From f987f5af492f2ac9d5aeebd351bcb49175556af2 Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Mon, 29 May 2023 01:06:09 +0200 Subject: Initial commit --- src/cube.sync-conflict-20230524-182143-JOKKFPA.c | 614 +++++++++++++++++++++++ 1 file changed, 614 insertions(+) create mode 100644 src/cube.sync-conflict-20230524-182143-JOKKFPA.c (limited to 'src/cube.sync-conflict-20230524-182143-JOKKFPA.c') diff --git a/src/cube.sync-conflict-20230524-182143-JOKKFPA.c b/src/cube.sync-conflict-20230524-182143-JOKKFPA.c new file mode 100644 index 0000000..e64acca --- /dev/null +++ b/src/cube.sync-conflict-20230524-182143-JOKKFPA.c @@ -0,0 +1,614 @@ +/* +# 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 . + +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 +#include +#include + +#ifdef DEBUG +#include +#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; + } +} -- cgit v1.3