Duo Trio Quart (Bitboards)

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Samuel Bak - White and Blue ¹

Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota ↩︎

Pawn-Duo, (Phalanx) ¹
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.

Contents

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
}

U64 pawnsWithWestNeighbors(U64 pawns) {
   return pawns & eastOne (pawns);
}

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

8/8/8/8/PPP5/8/5PP1/8

pawns               pawns with east     pawns with west     pawns with east
                    neighbors           neighbors           and west neighbors
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
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. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
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
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
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1 1 1 . . . . .     1 . . . . . . .     . . 1 . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . 1 1 .     . . . . . 1 . .     . . . . . . 1 .     . . . . . 1 1 .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .