7 October 2025 1:10:42.974 PM hyperball_monte_carlo_test(): Fortran77 version Test ball_monte_carlo(). TEST01 Use Monte Carlo to estimate integrals over the interior of the unit hyperball in M dimensions. The spatial dimension M = 3 N 1 X^2 Y^2 Z^2 X^4 X^2Y^2 Z^4 1 4.18879 1.95456 0.154962 0.222153 0.912032 0.723078E-01 0.117819E-01 2 4.18879 1.62731 1.05487 0.664254 1.26129 0.136638 0.210351 4 4.18879 0.734514 0.199887 0.971398 0.368033 0.651732E-01 0.305456 8 4.18879 0.517291 0.891092 0.408330 0.127877 0.109757 0.923969E-01 16 4.18879 0.983047 0.931486 1.06439 0.477341 0.159812 0.488477 32 4.18879 1.03570 0.703630 0.877538 0.497207 0.108907 0.378070 64 4.18879 0.789039 0.675452 0.839127 0.333270 0.656307E-01 0.350401 128 4.18879 0.915054 0.825066 0.886565 0.403059 0.112893 0.405476 256 4.18879 0.763896 0.872109 0.916547 0.300699 0.125996 0.422931 512 4.18879 0.815962 0.903185 0.817093 0.349506 0.120456 0.357843 1024 4.18879 0.855916 0.814805 0.822955 0.375218 0.117958 0.340883 2048 4.18879 0.843579 0.835054 0.831435 0.359523 0.122554 0.356660 4096 4.18879 0.853495 0.810376 0.844804 0.370678 0.119071 0.366617 8192 4.18879 0.843629 0.822722 0.843863 0.361941 0.119218 0.361640 16384 4.18879 0.820308 0.842325 0.838738 0.347649 0.118054 0.356431 32768 4.18879 0.839988 0.834583 0.842454 0.358756 0.120813 0.362220 65536 4.18879 0.842308 0.837056 0.838084 0.360922 0.120189 0.360257 Exact 4.18879 0.837758 0.837758 0.837758 0.359039 0.119680 0.359039 TEST02 Use Monte Carlo to estimate integrals over the interior of the unit hyperball in M dimensions. The spatial dimension M = 6 N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 5.16771 3.04274 0.142038 0.559680E-02 0.222997E-03 0.114102E-01 0.225440E-03 2 5.16771 2.62493 0.110915 0.113869E-01 0.234930E-02 0.147631E-01 0.924880E-03 4 5.16771 -0.170038E-01 0.601223 0.155288 0.723497 0.219124E-02 0.108755 8 5.16771 0.277771 0.233428 0.263582E-01 0.489504 0.179494E-02 0.202893 16 5.16771 0.107164 0.691127 0.306501E-01 0.439393 0.920459E-02 0.143656E-01 32 5.16771 -0.257685 0.861574 0.637342E-01 0.234514 0.892938E-02 0.109810 64 5.16771 -0.281593 0.816894 0.926378E-01 0.121491 0.556367E-02 0.762952E-01 128 5.16771 0.202221 0.769736 0.708359E-01 0.180174 0.333151E-02 0.555347E-01 256 5.16771 0.481350E-01 0.719478 0.780483E-01 0.170988 0.535052E-02 0.845573E-01 512 5.16771 -0.198148 0.653258 0.614065E-01 0.176476 0.549871E-02 0.881022E-01 1024 5.16771 0.612776E-01 0.662809 0.654038E-01 0.165125 0.594789E-02 0.784103E-01 2048 5.16771 -0.736841E-01 0.635707 0.639241E-01 0.185490 0.511389E-02 0.789078E-01 4096 5.16771 -0.158125E-01 0.641492 0.633989E-01 0.189354 0.544617E-02 0.834174E-01 8192 5.16771 -0.954104E-02 0.651746 0.661295E-01 0.195343 0.511429E-02 0.815556E-01 16384 5.16771 -0.141411E-02 0.652669 0.642869E-01 0.192642 0.536623E-02 0.775498E-01 32768 5.16771 0.470413E-02 0.637075 0.639778E-01 0.189994 0.548752E-02 0.812996E-01 65536 5.16771 0.590031E-02 0.642482 0.650386E-01 0.193155 0.534675E-02 0.805000E-01 Exact 5.16771 0.00000 0.645964 0.645964E-01 0.193789 0.538303E-02 0.807455E-01 hyperball_monte_carlo_test(): Normal end of execution. 7 October 2025 1:10:43.068 PM