Center Manhattan-Distance
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The Center Manhattan-Distance is the Manhattan-Distance or number of orthogonal King moves on the otherwise empty board from any square to the four squares {d4, d5, e4, e5} in the center of the board. In conjunction with Center Distance a constant array might be considered as the base of Piece-Square Tables. Center Manhattan-Distance is used in various evaluation terms, for instance to encourage the king to centralize in the ending, as well in Mop-up Evaluation.
Contents
Lookup
Rather than to calculate the Center Manhattan-Distance from square coordinates, taking the sum from the file- and rank- Center Distance each, a lookup of a small array is appropriate. This is how the Center Manhattan-Distance might be defined in C or C++:
const int arrCenterManhattanDistance[64] = { // char is sufficient as well, also unsigned
6, 5, 4, 3, 3, 4, 5, 6,
5, 4, 3, 2, 2, 3, 4, 5,
4, 3, 2, 1, 1, 2, 3, 4,
3, 2, 1, 0, 0, 1, 2, 3,
3, 2, 1, 0, 0, 1, 2, 3,
4, 3, 2, 1, 1, 2, 3, 4,
5, 4, 3, 2, 2, 3, 4, 5,
6, 5, 4, 3, 3, 4, 5, 6
};
Calculation
Avoid Memory lookup purists may use following calculation. The routine first extracts file and rank. If either is less than 4, its ones' complement is used, to get the file or rank wise Manhattan Center Distance from the two lower bits each (while the third lowest bit 2, is always set).
file = sq & 7; // 0 1 2 3 4 5 6 7 if (file < 4) file = ~file; // -1 -2 -3 -4 4 5 6 7 bit 2 is always set file &= 3; // 3 2 1 0 0 1 2 3
The file and rank distances are added for the final Manhattan Center Distance. The slight optimization considers each summand has bit 2 set, to perform the 'add' with a final post-mask 7, rather than to add two pre-masks with 3.
/**
* manhattanCenterDistance
* @author Gerd Isenberg
* @param sq square 0..63
* @return Manhattan Center Distance
*/
int manhattanCenterDistance(int sq) {
int file, rank;
file = sq & 7;
rank = sq >> 3;
file ^= (file-4) >> 8;
rank ^= (rank-4) >> 8;
return (file + rank) & 7;
}
with following generated x86 Assembly:
?manhattanCenterDistance PROC NEAR ; _sq$ = ecx 00000 8b d1 mov edx, ecx 00002 c1 f9 03 sar ecx, 3 00005 8d 41 fc lea eax, DWORD PTR [ecx-4] 00008 c1 f8 08 sar eax, 8 0000b 33 c1 xor eax, ecx 0000d 83 e2 07 and edx, 7 00010 8d 4a fc lea ecx, DWORD PTR [edx-4] 00013 c1 f9 08 sar ecx, 8 00016 33 ca xor ecx, edx 00018 03 c1 add eax, ecx 0001a 83 e0 07 and eax, 7 0001d c3 ret 0
See also
- Avoiding Branches
- Center Distance
- Corner-Distance in KBNK Endgame
- Manhattan-Distance
- Mop-up Evaluation
- Piece-Square Tables
Forum Posts
- Simple method for simple mates for programs without TBs by J. Wesley Cleveland, CCC, November 25, 2016 » Mop-up Evaluation, KBNK Endgame
