Simplify the PRNG code and usage #148
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This patch replaces RKISS by a simpler and faster PRNG, xorshift64* proposed by S. Vigna (2014). It is extremely simple, has a large enough period for Stockfish's needs (2^64), requires no warming-up (allowing such code to be removed), and offers slightly better randomness than MT19937. Paper: http://xorshift.di.unimi.it/ Reference source code (public domain): http://xorshift.di.unimi.it/xorshift64star.c The patch also simplifies how init_magics() searches for magics: - Old logic: seed the PRNG always with the same seed, then use optimized bit rotations to tailor the RNG sequence per rank. - New logic: seed the PRNG with an optimized seed per rank. This has two advantages: 1. Less code and less computation to perform during magics search (not ROTL). 2. More choices for random sequence tuning. The old logic only let us choose from 4096 bit rotation pairs. With the new one, we can look for the best seeds among 2^64 values. Indeed, the set of seeds[][] provided in the patch reduces the effort needed to find the magics: 64-bit SF: Old logic -> 5,783,789 rand64() calls needed to find the magics New logic -> 4,420,086 calls 32-bit SF: Old logic -> 2,175,518 calls New logic -> 1,895,955 calls In the 64-bit case, init_magics() take 25 ms less to complete (Intel Core i5). Finally, when playing with strength handicap, non-determinism is achieved by setting the seed of the static RNG only once. Afterwards, there is no need to skip output values. The bench only changes because the Zobrist keys are now different (since they are random numbers straight out of the PRNG). New bench: 7573215
With these seeds, magics are found even faster. On Intel Core i5, time spent in init_magics is now 185 ms, vs 245 ms with former logic (RKISS).
This time, the seed has been carefully chosen so that the
resulting Zobrist keys are particularly well-behaved:
1. All triplets of XORed keys are unique, implying that it
would take at least 7 keys to find a 64-bit collision
(test suggested by ceebo)
2. All pairs of XORed keys are unique modulo 2^32
3. The cardinality of { (key1 ^ key2) >> 48 } is as close
as possible to the maximum (65536)
Point 2 aims at ensuring a good distribution among the bits
that determine an TT entry's cluster, likewise point 3
among the bits that form the TT entry's key16 inside a
cluster.
Details:
Bitset card(key1^key2)
------ ---------------
RKISS
key16 64894 = 99.020% of theoretical maximum
low18 180117 = 99.293%
low32 305362 = 99.997%
Xorshift64*, old seed
key16 64918 = 99.057%
low18 179994 = 99.225%
low32 305350 = 99.993%
Xorshift64*, new seed
key16 65027 = 99.223%
low18 181118 = 99.845%
low32 305371 = 100.000%
Class is small enough that it doesn't deserve its own file. Suggested my Marco.
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Nice! Changes look good to me. |
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As the author of (part of) the code this patch replaces I am very happy it s
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Approved. RKiss was an overkill for Stockfish, so I'm happy that we can switch to something more simple. |
niklasf
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to niklasf/Stockfish
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Jan 5, 2017
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The patch replaces the concept of magic boosters by a set a well chosen PRNG seeds, allowing 30% quicker magics init; a simpler PRNG design particularly easy to seed; and for skill handicap play, does away with RNG sequence skipping.
Passed STC:
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 17668 W: 3628 L: 3500 D: 10540
and LTC:
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 73703 W: 12281 L: 12245 D: 49177