Double and Triple (Bitboards)

**[[Home]] * [[Board Representation]] * [[Bitboards]] * [[Pawn Pattern and Properties]] * Double and Triple**

[[toc]]
=By Square= 
Working in the **square centric world** of the board implies using a square index of one particular pawn, likely from [[Bitboard Serialization|bitboard traversal]].

For [[Doubled Pawn|doubled]] (twins) or multiple pawns on a file, we simply intersect the file-mask by own-pawns and perform a [[Population Count|population count]]. This symmetrical property appears to be equal for white and black pawns, except for the before- and behind semantic.
[[code format="cpp"]]
wPawnsOnFile = arrFiles[sqOfWhitePawn] & pawnBB[white];
if ( wPawnsOnFile & (wPawnsOnFile-1) ) -> white pawn is a least double pawn
if ( wPawnsOnFile & arrNortRay[sqOfWhitePawns] ) -> white pawn has own pawn ahead
if ( wPawnsOnFile & arrSoutRay[sqOfWhitePawns] ) -> white pawn has own pawn behind
[[code]]

[[code]]
arrFiles[d*]
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
[[code]]
The arrFiles might be condensed to eight bitboards only, instead of 64 - if we index by
[[code]]
file(sq) == sq & 7
[[code]]
instead of square.
[[#Multiple]]
=Multiple Pawns= 
Working in the **bitboard centric world** to determine pawn related pattern set-wise.

All pawns that are member of the [[Pawn Spans|rearspan]] of all own pawns, have at least one pawn in front on the same file. All pawns that are member of the [[Pawn Spans|frontspan]] of all own pawns, have at least one pawn behind on the same file.
[[code format="cpp"]]
// pawns with at least one pawn in front on the same file
U64 wPawnsBehindOwn(U64 wpawns) {return wpawns & wRearSpans(wpawns);}

// pawns with at least one pawn behind on the same file
U64 wPawnsInfrontOwn (U64 wpawns) {return wpawns & wFrontSpans(wpawns);}
[[code]]
Obviously, since each pawn in front of a pawn implies this pawn behind, the number of pawns in front is equal the number of pawns behind.
[[code format="cpp"]]
popCount(wPawnsBehindOwn) == popCount(wPawnsInfrontOwn)
[[code]]
The intersection of both sets implies at least a triple, thus a pawn in front and behind.
[[code format="cpp"]]
U64 wPawnsInfrontAndBehindOwn (U64 wpawns) {
   return wPawnsInfrontOwn(wpawns) &  wPawnsBehindOwn(wpawns);
}
[[code]]
If the intersection is empty on a file, it is a double pawn or a twin.
[[code format="cpp"]]
fileWithAtLeastTriple = fileFill(infrontAndBehindOwn);
rearTwin  = behindOwn  & ~fileWithAtLeastTriple;
frontTwin = infrontOwn & ~fileWithAtLeastTriple;
[[code]]

=Forum Posts=
* [[http://www.talkchess.com/forum/viewtopic.php?t=29689|Doubled and Backward Pawn Engine "Definitions"]] by [[Brian Richardson]], [[CCC]], September 07, 2009
* [[http://www.talkchess.com/forum/viewtopic.php?t=60133|Doubled pawns]] by [[Stefano Gemma]], [[CCC]], May 11, 2016

=What links here?=
[[include page="Double and Triple (Bitboards)" component="backlinks" limit="20" ]]
**[[Pawn Pattern and Properties|Up one Level]]**