6 October 2025 6:20:49.696 PM hypersphere_monte_carlo_test(): Fortran90 version Test hypersphere_monte_carlo(). TEST01 Use HYPERSPHERE01_SAMPLE to estimate integrals on the surface of the unit hypersphere. Spatial dimension = 3 N 1 X^2 Y^2 Z^2 X^4 X^2Y^2 Z^4 1 12.5664 0.873353 1.68088 10.0121 0.606973E-01 0.116820 7.97708 2 12.5664 6.77875 1.91311 3.87451 4.92199 0.451037 1.56472 4 12.5664 1.91777 5.04605 5.60255 0.553588 1.05150 3.62851 8 12.5664 5.91418 2.38709 4.26509 4.19594 0.718635 2.42433 16 12.5664 5.54638 5.30037 1.71962 3.35592 1.57106 0.732079 32 12.5664 4.43211 5.01675 3.11751 3.00218 0.814445 1.50152 64 12.5664 4.37480 3.63296 4.55861 2.84545 0.703489 3.05516 128 12.5664 4.00304 4.15489 4.40844 2.36251 0.842291 2.70546 256 12.5664 4.01017 4.11970 4.43650 2.35215 0.838689 2.74413 512 12.5664 3.91075 4.34432 4.31130 2.34858 0.809554 2.63609 1024 12.5664 4.15454 4.19879 4.21305 2.49652 0.826041 2.54525 2048 12.5664 4.21171 4.15890 4.19576 2.52623 0.848120 2.53078 4096 12.5664 4.22122 4.20840 4.13675 2.53990 0.848931 2.46366 8192 12.5664 4.17950 4.20343 4.18344 2.49869 0.839606 2.49484 16384 12.5664 4.13424 4.23263 4.19950 2.45620 0.839389 2.51127 32768 12.5664 4.14400 4.22915 4.19323 2.47978 0.837562 2.52889 65536 12.5664 4.20241 4.18491 4.17905 2.51847 0.840498 2.50025 Exact 12.5664 4.18879 4.18879 4.18879 2.51327 0.837758 2.51327 TEST02 Use HYPERSPHERE01_SAMPLE to estimate integrals on the surface of the unit hypersphere. Spatial dimension = 6 N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 31.0063 -23.3861 9.62718 0.110483 0.276605 0.434605E-03 0.647378E-04 2 31.0063 -21.2937 2.25065 0.161042 0.150047 0.203225 0.196563E-01 4 31.0063 3.51226 1.08204 0.285668 3.37503 0.204526E-01 3.24903 8 31.0063 4.83983 7.85392 0.601770 1.64000 0.101244E-01 0.611007E-01 16 31.0063 -0.441795 3.31626 0.298937 1.46328 0.719443E-01 1.42051 32 31.0063 -2.63429 5.79051 0.466848 1.83530 0.987530E-01 1.39975 64 31.0063 2.23219 4.92959 0.480663 1.20987 0.673015E-01 0.749816 128 31.0063 -1.95864 5.39598 0.614122 1.46531 0.577920E-01 1.50576 256 31.0063 -0.515952 5.88606 0.707936 1.85051 0.624686E-01 0.751741 512 31.0063 0.421535 5.87333 0.679091 1.79632 0.612826E-01 1.08119 1024 31.0063 0.619297E-01 5.14124 0.641112 2.02831 0.653546E-01 1.10864 2048 31.0063 0.251801 5.07242 0.621445 1.83675 0.696085E-01 1.07284 4096 31.0063 0.488556 5.10708 0.622799 1.99042 0.663191E-01 0.974083 8192 31.0063 -0.742024E-01 5.23271 0.634997 1.90099 0.656348E-01 1.00542 16384 31.0063 0.845433E-01 5.19502 0.648044 1.90506 0.653941E-01 0.957878 32768 31.0063 0.248270E-01 5.16814 0.647265 1.94966 0.634616E-01 0.976489 65536 31.0063 -0.279426E-01 5.18110 0.650914 1.94440 0.645652E-01 0.984730 Exact 31.0063 0.00000 5.16771 0.645964 1.93789 0.645964E-01 0.968946 HYPERSPHERE_MONTE_CARLO_TEST Normal end of execution. 6 October 2025 6:20:49.757 PM