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+/*
+# Cube representation, moves, transformations and indexing
+
+## String description
+
+The functions readcube() and writecube() use the following format.
+Each edge is represented by two letters denoting the sides it belongs to
+and one number denoting its orientation (0 oriented, 1 mis-oriented).
+Similarly, each corner is represented by three letters and a number
+(0 oriented, 1 twisted clockwise, 2 twisted counter-clockwise).
+Edge orientation is relative to the F / B axis, corner orientation is
+relative to the U / D axis.
+
+The correct order of the pieces is the same as that defined in the
+section "Internal cube representation", except that pieces are read
+left-to-right. Pieces are divided by slices, so the ordering is not the
+most intuitive, but it is more convenient for the internal representation.
+
+Whitespaces between pieces are ignored when reading the cube, and a
+single whitespace character is added between pieces when writing.
+
+For example, the solved cube looks like this:
+
+UF0 UB0 DB0 DF0 UR0 UL0 DL0 DR0 FR0 FL0 BL0 BR0 UFR0 UBL0 DFL0 DBR0 UFL0 UBR0 DFR0 DBL0
+
+The cube after the moves R'U'F looks like this:
+
+FL1 BR0 DB0 UR1 UF0 UB0 DL0 FR0 UL1 DF1 BL0 DR0 UBL1 DBR1 UFR2 DFR2 DFL2 UBL2 UFL2 DBL0
+
+More formats might be supported in the future.
+
+## Internal cube representation
+
+The cube_t data structure implemented in this file is designed to
+efficiently perform common operations on a 3x3x3 Rubik's cube when
+solving it with an iterative-deepening DFS search. It is not the most
+general, complete, easy to read or compact one.  Since the cube can
+be trivially reoriented before the search, we only encode permutations
+of the cube that keep the center pieces in a fixed position (that is,
+we do not encode the position of the centers).
+
+The cube state is encoded in two 64-bit integers, one for edges and one
+for centers. We explain how edges are encoded first, and the highlight
+the few differences with corners afterwards.
+
+For encoding edges, only the 60 least-significant bits are used. Each
+edge described by 5 bits. The position of a 5-bit block in the 64-bit
+integer determine the position of the edge piece in the cube, according
+to the following table (least-significant bits on the right):
+
+55-59 50-54 45-49 40-44 35-39 30-34 25-29 20-24 15-19 10-14  5-9   0-4
+  BR    BL    FL    FR    DR    DL    UL    UR    DF    DB    UB    UF
+ossee ossee ossee ossee ossee ossee ossee ossee ossee ossee ossee ossee
+
+For each edge, the 4 least-significant bits ('ssee' in the table)
+determine the piece. The two bits marked with 'ss' determine the internal
+slice the piece belongs to, i.e. they are either '00' for M, '01' for
+S or '10' for E. The other two bits (marked with 'ee') determine the
+actual edge piece among the 4 in the same slice, and they are assigned
+somewhat arbitarily. Using this representation and the ordering defined
+in the table above, the edges are correctly permuted when these 4 bits
+for each represent the numbers 0 to 11 in the correct order.
+
+The last bit determines the orientation. The orientation of an edge
+depends on its position, and it is defined being 0 if the edge can be
+moved to its place in the solved orientation by permutations in the
+subgroup <U, D, R, L, F2, B2>.
+
+Corners are encoded in the 48 least-significant bits, and are described
+by 6 bits each, their position being defined by the following table:
+
+ 35-39  30-34  25-29  20-24  15-19  10-14   5-9    0-4
+  DBL    DFL    UBR    UFL    DBR    DFL    UBL    UFR
+oooxcc oooxcc oooxcc oooxcc oooxcc oooxcc oooxcc oooxcc
+
+The bit marked with an 'x' describes the axis the corner belongs to.
+The 0 axis consists of the corners UFR, UBL, DFL and DBR, and the other
+four corners form the axis marked with 1. Then two bits are needed to
+identify the corner among the four of the same axis.  The last three bits
+determine the orientation, where one corner is defined to be oriented
+(marked with '000') if its top or bottom sticker faces the top or bottom
+side. A corner a clockwise turn away from being oriented, thus requiring
+a counter-clockwise turn to be oriented correctly, is marked with '001',
+and a corner a counter-clockwise turn away is marked with '010'.  The most
+significant bit is not used to determine the corner orientation, but it
+must always be set to '0' to simplify the moving operations (see below).
+
+## Basic moves
+
+The 18 basic moves of the cube could be performed by applying a suitable
+general permutation (see below), but they have instead been manually
+implemented with a few simple operations each, to improve performance.
+
+For each move we first permute the pieces. This amounts to shifting
+around 4 blocks of bits for edges and 4 for corners. Since in some cases
+adjacent pieces on the cube are also adjacent in the bit representation we
+use, we can save some operations by shifting multiple blocks together.
+For example, for the move U for edges we shift a block of 15 bits 5
+positions to the left and a block of 5 bits 15 positions to the right.
+
+There are some moves that change the orientation of the pieces. Namely,
+the moves F, F', B and B' change the orientation of the edges and those
+moves as well as R, R', L and L' change the orientation of the corners.
+Edge orientation is easy to address: we simply xor the edge representation
+by a bit mask with zeroes everywhere except for the 4 edges that need
+to be flipped (i.e. the ones on the twisted face).
+
+Corner orientation is harder to reproduce efficiently working only with
+bitwise operations, as it involves performing operations modulo 3.
+However, with the help of the extra bit we reserved, we are able to
+do this using only two additions and 3 bitwise operations, without
+any multiplication, division or modulo operation. The trick is
+to use the following formula to sum two numbers x, y in {0,1,2}:
+
+               ((x+y) + (x+y+1)/4) % 4
+
+The thrid bit is needed because x+y and x+y+1 can exceed 3.
+See below (in the code) for the details.
+
+## Inverting the cube
+
+TODO
+
+## Transformations (conjugations by full-cube rotations)
+
+TODO
+
+## Indexing
+
+TODO - subgroup description etc
+
+Ideas for pruning (for another file?):
+- Use corner separation + CO as main coordinate (~150k states)
+  - for huge tables, htr corners can be used (6 times larger)
+- Symmetry table, one entry or each main coordinate value with the
+  following info:
+  - index of the corresponding main symcoord (13 bits)
+  - transtorep (6 bits)
+  - base value for pruning table (5 bits, probably 4)
+  - pruning value for only main coord, i.e. fallback (4 bits)
+- To get a full coord for the cube:
+  - get first coord c, get the transtorep
+  - transform edges with transtorep
+  - get second coordinate e
+  - return c * MAXE + e
+  - This is still too big, so divide by a power of 2 to get the hashed index
+    - second coordinate: ep always, + varible number of eo bit (0 to 11)
+- Generate table:
+  - first probe for base value:
+    - solve coord using fallback table for pruning for 10k random states or so
+  - loop over all possible values (even if going for smaller table)
+    - with inverse-index strategy or what?
+  - use 1 bit per entry (more than base value or not)
+*/
+
+#include <stdbool.h>
+#include <stdint.h>
+#include <string.h>
+
+#ifdef DEBUG
+#include <stdio.h>
+#endif
+
+#include "cube.h"
+
+#define _error         0xFFFFFFFF
+
+#define _esize         5ULL
+#define _eoblock       0x10ULL /* 10000 */
+#define _epblock       0x0FULL /* 01111 */
+#define _eblock        0x1FULL /* 11111 */
+
+#define _csize         6ULL
+#define _coblock       0x18ULL /* 011000 */
+#define _cpblock       0x07ULL /* 000111 */
+#define _cblock        0x3FULL /* 111111 */
+
+#define _edge_uf       0ULL  /* 00 00 */
+#define _edge_ub       1ULL  /* 00 01 */
+#define _edge_db       2ULL  /* 00 10 */
+#define _edge_df       3ULL  /* 00 11 */
+#define _edge_ur       4ULL  /* 01 00 */
+#define _edge_ul       5ULL  /* 01 01 */
+#define _edge_dl       6ULL  /* 01 10 */
+#define _edge_dr       7ULL  /* 01 11 */
+#define _edge_fr       8ULL  /* 10 00 */
+#define _edge_fl       9ULL  /* 10 01 */
+#define _edge_bl       10ULL /* 10 10 */
+#define _edge_br       11ULL /* 10 11 */
+
+#define _corner_ufr    0ULL /* 0 00 */
+#define _corner_ubl    1ULL /* 0 01 */
+#define _corner_dfl    2ULL /* 0 10 */
+#define _corner_dbr    3ULL /* 0 11 */
+#define _corner_ufl    4ULL /* 1 00 */
+#define _corner_ubr    5ULL /* 1 01 */
+#define _corner_dfr    6ULL /* 1 10 */
+#define _corner_dbl    7ULL /* 1 11 */
+
+#define ESHIFT(i)      ((i) * _esize)
+#define EOSHIFT(i)     (4ULL + (i) * _esize)
+#define EMASK(i)       (_eblock << ESHIFT(i))
+#define EOMASK(i)      (_eoblock << ESHIFT(i))
+#define EPMASK(i)      (_epblock << ESHIFT(i))
+#define ESOLVED(ee)    (_edge_##ee << (_edge_##ee * _esize))
+#define EDGEAT(e, i)   (((e) & EMASK(i)) >> ESHIFT(i))
+#define EOAT(e, i)     (((e) & EOMASK(i)) >> EOSHIFT(i))
+#define EPAT(e, i)     (((e) & EPMASK(i)) >> ESHIFT(i))
+
+#define CSHIFT(i)      ((i) * _csize)
+#define COSHIFT(i)     (3ULL + (i) * _csize)
+#define CMASK(i)       (_cblock << CSHIFT(i))
+#define COMASK(i)      (_coblock << CSHIFT(i))
+#define CPMASK(i)      (_cpblock << CSHIFT(i))
+#define CSOLVED(ccc)   (_corner_##ccc << (_corner_##ccc * _csize))
+#define CORNERAT(c, i) (((c) & CMASK(i)) >> CSHIFT(i))
+#define COAT(c, i)     (((c) & COMASK(i)) >> COSHIFT(i))
+#define CPAT(c, i)     (((c) & CPMASK(i)) >> CSHIFT(i))
+
+#define _emask_u       (EMASK(uf) | EMASK(ul) | EMASK(ub) | EMASK(ur))
+#define _emask_d       (EMASK(df) | EMASK(dl) | EMASK(db) | EMASK(dr))
+#define _emask_r       (EMASK(ur) | EMASK(dr) | EMASK(fr) | EMASK(br))
+#define _emask_l       (EMASK(ul) | EMASK(dl) | EMASK(fl) | EMASK(bl))
+#define _emask_f       (EMASK(uf) | EMASK(df) | EMASK(fr) | EMASK(fl))
+#define _emask_b       (EMASK(ub) | EMASK(db) | EMASK(br) | EMASK(bl))
+
+#define _cmask_u       (CMASK(ufr) | CMASK(ufl) | CMASK(ubl) | CMASK(ubr))
+#define _cmask_d       (CMASK(dfr) | CMASK(dfl) | CMASK(dbl) | CMASK(dbr))
+#define _cmask_r       (CMASK(ufr) | CMASK(dfr) | CMASK(ubr) | CMASK(dbr))
+#define _cmask_l       (CMASK(ufl) | CMASK(dfl) | CMASK(ubl) | CMASK(dbl))
+#define _cmask_f       (CMASK(ufr) | CMASK(ufl) | CMASK(dfr) | CMASK(dfl))
+#define _cmask_b       (CMASK(ubr) | CMASK(ubl) | CMASK(dbr) | CMASK(dbl))
+
+#define _eomask        (EOMASK(uf) | EOMASK(ul) | EOMASK(ub) | EOMASK(ur) \
+                        EOMASK(df) | EOMASK(dl) | EOMASK(db) | EOMASK(dr) \
+                        EOMASK(fr) | EOMASK(fl) | EOMASK(bl) | EOMASK(br))
+#define _comask        (COMASK(ufr) | COMASK(ufl) | COMASK(ubl) | COMASK(ubr) \
+                        COMASK(dfr) | COMASK(dfl) | COMASK(dbl) | COMASK(dbr))
+
+static uint64_t permsign(uint64_t *, int);
+static uint64_t readep(char *);
+static uint64_t readeo(char *);
+static uint64_t readcp(char *);
+static uint64_t readco(char *);
+static uint64_t readmove(char);
+static uint64_t readmodifier(char);
+
+static char *edgestr[] = {
+        [_edge_uf] = "UF",
+        [_edge_ub] = "UB",
+        [_edge_db] = "DB",
+        [_edge_df] = "DF",
+        [_edge_ur] = "UR",
+        [_edge_ul] = "UL",
+        [_edge_dl] = "DL",
+        [_edge_dr] = "DR",
+        [_edge_fr] = "FR",
+        [_edge_fl] = "FL",
+        [_edge_bl] = "BL",
+        [_edge_br] = "BR"
+};
+static char *cornerstr[] = {
+        [_corner_ufr] = "UFR",
+        [_corner_ubl] = "UBL",
+        [_corner_dfl] = "DFL",
+        [_corner_dbr] = "DBR",
+        [_corner_ufl] = "UFL",
+        [_corner_ubr] = "UBR",
+        [_corner_dfr] = "DFR",
+        [_corner_dbl] = "DBL"
+};
+static char *movestr[] = {
+        [U] = "U", [U2] = "U2", [U3] = "U'",
+        [D] = "D", [D2] = "D2", [D3] = "D'",
+        [R] = "R", [R2] = "R2", [R3] = "R'",
+        [L] = "L", [L2] = "L2", [L3] = "L'",
+        [F] = "F", [F2] = "F2", [F3] = "F'",
+        [B] = "B", [B2] = "B2", [B3] = "B'",
+};
+
+cube_t solvedcube = {
+        .e = ESOLVED(uf) | ESOLVED(ul) | ESOLVED(ub) | ESOLVED(ur) |
+             ESOLVED(df) | ESOLVED(dl) | ESOLVED(db) | ESOLVED(dr) |
+             ESOLVED(fr) | ESOLVED(fl) | ESOLVED(bl) | ESOLVED(br),
+        .c = CSOLVED(ufr) | CSOLVED(ufl) | CSOLVED(ubl) | CSOLVED(ubr) |
+             CSOLVED(dfr) | CSOLVED(dfl) | CSOLVED(dbl) | CSOLVED(dbr),
+};
+cube_t errorcube = { .e = _error, .c = _error };
+
+
+static uint64_t
+permsign(uint64_t *a, int n)
+{
+        int i, j;
+        uint64_t ret;
+
+        ret = 0;
+
+        for (i = 0; i < n; i++)
+                for (j = i+1; j < n; j++)
+                        ret += a[i] > a[j] ? 1 : 0;
+
+        return ret % 2;
+}
+
+bool
+isconsistent(cube_t cube)
+{
+        uint64_t p[12], sum;
+        bool found[12];
+        int i;
+
+        sum = 0;
+
+        /* Check for EP consistency */
+        for (i = 0; i < 12; i++)
+                found[i] = false;
+        for (i = 0; i < 12; i++) {
+                p[i] = EPAT(cube.e, i);
+                found[p[i]] = true;
+        }
+        for (i = 0; i < 12; i++)
+                if (!found[i])
+                        return false;
+        sum = permsign(p, 12);
+
+        /* Check for CP consistency */
+        for (i = 0; i < 8; i++)
+                found[i] = false;
+        for (i = 0; i < 8; i++) {
+                p[i] = CPAT(cube.c, i);
+                found[p[i]] = true;
+        }
+        for (i = 0; i < 8; i++)
+                if (!found[i])
+                        return false;
+        sum += permsign(p, 8);
+
+        /* Check permutation parity */
+        if (sum % 2 != 0)
+                return false;
+
+        /* Check for EO parity */
+        for (i = 0, sum = 0; i < 12; i++)
+                sum += EOAT(cube.e, i);
+        if (sum % 2 != 0)
+                return false;
+
+        /* Check for CO parity */
+        for (i = 0, sum = 0; i < 8; i++)
+                sum += COAT(cube.c, i);
+        if (sum % 3 != 0)
+                return false;
+
+        /* Check that CO extra bit is zero */
+        for (i = 0; i < 8; i++)
+                if (cube.c & (1ULL << (5 + i * _csize)))
+                        return false;
+
+        return true;
+}
+
+bool
+issolved(cube_t cube)
+{
+        return cube.c == solvedcube.c && cube.e == solvedcube.e;
+}
+
+
+static uint64_t
+readep(char *str)
+{
+        if (!strncmp(str, "UF", 2))
+                return _edge_uf;
+        if (!strncmp(str, "UL", 2))
+                return _edge_ul;
+        if (!strncmp(str, "UB", 2))
+                return _edge_ub;
+        if (!strncmp(str, "UR", 2))
+                return _edge_ur;
+        if (!strncmp(str, "DF", 2))
+                return _edge_df;
+        if (!strncmp(str, "DL", 2))
+                return _edge_dl;
+        if (!strncmp(str, "DB", 2))
+                return _edge_db;
+        if (!strncmp(str, "DR", 2))
+                return _edge_dr;
+        if (!strncmp(str, "FR", 2))
+                return _edge_fr;
+        if (!strncmp(str, "FL", 2))
+                return _edge_fl;
+        if (!strncmp(str, "BL", 2))
+                return _edge_bl;
+        if (!strncmp(str, "BR", 2))
+                return _edge_br;
+
+        return _error;
+}
+
+static uint64_t
+readeo(char *str)
+{
+        if (*str == '0')
+                return 0ULL;
+        if (*str == '1')
+                return 1ULL;
+
+        return _error;
+}
+
+static uint64_t
+readcp(char *str)
+{
+        if (!strncmp(str, "UFR", 3) || !strncmp(str, "URF", 3))
+                return _corner_ufr;
+        if (!strncmp(str, "UFL", 3) || !strncmp(str, "ULF", 3))
+                return _corner_ufl;
+        if (!strncmp(str, "UBL", 3) || !strncmp(str, "ULB", 3))
+                return _corner_ubl;
+        if (!strncmp(str, "UBR", 3) || !strncmp(str, "URB", 3))
+                return _corner_ubr;
+        if (!strncmp(str, "DFR", 3) || !strncmp(str, "DRF", 3))
+                return _corner_dfr;
+        if (!strncmp(str, "DFL", 3) || !strncmp(str, "DLF", 3))
+                return _corner_dfl;
+        if (!strncmp(str, "DBL", 3) || !strncmp(str, "DLB", 3))
+                return _corner_dbl;
+        if (!strncmp(str, "DBR", 3) || !strncmp(str, "DRB", 3))
+                return _corner_dbr;
+
+        return _error;
+}
+
+static uint64_t
+readco(char *str)
+{
+        if (*str == '0')
+                return 0ULL;
+        if (*str == '1')
+                return 1ULL;
+        if (*str == '2')
+                return 2ULL;
+
+        return _error;
+}
+
+cube_t
+readcube(char *buf)
+{
+        int i;
+        uint64_t piece, orient;
+        cube_t ret = {0};
+        char *b = buf;
+
+        for (i = 0; i < 12; i++) {
+                while (*b == ' ' || *b == '\t' || *b == '\n')
+                        b++;
+                if ((piece = readep(b)) == _error)
+                        goto readcube_error;
+                b += 2;
+                if ((orient = readeo(b)) == _error)
+                        goto readcube_error;
+                b++;
+                ret.e |= (piece << ESHIFT(i)) | (orient << EOSHIFT(i));
+        }
+        for (i = 0; i < 8; i++) {
+                while (*b == ' ' || *b == '\t' || *b == '\n')
+                        b++;
+                if ((piece = readcp(b)) == _error)
+                        goto readcube_error;
+                b += 3;
+                if ((orient = readco(b)) == _error)
+                        goto readcube_error;
+                b++;
+                ret.c |= (piece << CSHIFT(i)) | (orient << COSHIFT(i));
+        }
+
+        return ret;
+
+readcube_error:
+        return errorcube;
+}
+
+void
+writecube(cube_t cube, char *buf)
+{
+        char *errormsg;
+        uint64_t piece;
+        size_t len;
+        int i;
+
+        if (!isconsistent(cube)) {
+                errormsg = "ERROR: cannot write inconsistent cube";
+                goto writecube_error;
+        }
+
+        for (i = 0; i < 12; i++) {
+                piece = EPAT(cube.e, i);
+                buf[4*i    ] = edgestr[piece][0];
+                buf[4*i + 1] = edgestr[piece][1];
+                buf[4*i + 2] = EOAT(cube.e, i) + '0';
+                buf[4*i + 3] = ' ';
+        }
+        for (i = 0; i < 8; i++) {
+                piece = CPAT(cube.c, i);
+                buf[48 + 5*i    ] = cornerstr[piece][0];
+                buf[48 + 5*i + 1] = cornerstr[piece][1];
+                buf[48 + 5*i + 2] = cornerstr[piece][2];
+                buf[48 + 5*i + 3] = COAT(cube.c, i) + '0';
+                buf[48 + 5*i + 4] = ' ';
+        }
+
+        buf[48+39] = '\0';
+
+        return;
+
+writecube_error:
+        len = strlen(errormsg);
+        strcpy(buf, errormsg);
+        buf[len] = '\n';
+        buf[len+1] = '\0';
+}
+
+
+static uint64_t
+readmove(char c)
+{
+        switch (c) {
+        case 'U':
+                return U;
+        case 'D':
+                return D;
+        case 'R':
+                return R;
+        case 'L':
+                return L;
+        case 'F':
+                return F;
+        case 'B':
+                return B;
+        default:
+                return _error;
+        }
+}
+
+static uint64_t
+readmodifier(char c)
+{
+        switch (c) {
+        case '1': /* Fallthrough */
+        case '2': /* Fallthrough */
+        case '3':
+                return c - '0' - 1;
+        case '\'':
+                return 2;
+        default:
+                return 0;
+        }
+}
+
+int
+readmoves(char *buf, move_t *m)
+{
+        int n;
+        uint64_t r;
+        char *b;
+
+        for (b = buf, n = 0; *b != '\0'; b++) {
+                while (*b == ' ' || *b == '\t' || *b == '\n')
+                        b++;
+                if ((r = readmove(*b)) == _error)
+                        return -1;
+                m[n] = (move_t)r;
+                if ((r = readmodifier(*(b+1))) != 0) {
+                        b++;
+                        m[n] += r;
+                }
+                n++;
+        }
+
+        return n;
+}
+
+void
+writemoves(move_t *m, int n, char *buf)
+{
+        int i;
+        char *b, *s;
+
+        for (i = 0, b = buf; i < n; i++, b++) {
+                s = movestr[m[i]];
+                strcpy(b, s);
+                b += strlen(s); 
+                *b = ' ';
+        }
+        *b = '\0';
+}
+
+
+cube_t
+move(move_t m, cube_t c)
+{
+        /* TODO - not implemented yet */
+
+        cube_t ret = {0};
+
+        switch (m) {
+        case U:
+                return ret;
+        default:
+                return ret;
+        }
+}