Scalar Tests Testing ran: Volume of unit n-sphere, n = 2, 3, 4 # points PI (4/3)*PI (1/2)*PI^2 2 4.000000 8.000000 16.000000 4 4.000000 6.000000 12.000000 8 3.500000 6.000000 8.000000 16 3.250000 5.500000 5.000000 32 3.375000 5.000000 5.000000 64 3.187500 4.625000 5.250000 128 3.281250 4.750000 5.625000 256 3.281250 4.250000 4.687500 512 3.242188 4.218750 4.750000 1024 3.171875 4.203125 4.890625 2048 3.123047 4.183594 4.929688 4096 3.125977 4.185547 4.910156 8192 3.144043 4.151367 4.855469 16384 3.138184 4.137695 4.904297 32768 3.141479 4.149902 4.906250 actual 3.141593 4.188790 4.934803 Testing ran0: Volume of unit n-sphere, n = 2, 3, 4 # points PI (4/3)*PI (1/2)*PI^2 2 4.000000 4.000000 8.000000 4 4.000000 4.000000 4.000000 8 4.500000 5.000000 2.000000 16 4.500000 5.000000 4.000000 32 3.625000 4.000000 3.500000 64 3.500000 4.625000 5.750000 128 3.531250 4.687500 6.000000 256 3.281250 4.437500 5.250000 512 3.210938 4.421875 5.187500 1024 3.082031 4.148438 4.796875 2048 3.144531 4.160156 4.992188 4096 3.158203 4.199219 4.968750 8192 3.146973 4.211914 5.042969 16384 3.140381 4.217773 4.952148 32768 3.133545 4.176025 4.930176 actual 3.141593 4.188790 4.934803 Testing ran1: Volume of unit n-sphere, n = 2, 3, 4 # points PI (4/3)*PI (1/2)*PI^2 2 4.000000 4.000000 0.000000 4 4.000000 4.000000 4.000000 8 4.500000 4.000000 2.000000 16 3.500000 3.500000 3.000000 32 3.375000 3.500000 4.000000 64 3.250000 3.625000 4.250000 128 3.218750 3.937500 4.750000 256 3.093750 3.875000 4.875000 512 3.148438 4.093750 5.125000 1024 3.089844 4.156250 5.031250 2048 3.140625 4.242188 5.187500 4096 3.156250 4.189453 5.062500 8192 3.133789 4.173828 4.955078 16384 3.138184 4.209473 4.924805 32768 3.150757 4.214600 4.944336 actual 3.141593 4.188790 4.934803 Testing ran2: Volume of unit n-sphere, n = 2, 3, 4 # points PI (4/3)*PI (1/2)*PI^2 2 0.000000 0.000000 0.000000 4 3.000000 6.000000 4.000000 8 2.500000 3.000000 2.000000 16 3.250000 5.000000 4.000000 32 3.375000 4.750000 5.000000 64 3.312500 4.625000 6.250000 128 3.312500 4.500000 5.625000 256 3.328125 4.468750 5.375000 512 3.273438 4.484375 5.062500 1024 3.183594 4.328125 4.906250 2048 3.121094 4.226563 5.070313 4096 3.139648 4.218750 4.964844 8192 3.145996 4.239258 5.000000 16384 3.155029 4.265137 5.048828 32768 3.147949 4.202393 4.979492 actual 3.141593 4.188790 4.934803 Testing ran3: Volume of unit n-sphere, n = 2, 3, 4 # points PI (4/3)*PI (1/2)*PI^2 2 2.000000 4.000000 0.000000 4 3.000000 6.000000 4.000000 8 2.500000 5.000000 6.000000 16 3.250000 4.000000 5.000000 32 3.375000 4.750000 6.500000 64 3.312500 4.000000 5.000000 128 3.000000 3.687500 4.500000 256 3.218750 4.125000 4.312500 512 3.210938 4.343750 5.093750 1024 3.191406 4.289063 4.937500 2048 3.175781 4.210938 4.726563 4096 3.169922 4.162109 4.894531 8192 3.169434 4.183594 4.921875 16384 3.180420 4.201660 4.949219 32768 3.161987 4.214600 5.011719 actual 3.141593 4.188790 4.934803 Vector Tests Testing ran0: Volume of unit n-sphere, n = 2, 3, 4 # points PI (4/3)*PI (1/2)*PI^2 2 2.000000 0.000000 0.000000 4 3.000000 2.000000 0.000000 8 4.000000 6.000000 4.000000 16 3.500000 5.500000 7.000000 32 3.250000 5.000000 6.000000 64 3.375000 5.125000 6.250000 128 3.375000 4.375000 5.750000 256 3.250000 4.437500 5.812500 512 3.203125 4.296875 5.468750 1024 3.101563 4.054688 4.828125 2048 3.136719 4.195313 4.960938 4096 3.100586 4.101563 4.789063 8192 3.116699 4.178711 4.886719 actual 3.141593 4.188790 4.934803 Testing ran1: Volume of unit n-sphere, n = 2, 3, 4 # points PI (4/3)*PI (1/2)*PI^2 2 4.000000 4.000000 0.000000 4 4.000000 6.000000 0.000000 8 3.500000 4.000000 2.000000 16 3.500000 4.000000 3.000000 32 3.125000 4.000000 4.000000 64 3.312500 4.250000 4.250000 128 3.062500 4.187500 3.875000 256 3.218750 4.312500 4.500000 512 3.195313 4.140625 4.531250 1024 3.156250 3.953125 4.484375 2048 3.125000 4.109375 4.750000 4096 3.134766 4.115234 4.781250 8192 3.133301 4.181641 4.886719 actual 3.141593 4.188790 4.934803 Testing ran2: Volume of unit n-sphere, n = 2, 3, 4 # points PI (4/3)*PI (1/2)*PI^2 2 4.000000 4.000000 0.000000 4 5.000000 6.000000 4.000000 8 4.000000 6.000000 6.000000 16 4.000000 6.500000 7.000000 32 3.250000 5.000000 6.000000 64 3.187500 4.750000 6.000000 128 3.250000 4.625000 5.625000 256 3.203125 4.218750 4.750000 512 3.257813 4.328125 4.812500 1024 3.234375 4.335938 5.218750 2048 3.136719 4.160156 4.929688 4096 3.131836 4.205078 5.050781 8192 3.124023 4.164063 4.886719 actual 3.141593 4.188790 4.934803 Testing ran3: Volume of unit n-sphere, n = 2, 3, 4 # points PI (4/3)*PI (1/2)*PI^2 2 2.000000 4.000000 8.000000 4 4.000000 8.000000 12.000000 8 4.000000 7.000000 8.000000 16 4.000000 6.500000 7.000000 32 3.500000 5.500000 6.500000 64 3.437500 5.250000 5.500000 128 3.250000 4.625000 4.875000 256 3.296875 4.437500 4.562500 512 3.187500 4.203125 4.906250 1024 3.191406 4.148438 4.765625 2048 3.181641 4.199219 4.648438 4096 3.135742 4.195313 4.750000 8192 3.123047 4.142578 4.765625 actual 3.141593 4.188790 4.934803