384853e+38 0 2.01e-26 2.99e+24 2.01e-26 86315661487498.53 0 2.99e+24 2.99e+24 2.01e-26 1.11165983529589e-11 2.99e+24 2.99e+24 2.99e+24 2.01e-26 3.333899154957826e-35 5.5e-79 2.01e-26 2.01e-26 2.01e-26 8.268315690384853e+38 5.5e-79 2.01e-26 2.99e+24 2.01e-26 86315661487498.53 5.5e-79 2.99e+24 2.99e+24 2.01e-26 1.11165983529589e-11 2.01e-26 2.01e-26 2.01e-26 2.01e-26 3.509182168450738e+38 1.01e-26 1.01e-26 1.01e-26 2.99e+24 9.983650737892871e-12 1.01e-26 1.01e-26 2.99e+24 2.99e+24 3.353865073488965e-35 0 2.01e-26 2.01e-26 2.99e+24 1.11165983529589e-11 0 2.01e-26 2.99e+24 2.99e+24 3.374118957422856e-35 0 2.99e+24 2.99e+24 2.99e+24 4.557265740116441e-37 2.99e+24 2.99e+24 2.99e+24 2.99e+24 1.934163652061004e-37 5.5e-79 2.01e-26 2.01e-26 2.99e+24 1.11165983529589e-11 5.5e-79 2.01e-26 2.99e+24 2.99e+24 3.374118957422856e-35 5.5e-79 2.99e+24 2.99e+24 2.99e+24 4.557265740116441e-37 2.01e-26 2.01e-26 2.01e-26 2.99e+24 7.077046312962523e-12 RJ - Error! Invalid input arguments. X = 0 Y = 1.9e-26 Z = 1.9e-26 P = 1 0 1.9e-26 1.9e-26 1 ***Error*** 2 3 4 5 0.1429757966715675 0.5 1 1 0.25 2.608105757997978 0.5 1 1 0.75 1.442864193614197 0.5 1 1 1 1.210841860059132 0.5 1 1 2 0.7670625432950464 0.5 1 2 0.25 2.008380291058661 0.5 1 2 0.75 1.136845217951276 0.5 1 2 1.5 0.7460643441600711 0.5 1 2 4 0.3794195060366037 0.5 1 5 0.25 1.370892718222587 0.5 1 5 0.75 0.7949204422899481 0.5 1 5 3 0.338529421141784 0.5 1 5 10 0.139847651098525 0.5 1 10 0.25 1.005572682199914 0.5 1 10 0.75 0.5908850286211613 0.5 1 10 5 0.1811791604390096 0.5 1 10 20 0.06283564851298871 0.5 1 100 0.25 0.3343272158567165 0.5 1 100 0.75 0.2006464395741285 0.5 1 100 50 0.01167793209710091 0.5 1 100 200 0.003581148146400939 toms577_test(): Normal end of execution. 26-Jul-2022 16:00:22