From 4d08bf731a099de2d174c73489636e1a12935aee Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Fri, 8 Sep 2023 18:28:30 +0200 Subject: New implementation, moved old to experiments/ --- src/array_cube.c | 712 ++++++++++++++++++++++++++++++++++++++++++++ src/cube.c | 888 ------------------------------------------------------- src/cube.h | 42 ++- 3 files changed, 746 insertions(+), 896 deletions(-) create mode 100644 src/array_cube.c delete mode 100644 src/cube.c (limited to 'src') diff --git a/src/array_cube.c b/src/array_cube.c new file mode 100644 index 0000000..3445658 --- /dev/null +++ b/src/array_cube.c @@ -0,0 +1,712 @@ +/* +In this implementation of the cube.h interface, the cube is represented +by two arrays of 8-bit unsigned integers, one for centers and one for +corners. The 4 leas-significant digits of each bit determine the piece, +the other 4 are used for orientation or kept to 0. + +Edges: + xxxopppp (x = unused, o = orientation, p = piece) + +Corners: + xooxpppp (x = unused, o = orientation, p = piece) + +The two bits for CO are shifted to make it possible to perform mod 3 +operations (sum, inverse) using only addition and bitwise operators. +See below for details. + +The third bit is needed because x+y+1 can exceed 4. +*/ + +#include +#include +#include + +#ifdef DEBUG +#include +#endif + +#include "cube.h" + +#define _c_ufr 0U +#define _c_ubl 1U +#define _c_dfl 2U +#define _c_dbr 3U +#define _c_ufl 4U +#define _c_ubr 5U +#define _c_dfr 6U +#define _c_dbl 7U + +#define _e_uf 0U +#define _e_ub 1U +#define _e_db 2U +#define _e_df 3U +#define _e_ur 4U +#define _e_ul 5U +#define _e_dl 6U +#define _e_dr 7U +#define _e_fr 8U +#define _e_fl 9U +#define _e_bl 10U +#define _e_br 11U + +#define _eoshift 4U +#define _coshift 5U + +#define _pbits 0xFU +#define _eobit 0x10U +#define _cobits 0xF0U +#define _cobits2 0x60U +#define _ctwist_cw 0x20U +#define _ctwist_ccw 0x40U +#define _eflip 0x10U +#define _error 0xFFU + +static char *cornerstr[] = { + [_c_ufr] = "UFR", + [_c_ubl] = "UBL", + [_c_dfl] = "DFL", + [_c_dbr] = "DBR", + [_c_ufl] = "UFL", + [_c_ubr] = "UBR", + [_c_dfr] = "DFR", + [_c_dbl] = "DBL" +}; + +static char *cornerstralt[] = { + [_c_ufr] = "URF", + [_c_ubl] = "ULB", + [_c_dfl] = "DLF", + [_c_dbr] = "DRB", + [_c_ufl] = "ULF", + [_c_ubr] = "URB", + [_c_dfr] = "DRF", + [_c_dbl] = "DLB" +}; + +static char *edgestr[] = { + [_e_uf] = "UF", + [_e_ub] = "UB", + [_e_db] = "DB", + [_e_df] = "DF", + [_e_ur] = "UR", + [_e_ul] = "UL", + [_e_dl] = "DL", + [_e_dr] = "DR", + [_e_fr] = "FR", + [_e_fl] = "FL", + [_e_bl] = "BL", + [_e_br] = "BR" +}; + +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 = { + .c = { + [_c_ufr] = _c_ufr, + [_c_ubl] = _c_ubl, + [_c_dfl] = _c_dfl, + [_c_dbr] = _c_dbr, + [_c_ufl] = _c_ufl, + [_c_ubr] = _c_ubr, + [_c_dfr] = _c_dfr, + [_c_dbl] = _c_dbl + }, + .e = { + [_e_uf] = _e_uf, + [_e_ub] = _e_ub, + [_e_db] = _e_db, + [_e_df] = _e_df, + [_e_ur] = _e_ur, + [_e_ul] = _e_ul, + [_e_dl] = _e_dl, + [_e_dr] = _e_dr, + [_e_fr] = _e_fr, + [_e_fl] = _e_fl, + [_e_bl] = _e_bl, + [_e_br] = _e_br + } +}; + +static cube_t errorcube = { .e = {0}, .c = {0} }; + +static uint8_t readco(char *); +static uint8_t readcp(char *); +static uint8_t readeo(char *); +static uint8_t readep(char *); +static uint8_t readmove(char); +static uint8_t readmodifier(char); +static int permsign(uint8_t *, int); +static cube_t compose(cube_t, cube_t); + +static uint8_t +readco(char *str) +{ + if (*str == '0') + return 0; + if (*str == '1') + return _ctwist_cw; + if (*str == '2') + return _ctwist_ccw; + +#ifdef DEBUG + fprintf(stderr, "Error reading CO\n"); +#endif + return _error; +} + +static uint8_t +readcp(char *str) +{ + uint8_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 uint8_t +readeo(char *str) +{ + if (*str == '0') + return 0; + if (*str == '1') + return _eflip; + +#ifdef DEBUG + fprintf(stderr, "Error reading EO\n"); +#endif + return _error; +} + +static uint8_t +readep(char *str) +{ + uint8_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; +} + +cube_t +readcube(char *buf) +{ + int i; + uint8_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[i] = piece | orient; + } + 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[i] = piece | orient; + } + + return ret; + +readcube_error: +#ifdef DEBUG + fprintf(stderr, "readcube error\n"); +#endif + return errorcube; +} + +void +writecube(cube_t cube, char *buf) +{ + char *errormsg; + uint8_t piece, orient; + size_t len; + int i; + + if (!isconsistent(cube)) { + errormsg = "ERROR: cannot write inconsistent cube"; + goto writecube_error; + } + + for (i = 0; i < 12; i++) { + piece = cube.e[i] & _pbits; + orient = (cube.e[i] & _eobit) >> _eoshift; + buf[4*i ] = edgestr[piece][0]; + buf[4*i + 1] = edgestr[piece][1]; + buf[4*i + 2] = orient + '0'; + buf[4*i + 3] = ' '; + } + for (i = 0; i < 8; i++) { + piece = cube.c[i] & _pbits; + orient = (cube.c[i] & _cobits) >> _coshift; + 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] = orient + '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 uint8_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 uint8_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 int +permsign(uint8_t *a, int n) +{ + int i, j; + uint8_t ret = 0; + + for (i = 0; i < n; i++) + for (j = i+1; j < n; j++) + ret += (a[i] & _pbits) > (a[j] & _pbits) ? 1 : 0; + + return ret % 2; +} + +bool +isconsistent(cube_t cube) +{ + int8_t p, psum, eosum, co, cosum; + bool found[12]; + int i; + + psum = 0; + for (i = 0; i < 12; i++) + found[i] = false; + for (i = 0; i < 12; i++) { + p = cube.e[i] & _pbits; + if (p >= 12) + goto inconsistent_ep; + found[p] = true; + } + for (i = 0; i < 12; i++) + if (!found[i]) + goto inconsistent_ep; + psum = permsign(cube.e, 12); + + for (i = 0; i < 8; i++) + found[i] = false; + for (i = 0; i < 8; i++) { + p = cube.c[i] & _pbits; + if (p >= 8) + goto inconsistent_cp; + found[p] = true; + } + for (i = 0; i < 8; i++) + if (!found[i]) + goto inconsistent_cp; + psum += permsign(cube.c, 8); + + if (psum % 2 != 0) + goto inconsistent_parity; + + eosum = 0; + for (i = 0; i < 12; i++) + eosum += (cube.e[i] & _eobit) >> _eoshift; + if (eosum % 2 != 0) + goto inconsistent_eo; + + cosum = 0; + for (i = 0; i < 8; i++) { + co = (cube.c[i] & _cobits) >> _coshift; + if (co > 2) + goto inconsistent_co; + cosum += co; + } + if (cosum % 3 != 0) + goto inconsistent_co; + + 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_co: +#ifdef DEBUG + fprintf(stderr, "Inconsistent CO\n"); +#endif + goto inconsistent_return; +inconsistent_return: + return false; +} + +bool +equal(cube_t cube1, cube_t cube2) +{ + uint8_t i; + + for (i = 0; i < 12; i++) + if (cube1.e[i] != cube2.e[i]) + return false; + + for (i = 0; i < 8; i++) + if (cube1.c[i] != cube2.c[i]) + return false; + + return true; +} + +bool +issolved(cube_t cube) +{ + return equal(cube, solvedcube); +} + +bool +iserror(cube_t cube) +{ + return equal(cube, errorcube); +} + +cube_t +move(cube_t c, move_t m) +{ + cube_t ret; + uint8_t aux, auy, auz; + +#ifdef DEBUG + if (!isconsistent(c)) + goto move_inconsistent; +#endif + +#define PERM4(r, i, j, k, l) \ + aux = r[i]; \ + r[i] = r[l]; \ + r[l] = r[k]; \ + r[k] = r[j]; \ + r[j] = aux; +#define PERM22(r, i, j, k, l) \ + aux = r[i]; \ + r[i] = r[j]; \ + r[j] = aux; \ + aux = r[k]; \ + r[k] = r[l]; \ + r[l] = aux; +#define CO(a, b) \ + aux = (a & _cobits) + (b & _cobits); \ + auy = (aux + _ctwist_cw) >> 2U; \ + auz = (aux + auy) & _cobits2; \ + a = (a & _pbits) | auz; +#define CO4(r, i, j, k, l) \ + CO(r[i], _ctwist_cw) \ + CO(r[j], _ctwist_cw) \ + CO(r[k], _ctwist_ccw) \ + CO(r[l], _ctwist_ccw) +#define EO4(r, i, j, k, l) \ + r[i] ^= _eobit; \ + r[j] ^= _eobit; \ + r[k] ^= _eobit; \ + r[l] ^= _eobit; + + ret = c; + + switch (m) { + case U: + PERM4(ret.e, _e_uf, _e_ul, _e_ub, _e_ur) + PERM4(ret.c, _c_ufr, _c_ufl, _c_ubl, _c_ubr) + + return ret; + case U2: + PERM22(ret.e, _e_uf, _e_ub, _e_ul, _e_ur) + PERM22(ret.c, _c_ufr, _c_ubl, _c_ufl, _c_ubr) + + return ret; + case U3: + PERM4(ret.e, _e_uf, _e_ur, _e_ub, _e_ul) + PERM4(ret.c, _c_ufr, _c_ubr, _c_ubl, _c_ufl) + + return ret; + case D: + PERM4(ret.e, _e_df, _e_dr, _e_db, _e_dl) + PERM4(ret.c, _c_dfr, _c_dbr, _c_dbl, _c_dfl) + + return ret; + case D2: + PERM22(ret.e, _e_df, _e_db, _e_dr, _e_dl) + PERM22(ret.c, _c_dfr, _c_dbl, _c_dbr, _c_dfl) + + return ret; + case D3: + PERM4(ret.e, _e_df, _e_dl, _e_db, _e_dr) + PERM4(ret.c, _c_dfr, _c_dfl, _c_dbl, _c_dbr) + + return ret; + case R: + PERM4(ret.e, _e_ur, _e_br, _e_dr, _e_fr) + PERM4(ret.c, _c_ufr, _c_ubr, _c_dbr, _c_dfr) + + CO4(ret.c, _c_ubr, _c_dfr, _c_ufr, _c_dbr) + + return ret; + case R2: + PERM22(ret.e, _e_ur, _e_dr, _e_fr, _e_br) + PERM22(ret.c, _c_ufr, _c_dbr, _c_ubr, _c_dfr) + + return ret; + case R3: + PERM4(ret.e, _e_ur, _e_fr, _e_dr, _e_br) + PERM4(ret.c, _c_ufr, _c_dfr, _c_dbr, _c_ubr) + + CO4(ret.c, _c_ubr, _c_dfr, _c_ufr, _c_dbr) + + return ret; + case L: + PERM4(ret.e, _e_ul, _e_fl, _e_dl, _e_bl) + PERM4(ret.c, _c_ufl, _c_dfl, _c_dbl, _c_ubl) + + CO4(ret.c, _c_ufl, _c_dbl, _c_dfl, _c_ubl) + + return ret; + case L2: + PERM22(ret.e, _e_ul, _e_dl, _e_fl, _e_bl) + PERM22(ret.c, _c_ufl, _c_dbl, _c_ubl, _c_dfl) + + return ret; + case L3: + PERM4(ret.e, _e_ul, _e_bl, _e_dl, _e_fl) + PERM4(ret.c, _c_ufl, _c_ubl, _c_dbl, _c_dfl) + + CO4(ret.c, _c_ufl, _c_dbl, _c_dfl, _c_ubl) + + return ret; + case F: + PERM4(ret.e, _e_uf, _e_fr, _e_df, _e_fl) + PERM4(ret.c, _c_ufr, _c_dfr, _c_dfl, _c_ufl) + + EO4(ret.e, _e_uf, _e_fr, _e_df, _e_fl) + CO4(ret.c, _c_ufr, _c_dfl, _c_dfr, _c_ufl) + + return ret; + case F2: + PERM22(ret.e, _e_uf, _e_df, _e_fr, _e_fl) + PERM22(ret.c, _c_ufr, _c_dfl, _c_ufl, _c_dfr) + + return ret; + case F3: + PERM4(ret.e, _e_uf, _e_fl, _e_df, _e_fr) + PERM4(ret.c, _c_ufr, _c_ufl, _c_dfl, _c_dfr) + + EO4(ret.e, _e_uf, _e_fr, _e_df, _e_fl) + CO4(ret.c, _c_ufr, _c_dfl, _c_dfr, _c_ufl) + + return ret; + case B: + PERM4(ret.e, _e_ub, _e_bl, _e_db, _e_br) + PERM4(ret.c, _c_ubr, _c_ubl, _c_dbl, _c_dbr) + + EO4(ret.e, _e_ub, _e_br, _e_db, _e_bl) + CO4(ret.c, _c_ubl, _c_dbr, _c_dbl, _c_ubr) + + return ret; + case B2: + PERM22(ret.e, _e_ub, _e_db, _e_br, _e_bl) + PERM22(ret.c, _c_ubr, _c_dbl, _c_ubl, _c_dbr) + + return ret; + case B3: + PERM4(ret.e, _e_ub, _e_br, _e_db, _e_bl) + PERM4(ret.c, _c_ubr, _c_dbr, _c_dbl, _c_ubl) + + EO4(ret.e, _e_ub, _e_br, _e_db, _e_bl) + CO4(ret.c, _c_ubl, _c_dbr, _c_dbl, _c_ubr) + + return ret; + default: + goto move_unknown; + } + +move_inconsistent: + fprintf(stderr, "move error, inconsistent cube\n"); + goto move_error; +move_unknown: + fprintf(stderr, "mover error, unknown move\n"); + goto move_error; +move_error: + return errorcube; +} + +cube_t +inverse(cube_t c) +{ + uint8_t i, piece, orien; + cube_t ret = {0}; + +#ifdef DEBUG + if (!isconsistent(c)) + goto inverse_inconsistent; +#endif + + for (i = 0; i < 12; i++) { + piece = c.e[i & _pbits]; + orien = piece & _eobit; + ret.e[piece & _pbits] = i | orien; + } + + for (i = 0; i < 8; i++) { + piece = c.c[i & _pbits]; + orien = ((piece << 1) | (piece >> 1)) & _cobits2; + ret.c[piece & _pbits] = i | orien; + } + + return ret; + +inverse_inconsistent: + fprintf(stderr, "inverse error, inconsistent cube\n"); + return errorcube; +} diff --git a/src/cube.c b/src/cube.c deleted file mode 100644 index 4372b5e..0000000 --- a/src/cube.c +++ /dev/null @@ -1,888 +0,0 @@ -/* -# 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 . - -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 -#include -#include - -#ifdef DEBUG -#include -#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; -} diff --git a/src/cube.h b/src/cube.h index b916f96..836bb5d 100644 --- a/src/cube.h +++ b/src/cube.h @@ -3,25 +3,51 @@ typedef enum { R, R2, R3, L, L2, L3, F, F2, F3, B, B2, B3 } move_t; + typedef struct { - uint64_t e; - uint64_t c; + uint8_t c[8]; + uint8_t e[12]; } cube_t; extern cube_t solvedcube; -extern cube_t errorcube; -bool isconsistent(cube_t); -bool issolved(cube_t); +/* +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 pieces are ordered such that 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 + +Whitespace (including newlines) between pieces is ignored when reading +the cube, and a single whitespace character is added between pieces +when writing. + +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. +*/ cube_t readcube(char *); void writecube(cube_t, char *); +bool isconsistent(cube_t); +bool equal(cube_t, cube_t); +bool issolved(cube_t); +bool iserror(cube_t); + int readmoves(char *, move_t *); void writemoves(move_t *, int, char *); cube_t move(cube_t, move_t); - -/* cube_t inverse(cube_t); -*/ -- cgit v1.3