[Cryptech Tech] Avalanche noise fascination
Fredrik Thulin
fredrik at thulin.net
Sat Nov 8 11:08:09 UTC 2014
Hi all
It's been a while since I reported on the status of the avalanche noise front.
I've upped my game considerably since last time, and am now using an STM32
(stm32f401rbt6 to be precise) and sampling a 42 MHz timer using DMA whenever
the amplified avalanche noise makes an input pin change from low to high.
Compared to my earlier use of an msp430, this indicates excellent assumed
accuracy. I'm saying assumed accuracy since the timing delta plot (attached in
two sizes, plus plot data as text) are very smooth looking to my human eye,
but I don't have a theoretical model to match this against so who knows if the
irregular "fallout" on the right is to be expected, is within probabilistic
limits etc.?
I'm fairly confident I could quite easily whiten the timer readings into
entropy that would pass the ent Chi-square test and probably then Dieharder
too, using for example the same technique that Benedikt has been using all
along - effectively xor:ing two consecutive readings and using the LSB of the
result.
In order to validate the workings of the circuit I'm trying to reduce the
whitening as much as possible, to ideally just use the raw LSB of every timer
value captured. That one would be '1' 50% of the times and '0' the other 50%
of the time, if every clock cycle is equally long (assuming infinite precision)
right? So no whitening beyond just using the LSB of each capture should be
necessary, and no von Neumann should be necessary either. If further whitening
*is* in fact required, it is to compensate for some imperfection in the
circuit, right?
I started with the timing deltas, and when I had code that resulted in what I
thought produced good looking graphs I went on to extracting entropy. After
somewhere around 1GB it was apparent from the Chi-square value of 'ent' that
some kind of imperfection was actually still present in the data produced. I
continued extracting data (which luckily I can now do at a rate around 35 kB/s
using only the rising flanks) and started implementing the Chi-square test
myself, in order to look not only at the end result value, but also at how
much each byte value contributed to the unexpectedly high result (447 using
these 3.9 GB).
This is when it became really fascinating =). After 3.9 GB of data, the Chi-
square test puts a bright spotlight on very apparent bit patterns in the LSBs!
I'm attaching the full output of my test program as well as the test program
itself. The highlight is this part:
> Highest:
> 86 / 01010110, off-by -10953, a*a = 119968209
> 82 / 01010010, off-by -11178, a*a = 124947684
>
> 109 / 01101101, off-by -11248, a*a = 126517504
> 169 / 10101001, off-by -11463, a*a = 131400369
> 127 / 01111111, off-by 12632, a*a = 159567424
> 255 / 11111111, off-by 12730, a*a = 162052900
>
> 63 / 00111111, off-by 13691, a*a = 187443481
> 64 / 01000000, off-by 13742, a*a = 188842564
> 85 / 01010101, off-by -13789, a*a = 190136521
>
> 0 / 00000000, off-by 17846, a*a = 318479716
>
> 0x0 at position 255, 0xff at position 251
>
> Chi-Square: 447.3987561728832
Look! There are 17k (0.11%) more occurrences of 00000000 than expected (that
is eight samples in a row from a 42 MHz timer with a LSB of '0'), and 13k more
than expected of alternating '1' and '0'.
I'm thrilled to go looking for what causes this and I do have some theories of
what to try, but I wanted to share this challenge with the rest of you since
some people on this list are no doubt more experienced than me in this field
=).
What are your theories of what is causing these bit patterns?
/Fredrik
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{3: 9536,
4: 33950,
5: 66077,
6: 103000,
7: 141291,
8: 175287,
9: 202374,
10: 221820,
11: 235665,
12: 245159,
13: 252718,
14: 256362,
15: 259601,
16: 259672,
17: 258713,
18: 255397,
19: 250731,
20: 245345,
21: 239546,
22: 231946,
23: 223710,
24: 216190,
25: 207096,
26: 199203,
27: 189727,
28: 181631,
29: 172204,
30: 163333,
31: 154924,
32: 146840,
33: 139578,
34: 131033,
35: 124048,
36: 116181,
37: 109344,
38: 102245,
39: 96741,
40: 90567,
41: 85223,
42: 79585,
43: 74784,
44: 70035,
45: 65213,
46: 61178,
47: 57222,
48: 53419,
49: 49567,
50: 46340,
51: 43032,
52: 40190,
53: 37422,
54: 34776,
55: 32534,
56: 30358,
57: 27950,
58: 26247,
59: 24434,
60: 22321,
61: 20870,
62: 19381,
63: 18068,
64: 16796,
65: 15762,
66: 14379,
67: 13231,
68: 12460,
69: 11542,
70: 10490,
71: 9738,
72: 9147,
73: 8463,
74: 7837,
75: 7100,
76: 6756,
77: 6173,
78: 5793,
79: 5256,
80: 4771,
81: 4533,
82: 4225,
83: 3903,
84: 3624,
85: 3397,
86: 3023,
87: 2770,
88: 2613,
89: 2391,
90: 2159,
91: 2107,
92: 1903,
93: 1772,
94: 1710,
95: 1535,
96: 1340,
97: 1238,
98: 1151,
99: 1128,
100: 967,
101: 919,
102: 832,
103: 790,
104: 739,
105: 664,
106: 636,
107: 543,
108: 545,
109: 469,
110: 501,
111: 406,
112: 377,
113: 331,
114: 312,
115: 287,
116: 284,
117: 271,
118: 212,
119: 190,
120: 184,
121: 163,
122: 173,
123: 140,
124: 137,
125: 124,
126: 126,
127: 91,
128: 93,
129: 95,
130: 80,
131: 72,
132: 72,
133: 79,
134: 52,
135: 56,
136: 55,
137: 43,
138: 55,
139: 37,
140: 38,
141: 39,
142: 31,
143: 28,
144: 19,
145: 22,
146: 26,
147: 26,
148: 18,
149: 15,
150: 20,
151: 7,
152: 15,
153: 12,
154: 12,
155: 11,
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157: 15,
158: 6,
159: 5,
160: 6,
161: 6,
162: 7,
163: 5}
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Expect 15447806 occurances of each byte for 3954638418 bytes of data (0.390625%)
0 / 00000000 - 0.391076% of total (15465652 / 3954638418), off-by 17846, a*a = 318479716, chisq = 20.62, incr 20.62
1 / 00000001 - 0.390688% of total (15450295 / 3954638418), off-by 2489, a*a = 6195121, chisq = 21.02, incr 0.40
2 / 00000010 - 0.390719% of total (15451533 / 3954638418), off-by 3727, a*a = 13890529, chisq = 21.92, incr 0.90
3 / 00000011 - 0.390757% of total (15453007 / 3954638418), off-by 5201, a*a = 27050401, chisq = 23.67, incr 1.75
4 / 00000100 - 0.390678% of total (15449907 / 3954638418), off-by 2101, a*a = 4414201, chisq = 23.95, incr 0.29
5 / 00000101 - 0.390644% of total (15448550 / 3954638418), off-by 744, a*a = 553536, chisq = 23.99, incr 0.04
6 / 00000110 - 0.390692% of total (15450465 / 3954638418), off-by 2659, a*a = 7070281, chisq = 24.45, incr 0.46
7 / 00000111 - 0.390710% of total (15451187 / 3954638418), off-by 3381, a*a = 11431161, chisq = 25.19, incr 0.74
8 / 00001000 - 0.390854% of total (15456846 / 3954638418), off-by 9040, a*a = 81721600, chisq = 30.48, incr 5.29
9 / 00001001 - 0.390766% of total (15453385 / 3954638418), off-by 5579, a*a = 31125241, chisq = 32.49, incr 2.01
10 / 00001010 - 0.390565% of total (15445439 / 3954638418), off-by -2367, a*a = 5602689, chisq = 32.85, incr 0.36
11 / 00001011 - 0.390652% of total (15448889 / 3954638418), off-by 1083, a*a = 1172889, chisq = 32.93, incr 0.08
12 / 00001100 - 0.390848% of total (15456617 / 3954638418), off-by 8811, a*a = 77633721, chisq = 37.96, incr 5.03
13 / 00001101 - 0.390680% of total (15449985 / 3954638418), off-by 2179, a*a = 4748041, chisq = 38.26, incr 0.31
14 / 00001110 - 0.390505% of total (15443056 / 3954638418), off-by -4750, a*a = 22562500, chisq = 39.72, incr 1.46
15 / 00001111 - 0.390845% of total (15456507 / 3954638418), off-by 8701, a*a = 75707401, chisq = 44.63, incr 4.90
16 / 00010000 - 0.390756% of total (15452985 / 3954638418), off-by 5179, a*a = 26822041, chisq = 46.36, incr 1.74
17 / 00010001 - 0.390746% of total (15452582 / 3954638418), off-by 4776, a*a = 22810176, chisq = 47.84, incr 1.48
18 / 00010010 - 0.390759% of total (15453095 / 3954638418), off-by 5289, a*a = 27973521, chisq = 49.65, incr 1.81
19 / 00010011 - 0.390554% of total (15444985 / 3954638418), off-by -2821, a*a = 7958041, chisq = 50.16, incr 0.52
20 / 00010100 - 0.390506% of total (15443092 / 3954638418), off-by -4714, a*a = 22221796, chisq = 51.60, incr 1.44
21 / 00010101 - 0.390403% of total (15439018 / 3954638418), off-by -8788, a*a = 77228944, chisq = 56.60, incr 5.00
22 / 00010110 - 0.390496% of total (15442720 / 3954638418), off-by -5086, a*a = 25867396, chisq = 58.28, incr 1.67
23 / 00010111 - 0.390696% of total (15450595 / 3954638418), off-by 2789, a*a = 7778521, chisq = 58.78, incr 0.50
24 / 00011000 - 0.390660% of total (15449197 / 3954638418), off-by 1391, a*a = 1934881, chisq = 58.91, incr 0.13
25 / 00011001 - 0.390656% of total (15449019 / 3954638418), off-by 1213, a*a = 1471369, chisq = 59.00, incr 0.10
26 / 00011010 - 0.390408% of total (15439236 / 3954638418), off-by -8570, a*a = 73444900, chisq = 63.75, incr 4.75
27 / 00011011 - 0.390667% of total (15449483 / 3954638418), off-by 1677, a*a = 2812329, chisq = 63.94, incr 0.18
28 / 00011100 - 0.390600% of total (15446824 / 3954638418), off-by -982, a*a = 964324, chisq = 64.00, incr 0.06
29 / 00011101 - 0.390567% of total (15445503 / 3954638418), off-by -2303, a*a = 5303809, chisq = 64.34, incr 0.34
30 / 00011110 - 0.390546% of total (15444698 / 3954638418), off-by -3108, a*a = 9659664, chisq = 64.97, incr 0.63
31 / 00011111 - 0.390825% of total (15455697 / 3954638418), off-by 7891, a*a = 62267881, chisq = 69.00, incr 4.03
32 / 00100000 - 0.390675% of total (15449784 / 3954638418), off-by 1978, a*a = 3912484, chisq = 69.25, incr 0.25
33 / 00100001 - 0.390563% of total (15445373 / 3954638418), off-by -2433, a*a = 5919489, chisq = 69.64, incr 0.38
34 / 00100010 - 0.390612% of total (15447294 / 3954638418), off-by -512, a*a = 262144, chisq = 69.65, incr 0.02
35 / 00100011 - 0.390634% of total (15448179 / 3954638418), off-by 373, a*a = 139129, chisq = 69.66, incr 0.01
36 / 00100100 - 0.390478% of total (15441976 / 3954638418), off-by -5830, a*a = 33988900, chisq = 71.86, incr 2.20
37 / 00100101 - 0.390576% of total (15445861 / 3954638418), off-by -1945, a*a = 3783025, chisq = 72.11, incr 0.24
38 / 00100110 - 0.390543% of total (15444546 / 3954638418), off-by -3260, a*a = 10627600, chisq = 72.79, incr 0.69
39 / 00100111 - 0.390543% of total (15444559 / 3954638418), off-by -3247, a*a = 10543009, chisq = 73.48, incr 0.68
40 / 00101000 - 0.390593% of total (15446532 / 3954638418), off-by -1274, a*a = 1623076, chisq = 73.58, incr 0.11
41 / 00101001 - 0.390443% of total (15440621 / 3954638418), off-by -7185, a*a = 51624225, chisq = 76.92, incr 3.34
42 / 00101010 - 0.390351% of total (15436988 / 3954638418), off-by -10818, a*a = 117029124, chisq = 84.50, incr 7.58
43 / 00101011 - 0.390434% of total (15440237 / 3954638418), off-by -7569, a*a = 57289761, chisq = 88.21, incr 3.71
44 / 00101100 - 0.390492% of total (15442560 / 3954638418), off-by -5246, a*a = 27520516, chisq = 89.99, incr 1.78
45 / 00101101 - 0.390473% of total (15441781 / 3954638418), off-by -6025, a*a = 36300625, chisq = 92.34, incr 2.35
46 / 00101110 - 0.390554% of total (15444992 / 3954638418), off-by -2814, a*a = 7918596, chisq = 92.85, incr 0.51
47 / 00101111 - 0.390592% of total (15446502 / 3954638418), off-by -1304, a*a = 1700416, chisq = 92.96, incr 0.11
48 / 00110000 - 0.390500% of total (15442847 / 3954638418), off-by -4959, a*a = 24591681, chisq = 94.55, incr 1.59
49 / 00110001 - 0.390680% of total (15449985 / 3954638418), off-by 2179, a*a = 4748041, chisq = 94.86, incr 0.31
50 / 00110010 - 0.390615% of total (15447408 / 3954638418), off-by -398, a*a = 158404, chisq = 94.87, incr 0.01
51 / 00110011 - 0.390568% of total (15445535 / 3954638418), off-by -2271, a*a = 5157441, chisq = 95.21, incr 0.33
52 / 00110100 - 0.390584% of total (15446178 / 3954638418), off-by -1628, a*a = 2650384, chisq = 95.38, incr 0.17
53 / 00110101 - 0.390536% of total (15444297 / 3954638418), off-by -3509, a*a = 12313081, chisq = 96.17, incr 0.80
54 / 00110110 - 0.390509% of total (15443227 / 3954638418), off-by -4579, a*a = 20967241, chisq = 97.53, incr 1.36
55 / 00110111 - 0.390790% of total (15454335 / 3954638418), off-by 6529, a*a = 42627841, chisq = 100.29, incr 2.76
56 / 00111000 - 0.390670% of total (15449567 / 3954638418), off-by 1761, a*a = 3101121, chisq = 100.49, incr 0.20
57 / 00111001 - 0.390647% of total (15448676 / 3954638418), off-by 870, a*a = 756900, chisq = 100.54, incr 0.05
58 / 00111010 - 0.390481% of total (15442128 / 3954638418), off-by -5678, a*a = 32239684, chisq = 102.63, incr 2.09
59 / 00111011 - 0.390779% of total (15453895 / 3954638418), off-by 6089, a*a = 37075921, chisq = 105.03, incr 2.40
60 / 00111100 - 0.390537% of total (15444320 / 3954638418), off-by -3486, a*a = 12152196, chisq = 105.81, incr 0.79
61 / 00111101 - 0.390786% of total (15454175 / 3954638418), off-by 6369, a*a = 40564161, chisq = 108.44, incr 2.63
62 / 00111110 - 0.390579% of total (15446004 / 3954638418), off-by -1802, a*a = 3247204, chisq = 108.65, incr 0.21
63 / 00111111 - 0.390971% of total (15461497 / 3954638418), off-by 13691, a*a = 187443481, chisq = 120.78, incr 12.13
64 / 01000000 - 0.390972% of total (15461548 / 3954638418), off-by 13742, a*a = 188842564, chisq = 133.01, incr 12.22
65 / 01000001 - 0.390608% of total (15447133 / 3954638418), off-by -673, a*a = 452929, chisq = 133.04, incr 0.03
66 / 01000010 - 0.390738% of total (15452288 / 3954638418), off-by 4482, a*a = 20088324, chisq = 134.34, incr 1.30
67 / 01000011 - 0.390558% of total (15445144 / 3954638418), off-by -2662, a*a = 7086244, chisq = 134.80, incr 0.46
68 / 01000100 - 0.390709% of total (15451142 / 3954638418), off-by 3336, a*a = 11128896, chisq = 135.52, incr 0.72
69 / 01000101 - 0.390536% of total (15444291 / 3954638418), off-by -3515, a*a = 12355225, chisq = 136.32, incr 0.80
70 / 01000110 - 0.390590% of total (15446434 / 3954638418), off-by -1372, a*a = 1882384, chisq = 136.44, incr 0.12
71 / 01000111 - 0.390682% of total (15450061 / 3954638418), off-by 2255, a*a = 5085025, chisq = 136.77, incr 0.33
72 / 01001000 - 0.390506% of total (15443085 / 3954638418), off-by -4721, a*a = 22287841, chisq = 138.21, incr 1.44
73 / 01001001 - 0.390467% of total (15441563 / 3954638418), off-by -6243, a*a = 38975049, chisq = 140.73, incr 2.52
74 / 01001010 - 0.390712% of total (15451237 / 3954638418), off-by 3431, a*a = 11771761, chisq = 141.50, incr 0.76
75 / 01001011 - 0.390540% of total (15444443 / 3954638418), off-by -3363, a*a = 11309769, chisq = 142.23, incr 0.73
76 / 01001100 - 0.390729% of total (15451923 / 3954638418), off-by 4117, a*a = 16949689, chisq = 143.33, incr 1.10
77 / 01001101 - 0.390544% of total (15444606 / 3954638418), off-by -3200, a*a = 10240000, chisq = 143.99, incr 0.66
78 / 01001110 - 0.390641% of total (15448422 / 3954638418), off-by 616, a*a = 379456, chisq = 144.01, incr 0.02
79 / 01001111 - 0.390676% of total (15449832 / 3954638418), off-by 2026, a*a = 4104676, chisq = 144.28, incr 0.27
80 / 01010000 - 0.390735% of total (15452169 / 3954638418), off-by 4363, a*a = 19035769, chisq = 145.51, incr 1.23
81 / 01010001 - 0.390523% of total (15443757 / 3954638418), off-by -4049, a*a = 16394401, chisq = 146.57, incr 1.06
82 / 01010010 - 0.390342% of total (15436628 / 3954638418), off-by -11178, a*a = 124947684, chisq = 154.66, incr 8.09
83 / 01010011 - 0.390590% of total (15446441 / 3954638418), off-by -1365, a*a = 1863225, chisq = 154.78, incr 0.12
84 / 01010100 - 0.390384% of total (15438264 / 3954638418), off-by -9542, a*a = 91049764, chisq = 160.68, incr 5.89
85 / 01010101 - 0.390276% of total (15434017 / 3954638418), off-by -13789, a*a = 190136521, chisq = 172.98, incr 12.31
86 / 01010110 - 0.390348% of total (15436853 / 3954638418), off-by -10953, a*a = 119968209, chisq = 180.75, incr 7.77
87 / 01010111 - 0.390510% of total (15443240 / 3954638418), off-by -4566, a*a = 20848356, chisq = 182.10, incr 1.35
88 / 01011000 - 0.390524% of total (15443809 / 3954638418), off-by -3997, a*a = 15976009, chisq = 183.13, incr 1.03
89 / 01011001 - 0.390675% of total (15449775 / 3954638418), off-by 1969, a*a = 3876961, chisq = 183.38, incr 0.25
90 / 01011010 - 0.390437% of total (15440367 / 3954638418), off-by -7439, a*a = 55338721, chisq = 186.97, incr 3.58
91 / 01011011 - 0.390466% of total (15441505 / 3954638418), off-by -6301, a*a = 39702601, chisq = 189.54, incr 2.57
92 / 01011100 - 0.390554% of total (15444984 / 3954638418), off-by -2822, a*a = 7963684, chisq = 190.05, incr 0.52
93 / 01011101 - 0.390543% of total (15444561 / 3954638418), off-by -3245, a*a = 10530025, chisq = 190.73, incr 0.68
94 / 01011110 - 0.390593% of total (15446557 / 3954638418), off-by -1249, a*a = 1560001, chisq = 190.84, incr 0.10
95 / 01011111 - 0.390736% of total (15452211 / 3954638418), off-by 4405, a*a = 19404025, chisq = 192.09, incr 1.26
96 / 01100000 - 0.390684% of total (15450147 / 3954638418), off-by 2341, a*a = 5480281, chisq = 192.45, incr 0.35
97 / 01100001 - 0.390676% of total (15449831 / 3954638418), off-by 2025, a*a = 4100625, chisq = 192.71, incr 0.27
98 / 01100010 - 0.390708% of total (15451080 / 3954638418), off-by 3274, a*a = 10719076, chisq = 193.41, incr 0.69
99 / 01100011 - 0.390655% of total (15448997 / 3954638418), off-by 1191, a*a = 1418481, chisq = 193.50, incr 0.09
100 / 01100100 - 0.390491% of total (15442523 / 3954638418), off-by -5283, a*a = 27910089, chisq = 195.30, incr 1.81
101 / 01100101 - 0.390565% of total (15445434 / 3954638418), off-by -2372, a*a = 5626384, chisq = 195.67, incr 0.36
102 / 01100110 - 0.390644% of total (15448574 / 3954638418), off-by 768, a*a = 589824, chisq = 195.71, incr 0.04
103 / 01100111 - 0.390638% of total (15448324 / 3954638418), off-by 518, a*a = 268324, chisq = 195.72, incr 0.02
104 / 01101000 - 0.390637% of total (15448264 / 3954638418), off-by 458, a*a = 209764, chisq = 195.74, incr 0.01
105 / 01101001 - 0.390462% of total (15441359 / 3954638418), off-by -6447, a*a = 41563809, chisq = 198.43, incr 2.69
106 / 01101010 - 0.390510% of total (15443261 / 3954638418), off-by -4545, a*a = 20657025, chisq = 199.77, incr 1.34
107 / 01101011 - 0.390385% of total (15438319 / 3954638418), off-by -9487, a*a = 90003169, chisq = 205.59, incr 5.83
108 / 01101100 - 0.390538% of total (15444373 / 3954638418), off-by -3433, a*a = 11785489, chisq = 206.35, incr 0.76
109 / 01101101 - 0.390341% of total (15436558 / 3954638418), off-by -11248, a*a = 126517504, chisq = 214.54, incr 8.19
110 / 01101110 - 0.390675% of total (15449774 / 3954638418), off-by 1968, a*a = 3873024, chisq = 214.80, incr 0.25
111 / 01101111 - 0.390780% of total (15453918 / 3954638418), off-by 6112, a*a = 37356544, chisq = 217.21, incr 2.42
112 / 01110000 - 0.390775% of total (15453724 / 3954638418), off-by 5918, a*a = 35022724, chisq = 219.48, incr 2.27
113 / 01110001 - 0.390713% of total (15451306 / 3954638418), off-by 3500, a*a = 12250000, chisq = 220.27, incr 0.79
114 / 01110010 - 0.390602% of total (15446907 / 3954638418), off-by -899, a*a = 808201, chisq = 220.33, incr 0.05
115 / 01110011 - 0.390512% of total (15443338 / 3954638418), off-by -4468, a*a = 19963024, chisq = 221.62, incr 1.29
116 / 01110100 - 0.390645% of total (15448580 / 3954638418), off-by 774, a*a = 599076, chisq = 221.66, incr 0.04
117 / 01110101 - 0.390644% of total (15448539 / 3954638418), off-by 733, a*a = 537289, chisq = 221.69, incr 0.03
118 / 01110110 - 0.390489% of total (15442430 / 3954638418), off-by -5376, a*a = 28901376, chisq = 223.56, incr 1.87
119 / 01110111 - 0.390815% of total (15455316 / 3954638418), off-by 7510, a*a = 56400100, chisq = 227.21, incr 3.65
120 / 01111000 - 0.390709% of total (15451111 / 3954638418), off-by 3305, a*a = 10923025, chisq = 227.92, incr 0.71
121 / 01111001 - 0.390710% of total (15451162 / 3954638418), off-by 3356, a*a = 11262736, chisq = 228.65, incr 0.73
122 / 01111010 - 0.390435% of total (15440277 / 3954638418), off-by -7529, a*a = 56685841, chisq = 232.32, incr 3.67
123 / 01111011 - 0.390570% of total (15445621 / 3954638418), off-by -2185, a*a = 4774225, chisq = 232.63, incr 0.31
124 / 01111100 - 0.390750% of total (15452736 / 3954638418), off-by 4930, a*a = 24304900, chisq = 234.20, incr 1.57
125 / 01111101 - 0.390647% of total (15448662 / 3954638418), off-by 856, a*a = 732736, chisq = 234.25, incr 0.05
126 / 01111110 - 0.390512% of total (15443352 / 3954638418), off-by -4454, a*a = 19838116, chisq = 235.53, incr 1.28
127 / 01111111 - 0.390944% of total (15460438 / 3954638418), off-by 12632, a*a = 159567424, chisq = 245.86, incr 10.33
128 / 10000000 - 0.390716% of total (15451395 / 3954638418), off-by 3589, a*a = 12880921, chisq = 246.70, incr 0.83
129 / 10000001 - 0.390583% of total (15446162 / 3954638418), off-by -1644, a*a = 2702736, chisq = 246.87, incr 0.17
130 / 10000010 - 0.390548% of total (15444744 / 3954638418), off-by -3062, a*a = 9375844, chisq = 247.48, incr 0.61
131 / 10000011 - 0.390573% of total (15445752 / 3954638418), off-by -2054, a*a = 4218916, chisq = 247.75, incr 0.27
132 / 10000100 - 0.390582% of total (15446091 / 3954638418), off-by -1715, a*a = 2941225, chisq = 247.94, incr 0.19
133 / 10000101 - 0.390713% of total (15451305 / 3954638418), off-by 3499, a*a = 12243001, chisq = 248.73, incr 0.79
134 / 10000110 - 0.390515% of total (15443451 / 3954638418), off-by -4355, a*a = 18966025, chisq = 249.96, incr 1.23
135 / 10000111 - 0.390786% of total (15454168 / 3954638418), off-by 6362, a*a = 40475044, chisq = 252.58, incr 2.62
136 / 10001000 - 0.390733% of total (15452096 / 3954638418), off-by 4290, a*a = 18404100, chisq = 253.77, incr 1.19
137 / 10001001 - 0.390669% of total (15449543 / 3954638418), off-by 1737, a*a = 3017169, chisq = 253.97, incr 0.20
138 / 10001010 - 0.390508% of total (15443174 / 3954638418), off-by -4632, a*a = 21455424, chisq = 255.36, incr 1.39
139 / 10001011 - 0.390598% of total (15446744 / 3954638418), off-by -1062, a*a = 1127844, chisq = 255.43, incr 0.07
140 / 10001100 - 0.390585% of total (15446222 / 3954638418), off-by -1584, a*a = 2509056, chisq = 255.59, incr 0.16
141 / 10001101 - 0.390580% of total (15446021 / 3954638418), off-by -1785, a*a = 3186225, chisq = 255.80, incr 0.21
142 / 10001110 - 0.390827% of total (15455794 / 3954638418), off-by 7988, a*a = 63808144, chisq = 259.93, incr 4.13
143 / 10001111 - 0.390863% of total (15457212 / 3954638418), off-by 9406, a*a = 88472836, chisq = 265.66, incr 5.73
144 / 10010000 - 0.390895% of total (15458499 / 3954638418), off-by 10693, a*a = 114340249, chisq = 273.06, incr 7.40
145 / 10010001 - 0.390650% of total (15448812 / 3954638418), off-by 1006, a*a = 1012036, chisq = 273.12, incr 0.07
146 / 10010010 - 0.390422% of total (15439772 / 3954638418), off-by -8034, a*a = 64545156, chisq = 277.30, incr 4.18
147 / 10010011 - 0.390748% of total (15452670 / 3954638418), off-by 4864, a*a = 23658496, chisq = 278.83, incr 1.53
148 / 10010100 - 0.390455% of total (15441076 / 3954638418), off-by -6730, a*a = 45292900, chisq = 281.77, incr 2.93
149 / 10010101 - 0.390400% of total (15438924 / 3954638418), off-by -8882, a*a = 78889924, chisq = 286.87, incr 5.11
150 / 10010110 - 0.390643% of total (15448501 / 3954638418), off-by 695, a*a = 483025, chisq = 286.90, incr 0.03
151 / 10010111 - 0.390641% of total (15448452 / 3954638418), off-by 646, a*a = 417316, chisq = 286.93, incr 0.03
152 / 10011000 - 0.390664% of total (15449338 / 3954638418), off-by 1532, a*a = 2347024, chisq = 287.08, incr 0.15
153 / 10011001 - 0.390553% of total (15444970 / 3954638418), off-by -2836, a*a = 8042896, chisq = 287.60, incr 0.52
154 / 10011010 - 0.390556% of total (15445079 / 3954638418), off-by -2727, a*a = 7436529, chisq = 288.09, incr 0.48
155 / 10011011 - 0.390487% of total (15442360 / 3954638418), off-by -5446, a*a = 29658916, chisq = 290.01, incr 1.92
156 / 10011100 - 0.390666% of total (15449432 / 3954638418), off-by 1626, a*a = 2643876, chisq = 290.18, incr 0.17
157 / 10011101 - 0.390650% of total (15448786 / 3954638418), off-by 980, a*a = 960400, chisq = 290.24, incr 0.06
158 / 10011110 - 0.390677% of total (15449845 / 3954638418), off-by 2039, a*a = 4157521, chisq = 290.51, incr 0.27
159 / 10011111 - 0.390816% of total (15455357 / 3954638418), off-by 7551, a*a = 57017601, chisq = 294.20, incr 3.69
160 / 10100000 - 0.390723% of total (15451685 / 3954638418), off-by 3879, a*a = 15046641, chisq = 295.17, incr 0.97
161 / 10100001 - 0.390591% of total (15446448 / 3954638418), off-by -1358, a*a = 1844164, chisq = 295.29, incr 0.12
162 / 10100010 - 0.390480% of total (15442059 / 3954638418), off-by -5747, a*a = 33028009, chisq = 297.43, incr 2.14
163 / 10100011 - 0.390649% of total (15448761 / 3954638418), off-by 955, a*a = 912025, chisq = 297.49, incr 0.06
164 / 10100100 - 0.390590% of total (15446418 / 3954638418), off-by -1388, a*a = 1926544, chisq = 297.61, incr 0.12
165 / 10100101 - 0.390551% of total (15444874 / 3954638418), off-by -2932, a*a = 8596624, chisq = 298.17, incr 0.56
166 / 10100110 - 0.390601% of total (15446843 / 3954638418), off-by -963, a*a = 927369, chisq = 298.23, incr 0.06
167 / 10100111 - 0.390655% of total (15448980 / 3954638418), off-by 1174, a*a = 1378276, chisq = 298.32, incr 0.09
168 / 10101000 - 0.390488% of total (15442407 / 3954638418), off-by -5399, a*a = 29149201, chisq = 300.21, incr 1.89
169 / 10101001 - 0.390335% of total (15436343 / 3954638418), off-by -11463, a*a = 131400369, chisq = 308.71, incr 8.51
170 / 10101010 - 0.390683% of total (15450105 / 3954638418), off-by 2299, a*a = 5285401, chisq = 309.06, incr 0.34
171 / 10101011 - 0.390387% of total (15438399 / 3954638418), off-by -9407, a*a = 88491649, chisq = 314.78, incr 5.73
172 / 10101100 - 0.390574% of total (15445797 / 3954638418), off-by -2009, a*a = 4036081, chisq = 315.04, incr 0.26
173 / 10101101 - 0.390577% of total (15445920 / 3954638418), off-by -1886, a*a = 3556996, chisq = 315.28, incr 0.23
174 / 10101110 - 0.390703% of total (15450876 / 3954638418), off-by 3070, a*a = 9424900, chisq = 315.89, incr 0.61
175 / 10101111 - 0.390532% of total (15444144 / 3954638418), off-by -3662, a*a = 13410244, chisq = 316.75, incr 0.87
176 / 10110000 - 0.390780% of total (15453919 / 3954638418), off-by 6113, a*a = 37368769, chisq = 319.17, incr 2.42
177 / 10110001 - 0.390736% of total (15452194 / 3954638418), off-by 4388, a*a = 19254544, chisq = 320.42, incr 1.25
178 / 10110010 - 0.390645% of total (15448594 / 3954638418), off-by 788, a*a = 620944, chisq = 320.46, incr 0.04
179 / 10110011 - 0.390628% of total (15447925 / 3954638418), off-by 119, a*a = 14161, chisq = 320.46, incr 0.00
180 / 10110100 - 0.390446% of total (15440714 / 3954638418), off-by -7092, a*a = 50296464, chisq = 323.72, incr 3.26
181 / 10110101 - 0.390534% of total (15444222 / 3954638418), off-by -3584, a*a = 12845056, chisq = 324.55, incr 0.83
182 / 10110110 - 0.390592% of total (15446490 / 3954638418), off-by -1316, a*a = 1731856, chisq = 324.66, incr 0.11
183 / 10110111 - 0.390624% of total (15447763 / 3954638418), off-by -43, a*a = 1849, chisq = 324.66, incr 0.00
184 / 10111000 - 0.390646% of total (15448644 / 3954638418), off-by 838, a*a = 702244, chisq = 324.71, incr 0.05
185 / 10111001 - 0.390659% of total (15449142 / 3954638418), off-by 1336, a*a = 1784896, chisq = 324.82, incr 0.12
186 / 10111010 - 0.390563% of total (15445374 / 3954638418), off-by -2432, a*a = 5914624, chisq = 325.20, incr 0.38
187 / 10111011 - 0.390595% of total (15446602 / 3954638418), off-by -1204, a*a = 1449616, chisq = 325.30, incr 0.09
188 / 10111100 - 0.390761% of total (15453186 / 3954638418), off-by 5380, a*a = 28944400, chisq = 327.17, incr 1.87
189 / 10111101 - 0.390505% of total (15443080 / 3954638418), off-by -4726, a*a = 22335076, chisq = 328.62, incr 1.45
190 / 10111110 - 0.390593% of total (15446528 / 3954638418), off-by -1278, a*a = 1633284, chisq = 328.72, incr 0.11
191 / 10111111 - 0.390888% of total (15458199 / 3954638418), off-by 10393, a*a = 108014449, chisq = 335.71, incr 6.99
192 / 11000000 - 0.390833% of total (15456037 / 3954638418), off-by 8231, a*a = 67749361, chisq = 340.10, incr 4.39
193 / 11000001 - 0.390765% of total (15453350 / 3954638418), off-by 5544, a*a = 30735936, chisq = 342.09, incr 1.99
194 / 11000010 - 0.390888% of total (15458197 / 3954638418), off-by 10391, a*a = 107972881, chisq = 349.08, incr 6.99
195 / 11000011 - 0.390522% of total (15443730 / 3954638418), off-by -4076, a*a = 16613776, chisq = 350.16, incr 1.08
196 / 11000100 - 0.390557% of total (15445131 / 3954638418), off-by -2675, a*a = 7155625, chisq = 350.62, incr 0.46
197 / 11000101 - 0.390643% of total (15448514 / 3954638418), off-by 708, a*a = 501264, chisq = 350.65, incr 0.03
198 / 11000110 - 0.390620% of total (15447627 / 3954638418), off-by -179, a*a = 32041, chisq = 350.65, incr 0.00
199 / 11000111 - 0.390865% of total (15457317 / 3954638418), off-by 9511, a*a = 90459121, chisq = 356.51, incr 5.86
200 / 11001000 - 0.390616% of total (15447446 / 3954638418), off-by -360, a*a = 129600, chisq = 356.52, incr 0.01
201 / 11001001 - 0.390418% of total (15439615 / 3954638418), off-by -8191, a*a = 67092481, chisq = 360.86, incr 4.34
202 / 11001010 - 0.390594% of total (15446577 / 3954638418), off-by -1229, a*a = 1510441, chisq = 360.96, incr 0.10
203 / 11001011 - 0.390568% of total (15445568 / 3954638418), off-by -2238, a*a = 5008644, chisq = 361.28, incr 0.32
204 / 11001100 - 0.390515% of total (15443463 / 3954638418), off-by -4343, a*a = 18861649, chisq = 362.50, incr 1.22
205 / 11001101 - 0.390497% of total (15442726 / 3954638418), off-by -5080, a*a = 25806400, chisq = 364.17, incr 1.67
206 / 11001110 - 0.390735% of total (15452157 / 3954638418), off-by 4351, a*a = 18931201, chisq = 365.40, incr 1.23
207 / 11001111 - 0.390671% of total (15449618 / 3954638418), off-by 1812, a*a = 3283344, chisq = 365.61, incr 0.21
208 / 11010000 - 0.390692% of total (15450460 / 3954638418), off-by 2654, a*a = 7043716, chisq = 366.07, incr 0.46
209 / 11010001 - 0.390495% of total (15442684 / 3954638418), off-by -5122, a*a = 26234884, chisq = 367.77, incr 1.70
210 / 11010010 - 0.390667% of total (15449480 / 3954638418), off-by 1674, a*a = 2802276, chisq = 367.95, incr 0.18
211 / 11010011 - 0.390507% of total (15443125 / 3954638418), off-by -4681, a*a = 21911761, chisq = 369.37, incr 1.42
212 / 11010100 - 0.390517% of total (15443524 / 3954638418), off-by -4282, a*a = 18335524, chisq = 370.55, incr 1.19
213 / 11010101 - 0.390453% of total (15441002 / 3954638418), off-by -6804, a*a = 46294416, chisq = 373.55, incr 3.00
214 / 11010110 - 0.390495% of total (15442665 / 3954638418), off-by -5141, a*a = 26429881, chisq = 375.26, incr 1.71
215 / 11010111 - 0.390438% of total (15440430 / 3954638418), off-by -7376, a*a = 54405376, chisq = 378.78, incr 3.52
216 / 11011000 - 0.390716% of total (15451386 / 3954638418), off-by 3580, a*a = 12816400, chisq = 379.61, incr 0.83
217 / 11011001 - 0.390631% of total (15448056 / 3954638418), off-by 250, a*a = 62500, chisq = 379.62, incr 0.00
218 / 11011010 - 0.390555% of total (15445045 / 3954638418), off-by -2761, a*a = 7623121, chisq = 380.11, incr 0.49
219 / 11011011 - 0.390682% of total (15450060 / 3954638418), off-by 2254, a*a = 5080516, chisq = 380.44, incr 0.33
220 / 11011100 - 0.390528% of total (15443954 / 3954638418), off-by -3852, a*a = 14837904, chisq = 381.40, incr 0.96
221 / 11011101 - 0.390743% of total (15452486 / 3954638418), off-by 4680, a*a = 21902400, chisq = 382.82, incr 1.42
222 / 11011110 - 0.390813% of total (15455255 / 3954638418), off-by 7449, a*a = 55487601, chisq = 386.41, incr 3.59
223 / 11011111 - 0.390888% of total (15458216 / 3954638418), off-by 10410, a*a = 108368100, chisq = 393.42, incr 7.02
224 / 11100000 - 0.390696% of total (15450604 / 3954638418), off-by 2798, a*a = 7828804, chisq = 393.93, incr 0.51
225 / 11100001 - 0.390557% of total (15445125 / 3954638418), off-by -2681, a*a = 7187761, chisq = 394.40, incr 0.47
226 / 11100010 - 0.390703% of total (15450907 / 3954638418), off-by 3101, a*a = 9616201, chisq = 395.02, incr 0.62
227 / 11100011 - 0.390474% of total (15441844 / 3954638418), off-by -5962, a*a = 35545444, chisq = 397.32, incr 2.30
228 / 11100100 - 0.390599% of total (15446762 / 3954638418), off-by -1044, a*a = 1089936, chisq = 397.39, incr 0.07
229 / 11100101 - 0.390438% of total (15440411 / 3954638418), off-by -7395, a*a = 54686025, chisq = 400.93, incr 3.54
230 / 11100110 - 0.390744% of total (15452516 / 3954638418), off-by 4710, a*a = 22184100, chisq = 402.37, incr 1.44
231 / 11100111 - 0.390698% of total (15450678 / 3954638418), off-by 2872, a*a = 8248384, chisq = 402.90, incr 0.53
232 / 11101000 - 0.390807% of total (15454993 / 3954638418), off-by 7187, a*a = 51652969, chisq = 406.24, incr 3.34
233 / 11101001 - 0.390440% of total (15440503 / 3954638418), off-by -7303, a*a = 53333809, chisq = 409.70, incr 3.45
234 / 11101010 - 0.390598% of total (15446721 / 3954638418), off-by -1085, a*a = 1177225, chisq = 409.77, incr 0.08
235 / 11101011 - 0.390747% of total (15452648 / 3954638418), off-by 4842, a*a = 23444964, chisq = 411.29, incr 1.52
236 / 11101100 - 0.390774% of total (15453707 / 3954638418), off-by 5901, a*a = 34821801, chisq = 413.54, incr 2.25
237 / 11101101 - 0.390596% of total (15446661 / 3954638418), off-by -1145, a*a = 1311025, chisq = 413.63, incr 0.08
238 / 11101110 - 0.390712% of total (15451243 / 3954638418), off-by 3437, a*a = 11812969, chisq = 414.39, incr 0.76
239 / 11101111 - 0.390811% of total (15455169 / 3954638418), off-by 7363, a*a = 54213769, chisq = 417.90, incr 3.51
240 / 11110000 - 0.390662% of total (15449256 / 3954638418), off-by 1450, a*a = 2102500, chisq = 418.04, incr 0.14
241 / 11110001 - 0.390716% of total (15451413 / 3954638418), off-by 3607, a*a = 13010449, chisq = 418.88, incr 0.84
242 / 11110010 - 0.390684% of total (15450136 / 3954638418), off-by 2330, a*a = 5428900, chisq = 419.23, incr 0.35
243 / 11110011 - 0.390524% of total (15443815 / 3954638418), off-by -3991, a*a = 15928081, chisq = 420.26, incr 1.03
244 / 11110100 - 0.390592% of total (15446485 / 3954638418), off-by -1321, a*a = 1745041, chisq = 420.38, incr 0.11
245 / 11110101 - 0.390700% of total (15450778 / 3954638418), off-by 2972, a*a = 8832784, chisq = 420.95, incr 0.57
246 / 11110110 - 0.390600% of total (15446836 / 3954638418), off-by -970, a*a = 940900, chisq = 421.01, incr 0.06
247 / 11110111 - 0.390700% of total (15450755 / 3954638418), off-by 2949, a*a = 8696601, chisq = 421.57, incr 0.56
248 / 11111000 - 0.390585% of total (15446244 / 3954638418), off-by -1562, a*a = 2439844, chisq = 421.73, incr 0.16
249 / 11111001 - 0.390826% of total (15455754 / 3954638418), off-by 7948, a*a = 63170704, chisq = 425.82, incr 4.09
250 / 11111010 - 0.390650% of total (15448784 / 3954638418), off-by 978, a*a = 956484, chisq = 425.88, incr 0.06
251 / 11111011 - 0.390705% of total (15450955 / 3954638418), off-by 3149, a*a = 9916201, chisq = 426.52, incr 0.64
252 / 11111100 - 0.390842% of total (15456373 / 3954638418), off-by 8567, a*a = 73393489, chisq = 431.28, incr 4.75
253 / 11111101 - 0.390656% of total (15449037 / 3954638418), off-by 1231, a*a = 1515361, chisq = 431.37, incr 0.10
254 / 11111110 - 0.390859% of total (15457053 / 3954638418), off-by 9247, a*a = 85507009, chisq = 436.91, incr 5.54
255 / 11111111 - 0.390947% of total (15460536 / 3954638418), off-by 12730, a*a = 162052900, chisq = 447.40, incr 10.49
First Chi-Square: 447.3987561728833
Sorted contributors: [183, 179, 198, 217, 200, 35, 50, 104, 34, 103, 78, 151, 65, 150, 197, 117, 5, 102, 116, 178, 184, 125, 57, 114, 163, 166, 246, 250, 157, 28, 145, 228, 139, 11, 234, 237, 167, 99, 187, 25, 202, 253, 94, 40, 190, 47, 182, 244, 185, 161, 83, 70, 164, 24, 240, 152, 248, 140, 156, 52, 129, 210, 27, 132, 137, 56, 141, 62, 207, 173, 37, 110, 89, 32, 172, 97, 79, 158, 131, 4, 13, 49, 123, 203, 219, 71, 51, 170, 29, 242, 96, 10, 101, 186, 33, 1, 208, 6, 67, 196, 225, 154, 218, 23, 224, 46, 19, 92, 153, 231, 165, 247, 245, 130, 174, 226, 30, 251, 77, 93, 39, 38, 98, 120, 68, 121, 75, 7, 74, 108, 238, 60, 133, 113, 53, 69, 216, 181, 128, 241, 175, 2, 220, 160, 243, 88, 81, 195, 76, 212, 136, 204, 206, 134, 80, 177, 95, 126, 115, 66, 106, 87, 54, 138, 221, 211, 230, 20, 72, 189, 14, 17, 235, 147, 124, 48, 205, 22, 209, 214, 16, 3, 44, 100, 18, 118, 188, 168, 155, 193, 9, 58, 162, 36, 236, 112, 227, 45, 59, 111, 176, 73, 91, 135, 61, 105, 55, 148, 213, 180, 41, 232, 233, 239, 215, 229, 90, 222, 119, 122, 159, 43, 31, 249, 142, 146, 201, 192, 252, 26, 15, 21, 12, 149, 8, 254, 143, 171, 107, 199, 84, 194, 191, 223, 144, 42, 86, 82, 109, 169, 127, 255, 63, 64, 85, 0]
Chi-square calculation again, sorted by contributing byte
183 / 10110111 - 0.390624% of total (15447763 / 3954638418), off-by -43, a*a = 1849, chisq = 0.00, incr 0.00
179 / 10110011 - 0.390628% of total (15447925 / 3954638418), off-by 119, a*a = 14161, chisq = 0.00, incr 0.00
198 / 11000110 - 0.390620% of total (15447627 / 3954638418), off-by -179, a*a = 32041, chisq = 0.00, incr 0.00
217 / 11011001 - 0.390631% of total (15448056 / 3954638418), off-by 250, a*a = 62500, chisq = 0.01, incr 0.00
200 / 11001000 - 0.390616% of total (15447446 / 3954638418), off-by -360, a*a = 129600, chisq = 0.02, incr 0.01
35 / 00100011 - 0.390634% of total (15448179 / 3954638418), off-by 373, a*a = 139129, chisq = 0.02, incr 0.01
50 / 00110010 - 0.390615% of total (15447408 / 3954638418), off-by -398, a*a = 158404, chisq = 0.03, incr 0.01
104 / 01101000 - 0.390637% of total (15448264 / 3954638418), off-by 458, a*a = 209764, chisq = 0.05, incr 0.01
34 / 00100010 - 0.390612% of total (15447294 / 3954638418), off-by -512, a*a = 262144, chisq = 0.07, incr 0.02
103 / 01100111 - 0.390638% of total (15448324 / 3954638418), off-by 518, a*a = 268324, chisq = 0.08, incr 0.02
78 / 01001110 - 0.390641% of total (15448422 / 3954638418), off-by 616, a*a = 379456, chisq = 0.11, incr 0.02
151 / 10010111 - 0.390641% of total (15448452 / 3954638418), off-by 646, a*a = 417316, chisq = 0.13, incr 0.03
65 / 01000001 - 0.390608% of total (15447133 / 3954638418), off-by -673, a*a = 452929, chisq = 0.16, incr 0.03
150 / 10010110 - 0.390643% of total (15448501 / 3954638418), off-by 695, a*a = 483025, chisq = 0.19, incr 0.03
197 / 11000101 - 0.390643% of total (15448514 / 3954638418), off-by 708, a*a = 501264, chisq = 0.23, incr 0.03
117 / 01110101 - 0.390644% of total (15448539 / 3954638418), off-by 733, a*a = 537289, chisq = 0.26, incr 0.03
5 / 00000101 - 0.390644% of total (15448550 / 3954638418), off-by 744, a*a = 553536, chisq = 0.30, incr 0.04
102 / 01100110 - 0.390644% of total (15448574 / 3954638418), off-by 768, a*a = 589824, chisq = 0.34, incr 0.04
116 / 01110100 - 0.390645% of total (15448580 / 3954638418), off-by 774, a*a = 599076, chisq = 0.37, incr 0.04
178 / 10110010 - 0.390645% of total (15448594 / 3954638418), off-by 788, a*a = 620944, chisq = 0.42, incr 0.04
184 / 10111000 - 0.390646% of total (15448644 / 3954638418), off-by 838, a*a = 702244, chisq = 0.46, incr 0.05
125 / 01111101 - 0.390647% of total (15448662 / 3954638418), off-by 856, a*a = 732736, chisq = 0.51, incr 0.05
57 / 00111001 - 0.390647% of total (15448676 / 3954638418), off-by 870, a*a = 756900, chisq = 0.56, incr 0.05
114 / 01110010 - 0.390602% of total (15446907 / 3954638418), off-by -899, a*a = 808201, chisq = 0.61, incr 0.05
163 / 10100011 - 0.390649% of total (15448761 / 3954638418), off-by 955, a*a = 912025, chisq = 0.67, incr 0.06
166 / 10100110 - 0.390601% of total (15446843 / 3954638418), off-by -963, a*a = 927369, chisq = 0.73, incr 0.06
246 / 11110110 - 0.390600% of total (15446836 / 3954638418), off-by -970, a*a = 940900, chisq = 0.79, incr 0.06
250 / 11111010 - 0.390650% of total (15448784 / 3954638418), off-by 978, a*a = 956484, chisq = 0.85, incr 0.06
157 / 10011101 - 0.390650% of total (15448786 / 3954638418), off-by 980, a*a = 960400, chisq = 0.91, incr 0.06
28 / 00011100 - 0.390600% of total (15446824 / 3954638418), off-by -982, a*a = 964324, chisq = 0.98, incr 0.06
145 / 10010001 - 0.390650% of total (15448812 / 3954638418), off-by 1006, a*a = 1012036, chisq = 1.04, incr 0.07
228 / 11100100 - 0.390599% of total (15446762 / 3954638418), off-by -1044, a*a = 1089936, chisq = 1.11, incr 0.07
139 / 10001011 - 0.390598% of total (15446744 / 3954638418), off-by -1062, a*a = 1127844, chisq = 1.18, incr 0.07
11 / 00001011 - 0.390652% of total (15448889 / 3954638418), off-by 1083, a*a = 1172889, chisq = 1.26, incr 0.08
234 / 11101010 - 0.390598% of total (15446721 / 3954638418), off-by -1085, a*a = 1177225, chisq = 1.34, incr 0.08
237 / 11101101 - 0.390596% of total (15446661 / 3954638418), off-by -1145, a*a = 1311025, chisq = 1.42, incr 0.08
167 / 10100111 - 0.390655% of total (15448980 / 3954638418), off-by 1174, a*a = 1378276, chisq = 1.51, incr 0.09
99 / 01100011 - 0.390655% of total (15448997 / 3954638418), off-by 1191, a*a = 1418481, chisq = 1.60, incr 0.09
187 / 10111011 - 0.390595% of total (15446602 / 3954638418), off-by -1204, a*a = 1449616, chisq = 1.70, incr 0.09
25 / 00011001 - 0.390656% of total (15449019 / 3954638418), off-by 1213, a*a = 1471369, chisq = 1.79, incr 0.10
202 / 11001010 - 0.390594% of total (15446577 / 3954638418), off-by -1229, a*a = 1510441, chisq = 1.89, incr 0.10
253 / 11111101 - 0.390656% of total (15449037 / 3954638418), off-by 1231, a*a = 1515361, chisq = 1.99, incr 0.10
94 / 01011110 - 0.390593% of total (15446557 / 3954638418), off-by -1249, a*a = 1560001, chisq = 2.09, incr 0.10
40 / 00101000 - 0.390593% of total (15446532 / 3954638418), off-by -1274, a*a = 1623076, chisq = 2.19, incr 0.11
190 / 10111110 - 0.390593% of total (15446528 / 3954638418), off-by -1278, a*a = 1633284, chisq = 2.30, incr 0.11
47 / 00101111 - 0.390592% of total (15446502 / 3954638418), off-by -1304, a*a = 1700416, chisq = 2.41, incr 0.11
182 / 10110110 - 0.390592% of total (15446490 / 3954638418), off-by -1316, a*a = 1731856, chisq = 2.52, incr 0.11
244 / 11110100 - 0.390592% of total (15446485 / 3954638418), off-by -1321, a*a = 1745041, chisq = 2.63, incr 0.11
185 / 10111001 - 0.390659% of total (15449142 / 3954638418), off-by 1336, a*a = 1784896, chisq = 2.75, incr 0.12
161 / 10100001 - 0.390591% of total (15446448 / 3954638418), off-by -1358, a*a = 1844164, chisq = 2.87, incr 0.12
83 / 01010011 - 0.390590% of total (15446441 / 3954638418), off-by -1365, a*a = 1863225, chisq = 2.99, incr 0.12
70 / 01000110 - 0.390590% of total (15446434 / 3954638418), off-by -1372, a*a = 1882384, chisq = 3.11, incr 0.12
164 / 10100100 - 0.390590% of total (15446418 / 3954638418), off-by -1388, a*a = 1926544, chisq = 3.24, incr 0.12
24 / 00011000 - 0.390660% of total (15449197 / 3954638418), off-by 1391, a*a = 1934881, chisq = 3.36, incr 0.13
240 / 11110000 - 0.390662% of total (15449256 / 3954638418), off-by 1450, a*a = 2102500, chisq = 3.50, incr 0.14
152 / 10011000 - 0.390664% of total (15449338 / 3954638418), off-by 1532, a*a = 2347024, chisq = 3.65, incr 0.15
248 / 11111000 - 0.390585% of total (15446244 / 3954638418), off-by -1562, a*a = 2439844, chisq = 3.81, incr 0.16
140 / 10001100 - 0.390585% of total (15446222 / 3954638418), off-by -1584, a*a = 2509056, chisq = 3.97, incr 0.16
156 / 10011100 - 0.390666% of total (15449432 / 3954638418), off-by 1626, a*a = 2643876, chisq = 4.14, incr 0.17
52 / 00110100 - 0.390584% of total (15446178 / 3954638418), off-by -1628, a*a = 2650384, chisq = 4.31, incr 0.17
129 / 10000001 - 0.390583% of total (15446162 / 3954638418), off-by -1644, a*a = 2702736, chisq = 4.49, incr 0.17
210 / 11010010 - 0.390667% of total (15449480 / 3954638418), off-by 1674, a*a = 2802276, chisq = 4.67, incr 0.18
27 / 00011011 - 0.390667% of total (15449483 / 3954638418), off-by 1677, a*a = 2812329, chisq = 4.85, incr 0.18
132 / 10000100 - 0.390582% of total (15446091 / 3954638418), off-by -1715, a*a = 2941225, chisq = 5.04, incr 0.19
137 / 10001001 - 0.390669% of total (15449543 / 3954638418), off-by 1737, a*a = 3017169, chisq = 5.24, incr 0.20
56 / 00111000 - 0.390670% of total (15449567 / 3954638418), off-by 1761, a*a = 3101121, chisq = 5.44, incr 0.20
141 / 10001101 - 0.390580% of total (15446021 / 3954638418), off-by -1785, a*a = 3186225, chisq = 5.64, incr 0.21
62 / 00111110 - 0.390579% of total (15446004 / 3954638418), off-by -1802, a*a = 3247204, chisq = 5.85, incr 0.21
207 / 11001111 - 0.390671% of total (15449618 / 3954638418), off-by 1812, a*a = 3283344, chisq = 6.07, incr 0.21
173 / 10101101 - 0.390577% of total (15445920 / 3954638418), off-by -1886, a*a = 3556996, chisq = 6.30, incr 0.23
37 / 00100101 - 0.390576% of total (15445861 / 3954638418), off-by -1945, a*a = 3783025, chisq = 6.54, incr 0.24
110 / 01101110 - 0.390675% of total (15449774 / 3954638418), off-by 1968, a*a = 3873024, chisq = 6.79, incr 0.25
89 / 01011001 - 0.390675% of total (15449775 / 3954638418), off-by 1969, a*a = 3876961, chisq = 7.04, incr 0.25
32 / 00100000 - 0.390675% of total (15449784 / 3954638418), off-by 1978, a*a = 3912484, chisq = 7.30, incr 0.25
172 / 10101100 - 0.390574% of total (15445797 / 3954638418), off-by -2009, a*a = 4036081, chisq = 7.56, incr 0.26
97 / 01100001 - 0.390676% of total (15449831 / 3954638418), off-by 2025, a*a = 4100625, chisq = 7.82, incr 0.27
79 / 01001111 - 0.390676% of total (15449832 / 3954638418), off-by 2026, a*a = 4104676, chisq = 8.09, incr 0.27
158 / 10011110 - 0.390677% of total (15449845 / 3954638418), off-by 2039, a*a = 4157521, chisq = 8.36, incr 0.27
131 / 10000011 - 0.390573% of total (15445752 / 3954638418), off-by -2054, a*a = 4218916, chisq = 8.63, incr 0.27
4 / 00000100 - 0.390678% of total (15449907 / 3954638418), off-by 2101, a*a = 4414201, chisq = 8.92, incr 0.29
13 / 00001101 - 0.390680% of total (15449985 / 3954638418), off-by 2179, a*a = 4748041, chisq = 9.23, incr 0.31
49 / 00110001 - 0.390680% of total (15449985 / 3954638418), off-by 2179, a*a = 4748041, chisq = 9.53, incr 0.31
123 / 01111011 - 0.390570% of total (15445621 / 3954638418), off-by -2185, a*a = 4774225, chisq = 9.84, incr 0.31
203 / 11001011 - 0.390568% of total (15445568 / 3954638418), off-by -2238, a*a = 5008644, chisq = 10.17, incr 0.32
219 / 11011011 - 0.390682% of total (15450060 / 3954638418), off-by 2254, a*a = 5080516, chisq = 10.49, incr 0.33
71 / 01000111 - 0.390682% of total (15450061 / 3954638418), off-by 2255, a*a = 5085025, chisq = 10.82, incr 0.33
51 / 00110011 - 0.390568% of total (15445535 / 3954638418), off-by -2271, a*a = 5157441, chisq = 11.16, incr 0.33
170 / 10101010 - 0.390683% of total (15450105 / 3954638418), off-by 2299, a*a = 5285401, chisq = 11.50, incr 0.34
29 / 00011101 - 0.390567% of total (15445503 / 3954638418), off-by -2303, a*a = 5303809, chisq = 11.84, incr 0.34
242 / 11110010 - 0.390684% of total (15450136 / 3954638418), off-by 2330, a*a = 5428900, chisq = 12.19, incr 0.35
96 / 01100000 - 0.390684% of total (15450147 / 3954638418), off-by 2341, a*a = 5480281, chisq = 12.55, incr 0.35
10 / 00001010 - 0.390565% of total (15445439 / 3954638418), off-by -2367, a*a = 5602689, chisq = 12.91, incr 0.36
101 / 01100101 - 0.390565% of total (15445434 / 3954638418), off-by -2372, a*a = 5626384, chisq = 13.28, incr 0.36
186 / 10111010 - 0.390563% of total (15445374 / 3954638418), off-by -2432, a*a = 5914624, chisq = 13.66, incr 0.38
33 / 00100001 - 0.390563% of total (15445373 / 3954638418), off-by -2433, a*a = 5919489, chisq = 14.04, incr 0.38
1 / 00000001 - 0.390688% of total (15450295 / 3954638418), off-by 2489, a*a = 6195121, chisq = 14.44, incr 0.40
208 / 11010000 - 0.390692% of total (15450460 / 3954638418), off-by 2654, a*a = 7043716, chisq = 14.90, incr 0.46
6 / 00000110 - 0.390692% of total (15450465 / 3954638418), off-by 2659, a*a = 7070281, chisq = 15.36, incr 0.46
67 / 01000011 - 0.390558% of total (15445144 / 3954638418), off-by -2662, a*a = 7086244, chisq = 15.82, incr 0.46
196 / 11000100 - 0.390557% of total (15445131 / 3954638418), off-by -2675, a*a = 7155625, chisq = 16.28, incr 0.46
225 / 11100001 - 0.390557% of total (15445125 / 3954638418), off-by -2681, a*a = 7187761, chisq = 16.74, incr 0.47
154 / 10011010 - 0.390556% of total (15445079 / 3954638418), off-by -2727, a*a = 7436529, chisq = 17.23, incr 0.48
218 / 11011010 - 0.390555% of total (15445045 / 3954638418), off-by -2761, a*a = 7623121, chisq = 17.72, incr 0.49
23 / 00010111 - 0.390696% of total (15450595 / 3954638418), off-by 2789, a*a = 7778521, chisq = 18.22, incr 0.50
224 / 11100000 - 0.390696% of total (15450604 / 3954638418), off-by 2798, a*a = 7828804, chisq = 18.73, incr 0.51
46 / 00101110 - 0.390554% of total (15444992 / 3954638418), off-by -2814, a*a = 7918596, chisq = 19.24, incr 0.51
19 / 00010011 - 0.390554% of total (15444985 / 3954638418), off-by -2821, a*a = 7958041, chisq = 19.76, incr 0.52
92 / 01011100 - 0.390554% of total (15444984 / 3954638418), off-by -2822, a*a = 7963684, chisq = 20.27, incr 0.52
153 / 10011001 - 0.390553% of total (15444970 / 3954638418), off-by -2836, a*a = 8042896, chisq = 20.79, incr 0.52
231 / 11100111 - 0.390698% of total (15450678 / 3954638418), off-by 2872, a*a = 8248384, chisq = 21.33, incr 0.53
165 / 10100101 - 0.390551% of total (15444874 / 3954638418), off-by -2932, a*a = 8596624, chisq = 21.88, incr 0.56
247 / 11110111 - 0.390700% of total (15450755 / 3954638418), off-by 2949, a*a = 8696601, chisq = 22.45, incr 0.56
245 / 11110101 - 0.390700% of total (15450778 / 3954638418), off-by 2972, a*a = 8832784, chisq = 23.02, incr 0.57
130 / 10000010 - 0.390548% of total (15444744 / 3954638418), off-by -3062, a*a = 9375844, chisq = 23.63, incr 0.61
174 / 10101110 - 0.390703% of total (15450876 / 3954638418), off-by 3070, a*a = 9424900, chisq = 24.24, incr 0.61
226 / 11100010 - 0.390703% of total (15450907 / 3954638418), off-by 3101, a*a = 9616201, chisq = 24.86, incr 0.62
30 / 00011110 - 0.390546% of total (15444698 / 3954638418), off-by -3108, a*a = 9659664, chisq = 25.48, incr 0.63
251 / 11111011 - 0.390705% of total (15450955 / 3954638418), off-by 3149, a*a = 9916201, chisq = 26.13, incr 0.64
77 / 01001101 - 0.390544% of total (15444606 / 3954638418), off-by -3200, a*a = 10240000, chisq = 26.79, incr 0.66
93 / 01011101 - 0.390543% of total (15444561 / 3954638418), off-by -3245, a*a = 10530025, chisq = 27.47, incr 0.68
39 / 00100111 - 0.390543% of total (15444559 / 3954638418), off-by -3247, a*a = 10543009, chisq = 28.15, incr 0.68
38 / 00100110 - 0.390543% of total (15444546 / 3954638418), off-by -3260, a*a = 10627600, chisq = 28.84, incr 0.69
98 / 01100010 - 0.390708% of total (15451080 / 3954638418), off-by 3274, a*a = 10719076, chisq = 29.53, incr 0.69
120 / 01111000 - 0.390709% of total (15451111 / 3954638418), off-by 3305, a*a = 10923025, chisq = 30.24, incr 0.71
68 / 01000100 - 0.390709% of total (15451142 / 3954638418), off-by 3336, a*a = 11128896, chisq = 30.96, incr 0.72
121 / 01111001 - 0.390710% of total (15451162 / 3954638418), off-by 3356, a*a = 11262736, chisq = 31.69, incr 0.73
75 / 01001011 - 0.390540% of total (15444443 / 3954638418), off-by -3363, a*a = 11309769, chisq = 32.42, incr 0.73
7 / 00000111 - 0.390710% of total (15451187 / 3954638418), off-by 3381, a*a = 11431161, chisq = 33.16, incr 0.74
74 / 01001010 - 0.390712% of total (15451237 / 3954638418), off-by 3431, a*a = 11771761, chisq = 33.92, incr 0.76
108 / 01101100 - 0.390538% of total (15444373 / 3954638418), off-by -3433, a*a = 11785489, chisq = 34.69, incr 0.76
238 / 11101110 - 0.390712% of total (15451243 / 3954638418), off-by 3437, a*a = 11812969, chisq = 35.45, incr 0.76
60 / 00111100 - 0.390537% of total (15444320 / 3954638418), off-by -3486, a*a = 12152196, chisq = 36.24, incr 0.79
133 / 10000101 - 0.390713% of total (15451305 / 3954638418), off-by 3499, a*a = 12243001, chisq = 37.03, incr 0.79
113 / 01110001 - 0.390713% of total (15451306 / 3954638418), off-by 3500, a*a = 12250000, chisq = 37.82, incr 0.79
53 / 00110101 - 0.390536% of total (15444297 / 3954638418), off-by -3509, a*a = 12313081, chisq = 38.62, incr 0.80
69 / 01000101 - 0.390536% of total (15444291 / 3954638418), off-by -3515, a*a = 12355225, chisq = 39.42, incr 0.80
216 / 11011000 - 0.390716% of total (15451386 / 3954638418), off-by 3580, a*a = 12816400, chisq = 40.25, incr 0.83
181 / 10110101 - 0.390534% of total (15444222 / 3954638418), off-by -3584, a*a = 12845056, chisq = 41.08, incr 0.83
128 / 10000000 - 0.390716% of total (15451395 / 3954638418), off-by 3589, a*a = 12880921, chisq = 41.92, incr 0.83
241 / 11110001 - 0.390716% of total (15451413 / 3954638418), off-by 3607, a*a = 13010449, chisq = 42.76, incr 0.84
175 / 10101111 - 0.390532% of total (15444144 / 3954638418), off-by -3662, a*a = 13410244, chisq = 43.63, incr 0.87
2 / 00000010 - 0.390719% of total (15451533 / 3954638418), off-by 3727, a*a = 13890529, chisq = 44.53, incr 0.90
220 / 11011100 - 0.390528% of total (15443954 / 3954638418), off-by -3852, a*a = 14837904, chisq = 45.49, incr 0.96
160 / 10100000 - 0.390723% of total (15451685 / 3954638418), off-by 3879, a*a = 15046641, chisq = 46.46, incr 0.97
243 / 11110011 - 0.390524% of total (15443815 / 3954638418), off-by -3991, a*a = 15928081, chisq = 47.49, incr 1.03
88 / 01011000 - 0.390524% of total (15443809 / 3954638418), off-by -3997, a*a = 15976009, chisq = 48.53, incr 1.03
81 / 01010001 - 0.390523% of total (15443757 / 3954638418), off-by -4049, a*a = 16394401, chisq = 49.59, incr 1.06
195 / 11000011 - 0.390522% of total (15443730 / 3954638418), off-by -4076, a*a = 16613776, chisq = 50.66, incr 1.08
76 / 01001100 - 0.390729% of total (15451923 / 3954638418), off-by 4117, a*a = 16949689, chisq = 51.76, incr 1.10
212 / 11010100 - 0.390517% of total (15443524 / 3954638418), off-by -4282, a*a = 18335524, chisq = 52.95, incr 1.19
136 / 10001000 - 0.390733% of total (15452096 / 3954638418), off-by 4290, a*a = 18404100, chisq = 54.14, incr 1.19
204 / 11001100 - 0.390515% of total (15443463 / 3954638418), off-by -4343, a*a = 18861649, chisq = 55.36, incr 1.22
206 / 11001110 - 0.390735% of total (15452157 / 3954638418), off-by 4351, a*a = 18931201, chisq = 56.58, incr 1.23
134 / 10000110 - 0.390515% of total (15443451 / 3954638418), off-by -4355, a*a = 18966025, chisq = 57.81, incr 1.23
80 / 01010000 - 0.390735% of total (15452169 / 3954638418), off-by 4363, a*a = 19035769, chisq = 59.04, incr 1.23
177 / 10110001 - 0.390736% of total (15452194 / 3954638418), off-by 4388, a*a = 19254544, chisq = 60.29, incr 1.25
95 / 01011111 - 0.390736% of total (15452211 / 3954638418), off-by 4405, a*a = 19404025, chisq = 61.55, incr 1.26
126 / 01111110 - 0.390512% of total (15443352 / 3954638418), off-by -4454, a*a = 19838116, chisq = 62.83, incr 1.28
115 / 01110011 - 0.390512% of total (15443338 / 3954638418), off-by -4468, a*a = 19963024, chisq = 64.12, incr 1.29
66 / 01000010 - 0.390738% of total (15452288 / 3954638418), off-by 4482, a*a = 20088324, chisq = 65.42, incr 1.30
106 / 01101010 - 0.390510% of total (15443261 / 3954638418), off-by -4545, a*a = 20657025, chisq = 66.76, incr 1.34
87 / 01010111 - 0.390510% of total (15443240 / 3954638418), off-by -4566, a*a = 20848356, chisq = 68.11, incr 1.35
54 / 00110110 - 0.390509% of total (15443227 / 3954638418), off-by -4579, a*a = 20967241, chisq = 69.47, incr 1.36
138 / 10001010 - 0.390508% of total (15443174 / 3954638418), off-by -4632, a*a = 21455424, chisq = 70.86, incr 1.39
221 / 11011101 - 0.390743% of total (15452486 / 3954638418), off-by 4680, a*a = 21902400, chisq = 72.28, incr 1.42
211 / 11010011 - 0.390507% of total (15443125 / 3954638418), off-by -4681, a*a = 21911761, chisq = 73.69, incr 1.42
230 / 11100110 - 0.390744% of total (15452516 / 3954638418), off-by 4710, a*a = 22184100, chisq = 75.13, incr 1.44
20 / 00010100 - 0.390506% of total (15443092 / 3954638418), off-by -4714, a*a = 22221796, chisq = 76.57, incr 1.44
72 / 01001000 - 0.390506% of total (15443085 / 3954638418), off-by -4721, a*a = 22287841, chisq = 78.01, incr 1.44
189 / 10111101 - 0.390505% of total (15443080 / 3954638418), off-by -4726, a*a = 22335076, chisq = 79.46, incr 1.45
14 / 00001110 - 0.390505% of total (15443056 / 3954638418), off-by -4750, a*a = 22562500, chisq = 80.92, incr 1.46
17 / 00010001 - 0.390746% of total (15452582 / 3954638418), off-by 4776, a*a = 22810176, chisq = 82.39, incr 1.48
235 / 11101011 - 0.390747% of total (15452648 / 3954638418), off-by 4842, a*a = 23444964, chisq = 83.91, incr 1.52
147 / 10010011 - 0.390748% of total (15452670 / 3954638418), off-by 4864, a*a = 23658496, chisq = 85.44, incr 1.53
124 / 01111100 - 0.390750% of total (15452736 / 3954638418), off-by 4930, a*a = 24304900, chisq = 87.02, incr 1.57
48 / 00110000 - 0.390500% of total (15442847 / 3954638418), off-by -4959, a*a = 24591681, chisq = 88.61, incr 1.59
205 / 11001101 - 0.390497% of total (15442726 / 3954638418), off-by -5080, a*a = 25806400, chisq = 90.28, incr 1.67
22 / 00010110 - 0.390496% of total (15442720 / 3954638418), off-by -5086, a*a = 25867396, chisq = 91.95, incr 1.67
209 / 11010001 - 0.390495% of total (15442684 / 3954638418), off-by -5122, a*a = 26234884, chisq = 93.65, incr 1.70
214 / 11010110 - 0.390495% of total (15442665 / 3954638418), off-by -5141, a*a = 26429881, chisq = 95.36, incr 1.71
16 / 00010000 - 0.390756% of total (15452985 / 3954638418), off-by 5179, a*a = 26822041, chisq = 97.10, incr 1.74
3 / 00000011 - 0.390757% of total (15453007 / 3954638418), off-by 5201, a*a = 27050401, chisq = 98.85, incr 1.75
44 / 00101100 - 0.390492% of total (15442560 / 3954638418), off-by -5246, a*a = 27520516, chisq = 100.63, incr 1.78
100 / 01100100 - 0.390491% of total (15442523 / 3954638418), off-by -5283, a*a = 27910089, chisq = 102.44, incr 1.81
18 / 00010010 - 0.390759% of total (15453095 / 3954638418), off-by 5289, a*a = 27973521, chisq = 104.25, incr 1.81
118 / 01110110 - 0.390489% of total (15442430 / 3954638418), off-by -5376, a*a = 28901376, chisq = 106.12, incr 1.87
188 / 10111100 - 0.390761% of total (15453186 / 3954638418), off-by 5380, a*a = 28944400, chisq = 107.99, incr 1.87
168 / 10101000 - 0.390488% of total (15442407 / 3954638418), off-by -5399, a*a = 29149201, chisq = 109.88, incr 1.89
155 / 10011011 - 0.390487% of total (15442360 / 3954638418), off-by -5446, a*a = 29658916, chisq = 111.80, incr 1.92
193 / 11000001 - 0.390765% of total (15453350 / 3954638418), off-by 5544, a*a = 30735936, chisq = 113.79, incr 1.99
9 / 00001001 - 0.390766% of total (15453385 / 3954638418), off-by 5579, a*a = 31125241, chisq = 115.81, incr 2.01
58 / 00111010 - 0.390481% of total (15442128 / 3954638418), off-by -5678, a*a = 32239684, chisq = 117.89, incr 2.09
162 / 10100010 - 0.390480% of total (15442059 / 3954638418), off-by -5747, a*a = 33028009, chisq = 120.03, incr 2.14
36 / 00100100 - 0.390478% of total (15441976 / 3954638418), off-by -5830, a*a = 33988900, chisq = 122.23, incr 2.20
236 / 11101100 - 0.390774% of total (15453707 / 3954638418), off-by 5901, a*a = 34821801, chisq = 124.48, incr 2.25
112 / 01110000 - 0.390775% of total (15453724 / 3954638418), off-by 5918, a*a = 35022724, chisq = 126.75, incr 2.27
227 / 11100011 - 0.390474% of total (15441844 / 3954638418), off-by -5962, a*a = 35545444, chisq = 129.05, incr 2.30
45 / 00101101 - 0.390473% of total (15441781 / 3954638418), off-by -6025, a*a = 36300625, chisq = 131.40, incr 2.35
59 / 00111011 - 0.390779% of total (15453895 / 3954638418), off-by 6089, a*a = 37075921, chisq = 133.80, incr 2.40
111 / 01101111 - 0.390780% of total (15453918 / 3954638418), off-by 6112, a*a = 37356544, chisq = 136.22, incr 2.42
176 / 10110000 - 0.390780% of total (15453919 / 3954638418), off-by 6113, a*a = 37368769, chisq = 138.64, incr 2.42
73 / 01001001 - 0.390467% of total (15441563 / 3954638418), off-by -6243, a*a = 38975049, chisq = 141.16, incr 2.52
91 / 01011011 - 0.390466% of total (15441505 / 3954638418), off-by -6301, a*a = 39702601, chisq = 143.73, incr 2.57
135 / 10000111 - 0.390786% of total (15454168 / 3954638418), off-by 6362, a*a = 40475044, chisq = 146.35, incr 2.62
61 / 00111101 - 0.390786% of total (15454175 / 3954638418), off-by 6369, a*a = 40564161, chisq = 148.98, incr 2.63
105 / 01101001 - 0.390462% of total (15441359 / 3954638418), off-by -6447, a*a = 41563809, chisq = 151.67, incr 2.69
55 / 00110111 - 0.390790% of total (15454335 / 3954638418), off-by 6529, a*a = 42627841, chisq = 154.43, incr 2.76
148 / 10010100 - 0.390455% of total (15441076 / 3954638418), off-by -6730, a*a = 45292900, chisq = 157.36, incr 2.93
213 / 11010101 - 0.390453% of total (15441002 / 3954638418), off-by -6804, a*a = 46294416, chisq = 160.36, incr 3.00
180 / 10110100 - 0.390446% of total (15440714 / 3954638418), off-by -7092, a*a = 50296464, chisq = 163.61, incr 3.26
41 / 00101001 - 0.390443% of total (15440621 / 3954638418), off-by -7185, a*a = 51624225, chisq = 166.96, incr 3.34
232 / 11101000 - 0.390807% of total (15454993 / 3954638418), off-by 7187, a*a = 51652969, chisq = 170.30, incr 3.34
233 / 11101001 - 0.390440% of total (15440503 / 3954638418), off-by -7303, a*a = 53333809, chisq = 173.75, incr 3.45
239 / 11101111 - 0.390811% of total (15455169 / 3954638418), off-by 7363, a*a = 54213769, chisq = 177.26, incr 3.51
215 / 11010111 - 0.390438% of total (15440430 / 3954638418), off-by -7376, a*a = 54405376, chisq = 180.78, incr 3.52
229 / 11100101 - 0.390438% of total (15440411 / 3954638418), off-by -7395, a*a = 54686025, chisq = 184.32, incr 3.54
90 / 01011010 - 0.390437% of total (15440367 / 3954638418), off-by -7439, a*a = 55338721, chisq = 187.91, incr 3.58
222 / 11011110 - 0.390813% of total (15455255 / 3954638418), off-by 7449, a*a = 55487601, chisq = 191.50, incr 3.59
119 / 01110111 - 0.390815% of total (15455316 / 3954638418), off-by 7510, a*a = 56400100, chisq = 195.15, incr 3.65
122 / 01111010 - 0.390435% of total (15440277 / 3954638418), off-by -7529, a*a = 56685841, chisq = 198.82, incr 3.67
159 / 10011111 - 0.390816% of total (15455357 / 3954638418), off-by 7551, a*a = 57017601, chisq = 202.51, incr 3.69
43 / 00101011 - 0.390434% of total (15440237 / 3954638418), off-by -7569, a*a = 57289761, chisq = 206.22, incr 3.71
31 / 00011111 - 0.390825% of total (15455697 / 3954638418), off-by 7891, a*a = 62267881, chisq = 210.25, incr 4.03
249 / 11111001 - 0.390826% of total (15455754 / 3954638418), off-by 7948, a*a = 63170704, chisq = 214.34, incr 4.09
142 / 10001110 - 0.390827% of total (15455794 / 3954638418), off-by 7988, a*a = 63808144, chisq = 218.47, incr 4.13
146 / 10010010 - 0.390422% of total (15439772 / 3954638418), off-by -8034, a*a = 64545156, chisq = 222.65, incr 4.18
201 / 11001001 - 0.390418% of total (15439615 / 3954638418), off-by -8191, a*a = 67092481, chisq = 226.99, incr 4.34
192 / 11000000 - 0.390833% of total (15456037 / 3954638418), off-by 8231, a*a = 67749361, chisq = 231.38, incr 4.39
252 / 11111100 - 0.390842% of total (15456373 / 3954638418), off-by 8567, a*a = 73393489, chisq = 236.13, incr 4.75
26 / 00011010 - 0.390408% of total (15439236 / 3954638418), off-by -8570, a*a = 73444900, chisq = 240.88, incr 4.75
15 / 00001111 - 0.390845% of total (15456507 / 3954638418), off-by 8701, a*a = 75707401, chisq = 245.78, incr 4.90
21 / 00010101 - 0.390403% of total (15439018 / 3954638418), off-by -8788, a*a = 77228944, chisq = 250.78, incr 5.00
12 / 00001100 - 0.390848% of total (15456617 / 3954638418), off-by 8811, a*a = 77633721, chisq = 255.81, incr 5.03
149 / 10010101 - 0.390400% of total (15438924 / 3954638418), off-by -8882, a*a = 78889924, chisq = 260.91, incr 5.11
8 / 00001000 - 0.390854% of total (15456846 / 3954638418), off-by 9040, a*a = 81721600, chisq = 266.20, incr 5.29
254 / 11111110 - 0.390859% of total (15457053 / 3954638418), off-by 9247, a*a = 85507009, chisq = 271.74, incr 5.54
143 / 10001111 - 0.390863% of total (15457212 / 3954638418), off-by 9406, a*a = 88472836, chisq = 277.47, incr 5.73
171 / 10101011 - 0.390387% of total (15438399 / 3954638418), off-by -9407, a*a = 88491649, chisq = 283.19, incr 5.73
107 / 01101011 - 0.390385% of total (15438319 / 3954638418), off-by -9487, a*a = 90003169, chisq = 289.02, incr 5.83
199 / 11000111 - 0.390865% of total (15457317 / 3954638418), off-by 9511, a*a = 90459121, chisq = 294.88, incr 5.86
84 / 01010100 - 0.390384% of total (15438264 / 3954638418), off-by -9542, a*a = 91049764, chisq = 300.77, incr 5.89
194 / 11000010 - 0.390888% of total (15458197 / 3954638418), off-by 10391, a*a = 107972881, chisq = 307.76, incr 6.99
191 / 10111111 - 0.390888% of total (15458199 / 3954638418), off-by 10393, a*a = 108014449, chisq = 314.75, incr 6.99
223 / 11011111 - 0.390888% of total (15458216 / 3954638418), off-by 10410, a*a = 108368100, chisq = 321.77, incr 7.02
144 / 10010000 - 0.390895% of total (15458499 / 3954638418), off-by 10693, a*a = 114340249, chisq = 329.17, incr 7.40
42 / 00101010 - 0.390351% of total (15436988 / 3954638418), off-by -10818, a*a = 117029124, chisq = 336.75, incr 7.58
86 / 01010110 - 0.390348% of total (15436853 / 3954638418), off-by -10953, a*a = 119968209, chisq = 344.51, incr 7.77
82 / 01010010 - 0.390342% of total (15436628 / 3954638418), off-by -11178, a*a = 124947684, chisq = 352.60, incr 8.09
109 / 01101101 - 0.390341% of total (15436558 / 3954638418), off-by -11248, a*a = 126517504, chisq = 360.79, incr 8.19
169 / 10101001 - 0.390335% of total (15436343 / 3954638418), off-by -11463, a*a = 131400369, chisq = 369.30, incr 8.51
127 / 01111111 - 0.390944% of total (15460438 / 3954638418), off-by 12632, a*a = 159567424, chisq = 379.63, incr 10.33
255 / 11111111 - 0.390947% of total (15460536 / 3954638418), off-by 12730, a*a = 162052900, chisq = 390.12, incr 10.49
63 / 00111111 - 0.390971% of total (15461497 / 3954638418), off-by 13691, a*a = 187443481, chisq = 402.25, incr 12.13
64 / 01000000 - 0.390972% of total (15461548 / 3954638418), off-by 13742, a*a = 188842564, chisq = 414.47, incr 12.22
85 / 01010101 - 0.390276% of total (15434017 / 3954638418), off-by -13789, a*a = 190136521, chisq = 426.78, incr 12.31
0 / 00000000 - 0.391076% of total (15465652 / 3954638418), off-by 17846, a*a = 318479716, chisq = 447.40, incr 20.62
Second Chi-Square: 447.3987561728832
Lowest:
183 / 10110111, off-by -43, a*a = 1849
179 / 10110011, off-by 119, a*a = 14161
198 / 11000110, off-by -179, a*a = 32041
217 / 11011001, off-by 250, a*a = 62500
200 / 11001000, off-by -360, a*a = 129600
35 / 00100011, off-by 373, a*a = 139129
50 / 00110010, off-by -398, a*a = 158404
104 / 01101000, off-by 458, a*a = 209764
34 / 00100010, off-by -512, a*a = 262144
103 / 01100111, off-by 518, a*a = 268324
Highest:
86 / 01010110, off-by -10953, a*a = 119968209
82 / 01010010, off-by -11178, a*a = 124947684
109 / 01101101, off-by -11248, a*a = 126517504
169 / 10101001, off-by -11463, a*a = 131400369
127 / 01111111, off-by 12632, a*a = 159567424
255 / 11111111, off-by 12730, a*a = 162052900
63 / 00111111, off-by 13691, a*a = 187443481
64 / 01000000, off-by 13742, a*a = 188842564
85 / 01010101, off-by -13789, a*a = 190136521
0 / 00000000, off-by 17846, a*a = 318479716
0x0 at position 255, 0xff at position 251
Chi-Square: 447.3987561728832
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