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PCG — Java Implementation. High quality fast random number generator
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KilianB/pcg-java
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PCG is a family of simple fast space-efficient statistically good algorithms for random number generation. Unlike many general-purpose RNGs, they are also hard to predict.
This implementation is based on Melissa E. O'NeillC code andpaperPCG: A Family of Simple FastSpace-Efficient Statistically Good Algorithms for Random Number Generation.
You are highly advised to check out her website for further information:www.pcg-random.orgJava implementation featuring a 64 bit state RNG with 32 bit output.
- High quality number generator
- Thread safe
- Quick advance and rewind allowing to reset the generator to a previous state or to skip the next k numbers
- Calculate the distance between different generator instances
- Extends the random interface to conveniently uses methods like
Collection.sort - Allows to split instances like
SplittableRandom
Note: The PCG family isnot cryptographically secure!
- Either download thepre build jar files and add them to your build path manually
- Use Maven, gradle or ivy via maven central
<!-- Java 10 Version --><dependency> <groupId>dev.brachtendorf</groupId> <artifactId>pcg-java-10</artifactId> <version>1.0.1</version></dependency><!-- Java 8 Version --><dependency> <groupId>dev.brachtendorf</groupId> <artifactId>pcg-java-8</artifactId> <version>1.0.1</version></dependency>Several different random number generators are bundled in this package. Pick one which suits your needs
// Uniquely seedPcgRRrng =newPcgRR();intrandomInt =rng.nextInt();doublenextGaus =rng.nextGaus();
Exand additional features and examples.
/* Next to randomly setting the internal state (seeding) the pcg family also allows to select one ofmany streams which all follow a different random number sequence ensuring that internal stagesnever converge between instance. */longseed =0;longstreamNumber =0;PcgRRrng =newPcgRR(seed,streamNumber);/* This istance will produce the same output when generating a number but they don't share areference*/PcgRRrngClone =rng.split();rng.nextInt() ==rngClone.nextInt()// TRUE/* This instance does not share a state and has a different seed and stream number!*/RngRRdistinctRng =rng.splitDistinct();//DistancerngClone =rng.split();for(inti =0;i <100;i++;){rng.nextInt();}rngClone.distance(rng)// 100//Rewind or fast skip x numbersintrandomInt =rng.nextInt()rng.advance(-1)// rewind 1 steprandomInt ==rng.Next()// TRUE
| Generator | Description | Thread safety | Notes |
| PcgRR | Balance speed with statistical performance and reasonable security.See chapter 6.3.1 in the paper. | Yes synchronization* | Recommended for multi threaded use |
| PcgRS | Instead of rotating the bits perform an implied shift.See chapter 6.3.2 in the paper.Slightly worse statistical performance** | Yes synchronization* | This generator is supposed to be faster due to performing a shift instead of rotating bits. But in benchmarks it performed slightly worse than the RR version. No real reason to pick this one over the RR at the moment. |
| PcgRSFast |
| No! | The go to instance when thread safety is not desired |
| PcgRSUFast |
| No! | This is a more lets seehow quick we can get approach instead of a reasonable class. Usually the PcgRSFast is preferable. |
- 3 separate implementations with different synchronization approaches were implemented and benchmarked with synchronization outperforminglocks and cas instructions by far.** when speaking about less statistical performance we are still way beyond everything generated by java random or mt!
Statistical and performance benchmarks were performed using pract rand and Oracle's jmh harness respectively
PractRand Test Suite
rng=PcgRSUFast stdin32, seed=Randomlength= 64 gigabytes (2^36 bytes), time= 2351 seconds Test Name Raw Processed Evaluation BCFN(2+0,13-0,T) R= +1.0 p = 0.335 normal BCFN(2+1,13-0,T) R= -2.7 p = 0.865 normal BCFN(2+2,13-0,T) R= +0.7 p = 0.386 normalClick here to expand the full report
rng=PcgRSUFast stdin32, seed=Randomlength= 64 gigabytes (2^36 bytes), time= 2351 seconds Test Name Raw Processed Evaluation BCFN(2+0,13-0,T) R= +1.0 p = 0.335 normal BCFN(2+1,13-0,T) R= -2.7 p = 0.865 normal BCFN(2+2,13-0,T) R= +0.7 p = 0.386 normal BCFN(2+3,13-0,T) R= +4.2 p = 0.044 normal BCFN(2+4,13-0,T) R= +1.2 p = 0.315 normal BCFN(2+5,13-0,T) R= -0.8 p = 0.627 normal BCFN(2+6,13-0,T) R= +1.8 p = 0.233 normal BCFN(2+7,13-0,T) R= -2.3 p = 0.824 normal BCFN(2+8,13-1,T) R= -1.9 p = 0.781 normal BCFN(2+9,13-1,T) R= -4.7 p = 0.976 normal BCFN(2+10,13-2,T) R= +3.5 p = 0.078 normal BCFN(2+11,13-3,T) R= +2.7 p = 0.136 normal BCFN(2+12,13-3,T) R= -3.7 p = 0.944 normal BCFN(2+13,13-4,T) R= -0.3 p = 0.532 normal BCFN(2+14,13-5,T) R= -0.4 p = 0.543 normal BCFN(2+15,13-5,T) R= +1.6 p = 0.236 normal BCFN(2+16,13-6,T) R= -0.2 p = 0.494 normal BCFN(2+17,13-6,T) R= +1.5 p = 0.243 normal BCFN(2+18,13-7,T) R= -2.0 p = 0.793 normal BCFN(2+19,13-8,T) R= -3.2 p = 0.960 normal BCFN(2+20,13-8,T) R= -3.1 p = 0.956 normal BCFN(2+21,13-9,T) R= -2.3 p = 0.891 normal BCFN(2+22,13-9,T) R= -2.1 p = 0.860 normal DC6-9x1Bytes-1 R= +1.9 p = 0.191 normal Gap-16:A R= +0.5 p = 0.435 normal Gap-16:B R= +0.9 p = 0.270 normal FPF-14+6/16:(0,14-0) R= +3.2 p = 0.014 normal FPF-14+6/16:(1,14-0) R= -1.2 p = 0.806 normal FPF-14+6/16:(2,14-0) R= -1.5 p = 0.861 normal FPF-14+6/16:(3,14-0) R= -1.0 p = 0.751 normal FPF-14+6/16:(4,14-0) R= +0.5 p = 0.356 normal FPF-14+6/16:(5,14-0) R= +1.4 p = 0.158 normal FPF-14+6/16:(6,14-0) R= -1.3 p = 0.825 normal FPF-14+6/16:(7,14-0) R= -0.5 p = 0.638 normal FPF-14+6/16:(8,14-0) R= -0.1 p = 0.538 normal FPF-14+6/16:(9,14-0) R= -0.4 p = 0.609 normal FPF-14+6/16:(10,14-0) R= +0.6 p = 0.331 normal FPF-14+6/16:(11,14-0) R= +0.2 p = 0.433 normal FPF-14+6/16:(12,14-1) R= +0.1 p = 0.467 normal FPF-14+6/16:(13,14-2) R= +0.3 p = 0.421 normal FPF-14+6/16:(14,14-2) R= +0.3 p = 0.427 normal FPF-14+6/16:(15,14-3) R= +1.2 p = 0.198 normal FPF-14+6/16:(16,14-4) R= +0.6 p = 0.336 normal FPF-14+6/16:(17,14-5) R= -1.8 p = 0.904 normal FPF-14+6/16:(18,14-5) R= -2.6 p = 0.973 normal FPF-14+6/16:(19,14-6) R= +0.4 p = 0.380 normal FPF-14+6/16:(20,14-7) R= -0.8 p = 0.713 normal FPF-14+6/16:(21,14-8) R= +3.1 p = 0.023 normal FPF-14+6/16:(22,14-8) R= +0.8 p = 0.281 normal FPF-14+6/16:(23,14-9) R= +0.0 p = 0.464 normal FPF-14+6/16:(24,14-10) R= -1.6 p = 0.888 normal FPF-14+6/16:(25,14-11) R= -0.9 p = 0.694 normal FPF-14+6/16:(26,14-11) R= -0.4 p = 0.539 normal FPF-14+6/16:all R= +0.1 p = 0.478 normal FPF-14+6/16:cross R= +1.4 p = 0.091 normal BRank(12):128(16) R= -0.1 p~= 0.520 normal BRank(12):256(8) R= -0.2 p~= 0.490 normal BRank(12):384(2) R= +1.6 p~= 0.168 normal BRank(12):512(8) R= +2.5 p~= 0.020 normal BRank(12):768(2) R= -0.2 p~= 0.554 normal BRank(12):1K(4) R= +0.4 p~= 0.340 normal BRank(12):1536(1) R= -0.7 p~= 0.689 normal BRank(12):2K(4) R= +1.7 p~= 0.060 normal BRank(12):3K(1) R= +1.8 p~= 0.146 normal BRank(12):4K(2) R= -0.2 p~= 0.554 normal BRank(12):6K(1) R= -0.7 p~= 0.689 normal BRank(12):8K(2) R= +0.8 p~= 0.293 normal BRank(12):12K(1) R= -0.7 p~= 0.689 normal mod3n(5):(0,9-0) R= -2.8 p = 0.921 normal mod3n(5):(1,9-0) R= +0.7 p = 0.369 normal mod3n(5):(2,9-0) R= -0.9 p = 0.675 normal mod3n(5):(3,9-0) R= +0.6 p = 0.388 normal mod3n(5):(4,9-0) R= +0.5 p = 0.408 normal mod3n(5):(5,9-0) R= +2.0 p = 0.166 normal mod3n(5):(6,9-0) R= -1.2 p = 0.721 normal mod3n(5):(7,9-0) R= -1.2 p = 0.727 normal mod3n(5):(8,9-1) R= -1.0 p = 0.696 normal mod3n(5):(9,9-1) R= +1.1 p = 0.292 normal mod3n(5):(10,9-2) R= -1.9 p = 0.829 normal mod3n(5):(11,9-2) R= +1.8 p = 0.187 normal mod3n(5):(12,9-3) R= -0.3 p = 0.556 normal mod3n(5):(13,9-3) R= +1.3 p = 0.255 normal mod3n(5):(14,9-4) R= +0.1 p = 0.468 normal mod3n(5):(15,9-4) R= +1.5 p = 0.216 normal TMFn(2+0):wl R= -0.2 p~= 0.5 normal TMFn(2+1):wl R= +0.2 p~= 0.5 normal TMFn(2+2):wl R= -1.3 p~= 0.7 normal TMFn(2+3):wl R= +0.7 p~= 0.4 normal TMFn(2+4):wl R= +1.8 p~= 0.3 normal TMFn(2+5):wl R= +0.8 p~= 0.4 normal TMFn(2+6):wl R= +1.9 p~= 0.3 normal TMFn(2+7):wl R= +2.2 p~= 0.2 normal TMFn(2+8):wl R= -0.9 p~= 0.6 normal TMFn(2+9):wl R= +1.2 p~= 0.3 normal TMFn(2+10):wl R= +1.5 p~= 0.3 normal TMFn(2+11):wl R= +5.2 p~= 0.08 normal [Low1/8]BCFN(2+0,13-0,T) R= +1.8 p = 0.232 normal [Low1/8]BCFN(2+1,13-0,T) R= +2.0 p = 0.205 normal [Low1/8]BCFN(2+2,13-0,T) R= -0.0 p = 0.500 normal [Low1/8]BCFN(2+3,13-0,T) R= -1.0 p = 0.657 normal [Low1/8]BCFN(2+4,13-0,T) R= +0.7 p = 0.390 normal [Low1/8]BCFN(2+5,13-1,T) R= +1.3 p = 0.299 normal [Low1/8]BCFN(2+6,13-1,T) R= +1.6 p = 0.248 normal [Low1/8]BCFN(2+7,13-2,T) R= +2.7 p = 0.134 normal [Low1/8]BCFN(2+8,13-3,T) R= +0.7 p = 0.377 normal [Low1/8]BCFN(2+9,13-3,T) R= -3.1 p = 0.903 normal [Low1/8]BCFN(2+10,13-4,T) R= -2.5 p = 0.854 normal [Low1/8]BCFN(2+11,13-5,T) R= -3.1 p = 0.910 normal [Low1/8]BCFN(2+12,13-5,T) R= +3.3 p = 0.095 normal [Low1/8]BCFN(2+13,13-6,T) R= -2.8 p = 0.892 normal [Low1/8]BCFN(2+14,13-6,T) R= +1.2 p = 0.281 normal [Low1/8]BCFN(2+15,13-7,T) R= +1.2 p = 0.277 normal [Low1/8]BCFN(2+16,13-8,T) R= +0.8 p = 0.305 normal [Low1/8]BCFN(2+17,13-8,T) R= +0.8 p = 0.311 normal [Low1/8]BCFN(2+18,13-9,T) R= -2.4 p = 0.908 normal [Low1/8]BCFN(2+19,13-9,T) R= +0.4 p = 0.339 normal [Low1/8]DC6-9x1Bytes-1 R= +0.8 p = 0.401 normal [Low1/8]Gap-16:A R= -0.7 p = 0.746 normal [Low1/8]Gap-16:B R= -0.2 p = 0.556 normal [Low1/8]FPF-14+6/16:(0,14-0) R= +1.1 p = 0.224 normal [Low1/8]FPF-14+6/16:(1,14-0) R= -1.9 p = 0.911 normal [Low1/8]FPF-14+6/16:(2,14-0) R= -1.7 p = 0.889 normal [Low1/8]FPF-14+6/16:(3,14-0) R= +0.4 p = 0.398 normal [Low1/8]FPF-14+6/16:(4,14-0) R= +2.1 p = 0.069 normal [Low1/8]FPF-14+6/16:(5,14-0) R= -0.4 p = 0.601 normal [Low1/8]FPF-14+6/16:(6,14-0) R= +2.2 p = 0.062 normal [Low1/8]FPF-14+6/16:(7,14-0) R= +0.5 p = 0.359 normal [Low1/8]FPF-14+6/16:(8,14-0) R= -0.5 p = 0.631 normal [Low1/8]FPF-14+6/16:(9,14-1) R= -2.3 p = 0.949 normal [Low1/8]FPF-14+6/16:(10,14-2) R= -0.6 p = 0.675 normal [Low1/8]FPF-14+6/16:(11,14-2) R= -1.4 p = 0.843 normal [Low1/8]FPF-14+6/16:(12,14-3) R= -0.5 p = 0.630 normal [Low1/8]FPF-14+6/16:(13,14-4) R= -0.6 p = 0.655 normal [Low1/8]FPF-14+6/16:(14,14-5) R= +0.2 p = 0.443 normal [Low1/8]FPF-14+6/16:(15,14-5) R= -0.7 p = 0.698 normal [Low1/8]FPF-14+6/16:(16,14-6) R= -0.1 p = 0.530 normal [Low1/8]FPF-14+6/16:(17,14-7) R= -1.5 p = 0.854 normal [Low1/8]FPF-14+6/16:(18,14-8) R= +1.0 p = 0.223 normal [Low1/8]FPF-14+6/16:(19,14-8) R= -1.1 p = 0.778 normal [Low1/8]FPF-14+6/16:(20,14-9) R= +0.9 p = 0.252 normal [Low1/8]FPF-14+6/16:(21,14-10) R= -0.2 p = 0.522 normal [Low1/8]FPF-14+6/16:(22,14-11) R= +0.4 p = 0.340 normal [Low1/8]FPF-14+6/16:(23,14-11) R= +1.7 p = 0.116 normal [Low1/8]FPF-14+6/16:all R= -0.4 p = 0.615 normal [Low1/8]FPF-14+6/16:cross R= -0.3 p = 0.565 normal [Low1/8]BRank(12):128(8) R= +1.5 p~= 0.080 normal [Low1/8]BRank(12):256(8) R= -0.7 p~= 0.670 normal [Low1/8]BRank(12):384(2) R= +0.8 p~= 0.293 normal [Low1/8]BRank(12):512(4) R= -0.8 p~= 0.670 normal [Low1/8]BRank(12):768(1) R= +0.4 p~= 0.366 normal [Low1/8]BRank(12):1K(4) R= -1.4 p~= 0.890 normal [Low1/8]BRank(12):1536(1) R= -0.7 p~= 0.689 normal [Low1/8]BRank(12):2K(2) R= -0.2 p~= 0.554 normal [Low1/8]BRank(12):3K(1) R= +0.4 p~= 0.366 normal [Low1/8]BRank(12):4K(2) R= -1.0 p~= 0.744 normal [Low1/8]BRank(12):6K(1) R= -0.7 p~= 0.689 normal [Low1/8]mod3n(5):(0,9-0) R= +1.0 p = 0.303 normal [Low1/8]mod3n(5):(1,9-0) R= -2.1 p = 0.849 normal [Low1/8]mod3n(5):(2,9-0) R= +3.5 p = 0.044 normal [Low1/8]mod3n(5):(3,9-0) R= -0.4 p = 0.577 normal [Low1/8]mod3n(5):(4,9-0) R= +0.4 p = 0.421 normal [Low1/8]mod3n(5):(5,9-1) R= +1.0 p = 0.306 normal [Low1/8]mod3n(5):(6,9-1) R= -1.1 p = 0.712 normal [Low1/8]mod3n(5):(7,9-2) R= -1.6 p = 0.790 normal [Low1/8]mod3n(5):(8,9-2) R= -1.4 p = 0.756 normal [Low1/8]mod3n(5):(9,9-3) R= -2.8 p = 0.926 normal [Low1/8]mod3n(5):(10,9-3) R= -0.0 p = 0.494 normal [Low1/8]mod3n(5):(11,9-4) R= -0.2 p = 0.530 normal [Low1/8]mod3n(5):(12,9-4) R= +3.5 p = 0.047 normal [Low1/8]mod3n(5):(13,9-5) R= +2.5 p = 0.108 normal [Low1/8]mod3n(5):(14,9-5) R= -1.8 p = 0.830 normal [Low1/8]mod3n(5):(15,9-6) R= +3.7 p = 0.042 normal [Low1/8]TMFn(2+0):wl R= -2.0 p~= 0.7 normal [Low1/8]TMFn(2+1):wl R= -1.5 p~= 0.7 normal [Low1/8]TMFn(2+2):wl R= -3.7 p~= 0.9 normal [Low1/8]TMFn(2+3):wl R= -3.4 p~= 0.8 normal [Low1/8]TMFn(2+4):wl R= -0.2 p~= 0.5 normal [Low1/8]TMFn(2+5):wl R= +0.6 p~= 0.4 normal [Low1/8]TMFn(2+6):wl R= +0.3 p~= 0.4 normal [Low1/8]TMFn(2+7):wl R= -0.1 p~= 0.5 normal [Low1/8]TMFn(2+8):wl R= +2.3 p~= 0.2 normal [Low1/16]BCFN(2+0,13-0,T) R= +0.9 p = 0.356 normal [Low1/16]BCFN(2+1,13-0,T) R= +0.9 p = 0.360 normal [Low1/16]BCFN(2+2,13-0,T) R= +0.4 p = 0.435 normal [Low1/16]BCFN(2+3,13-0,T) R= +4.1 p = 0.050 normal [Low1/16]BCFN(2+4,13-1,T) R= -0.6 p = 0.587 normal [Low1/16]BCFN(2+5,13-1,T) R= +0.3 p = 0.450 normal [Low1/16]BCFN(2+6,13-2,T) R= +1.5 p = 0.261 normal [Low1/16]BCFN(2+7,13-3,T) R= +6.2 p = 9.3e-3 normal [Low1/16]BCFN(2+8,13-3,T) R= -0.6 p = 0.581 normal [Low1/16]BCFN(2+9,13-4,T) R= +1.4 p = 0.269 normal [Low1/16]BCFN(2+10,13-5,T) R= -2.0 p = 0.795 normal [Low1/16]BCFN(2+11,13-5,T) R= +1.6 p = 0.239 normal [Low1/16]BCFN(2+12,13-6,T) R= -0.7 p = 0.577 normal [Low1/16]BCFN(2+13,13-6,T) R= -0.3 p = 0.517 normal [Low1/16]BCFN(2+14,13-7,T) R= +0.4 p = 0.381 normal [Low1/16]BCFN(2+15,13-8,T) R= +0.5 p = 0.359 normal [Low1/16]BCFN(2+16,13-8,T) R= +2.8 p = 0.116 normal [Low1/16]BCFN(2+17,13-9,T) R= +0.6 p = 0.314 normal [Low1/16]BCFN(2+18,13-9,T) R= +1.0 p = 0.263 normal [Low1/16]DC6-9x1Bytes-1 R= -2.5 p = 0.942 normal [Low1/16]Gap-16:A R= -2.1 p = 0.957 normal [Low1/16]Gap-16:B R= -0.2 p = 0.551 normal [Low1/16]FPF-14+6/16:(0,14-0) R= -0.2 p = 0.566 normal [Low1/16]FPF-14+6/16:(1,14-0) R= -1.3 p = 0.828 normal [Low1/16]FPF-14+6/16:(2,14-0) R= +2.1 p = 0.075 normal [Low1/16]FPF-14+6/16:(3,14-0) R= +0.9 p = 0.263 normal [Low1/16]FPF-14+6/16:(4,14-0) R= -1.2 p = 0.811 normal [Low1/16]FPF-14+6/16:(5,14-0) R= -1.5 p = 0.863 normal [Low1/16]FPF-14+6/16:(6,14-0) R= -0.0 p = 0.505 normal [Low1/16]FPF-14+6/16:(7,14-0) R= -0.3 p = 0.592 normal [Low1/16]FPF-14+6/16:(8,14-1) R= +2.2 p = 0.062 normal [Low1/16]FPF-14+6/16:(9,14-2) R= +1.7 p = 0.120 normal [Low1/16]FPF-14+6/16:(10,14-2) R= -1.3 p = 0.815 normal [Low1/16]FPF-14+6/16:(11,14-3) R= +0.5 p = 0.363 normal [Low1/16]FPF-14+6/16:(12,14-4) R= +2.4 p = 0.047 normal [Low1/16]FPF-14+6/16:(13,14-5) R= -2.1 p = 0.939 normal [Low1/16]FPF-14+6/16:(14,14-5) R= +1.9 p = 0.092 normal [Low1/16]FPF-14+6/16:(15,14-6) R= -0.1 p = 0.520 normal [Low1/16]FPF-14+6/16:(16,14-7) R= +0.1 p = 0.455 normal [Low1/16]FPF-14+6/16:(17,14-8) R= -0.7 p = 0.690 normal [Low1/16]FPF-14+6/16:(18,14-8) R= -1.3 p = 0.815 normal [Low1/16]FPF-14+6/16:(19,14-9) R= +2.5 p = 0.054 normal [Low1/16]FPF-14+6/16:(20,14-10) R= +1.5 p = 0.141 normal [Low1/16]FPF-14+6/16:(21,14-11) R= -1.4 p = 0.866 normal [Low1/16]FPF-14+6/16:(22,14-11) R= -0.3 p = 0.523 normal [Low1/16]FPF-14+6/16:all R= +0.3 p = 0.438 normal [Low1/16]FPF-14+6/16:cross R= +2.6 p = 0.014 normal [Low1/16]BRank(12):128(8) R= -0.3 p~= 0.500 normal [Low1/16]BRank(12):256(4) R= +2.2 p~= 0.030 normal [Low1/16]BRank(12):384(2) R= -1.0 p~= 0.744 normal [Low1/16]BRank(12):512(4) R= -0.8 p~= 0.670 normal [Low1/16]BRank(12):768(1) R= -0.7 p~= 0.689 normal [Low1/16]BRank(12):1K(2) R= -1.0 p~= 0.744 normal [Low1/16]BRank(12):1536(1) R= -0.7 p~= 0.689 normal [Low1/16]BRank(12):2K(2) R= -0.2 p~= 0.554 normal [Low1/16]BRank(12):3K(1) R= -0.7 p~= 0.689 normal [Low1/16]BRank(12):4K(1) R= +0.4 p~= 0.366 normal [Low1/16]mod3n(5):(0,9-0) R= -1.6 p = 0.792 normal [Low1/16]mod3n(5):(1,9-0) R= +2.2 p = 0.134 normal [Low1/16]mod3n(5):(2,9-0) R= +2.0 p = 0.163 normal [Low1/16]mod3n(5):(3,9-0) R= -3.5 p = 0.962 normal [Low1/16]mod3n(5):(4,9-1) R= -4.4 p = 0.987 normal [Low1/16]mod3n(5):(5,9-1) R= +1.3 p = 0.262 normal [Low1/16]mod3n(5):(6,9-2) R= +1.1 p = 0.287 normal [Low1/16]mod3n(5):(7,9-2) R= -1.6 p = 0.794 normal [Low1/16]mod3n(5):(8,9-3) R= -4.5 p =1-7.5e-3 normal [Low1/16]mod3n(5):(9,9-3) R= -1.8 p = 0.811 normal [Low1/16]mod3n(5):(10,9-4) R= +0.3 p = 0.423 normal [Low1/16]mod3n(5):(11,9-4) R= +2.2 p = 0.132 normal [Low1/16]mod3n(5):(12,9-5) R= -2.1 p = 0.871 normal [Low1/16]mod3n(5):(13,9-5) R= +0.2 p = 0.434 normal [Low1/16]mod3n(5):(14,9-6) R= -1.3 p = 0.729 normal [Low1/16]mod3n(5):(15,9-6) R= -2.1 p = 0.893 normal [Low1/16]TMFn(2+0):wl R= +3.2 p~= 0.2 normal [Low1/16]TMFn(2+1):wl R= +0.3 p~= 0.4 normal [Low1/16]TMFn(2+2):wl R= -0.9 p~= 0.6 normal [Low1/16]TMFn(2+3):wl R= +1.0 p~= 0.4 normal [Low1/16]TMFn(2+4):wl R= -1.2 p~= 0.7 normal [Low1/16]TMFn(2+5):wl R= -2.9 p~= 0.8 normal [Low1/16]TMFn(2+6):wl R= +0.2 p~= 0.5 normal [Low1/16]TMFn(2+7):wl R= +1.0 p~= 0.4 normal [Low1/32]BCFN(2+0,13-0,T) R= +2.2 p = 0.184 normal [Low1/32]BCFN(2+1,13-0,T) R= +4.8 p = 0.028 normal [Low1/32]BCFN(2+2,13-1,T) R= +0.7 p = 0.376 normal [Low1/32]BCFN(2+3,13-1,T) R= -3.3 p = 0.914 normal [Low1/32]BCFN(2+4,13-1,T) R= -2.2 p = 0.817 normal [Low1/32]BCFN(2+5,13-2,T) R= -1.4 p = 0.706 normal [Low1/32]BCFN(2+6,13-3,T) R= -0.2 p = 0.522 normal [Low1/32]BCFN(2+7,13-3,T) R= -1.8 p = 0.769 normal [Low1/32]BCFN(2+8,13-4,T) R= +1.7 p = 0.236 normal [Low1/32]BCFN(2+9,13-5,T) R= +0.5 p = 0.399 normal [Low1/32]BCFN(2+10,13-5,T) R= +3.0 p = 0.113 normal [Low1/32]BCFN(2+11,13-6,T) R= -1.2 p = 0.675 normal [Low1/32]BCFN(2+12,13-6,T) R= +3.3 p = 0.094 normal [Low1/32]BCFN(2+13,13-7,T) R= +7.2 p = 8.3e-3 normal [Low1/32]BCFN(2+14,13-8,T) R= +6.1 p = 0.018 normal [Low1/32]BCFN(2+15,13-8,T) R= +8.5 p = 4.5e-3 normal [Low1/32]BCFN(2+16,13-9,T) R= +12.7 p = 5.8e-4 normal [Low1/32]BCFN(2+17,13-9,T) R= +6.1 p = 0.019 normal [Low1/32]DC6-9x1Bytes-1 R= +2.8 p = 0.116 normal [Low1/32]Gap-16:A R= +0.7 p = 0.415 normal [Low1/32]Gap-16:B R= -1.2 p = 0.802 normal [Low1/32]FPF-14+6/16:(0,14-0) R= -1.2 p = 0.795 normal [Low1/32]FPF-14+6/16:(1,14-0) R= +0.4 p = 0.394 normal [Low1/32]FPF-14+6/16:(2,14-0) R= -3.0 p = 0.984 normal [Low1/32]FPF-14+6/16:(3,14-0) R= +0.6 p = 0.338 normal [Low1/32]FPF-14+6/16:(4,14-0) R= -1.2 p = 0.795 normal [Low1/32]FPF-14+6/16:(5,14-0) R= -0.8 p = 0.712 normal [Low1/32]FPF-14+6/16:(6,14-0) R= +1.0 p = 0.239 normal [Low1/32]FPF-14+6/16:(7,14-1) R= +0.8 p = 0.289 normal [Low1/32]FPF-14+6/16:(8,14-2) R= +2.0 p = 0.079 normal [Low1/32]FPF-14+6/16:(9,14-2) R= +0.7 p = 0.323 normal [Low1/32]FPF-14+6/16:(10,14-3) R= +0.9 p = 0.262 normal [Low1/32]FPF-14+6/16:(11,14-4) R= +0.6 p = 0.342 normal [Low1/32]FPF-14+6/16:(12,14-5) R= -1.1 p = 0.782 normal [Low1/32]FPF-14+6/16:(13,14-5) R= -2.4 p = 0.959 normal [Low1/32]FPF-14+6/16:(14,14-6) R= +2.7 p = 0.034 normal [Low1/32]FPF-14+6/16:(15,14-7) R= -0.2 p = 0.543 normal [Low1/32]FPF-14+6/16:(16,14-8) R= -0.9 p = 0.724 normal [Low1/32]FPF-14+6/16:(17,14-8) R= -0.9 p = 0.734 normal [Low1/32]FPF-14+6/16:(18,14-9) R= -0.4 p = 0.580 normal [Low1/32]FPF-14+6/16:(19,14-10) R= +0.4 p = 0.358 normal [Low1/32]FPF-14+6/16:(20,14-11) R= +0.6 p = 0.296 normal [Low1/32]FPF-14+6/16:(21,14-11) R= -1.0 p = 0.730 normal [Low1/32]FPF-14+6/16:all R= -0.8 p = 0.730 normal [Low1/32]FPF-14+6/16:cross R= -0.7 p = 0.736 normal [Low1/32]BRank(12):128(8) R= -1.9 p~= 0.990 normal [Low1/32]BRank(12):256(4) R= -0.1 p~= 0.490 normal [Low1/32]BRank(12):384(2) R= -0.2 p~= 0.554 normal [Low1/32]BRank(12):512(4) R= +0.4 p~= 0.340 normal [Low1/32]BRank(12):768(1) R= +1.8 p~= 0.146 normal [Low1/32]BRank(12):1K(2) R= -0.2 p~= 0.554 normal [Low1/32]BRank(12):1536(1) R= -0.7 p~= 0.689 normal [Low1/32]BRank(12):2K(2) R= -0.2 p~= 0.554 normal [Low1/32]BRank(12):3K(1) R= -0.7 p~= 0.689 normal [Low1/32]BRank(12):4K(1) R= +0.4 p~= 0.366 normal [Low1/32]mod3n(5):(0,9-0) R= -2.2 p = 0.861 normal [Low1/32]mod3n(5):(1,9-0) R= +2.0 p = 0.165 normal [Low1/32]mod3n(5):(2,9-0) R= -1.9 p = 0.834 normal [Low1/32]mod3n(5):(3,9-1) R= -0.2 p = 0.544 normal [Low1/32]mod3n(5):(4,9-1) R= +2.2 p = 0.140 normal [Low1/32]mod3n(5):(5,9-2) R= -2.8 p = 0.920 normal [Low1/32]mod3n(5):(6,9-2) R= -2.1 p = 0.860 normal [Low1/32]mod3n(5):(7,9-3) R= +0.2 p = 0.443 normal [Low1/32]mod3n(5):(8,9-3) R= +2.4 p = 0.114 normal [Low1/32]mod3n(5):(9,9-4) R= -1.9 p = 0.832 normal [Low1/32]mod3n(5):(10,9-4) R= -0.2 p = 0.515 normal [Low1/32]mod3n(5):(11,9-5) R= +1.6 p = 0.194 normal [Low1/32]mod3n(5):(12,9-5) R= +0.7 p = 0.322 normal [Low1/32]mod3n(5):(13,9-6) R= -1.8 p = 0.846 normal [Low1/32]mod3n(5):(14,9-6) R= -1.2 p = 0.719 normal [Low1/32]mod3n(5):(15,9-6) R= -2.0 p = 0.882 normal [Low1/32]TMFn(2+0):wl R= +1.5 p~= 0.3 normal [Low1/32]TMFn(2+1):wl R= +0.3 p~= 0.5 normal [Low1/32]TMFn(2+2):wl R= +1.2 p~= 0.3 normal [Low1/32]TMFn(2+3):wl R= -2.9 p~= 0.8 normal [Low1/32]TMFn(2+4):wl R= +0.1 p~= 0.5 normal [Low1/32]TMFn(2+5):wl R= -0.0 p~= 0.5 normal [Low1/32]TMFn(2+6):wl R= +1.2 p~= 0.3 normal [Low1/64]BCFN(2+0,13-1,T) R= +3.9 p = 0.060 normal [Low1/64]BCFN(2+1,13-1,T) R= +1.8 p = 0.223 normal [Low1/64]BCFN(2+2,13-1,T) R= -0.8 p = 0.623 normal [Low1/64]BCFN(2+3,13-1,T) R= -2.5 p = 0.846 normal [Low1/64]BCFN(2+4,13-2,T) R= +2.1 p = 0.192 normal [Low1/64]BCFN(2+5,13-3,T) R= +2.7 p = 0.133 normal [Low1/64]BCFN(2+6,13-3,T) R= -0.5 p = 0.569 normal [Low1/64]BCFN(2+7,13-4,T) R= +2.8 p = 0.125 normal [Low1/64]BCFN(2+8,13-5,T) R= -1.5 p = 0.721 normal [Low1/64]BCFN(2+9,13-5,T) R= +6.2 p = 0.012 normal [Low1/64]BCFN(2+10,13-6,T) R= +6.0 p = 0.016 normal [Low1/64]BCFN(2+11,13-6,T) R= +0.7 p = 0.352 normal [Low1/64]BCFN(2+12,13-7,T) R= +7.0 p = 9.3e-3 normal [Low1/64]BCFN(2+13,13-8,T) R= +4.7 p = 0.042 normal [Low1/64]BCFN(2+14,13-8,T) R= +7.2 p = 9.6e-3 normal [Low1/64]BCFN(2+15,13-9,T) R= +6.4 p = 0.017 normal [Low1/64]BCFN(2+16,13-9,T) R= +3.7 p = 0.068 normal [Low1/64]DC6-9x1Bytes-1 R= +1.7 p = 0.258 normal [Low1/64]Gap-16:A R= +3.0 p = 0.038 normal [Low1/64]Gap-16:B R= +3.0 p = 0.018 normal [Low1/64]FPF-14+6/16:(0,14-0) R= -0.3 p = 0.580 normal [Low1/64]FPF-14+6/16:(1,14-0) R= +1.6 p = 0.130 normal [Low1/64]FPF-14+6/16:(2,14-0) R= -0.3 p = 0.596 normal [Low1/64]FPF-14+6/16:(3,14-0) R= +0.5 p = 0.370 normal [Low1/64]FPF-14+6/16:(4,14-0) R= -1.8 p = 0.897 normal [Low1/64]FPF-14+6/16:(5,14-0) R= -0.5 p = 0.627 normal [Low1/64]FPF-14+6/16:(6,14-1) R= -0.3 p = 0.580 normal [Low1/64]FPF-14+6/16:(7,14-2) R= +1.3 p = 0.191 normal [Low1/64]FPF-14+6/16:(8,14-2) R= -0.6 p = 0.674 normal [Low1/64]FPF-14+6/16:(9,14-3) R= -1.9 p = 0.913 normal [Low1/64]FPF-14+6/16:(10,14-4) R= +2.2 p = 0.062 normal [Low1/64]FPF-14+6/16:(11,14-5) R= -1.5 p = 0.864 normal [Low1/64]FPF-14+6/16:(12,14-5) R= -1.6 p = 0.870 normal [Low1/64]FPF-14+6/16:(13,14-6) R= -0.9 p = 0.722 normal [Low1/64]FPF-14+6/16:(14,14-7) R= -1.6 p = 0.875 normal [Low1/64]FPF-14+6/16:(15,14-8) R= -1.1 p = 0.775 normal [Low1/64]FPF-14+6/16:(16,14-8) R= -1.5 p = 0.866 normal [Low1/64]FPF-14+6/16:(17,14-9) R= +1.2 p = 0.186 normal [Low1/64]FPF-14+6/16:(18,14-10) R= +0.6 p = 0.309 normal [Low1/64]FPF-14+6/16:(19,14-11) R= -0.2 p = 0.474 normal [Low1/64]FPF-14+6/16:(20,14-11) R= +1.0 p = 0.215 normal [Low1/64]FPF-14+6/16:all R= -0.6 p = 0.669 normal [Low1/64]FPF-14+6/16:cross R= +0.7 p = 0.215 normal [Low1/64]BRank(12):128(8) R= -1.1 p~= 0.860 normal [Low1/64]BRank(12):256(4) R= +1.7 p~= 0.060 normal [Low1/64]BRank(12):384(1) R= +0.4 p~= 0.366 normal [Low1/64]BRank(12):512(4) R= -1.4 p~= 0.890 normal [Low1/64]BRank(12):768(1) R= -0.7 p~= 0.689 normal [Low1/64]BRank(12):1K(2) R= -0.2 p~= 0.554 normal [Low1/64]BRank(12):1536(1) R= -0.7 p~= 0.689 normal [Low1/64]BRank(12):2K(2) R= -0.2 p~= 0.554 normal [Low1/64]BRank(12):3K(1) R= +0.4 p~= 0.366 normal [Low1/64]mod3n(5):(0,9-0) R= +2.2 p = 0.140 normal [Low1/64]mod3n(5):(1,9-0) R= -1.8 p = 0.815 normal [Low1/64]mod3n(5):(2,9-1) R= +0.5 p = 0.395 normal [Low1/64]mod3n(5):(3,9-1) R= +0.2 p = 0.459 normal [Low1/64]mod3n(5):(4,9-2) R= +2.0 p = 0.155 normal [Low1/64]mod3n(5):(5,9-2) R= +1.2 p = 0.267 normal [Low1/64]mod3n(5):(6,9-3) R= +4.4 p = 0.019 normal [Low1/64]mod3n(5):(7,9-3) R= +1.5 p = 0.221 normal [Low1/64]mod3n(5):(8,9-4) R= -0.3 p = 0.544 normal [Low1/64]mod3n(5):(9,9-4) R= -1.0 p = 0.677 normal [Low1/64]mod3n(5):(10,9-5) R= -1.1 p = 0.688 normal [Low1/64]mod3n(5):(11,9-5) R= -2.1 p = 0.868 normal [Low1/64]mod3n(5):(12,9-6) R= -0.3 p = 0.501 normal [Low1/64]mod3n(5):(13,9-6) R= -0.1 p = 0.472 normal [Low1/64]mod3n(5):(14,9-6) R= -0.7 p = 0.604 normal [Low1/64]mod3n(5):(15,9-6) R= +2.6 p = 0.091 normal [Low1/64]TMFn(2+0):wl R= -2.8 p~= 0.8 normal [Low1/64]TMFn(2+1):wl R= -0.9 p~= 0.6 normal [Low1/64]TMFn(2+2):wl R= -0.6 p~= 0.6 normal [Low1/64]TMFn(2+3):wl R= -2.1 p~= 0.8 normal [Low1/64]TMFn(2+4):wl R= +0.3 p~= 0.5 normal [Low1/64]TMFn(2+5):wl R= -0.5 p~= 0.6 normal [Low4/16]BCFN(2+0,13-0,T) R= -2.6 p = 0.855 normal [Low4/16]BCFN(2+1,13-0,T) R= -0.8 p = 0.621 normal [Low4/16]BCFN(2+2,13-0,T) R= -3.3 p = 0.912 normal [Low4/16]BCFN(2+3,13-0,T) R= +0.4 p = 0.437 normal [Low4/16]BCFN(2+4,13-0,T) R= +1.0 p = 0.339 normal [Low4/16]BCFN(2+5,13-0,T) R= +3.7 p = 0.066 normal [Low4/16]BCFN(2+6,13-1,T) R= -3.4 p = 0.918 normal [Low4/16]BCFN(2+7,13-1,T) R= +1.2 p = 0.303 normal [Low4/16]BCFN(2+8,13-2,T) R= +2.3 p = 0.173 normal [Low4/16]BCFN(2+9,13-3,T) R= +1.6 p = 0.246 normal [Low4/16]BCFN(2+10,13-3,T) R= -2.1 p = 0.801 normal [Low4/16]BCFN(2+11,13-4,T) R= -3.1 p = 0.906 normal [Low4/16]BCFN(2+12,13-5,T) R= +3.4 p = 0.090 normal [Low4/16]BCFN(2+13,13-5,T) R= -3.5 p = 0.939 normal [Low4/16]BCFN(2+14,13-6,T) R= +4.4 p = 0.047 normal [Low4/16]BCFN(2+15,13-6,T) R= +0.9 p = 0.327 normal [Low4/16]BCFN(2+16,13-7,T) R= +0.3 p = 0.402 normal [Low4/16]BCFN(2+17,13-8,T) R= -0.0 p = 0.437 normal [Low4/16]BCFN(2+18,13-8,T) R= +0.6 p = 0.335 normal [Low4/16]BCFN(2+19,13-9,T) R= +2.3 p = 0.139 normal [Low4/16]BCFN(2+20,13-9,T) R= -2.6 p = 0.945 normal [Low4/16]DC6-9x1Bytes-1 R= +3.6 p = 0.029 normal [Low4/16]Gap-16:A R= +1.0 p = 0.308 normal [Low4/16]Gap-16:B R= -0.4 p = 0.606 normal [Low4/16]FPF-14+6/16:(0,14-0) R= +1.7 p = 0.119 normal [Low4/16]FPF-14+6/16:(1,14-0) R= -2.3 p = 0.946 normal [Low4/16]FPF-14+6/16:(2,14-0) R= +0.1 p = 0.461 normal [Low4/16]FPF-14+6/16:(3,14-0) R= +0.7 p = 0.316 normal [Low4/16]FPF-14+6/16:(4,14-0) R= +2.8 p = 0.024 normal [Low4/16]FPF-14+6/16:(5,14-0) R= -2.0 p = 0.918 normal [Low4/16]FPF-14+6/16:(6,14-0) R= -1.2 p = 0.803 normal [Low4/16]FPF-14+6/16:(7,14-0) R= +1.6 p = 0.137 normal [Low4/16]FPF-14+6/16:(8,14-0) R= -0.0 p = 0.508 normal [Low4/16]FPF-14+6/16:(9,14-0) R= +2.4 p = 0.048 normal [Low4/16]FPF-14+6/16:(10,14-1) R= -0.6 p = 0.672 normal [Low4/16]FPF-14+6/16:(11,14-2) R= +1.0 p = 0.238 normal [Low4/16]FPF-14+6/16:(12,14-2) R= +1.5 p = 0.156 normal [Low4/16]FPF-14+6/16:(13,14-3) R= +0.9 p = 0.269 normal [Low4/16]FPF-14+6/16:(14,14-4) R= -1.3 p = 0.825 normal [Low4/16]FPF-14+6/16:(15,14-5) R= -0.8 p = 0.715 normal [Low4/16]FPF-14+6/16:(16,14-5) R= +1.4 p = 0.156 normal [Low4/16]FPF-14+6/16:(17,14-6) R= +1.6 p = 0.138 normal [Low4/16]FPF-14+6/16:(18,14-7) R= +0.9 p = 0.249 normal [Low4/16]FPF-14+6/16:(19,14-8) R= -1.2 p = 0.799 normal [Low4/16]FPF-14+6/16:(20,14-8) R= +0.8 p = 0.280 normal [Low4/16]FPF-14+6/16:(21,14-9) R= -2.7 p = 0.989 normal [Low4/16]FPF-14+6/16:(22,14-10) R= -0.8 p = 0.691 normal [Low4/16]FPF-14+6/16:(23,14-11) R= -1.0 p = 0.741 normal [Low4/16]FPF-14+6/16:(24,14-11) R= -1.2 p = 0.794 normal [Low4/16]FPF-14+6/16:all R= +1.5 p = 0.155 normal [Low4/16]FPF-14+6/16:cross R= +0.7 p = 0.231 normal [Low4/16]BRank(12):128(8) R= -0.7 p~= 0.750 normal [Low4/16]BRank(12):256(8) R= -1.5 p~= 0.940 normal [Low4/16]BRank(12):384(2) R= -1.0 p~= 0.744 normal [Low4/16]BRank(12):512(4) R= -1.4 p~= 0.890 normal [Low4/16]BRank(12):768(2) R= -1.0 p~= 0.744 normal [Low4/16]BRank(12):1K(4) R= -0.1 p~= 0.490 normal [Low4/16]BRank(12):1536(1) R= +1.8 p~= 0.146 normal [Low4/16]BRank(12):2K(2) R= -1.0 p~= 0.744 normal [Low4/16]BRank(12):3K(1) R= -0.7 p~= 0.689 normal [Low4/16]BRank(12):4K(2) R= -1.0 p~= 0.744 normal [Low4/16]BRank(12):6K(1) R= -0.7 p~= 0.689 normal [Low4/16]BRank(12):8K(1) R= -0.7 p~= 0.689 normal [Low4/16]mod3n(5):(0,9-0) R= -4.5 p = 0.989 normal [Low4/16]mod3n(5):(1,9-0) R= +2.9 p = 0.075 normal [Low4/16]mod3n(5):(2,9-0) R= -0.6 p = 0.621 normal [Low4/16]mod3n(5):(3,9-0) R= +2.8 p = 0.081 normal [Low4/16]mod3n(5):(4,9-0) R= -0.2 p = 0.538 normal [Low4/16]mod3n(5):(5,9-0) R= +2.7 p = 0.094 normal [Low4/16]mod3n(5):(6,9-1) R= -2.3 p = 0.872 normal [Low4/16]mod3n(5):(7,9-1) R= +1.8 p = 0.180 normal [Low4/16]mod3n(5):(8,9-2) R= +2.4 p = 0.120 normal [Low4/16]mod3n(5):(9,9-2) R= +2.8 p = 0.084 normal [Low4/16]mod3n(5):(10,9-3) R= +0.5 p = 0.394 normal [Low4/16]mod3n(5):(11,9-3) R= +5.6 p = 4.5e-3 normal [Low4/16]mod3n(5):(12,9-4) R= +1.4 p = 0.237 normal [Low4/16]mod3n(5):(13,9-4) R= +1.1 p = 0.281 normal [Low4/16]mod3n(5):(14,9-5) R= -1.5 p = 0.779 normal [Low4/16]mod3n(5):(15,9-5) R= +0.8 p = 0.315 normal [Low4/16]TMFn(2+0):wl R= -0.9 p~= 0.6 normal [Low4/16]TMFn(2+1):wl R= -2.5 p~= 0.8 normal [Low4/16]TMFn(2+2):wl R= -1.9 p~= 0.7 normal [Low4/16]TMFn(2+3):wl R= +0.3 p~= 0.5 normal [Low4/16]TMFn(2+4):wl R= +0.6 p~= 0.4 normal [Low4/16]TMFn(2+5):wl R= -0.8 p~= 0.6 normal [Low4/16]TMFn(2+6):wl R= +0.6 p~= 0.4 normal [Low4/16]TMFn(2+7):wl R= +1.0 p~= 0.4 normal [Low4/16]TMFn(2+8):wl R= +0.1 p~= 0.5 normal [Low4/16]TMFn(2+9):wl R= +2.3 p~= 0.2 normal [Low4/32]BCFN(2+0,13-0,T) R= +0.8 p = 0.372 normal [Low4/32]BCFN(2+1,13-0,T) R= +5.1 p = 0.021 normal [Low4/32]BCFN(2+2,13-0,T) R= +2.6 p = 0.144 normal [Low4/32]BCFN(2+3,13-0,T) R= -0.1 p = 0.518 normal [Low4/32]BCFN(2+4,13-0,T) R= -1.4 p = 0.719 normal [Low4/32]BCFN(2+5,13-1,T) R= -2.7 p = 0.870 normal [Low4/32]BCFN(2+6,13-1,T) R= -3.2 p = 0.910 normal [Low4/32]BCFN(2+7,13-2,T) R= -1.1 p = 0.660 normal [Low4/32]BCFN(2+8,13-3,T) R= -4.0 p = 0.955 normal [Low4/32]BCFN(2+9,13-3,T) R= +2.4 p = 0.161 normal [Low4/32]BCFN(2+10,13-4,T) R= +2.7 p = 0.138 normal [Low4/32]BCFN(2+11,13-5,T) R= +4.0 p = 0.058 normal [Low4/32]BCFN(2+12,13-5,T) R= +0.8 p = 0.351 normal [Low4/32]BCFN(2+13,13-6,T) R= -2.8 p = 0.889 normal [Low4/32]BCFN(2+14,13-6,T) R= +2.2 p = 0.172 normal [Low4/32]BCFN(2+15,13-7,T) R= -0.4 p = 0.511 normal [Low4/32]BCFN(2+16,13-8,T) R= -3.0 p = 0.948 normal [Low4/32]BCFN(2+17,13-8,T) R= -2.6 p = 0.898 normal [Low4/32]BCFN(2+18,13-9,T) R= -2.8 p = 0.961 normal [Low4/32]BCFN(2+19,13-9,T) R= -1.5 p = 0.739 normal [Low4/32]DC6-9x1Bytes-1 R= +2.0 p = 0.183 normal [Low4/32]Gap-16:A R= +3.3 p = 0.016 normal [Low4/32]Gap-16:B R= +3.0 p = 0.018 normal [Low4/32]FPF-14+6/16:(0,14-0) R= -1.2 p = 0.812 normal [Low4/32]FPF-14+6/16:(1,14-0) R= -1.0 p = 0.752 normal [Low4/32]FPF-14+6/16:(2,14-0) R= +1.5 p = 0.147 normal [Low4/32]FPF-14+6/16:(3,14-0) R= +1.3 p = 0.189 normal [Low4/32]FPF-14+6/16:(4,14-0) R= +1.1 p = 0.216 normal [Low4/32]FPF-14+6/16:(5,14-0) R= +1.0 p = 0.245 normal [Low4/32]FPF-14+6/16:(6,14-0) R= -0.6 p = 0.670 normal [Low4/32]FPF-14+6/16:(7,14-0) R= -1.5 p = 0.855 normal [Low4/32]FPF-14+6/16:(8,14-0) R= +1.1 p = 0.220 normal [Low4/32]FPF-14+6/16:(9,14-1) R= -1.1 p = 0.795 normal [Low4/32]FPF-14+6/16:(10,14-2) R= -0.1 p = 0.517 normal [Low4/32]FPF-14+6/16:(11,14-2) R= +2.0 p = 0.086 normal [Low4/32]FPF-14+6/16:(12,14-3) R= +1.4 p = 0.170 normal [Low4/32]FPF-14+6/16:(13,14-4) R= +1.9 p = 0.100 normal [Low4/32]FPF-14+6/16:(14,14-5) R= +0.5 p = 0.358 normal [Low4/32]FPF-14+6/16:(15,14-5) R= +0.5 p = 0.352 normal [Low4/32]FPF-14+6/16:(16,14-6) R= -1.3 p = 0.825 normal [Low4/32]FPF-14+6/16:(17,14-7) R= +0.7 p = 0.314 normal [Low4/32]FPF-14+6/16:(18,14-8) R= -0.7 p = 0.689 normal [Low4/32]FPF-14+6/16:(19,14-8) R= -0.2 p = 0.524 normal [Low4/32]FPF-14+6/16:(20,14-9) R= -0.8 p = 0.700 normal [Low4/32]FPF-14+6/16:(21,14-10) R= -1.8 p = 0.925 normal [Low4/32]FPF-14+6/16:(22,14-11) R= +1.8 p = 0.114 normal [Low4/32]FPF-14+6/16:(23,14-11) R= -0.2 p = 0.473 normal [Low4/32]FPF-14+6/16:all R= +0.8 p = 0.294 normal [Low4/32]FPF-14+6/16:cross R= -1.0 p = 0.851 normal [Low4/32]BRank(12):128(8) R= +0.1 p~= 0.450 normal [Low4/32]BRank(12):256(8) R= +1.6 p~= 0.060 normal [Low4/32]BRank(12):384(2) R= -1.0 p~= 0.744 normal [Low4/32]BRank(12):512(4) R= -1.4 p~= 0.890 normal [Low4/32]BRank(12):768(1) R= +0.4 p~= 0.366 normal [Low4/32]BRank(12):1K(4) R= -0.8 p~= 0.670 normal [Low4/32]BRank(12):1536(1) R= -0.7 p~= 0.689 normal [Low4/32]BRank(12):2K(2) R= -0.2 p~= 0.554 normal [Low4/32]BRank(12):3K(1) R= -0.7 p~= 0.689 normal [Low4/32]BRank(12):4K(2) R= -0.2 p~= 0.554 normal [Low4/32]BRank(12):6K(1) R= -0.7 p~= 0.689 normal [Low4/32]mod3n(5):(0,9-0) R= -1.2 p = 0.729 normal [Low4/32]mod3n(5):(1,9-0) R= -2.7 p = 0.912 normal [Low4/32]mod3n(5):(2,9-0) R= -0.1 p = 0.528 normal [Low4/32]mod3n(5):(3,9-0) R= +1.2 p = 0.283 normal [Low4/32]mod3n(5):(4,9-0) R= +3.6 p = 0.039 normal [Low4/32]mod3n(5):(5,9-1) R= -3.8 p = 0.974 normal [Low4/32]mod3n(5):(6,9-1) R= +2.1 p = 0.145 normal [Low4/32]mod3n(5):(7,9-2) R= -0.1 p = 0.519 normal [Low4/32]mod3n(5):(8,9-2) R= +0.7 p = 0.351 normal [Low4/32]mod3n(5):(9,9-3) R= +0.6 p = 0.367 normal [Low4/32]mod3n(5):(10,9-3) R= +1.1 p = 0.289 normal [Low4/32]mod3n(5):(11,9-4) R= +0.7 p = 0.354 normal [Low4/32]mod3n(5):(12,9-4) R= +1.1 p = 0.281 normal [Low4/32]mod3n(5):(13,9-5) R= -1.4 p = 0.752 normal [Low4/32]mod3n(5):(14,9-5) R= +0.1 p = 0.450 normal [Low4/32]mod3n(5):(15,9-6) R= -1.6 p = 0.798 normal [Low4/32]TMFn(2+0):wl R= -2.0 p~= 0.8 normal [Low4/32]TMFn(2+1):wl R= -0.6 p~= 0.6 normal [Low4/32]TMFn(2+2):wl R= +2.0 p~= 0.2 normal [Low4/32]TMFn(2+3):wl R= +1.6 p~= 0.3 normal [Low4/32]TMFn(2+4):wl R= -3.0 p~= 0.8 normal [Low4/32]TMFn(2+5):wl R= -0.0 p~= 0.5 normal [Low4/32]TMFn(2+6):wl R= -1.2 p~= 0.7 normal [Low4/32]TMFn(2+7):wl R= +1.7 p~= 0.3 normal [Low4/32]TMFn(2+8):wl R= +2.5 p~= 0.2 normal [Low4/64]BCFN(2+0,13-0,T) R= +1.2 p = 0.307 normal [Low4/64]BCFN(2+1,13-0,T) R= -5.5 p = 0.989 normal [Low4/64]BCFN(2+2,13-0,T) R= -2.5 p = 0.847 normal [Low4/64]BCFN(2+3,13-0,T) R= +1.3 p = 0.294 normal [Low4/64]BCFN(2+4,13-1,T) R= +2.1 p = 0.198 normal [Low4/64]BCFN(2+5,13-1,T) R= -0.9 p = 0.635 normal [Low4/64]BCFN(2+6,13-2,T) R= -3.0 p = 0.894 normal [Low4/64]BCFN(2+7,13-3,T) R= -1.7 p = 0.746 normal [Low4/64]BCFN(2+8,13-3,T) R= +0.2 p = 0.453 normal [Low4/64]BCFN(2+9,13-4,T) R= -3.1 p = 0.908 normal [Low4/64]BCFN(2+10,13-5,T) R= -1.7 p = 0.746 normal [Low4/64]BCFN(2+11,13-5,T) R= -2.0 p = 0.794 normal [Low4/64]BCFN(2+12,13-6,T) R= -1.1 p = 0.651 normal [Low4/64]BCFN(2+13,13-6,T) R= -2.0 p = 0.790 normal [Low4/64]BCFN(2+14,13-7,T) R= -1.4 p = 0.708 normal [Low4/64]BCFN(2+15,13-8,T) R= +1.6 p = 0.213 normal [Low4/64]BCFN(2+16,13-8,T) R= -0.4 p = 0.506 normal [Low4/64]BCFN(2+17,13-9,T) R= +1.4 p = 0.212 normal [Low4/64]BCFN(2+18,13-9,T) R= +4.4 p = 0.046 normal [Low4/64]DC6-9x1Bytes-1 R= -0.6 p = 0.699 normal [Low4/64]Gap-16:A R= +1.4 p = 0.220 normal [Low4/64]Gap-16:B R= +4.6 p = 7.2e-4 normalish [Low4/64]FPF-14+6/16:(0,14-0) R= -0.5 p = 0.635 normal [Low4/64]FPF-14+6/16:(1,14-0) R= +1.7 p = 0.121 normal [Low4/64]FPF-14+6/16:(2,14-0) R= -1.7 p = 0.892 normal [Low4/64]FPF-14+6/16:(3,14-0) R= -0.9 p = 0.731 normal [Low4/64]FPF-14+6/16:(4,14-0) R= +3.2 p = 0.012 normal [Low4/64]FPF-14+6/16:(5,14-0) R= -1.0 p = 0.764 normal [Low4/64]FPF-14+6/16:(6,14-0) R= +1.5 p = 0.145 normal [Low4/64]FPF-14+6/16:(7,14-0) R= +1.2 p = 0.208 normal [Low4/64]FPF-14+6/16:(8,14-1) R= +0.2 p = 0.461 normal [Low4/64]FPF-14+6/16:(9,14-2) R= -1.4 p = 0.845 normal [Low4/64]FPF-14+6/16:(10,14-2) R= +1.5 p = 0.143 normal [Low4/64]FPF-14+6/16:(11,14-3) R= -0.6 p = 0.678 normal [Low4/64]FPF-14+6/16:(12,14-4) R= +0.4 p = 0.382 normal [Low4/64]FPF-14+6/16:(13,14-5) R= -2.0 p = 0.928 normal [Low4/64]FPF-14+6/16:(14,14-5) R= +0.1 p = 0.464 normal [Low4/64]FPF-14+6/16:(15,14-6) R= +0.4 p = 0.392 normal [Low4/64]FPF-14+6/16:(16,14-7) R= -0.5 p = 0.633 normal [Low4/64]FPF-14+6/16:(17,14-8) R= -1.9 p = 0.917 normal [Low4/64]FPF-14+6/16:(18,14-8) R= -2.2 p = 0.950 normal [Low4/64]FPF-14+6/16:(19,14-9) R= +0.1 p = 0.437 normal [Low4/64]FPF-14+6/16:(20,14-10) R= -0.9 p = 0.721 normal [Low4/64]FPF-14+6/16:(21,14-11) R= +0.8 p = 0.248 normal [Low4/64]FPF-14+6/16:(22,14-11) R= +3.5 p = 0.023 normal [Low4/64]FPF-14+6/16:all R= +1.0 p = 0.261 normal [Low4/64]FPF-14+6/16:cross R= -1.1 p = 0.867 normal [Low4/64]BRank(12):128(8) R= +0.5 p~= 0.300 normal [Low4/64]BRank(12):256(4) R= -0.2 p~= 0.500 normal [Low4/64]BRank(12):384(2) R= +0.8 p~= 0.293 normal [Low4/64]BRank(12):512(4) R= -1.4 p~= 0.890 normal [Low4/64]BRank(12):768(1) R= +0.4 p~= 0.366 normal [Low4/64]BRank(12):1K(2) R= -1.0 p~= 0.744 normal [Low4/64]BRank(12):1536(1) R= +0.4 p~= 0.366 normal [Low4/64]BRank(12):2K(2) R= -1.0 p~= 0.744 normal [Low4/64]BRank(12):3K(1) R= +0.4 p~= 0.366 normal [Low4/64]BRank(12):4K(1) R= -0.7 p~= 0.689 normal [Low4/64]mod3n(5):(0,9-0) R= -0.1 p = 0.514 normal [Low4/64]mod3n(5):(1,9-0) R= +0.7 p = 0.358 normal [Low4/64]mod3n(5):(2,9-0) R= -0.1 p = 0.515 normal [Low4/64]mod3n(5):(3,9-0) R= +0.1 p = 0.489 normal [Low4/64]mod3n(5):(4,9-1) R= +1.9 p = 0.173 normal [Low4/64]mod3n(5):(5,9-1) R= -0.8 p = 0.654 normal [Low4/64]mod3n(5):(6,9-2) R= +0.8 p = 0.346 normal [Low4/64]mod3n(5):(7,9-2) R= +3.3 p = 0.052 normal [Low4/64]mod3n(5):(8,9-3) R= -2.2 p = 0.870 normal [Low4/64]mod3n(5):(9,9-3) R= -1.4 p = 0.760 normal [Low4/64]mod3n(5):(10,9-4) R= +1.0 p = 0.290 normal [Low4/64]mod3n(5):(11,9-4) R= +2.5 p = 0.108 normal [Low4/64]mod3n(5):(12,9-5) R= +1.4 p = 0.216 normal [Low4/64]mod3n(5):(13,9-5) R= +1.1 p = 0.258 normal [Low4/64]mod3n(5):(14,9-6) R= +0.6 p = 0.323 normal [Low4/64]mod3n(5):(15,9-6) R= +0.3 p = 0.376 normal [Low4/64]TMFn(2+0):wl R= -1.8 p~= 0.7 normal [Low4/64]TMFn(2+1):wl R= +0.1 p~= 0.5 normal [Low4/64]TMFn(2+2):wl R= +1.0 p~= 0.4 normal [Low4/64]TMFn(2+3):wl R= -3.0 p~= 0.8 normal [Low4/64]TMFn(2+4):wl R= -0.3 p~= 0.5 normal [Low4/64]TMFn(2+5):wl R= -0.6 p~= 0.6 normal [Low4/64]TMFn(2+6):wl R= +2.5 p~= 0.2 normal [Low4/64]TMFn(2+7):wl R= +4.3 p~= 0.1 normal [Low8/32]BCFN(2+0,13-0,T) R= -2.5 p = 0.846 normal [Low8/32]BCFN(2+1,13-0,T) R= +2.1 p = 0.192 normal [Low8/32]BCFN(2+2,13-0,T) R= +1.4 p = 0.286 normal [Low8/32]BCFN(2+3,13-0,T) R= +1.9 p = 0.217 normal [Low8/32]BCFN(2+4,13-0,T) R= +0.3 p = 0.442 normal [Low8/32]BCFN(2+5,13-0,T) R= -1.4 p = 0.719 normal [Low8/32]BCFN(2+6,13-1,T) R= +1.5 p = 0.267 normal [Low8/32]BCFN(2+7,13-1,T) R= +3.1 p = 0.108 normal [Low8/32]BCFN(2+8,13-2,T) R= +0.9 p = 0.347 normal [Low8/32]BCFN(2+9,13-3,T) R= +5.8 p = 0.013 normal [Low8/32]BCFN(2+10,13-3,T) R= -2.3 p = 0.832 normal [Low8/32]BCFN(2+11,13-4,T) R= +2.2 p = 0.183 normal [Low8/32]BCFN(2+12,13-5,T) R= -2.8 p = 0.881 normal [Low8/32]BCFN(2+13,13-5,T) R= -1.1 p = 0.658 normal [Low8/32]BCFN(2+14,13-6,T) R= -0.1 p = 0.478 normal [Low8/32]BCFN(2+15,13-6,T) R= +2.6 p = 0.142 normal [Low8/32]BCFN(2+16,13-7,T) R= -2.3 p = 0.844 normal [Low8/32]BCFN(2+17,13-8,T) R= +1.7 p = 0.206 normal [Low8/32]BCFN(2+18,13-8,T) R= -0.6 p = 0.538 normal [Low8/32]BCFN(2+19,13-9,T) R= -1.9 p = 0.813 normal [Low8/32]BCFN(2+20,13-9,T) R= -1.2 p = 0.673 normal [Low8/32]DC6-9x1Bytes-1 R= -0.0 p = 0.542 normal [Low8/32]Gap-16:A R= -0.2 p = 0.627 normal [Low8/32]Gap-16:B R= +0.1 p = 0.470 normal [Low8/32]FPF-14+6/16:(0,14-0) R= +0.8 p = 0.281 normal [Low8/32]FPF-14+6/16:(1,14-0) R= -1.6 p = 0.874 normal [Low8/32]FPF-14+6/16:(2,14-0) R= -2.7 p = 0.973 normal [Low8/32]FPF-14+6/16:(3,14-0) R= +1.4 p = 0.157 normal [Low8/32]FPF-14+6/16:(4,14-0) R= +0.3 p = 0.428 normal [Low8/32]FPF-14+6/16:(5,14-0) R= -1.1 p = 0.774 normal [Low8/32]FPF-14+6/16:(6,14-0) R= +0.7 p = 0.317 normal [Low8/32]FPF-14+6/16:(7,14-0) R= -0.1 p = 0.516 normal [Low8/32]FPF-14+6/16:(8,14-0) R= -1.9 p = 0.916 normal [Low8/32]FPF-14+6/16:(9,14-0) R= +1.5 p = 0.152 normal [Low8/32]FPF-14+6/16:(10,14-1) R= -1.1 p = 0.795 normal [Low8/32]FPF-14+6/16:(11,14-2) R= +0.1 p = 0.477 normal [Low8/32]FPF-14+6/16:(12,14-2) R= -1.6 p = 0.876 normal [Low8/32]FPF-14+6/16:(13,14-3) R= -1.5 p = 0.857 normal [Low8/32]FPF-14+6/16:(14,14-4) R= -0.5 p = 0.645 normal [Low8/32]FPF-14+6/16:(15,14-5) R= +1.2 p = 0.201 normal [Low8/32]FPF-14+6/16:(16,14-5) R= +1.2 p = 0.205 normal [Low8/32]FPF-14+6/16:(17,14-6) R= -1.8 p = 0.898 normal [Low8/32]FPF-14+6/16:(18,14-7) R= -0.1 p = 0.520 normal [Low8/32]FPF-14+6/16:(19,14-8) R= +0.8 p = 0.278 normal [Low8/32]FPF-14+6/16:(20,14-8) R= -0.4 p = 0.591 normal [Low8/32]FPF-14+6/16:(21,14-9) R= +1.9 p = 0.097 normal [Low8/32]FPF-14+6/16:(22,14-10) R= -0.1 p = 0.489 normal [Low8/32]FPF-14+6/16:(23,14-11) R= +0.5 p = 0.314 normal [Low8/32]FPF-14+6/16:(24,14-11) R= +0.0 p = 0.426 normal [Low8/32]FPF-14+6/16:all R= -1.3 p = 0.840 normal [Low8/32]FPF-14+6/16:cross R= +0.9 p = 0.180 normal [Low8/32]BRank(12):128(8) R= +0.5 p~= 0.300 normal [Low8/32]BRank(12):256(8) R= +0.6 p~= 0.250 normal [Low8/32]BRank(12):384(2) R= -1.0 p~= 0.744 normal [Low8/32]BRank(12):512(4) R= -1.4 p~= 0.890 normal [Low8/32]BRank(12):768(2) R= -0.2 p~= 0.554 normal [Low8/32]BRank(12):1K(4) R= -0.8 p~= 0.670 normal [Low8/32]BRank(12):1536(1) R= -0.7 p~= 0.689 normal [Low8/32]BRank(12):2K(2) R= +0.8 p~= 0.293 normal [Low8/32]BRank(12):3K(1) R= -0.7 p~= 0.689 normal [Low8/32]BRank(12):4K(2) R= -0.2 p~= 0.554 normal [Low8/32]BRank(12):6K(1) R= -0.7 p~= 0.689 normal [Low8/32]BRank(12):8K(1) R= +0.4 p~= 0.366 normal [Low8/32]mod3n(5):(0,9-0) R= -0.6 p = 0.615 normal [Low8/32]mod3n(5):(1,9-0) R= -0.0 p = 0.512 normal [Low8/32]mod3n(5):(2,9-0) R= -0.0 p = 0.504 normal [Low8/32]mod3n(5):(3,9-0) R= +0.6 p = 0.377 normal [Low8/32]mod3n(5):(4,9-0) R= +2.0 p = 0.163 normal [Low8/32]mod3n(5):(5,9-0) R= +0.8 p = 0.339 normal [Low8/32]mod3n(5):(6,9-1) R= +0.2 p = 0.455 normal [Low8/32]mod3n(5):(7,9-1) R= -0.6 p = 0.612 normal [Low8/32]mod3n(5):(8,9-2) R= -1.3 p = 0.744 normal [Low8/32]mod3n(5):(9,9-2) R= -0.1 p = 0.510 normal [Low8/32]mod3n(5):(10,9-3) R= -1.7 p = 0.796 normal [Low8/32]mod3n(5):(11,9-3) R= +2.8 p = 0.087 normal [Low8/32]mod3n(5):(12,9-4) R= +0.9 p = 0.315 normal [Low8/32]mod3n(5):(13,9-4) R= -1.0 p = 0.676 normal [Low8/32]mod3n(5):(14,9-5) R= -3.5 p = 0.982 normal [Low8/32]mod3n(5):(15,9-5) R= -1.8 p = 0.827 normal [Low8/32]TMFn(2+0):wl R= +0.7 p~= 0.4 normal [Low8/32]TMFn(2+1):wl R= +0.5 p~= 0.4 normal [Low8/32]TMFn(2+2):wl R= +0.5 p~= 0.4 normal [Low8/32]TMFn(2+3):wl R= +2.5 p~= 0.2 normal [Low8/32]TMFn(2+4):wl R= +0.3 p~= 0.4 normal [Low8/32]TMFn(2+5):wl R= -3.7 p~= 0.9 normal [Low8/32]TMFn(2+6):wl R= -0.4 p~= 0.6 normal [Low8/32]TMFn(2+7):wl R= +1.1 p~= 0.3 normal [Low8/32]TMFn(2+8):wl R= -0.8 p~= 0.6 normal [Low8/32]TMFn(2+9):wl R= +1.4 p~= 0.3 normal [Low8/64]BCFN(2+0,13-0,T) R= -3.1 p = 0.900 normal [Low8/64]BCFN(2+1,13-0,T) R= +0.5 p = 0.419 normal [Low8/64]BCFN(2+2,13-0,T) R= -0.3 p = 0.547 normal [Low8/64]BCFN(2+3,13-0,T) R= +3.1 p = 0.101 normal [Low8/64]BCFN(2+4,13-0,T) R= +2.3 p = 0.170 normal [Low8/64]BCFN(2+5,13-1,T) R= -1.8 p = 0.762 normal [Low8/64]BCFN(2+6,13-1,T) R= -1.7 p = 0.753 normal [Low8/64]BCFN(2+7,13-2,T) R= -0.6 p = 0.592 normal [Low8/64]BCFN(2+8,13-3,T) R= +0.3 p = 0.439 normal [Low8/64]BCFN(2+9,13-3,T) R= +3.8 p = 0.067 normal [Low8/64]BCFN(2+10,13-4,T) R= -0.9 p = 0.630 normal [Low8/64]BCFN(2+11,13-5,T) R= -1.1 p = 0.657 normal [Low8/64]BCFN(2+12,13-5,T) R= -1.1 p = 0.653 normal [Low8/64]BCFN(2+13,13-6,T) R= +0.4 p = 0.406 normal [Low8/64]BCFN(2+14,13-6,T) R= -3.6 p = 0.953 normal [Low8/64]BCFN(2+15,13-7,T) R= -2.0 p = 0.795 normal [Low8/64]BCFN(2+16,13-8,T) R= -2.2 p = 0.837 normal [Low8/64]BCFN(2+17,13-8,T) R= -0.5 p = 0.516 normal [Low8/64]BCFN(2+18,13-9,T) R= +1.0 p = 0.267 normal [Low8/64]BCFN(2+19,13-9,T) R= -0.5 p = 0.506 normal [Low8/64]DC6-9x1Bytes-1 R= -1.7 p = 0.867 normal [Low8/64]Gap-16:A R= -0.7 p = 0.739 normal [Low8/64]Gap-16:B R= +1.4 p = 0.162 normal [Low8/64]FPF-14+6/16:(0,14-0) R= -0.9 p = 0.728 normal [Low8/64]FPF-14+6/16:(1,14-0) R= -1.3 p = 0.820 normal [Low8/64]FPF-14+6/16:(2,14-0) R= +1.9 p = 0.093 normal [Low8/64]FPF-14+6/16:(3,14-0) R= -1.2 p = 0.797 normal [Low8/64]FPF-14+6/16:(4,14-0) R= -0.8 p = 0.726 normal [Low8/64]FPF-14+6/16:(5,14-0) R= -1.9 p = 0.912 normal [Low8/64]FPF-14+6/16:(6,14-0) R= +2.5 p = 0.041 normal [Low8/64]FPF-14+6/16:(7,14-0) R= +0.8 p = 0.290 normal [Low8/64]FPF-14+6/16:(8,14-0) R= +1.5 p = 0.145 normal [Low8/64]FPF-14+6/16:(9,14-1) R= +1.3 p = 0.176 normal [Low8/64]FPF-14+6/16:(10,14-2) R= -0.1 p = 0.526 normal [Low8/64]FPF-14+6/16:(11,14-2) R= -0.8 p = 0.709 normal [Low8/64]FPF-14+6/16:(12,14-3) R= -0.4 p = 0.600 normal [Low8/64]FPF-14+6/16:(13,14-4) R= +0.4 p = 0.380 normal [Low8/64]FPF-14+6/16:(14,14-5) R= -0.9 p = 0.744 normal [Low8/64]FPF-14+6/16:(15,14-5) R= +1.4 p = 0.170 normal [Low8/64]FPF-14+6/16:(16,14-6) R= -0.8 p = 0.718 normal [Low8/64]FPF-14+6/16:(17,14-7) R= +0.0 p = 0.473 normal [Low8/64]FPF-14+6/16:(18,14-8) R= +0.7 p = 0.293 normal [Low8/64]FPF-14+6/16:(19,14-8) R= -2.2 p = 0.954 normal [Low8/64]FPF-14+6/16:(20,14-9) R= +1.8 p = 0.114 normal [Low8/64]FPF-14+6/16:(21,14-10) R= -0.2 p = 0.520 normal [Low8/64]FPF-14+6/16:(22,14-11) R= +2.1 p = 0.087 normal [Low8/64]FPF-14+6/16:(23,14-11) R= -1.1 p = 0.773 normal [Low8/64]FPF-14+6/16:all R= +0.3 p = 0.423 normal [Low8/64]FPF-14+6/16:cross R= -1.0 p = 0.856 normal [Low8/64]BRank(12):128(8) R= -0.3 p~= 0.500 normal [Low8/64]BRank(12):256(8) R= +0.1 p~= 0.450 normal [Low8/64]BRank(12):384(2) R= +0.6 p~= 0.322 normal [Low8/64]BRank(12):512(4) R= -0.1 p~= 0.490 normal [Low8/64]BRank(12):768(1) R= -0.7 p~= 0.689 normal [Low8/64]BRank(12):1K(4) R= -0.8 p~= 0.670 normal [Low8/64]BRank(12):1536(1) R= -0.7 p~= 0.689 normal [Low8/64]BRank(12):2K(2) R= -0.2 p~= 0.554 normal [Low8/64]BRank(12):3K(1) R= +0.4 p~= 0.366 normal [Low8/64]BRank(12):4K(2) R= -0.2 p~= 0.554 normal [Low8/64]BRank(12):6K(1) R= -0.7 p~= 0.689 normal [Low8/64]mod3n(5):(0,9-0) R= +4.7 p = 0.011 normal [Low8/64]mod3n(5):(1,9-0) R= -1.2 p = 0.727 normal [Low8/64]mod3n(5):(2,9-0) R= -0.3 p = 0.553 normal [Low8/64]mod3n(5):(3,9-0) R= +0.9 p = 0.327 normal [Low8/64]mod3n(5):(4,9-0) R= +1.6 p = 0.219 normal [Low8/64]mod3n(5):(5,9-1) R= +0.2 p = 0.462 normal [Low8/64]mod3n(5):(6,9-1) R= -1.4 p = 0.760 normal [Low8/64]mod3n(5):(7,9-2) R= +1.0 p = 0.302 normal [Low8/64]mod3n(5):(8,9-2) R= +2.8 p = 0.088 normal [Low8/64]mod3n(5):(9,9-3) R= -2.8 p = 0.925 normal [Low8/64]mod3n(5):(10,9-3) R= -0.4 p = 0.575 normal [Low8/64]mod3n(5):(11,9-4) R= -1.6 p = 0.784 normal [Low8/64]mod3n(5):(12,9-4) R= -0.8 p = 0.642 normal [Low8/64]mod3n(5):(13,9-5) R= -0.2 p = 0.500 normal [Low8/64]mod3n(5):(14,9-5) R= +1.9 p = 0.158 normal [Low8/64]mod3n(5):(15,9-6) R= +1.0 p = 0.261 normal [Low8/64]TMFn(2+0):wl R= -0.7 p~= 0.6 normal [Low8/64]TMFn(2+1):wl R= -3.3 p~= 0.8 normal [Low8/64]TMFn(2+2):wl R= +3.6 p~= 0.1 normal [Low8/64]TMFn(2+3):wl R= +2.3 p~= 0.2 normal [Low8/64]TMFn(2+4):wl R= -2.4 p~= 0.8 normal [Low8/64]TMFn(2+5):wl R= -1.0 p~= 0.6 normal [Low8/64]TMFn(2+6):wl R= +0.6 p~= 0.4 normal [Low8/64]TMFn(2+7):wl R= +3.0 p~= 0.2 normal [Low8/64]TMFn(2+8):wl R= +2.3 p~= 0.2 normalPracRand was advertised by pcg-random.com and according to it's docs outperforms dieharder and testu01 in it's analysis. I mainly choose it because it was already prebuild for windows and I did not have to switch to linux to build the other tools myself. You are more than welcome to go ahead and run benchmarks usingTestU01 orDieharder and report back.
Performed with OpenJDKsjmh benchmark harness testing the throughput ofnextInt. Higher numbers are betterJmh parameters
- Single:
java -jar benchmarks.jar -f 5 -tu us -w15 - Multi:
java -jar benchmarks.jar -f 5 -tu us -w15 -t 4 -e "Fast|Splittable"
wmic:root\cli>cpu get caption, name, numberofcores, maxclockspeedCaption MaxClockSpeed Name NumberOfCoresIntel64 Family 6 Model 94 Stepping 3 3301 Intel(R) Core(TM) i5-6600 CPU @ 3.30GHz 4
| RNG | Mode | Cnt | Score | Error | Units |
|---|---|---|---|---|---|
| JdkRandom | thrpt | 25 | 104,803 | ± 0,955 | ops/us |
| JdkSplittable | thrpt | 25 | 307,956 | ± 6,684 | ops/us |
| MersenneTwister | thrpt | 25 | 127,690 | ± 0,854 | ops/us |
| MersenneTwisterFast | thrpt | 25 | 163,238 | ± 2,404 | ops/us |
| PcgRR | thrpt | 25 | 215,295 | ± 2,442 | ops/us |
| PcgRS | thrpt | 25 | 216,910 | ± 1,022 | ops/us |
| PcgRSFast | thrpt | 25 | 326,687 | ± 1,587 | ops/us |
| PcgRSUFast | thrpt | 25 | 335,159 | ± 1,381 | ops/us |
Be aware of the axis scales. The PCG family performs really well in single threaded environments. In multithreading the CAS instruction is capping the execution speed. Note that while JdkRandom and PCU's are thread safe they rely on Compare And Swap instructions which, if contested (higher contention) result in a lower throughput (In other words the more threads try to access a thread safe instance the slower it will overall get).
Next take a look at the thread safe implementation under high congestion (the synchronized block, lock or cas instructions are constantly contested).As you can see under really high stress the locked version performs the best, but does it really warrant the trade off to be more than 4 times slowerif it does not get raced? Probably not but it has to be decided on a case by case basis.
To avoid object creation overhead a good way to implement high throughput rngs for multi threaded environments is to use make use of the PcgRSFast implementation combined with theThreadlocal class instance to be used within executor pools. (TODO link to GA for example)
The code is provided as is with no guarantee on correct implementation or liability. Please check it for yourself and if you find any errors open an issue and optionally a pull request. It would be nice if you let me know if the code was to use for your.