06 October 2025   6:45:33.673 PM
 
sphere_monte_carlo_test():
  Fortran90 version
  Test sphere_monte_carlo().
 
TEST01
  Use SPHERE01_SAMPLE to estimate integrals 
  over the surface of the unit sphere in 3D.
 
         N        1              X^2             Y^2             Z^2             X^4           X^2Y^2           Z^4
 
         1     12.5664         12.0203        0.134559        0.411491         11.4980        0.128712        0.134745E-01
         2     12.5664         4.52390         5.13574         2.90673         2.10215         1.46155        0.688057    
         4     12.5664         3.18794         5.19018         4.18825         1.62129        0.580505         1.49500    
         8     12.5664         4.46329         4.15657         3.94651         2.74831        0.954945         2.58805    
        16     12.5664         6.03585         2.50769         4.02283         3.81427        0.795603         2.08813    
        32     12.5664         4.50796         4.00656         4.05186         2.66670        0.812194         2.27929    
        64     12.5664         4.99963         4.33788         3.22886         3.30649        0.876893         1.53559    
       128     12.5664         3.92297         4.71109         3.93232         2.15252        0.912859         2.22880    
       256     12.5664         4.09766         4.31262         4.15609         2.47903        0.886657         2.60372    
       512     12.5664         4.05083         4.14956         4.36598         2.37596        0.821142         2.68618    
      1024     12.5664         4.29580         4.02427         4.24630         2.60365        0.834501         2.54000    
      2048     12.5664         4.27177         4.17576         4.11884         2.56743        0.863388         2.42928    
      4096     12.5664         4.15873         4.18689         4.22075         2.49859        0.815797         2.53856    
      8192     12.5664         4.19175         4.15416         4.22046         2.51997        0.837250         2.53925    
     16384     12.5664         4.17510         4.20588         4.18539         2.50576        0.840190         2.51757    
     32768     12.5664         4.13717         4.19614         4.23305         2.46369        0.836312         2.54752    
     65536     12.5664         4.19101         4.18977         4.18560         2.50714        0.842347         2.50542    
 
     Exact     12.5664         4.18879         4.18879         4.18879         2.51327        0.837758         2.51327    
 
sphere_monte_carlo_test():
  Normal end of execution.
 
06 October 2025   6:45:33.698 PM