├── .gitignore
├── makefile
├── src
    ├── prun.h
    ├── sym.h
    ├── move.h
    ├── solve.h
    ├── coord.h
    ├── cubie.h
    ├── face.cpp
    ├── face.h
    ├── cubie.cpp
    ├── sym.cpp
    ├── test.cpp
    ├── coord.cpp
    ├── main.cpp
    ├── move.cpp
    ├── solve.cpp
    └── prun.cpp
├── README.md
└── LICENSE


/.gitignore:
--------------------------------------------------------------------------------
 1 | # Prerequisites
 2 | *.d
 3 | 
 4 | # Compiled Object files
 5 | *.slo
 6 | *.lo
 7 | *.o
 8 | *.obj
 9 | 
10 | # Precompiled Headers
11 | *.gch
12 | *.pch
13 | 
14 | # Compiled Dynamic libraries
15 | *.so
16 | *.dylib
17 | *.dll
18 | 
19 | # Fortran module files
20 | *.mod
21 | *.smod
22 | 
23 | # Compiled Static libraries
24 | *.lai
25 | *.la
26 | *.a
27 | *.lib
28 | 
29 | # Executables
30 | *.exe
31 | *.out
32 | *.app
33 | 
34 | # Project specific
35 | twophase
36 | twophase*.tbl
37 | .depend
38 | .idea
39 | CMakeLists.txt
40 | cmake-build-debug
41 | 


--------------------------------------------------------------------------------
/makefile:
--------------------------------------------------------------------------------
 1 | C=gcc
 2 | CXX=g++
 3 | RM=rm -f
 4 | CPPFLAGS=-std=c++11 -lpthread -O3
 5 | LDFLAGS=
 6 | LDLIBS=-lpthread
 7 | 
 8 | SRCS=$(patsubst %,src/%,main.cpp coord.cpp cubie.cpp face.cpp move.cpp prun.cpp solve.cpp sym.cpp)
 9 | OBJS=$(subst .cpp,.o,$(SRCS))
10 | 
11 | all: tool
12 | 
13 | tool: $(OBJS)
14 | 	$(CXX) $(LDFLAGS) -o twophase $(OBJS) $(LDLIBS) 
15 | 
16 | depend: .depend
17 | 
18 | .depend: $(SRCS)
19 | 	$(RM) ./.depend
20 | 	$(CXX) $(CPPFLAGS) -MM $^>>./.depend;
21 | 
22 | clean:
23 | 	$(RM) $(OBJS)
24 | 
25 | distclean: clean
26 | 	$(RM) *~ .depend
27 | 
28 | include .depend
29 | 


--------------------------------------------------------------------------------
/src/prun.h:
--------------------------------------------------------------------------------
 1 | /**
 2 |  * Pruning table generation and lookup.
 3 |  */
 4 | 
 5 | #ifndef __PRUN__
 6 | #define __PRUN__
 7 | 
 8 | #include <cstdint>
 9 | #include "coord.h"
10 | #include "sym.h"
11 | 
12 | namespace prun {
13 | 
14 |   const int N_FS1TWIST = sym::N_FSLICE1 * coord::N_TWIST;
15 |   const int N_CORNUD2 = sym::N_CORNERS * coord::N_UDEDGES2;
16 |   const int N_CSLICE2 = coord::N_CORNERS * coord::N_SLICE2;
17 | 
18 |   #ifdef AX
19 |     using prun1 = uint64_t;
20 |   #else
21 |     using prun1 = uint32_t;
22 |   #endif
23 | 
24 |   extern prun1  *phase1;
25 |   extern uint8_t *phase2;
26 |   extern uint8_t *precheck;
27 | 
28 |   int get_phase1(int flip, int slice, int twist, int togo, move::mask& next);
29 |   int get_phase2(int corners, int udedges);
30 |   int get_precheck(int corners, int slice);
31 | 
32 |   bool init(bool file = true);
33 | 
34 | }
35 | 
36 | #endif
37 | 


--------------------------------------------------------------------------------
/src/sym.h:
--------------------------------------------------------------------------------
 1 | /**
 2 |  * Symmetry definition and reduction/conjugation tables.
 3 |  */
 4 | 
 5 | #ifndef __SYM__
 6 | #define __SYM__
 7 | 
 8 | #include "coord.h"
 9 | #include "cubie.h"
10 | #include "move.h"
11 | 
12 | namespace sym {
13 | 
14 |   const int COUNT = 48;
15 | 
16 |   #ifdef F5
17 |     const int COUNT_SUB = 4; // number of symmetries used for reduction
18 |     const int N_FSLICE1 = 255664;
19 |     const int N_CORNERS = 10368;
20 |     const int ROT = 36; // 90 degree rotation around FB-axis
21 |   #else
22 |     const int COUNT_SUB = 16;
23 |     const int N_FSLICE1 = 64430;
24 |     const int N_CORNERS = 2768;
25 |     const int ROT = 16; // 120 degree rotation around axis through URF and DLB corner
26 |   #endif
27 | 
28 |   extern cubie::cube cubes[COUNT];
29 |   extern int inv[COUNT];
30 |   extern int effect[COUNT][3];
31 | 
32 |   extern int conj_move[move::COUNT][COUNT];
33 |   extern uint16_t conj_twist[coord::N_TWIST][COUNT_SUB];
34 |   extern uint16_t conj_udedges2[coord::N_UDEDGES2][COUNT_SUB];
35 | 
36 |   extern uint32_t fslice1_sym[coord::N_FSLICE1];
37 |   extern uint32_t corners_sym[coord::N_CORNERS];
38 |   extern uint32_t fslice1_raw[N_FSLICE1];
39 |   extern uint16_t corners_raw[N_CORNERS];
40 |   extern uint16_t fslice1_selfs[N_FSLICE1];
41 |   extern uint16_t corners_selfs[N_CORNERS];
42 | 
43 |   inline bool eff_inv(int eff) { return eff & 1; }
44 |   inline bool eff_flip(int eff) { return eff & 2; }
45 |   inline int eff_shift(int eff) { return eff >> 2; }
46 |   inline int coord_c(int coord) { return coord / COUNT_SUB; }
47 |   inline int coord_s(int coord) { return coord % COUNT_SUB; }
48 | 
49 |   void init();
50 | 
51 | }
52 | 
53 | #endif
54 | 


--------------------------------------------------------------------------------
/src/move.h:
--------------------------------------------------------------------------------
 1 | /**
 2 |  * All kinds of moveset definitions and setup
 3 |  */
 4 | 
 5 | #ifndef __MOVE__
 6 | #define __MOVE__
 7 | 
 8 | #include <cstdint>
 9 | #include <string>
10 | #include <vector>
11 | 
12 | #include "cubie.h"
13 | 
14 | namespace move {
15 | 
16 |   using mask = uint64_t;
17 | 
18 |   #ifdef QT
19 |     #ifdef AX
20 |       const int COUNT = 30;
21 |       const int COUNT1 = 24;
22 |       const int split[] = {
23 |         -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
24 |         8, 10, 12, 16, 18, 20
25 |       }; // split extra half-turns into quarter-turn (for cleaner phase 2 implementation)
26 |     #else
27 |       const int COUNT = 16;
28 |       const int COUNT1 = 12;
29 |       const int split[] = {
30 |         -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
31 |         4, 6, 8, 10
32 |       };
33 |     #endif
34 |   #else
35 |     #ifdef AX
36 |       const int COUNT = 45;
37 |       const int COUNT1 = 45;
38 |     #else
39 |       const int COUNT = 18;
40 |       const int COUNT1 = 18;
41 |     #endif
42 |   #endif
43 | 
44 |   extern std::string names[COUNT];
45 |   extern cubie::cube cubes[COUNT];
46 |   extern int inv[COUNT];
47 | 
48 |   extern mask next[COUNT]; // successor moves that should be explored
49 |   extern mask next_p1p2[COUNT]; // `next` for phase1 to phase 2 transition
50 |   extern mask qt_skip[COUNT]; // to avoid ever trying M^3 = M' in QT mode
51 | 
52 |   extern mask p1mask; // phase 1 moves
53 |   extern mask p2mask; // phase 2 moves
54 | 
55 |   inline mask bit(int m) {
56 |     return mask(1) << m;
57 |   }
58 |   inline bool in(int m, mask mm) {
59 |     return mm & bit(m);
60 |   }
61 | 
62 |   // Convert solution to AXHT; especially useful when solving in AXQT
63 |   std::string compress(const std::vector<int>& mseq);
64 | 
65 |   /* Compute solution lengths in different metrics */
66 |   int len_ht(const std::vector<int>& mseq);
67 |   int len_axht(const std::vector<int>& mseq);
68 |   int len_qt(const std::vector<int>& mseq);
69 |   int len_axqt(const std::vector<int>& mseq);
70 | 
71 |   void init();
72 | 
73 | }
74 | 
75 | #endif
76 | 


--------------------------------------------------------------------------------
/src/solve.h:
--------------------------------------------------------------------------------
 1 | #ifndef __SOLVE__
 2 | #define __SOLVE__
 3 | 
 4 | #include <condition_variable>
 5 | #include <mutex>
 6 | #include <queue>
 7 | #include <utility>
 8 | #include <thread>
 9 | # include "move.h"
10 | 
11 | namespace solve {
12 | 
13 |   using searchres = std::pair<std::vector<int>, int>; // moves + search direction
14 |   inline bool cmp(const searchres& s1, const searchres&  s2) { return s1.first.size() < s2.first.size(); }
15 | 
16 |   // Container with coords of a starting position
17 |   struct coordc {
18 |     int flip;
19 |     int slice;
20 |     int twist;
21 |     int uedges;
22 |     int dedges;
23 |     int corners;
24 |   };
25 | 
26 |   // Number of search directions
27 |   #ifdef F5
28 |     const int N_DIRS = 4;
29 |   #else
30 |     const int N_DIRS = 6;
31 |   #endif
32 | 
33 |   class Engine {
34 | 
35 |     int n_threads; // number of search threads
36 |     int n_splits; // number of sub-searches every search is split into
37 |     int n_sols; // number of solutions to find
38 |     int max_len; // find solutions with at most this length; -1 means simply search for the full `tlimit`
39 |     int tlim; // search for this amount of milliseconds
40 | 
41 |     coordc dirs[N_DIRS]; // search directions
42 |     move::mask masks[move::COUNT1]; // split masks
43 |     int depths[N_DIRS]; // current search depths per direction
44 |     int splits[N_DIRS]; // current search splits per direction
45 | 
46 |     bool done; // indicate that we are done
47 |     int lenlim; // only look for solution that are strictly shorter than this
48 |     std::mutex job_mtx; // thread-safety for selection of the next search task
49 |     std::mutex sol_mtx; // thread-safety for reporting a solution
50 |     std::priority_queue<searchres, std::vector<searchres>, decltype(&cmp)> sols {cmp}; // already found solutions
51 |     std::vector<std::thread> threads; // search threads
52 | 
53 |     // Tools for implementing a required timeout
54 |     std::mutex tout_mtx;
55 |     std::condition_variable tout_cvar;
56 | 
57 |     public:
58 |       Engine(
59 |         int n_threads, int tlim,
60 |         int n_sols = 1, int max_len = -1, int n_splits = 1
61 |       );
62 |       void prepare(); // setup all threads
63 |       void solve(const cubie::cube& c, std::vector<std::vector<int>>& res); // actual solve
64 |       void finish(); // wait for all threads to shutdown (mostly for clean program exit)
65 |       void report_sol(searchres& sol); // report a solution; never call this from the outside
66 | 
67 |     void thread(); // search thread
68 | 
69 |   };
70 | 
71 | }
72 | 
73 | #endif
74 | 


--------------------------------------------------------------------------------
/src/coord.h:
--------------------------------------------------------------------------------
 1 | /**
 2 |  * Coord definitions, utilities and move tables.
 3 |  */
 4 | 
 5 | #ifndef __COORD__
 6 | #define __COORD__
 7 | 
 8 | #include "cubie.h"
 9 | #include "move.h"
10 | 
11 | namespace coord {
12 | 
13 |   const int N_FLIP = 2048; // 2^(12 - 1)
14 |   const int N_TWIST = 2187; // 3^(8 - 1)
15 |   const int N_SLICE1 = 495; // binom(12, 4)
16 |   const int N_FSLICE1 = 1013760; // N_FLIP * N_SLICE
17 | 
18 |   const int N_SLICE = 11880; // 12! / 8!
19 |   const int N_UEDGES = 11880; // 12! / 8!
20 |   const int N_DEDGES = 11880; // 12! / 8!
21 | 
22 |   const int N_SLICE2 = 24; // 4!
23 |   const int N_UDEDGES2 = 40320; // 8!
24 |   const int N_CORNERS = 40320; // 8!
25 | 
26 |   const int SLICE1_SOLVED = 494; // SLICE1 is not 0 at the end of phase 1
27 | 
28 |   extern uint16_t move_flip[N_FLIP][move::COUNT];
29 |   extern uint16_t move_twist[N_TWIST][move::COUNT];
30 |   extern uint16_t move_edges4[N_SLICE][move::COUNT];
31 |   extern uint16_t move_corners[N_CORNERS][move::COUNT];
32 |   extern uint16_t move_udedges2[N_UDEDGES2][move::COUNT]; // primarily for faster phase 2 table generation
33 | 
34 |   int get_flip(const cubie::cube& c);
35 |   int get_twist(const cubie::cube& c);
36 |   int get_slice(const cubie::cube& c);
37 |   int get_uedges(const cubie::cube& c);
38 |   int get_dedges(const cubie::cube& c);
39 |   int get_corners(const cubie::cube& c);
40 | 
41 |   void set_flip(cubie::cube& c, int flip);
42 |   void set_twist(cubie::cube& c, int twist);
43 |   void set_slice(cubie::cube& c, int slice);
44 |   void set_uedges(cubie::cube& c, int uedges);
45 |   void set_dedges(cubie::cube& c, int dedges);
46 |   void set_corners(cubie::cube& c, int corners);
47 | 
48 |   int get_slice1(const cubie::cube& c); // faster table generation
49 |   void set_slice1(cubie::cube& c, int slice1);
50 |   int get_udedges2(const cubie::cube& c);
51 |   void set_udedges2(cubie::cube& c, int udedges2);
52 |   inline int merge_udedges2(int uedges, int dedges) { return 24 * uedges + (dedges % 24); };
53 | 
54 |   inline int slice_to_slice1(int slice) { return slice / 24; }
55 |   inline int slice1_to_slice(int slice1) { return 24 * slice1; }
56 |   inline int slice_to_slice2(int slice) { return slice - N_SLICE2 * SLICE1_SOLVED; }
57 |   inline int slice2_to_slice(int slice2) { return slice2 + N_SLICE2 * SLICE1_SOLVED; }
58 |   inline int fslice1(int flip, int slice1) { return N_FLIP * slice1 + flip; }
59 |   inline int fslice1_to_flip(int fslice1) { return fslice1 % N_FLIP; }
60 |   inline int fslice1_to_slice1(int fslice1) { return fslice1 / N_FLIP; }
61 | 
62 |   void init();
63 | 
64 | }
65 | 
66 | #endif
67 | 


--------------------------------------------------------------------------------
/src/cubie.h:
--------------------------------------------------------------------------------
 1 | /**
 2 |  * Cubie definitions, cubie-cube representation + methods for manipulating it
 3 |  */
 4 | 
 5 | #ifndef __CUBIE__
 6 | #define __CUBIE__
 7 | 
 8 | #include <string>
 9 | 
10 | namespace cubie {
11 | 
12 |   /* All cubie definitions are plain integers for making uniform handling much easier */
13 | 
14 |   namespace corner { // definition of corner cubies
15 |     const int COUNT = 8;
16 | 
17 |     const int URF = 0;
18 |     const int UFL = 1;
19 |     const int ULB = 2;
20 |     const int UBR = 3;
21 |     const int DFR = 4;
22 |     const int DLF = 5;
23 |     const int DBL = 6;
24 |     const int DRB = 7;
25 | 
26 |     const std::string NAMES[] = {
27 |       "URF", "UFL", "ULB", "UBR", "DFR", "DLF", "DBL", "DRB"
28 |     };
29 |   }
30 |   using namespace corner;
31 | 
32 |   namespace edge { // definition of edge cubies
33 |     const int COUNT = 12;
34 | 
35 |     const int UR = 0;
36 |     const int UF = 1;
37 |     const int UL = 2;
38 |     const int UB = 3;
39 |     const int DR = 4;
40 |     const int DF = 5;
41 |     const int DL = 6;
42 |     const int DB = 7;
43 |     // SLICE-edges last s.t. UDEDGES2 is easier to handle
44 |     const int FR = 8;
45 |     const int FL = 9;
46 |     const int BL = 10;
47 |     const int BR = 11;
48 | 
49 |     const std::string NAMES[] = {
50 |       "UR", "UF", "UL", "UB", "DR", "DF", "DL", "DB", "FR", "FL", "BL", "BR"
51 |     };
52 |   }
53 |   using namespace edge;
54 | 
55 |   struct cube {
56 |     int cperm[corner::COUNT]; // corner cubie permutation
57 |     int eperm[edge::COUNT]; // edge cubie permutation
58 |     int cori[corner::COUNT]; // corner cubie orientation; 0 if U/D-facelet on U/D-face; 1 clockwise rot; 2 c-clock
59 |     int eori[edge::COUNT]; // edge cubie orientation; 0 if U/D-facelet on U/D-face or same for F/B for slice edges
60 |   };
61 | 
62 |   const cube SOLVED_CUBE = {
63 |     {URF, UFL, ULB, UBR, DFR, DLF, DBL, DRB},
64 |     {UR, UF, UL, UB, DR, DF, DL, DB, FR, FL, BL, BR},
65 |     {}, {}
66 |   }; // cubie-cube in solved state
67 | 
68 |   /* Explicitly pass result cube to avoid unnecessary copying during table generation */
69 | 
70 |   namespace corner {
71 |     void mul(const cube& c1, const cube& c2, cube& into); // multiply only corner cubies
72 |   }
73 |   namespace edge {
74 |     void mul(const cube& c1, const cube& c2, cube& into); // multiply only edge cubies
75 |   }
76 | 
77 |   void mul(const cube& c1, const cube& c2, cube& into); // fully multiply two cubes
78 |   void inv(const cube& c, cube& into); // compute the inverse cube
79 |   void shuffle(cube& c); // generate a uniformly random cube
80 |   int check(const cube& c); // check a cube for being solvable
81 | 
82 |   bool operator==(const cube& c1, const cube& c2);
83 |   bool operator!=(const cube& c1, const cube& c2);
84 | 
85 | }
86 | 
87 | #endif
88 | 


--------------------------------------------------------------------------------
/src/face.cpp:
--------------------------------------------------------------------------------
 1 | #include "face.h"
 2 | 
 3 | #include <string>
 4 | #include <unordered_map>
 5 | 
 6 | namespace face {
 7 | 
 8 |   // True modulo function that also works properly for negative numbers
 9 |   int mod(int a, int m) {
10 |     return a > 0 ? a % m : (a % m + m) % m;
11 |   }
12 | 
13 |   // Converts a cubelet and its orientation into a single unique code-number
14 |   int encode(const std::string& cubelet, int ori) {
15 |     int res = 0;
16 |     for (int i = 0; i < cubelet.size(); i++)
17 |       res = color::COUNT * res + color::FROM_NAME.at(cubelet[mod(i - ori, cubelet.size())]);
18 |     return res;
19 |   }
20 | 
21 |   // Map code to cubie ID and orientation
22 |   std::unordered_map<int, std::pair<int, int>> corners;
23 |   std::unordered_map<int, std::pair<int, int>> edges;
24 | 
25 |   void init() {
26 |     for (int corner = 0; corner < cubie::corner::COUNT; corner++) {
27 |       for (int ori = 0; ori < 3; ori++)
28 |         corners[encode(cubie::corner::NAMES[corner], ori)] = std::make_pair(corner, ori);
29 |     }
30 |     for (int edge = 0; edge < cubie::edge::COUNT; edge++) {
31 |       for (int ori = 0; ori < 2; ori++)
32 |         edges[encode(cubie::edge::NAMES[edge], ori)] = std::make_pair(edge, ori);
33 |     }
34 |   }
35 | 
36 |   int to_cubie(const std::string& s, cubie::cube& c) {
37 |     for (int i = 0; i < N_FACELETS; i++) {
38 |       if (color::FROM_NAME.find(s[i]) == color::FROM_NAME.end())
39 |         return 1; // invalid color
40 |       if ((i - 4) % 9 == 0 && color::FROM_NAME.at(s[i]) != i / 9)
41 |         return 2; // invalid center facelet (they are always fixed)
42 |     }
43 | 
44 |     for (int corner = 0; corner < cubie::corner::COUNT; corner++) {
45 |       char cornlet[3];
46 |       for (int i = 0; i < 3; i++)
47 |         cornlet[i] = s[CORNLETS[corner][i]];
48 |       auto tmp = corners.find(encode(std::string(cornlet, 3), 0));
49 |       if (tmp == corners.end())
50 |         return 3; // invalid corner cubie
51 |       c.cperm[corner] = tmp->second.first;
52 |       c.cori[corner] = tmp->second.second;
53 |     }
54 | 
55 |     for (int edge = 0; edge < cubie::edge::COUNT; edge++) {
56 |       char edgelet[2];
57 |       for (int i = 0; i < 2; i++)
58 |         edgelet[i] = s[EDGELETS[edge][i]];
59 |       auto tmp = edges.find(encode(std::string(edgelet, 2), 0));
60 |       if (tmp == edges.end())
61 |         return 4; // invalid edge cubie
62 |       c.eperm[edge] = tmp->second.first;
63 |       c.eori[edge] = tmp->second.second;
64 |     }
65 | 
66 |     return 0;
67 |   }
68 | 
69 |   // Assumes the given cube to be valid
70 |   std::string from_cubie(const cubie::cube& c) {
71 |     char s[N_FACELETS];
72 | 
73 |     for (int color = 0; color < color::COUNT; color++)
74 |       s[9 * color + 4] = color::NAMES[color];
75 |     for (int corner = 0; corner < cubie::corner::COUNT; corner++) {
76 |       for (int i = 0; i < 3; i++)
77 |         // Corner twist is defined clockwise
78 |         s[CORNLETS[corner][i]] = cubie::corner::NAMES[c.cperm[corner]][mod(i - c.cori[corner], 3)];
79 |     }
80 |     for (int edge = 0; edge < cubie::edge::COUNT; edge++) {
81 |       for (int i = 0; i < 2; i++)
82 |         s[EDGELETS[edge][i]] = cubie::edge::NAMES[c.eperm[edge]][mod(i - c.eori[edge], 2)];
83 |     }
84 | 
85 |     return std::string(s, N_FACELETS);
86 |   }
87 | 
88 | }
89 | 


--------------------------------------------------------------------------------
/src/face.h:
--------------------------------------------------------------------------------
 1 | /**
 2 |  * Since `cubie::cube`s (especially the orientation part) are quite tricky to deal with, we use a more convenient
 3 |  * representation to interface with the outside world, the face-cube. Having defined an ordering over all 54 stickers
 4 |  * on the physical cube, a list of the colors for each sticker (in terms of the faces U, R, F, D, L and B not the
 5 |  * actual cube colors) uniquely specifies any cube-state.
 6 |  *
 7 |  * The facelet positions are defined as shown in the folded-up Rubik's cube depicted below.
 8 |  *
 9 |  *          +--+-----+
10 |  *          |U1|U2|U3|
11 |  *          |--+--+--|
12 |  *          |U4|U5|U6|
13 |  *          |--+--+--|
14 |  *          |U7|U8|U9|
15 |  * +--+--+--+--+--+--+--+--+--+--+--+--+
16 |  * |L1|L2|L3|F1|F2|F3|R1|R2|R3|B1|B2|B3|
17 |  * |--+--+--|--+--+--|--+--+--|--+--+--|
18 |  * |L4|L5|L6|F4|F5|F6|R4|R5|R6|B4|B5|B6|
19 |  * |--+--+--|--+--+--|--+--+--|--+--+--|
20 |  * |L7|L8|L9|F7|F8|F9|R7|R8|R9|B7|B8|B9|
21 |  * +--+--+--+--+--+--+--+--+--+--+--+--+
22 |  *          |D1|D2|D3|
23 |  *          |--+--+--|
24 |  *          |D4|D5|D6|
25 |  *          |--+--+--|
26 |  *          |D7|D8|D9|
27 |  *          +--+--+--+
28 |  *
29 |  * A facelet string simply lists the colors of every facelet position with the faces being in order U, R, F, D, L, B
30 |  * and the facelets within a face sorted by their index, i.e. U1U2U3U4U5U6U7U8U9R1R2... where U1, U2, ... are the
31 |  * colors of the corresponding facelets.
32 |  *
33 |  * Note that facelet X5 (i.e. the center sticker of face X) must always be of color X. It also does not matter which
34 |  * of the actual cube colors (like red, orange, etc.) is assigned to which face, the assignment must only be consistent
35 |  * with respect to the neighborhood relations, i.e. for example if white is considered as the F-face, then yellow must
36 |  * be B (as it is always on the opposite side on a physical cube).
37 |  */
38 | 
39 | #ifndef __FACE__
40 | #define __FACE__
41 | 
42 | #include <string>
43 | #include <unordered_map>
44 | #include "cubie.h"
45 | 
46 | namespace face {
47 | 
48 |   const int N_FACELETS = 54; // number of facelets (stickers) = 9 * 6
49 | 
50 |   namespace color {
51 |     const int COUNT = 6; // number of colors/faces of a cube
52 | 
53 |     /* Color/Face ordering */
54 |     const int U = 0;
55 |     const int R = 1;
56 |     const int F = 2;
57 |     const int D = 3;
58 |     const int L = 4;
59 |     const int B = 5;
60 | 
61 |     const char NAMES[] = {'U', 'R', 'F', 'D', 'L', 'B'};
62 | 
63 |     // Maps color character to corresponding color ID
64 |     const std::unordered_map<char, int> FROM_NAME = {
65 |       {'U', U}, {'R', R}, {'F', F}, {'D', D}, {'L', L}, {'B', B}
66 |     };
67 |   }
68 | 
69 |   /* Map corner/edge IDs to corresponding facelet positions */
70 |   const int CORNLETS[][3] = {
71 |     {8, 9, 20}, {6, 18, 38}, {0, 36, 47}, {2, 45, 11},
72 |     {29, 26, 15}, {27, 44, 24}, {33, 53, 42}, {35, 17, 51}
73 |   };
74 |   const int EDGELETS[][2] = {
75 |     {5, 10}, {7, 19}, {3, 37}, {1, 46}, {32, 16}, {28, 25},
76 |     {30, 43}, {34, 52}, {23, 12}, {21, 41}, {50, 39}, {48, 14}
77 |   };
78 | 
79 |   /* Routines for converting a facelet-string to a cubie-cube and vice-versa */
80 |   int to_cubie(const std::string& s, cubie::cube &c);
81 |   std::string from_cubie(const cubie::cube &c);
82 | 
83 |   // Initializes the face-level; to be called before accessing anything from this file
84 |   void init();
85 | 
86 | }
87 | 
88 | #endif
89 | 


--------------------------------------------------------------------------------
/src/cubie.cpp:
--------------------------------------------------------------------------------
  1 | #include "cubie.h"
  2 | 
  3 | #include <algorithm>
  4 | #include <random>
  5 | #include "coord.h"
  6 | 
  7 | namespace cubie {
  8 | 
  9 |   /* Faster than tricky if-else sequences for handling mirrored states */
 10 |   int mul_coris[][6] = {
 11 |     {0, 1, 2, 3, 4, 5},
 12 |     {1, 2, 0, 4, 5, 3},
 13 |     {2, 0, 1, 5, 3, 4},
 14 |     {3, 5, 4, 0, 2, 1},
 15 |     {4, 3, 5, 1, 0, 2},
 16 |     {5, 4, 3, 2, 1, 0}
 17 |   };
 18 |   int inv_cori[] = {
 19 |     0, 2, 1, 3, 4, 5
 20 |   };
 21 | 
 22 |   std::random_device device;
 23 |   std::mt19937 gen(device());
 24 | 
 25 |   void corner::mul(const cubie::cube& c1, const cubie::cube& c2, cubie::cube& into) {
 26 |     for (int i = 0; i < corner::COUNT; i++) {
 27 |       into.cperm[i] = c1.cperm[c2.cperm[i]];
 28 |       into.cori[i] = mul_coris[c1.cori[c2.cperm[i]]][c2.cori[i]];
 29 |     }
 30 |   }
 31 | 
 32 |   void edge::mul(const cubie::cube& c1, const cubie::cube& c2, cubie::cube& into) {
 33 |     for (int i = 0; i < edge::COUNT; i++) {
 34 |       into.eperm[i] = c1.eperm[c2.eperm[i]];
 35 |       into.eori[i] = (c1.eori[c2.eperm[i]] + c2.eori[i]) & 1;
 36 |     }
 37 |   }
 38 | 
 39 |   // Permutation partiy =  #inversions % 2
 40 |   bool parity(const int perm[], int len) {
 41 |     int par = 0;
 42 |     for (int i = 0; i < len; i++) {
 43 |       for (int j = 0; j < i; j++) {
 44 |         if (perm[j] > perm[i])
 45 |           par++;
 46 |       }
 47 |     }
 48 |     return par & 1;
 49 |   }
 50 | 
 51 |   void mul(const cubie::cube& c1, const cubie::cube& c2, cubie::cube& into) {
 52 |     corner::mul(c1, c2, into);
 53 |     edge::mul(c1, c2, into);
 54 |   }
 55 | 
 56 |   void inv(const cube& c, cube& into) {
 57 |     for (int corner = 0; corner < corner::COUNT; corner++)
 58 |       into.cperm[c.cperm[corner]] = corner; // inv[a[i]] = i
 59 |     for (int edge = 0; edge < edge::COUNT; edge++)
 60 |       into.eperm[c.eperm[edge]] = edge;
 61 |     for (int i = 0; i < corner::COUNT; i++)
 62 |       into.cori[i] = inv_cori[c.cori[into.cperm[i]]];
 63 |     for (int i = 0; i < edge::COUNT; i++)
 64 |       into.eori[i] = c.eori[into.eperm[i]];
 65 |   }
 66 | 
 67 |   int check(const cube& c) {
 68 |     bool corners[corner::COUNT] = {};
 69 |     int cori_sum = 0;
 70 | 
 71 |     for (int i = 0; i < corner::COUNT; i++) {
 72 |       if (c.cperm[i] < 0 || c.cperm[i] >= corner::COUNT)
 73 |         return 1; // invalid corner cubie
 74 |       corners[c.cperm[i]] = true;
 75 |       if (c.cori[i] < 0 || c.cori[i] >= 3)
 76 |         return 2; // invalid corner orientation
 77 |       cori_sum += c.cori[i];
 78 |     }
 79 |     if (cori_sum % 3 != 0)
 80 |       return 3; // invalid twist parity
 81 |     for (bool corner : corners) {
 82 |       if (!corner)
 83 |         return 4; // missing corner
 84 |     }
 85 | 
 86 |     bool edges[edge::COUNT] = {};
 87 |     int eori_sum = 0;
 88 | 
 89 |     for (int i = 0; i < edge::COUNT; i++) {
 90 |       if (c.eperm[i] < 0 || c.eperm[i] >= edge::COUNT)
 91 |         return 5; // invalid edge cubie
 92 |       edges[c.eperm[i]] = true;
 93 |       if (c.eori[i] < 0 || c.eori[i] >= 2)
 94 |         return 6; // invalid edge orientation
 95 |       eori_sum += c.eori[i];
 96 |     }
 97 |     if ((eori_sum & 1) != 0)
 98 |       return 7; // invalid flip parity
 99 |     for (bool edge : edges) {
100 |       if (!edge)
101 |         return 8; // missing edge
102 |     }
103 | 
104 |     if (parity(c.cperm, corner::COUNT) != parity(c.eperm, edge::COUNT))
105 |       return 9; // corner and edge permutation parity mismatch
106 |     return 0;
107 |   }
108 | 
109 |   void shuffle(cube& c) {
110 |     for (int i = 0; i < corner::COUNT; i++)
111 |       c.cperm[i] = i;
112 |     for (int i = 0; i < edge::COUNT; i++)
113 |       c.eperm[i] = i;
114 | 
115 |     coord::set_corners(c, std::uniform_int_distribution<int>(0, coord::N_CORNERS)(gen));
116 |     std::shuffle(c.eperm, c.eperm + edge::COUNT, gen); // no coordinate for all edges
117 |     if (parity(c.cperm, corner::COUNT) != parity(c.eperm, edge::COUNT))
118 |       std::swap(c.cperm[corner::COUNT - 2], c.cperm[corner::COUNT - 1]); // flip parity
119 | 
120 |     coord::set_twist(c, std::uniform_int_distribution<int>(0, coord::N_TWIST - 1)(gen));
121 |     coord::set_flip(c, std::uniform_int_distribution<int>(0, coord::N_FLIP - 1)(gen));
122 |   }
123 | 
124 |   // We could maybe make this faster, but it is not performance critical anyways
125 |   bool operator==(const cube& c1, const cube& c2) {
126 |     return
127 |       std::equal(c1.cperm, c1.cperm + corner::COUNT, c2.cperm) &&
128 |       std::equal(c1.eperm, c1.eperm + edge::COUNT, c2.eperm) &&
129 |       std::equal(c1.cori, c1.cori + corner::COUNT, c2.cori) &&
130 |       std::equal(c1.eori, c1.eori + edge::COUNT, c2.eori)
131 |     ;
132 |   }
133 | 
134 |   bool operator!=(const cube& c1, const cube& c2) {
135 |     return !(c1 == c2);
136 |   }
137 | 
138 | }
139 | 


--------------------------------------------------------------------------------
/src/sym.cpp:
--------------------------------------------------------------------------------
  1 | #include "sym.h"
  2 | 
  3 | namespace sym {
  4 | 
  5 |   using namespace cubie::corner;
  6 |   using namespace cubie::edge;
  7 | 
  8 |   const uint32_t EMPTY = ~uint32_t(0);
  9 | 
 10 |   cubie::cube cubes[COUNT];
 11 |   int inv[COUNT];
 12 |   int effect[COUNT][3];
 13 | 
 14 |   int conj_move[move::COUNT][COUNT];
 15 |   uint16_t conj_twist[coord::N_TWIST][COUNT_SUB];
 16 |   uint16_t conj_udedges2[coord::N_UDEDGES2][COUNT_SUB];
 17 | 
 18 |   uint32_t fslice1_sym[coord::N_FSLICE1];
 19 |   uint32_t corners_sym[coord::N_CORNERS];
 20 |   uint32_t fslice1_raw[N_FSLICE1];
 21 |   uint16_t corners_raw[N_CORNERS];
 22 |   uint16_t fslice1_selfs[N_FSLICE1];
 23 |   uint16_t corners_selfs[N_CORNERS];
 24 | 
 25 |   void init_base() {
 26 |     cubie::cube c = cubie::SOLVED_CUBE;
 27 |     cubie::cube tmp;
 28 | 
 29 |     cubie::cube lr2 = {
 30 |       {UFL, URF, UBR, ULB, DLF, DFR, DRB, DBL},
 31 |       {UL, UF, UR, UB, DL, DF, DR, DB, FL, FR, BR, BL},
 32 |       {3, 3, 3, 3, 3, 3, 3, 3}, {} // special mirror ori
 33 |     };
 34 |     cubie::cube u4 = {
 35 |       {UBR, URF, UFL, ULB, DRB, DFR, DLF, DBL},
 36 |       {UB, UR, UF, UL, DB, DR, DF, DL, BR, FR, FL, BL},
 37 |       {}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1}
 38 |     };
 39 |     cubie::cube f2 = {
 40 |       {DLF, DFR, DRB, DBL, UFL, URF, UBR, ULB},
 41 |       {DL, DF, DR, DB, UL, UF, UR, UB, FL, FR, BR, BL},
 42 |       {}, {}
 43 |     };
 44 |     cubie::cube urf3 = {
 45 |       {URF, DFR, DLF, UFL, UBR, DRB, DBL, ULB},
 46 |       {UF, FR, DF, FL, UB, BR, DB, BL, UR, DR, DL, UL},
 47 |       {1, 2, 1, 2, 2, 1, 2, 1},
 48 |       {1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1}
 49 |     };
 50 | 
 51 |     // First 4 symmetries are the ones used in F5 mode
 52 |     for (int i = 0; i < COUNT; i++) {
 53 |       cubes[i] = c;
 54 | 
 55 |       cubie::mul(c, lr2, tmp);
 56 |       std::swap(tmp, c);
 57 | 
 58 |       if (i % 2 == 1) {
 59 |         cubie::mul(c, f2, tmp);
 60 |         std::swap(tmp, c);
 61 |       }
 62 |       if (i % 4 == 3) {
 63 |         cubie::mul(c, u4, tmp);
 64 |         std::swap(tmp, c);
 65 |       }
 66 |       if (i % 16 == 15) {
 67 |         cubie::mul(c, urf3, tmp);
 68 |         std::swap(tmp, c);
 69 |       }
 70 |     }
 71 | 
 72 |     /* Maybe not the most efficient, but overall time spent here completely negligible. */
 73 | 
 74 |     for (int i = 0; i < COUNT; i++) {
 75 |       for (int j = 0; j < COUNT; j++) {
 76 |         cubie::mul(cubes[i], cubes[j], c);
 77 |         if (c == cubie::SOLVED_CUBE) {
 78 |           inv[i] = j;
 79 |           break;
 80 |         }
 81 |       }
 82 |     }
 83 | 
 84 |     for (int m = 0; m < move::COUNT; m++) {
 85 |       for (int s = 0; s < COUNT; s++) {
 86 |         cubie::mul(cubes[s], move::cubes[m], tmp);
 87 |         cubie::mul(tmp, cubes[inv[s]], c);
 88 |         for (int conj = 0; conj < move::COUNT; conj++) {
 89 |           if (c == move::cubes[conj]) {
 90 |             conj_move[m][s] = conj;
 91 |             break;
 92 |           }
 93 |         }
 94 |       }
 95 |     }
 96 | 
 97 |     /* Figure this out right here instead of defining even more "weird" constants */
 98 |     int per_axis = move::COUNT1 / 3;
 99 |     int per_face = 3;
100 |     #ifdef QT
101 |       per_face -= 1;
102 |     #endif
103 |     for (int s = 0; s < COUNT; s++) {
104 |       for (int ax = 0; ax < 3; ax++) {
105 |         effect[s][ax] = (conj_move[per_axis * ax][inv[s]] / per_axis) << 2; // shift
106 |         effect[s][ax] |= (conj_move[per_axis * ax][inv[s]] % per_axis >= per_face) << 1; // flip
107 |         effect[s][ax] |= (conj_move[per_axis * ax][inv[s]] % per_face != 0); // inv
108 |       }
109 |     }
110 |   }
111 | 
112 |   void init_conjcoord(
113 |     uint16_t conj_coord[][COUNT_SUB],
114 |     int n_coords,
115 |     int (*get_coord)(const cubie::cube&),
116 |     void (*set_coord)(cubie::cube&, int),
117 |     void (*mul)(const cubie::cube&, const cubie::cube&, cubie::cube&)
118 |   ) {
119 |     cubie::cube c1 = cubie::SOLVED_CUBE; // make sure all multiplications will work
120 |     cubie::cube c2;
121 |     cubie::cube tmp;
122 | 
123 |     for (int coord = 0; coord < n_coords; coord++) {
124 |       set_coord(c1, coord);
125 |       conj_coord[coord][0] = coord; // sym 0 is identity
126 |       for (int s = 1; s < COUNT_SUB; s++) {
127 |         mul(cubes[s], c1, tmp);
128 |         mul(tmp, cubes[inv[s]], c2);
129 |         conj_coord[coord][s] = get_coord(c2);
130 |       }
131 |     }
132 |   }
133 | 
134 |   void init_fslice1() {
135 |     std::fill(fslice1_sym, fslice1_sym + coord::N_FSLICE1, EMPTY);
136 | 
137 |     cubie::cube c1 = cubie::SOLVED_CUBE;
138 |     cubie::cube c2;
139 |     cubie::cube tmp;
140 |     int cls = 0;
141 | 
142 |     for (int slice1 = 0; slice1 < coord::N_SLICE1; slice1++) {
143 |       coord::set_slice1(c1, slice1); // SLICE is slightly more expensive to set
144 |       for (int flip = 0; flip < coord::N_FLIP; flip++) {
145 |         coord::set_flip(c1, flip);
146 |         int fslice1 = coord::fslice1(flip, slice1);
147 | 
148 |         if (fslice1_sym[fslice1] != EMPTY)
149 |           continue;
150 |         fslice1_sym[fslice1] = COUNT_SUB * cls;
151 |         fslice1_raw[cls] = fslice1;
152 |         fslice1_selfs[cls] = 1; // symmetry 0 is identity and always a self-sym
153 | 
154 |         for (int s = 1; s < COUNT_SUB; s++) {
155 |           cubie::edge::mul(cubes[inv[s]], c1, tmp);
156 |           cubie::edge::mul(tmp, cubes[s], c2);
157 |           int fslice11 = coord::fslice1(coord::get_flip(c2), coord::get_slice1(c2));
158 |           if (fslice1_sym[fslice11] == EMPTY)
159 |             fslice1_sym[fslice11] = COUNT_SUB * cls + s;
160 |           else if (fslice11 == fslice1) // collect self-symmetries
161 |             fslice1_selfs[cls] |= 1 << s;
162 |         }
163 |         cls++;
164 |       }
165 |     }
166 |   }
167 | 
168 |   void init_corners() {
169 |     std::fill(corners_sym, corners_sym + coord::N_CORNERS, EMPTY);
170 | 
171 |     cubie::cube c1 = cubie::SOLVED_CUBE;
172 |     cubie::cube c2;
173 |     cubie::cube tmp;
174 |     int cls = 0;
175 | 
176 |     for (int corners = 0; corners < coord::N_CORNERS; corners++) {
177 |       coord::set_corners(c1, corners);
178 | 
179 |       if (corners_sym[corners] != EMPTY)
180 |         continue;
181 |       corners_sym[corners] = COUNT_SUB * cls;
182 |       corners_raw[cls] = corners;
183 |       corners_selfs[cls] = 1;
184 | 
185 |       for (int s = 1; s < COUNT_SUB; s++) {
186 |         cubie::corner::mul(cubes[inv[s]], c1, tmp);
187 |         cubie::corner::mul(tmp, cubes[s], c2);
188 |         int corners1 = coord::get_corners(c2);
189 |         if (corners_sym[corners1] == EMPTY)
190 |           corners_sym[corners1] = COUNT_SUB * cls + s;
191 |         else if (corners1 == corners)
192 |           corners_selfs[cls] |= 1 << s;
193 |       }
194 |       cls++;
195 |     }
196 |   }
197 | 
198 |   void init() {
199 |     init_base();
200 |     init_conjcoord(conj_twist, coord::N_TWIST, coord::get_twist, coord::set_twist, cubie::corner::mul);
201 |     init_conjcoord(conj_udedges2, coord::N_UDEDGES2, coord::get_udedges2, coord::set_udedges2, cubie::edge::mul);
202 |     init_fslice1();
203 |     init_corners();
204 |   }
205 | 
206 | }
207 | 


--------------------------------------------------------------------------------
/src/test.cpp:
--------------------------------------------------------------------------------
  1 | /**
  2 |  * Tests & sanity checks for individual parts of the solver; very useful during development.
  3 |  */
  4 | 
  5 | #include <bitset>
  6 | #include <chrono>
  7 | #include <iostream>
  8 | #include <strings.h>
  9 | 
 10 | #include "coord.h"
 11 | #include "cubie.h"
 12 | #include "move.h"
 13 | #include "prun.h"
 14 | #include "sym.h"
 15 | 
 16 | inline void ok() { std::cout << "Ok." << std::endl; }
 17 | inline void error() { std::cout << "Error." << std::endl; }
 18 | 
 19 | void test_cubie() {
 20 |   std::cout << "Testing cubie level ..." << std::endl;
 21 |   cubie::cube c = cubie::SOLVED_CUBE;
 22 | 
 23 |   cubie::cube tmp1, tmp2;
 24 |   cubie::inv(c, tmp1);
 25 |   if (c != tmp1)
 26 |     error();
 27 |   cubie::mul(c, tmp1, tmp2);
 28 |   if (c != tmp2)
 29 |     error();
 30 | 
 31 |   cubie::shuffle(c);
 32 |   cubie::inv(c, tmp1);
 33 |   cubie::mul(c, tmp1, tmp2);
 34 |   if (tmp2 != cubie::SOLVED_CUBE)
 35 |     error();
 36 | 
 37 |   for (int i = 0; i < 100; i++) {
 38 |     cubie::shuffle(c);
 39 |     if (cubie::check(c) != 0)
 40 |       error();
 41 |   }
 42 |   cubie::shuffle(c);
 43 |   std::swap(c.cperm[0], c.cperm[1]);
 44 |   if (check(c) == 0)
 45 |     error();
 46 | 
 47 |   ok();
 48 | }
 49 | 
 50 | void test_getset(int (*get_coord)(const cubie::cube&), void (*set_coord)(cubie::cube&, int), int count) {
 51 |   cubie::cube c;
 52 |   for (int i = 0; i < count; i++) {
 53 |     set_coord(c, i);
 54 |     if (get_coord(c) != i)
 55 |       error();
 56 |   }
 57 |   ok();
 58 | }
 59 | 
 60 | void test_movecoord(uint16_t move_coord[][move::COUNT], int n_coord, move::mask moves = move::p1mask | move::p2mask) {
 61 |   for (int coord = 0; coord < n_coord; coord++) {
 62 |     for (; moves; moves &= moves - 1) {
 63 |       int m = ffsll(moves) - 1;
 64 |       if (move_coord[move_coord[coord][m]][move::inv[m]] != coord)
 65 |         error();
 66 |       if (move_coord[move_coord[coord][move::inv[m]]][m] != coord)
 67 |         error();
 68 |     }
 69 |   }
 70 |   ok();
 71 | }
 72 | 
 73 | void test_coord() {
 74 |   std::cout << "Testing coord level ..." << std::endl;
 75 |   test_getset(coord::get_flip, coord::set_flip, coord::N_FLIP);
 76 |   test_getset(coord::get_twist, coord::set_twist, coord::N_TWIST);
 77 |   test_getset(coord::get_slice, coord::set_slice, coord::N_SLICE);
 78 |   test_getset(coord::get_uedges, coord::set_uedges, coord::N_UEDGES);
 79 |   test_getset(coord::get_dedges, coord::set_dedges, coord::N_DEDGES);
 80 |   test_getset(coord::get_corners, coord::set_corners, coord::N_CORNERS);
 81 | 
 82 |   test_getset(coord::get_slice1, coord::set_slice1, coord::N_SLICE1);
 83 |   test_getset(coord::get_udedges2, coord::set_udedges2, coord::N_UDEDGES2);
 84 | 
 85 |   test_movecoord(coord::move_flip, coord::N_FLIP);
 86 |   test_movecoord(coord::move_twist, coord::N_TWIST);
 87 |   test_movecoord(coord::move_edges4, coord::N_SLICE);
 88 |   test_movecoord(coord::move_corners, coord::N_CORNERS);
 89 |   test_movecoord(coord::move_udedges2, coord::N_UDEDGES2, move::p2mask);
 90 | }
 91 | 
 92 | void test_move() {
 93 |   std::cout << "Testing move level ..." << std::endl;
 94 | 
 95 |   cubie::cube c;
 96 |   for (int m = 0; m < move::COUNT; m++) {
 97 |     if (move::inv[move::inv[m]] != m)
 98 |       error();
 99 |     cubie::mul(move::cubes[m], move::cubes[move::inv[m]], c);
100 |     if (c != cubie::SOLVED_CUBE)
101 |       error();
102 |     cubie::mul(move::cubes[move::inv[m]], move::cubes[m], c);
103 |     if (c != cubie::SOLVED_CUBE)
104 |       error();
105 |   }
106 |   ok();
107 | 
108 |   std::cout << "Phase 1: ";
109 |   for (int m = 0; m < move::COUNT; m++) {
110 |     if (move::in(m, move::p1mask))
111 |       std::cout << move::names[m] << " ";
112 |   }
113 |   std::cout << std::endl;
114 |   std::cout << "Phase 2: ";
115 |   for (int m = 0; m < move::COUNT; m++) {
116 |     if (move::in(m, move::p2mask))
117 |       std::cout << move::names[m] << " ";
118 |   }
119 |   std::cout << std::endl;
120 | 
121 |   std::cout << "Forbidden:" << std::endl;
122 |   for (int m = 0; m < move::COUNT; m++) {
123 |     std::cout << move::names[m] << ": ";
124 |     for (int m1 = 0; m1 < move::COUNT; m1++) {
125 |       if (!move::in(m1, move::next[m]))
126 |         std::cout << move::names[m1] << " ";
127 |     }
128 |     if (move::qt_skip[m] != 0) {
129 |       std::cout << "| ";
130 |       for (int m1 = 0; m1 < move::COUNT; m1++) {
131 |         if (move::in(m1, move::qt_skip[m]))
132 |           std::cout << move::names[m1] << " ";
133 |       }
134 |     }
135 |     std::cout << std::endl;
136 |   }
137 | 
138 | }
139 | 
140 | void test_conj(uint16_t conj_coord[][sym::COUNT_SUB], int n_coord) {
141 |   for (int coord = 0; coord < n_coord; coord++) {
142 |     for (int s = 0; s < sym::COUNT_SUB; s++) {
143 |       if (conj_coord[conj_coord[coord][s]][sym::inv[s]] != coord)
144 |         error();
145 |       if (conj_coord[conj_coord[coord][sym::inv[s]]][s] != coord)
146 |         error();
147 |     }
148 |   }
149 |   ok();
150 | }
151 | 
152 | void test_sym() {
153 |   std::cout << "Testing sym level ..." << std::endl;
154 |   test_conj(sym::conj_twist, coord::N_TWIST);
155 |   test_conj(sym::conj_udedges2, coord::N_UDEDGES2);
156 | }
157 | 
158 | void test_prun() {
159 |   std::cout << "Testing pruning ..." << std::endl;
160 | 
161 |   srand(0);
162 |   int n_moves = std::bitset<64>(move::p1mask).count(); // make sure not to consider B-moves in F5-mode
163 | 
164 |   for (int i = 0; i < 1000; i++) {
165 |     int flip = rand() % coord::N_FLIP;
166 |     int slice = rand() % coord::N_SLICE;
167 |     int twist = rand() % coord::N_TWIST;
168 | 
169 |     move::mask next;
170 |     move::mask next1;
171 |     move::mask tmp;
172 |     int togo = prun::get_phase1(flip, slice, twist, 100, tmp);
173 | 
174 |     int dist = prun::get_phase1(flip, slice, twist, togo, next);
175 |     next &= move::p1mask;
176 | 
177 |     next1 = 0;
178 |     for (int m = 0; m < n_moves; m++) {
179 |       int flip1 = coord::move_flip[flip][m];
180 |       int slice1 = coord::move_edges4[slice][m];
181 |       int twist1 = coord::move_twist[twist][m];
182 |       if (prun::get_phase1(flip1, slice1, twist1, 100, tmp) < dist)
183 |         next1 |= move::bit(m);
184 |     }
185 |     if (next1 != next)
186 |       error();
187 | 
188 |     dist = prun::get_phase1(flip, slice, twist, togo + 1, next);
189 |     next &= move::p1mask;
190 | 
191 |     next1 = 0;
192 |     for (int m = 0; m < n_moves; m++) {
193 |       int flip1 = coord::move_flip[flip][m];
194 |       int slice1 = coord::move_edges4[slice][m];
195 |       int twist1 = coord::move_twist[twist][m];
196 |       if (prun::get_phase1(flip1, slice1, twist1, 100, tmp) <= dist)
197 |         next1 |= move::bit(m);
198 |     }
199 |     if (next1 != next)
200 |       error();
201 |   }
202 | 
203 |   ok();
204 | }
205 | 
206 | bool check(const cubie::cube &c, const std::vector<int>& sol) {
207 |   cubie::cube c1;
208 |   cubie::cube c2;
209 | 
210 |   c1 = c;
211 |   for (int m : sol) {
212 |     cubie::mul(c1, move::cubes[m], c2);
213 |     std::swap(c1, c2);
214 |   }
215 | 
216 |   return c1 == cubie::SOLVED_CUBE;
217 | }
218 | 
219 | int main() {
220 |   auto tick = std::chrono::high_resolution_clock::now();
221 |   move::init();
222 |   coord::init();
223 |   sym::init();
224 |   prun::init();
225 |   std::cout << std::chrono::duration_cast<std::chrono::microseconds>(std::chrono::high_resolution_clock::now() - tick).count() / 1000. << "ms" << std::endl;
226 | 
227 |   test_cubie();
228 |   test_coord();
229 |   test_move();
230 |   test_sym();
231 |   test_prun();
232 | 
233 |   return 0;
234 | }
235 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | # rob-twophase v2.0
 2 | 
 3 | This is an extremely efficient Rubik's Cube solving algorithm designed particularly for the use by high-speed robots. At its core, it is a highly optimized C++ version of Herbert Kociemba's two-phase algorithm that combines many of the best tricks from the excellent implementations [`RubiksCube-TwophaseSolver`](https://github.com/hkociemba/RubiksCube-TwophaseSolver), [`min2phase`](https://github.com/cs0x7f/min2phase) and [`cube20src`](https://github.com/rokicki/cube20src) with some further improvements of my own. Additionally, it includes several features that (to the best of my knowledge) cannot be found elsewhere at the moment. First and foremost, `rob-twophase` is able to directly consider the mechanics of axial robots (i.e. that they can move opposite faces in parallel or that a 180-degree turn takes about twice as long as a 90-degree one) yielding 15-20% faster to execute solutions on average. Secondly, it supports single-solve multi-threading with an arbitrary number of threads yielding 10+ times speed-ups even on moderate hardware. Finally, it can search for multiple solutions at once allowing post-selection to consider additional execution parameters (like for instance turn transitions). If you are planning to challenge the official Guinness World Record for the fastest robot to solve a Rubik's Cube, `rob-twophase` is most likely the solver you will want to use.
 4 | 
 5 | **New in Version 2.0:**
 6 | 
 7 | * Considerably faster solving performance by less table decomposition and proper elimination of redundant maneuvers in QT-modes.
 8 | * Significantly faster initial table generation (also through better coordinates).
 9 | * Much better utilization of high thread-counts via the `-s` parameter.
10 | * Return more than one solution with `-n`.
11 | * Automatically compress QT-mode solutions back to HT using the `-c` option.
12 | * Cleaner code by major refactoring and elimination of questionable "optimizations".
13 | 
14 | ## Usage
15 | 
16 | The easiest way to use `rob-twophase` is to use the small interactive CMD-utility that it compiles to via `make`. Interfacing with this tool via pipes to STDIN/STDOUT should be more than sufficient for most applications (this is also what I do for my own robots). If you want to interface with it directly in C++ best have a look at `src/main.cpp` to see how to use the internal solver engine. The solving mode needs to be selected during compile time via compiler-flags (both for efficiency but also simplicity reasons). Simply add them to `CPPFLAGS` if you are using the provided `makefile`. `-DQT` solves in the quarter-turn metric (only 90-degree moves), `-DAX` in the axial metric (opposite faces can be manipulated at the same time) and `-DF5` uses only 5 faces (never turning the B-face). All three of those flags can be combined arbitrarily.
17 | 
18 | The CMD-program provides the following options:
19 | 
20 | * `-c` (default OFF): Compress solutions to AXHT. This is especially useful when solving in AXQT as properly merging move sequences like `D (U D)` is not entirely trivial without having all the proper move definitions at the ready.
21 | 
22 | * `-l` (default -1): Maximum solution length. The search will stop once a solution of at most this length is found. With `-1` the solver will simply search for the full time-limit and eventually return the best solution found.
23 | 
24 | * `-m` (default 10): Time-limit in milliseconds.
25 | 
26 | * `-n` (default 1): Number of solutions to return, i.e. it will return the best `-n` solutions found.
27 | 
28 | * `-s` (default 1): Number of splits for every IDA-search task. This is an advanced parallelization parameter most relevant for high thread-counts. As a very rough guide, choose it so that `-t / -s` is close to 6 (or close to 4 when using `-DF5`).
29 | 
30 | * `-t` (default 1): Number of threads. Best set this as the number of processor threads you have (typically number of cores times two), i.e. use hyper-threading.
31 | 
32 | * `-w` (default 0): Number of random warmup solves to perform on start-up to optimally prepare the cache for the robot solves that matter.
33 | 
34 | When first starting `rob-twophase`, it will generate fairly big tables which may take several seconds to minutes (see section below). Those are then persisted in files to make further start-ups very quick. After starting it can solve cubes by typing `solve FACECUBE` (see [`src/face.h`](https://github.com/efrantar/rob-twophase/blob/master/src/face.h) for a detailed documentation of Kociemba's face-cube representation), generate scrambles with `scramble` or run benchmarks with `bench`. Note that the program is already designed to be directly used by robots (for example via pipe communication) and thereby of course also does things such as always preloading all threads to ensure maximum solving speed.
35 | 
36 | ## Performance
37 | 
38 | All benchmarks were run on a stock AMD Ryzen 5 3600 (6 cores, 12 threads) processor (hence `-t 12 -s 2`) combined with standard clocked DDR4 memory and use exactly the same set of 10000 uniformly random cubes (file `bench.cubes`).
39 | 
40 | The first table gives for each solving mode (indicated by the compiler flags) the average solution length (number of moves) when running the solver with a timelimit of 10ms (`-m 10`) per cube in the various metrics (half-turn HT, quarter-turn QT, axial half-turn AXHT and axial quarter-turn AXQT). The number in bold is the length in the metric that is being solved in (i.e. the number that is relevant), the other values are just given to illustrate the gains from directly solving in the appropriate metric.
41 | 
42 | | `-DQT` | `-DAX` | `-DF5` | HT        | QT        | AXHT      | AXQT      | Setup Time | Table Size |
43 | | :----: | :----: | :----: | :-:       | :-:       | :--:      | :--:      | :--------: | :--------: |
44 | | -      | -      | -      | **18.56** | *26.46*   | *17.00*   | *24.60*   | 38s        | 676MB      |
45 | | YES    | -      | -      | *19.84*   | **24.22** | *17.97*   | *22.21*   | 26s        | 676MB      |
46 | | -      | YES    | -      | *21.83*   | *31.05*   | **14.71** | *22.95*   | 98s        | 1.2GB      |
47 | | YES    | YES    | -      | *22.76*   | *27.03*   | *16.40*   | **19.91** | 57s        | 1.2GB      |
48 | | -      | -      | YES    | **20.61** | *29.51*   | *18.90*   | *27.50*   | 125s       | 2.7GB      |
49 | | YES    | -      | YES    | *22.07*   | **26.98** | *19.99*   | *24.78*   | 85s        | 2.7GB      |
50 | | -      | YES    | YES    | *23.65*   | *33.34*   | **16.85** | *25.50*   | 287s       | 4.9GB      |
51 | | YES    | YES    | YES    | *25.08*   | *29.94*   | *18.38*   | **22.49** | 162s       | 4.9GB      |
52 | 
53 | Finally, a speed comparison with Tomas Rokicki's [`cube20src`](https://github.com/rokicki/cube20src) solver which was used to prove that God's number is 20 (and is probably the next fastest available solver). `rob-twophase` learned many great tricks from this extremely optimized implementation. Furthermore, `cube20src` clearly remains the best choice for batch-solving a very large number of cubes. However, it does (at least as of right now) not support robot metrics or single-solve multi-threading. In general, `rob-twophase` is slightly faster in single-threaded mode (apart from shorter QT searches it seems) but dramatically faster when multi-threading. The table below gives the average solving time for different move-bounds and metrics (using again `bench.cubes`).
54 | 
55 | | Metric | Max #Moves | `rob-twophase` w. `-t 1` | `rob-twophase` w. `-t 12` | `cube20src` |
56 | | :----: | :--------: | :----------------------: | :-----------------------: | :---------: |
57 | | HT     | 20         | 00.48ms                  | **00.02ms**               | 00.55ms     |
58 | | HT     | 19         | 41.51ms                  | **04.37ms**               | 53.04ms     |
59 | | QT     | 26         | 11.20ms                  | **00.96ms**               | 10.26ms     |
60 | | QT     | 25         | 71.43ms                  | **07.13ms**               | 77.94ms     |
61 | 


--------------------------------------------------------------------------------
/src/coord.cpp:
--------------------------------------------------------------------------------
  1 | #include "coord.h"
  2 | 
  3 | #include <algorithm>
  4 | #include <bitset>
  5 | #include <cstring>
  6 | 
  7 | #include "cubie.h"
  8 | 
  9 | namespace coord {
 10 | 
 11 |   const int N_C12K4 = 495; // binom(12, 4)
 12 |   const int N_PERM4 = 24; // 4!
 13 | 
 14 |   uint16_t move_flip[N_FLIP][move::COUNT];
 15 |   uint16_t move_twist[N_TWIST][move::COUNT];
 16 |   uint16_t move_edges4[N_SLICE][move::COUNT];
 17 |   uint16_t move_corners[N_CORNERS][move::COUNT];
 18 |   uint16_t move_udedges2[N_UDEDGES2][move::COUNT];
 19 | 
 20 |   /* Used for en-/decoding pos-perm coords */
 21 |   uint8_t enc_perm[1 << (4 * 2)]; // encode 4-elem perm as 8 bits
 22 |   uint8_t dec_perm[N_PERM4];
 23 |   uint16_t enc_comb[1 << 12]; // encode 4-elem comb as 12-bit mask with exactly 4 bits on
 24 |   uint16_t dec_comb[N_C12K4];
 25 | 
 26 |   int binarize_perm(int perm[]) {
 27 |     int bin = 0;
 28 |     for (int i = 3; i >= 0; i--)
 29 |       bin = (bin << 2) | perm[i];
 30 |     return bin;
 31 |   }
 32 | 
 33 |   void init_encdec() {
 34 |     int perm[] = {0, 1, 2, 3};
 35 |     for (int i = 0; i < N_PERM4; i++) {
 36 |       int bin = binarize_perm(perm);
 37 |       enc_perm[bin] = i;
 38 |       dec_perm[i] = bin;
 39 |       std::next_permutation(perm, perm + 4);
 40 |     }
 41 | 
 42 |     int i = 0;
 43 |     for (int comb = 0; comb < (1 << cubie::edge::COUNT); comb++) {
 44 |       if (std::bitset<cubie::edge::COUNT>(comb).count() == 4) {
 45 |         enc_comb[comb] = i;
 46 |         dec_comb[i] = comb;
 47 |         i++;
 48 |       }
 49 |     }
 50 |   }
 51 | 
 52 |   int get_ori(const int oris[], int len, int n_oris) {
 53 |     int val = 0;
 54 |     for (int i = 0; i < len - 1; i++) // last ori can be reconstructed by parity
 55 |       val = n_oris * val + oris[i];
 56 |     return val;
 57 |   }
 58 | 
 59 |   void set_ori(int val, int oris[], int len, int n_oris) {
 60 |     int par = 0;
 61 |     for (int i = len - 2; i >= 0; i--) {
 62 |       oris[i] = val % n_oris;
 63 |       par += oris[i];
 64 |       val /= n_oris;
 65 |     }
 66 |     // Ori parity must always be 0
 67 |     oris[len - 1] = (n_oris - par % n_oris) % n_oris;
 68 |   }
 69 | 
 70 |   // `mask` indicates which 4 edges to compute the coordinate for
 71 |   int get_combperm(const int cubies[], int len, int mask) {
 72 |     int min_cubie = ffs(mask) - 1;
 73 | 
 74 |     int comb = 0;
 75 |     int perm = 0;
 76 | 
 77 |     for (int i = len - 1; i >= 0; i--) {
 78 |       if (mask & (1 << cubies[i])) {
 79 |         comb |= 1 << i;
 80 |         perm = (perm << 2) | (cubies[i] - min_cubie);
 81 |       }
 82 |     }
 83 | 
 84 |     return N_PERM4 * enc_comb[comb] + enc_perm[perm];
 85 |   }
 86 | 
 87 |   void set_combperm(int comb, int perm, int cubies[], int len, int min_cubie) {
 88 |     comb = dec_comb[comb];
 89 |     perm = dec_perm[perm];
 90 | 
 91 |     int cubie = 0;
 92 |     for (int i = 0; i < len; i++) {
 93 |       if (cubie == min_cubie)
 94 |         cubie += 4;
 95 |       if (comb & (1 << i)) {
 96 |         cubies[i] = (perm & 0x3) + min_cubie;
 97 |         perm >>= 2;
 98 |       } else
 99 |         cubies[i] = cubie++;
100 |     }
101 |   }
102 | 
103 |   /* Faster than using `*_comperm()` twice */
104 | 
105 |   int get_perm8(const int cubies[]) {
106 |     int comb1 = 0;
107 |     int perm1 = 0;
108 |     int perm2 = 0;
109 | 
110 |     for (int i = 7; i >= 0; i--) {
111 |       if (cubies[i] < 4) {
112 |         comb1 |= 1 << i;
113 |         perm1 = (perm1 << 2) | cubies[i];
114 |       } else
115 |         perm2 = (perm2 << 2) | (cubies[i] - 4);
116 |     }
117 | 
118 |     comb1 = enc_comb[comb1];
119 |     perm1 = enc_perm[perm1];
120 |     perm2 = enc_perm[perm2];
121 |     return N_PERM4 * (N_PERM4 * comb1 + perm1) + perm2;
122 |   }
123 | 
124 |   void set_perm8(int perm8, int cubies[]) {
125 |     int perm2 = dec_perm[perm8 % N_PERM4];
126 |     int comb1 = dec_comb[(perm8 / N_PERM4) / N_PERM4];
127 |     int perm1 = dec_perm[(perm8 / N_PERM4) % N_PERM4];
128 | 
129 |     for (int i = 0; i < 8; i++) {
130 |       if (comb1 & (1 << i)) {
131 |         cubies[i] = perm1 & 0x3;
132 |         perm1 >>= 2;
133 |       } else {
134 |         cubies[i] = (perm2 & 0x3) + 4;
135 |         perm2 >>= 2;
136 |       }
137 |     }
138 |   }
139 | 
140 |   int get_twist(const cubie::cube& c) {
141 |     return get_ori(c.cori, cubie::corner::COUNT, 3);
142 |   }
143 | 
144 |   void set_twist(cubie::cube& c, int twist) {
145 |     set_ori(twist, c.cori, cubie::corner::COUNT, 3);
146 |   }
147 | 
148 |   int get_flip(const cubie::cube& c) {
149 |     return get_ori(c.eori, cubie::edge::COUNT, 2);
150 |   }
151 | 
152 |   void set_flip(cubie::cube& c, int flip) {
153 |     set_ori(flip, c.eori, cubie::edge::COUNT, 2);
154 |   }
155 | 
156 |   int get_slice(const cubie::cube& c) {
157 |     return get_combperm(c.eperm, cubie::edge::COUNT, 0xf00);
158 |   }
159 | 
160 |   void set_slice(cubie::cube& c, int slice) {
161 |     set_combperm(slice / N_PERM4, slice % N_PERM4, c.eperm, cubie::edge::COUNT, cubie::edge::FR);
162 |   }
163 | 
164 |   int get_uedges(const cubie::cube& c) {
165 |     return get_combperm(c.eperm, cubie::edge::COUNT, 0x00f);
166 |   }
167 | 
168 |   void set_uedges(cubie::cube& c, int uedges) {
169 |     set_combperm(uedges / N_PERM4, uedges % N_PERM4, c.eperm, cubie::edge::COUNT, cubie::edge::UR);
170 |   }
171 | 
172 |   int get_dedges(const cubie::cube& c) {
173 |     return get_combperm(c.eperm, cubie::edge::COUNT, 0x0f0);
174 |   }
175 | 
176 |   void set_dedges(cubie::cube& c, int dedges) {
177 |     set_combperm(dedges / N_PERM4, dedges % N_PERM4, c.eperm, cubie::edge::COUNT, cubie::edge::DR);
178 |   }
179 | 
180 |   int get_corners(const cubie::cube& c) {
181 |     return get_perm8(c.cperm);
182 |   }
183 | 
184 |   void set_corners(cubie::cube& c, int corners) {
185 |     set_perm8(corners, c.cperm);
186 |   }
187 | 
188 |   /* Dedicated methods again more efficient than `*_posperm()` */
189 | 
190 |   int get_slice1(const cubie::cube& c) {
191 |     int slice1 = 0;
192 |     for (int i = cubie::edge::COUNT - 1; i >= 0; i--) {
193 |       if (c.eperm[i] >= cubie::edge::FR)
194 |         slice1 |= 1 << i;
195 |     }
196 |     return enc_comb[slice1];
197 |   }
198 | 
199 |   void set_slice1(cubie::cube& c, int slice1) {
200 |     slice1 = dec_comb[slice1];
201 |     int j = cubie::edge::FR;
202 |     int cubie = 0;
203 |     for (int i = 0; i < cubie::edge::COUNT; i++)
204 |       c.eperm[i] = (slice1 & (1 << i)) ? j++ : cubie++;
205 |   }
206 | 
207 |   int get_udedges2(const cubie::cube& c) {
208 |     return get_perm8(c.eperm);
209 |   }
210 | 
211 |   void set_udedges2(cubie::cube& c, int udedges2) {
212 |     set_perm8(udedges2, c.eperm);
213 |   }
214 | 
215 |   // Computing only exactly the moves that are needed and storing them tightly would only make things more complicated
216 |   // during solving (in exchange for completely negligible setup/memory-gains)
217 |   void init_move(
218 |     uint16_t move_coord[][move::COUNT],
219 |     int n_coord,
220 |     int (*get_coord)(const cubie::cube&),
221 |     void (*set_coord)(cubie::cube&, int),
222 |     void (*mul)(const cubie::cube&, const cubie::cube&, cubie::cube&),
223 |     bool phase2 = false
224 |   ) {
225 |     cubie::cube c1 = cubie::SOLVED_CUBE; // coords only affect perm or ori -> one would be uninitialized
226 |     cubie::cube c2;
227 | 
228 |     for (int coord = 0; coord < n_coord; coord++) {
229 |       set_coord(c1, coord);
230 | 
231 |       if (phase2) { // UDEDGES2 is only defined for phase 2 moves
232 |         for (move::mask moves = move::p2mask; moves; moves &= moves - 1) {
233 |           int m = ffsll(moves) - 1;
234 |           mul(c1, move::cubes[m], c2);
235 |           move_coord[coord][m] = get_coord(c2);
236 |         }
237 |       } else {
238 |         for (int m = 0; m < move::COUNT; m++) {
239 |           mul(c1, move::cubes[m], c2);
240 |           move_coord[coord][m] = get_coord(c2);
241 |         }
242 |       }
243 |     }
244 |   }
245 | 
246 |   void init() {
247 |     init_encdec();
248 | 
249 |     init_move(move_flip, N_FLIP, get_flip, set_flip, cubie::edge::mul);
250 |     init_move(move_twist, N_TWIST, get_twist, set_twist, cubie::corner::mul);
251 |     init_move(move_edges4, N_SLICE, get_slice, set_slice, cubie::edge::mul);
252 |     init_move(move_corners, N_CORNERS, get_corners, set_corners, cubie::corner::mul);
253 |     init_move(move_udedges2, N_UDEDGES2, get_udedges2, set_udedges2, cubie::edge::mul, true);
254 |   }
255 | 
256 | }
257 | 


--------------------------------------------------------------------------------
/src/main.cpp:
--------------------------------------------------------------------------------
  1 | #include <algorithm>
  2 | #include <fstream>
  3 | #include <getopt.h>
  4 | #include <iostream>
  5 | #include <vector>
  6 | #include <numeric>
  7 | 
  8 | #include "cubie.h"
  9 | #include "coord.h"
 10 | #include "face.h"
 11 | #include "move.h"
 12 | #include "prun.h"
 13 | #include "solve.h"
 14 | #include "sym.h"
 15 | 
 16 | const std::string BENCH_FILE = "bench.cubes";
 17 | 
 18 | void usage() {
 19 |   std::cout << "Usage: ./twophase "
 20 |     << "[-c] [-l MAX_LEN = 1] [-m MILLIS = 10] [-n N_SOLS = 1] [-s N_SPLITS = 1] [-t N_THREADS = 1] [-w N_WARMUPS = 0]"
 21 |   << std::endl;
 22 |   exit(1);
 23 | }
 24 | 
 25 | void init() {
 26 |   auto tick = std::chrono::high_resolution_clock::now();
 27 |   std::cout << "Loading tables ..." << std::endl;
 28 | 
 29 |   face::init();
 30 |   move::init();
 31 |   coord::init();
 32 |   sym::init();
 33 |   if (prun::init(true)) {
 34 |     std::cout << "Error." << std::endl;
 35 |     exit(1);
 36 |   }
 37 | 
 38 |   std::cout << "Done. " << std::chrono::duration_cast<std::chrono::milliseconds>(
 39 |     std::chrono::high_resolution_clock::now() - tick
 40 |   ).count() / 1000. << "s" << std::endl << std::endl;
 41 | }
 42 | 
 43 | void warmup(solve::Engine& solver, int count) {
 44 |   if (count == 0)
 45 |     return;
 46 | 
 47 |   std::cout << "Warming up ..." << std::endl;
 48 |   cubie::cube c;
 49 |   std::vector<std::vector<int>> sols;
 50 |   for (int i = 0; i < count; i++) {
 51 |     cubie::shuffle(c);
 52 |     solver.prepare();
 53 |     solver.solve(c, sols);
 54 |     solver.finish();
 55 |     std::cout << i << std::endl;
 56 |   }
 57 |   std::cout << "Done." << std::endl << std::endl;
 58 | }
 59 | 
 60 | bool check(const cubie::cube &c, const std::vector<int>& sol) {
 61 |   cubie::cube c1;
 62 |   cubie::cube c2;
 63 | 
 64 |   c1 = c;
 65 |   for (int m : sol) {
 66 |     cubie::mul(c1, move::cubes[m], c2);
 67 |     std::swap(c1, c2);
 68 |   }
 69 | 
 70 |   return c1 == cubie::SOLVED_CUBE;
 71 | }
 72 | 
 73 | double mean(const std::vector<std::vector<int>>& sols, int (*len)(const std::vector<int>&)) {
 74 |   double total = 0;
 75 |   for (auto& sol : sols)
 76 |     total += len(sol);
 77 |   return total / sols.size();
 78 | }
 79 | 
 80 | int main(int argc, char *argv[]) {
 81 |   int n_threads = 1;
 82 |   int tlim = 10;
 83 |   int n_sols = 1;
 84 |   int max_len = -1;
 85 |   int n_splits = 1;
 86 |   bool compress = false;
 87 |   int n_warmups = 0;
 88 | 
 89 |   try {
 90 |     int opt;
 91 |     while ((opt = getopt(argc, argv, "cl:m:n:s:t:w:")) != -1) {
 92 |       switch (opt) {
 93 |         case 'c':
 94 |           compress = true;
 95 |           break;
 96 |         case 'l':
 97 |           max_len = std::stoi(optarg);
 98 |           break;
 99 |         case 'm':
100 |           tlim = std::stoi(optarg);
101 |           break;
102 |         case 'n':
103 |           if ((n_sols = std::stoi(optarg)) <= 0) {
104 |             std::cout << "Error: Number of solutions (-n) must be >= 1." << std::endl;
105 |             return 1;
106 |           }
107 |           break;
108 |         case 's':
109 |           if ((n_splits = std::stoi(optarg)) <= 0) {
110 |             std::cout << "Error: Number of job splits (-s) must be >= 1." << std::endl;
111 |             return 1;
112 |           }
113 |           break;
114 |         case 't':
115 |           if ((n_threads = std::stoi(optarg)) <= 0) {
116 |             std::cout << "Error: Number of solver threads (-t) must be >= 1." << std::endl;
117 |             return 1;
118 |           }
119 |           break;
120 |         case 'w':
121 |           if ((n_warmups = std::stoi(optarg)) <= 0) {
122 |             std::cout << "Error: Number of warmup solves (-w) must be >= 0." << std::endl;
123 |             return 1;
124 |           }
125 |           break;
126 |         default:
127 |           usage();
128 |       }
129 |     }
130 |   } catch (...) { // catch any integer conversion errors
131 |     usage();
132 |   }
133 | 
134 |   std::cout << "This is rob-twophase v2.0; copyright Elias Frantar 2020." << std::endl << std::endl;
135 |   init();
136 |   solve::Engine solver(n_threads, tlim, n_sols, max_len, n_splits);
137 |   warmup(solver, n_warmups);
138 | 
139 |   std::cout << "Enter >>solve FACECUBE<< to solve, >>scramble<< to scramble or >>bench<< to benchmark." << std::endl << std::endl;
140 | 
141 |   std::string mode;
142 |   while (std::cin) {
143 |     solver.prepare();
144 |     std::cout << "Ready!" << std::endl;
145 | 
146 |     std::cin >> mode;
147 |     if (mode == "bench") {
148 |       try {
149 |         std::ifstream fstream;
150 |         fstream.open(BENCH_FILE);
151 | 
152 |         std::string s;
153 |         std::vector<cubie::cube> cubes;
154 |         while (std::getline(fstream, s)) {
155 |           cubie::cube c;
156 |           face::to_cubie(s, c);
157 |           cubes.push_back(c);
158 |         }
159 |         if (cubes.size() == 0) {
160 |           std::cout << "Error." << std::endl;
161 |           continue;
162 |         }
163 | 
164 |         std::vector<std::vector<int>> sols;
165 |         std::vector<int> times(cubes.size());
166 |         int failed = 0;
167 | 
168 |         std::cout << "Benchmarking ..." << std::endl;
169 |         for (int i = 0; i < cubes.size(); i++) {
170 |           std::cout << i << std::endl;
171 | 
172 |           solver.prepare();
173 |           auto tick = std::chrono::high_resolution_clock::now();
174 |           std::vector<std::vector<int>> tmp;
175 |           solver.solve(cubes[i], tmp);
176 |           times[i] = std::chrono::duration_cast<std::chrono::microseconds>(
177 |             std::chrono::high_resolution_clock::now() - tick
178 |           ).count() / 1000.;
179 |           solver.finish();
180 | 
181 |           if (tmp.size() == 0 || !check(cubes[i], tmp[0])) {
182 |             std::cout << face::from_cubie(cubes[i]) << std::endl;
183 |             failed++;
184 |           }
185 |           else
186 |             sols.push_back(tmp[0]);
187 |         }
188 | 
189 |         std::cout << std::endl;
190 |         std::cout << "Failed: " << failed << std::endl;
191 |         std::cout << "Avg. Time: " << std::accumulate(times.begin(), times.end(), 0.) / times.size() << " ms" << std::endl;
192 |         std::cout << "Avg. Moves: "
193 |           << mean(sols, move::len_ht) << " (HT), "
194 |           << mean(sols, move::len_qt) << " (QT), "
195 |           << mean(sols, move::len_axht) << " (AXHT), "
196 |           << mean(sols, move::len_axqt) << " (AXQT)"
197 |         << std::endl;
198 | 
199 |         int freq[100];
200 |         int min = 100;
201 |         int max = 0;
202 |         for (auto& sol : sols) {
203 |           freq[sol.size()]++;
204 |           min = std::min(min, (int) sol.size()); // errors without casting ...
205 |           max = std::max(max, (int) sol.size());
206 |         }
207 | 
208 |         std::cout << std::endl;
209 |         std::cout << "Distribution:" << std::endl;
210 |         for (int len = min; len <= max; len++)
211 |           std::cout << len << ": " << freq[len] << std::endl;
212 |         std::cout << std::endl;
213 |       } catch (...) { // any file reading errors
214 |         std::cout << "Error." << std::endl;
215 |         continue;
216 |       }
217 |     } else {
218 |       cubie::cube c;
219 |       std::vector<std::vector<int>> sols;
220 | 
221 |       if (mode == "solve") {
222 |         std::string fcube;
223 |         std::cin >> fcube;
224 |         int err = face::to_cubie(fcube, c);
225 |         if (err != 0) {
226 |           std::cout << "Face-error " << err << "." << std::endl;
227 |           continue;
228 |         }
229 |         err = cubie::check(c);
230 |         if (err != 0) {
231 |           std::cout << "Cubie-error " << err << "." << std::endl;
232 |           continue;
233 |         }
234 |       } else if (mode == "scramble") {
235 |         cubie::shuffle(c);
236 |         cubie::cube tmp;
237 |         cubie::inv(c, tmp);
238 |         std::cout << face::from_cubie(tmp) << std::endl; // the solution we find will actually be a scramble for the inverse
239 |       } else {
240 |         std::cout << "Error." << std::endl;
241 |         continue;
242 |       }
243 | 
244 |       auto tick = std::chrono::high_resolution_clock::now();
245 |       solver.solve(c, sols);
246 |       std::cout << std::chrono::duration_cast<std::chrono::microseconds>(
247 |         std::chrono::high_resolution_clock::now() - tick
248 |       ).count() / 1000. << "ms" << std::endl;
249 | 
250 |       for (std::vector<int>& sol : sols) {
251 |         int len = sol.size(); // always print uncompressed length
252 |         if (compress)
253 |           std::cout << move::compress(sol) << " ";
254 |         else {
255 |           for (int m : sol)
256 |             std::cout << move::names[m] << " ";
257 |         }
258 |         std::cout << "(" << len << ")" << std::endl;
259 |       }
260 |     }
261 |   }
262 |   solver.finish(); // clean exit
263 | 
264 |   return 0;
265 | }
266 | 


--------------------------------------------------------------------------------
/src/move.cpp:
--------------------------------------------------------------------------------
  1 | #include "move.h"
  2 | 
  3 | namespace move {
  4 | 
  5 |   using namespace cubie::corner;
  6 |   using namespace cubie::edge;
  7 | 
  8 |   /* Select moves and order according to used metric */
  9 |   #ifdef QT
 10 |     #ifdef AX
 11 |         const int map[] = {
 12 |           // U, U2, U', D, D2, D'
 13 |           0, -1, 1, 2, -1, 3,
 14 |           // (U D), (U D2), (U D'), (U2 D), (U2 D2), (U2 D'), (U' D), (U' D2), (U' D')
 15 |           4, -1, 5, -1, -1, -1, 6, -1, 7,
 16 |           // R, R2, R', L, L2, L'
 17 |           8, 24, 9, 10, 25, 11,
 18 |           // (R L), (R L2), (R L'), (R2 L), (R2 L2), (R2 L'), (R' L), (R' L2), (R' L')
 19 |           12, -1, 13, -1, 26, -1, 14, -1, 15,
 20 |           // F, F2, F', B, B2, B'
 21 |           16, 27, 17, 18, 28, 19,
 22 |           // (F B), (F B2), (F B'), (F2 B), (F2 B2), (F2 B'), (F' B), (F' B2), (F' B')
 23 |           20, -1, 21, -1, 29, -1, 22, -1, 23
 24 |         };
 25 |       #else
 26 |         const int map[] = {
 27 |           0, -1, 1, 2, -1, 3,
 28 |           -1, -1, -1, -1, -1, -1, -1, -1, -1,
 29 |           4, 12, 5, 6, 13, 7,
 30 |           -1, -1, -1, -1, -1, -1, -1, -1, -1,
 31 |           8, 14, 9, 10, 15, 11,
 32 |           -1, -1, -1, -1, -1, -1, -1, -1, -1
 33 |         };
 34 |       #endif
 35 |   #else
 36 |     #ifdef AX
 37 |       const int map[] = {
 38 |         0, 1, 2, 3, 4, 5,
 39 |         6, 7, 8, 9, 10, 11, 12, 13, 14,
 40 |         15, 16, 17, 18, 19, 20,
 41 |         21, 22, 23, 24, 25, 26, 27, 28, 29,
 42 |         30, 31, 32, 33, 34, 35,
 43 |         36, 37, 38, 39, 40, 41, 42, 43, 44
 44 |       };
 45 |     #else
 46 |       const int map[] = {
 47 |         0, 1, 2, 3, 4, 5,
 48 |         -1, -1, -1, -1, -1, -1, -1, -1, -1,
 49 |         6, 7, 8, 9, 10, 11,
 50 |         -1, -1, -1, -1, -1, -1, -1, -1, -1,
 51 |         12, 13, 14, 15, 16, 17,
 52 |         -1, -1, -1, -1, -1, -1, -1, -1, -1
 53 |       };
 54 |     #endif
 55 |   #endif
 56 | 
 57 |   std::string names[COUNT];
 58 |   cubie::cube cubes[COUNT];
 59 |   int inv[COUNT];
 60 | 
 61 |   mask next[COUNT];
 62 |   mask next_p1p2[COUNT];
 63 |   mask qt_skip[COUNT];
 64 | 
 65 |   mask p1mask = bit(45) - 1;
 66 |   mask p2mask = 0x10482097fff; // 000010000 010010 000010000 010010 111111111 111111;
 67 | 
 68 |   // For full set of 45 moves no matter the solving mode
 69 |   std::string names1[45];
 70 |   int merge[45][45];
 71 |   int unmap[COUNT];
 72 | 
 73 |   // Translate bitmask from full moveset to configured one
 74 |   mask reindex(mask mm) {
 75 |     mask mm1 = 0;
 76 |     for (int m = 0; m < 45; m++) {
 77 |       if (map[m] != -1 && in(m, mm)) // drop unmapped moves
 78 |         mm1 |= bit(map[m]);
 79 |     }
 80 |     return mm1;
 81 |   }
 82 | 
 83 |   // Build full moveset first, then remap to configured one
 84 |   void init() {
 85 |     for (int m = 0; m < 45; m++) {
 86 |       if (map[m] != -1)
 87 |         unmap[map[m]] = m;
 88 |     }
 89 | 
 90 |     cubie::cube cubes1[45];
 91 |     int inv1[45];
 92 |     // Not initializing the following arrays apparently causes problems on MacOS
 93 |     mask next1[45] = {0};
 94 |     mask qt_skip1[45] = {0};
 95 | 
 96 |     std::string fnames[] = {"U", "D", "R", "L", "F", "B"};
 97 |     std::string pnames[] = {"", "2", "'"};
 98 |     cubie::cube fcubes[] = {
 99 |       { // U
100 |         {UBR, URF, UFL, ULB, DFR, DLF, DBL, DRB},
101 |         {UB, UR, UF, UL, DR, DF, DL, DB, FR, FL, BL, BR},
102 |         {}, {}
103 |       },
104 |       { // D
105 |         {URF, UFL, ULB, UBR, DLF, DBL, DRB, DFR},
106 |         {UR, UF, UL, UB, DF, DL, DB, DR, FR, FL, BL, BR},
107 |         {}, {}
108 |       },
109 |       { // R
110 |         {DFR, UFL, ULB, URF, DRB, DLF, DBL, UBR},
111 |         {FR, UF, UL, UB, BR, DF, DL, DB, DR, FL, BL, UR},
112 |         {2, 0, 0, 1, 1, 0, 0, 2}, {}
113 |       },
114 |       { // L
115 |         {URF, ULB, DBL, UBR, DFR, UFL, DLF, DRB},
116 |         {UR, UF, BL, UB, DR, DF, FL, DB, FR, UL, DL, BR},
117 |         {0, 1, 2, 0, 0, 2, 1, 0}, {}
118 |       },
119 |       { // F
120 |         {UFL, DLF, ULB, UBR, URF, DFR, DBL, DRB},
121 |         {UR, FL, UL, UB, DR, FR, DL, DB, UF, DF, BL, BR},
122 |         {1, 2, 0, 0, 2, 1, 0, 0},
123 |         {0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0}
124 |       },
125 |       { // B
126 |         {URF, UFL, UBR, DRB, DFR, DLF, ULB, DBL},
127 |         {UR, UF, UL, BR, DR, DF, DL, BL, FR, FL, UB, DB},
128 |         {0, 0, 1, 2, 0, 0, 2, 1},
129 |         {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1}
130 |       }
131 |     };
132 | 
133 |     for (int ax = 0; ax < 3; ax++) {
134 |       int i1 = 15 * ax; // index to start first face moves
135 |       int i2 = 15 * ax + 3; // index to start of second face moves
136 |       int i3 = 15 * ax + 6; // index to start of axial moves
137 | 
138 |       int f1 = 2 * ax; // first face
139 |       int f2 = 2 * ax + 1; // second face
140 | 
141 |       for (int cnt = 0; cnt < 3; cnt++) {
142 |         int m = i1 + cnt;
143 |         names1[m] = fnames[f1] + pnames[cnt];
144 |         if (cnt == 0)
145 |           cubes1[m] = fcubes[f1];
146 |         else
147 |           cubie::mul(cubes1[m - 1], fcubes[f1], cubes1[m]);
148 |         inv1[m] = i1 + (2 - cnt);
149 |         next1[m] |= mask(0x7) << i1; // block any moves on same face
150 |         #ifdef AX
151 |           next1[m] |= mask(0x38) << i1; // block also moves on opposite face
152 |         #endif
153 |         #ifdef QT
154 |           if (cnt == 0) { // block all axial moves but the ones with M
155 |             next1[m] |= mask(0x1ff ^ (0x7 << 3 * cnt)) << i3;
156 |             continue;
157 |           }
158 |         #endif
159 |         next1[m] |= mask(0x1ff) << i3; // block all axial moves
160 |       }
161 |       for (int cnt = 0; cnt < 3; cnt++) {
162 |         int m = i2 + cnt;
163 |         names1[m] = fnames[f2] + pnames[cnt];
164 |         if (cnt == 0)
165 |           cubes1[m] = fcubes[f2];
166 |         else
167 |           cubie::mul(cubes1[m - 1], fcubes[f2], cubes1[m]);
168 |         inv1[m] = i2 + (2 - cnt);
169 |         next1[m] |= mask(0x3f) << i1; // block all simple moves on both faces
170 |         #ifdef QT
171 |           if (cnt == 0) { // block all axial moves but the ones with M
172 |             next1[m] |= mask(0x1ff ^ (0x49 << cnt)) << i3; // 0x49 == 0b1001001
173 |             continue;
174 |           }
175 |         #endif
176 |         next1[m] |= mask(0x1ff) << i3;
177 |       }
178 |       for (int cnt1 = 0; cnt1 < 3; cnt1++) {
179 |         for (int cnt2 = 0; cnt2 < 3; cnt2++) {
180 |           int m = i3 + 3 * cnt1 + cnt2;
181 |           names1[m] = "(" + names1[i1 + cnt1] + " " + names1[i2 + cnt2] + ")";
182 |           cubie::mul(cubes1[i1 + cnt1], cubes1[i2 + cnt2], cubes1[m]);
183 |           inv1[m] = i3 + 3 * (2 - cnt1) + (2 - cnt2);
184 |           next1[m] |= mask(0x7fff) << 15 * ax; // block all simple and axial moves
185 |         }
186 |       }
187 | 
188 |       qt_skip1[i1] |= bit(i1);
189 |       qt_skip1[i1] |= bit(i3);
190 |       qt_skip1[i2] |= bit(i2);
191 |       qt_skip1[i2] |= bit(i3);
192 |       qt_skip1[i3] |= bit(i3);
193 |     }
194 |     // Half-slice moves commute
195 |     next1[25] |= bit(10);
196 |     next1[40] |= bit(10) | bit(25);
197 |     #ifdef QT
198 |     // Allow repetitions of purely clockwise moves
199 |       for (int m : {0, 3, 6, 15, 18, 21, 30, 33, 36})
200 |         next1[m] ^= bit(m);
201 |     #endif
202 |     // Was built by blocking moves, but should actually indicate permitted ones
203 |     for (int m = 0; m < 45; m++)
204 |       next1[m] = ~next1[m];
205 | 
206 |     for (int m = 0; m < 45; m++) {
207 |       if (map[m] == -1)
208 |         continue;
209 |       int i = map[m];
210 | 
211 |       names[i] = names1[m];
212 |       cubes[i] = cubes1[m];
213 |       inv[i] = map[inv1[m]];
214 |       next[i] = reindex(next1[m]);
215 |       qt_skip[i] = reindex(qt_skip1[m]);
216 |     }
217 | 
218 |     #ifdef QT
219 |       // Unmapped moves are skipped automatically during reindexing
220 |       p1mask &= ~0x10482090000; // 000010000 010010 000010000 010010 000000000 000000
221 |     #endif
222 |     #ifdef F5
223 |       mask tmp = ~(mask(0xfff) << 33);
224 |       p1mask &= tmp;
225 |       p2mask &= tmp;
226 |     #endif
227 |     p1mask = reindex(p1mask);
228 |     p2mask = reindex(p2mask);
229 | 
230 |     for (int m = 0; m < COUNT; m++) {
231 |       if (p2mask & move::bit(m))
232 |         next_p1p2[m] = next[m]; // we can do normal blocking for phase 2 moves
233 |       else {
234 |         #ifndef AX
235 |           #ifdef QT
236 |             next_p1p2[m] = ~(mask(0x3) << 2 * (m / 2));
237 |             if (m / 2 > 1)
238 |               next_p1p2[m] &= ~(move::bit(COUNT1 + (m / 2) - 2));
239 |           #else
240 |             next_p1p2[m] = ~(mask(0x7) << 3 * (m / 3));
241 |           #endif
242 |         #else
243 |           next_p1p2[m] = next[m]; // no commutativity problems in axial mode
244 |         #endif
245 |       }
246 |     }
247 | 
248 |     cubie::cube c;
249 |     for (int m1 = 0; m1 < 45; m1++) {
250 |       for (int m2 = 0; m2 < 45; m2++) {
251 |         merge[m1][m2] = -1;
252 |         cubie::mul(cubes1[m1], cubes1[m2], c);
253 |         for (int i = 0; i < 45; i++) {
254 |           if (c == cubes1[i]) {
255 |             merge[m1][m2] = i;
256 |             break;
257 |           }
258 |         }
259 |       }
260 |     }
261 |   }
262 | 
263 |   void compress1(const std::vector<int>& mseq, std::vector<int>& into) {
264 |     into.clear();
265 |     for (int m : mseq) {
266 |       m = unmap[m];
267 |       if (into.size() == 0 || merge[into.back()][m] == -1)
268 |         into.push_back(m);
269 |       else {
270 |         int tmp = into.back();
271 |         into.pop_back();
272 |         into.push_back(merge[tmp][m]);
273 |       }
274 |     }
275 |   }
276 | 
277 |   std::string compress(const std::vector<int>& mseq) {
278 |     std::vector<int> comp;
279 |     compress1(mseq, comp);
280 | 
281 |     // Faster string building probably not worth it in a function like this
282 |     std::string s;
283 |     for (int i = 0; i < comp.size(); i++) {
284 |       s += names1[comp[i]];
285 |       if (i != comp.size() - 1)
286 |         s += " ";
287 |     }
288 |     return s;
289 |   }
290 | 
291 |   int len(const std::vector<int>& mseq, int cost[]) {
292 |     std::vector<int> comp;
293 |     compress1(mseq, comp);
294 | 
295 |     int res = 0;
296 |     for (int m : comp)
297 |       res += cost[m];
298 |     return res;
299 |   }
300 | 
301 |   int len_ht(const std::vector<int>& mseq) {
302 |     int cost[] = {
303 |       1, 1, 1, 1, 1, 1,
304 |       2, 2, 2, 2, 2, 2, 2, 2, 2,
305 |       1, 1, 1, 1, 1, 1,
306 |       2, 2, 2, 2, 2, 2, 2, 2, 2,
307 |       1, 1, 1, 1, 1, 1,
308 |       2, 2, 2, 2, 2, 2, 2, 2, 2
309 |     };
310 |     return len(mseq, cost);
311 |   }
312 | 
313 |   int len_axht(const std::vector<int>& mseq) {
314 |     int cost[] = {
315 |       1, 1, 1, 1, 1, 1,
316 |       1, 1, 1, 1, 1, 1, 1, 1, 1,
317 |       1, 1, 1, 1, 1, 1,
318 |       1, 1, 1, 1, 1, 1, 1, 1, 1,
319 |       1, 1, 1, 1, 1, 1,
320 |       1, 1, 1, 1, 1, 1, 1, 1, 1
321 |     };
322 |     return len(mseq, cost);
323 |   }
324 | 
325 |   int len_qt(const std::vector<int>& mseq) {
326 |     int cost[] = {
327 |       1, 2, 1, 1, 2, 1,
328 |       2, 3, 2, 3, 4, 3, 2, 3, 2,
329 |       1, 2, 1, 1, 2, 1,
330 |       2, 3, 2, 3, 4, 3, 2, 3, 2,
331 |       1, 2, 1, 1, 2, 1,
332 |       2, 3, 2, 3, 4, 3, 2, 3, 2
333 |     };
334 |     return len(mseq, cost);
335 |   }
336 | 
337 |   int len_axqt(const std::vector<int>& mseq) {
338 |     int cost[] = {
339 |       1, 2, 1, 1, 2, 1,
340 |       1, 2, 1, 2, 2, 2, 1, 2, 1,
341 |       1, 2, 1, 1, 2, 1,
342 |       1, 2, 1, 2, 2, 2, 1, 2, 1,
343 |       1, 2, 1, 1, 2, 1,
344 |       1, 2, 1, 2, 2, 2, 1, 2, 1
345 |     };
346 |     return len(mseq, cost);
347 |   }
348 | 
349 | }
350 | 


--------------------------------------------------------------------------------
/src/solve.cpp:
--------------------------------------------------------------------------------
  1 | #include "solve.h"
  2 | 
  3 | #include <algorithm>
  4 | #include <cstring>
  5 | #include <thread>
  6 | #include "prun.h"
  7 | #include "sym.h"
  8 | 
  9 | namespace solve {
 10 | 
 11 |   class Search {
 12 | 
 13 |     int dir; // ID of search direction
 14 |     const coordc& cube; // starting position
 15 |     int p1depth; // phase 1 search depth
 16 |     move::mask d0moves; // mask for initial moves to consider
 17 |     bool& done; // when to terminate the search
 18 |     int& lenlim; // only find strictly shorter solutions
 19 |     Engine& solver; // report solutions to
 20 | 
 21 |     /* Keep track of reconstructed edges that remain valid in the current search path */
 22 |     int uedges[50];
 23 |     int dedges[50];
 24 |     int edges_depth;
 25 | 
 26 |     int moves[50]; // current (partial) solution
 27 | 
 28 |   private:
 29 |     void phase1(
 30 |       int depth, int togo, int flip, int slice, int twist, int corners, move::mask next, move::mask qt_skip
 31 |     ); // phase 1 search; iterates through all solution with exactly `togo` moves
 32 |     bool phase2(
 33 |       int depth, int togo, int slice, int udedges2, int corners, move::mask next, move::mask qt_skip
 34 |     ); // phase 2 search; returns once any solution is found
 35 | 
 36 |   public:
 37 |     Search(
 38 |       int dir,
 39 |       const coordc& cube,
 40 |       int p1depth, move::mask d0moves,
 41 |       bool& done, int& lenlim, Engine& solver
 42 |     ) : dir(dir), cube(cube), p1depth(p1depth), d0moves(d0moves), done(done), lenlim(lenlim), solver(solver) {};
 43 |     void run(); // perform the search
 44 | 
 45 |   };
 46 | 
 47 |   void Search::run() {
 48 |     uedges[0] = cube.uedges;
 49 |     dedges[0] = cube.dedges;
 50 |     edges_depth = 0;
 51 | 
 52 |     move::mask next;
 53 |     prun::get_phase1(cube.flip, cube.slice, cube.twist, p1depth, next);
 54 |     next &= move::p1mask & d0moves; // block B-moves in F5 mode here and select current search split
 55 |     phase1(0, p1depth, cube.flip, cube.slice, cube.twist, cube.corners, next, 0);
 56 |   }
 57 | 
 58 |   void Search::phase1(
 59 |     int depth, int togo, int flip, int slice, int twist, int corners, move::mask next, move::mask qt_skip
 60 |   ) {
 61 |     if (done)
 62 |       return;
 63 |     if (togo == 0) {
 64 |       int tmp = prun::get_precheck(corners, slice);
 65 |       if (tmp >= lenlim - depth) // phase 2 precheck, only reconstruct edges if successful
 66 |         return;
 67 | 
 68 |       for (int i = edges_depth + 1; i <= depth; i++) {
 69 |         uedges[i] = coord::move_edges4[uedges[i - 1]][moves[i - 1]];
 70 |         dedges[i] = coord::move_edges4[dedges[i - 1]][moves[i - 1]];
 71 |       }
 72 |       edges_depth = depth - 1;
 73 |       int udedges2 = coord::merge_udedges2(uedges[depth], dedges[depth]);
 74 | 
 75 |       int delta = 1;
 76 |       #ifndef AX
 77 |         #ifdef QT
 78 |           delta++; // in vanilla QT mode the perm-parity indicates whether solution length is odd or even
 79 |         #endif
 80 |       #endif
 81 |       for (int togo1 = std::max(prun::get_phase2(corners, udedges2), tmp); togo1 < lenlim - depth; togo1 += delta) {
 82 |         if (phase2(depth, togo1, slice, udedges2, corners, move::p2mask & move::next_p1p2[moves[depth - 1]], qt_skip))
 83 |           return; // once we have found a phase 2 solution, there cannot be any shorter ones -> quit
 84 |       }
 85 |       return;
 86 |     }
 87 | 
 88 |     depth++;
 89 |     togo--;
 90 |     while (next) {
 91 |       int m = ffsll(next) -  1; // get rightmost move index (`ffsll()` uses 1-based indexing)
 92 |       next &= next - 1;
 93 | 
 94 |       int flip1 = coord::move_flip[flip][m];
 95 |       int slice1 = coord::move_edges4[slice][m];
 96 |       int twist1 = coord::move_twist[twist][m];
 97 |       move::mask next1;
 98 |       int dist1 = prun::get_phase1(flip1, slice1, twist1, togo, next1);
 99 | 
100 |       // Check inside loop to avoid unnecessary recursion unwinds
101 |       if (dist1 == togo || dist1 + togo >= 5) { // Rokicki optimization
102 |         int corners1 = coord::move_corners[corners][m];
103 |         moves[depth - 1] = m;
104 | 
105 |         next1 &= move::p1mask & move::next[m];
106 |         move::mask qt_skip1;
107 |         #ifdef QT // let `qt_skip` get completely optimized away when not in QT-mode
108 |           qt_skip1 = move::qt_skip[m];
109 |           next1 &= ~(qt_skip & qt_skip1);
110 |         #endif
111 |         phase1(depth, togo, flip1, slice1, twist1, corners1, next1, qt_skip1);
112 |       }
113 |     }
114 | 
115 |     // We always want to maintain the maximum number of already reconstructed EDGES coordinates, hence we only
116 |     // decrement when the depth level gets lower than the current valid index (note that we will typically also
117 |     // visit other deeper branches in between that might not have any effect on this)
118 |     if (edges_depth == depth - 1)
119 |       edges_depth--;
120 |   }
121 | 
122 |   bool Search::phase2(
123 |     int depth, int togo, int slice, int udedges2, int corners, move::mask next, move::mask qt_skip
124 |   ) {
125 |     if (togo == 0) {
126 |       if (slice != coord::N_SLICE2 * coord::SLICE1_SOLVED) // check if SLICE2 is also solved
127 |         return false;
128 | 
129 |       searchres sol = {std::vector<int>(depth), dir };
130 |       for (int i = 0; i < depth; i++)
131 |         sol.first[i] = moves[i];
132 |       solver.report_sol(sol);
133 | 
134 |       return true; // we will not find any shorter solutions
135 |     }
136 | 
137 |     while (next) {
138 |       int m = ffsll(next) -  1; // get rightmost move index (`ffsll()` uses 1-based indexing)
139 |       next &= next - 1;
140 | 
141 |       int slice1 = coord::move_edges4[slice][m];
142 |       int udedges21 = coord::move_udedges2[udedges2][m];
143 |       int corners1 = coord::move_corners[corners][m];
144 | 
145 |       if (prun::get_phase2(corners1, udedges21) < togo) {
146 |         #ifdef QT
147 |           // As we never want to leave the set of phase 2 cubes (which we would by doing only a quarter-turn on an axis
148 |           // for which only double-moves are permitted), we need special handling of the double moves. The simplest way
149 |           // to do this is to treat a double moves simply as if two consecutive quarter-turns were added to the current
150 |           // search path.
151 |           if (m >= move::COUNT1) {
152 |             if (togo <= 1) // we cannot do half turns when only a single quarter-turn is permitted
153 |               break;
154 | 
155 |             int tmp = move::split[m];
156 |             moves[depth] = tmp;
157 |             moves[depth + 1] = tmp;
158 | 
159 |             move::mask next1 = move::p2mask & move::next[m];
160 |             move::mask qt_skip1 = move::qt_skip[m];
161 |             next1 &= ~(qt_skip & qt_skip1);
162 | 
163 |             if (phase2(depth + 2, togo - 2, slice1, udedges21, corners1, next1, qt_skip1))
164 |               return true;
165 |             continue;
166 |           }
167 |         #endif
168 | 
169 |         moves[depth] = m;
170 |         if (phase2(depth + 1, togo - 1, slice1, udedges21, corners1, move::p2mask & move::next[m], 0))
171 |           return true; // return as soon as we have a solution
172 |       }
173 |     }
174 | 
175 |     return false;
176 |   }
177 | 
178 |   Engine::Engine(
179 |     int n_threads, int tlim,
180 |     int n_sols, int max_len, int n_splits
181 |   ) : n_threads(n_threads), tlim(tlim), n_sols(n_sols), max_len(max_len), n_splits(n_splits) {
182 |     int tmp = (move::COUNT1 + n_splits - 1) / n_splits; // ceil to make sure that we always include all moves
183 |     for (int i = 0; i < n_splits; i++)
184 |       masks[i] = (move::mask(1) << tmp) - 1 << tmp * i;
185 |     done = true; // make sure that the first `prepare()` will actually do something
186 |   }
187 | 
188 |   void Engine::thread() {
189 |     int mindir = 0;
190 |     do {
191 |       /* Select next job to execute; don't forget to lock */
192 |       job_mtx.lock();
193 |       for (int dir = 0; dir < N_DIRS; dir++) {
194 |         if (depths[dir] < depths[mindir])
195 |           mindir = dir;
196 |       }
197 |       int split = splits[mindir]++;
198 |       int togo = depths[mindir];
199 |       if (splits[mindir] == n_splits) {
200 |         depths[mindir]++;
201 |         splits[mindir] = 0;
202 |       }
203 |       job_mtx.unlock();
204 | 
205 |       Search search(mindir, dirs[mindir], togo, masks[split], done, lenlim, *this);
206 |       search.run();
207 |     } while (!done); // we should never actually get to the truly optimal depth anyways in general
208 |   }
209 | 
210 |   void Engine::prepare() {
211 |     if (!done) // avoid double preparation
212 |       return;
213 |     finish();
214 | 
215 |     job_mtx.lock(); // make spawned threads wait for initialization of the cube to be solved
216 |     for (int i = 0; i < n_threads; i++)
217 |       threads.push_back(std::thread([&]() { this->thread(); }));
218 | 
219 |     done = false;
220 |     lenlim = max_len > 0 ? max_len + 1: 50; // only search for strictly shorter solutions than this
221 |     // `sols` is always emptied after a solve
222 |   }
223 | 
224 |   void Engine::solve(const cubie::cube& c, std::vector<std::vector<int>>& res) {
225 |     prepare(); // make sure we are prepared; will do nothing if that should already be the case
226 | 
227 |     cubie::cube tmp1, tmp2;
228 |     cubie::cube invc;
229 |     cubie::inv(c, invc);
230 | 
231 |     for (int dir = 0; dir < N_DIRS; dir++) {
232 |       const cubie::cube& c1 = (dir & 1) ? invc : c; // reference is enough, we do not need to copy
233 |       int rot = sym::ROT * (dir / 2);
234 |       cubie::mul(sym::cubes[sym::inv[rot]], c1, tmp1);
235 |       cubie::mul(tmp1, sym::cubes[rot], tmp2);
236 | 
237 |       dirs[dir].flip = coord::get_flip(tmp2);
238 |       dirs[dir].slice = coord::get_slice(tmp2);
239 |       dirs[dir].twist = coord::get_twist(tmp2);
240 |       dirs[dir].uedges = coord::get_uedges(tmp2);
241 |       dirs[dir].dedges = coord::get_dedges(tmp2);
242 |       dirs[dir].corners = coord::get_corners(tmp2);
243 | 
244 |       move::mask tmp; // simply ignore, makes no sense anyways without proper `togo`
245 |       depths[dir] = prun::get_phase1(dirs[dir].flip, dirs[dir].slice, dirs[dir].twist, 100, tmp);
246 |       splits[dir] = 0;
247 |     }
248 | 
249 |     job_mtx.unlock(); // start solving
250 | 
251 |     { // timeout
252 |       std::unique_lock<std::mutex> lock(tout_mtx);
253 |       tout_cvar.wait_for(lock, std::chrono::milliseconds(tlim), [&]{ return done; });
254 |       if (!done)
255 |         done = true; // if we get here, this was a timeout
256 |     }
257 |     std::lock_guard<std::mutex> lock(sol_mtx); // make sure no thread is writing any more solutions
258 | 
259 |     res.resize(sols.size());
260 |     for (int i = 0; i < res.size(); i++) {
261 |       const searchres& sol = sols.top();
262 |       res[i].resize(sol.first.size());
263 | 
264 |       int rot = sym::ROT * (sol.second / 2);
265 |       for (int j = 0; j < res[i].size(); j++) // undo rotation
266 |         res[i][j] = sym::conj_move[sol.first[j]][rot];
267 |       if (sol.second & 1) { // undo inversion
268 |         for (int j = 0; j < res[i].size(); j++)
269 |           res[i][j] = move::inv[res[i][j]];
270 |         std::reverse(res[i].begin(), res[i].end());
271 |       }
272 | 
273 |       sols.pop();
274 |     }
275 |     std::reverse(res.begin(), res.end()); // return solutions in order of increasing length
276 |   }
277 | 
278 |   void Engine::report_sol(searchres& sol) {
279 |     std::lock_guard<std::mutex> lock(sol_mtx);
280 | 
281 |     if (done) // prevent any type of reporting after the solver has terminated (important for threading)
282 |       return;
283 | 
284 |     sols.push(sol); // usually we only get here if we actually have a solution that will be added
285 |     if (sols.size() > n_sols)
286 |       sols.pop();
287 |     if (sols.size() == n_sols) {
288 |       lenlim = sols.top().first.size(); // only search for strictly shorter solutions
289 | 
290 |       if (lenlim <= max_len) { // already found a solution that is short enough
291 |         done = true; // end searching
292 |         // Wake up timeout
293 |         std::lock_guard<std::mutex> lock(tout_mtx);
294 |         tout_cvar.notify_one();
295 |       }
296 |     }
297 |   }
298 | 
299 |   void Engine::finish() {
300 |     for (std::thread& t : threads) // wait for all existing threads to actually finish
301 |       t.join();
302 |     threads.clear(); // they are now invalid
303 |   }
304 | 
305 | }
306 | 


--------------------------------------------------------------------------------
/src/prun.cpp:
--------------------------------------------------------------------------------
  1 | #include "prun.h"
  2 | 
  3 | #include <bitset>
  4 | #include <iostream>
  5 | #include <cstring>
  6 | 
  7 | namespace prun {
  8 |   const std::string SAVE = "twophase-"
  9 |     #ifdef AX
 10 |       "ax"
 11 |     #endif
 12 |     #ifdef QT
 13 |       "qt"
 14 |     #else
 15 |       "ht"
 16 |     #endif
 17 |     #ifdef F5
 18 |       "-f5"
 19 |     #endif
 20 |     ".tbl"
 21 |   ;
 22 | 
 23 |   const int EMPTY = 0xff;
 24 | 
 25 |   #ifdef AX
 26 |     const int BITS_PER_AX = 16; // bits used for encoding an axis in the ext. phase 1 table
 27 |   #else
 28 |     const int BITS_PER_AX = 8;
 29 |   #endif
 30 |   #ifdef QT
 31 |     const int BITS_PER_M = 2; // bits per move
 32 |     const int N_SIMP = 4; // number of simple moves
 33 |     const int N_AX = 4; // number of axial moves
 34 |   #else
 35 |     const int BITS_PER_M = 1;
 36 |     const int N_SIMP = 6;
 37 |     const int N_AX = 9;
 38 |   #endif
 39 | 
 40 |   // Used to remap symmetry ext. phase 1 table entries back to actual situation
 41 |   move::mask remap[2][16][1 << BITS_PER_AX];
 42 | 
 43 |   prun1 *phase1;
 44 |   uint8_t *phase2;
 45 |   uint8_t *precheck;
 46 | 
 47 |   inline int ones(int count) { return (1 << count) - 1; }
 48 | 
 49 |   int rev(int movec, int count, int off = 0, int step = BITS_PER_M) {
 50 |     movec >>= step * off;
 51 | 
 52 |     int rev = 0;
 53 |     for (int i = 0; i < step * count; i += step) {
 54 |       rev = (rev << step) | (movec & ones(step));
 55 |       movec >>= step;
 56 |     }
 57 |     return rev << step * off;
 58 |   }
 59 | 
 60 |   int inv(int mask) {
 61 |     int n_per_face = N_SIMP / 2;
 62 | 
 63 |     int inv = rev(mask, n_per_face) | rev(mask, n_per_face, n_per_face);
 64 |     #ifdef AX
 65 |       inv |= rev(mask, N_AX, N_SIMP);
 66 |     #endif
 67 |     return inv;
 68 |   }
 69 |   
 70 |   int flip(int mask) {
 71 |     int per_face = N_SIMP / 2;
 72 |     int flipped = rev(mask, 2, 0, BITS_PER_M * per_face);
 73 | 
 74 |     #ifdef AX
 75 |       mask >>= BITS_PER_M * N_SIMP;
 76 | 
 77 |       // Flipping an axis means to transpose the axial move-mask (M N) (M N2) (M N') ... to (N M) (N M2) (N M') ...
 78 |       int fax = 0;
 79 |       for (int i = 0; i < per_face; i++) {
 80 |         for (int j = 0; j < per_face; j++)
 81 |           fax |= ((mask >> BITS_PER_M * (per_face * i + j)) & ones(BITS_PER_M)) << BITS_PER_M * (per_face * j + i);
 82 |       }
 83 |       flipped |= fax << BITS_PER_M * N_SIMP;
 84 |     #endif
 85 | 
 86 |     return flipped;
 87 |   }
 88 | 
 89 |   void init_base() {
 90 |     /* It is probably cleanest to simply handle the special HT case individually */
 91 |     #ifndef AX
 92 |       #ifndef QT
 93 |         for (int eff = 0; eff < 16; eff++) {
 94 |           for (int mask = 0; mask < 256; mask++) {
 95 |             int mask1 = mask & 0xf;
 96 |             int mask2 = (mask & 0xf0) >> 4;
 97 | 
 98 |             if (sym::eff_inv(eff)) {
 99 |               mask1 = rev(mask1, 3, 1) | (mask1 & 1);
100 |               mask2 = rev(mask2, 3, 1) | (mask2 & 1);
101 |             }
102 |             if (sym::eff_flip(eff))
103 |               std::swap(mask1, mask2);
104 | 
105 |             remap[0][eff][mask] = ((mask1 & 1) ? 0 : ~(mask1 >> 1) & 0x7) << 6 * sym::eff_shift(eff);
106 |             remap[1][eff][mask] = ((mask1 & 1) ? ~(mask1 >> 1) & 0x7 : 0x7) << 6 * sym::eff_shift(eff);
107 |             remap[0][eff][mask] |= ((mask2 & 1) ? 0 : ~(mask2 >> 1) & 0x7) << 6 * sym::eff_shift(eff) + 3;
108 |             remap[1][eff][mask] |= ((mask2 & 1) ? ~(mask2 >> 1) & 0x7 : 0x7) << 6 * sym::eff_shift(eff) + 3;
109 |           }
110 |         }
111 |         return;
112 |       #endif
113 |     #endif
114 | 
115 |     for (int eff = 0; eff < 16; eff++) {
116 |       for (int mask = 0; mask < (1 << BITS_PER_AX); mask++) {
117 |         move::mask mask1 = mask;
118 |         #ifndef QT
119 |           mask1 >>= 1; // first bit encodes direction in HT
120 |         #endif
121 | 
122 |         if (sym::eff_inv(eff))
123 |           mask1 = inv(mask1);
124 |         if (sym::eff_flip(eff))
125 |           mask1 = flip(mask1);
126 | 
127 |         #ifdef QT
128 |           remap[0][eff][mask] = 0;
129 |           remap[1][eff][mask] = 0;
130 |           for (int i = 0; i < BITS_PER_AX / 2; i++) {
131 |             remap[0][eff][mask] |= ((mask1 & 0x3) == 0) << i;
132 |             remap[1][eff][mask] |= ((mask1 & 0x3) <= 1) << i;
133 |             mask1 >>= 2;
134 |           }
135 |           remap[0][eff][mask] <<= (BITS_PER_AX / 2) * sym::eff_shift(eff);
136 |           remap[1][eff][mask] <<= (BITS_PER_AX / 2) * sym::eff_shift(eff);
137 |         #else
138 |           move::mask o = ones(BITS_PER_AX - 1); // first bit indicates direction but is not a move
139 |           remap[0][eff][mask] = ((mask & 1) ? 0 : ~mask1 & o) << (BITS_PER_AX - 1) * sym::eff_shift(eff);
140 |           remap[1][eff][mask] = ((mask & 1) ? ~mask1 & o : o) << (BITS_PER_AX - 1) * sym::eff_shift(eff);
141 |         #endif
142 |       }
143 |     }
144 |   }
145 | 
146 |   void init_phase1() {
147 |     int n_moves = std::bitset<64>(move::p1mask).count(); // make sure not to consider B-moves in F5-mode
148 | 
149 |     phase1 = new prun1[N_FS1TWIST];
150 |     std::fill(phase1, phase1 + N_FS1TWIST, EMPTY);
151 | 
152 |     phase1[coord::N_TWIST * sym::coord_c(sym::fslice1_sym[coord::fslice1(0, coord::SLICE1_SOLVED)])] = 0;
153 |     int count = 0;
154 |     int dist = 0;
155 | 
156 |     while (count < N_FS1TWIST) {
157 |       int coord = 0;
158 | 
159 |       for (int fs1sym = 0; fs1sym < sym::N_FSLICE1; fs1sym++) {
160 |         int fslice1 = sym::fslice1_raw[fs1sym];
161 |         int flip = coord::fslice1_to_flip(fslice1);
162 |         int slice = coord::slice1_to_slice(coord::fslice1_to_slice1(fslice1));
163 | 
164 |         for (int twist = 0; twist < coord::N_TWIST; twist++) {
165 |           if ((phase1[coord] & 0xff) == dist) {
166 |             count++;
167 |             int deltas[move::COUNT1]; // easier encoding if B-face always exists (F5-mode ignores it anyways)
168 | 
169 |             for (int m = 0; m < n_moves; m++) {
170 |               int slice11 = coord::slice_to_slice1(coord::move_edges4[slice][m]);
171 |               int fslice11 = coord::fslice1(coord::move_flip[flip][m], slice11);
172 |               int tmp = sym::fslice1_sym[fslice11];
173 |               int twist1 = sym::conj_twist[coord::move_twist[twist][m]][sym::coord_s(tmp)];
174 |               int fs1sym1 = sym::coord_c(tmp);
175 |               int coord1 = coord::N_TWIST * fs1sym1 + twist1;
176 | 
177 |               if (phase1[coord1] == EMPTY)
178 |                 phase1[coord1] = dist + 1;
179 |               deltas[m] = (phase1[coord1] & 0xff) - dist;
180 |               coord1 -= twist1; // only TWIST part changes below
181 | 
182 |               int selfs = sym::fslice1_selfs[fs1sym1] >> 1;
183 |               for (int s = 1; selfs > 0; s++) { // bit 0 is always on
184 |                 if (selfs & 1) {
185 |                   int coord2 = coord1 + sym::conj_twist[twist1][s];
186 |                   if (phase1[coord2] == EMPTY)
187 |                     phase1[coord2] = dist + 1;
188 |                 }
189 |                 selfs >>= 1;
190 |               }
191 |             }
192 | 
193 |             prun1 prun = 0;
194 |             #ifdef QT
195 |               // In QT there is enough space to simply encode the effect of every move in 2 bits
196 |               for (int m = n_moves - 1; m >= 0; m--)
197 |                   prun = (prun << 2) | (deltas[m] + 1);
198 |             #else
199 |               #ifndef AX
200 |                 int n_ax = 6; // in standard (HT) mode we have to treat every face as an individual axis for encoding
201 |                 int bits_per_ax = 4;
202 |               #else
203 |                 int n_ax = 3;
204 |                 int bits_per_ax = BITS_PER_AX;
205 |               #endif
206 |                 /* Encode from left to right to preserve indexing of moves */
207 |                 for (int ax = n_ax - 1; ax >= 0; ax--) {
208 |                   bool away = false; // first bit of axis encoding (whether any move brings us further from the goal)
209 |                   for (int i = ax * (bits_per_ax - 1); i < (ax + 1) * (bits_per_ax - 1); i++) {
210 |                     if (deltas[i] != 0) {
211 |                       if (deltas[i] > 0)
212 |                         away = true;
213 |                       break; // stop immediately once we found a value != 0
214 |                     }
215 |                   }
216 | 
217 |                   int tmp = 0;
218 |                   for (int i = (ax + 1) * (bits_per_ax - 1) - 1; i >= ax * (bits_per_ax - 1); i--)
219 |                     tmp = (tmp | (away ? deltas[i] : deltas[i] + 1)) << 1;
220 |                   tmp |= away;
221 | 
222 |                   prun = (prun << bits_per_ax) | tmp;
223 |                 }
224 |             #endif
225 |             phase1[coord] |= prun << 8;
226 |           }
227 |           coord++;
228 |         }
229 |       }
230 | 
231 |       std::cout << dist << " " << count << std::endl;
232 |       dist++;
233 |     }
234 |   }
235 | 
236 |   void init_phase2() {
237 |     phase2 = new uint8_t[N_CORNUD2];
238 |     std::fill(phase2, phase2 + N_CORNUD2, EMPTY);
239 | 
240 |     phase2[0] = 0;
241 |     int count = 0;
242 |     int dist = 0;
243 | 
244 |     while (count < N_CORNUD2) {
245 |       int coord = 0;
246 | 
247 |       for (int csym = 0; csym < sym::N_CORNERS; csym++) {
248 |         int corners = sym::corners_raw[csym];
249 | 
250 |         for (int udedges2 = 0; udedges2 < coord::N_UDEDGES2; udedges2++) {
251 |           if (phase2[coord] == dist) {
252 |             count++;
253 | 
254 |             for (move::mask moves = move::p2mask; moves; moves &= moves - 1) {
255 |               int m = ffsll(moves) - 1;
256 | 
257 |               int dist1 = dist + 1;
258 |               #ifdef QT
259 |                 if (m >= move::COUNT1)
260 |                   dist1++; // half-turns cost 2 in QTM
261 |               #endif
262 | 
263 |               int corners1 = coord::move_corners[corners][m];
264 |               int udedges21 = coord::move_udedges2[udedges2][m];
265 |               int tmp = sym::corners_sym[corners1];
266 |               udedges21 = sym::conj_udedges2[udedges21][sym::coord_s(tmp)];
267 |               int csym1 = sym::coord_c(tmp);
268 |               int coord1 = coord::N_UDEDGES2 * csym1 + udedges21;
269 | 
270 |               if (phase2[coord1] <= dist1)
271 |                 continue;
272 |               phase2[coord1] = dist1;
273 |               coord1 -= udedges21;
274 | 
275 |               int selfs = sym::corners_selfs[csym1] >> 1;
276 |               for (int s = 1; selfs > 0; s++) {
277 |                 if (selfs & 1) {
278 |                   int coord2 = coord1 + sym::conj_udedges2[udedges21][s];
279 |                   if (phase2[coord2] > dist1)
280 |                     phase2[coord2] = dist1;
281 |                 }
282 |                 selfs >>= 1;
283 |               }
284 |             }
285 |           }
286 |           coord++;
287 |         }
288 |       }
289 | 
290 |       std::cout << dist << " " << count << std::endl;
291 |       dist++;
292 |     }
293 |   }
294 | 
295 |   void init_precheck() {
296 |     precheck = new uint8_t[N_CSLICE2];
297 |     std::fill(precheck, precheck + N_CSLICE2, EMPTY);
298 | 
299 |     precheck[0] = 0;
300 |     int dist = 0;
301 |     int count = 0;
302 | 
303 |     while (count < N_CSLICE2) {
304 |       int coord = 0;
305 | 
306 |       for (int corners = 0; corners < coord::N_CORNERS; corners++) {
307 |         for (int slice2 = 0; slice2 < coord::N_SLICE2; slice2++) {
308 |           if (precheck[coord] == dist) {
309 |             count++;
310 |             int slice = coord::slice2_to_slice(slice2);
311 | 
312 |             for (move::mask moves = move::p2mask; moves; moves &= moves - 1) {
313 |               int m = ffsll(moves) - 1;
314 | 
315 |               int dist1 = dist + 1;
316 |               #ifdef QT
317 |                 if (m >= move::COUNT1)
318 |                   dist1++; // half-turns cost 2 in QTM
319 |               #endif
320 | 
321 |               int corners1 = coord::move_corners[corners][m];
322 |               int slice21 = coord::slice_to_slice2(coord::move_edges4[slice][m]);
323 | 
324 |               int coord1 = coord::N_SLICE2 * corners1 + slice21;
325 |               if (precheck[coord1] > dist1)
326 |                 precheck[coord1] = dist1;
327 |             }
328 |           }
329 |           coord++;
330 |         }
331 |       }
332 | 
333 |       std::cout << dist << " " << count << std::endl;
334 |       dist++;
335 |     }
336 |   }
337 | 
338 |   int get_phase1(int flip, int slice, int twist, int togo, move::mask& next) {
339 |     int tmp = sym::fslice1_sym[coord::fslice1(flip, coord::slice_to_slice1(slice))];
340 |     int s = sym::coord_s(tmp);
341 |     prun1 prun = phase1[coord::N_TWIST * sym::coord_c(tmp) + sym::conj_twist[twist][s]];
342 | 
343 |     int dist = prun & 0xff;
344 |     int delta = togo - dist;
345 | 
346 |     // `delta` < 0 case can never happen during a real search
347 |     if (delta > 1)
348 |       next = move::p1mask; // all moves are possible
349 |     else {
350 |       prun >>= 8; // get rid of dist
351 |       next = 0;
352 |       for (int ax = 0; ax < 3; ax++) {
353 |         next |= remap[delta][sym::effect[s][ax]][prun & ones(BITS_PER_AX)];
354 |         prun >>= BITS_PER_AX;
355 |       }
356 |     }
357 | 
358 |     return dist;
359 |   }
360 | 
361 |   int get_phase2(int corners, int udedges) {
362 |     int tmp = sym::corners_sym[corners];
363 |     return phase2[coord::N_UDEDGES2 * sym::coord_c(tmp) + sym::conj_udedges2[udedges][sym::coord_s(tmp)]];
364 |   }
365 | 
366 |   int get_precheck(int corners, int slice) {
367 |     return precheck[coord::N_SLICE2 * corners + coord::slice_to_slice2(slice)];
368 |   }
369 | 
370 |   bool init(bool file) {
371 |     init_base();
372 | 
373 |     if (!file) {
374 |       init_phase1();
375 |       init_phase2();
376 |       init_precheck();
377 |       return true;
378 |     }
379 | 
380 |     FILE *f = fopen(SAVE.c_str(), "rb");
381 |     int err = 0;
382 | 
383 |     if (f == NULL) {
384 |       init_phase1();
385 |       init_phase2();
386 |       init_precheck();
387 | 
388 |       f = fopen(SAVE.c_str(), "wb");
389 |       if (fwrite(phase1, sizeof(prun1), N_FS1TWIST, f) != N_FS1TWIST)
390 |         err = 1;
391 |       if (fwrite(phase2, sizeof(uint8_t), N_CORNUD2, f) != N_CORNUD2)
392 |         err = 1;
393 |       if (fwrite(precheck, sizeof(uint8_t), N_CSLICE2, f) != N_CSLICE2)
394 |         err = 1;
395 |       if (err)
396 |         remove(SAVE.c_str()); // delete file if there was some error writing it
397 |     } else {
398 |       phase1 = new prun1[N_FS1TWIST];
399 |       phase2 = new uint8_t[N_CORNUD2];
400 |       precheck = new uint8_t[N_CSLICE2];
401 |       if (fread(phase1, sizeof(prun1), N_FS1TWIST, f) != N_FS1TWIST)
402 |         err = 1;
403 |       if (fread(phase2, sizeof(uint8_t), N_CORNUD2, f) != N_CORNUD2)
404 |         err = 1;
405 |       if (fread(precheck, sizeof(uint8_t), N_CSLICE2, f) != N_CSLICE2)
406 |         err = 1;
407 |     }
408 | 
409 |     fclose(f);
410 |     return err;
411 |   }
412 | 
413 | }
414 | 


--------------------------------------------------------------------------------
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--------------------------------------------------------------------------------
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411 | modify it is void, and will automatically terminate your rights under
412 | this License (including any patent licenses granted under the third
413 | paragraph of section 11).
414 | 
415 |   However, if you cease all violation of this License, then your
416 | license from a particular copyright holder is reinstated (a)
417 | provisionally, unless and until the copyright holder explicitly and
418 | finally terminates your license, and (b) permanently, if the copyright
419 | holder fails to notify you of the violation by some reasonable means
420 | prior to 60 days after the cessation.
421 | 
422 |   Moreover, your license from a particular copyright holder is
423 | reinstated permanently if the copyright holder notifies you of the
424 | violation by some reasonable means, this is the first time you have
425 | received notice of violation of this License (for any work) from that
426 | copyright holder, and you cure the violation prior to 30 days after
427 | your receipt of the notice.
428 | 
429 |   Termination of your rights under this section does not terminate the
430 | licenses of parties who have received copies or rights from you under
431 | this License.  If your rights have been terminated and not permanently
432 | reinstated, you do not qualify to receive new licenses for the same
433 | material under section 10.
434 | 
435 |   9. Acceptance Not Required for Having Copies.
436 | 
437 |   You are not required to accept this License in order to receive or
438 | run a copy of the Program.  Ancillary propagation of a covered work
439 | occurring solely as a consequence of using peer-to-peer transmission
440 | to receive a copy likewise does not require acceptance.  However,
441 | nothing other than this License grants you permission to propagate or
442 | modify any covered work.  These actions infringe copyright if you do
443 | not accept this License.  Therefore, by modifying or propagating a
444 | covered work, you indicate your acceptance of this License to do so.
445 | 
446 |   10. Automatic Licensing of Downstream Recipients.
447 | 
448 |   Each time you convey a covered work, the recipient automatically
449 | receives a license from the original licensors, to run, modify and
450 | propagate that work, subject to this License.  You are not responsible
451 | for enforcing compliance by third parties with this License.
452 | 
453 |   An "entity transaction" is a transaction transferring control of an
454 | organization, or substantially all assets of one, or subdividing an
455 | organization, or merging organizations.  If propagation of a covered
456 | work results from an entity transaction, each party to that
457 | transaction who receives a copy of the work also receives whatever
458 | licenses to the work the party's predecessor in interest had or could
459 | give under the previous paragraph, plus a right to possession of the
460 | Corresponding Source of the work from the predecessor in interest, if
461 | the predecessor has it or can get it with reasonable efforts.
462 | 
463 |   You may not impose any further restrictions on the exercise of the
464 | rights granted or affirmed under this License.  For example, you may
465 | not impose a license fee, royalty, or other charge for exercise of
466 | rights granted under this License, and you may not initiate litigation
467 | (including a cross-claim or counterclaim in a lawsuit) alleging that
468 | any patent claim is infringed by making, using, selling, offering for
469 | sale, or importing the Program or any portion of it.
470 | 
471 |   11. Patents.
472 | 
473 |   A "contributor" is a copyright holder who authorizes use under this
474 | License of the Program or a work on which the Program is based.  The
475 | work thus licensed is called the contributor's "contributor version".
476 | 
477 |   A contributor's "essential patent claims" are all patent claims
478 | owned or controlled by the contributor, whether already acquired or
479 | hereafter acquired, that would be infringed by some manner, permitted
480 | by this License, of making, using, or selling its contributor version,
481 | but do not include claims that would be infringed only as a
482 | consequence of further modification of the contributor version.  For
483 | purposes of this definition, "control" includes the right to grant
484 | patent sublicenses in a manner consistent with the requirements of
485 | this License.
486 | 
487 |   Each contributor grants you a non-exclusive, worldwide, royalty-free
488 | patent license under the contributor's essential patent claims, to
489 | make, use, sell, offer for sale, import and otherwise run, modify and
490 | propagate the contents of its contributor version.
491 | 
492 |   In the following three paragraphs, a "patent license" is any express
493 | agreement or commitment, however denominated, not to enforce a patent
494 | (such as an express permission to practice a patent or covenant not to
495 | sue for patent infringement).  To "grant" such a patent license to a
496 | party means to make such an agreement or commitment not to enforce a
497 | patent against the party.
498 | 
499 |   If you convey a covered work, knowingly relying on a patent license,
500 | and the Corresponding Source of the work is not available for anyone
501 | to copy, free of charge and under the terms of this License, through a
502 | publicly available network server or other readily accessible means,
503 | then you must either (1) cause the Corresponding Source to be so
504 | available, or (2) arrange to deprive yourself of the benefit of the
505 | patent license for this particular work, or (3) arrange, in a manner
506 | consistent with the requirements of this License, to extend the patent
507 | license to downstream recipients.  "Knowingly relying" means you have
508 | actual knowledge that, but for the patent license, your conveying the
509 | covered work in a country, or your recipient's use of the covered work
510 | in a country, would infringe one or more identifiable patents in that
511 | country that you have reason to believe are valid.
512 | 
513 |   If, pursuant to or in connection with a single transaction or
514 | arrangement, you convey, or propagate by procuring conveyance of, a
515 | covered work, and grant a patent license to some of the parties
516 | receiving the covered work authorizing them to use, propagate, modify
517 | or convey a specific copy of the covered work, then the patent license
518 | you grant is automatically extended to all recipients of the covered
519 | work and works based on it.
520 | 
521 |   A patent license is "discriminatory" if it does not include within
522 | the scope of its coverage, prohibits the exercise of, or is
523 | conditioned on the non-exercise of one or more of the rights that are
524 | specifically granted under this License.  You may not convey a covered
525 | work if you are a party to an arrangement with a third party that is
526 | in the business of distributing software, under which you make payment
527 | to the third party based on the extent of your activity of conveying
528 | the work, and under which the third party grants, to any of the
529 | parties who would receive the covered work from you, a discriminatory
530 | patent license (a) in connection with copies of the covered work
531 | conveyed by you (or copies made from those copies), or (b) primarily
532 | for and in connection with specific products or compilations that
533 | contain the covered work, unless you entered into that arrangement,
534 | or that patent license was granted, prior to 28 March 2007.
535 | 
536 |   Nothing in this License shall be construed as excluding or limiting
537 | any implied license or other defenses to infringement that may
538 | otherwise be available to you under applicable patent law.
539 | 
540 |   12. No Surrender of Others' Freedom.
541 | 
542 |   If conditions are imposed on you (whether by court order, agreement or
543 | otherwise) that contradict the conditions of this License, they do not
544 | excuse you from the conditions of this License.  If you cannot convey a
545 | covered work so as to satisfy simultaneously your obligations under this
546 | License and any other pertinent obligations, then as a consequence you may
547 | not convey it at all.  For example, if you agree to terms that obligate you
548 | to collect a royalty for further conveying from those to whom you convey
549 | the Program, the only way you could satisfy both those terms and this
550 | License would be to refrain entirely from conveying the Program.
551 | 
552 |   13. Use with the GNU Affero General Public License.
553 | 
554 |   Notwithstanding any other provision of this License, you have
555 | permission to link or combine any covered work with a work licensed
556 | under version 3 of the GNU Affero General Public License into a single
557 | combined work, and to convey the resulting work.  The terms of this
558 | License will continue to apply to the part which is the covered work,
559 | but the special requirements of the GNU Affero General Public License,
560 | section 13, concerning interaction through a network will apply to the
561 | combination as such.
562 | 
563 |   14. Revised Versions of this License.
564 | 
565 |   The Free Software Foundation may publish revised and/or new versions of
566 | the GNU General Public License from time to time.  Such new versions will
567 | be similar in spirit to the present version, but may differ in detail to
568 | address new problems or concerns.
569 | 
570 |   Each version is given a distinguishing version number.  If the
571 | Program specifies that a certain numbered version of the GNU General
572 | Public License "or any later version" applies to it, you have the
573 | option of following the terms and conditions either of that numbered
574 | version or of any later version published by the Free Software
575 | Foundation.  If the Program does not specify a version number of the
576 | GNU General Public License, you may choose any version ever published
577 | by the Free Software Foundation.
578 | 
579 |   If the Program specifies that a proxy can decide which future
580 | versions of the GNU General Public License can be used, that proxy's
581 | public statement of acceptance of a version permanently authorizes you
582 | to choose that version for the Program.
583 | 
584 |   Later license versions may give you additional or different
585 | permissions.  However, no additional obligations are imposed on any
586 | author or copyright holder as a result of your choosing to follow a
587 | later version.
588 | 
589 |   15. Disclaimer of Warranty.
590 | 
591 |   THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
592 | APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
596 | PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
597 | IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
599 | 
600 |   16. Limitation of Liability.
601 | 
602 |   IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
610 | SUCH DAMAGES.
611 | 
612 |   17. Interpretation of Sections 15 and 16.
613 | 
614 |   If the disclaimer of warranty and limitation of liability provided
615 | above cannot be given local legal effect according to their terms,
616 | reviewing courts shall apply local law that most closely approximates
617 | an absolute waiver of all civil liability in connection with the
618 | Program, unless a warranty or assumption of liability accompanies a
619 | copy of the Program in return for a fee.
620 | 
621 |                      END OF TERMS AND CONDITIONS
622 | 
623 |             How to Apply These Terms to Your New Programs
624 | 
625 |   If you develop a new program, and you want it to be of the greatest
626 | possible use to the public, the best way to achieve this is to make it
627 | free software which everyone can redistribute and change under these terms.
628 | 
629 |   To do so, attach the following notices to the program.  It is safest
630 | to attach them to the start of each source file to most effectively
631 | state the exclusion of warranty; and each file should have at least
632 | the "copyright" line and a pointer to where the full notice is found.
633 | 
634 |     <one line to give the program's name and a brief idea of what it does.>
635 |     Copyright (C) <year>  <name of author>
636 | 
637 |     This program is free software: you can redistribute it and/or modify
638 |     it under the terms of the GNU General Public License as published by
639 |     the Free Software Foundation, either version 3 of the License, or
640 |     (at your option) any later version.
641 | 
642 |     This program is distributed in the hope that it will be useful,
643 |     but WITHOUT ANY WARRANTY; without even the implied warranty of
644 |     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
645 |     GNU General Public License for more details.
646 | 
647 |     You should have received a copy of the GNU General Public License
648 |     along with this program.  If not, see <https://www.gnu.org/licenses/>.
649 | 
650 | Also add information on how to contact you by electronic and paper mail.
651 | 
652 |   If the program does terminal interaction, make it output a short
653 | notice like this when it starts in an interactive mode:
654 | 
655 |     <program>  Copyright (C) <year>  <name of author>
656 |     This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
657 |     This is free software, and you are welcome to redistribute it
658 |     under certain conditions; type `show c' for details.
659 | 
660 | The hypothetical commands `show w' and `show c' should show the appropriate
661 | parts of the General Public License.  Of course, your program's commands
662 | might be different; for a GUI interface, you would use an "about box".
663 | 
664 |   You should also get your employer (if you work as a programmer) or school,
665 | if any, to sign a "copyright disclaimer" for the program, if necessary.
666 | For more information on this, and how to apply and follow the GNU GPL, see
667 | <https://www.gnu.org/licenses/>.
668 | 
669 |   The GNU General Public License does not permit incorporating your program
670 | into proprietary programs.  If your program is a subroutine library, you
671 | may consider it more useful to permit linking proprietary applications with
672 | the library.  If this is what you want to do, use the GNU Lesser General
673 | Public License instead of this License.  But first, please read
674 | <https://www.gnu.org/licenses/why-not-lgpl.html>.
675 | 


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