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Added a reference to new titboard engine (TDFA), as well as some new data on speed comparison between titboards and magic bitboards. Clarified the explanation for why titboards are not commonly used.
'''Titboards''',<br/>
a bitboard-based [[Move Generation|move generation]] technique invented by [[Zach Wegner]] <ref>[http://www.open-aurec.com/wbforum/viewtopic.php?f=4&t=5623&p=27838 Yet another new bitboard move generation method] by [[Zach Wegner]], [[Computer Chess Forums|Winboard Forum]], September 22, 2006</ref> and first implemented by Malik Tremain <ref name="TDFA">[https://github.com/TiltedDFA/TDFA TDFA - Titboard Engine] by Malik Tremain, January 22, 2024</ref>. Titboards are based on an extension of bitboards to ternary boards, hence the name ("bit" means binary digit, "tit" mean [https://en.wikipedia.org/wiki/Ternary_numeral_system ternary digit]). Titboards are only used for move generation, not for any other purposes that typical bitboard attack-getters will be used for.
The idea of titboards is to eliminate [[BitScan|bitscans]]. Typical bitboard move generation techniques generate a bitboard, intersect it with the set of allowable [[Squares|squares]] (empty or enemy-occupied), and then [[Bitboard Serialization|serialize]] that into a list of moves. Titboards take a bitboard occupancy for each side for just one rank, file, or diagonal, and convert them to ternary representations and add them together. This index can determine which squares can actually be moved to, instead of just attacked. It is used in a lookup table of 3^7=2187 entries per [[Direction|direction]] per square.
Titboards are not typically used (there is no one known engine that implements them<ref name="TDFA"/>). The reasons behind this This is because they are that they use currently slower than modern alternatives while being harder to implement. They require a large amount of memory look-up table (more than ~8.9 MB) and they work very differently from modern generation techniques likes [[Magic Bitboards]]), and where they require each direction to be calculated individually {File, Rank, Diagonal, Anti-Diagonal}. For each direction they must keep another attack generation method beside require the input of (square, us, them due ), as a pose to their inflexibility. Modern cpus also have built-in bitscan instructions(square, further obsoleting ternary boardsoccupied) which is more commonly used.
=Speed=
Testing shows that titboards have no speed advantage over magic bitboardson modern hardware, however, the gap seemingly narrows on older CPUs that offer less efficient bitscan operations. A full array of results can be found here<ref>[https://github.com/TiltedDFA/TDFA/blob/3c4110f860f9c98b619a3f2565d139c92fe606c8/RunResults.txt TDFA - Perft result comparison]</ref>.
<pre>
Titboard perft group:
Pext perft group:
Magic Bitboard perft group:
</pre>
