Pawn Attacks (Bitboards)

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A pawn captures diagonally forward, and controls or attacks one (rook pawn) or two squares one step ahead in diagonal direction(s). For white versus black pawns forward and backward are considered relative from either whites or blacks point of view.

=Single Pawn=

Attacks
To get attacks, we use a lookup of pre-calculated pawn-attacks, similar to knight- and king-attacks, except the need to consider color of the pawn. whitePawnAttacks = arrPawnAttacks[white][sqOfWhitePawn]; if ( whitePawnAttacks & pieceBB[black] ) -> pseudo legal captures possible

arrPawnAttacks[white][d4] . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

Captures
Only intersection with the opponent pieces is required. We may include a possible en passant target square.

=Pawns set-wise= Working in the bitboard centric world to determine attacks and properties set-wise.

Attacks
Generate all squares that are attacked by pawns of a color. It makes sense to keep disjoint sets for both attacking directions. For move geneneration purpose, disjoint east-west attacks has the advantage of unique source-target relation ship (+-7,9). After obtaining the direction-wise target-set a reverse shift is sufficient to get the source-set without further intersections and wrap issues.

The code snippets rely on shifting bitboards, specially by one step only. U64 wPawnEastAttacks(U64 wpawns) {return noEaOne(wpawns);} U64 wPawnWestAttacks(U64 wpawns) {return noWeOne(wpawns);}

U64 bPawnEastAttacks(U64 bpawns) {return soEaOne(bpawns);} U64 bPawnWestAttacks(U64 bpawns) {return soWeOne(bpawns);} A bit-wise boolean instruction to combine those disjoint sets: U64 wPawnAnyAttacks(U64 wpawns) { return wPawnEastAttacks(wpawns) | wPawnWestAttacks(wpawns); }

U64 wPawnDblAttacks(U64 wpawns) { return wPawnEastAttacks(wpawns) & wPawnWestAttacks(wpawns); }

U64 wPawnSingleAttacks(U64 wpawns) { return wPawnEastAttacks(wpawns) ^ wPawnWestAttacks(wpawns); } and similar for black.

white pawns      white pawns << 9  &       notAFile     ==   wPawnEastAttacks . . . . . . . .    . . . . . . . .      . 1 1 1 1 1 1 1      . . . . . . . . . . . . . . . .     . . . . . . . .      . 1 1 1 1 1 1 1      . . . . . . . . . . . . . . . .     . . . . . . . .      . 1 1 1 1 1 1 1      . . . . . . . . . . . . . . . .     . . . . . . . .      . 1 1 1 1 1 1 1      . . . . . . . . . . . . . . . .     h. . c. . . .     . 1 1 1 1 1 1 1      . . . c. . . . . . c. . . . .    . a b. d. f g. 1 1 1 1 1 1 1     . a b. d. f g a b. d. f g h. . . . . . . .     . 1 1 1 1 1 1 1      . . . . . . . . . . . . . . . .     / . . . . . . .      . 1 1 1 1 1 1 1      / . . . . . ..

white pawns      white pawns << 7  &       notHFile     ==  wPawnWestAttacks . . . . . . . .    . . . . . . . .      1 1 1 1 1 1 1 .      . . . . . . . . . . . . . . . .     . . . . . . . .      1 1 1 1 1 1 1 .      . . . . . . . . . . . . . . . .     . . . . . . . .      1 1 1 1 1 1 1 .      . . . . . . . . . . . . . . . .     . . . . . . . .      1 1 1 1 1 1 1 .      . . . . . . . . . . . . . . . .     . c. . . . . .     1 1 1 1 1 1 1 .      . c. . . . . . . . c. . . . .    b. d. f g h. 1 1 1 1 1 1 1 .     b. d. f g h. a b. d. f g h. . . . . . . a     1 1 1 1 1 1 1. . . . . . . . . . . . . . . . .    . . . . . . . \      1 1 1 1 1 1 1 .      . . . . . . . \

white pawns                                                 wPawnAnyAttacks . . . . . . . .                                              . . . . . . . .  . . . . . . . .                                               . . . . . . . .  . . . . . . . .                                               . . . . . . . .  . . . . . . . .                                               . . . . . . . .  . . . . . . . .                                               . c. c. . . . . . c. . . . .                                              b a 1. 1 g 1 g a b. d. f g h. . . . . . . . . . . . . . . .                                               . . . . . . ..

Attack Maps
One idea to combine pawn-attacks is about safe squares or push-targets for white respectively black pawns. A kind if of set-wise static exchange evaluation - only considering pawn-attacks from both sides. A square is assumed safe, if the number of own pawn defends if greater or equal than opponent pawn attacks. That is true if the own side defends a square twice, or the opposite side has no attacks at all, or own side attacks once and opponent not twice. U64 wSafePawnSquares(U64 wpawns, U64 bpawns) { U64 wPawnEastAttacks = wPawnEastAttacks (wpawns); U64 wPawnWestAttacks = wPawnWestAttacks (wpawns); U64 bPawnEastAttacks = bPawnEastAttacks (bpawns); U64 bPawnWestAttacks = bPawnWestAttacks (bpawns); U64 wPawnDblAttacks =  wPawnEastAttacks &  wPawnWestAttacks; U64 wPawnOddAttacks =  wPawnEastAttacks ^  wPawnWestAttacks; U64 bPawnDblAttacks =  bPawnEastAttacks &  bPawnWestAttacks; U64 bPawnAnyAttacks =  bPawnEastAttacks |  bPawnWestAttacks; return wPawnDblAttacks |~bPawnAnyAttacks | (wPawnOddAttacks &~bPawnDblAttacks); } Those attack maps are among other things useful to decide about candidates and backward pawns.

Captures
As usual, capture targets are the intersection of attack-sets with opponent pieces. Except en passant captures of course. A reverse shift of disjoint direction-wise sets obtains the pawns which may capture.

To find the pawn set, which can actually capture, on the fly, we can start with the target squares as well: U64 wPawnsAble2CaptureEast(U64 wpawns, U64 bpieces) { return wpawns & bPawnWestAttacks(bpieces); }

U64 wPawnsAble2CaptureWest(U64 wpawns, U64 bpieces) { return wpawns & bPawnEastAttacks(bpieces); }

U64 wPawnsAble2CaptureAny(U64 wpawns, U64 bpieces) { return wpawns & bPawnAnyAttacks(bpieces); }

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