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'''[[Main Page|Home]] * [[Board Representation]] * [[Bitboards]] * [[Pawn Pattern and Properties]] * Pawn Attacks'''
A pawn captures diagonally forward, and controls or attacks one (rook pawn) or two squares one step ahead in diagonal [[Direction|direction(s)]]. For white versus black pawns forward and backward are considered relative from either whites or blacks point of view.
=Single Pawn=
<span id="AttacksOfaSinglePawn"></span>
==Attacks==
To get attacks, we use a lookup of pre-calculated pawn-atacks, similar to knight- and king-attacks, except the need to consider color of the pawn.
<pre>
whitePawnAttacks = arrPawnAttacks[white][sqOfWhitePawn];
if ( whitePawnAttacks & pieceBB[black] ) -> pseudo legal captures possible
</pre>
<pre>
arrPawnAttacks[white][d4]
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . 1 . 1 . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
</pre>
==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.
<span id="PawnAttacks"></span>
==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 Generation|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 [[General Setwise Operations#ShiftingBitboards|shifting bitboards]], specially by [[General Setwise Operations#OneStepOnly|one step only]].''
<pre>
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);}
</pre>
A bit-wise boolean instruction to combine those disjoint sets:
<pre>
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);
}
</pre>
and similar for black.
<pre>
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 . . . . . . . .
. . . . . . . . . . . . . . . .
</pre>
<span id="PawnAttackMaps"></span>
==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.
<pre>
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);
}
</pre>
Those attack maps are among other things useful to decide about [[Candidates (Bitboards)|candidates]] and [[Backward Pawns (Bitboards)|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:
<pre>
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);
}
</pre>
'''[[Pawn Pattern and Properties|Up one Level]]'''
A pawn captures diagonally forward, and controls or attacks one (rook pawn) or two squares one step ahead in diagonal [[Direction|direction(s)]]. For white versus black pawns forward and backward are considered relative from either whites or blacks point of view.
=Single Pawn=
<span id="AttacksOfaSinglePawn"></span>
==Attacks==
To get attacks, we use a lookup of pre-calculated pawn-atacks, similar to knight- and king-attacks, except the need to consider color of the pawn.
<pre>
whitePawnAttacks = arrPawnAttacks[white][sqOfWhitePawn];
if ( whitePawnAttacks & pieceBB[black] ) -> pseudo legal captures possible
</pre>
<pre>
arrPawnAttacks[white][d4]
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . 1 . 1 . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
</pre>
==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.
<span id="PawnAttacks"></span>
==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 Generation|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 [[General Setwise Operations#ShiftingBitboards|shifting bitboards]], specially by [[General Setwise Operations#OneStepOnly|one step only]].''
<pre>
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);}
</pre>
A bit-wise boolean instruction to combine those disjoint sets:
<pre>
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);
}
</pre>
and similar for black.
<pre>
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 . . . . . . . .
. . . . . . . . . . . . . . . .
</pre>
<span id="PawnAttackMaps"></span>
==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.
<pre>
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);
}
</pre>
Those attack maps are among other things useful to decide about [[Candidates (Bitboards)|candidates]] and [[Backward Pawns (Bitboards)|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:
<pre>
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);
}
</pre>
'''[[Pawn Pattern and Properties|Up one Level]]'''
