Magics
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Magics
Hi, have been away from site for some time, was wondering if there were any improvement to the magics in magic move generation.
In particular, the shifts for the bishop I have are:
58, 59, 59, 59, 59, 59, 59, 58,
59, 59, 59, 59, 59, 59, 59, 59,
60, 60, 57, 57, 57, 57, 59, 59,
59, 59, 57, 55, 55, 57, 59, 59,
59, 59, 57, 55, 55, 57, 59, 59,
59, 59, 57, 57, 57, 57, 59, 60,
59, 59, 59, 59, 59, 59, 59, 59,
58, 59, 59, 59, 59, 59, 59, 58
Of particular interest are squares 16,17,47 which have been reduced from 59(32 entries) to 60(16 entries) thanks to Richard Pijl.
So perhaps all of the '59 shift' squares can go to '60 shift'. and maybe other squares can also have their tables halved in size too.
So I was curious if any more magics have been produced to improve what I have.
I've tried to figure out how to generate them but appears to be a very difficult problem.
Any thoughts?
In particular, the shifts for the bishop I have are:
58, 59, 59, 59, 59, 59, 59, 58,
59, 59, 59, 59, 59, 59, 59, 59,
60, 60, 57, 57, 57, 57, 59, 59,
59, 59, 57, 55, 55, 57, 59, 59,
59, 59, 57, 55, 55, 57, 59, 59,
59, 59, 57, 57, 57, 57, 59, 60,
59, 59, 59, 59, 59, 59, 59, 59,
58, 59, 59, 59, 59, 59, 59, 58
Of particular interest are squares 16,17,47 which have been reduced from 59(32 entries) to 60(16 entries) thanks to Richard Pijl.
So perhaps all of the '59 shift' squares can go to '60 shift'. and maybe other squares can also have their tables halved in size too.
So I was curious if any more magics have been produced to improve what I have.
I've tried to figure out how to generate them but appears to be a very difficult problem.
Any thoughts?
Colin

 Posts: 2192
 Joined: Wed Mar 08, 2006 7:47 pm
 Location: Hattingen, Germany
Re: Magics
There are some more bishop squares with N1 bits:
https://chessprogramming.wikispaces.com ... ics+so+far
The latest trend seems to use fixed shift magics, and magic packing.
https://chessprogramming.wikispaces.com ... ics+so+far
The latest trend seems to use fixed shift magics, and magic packing.
Re: Magics
Thanks, those magics seem a good improvement on what I have.
I'm curious about Fixed Shift Magics, I can't seem to see anything that explains what they are/how they work.
Can anyone point me in the right direction...
I see this site has Fixed Shift Magics, http://www.openaurec.com/wbforum/viewt ... =4&t=51162 but its unclear how to use them.
Thanks
I'm curious about Fixed Shift Magics, I can't seem to see anything that explains what they are/how they work.
Can anyone point me in the right direction...
I see this site has Fixed Shift Magics, http://www.openaurec.com/wbforum/viewt ... =4&t=51162 but its unclear how to use them.
Thanks
Colin
Re: Magics
see https://chessprogramming.wikispaces.com ... ft%20Fancy
The only difference of fixed shift magics is to always shift the product of the magicmultiplication by the constant 52 (=6412) for rooks and not having to look up a variable in a separate array.
This idea is not new. It just requires more memory for less computation. The novelty is the idea to have the resulting bitboard data overlap.
regards
Edmund
The only difference of fixed shift magics is to always shift the product of the magicmultiplication by the constant 52 (=6412) for rooks and not having to look up a variable in a separate array.
This idea is not new. It just requires more memory for less computation. The novelty is the idea to have the resulting bitboard data overlap.
regards
Edmund
Re: Magics
Thanks, I don't think I get it, but this is what I think I think:
Will use pseduo java code with the ROOK case:
long is 64 bit
int is 32 bit
Consider any occupancy, and any square:
long occ = any_occupancy;
int sq = any_square
Apply mask (identical to magic move generation):
occ &= rook_mask[sq];
Multiply by magic number for that square
occ *= rook_magic[sq];
Get top 12 bits:
int index = (int)( occ >>> 52);
Then is there an array for each square of size 4096?
Moves = magicArray[sq][index];
And this is where I'm stuck, since this is just normal magic move generation but all arrays are large (4096).
Thats as much as I can understand for now
Will use pseduo java code with the ROOK case:
long is 64 bit
int is 32 bit
Consider any occupancy, and any square:
long occ = any_occupancy;
int sq = any_square
Apply mask (identical to magic move generation):
occ &= rook_mask[sq];
Multiply by magic number for that square
occ *= rook_magic[sq];
Get top 12 bits:
int index = (int)( occ >>> 52);
Then is there an array for each square of size 4096?
Moves = magicArray[sq][index];
And this is where I'm stuck, since this is just normal magic move generation but all arrays are large (4096).
Thats as much as I can understand for now
Colin
Re: Magics
Yes, you have it right. See this threadcms271828 wrote:Get top 12 bits:
int index = (int)( occ >>> 52);
Then is there an array for each square of size 4096?
Moves = magicArray[sq][index];
And this is where I'm stuck, since this is just normal magic move generation but all arrays are large (4096).
http://www.talkchess.com/forum/viewtopi ... at&start=0
Robert P.
Re: Magics
True .. the size for each square is 4096. But the good thing is, with certain magic keys you can drive the density down. For example with square 0 (the most difficult one to get a proper compression) you can get a density of about 3/4, and the central squares have densities much lower. Now with this in mind you can start "packing" the data in the array.cms271828 wrote:Then is there an array for each square of size 4096?
Moves = magicArray[sq][index];
Onno started off by finding magic keys that minimise the density and maximise the largest gaps between bits and then manually he fitted the tables together.
Eventually you don't have an array magicArray[sq][index] but just magicArray[index] and a second offsetArray[sq], which tells for every square where to start looking for the relevant data in the large array.
regards
Edmund
Re: Magics
Thanks, I set it up using
I have a8 = 0, h1 = 63
But I have a problem with the bishops...
Firstly, I create the index into the table with..
Now for square 2 (c8), with occupancy (b7,d7,e6,f5) = 0x20100A00
I obtain index = 9794.
And for square 6 (g8), with occupancy (e6) = 0x100000
I obtain index = 9794
Clearly there's an error, since those occupancies have different attack sets.
I'm not sure what I'm doing wrong, is the bishop shift not 52?
Also data is taken from the 8th entry here http://www.openaurec.com/wbforum/viewt ... =4&t=51162
Please help me figure this out, thanks
Code: Select all
unsigned long long lookup_table[97264];
struct
{
unsigned long long factor;
int position;
}
bishop_magics[64] =
{
{ 0x007bfeffbfeffbffull, 16530 },
{ 0x003effbfeffbfe08ull, 9162 },
{ 0x0000401020200000ull, 9674 },
{ 0x0000200810000000ull, 18532 },
{ 0x0000110080000000ull, 19172 },
{ 0x0000080100800000ull, 17700 },
{ 0x0007efe0bfff8000ull, 5730 },
{ 0x00000fb0203fff80ull, 19661 },
{ 0x00007dff7fdff7fdull, 17065 },
{ 0x0000011fdff7efffull, 12921 },
{ 0x0000004010202000ull, 15683 },
{ 0x0000002008100000ull, 17764 },
{ 0x0000001100800000ull, 19684 },
{ 0x0000000801008000ull, 18724 },
{ 0x000007efe0bfff80ull, 4108 },
{ 0x000000080f9fffc0ull, 12936 },
{ 0x0000400080808080ull, 15747 },
{ 0x0000200040404040ull, 4066 },
{ 0x0000400080808080ull, 14359 },
{ 0x0000200200801000ull, 36039 },
{ 0x0000240080840000ull, 20457 },
{ 0x0000080080840080ull, 43291 },
{ 0x0000040010410040ull, 5606 },
{ 0x0000020008208020ull, 9497 },
{ 0x0000804000810100ull, 15715 },
{ 0x0000402000408080ull, 13388 },
{ 0x0000804000810100ull, 5986 },
{ 0x0000404004010200ull, 11814 },
{ 0x0000404004010040ull, 92656 },
{ 0x0000101000804400ull, 9529 },
{ 0x0000080800104100ull, 18118 },
{ 0x0000040400082080ull, 5826 },
{ 0x0000410040008200ull, 4620 },
{ 0x0000208020004100ull, 12958 },
{ 0x0000110080040008ull, 55229 },
{ 0x0000020080080080ull, 9892 },
{ 0x0000404040040100ull, 33767 },
{ 0x0000202040008040ull, 20023 },
{ 0x0000101010002080ull, 6515 },
{ 0x0000080808001040ull, 6483 },
{ 0x0000208200400080ull, 19622 },
{ 0x0000104100200040ull, 6274 },
{ 0x0000208200400080ull, 18404 },
{ 0x0000008840200040ull, 14226 },
{ 0x0000020040100100ull, 17990 },
{ 0x007fff80c0280050ull, 18920 },
{ 0x0000202020200040ull, 13862 },
{ 0x0000101010100020ull, 19590 },
{ 0x0007ffdfc17f8000ull, 5884 },
{ 0x0003ffefe0bfc000ull, 12946 },
{ 0x0000000820806000ull, 5570 },
{ 0x00000003ff004000ull, 18740 },
{ 0x0000000100202000ull, 6242 },
{ 0x0000004040802000ull, 12326 },
{ 0x007ffeffbfeff820ull, 4156 },
{ 0x003fff7fdff7fc10ull, 12876 },
{ 0x0003ffdfdfc27f80ull, 17047 },
{ 0x000003ffefe0bfc0ull, 17780 },
{ 0x0000000008208060ull, 2494 },
{ 0x0000000003ff0040ull, 17716 },
{ 0x0000000001002020ull, 17067 },
{ 0x0000000040408020ull, 9465 },
{ 0x00007ffeffbfeff9ull, 16196 },
{ 0x007ffdff7fdff7fdull, 6166 }
},
rook_magics[64] =
{
{ 0x00a801f7fbfeffffull, 85487 },
{ 0x00180012000bffffull, 43101 },
{ 0x0040080010004004ull, 0 },
{ 0x0040040008004002ull, 49085 },
{ 0x0040020004004001ull, 93168 },
{ 0x0020008020010202ull, 78956 },
{ 0x0040004000800100ull, 60703 },
{ 0x0810020990202010ull, 64799 },
{ 0x000028020a13fffeull, 30640 },
{ 0x003fec008104ffffull, 9256 },
{ 0x00001800043fffe8ull, 28647 },
{ 0x00001800217fffe8ull, 10404 },
{ 0x0000200100020020ull, 63775 },
{ 0x0000200080010020ull, 14500 },
{ 0x0000300043ffff40ull, 52819 },
{ 0x000038010843fffdull, 2048 },
{ 0x00d00018010bfff8ull, 52037 },
{ 0x0009000c000efffcull, 16435 },
{ 0x0004000801020008ull, 29104 },
{ 0x0002002004002002ull, 83439 },
{ 0x0001002002002001ull, 86842 },
{ 0x0001001000801040ull, 27623 },
{ 0x0000004040008001ull, 26599 },
{ 0x0000802000200040ull, 89583 },
{ 0x0040200010080010ull, 7042 },
{ 0x0000080010040010ull, 84463 },
{ 0x0004010008020008ull, 82415 },
{ 0x0000020020040020ull, 95216 },
{ 0x0000010020020020ull, 35015 },
{ 0x0000008020010020ull, 10790 },
{ 0x0000008020200040ull, 53279 },
{ 0x0000200020004081ull, 70684 },
{ 0x0040001000200020ull, 38640 },
{ 0x0000080400100010ull, 32743 },
{ 0x0004010200080008ull, 68894 },
{ 0x0000200200200400ull, 62751 },
{ 0x0000200100200200ull, 41670 },
{ 0x0000200080200100ull, 25575 },
{ 0x0000008000404001ull, 3042 },
{ 0x0000802000200040ull, 36591 },
{ 0x00ffffb50c001800ull, 69918 },
{ 0x007fff98ff7fec00ull, 9092 },
{ 0x003ffff919400800ull, 17401 },
{ 0x001ffff01fc03000ull, 40688 },
{ 0x0000010002002020ull, 96240 },
{ 0x0000008001002020ull, 91632 },
{ 0x0003fff673ffa802ull, 32495 },
{ 0x0001fffe6fff9001ull, 51133 },
{ 0x00ffffd800140028ull, 78319 },
{ 0x007fffe87ff7ffecull, 12595 },
{ 0x003fffd800408028ull, 5152 },
{ 0x001ffff111018010ull, 32110 },
{ 0x000ffff810280028ull, 13894 },
{ 0x0007fffeb7ff7fd8ull, 2546 },
{ 0x0003fffc0c480048ull, 41052 },
{ 0x0001ffffa2280028ull, 77676 },
{ 0x00ffffe4ffdfa3baull, 73580 },
{ 0x007ffb7fbfdfeff6ull, 44947 },
{ 0x003fffbfdfeff7faull, 73565 },
{ 0x001fffeff7fbfc22ull, 17682 },
{ 0x000ffffbf7fc2ffeull, 56607 },
{ 0x0007fffdfa03ffffull, 56135 },
{ 0x0003ffdeff7fbdecull, 44989 },
{ 0x0001ffff99ffab2full, 21479 }
};
But I have a problem with the bishops...
Firstly, I create the index into the table with..
Code: Select all
int index = (int) ((occ * bishop_magics[sq]) >>> 52) + bishop_pos[sq];
I obtain index = 9794.
And for square 6 (g8), with occupancy (e6) = 0x100000
I obtain index = 9794
Clearly there's an error, since those occupancies have different attack sets.
I'm not sure what I'm doing wrong, is the bishop shift not 52?
Also data is taken from the 8th entry here http://www.openaurec.com/wbforum/viewt ... =4&t=51162
Please help me figure this out, thanks
Colin