Difference between revisions of "Hyperbola Quintessence"
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* [http://www.talkchess.com/forum/viewtopic.php?t=58795 Comparison of bitboard attack-getter variants] by [[Sven Schüle]], [[CCC]], January 04, 2016 | * [http://www.talkchess.com/forum/viewtopic.php?t=58795 Comparison of bitboard attack-getter variants] by [[Sven Schüle]], [[CCC]], January 04, 2016 | ||
* [http://www.talkchess.com/forum/viewtopic.php?t=58667&start=106 Re: The wrong way] by [[Aleks Peshkov]], [[CCC]], January 05, 2016 » [[SSSE3#SSSE3Version|SSSE3 Hyperbola Quintessence]] | * [http://www.talkchess.com/forum/viewtopic.php?t=58667&start=106 Re: The wrong way] by [[Aleks Peshkov]], [[CCC]], January 05, 2016 » [[SSSE3#SSSE3Version|SSSE3 Hyperbola Quintessence]] | ||
+ | * [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=71312 Understanding first rank attack state generation] by [[Kalyankumar Ramaseshan]], [[CCC]], July 18, 2019 » [[First Rank Attacks]] | ||
=External Links= | =External Links= | ||
+ | * [https://github.com/abulmo/hqperft GitHub - abulmo/hqperft: Chess move generation based on (H)yperbola (Q)uintessence & range attacks] by [[Richard Delorme]] » [[Perft]] | ||
* [http://www.youtube.com/watch?v=bCH4YK6oq8M&list=SPQV5mozTHmacMeRzJCW_8K3qw2miYqd0c&index=9 Sliding Pieces (Part 1) - Advanced Java Chess Engine Tutorial 8] by [[Jonathan Warkentin]] | * [http://www.youtube.com/watch?v=bCH4YK6oq8M&list=SPQV5mozTHmacMeRzJCW_8K3qw2miYqd0c&index=9 Sliding Pieces (Part 1) - Advanced Java Chess Engine Tutorial 8] by [[Jonathan Warkentin]] | ||
* [http://timcooijmans.blogspot.co.uk/2014/04/hyperbola-quintessence-for-rooks-along.html Hyperbola Quintessence for rooks along ranks] by [https://www.blogger.com/profile/11033414990764447420 Tim Cooijmans], April 6, 2014 <ref>[http://www.talkchess.com/forum/viewtopic.php?t=58795&start=10 Re: Comparison of bitboard attack-getter variants] by [[Matthew R. Brades]], [[CCC]], January 04, 2016</ref> | * [http://timcooijmans.blogspot.co.uk/2014/04/hyperbola-quintessence-for-rooks-along.html Hyperbola Quintessence for rooks along ranks] by [https://www.blogger.com/profile/11033414990764447420 Tim Cooijmans], April 6, 2014 <ref>[http://www.talkchess.com/forum/viewtopic.php?t=58795&start=10 Re: Comparison of bitboard attack-getter variants] by [[Matthew R. Brades]], [[CCC]], January 04, 2016</ref> | ||
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* [https://en.wikipedia.org/wiki/Aether_(classical_element)#Fifth_element Quintessence the Fifth Element from Wikipedia] | * [https://en.wikipedia.org/wiki/Aether_(classical_element)#Fifth_element Quintessence the Fifth Element from Wikipedia] | ||
==Misc== | ==Misc== | ||
− | * [[ | + | * [[:Category:Focus|Focus]] - [https://en.wikipedia.org/wiki/Hocus_Pocus_%28song%29 Hocus Pocus], [https://en.wikipedia.org/wiki/Pinkpop_Festival Pinkpop Festival] 1972, [https://en.wikipedia.org/wiki/Geleen Geleen], [https://en.wikipedia.org/wiki/YouTube YouTube] Video |
: {{#evu:https://www.youtube.com/watch?v=5-adsDeltaM|alignment=left|valignment=top}} | : {{#evu:https://www.youtube.com/watch?v=5-adsDeltaM|alignment=left|valignment=top}} | ||
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'''[[Sliding Piece Attacks|Up one Level]]''' | '''[[Sliding Piece Attacks|Up one Level]]''' | ||
− | [[Category:Samuel Bak]][[Category:Focus]] | + | [[Category:Samuel Bak]] |
+ | [[Category:Focus]] |
Latest revision as of 21:03, 19 July 2019
Home * Board Representation * Bitboards * Sliding Piece Attacks * Hyperbola Quintessence
Hyperbola Quintessence applies the o^(o-2r)-trick also for vertical or diagonal negative Rays - by reversing the bit-order of up to one bit per rank or byte with a vertical flip aka x86-64 bswap [2] . It is somehow a resurrection of the reverse bitboards idea of Ryan Mack's Hyperbola Project on the fly, and was created by Gerd Isenberg. Improvements by Aleks Peshkov [3] made it applicable and competitive.
Code samples and bitboard diagrams rely on Little endian file and rank mapping. |
Contents
Reverse Math
Assume following masked occupancy on a file, diagonal or anti-diagonal - for simplicity as a flat byte (in a real bitboard with masked files or diagonals you have 6..8 scratch-bits between the bits of this byte). Thus, vertical flip reverses the bits of this byte.
o' = reverse(o) r' = reverse(r) normal reversed o 11010101 10101011 o' occupancy including slider r 00010000 00001000 r' slider o-r 11000101 10100011 o'-r' 1. sub clears the slider o-2r 10110101 10011011 o'-2r' 2. sub borrows "one" from next blocker |......| \....../ normal 10110101 \..../ 11011001 <--XXXX re-reverse single xor 01101100 -> to get the attack set
The first subtraction of (o-2r) is done implicitly by masking off the line, removing the slider from the occupied set. The second subtraction borrows a "one" from the next nearest blocker in msb-direction, falling through all unset bits outside the line. Of course, if no blocker is available, it borrows a "one" in usual arithmetical manner from the hidden 2^N. Only the changed bits (from original o, o') are the appropriate sliding attacks, including the blocker but excluding the slider. The result finally needs to be intersected with the same line mask as previously the occupancy, to clear the wrapped borrow one bits outside the file or diagonal. The fine optimization by Aleks Peshkov covers the final union of positive and negative ray-attacks. Since opposed ray-directions are always disjoint sets, using xor instead of bitwise or safes two instructions per line-attack. That is because bit-reversal or any mirroring or flipping is own inverse and distributive over xor.
reverse(a ^ b) == reverse (a) ^ reverse(b)
thus
lineAttacks = o^(o-2r) ^ reverse((o'-2r')^o') lineAttacks = o^(o-2r) ^ reverse( o'-2r') ^ reverse(o') lineAttacks = o^(o-2r) ^ reverse( o'-2r') ^ o
and finally
lineAttacks = (o-2r) ^ reverse( o'-2r')
Beside shorter code this reduces register pressure - and clearly outperforms kindergarten bitboards - ipc-wise, in code size and memory requirements.
Source Code
C
The three C-routines only differ by the line-mask applied:
U64 diagonalAttacks(U64 occ, enumSquare sq) { U64 forward, reverse; forward = occ & smsk[sq].diagonalMaskEx; reverse = _byteswap_uint64(forward); forward -= smsk[sq].bitMask; reverse -= _byteswap_uint64(smsk[sq].bitMask); forward ^= _byteswap_uint64(reverse); forward &= smsk[sq].diagonalMaskEx; return forward; } U64 antiDiagAttacks(U64 occ, enumSquare sq) { U64 forward, reverse; forward = occ & smsk[sq].antidiagMaskEx; reverse = _byteswap_uint64(forward); forward -= smsk[sq].bitMask; reverse -= _byteswap_uint64(smsk[sq].bitMask); forward ^= _byteswap_uint64(reverse); forward &= smsk[sq].antidiagMaskEx; return forward; } U64 fileAttacks(U64 occ, enumSquare sq) { U64 forward, reverse; forward = occ & smsk[sq].fileMaskEx; reverse = _byteswap_uint64(forward); forward -= smsk[sq].bitMask; reverse -= _byteswap_uint64(smsk[sq].bitMask); forward ^= _byteswap_uint64(reverse); forward &= smsk[sq].fileMaskEx; return forward; } U64 bishopAttacks(U64 occ, enumSquare sq) { return diagonalAttacks (occ, sq) + antiDiagAttacks (occ, sq); }
For better locality of the line-attacks on the otherwise empty board, we may use an properly aligned array of structs.
struct { U64 bitMask; // 1 << sq for convenience U64 diagonalMaskEx; U64 antidiagMaskEx; U64 fileMaskEx; } smsk[64]; // 2 KByte
Using x86-64 bswap makes it quite competitive for bishops and files, on AMD K8 or K10 it has a latency of one cycle with a throughput of 1/3, like other cheap instructions. However, Intel is tad slower - while the recent Core 2 duo processors perform 128-bit SIMD-instructions with 128-bit alus, that is bitwise logical instructions with a latency of one cycle and throughput of 1/3, the general purpose bswap-instruction takes four cycles with a throughput of one. In Intel 64 and IA32 Architectures Optimization Reference Manual [4] , it is therefor recommend (5.6.5. endian conversion) to use the SSSE3 pshufb instruction to swap bytes, available through intrinsic [5] , see SSSE3 Hyperbola Quintessence for bishop attacks.
As long there is no fast bit reversal instruction, there is no general solution for all four lines, and the rook attack-getter still needs some standard technique for the rank-attacks. Tim Cooijmans proposed to map the rank to the main diagonal before applying HQ, and to re-map the calculated attacks back to the original rank [6] .
Generalized Set-wise Attacks
Hyperbola quintessence can be generalized to work on whole sets of sliding pieces instead on individual pieces, whose ranks to be masked. The problem arising, when not masking the rank of the piece is that attacks wrap around the board during subtraction. This is shown below:
........ ........ 11111111 ........ ........ 11111111 ........ ........ 11111111 r = ........ , o = ........ this leads to o - 2*r = 11111111 ........ ........ 11111111 ........ ........ 11111111 ....1... ....1... 11111... ........ ........ ........ instead of ........ ........ ........ ........ ........ ........ 11111... ........
This is not the intended result. It can be avioded, by bitwise adding an overflow barrier on the right-hand side. Afterwards this barrier needs to be removed from the attack set:
u64 right = 0x0101010101010101ULL; ......1. 1..1..1. 1...1111 ....1... 1...1... .1111..1 ......1. 11....1. 1.111111 r = .....1.. o = .11..1.. now: ((o | right) - 2*r) = .1.111.1 ........ ........ ........ ......1. ......1. 1111111. .......1 .......1 1111111. 1....... 1....... 1......1 Note, that the 4th rank was not flooded by the subtraction! Next, the blockers are removed as usual: ...111.1 1111...1 .11111.1 o ^ ((o | right) - 2*r) = ..111..1 ........ 111111.. 11111111 .......1 The last step is to remove the barrier at the right side that became visible after the last operation. ...111.. 1111... .11111.. (o ^ ((o | right) - 2*r) & ~right = ..111... ........ 111111.. 1111111. ........ This is the correct attack set for the left direction.
the complete algorithm for the left direction is therefore:
const u64 right = 0x0101010101010101ULL; u64 leftAttacks = ((o ^ ((o | right) - 2*r) & ~right);
For the right-hand direction, the bits need to be reversed rank-wise.
x86-64 assembly
The VC2005 generated x86-64 assembly of bishopAttacks indicates what ipc-monster Hyperbola Quintessence is:
occ$ = 16 sq$ = 24 ?bishopAttacks@@YA_K_KI@Z PROC 00000 40 53 push rbx 00002 8b c2 mov eax, edx 00004 4c 8d 15 00 00 00 00 lea r10, OFFSET FLAT:?smsk 0000b 48 c1 e0 05 shl rax, 5 0000f 4a 8b 5c 10 08 mov rbx, QWORD PTR [rax+r10+8] ; diagonalMaskEx 00014 4e 8b 4c 10 10 mov r9, QWORD PTR [rax+r10+16] ; antidiagMaskEx 00019 4e 8b 14 10 mov r10, QWORD PTR [rax+r10] ; r := 1 << sq 0001d 4c 8b db mov r11, rbx ; diagonalMaskEx 00020 49 8b d1 mov rdx, r9 ; antidiagMaskEx 00023 4d 8b c2 mov r8, r10 ; r := 1 << sq 00026 48 23 d1 and rdx, rcx ; anti & occ 00029 4c 23 d9 and r11, rcx ; dia & occ 0002c 49 0f c8 bswap r8 ; r' 0002f 48 8b c2 mov rax, rdx ; ant 00032 49 8b cb mov rcx, r11 ; dia 00035 49 2b d2 sub rdx, r10 ; ant - r 00038 48 0f c8 bswap rax ; ant' 0003b 48 0f c9 bswap rcx ; dia' 0003e 4d 2b da sub r11, r10 ; dia - r 00041 49 2b c0 sub rax, r8 ; ant' - r' 00044 49 2b c8 sub rcx, r8 ; dia' - r' 00047 48 0f c8 bswap rax ;(ant' - r')' 0004a 48 0f c9 bswap rcx ;(dia' - r')' 0004d 48 33 c2 xor rax, rdx ; ant := (ant' - r')' ^ (ant - r) 00050 49 33 cb xor rcx, r11 ; dia := (dia' - r')' ^ (dia - r) 00053 49 23 c1 and rax, r9 ; ant &= antidiagMaskEx 00056 48 23 cb and rcx, rbx ; dia &= diagonalMaskEx 00059 48 03 c1 add rax, rcx ; attacks := dia + ant 0005c 5b pop rbx 0005d c3 ret 0 ?bishopAttacks@@YA_K_KI@Z ENDP
Java
Java programmer may try Long.reverseBytes:
static private final long[] bitMask = { 0x0000000000000001, 0x0000000000000002, 0x0000000000000004, 0x0000000000000008, 0x0000000000000010, 0x0000000000000020, 0x0000000000000040, 0x0000000000000080, ... }; static private final long[] diagonalMaskEx = { 0x8040201008040200, 0x0080402010080400, 0x0000804020100800, 0x0000008040201000, 0x0000000080402000, 0x0000000000804000, 0x0000000000008000, 0x0000000000000000, ... }; /** * @param occ - occupancy * sq - from square * @return diagonal attacks from sq with occupancy occ */ static public long diagonalAttacks(long occ, int sq) { long forward = occ & diagonalMaskEx[sq]; long reverse = Long.reverseBytes(forward); forward -= bitMask[sq]; reverse -= bitMask[sq^56]; forward ^= Long.reverseBytes(reverse); forward &= diagonalMaskEx[sq]; return forward; }
Long.reverse for a generalized attack getter even for ranks is too expensive, except a JVM can use a machine instruction rather than a bit-reversal routine:
/** * @param occ - occupancy * line - {0..3} {rank, file, diagonal, antidiagonal} * sq - from square * @return attacks from sq on line with occupancy occ */ static public long attacks(long occ, int line, int sq) { long forward = occ & maskEx[sq][line]; long reverse = Long.reverse(forward); forward -= bitMask[sq]; reverse -= bitMask[sq^63]; forward ^= Long.reverse(reverse); forward &= maskEx[sq][line]; return forward; }
See also
- Reverse Bitboards
- Obstruction Difference
- SBAMG
- SSSE3 Hyperbola Quintessence
- Subtracting a Rook from a Blocking Piece
Forum Posts
- Re: BitBoard Tests Magic v Non-Rotated 32 Bits v 64 Bits by Aleks Peshkov, CCC, August 25, 2007
- Hyperbola Quiesscene: hardly any improvement by trojanfoe, CCC, January 13, 2009
- Comparison of bitboard attack-getter variants by Sven Schüle, CCC, January 04, 2016
- Re: The wrong way by Aleks Peshkov, CCC, January 05, 2016 » SSSE3 Hyperbola Quintessence
- Understanding first rank attack state generation by Kalyankumar Ramaseshan, CCC, July 18, 2019 » First Rank Attacks
External Links
- GitHub - abulmo/hqperft: Chess move generation based on (H)yperbola (Q)uintessence & range attacks by Richard Delorme » Perft
- Sliding Pieces (Part 1) - Advanced Java Chess Engine Tutorial 8 by Jonathan Warkentin
- Hyperbola Quintessence for rooks along ranks by Tim Cooijmans, April 6, 2014 [7]
Hyperbola
Quintessence
- Quintessence from Wikipedia
- Quintessence (physics) from Wikipedia
- Quintessence the Fifth Element from Wikipedia
Misc
- Focus - Hocus Pocus, Pinkpop Festival 1972, Geleen, YouTube Video
References
- ↑ Samuel Bak - represented by Pucker Gallery since 1969
- ↑ _byteswap_uint64 Visual C++ Developer Center - Run-Time Library Reference
- ↑ Re: BitBoard Tests Magic v Non-Rotated 32 Bits v 64 Bits by Aleks Peshkov, CCC, August 25, 2007
- ↑ Intel 64 and IA32 Architectures Optimization Reference Manual (pdf)
- ↑ _mm_shuffle_epi8 Visual C++ Developer Center - Run-Time Library Reference
- ↑ Hyperbola Quintessence for rooks along ranks by Tim Cooijmans, April 6, 2014
- ↑ Re: Comparison of bitboard attack-getter variants by Matthew R. Brades, CCC, January 04, 2016