New implementation, moved old to experiments/

1 files changed, 888 insertions, 0 deletions

diff --git a/experiments/cube.c b/experiments/cube.c
new file mode 100644
index 0000000..4372b5e
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+++ b/experiments/cube.c
@@ -0,0 +1,888 @@
+/*
+# Cube representation, moves, transformations and (tentatively) indexing
+
+## Textual 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 \ (no newline)
+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 \ (no newline)
+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.
+
+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.  We can
+apply this operation to multiple pairs of bits representing ternary
+digits at once using binary operations.  See the function coapply()
+below for the details.
+
+## Inverting the cube
+
+TODO
+
+## Transformations (conjugations by full-cube rotations)
+
+TODO
+
+## Indexing (tentative)
+
+TODO - subgroup description etc
+
+*/
+
+#include <stdbool.h>
+#include <stdint.h>
+#include <string.h>
+
+#ifdef DEBUG
+#include <stdio.h>
+#endif
+
+#include "cube.h"
+
+#define _error         0xFFFFFFFF
+
+#define _eoblock       0x10ULL    /* 10000 */
+#define _epblock       0x0FULL    /* 01111 */
+#define _eblock        0x1FULL    /* 11111 */
+#define _eblock2       0x3FFULL   /* 1111111111 */
+
+#define _coblock       0x18ULL    /* 011000 */
+#define _cpblock       0x07ULL    /* 000111 */
+#define _cblock        0x3FULL    /* 111111 */
+#define _cblock2       0xFFFULL   /* 111111111111 */
+
+#define _eomask        0x842108421084210ULL /* 10000 repeated 12 times */
+#define _comask        0x618618618618ULL    /* 011000 repeated 8 times */
+#define _coonemask     0x208208208208ULL    /* 001000 repeated 8 times */
+#define _coextramask   0x820820820820ULL    /* 100000 repeated 8 times */
+
+#define _emask_u (_eblock2 | _eblock2 << 20ULL)
+#define _emask_d (_eblock2 << 10ULL | _eblock2 << 30ULL)
+#define _emask_r (_eblock << 20ULL | _eblock2 << 35ULL | _eblock << 55ULL)
+#define _emask_l (_eblock2 << 45ULL | _eblock2 << 25ULL)
+#define _emask_f (_eblock | _eblock << 15ULL | _eblock2 << 40ULL)
+#define _emask_b (_eblock2 << 5ULL | _eblock2 << 50ULL)
+
+#define _cmask_u (_cblock2 | _cblock2 << 24ULL)
+#define _cmask_d (_cblock2 << 12ULL | _cblock2 << 36ULL)
+#define _cmask_r (_cblock | _cblock << 18ULL | _cblock2 << 30ULL)
+#define _cmask_l (_cblock2 << 6ULL | _cblock << 24ULL | _cblock << 42ULL)
+#define _cmask_f (_cblock | _cblock << 12ULL | _cblock << 24ULL | _cblock << 36ULL)
+#define _cmask_b (_cblock << 6ULL | _cblock << 18ULL | _cblock << 30ULL | _cblock << 42ULL)
+
+#define _eomask_f (1ULL << 4ULL | 1ULL << 19ULL | 1ULL << 44ULL | 1ULL << 49ULL)
+#define _eomask_b (1ULL << 9ULL | 1ULL << 14ULL | 1ULL << 54ULL | 1ULL << 59ULL)
+
+#define _comask_r (2ULL << 3ULL | 1ULL << 33ULL | 2ULL << 21ULL | 1ULL << 39ULL)
+#define _comask_l (1ULL << 27ULL | 2ULL << 9ULL | 2ULL << 15ULL | 1ULL << 45ULL)
+#define _comask_f (1ULL << 3ULL | 1ULL << 15ULL | 2ULL << 27ULL | 2ULL << 39ULL)
+#define _comask_b (1ULL << 9ULL | 1ULL << 21ULL | 2ULL << 33ULL | 2ULL << 45ULL)
+
+static inline uint64_t coapply(uint64_t, uint64_t);
+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[] = {
+        "UF", "UB", "DB", "DF",
+        "UR", "UL", "DL", "DR",
+        "FR", "FL", "BL", "BR"
+};
+static char *cornerstr[] = {
+        "UFR", "UBL", "DFL", "DBR",
+        "UFL", "UBR", "DFR", "DBL"
+};
+static char *cornerstralt[] = {
+        "URF", "ULB", "DLF", "DRB",
+        "ULF", "URB", "DRF", "DLB"
+};
+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 = 0x5A928398A418820ULL, .c = 0x1C61440C2040ULL };
+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 x, p[12], sum, co;
+        bool found[12];
+        int i;
+
+        sum = 0;
+
+        /* Check for EP consistency */
+        for (i = 0; i < 12; i++)
+                found[i] = false;
+        for (i = 0, x = cube.e; i < 12; i++, x >>= 5ULL) {
+                p[i] = x & _epblock;
+                if (p[i] >= 12)
+                        goto inconsistent_ep;
+                found[p[i]] = true;
+        }
+        for (i = 0; i < 12; i++)
+                if (!found[i])
+                        goto inconsistent_ep;
+        sum = permsign(p, 12);
+
+        /* Check for CP consistency */
+        for (i = 0; i < 8; i++)
+                found[i] = false;
+        for (i = 0, x = cube.c; i < 8; i++, x >>= 6ULL) {
+                p[i] = x & _cpblock;
+                if (p[i] >= 8)
+                        goto inconsistent_cp;
+                found[p[i]] = true;
+        }
+        for (i = 0; i < 8; i++)
+                if (!found[i])
+                        goto inconsistent_cp;
+        sum += permsign(p, 8);
+
+        /* Check permutation parity */
+        if (sum % 2 != 0)
+                goto inconsistent_parity;
+
+        /* Check for EO parity */
+        for (i = 0, sum = 0, x = cube.e; i < 12; i++, x >>= 5ULL)
+                sum += (x & _eoblock) >> 4ULL;
+        if (sum % 2 != 0)
+                goto inconsistent_eo;
+
+        /* Check for CO parity */
+        for (i = 0, sum = 0, x = cube.c; i < 8; i++, x >>= 6ULL) {
+                co = (x & _coblock) >> 3ULL;
+                if (co > 2)
+                        goto inconsistent_co3;
+                sum += co;
+        }
+        if (sum % 3 != 0)
+                goto inconsistent_co;
+
+        /* Check that CO extra bit is zero */
+        if (cube.c & _coextramask)
+                goto inconsistent_coextra;
+
+        return true;
+
+inconsistent_ep:
+#ifdef DEBUG
+        fprintf(stderr, "Inconsistent EP\n");
+#endif
+        goto inconsistent_return;
+inconsistent_cp:
+#ifdef DEBUG
+        fprintf(stderr, "Inconsistent CP\n");
+#endif
+        goto inconsistent_return;
+inconsistent_parity:
+#ifdef DEBUG
+        fprintf(stderr, "Inconsistent parity\n");
+#endif
+        goto inconsistent_return;
+inconsistent_eo:
+#ifdef DEBUG
+        fprintf(stderr, "Inconsistent EO\n");
+#endif
+        goto inconsistent_return;
+inconsistent_co3:
+#ifdef DEBUG
+        fprintf(stderr, "Inconsistent CO=3\n");
+#endif
+        goto inconsistent_return;
+inconsistent_co:
+#ifdef DEBUG
+        fprintf(stderr, "Inconsistent CO\n");
+#endif
+        goto inconsistent_return;
+inconsistent_coextra:
+#ifdef DEBUG
+        fprintf(stderr, "Inconsistent extra bit for CO\n");
+#endif
+        goto inconsistent_return;
+inconsistent_return:
+        return false;
+}
+
+bool
+issolved(cube_t cube)
+{
+        return cube.c == solvedcube.c && cube.e == solvedcube.e;
+}
+
+
+static uint64_t
+readep(char *str)
+{
+        uint64_t e;
+
+        for (e = 0; e < 12; e++)
+                if (!strncmp(str, edgestr[e], 2))
+                        return e;
+
+#ifdef DEBUG
+        fprintf(stderr, "Error reading EP\n");
+#endif
+        return _error;
+}
+
+static uint64_t
+readeo(char *str)
+{
+        if (*str == '0')
+                return 0ULL;
+        if (*str == '1')
+                return 1ULL;
+
+#ifdef DEBUG
+        fprintf(stderr, "Error reading EO\n");
+#endif
+        return _error;
+}
+
+static uint64_t
+readcp(char *str)
+{
+        uint64_t c;
+
+        for (c = 0; c < 8; c++)
+                if (!strncmp(str, cornerstr[c], 3) ||
+                    !strncmp(str, cornerstralt[c], 3))
+                        return c;
+
+#ifdef DEBUG
+        fprintf(stderr, "Error reading CP\n");
+#endif
+        return _error;
+}
+
+static uint64_t
+readco(char *str)
+{
+        if (*str == '0')
+                return 0ULL;
+        if (*str == '1')
+                return 1ULL;
+        if (*str == '2')
+                return 2ULL;
+
+#ifdef DEBUG
+        fprintf(stderr, "Error reading CO\n");
+#endif
+        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 << (i * 5ULL)) | (orient << (i * 5ULL + 4ULL));
+        }
+        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 << (i * 6ULL)) | (orient << (i * 6ULL + 3ULL));
+        }
+
+        return ret;
+
+readcube_error:
+#ifdef DEBUG
+        fprintf(stderr, "readcube error\n");
+#endif
+        return errorcube;
+}
+
+void
+writecube(cube_t cube, char *buf)
+{
+        char *errormsg;
+        uint64_t piece, orien, x;
+        size_t len;
+        int i;
+
+        if (!isconsistent(cube)) {
+                errormsg = "ERROR: cannot write inconsistent cube";
+                goto writecube_error;
+        }
+
+        for (i = 0, x = cube.e; i < 12; i++, x >>= 5ULL) {
+                piece = x & _epblock;
+                orien = (x & _eoblock) >> 4ULL;
+                buf[4*i    ] = edgestr[piece][0];
+                buf[4*i + 1] = edgestr[piece][1];
+                buf[4*i + 2] = orien + '0';
+                buf[4*i + 3] = ' ';
+        }
+        for (i = 0, x = cube.c; i < 8; i++, x >>= 6ULL) {
+                piece = x & _cpblock;
+                orien = (x & _coblock) >> 3ULL;
+                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] = orien + '0';
+                buf[48 + 5*i + 4] = ' ';
+        }
+
+        buf[48+39] = '\0';
+
+        return;
+
+writecube_error:
+#ifdef DEBUG
+        fprintf(stderr, "writecube error, see stdout for details\n");
+#endif
+        len = strlen(errormsg);
+        memcpy(buf, errormsg, len);
+        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 (*b == '\0')
+                        return n;
+                if ((r = readmove(*b)) == _error)
+                        goto readmoves_error;
+                m[n] = (move_t)r;
+                if ((r = readmodifier(*(b+1))) != 0) {
+                        b++;
+                        m[n] += r;
+                }
+                n++;
+        }
+
+        return n;
+
+readmoves_error:
+#ifdef DEBUG
+        fprintf(stderr, "readmoves error\n");
+#endif
+        return -1;
+}
+
+void
+writemoves(move_t *m, int n, char *buf)
+{
+        int i;
+        size_t len;
+        char *b, *s;
+
+        for (i = 0, b = buf; i < n; i++, b++) {
+                s = movestr[m[i]];
+                len = strlen(s);
+                memcpy(b, s, len);
+                b += len;       
+                *b = ' ';
+        }
+        *b = '\0';
+}
+
+
+static inline uint64_t
+coapply(uint64_t c, uint64_t m)
+{
+        uint64_t z, b;
+
+        z = c + m;
+        b = ((z + _coonemask) & _coextramask) >> 2ULL;
+
+        return (z + b) & ~_coextramask;
+}
+
+cube_t
+move(cube_t c, move_t m)
+{
+        cube_t ret = {0};
+
+#ifdef DEBUG
+        if (!isconsistent(c)) {
+                fprintf(stderr, "move error, inconsistent cube\n");
+                goto move_error;
+        }
+#endif
+
+        switch (m) {
+        case U:
+                ret.e = c.e & ~_emask_u;
+                ret.e |=
+                    (c.e & _eblock) << 25ULL |
+                    (c.e & _eblock << 5ULL) << 15ULL |
+                    (c.e & _eblock2 << 20ULL) >> 20ULL;
+
+                ret.c = c.c & ~_cmask_u;
+                ret.c |=
+                    (c.c & _cblock2) << 24ULL |
+                    (c.c & _cblock << 24ULL) >> 18ULL |
+                    (c.c & _cblock << 30ULL) >> 30ULL;
+
+                return ret;
+        case U2:
+                ret.e = c.e & ~_emask_u;
+                ret.e |=
+                    (c.e & (_eblock | _eblock << 20ULL)) << 5ULL |
+                    (c.e & (_eblock << 5ULL | _eblock << 25ULL)) >> 5ULL;
+
+                ret.c = c.c & ~_cmask_u;
+                ret.c |=
+                    (c.c & (_cblock | _cblock << 24ULL)) << 6ULL |
+                    (c.c & (_cblock << 6ULL | _cblock << 30ULL)) >> 6ULL;
+
+                return ret;
+        case U3:
+                ret.e = c.e & ~_emask_u;
+                ret.e |=
+                    (c.e & _eblock2) << 20ULL |
+                    (c.e & _eblock << 25ULL) >> 25ULL |
+                    (c.e & _eblock << 20ULL) >> 15ULL;
+
+                ret.c = c.c & ~_cmask_u;
+                ret.c |=
+                    (c.c & _cblock) << 30ULL |
+                    (c.c & _cblock << 6ULL) << 18ULL |
+                    (c.c & _cblock2 << 24ULL) >> 24ULL;
+
+                return ret;
+        case D:
+                ret.e = c.e & ~_emask_d;
+                ret.e |=
+                    (c.e & _eblock2 << 10ULL) << 20ULL |
+                    (c.e & _eblock << 30ULL) >> 15ULL |
+                    (c.e & _eblock << 35ULL) >> 25ULL;
+
+                ret.c = c.c & ~_cmask_d;
+                ret.c |=
+                    (c.c & _cblock2 << 12ULL) << 24ULL |
+                    (c.c & _cblock << 36ULL) >> 18ULL |
+                    (c.c & _cblock << 42ULL) >> 30ULL;
+
+                return ret;
+        case D2:
+                ret.e = c.e & ~_emask_d;
+                ret.e |=
+                    (c.e & (_eblock << 10ULL | _eblock << 30ULL)) << 5ULL |
+                    (c.e & (_eblock << 15ULL | _eblock << 35ULL)) >> 5ULL;
+
+                ret.c = c.c & ~_cmask_d;
+                ret.c |=
+                    (c.c & (_cblock << 12ULL | _cblock << 36ULL)) << 6ULL |
+                    (c.c & (_cblock << 18ULL | _cblock << 42ULL)) >> 6ULL;
+
+                return ret;
+        case D3:
+                ret.e = c.e & ~_emask_d;
+                ret.e |=
+                    (c.e & _eblock << 10ULL) << 25ULL |
+                    (c.e & _eblock << 15ULL) << 15ULL |
+                    (c.e & _eblock2 << 30ULL) >> 20ULL;
+
+                ret.c = c.c & ~_cmask_d;
+                ret.c |=
+                    (c.c & _cblock << 12ULL) << 30ULL |
+                    (c.c & _cblock << 18ULL) << 18ULL |
+                    (c.c & _cblock2 << 36ULL) >> 24ULL;
+
+                return ret;
+        case R:
+                ret.e = c.e & ~_emask_r;
+                ret.e |=
+                    (c.e & _eblock << 20ULL) << 35ULL |
+                    (c.e & _eblock << 55ULL) >> 20ULL |
+                    (c.e & _eblock << 35ULL) << 5ULL |
+                    (c.e & _eblock << 40ULL) >> 20ULL;
+
+                ret.c = c.c & ~_cmask_r;
+                ret.c |=
+                    (c.c & _cblock) << 30ULL |
+                    (c.c & _cblock << 30ULL) >> 12ULL |
+                    (c.c & _cblock << 18ULL) << 18ULL |
+                    (c.c & _cblock << 36ULL) >> 36ULL;
+
+                ret.c = coapply(ret.c, _comask_r);
+
+                return ret;
+        case R2:
+                ret.e = c.e & ~_emask_r;
+                ret.e |=
+                    (c.e & (_eblock << 20ULL | _eblock << 40ULL)) << 15ULL |
+                    (c.e & (_eblock << 35ULL | _eblock << 55ULL)) >> 15ULL;
+
+                ret.c = c.c & ~_cmask_r;
+                ret.c |=
+                    (c.c & _cblock) << 18ULL |
+                    (c.c & _cblock << 18ULL) >> 18ULL |
+                    (c.c & _cblock << 30ULL) << 6ULL |
+                    (c.c & _cblock << 36ULL) >> 6ULL;
+
+                return ret;
+        case R3:
+                ret.e = c.e & ~_emask_r;
+                ret.e |=
+                    (c.e & (_eblock << 20ULL | _eblock << 35ULL)) << 20ULL |
+                    (c.e & _eblock << 55ULL) >> 35ULL |
+                    (c.e & _eblock << 40ULL) >> 5ULL;
+
+                ret.c = c.c & ~_cmask_r;
+                ret.c |=
+                    (c.c & _cblock) << 36ULL |
+                    (c.c & _cblock << 30ULL) >> 30ULL |
+                    (c.c & _cblock << 18ULL) << 12ULL |
+                    (c.c & _cblock << 36ULL) >> 18ULL;
+
+                ret.c = coapply(ret.c, _comask_r);
+
+                return ret;
+        case L:
+                ret.e = c.e & ~_emask_l;
+                ret.e |=
+                    (c.e & _eblock2 << 25ULL) << 20ULL |
+                    (c.e & _eblock << 45ULL) >> 15ULL |
+                    (c.e & _eblock << 50ULL) >> 25ULL;
+
+                ret.c = c.c & ~_cmask_l;
+                ret.c |=
+                    (c.c & _cblock << 6ULL) << 18ULL |
+                    (c.c & _cblock << 12ULL) << 30ULL |
+                    (c.c & _cblock << 24ULL) >> 12ULL |
+                    (c.c & _cblock << 42ULL) >> 36ULL;
+
+                ret.c = coapply(ret.c, _comask_l);
+
+                return ret;
+        case L2:
+                ret.e = c.e & ~_emask_l;
+                ret.e |=
+                    (c.e & (_eblock << 25ULL | _eblock << 45ULL)) << 5ULL |
+                    (c.e & (_eblock << 30ULL | _eblock << 50ULL)) >> 5ULL;
+
+                ret.c = c.c & ~_cmask_l;
+                ret.c |=
+                    (c.c & _cblock << 6ULL) << 6ULL |
+                    (c.c & _cblock << 12ULL) >> 6ULL |
+                    (c.c & _cblock << 24ULL) << 18ULL |
+                    (c.c & _cblock << 42ULL) >> 18ULL;
+
+                return ret;
+        case L3:
+                ret.e = c.e & ~_emask_l;
+                ret.e |=
+                    (c.e & _eblock << 25ULL) << 25ULL |
+                    (c.e & _eblock << 30ULL) << 15ULL |
+                    (c.e & _eblock2 << 45ULL) >> 20ULL;
+
+                ret.c = c.c & ~_cmask_l;
+                ret.c |=
+                    (c.c & _cblock << 6ULL) << 36ULL |
+                    (c.c & _cblock << 12ULL) << 12ULL |
+                    (c.c & _cblock << 24ULL) >> 18ULL |
+                    (c.c & _cblock << 42ULL) >> 30ULL;
+
+                ret.c = coapply(ret.c, _comask_l);
+
+                return ret;
+        case F:
+                ret.e = c.e & ~_emask_f;
+                ret.e |=
+                    (c.e & _eblock) << 40ULL |
+                    (c.e & _eblock << 15ULL) << 30ULL |
+                    (c.e & _eblock << 40ULL) >> 25ULL |
+                    (c.e & _eblock << 45ULL) >> 45ULL;
+
+                ret.e ^= _eomask_f;
+
+                ret.c = c.c & ~_cmask_f;
+                ret.c |=
+                    (c.c & _cblock) << 36ULL |
+                    (c.c & (_cblock << 24ULL | _cblock << 36ULL)) >> 24ULL |
+                    (c.c & _cblock << 12ULL) << 12ULL;
+
+                ret.c = coapply(ret.c, _comask_f);
+                
+                return ret;
+        case F2:
+                ret.e = c.e & ~_emask_f;
+                ret.e |=
+                    (c.e & _eblock) << 15ULL |
+                    (c.e & _eblock << 15ULL) >> 15ULL |
+                    (c.e & _eblock << 40ULL) << 5ULL |
+                    (c.e & _eblock << 45ULL) >> 5ULL;
+
+                ret.c = c.c & ~_cmask_f;
+                ret.c |=
+                    (c.c & (_cblock | _cblock << 24ULL)) << 12ULL |
+                    (c.c & (_cblock << 12ULL | _cblock << 36ULL)) >> 12ULL;
+
+                return ret;
+        case F3:
+                ret.e = c.e & ~_emask_f;
+                ret.e |=
+                    (c.e & _eblock) << 45ULL |
+                    (c.e & _eblock << 15ULL) << 25ULL |
+                    (c.e & _eblock << 40ULL) >> 40ULL |
+                    (c.e & _eblock << 45ULL) >> 30ULL;
+
+                ret.e ^= _eomask_f;
+
+                ret.c = c.c & ~_cmask_f;
+                ret.c |=
+                    (c.c & (_cblock | _cblock << 12ULL)) << 24ULL |
+                    (c.c & _cblock << 24ULL) >> 12ULL |
+                    (c.c & _cblock << 36ULL) >> 36ULL;
+
+                ret.c = coapply(ret.c, _comask_f);
+                
+                return ret;
+        case B:
+                ret.e = c.e & ~_emask_b;
+                ret.e |=
+                    (c.e & _eblock2 << 5ULL) << 45ULL |
+                    (c.e & _eblock << 50ULL) >> 40ULL |
+                    (c.e & _eblock << 55ULL) >> 50ULL;
+
+                ret.e ^= _eomask_b;
+
+                ret.c = c.c & ~_cmask_b;
+                ret.c |=
+                    (c.c & _cblock << 6ULL) << 36ULL |
+                    (c.c & _cblock << 18ULL) << 12ULL |
+                    (c.c & (_cblock << 30ULL | _cblock << 42ULL)) >> 24ULL;
+
+                ret.c = coapply(ret.c, _comask_b);
+
+                return ret;
+        case B2:
+                ret.e = c.e & ~_emask_b;
+                ret.e |=
+                    (c.e & (_eblock << 5ULL | _eblock << 50ULL)) << 5ULL |
+                    (c.e & (_eblock << 10ULL | _eblock << 55ULL)) >> 5ULL;
+
+                ret.c = c.c & ~_cmask_b;
+                ret.c |=
+                    (c.c & (_cblock << 6ULL | _cblock << 30ULL)) << 12ULL |
+                    (c.c & (_cblock << 18ULL | _cblock << 42ULL)) >> 12ULL;
+
+                return ret;
+        case B3:
+                ret.e = c.e & ~_emask_b;
+                ret.e |=
+                    (c.e & _eblock << 5ULL) << 50ULL |
+                    (c.e & _eblock << 10ULL) << 40ULL |
+                    (c.e & _eblock2 << 50ULL) >> 45ULL;
+
+                ret.e ^= _eomask_b;
+
+                ret.c = c.c & ~_cmask_b;
+                ret.c |=
+                    (c.c & (_cblock << 6ULL | _cblock << 18ULL)) << 24ULL |
+                    (c.c & _cblock << 30ULL) >> 12ULL |
+                    (c.c & _cblock << 42ULL) >> 36ULL;
+
+                ret.c = coapply(ret.c, _comask_b);
+
+                return ret;
+        default:
+                goto move_unknown;
+        }
+
+move_unknown:
+#ifdef DEBUG
+        fprintf(stderr, "move error, unknow move\n");
+#endif
+        goto move_error;
+move_error:
+        return errorcube;
+}