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An Isolated Pawn or Isolani has no friendly pawns on adjacent files .

Isolani by Square

To determine whether a pawn is isolated, we simply lookup an array with neighboring file-masks. If the intersection of neighbored files with own pawns is empty, the pawn is isolated. This symmetrical property appears to be equal for white and black pawns.

if ( (arrNeighborFiles[sqOfWhitePawn] & pawnBB[white]) == 0 ) -> pawn is isolated

arrNeighborFiles[d*]
. . 1 . 1 . . .
. . 1 . 1 . . .
. . 1 . 1 . . .
. . 1 . 1 . . .
. . 1 . 1 . . .
. . 1 . 1 . . .
. . 1 . 1 . . .
. . 1 . 1 . . .

The arrNeighborFiles might be condensed to eight bitboards only, instead of 64 - if we index by

file(sq) == sq & 7

instead of square.

Isolanis and Half-isolanis set-wise

Isolated pawns are the relative complement of pawns with the union of their own attack fills over the whole file. To keep disjoint pawns with no neighbor on either east or west adjacent files has the advantage of greater versatility. Isolanis are the intersection of them, half-isolanis the exclusive or:

U64 noNeighborOnEastFile (U64 pawns) {
    return pawns & ~westAttackFileFill(pawns);
}
 
U64 noNeighborOnWestFile (U64 pawns) {
    return pawns & ~eastAttackFileFill(pawns);
}
 
U64 isolanis(U64 pawns) {
   return  noNeighborOnEastFile(pawns)
         & noNeighborOnWestFile(pawns);
}
 
U64 halfIsolanis(U64 pawns) {
   return  noNeighborOnEastFile(pawns)
         ^ noNeighborOnWestFile(pawns);
}

Hanging pawns

Hanging pawns are a duo of open and half-isolated pawns.

U64 wHangingPawns(U64 wpawns, U64 bpawns) {
   return wOpenPawns(wpawns, bpawns)
        & halfIsolanis(wpawns) & duo(wpawns);
}

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