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Perft

4,852 bytes added, 07:48, 11 October 2021
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'''Perft''', ('''perf'''ormance '''t'''est, move path enumeration)<br/>
a [[Debugging|debugging ]] function to walk the move generation tree of strictly [[Legal Move|legal moves]] to count all the [[Leaf Node|leaf nodes]] of a certain [[Depth|depth]], which can be compared to [[Perft Results|predetermined values]] and used to isolate [[Engine Testing#bugs|bugs]]. In perft, nodes are only counted at the end after the last [[Make Move|makemove]]. Thus "higher" [[Terminal Node|terminal nodes]] (e.g. mate or stalemate) are not counted, instead the number of move paths of a certain depth. Perft ignores draws by [[Repetitions|repetition]], by the [[Fifty-move Rule|fifty-move rule]] and by [[Material#InsufficientMaterial|insufficient material]]. By recording the amount of time taken for each iteration, it's possible to compare the performance of different move generators or the same generator on different machines, though this must be done with caution since there are variations to perft.
=Perft function=
A simple perft function in [[C]] looks as followsthe following:
<pre>
typedef unsigned long long u64;
u64 Perft(int depth)
{
MOVE move_list[256]; int n_moves, i; u64 nodes = 0;
if (depth == 0) return 11ULL;
n_moves = GenerateLegalMoves(move_list); for (i = 0; i < n_moves; i++) { MakeMove(move_list[i]); nodes += Perft(depth - 1); UndoMove(move_list[i]); } return nodes;
}
</pre>
=Speed up===<span id="Bulk"></span>Bulk-counting==Assuming the above code used a legal move generator. The algorithm is simple, short but it makes moves for every node even they are the leave (ends of branches). It could improve speed significantly: instead of counting nodes at "depth 0", legal move generators can take advantage of the fact that the number of moves generated at "depth 1" represents the accurate perft Perft value for that branch. Therefore they can skip the last [[Make Move|makemove]]/[[Unmake Move|undomove]], which gives much faster results and is a better indicator of the raw move generator speed (versus move generator + make/unmake). However, this can cause some confusion when comparing perft Perft valuesand may make the task of collecting some extra information such as the number of captures and checks be almost impossible.
<pre>
typedef unsigned long long u64Perft(int depth /* assuming >= 1 */){ MOVE move_list[256]; int n_moves, i; u64 nodes = 0;  n_moves = GenerateLegalMoves(move_list);
u64 Perft if (int depth== 1){ MOVE move_list[256]; int return (u64) n_moves, i; u64 nodes = 0;
n_moves = GenerateLegalMoves(move_list); for (i = 0; i < n_moves; i++) { if (depth == 1) nodes++; else { MakeMove(move_list[i]); nodes += Perft(depth - 1); UndoMove(move_list[i]); } } return nodes;
}
</pre>
==Perft function with pseudo move generatorPseudo Legal Moves==To generate legal moves some programs have to make moves first, call a function to check if the function IsIncheck position incheck and then undo those moves. That makes the above Perft function to make and undo moves twice for all moves. Bellow Below code can avoid that problem and run much faster:
<pre>
typedef unsigned long long u64;
 
u64 Perft(int depth)
{
MOVE move_list[256]; int n_moves, i; u64 nodes = 0;
if (depth == 0) return 11ULL;
n_moves = GenerateMoves(move_list); for (i = 0; i < n_moves; i++) { MakeMove(move_list[i]); if (!IsIncheck()) nodes += Perft(depth - 1); UndoMove(move_list[i]); } return nodes;
}
</pre>
<span id==Hashing== Perft can receive another speed boost by [[Hash Table|hashing]] node counts, with a small chance for inaccurate results. Sometimes this is used as a sanity check to make sure the hash table and keys are working correctly. =Divide= The Divide command is often implemented as a variation of Perft, listing all moves and for each move, the perft of the decremented depth. However, some programs already give "Bulkdivided"output for Perft. Below is output of [[Stockfish]] when computing perft 5 for start position: <pre>go perft 5a2a3: 181046b2b3: 215255c2c3: 222861d2d3: 328511e2e3: 402988f2f3: 178889g2g3: 217210h2h3: 181044a2a4: 217832b2b4: 216145c2c4: 240082d2d4: 361790e2e4: 405385f2f4: 198473g2g4: 214048h2h4: 218829b1a3: 198572b1c3: 234656g1f3: 233491g1h3: 198502 Nodes searched: 4865609</spanpre>
=Purposes=
Perft is mostly for debugging purposes. It works mainly with functions: move generators, make move, unmake move. They all are very basic and vital for chess engines. By comparing Perft results developers can find out if those functions work correctly or not. If they are incorrect developers can narrow quickly by comparing branches, then call Perft for wrong branches with lower depth, repeat until finding direct positions which give the wrong result.
=Hashing= Other purposes:Perft can receive another speed boost by [[Hash Table|hashing]] node counts* give a quick glance at how good/bad their generators/make/unmake functions are, compared with the speed of other engines* calculate branch factors* a small chance for inaccurate factor to estimate how the complexity of chess variants, by comparing branch factors or Perft results. Sometimes this is used as at a sanity check to make sure the hash table and keys are working correctly.given depth for their starting positions
<span id="History"></span>=Perft History=
Supposably, perft was first implemented within the [[Cobol]] program [[RSCE-1]] by [[Rolf C. Smith#RCSmith|R.C. Smith]], submitted to the [https://en.wikipedia.org/wiki/United_States_Chess_Federation USCF] for evaluation, and subject of an [[Timeline#1978|1978]] [[Computerworld]] article <ref>[http://news.google.com/newspapers?nid=849&dat=19780417&id=h8lOAAAAIBAJ&sjid=DEoDAAAAIBAJ&pg=6180,1080528 Written in Cobol - Program Written as Chess Buff's Research Aid] by Brad Schultz, [[Computerworld]], April 17, 1978, Page 37</ref> . RSCE-1's purpose was not to play chess games, but position analysis, to find forced [[Checkmate|mates]], and to perform a move path enumeration of up to three [[Ply|plies]], with the [[Perft Results|perft(3) result]] of 8,902 from the [[Initial Position|initial position]] already mentioned <ref>[http://www.talkchess.com/forum/viewtopic.php?t=41373 Perft(3) from 1978, with a twist!] by [[Steven Edwards]], [[CCC]], December 08, 2011</ref>. [[Ken Thompson]] may have calculated perft(3) and perft(4) earlier than this date with [[Belle]]. [[Steven Edwards]] suggested the move path enumeration in 1995 as implemented in [[Spector]] <ref>[https://groups.google.com/d/msg/rec.games.chess.computer/M8V1AzkfOok/YV9lcfOlfgIJ Re: Speed of Move Generator] by [[Steven Edwards]], [[Computer Chess Forums|rgcc]], August 16, 1995</ref> and has since been actively involved in Perft computations, while the term "Perft" was likely coined by a [[Crafty]] command, despite its initial implementation was not conform to the above definition <ref>[https://groups.google.com/d/msg/rec.games.chess.computer/2nqtCdHC-r0/ENqomE2u51kJ Re: complete opening tree stats] by [[Robert Hyatt]], [[Computer Chess Forums|rgcc]], February 05, 1998</ref>.
<span id="15"></span>
In '''August 2017''', [[Ankan Banerjee]], who already confirmed Peter Österlund's perft('''14''') in September 2016 <ref>[http://www.talkchess.com/forum/viewtopic.php?t=61119&start=30 Re: yet another attempt on Perft(14)] by [[Ankan Banerjee]], [[CCC]], September 09, 2016</ref>, computed perft('''15''') of 2,015,099,950,053,364,471,960 with his [[GPU]] perft program <ref>[https://github.com/ankan-ban/perft_gpu ankan-ban/perft_gpu · GitHub]</ref>, running it several days two times with different [[Zobrist Hashing|zobrist keys]] on a cluster of [https://en.wikipedia.org/wiki/Nvidia_DGX-1 Nvidia DGX-1] server systems <ref>[https://www.nvidia.com/en-us/data-center/dgx-1/ DGX-1 for AI Research | NVIDIA]</ref>. His program starts exploring the tree in [[Depth-First|depth first]] manner on CPU. When a certain depth is reached a GPU function (kernel) is launched to compute perft of the subtree in [[Best-First|breadth first]] manner <ref>[http://www.talkchess.com/forum/viewtopic.php?t=64983&start=9 Re: Perft(15): comparison of estimates with Ankan's result] by [[Ankan Banerjee]], [[CCC]], August 26, 2017</ref>. Ankan Banerjee dedicated his computations in honor to [[Steven Edwards]] - whose tireless efforts for verifying perft(14) encouraged him to verify perft(14) and take up the challenge to compute perft(15) <ref>[http://www.talkchess.com/forum/viewtopic.php?t=64983&start=4 Re: perft(15)] by [[Ankan Banerjee]], [[CCC]], August 25, 2017</ref>.
 =Quotes=by [[Robert Hyatt]] in a forum post, June 12, 2020 <span idref>[http://talkchess.com/forum3/viewtopic.php?f=7&t="Divide">74153 Re: Perft speed and depth questions] by [[Mark Buisseret]], [[Computer Chess Forums|CCRL Discussion Board]], June 12, 2020</spanref>:=Divide= The Divide command is often implemented as I believe I was the first to use this. Back in the 80's. We rewrote the move generator in Cray Blitz in assembly language. It was a variation of pain to debug. I decided on the "perft" approach solely to test/debug the move generator. We'd run two versions, one FORTRAN, one assembly, listing all moves and for each we tested and debugged until they matched. I carried this over into Crafty as early versions went through several different approaches on movegeneration. Starting with the Slate/Atkin approach, then rotated bit boards (which took some time to debug), and the perft magic. It was really intended solely for that purpose. Then several started to use it as a benchmark for speed. I never followed that path since move generation is a very small part of the decremented depthoverall CPU time burned. Speed here is not so important. HoweverI doubt anyone's move generator takes more than 10% of total search time, some programs already give "divided" output for which means a 20% improvement in perftnumbers is only a 2% overall speed gain. I would not worry about anything but matching the node counts exactly...
=Results=
* [[Perft Results]]
* [[Chess960 Perft Results]]
* [[Chinese Chess Perft Results]]
=Publications=
* [[Aart Bik]] ('''2012'''). ''Computing Deep Perft and Divide Numbers for Checkers''. [[ICGA Journal#35_4|ICGA Journal, Vol. 35, No. 4]] » [[Checkers]]
* [[Daniel Shawul|Daniel S. Abdi]] ('''2013'''). ''Monte carlo methods for estimating game tree size''. <ref>[http://www.talkchess.com/forum/viewtopic.php?t=47740&topic_view=flat&start=11 Re: MC methods] by [[Daniel Shawul]], [[CCC]], April 13, 2013</ref> » [[Monte-Carlo Tree Search]]
 
=Perft in other Games=
* [http://tonyjh.com/chess/technical/ Perft for other forms of Chess] by [[Tony Hecker]]
* [http://checker-board.blogspot.com/2009/02/perft-for-checkers.html Perft for Checkers] by [[Martin Fierz]]
* [http://www.aartbik.com/strategy.php Perft for Checkers and Reversi/Othello] by [[Aart Bik]]
=Forum Posts=
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=71379 You gotta love Perft... just not too much!] by [[Martin Bryant]], [[CCC]], July 27, 2019
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=71550 Shogi Perft numbers] by [[Toni Helminen]], [[CCC]], August 14, 2019 » [[Shogi]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=72669 LastEmperor - Chess960 perft tool] by [[Toni Helminen|JohnWoe]], [[CCC]], December 28, 2019 » [[Chess960 Perft Results]]
==2020 ...==
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=73493 Where to enter/read position into hash table in perft?] by [[Marcel Vanthoor]], [[CCC]], March 28, 2020 » [[Transposition Table]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=73558 Count the number of nodes of perft(14) and beyond] by [[Marc-Philippe Huget]], [[CCC]], April 04, 2020
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=73625 magic bitboard perft] by [[Richard Delorme]], [[CCC]], April 11, 2020 » [[Magic Bitboards]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=73577 Perft speed optimization] by [[Marcel Vanthoor]], [[CCC]], April 06, 2020
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=73812 Request for InDoubleCheck PERFTS EPDs] by [[Chris Whittington]], [[CCC]], May 02, 2020 » [[Double Check]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=74153 Perft speed and depth questions] by [[Mark Buisseret]], [[CCC]], June 12, 2020
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=75877 Place to find correct perft result from a fen position] by [[Elias Nilsson]], [[CCC]], November 20, 2020 » [[Perft Results]]
'''2021'''
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=76430 Chinese chess Xiangqi perft results] by [[Maksim Korzh]], [[CCC]], January 27, 2021 » [[Chinese Chess Perft Results]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=77054 PERFT transposition table funny?!] by [[Martin Bryant]], [[CCC]], April 10, 2021 » [[Transposition Table]], [[Memory]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=2&t=77069 Perft 7 -> 1.6 trillion moves] by [[Michael Byrne|MikeB]], [[CCC]], April 12, 2021
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=77350 Being silly with perft and legal move generation] by [[Jakob Progsch]], [[CCC]], May 19, 2021 » [[Move Generation#Legal|Legal Move Generation]], [[En passant]]
* [http://talkchess.com/forum3/viewtopic.php?f=7&t=78119 Perft position to debug check-evasions via en passant capture] by [[Roland Tomasi]], [[CCC]], September 06, 2021
* [http://talkchess.com/forum3/viewtopic.php?f=7&t=78241 Perft test] by [[Pierluigi Meloni]], [[CCC]], September 24, 2021
* [http://talkchess.com/forum3/viewtopic.php?f=7&t=78230 Gigantua: 1.5 Giganodes per Second per Core move generator] by [[Daniel Infuehr]], [[CCC]], September 22, 2021
* [http://talkchess.com/forum3/viewtopic.php?f=7&t=78352 Gigantua: 2 Gigamoves per Second per Core move generator - Sourcecode Release] by [[Daniel Infuehr]], [[CCC]], October 07, 2021
=External Links=
* [https://en.wikipedia.org/wiki/Performance_testing Performance testing from Wikipedia]
* [https://web.archive.org/web/20061014115710/http://www.albert.nu/programs/dperft/ Distributed Perft Project] ([https://en.wikipedia.org/wiki/Wayback_Machine Wayback Machine])
==Perft in other Games==
* [http://tonyjh.com/chess/technical/ Perft for other forms of Chess] by [[Tony Hecker]]
* [http://checker-board.blogspot.com/2009/02/perft-for-checkers.html Perft for Checkers] by [[Martin Fierz]]
* [http://www.aartbik.com/strategy.php Perft for Checkers and Reversi/Othello] by [[Aart Bik]]
==Implementations==
* [httphttps://home.hccnet.nl/h.g.muller/dwnldpage.html µ-Max Dowload Page - qperft] by [[Harm Geert Muller]] » [[Micro-Max]]
* [https://github.com/ankan-ban/perft_gpu ankan-ban/perft_gpu · GitHub] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=48387 Fast perft on GPU (upto 20 Billion nps w/o hashing)] by [[Ankan Banerjee]], [[CCC]], June 22, 2013</ref>
* [http://cinnamonchess.altervista.org/auriga Auriga] by [[Giuseppe Cannella]] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=58406 Auriga - distributed and collaborative Perft] by [[Giuseppe Cannella]], [[CCC]], November 28, 2015</ref>
* [http://www.craftychess.com/documentation/craftydoc.html Crafty Command Documentation] by [[Robert Hyatt]], see perft <depth> » [[Crafty]]
* [https://github.com/abulmo/hqperft hqperft: Chess move generation based on (H)yperbola (Q)uintessence & range attacks] by [[Richard Delorme]] » [[Hyperbola Quintessence]]
* [https://github.com/jniemann66/juddperft GitHub - jniemann66/juddperft: Chess move generation engine] by [[Judd Niemann]]
* [http://www.rocechess.ch/perft.html perft, divide, debugging a move generator] from [[ROCE]] by [[Roman Hartmann]]
* [http://marcelk.net/rookie/nostalgia/v3/perft-random.epd perft-random.epd] by [[Marcel van Kervinck]] » [[Rookie]]
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