Duo Trio Quart (Bitboards)

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Pawn-Duo, (Phalanx) two adjacent pawns of the same color on the same rank that mutually cover the other's stop square. A Trio are three horizontal friendly pawns, a Quart four horizontal friendly pawns.

Working in the bitboard centric world to determine pawn related pattern set-wise.

The code snippets rely on shifting bitboards, specially by one step only.

=Neighbors= To get pawns with east or west neighbors is simple: U64 pawnsWithEastNeighbors(U64 pawns) { return pawns & westOne (pawns); }

U64 pawnsWithWestNeighbors(U64 pawns) { return pawnsWithEastNeighbors(pawns) << 1; // * 2 } or U64 pawnsWithWestNeighbors(U64 pawns) { return pawns & eastOne (pawns); }

U64 pawnsWithEastNeighbors(U64 pawns) { return pawnsWithWestNeighbors(pawns) >> 1; }

pawns              pawns with east     pawns with west     pawns with east neighbors          neighbors           and west neighbors . . . . . . . .    . . . . . . . .     . . . . . . . .     . . . . . . . . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . 1 1 1 . . . . .     1 1 . . . . . .     . 1 1 . . . . .     . 1 . . . . . . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . . . . . . 1 1 .     . . . . . 1 . .     . . . . . . 1 .     . . . . . . . . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . =Neighbor Algebra= Pawns with east or west neighbors are at least member of a duo. Pawns with east and west neighbors at least member of a trio. If two neighbors have both east and west neighbors, it is at least a quart.

An exclusive pawn duo is therefor a pawn with one neighbor, while this neighbor has no other neighbor as well. U64 duo (U64 pawns) { U64 withWestNeighbors = pawnsWithWestNeighbors(pawns); U64 withEastNeighbors = withWestNeighbors >> 1;

U64 withOneExclusiveNeighbor = withWestNeighbors ^ withEastNeighbors; U64 withExclusiveWestNeighbor = withWestNeighbors & withOneExclusiveNeighbor; U64 withExclusiveEastNeighbor = withEastNeighbors & withOneExclusiveNeighbor;

U64 duoWestOne = withEclusiveEastNeighbor & (withEclusiveWestNeighbor >> 1); U64 duoEastOne = duoWestOne << 1; return duoWestOne | duoEastOne; }

pawns              pawns with excl. pawns with excl. duo east neighbor      west neighbor . . . . . . . .    . . . . . . . .     . . . . . . . .     . . . . . . . . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . 1 1 1 . . . . .     1 . . . . . . .     . . 1 . . . . .     . . . . . . . . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . . . . . . 1 1 .     . . . . . 1 . .     . . . . . . 1 .     . . . . . 1 1 . . . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . . =See also=
 * Stop Square
 * Hanging Pawns
 * Pawn Islands (Bitboards)
 * Phalanx (Engine)

=Forum Posts=
 * The phalanx concept by Lyudmil Tsvetkov, CCC, May 21, 2014

=External Links=
 * Pawn Structure (General) | Page 5 of 5 | Phalanx Formation
 * Duet from Wikipedia
 * Phalanx from Wikipedia
 * Trio from Wikipedia
 * Kinga Głyk Trio - Walking Baby, VisionInMusica, Terni, March 10, 2017, YouTube Video
 * Kinga Głyk, Irek Głyk, Rafal Stepien


 * Quart (disambiguation) from Wikipedia
 * Panta Rhei plays Bartók's Quarts, 1977, YouTube Video

=References=

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