#include "negamax_cnn1986.h" // =================================================================== // Globals // =================================================================== const float infty = 3.0; char negamax_cnn1986_ptn[9]; uint8_t negamax_cnn1986_search_depth = 3; // =================================================================== // Implementation of a small convolutional neural network // =================================================================== static float flattened[CONV_NUM+2]; static float dense1[DENSE1_NUM]; static float dense2[DENSE2_NUM]; #ifndef DETERMINISTIC union u_f { uint32_t u; float f; }; static uint32_t state = 1; static union u_f fudge; #define DOXORSHIFT { \ state ^= state << 13; \ state ^= state >> 17; \ state ^= state << 5; \ fudge.u = 0x3f800000 | state >> 10; \ fudge.f = (fudge.f - 1.5) * 0.01; \ } #endif #define RELU(x) ((x) = ((x)<0)?0:(x)) float cnn1986_evaluate_black_win(void) { /* ------------------ * * Convolution layer * * ------------------ */ // for each kernel for (uint8_t kern = 0; kern < KERN_NUM; kern++) { // the stride is 1, march across the board for (uint8_t bx = 0; bx < KERN_OSIZE; bx++) { for (uint8_t by = 0; by < KERN_OSIZE; by++) { flattened[kern+KERN_NUM*(bx+by*KERN_OSIZE)] = conv2d_biases[kern]; // Compute the convolution for this position for (uint8_t ky = 0; ky < KERN_SIZE; ky++) { for (uint8_t kx = 0; kx < KERN_SIZE; kx++) { for (uint8_t c = 0; c < KERN_CHAN; c++) { // Where we are on the board const uint8_t loc = kx+bx+(ky+by)*5; // Look up what's on the board at this location, and // multiply it. For c=0 we have to do some extra work float lookup = 0; if (COUNT_AT(loc)>c) { if (c==0) { if (STONE_AT(loc) == STONE_STANDING) { lookup = (colours[loc] & 1) ? +0.25 : -0.25; } else if (STONE_AT(loc) == STONE_CAPSTONE) { lookup = (colours[loc] & 1) ? +1.00 : -1.00; } else { lookup = (colours[loc] & 1) ? +0.50 : -0.50; } } else { lookup = (colours[loc] & (1< 1.0) { return 1.0; } else if (output < 0.0) { return -1.0; } return 2*output-1.0; } // =================================================================== // α-β negamax using the above evaluator // =================================================================== static void previous_ply(void) { if (ply>0) ply--; if (ply == 1) { current_colour = C_WHITE; } else { if (current_colour == C_BLACK) current_colour = C_WHITE; else current_colour = C_BLACK; } } static inline void push_stones(const int8_t location, const uint8_t count, const uint8_t new_colours, const enum STONE_VARIANT top_stone) { colours[location] = (colours[location] << count) | new_colours; celldat[location] = top_stone | ((celldat[location] + ((count << NUM_SHIFT))) & NUM_MASK); } static float val; static enum WIN_TYPE w; // UP DOWN LEFT RIGHT static const int8_t deltas[4] = { +5, -5, -1, +1}; #define WIN_EVALUATE_OR_RECURSE(store,reset) { \ w = 0xFF; \ if (ply >= 2*5 - 2) w = check_win(); \ if (w < 0xFF) { \ /* Somebody won, assign weights accordingly. Note in particular that draws are only worth ∞/2 ;) */ \ if (w == WIN_ROAD_BLACK || w == WIN_FLAT_BLACK) \ val = infty; \ else if (w == WIN_DRAW) val = infty/2.0; \ else val = -infty; \ val *= colour; \ } else if (cur_depth == negamax_cnn1986_search_depth) { \ /* We're at the bottom, evaluate */ \ val = colour * cnn1986_evaluate_black_win(); \ } else { \ /* We're not at the bottom, recurse first */ \ next_ply(); \ val = -negamax_cnn1986(cur_depth + 1, -beta, -alpha, -colour); \ previous_ply(); \ } \ { reset }; \ /* Prune */ \ if (val >= beta) return beta; \ /* Update the optimal value, which alpha carries */ \ if (val > alpha) { \ alpha = val; \ if (cur_depth == 0) { store }; \ } \ } float negamax_cnn1986(const uint8_t cur_depth, float alpha, float beta, const float colour) { const uint8_t black = (ply & 1), material = (black) ? black_count : white_count, flat = material & 127, cap = (ply > 2 && (material & 128)), standing = (ply > 2 && (material & 127)); // Step across the board for (uint8_t row = 0; row < 5; row++) { for (uint8_t col = 0; col < 5; col++) { // Try all valid actions for this square. Is it empty? const uint8_t loc = THE_COORDS(col, row); const uint8_t count = (COUNT_AT(loc) > 5) ? 5 : COUNT_AT(loc); // Only try moves after CPS if (count && ((colours[loc] & 1) == current_colour) && ply>2) { // There are stones, can we move them in a given direction? // Pre-compute end-stops uint8_t end_stops[4][2]; // (end, not_crush) // UP DOWN LEFT RIGHT end_stops[0][0] = (4-row > count) ? count : 4-row; end_stops[1][0] = (row > count) ? count : row; end_stops[2][0] = (col > count) ? count : col; end_stops[3][0] = (4-col > count) ? count : 4-col; const uint8_t cap_top = STONE_AT(loc) == STONE_CAPSTONE; for (uint8_t d = 0; d < 4; d++){ end_stops[d][1] = 1; const uint8_t stop = end_stops[d][0]; end_stops[d][0] = 0; for (uint8_t k = 1; k <= stop; k++) { const uint8_t stone = STONE_AT(loc+k*deltas[d]); if (stone == STONE_STANDING) { if (cap_top) { end_stops[d][1] = 0; end_stops[d][0]++; } break; } else if (stone == STONE_CAPSTONE) { break; } end_stops[d][0]++; } } uint16_t colours_backup[5]; uint8_t celldat_backup[5], drops[5]; // we only use 4, the // fifth is to skip a // bounds check at (*) // Back up the row of the board for (uint8_t y = 0; y < 5; y++) { colours_backup[y] = colours[THE_COORDS(col, y)]; celldat_backup[y] = celldat[THE_COORDS(col, y)]; } // I'm not a huge fan of looping through enums, but it's // better than manually unrolling this. Sufficiently smart // compilers? for (enum MOVE_DIRECTION dir = M_UP; dir <= M_RIGHT; dir++) { // Back-up the column once we start looking horizontally if (dir == M_LEFT) { for (uint8_t x = 0; x < 5; x++) { colours_backup[x] = colours[THE_COORDS(x, row)]; celldat_backup[x] = celldat[THE_COORDS(x, row)]; } } /* * We don't do anything terribly efficient here just try * all the ordered partitions of num ∈ {1 … end_stop}, and * skip the partition if it calls for multiple stones at * the end with a crush. */ uint8_t gaps, t, idx, mask; for (uint8_t num = 1; num <= count; num++) { for (uint8_t steps = 1; steps <= end_stops[dir][0] && steps <= num; steps++) { gaps = 0b00000111 >> (4-steps); do { // Ensure legal move if we have to crush const uint8_t last_drop_check = (num > 1) ? (gaps & 1<<(num - 2)) : 1; if (end_stops[dir][1] || last_drop_check) { // Translate to a drop sequence drops[0] = 1; mask = 1; idx = 0; for (uint8_t d = 0; d + 1 < num; d++) { if (gaps & mask) { idx++; drops[idx] = 1; // (*) we don't need to bounds check } else { drops[idx] += 1; } mask <<= 1; } // Do it, and manually check for win if it's valid uint8_t j = num; for (uint8_t k = 0; k < steps; k++) { j -= drops[k]; push_stones(loc+(k+1)*deltas[dir], drops[k], (colours[loc] >> j) & (0xFFFF >> (0x10 - drops[k])), (k == steps - 1) ? STONE_AT(loc) : STONE_FLAT); } // Then we drop them from the source colours[loc] >>= num; const uint8_t dec_count = celldat[loc] - (num << NUM_SHIFT); celldat[loc] = dec_count & NUM_MASK; // First check for wins, if we're at the bottom // evaluate, otherwise recurse WIN_EVALUATE_OR_RECURSE({ // If we did update the optimal value, store // this move generate_move(loc, dir, steps, drops, negamax_cnn1986_ptn); },{ // Reset the board data after recursing or // before returning if (dir <= M_DOWN) { for (uint8_t y = 0; y < 5; y++) { colours[THE_COORDS(col, y)] = colours_backup[y]; celldat[THE_COORDS(col, y)] = celldat_backup[y]; } } else { for (uint8_t x = 0; x < 5; x++) { colours[THE_COORDS(x, row)] = colours_backup[x]; celldat[THE_COORDS(x, row)] = celldat_backup[x]; } } }); } /* * With thanks to * https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation * we have the following magic to generate the next * permutation of steps-many set bits */ t = (gaps | (gaps - 1)); gaps = (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(gaps) + 1)); } while (gaps && (gaps + 1 <= (1<<(num-1)))); } } } } else if (material && count == 0) { // Empty square, try placements if (flat) { // Generate the placement if (black) black_count--; else white_count--; colours[loc] = current_colour; celldat[loc] = NUM_INC | STONE_FLAT; WIN_EVALUATE_OR_RECURSE({ // If we did update the optimal value, store generate_place(loc, STONE_FLAT, negamax_cnn1986_ptn); },{ // Reset the state celldat[loc] = 0; if (black) black_count++; else white_count++; }); // Do the same for walls, can't happen without flats if (standing) { if (black) black_count--; else white_count--; colours[loc] = current_colour; celldat[loc] = NUM_INC | STONE_STANDING; WIN_EVALUATE_OR_RECURSE({ generate_place(loc, STONE_STANDING, negamax_cnn1986_ptn); },{ celldat[loc] = 0; if (black) black_count++; else white_count++; }); } } // and for caps if (cap) { if (black) black_count &= 127; else white_count &= 127; colours[loc] = current_colour; celldat[loc] = NUM_INC | STONE_CAPSTONE; WIN_EVALUATE_OR_RECURSE({ generate_place(loc, STONE_CAPSTONE, negamax_cnn1986_ptn); },{ celldat[loc] = 0; if (black) black_count |= 128; else white_count |= 128; }); } } negamax_cnn1986_display_progress(cur_depth); } } return alpha; } inline float negamax_cnn1986_generate(void) { return negamax_cnn1986(0, -infty, infty, (ply&1)?1.0:-1.0); }