19 December  2023   8:12:19.178 AM      
 
sphere_monte_carlo_test():
  Fortran77 version
  Test sphere_monte_carlo().
 
TEST01
  Use SPHERE01_SAMPLE to estimate integrals
  over the surface of the unit sphere.
 
         N        1              X^2             Y^2             Z^2             X^4           X^2Y^2           Z^4
 
         1     12.5664         10.5339        0.835154         1.19727         8.83023        0.700080        0.114071    
         2     12.5664         4.28968         2.47122         5.80547         1.57859        0.709761         2.68539    
         4     12.5664         1.56372         3.30088         7.70177        0.672040        0.257850         6.14261    
         8     12.5664         1.84747         6.81078         3.90812        0.859633        0.456343         1.85661    
        16     12.5664         3.17624         4.98900         4.40113         1.36133         1.03992         2.89549    
        32     12.5664         5.07425         3.92917         3.56295         3.06785         1.00885         1.94710    
        64     12.5664         3.75023         4.36541         4.45073         2.22941        0.696132         2.75584    
       128     12.5664         4.25770         3.74421         4.56445         2.56305        0.793423         2.75939    
       256     12.5664         4.19827         4.28120         4.08690         2.54469        0.843342         2.47283    
       512     12.5664         3.94159         4.26918         4.35560         2.33799        0.768640         2.70099    
      1024     12.5664         4.33650         4.13726         4.09261         2.63774        0.889952         2.48749    
      2048     12.5664         4.08640         4.32941         4.15056         2.43336        0.836960         2.48845    
      4096     12.5664         4.21149         4.11647         4.23842         2.52601        0.828100         2.53557    
      8192     12.5664         4.18569         4.14896         4.23172         2.50069        0.837680         2.53923    
     16384     12.5664         4.14831         4.19980         4.21825         2.47607        0.833538         2.53489    
     32768     12.5664         4.15185         4.16627         4.24826         2.47339        0.825077         2.55324    
 
     Exact     12.5664         4.18879         4.18879         4.18879         2.51327        0.837758         2.51327    
 
sphere_monte_carlo_test():
  Normal end of execution.
 
19 December  2023   8:12:19.195 AM