Random/LFSR on P2

17172747677

Comments

  • TonyB_TonyB_ Posts: 1,221
    edited 2019-05-02 - 21:41:09
    TonyB_ wrote: »
    evanh wrote: »
    I've just done a compare against your most recent selection of ++ candidates - https://forums.parallax.com/discussion/comment/1468718/#Comment_1468718 - and note that, although the rankings differ, the pfreq/zfreq/nzfreq ChiSquare totals all match. Tony, I assume you've been ranking pfreq with higher priority.

    Evan, I've changed the Chi-Square titles in that post to pchi/zchi/nzchi. I give equal weight to prank, zrank and nzrank. I sum the ranks (i.e. prank+zrank+nzrank) to get an overall ranking and the lowest one is given a rank of 1. I do not sum pchi+zchi+nzchi. If prank+zrank+nzrank is the same integer for two different [a,b,c,d] then I use prank as the tie-breaker.

    Evan, I've checked my QuickBASIC code in xoro32r.bas (attached) and there is equal weighting, but it can be different if variables pw/zw/nzw are not all 1. Search for "paths" in xoro32r.bas to see where the files go. xoro32.abc lists the 84 full-length candidates as aabbcc. This file and the 84*3=252 binary files (aabbcc.pb, aabbcc.zb and aabbcc.nzb) are needed before xoro32r.bas can run.

    Have you created the binary files for scramblers other than ++ yet?
    Formerly known as TonyB
  • TonyB_ wrote: »
    Have you created the binary files for scramblers other than ++ yet?

    I had but they're deleted again. I'm doing them over with ChiSquare totals included now.

    I'll get back to you later.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • evanhevanh Posts: 7,502
    edited 2019-05-03 - 13:40:19
    Okay, I had started to write my own sorting and ranking routines while these reruns were underway, but then realised I wanted to put all ChiSquare totals from every algorithm variant in the one database so that they can be sorted as one big group. So, for the moment, I've just opted to merge into one large CSV file and use a spreadsheet to do the sorting. It's easy to make new spreadsheet columns with linear fills for making the ranking columns.

    PS: I've adopted using sum of the rankings to make the final sort, thanks.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • evanhevanh Posts: 7,502
    edited 2019-05-09 - 07:26:59
    Done at last, all eight scrambler variations. I had some breaks in the process.

    Here's the resulting concatenated CSV file, distscore-s16.csv, and sortable spreadsheet and also a post-sorted exported CSV for easy reading of the example sort: sumRank = 3 x pRank + zRank + nzRank.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • evanh wrote: »
    Done at last, all eight scrambler variations. I had some breaks in the process.

    Here's the resulting concatenated CSV file, distscore-s16.csv, and sortable spreadsheet and also a post-sorted exported CSV for easy reading of the example sort: sumRank = 3 x pRank + zRank + nzRank.

    Many thanks, Evan. I think a weighting of 3 is somewhat excessive for prank and csv files with 1 and 2 would be useful to have. xoroshiro32[10,3,11,10]--+ would still be top for all three and the question is how does it perform in PractRand tests?

    xoroshiro32[13,5,10,9]--- is slightly better than the ++ in P2 rev B, but the former would need a bit more logic than the latter probably as all as the signs are negative.
    Formerly known as TonyB
  • evanhevanh Posts: 7,502
    edited 2019-05-09 - 13:46:55
    Hmm, I suppose you can't load any recent spreadsheet. EDIT: The CSV is loadable by any spreadsheet software though.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • TonyB_ wrote: »
    evanh wrote: »
    Done at last, all eight scrambler variations. I had some breaks in the process.

    Here's the resulting concatenated CSV file, distscore-s16.csv, and sortable spreadsheet and also a post-sorted exported CSV for easy reading of the example sort: sumRank = 3 x pRank + zRank + nzRank.

    Many thanks, Evan. I think a weighting of 3 is somewhat excessive for prank and csv files with 1 and 2 would be useful to have. xoroshiro32[10,3,11,10]--+ would still be top for all three and the question is how does it perform in PractRand tests?

    xoroshiro32[13,5,10,9]--- is slightly better than the ++ in P2 rev B, but the former would need a bit more logic than the latter probably as all as the signs are negative.

    Some more thoughts on distscore-s16.csv.txt:

    1. As mentioned before, I prefer pchi/zchi/nzchi to pfchi/zfchi/nzfchi.
    2. An overall rank orank (1,2,3,etc.) would be a helpful addition or change sumrank to orank.
    3. The top 20 contain only seven different [a,b,c,d].
    4. The similiarity in positive/negative pairs is obvious, especially [14,2,9,5]++-/--+ which are almost identical.
    5. In the absence of a different algorithm with 32-bit state, a P3 could use one of the top three.
    Formerly known as TonyB
  • Here's some snippets of other examples:
    sumRank = 3 x pRank + 2 x zRank + nzRank
    
    Algorithm	Candidate	pfChi	zfChi	nzfChi	pRank	zRank	nzRank	sumRank
    Xoroshiro32(16)-s1-s0+	[10 3 11 10]	10	123	483	13	8	18	73
    Xoroshiro32(16)s1+s0-	[10 3 11 10]	14	132	567	26	10	30	128
    Xoroshiro32(16)-s1-s0-	[13 5 10 9]	12	315	296	21	38	2	141
    Xoroshiro32(16)-s1-s0+	[13 5 8 10]	6	433	549	3	59	28	155
    Xoroshiro32(16)++	[13 5 10 9]	24	327	265	38	42	1	199
    Xoroshiro32(16)s1+s0-	[14 2 9 5]	47	115	418	63	4	10	207
    Xoroshiro32(16)-s1-s0+	[14 2 9 5]	47	117	415	64	6	8	212
    Xoroshiro32(16)-s1-s0+	[2 1 11 11]	6	505	763	4	70	73	225
    Xoroshiro32(16)s1+s0-	[13 5 8 10]	14	467	674	27	63	54	261
    Xoroshiro32(16)s1+s0-	[2 1 11 11]	33	399	631	52	53	41	303
    Xoroshiro32(16)s1-s0-	[14 2 7 10]	25	546	614	39	78	38	311
    Xoroshiro32(16)++	[13 5 8 10]	50	337	567	66	44	31	317
    Xoroshiro32(16)-s1+s0+	[14 2 7 10]	12	644	750	22	105	72	348
    Xoroshiro32(16)-s1+s0-	[13 5 8 13]	124	85	348	133	1	3	404
    Xoroshiro32(16)-s1-s0-	[13 5 8 10]	73	346	602	94	46	35	409
    Xoroshiro32(16)s1-s0+	[14 2 9 5]	46	372	1159	60	47	149	423
    Xoroshiro32(16)s1+s0-	[8 1 7 5]	76	309	686	99	36	57	426
    Xoroshiro32(16)s1-s0-	[13 5 10 9]	59	595	430	77	93	11	428
    Xoroshiro32(16)++	[14 2 9 9]	68	192	1119	89	18	139	442
    Xoroshiro32(16)s1-s0+	[2 1 11 11]	12	803	938	23	136	103	444
    Xoroshiro32(16)-s1+s0+	[13 5 10 9]	47	681	499	65	114	21	444
    Xoroshiro32(16)-s1-s0+	[8 1 7 5]	79	314	701	103	37	61	444
    Xoroshiro32(16)-s1+s0-	[14 2 9 5]	52	373	1146	70	48	144	450
    Xoroshiro32(16)-s1+s0-	[8 1 7 5]	51	504	990	67	69	113	452
    Xoroshiro32(16)s1-s0+	[8 1 7 5]	52	506	996	71	71	114	469
    Xoroshiro32(16)-s1-s0-	[14 2 9 9]	89	183	1112	109	17	138	499
    Xoroshiro32(16)-s1+s0-	[2 8 7 3]	10	839	1228	14	142	176	502
    Xoroshiro32(16)s1-s0+	[2 8 7 3]	11	837	1229	18	140	178	512
    Xoroshiro32(16)-s1-s0-	[7 1 8 6]	99	528	605	116	73	36	530
    Xoroshiro32(16)-s1-s0+	[6 2 3 6]	29	569	1472	43	86	236	537
    Xoroshiro32(16)s1+s0-	[6 2 3 6]	29	575	1483	44	88	238	546
    Xoroshiro32(16)s1+s0-	[14 11 3 12]	158	162	742	151	13	70	549
    Xoroshiro32(16)++	[7 1 8 6]	109	532	597	123	74	34	551
    
    sumRank = 3 x pRank + zRank + 2 x nzRank
    
    Algorithm	Candidate	pfChi	zfChi	nzfChi	pRank	zRank	nzRank	sumRank
    Xoroshiro32(16)-s1-s0+	[10 3 11 10]	10	123	483	13	8	18	83
    Xoroshiro32(16)-s1-s0-	[13 5 10 9]	12	315	296	21	38	2	105
    Xoroshiro32(16)-s1-s0+	[13 5 8 10]	6	433	549	3	59	28	124
    Xoroshiro32(16)s1+s0-	[10 3 11 10]	14	132	567	26	10	30	148
    Xoroshiro32(16)++	[13 5 10 9]	24	327	265	38	42	1	158
    Xoroshiro32(16)s1+s0-	[14 2 9 5]	47	115	418	63	4	10	213
    Xoroshiro32(16)-s1-s0+	[14 2 9 5]	47	117	415	64	6	8	214
    Xoroshiro32(16)-s1-s0+	[2 1 11 11]	6	505	763	4	70	73	228
    Xoroshiro32(16)s1+s0-	[13 5 8 10]	14	467	674	27	63	54	252
    Xoroshiro32(16)s1-s0-	[14 2 7 10]	25	546	614	39	78	38	271
    Xoroshiro32(16)s1+s0-	[2 1 11 11]	33	399	631	52	53	41	291
    Xoroshiro32(16)++	[13 5 8 10]	50	337	567	66	44	31	304
    Xoroshiro32(16)-s1+s0+	[14 2 7 10]	12	644	750	22	105	72	315
    Xoroshiro32(16)s1-s0-	[13 5 10 9]	59	595	430	77	93	11	346
    Xoroshiro32(16)-s1+s0+	[13 5 10 9]	47	681	499	65	114	21	351
    Xoroshiro32(16)-s1-s0-	[13 5 8 10]	73	346	602	94	46	35	398
    Xoroshiro32(16)-s1+s0-	[13 5 8 13]	124	85	348	133	1	3	406
    Xoroshiro32(16)s1-s0+	[2 1 11 11]	12	803	938	23	136	103	411
    Xoroshiro32(16)s1+s0-	[8 1 7 5]	76	309	686	99	36	57	447
    Xoroshiro32(16)-s1-s0+	[8 1 7 5]	79	314	701	103	37	61	468
    Xoroshiro32(16)-s1-s0-	[7 1 8 6]	99	528	605	116	73	36	493
    Xoroshiro32(16)-s1+s0-	[8 1 7 5]	51	504	990	67	69	113	496
    Xoroshiro32(16)++	[7 1 8 6]	109	532	597	123	74	34	511
    Xoroshiro32(16)s1-s0+	[8 1 7 5]	52	506	996	71	71	114	512
    Xoroshiro32(16)s1-s0+	[14 2 9 5]	46	372	1159	60	47	149	525
    Xoroshiro32(16)-s1+s0-	[2 8 7 3]	10	839	1228	14	142	176	536
    Xoroshiro32(16)-s1+s0-	[14 2 9 5]	52	373	1146	70	48	144	546
    Xoroshiro32(16)s1-s0+	[2 8 7 3]	11	837	1229	18	140	178	550
    Xoroshiro32(16)++	[14 2 9 9]	68	192	1119	89	18	139	563
    
    sumRank = 2 x pRank + zRank + nzRank
    
    Algorithm	Candidate	pfChi	zfChi	nzfChi	pRank	zRank	nzRank	sumRank
    Xoroshiro32(16)-s1-s0+	[10 3 11 10]	10	123	483	13	8	18	52
    Xoroshiro32(16)-s1-s0-	[13 5 10 9]	12	315	296	21	38	2	82
    Xoroshiro32(16)s1+s0-	[10 3 11 10]	14	132	567	26	10	30	92
    Xoroshiro32(16)-s1-s0+	[13 5 8 10]	6	433	549	3	59	28	93
    Xoroshiro32(16)++	[13 5 10 9]	24	327	265	38	42	1	119
    Xoroshiro32(16)s1+s0-	[14 2 9 5]	47	115	418	63	4	10	140
    Xoroshiro32(16)-s1-s0+	[14 2 9 5]	47	117	415	64	6	8	142
    Xoroshiro32(16)-s1-s0+	[2 1 11 11]	6	505	763	4	70	73	151
    Xoroshiro32(16)s1+s0-	[13 5 8 10]	14	467	674	27	63	54	171
    Xoroshiro32(16)s1-s0-	[14 2 7 10]	25	546	614	39	78	38	194
    Xoroshiro32(16)s1+s0-	[2 1 11 11]	33	399	631	52	53	41	198
    Xoroshiro32(16)++	[13 5 8 10]	50	337	567	66	44	31	207
    Xoroshiro32(16)-s1+s0+	[14 2 7 10]	12	644	750	22	105	72	221
    Xoroshiro32(16)s1-s0-	[13 5 10 9]	59	595	430	77	93	11	258
    Xoroshiro32(16)-s1+s0+	[13 5 10 9]	47	681	499	65	114	21	265
    Xoroshiro32(16)-s1-s0-	[13 5 8 10]	73	346	602	94	46	35	269
    Xoroshiro32(16)-s1+s0-	[13 5 8 13]	124	85	348	133	1	3	270
    Xoroshiro32(16)s1-s0+	[2 1 11 11]	12	803	938	23	136	103	285
    Xoroshiro32(16)s1+s0-	[8 1 7 5]	76	309	686	99	36	57	291
    Xoroshiro32(16)-s1-s0+	[8 1 7 5]	79	314	701	103	37	61	304
    Xoroshiro32(16)s1-s0+	[14 2 9 5]	46	372	1159	60	47	149	316
    Xoroshiro32(16)-s1+s0-	[8 1 7 5]	51	504	990	67	69	113	316
    Xoroshiro32(16)s1-s0+	[8 1 7 5]	52	506	996	71	71	114	327
    Xoroshiro32(16)-s1+s0-	[14 2 9 5]	52	373	1146	70	48	144	332
    Xoroshiro32(16)++	[14 2 9 9]	68	192	1119	89	18	139	335
    Xoroshiro32(16)-s1-s0-	[7 1 8 6]	99	528	605	116	73	36	341
    Xoroshiro32(16)-s1+s0-	[2 8 7 3]	10	839	1228	14	142	176	346
    Xoroshiro32(16)s1-s0+	[2 8 7 3]	11	837	1229	18	140	178	354
    Xoroshiro32(16)++	[7 1 8 6]	109	532	597	123	74	34	354
    
    sumRank = pRank + zRank + nzRank
    
    Algorithm	Candidate	pfChi	zfChi	nzfChi	pRank	zRank	nzRank	sumRank
    Xoroshiro32(16)-s1-s0+	[10 3 11 10]	10	123	483	13	8	18	39
    Xoroshiro32(16)-s1-s0-	[13 5 10 9]	12	315	296	21	38	2	61
    Xoroshiro32(16)s1+s0-	[10 3 11 10]	14	132	567	26	10	30	66
    Xoroshiro32(16)s1+s0-	[14 2 9 5]	47	115	418	63	4	10	77
    Xoroshiro32(16)-s1-s0+	[14 2 9 5]	47	117	415	64	6	8	78
    Xoroshiro32(16)++	[13 5 10 9]	24	327	265	38	42	1	81
    Xoroshiro32(16)-s1-s0+	[13 5 8 10]	6	433	549	3	59	28	90
    Xoroshiro32(16)-s1+s0-	[13 5 8 13]	124	85	348	133	1	3	137
    Xoroshiro32(16)++	[13 5 8 10]	50	337	567	66	44	31	141
    Xoroshiro32(16)s1+s0-	[13 5 8 10]	14	467	674	27	63	54	144
    Xoroshiro32(16)s1+s0-	[2 1 11 11]	33	399	631	52	53	41	146
    Xoroshiro32(16)-s1-s0+	[2 1 11 11]	6	505	763	4	70	73	147
    Xoroshiro32(16)s1-s0-	[14 2 7 10]	25	546	614	39	78	38	155
    Xoroshiro32(16)-s1-s0-	[13 5 8 10]	73	346	602	94	46	35	175
    Xoroshiro32(16)s1-s0-	[13 5 10 9]	59	595	430	77	93	11	181
    Xoroshiro32(16)s1+s0-	[8 1 7 5]	76	309	686	99	36	57	192
    Xoroshiro32(16)-s1+s0+	[14 2 7 10]	12	644	750	22	105	72	199
    Xoroshiro32(16)-s1+s0+	[13 5 10 9]	47	681	499	65	114	21	200
    Xoroshiro32(16)-s1-s0+	[8 1 7 5]	79	314	701	103	37	61	201
    Xoroshiro32(16)-s1-s0-	[7 2 14 13]	253	88	392	206	2	7	215
    Xoroshiro32(16)-s1-s0-	[7 1 8 6]	99	528	605	116	73	36	225
    Xoroshiro32(16)++	[7 1 8 6]	109	532	597	123	74	34	231
    Xoroshiro32(16)s1+s0-	[14 11 3 12]	158	162	742	151	13	70	234
    Xoroshiro32(16)++	[14 2 9 9]	68	192	1119	89	18	139	246
    Xoroshiro32(16)-s1+s0-	[8 1 7 5]	51	504	990	67	69	113	249
    Xoroshiro32(16)-s1+s0-	[13 13 14 6]	213	122	704	184	7	62	253
    Xoroshiro32(16)s1-s0+	[13 5 8 13]	264	139	555	213	11	29	253
    Xoroshiro32(16)s1-s0+	[14 2 9 5]	46	372	1159	60	47	149	256
    Xoroshiro32(16)s1-s0+	[8 1 7 5]	52	506	996	71	71	114	256
    Xoroshiro32(16)s1-s0+	[2 1 11 11]	12	803	938	23	136	103	262
    Xoroshiro32(16)-s1+s0-	[14 2 9 5]	52	373	1146	70	48	144	262
    Xoroshiro32(16)-s1-s0-	[14 2 9 9]	89	183	1112	109	17	138	264
    
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • Yeah, both --+ and --- would be more logic. Maybe that's why they are slightly better scoring.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • TonyB_ wrote: »
    5. In the absence of a different algorithm with 32-bit state, a P3 could use one of the top three.
    evanh wrote: »
    Yeah, both --+ and --- would be more logic. Maybe that's why they are slightly better scoring.
    I would be curious if any of the those variants would respond even better to rotl(+/-s1 +/-s0, D ) +/- s0 * 5
    It would seem that the best case would be a better pchi/zchi/nzchi scoring one that does not use --+ or ---, and yet also excels at PractRand scoring by >= 70% (which we have seen over the current ++).
  • evanh wrote: »
    Here's some snippets of other examples:

    Evan, thanks for these other weightings. zrank and nzrank should always be the same, I think.
    TonyB_ wrote: »
    5. In the absence of a different algorithm with 32-bit state, a P3 could use one of the top three.
    evanh wrote: »
    Yeah, both --+ and --- would be more logic. Maybe that's why they are slightly better scoring.
    I would be curious if any of the those variants would respond even better to rotl(+/-s1 +/-s0, D ) +/- s0 * 5
    It would seem that the best case would be a better pchi/zchi/nzchi scoring one that does not use --+ or ---, and yet also excels at PractRand scoring by >= 70% (which we have seen over the current ++).

    neg(x) = not(x)+1, therefore -s1-s0 = !s1+!s0+2, hence extra logic for carry input (into bit 1) not needed with ++.

    I agree that s0 * 5 would be worth testing with full set of +/- scramblers, but I don't do the tests.

    Also xoroshiro32[10,3,11,10]--+ might not have a very good PractRand score, despite very good distributions.
    Formerly known as TonyB
  • TonyB_ wrote: »
    Also xoroshiro32[10,3,11,10]--+ might not have a very good PractRand score, despite very good distributions.
    True, the two don't seem to correlate at all.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • evanh wrote: »
    TonyB_ wrote: »
    Also xoroshiro32[10,3,11,10]--+ might not have a very good PractRand score, despite very good distributions.
    True, the two don't seem to correlate at all.

    Are PractRand scores for [13,5,10,9]--- and [13,5,8,10]--+ better or worse than ++ versions?
    Formerly known as TonyB
  • Hmm, the gridding scripts are oriented towards running a selection of candidates of a single algorithm at a time. Without rewriting things, I'll have to make a config file for each scrambler variation and run them independently ...
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • TonyB_ wrote: »
    neg(x) = not(x)+1, therefore -s1-s0 = !s1+!s0+2, hence extra logic for carry input (into bit 1) not needed with ++.
    I believe that may also be expressed as: 1 + !(s1+s0), if that helps.
    Removing the constant sum would likely need to be characterized independently, though probably would have minimal impact.

  • evanhevanh Posts: 7,502
    edited 2019-05-10 - 16:05:32
    That'll still force a depth 3 summing. Or at least it does when combined with the s0 * 5.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • xoroshironotxoroshironot Posts: 103
    edited 2019-05-10 - 22:53:52
    evanh wrote: »
    That'll still force a depth 3 summing.
    Assuming the + 1 could be dropped, then just NOT gating the (+s1+s0) result before or after the ROTL.

    Edit: Cannot drop constant sum in --+ or --- without bumping into the final output NOT/sum issue again discussed way back (required use of E constant):
    Using s1=s0=0 in Tony's example, !0+!0<>0, so missing value in output would no longer be zero.
  • I'm learning more about Bash, that's for sure. This
    		chirecords[$a]=$( printf "${chirecords[$a]}\t$(($a + 1))" )
    
    and this
    		chirecords[$a]+=$'\t'$(($a + 1))
    
    do the same job.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • Some gridding scores:
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [13 5 10 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M  512M  512M  512M  512M  512M    1G    1G    1G  512M  512M  512M  512M  512M
     04 |  512M  512M    1G    1G    1G    1G    2G  512M    1G    1G    1G    1G    2G    1G    1G    1G
      Exponent Minimum = 29   Exponent Average = 29.395
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [13 5 8 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M    1G    1G    1G    1G    1G  512M    1G    1G    1G    1G    1G    1G    1G
     04 |  512M    1G  512M  256M  256M  512M  512M    1G  256M  256M    1G  256M  512M  512M    2G    1G
      Exponent Minimum = 28   Exponent Average = 29.270
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [14 2 9 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M  512M  512M  512M  512M  512M    1G  512M  256M  512M  512M  512M    1G  512M
     04 |  256M  512M    1G    1G    1G    2G    2G    1G    1G  512M  512M    1G  512M    1G    2G  256M
      Exponent Minimum = 28   Exponent Average = 29.250
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [7 1 8 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M  128M  256M  128M   64M   32M   32M   32M   16M   16M  128M   64M  128M   64M   64M
     08 |  512M  256M   64M  128M  256M  512M  512M  256M  512M  256M   64M   64M  128M    1G    1G    1G
     04 |  256M  256M  256M  512M  256M    1G  512M    1G    1G  512M  512M    1G  512M    1G    1G    1G
      Exponent Minimum = 24   Exponent Average = 27.708
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [7 2 14 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M    1G  512M  512M    1G    1G
     04 |  256M  256M  512M  512M  512M  512M  512M    1G  512M  512M  256M  512M    1G    2G    2G    1G
      Exponent Minimum = 28   Exponent Average = 29.166
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [7 2 14 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M    1G  512M    1G    1G    1G    1G  128M  256M  128M    1G    1G  256M
     08 |   32M  128M  512M    1G    1G    1G  512M  512M  512M  256M  512M  256M  256M  256M  128M  128M
     04 |  256M    1G  256M  512M    1G    1G  512M  512M  512M  256M   32M   64M   32M  512M  256M   64M
      Exponent Minimum = 25   Exponent Average = 28.479
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [14 2 7 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  256M  256M  512M  512M  512M  512M  256M  256M  512M  256M  512M
     08 |  128M  256M  256M  128M  256M  128M  128M   64M   32M   32M   32M   64M   64M   64M   64M  128M
     04 |  256M    1G  512M  256M  512M   64M   64M  256M  128M  256M  512M   64M   64M  256M   64M    1G
      Exponent Minimum = 25   Exponent Average = 27.645
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [14 2 9 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  256M  512M   16M    8M    8M   16M  512M  512M
     08 |  512M  512M  512M  512M  512M  512M  256M   64M   32M   16M   32M   64M  128M  256M  512M  512M
     04 |  512M  512M  512M  256M  128M  256M  256M  256M   64M    1G    4M    2M    2M    4M  512M    4G
      Exponent Minimum = 21   Exponent Average = 27.312
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [11 1 2 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |   16M   16M   16M   32M   16M   16M   32M   32M   16M   32M   16M   64M   16M   32M   32M   32M
     04 |  256M  512M  512M  512M  512M  256M  512M    1G  512M  512M  512M    2G  256M  256M  512M  512M
      Exponent Minimum = 24   Exponent Average = 27.500
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [8 7 15 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   64M   32M  128M  256M  256M  512M   64M   64M   64M   64M  256M  512M  512M  128M  128M  128M
     08 |   32M  128M  512M  512M  512M  512M   32M   32M  512M  256M  128M  512M  512M   64M   64M  128M
     04 |   16M    8M   32M   64M   64M  512M  256M   32M   16M   16M   64M  256M  128M   64M   64M   32M
      Exponent Minimum = 23   Exponent Average = 26.770
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [8 1 7 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M   32M  256M  128M   64M   32M   32M   16M   16M   64M   64M   64M   64M   64M   64M
     08 |    1G  128M  128M  128M  256M  512M  256M  256M  512M   64M   64M  128M  512M  512M    1G    1G
     04 |  256M  256M  256M  256M  512M  512M   32M  256M    1G    1G  256M  512M    1G  256M    2G    1G
      Exponent Minimum = 24   Exponent Average = 27.479
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [3 3 10 2].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    4M   32M  256M    1G   16M    2M    2M    2M    2M   16M    4M    4M    4M    2M    8M    2M
     04 |  256M  256M  512M  512M  512M  512M  512M  256M  256M  512M  512M  512M  512M  512M  512M  512M
      Exponent Minimum = 21   Exponent Average = 26.916
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [13 13 14 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1M    1M    2M    2M    2M    2M    2M    2M    2M    2M    4M    2M    4M    4M    4M    2M
     04 |  128M  256M  256M  128M  128M  128M  256M  128M  256M  256M  128M  256M  512M  256M  256M  128M
      Exponent Minimum = 20   Exponent Average = 25.916
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [4 1 9 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |    2M    2M    2M    2M    2M    2M    2M    2M    2M    2M    2M    2M    2M    2M    2M    2M
     08 |    4M    2M    2M    4M   16M    1M    1M    1M    1M   64M   64M   64M  128M  128M   64M  256M
     04 |    1G    1G    1G  512M    1G  512M    1G    1G  512M    1G    1G    1G  512M    1G    1G    2G
      Exponent Minimum = 20   Exponent Average = 24.770
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)++ candidate [14 12 13 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  256M
     08 |    2M    4M   16M   16M    4M    4M    2M    4M   16M  512M  256M  256M  256M  512M    8M    4M
     04 |  512M  256M  512M  256M  512M  512M  256M  256M  256M  256M  256M  512M  512M    1G    1G   64M
      Exponent Minimum = 21   Exponent Average = 27.250
    
    
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [10 3 11 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1G  512M  512M    1G  512M  512M    1G  512M  512M  512M    1G    1G  256M  512M  512M    1G
     04 |  256M  512M  512M  256M  512M    1G  512M    1G    1G    2G    1G    1G  512M  512M    1G    1G
      Exponent Minimum = 28   Exponent Average = 29.250
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [13 5 8 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M    1G    1G    1G  512M    1G    1G  512M    1G    1G    1G    1G  512M    1G    1G
     04 |  512M    1G  512M  256M  512M  512M  512M    1G  256M  512M    1G  256M  512M  512M    2G    1G
      Exponent Minimum = 28   Exponent Average = 29.291
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [14 2 9 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  256M  512M  512M  512M    1G  256M  512M  512M  512M  512M    1G    1G    1G  512M    1G  512M
     08 |  128M    1G  512M    1G  512M  256M  512M    1G    1G    1G    1G    1G    1G    1G    1G    1G
     04 |    1G  128M    1G    1G    1G    1G  128M  512M    1G  256M  256M  256M  256M    1G  512M  128M
      Exponent Minimum = 27   Exponent Average = 29.166
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [2 1 11 11].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  256M  128M  256M  128M  128M  128M  256M  128M  128M  256M  256M  128M  256M  256M  256M
     08 |    8M    8M    8M    8M    8M    8M    8M    8M    8M   64M    8M   16M    8M    8M  128M   32M
     04 |  512M  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  256M  512M  512M
      Exponent Minimum = 23   Exponent Average = 26.708
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [8 1 7 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M   32M  256M  128M   64M   32M   32M   16M   16M   64M   64M   32M   64M   64M   32M
     08 |    1G  256M  128M  128M  256M  512M  256M  512M  512M   64M   32M  128M  512M  512M  512M  512M
     04 |  256M  256M  512M  256M  512M    1G   32M  256M    1G    1G  256M  512M    1G  512M    2G    1G
      Exponent Minimum = 24   Exponent Average = 27.479
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [6 2 3 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1G  512M    1G    1G    1G    1G    2G    1G    1G    1G    1G    1G  512M    1G    1G    1G
     04 |  512M  512M    1G    1G  512M    1G    1G    1G    2G    2G    2G    4G  512M    1G    2G    2G
      Exponent Minimum = 29   Exponent Average = 29.708
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [14 11 3 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  256M  512M  128M  128M  256M  256M  512M  256M  512M  512M  512M  128M   64M  128M  128M   64M
     08 |   32M   64M  256M  256M  256M  256M  256M   64M   64M   32M   32M   64M   64M   32M   64M   32M
     04 |   64M  256M   32M   32M   64M   64M  256M  256M  256M  512M  128M   32M   16M   32M   32M   16M
      Exponent Minimum = 24   Exponent Average = 26.750
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [13 13 14 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    2M    2M    8M   32M    4M    2M    2M    2M    2M    2M   16M   64M   32M   16M    8M    4M
     04 |  256M  256M  256M  256M  256M  256M  256M  256M  256M  256M  512M  256M  512M  512M  512M  512M
      Exponent Minimum = 21   Exponent Average = 26.625
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [8 7 15 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   64M  128M  512M  128M  128M  128M   32M   16M  128M  128M   64M  256M  256M  128M  128M  128M
     08 |   64M  128M  256M  256M  512M  512M   16M    8M  128M  256M   32M  128M  256M   64M   64M  128M
     04 |   16M   32M  128M   32M   32M  512M   64M   32M   32M   32M   32M  128M   64M   64M   32M   32M
      Exponent Minimum = 23   Exponent Average = 26.395
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [7 2 14 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |    1G  512M    1G  512M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M  512M    1G  512M  512M    1G    1G
     04 |  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M  256M  512M    2G    1G    1G    1G
      Exponent Minimum = 28   Exponent Average = 29.208
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [13 5 8 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  256M  256M  512M    1G  256M  512M  512M  512M    1G  512M  512M  512M  512M  512M  512M    1G
     04 |  128M  512M  512M    1G    1G    1G  512M  512M  512M  512M  512M  512M  512M  512M    1G    1G
      Exponent Minimum = 27   Exponent Average = 29.062
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [12 10 13 7].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |   64M   16M   16M   32M   64M   32M   32M  256M  512M  512M  512M    1G  512M  512M    1G    1G
     04 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M    1G  512M    1G
      Exponent Minimum = 24   Exponent Average = 28.500
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [2 8 7 3].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  256M  512M  256M  512M  512M  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M    1G  512M  512M  512M  512M  512M  512M  256M  256M  512M  512M    1G  512M    1G  512M
     04 |  256M   64M    1G  512M  512M  512M  512M    1G    2G  512M    2G    2G    1G  512M    2G    1G
      Exponent Minimum = 26   Exponent Average = 29.125
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [9 2 14 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  128M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  256M
     04 |  128M  128M  512M  512M  512M  256M  256M  256M  256M  512M  256M    1G  512M  512M    1G  512M
      Exponent Minimum = 27   Exponent Average = 28.791
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1+s0- candidate [13 3 14 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  256M  512M
     08 |    8M   32M   64M  128M  256M  256M  256M  256M  256M  256M   32M   32M  128M  512M    8M    8M
     04 |  128M  128M  512M  512M  512M  512M  512M  512M  512M    1G    1G  512M  512M  512M   64M  512M
      Exponent Minimum = 23   Exponent Average = 27.979
    
    
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [2 1 11 11].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  256M  256M  128M  128M  128M  128M  128M  128M  128M  256M  256M  128M  256M  256M  512M
     08 |    8M    8M    8M    8M    8M    8M    8M    8M    8M   64M   16M   16M    8M    8M  128M   32M
     04 |  256M  256M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M  512M  128M  512M  512M
      Exponent Minimum = 23   Exponent Average = 26.708
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [14 2 9 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M    1G    1G  512M  256M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M
     08 |  256M    1G  512M    1G  512M  256M  512M    1G    1G    1G    1G    1G    1G    1G    1G    1G
     04 |  512M  128M    1G    1G    1G    2G  128M  512M    1G  256M  256M  256M  256M    1G  512M  256M
      Exponent Minimum = 27   Exponent Average = 29.187
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [8 1 7 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M   32M  512M  128M   64M   32M   32M   16M   16M   64M   64M   64M   64M   64M   32M
     08 |  512M  128M  128M  256M  256M  256M  128M  256M  512M  128M   64M  128M  512M  512M  512M    1G
     04 |  256M  512M  512M  256M    1G    1G   32M  256M    1G    1G  256M  512M    1G  256M    2G    1G
      Exponent Minimum = 24   Exponent Average = 27.520
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [2 8 7 3].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  256M  512M  256M  512M  256M  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1G    1G  512M  512M  512M  512M  512M  256M  128M  128M  512M  256M  256M  512M    1G  512M
     04 |  128M   64M  512M  512M  512M  512M  512M    2G    2G    1G    2G    2G    1G  512M    2G    1G
      Exponent Minimum = 26   Exponent Average = 29.000
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [13 5 8 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M   32M   64M   64M   64M  128K   64K   64M   64M   64M   64M   64M   64M   64M   64M
     08 |  256M  256M  512M  512M   64M   32M   64K   32K  256M  512M    1G    1G  512M  512M  512M  512M
     04 |  128M  256M  256M  256M  512M  512M    1G  512M    2G    1G    1G  512M    1G  128M  512M  512M
      Exponent Minimum = 15   Exponent Average = 26.791
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [13 13 14 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    2M    2M    8M   16M    4M    2M    2M    2M    2M    2M    8M   64M   32M   16M    8M    2M
     04 |  256M  256M  256M  256M  256M  256M  512M  256M  256M  256M  512M  256M  256M  512M  512M  512M
      Exponent Minimum = 21   Exponent Average = 26.562
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [14 2 9 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M    1G    1G  512M    1G    1G  512M    1G  512M  512M    1G    1G  512M
     08 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M  512M
     04 |  256M  512M    1G    1G    1G    2G  512M  512M    2G  512M  512M  512M  512M    1G    2G  256M
      Exponent Minimum = 28   Exponent Average = 29.333
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [13 3 14 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    8M   32M  128M  128M  256M  512M  256M  256M   64K  256M   32M   32M  128M  256M   16M    8M
     04 |  128M  128M  512M    1G  512M  256M  512M  512M  512M    1G    1G  256M    1G  256M  128M  512M
      Exponent Minimum = 16   Exponent Average = 27.791
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [10 3 11 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1G  512M  512M  512M  512M  512M  512M    1G  512M  512M    1G    1G  512M  512M    1G  512M
     04 |  512M  512M  512M  512M  512M    1G    1G    1G    1G    1G    1G    1G  512M    1G    1G  512M
      Exponent Minimum = 29   Exponent Average = 29.291
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [10 3 11 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M    1G  256M  128M  128M  128M  256M  128M  128M  512M  512M  512M  512M    1G
     04 |  512M  256M  512M    1G  512M  512M  512M    1G    1G    1G  256M  128M  128M    2G  512M  512M
      Exponent Minimum = 27   Exponent Average = 28.791
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [13 5 8 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M    1G    1G    1G    1G    1G    2G  512M    1G    1G    1G    1G    1G    1G    1G
     04 |  512M    1G  512M  256M  512M  512M  512M    2G  256M  512M    1G  128M  512M  512M    2G    1G
      Exponent Minimum = 27   Exponent Average = 29.354
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [14 11 3 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  256M  256M  128M  256M  256M  256M  512M  128M  512M  512M  512M  256M   32M  128M  128M   64M
     08 |   32M   64M  256M  256M  256M  512M  256M   64M   64M   32M   32M   64M   64M   64M   64M   64M
     04 |   64M  128M   32M   64M   64M   64M  256M  256M  256M  512M  128M   64M    8M   32M   32M   16M
      Exponent Minimum = 23   Exponent Average = 26.791
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [3 3 10 2].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  256M  512M  512M  512M  512M  256M  256M  512M  256M  512M  512M  512M  512M  256M  256M  256M
     08 |    4M  128M  512M    1G    2M    2M    2M    2M    2M   16M    4M    4M    2M   64M    2M    4M
     04 |  256M  256M  256M  512M  256M  512M  512M  128M  128M  256M  512M  256M  256M  512M  512M  256M
      Exponent Minimum = 21   Exponent Average = 26.666
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [15 3 6 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M   64M  128M  256M  512M  512M  512M  512M
     08 |  256M  512M  512M  512M  512M    1G  512M  512M  512M  512M  512M  512M  512M    1G  512M  512M
     04 |  256M  256M  256M  512M  512M  512M  512M  512M  512M  512M  256M  512M  512M  256M  512M  512M
      Exponent Minimum = 26   Exponent Average = 28.791
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [13 5 8 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  256M  512M    1G    1G  128M  512M  512M  512M  512M    1G    1G  512M  512M  512M  256M  512M
     04 |  128M  512M  512M  512M    1G    2G  512M    1G  512M  512M  512M  512M  512M  512M  512M    1G
      Exponent Minimum = 27   Exponent Average = 29.062
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [9 2 14 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M    1G  512M
     08 |    1G    1G    1G    1G    1G  512M    1G  512M    1G  128M  128M  128M  512M  512M  512M    1G
     04 |  256M  512M  512M  512M    1G    1G  512M  512M  512M  512M  512M    1G  256M  256M  512M  512M
      Exponent Minimum = 27   Exponent Average = 29.041
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [14 2 7 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  256M  512M  256M  256M  512M  512M  512M  512M  128M   64M  512M  256M  512M
     08 |  128M  128M  128M  128M  128M  128M   64M   64M   32M   16M   32M   32M  128M   64M   64M  128M
     04 |  256M  256M  128M   64M  512M   64M   64M  256M  256M  128M  512M   32M   16M  128M   64M  256M
      Exponent Minimum = 24   Exponent Average = 27.208
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0+ candidate [3 11 14 7].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  128M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M   64M   64M   64M  128M   64M  128M  128M  256M  128M  128M  256M  512M    1G  512M
     04 |  256M  512M    1G    1G    1G  512M  128M   32M  128M    2G  256M  128M  256M  256M  128M  512M
      Exponent Minimum = 25   Exponent Average = 28.250
    
    
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [14 2 7 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  256M  256M  512M  512M  512M  512M   64M  512M  512M  256M  512M
     08 |  128M  256M  256M  128M  256M  128M   64M   64M   32M   32M   32M   64M  128M   64M   64M  128M
     04 |  256M  256M  256M  256M  512M   64M   64M  256M  128M  128M  512M   16M  128M  512M   64M    1G
      Exponent Minimum = 24   Exponent Average = 27.541
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [13 5 10 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M  512M  512M  512M  512M    1G    1G    1G    1G  512M    1G  512M  512M  512M
     04 |  512M  512M  512M    1G    1G    1G    2G  512M    1G    1G  512M    1G    2G    1G    1G    1G
      Exponent Minimum = 29   Exponent Average = 29.375
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [7 1 8 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   16M  128M  256M  128M   64M   64M   32M   32M   16M   16M   64M  128M  128M   64M   32M
     08 |  512M  128M   64M  128M  256M  512M  256M  128M  256M  256M   64M   32M  128M    1G    1G  512M
     04 |  512M  256M  256M  256M  256M    1G  512M  512M    1G  512M  512M    1G    1G    2G    1G    1G
      Exponent Minimum = 24   Exponent Average = 27.583
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [15 6 2 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  256M  512M    2M    1M    2M    1M    1M    1M   16M  256M  512M  512M  256M  512M
     08 |  128M   64M   64M   64M   32M   64M   64M  128M  128M  128M  256M  512M  256M  256M  256M  512M
     04 |  256M  128M   64M  256M  512K  256K  512K  256K  256K  256K    4M   64M  128M  256M   64M    1G
      Exponent Minimum = 18   Exponent Average = 25.312
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [7 2 14 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M  256M  512M  512M    1G  512M  512M  512M  512M    1G  512M  512M  512M  512M
     04 |  256M  512M  512M  512M  512M    1G  512M    1G  512M  512M  256M  512M    1G    1G    1G    1G
      Exponent Minimum = 28   Exponent Average = 29.104
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [14 2 9 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M    1G  512M  512M  512M    1G  512M  512M    1G  512M
     08 |  512M  512M  512M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M    1G    1G  512M
     04 |  256M  512M    1G    1G  512M    2G    2G    1G    2G  512M  512M    1G  512M    1G    2G  256M
      Exponent Minimum = 28   Exponent Average = 29.354
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [3 11 14 7].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  128M  256M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M   64M   64M   64M   64M   64M  128M  128M  256M  128M  128M  256M  512M    1G  512M
     04 |  256M  512M    1G    1G    1G  512M  128M   32M   64M  512M  256M  256M  512M  256M  128M  512M
      Exponent Minimum = 25   Exponent Average = 28.187
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [10 7 11 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M    1G  512M  512M  512M  512M  512M  512M  512M  512M  512M  256M  256M    1G    1G    1G
     04 |  512M    1G    1G  512M  512M    1G    1G  256M  512M    1G  512M    2G  512M  512M    1G    1G
      Exponent Minimum = 28   Exponent Average = 29.208
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [8 7 15 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   64M   64M  128M  256M  256M  512M   64M  128M  128M  128M  256M  512M  256M  256M  128M  128M
     08 |   32M  128M  512M  256M  256M  512M   32M   64M  256M  512M  128M  512M  512M  128M   64M  128M
     04 |   16M   16M   32M   64M   64M  512M  256M   32M   32M   32M   64M  256M  128M   64M   64M   32M
      Exponent Minimum = 24   Exponent Average = 26.916
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [8 1 7 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M   64M  256M  128M   64M   32M   32M   16M   16M   64M   64M   64M   64M   64M   32M
     08 |    1G  256M  128M  128M  256M  512M  128M  256M  512M   64M   64M  128M    1G    1G  512M  512M
     04 |  256M  256M  512M  256M    1G    1G   32M  512M    1G  512M  256M  512M    1G  256M    2G    1G
      Exponent Minimum = 24   Exponent Average = 27.541
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [4 1 9 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |    4M    4M    4M    4M    4M    2M    2M    4M    4M    4M    4M    4M    4M    4M    4M    4M
     08 |    4M    2M    4M    4M   16M    1M    1M    2M    2M   64M   64M   64M  128M  128M   64M  256M
     04 |    1G    1G    1G    1G    1G  512M    1G    1G    1G  512M    1G    1G  512M  512M    2G    2G
      Exponent Minimum = 20   Exponent Average = 25.145
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [7 2 14 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M    1G  512M  512M  512M  512M    1G    1G    1G    1G  128M  256M  128M    1G    1G  256M
     08 |   32M  128M  256M  512M    1G    1G  512M  512M  512M  256M  512M  512M  128M  128M  256M  128M
     04 |  128M  512M  256M  512M    1G    1G  512M  512M  512M  256M   32M   64M   32M  512M  256M   64M
      Exponent Minimum = 25   Exponent Average = 28.395
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [8 9 13 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  256M  256M  256M  256M  512M  512M  512M  512M
     08 |  128M  512M    1G    1G  512M    1G    1G  512M    1G  512M  256M  256M  128M  256M  256M  256M
     04 |  256M  256M  512M    1G    1G    1G    1G    1G  512M    2G  512M   64M  256M  512M  512M  256M
      Exponent Minimum = 26   Exponent Average = 28.833
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)s1-s0- candidate [13 5 8 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M    1G    1G    1G    1G    2G  512M    1G    1G    1G    1G    1G    1G    1G
     04 |  512M    1G  512M  512M  512M    1G  512M    2G  256M  512M    1G  512M  512M  512M    2G    1G
      Exponent Minimum = 28   Exponent Average = 29.416
    
    
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [14 2 7 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  256M  256M  512M  512M  512M  512M   64M  512M  512M  256M  512M
     08 |  128M  256M  256M  256M  256M  128M  128M   32M   32M   16M   32M   32M   64M   64M   64M  128M
     04 |  256M  128M  256M  256M    1G   64M   64M  256M  128M  128M  512M   16M  128M    1G   64M    1G
      Exponent Minimum = 24   Exponent Average = 27.520
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [13 5 10 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M  512M  512M  512M  512M    1G    1G    1G    1G    1G    1G  512M  512M  512M
     04 |  512M  512M  512M    1G    1G    1G    2G  512M    1G    1G  512M    1G    1G    2G    1G  512M
      Exponent Minimum = 29   Exponent Average = 29.395
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [7 1 8 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   16M  128M  128M  128M   64M   64M   32M   32M   16M   16M   64M   64M  128M   64M   64M
     08 |  512M  128M   64M   64M  256M    1G  256M  128M  256M  256M   64M   32M  128M  512M  512M  512M
     04 |  256M  512M  256M  512M  256M    1G  512M    1G    1G    1G  512M    1G    1G    2G    1G    1G
      Exponent Minimum = 24   Exponent Average = 27.583
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [15 6 2 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M    2M    1M    2M    1M    1M    1M   16M  256M  256M  512M  256M  512M
     08 |   64M   64M   64M   64M   32M   64M   64M  128M  128M  128M  256M  512M  512M  256M  256M  256M
     04 |  512M  128M  128M  128M  512K  256K  512K  256K  256K  256K    4M   64M   64M  256M   64M    1G
      Exponent Minimum = 18   Exponent Average = 25.291
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [14 2 9 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M    1G    1G  512M  512M  512M  512M  512M    1G  512M
     08 |  512M  512M  512M  512M  512M  512M  512M    1G    1G    1G  512M  512M  512M    1G  512M  512M
     04 |  128M  512M    1G    1G    1G    2G    2G    1G    2G  512M  512M    1G    1G    1G    2G  256M
      Exponent Minimum = 27   Exponent Average = 29.395
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [3 11 14 7].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  128M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M   64M   64M   64M  128M   64M  128M  128M  128M  128M  128M  256M  256M    1G  512M
     04 |  256M  512M    1G    1G    1G  512M  128M   32M  128M    2G  128M  256M  256M  128M  128M  512M
      Exponent Minimum = 25   Exponent Average = 28.187
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [8 1 7 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M   32M  256M  128M   64M   32M   32M   16M   16M   64M   64M   32M   64M   64M   64M
     08 |    1G  256M  128M  128M  256M  512M  128M  256M  256M   64M   32M  128M  512M    1G  512M    1G
     04 |  256M  256M  512M  256M    1G    1G   32M  512M    1G  512M  256M  512M    1G  256M    2G    1G
      Exponent Minimum = 24   Exponent Average = 27.479
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [7 2 14 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M    1G    1G  512M    1G    1G  128M  256M  128M  512M    1G  512M
     08 |   64M  128M  256M  512M    1G    1G  512M  512M    1G  256M  512M  256M  256M  256M  256M  128M
     04 |  256M  512M  256M  512M    1G    1G  512M  512M  512M  256M   32M   64M   32M  512M    1G  256M
      Exponent Minimum = 25   Exponent Average = 28.541
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [10 7 11 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1G  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M    1G    1G    1G
     04 |  512M    2G    1G  512M  512M    1G    1G  256M  512M    1G  512M    2G  512M    1G    1G    1G
      Exponent Minimum = 28   Exponent Average = 29.291
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [11 1 2 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |   32M   32M   32M   32M   32M   32M   64M   32M   16M   16M   16M   32M   32M   16M   32M   32M
     04 |  256M  512M  256M  512M  512M  256M    1G    1G  512M  512M  512M    4G  256M  512M  512M  512M
      Exponent Minimum = 24   Exponent Average = 27.625
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [7 2 14 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1G  512M  512M  256M  512M  512M    1G  512M  512M  512M  512M    1G    1G    1G    1G    1G
     04 |  256M  512M  512M  512M  512M  512M  512M    1G  512M  512M  256M  512M    1G    1G    1G    1G
      Exponent Minimum = 28   Exponent Average = 29.187
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [13 13 14 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1M    2M    2M    2M    2M    2M    2M    2M    2M    2M    4M    4M    2M    4M    2M    2M
     04 |  128M  128M  256M  128M  128M  128M  256M  256M  256M  256M  128M  256M  256M  256M  256M  256M
      Exponent Minimum = 20   Exponent Average = 25.895
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0+ candidate [4 1 9 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |    4M    4M    4M    4M    4M    4M    4M    4M    4M    4M    4M    4M    4M    4M    4M    4M
     08 |    8M    4M    4M    4M   16M    2M    1M    2M    1M   64M   64M   64M  128M  128M   64M  512M
     04 |    1G    1G    1G    1G    1G  512M    1G    1G  512M    1G    1G    1G  512M  512M    1G    2G
      Exponent Minimum = 20   Exponent Average = 25.229
    
    
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [8 1 7 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M   32M  256M  128M   64M   32M   32M   16M   16M   64M   64M   64M   64M   64M   64M
     08 |    1G  128M  128M  128M  256M  512M  128M  256M  512M  128M   64M  128M    1G  512M  512M    1G
     04 |  256M  512M  512M  256M    1G    1G   32M  256M    1G    1G  256M  512M    1G  512M    2G    1G
      Exponent Minimum = 24   Exponent Average = 27.583
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [13 5 8 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   64M   64M   32M   64M   64M   32M   64K  128K   64M   64M   64M   64M   64M   64M   64M   64M
     08 |  256M  256M  256M  512M   64M   16M   32K   64K  256M  512M  512M  512M  512M  512M    1G  512M
     04 |  128M  512M  128M  128M    1G    1G    1G  512M  256M  256M    2G  512M    2G  128M  512M  512M
      Exponent Minimum = 15   Exponent Average = 26.708
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [14 2 9 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  256M  512M  512M  512M  512M  256M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M
     08 |  128M    1G  512M    1G  512M  512M  512M  512M    1G    1G    1G    1G    1G    1G    2G    1G
     04 |    1G  128M    1G    2G    1G    2G  128M  512M    1G  256M  256M  256M  256M    1G  512M  128M
      Exponent Minimum = 27   Exponent Average = 29.145
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [2 8 7 3].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  256M  512M  512M  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M    1G  512M  512M  512M  512M  256M  256M  128M  128M  512M  512M    1G  512M    1G  512M
     04 |  256M  128M    1G  512M  512M  512M  512M    2G    2G  512M    2G    1G    1G  512M    2G    1G
      Exponent Minimum = 27   Exponent Average = 29.083
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [13 13 14 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    2M    2M    8M   16M    4M    2M    2M    2M    2M    2M    8M   64M   32M   32M    8M    4M
     04 |  256M  256M  256M  256M  256M  256M  512M  256M  256M  256M  256M  512M  256M  512M  512M  512M
      Exponent Minimum = 21   Exponent Average = 26.604
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [2 1 11 11].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  128M  256M  128M  128M  128M  128M  128M  128M  128M  256M  256M  128M  256M  512M  512M
     08 |    8M    8M    8M    8M    8M    8M    8M    8M    8M  128M    8M   16M    8M    8M  128M   32M
     04 |  512M  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  128M  512M  512M
      Exponent Minimum = 23   Exponent Average = 26.708
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [13 5 8 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M    1G    1G    1G    1G    1G    2G  512M    1G    1G    1G    1G    1G    1G    1G
     04 |  512M    1G  512M  256M  512M  512M  512M    1G  256M  512M    1G  256M  512M  512M    2G    1G
      Exponent Minimum = 28   Exponent Average = 29.354
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [13 3 14 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    8M   32M  128M  256M  256M  512M  256M  256M  256M  256M   32M   32M   64M  128M   16M    8M
     04 |  128M  256M  512M  512M  512M  512M  512M  512M  512M    1G    1G  512M    1G  256M  128M  512M
      Exponent Minimum = 23   Exponent Average = 28.062
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [14 2 9 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M    1G    1G  512M    1G    1G    1G  512M  512M    1G    1G    1G  512M
     08 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     04 |  256M  512M    1G    1G    1G    2G  512M  512M    2G  512M    1G    1G  512M    1G    1G  256M
      Exponent Minimum = 28   Exponent Average = 29.354
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [14 11 3 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  256M  512M  128M  256M  256M  256M  512M  128M  512M  512M  256M  128M   32M   64M  256M   64M
     08 |   64M   64M  256M  256M  256M  512M  256M   64M   64M   32M   32M   64M   32M   64M   64M   64M
     04 |   64M  128M   32M   64M   64M   64M  256M  256M  256M  512M   64M   32M    8M   16M   64M   16M
      Exponent Minimum = 23   Exponent Average = 26.729
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [10 3 11 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1G  512M  512M  512M  512M  512M  512M    1G  512M  512M    1G    1G    1G  512M    1G    1G
     04 |  256M  512M  512M  256M  512M    1G  512M    1G    1G    1G    1G    1G  512M  512M  512M    1G
      Exponent Minimum = 28   Exponent Average = 29.250
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [15 3 6 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M   64M   64M  256M  512M  512M  512M  512M
     08 |  256M  512M  512M  512M  512M    1G  512M  512M  256M  512M  256M  512M  512M  512M  512M  256M
     04 |  256M  256M  256M  256M  512M  512M  512M  512M  512M  512M  256M  512M  512M  256M  512M  512M
      Exponent Minimum = 26   Exponent Average = 28.666
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [3 3 10 2].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  256M  512M  256M  512M  256M
     08 |    4M  128M  512M  512M    2M    2M    2M    2M    2M    8M    4M    2M    2M   64M    2M    2M
     04 |  256M  256M  256M  512M  256M  512M  512M  128M  128M  256M  512M  256M  256M  512M  512M  256M
      Exponent Minimum = 21   Exponent Average = 26.645
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [10 3 11 12].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M    1G  256M  128M  128M  128M  256M  128M  128M  512M    1G    1G  512M    1G
     04 |  512M  256M  512M    1G  512M  512M  512M    1G    1G    1G  256M  128M  128M    2G    2G  512M
      Exponent Minimum = 27   Exponent Average = 28.875
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1+s0- candidate [13 5 8 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M    1G    1G  128M  256M  512M  512M    1G    1G    1G  512M  512M  512M  512M    1G
     04 |  128M  256M  512M  512M    1G    1G  512M  512M    1G    1G  512M  512M  512M  512M  512M    1G
      Exponent Minimum = 27   Exponent Average = 29.104
    
    
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • Did less of the final two scrambler variations:
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0+ candidate [10 3 11 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1G    1G  512M  512M  512M  512M  512M  512M  512M  512M    1G    1G  512M  512M    1G    1G
     04 |  256M  512M  512M  256M  512M    1G  512M    1G    1G    1G    1G    1G  512M  512M    1G  512M
      Exponent Minimum = 28   Exponent Average = 29.229
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0+ candidate [13 5 8 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M    1G    1G    1G  512M    1G    1G  512M    1G    1G    1G  512M  512M    1G    1G
     04 |  512M    2G  512M  256M  256M  512M  512M    1G  256M  256M    1G  256M  256M  256M    2G    1G
      Exponent Minimum = 28   Exponent Average = 29.208
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0+ candidate [14 2 9 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  256M  512M    1G  512M  512M  256M  512M  512M  512M    1G  512M    1G    1G    1G    1G  512M
     08 |  128M    1G  512M  512M  512M  512M  512M    1G    1G    1G    1G    1G    1G    1G    1G    1G
     04 |  512M  128M    1G    1G    1G    1G  128M  512M    1G  256M  256M  256M  256M    1G  512M  128M
      Exponent Minimum = 27   Exponent Average = 29.166
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0+ candidate [2 1 11 11].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  256M  128M  128M  128M  128M  128M  128M  128M  256M  256M  128M  256M  256M  256M
     08 |    8M    8M    8M    8M    8M    8M    8M    8M    8M   64M    8M   16M    8M    8M  128M   32M
     04 |  256M  512M  512M  512M  512M  256M  512M    1G  512M  512M  512M  512M  512M    2G  512M  512M
      Exponent Minimum = 23   Exponent Average = 26.770
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0+ candidate [8 1 7 5].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M   64M  256M  128M   64M   32M   32M   32M   16M   64M   64M   64M   64M   64M   32M
     08 |    1G  128M  128M  128M  256M  256M  128M  256M  512M  128M   32M  128M  512M  512M  512M  512M
     04 |  256M  256M  512M  256M  512M    1G   32M  256M  512M  512M  256M  512M    1G  512M    2G  512M
      Exponent Minimum = 24   Exponent Average = 27.416
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0+ candidate [6 2 3 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |    1G    1G    1G    1G    1G    1G    2G    1G    1G    1G    2G    1G    1G    1G    1G  512M
     04 |  256M    1G    1G    1G  512M    1G    1G    1G    1G    2G    2G    2G  512M    1G    2G    2G
      Exponent Minimum = 28   Exponent Average = 29.708
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0- candidate [13 5 10 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M  512M  512M  512M  512M  512M  512M    1G    1G    1G    1G  512M  512M  512M  512M
     04 |  512M  512M  512M    1G    1G    1G    2G  512M    1G    1G  512M    1G    2G    1G    1G    1G
      Exponent Minimum = 29   Exponent Average = 29.354
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0- candidate [13 5 8 10].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
     08 |  512M  512M    1G    1G    1G    1G    1G    1G  512M    1G    1G    1G    1G    1G    1G    1G
     04 |  512M    1G  512M  256M  256M  512M  512M    1G  256M  256M    1G  256M  256M  256M    2G    1G
      Exponent Minimum = 28   Exponent Average = 29.250
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0- candidate [7 2 14 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M    1G    1G    1G    1G    1G  128M  256M  128M  512M  512M  512M
     08 |   32M  128M  512M    1G    1G    1G  512M  512M  512M    1G  512M  512M  128M  128M  256M  128M
     04 |  128M    1G  256M  512M    1G    1G  512M  512M  512M  256M   32M   64M   32M  256M    1G  256M
      Exponent Minimum = 25   Exponent Average = 28.541
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0- candidate [7 1 8 6].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   32M   32M  128M  256M  128M   64M   32M   32M   32M   16M   16M  128M  128M  128M   64M   32M
     08 |  512M  128M   64M  128M  256M    1G  512M  128M  256M  256M   64M   64M  128M    1G  512M  512M
     04 |  512M  256M  256M  256M  256M    1G  512M    1G  512M  512M  512M    1G    1G    2G    1G    1G
      Exponent Minimum = 24   Exponent Average = 27.645
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0- candidate [14 2 9 9].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M  512M
     08 |  512M  512M    1G  512M  512M  512M  512M  512M    1G  512M  512M  512M  512M    1G    1G  512M
     04 |  256M  512M    1G    1G    1G    2G    2G    1G    1G  512M  512M    1G  512M    1G    2G  256M
      Exponent Minimum = 28   Exponent Average = 29.333
    
    
    __________________________________________________________________________________________________________
      Gridded scores of single iterated Xoroshiro32(16)-s1-s0- candidate [8 7 15 13].
          Byte Sampled Double Full Period = 8 GB
          PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
        |===00====01====02====03====04====05====06====07====08====09====10====11====12====13====14====15==
     16 |   64M   64M  128M  256M  128M  512M   64M   64M   64M  128M  256M  512M  256M  128M  128M  128M
     08 |   64M  128M  512M  512M  512M  512M   32M   32M  256M  256M  128M  512M  512M   64M   64M  128M
     04 |   16M   16M   32M   64M   32M  512M  256M   32M   16M   32M   64M  256M   64M   64M   64M   32M
      Exponent Minimum = 24   Exponent Average = 26.770
    
    
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • To me, the best looking one there is Xoroshiro32(16)s1+s0- candidate [6 2 3 6].
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • Ha! I've now got a script that can sort each distribution results. I've realised this is still useful independently of the single large spreadsheet sorting.

    It runs quite smoothly. The slowest part is the built-in sort command. Took me a while to learn how to use it. In particular making [tab] as the sole field separator. The IFS variable wasn't playing ball for a while.
    	d=${#chirecords[*]}    # Total number records.  Note: @ and * perform the same job in most cases
    	printf "Sorting pRanking ... "
    	chirecords=($( sort -nt$'\t' -k3,3 -k4,4 <<<"${chirecords[*]}" ))  # The entire array in one go!
    	a=0; echo $d
    	while [ $a -lt $d ]; do
    		chirecords[$a]+=$'\t'$(($a + 1))
    		a=$(($a + 1))
    	done
    
    	printf "Sorting zRanking ... "
    	chirecords=($( sort -nt$'\t' -k4,4 -k3,3 <<<"${chirecords[*]}" ))  # The entire array in one go!
    	a=0; echo $d
    	while [ $a -lt $d ]; do
    		chirecords[$a]+=$'\t'$(($a + 1))
    		a=$(($a + 1))
    	done
    
    	printf "Sorting nzRanking ... "
    	chirecords=($( sort -nt$'\t' -k5,5 -k3,3 <<<"${chirecords[*]}" ))  # The entire array in one go!
    	a=0; echo $d
    	while [ $a -lt $d ]; do
    		chirecords[$a]+=$'\t'$(($a + 1))
    		a=$(($a + 1))
    	done
    
    	printf "Sorting sumRanking ... "
    	a=0
    	while [ $a -lt $d ]; do
    		IFS=$'\t\n' read line line line line line prank zrank nzrank line <<<${chirecords[$a]}
    		chirecords[$a]+=$'\t'$(($prank * 2 + $zrank + $nzrank))
    		a=$(($a + 1))
    	done
    	chirecords=($( sort -nt$'\t' -k9,9 -k3,3 <<<"${chirecords[*]}" ))  # The entire array in one go!
    	echo $d
    
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • evanhevanh Posts: 7,502
    edited 2019-05-26 - 14:28:47
    Doh! I made a tiny typo in the .cfg file so now have to redo two of the runs.

    I didin't notice until comparing the sorted chi rankings and it kind of stood out when three files were byte for byte identical. The first of the three is correct, so not rerunning that one.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
  • Thanks for the last lot of results, Evan. I'll wait to see what the error you found means. It seems there is little difference in PractRand scores for different +/- scrambler options with the same candidate.

    I've been doing a lot of tiring demolition work lately but I had a day off today hence my return from lurkdom. I think it could be worthwhile calculating the distributions for the following:
    	rotl (+/- s1 +/- s0, d) + (+/- s0 +/- s0*4)
    
     0	rotl (+s1 + s0, d) + s0*5
     1	rotl (-s1 + s0, d) + s0*5
     2	rotl (+s1 - s0, d) + s0*5
     3	rotl (-s1 - s0, d) + s0*5
     4	rotl (+s1 + s0, d) + s0*3
     5	rotl (-s1 + s0, d) + s0*3
     6	rotl (+s1 - s0, d) + s0*3
     7	rotl (-s1 - s0, d) + s0*3
     8	rotl (+s1 + s0, d) - s0*3
     9	rotl (-s1 + s0, d) - s0*3
    10	rotl (+s1 - s0, d) - s0*3
    11	rotl (-s1 - s0, d) - s0*3
    12	rotl (+s1 + s0, d) - s0*5
    13	rotl (-s1 + s0, d) - s0*5
    14	rotl (+s1 - s0, d) - s0*5
    15	rotl (-s1 - s0, d) - s0*5
    

    This is twice the work compared to previously, but it does include s0*3 as well as s0*5.
    Formerly known as TonyB
  • It's all the s0*5 I'm doing at the moment.
    "... peers into the actual workings of a quantum jump for the first time. The results
    reveal a surprising finding that contradicts Danish physicist Niels Bohr's established view
    —the jumps are neither abrupt nor as random as previously thought."
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