Here are sample outputs from KonStat2, the program created by compiling and
linking together KonStat2.c, Konton2.c, and (optionally)
snow2.c. All these tests are documented in the
The Tests in KonStat2.c section of
the Konton2 page. For the source code, see the
Konton2 Source Code section of the Konton2 page. The source code for the
generators is in BadPRNGs.zip
(6 KB--5768 bytes).
Below are some results for weak, but widely used, PRNGs. These results are provided to show how weak the generators really are and to show what bad results from KonStat2 look like.
This is Prof. Marsaglia's multiply-with-carry generator.
the test sequence length = 128 MB ------------------------------------------------------------------------------ MultWithCarry.bin cumulative sums, 1 sequence the bit runs statistic = 21.34037 [P = 0.0188]* the alt. 1 bit runs statistic = 9.77794 [P = 0.4602] the alt. 2 bit runs statistic = 9.57193 [P = 0.4788] the alt. 3 bit runs statistic = 24.12542 [P = 0.0073]** the alt. 4 bit runs statistic = 8.88542 [P = 0.5430] the alt. 5 bit runs statistic = 17.37564 [P = 0.0665]* the block bit freq. statistic = 263.31780 [P = 0.3633] the bit frequency statistic = 0.61551 [P = 0.4327] the tidbit frequency statistic = 1.45322 [P = 0.6931] the nibble frequency statistic = 13.65053 [P = 0.5522] the byte frequency statistic = 232.90118 [P = 0.8361] the bit 0 statistic = 0.56083 [P = 0.4539] the bit 1 statistic = 0.05201 [P = 0.8196] the bit 2 statistic = 0.09796 [P = 0.7543] the bit 3 statistic = 0.64025 [P = 0.4236] the bit 4 statistic = 0.23298 [P = 0.6293] the bit 5 statistic = 6.85205 [P = 0.0089]** the bit 6 statistic = 0.16193 [P = 0.6874] the bit 7 statistic = 0.07601 [P = 0.7828] the overall bit statistic = 8.67401 [P = 0.3705] the 8-bit-sum statistic = 9.51335 [P = 0.3009] the 16-bit-sum statistic = 1.48758 [P = 0.4753] the 32-bit-sum statistic = 1.34814 [P = 0.5096] the odd/even-bit-sum statistic = 59.50766 [P = 0.6015] the 64-bit matrix statistic = 467.16250 [P = 0.0000]**** the 128-bit matrix statistic = 444.00335 [P = 0.0000]**** the 256-bit matrix statistic = 365.70023 [P = 0.0000]**** the 512-bit matrix statistic = 419.27180 [P = 0.0000]**** the 1024-bit matrix statistic = 470.12866 [P = 0.0000]**** the 2048-bit matrix statistic = 478.00998 [P = 0.0000]**** the bit prediction A statistic = 0.01088 [P = 0.9169]^ the bit prediction B statistic = 1.43695 [P = 0.2306] the bit prediction C statistic = 1.29991 [P = 0.2542] the bit prediction D statistic = 1.01766 [P = 0.3131] the bit prediction E statistic = 0.01819 [P = 0.8927] the byte prediction A statistic = 0.41582 [P = 0.5190] the byte prediction B statistic = 1.01204 [P = 0.3144] the byte prediction C statistic = 0.08525 [P = 0.7703] the byte prediction D statistic = 0.31719 [P = 0.5733] the byte repetition statistic = 1.16200 [P = 0.2811] the 2-byte AND statistic = 1.85870 [P = 0.9322]^ the 4-byte AND statistic = 1.78973 [P = 0.4087] the 4-byte AND-OR statistic = 0.44911 [P = 0.7989] the 2-byte up/down statistic = 0.76430 [P = 0.6824] the 4-byte up/down statistic = 3.30606 [P = 0.8553] the rect. distance statistic = 6.00548 [P = 0.4226] the 4-byte collision statistic = 0.66099 [P = 0.4162] the 6-byte collision statistic = 1.47421 [P = 0.2247] the 8-byte collision statistic = 0.00101 [P = 0.9747]^ the 12-byte collision statistic = 0.11765 [P = 0.7316] the 16-byte collision statistic = 0.01232 [P = 0.9116]^ the 24-byte collision statistic = 0.08296 [P = 0.7733] the 32-byte collision statistic = 1.89146 [P = 0.1690] the 1-byte offset XOR statistic = 248.16724 [P = 0.6086] the 2-byte offset XOR statistic = 238.44331 [P = 0.7642] the 6-byte offset XOR statistic = 245.55624 [P = 0.6531] the 24-byte offset XOR stat. = 247.89907 [P = 0.6133] the 120-byte offset XOR stat. = 230.74997 [P = 0.8600] the 720-byte offset XOR stat. = 250.72386 [P = 0.5639] the 5040-byte offset XOR stat. = 272.64686 [P = 0.2138] the 40320-byte offset XOR stat. = 259.02937 [P = 0.4180] the 362880-byte off. XOR stat. = 216.97292 [P = 0.9596]^ the mod 3 statistic = 6.05138 [P = 0.0485]* the mod 5 statistic = 1.12610 [P = 0.8901] the mod 7 statistic = 2.62559 [P = 0.8542] the mod 11 statistic = 3.53147 [P = 0.9660]^ the mod 13 statistic = 7.13359 [P = 0.8487] the mod 17 statistic = 10.11267 [P = 0.8607] the mod 19 statistic = 11.95394 [P = 0.8496] the mod 23 statistic = 35.00070 [P = 0.0387]* ------------------------------------------------------------------------------
This is Prof. Marsaglia's multiply-with-carry generator.
the test sequence length = 128 MB ------------------------------------------------------------------------------ MultWithCarry2.bin cumulative sums, 1 sequence the bit runs statistic = 18.61015 [P = 0.0455]* the alt. 1 bit runs statistic = 5.71166 [P = 0.8389] the alt. 2 bit runs statistic = 6.93328 [P = 0.7317] the alt. 3 bit runs statistic = 11.12408 [P = 0.3479] the alt. 4 bit runs statistic = 2.16570 [P = 0.9949]^^ the alt. 5 bit runs statistic = 10.34059 [P = 0.4111] the block bit freq. statistic = 185.33220 [P = 0.9997]^^^ the bit frequency statistic = 2.05502 [P = 0.1517] the tidbit frequency statistic = 2.34655 [P = 0.5037] the nibble frequency statistic = 5.84765 [P = 0.9822]^ the byte frequency statistic = 190.55014 [P = 0.9991]^^^ the bit 0 statistic = 1.06824 [P = 0.3013] the bit 1 statistic = 4.65736 [P = 0.0309]* the bit 2 statistic = 0.19623 [P = 0.6578] the bit 3 statistic = 0.42470 [P = 0.5146] the bit 4 statistic = 0.40998 [P = 0.5220] the bit 5 statistic = 0.31479 [P = 0.5748] the bit 6 statistic = 0.46194 [P = 0.4967] the bit 7 statistic = 2.53895 [P = 0.1111] the overall bit statistic = 10.07218 [P = 0.2600] the 8-bit-sum statistic = 22.89856 [P = 0.0035]** the 16-bit-sum statistic = 5.71949 [P = 0.0573]* the 32-bit-sum statistic = 1.98163 [P = 0.3713] the odd/even-bit-sum statistic = 56.99971 [P = 0.6889] the 64-bit matrix statistic = 821.00119 [P = 0.0000]**** the 128-bit matrix statistic = 821.40926 [P = 0.0000]**** the 256-bit matrix statistic = 746.21045 [P = 0.0000]**** the 512-bit matrix statistic = 768.37405 [P = 0.0000]**** the 1024-bit matrix statistic = 861.58742 [P = 0.0000]**** the 2048-bit matrix statistic = 723.47546 [P = 0.0000]**** the bit prediction A statistic = 1.81420 [P = 0.1780] the bit prediction B statistic = 0.20510 [P = 0.6506] the bit prediction C statistic = 15.54334 [P = 0.0001]**** the bit prediction D statistic = 15.09994 [P = 0.0001]*** the bit prediction E statistic = 6.44467 [P = 0.0111]* the byte prediction A statistic = 0.23323 [P = 0.6291] the byte prediction B statistic = 0.94364 [P = 0.3313] the byte prediction C statistic = 0.38603 [P = 0.5344] the byte prediction D statistic = 0.00277 [P = 0.9581]^ the byte repetition statistic = 15.30317 [P = 0.0001]**** the 2-byte AND statistic = 8.98962 [P = 0.1742] the 4-byte AND statistic = 4.46144 [P = 0.1075] the 4-byte AND-OR statistic = 2.16536 [P = 0.3387] the 2-byte up/down statistic = 4.33930 [P = 0.1142] the 4-byte up/down statistic = 9.05688 [P = 0.2486] the rect. distance statistic = 1.97946 [P = 0.9216]^ the 4-byte collision statistic = 3.80731 [P = 0.0510]* the 6-byte collision statistic = 2.57542 [P = 0.1085] the 8-byte collision statistic = 0.06508 [P = 0.7986] the 12-byte collision statistic = 0.00240 [P = 0.9609]^ the 16-byte collision statistic = 0.21041 [P = 0.6465] the 24-byte collision statistic = 3.02480 [P = 0.0820]* the 32-byte collision statistic = 4.52600 [P = 0.0334]* the 1-byte offset XOR statistic = 260.45572 [P = 0.3938] the 2-byte offset XOR statistic = 251.69691 [P = 0.5467] the 6-byte offset XOR statistic = 228.59588 [P = 0.8815] the 24-byte offset XOR stat. = 228.30978 [P = 0.8842] the 120-byte offset XOR stat. = 236.47548 [P = 0.7914] the 720-byte offset XOR stat. = 224.06919 [P = 0.9192]^ the 5040-byte offset XOR stat. = 216.14919 [P = 0.9630]^ the 40320-byte offset XOR stat. = 239.74406 [P = 0.7453] the 362880-byte off. XOR stat. = 221.93694 [P = 0.9335]^ the mod 3 statistic = 2.18008 [P = 0.3362] the mod 5 statistic = 1.92580 [P = 0.7494] the mod 7 statistic = 5.31293 [P = 0.5043] the mod 11 statistic = 6.35357 [P = 0.7847] the mod 13 statistic = 11.35326 [P = 0.4989] the mod 17 statistic = 6.78415 [P = 0.9772]^ the mod 19 statistic = 16.05819 [P = 0.5885] the mod 23 statistic = 15.48308 [P = 0.8407] ------------------------------------------------------------------------------
This is Prof. Marsaglia's three shift generator.
the test sequence length = 128 MB ------------------------------------------------------------------------------ ThreeShift.bin cumulative sums, 1 sequence the bit runs statistic = 28.90448 [P = 0.0013]** the alt. 1 bit runs statistic = 31.27437 [P = 0.0005]*** the alt. 2 bit runs statistic = 20.98344 [P = 0.0212]* the alt. 3 bit runs statistic = 20.40885 [P = 0.0256]* the alt. 4 bit runs statistic = 25.77148 [P = 0.0041]** the alt. 5 bit runs statistic = 33.59695 [P = 0.0002]*** the block bit freq. statistic = 242.37141 [P = 0.7203] the bit frequency statistic = 0.03391 [P = 0.8539] the tidbit frequency statistic = 0.17799 [P = 0.9811]^ the nibble frequency statistic = 6.81654 [P = 0.9625]^ the byte frequency statistic = 155.17106 [P = 1.0000]^^^^ the bit 0 statistic = 0.78706 [P = 0.3750] the bit 1 statistic = 0.32102 [P = 0.5710] the bit 2 statistic = 0.07374 [P = 0.7860] the bit 3 statistic = 0.34128 [P = 0.5591] the bit 4 statistic = 0.21405 [P = 0.6436] the bit 5 statistic = 0.17962 [P = 0.6717] the bit 6 statistic = 0.17209 [P = 0.6783] the bit 7 statistic = 0.30118 [P = 0.5831] the overall bit statistic = 2.39004 [P = 0.9667]^ the 8-bit-sum statistic = 3.29380 [P = 0.9146]^ the 16-bit-sum statistic = 0.19181 [P = 0.9085]^ the 32-bit-sum statistic = 0.98919 [P = 0.6098] the odd/even-bit-sum statistic = 30.24538 [P = 0.9998]^^^ the 64-bit matrix statistic = 178.88945 [P = 0.9999]^^^^ the 128-bit matrix statistic = 242.61484 [P = 0.7012] the 256-bit matrix statistic = 238.77780 [P = 0.7594] the 512-bit matrix statistic = 249.68868 [P = 0.5821] the 1024-bit matrix statistic = 231.75651 [P = 0.8491] the 2048-bit matrix statistic = 254.64798 [P = 0.4944] the bit prediction A statistic = 0.01245 [P = 0.9112]^ the bit prediction B statistic = 1.41088 [P = 0.2349] the bit prediction C statistic = 0.08145 [P = 0.7753] the bit prediction D statistic = 11.93461 [P = 0.0006]*** the bit prediction E statistic = 409.62509 [P = 0.0000]**** the byte prediction A statistic = 0.00221 [P = 0.9625]^ the byte prediction B statistic = 0.94095 [P = 0.3320] the byte prediction C statistic = 1.75369 [P = 0.1854] the byte prediction D statistic = 0.00016 [P = 0.9901]^^ the byte repetition statistic = 0.05864 [P = 0.8087] the 2-byte AND statistic = 2.41195 [P = 0.8782] the 4-byte AND statistic = 0.30152 [P = 0.8601] the 4-byte AND-OR statistic = 0.00634 [P = 0.9968]^^ the 2-byte up/down statistic = 4.14185 [P = 0.1261] the 4-byte up/down statistic = 8.31066 [P = 0.3060] the rect. distance statistic = 5.26055 [P = 0.5109] the 4-byte collision statistic = 0.01183 [P = 0.9134]^ the 6-byte collision statistic = 0.03237 [P = 0.8572] the 8-byte collision statistic = 1.78534 [P = 0.1815] the 12-byte collision statistic = 1.13942 [P = 0.2858] the 16-byte collision statistic = 1.24056 [P = 0.2654] the 24-byte collision statistic = 0.00064 [P = 0.9798]^ the 32-byte collision statistic = 0.35327 [P = 0.5523] the 1-byte offset XOR statistic = 141.67310 [P = 1.0000]^^^^ the 2-byte offset XOR statistic = 145.94541 [P = 1.0000]^^^^ the 6-byte offset XOR statistic = 152.53059 [P = 1.0000]^^^^ the 24-byte offset XOR stat. = 202.56534 [P = 0.9933]^^ the 120-byte offset XOR stat. = 216.22385 [P = 0.9627]^ the 720-byte offset XOR stat. = 201.18204 [P = 0.9945]^^ the 5040-byte offset XOR stat. = 216.09203 [P = 0.9632]^ the 40320-byte offset XOR stat. = 196.86336 [P = 0.9972]^^ the 362880-byte off. XOR stat. = 201.85962 [P = 0.9940]^^ the mod 3 statistic = 0.54010 [P = 0.7633] the mod 5 statistic = 0.86088 [P = 0.9301]^ the mod 7 statistic = 2.34645 [P = 0.8852] the mod 11 statistic = 7.13684 [P = 0.7125] the mod 13 statistic = 4.51058 [P = 0.9724]^ the mod 17 statistic = 13.47458 [P = 0.6378] the mod 19 statistic = 8.20732 [P = 0.9754]^ the mod 23 statistic = 16.78600 [P = 0.7751] ------------------------------------------------------------------------------
This is Prof. Marsaglia's three shift generator.
the test sequence length = 128 MB ------------------------------------------------------------------------------ ThreeShift2.bin cumulative sums, 1 sequence the bit runs statistic = 31.86047 [P = 0.0004]*** the alt. 1 bit runs statistic = 33.09616 [P = 0.0003]*** the alt. 2 bit runs statistic = 33.22319 [P = 0.0002]*** the alt. 3 bit runs statistic = 33.76092 [P = 0.0002]*** the alt. 4 bit runs statistic = 17.39410 [P = 0.0661]* the alt. 5 bit runs statistic = 26.00328 [P = 0.0037]** the block bit freq. statistic = 237.31466 [P = 0.7931] the bit frequency statistic = 0.00463 [P = 0.9457]^ the tidbit frequency statistic = 0.53047 [P = 0.9121]^ the nibble frequency statistic = 7.76862 [P = 0.9327]^ the byte frequency statistic = 197.17987 [P = 0.9971]^^ the bit 0 statistic = 0.06154 [P = 0.8041] the bit 1 statistic = 0.29590 [P = 0.5865] the bit 2 statistic = 0.39813 [P = 0.5281] the bit 3 statistic = 1.07790 [P = 0.2992] the bit 4 statistic = 0.00636 [P = 0.9364]^ the bit 5 statistic = 0.06180 [P = 0.8037] the bit 6 statistic = 0.09613 [P = 0.7565] the bit 7 statistic = 0.83525 [P = 0.3608] the overall bit statistic = 2.83301 [P = 0.9444]^ the 8-bit-sum statistic = 4.23350 [P = 0.8355] the 16-bit-sum statistic = 0.12071 [P = 0.9414]^ the 32-bit-sum statistic = 2.12444 [P = 0.3457] the odd/even-bit-sum statistic = 40.81039 [P = 0.9865]^ the 64-bit matrix statistic = 228.91071 [P = 0.8785] the 128-bit matrix statistic = 234.61117 [P = 0.8155] the 256-bit matrix statistic = 248.46828 [P = 0.6034] the 512-bit matrix statistic = 246.29446 [P = 0.6407] the 1024-bit matrix statistic = 232.63462 [P = 0.8392] the 2048-bit matrix statistic = 216.00142 [P = 0.9636]^ the bit prediction A statistic = 1.14204 [P = 0.2852] the bit prediction B statistic = 1.21452 [P = 0.2704] the bit prediction C statistic = 0.59839 [P = 0.4392] the bit prediction D statistic = 1.47570 [P = 0.2244] the bit prediction E statistic = 480.73185 [P = 0.0000]**** the byte prediction A statistic = 1.12354 [P = 0.2892] the byte prediction B statistic = 0.46540 [P = 0.4951] the byte prediction C statistic = 1.23470 [P = 0.2665] the byte prediction D statistic = 1.01483 [P = 0.3137] the byte repetition statistic = 0.12354 [P = 0.7252] the 2-byte AND statistic = 3.24229 [P = 0.7779] the 4-byte AND statistic = 1.19532 [P = 0.5501] the 4-byte AND-OR statistic = 1.16656 [P = 0.5581] the 2-byte up/down statistic = 0.89157 [P = 0.6403] the 4-byte up/down statistic = 1.38613 [P = 0.9860]^ the rect. distance statistic = 5.73776 [P = 0.4532] the 4-byte collision statistic = 1.49842 [P = 0.2209] the 6-byte collision statistic = 4.17697 [P = 0.0410]* the 8-byte collision statistic = 5.71057 [P = 0.0169]* the 12-byte collision statistic = 0.29130 [P = 0.5894] the 16-byte collision statistic = 0.74052 [P = 0.3895] the 24-byte collision statistic = 0.06960 [P = 0.7919] the 32-byte collision statistic = 1.48062 [P = 0.2237] the 1-byte offset XOR statistic = 191.58608 [P = 0.9989]^^ the 2-byte offset XOR statistic = 193.37286 [P = 0.9984]^^ the 6-byte offset XOR statistic = 227.30907 [P = 0.8932] the 24-byte offset XOR stat. = 185.75098 [P = 0.9996]^^^ the 120-byte offset XOR stat. = 208.50528 [P = 0.9850]^ the 720-byte offset XOR stat. = 198.24582 [P = 0.9965]^^ the 5040-byte offset XOR stat. = 199.79156 [P = 0.9956]^^ the 40320-byte offset XOR stat. = 194.43655 [P = 0.9981]^^ the 362880-byte off. XOR stat. = 221.19087 [P = 0.9381]^ the mod 3 statistic = 1.32072 [P = 0.5167] the mod 5 statistic = 1.14364 [P = 0.8873] the mod 7 statistic = 6.84371 [P = 0.3355] the mod 11 statistic = 6.23042 [P = 0.7955] the mod 13 statistic = 6.71285 [P = 0.8760] the mod 17 statistic = 20.65000 [P = 0.1924] the mod 19 statistic = 16.76349 [P = 0.5394] the mod 23 statistic = 11.34133 [P = 0.9695]^ ------------------------------------------------------------------------------
An LCG (linear congruent generator); all the bits are used.
the test sequence length = 128 MB ------------------------------------------------------------------------------ LCG.bin cumulative sums, 1 sequence the bit runs statistic = 5.05564 [P = 0.8874] the alt. 1 bit runs statistic = 4.35599 [P = 0.9299]^ the alt. 2 bit runs statistic = 4.01721 [P = 0.9466]^ the alt. 3 bit runs statistic = 3.07899 [P = 0.9795]^ the alt. 4 bit runs statistic = 2.77843 [P = 0.9862]^ the alt. 5 bit runs statistic = 2.55245 [P = 0.9901]^^ the block bit freq. statistic = 133.50982 [P = 1.0000]^^^^ the bit frequency statistic = 0.01562 [P = 0.9005]^ the tidbit frequency statistic = 0.25147 [P = 0.9689]^ the nibble frequency statistic = 3.51307 [P = 0.9989]^^ the byte frequency statistic = 60.32960 [P = 1.0000]^^^^ the bit 0 statistic = 0.00000 [P = 1.0000]^^^^ the bit 1 statistic = 0.06458 [P = 0.7994] the bit 2 statistic = 0.21103 [P = 0.6460] the bit 3 statistic = 0.01259 [P = 0.9107]^ the bit 4 statistic = 0.03143 [P = 0.8593] the bit 5 statistic = 0.12598 [P = 0.7226] the bit 6 statistic = 0.02184 [P = 0.8825] the bit 7 statistic = 0.49125 [P = 0.4834] the overall bit statistic = 0.95869 [P = 0.9985]^^ the 8-bit-sum statistic = 1.34618 [P = 0.9950]^^ the 16-bit-sum statistic = 0.39041 [P = 0.8227] the 32-bit-sum statistic = 1.79080 [P = 0.4084] the odd/even-bit-sum statistic = 34537.31272 [P = 0.0000]**** the 64-bit matrix statistic = 7211015.13128 [P = 0.0000]**** the 128-bit matrix statistic = 15489383.63719 [P = 0.0000]**** the 256-bit matrix statistic = 127423131.18270 [P = 0.0000]**** the 512-bit matrix statistic = 90917461.20765 [P = 0.0000]**** the 1024-bit matrix statistic = 134647910.52035 [P = 0.0000]**** the 2048-bit matrix statistic = 231359649.71710 [P = 0.0000]**** the bit prediction A statistic = 5.35302 [P = 0.0207]* the bit prediction B statistic = 0.00470 [P = 0.9454]^ the bit prediction C statistic = 0.45544 [P = 0.4998] the bit prediction D statistic = 31608.08264 [P = 0.0000]**** the bit prediction E statistic = 14073.87454 [P = 0.0000]**** the byte prediction A statistic = 0.01106 [P = 0.9162]^ the byte prediction B statistic = 3.35158 [P = 0.0671]* the byte prediction C statistic = 6700927.35189 [P = 0.0000]**** the byte prediction D statistic = 2549.49280 [P = 0.0000]**** the byte repetition statistic = 0.02275 [P = 0.8801] the 2-byte AND statistic = 1.42607 [P = 0.9643]^ the 4-byte AND statistic = 0.98707 [P = 0.6105] the 4-byte AND-OR statistic = 1.89494 [P = 0.3877] the 2-byte up/down statistic = 0.75471 [P = 0.6857] the 4-byte up/down statistic = 4.67893 [P = 0.6991] the rect. distance statistic = 7.80937 [P = 0.2524] the 4-byte collision statistic = 0.00152 [P = 0.9689]^ the 6-byte collision statistic = 1375.26032 [P = 0.0000]**** the 8-byte collision statistic = 2041.14882 [P = 0.0000]**** the 12-byte collision statistic = 5191.63452 [P = 0.0000]**** the 16-byte collision statistic = 8286.76922 [P = 0.0000]**** the 24-byte collision statistic = 9741.26973 [P = 0.0000]**** the 32-byte collision statistic = 8698.72023 [P = 0.0000]**** the 1-byte offset XOR statistic = 103.35053 [P = 1.0000]^^^^ the 2-byte offset XOR statistic = 134.03212 [P = 1.0000]^^^^ the 6-byte offset XOR statistic = 129.52161 [P = 1.0000]^^^^ the 24-byte offset XOR stat. = 52941182.94312 [P = 0.0000]**** the 120-byte offset XOR stat. = 64680471.58277 [P = 0.0000]**** the 720-byte offset XOR stat. = 73158262.52719 [P = 0.0000]**** the 5040-byte offset XOR stat. = 61323098.11674 [P = 0.0000]**** the 40320-byte offset XOR stat. = 281674118.87189 [P = 0.0000]**** the 362880-byte off. XOR stat. = 277369460.94319 [P = 0.0000]**** the mod 3 statistic = 0.01809 [P = 0.9910]^^ the mod 5 statistic = 2.62679 [P = 0.6221] the mod 7 statistic = 1.58704 [P = 0.9535]^ the mod 11 statistic = 1.48588 [P = 0.9990]^^ the mod 13 statistic = 2.80027 [P = 0.9968]^^ the mod 17 statistic = 3.62414 [P = 0.9994]^^^ the mod 19 statistic = 4.57590 [P = 0.9994]^^^ the mod 23 statistic = 2.94857 [P = 1.0000]^^^^ ------------------------------------------------------------------------------
A truncated LCG; only the highest order 8 bits are used.
the test sequence length = 128 MB ------------------------------------------------------------------------------ TruncLCG.bin cumulative sums, 1 sequence the bit runs statistic = 18.71948 [P = 0.0440]* the alt. 1 bit runs statistic = 6.06415 [P = 0.8098] the alt. 2 bit runs statistic = 6.84945 [P = 0.7396] the alt. 3 bit runs statistic = 9.11564 [P = 0.5212] the alt. 4 bit runs statistic = 9.20846 [P = 0.5124] the alt. 5 bit runs statistic = 8.40617 [P = 0.5892] the block bit freq. statistic = 246.18415 [P = 0.6591] the bit frequency statistic = 0.33317 [P = 0.5638] the tidbit frequency statistic = 2.28856 [P = 0.5147] the nibble frequency statistic = 9.80609 [P = 0.8318] the byte frequency statistic = 226.67279 [P = 0.8987] the bit 0 statistic = 0.00000 [P = 1.0000]^^^^ the bit 1 statistic = 0.00000 [P = 1.0000]^^^^ the bit 2 statistic = 0.00000 [P = 1.0000]^^^^ the bit 3 statistic = 0.47493 [P = 0.4907] the bit 4 statistic = 0.83179 [P = 0.3618] the bit 5 statistic = 0.02043 [P = 0.8863] the bit 6 statistic = 0.22098 [P = 0.6383] the bit 7 statistic = 0.63474 [P = 0.4256] the overall bit statistic = 2.18286 [P = 0.9749]^ the 8-bit-sum statistic = 7.34750 [P = 0.4996] the 16-bit-sum statistic = 3.28656 [P = 0.1933] the 32-bit-sum statistic = 4.97692 [P = 0.0830]* the odd/even-bit-sum statistic = 58.03336 [P = 0.6535] the 64-bit matrix statistic = 138.30190 [P = 1.0000]^^^^ the 128-bit matrix statistic = 136.88369 [P = 1.0000]^^^^ the 256-bit matrix statistic = 140.55586 [P = 1.0000]^^^^ the 512-bit matrix statistic = 156.42707 [P = 1.0000]^^^^ the 1024-bit matrix statistic = 2771.70373 [P = 0.0000]**** the 2048-bit matrix statistic = 10356.46990 [P = 0.0000]**** the bit prediction A statistic = 0.14450 [P = 0.7039] the bit prediction B statistic = 0.05795 [P = 0.8098] the bit prediction C statistic = 0.14269 [P = 0.7056] the bit prediction D statistic = 0.78573 [P = 0.3754] the bit prediction E statistic = 0.23214 [P = 0.6299] the byte prediction A statistic = 0.26498 [P = 0.6067] the byte prediction B statistic = 0.09867 [P = 0.7534] the byte prediction C statistic = 3.77992 [P = 0.0519]* the byte prediction D statistic = 9.96278 [P = 0.0016]** the byte repetition statistic = 0.01135 [P = 0.9151]^ the 2-byte AND statistic = 7.91800 [P = 0.2442] the 4-byte AND statistic = 0.93058 [P = 0.6280] the 4-byte AND-OR statistic = 4.07658 [P = 0.1303] the 2-byte up/down statistic = 0.02418 [P = 0.9880]^ the 4-byte up/down statistic = 8.38307 [P = 0.3000] the rect. distance statistic = 4.91385 [P = 0.5549] the 4-byte collision statistic = 1.93886 [P = 0.1638] the 6-byte collision statistic = 3.53793 [P = 0.0600]* the 8-byte collision statistic = 3.45042 [P = 0.0632]* the 12-byte collision statistic = 2.09892 [P = 0.1474] the 16-byte collision statistic = 2.39279 [P = 0.1219] the 24-byte collision statistic = 1.62709 [P = 0.2021] the 32-byte collision statistic = 0.39016 [P = 0.5322] the 1-byte offset XOR statistic = 200.72129 [P = 0.9949]^^ the 2-byte offset XOR statistic = 172.39521 [P = 1.0000]^^^^ the 6-byte offset XOR statistic = 208.41360 [P = 0.9851]^ the 24-byte offset XOR stat. = 128.02246 [P = 1.0000]^^^^ the 120-byte offset XOR stat. = 179.41597 [P = 0.9999]^^^^ the 720-byte offset XOR stat. = 570.16257 [P = 0.0000]**** the 5040-byte offset XOR stat. = 159.17181 [P = 1.0000]^^^^ the 40320-byte offset XOR stat. = 223.48190 [P = 0.9233]^ the 362880-byte off. XOR stat. = 192.92493 [P = 0.9986]^^ the mod 3 statistic = 0.15097 [P = 0.9273]^ the mod 5 statistic = 5.34490 [P = 0.2537] the mod 7 statistic = 1.12300 [P = 0.9805]^ the mod 11 statistic = 7.48907 [P = 0.6786] the mod 13 statistic = 5.36929 [P = 0.9445]^ the mod 17 statistic = 12.88239 [P = 0.6813] the mod 19 statistic = 25.49155 [P = 0.1120] the mod 23 statistic = 14.75663 [P = 0.8725] ------------------------------------------------------------------------------
A truncated LCG; only the highest order 8 bits are used.
the test sequence length = 128 MB ------------------------------------------------------------------------------ TruncLCG2.bin cumulative sums, 1 sequence the bit runs statistic = 6.01126 [P = 0.8143] the alt. 1 bit runs statistic = 15.72475 [P = 0.1078] the alt. 2 bit runs statistic = 5.07927 [P = 0.8858] the alt. 3 bit runs statistic = 6.93506 [P = 0.7316] the alt. 4 bit runs statistic = 5.32753 [P = 0.8683] the alt. 5 bit runs statistic = 6.18453 [P = 0.7995] the block bit freq. statistic = 247.10985 [P = 0.6436] the bit frequency statistic = 0.65916 [P = 0.4169] the tidbit frequency statistic = 2.34286 [P = 0.5044] the nibble frequency statistic = 10.28605 [P = 0.8014] the byte frequency statistic = 251.42729 [P = 0.5515] the bit 0 statistic = 0.00000 [P = 1.0000]^^^^ the bit 1 statistic = 0.00000 [P = 1.0000]^^^^ the bit 2 statistic = 0.00000 [P = 1.0000]^^^^ the bit 3 statistic = 1.97954 [P = 0.1594] the bit 4 statistic = 0.00063 [P = 0.9800]^ the bit 5 statistic = 0.03058 [P = 0.8612] the bit 6 statistic = 0.08016 [P = 0.7771] the bit 7 statistic = 1.04588 [P = 0.3065] the overall bit statistic = 3.13679 [P = 0.9255]^ the 8-bit-sum statistic = 7.77556 [P = 0.4557] the 16-bit-sum statistic = 0.53393 [P = 0.7657] the 32-bit-sum statistic = 0.09755 [P = 0.9524]^ the odd/even-bit-sum statistic = 64.90341 [P = 0.4101] the 64-bit matrix statistic = 171.32398 [P = 1.0000]^^^^ the 128-bit matrix statistic = 148.65505 [P = 1.0000]^^^^ the 256-bit matrix statistic = 171.98223 [P = 1.0000]^^^^ the 512-bit matrix statistic = 129.82734 [P = 1.0000]^^^^ the 1024-bit matrix statistic = 2967.26066 [P = 0.0000]**** the 2048-bit matrix statistic = 7824.05938 [P = 0.0000]**** the bit prediction A statistic = 0.01945 [P = 0.8891] the bit prediction B statistic = 1.84375 [P = 0.1745] the bit prediction C statistic = 0.12287 [P = 0.7259] the bit prediction D statistic = 0.33706 [P = 0.5615] the bit prediction E statistic = 0.45413 [P = 0.5004] the byte prediction A statistic = 0.14481 [P = 0.7035] the byte prediction B statistic = 3.31621 [P = 0.0686]* the byte prediction C statistic = 2.12318 [P = 0.1451] the byte prediction D statistic = 0.00371 [P = 0.9514]^ the byte repetition statistic = 0.00736 [P = 0.9316]^ the 2-byte AND statistic = 4.73499 [P = 0.5782] the 4-byte AND statistic = 1.99483 [P = 0.3688] the 4-byte AND-OR statistic = 0.02776 [P = 0.9862]^ the 2-byte up/down statistic = 1.25753 [P = 0.5333] the 4-byte up/down statistic = 3.62314 [P = 0.8220] the rect. distance statistic = 4.46772 [P = 0.6136] the 4-byte collision statistic = 0.55229 [P = 0.4574] the 6-byte collision statistic = 0.02980 [P = 0.8629] the 8-byte collision statistic = 0.44193 [P = 0.5062] the 12-byte collision statistic = 0.60693 [P = 0.4359] the 16-byte collision statistic = 1.14412 [P = 0.2848] the 24-byte collision statistic = 0.92082 [P = 0.3373] the 32-byte collision statistic = 1.16313 [P = 0.2808] the 1-byte offset XOR statistic = 228.31838 [P = 0.8841] the 2-byte offset XOR statistic = 206.07472 [P = 0.9891]^ the 6-byte offset XOR statistic = 208.42180 [P = 0.9851]^ the 24-byte offset XOR stat. = 167.68973 [P = 1.0000]^^^^ the 120-byte offset XOR stat. = 175.18560 [P = 1.0000]^^^^ the 720-byte offset XOR stat. = 167.56437 [P = 1.0000]^^^^ the 5040-byte offset XOR stat. = 187.56319 [P = 0.9995]^^^ the 40320-byte offset XOR stat. = 688.70363 [P = 0.0000]**** the 362880-byte off. XOR stat. = 145.20129 [P = 1.0000]^^^^ the mod 3 statistic = 1.81484 [P = 0.4036] the mod 5 statistic = 2.52803 [P = 0.6396] the mod 7 statistic = 3.80975 [P = 0.7024] the mod 11 statistic = 15.96486 [P = 0.1006] the mod 13 statistic = 21.95450 [P = 0.0380]* the mod 17 statistic = 16.14867 [P = 0.4426] the mod 19 statistic = 17.64951 [P = 0.4790] the mod 23 statistic = 37.09088 [P = 0.0231]* ------------------------------------------------------------------------------
A truncated LCG; only the highest order 8 bits are used.
the test sequence length = 128 MB ------------------------------------------------------------------------------ TruncLCG3.bin cumulative sums, 1 sequence the bit runs statistic = 10.12428 [P = 0.4297] the alt. 1 bit runs statistic = 10.39651 [P = 0.4064] the alt. 2 bit runs statistic = 8.67241 [P = 0.5634] the alt. 3 bit runs statistic = 11.05357 [P = 0.3534] the alt. 4 bit runs statistic = 11.58872 [P = 0.3135] the alt. 5 bit runs statistic = 12.80302 [P = 0.2349] the block bit freq. statistic = 240.66077 [P = 0.7461] the bit frequency statistic = 0.24671 [P = 0.6194] the tidbit frequency statistic = 0.66090 [P = 0.8824] the nibble frequency statistic = 20.22806 [P = 0.1634] the byte frequency statistic = 246.06528 [P = 0.6446] the bit 0 statistic = 0.00000 [P = 1.0000]^^^^ the bit 1 statistic = 0.00000 [P = 1.0000]^^^^ the bit 2 statistic = 0.00000 [P = 1.0000]^^^^ the bit 3 statistic = 0.05399 [P = 0.8163] the bit 4 statistic = 2.48967 [P = 0.1146] the bit 5 statistic = 0.00039 [P = 0.9843]^ the bit 6 statistic = 0.63474 [P = 0.4256] the bit 7 statistic = 0.13815 [P = 0.7101] the overall bit statistic = 3.31694 [P = 0.9129]^ the 8-bit-sum statistic = 2.89816 [P = 0.9406]^ the 16-bit-sum statistic = 0.26700 [P = 0.8750] the 32-bit-sum statistic = 0.30108 [P = 0.8602] the odd/even-bit-sum statistic = 58.53430 [P = 0.6360] the 64-bit matrix statistic = 130.23264 [P = 1.0000]^^^^ the 128-bit matrix statistic = 127.77112 [P = 1.0000]^^^^ the 256-bit matrix statistic = 121.52768 [P = 1.0000]^^^^ the 512-bit matrix statistic = 112.95317 [P = 1.0000]^^^^ the 1024-bit matrix statistic = 16700.58220 [P = 0.0000]**** the 2048-bit matrix statistic = 16594.21460 [P = 0.0000]**** the bit prediction A statistic = 0.16075 [P = 0.6885] the bit prediction B statistic = 0.05602 [P = 0.8129] the bit prediction C statistic = 2.15525 [P = 0.1421] the bit prediction D statistic = 0.00296 [P = 0.9566]^ the bit prediction E statistic = 0.47023 [P = 0.4929] the byte prediction A statistic = 1.50313 [P = 0.2202] the byte prediction B statistic = 0.71017 [P = 0.3994] the byte prediction C statistic = 1.21327 [P = 0.2707] the byte prediction D statistic = 0.78677 [P = 0.3751] the byte repetition statistic = 0.43022 [P = 0.5119] the 2-byte AND statistic = 12.02843 [P = 0.0613]* the 4-byte AND statistic = 0.12888 [P = 0.9376]^ the 4-byte AND-OR statistic = 1.87486 [P = 0.3916] the 2-byte up/down statistic = 0.20012 [P = 0.9048]^ the 4-byte up/down statistic = 7.89042 [P = 0.3424] the rect. distance statistic = 3.41928 [P = 0.7547] the 4-byte collision statistic = 1.61266 [P = 0.2041] the 6-byte collision statistic = 3.62746 [P = 0.0568]* the 8-byte collision statistic = 1.34429 [P = 0.2463] the 12-byte collision statistic = 3.16990 [P = 0.0750]* the 16-byte collision statistic = 3.00646 [P = 0.0829]* the 24-byte collision statistic = 0.02316 [P = 0.8790] the 32-byte collision statistic = 5.23209 [P = 0.0222]* the 1-byte offset XOR statistic = 202.82902 [P = 0.9930]^^ the 2-byte offset XOR statistic = 213.75191 [P = 0.9716]^ the 6-byte offset XOR statistic = 197.78246 [P = 0.9968]^^ the 24-byte offset XOR stat. = 159.22333 [P = 1.0000]^^^^ the 120-byte offset XOR stat. = 151.63338 [P = 1.0000]^^^^ the 720-byte offset XOR stat. = 174.26952 [P = 1.0000]^^^^ the 5040-byte offset XOR stat. = 168.38416 [P = 1.0000]^^^^ the 40320-byte offset XOR stat. = 196.71726 [P = 0.9973]^^ the 362880-byte off. XOR stat. = 178.84662 [P = 0.9999]^^^^ the mod 3 statistic = 0.85556 [P = 0.6520] the mod 5 statistic = 2.32098 [P = 0.6770] the mod 7 statistic = 3.31455 [P = 0.7685] the mod 11 statistic = 10.07785 [P = 0.4337] the mod 13 statistic = 10.14538 [P = 0.6032] the mod 17 statistic = 7.52910 [P = 0.9617]^ the mod 19 statistic = 18.44778 [P = 0.4265] the mod 23 statistic = 16.77686 [P = 0.7756] ------------------------------------------------------------------------------
A radically truncated LCG; only the highest order bit is used.
the test sequence length = 128 MB ------------------------------------------------------------------------------ RTLCG.bin cumulative sums, 1 sequence the bit runs statistic = 2.01170 [P = 0.9962]^^ the alt. 1 bit runs statistic = 6.96594 [P = 0.7287] the alt. 2 bit runs statistic = 10.77743 [P = 0.3751] the alt. 3 bit runs statistic = 4.97440 [P = 0.8929] the alt. 4 bit runs statistic = 2.54507 [P = 0.9902]^^ the alt. 5 bit runs statistic = 4.39488 [P = 0.9278]^ the block bit freq. statistic = 194.31303 [P = 0.9984]^^ the bit frequency statistic = 0.36056 [P = 0.5482] the tidbit frequency statistic = 2.95156 [P = 0.3992] the nibble frequency statistic = 11.87077 [P = 0.6888] the byte frequency statistic = 232.39289 [P = 0.8420] the bit 0 statistic = 0.00000 [P = 0.9988]^^ the bit 1 statistic = 0.56160 [P = 0.4536] the bit 2 statistic = 9.00429 [P = 0.0027]** the bit 3 statistic = 0.36717 [P = 0.5446] the bit 4 statistic = 0.07160 [P = 0.7890] the bit 5 statistic = 0.31848 [P = 0.5725] the bit 6 statistic = 0.10410 [P = 0.7470] the bit 7 statistic = 0.31440 [P = 0.5750] the overall bit statistic = 10.74165 [P = 0.2168] the 8-bit-sum statistic = 4.62658 [P = 0.7966] the 16-bit-sum statistic = 2.49322 [P = 0.2875] the 32-bit-sum statistic = 0.40922 [P = 0.8150] the odd/even-bit-sum statistic = 88.45713 [P = 0.0189]* the 64-bit matrix statistic = 181.23642 [P = 0.9999]^^^ the 128-bit matrix statistic = 171.77586 [P = 1.0000]^^^^ the 256-bit matrix statistic = 10501.19028 [P = 0.0000]**** the 512-bit matrix statistic = 33622.09766 [P = 0.0000]**** the 1024-bit matrix statistic = 9356.30616 [P = 0.0000]**** the 2048-bit matrix statistic = 1115713.61697 [P = 0.0000]**** the bit prediction A statistic = 0.00778 [P = 0.9297]^ the bit prediction B statistic = 0.52727 [P = 0.4678] the bit prediction C statistic = 1.11031 [P = 0.2920] the bit prediction D statistic = 0.54903 [P = 0.4587] the bit prediction E statistic = 1.14988 [P = 0.2836] the byte prediction A statistic = 0.24132 [P = 0.6233] the byte prediction B statistic = 0.22135 [P = 0.6380] the byte prediction C statistic = 0.01692 [P = 0.8965] the byte prediction D statistic = 0.00518 [P = 0.9426]^ the byte repetition statistic = 0.12064 [P = 0.7283] the 2-byte AND statistic = 3.55839 [P = 0.7362] the 4-byte AND statistic = 0.02793 [P = 0.9861]^ the 4-byte AND-OR statistic = 1.64117 [P = 0.4402] the 2-byte up/down statistic = 0.12771 [P = 0.9381]^ the 4-byte up/down statistic = 4.12108 [P = 0.7657] the rect. distance statistic = 3.87960 [P = 0.6930] the 4-byte collision statistic = 0.57986 [P = 0.4464] the 6-byte collision statistic = 0.65509 [P = 0.4183] the 8-byte collision statistic = 0.58082 [P = 0.4460] the 12-byte collision statistic = 1.16831 [P = 0.2797] the 16-byte collision statistic = 0.24995 [P = 0.6171] the 24-byte collision statistic = 1.05681 [P = 0.3039] the 32-byte collision statistic = 0.13766 [P = 0.7106] the 1-byte offset XOR statistic = 270.36262 [P = 0.2431] the 2-byte offset XOR statistic = 160.65096 [P = 1.0000]^^^^ the 6-byte offset XOR statistic = 134.37023 [P = 1.0000]^^^^ the 24-byte offset XOR stat. = 192.85789 [P = 0.9986]^^ the 120-byte offset XOR stat. = 183.04276 [P = 0.9998]^^^ the 720-byte offset XOR stat. = 137.43090 [P = 1.0000]^^^^ the 5040-byte offset XOR stat. = 222.47646 [P = 0.9301]^ the 40320-byte offset XOR stat. = 365.30426 [P = 0.0000]**** the 362880-byte off. XOR stat. = 792.82514 [P = 0.0000]**** the mod 3 statistic = 0.98538 [P = 0.6110] the mod 5 statistic = 2.29664 [P = 0.6814] the mod 7 statistic = 3.04907 [P = 0.8027] the mod 11 statistic = 6.66866 [P = 0.7563] the mod 13 statistic = 5.68887 [P = 0.9309]^ the mod 17 statistic = 11.99369 [P = 0.7444] the mod 19 statistic = 31.15449 [P = 0.0276]* the mod 23 statistic = 29.10191 [P = 0.1420] ------------------------------------------------------------------------------