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Random/LFSR on P2

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  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-08 10:42
    evanh wrote: »
    I've wiped all the parity sourced Practrand report files and started the culling and gridding runs afresh.

    EDIT: Here's the culled tables, both with and without parity, for comparison. Notably [11 10 12]s parity scores means it shouldn't be included now but I've thrown it in to fill the final score chart. 
    __________________________________________________________________________________________________________

  Xoroshiro32(16)+ PractRand Score Table.  Build 2018-07-06 03:34:09 +1200
    PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
    Scoring ran from 2018-07-06 03:08:16 to 2018-07-06 03:33:18.  Byte Sampled Double Full Period = 8 GB
__________________________________________________________________________________________________________
                Sampling apertures of the generator output, labelled as most to least bit-significance
  Candidate    ----------------------------------------------------------------------------------------
[ A  B  C]  15:00  6:15  5:14  4:13  3:12  2:11  1:10  0:09 15:08 14:07 13:06 12:05 11:04 10:03  9:02  8:01  7:00
==========================================================================================================
[14  2  7]                                             256K  512M  512M  256M  256M  256M  128M  256M   16M   64K
[13  5  8]                                             256K  128M   64M  128M  128M   64M  128M  256M   16M   64K
[10  3 11]                                             256K  256M  256M  256M  256M  256M  256M  128M   16M   64K
[15  3  6]                                             256K  256M  512M  256M  512M  256M  256M  256M   16M   64K
[11 10 12]                                             256K   64M  128M  128M  256M  128M   64M  256M   16M   64K
[ 3  2  6]                                                                                         2M    1M   64K
[ 6  2  3]                                                                                       512K  512K   64K
[10  7 11]                                             256K  256M  256M  256M   64M   64M   64M  256M   16M   64K
[ 8  9 13]                                             256K  256M  256M  256M  128M  512M  256M  512M   16M   64K
[13  9  8]                                             256K  256M  256M   64M  128M  256M  256M   64M   16M   64K

__________________________________________________________________________________________________________

  Xoroshiro32(16)+p PractRand Score Table.  Build 2018-07-08 18:42:39 +1200
    PractRand v0.93 options:  stdin -multithreaded -te 1 -tf 2 -tlmin 1KB
    Scoring ran from 2018-07-08 18:20:49 to 2018-07-08 18:41:57.  Byte Sampled Double Full Period = 8 GB
__________________________________________________________________________________________________________
                Sampling apertures of the generator output, labelled as most to least bit-significance
  Candidate    ----------------------------------------------------------------------------------------
[ A  B  C]  15:00  6:15  5:14  4:13  3:12  2:11  1:10  0:09 15:08 14:07 13:06 12:05 11:04 10:03  9:02  8:01  7:00
==========================================================================================================
[14  2  7]   512M                                            512M  512M  256M  256M  256M  128M  256M   16M  512M
[13  5  8]   128M                                            128M   64M  128M  128M   64M  128M  256M   16M  128M
[10  3 11]   512M                                            256M  256M  256M  256M  256M  256M  128M   16M  256M
[15  3  6]   512M                                            256M  512M  256M  512M  256M  256M  256M   16M  256M
[11 10 12]                                                    64M  128M  128M  256M  128M   64M  256M         16M
[ 3  2  6]                                                                                         2M            
[ 6  2  3]                                                                                       512K            
[10  7 11]   256M                                            256M  256M  256M   64M   64M   64M  256M   16M  512M
[ 8  9 13]   256M                                            256M  256M  256M  128M  512M  256M  512M   16M  512M
[13  9  8]    64M                                            256M  256M   64M  128M  256M  256M   64M   16M  512M

    Here's completely updated frequency distribution reports for the ten candidates:

    Thanks, Evan. [14,2,7]+p pair/XORO32 distribution is better than [14,2,7]+. Table updated at
    http://forums.parallax.com/discussion/comment/1441593/#Comment_1441593

    Above results confirm several points:

    1. Best xoroshiro32+ triple is [14,2,7].
    2. Parity trick makes a huge improvement to bit 0.
    3. Bit 1 is much better than bit 0 without parity but weaker than higher bits.
    4. Improved bit 0 with parity masks relatively weak bit 1 for [7:0].
  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-08 12:18
    Comparison of xoroshiro32+/+p/++:

    PractRand scores, single iteration 
    # a,  b,  c,  d,  15:0, 15:8, 14:7, 13:6, 12:5, 11:4, 10:3,  9:2,  8:1,  7:0
 14,  2,  7,  +,   64K, 512M, 512M, 256M, 256M, 256M, 128M, 256M,  16M,  64K
 14,  2,  7, +p,  512M, 512M, 512M, 256M, 256M, 256M, 128M, 256M,  16M, 512M
 14,  2,  7,  5,  256M,   1G,   1G,   1G,   1G,   1G,   1G,   1G,   1G,   1G

    Pair/XORO32 frequency, double iteration
    Actual and Expected 
    # a,  b,  c,  d,     pfreq0,     pfreq1,     pfreq2,     pfreq3,     pfreq4,     pfreq5,     pfreq6,     pfreq7,     pfreq8,     pfreq9,    pfreq10,    pfreq11,    pfreq12,   pfreq13+
 14,  2,  7,  +, 1360520517, 1842746126,  858490998,  200964795,   29117354,    2902521,     212668,      11793,        509,         14,          1,          0,          0,          0
 14,  2,  7, +p, 1419103690, 1764224504,  850000354,  220741984,   36364139,    4160939,     348172,      22317,       1148,         45,          4,          0,          0,          0
 14,  2,  7,  5, 1576661053, 1583423321,  791674049,  262776786,   65121487,   12864448,    2110786,     295138,      35867,       3945,        372,         41,          3,          0
#expected, , , , 1580030169, 1580030169,  790015084,  263338361,   65834590,   13166918,    2194486,     313498,      39187,       4354,        435,         40,          3,          0

    Pair/XORO32 frequency, double iteration
    |Actual-Expected|/Expected 
    # a,  b,  c,  d,     pfreq0,     pfreq1,     pfreq2,     pfreq3,     pfreq4,     pfreq5,     pfreq6,     pfreq7,     pfreq8,     pfreq9,    pfreq10,    pfreq11,    pfreq12
 14,  2,  7,  +, 0.13892750, 0.16627274, 0.08667671, 0.23685712, 0.55771952, 0.77955957, 0.90308983, 0.96238253, 0.98701099, 0.99678456, 0.99770114, 1.00000000, 1.00000000
 14,  2,  7, +p, 0.10185025, 0.11657646, 0.07592927, 0.16175530, 0.44764387, 0.68398534, 0.84134234, 0.92881294, 0.97070457, 0.98966467, 0.99080459, 1.00000000, 1.00000000
 14,  2,  7,  5, 0.00213231, 0.00214752, 0.00209991, 0.00213252, 0.01083173, 0.02297196, 0.03814104, 0.05856496, 0.08472197, 0.09393661, 0.14482758, 0.02500000, 0.00000000
  • evanhevanh Posts: 16,037
    The question marked 15:0 score in your Xoroshiro32+ above is 64K. 
    __________________________________________________________________________________________________________
  PractRand scoring of Xoroshiro32(16)+ candidate [14 2 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 |   64K    2M    2M    2M    2M    2M    2M    2M   64K    1M    1M    1M    1M  256K  256K  256K
 15 |  256M  256M  256M  256M  256M  256M  256M  256M  256M  256M  512M  512M  512M  512M  512M  512M
 14 |   64M  128M  128M  128M  128M  128M  128M  128M  128M  128M  128M  128M  128M  128M   64M   64M
 13 |   32M   64M   64M   64M   64M   64M  128M  128M   64M   64M  128M  256M  256M  256M  256M   32M
 12 |    2M    8M   16M   16M   64M    2M    2M    2M    2M    2M    2M    2M    2M    2M    2M    2M
 11 |  512M  256M  128M  256M  256M  256M  128M  256M  128M  256M  512M    1G    4G  512M    1G    1G
 10 |  256M   32M   32M  512M  512M  512M  512M  128M  256M  256M  512M  512M    1G    1G  256M    1G
 09 |    1G    1G  128M  128M    2G    2G    4G    4G    2G    2G    2G    2G    2G    2G    1G    2G
 08 |   64K   16M  256M  128M  256M  256M  256M  512M  512M  256K  256K  256K  256K  256K  256K  256K
 07 |  256M  256M  512M    1G  512M  512M  512M  256M  256M  256M  512M    1G    1G    1G    1G    1G
 06 |  256K   32M   64M  128M  128M  128M  256M  256M   64M  128M  128M  256K  256K  256K  256K  256K
 05 |  512M    1G  128M  256M  256M    1G    1G  256M  256M  256M  256M  256M  256M    1G    1G    1G
 04 |   64K   16M  256M   64M  256M  512M  256M  256M    1G  512M  512M  512M  256M   64K   64K   64K
 03 |  256K  128M    1G    1G    1G    1G    1G    2G    1G    1G  512M    2G    1G    1G  256K  256K
 02 |    8K   16M  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M    8K
 01 |    8K    2M   64M  128M  512M    1G    1G    1G    1G    1G  256M  512M    1G  512M    1G    1G
  Lowest Exponent = 13   Exponent Average = 26.335
  • TonyB_TonyB_ Posts: 2,196
    TonyB_ wrote: »
    I'm most interested currently in which 16-bit subsample of double-iterated xoroshiro32++ [14,2,7,5], i.e. the P2 v1 XORO32 instruction, has the highest PractRand score. Frequency test results below suggest it will be [25:10].
    # a,  b,  c,  d, size, lsb, low freq, high freq
 14,  2,  7,  5,   16, 	0,    0FFFF,    10000
...
 14,  2,  7,  5,   16, 	7,    0FEE8,    1011A
 14,  2,  7,  5,   16, 	8,    0FACD,    10532
 14,  2,  7,  5,   16, 	9,    0F815,    1092D
 14,  2,  7,  5,   16, 	10,   0F64A,    10A52
 14,  2,  7,  5,   16, 	11,   0F8AB,    107D6
 14,  2,  7,  5,   16, 	12,   0FD88,    1025F
...
 14,  2,  7,  5,   16, 	16,   0FFFF,    10000

    How much better will the top score be than [15:0] or [31:16], I wonder?

    Thanks, Evan. Do you think you might have time this week to do 16-bit double iteration tests for [14,2,7,5]? The results would have practical use on the P2 v1 and FPGA implementions. The three scores needed are [15:0], [31:16] and whichever other one is the highest.
  • evanhevanh Posts: 16,037
    edited 2018-07-08 13:07
    How much info are you wanting? Just a few Practrand scores only? I could hand build and score a few individual cases one by one I guess.

    What's the chances of doing any more later? If this is likely to recur I should probably work on getting the automation to do it. EDIT: We could grid them all too then.

  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-08 17:55
    evanh wrote: »
    How much info are you wanting? Just a few Practrand scores only? I could hand build and score a few individual cases one by one I guess.

    What's the chances of doing any more later? If this is likely to recur I should probably work on getting the automation to do it. EDIT: We could grid them all too then.

    [15:0], [31:16] and [25:10] if individual, just to see the difference. Automated grid to test all 16-bit subsamples (and possibly higher) could be handy, though.
  • evanhevanh Posts: 16,037
    edited 2018-07-08 17:33
    Damn it. There has still been more BCFN glitches getting by undetected. This time at least no need to start over.

    Latest scoring logic: 
    if [ ! -f "$PRreport" ]; then # If no pre-existing Practrand report then run and score the case

	"$RNGbin" | stdbuf -o L $PRcommand >"$PRreport"
	if [ $? -ne 0 ]; then
		printf "Aborted ${RNGbin} - PractRand error\n"
		exit 2
	fi
fi

# Output the score to console/logfile.  This is not score extraction for score table.
extract_score
if [ $bcfncnt -eq $failcnt ]; then  # probably incorrect score due to too sensitive BCFN testing
	if [ $bcfncnt -gt 2 ];then
		printf "Passing because "

	else # rerun testing from +1 power
		mv "$PRreport" "${PRreport}.tmp"
		printf "BCFNs: $bcfncnt, ${RNGbin}, PractRand score: ${scoresize}B - Trying larger ...\n"
		scoresizedn=$scoresize
		sizeup=$(( $sizekb * 2 ))
		"$RNGbin" | stdbuf -o L $PRcommand -tlmin "${sizeup}KB" >"$PRreport"

		extract_score
		if [ $sizekb -eq $sizeup ] && [ $bcfncnt -gt 0 ]; then # recuring fails
			if [ $bcfncnt -lt $failcnt ] || [ $bcfncnt -gt 2 ]; then # initial score was valid, revert
				rm "$PRreport"
				mv "${PRreport}.tmp" "$PRreport"
				printf "BCFNs: $bcfncnt, Fails: $failcnt, Reverted - "
				scoresize=$scoresizedn
				bcfncnt=0

			else # two BCFN glitches in a row!  raise another power, rerun again
				printf "BCFNs: $bcfncnt, Fails: $failcnt, ${RNGbin}  - Larger again ...\n"
				sizeup=$(( $sizekb * 2 ))
				"$RNGbin" | stdbuf -o L $PRcommand -tlmin "${sizeup}KB" >"$PRreport"

				extract_score
				if [ $sizekb -eq $sizeup ]; then # plain giving up at three tries, revert
					rm "$PRreport"
					mv "${PRreport}.tmp" "$PRreport"
					printf "BCFNs: $bcfncnt, Fails: $failcnt, Reverted - "
					scoresize=$scoresizedn
					bcfncnt=0

				else # got through it, any more glitches for this case won't be detected on this run
					rm "${PRreport}.tmp"
				fi
			fi
		else # revised report is normal, BCFN glitch cleared
			rm "${PRreport}.tmp"
			if [ $bcfncnt -lt $failcnt ]; then # report the correction
				printf "BCFNs: $bcfncnt, Fails: $failcnt, Accepted - "
			fi
		fi
	fi
	if [ $bcfncnt -eq $failcnt ]; then
		printf "BCFN & Fails: $failcnt, "
	fi
fi
printf "${RNGbin}, PractRand score: ${scoresize}B\n"

rm "$RNGbin"
  • evanhevanh Posts: 16,037
    Revised chart attached:
    scores_xo+s16.png
    992 x 686 - 72K
    zip
    zip
    scores_xo+s16.zip
    96K
  • TonyB_TonyB_ Posts: 2,196
    TonyB_ wrote: »
    evanh wrote: »
    TonyB_ wrote: »
    TonyB_ wrote: »
    I'm most interested currently in which 16-bit subsample of double-iterated xoroshiro32++ [14,2,7,5], i.e. the P2 v1 XORO32 instruction, has the highest PractRand score. Frequency test results below suggest it will be [25:10].
    # a,  b,  c,  d, size, lsb, low freq, high freq
 14,  2,  7,  5,   16, 	0,    0FFFF,    10000
...
 14,  2,  7,  5,   16, 	7,    0FEE8,    1011A
 14,  2,  7,  5,   16, 	8,    0FACD,    10532
 14,  2,  7,  5,   16, 	9,    0F815,    1092D
 14,  2,  7,  5,   16, 	10,   0F64A,    10A52
 14,  2,  7,  5,   16, 	11,   0F8AB,    107D6
 14,  2,  7,  5,   16, 	12,   0FD88,    1025F
...
 14,  2,  7,  5,   16, 	16,   0FFFF,    10000

    How much better will the top score be than [15:0] or [31:16], I wonder?

    Thanks, Evan. Do you think you might have time this week to do 16-bit double iteration tests for [14,2,7,5]? The results would have practical use on the P2 v1 and FPGA implementions. The three scores needed are [15:0], [31:16] and whichever other one is the highest.

    How much info are you wanting? Just a few Practrand scores only? I could hand build and score a few individual cases one by one I guess.

    What's the chances of doing any more later? If this is likely to recur I should probably work on getting the automation to do it. EDIT: We could grid them all too then.

    [15:0], [31:16] and [25:10] if individual, just to see the difference. Automated grid to test all 16-bit subsamples (and possibly higher) could be handy, though.

    Is is Thursday already? Time flies!

  • evanhevanh Posts: 16,037
    Bouncing around the walls again? Hehe. Yeah, I went all in for automatic testing of double iterating the generator. The C source was quick to change although it did require concentration for keeping sorted the separation of word widths. I needed to be fresh for sure.

    While working my way through the scripts it started getting messy enough that I decided to do a cleaning round ... and that proved troublesome due to ripple effects right throughout.

    Had a day off. Started a functioning culling run today - Looking to be twice the number of passing candidates with 512 MB threshold. Again, none of the [14 2 7 x] candidates made the grade.

    I've only just finished the gridding clean-up right now. I'll have a grid done for [14 2 7 5] first ...

  • evanhevanh Posts: 16,037
    edited 2018-07-12 14:11
    I've done the faster half (even-sized apertures) first:
    Full 16x16 single iterated grid: Lowest Exponent = 27, Exponent Average = 30.957
    Even 8x16 single iterated grid: Lowest Exponent = 27, Exponent Average = 30.242
    Even 16x32 double iterated grid: Lowest Exponent = 26, Exponent Average = 31.126
    Note the heightened average even though the worst case is lower. And it'll be higher again with the odds included. 
    __________________________________________________________________________________________________________
  Gridded scores of single iterated Xoroshiro32(16)++ candidate [14 2 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 |  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
 15 |    4G    2G    8G    8G    4G    4G    4G    2G    4G    4G    4G    8G    4G    8G    4G   16G
 14 |    4G    4G    4G    2G    2G    2G    1G    2G    1G    2G    2G    2G    4G    4G    4G    2G
 13 |    2G    4G    4G    4G    4G    4G    4G    4G    4G    2G    4G    2G    4G    4G    2G    2G
 12 |  512M  512M    1G    1G  512M  512M    1G    1G    1G  512M    1G    1G    1G    1G  512M  512M
 11 |    2G    2G    4G    4G    4G    2G    4G    4G    4G    2G    2G    4G    4G    4G    4G    4G
 10 |    2G    2G    1G    2G    2G    2G    1G    2G    2G    2G    2G    2G    2G    2G    2G    2G
 09 |    2G    4G    4G    4G    4G    8G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G
 08 |    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G  256M  512M    1G    1G    1G    1G
 07 |    8G    2G    4G    4G    4G    4G    8G    8G    8G    8G    4G    4G    4G    8G    8G    4G
 06 |    4G    2G  512M    2G    1G    2G    2G    4G    2G    2G    2G    2G    1G    2G    4G    2G
 05 |    4G    2G    4G    4G    4G    2G    4G    2G    4G    4G    4G    4G    2G    2G    2G    4G
 04 |  128M    1G    2G    1G    1G    2G    1G    2G    2G    1G    1G    2G    1G  512M    1G  512M
 03 |    2G    4G    2G    4G    4G    4G    2G    4G    4G    4G    4G    4G    4G    4G    4G    2G
 02 |    1G    2G    2G    2G    2G    2G    2G    2G    2G    1G    1G    2G    2G    2G  512M  512M
 01 |    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G

    __________________________________________________________________________________________________________
  Gridded scores of single iterated Xoroshiro32(16)++ candidate [14 2 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 |  256M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M  512M
 14 |    4G    4G    4G    2G    2G    2G    1G    2G    1G    2G    2G    2G    4G    4G    4G    2G
 12 |  512M  512M    1G    1G  512M  512M    1G    1G    1G  512M    1G    1G    1G    1G  512M  512M
 10 |    2G    2G    1G    2G    2G    2G    1G    2G    2G    2G    2G    2G    2G    2G    2G    2G
 08 |    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G  256M  512M    1G    1G    1G    1G
 06 |    4G    2G  512M    2G    1G    2G    2G    4G    2G    2G    2G    2G    1G    2G    4G    2G
 04 |  128M    1G    2G    1G    1G    2G    1G    2G    2G    1G    1G    2G    1G  512M    1G  512M
 02 |    1G    2G    2G    2G    2G    2G    2G    2G    2G    1G    1G    2G    2G    2G  512M  512M

    __________________________________________________________________________________________________________
  Gridded scores of double iterated Xoroshiro32(16)++ candidate [14 2 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====17====18====19====20====21====22====23====24====25====26====27====28====29====30====31=
 32 |  256M    1G    1G    1G    1G    2G  512M  512M  512M  256M  256M  256M    1G    1G    1G    1G  256M    1G    1G    2G    2G    1G  512M  512M    1G    1G  512M    1G    1G    1G    1G    1G
 30 |    8G    8G    4G    8G    4G   16G    8G   16G    8G   16G    8G    8G    4G    8G    4G    8G    4G    4G    4G    4G    4G    4G    4G    8G    8G    4G    4G    8G    8G   16G    8G    8G
 28 |    2G    2G    4G    4G    2G    4G    1G    4G    2G    4G    4G    4G    2G    1G    2G    8G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    4G    4G    4G
 26 |    8G    8G    4G    8G    4G   16G    8G   16G    8G   16G    8G    8G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    8G    8G
 24 |    2G    2G    2G    2G    2G    2G    2G    4G    2G    2G    2G    2G    2G    2G    2G    4G    2G    2G    2G    2G    2G    4G    4G    2G    2G    2G    2G    2G    2G    2G    4G    2G
 22 |    2G    2G    2G    4G    4G    4G    4G    4G    8G    8G    8G    8G    4G    4G    4G    8G    8G    8G    8G    4G    4G    8G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G
 20 |    2G    1G    1G    1G    2G    4G    2G    2G    2G    4G    2G    2G    1G    2G    2G    2G    2G    4G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    1G    2G    2G    2G
 18 |    4G    2G    4G    2G    2G    4G    4G    4G    4G    4G    8G    8G    2G    2G    4G    4G    4G    8G    4G    4G   16G    4G    4G    4G    8G    8G    4G    4G    4G    2G    2G    4G
 16 |  512M    1G    1G    1G    1G    1G    1G    1G  512M  256M  128M  128M    1G    1G  512M  512M  512M  512M  512M    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G
 14 |    2G    2G    2G    4G    2G   16G    2G    4G    2G    4G    8G   16G    4G    4G    2G    2G    2G    2G    2G    4G    2G    2G    4G    8G    4G    8G    8G   16G   16G    8G    4G    4G
 12 |    1G  512M    1G    1G  512M    1G    4G    2G    1G    1G    1G    1G    2G    2G    2G    2G  512M    1G    1G    1G  512M    1G    1G  256M  256M    1G    1G    4G    4G    8G    4G    2G
 10 |    2G    8G    4G    2G    2G    1G    1G    1G    1G    2G    4G    8G    8G    1G  512M    1G    2G    8G    4G    4G    2G    1G    1G    2G    1G    1G    2G    8G    4G    8G  512M    1G
 08 |   64M  512M    1G    2G  512M    1G  128M  128M    1G    2G    4G    4G    4G    2G    2G  256M   64M  512M    1G    2G  512M    1G  128M  128M    1G    4G    2G    1G    1G    2G    2G  256M
 06 |    2G    2G    2G    2G    4G    2G    4G    8G    4G    2G    4G    4G    2G    4G    4G    4G    2G    2G    2G    2G    4G    2G    4G    4G    4G    2G    4G    8G    2G    4G    4G    4G
 04 |    2G    1G    1G    2G    4G    1G    2G    1G    4G    1G    2G    2G    1G    1G    2G    2G    2G    1G    1G    2G    4G    1G    2G    1G    4G    1G    2G    2G    1G    1G    2G    2G
 02 |    2G    1G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G  512M    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G  512M    2G    2G    2G
  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-12 14:54
    Thanks for the results, Evan.
  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-13 10:43
    Here are the double-iterated xoroshiro32++ [14,2,7,5] low and high frequencies for selected 16-bit subsamples, with PractRand scores above appended:
    # a,  b,  c,  d, size, lsb, low freq, high freq, PractRand score
 14,  2,  7,  5,   16, 	0,    0FFFF,    10000,  512M
...
 14,  2,  7,  5,   16, 	7,    0FEE8,    1011A,    1G
 14,  2,  7,  5,   16, 	8,    0FACD,    10532,  512M
 14,  2,  7,  5,   16, 	9,    0F815,    1092D,  256M
 14,  2,  7,  5,   16, 	10,   0F64A,    10A52,  128M
 14,  2,  7,  5,   16, 	11,   0F8AB,    107D6,  128M
 14,  2,  7,  5,   16, 	12,   0FD88,    1025F,    1G
...
 14,  2,  7,  5,   16, 	16,   0FFFF,    10000,  512M

    The subsamples with the greatest frequency variations have the lowest PractRand scores. This is the opposite of what I predicted they might be.

  • evanhevanh Posts: 16,037
    Tony,
    I gather you've got access to another computer to generate those numbers with.

  • evanhevanh Posts: 16,037
    At any rate, Practrand scoring has consistently matched the distribution scores all along. I've been a little surprised by how good your numbers are for predictability.

    I guess you could say we've done a pretty good job verifying distribution scoring as a rapid candidate selection method. My Practrand based mass scoring approach has been a good test bed for doing the proving but it isn't practical to carry on using for longer worded engines. Although shorter engines would be fine.
  • evanhevanh Posts: 16,037
    edited 2018-07-13 03:17
    I'd like to continue down current track. Finish the double iteration mass scoring. Then also do some testing of XoroshiroXX** as well - Try and get a gauge on the Prop2's free running generator too.

  • evanhevanh Posts: 16,037
    edited 2018-07-13 03:54
    Full 32x32 double iterated grid: Lowest Exponent = 26, Exponent Average = 31.839.

    Compared to an average of 30.957 for the single iterated grid scoring, that's not far off average scores being doubled in value. And lowest is half value.

    So, based on this one candidate, double iterating destabilises the quality a little ... and distribution likewise?
    __________________________________________________________________________________________________________
  Gridded scores of double iterated Xoroshiro32(16)++ candidate [14 2 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====17====18====19====20====21====22====23====24====25====26====27====28====29====30====31=
 32 |  256M    1G    1G    1G    1G    2G  512M  512M  512M  256M  256M  256M    1G    1G    1G    1G  256M    1G    1G    2G    2G    1G  512M  512M    1G    1G  512M    1G    1G    1G    1G    1G
 31 |    8G    8G   16G    8G   16G    8G   16G   16G   16G   16G   16G   16G   16G   16G   16G   16G    8G    8G    8G    8G    8G    8G   16G   16G   16G    8G   16G   16G   16G   16G   16G   16G
 30 |    8G    8G    4G    8G    4G   16G    8G   16G    8G   16G    8G    8G    4G    8G    4G    8G    4G    4G    4G    4G    4G    4G    4G    8G    8G    4G    4G    8G    8G   16G    8G    8G
 29 |   32G   16G   16G   16G   16G    4G    8G   16G   16G   16G   32G    8G    8G    8G   32G   32G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G   16G   16G   16G   16G
 28 |    2G    2G    4G    4G    2G    4G    1G    4G    2G    4G    4G    4G    2G    1G    2G    8G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    4G    4G    4G
 27 |   16G   16G    8G    4G    8G   16G    8G    8G    8G    8G   16G   16G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G   16G   16G
 26 |    8G    8G    4G    8G    4G   16G    8G   16G    8G   16G    8G    8G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    8G    8G
 25 |    8G   16G    8G    8G    8G    8G    8G    8G    8G    8G   16G   16G    8G   16G   16G   16G   16G   16G   16G    8G   16G    8G    8G    8G    8G    8G    8G    8G    8G    8G   16G   16G
 24 |    2G    2G    2G    2G    2G    2G    2G    4G    2G    2G    2G    2G    2G    2G    2G    4G    2G    2G    2G    2G    2G    4G    4G    2G    2G    2G    2G    2G    2G    2G    4G    2G
 23 |    8G    8G   16G    4G    4G    4G    4G    4G    4G    4G    8G   16G    8G    8G   16G   16G   32G   16G    8G    8G   16G   16G    8G    8G    8G    8G    8G    8G    8G    8G    8G    8G
 22 |    2G    2G    2G    4G    4G    4G    4G    4G    8G    8G    8G    8G    4G    4G    4G    8G    8G    8G    8G    4G    4G    8G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G
 21 |    4G    4G    4G    8G   16G    4G    4G    4G    4G    4G    8G   16G    8G    8G    8G    8G   16G   16G   16G    8G    8G    8G    8G    8G    8G    8G    8G    4G    8G    8G    8G    8G
 20 |    2G    1G    1G    1G    2G    4G    2G    2G    2G    4G    2G    2G    1G    2G    2G    2G    2G    4G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    1G    2G    2G    2G
 19 |    8G    4G    4G    4G    8G   16G   16G    4G    4G    4G    8G    8G    4G    8G    8G    8G   16G    8G   16G   16G    8G    8G    8G   16G   16G   16G    8G    8G    8G    4G    8G    8G
 18 |    4G    2G    4G    2G    2G    4G    4G    4G    4G    4G    8G    8G    2G    2G    4G    4G    4G    8G    4G    4G   16G    4G    4G    4G    8G    8G    4G    4G    4G    2G    2G    4G
 17 |    8G    4G    4G    8G    4G    4G    4G    8G    4G    2G    4G   16G    4G    4G    8G    8G    8G    8G   16G    8G   16G   16G    8G    8G   16G    8G   16G   16G   16G    8G    8G    8G
 16 |  512M    1G    1G    1G    1G    1G    1G    1G  512M  256M  128M  128M    1G    1G  512M  512M  512M  512M  512M    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G
 15 |    4G    8G    8G    8G    8G    8G    4G    8G   16G    8G    4G   16G    8G    8G    8G    4G    4G    8G    8G   16G   16G   16G   16G   16G    8G   16G   16G    8G   16G   16G    8G    8G
 14 |    2G    2G    2G    4G    2G   16G    2G    4G    2G    4G    8G   16G    4G    4G    2G    2G    2G    2G    2G    4G    2G    2G    4G    8G    4G    8G    8G   16G   16G    8G    4G    4G
 13 |    4G    4G    8G    4G    8G    8G    8G    4G    4G    8G    8G   16G   16G   16G    8G    4G    4G    4G    8G    4G    4G    4G    4G    4G    8G    8G   16G   16G   16G   16G    8G    8G
 12 |    1G  512M    1G    1G  512M    1G    4G    2G    1G    1G    1G    1G    2G    2G    2G    2G  512M    1G    1G    1G  512M    1G    1G  256M  256M    1G    1G    4G    4G    8G    4G    2G
 11 |    4G    4G    4G    4G    4G    2G    4G    4G    8G    4G    8G    8G    8G    2G    4G    8G    4G    4G    4G    4G    4G    2G    8G    2G    2G    4G    8G    8G    8G    8G    8G    8G
 10 |    2G    8G    4G    2G    2G    1G    1G    1G    1G    2G    4G    8G    8G    1G  512M    1G    2G    8G    4G    4G    2G    1G    1G    2G    1G    1G    2G    8G    4G    8G  512M    1G
 09 |    1G    8G    8G    8G    4G  512M  512M  512M    4G    8G    8G    8G    8G    4G    1G  512M    1G    8G    8G    8G    4G  512M  512M    1G    8G    8G    8G    8G    8G    8G    1G  512M
 08 |   64M  512M    1G    2G  512M    1G  128M  128M    1G    2G    4G    4G    4G    2G    2G  256M   64M  512M    1G    2G  512M    1G  128M  128M    1G    4G    2G    1G    1G    2G    2G  256M
 07 |  512M    1G    4G    4G    8G    4G    4G  256M    2G    8G    8G    8G    4G    8G    8G    8G  256M  512M    8G    4G    8G    4G    8G  256M    2G    8G    8G    8G    8G    8G    8G    8G
 06 |    2G    2G    2G    2G    4G    2G    4G    8G    4G    2G    4G    4G    2G    4G    4G    4G    2G    2G    2G    2G    4G    2G    4G    4G    4G    2G    4G    8G    2G    4G    4G    4G
 05 |    4G    4G    4G    4G    4G    4G    4G    4G    4G    2G    4G    4G    4G    4G    4G    2G    4G    4G    4G    4G    4G    4G    4G    4G    4G    2G    4G    4G    4G    4G    4G    4G
 04 |    2G    1G    1G    2G    4G    1G    2G    1G    4G    1G    2G    2G    1G    1G    2G    2G    2G    1G    1G    2G    4G    1G    2G    1G    4G    1G    2G    2G    1G    1G    2G    2G
 03 |    4G    2G    2G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    4G    2G    2G    4G    4G    4G    4G    4G    2G    4G    4G    4G    4G    4G    4G    2G
 02 |    2G    1G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G  512M    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G    2G  512M    2G    2G    2G
 01 |  512M    1G    1G    1G    1G    1G    1G    1G    1G  512M    1G    1G    1G    1G    1G    1G  512M    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G    1G
  • evanhevanh Posts: 16,037
    evanh wrote: »
    I'd like to continue down current track. Finish the double iteration mass scoring. Then also do some testing of XoroshiroXX** as well - Try and get a gauge on the Prop2's free running generator too.
    Running at about 3 hours per grid (for easy half). Currently at #4 of 53 candidates, so maybe another week to finish the gridding.

  • evanhevanh Posts: 16,037
    edited 2018-07-13 12:07
    Hmm, one thing that has been getting on my wick is the amount of unusable RAM on PCs these days. It crazily increases with total RAM installed. This newish Ryzen setup I've got is losing about 600 MB for no apparent reason. Given the CPU has the whole memory controller built-in, the loses aren't likely to change with motherboards. EDIT: I'd be okay at 1% of that, say 5 MB unusable.
    CPU AuthenticAMD, Features Code 178BFBFF, Model Code 00800F11
    AMD Ryzen 7 1700X Eight-Core Processor
    Measured - Minimum 3992 MHz, Maximum 3992 MHz
    get_nprocs() - CPUs 16, Configured CPUs 16
    get_phys_pages() and size - RAM Size 31.41 GB, Page Size 4096 Bytes
    ...

    And here's with one DIMM removed. Now the unusable amount is down to about 340 MB. I totally don't get why it's dynamic at all.
    CPU AuthenticAMD, Features Code 178BFBFF, Model Code 00800F11
    AMD Ryzen 7 1700X Eight-Core Processor
    Measured - Minimum 3992 MHz, Maximum 3993 MHz
    get_nprocs() - CPUs 16, Configured CPUs 16
    get_phys_pages() and size - RAM Size 15.66 GB, Page Size 4096 Bytes

    Back to random number testing now. :) I note me CPU cooler is in need of a dust out too. Packed dust forming into top and bottom fins.

    EDIT2: Big Oops! Those Physical RAM sizes weren't actually truly the amount of DRAM addressable. Asking google the right question made a huge difference to my understanding. Turns out those numbers exclude the whole Linux kernel space! And that has a reserved space that sizes as a percentage of the physical RAM installed.

    Here's some corrected numbers:
    evanh@controlled:~/hoard/coding/rng_testing$ dmesg|grep Memory:
    [ 0.000000] Memory: 16289976K/16710308K available (12300K kernel code, 2470K rwdata, 4240K rodata, 2408K init, 2416K bss, 420332K reserved, 0K cma-reserved)
    User available (16289976 KB) + Kernel reserved (420332 KB) = Kernel available (16710308 KB)
    + Kernel code&data (23834 KB) = CPU addressable DRAM (16734142 KB).

    Installed DRAM (16 GB = 16777216 KB) - Addressable (16734142 KB) = 43074 KB unaccounted for.
    evanh@controlled:~/hoard/coding/rng_testing$ dmesg|grep Memory:
    [ 0.000000] Memory: 32805040K/33487524K available (12300K kernel code, 2470K rwdata, 4240K rodata, 2408K init, 2416K bss, 682484K reserved, 0K cma-reserved)
    User available (32805040 KB) + Kernel reserved (682484 KB) = Kernel available (33487524 KB)
    + Kernel code&data (23834 KB) = CPU addressable DRAM (33511358 KB).

    Installed DRAM (32 GB = 33554432 KB) - Addressable (33511358 KB) = 43074 KB unaccounted for.

    Yay! The unusable space is a much smaller, and fixed amount, of slightly over 42 MB. I can handle that. :)


    EDIT3: Looks like I've assumed too much again. My older PC doesn't conform to the above allocations. It seems that all kernel code and data must reside within the "reserved" space. So, the 23834 KB piece is gobbled up and that leaves a bit over 65 MB unaccounted for. It's only 1.5 MB unaccounted on the older PC!
    evanh@control:~$ dmesg |grep Memory:
    [ 0.000000] Memory: 8043912K/8387064K available (12300K kernel code, 2470K rwdata, 4240K rodata, 2404K init, 2416K bss, 343152K reserved, 0K cma-reserved)
  • TonyB_TonyB_ Posts: 2,196
    evanh wrote: »
    TonyB_ wrote: »
    Here are the double-iterated xoroshiro32++ [14,2,7,5] low and high frequencies for selected 16-bit subsamples, with PractRand scores above appended:
    # a,  b,  c,  d, size, lsb, low freq, high freq, PractRand score
 14,  2,  7,  5,   16, 	0,    0FFFF,    10000,  512M
...
 14,  2,  7,  5,   16, 	7,    0FEE8,    1011A,    1G
 14,  2,  7,  5,   16, 	8,    0FACD,    10532,  512M
 14,  2,  7,  5,   16, 	9,    0F815,    1092D,  256M
 14,  2,  7,  5,   16, 	10,   0F64A,    10A52,  128M
 14,  2,  7,  5,   16, 	11,   0F8AB,    107D6,  128M
 14,  2,  7,  5,   16, 	12,   0FD88,    1025F,    1G
...
 14,  2,  7,  5,   16, 	16,   0FFFF,    10000,  512M

    The subsamples with the greatest frequency variations have the lowest PractRand scores. This is the opposite of what I predicted they might be.

    Tony,
    I gather you've got access to another computer to generate those numbers with.

    Evan, I added your PractRand scores. I can test low and high frequencies up to 16 bits.
  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-13 11:04
    If the equidistribution is disturbed by a fairly small amount then PractRand scores go up a bit, but too much disturbance makes the quality worse.
  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-13 13:18
    evanh wrote: »
    Full 32x32 double iterated grid: Lowest Exponent = 26, Exponent Average = 31.839.

    Compared to an average of 30.957 for the single iterated grid scoring, that's not far off average scores being doubled in value. And lowest is half value.

    So, based on this one candidate, double iterating destabilises the quality a little ... and distribution likewise?

    Looking at max scores, single iterated has one 16G for 15-bit, several 8G for 7-bit, plus 3-, 2- and 1-bit. Double iterated has four 32G for 29-bit and one for 23-bit, with more maximums for 15-bit and under than single-iterated, as would be expected.

    Some double-iterated scores are lower, e.g. 8-bit [7:0]. Would it be worthwhile appending +/-/= to the double-iterated scores to show how they compare to single?

    As for the distribution, the only one we have is 32-bit [31:0]. As the period is 2^32-1, each non-zero output would occur exactly once and zero never if they were equidistributed, which is not the case and the distribution is a binomial one instead. I don't know what the expected distributions are for less than 32-bit. The average frequency for 16-bit is 2^16, but there is no equation that can predict the distribution that I know of and the results will vary for each lsb, as my tests have shown.

    Running full double-iterated grid tests for all non-culled candidates might not be the best use of the resources at the moment. I'd like to know:

    1. Does the 32-bit distribution (pair/XORO32) vary with different lsb's for [14,2,7,5]? The ones to try are 5 or 19 or 20 as these have 2G score and 0 is only 256M. The C code would need a new constant to rotate the 32-bit output before incrementing the 4GB byte array.

    2. How long does each 32-bit distribution test take? About a minute? I'd prefer to see all the [31:0] pair and zero distributions before any more PractRand grid tests. Which [a,b,c,d] is closest to the ideal? Currently it's [3,2,6,5] for pair frequency but lots of candidates have not been tested yet.

    3. What is the distribution for scro's generator with 32-bit output and max score of 32G? Is it a binomial?
  • evanhevanh Posts: 16,037
    edited 2018-07-13 12:52
    Oh, ah, I couldn't run that same distribution code for a 32-bit output word. The memory allocation would be 2^64 or 16 x 1024^6 or 16 EB.

    EDIT: Or was it based on period length? I never really studied the purpose.

    EDIT2: Array index is formed from the pairing: 
        ipair = (next_prn << 16) | prev_prn;
    So that means a 32-bit output word would require 64-bit indexes.

  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-13 13:25
    deleted
  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-13 13:25
    deleted
  • evanhevanh Posts: 16,037
    So you're really wanting a distribution run for each and every grid score then.
  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-13 13:25
    deleted
  • evanhevanh Posts: 16,037
    Rotation is the columns the grids. If I start doing some I may as well do the lot.

  • TonyB_TonyB_ Posts: 2,196
    edited 2018-07-13 13:24
    Point 1 could well be a dud - how can rotating bits change the distribution?
  • TonyB_TonyB_ Posts: 2,196
    Point 1 was no good. Rotating will change the array index, but the number of different outputs that occur 0, 1, 2, etc., times will not change.
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