text: #include <assert.h>
  #include <limits.h>
  #include <math.h>
  #include <stdio.h>
  #include <stdlib.h>
  #include <string.h>
  
  //#define DEBUG
  
  #include "board.h"
  #include "debug.h"
  #include "move.h"
  #include "random.h"
  #include "tactics/util.h"
  #include "uct/internal.h"
  #include "uct/tree.h"
  #include "uct/policy/generic.h"
  
  /* This implements the UCB1 policy with an extra AMAF heuristics. */
  
  struct ucb1_policy_amaf {
  	/* This is what the Modification of UCT with Patterns in Monte Carlo Go
  	 * paper calls 'p'. Original UCB has this on 2, but this seems to
  	 * produce way too wide searches; reduce this to get deeper and
  	 * narrower readouts - try 0.2. */
  	floating_t explore_p;
  	/* Rescale virtual loss value to square root of #threads. This mitigates
  	 * the number of virtual losses added in case of a large amount of
  	 * threads; it seems that with linear virtual losses, overly diverse
  	 * exploration caused by this may cause a wrong mean value computed
  	 * for the parent node. */
  	bool vloss_sqrt;
  	/* In distributed mode, encourage different slaves to work on different
  	 * parts of the tree by adding virtual wins to different nodes. */
  	int virtual_win;
  	int root_virtual_win;
  	int vwin_min_playouts;
  	/* First Play Urgency - if set to less than infinity (the MoGo paper
  	 * above reports 1.0 as the best), new branches are explored only
  	 * if none of the existing ones has higher urgency than fpu. */
  	floating_t fpu;
  	unsigned int equiv_rave;
  	bool sylvain_rave;
          /* Give more weight to moves played earlier. */
  	int distance_rave;
  	/* Give 0 or negative rave bonus to ko threats before taking the ko.
  	   1=normal bonus, 0=no bonus, -1=invert rave bonus, -2=double penalty... */
  	int threat_rave;
  	/* Coefficient of local tree values embedded in RAVE. */
  	floating_t ltree_rave;
  	/* Coefficient of criticality embedded in RAVE. */
  	floating_t crit_rave;
  	int crit_min_playouts;
  	floating_t crit_plthres_coef;
  	bool crit_negative;
  	bool crit_negflip;
  	bool crit_amaf;
  	bool crit_lvalue;
  };
  
  
  static inline floating_t fast_sqrt(unsigned int x)
  {
  	static const floating_t table[] = {
  		0, 1, 1.41421356237309504880, 1.73205080756887729352,
  		2.00000000000000000000, 2.23606797749978969640,
  		2.44948974278317809819, 2.64575131106459059050,
  		2.82842712474619009760, 3.00000000000000000000,
  		3.16227766016837933199, 3.31662479035539984911,
  		3.46410161513775458705, 3.60555127546398929311,
  		3.74165738677394138558, 3.87298334620741688517,
  		4.00000000000000000000, 4.12310562561766054982,
  		4.24264068711928514640, 4.35889894354067355223,
  		4.47213595499957939281, 4.58257569495584000658,
  		4.69041575982342955456, 4.79583152331271954159,
  		4.89897948556635619639, 5.00000000000000000000,
  		5.09901951359278483002, 5.19615242270663188058,
  		5.29150262212918118100, 5.38516480713450403125,
  		5.47722557505166113456, 5.56776436283002192211,
  		5.65685424949238019520, 5.74456264653802865985,
  		5.83095189484530047087, 5.91607978309961604256,
  		6.00000000000000000000, 6.08276253029821968899,
  		6.16441400296897645025, 6.24499799839839820584,
  		6.32455532033675866399, 6.40312423743284868648,
  		6.48074069840786023096, 6.55743852430200065234,
  		6.63324958071079969822, 6.70820393249936908922,
  		6.78232998312526813906, 6.85565460040104412493,
  		6.92820323027550917410, 7.00000000000000000000,
  		7.07106781186547524400, 7.14142842854284999799,
  		7.21110255092797858623, 7.28010988928051827109,
  		7.34846922834953429459, 7.41619848709566294871,
  		7.48331477354788277116, 7.54983443527074969723,
  		7.61577310586390828566, 7.68114574786860817576,
  		7.74596669241483377035, 7.81024967590665439412,
  		7.87400787401181101968, 7.93725393319377177150,
  	};
  	if (x < sizeof(table) / sizeof(*table)) {
  		return table[x];
  	} else {
  		return sqrt(x);
  	}
  }
  
  #define URAVE_DEBUG if (0)
  static inline floating_t
  ucb1rave_evaluate(struct uct_policy *p, struct tree *tree, struct uct_descent *descent, int parity)
  {
  	struct ucb1_policy_amaf *b = p->data;
  	struct tree_node *node = descent->node;
  	struct tree_node *lnode = descent->lnode;
  
  	struct move_stats n = node->u, r = node->amaf;
  	if (p->uct->amaf_prior) {
  		stats_merge(&r, &node->prior);
  	} else {
  		stats_merge(&n, &node->prior);
  	}
  
  	if (p->uct->virtual_loss) {
  		/* Add virtual loss if we need to; this is used to discourage
  		 * other threads from visiting this node in case of multiple
  		 * threads doing the tree search. */
  		floating_t vloss_coeff = b->vloss_sqrt ? sqrt(p->uct->threads) / p->uct->threads : 1.;
  		struct move_stats c = { .value = parity > 0 ? 0. : 1., .playouts = node->descents * vloss_coeff };
  		stats_merge(&n, &c);
  	}
  
  	/* Local tree heuristics. */
  	assert(!lnode || lnode->parent);
  	if (p->uct->local_tree && b->ltree_rave > 0 && lnode
  	    && (p->uct->local_tree_rootchoose || lnode->parent->parent)) {
  		struct move_stats l = lnode->u;
  		l.playouts = ((floating_t) l.playouts) * b->ltree_rave / LTREE_PLAYOUTS_MULTIPLIER;
  		URAVE_DEBUG fprintf(stderr, "[ltree] adding [%s] %f%%%d to [%s] RAVE %f%%%d\n",
  			coord2sstr(node_coord(lnode), tree->board), l.value, l.playouts,
  			coord2sstr(node_coord(node), tree->board), r.value, r.playouts);
  		stats_merge(&r, &l);
  	}
  
  	/* Criticality heuristics. */
  	if (b->crit_rave > 0 && (b->crit_plthres_coef > 0
  				 ? node->u.playouts > tree->root->u.playouts * b->crit_plthres_coef
  				 : node->u.playouts > b->crit_min_playouts)) {
  		floating_t crit = tree_node_criticality(tree, node);
  		if (b->crit_negative || crit > 0) {
  			floating_t val = 1.0f;
  			if (b->crit_negflip && crit < 0) {
  				val = 0;
  				crit = -crit;
  			}
  			struct move_stats c = {
  				.value = tree_node_get_value(tree, parity, val),
  				.playouts = crit * r.playouts * b->crit_rave
  			};
  			URAVE_DEBUG fprintf(stderr, "[crit] adding %f%%%d to [%s] RAVE %f%%%d\n",
  				c.value, c.playouts,
  				coord2sstr(node_coord(node), tree->board), r.value, r.playouts);
  			stats_merge(&r, &c);
  		}
  	}
  
  	floating_t value = 0;
  	if (n.playouts) {
  		if (r.playouts) {
  			/* At the beginning, beta is at 1 and RAVE is used.
  			 * At b->equiv_rate, beta is at 1/3 and gets steeper on. */
  			floating_t beta;
  			if (b->sylvain_rave) {
  				beta = (floating_t) r.playouts / (r.playouts + n.playouts
  					+ (floating_t) n.playouts * r.playouts / b->equiv_rave);
  			} else {
  				/* XXX: This can be cached in descend; but we don't use this by default. */
  				beta = sqrt(b->equiv_rave / (3 * node->parent->u.playouts + b->equiv_rave));
  			}
  
  			value = beta * r.value + (1.f - beta) * n.value;
  			URAVE_DEBUG fprintf(stderr, "\t%s value = %f * %f + (1 - %f) * %f (prior %f)\n",
  			        coord2sstr(node_coord(node), tree->board), beta, r.value, beta, n.value, node->prior.value);
  		} else {
  			value = n.value;
  			URAVE_DEBUG fprintf(stderr, "\t%s value = %f (prior %f)\n",
  			        coord2sstr(node_coord(node), tree->board), n.value, node->prior.value);
  		}
  	} else if (r.playouts) {
  		value = r.value;
  		URAVE_DEBUG fprintf(stderr, "\t%s value = rave %f (prior %f)\n",
  			coord2sstr(node_coord(node), tree->board), r.value, node->prior.value);
  	}
  	descent->value.playouts = r.playouts + n.playouts;
  	descent->value.value = value;
  
  	return tree_node_get_value(tree, parity, value);
  }
  
  void
  ucb1rave_descend(struct uct_policy *p, struct tree *tree, struct uct_descent *descent, int parity, bool allow_pass)
  {
  	struct ucb1_policy_amaf *b = p->data;
  	floating_t nconf = 1.f;
  	if (b->explore_p > 0)
  		nconf = sqrt(log(descent->node->u.playouts + descent->node->prior.playouts));
  	struct uct *u = p->uct;
  	int vwin = 0;
  	if (u->max_slaves > 0 && u->slave_index >= 0)
  		vwin = descent->node == tree->root ? b->root_virtual_win : b->virtual_win;
  	int child = 0;
  
  	uctd_try_node_children(tree, descent, allow_pass, parity, u->tenuki_d, di, urgency) {
  		struct tree_node *ni = di.node;
  		urgency = ucb1rave_evaluate(p, tree, &di, parity);
  
  		/* In distributed mode, encourage different slaves to work on different
  		 * parts of the tree. We rely on the fact that children (if they exist)
  		 * are the same and in the same order in all slaves. */
  		if (vwin > 0 && ni->u.playouts > b->vwin_min_playouts && (child - u->slave_index) % u->max_slaves == 0)
  			urgency += vwin / (ni->u.playouts + vwin);
  
  		if (ni->u.playouts > 0 && b->explore_p > 0) {
  			urgency += b->explore_p * nconf / fast_sqrt(ni->u.playouts);
  
  		} else if (ni->u.playouts + ni->amaf.playouts + ni->prior.playouts == 0) {
  			/* assert(!u->even_eqex); */
  			urgency = b->fpu;
  		}
  	} uctd_set_best_child(di, urgency);
  
  	uctd_get_best_child(descent);
  }
  
  
  /* Return the length of the current ko (number of moves up to to the last ko capture),
   * 0 if the sequence is empty or doesn't start with a ko capture.
   *   B captures a ko
   *   W plays a ko threat
   *   B answers ko threat
   *   W re-captures the ko  <- return 4
   *   B plays a ko threat
   *   W connects the ko */
  static inline int ko_length(bool *ko_capture_map, int map_length)
  {
  	if (map_length <= 0 || !ko_capture_map[0]) return 0;
  	int length = 1;
  	while (length + 2 < map_length && ko_capture_map[length + 2]) length += 3;
  	return length;
  }
  
  void
  ucb1amaf_update(struct uct_policy *p, struct tree *tree, struct tree_node *node,
  		enum stone node_color, enum stone player_color,
  		struct playout_amafmap *map, struct board *final_board,
  		floating_t result)
  {
  	struct ucb1_policy_amaf *b = p->data;
  	enum stone winner_color = result > 0.5 ? S_BLACK : S_WHITE;
  
  	/* Record of the random playout - for each intersection coord,
  	 * first_move[coord] is the index map->game of the first move
  	 * at this coordinate, or INT_MAX if the move was not played.
  	 * The parity gives the color of this move.
  	 */
  	int first_map[board_size2(final_board)+1];
  	int *first_move = &first_map[1]; // +1 for pass
  
  #if 0
  	struct board bb; bb.size = 9+2;
  	for (struct tree_node *ni = node; ni; ni = ni->parent)
  		fprintf(stderr, "%s ", coord2sstr(node_coord(ni), &bb));
  	fprintf(stderr, "[color %d] update result %d (color %d)\n",
  			node_color, result, player_color);
  #endif
  
  	/* Initialize first_move */
  	for (int i = pass; i < board_size2(final_board); i++) first_move[i] = INT_MAX;
  	int move;
  	assert(map->gamelen > 0);
  	for (move = map->gamelen - 1; move >= map->game_baselen; move--)
  		first_move[map->game[move]] = move;
  
  	while (node) {
  		if (!b->crit_amaf && !is_pass(node_coord(node))) {
  			stats_add_result(&node->winner_owner, board_local_value(b->crit_lvalue, final_board, node_coord(node), winner_color), 1);
  			stats_add_result(&node->black_owner, board_local_value(b->crit_lvalue, final_board, node_coord(node), S_BLACK), 1);
  		}
  		stats_add_result(&node->u, result, 1);
  
  		bool *ko_capture_map = &map->is_ko_capture[move+1];
  		int max_threat_dist = b->threat_rave <= 0 ? ko_length(ko_capture_map, map->gamelen - (move+1)) : -1;
  
  		/* This loop ignores symmetry considerations, but they should
  		 * matter only at a point when AMAF doesn't help much. */
  		assert(map->game_baselen >= 0);
  		for (struct tree_node *ni = node->children; ni; ni = ni->sibling) {
  			if (is_pass(node_coord(ni))) continue;
  
  			/* Use the child move only if it was first played by the same color. */
  			int first = first_move[node_coord(ni)];
  			if (first == INT_MAX) continue;
  			assert(first > move && first < map->gamelen);
  			int distance = first - (move + 1);
  			if (distance & 1) continue;
  
  			int weight = 1;
  			floating_t res = result;
  
  			/* Don't give amaf bonus to a ko threat before taking the ko.
  			 * http://www.grappa.univ-lille3.fr/~coulom/Aja_PhD_Thesis.pdf
  			 */
  			if (distance <= max_threat_dist && distance % 6 == 4) {
  				weight = - b->threat_rave;
  				res = 1.0 - res;
  			} else if (b->distance_rave != 0) {
  				/* Give more weight to moves played earlier */
  				weight += b->distance_rave * (map->gamelen - first) / (map->gamelen - move);
  			}
  			stats_add_result(&ni->amaf, res, weight);
  
  			if (b->crit_amaf) {
  				stats_add_result(&ni->winner_owner, board_local_value(b->crit_lvalue, final_board, node_coord(ni), winner_color), 1);
  				stats_add_result(&ni->black_owner, board_local_value(b->crit_lvalue, final_board, node_coord(ni), S_BLACK), 1);
  			}
  #if 0
  			struct board bb; bb.size = 9+2;
  			fprintf(stderr, "* %s<%"PRIhash"> -> %s<%"PRIhash"> [%d/%f => %d/%f]\n",
  				coord2sstr(node_coord(node), &bb), node->hash,
  				coord2sstr(node_coord(ni), &bb), ni->hash,
  				player_color, result, move, res);
  #endif
  		}
  		if (node->parent) {
  			assert(move >= 0 && map->game[move] == node_coord(node) && first_move[node_coord(node)] > move);
  			first_move[node_coord(node)] = move;
  			move--;
  		}
  		node = node->parent;
  	}
  }
  
  void
  ucb1amaf_done(struct uct_policy *p)
  {
  	free(p->data);
  	free(p);
  }
  
  
  struct uct_policy *
  policy_ucb1amaf_init(struct uct *u, char *arg, struct board *board)
  {
  	struct uct_policy *p = calloc2(1, sizeof(*p));
  	struct ucb1_policy_amaf *b = calloc2(1, sizeof(*b));
  	p->uct = u;
  	p->data = b;
  	p->done = ucb1amaf_done;
  	p->choose = uctp_generic_choose;
  	p->winner = uctp_generic_winner;
  	p->evaluate = ucb1rave_evaluate;
  	p->descend = ucb1rave_descend;
  	p->update = ucb1amaf_update;
  	p->wants_amaf = true;
  
  	b->explore_p = 0;
  	b->equiv_rave = board_large(board) ? 4000 : 3000;
  	b->fpu = INFINITY;
  	b->sylvain_rave = true;
  	b->distance_rave = 3;
  	b->threat_rave = 0;
  	b->ltree_rave = 0.75f;
  
  	b->crit_rave = 1.1f;
  	b->crit_min_playouts = 2000;
  	b->crit_negative = 1;
  	b->crit_amaf = 0;
  
  	b->vloss_sqrt = true;
  
  	b->virtual_win = 5;
  	b->root_virtual_win = 30;
  	b->vwin_min_playouts = 1000;
  
  	if (arg) {
  		char *optspec, *next = arg;
  		while (*next) {
  			optspec = next;
  			next += strcspn(next, ":");
  			if (*next) { *next++ = 0; } else { *next = 0; }
  
  			char *optname = optspec;
  			char *optval = strchr(optspec, '=');
  			if (optval) *optval++ = 0;
  
  			if (!strcasecmp(optname, "explore_p")) {
  				b->explore_p = atof(optval);
  			} else if (!strcasecmp(optname, "fpu") && optval) {
  				b->fpu = atof(optval);
  			} else if (!strcasecmp(optname, "equiv_rave") && optval) {
  				b->equiv_rave = atof(optval);
  			} else if (!strcasecmp(optname, "sylvain_rave")) {
  				b->sylvain_rave = !optval || *optval == '1';
  			} else if (!strcasecmp(optname, "distance_rave") && optval) {
  				b->distance_rave = atoi(optval);
  			} else if (!strcasecmp(optname, "threat_rave") && optval) {
  				b->threat_rave = atoi(optval);
  			} else if (!strcasecmp(optname, "ltree_rave") && optval) {
  				b->ltree_rave = atof(optval);
  			} else if (!strcasecmp(optname, "crit_rave") && optval) {
  				b->crit_rave = atof(optval);
  			} else if (!strcasecmp(optname, "crit_min_playouts") && optval) {
  				b->crit_min_playouts = atoi(optval);
  			} else if (!strcasecmp(optname, "crit_plthres_coef") && optval) {
  				b->crit_plthres_coef = atof(optval);
  			} else if (!strcasecmp(optname, "crit_negative")) {
  				b->crit_negative = !optval || *optval == '1';
  			} else if (!strcasecmp(optname, "crit_negflip")) {
  				b->crit_negflip = !optval || *optval == '1';
  			} else if (!strcasecmp(optname, "crit_amaf")) {
  				b->crit_amaf = !optval || *optval == '1';
  			} else if (!strcasecmp(optname, "crit_lvalue")) {
  				b->crit_lvalue = !optval || *optval == '1';
  			} else if (!strcasecmp(optname, "virtual_win") && optval) {
  				b->virtual_win = atoi(optval);
  			} else if (!strcasecmp(optname, "root_virtual_win") && optval) {
  				b->root_virtual_win = atoi(optval);
  			} else if (!strcasecmp(optname, "vwin_min_playouts") && optval) {
  				b->vwin_min_playouts = atoi(optval);
  			} else if (!strcasecmp(optname, "vloss_sqrt")) {
  				b->vloss_sqrt = !optval || *optval == '1';
  			} else {
  				fprintf(stderr, "ucb1amaf: Invalid policy argument %s or missing value\n",
  					optname);
  				exit(1);
  			}
  		}
  	}
  
  	return p;
  }
  