Random/LFSR on P2

1232426282977

Comments

  • evanhevanh Posts: 7,502
    edited 2017-10-27 - 11:33:33
    evanh wrote: »
    I've arbitrarily tried a few of those ideas myself. Most end up with total fails on Practrand, some have given equivalent quality ... hmm, I've not tried to use all bits at once though, since that part I'd long moved outside the generator code. Good point, I'll have another fiddle ...

    Tony,
    Ha! That was silly of me, not doing a non-truncated scoring run. Turns out I had succeeded there all by myself. Here's two score tables. The first table is of the regular Xoroshiro algorithm with simple summing of the two halves of the state.

    The second table is one of my earlier spins, a couple of weeks back last weekend, from your prompting - The iterator hasn't changed but the summing gets dynamically modified. It sums the two halves still but a copy of the state is rotated based on high three bits of s1 before the summing.

    PS: Word0 is the full summing, without any truncation, that produces complete 16-bit results for every iteration.
      Xoroshiro32+ PractRand Score Table - Run 2017-10-27 23:25:54 +1300
    
    Combination    Word0   Word1   Word2  msByte  Byte04   Byte2   Byte1   msBit
    =============================================================================
     [ 1  2  8]    512K     32M     64M     16M     64M     64M     32M      1G
     [ 2  1 11]    512K      8M      8M    128K    128K    128K    256K      1G
     [ 2  1 15]     64K    128K    128K     32K     32K     64K     32K      1G
     [ 2  2  7]    512K      8M      8M     32M     32M     32M      4M      1G
     [ 2  6 15]    512K      2M      4M     16M    128K    128K    128K      1G
     [ 2  8  7]    512K      8M     16M    128M     32M     32M      4M      1G
     [ 2  9  9]    256K    256K    256K     16K    128K    512K     64M      1G
     [ 2 11  3]    512K      2M      4M    512K    256K    256K    256K      1G
     [ 3  2  6]    512K     64M     32M      2M      2M      2M      1M      1G
     [ 3  3 10]    512K     16M     16M    256K    256K    512K     64M      1G
     [ 3 11  2]    256K    256K    512K    128K     64K     64K     64K      1G
     [ 3 11 14]    512K      4M      4M    256K    256K    512K    512K      1G
     [ 4  1  9]    512K    512K      1M    512K      8M    256K    512K    512M
     [ 4  7 15]    512K     64M     64M    128M    512K    512K    512K      1G
     [ 4  8  5]    512K    512M    128M     32M      8M      4M      2M      1G
     [ 5  2  6]    512K    128M    128M      8M      4M      4M      4M      1G
     [ 5  8  4]    512K      4M     16M      4M      1M    256K    128K     64M
     [ 5 14 12]    512K    128M     64M      2M      4M     16M    128M      1G
     [ 6  2  3]    512K     32M     32M      1M      1M      1M      2M      2M
     [ 6  2  5]    512K     16M     16M    256K    512K    512K    512K      4M
     [ 6  2 11]    512K    512M    256M      8M      8M    256M    128M      1G
     [ 6  3 15]    512K     32M     32M      1M      1M      2M      4M      1G
     [ 6 14 11]    512K    128M    128M     32M     64M    128M     16M      1G
     [ 7  1  8]    512K     64M    128M     16M    128M     16M     16M      1G
     [ 7  2  2]    512K     16M     16M      2M      2M      4M      4M      4M
     [ 7  2 10]    512K      1G    512M    128M    256M     64M     32M      1G
     [ 7  2 14]    512K    512M    256M      4M      8M     32M     32M    256M
     [ 7  8  2]    512K    512M    512M     64M      8M      4M      4M    512M
     [ 7 10 10]    512K    128M    256M     32M     32M    256M    128M      1G
     [ 7 15  8]    512K      2M      2M    256K      1M    512K    256K      1G
     [ 8  1  7]    512K      1M      4M      1M      1M      1M      1M     64M
     [ 8  2  1]    512K     32M     64M      8M      8M     16M     16M     16M
     [ 8  5 13]    512K     32M     64M     16M      8M    128M    128M      1G
     [ 8  7 15]    512K      2M      2M    512K      2M      2M      1M      1G
     [ 8  9 13]    512K    512M    128M    512M      1G    512M    128M      1G
     [ 8 15  7]    256K    512K      1M    256K    512K    512K    256K      1G
     [ 9  1  4]    512K     32M     64M      8M     16M     16M     16M     64M
     [ 9  2 14]    512K      2G      1G    128M    256M     64M    128M      1G
     [ 9  8 14]    512K     16M     32M    256M     32M     32M     64M      1G
     [ 9  9  2]    512K     32M     64M     16M     16M     16M     32M     64M
     [10  2  7]    512K    256M    128M     16M     16M     64M     32M      1G
     [10  3  3]    512K     64M     64M     32M     32M     32M     64M    256M
     [10  3 11]    512K      2G      1G    256M    256M    512M    128M      1G
     [10  5 13]    512K      2G    512M      1G    512M    256M    128M    512M
     [10  7 11]    512K    512M    128M    512M    128M    512M    128M      1G
     [10 10  7]    512K     16M     16M     16M     16M    512M    128M    512M
     [11  1  2]    512K    256M    256M     32M     32M     32M     32M      1G
     [11  1 14]    512K      1G      1G     32M     16M     16M     16M      1G
     [11  2  6]    512K    512M    512M     32M     64M    512M    128M    512M
     [11  3 10]    512K     32M     32M     64M      1M    128K     64K    128M
     [11  7 10]    256K      4M      8M     32M    128K    128K     64K      1G
     [11  8 12]    512K    256M    256M    512M    512M    512M    128M      1G
     [11 10 12]    512K    128M    128M      1G    512M    512M    128M      1G
     [11 11 14]    512K     64M    128M     16M     16M     16M      8M      1G
     [11 14  6]    512K    256M    128M    256M     64M    512M    128M      1G
     [12  4 15]    512K    512M      1G    128M     64M     16M     16M      1G
     [12  8 11]    256K      4M      4M     64M    128K    128K     64K      1G
     [12 10 11]    512K      2M      2M    128K    128K    128K     64K      1G
     [12 10 13]    512K     32M     64M     16M     16M     32M      8M      1G
     [12 14  5]    512K     32M     32M    128M    128M     64M     64M      1G
     [13  3 14]    512K    512M    512M     64M     32M     16M      8M      1G
     [13  5  8]    512K    256M    256M    512M    128M    256M    128M      1G
     [13  5 10]    512K     64M     32M     64M     16M    256K    256K      1G
     [13  9  8]    512K    128M     64M    512M    512M    512M    128M      1G
     [13 10 12]    512K      2M      2M    128K    128K    128K     64K    512M
     [13 11 14]    512K     16M     16M      8M      8M      8M      8M      1G
     [13 12 14]    512K     16M     16M      8M      8M      4M      4M      1G
     [13 13 14]    512K     16M     16M      8M      8M      8M      8M      1G
     [14  1 11]    512K     64M     32M    256K    256K    256K    256K      1G
     [14  2  7]    512K      1G    512M      1G    512M    512M    128M      1G
     [14  2  9]    512K    512M    256M    128M    128M     64M    128M      1G
     [14  3 13]    512K     16M     16M      1M    256K     64K     64K      1G
     [14  8  9]    512K    128M     64M      1G     64M     64M     64M      1G
     [14 11  3]    512K    512M    512M    256M    128M    128M     64M      1G
     [14 11 11]    512K     16M      8M    256K    256K    128K    256K      1G
     [14 11 13]    256K    512K    512K    128K     64K     64K     64K      1G
     [14 12 13]    128K    512K    256K    128K     64K     64K     64K      1G
     [14 13 13]    128K    128K    256K     64K     64K    128K     64K    256M
     [15  1  2]    512K      2M      2M      1M    512K    512K    256K      1G
     [15  3  6]    512K      1G    512M    512M    512M    256M    128M      1G
     [15  4 12]    512K    128M     64M    128M      8M    256K    256K      1G
     [15  6  2]    512K    128M    256M    128M    128M     32M     16M      1G
     [15  7  4]    512K    512M    128M    512M    512M    256M    128M      1G
     [15  7  8]    512K     64M     64M     32M     32M      4M      2M    512M
    
      Xoroshiro32r+ PractRand Score Table - Run 2017-10-27 22:41:34 +1300
    
    Combination    Word0   Word1   Word2  msByte  Byte04   Byte2   Byte1   msBit
    =============================================================================
     [ 1  2  8]     16M     32M     16M     32M     16M      1M      1M     32M
     [ 2  1 11]      8M     16M     16M    512K    512K    512K    512K    512M
     [ 2  1 15]    128K    256K    256K    128K    128K    128K     64K      8M
     [ 2  2  7]      4M      8M      8M     16M      2M      1M      1M      8M
     [ 2  6 15]      1M      1M      1M      2M    128K    128K    256K      1G
     [ 2  8  7]     32M     64M     32M     16M      4M      1M      1M      4M
     [ 2  9  9]    512K      4M      4M    512K      2M      1M      1M    256M
     [ 2 11  3]      4M      4M      4M    512K    512K    512K    512K      1G
     [ 3  2  6]     16M     64M     32M      4M      4M      1M      2M    512M
     [ 3  3 10]     16M     32M     32M      4M      2M      4M      4M      1G
     [ 3 11  2]    256K    512K    256K    256K    128K    128K    128K     32M
     [ 3 11 14]      8M      8M      4M      1M    512K    512K    512K     64M
     [ 4  1  9]      1M      1M      2M      4M      1M      2M      2M     64M
     [ 4  7 15]     16M     16M     16M      1M    256K    256K    512K      1G
     [ 4  8  5]     64M    128M     64M     16M      2M      1M      2M      1G
     [ 5  2  6]     64M     64M     64M      4M      2M      2M      4M      1G
     [ 5  8  4]      2M      8M      8M      2M    512K    512K    256K      1G
     [ 5 14 12]    256M    256M    128M      8M     16M     32M    128M      1G
     [ 6  2  3]     32M     32M     16M      4M      1M      1M      1M    128M
     [ 6  2  5]     16M      8M      8M      1M      2M      2M    512K      1G
     [ 6  2 11]    256M    512M    128M      8M     16M     64M     64M      1G
     [ 6  3 15]     64M     64M     64M      2M      1M      2M      2M     32M
     [ 6 14 11]     64M    128M     64M      4M      8M     32M     64M      1G
     [ 7  1  8]     64M    128M     64M      8M      2M      4M      8M    512M
     [ 7  2  2]     16M     32M     16M      4M      1M      2M      2M      1G
     [ 7  2 10]     32M      1G    256M      8M     64M     64M     16M      1G
     [ 7  2 14]    512M      1G    256M      8M      8M     32M     64M    512M
     [ 7  8  2]    128M    256M    128M     32M      2M      1M      2M      1G
     [ 7 10 10]     64M    256M     64M      2M     32M     32M     16M      1G
     [ 7 15  8]      2M      4M      4M      2M      1M      1M      2M     32M
     [ 8  1  7]      2M      4M      8M      4M      2M      4M      4M    128M
     [ 8  2  1]     32M    128M    128M      2M      1M      4M      4M    256M
     [ 8  5 13]     32M    128M    128M     16M     64M    256M    128M    256M
     [ 8  7 15]      2M      4M      4M      1M    512K      1M      1M      8M
     [ 8  9 13]    512M      1G    512M     64M    128M    128M    128M      1G
     [ 8 15  7]      1M      1M      1M      1M    512K    512K    512K     16M
     [ 9  1  4]      8M     32M     32M     16M     32M     16M     16M      1G
     [ 9  2 14]    512M      2G      1G     16M     32M    128M    256M      1G
     [ 9  8 14]      8M     16M     16M      2M      1M      1M    512K      1G
     [ 9  9  2]      8M    128M    128M      8M      8M     16M     32M      1G
     [10  2  7]     16M    256M    128M     32M      8M     16M     32M      1G
     [10  3  3]     32M    128M    128M      4M     64M    128M     64M      1G
     [10  3 11]     16M      1G    512M     16M    256M    512M    512M      1G
     [10  5 13]     32M      2G      1G     32M    128M    256M    512M      1G
     [10  7 11]     16M    256M    256M     32M    128M    128M    128M      1G
     [10 10  7]     16M     32M     32M     32M      4M      8M     16M    512M
     [11  1  2]     32M    512M    128M      1M     16M     64M     32M      1G
     [11  1 14]     16M      1G    512M      4M     64M     32M     32M      1G
     [11  2  6]     32M    512M    512M     64M     32M     64M    256M      1G
     [11  3 10]      8M     32M     16M      4M      2M      1M    512K      1G
     [11  7 10]      2M      8M      4M    512K    512K    512K    512K      1G
     [11  8 12]     16M    128M    128M      4M     16M     32M      8M      1G
     [11 10 12]     16M    128M     64M      4M      2M      1M    256K      1G
     [11 11 14]     16M     64M     64M      2M     16M     16M     16M      1G
     [11 14  6]     32M    256M    256M     32M     16M     32M     64M      1G
     [12  4 15]     16M    512M    512M     16M     64M    128M    128M      1G
     [12  8 11]      2M      8M      4M    256K    512K    256K    256K      1G
     [12 10 11]      2M      4M      4M    256K    512K    256K    256K      1G
     [12 10 13]     16M    128M     64M      2M      2M      1M    256K     64M
     [12 14  5]     32M    128M    128M     32M     64M     64M     32M      1G
     [13  3 14]     32M    256M    128M      4M     32M     32M     16M      1G
     [13  5  8]     32M    256M    128M    128M    128M     64M    128M      1G
     [13  5 10]     32M     64M     32M      4M      2M      2M      2M      1G
     [13  9  8]     32M    256M    128M     64M     64M     32M     16M      1G
     [13 10 12]      1M      2M      2M    128K    256K    256K    128K    128M
     [13 11 14]     16M     32M     16M      2M      1M    256K    256K    256M
     [13 12 14]      8M     16M     16M      2M    512K    256K    128K      4M
     [13 13 14]      8M     16M     32M      2M     16M    256K    128K    128M
     [14  1 11]     32M     64M     32M      1M      1M    512K    512K      1G
     [14  2  7]     32M    128M     64M     64M    128M     32M     16M      1G
     [14  2  9]     32M    256M     64M     32M     16M      8M      8M      1G
     [14  3 13]      4M      8M      4M    512K    256K    128K    128K      1G
     [14  8  9]     32M    128M     32M     16M      8M      1M      1M      1G
     [14 11  3]     32M    256M    128M     16M     16M      2M      2M      1G
     [14 11 11]     16M     32M     16M      1M    512K    512K    256K      1G
     [14 11 13]    512K      1M    512K    256K    256K    128K    128K     16M
     [14 12 13]      1M      1M    512K    256K    256K    128K    128K     32M
     [14 13 13]    512K      1M    512K    256K    256K    128K    128K      8M
     [15  1  2]      2M      4M      4M      1M      1M    256K    256K      1M
     [15  3  6]     64M     64M     16M     32M    128M      8M      2M    512M
     [15  4 12]     32M     32M     16M      8M    512K      1M      1M      1G
     [15  6  2]     16M     64M     32M     16M     32M     32M     32M    128M
     [15  7  4]     32M    128M     64M     32M     64M     32M      8M      1G
     [15  7  8]     16M     32M     16M      8M      4M    512K    512K    256M
    
    "... 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 2017-10-27 - 11:49:21
    For the "r+" algorithm, the code changes from
    	uint64_t  result = (s0 + s1) & ACCUM_MASK;
    
    to this
    	int  shift = s1 >> (ACCUM_SIZE-3);
    	uint64_t  result = (rotl( s0, shift ) + rotl( s1, shift )) & ACCUM_MASK;
    
    It was just a quick hack to see what happened using the existing rotl() function as defined in my earlier source.

    I remember getting the idea from watching Melissa's lecture where she talks about using the high bits for dynamically rotating in her algorithms.
    "... 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 tables, Evan. Are they better than the normal Xoroshiro+?

    Have you had a chance to try the parity idea, sum and state?
    Formerly known as TonyB
  • Only Xoroshiro32+ [14,2,7] is relevant for the parity tests.
    Formerly known as TonyB
  • That's 31 consecutive shifts and XORs, right?
    "... 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_TonyB_ Posts: 1,221
    edited 2017-10-31 - 20:25:29
    Yes or 15 for the sum, in the absence of a parity flag.
    Formerly known as TonyB
  • TonyB_TonyB_ Posts: 1,221
    edited 2017-10-27 - 13:16:34
    Someone is saying that Xoroshiro32+ cannot possibly be as a good as an 8-bit Complementary Multiply-With-Carry PRNG and that CMWC in fact "is in an entirely different league."

    Here's the pseudo-code:
    ;set constants
    
    a = 253
    ;b = 8
    ;r = 8	
    
    ;initialise variables
    
    c = 0
    i = 0
    x[0] = 82
    x[1] = 97
    x[2] = 120
    x[3] = 111
    x[4] = 102
    x[5] = 116
    x[6] = 20
    x[7] = 12
    
    ;iterate CMWC
    
    t := a * x[i] + c
    c := t / 256			;high byte of t
    x[i] := (t mod 256) xor 255	;1's complement of low byte of t
    prn := x[i]
    i := (i + 1) and 7
    
    ;a,c,i,x[i] are 8-bit
    ;t is 16-bit
    ;Period > 2^66
    
    

    I like to know how this compares to the top byte of Xoroshiro32+ [14,2,7] but I don't have the testing tools.
    Formerly known as TonyB
  • evanhevanh Posts: 7,502
    edited 2017-10-27 - 13:09:30
    It's virtually identical scores to original Xoroshiro (including the lsbit) when the lsbit is replaced with parity, just a few more non-512K word0 scores. When the sum is shifted down one bit and the parity place as msbit then it all goes to shit.

    Here's the two modifications to algorithm:
    	int  shift;
    	uint64_t  result, parity = 0;
    
    
    	for( shift=1; shift < ACCUM_SIZE; shift++ )  {
    		parity = parity ^ (s0 >> shift) ^ (s1 >> shift);
    	}
    
    	result = (((s0 + s1) & -2LL) | (parity & 1LL)) & ACCUM_MASK;
    
    	int  shift;
    	uint64_t  result, parity = 0;
    
    
    	for( shift=1; shift < ACCUM_SIZE; shift++ )  {
    		parity = parity ^ (s0 >> shift) ^ (s1 >> shift);
    	}
    
    	result = (((s0 + s1) >> 1) | (parity << (ACCUM_SIZE-1))) & ACCUM_MASK;
    

    EDIT: Oops, I see a bug in the second code snippet. Doesn't matter though, the first one proves that parity is no good.

    EDIT2: Hmm, I've also left out the lsbit of s0 and s1 ... I'll do that all again ... but I doubt it'll make it better ...
    "... 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 2017-10-27 - 13:01:11
    Here's the score table for first parity modification above:
      Xoroshiro32p+ PractRand Score Table - Run 2017-10-28 01:45:41 +1300
    
    Combination    Word0   Word1   Word2  msByte  Byte04   Byte2   Byte1   msBit
    =============================================================================
     [ 1  2  8]    512K     32M     64M     16M     64M     64M     32M      1G
     [ 2  1 11]    512K      8M      8M    128K    128K    128K    256K      1G
     [ 2  1 15]     64K    128K    128K     32K     32K     64K     32K      1G
     [ 2  2  7]    512K      8M      8M     32M     32M     32M      4M      1G
     [ 2  6 15]    512K      2M      4M     16M    128K    128K    128K      1G
     [ 2  8  7]    512K      8M     16M    128M     32M     32M      4M      1G
     [ 2  9  9]    128K    256K    256K     16K    128K    512K     64M      1G
     [ 2 11  3]    512K      2M      4M    512K    256K    256K    256K      1G
     [ 3  2  6]    512K     64M     32M      2M      2M      2M      1M      1G
     [ 3  3 10]    512K     16M     16M    256K    256K    512K     64M      1G
     [ 3 11  2]    256K    256K    512K    128K     64K     64K     64K      1G
     [ 3 11 14]    512K      4M      4M    256K    256K    512K    512K      1G
     [ 4  1  9]    512K    512K      1M    512K      8M    256K    512K    512M
     [ 4  7 15]    512K     64M     64M    128M    512K    512K    512K      1G
     [ 4  8  5]    512K    512M    128M     32M      8M      4M      2M      1G
     [ 5  2  6]    512K    128M    128M      8M      4M      4M      4M      1G
     [ 5  8  4]    512K      4M     16M      4M      1M    256K    128K     64M
     [ 5 14 12]    512K    128M     64M      2M      4M     16M    128M      1G
     [ 6  2  3]    512K     32M     32M      1M      1M      1M      2M      2M
     [ 6  2  5]    512K     16M     16M    256K    512K    512K    512K      4M
     [ 6  2 11]    512K    512M    256M      8M      8M    256M    128M      1G
     [ 6  3 15]    512K     32M     32M      1M      1M      2M      4M      1G
     [ 6 14 11]    512K    128M    128M     32M     64M    128M     16M      1G
     [ 7  1  8]    512K     64M    128M     16M    128M     16M     16M      1G
     [ 7  2  2]    512K     16M     16M      2M      2M      4M      4M      4M
     [ 7  2 10]    512K      1G    512M    128M    256M     64M     32M      1G
     [ 7  2 14]    512K    512M    256M      4M      8M     32M     32M    256M
     [ 7  8  2]    512K    512M    512M     64M      8M      4M      4M    512M
     [ 7 10 10]    512K    128M    256M     32M     32M    256M    128M      1G
     [ 7 15  8]    512K      2M      2M    256K      1M    512K    256K      1G
     [ 8  1  7]    512K      1M      4M      1M      1M      1M      1M     64M
     [ 8  2  1]    512K     32M     64M      8M      8M     16M     16M     16M
     [ 8  5 13]    512K     32M     64M     16M      8M    128M    128M      1G
     [ 8  7 15]    512K      2M      2M    512K      2M      2M      1M      1G
     [ 8  9 13]    512K    512M    128M    512M      1G    512M    128M      1G
     [ 8 15  7]    512K    512K      1M    256K    512K    512K    256K      1G
     [ 9  1  4]    512K     32M     64M      8M     16M     16M     16M     64M
     [ 9  2 14]    512K      2G      1G    128M    256M     64M    128M      1G
     [ 9  8 14]    512K     16M     32M    256M     32M     32M     64M      1G
     [ 9  9  2]    512K     32M     64M     16M     16M     16M     32M     64M
     [10  2  7]    512K    256M    128M     16M     16M     64M     32M      1G
     [10  3  3]    512K     64M     64M     32M     32M     32M     64M    256M
     [10  3 11]    512K      2G      1G    256M    256M    512M    128M      1G
     [10  5 13]    512K      2G    512M      1G    512M    256M    128M    512M
     [10  7 11]    512K    512M    128M    512M    128M    512M    128M      1G
     [10 10  7]    512K     16M     16M     16M     16M    512M    128M    512M
     [11  1  2]    512K    256M    256M     32M     32M     32M     32M      1G
     [11  1 14]    512K      1G      1G     32M     16M     16M     16M      1G
     [11  2  6]    512K    512M    512M     32M     64M    512M    128M    512M
     [11  3 10]    512K     32M     32M     64M      1M    128K     64K    128M
     [11  7 10]    512K      4M      8M     32M    128K    128K     64K      1G
     [11  8 12]    512K    256M    256M    512M    512M    512M    128M      1G
     [11 10 12]    512K    128M    128M      1G    512M    512M    128M      1G
     [11 11 14]    512K     64M    128M     16M     16M     16M      8M      1G
     [11 14  6]    512K    256M    128M    256M     64M    512M    128M      1G
     [12  4 15]    512K    512M      1G    128M     64M     16M     16M      1G
     [12  8 11]    512K      4M      4M     64M    128K    128K     64K      1G
     [12 10 11]    512K      2M      2M    128K    128K    128K     64K      1G
     [12 10 13]    512K     32M     64M     16M     16M     32M      8M      1G
     [12 14  5]    512K     32M     32M    128M    128M     64M     64M      1G
     [13  3 14]    512K    512M    512M     64M     32M     16M      8M      1G
     [13  5  8]    512K    256M    256M    512M    128M    256M    128M      1G
     [13  5 10]    512K     64M     32M     64M     16M    256K    256K      1G
     [13  9  8]    512K    128M     64M    512M    512M    512M    128M      1G
     [13 10 12]    512K      2M      2M    128K    128K    128K     64K    512M
     [13 11 14]    512K     16M     16M      8M      8M      8M      8M      1G
     [13 12 14]    512K     16M     16M      8M      8M      4M      4M      1G
     [13 13 14]    512K     16M     16M      8M      8M      8M      8M      1G
     [14  1 11]    512K     64M     32M    256K    256K    256K    256K      1G
     [14  2  7]    512K      1G    512M      1G    512M    512M    128M      1G
     [14  2  9]    512K    512M    256M    128M    128M     64M    128M      1G
     [14  3 13]    512K     16M     16M      1M    256K     64K     64K      1G
     [14  8  9]    512K    128M     64M      1G     64M     64M     64M      1G
     [14 11  3]    512K    512M    512M    256M    128M    128M     64M      1G
     [14 11 11]    512K     16M      8M    256K    256K    128K    256K      1G
     [14 11 13]    256K    512K    512K    128K     64K     64K     64K      1G
     [14 12 13]    256K    512K    256K    128K     64K     64K     64K      1G
     [14 13 13]    256K    128K    256K     64K     64K    128K     64K    256M
     [15  1  2]    512K      2M      2M      1M    512K    512K    256K      1G
     [15  3  6]    512K      1G    512M    512M    512M    256M    128M      1G
     [15  4 12]    512K    128M     64M    128M      8M    256K    256K      1G
     [15  6  2]    512K    128M    256M    128M    128M     32M     16M      1G
     [15  7  4]    512K    512M    128M    512M    512M    256M    128M      1G
     [15  7  8]    512K     64M     64M     32M     32M      4M      2M    512M
    
    "... 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."
  • So state parity no good. How about sum parity?
    Formerly known as TonyB
  • TonyB_TonyB_ Posts: 1,221
    edited 2017-10-27 - 13:16:13
    Mistake in CMWC pseudo-code above corrected.
    Formerly known as TonyB
  • TonyB_ wrote: »
    Someone is saying that Xoroshiro32+ cannot possibly be as a good as an 8-bit Complementary Multiply-With-Carry PRNG and that CWMC in fact "is in an entirely different league."
    Probably quite right. The geometric tests that Melissa demo'd always came up nice and fuzzy looking with that type of algorithm. She strongly advocates for them because they fit modern CPUs really well.

    However, the problem with those type is they're costly to have a hardware implementation because of the multiply.
    "... 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."
  • Here's the repaired snippet:
    	int  shift;
    	uint64_t  result, parity = s0 ^ s1;
    
    
    	for( shift=1; shift < ACCUM_SIZE; shift++ )  {
    		parity = parity ^ (s0 >> shift) ^ (s1 >> shift);
    	}
    
    	result = (((s0 + s1) & -2LL) | (parity & 1LL)) & ACCUM_MASK;
    

    And the score table still looks the same:
      Xoroshiro32r+ PractRand Score Table - Run 2017-10-28 02:23:10 +1300
    
    Combination    Word0   Word1   Word2  msByte  Byte04   Byte2   Byte1   msBit
    =============================================================================
     [ 1  2  8]    512K     32M     64M     16M     64M     64M     32M      1G
     [ 2  1 11]    512K      8M      8M    128K    128K    128K    256K      1G
     [ 2  1 15]     64K    128K    128K     32K     32K     64K     32K      1G
     [ 2  2  7]    512K      8M      8M     32M     32M     32M      4M      1G
     [ 2  6 15]    512K      2M      4M     16M    128K    128K    128K      1G
     [ 2  8  7]    512K      8M     16M    128M     32M     32M      4M      1G
     [ 2  9  9]    256K    256K    256K     16K    128K    512K     64M      1G
     [ 2 11  3]    512K      2M      4M    512K    256K    256K    256K      1G
     [ 3  2  6]    512K     64M     32M      2M      2M      2M      1M      1G
     [ 3  3 10]    512K     16M     16M    256K    256K    512K     64M      1G
     [ 3 11  2]    512K    256K    512K    128K     64K     64K     64K      1G
     [ 3 11 14]    512K      4M      4M    256K    256K    512K    512K      1G
     [ 4  1  9]    512K    512K      1M    512K      8M    256K    512K    512M
     [ 4  7 15]    512K     64M     64M    128M    512K    512K    512K      1G
     [ 4  8  5]    512K    512M    128M     32M      8M      4M      2M      1G
     [ 5  2  6]    512K    128M    128M      8M      4M      4M      4M      1G
     [ 5  8  4]    512K      4M     16M      4M      1M    256K    128K     64M
     [ 5 14 12]    512K    128M     64M      2M      4M     16M    128M      1G
     [ 6  2  3]    512K     32M     32M      1M      1M      1M      2M      2M
     [ 6  2  5]    512K     16M     16M    256K    512K    512K    512K      4M
     [ 6  2 11]    512K    512M    256M      8M      8M    256M    128M      1G
     [ 6  3 15]    512K     32M     32M      1M      1M      2M      4M      1G
     [ 6 14 11]    512K    128M    128M     32M     64M    128M     16M      1G
     [ 7  1  8]    512K     64M    128M     16M    128M     16M     16M      1G
     [ 7  2  2]    512K     16M     16M      2M      2M      4M      4M      4M
     [ 7  2 10]    512K      1G    512M    128M    256M     64M     32M      1G
     [ 7  2 14]    512K    512M    256M      4M      8M     32M     32M    256M
     [ 7  8  2]    512K    512M    512M     64M      8M      4M      4M    512M
     [ 7 10 10]    512K    128M    256M     32M     32M    256M    128M      1G
     [ 7 15  8]    512K      2M      2M    256K      1M    512K    256K      1G
     [ 8  1  7]    512K      1M      4M      1M      1M      1M      1M     64M
     [ 8  2  1]    512K     32M     64M      8M      8M     16M     16M     16M
     [ 8  5 13]    512K     32M     64M     16M      8M    128M    128M      1G
     [ 8  7 15]    512K      2M      2M    512K      2M      2M      1M      1G
     [ 8  9 13]    512K    512M    128M    512M      1G    512M    128M      1G
     [ 8 15  7]    512K    512K      1M    256K    512K    512K    256K      1G
     [ 9  1  4]    512K     32M     64M      8M     16M     16M     16M     64M
     [ 9  2 14]    512K      2G      1G    128M    256M     64M    128M      1G
     [ 9  8 14]    512K     16M     32M    256M     32M     32M     64M      1G
     [ 9  9  2]    512K     32M     64M     16M     16M     16M     32M     64M
     [10  2  7]    512K    256M    128M     16M     16M     64M     32M      1G
     [10  3  3]    512K     64M     64M     32M     32M     32M     64M    256M
     [10  3 11]    512K      2G      1G    256M    256M    512M    128M      1G
     [10  5 13]    512K      2G    512M      1G    512M    256M    128M    512M
     [10  7 11]    512K    512M    128M    512M    128M    512M    128M      1G
     [10 10  7]    512K     16M     16M     16M     16M    512M    128M    512M
     [11  1  2]    512K    256M    256M     32M     32M     32M     32M      1G
     [11  1 14]    512K      1G      1G     32M     16M     16M     16M      1G
     [11  2  6]    512K    512M    512M     32M     64M    512M    128M    512M
     [11  3 10]    512K     32M     32M     64M      1M    128K     64K    128M
     [11  7 10]    512K      4M      8M     32M    128K    128K     64K      1G
     [11  8 12]    512K    256M    256M    512M    512M    512M    128M      1G
     [11 10 12]    512K    128M    128M      1G    512M    512M    128M      1G
     [11 11 14]    512K     64M    128M     16M     16M     16M      8M      1G
     [11 14  6]    512K    256M    128M    256M     64M    512M    128M      1G
     [12  4 15]    512K    512M      1G    128M     64M     16M     16M      1G
     [12  8 11]    512K      4M      4M     64M    128K    128K     64K      1G
     [12 10 11]    512K      2M      2M    128K    128K    128K     64K      1G
     [12 10 13]    512K     32M     64M     16M     16M     32M      8M      1G
     [12 14  5]    512K     32M     32M    128M    128M     64M     64M      1G
     [13  3 14]    512K    512M    512M     64M     32M     16M      8M      1G
     [13  5  8]    512K    256M    256M    512M    128M    256M    128M      1G
     [13  5 10]    512K     64M     32M     64M     16M    256K    256K      1G
     [13  9  8]    512K    128M     64M    512M    512M    512M    128M      1G
     [13 10 12]    512K      2M      2M    128K    128K    128K     64K    512M
     [13 11 14]    512K     16M     16M      8M      8M      8M      8M      1G
     [13 12 14]    512K     16M     16M      8M      8M      4M      4M      1G
     [13 13 14]    512K     16M     16M      8M      8M      8M      8M      1G
     [14  1 11]    512K     64M     32M    256K    256K    256K    256K      1G
     [14  2  7]    512K      1G    512M      1G    512M    512M    128M      1G
     [14  2  9]    512K    512M    256M    128M    128M     64M    128M      1G
     [14  3 13]    512K     16M     16M      1M    256K     64K     64K      1G
     [14  8  9]    512K    128M     64M      1G     64M     64M     64M      1G
     [14 11  3]    512K    512M    512M    256M    128M    128M     64M      1G
     [14 11 11]    512K     16M      8M    256K    256K    128K    256K      1G
     [14 11 13]    512K    512K    512K    128K     64K     64K     64K      1G
     [14 12 13]    256K    512K    256K    128K     64K     64K     64K      1G
     [14 13 13]    256K    128K    256K     64K     64K    128K     64K    256M
     [15  1  2]    512K      2M      2M      1M    512K    512K    256K      1G
     [15  3  6]    512K      1G    512M    512M    512M    256M    128M      1G
     [15  4 12]    512K    128M     64M    128M      8M    256K    256K      1G
     [15  6  2]    512K    128M    256M    128M    128M     32M     16M      1G
     [15  7  4]    512K    512M    128M    512M    512M    256M    128M      1G
     [15  7  8]    512K     64M     64M     32M     32M      4M      2M    512M
    
    "... 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: »
    However, the problem with those type is they're costly to have a hardware implementation because of the multiply.
    Actually, even the dynamic rotation I've used is probably too expensive.
    "... 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: »
    So state parity no good. How about sum parity?
    More of the same I suspect.
    "... 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_TonyB_ Posts: 1,221
    edited 2017-10-27 - 13:44:30
    evanh wrote: »
    TonyB_ wrote: »
    Someone is saying that Xoroshiro32+ cannot possibly be as a good as an 8-bit Complementary Multiply-With-Carry PRNG and that CMWC in fact "is in an entirely different league."
    Probably quite right. The geometric tests that Melissa demo'd always came up nice and fuzzy looking with that type of algorithm. She strongly advocates for them because they fit modern CPUs really well.

    However, the problem with those type is they're costly to have a hardware implementation because of the multiply.

    CMWC is yet another PRNG by the late Prof. Marsaglia.

    The numbers in the pseudo-code were chosen to make it as easy as possible to implement on 8-bit CPUs but does that affect the quality? Multiply by 253 is a byte shift and three subtracts.

    Formerly known as TonyB
  • x[0],x[1],...,x[r-1] = x[0],...,x[7] for r=8 is the lag table and the next PRN is a function of the rth previous one.
    Formerly known as TonyB
  • evanhevanh Posts: 7,502
    edited 2017-10-27 - 13:57:11
    Is there a 64-bit version? There's a lot more calibration adjustments possible in that algorithm than for the Xorshift/Xoroshiro algorithms.
    "... 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."
  • Why's it called a "lag" table?
    "... 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."
  • There are different versions, e.g. 32-bit with r=256 or r=4096, but if you're interested please test this 8-bit version first! I could generate the first 16 PRNs tonight as a check. Seeding the lag table correctly is an issue that Xoroshiro+ doesn't have.
    Formerly known as TonyB
  • evanhevanh Posts: 7,502
    edited 2017-10-27 - 14:07:37
    Huh! It worked! That was totally unexpected ...

    Here's the scores from sum parity replacing the lsbit:
      Xoroshiro32p+ PractRand Score Table - Run 2017-10-28 03:01:16 +1300
    
    Combination    Word0   Word1   Word2  msByte  Byte04   Byte2   Byte1   msBit
    =============================================================================
     [ 1  2  8]      8M     32M     64M     16M     64M     64M     32M      1G
     [ 2  1 11]      8M      8M      8M    128K    128K    128K    256K      1G
     [ 2  1 15]     64K    128K    128K     32K     32K     64K     32K      1G
     [ 2  2  7]      4M      8M      8M     32M     32M     32M      4M      1G
     [ 2  6 15]      1M      2M      4M     16M    128K    128K    128K      1G
     [ 2  8  7]      4M      8M     16M    128M     32M     32M      4M      1G
     [ 2  9  9]    256K    256K    256K     16K    128K    512K     64M      1G
     [ 2 11  3]      2M      2M      4M    512K    256K    256K    256K      1G
     [ 3  2  6]     16M     64M     32M      2M      2M      2M      1M      1G
     [ 3  3 10]     16M     16M     16M    256K    256K    512K     64M      1G
     [ 3 11  2]    256K    256K    512K    128K     64K     64K     64K      1G
     [ 3 11 14]      8M      4M      4M    256K    256K    512K    512K      1G
     [ 4  1  9]      1M    512K      1M    512K      8M    256K    512K    512M
     [ 4  7 15]     16M     64M     64M    128M    512K    512K    512K      1G
     [ 4  8  5]     16M    512M    128M     32M      8M      4M      2M      1G
     [ 5  2  6]     16M    128M    128M      8M      4M      4M      4M      1G
     [ 5  8  4]      2M      4M     16M      4M      1M    256K    128K     64M
     [ 5 14 12]     16M    128M     64M      2M      4M     16M    128M      1G
     [ 6  2  3]     16M     32M     32M      1M      1M      1M      2M      2M
     [ 6  2  5]      8M     16M     16M    256K    512K    512K    512K      4M
     [ 6  2 11]     16M    512M    256M      8M      8M    256M    128M      1G
     [ 6  3 15]     16M     32M     32M      1M      1M      2M      4M      1G
     [ 6 14 11]     16M    128M    128M     32M     64M    128M     16M      1G
     [ 7  1  8]      1M     64M    128M     16M    128M     16M     16M      1G
     [ 7  2  2]      8M     16M     16M      2M      2M      4M      4M      4M
     [ 7  2 10]     16M      1G    512M    128M    256M     64M     32M      1G
     [ 7  2 14]     16M    512M    256M      4M      8M     32M     32M    256M
     [ 7  8  2]     16M    512M    512M     64M      8M      4M      4M    512M
     [ 7 10 10]     16M    128M    256M     32M     32M    256M    128M      1G
     [ 7 15  8]      1M      2M      2M    256K      1M    512K    256K      1G
     [ 8  1  7]      1M      1M      4M      1M      1M      1M      1M     64M
     [ 8  2  1]      4M     32M     64M      8M      8M     16M     16M     16M
     [ 8  5 13]     16M     32M     64M     16M      8M    128M    128M      1G
     [ 8  7 15]      1M      2M      2M    512K      2M      2M      1M      1G
     [ 8  9 13]     16M    512M    128M    512M      1G    512M    128M      1G
     [ 8 15  7]    512K    512K      1M    256K    512K    512K    256K      1G
     [ 9  1  4]     16M     32M     64M      8M     16M     16M     16M     64M
     [ 9  2 14]     16M      2G      1G    128M    256M     64M    128M      1G
     [ 9  8 14]      8M     16M     32M    256M     32M     32M     64M      1G
     [ 9  9  2]     16M     32M     64M     16M     16M     16M     32M     64M
     [10  2  7]     16M    256M    128M     16M     16M     64M     32M      1G
     [10  3  3]     16M     64M     64M     32M     32M     32M     64M    256M
     [10  3 11]     16M      2G      1G    256M    256M    512M    128M      1G
     [10  5 13]     16M      2G    512M      1G    512M    256M    128M    512M
     [10  7 11]     16M    512M    128M    512M    128M    512M    128M      1G
     [10 10  7]     16M     16M     16M     16M     16M    512M    128M    512M
     [11  1  2]     16M    256M    256M     32M     32M     32M     32M      1G
     [11  1 14]     16M      1G      1G     32M     16M     16M     16M      1G
     [11  2  6]     16M    512M    512M     32M     64M    512M    128M    512M
     [11  3 10]      8M     32M     32M     64M      1M    128K     64K    128M
     [11  7 10]      4M      4M      8M     32M    128K    128K     64K      1G
     [11  8 12]     16M    256M    256M    512M    512M    512M    128M      1G
     [11 10 12]     16M    128M    128M      1G    512M    512M    128M      1G
     [11 11 14]     16M     64M    128M     16M     16M     16M      8M      1G
     [11 14  6]     16M    256M    128M    256M     64M    512M    128M      1G
     [12  4 15]     16M    512M      1G    128M     64M     16M     16M      1G
     [12  8 11]      2M      4M      4M     64M    128K    128K     64K      1G
     [12 10 11]      2M      2M      2M    128K    128K    128K     64K      1G
     [12 10 13]     16M     32M     64M     16M     16M     32M      8M      1G
     [12 14  5]     16M     32M     32M    128M    128M     64M     64M      1G
     [13  3 14]     16M    512M    512M     64M     32M     16M      8M      1G
     [13  5  8]     16M    256M    256M    512M    128M    256M    128M      1G
     [13  5 10]     16M     64M     32M     64M     16M    256K    256K      1G
     [13  9  8]     16M    128M     64M    512M    512M    512M    128M      1G
     [13 10 12]      1M      2M      2M    128K    128K    128K     64K    512M
     [13 11 14]     16M     16M     16M      8M      8M      8M      8M      1G
     [13 12 14]     16M     16M     16M      8M      8M      4M      4M      1G
     [13 13 14]     16M     16M     16M      8M      8M      8M      8M      1G
     [14  1 11]     16M     64M     32M    256K    256K    256K    256K      1G
     [14  2  7]     16M      1G    512M      1G    512M    512M    128M      1G
     [14  2  9]     16M    512M    256M    128M    128M     64M    128M      1G
     [14  3 13]      8M     16M     16M      1M    256K     64K     64K      1G
     [14  8  9]     16M    128M     64M      1G     64M     64M     64M      1G
     [14 11  3]     16M    512M    512M    256M    128M    128M     64M      1G
     [14 11 11]      8M     16M      8M    256K    256K    128K    256K      1G
     [14 11 13]    512K    512K    512K    128K     64K     64K     64K      1G
     [14 12 13]    256K    512K    256K    128K     64K     64K     64K      1G
     [14 13 13]    256K    128K    256K     64K     64K    128K     64K    256M
     [15  1  2]      2M      2M      2M      1M    512K    512K    256K      1G
     [15  3  6]     16M      1G    512M    512M    512M    256M    128M      1G
     [15  4 12]     16M    128M     64M    128M      8M    256K    256K      1G
     [15  6  2]     16M    128M    256M    128M    128M     32M     16M      1G
     [15  7  4]     16M    512M    128M    512M    512M    256M    128M      1G
     [15  7  8]     16M     64M     64M     32M     32M      4M      2M    512M
    

    And the relevant source snippet:
    	int  shift;
    	uint64_t  result = (s0 + s1) & ACCUM_MASK;
    	uint64_t  parity = result;
    
    
    	for( shift=1; shift < ACCUM_SIZE; shift++ )  {
    		parity = parity ^ (result >> shift);
    	}
    
    	result = ((result & -2LL) | (parity & 1LL)) & ACCUM_MASK;
    
    "... 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_TonyB_ Posts: 1,221
    edited 2017-10-27 - 17:17:38
    Excellent! Not totally unexpected as David Roberts did it first. Thanks a lot for the testing, Evan.

    This also proves that the state on its own without summing is hopeless.
    Formerly known as TonyB
  • Interesting, examining the results I now see that the best word0 score is 16M. Still doesn't make it to the nominal good scores, I'd want at least 256M, but of note the whole column is pretty much 32x better than what was achieved without the parity.
    "... 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_TonyB_ Posts: 1,221
    edited 2017-10-27 - 14:29:32
    evanh wrote: »
    Why's it called a "lag" table?

    Because PRN[n] is a function of PRN[n-r] not PRN[n-1]. If r=4096, a new PRN won't be used to generate another PRN until 4096 (or 4095) more iterations have been done, hence the lag.

    Formerly known as TonyB
  • TonyB_TonyB_ Posts: 1,221
    edited 2017-10-27 - 17:18:03
    deleted
    Formerly known as TonyB
  • TonyB_TonyB_ Posts: 1,221
    edited 2017-10-27 - 14:46:36
    As sum[0] is not good, would the parity of sum[15:1] give better results?

    EDIT:
    This would take too long to be worth doing on the P2, probably.
    Formerly known as TonyB
  • cgraceycgracey Posts: 11,487
    edited 2017-10-27 - 14:51:00
    If XORO32 can be used to produce a high-quality 16-bit result per iteration, then I could enhance the instruction to do TWO iterations, get 16-bit sums from each, and substitute the high-quality 32-bit PRNG result into the next instruction's S value. Meanwhile, the double iteration would be written back to the original D in the XORO32 instruction.
  • Not sure if I've got me head fully around your intent there but two consecutive Xoroshiro32's can not a make a one Xoroshiro64. The period in particular is still that of the Xoroshiro32.

    That said, I'm all for squeezing 16 useful bits out of the XORO32 instruction.
    "... 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 2017-10-27 - 15:31:51
    TonyB_ wrote: »
    As sum[0] is not good, would the parity of sum[15:1] give better results?

    The outcomes are just boggling me now! For this tiny change, I think it's the worst lsbit result I've had yet!

    So the only change is start by setting parity to zero instead of whatever the sum was. This effectively skips the lsbit of the sum for the parity.
    	int  shift;
    	uint64_t  result = (s0 + s1) & ACCUM_MASK;
    	uint64_t  parity = 0;
    
    
    	for( shift=1; shift < ACCUM_SIZE; shift++ )  {
    		parity = parity ^ (result >> shift);
    	}
    
    	result = ((result & -2LL) | (parity & 1LL)) & ACCUM_MASK;
    
      Xoroshiro32p+ PractRand Score Table - Run 2017-10-28 04:21:39 +1300
    
    Combination    Word0   Word1   Word2  msByte  Byte04   Byte2   Byte1   msBit
    =============================================================================
     [ 1  2  8]      8K     32M     64M     16M     64M     64M     32M      1G
     [ 2  1 11]     16K      8M      8M    128K    128K    128K    256K      1G
     [ 2  1 15]      8K    128K    128K     32K     32K     64K     32K      1G
     [ 2  2  7]      8K      8M      8M     32M     32M     32M      4M      1G
     [ 2  6 15]     16K      2M      4M     16M    128K    128K    128K      1G
     [ 2  8  7]      8K      8M     16M    128M     32M     32M      4M      1G
     [ 2  9  9]     16K    256K    256K     16K    128K    512K     64M      1G
     [ 2 11  3]     16K      2M      4M    512K    256K    256K    256K      1G
     [ 3  2  6]     16K     64M     32M      2M      2M      2M      1M      1G
     [ 3  3 10]     16K     16M     16M    256K    256K    512K     64M      1G
     [ 3 11  2]      4K    256K    512K    128K     64K     64K     64K      1G
     [ 3 11 14]      8K      4M      4M    256K    256K    512K    512K      1G
     [ 4  1  9]      8K    512K      1M    512K      8M    256K    512K    512M
     [ 4  7 15]     16K     64M     64M    128M    512K    512K    512K      1G
     [ 4  8  5]     16K    512M    128M     32M      8M      4M      2M      1G
     [ 5  2  6]      8K    128M    128M      8M      4M      4M      4M      1G
     [ 5  8  4]      8K      4M     16M      4M      1M    256K    128K     64M
     [ 5 14 12]     16K    128M     64M      2M      4M     16M    128M      1G
     [ 6  2  3]      8K     32M     32M      1M      1M      1M      2M      2M
     [ 6  2  5]     16K     16M     16M    256K    512K    512K    512K      4M
     [ 6  2 11]     16K    512M    256M      8M      8M    256M    128M      1G
     [ 6  3 15]      8K     32M     32M      1M      1M      2M      4M      1G
     [ 6 14 11]      8K    128M    128M     32M     64M    128M     16M      1G
     [ 7  1  8]      8K     64M    128M     16M    128M     16M     16M      1G
     [ 7  2  2]     16K     16M     16M      2M      2M      4M      4M      4M
     [ 7  2 10]      8K      1G    512M    128M    256M     64M     32M      1G
     [ 7  2 14]      8K    512M    256M      4M      8M     32M     32M    256M
     [ 7  8  2]      8K    512M    512M     64M      8M      4M      4M    512M
     [ 7 10 10]      8K    128M    256M     32M     32M    256M    128M      1G
     [ 7 15  8]     16K      2M      2M    256K      1M    512K    256K      1G
     [ 8  1  7]      8K      1M      4M      1M      1M      1M      1M     64M
     [ 8  2  1]     16K     32M     64M      8M      8M     16M     16M     16M
     [ 8  5 13]      8K     32M     64M     16M      8M    128M    128M      1G
     [ 8  7 15]     16K      2M      2M    512K      2M      2M      1M      1G
     [ 8  9 13]     16K    512M    128M    512M      1G    512M    128M      1G
     [ 8 15  7]     16K    512K      1M    256K    512K    512K    256K      1G
     [ 9  1  4]     16K     32M     64M      8M     16M     16M     16M     64M
     [ 9  2 14]      8K      2G      1G    128M    256M     64M    128M      1G
     [ 9  8 14]     16K     16M     32M    256M     32M     32M     64M      1G
     [ 9  9  2]      4K     32M     64M     16M     16M     16M     32M     64M
     [10  2  7]     16K    256M    128M     16M     16M     64M     32M      1G
     [10  3  3]     16K     64M     64M     32M     32M     32M     64M    256M
     [10  3 11]      8K      2G      1G    256M    256M    512M    128M      1G
     [10  5 13]     16K      2G    512M      1G    512M    256M    128M    512M
     [10  7 11]      4K    512M    128M    512M    128M    512M    128M      1G
     [10 10  7]      8K     16M     16M     16M     16M    512M    128M    512M
     [11  1  2]     16K    256M    256M     32M     32M     32M     32M      1G
     [11  1 14]      8K      1G      1G     32M     16M     16M     16M      1G
     [11  2  6]      8K    512M    512M     32M     64M    512M    128M    512M
     [11  3 10]     16K     32M     32M     64M      1M    128K     64K    128M
     [11  7 10]      8K      4M      8M     32M    128K    128K     64K      1G
     [11  8 12]     16K    256M    256M    512M    512M    512M    128M      1G
     [11 10 12]     16K    128M    128M      1G    512M    512M    128M      1G
     [11 11 14]     16K     64M    128M     16M     16M     16M      8M      1G
     [11 14  6]      8K    256M    128M    256M     64M    512M    128M      1G
     [12  4 15]     16K    512M      1G    128M     64M     16M     16M      1G
     [12  8 11]      8K      4M      4M     64M    128K    128K     64K      1G
     [12 10 11]     16K      2M      2M    128K    128K    128K     64K      1G
     [12 10 13]      8K     32M     64M     16M     16M     32M      8M      1G
     [12 14  5]     16K     32M     32M    128M    128M     64M     64M      1G
     [13  3 14]      8K    512M    512M     64M     32M     16M      8M      1G
     [13  5  8]     16K    256M    256M    512M    128M    256M    128M      1G
     [13  5 10]     16K     64M     32M     64M     16M    256K    256K      1G
     [13  9  8]     16K    128M     64M    512M    512M    512M    128M      1G
     [13 10 12]     16K      2M      2M    128K    128K    128K     64K    512M
     [13 11 14]     16K     16M     16M      8M      8M      8M      8M      1G
     [13 12 14]      8K     16M     16M      8M      8M      4M      4M      1G
     [13 13 14]      8K     16M     16M      8M      8M      8M      8M      1G
     [14  1 11]      8K     64M     32M    256K    256K    256K    256K      1G
     [14  2  7]     16K      1G    512M      1G    512M    512M    128M      1G
     [14  2  9]     16K    512M    256M    128M    128M     64M    128M      1G
     [14  3 13]     16K     16M     16M      1M    256K     64K     64K      1G
     [14  8  9]     16K    128M     64M      1G     64M     64M     64M      1G
     [14 11  3]      8K    512M    512M    256M    128M    128M     64M      1G
     [14 11 11]     16K     16M      8M    256K    256K    128K    256K      1G
     [14 11 13]      8K    512K    512K    128K     64K     64K     64K      1G
     [14 12 13]      8K    512K    256K    128K     64K     64K     64K      1G
     [14 13 13]      8K    128K    256K     64K     64K    128K     64K    256M
     [15  1  2]      8K      2M      2M      1M    512K    512K    256K      1G
     [15  3  6]      8K      1G    512M    512M    512M    256M    128M      1G
     [15  4 12]     16K    128M     64M    128M      8M    256K    256K      1G
     [15  6  2]      8K    128M    256M    128M    128M     32M     16M      1G
     [15  7  4]     16K    512M    128M    512M    512M    256M    128M      1G
     [15  7  8]     16K     64M     64M     32M     32M      4M      2M    512M
    
    "... 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 2017-10-27 - 15:48:18
    hmm, I don't know. I'm tired.

    EDIT: I tried starting parity as 1 instead of 0 for the hell of it but no surprise word0 stays full of 8K and 16K scores.
    "... 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."
Sign In or Register to comment.