Find magics on the fly
authorMarco Costalba <mcostalba@gmail.com>
Tue, 7 Jun 2011 13:12:07 +0000 (15:12 +0200)
committerMarco Costalba <mcostalba@gmail.com>
Tue, 7 Jun 2011 19:59:12 +0000 (20:59 +0100)
Good result for 32 bit case where computation is very fast,
still not satisfying on 64 bit case where the magics seem
a bit harder to get.

No functional change.

Signed-off-by: Marco Costalba <mcostalba@gmail.com>
src/bitboard.cpp
src/bitboard.h

index 88682948c3f7d724ce9dd05e6b313b74955f48a5..8c70a8e27b10820e27f288f28febfced33f91657 100644 (file)
   along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
 
+#include <cstring>
 #include <iostream>
 
 #include "bitboard.h"
 #include "bitcount.h"
+#include "rkiss.h"
 
 // Global bitboards definitions with static storage duration are
 // automatically set to zero before enter main().
 Bitboard RMask[64];
+Bitboard RMult[64];
 Bitboard* RAttacks[64];
 int RShift[64];
 
 Bitboard BMask[64];
+Bitboard BMult[64];
 Bitboard* BAttacks[64];
 int BShift[64];
 
@@ -53,117 +57,6 @@ Bitboard QueenPseudoAttacks[64];
 
 uint8_t BitCount8Bit[256];
 
-#if defined(IS_64BIT)
-
-static const uint64_t DeBruijnMagic = 0x218A392CD3D5DBFULL;
-
-const uint64_t BMult[64] = {
-  0x0440049104032280ULL, 0x1021023C82008040ULL, 0x0404040082000048ULL,
-  0x48C4440084048090ULL, 0x2801104026490000ULL, 0x4100880442040800ULL,
-  0x0181011002E06040ULL, 0x9101004104200E00ULL, 0x1240848848310401ULL,
-  0x2000142828050024ULL, 0x00001004024D5000ULL, 0x0102044400800200ULL,
-  0x8108108820112000ULL, 0xA880818210C00046ULL, 0x4008008801082000ULL,
-  0x0060882404049400ULL, 0x0104402004240810ULL, 0x000A002084250200ULL,
-  0x00100B0880801100ULL, 0x0004080201220101ULL, 0x0044008080A00000ULL,
-  0x0000202200842000ULL, 0x5006004882D00808ULL, 0x0000200045080802ULL,
-  0x0086100020200601ULL, 0xA802080A20112C02ULL, 0x0080411218080900ULL,
-  0x000200A0880080A0ULL, 0x9A01010000104000ULL, 0x0028008003100080ULL,
-  0x0211021004480417ULL, 0x0401004188220806ULL, 0x00825051400C2006ULL,
-  0x00140C0210943000ULL, 0x0000242800300080ULL, 0x00C2208120080200ULL,
-  0x2430008200002200ULL, 0x1010100112008040ULL, 0x8141050100020842ULL,
-  0x0000822081014405ULL, 0x800C049E40400804ULL, 0x4A0404028A000820ULL,
-  0x0022060201041200ULL, 0x0360904200840801ULL, 0x0881A08208800400ULL,
-  0x0060202C00400420ULL, 0x1204440086061400ULL, 0x0008184042804040ULL,
-  0x0064040315300400ULL, 0x0C01008801090A00ULL, 0x0808010401140C00ULL,
-  0x04004830C2020040ULL, 0x0080005002020054ULL, 0x40000C14481A0490ULL,
-  0x0010500101042048ULL, 0x1010100200424000ULL, 0x0000640901901040ULL,
-  0x00000A0201014840ULL, 0x00840082AA011002ULL, 0x010010840084240AULL,
-  0x0420400810420608ULL, 0x8D40230408102100ULL, 0x4A00200612222409ULL,
-  0x0A08520292120600ULL
-};
-
-const uint64_t RMult[64] = {
-  0x0A8002C000108020ULL, 0x4440200140003000ULL, 0x8080200010011880ULL,
-  0x0380180080141000ULL, 0x1A00060008211044ULL, 0x410001000A0C0008ULL,
-  0x9500060004008100ULL, 0x0100024284A20700ULL, 0x0000802140008000ULL,
-  0x0080C01002A00840ULL, 0x0402004282011020ULL, 0x9862000820420050ULL,
-  0x0001001448011100ULL, 0x6432800200800400ULL, 0x040100010002000CULL,
-  0x0002800D0010C080ULL, 0x90C0008000803042ULL, 0x4010004000200041ULL,
-  0x0003010010200040ULL, 0x0A40828028001000ULL, 0x0123010008000430ULL,
-  0x0024008004020080ULL, 0x0060040001104802ULL, 0x00582200028400D1ULL,
-  0x4000802080044000ULL, 0x0408208200420308ULL, 0x0610038080102000ULL,
-  0x3601000900100020ULL, 0x0000080080040180ULL, 0x00C2020080040080ULL,
-  0x0080084400100102ULL, 0x4022408200014401ULL, 0x0040052040800082ULL,
-  0x0B08200280804000ULL, 0x008A80A008801000ULL, 0x4000480080801000ULL,
-  0x0911808800801401ULL, 0x822A003002001894ULL, 0x401068091400108AULL,
-  0x000004A10A00004CULL, 0x2000800640008024ULL, 0x1486408102020020ULL,
-  0x000100A000D50041ULL, 0x00810050020B0020ULL, 0x0204000800808004ULL,
-  0x00020048100A000CULL, 0x0112000831020004ULL, 0x0009000040810002ULL,
-  0x0440490200208200ULL, 0x8910401000200040ULL, 0x6404200050008480ULL,
-  0x4B824A2010010100ULL, 0x04080801810C0080ULL, 0x00000400802A0080ULL,
-  0x8224080110026400ULL, 0x40002C4104088200ULL, 0x01002100104A0282ULL,
-  0x1208400811048021ULL, 0x3201014A40D02001ULL, 0x0005100019200501ULL,
-  0x0101000208001005ULL, 0x0002008450080702ULL, 0x001002080301D00CULL,
-  0x410201CE5C030092ULL
-};
-
-#else // if !defined(IS_64BIT)
-
-static const uint32_t DeBruijnMagic = 0x783A9B23;
-
-const uint64_t BMult[64] = {
-  0x54142844C6A22981ULL, 0x710358A6EA25C19EULL, 0x704F746D63A4A8DCULL,
-  0xBFED1A0B80F838C5ULL, 0x90561D5631E62110ULL, 0x2804260376E60944ULL,
-  0x84A656409AA76871ULL, 0xF0267F64C28B6197ULL, 0x70764EBB762F0585ULL,
-  0x92AA09E0CFE161DEULL, 0x41EE1F6BB266F60EULL, 0xDDCBF04F6039C444ULL,
-  0x5A3FAB7BAC0D988AULL, 0xD3727877FA4EAA03ULL, 0xD988402D868DDAAEULL,
-  0x812B291AFA075C7CULL, 0x94FAF987B685A932ULL, 0x3ED867D8470D08DBULL,
-  0x92517660B8901DE8ULL, 0x2D97E43E058814B4ULL, 0x880A10C220B25582ULL,
-  0xC7C6520D1F1A0477ULL, 0xDBFC7FBCD7656AA6ULL, 0x78B1B9BFB1A2B84FULL,
-  0x2F20037F112A0BC1ULL, 0x657171EA2269A916ULL, 0xC08302B07142210EULL,
-  0x0880A4403064080BULL, 0x3602420842208C00ULL, 0x852800DC7E0B6602ULL,
-  0x595A3FBBAA0F03B2ULL, 0x9F01411558159D5EULL, 0x2B4A4A5F88B394F2ULL,
-  0x4AFCBFFC292DD03AULL, 0x4A4094A3B3F10522ULL, 0xB06F00B491F30048ULL,
-  0xD5B3820280D77004ULL, 0x8B2E01E7C8E57A75ULL, 0x2D342794E886C2E6ULL,
-  0xC302C410CDE21461ULL, 0x111F426F1379C274ULL, 0xE0569220ABB31588ULL,
-  0x5026D3064D453324ULL, 0xE2076040C343CD8AULL, 0x93EFD1E1738021EEULL,
-  0xB680804BED143132ULL, 0x44E361B21986944CULL, 0x44C60170EF5C598CULL,
-  0xF4DA475C195C9C94ULL, 0xA3AFBB5F72060B1DULL, 0xBC75F410E41C4FFCULL,
-  0xB51C099390520922ULL, 0x902C011F8F8EC368ULL, 0x950B56B3D6F5490AULL,
-  0x3909E0635BF202D0ULL, 0x5744F90206EC10CCULL, 0xDC59FD76317ABBC1ULL,
-  0x881C7C67FCBFC4F6ULL, 0x47CA41E7E440D423ULL, 0xEB0C88112048D004ULL,
-  0x51C60E04359AEF1AULL, 0x1AA1FE0E957A5554ULL, 0xDD9448DB4F5E3104ULL,
-  0xDC01F6DCA4BEBBDCULL,
-};
-
-const uint64_t RMult[64] = {
-  0xD7445CDEC88002C0ULL, 0xD0A505C1F2001722ULL, 0xE065D1C896002182ULL,
-  0x9A8C41E75A000892ULL, 0x8900B10C89002AA8ULL, 0x9B28D1C1D60005A2ULL,
-  0x015D6C88DE002D9AULL, 0xB1DBFC802E8016A9ULL, 0x149A1042D9D60029ULL,
-  0xB9C08050599E002FULL, 0x132208C3AF300403ULL, 0xC1000CE2E9C50070ULL,
-  0x9D9AA13C99020012ULL, 0xB6B078DAF71E0046ULL, 0x9D880182FB6E002EULL,
-  0x52889F467E850037ULL, 0xDA6DC008D19A8480ULL, 0x468286034F902420ULL,
-  0x7140AC09DC54C020ULL, 0xD76FFFFA39548808ULL, 0xEA901C4141500808ULL,
-  0xC91004093F953A02ULL, 0x02882AFA8F6BB402ULL, 0xAEBE335692442C01ULL,
-  0x0E904A22079FB91EULL, 0x13A514851055F606ULL, 0x76C782018C8FE632ULL,
-  0x1DC012A9D116DA06ULL, 0x3C9E0037264FFFA6ULL, 0x2036002853C6E4A2ULL,
-  0xE3FE08500AFB47D4ULL, 0xF38AF25C86B025C2ULL, 0xC0800E2182CF9A40ULL,
-  0x72002480D1F60673ULL, 0x2500200BAE6E9B53ULL, 0xC60018C1EEFCA252ULL,
-  0x0600590473E3608AULL, 0x46002C4AB3FE51B2ULL, 0xA200011486BCC8D2ULL,
-  0xB680078095784C63ULL, 0x2742002639BF11AEULL, 0xC7D60021A5BDB142ULL,
-  0xC8C04016BB83D820ULL, 0xBD520028123B4842ULL, 0x9D1600344AC2A832ULL,
-  0x6A808005631C8A05ULL, 0x604600A148D5389AULL, 0xE2E40103D40DEA65ULL,
-  0x945B5A0087C62A81ULL, 0x012DC200CD82D28EULL, 0x2431C600B5F9EF76ULL,
-  0xFB142A006A9B314AULL, 0x06870E00A1C97D62ULL, 0x2A9DB2004A2689A2ULL,
-  0xD3594600CAF5D1A2ULL, 0xEE0E4900439344A7ULL, 0x89C4D266CA25007AULL,
-  0x3E0013A2743F97E3ULL, 0x0180E31A0431378AULL, 0x3A9E465A4D42A512ULL,
-  0x98D0A11A0C0D9CC2ULL, 0x8E711C1ABA19B01EULL, 0x8DCDC836DD201142ULL,
-  0x5AC08A4735370479ULL,
-};
-
-#endif // defined(IS_64BIT)
-
-
 namespace {
 
   CACHE_LINE_ALIGNMENT
@@ -172,8 +65,8 @@ namespace {
   Bitboard RAttacksTable[0x19000];
   Bitboard BAttacksTable[0x1480];
 
-  void init_sliding_attacks(Bitboard attacksTable[], Bitboard* attacks[], Bitboard mask[],
-                            int shift[], const Bitboard mult[], Square deltas[]);
+  void do_magics(Bitboard magic[], Bitboard* attack[], Bitboard attTabl[],
+                 Bitboard mask[], int shift[], Square deltas[]);
 }
 
 
@@ -201,13 +94,13 @@ void print_bitboard(Bitboard b) {
 #if defined(IS_64BIT) && !defined(USE_BSFQ)
 
 Square first_1(Bitboard b) {
-  return Square(BSFTable[((b & -b) * DeBruijnMagic) >> 58]);
+  return Square(BSFTable[((b & -b) * 0x218A392CD3D5DBFULL) >> 58]);
 }
 
 Square pop_1st_bit(Bitboard* b) {
   Bitboard bb = *b;
   *b &= (*b - 1);
-  return Square(BSFTable[((bb & -bb) * DeBruijnMagic) >> 58]);
+  return Square(BSFTable[((bb & -bb) * 0x218A392CD3D5DBFULL) >> 58]);
 }
 
 #elif !defined(USE_BSFQ)
@@ -215,7 +108,7 @@ Square pop_1st_bit(Bitboard* b) {
 Square first_1(Bitboard b) {
   b ^= (b - 1);
   uint32_t fold = unsigned(b) ^ unsigned(b >> 32);
-  return Square(BSFTable[(fold * DeBruijnMagic) >> 26]);
+  return Square(BSFTable[(fold * 0x783A9B23) >> 26]);
 }
 
 // Use type-punning
@@ -242,12 +135,12 @@ Square pop_1st_bit(Bitboard* bb) {
 
    if (u.dw.l)
    {
-       ret = Square(BSFTable[((u.dw.l ^ (u.dw.l - 1)) * DeBruijnMagic) >> 26]);
+       ret = Square(BSFTable[((u.dw.l ^ (u.dw.l - 1)) * 0x783A9B23) >> 26]);
        u.dw.l &= (u.dw.l - 1);
        *bb = u.b;
        return ret;
    }
-   ret = Square(BSFTable[((~(u.dw.h ^ (u.dw.h - 1))) * DeBruijnMagic) >> 26]);
+   ret = Square(BSFTable[((~(u.dw.h ^ (u.dw.h - 1))) * 0x783A9B23) >> 26]);
    u.dw.h &= (u.dw.h - 1);
    *bb = u.b;
    return ret;
@@ -310,10 +203,10 @@ void init_bitboards() {
           Bitboard b = 1ULL << i;
           b ^= b - 1;
           b ^= b >> 32;
-          BSFTable[uint32_t(b * DeBruijnMagic) >> 26] = i;
+          BSFTable[uint32_t(b * 0x783A9B23) >> 26] = i;
       }
       else
-          BSFTable[((1ULL << i) * DeBruijnMagic) >> 58] = i;
+          BSFTable[((1ULL << i) * 0x218A392CD3D5DBFULL) >> 58] = i;
 
   int steps[][9] = {
     {0}, {7,9,0}, {17,15,10,6,-6,-10,-15,-17,0}, {0}, {0}, {0}, {9,7,-7,-9,8,1,-1,-8,0}
@@ -333,8 +226,8 @@ void init_bitboards() {
   Square RDeltas[] = { DELTA_N,  DELTA_E,  DELTA_S,  DELTA_W  };
   Square BDeltas[] = { DELTA_NE, DELTA_SE, DELTA_SW, DELTA_NW };
 
-  init_sliding_attacks(RAttacksTable, RAttacks, RMask, RShift, RMult, RDeltas);
-  init_sliding_attacks(BAttacksTable, BAttacks, BMask, BShift, BMult, BDeltas);
+  do_magics(BMult, BAttacks, BAttacksTable, BMask, BShift, BDeltas);
+  do_magics(RMult, RAttacks, RAttacksTable, RMask, RShift, RDeltas);
 
   for (Square s = SQ_A1; s <= SQ_H8; s++)
   {
@@ -396,31 +289,77 @@ namespace {
     return attacks;
   }
 
-  void init_sliding_attacks(Bitboard attacksTable[], Bitboard* attacks[], Bitboard mask[],
-                            int shift[], const Bitboard mult[], Square deltas[]) {
+  template<bool Is64>
+  Bitboard pick_magic(Bitboard mask, RKISS& rk, int booster) {
 
-    Bitboard occupancy, index, excluded;
-    int maxKey, offset = 0;
+    Bitboard magic;
+    int lsb;
+
+    if (!Is64)
+        lsb = first_1(mask);
+
+    // Advance PRNG state of a quantity known to be the optimal to
+    // quickly retrieve all the magics.
+    for (int i = 0; i < booster; i++)
+        rk.rand<Bitboard>();
+
+    while (true)
+    {
+        magic = rk.rand<Bitboard>() & rk.rand<Bitboard>();
+        magic &= Is64 ? rk.rand<Bitboard>() : (rk.rand<Bitboard>() | rk.rand<Bitboard>());
+
+        if (   BitCount8Bit[(mask * magic) >> 56] >= 6
+            && (Is64 || BitCount8Bit[(lsb * magic) >> 56]))
+            return magic;
+    }
+  }
+
+  void do_magics(Bitboard magic[], Bitboard* attack[], Bitboard attTabl[],
+                 Bitboard mask[], int shift[], Square deltas[]) {
+
+    const int  MagicBoosters32[] = { 43, 53, 76, 17, 51, 65, 55, 23 };
+    const int  MagicBoosters64[] = { 26, 21, 21, 32, 31,  9,  5, 11 };
+
+    RKISS rk;
+    Bitboard occupancy[4096], proofs[4096], excluded;
+    int key, maxKey, index, booster, offset = 0;
 
     for (Square s = SQ_A1; s <= SQ_H8; s++)
     {
         excluded = ((Rank1BB | Rank8BB) & ~rank_bb(s)) | ((FileABB | FileHBB) & ~file_bb(s));
 
-        attacks[s] = &attacksTable[offset];
-        mask[s]    = sliding_attacks(s, EmptyBoardBB, deltas, excluded);
-        shift[s]   = (CpuIs64Bit ? 64 : 32) - count_1s<CNT64>(mask[s]);
+        attack[s] = &attTabl[offset];
+        mask[s]   = sliding_attacks(s, EmptyBoardBB, deltas, excluded);
+        shift[s]  = (CpuIs64Bit ? 64 : 32) - count_1s<CNT64>(mask[s]);
 
-        maxKey = 1 << count_1s<CNT64>(mask[s]);
+        maxKey = 1 << count_1s<CNT32>(mask[s]);
+        booster = CpuIs64Bit ? MagicBoosters64[square_rank(s)] : MagicBoosters32[square_rank(s)];
 
-        for (int key = 0; key < maxKey; key++)
+        // First compute occupancy and attacks for square 's'
+        for (key = 0; key < maxKey; key++)
         {
-            occupancy = submask(mask[s], key);
+            occupancy[key] = submask(mask[s], key);
+            proofs[key] = sliding_attacks(s, occupancy[key], deltas, EmptyBoardBB);
+        }
 
-            index = CpuIs64Bit ? occupancy * mult[s]
-                               : unsigned(occupancy * mult[s] ^ (occupancy >> 32) * (mult[s] >> 32));
+        // Then find a possible magic and corresponding attacks
+        do {
+            magic[s] = pick_magic<CpuIs64Bit>(mask[s], rk, booster);
+            memset(attack[s], 0, maxKey * sizeof(Bitboard));
+
+            for (key = 0; key < maxKey; key++)
+            {
+                index = CpuIs64Bit ? unsigned((occupancy[key] * magic[s]) >> shift[s])
+                                   : unsigned(occupancy[key] * magic[s] ^ (occupancy[key] >> 32) * (magic[s] >> 32)) >> shift[s];
+
+                if (!attack[s][index])
+                    attack[s][index] = proofs[key];
+
+                else if (attack[s][index] != proofs[key])
+                    break;
+            }
+        } while (key != maxKey);
 
-            attacks[s][index >> shift[s]] = sliding_attacks(s, occupancy, deltas, EmptyBoardBB);
-        }
         offset += maxKey;
     }
   }
index 404178dcc4b73f2c7e564b173c637c3d29ba29b9..0177df8cdb02c7345e991c3de6046ff412a7b03a 100644 (file)
@@ -60,12 +60,12 @@ extern Bitboard SquaresInFrontMask[2][64];
 extern Bitboard PassedPawnMask[2][64];
 extern Bitboard AttackSpanMask[2][64];
 
-extern const uint64_t RMult[64];
+extern uint64_t RMult[64];
 extern int RShift[64];
 extern Bitboard RMask[64];
 extern Bitboard* RAttacks[64];
 
-extern const uint64_t BMult[64];
+extern uint64_t BMult[64];
 extern int BShift[64];
 extern Bitboard BMask[64];
 extern Bitboard* BAttacks[64];