03 January 2014 11:50:53 AM HYPERBALL_VOLUME_MONTE_CARLO: C++ version Use a Monte Carlo approach to estimate the volume of the unit hyperball in M dimensions. HYPERBALL_VOLUME_MONTE_CARLO: Using default seed for random number generator. The spatial dimension is 6 The random number seed is 123456789 Log(N) N Estimate Error 0 1 0 5.2 1 2 0 5.2 2 4 0 5.2 3 8 0 5.2 4 16 0 5.2 5 32 6 0.83 6 64 3 2.2 7 128 6 0.83 8 256 5.25 0.082 9 512 4.875 0.29 10 1024 4.8125 0.36 11 2048 5.28125 0.11 12 4096 5.234375 0.067 13 8192 5.4296875 0.26 14 16384 5.328125 0.16 15 32768 5.1796875 0.012 16 65536 5.206054688 0.038 17 131072 5.22265625 0.055 18 262144 5.184082031 0.016 19 524288 5.161987305 0.0057 20 1048576 5.161743164 0.006 21 2097152 5.16003418 0.0077 22 4194304 5.154342651 0.013 23 8388608 5.161132812 0.0066 24 16777216 5.163551331 0.0042 25 33554432 5.16340065 0.0043 oo oo 5.16771278 0 HYPERBALL_VOLUME_MONTE_CARLO: Normal end of execution. 03 January 2014 11:51:00 AM