**Move Generation with Perfect Hash Functions**

by Trevor Fenner and Mark Levene

Issue is sliding piece attacks. The paper is quite interesting, stunning modulo math. The authors map masked and normalized (shifted to bit zero) files, diagonal or antidiagonal occupancies to vectors of eight (or nine) consecutive bits, quite similar as kindergarten bitboards does.

They use modulo 514 for the diagonals and modulo 257 for the anti-diagonals to get 8 (or even nine for the diagonals) bits as an index. That can be done most efficiently by reciprocal multiplication - this is how vc2005 implements the mod for x64 processors. One 64*64=128 bit mul, one shift and one further imul, sub. Of course using 64-bit div to get the remainder burns even more cycles.

Code: Select all

```
% 514
mov r11d, r10 ; masked diagonal
mov rax, ff00ff00ff00ff01H
mul r10
shr rdx, 9
imul edx, 514 ; 00000202H
sub r11d, edx
% 257
mov r11d, r10 ; masked diagonal
mov rax, ff00ff00ff00ff01H
mul r10
shr rdx, 8
imul edx, 257 ; 00000101H
sub r11d, edx
```

Code: Select all

```
mov rax, 0101010101010101H
imul rdx, rax
shr rdx, 56
```

Despite huge rook-tables most prefer magic-bitboards over kindergarten, since it covers both lines of a rook or bishop in one run with only one and, mul, shift->lookup.

My question is - how can they conclude they are competitive over magic-botboards - if they even can not beat kindergarten-bitboards by margins - not to mention table size and inner six bit only? To compare a Matlab 32-bit implementation with a loop-version to get the sliding attacks? Because Sam Tannous claimed small improvement over rotated with some high level hashing directories - and Bob Hyatt reported similar performance of rotated versus magic in crafty?

Strange conclusions, for Reference see Bob's post the authors mention in their paper:

http://64.68.157.89/forum/viewtopic.php ... 41&t=16002

Further references:

http://chessprogramming.wikispaces.com/ ... ctionaries

http://chessprogramming.wikispaces.com/Magic+Bitboards

http://chessprogramming.wikispaces.com/ ... +Bitboards

Did I miss something on superfast matlab modulo?

Cheers,

Gerd