yosys/passes/cmds/qwp.cc

/*
 *  yosys -- Yosys Open SYnthesis Suite
 *
 *  Copyright (C) 2012  Clifford Wolf <clifford@clifford.at>
 *
 *  Permission to use, copy, modify, and/or distribute this software for any
 *  purpose with or without fee is hereby granted, provided that the above
 *  copyright notice and this permission notice appear in all copies.
 *
 *  THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 *  WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 *  MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 *  ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 *  WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 *  ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 *  OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 *
 */

#include "kernel/yosys.h"
#include "kernel/sigtools.h"

#undef LOG_MATRICES
#undef PYPLOT_EDGES

USING_YOSYS_NAMESPACE
PRIVATE_NAMESPACE_BEGIN

static uint32_t xorshift32_state;

static double xorshift32()
{
	xorshift32_state ^= xorshift32_state << 13;
	xorshift32_state ^= xorshift32_state >> 17;
	xorshift32_state ^= xorshift32_state << 5;
	return (xorshift32_state % 1000000) / 1e6;
}

struct QwpConfig
{
	bool ltr;
	bool alpha;
	bool verbose;
	double grid;

	std::ofstream dump_file;

	QwpConfig() {
		ltr = false;
		alpha = false;
		verbose = false;
		grid = 1.0 / 16;
	}
};

struct QwpWorker
{
	QwpConfig &config;
	Module *module;
	char direction;

	struct Node {
		Cell *cell;
		bool tied, alt_tied;

		// pos = position in current direction
		// alt_pos = position in the other direction
		double pos, alt_pos;

		Node() {
			cell = nullptr;
			tied = false;
			pos = xorshift32();
			alt_tied = false;
			alt_pos = xorshift32();
		}

		void tie(double v) {
			tied = true;
			pos = v;
		}

		void alt_tie(double v) {
			alt_tied = true;
			alt_pos = v;
		}

		void swap_alt() {
			std::swap(tied, alt_tied);
			std::swap(pos, alt_pos);
		}

		void proj_left(double midpos) {
			cell = nullptr;
			tie(pos > midpos ? midpos : pos);
		}

		void proj_right(double midpos) {
			cell = nullptr;
			tie(pos < midpos ? midpos : pos);
		}
	};

	vector<Node> nodes;
	dict<pair<int, int>, double> edges;
	dict<Cell*, int> cell_to_node;

	// worker state variables
	double midpos;
	double radius;
	double alt_midpos;
	double alt_radius;

	QwpWorker(QwpConfig &config, Module *module, char direction = 'x') : config(config), module(module), direction(direction)
	{
		log_assert(direction == 'x' || direction == 'y');
	}

	void load_module()
	{
		log_assert(direction == 'x');

		SigMap sigmap(module);
		dict<SigBit, pool<int>> bits_to_nodes;

		if (config.ltr || config.alpha)
		{
			dict<Wire*, double> alpha_inputs, alpha_outputs;

			if (config.alpha)
			{
				dict<string, Wire*> alpha_order;

				for (auto wire : module->wires()) {
					if (wire->port_input || wire->port_output)
						alpha_order[wire->name.str()] = wire;
				}

				alpha_order.sort();

				for (auto &it : alpha_order) {
					if (it.second->port_input) {
						int idx = GetSize(alpha_inputs);
						alpha_inputs[it.second] = idx + 0.5;
					}
					if (it.second->port_output) {
						int idx = GetSize(alpha_outputs);
						alpha_outputs[it.second] = idx + 0.5;
					}
				}
			}

			for (auto wire : module->wires())
			{
				if (!wire->port_input && !wire->port_output)
					continue;

				int idx = GetSize(nodes);
				nodes.push_back(Node());

				if (config.ltr) {
					if (wire->port_input)
						nodes[idx].tie(0.0);
					else
						nodes[idx].tie(1.0);
				}

				if (config.alpha) {
					if (wire->port_input)
						nodes[idx].alt_tie(alpha_inputs.at(wire) / GetSize(alpha_inputs));
					else
						nodes[idx].alt_tie(alpha_outputs.at(wire) / GetSize(alpha_outputs));
				}

				for (auto bit : sigmap(wire))
					bits_to_nodes[bit].insert(idx);
			}
		}

		for (auto cell : module->selected_cells())
		{
			log_assert(cell_to_node.count(cell) == 0);
			int idx = GetSize(nodes);
			nodes.push_back(Node());

			cell_to_node[cell] = GetSize(nodes);
			nodes[idx].cell = cell;

			for (auto &conn : cell->connections())
			for (auto bit : sigmap(conn.second))
				bits_to_nodes[bit].insert(idx);
		}

		for (auto &it : bits_to_nodes)
		{
			if (GetSize(it.second) > 100)
				continue;

			for (int idx1 : it.second)
			for (int idx2 : it.second)
				if (idx1 < idx2)
					edges[pair<int, int>(idx1, idx2)] += 1.0 / GetSize(it.second);
		}
	}

	void solve(bool alt_mode = false)
	{
		// A := constraint_matrix
		// y := constraint_rhs_vector
		//
		// AA = A' * A
		// Ay = A' * y
		//
		// M := [AA Ay]

		if (config.verbose)
			log("> System size: %d^2\n", GetSize(nodes));

		// Row major order
		int N = GetSize(nodes), N1 = N+1;
		vector<double> M(N * N1);

		if (config.verbose)
			log("> Edge constraints: %d\n", GetSize(edges));

		// Edge constraints:
		//   A[i,:] := [ 0 0 .... 0 weight 0 ... 0 -weight 0 ... 0 0], y[i] := 0
		//
		// i.e. nonzero columns in A[i,:] at the two node indices.
		for (auto &edge : edges)
		{
			int idx1 = edge.first.first;
			int idx2 = edge.first.second;
			double weight = edge.second * (1.0 + xorshift32() * 1e-3);

			M[idx1 + idx1*N1] += weight * weight;
			M[idx2 + idx2*N1] += weight * weight;

			M[idx1 + idx2*N1] += -weight * weight;
			M[idx2 + idx1*N1] += -weight * weight;
		}

		if (config.verbose)
			log("> Node constraints: %d\n", GetSize(nodes));

		// Node constraints:
		//   A[i,:] := [ 0 0 .... 0 weight 0 ... 0 0], y[i] := weight * pos
		//
		// i.e. nonzero column in A[i,:] at the node index
		//
		// "tied" nodes have a large weight, pinning them in position. Untied
		// nodes have a small weight, giving then a tiny preference to stay at
		// the current position, making sure that AA never is singular.
		for (int idx = 0; idx < GetSize(nodes); idx++)
		{
			auto &node = nodes[idx];
			double rhs = (alt_mode ? node.alt_pos : node.pos);

			double weight = 1e-3;
			if (alt_mode ? node.alt_tied : node.tied)
				weight = 1e3;
			weight *= (1.0 + xorshift32() * 1e-3);

			M[idx + idx*N1] += weight * weight;
			M[N + idx*N1] += rhs * weight * weight;
		}

#ifdef LOG_MATRICES
		log("\n");
		for (int i = 0; i < N; i++) {
			for (int j = 0; j < N+1; j++)
				log(" %10.2e", M[(N+1)*i + j]);
			log("\n");
		}
#endif

		if (config.verbose)
			log("> Solving\n");

		// Solve "AA*x = Ay"
		// (least squares fit for "A*x = y")
		//
		// Using gaussian elimination to get M := [Id x]

		vector<int> pivot_cache;
		vector<int> queue;

		for (int i = 0; i < N; i++)
			queue.push_back(i);

		// gaussian elimination
		for (int i = 0; i < N; i++)
		{
			if (config.verbose && N > 15 && ((i+1) % (N/15)) == 0)
				log("> Solved %d%%: %d/%d\n", (100*(i+1))/N, i+1, N);

			// find best row
			int best_row = queue.front();
			int best_row_queue_idx = 0;
			double best_row_absval = 0;

			for (int k = 0; k < GetSize(queue); k++) {
				int row = queue[k];
				double absval = fabs(M[i + row*N1]);
				if (absval > best_row_absval) {
					best_row = row;
					best_row_queue_idx = k;
					best_row_absval = absval;
				}
			}

			int row = best_row;
			pivot_cache.push_back(row);

			queue[best_row_queue_idx] = queue.back();
			queue.pop_back();

			// normalize row
			for (int k = i+1; k < N1; k++)
				M[k + row*N1] /= M[i + row*N1];
			M[i + row*N1] = 1.0;

			// elimination
			for (int other_row : queue) {
				double d = M[i + other_row*N1];
				for (int k = i+1; k < N1; k++)
					M[k + other_row*N1] -= d*M[k + row*N1];
				M[i + other_row*N1] = 0.0;
			}
		}

		if (config.verbose)
			log("> Solved\n");

		log_assert(queue.empty());
		log_assert(GetSize(pivot_cache) == N);

		// back substitution
		for (int i = N-1; i >= 0; i--)
		for (int j = i+1; j < N; j++)
		{
			int row = pivot_cache[i];
			int other_row = pivot_cache[j];
			M[N + row*N1] -= M[j + row*N1] * M[N + other_row*N1];
			M[j + row*N1] = 0.0;
		}

#ifdef LOG_MATRICES
		log("\n");
		for (int i = 0; i < N; i++) {
			for (int j = 0; j < N+1; j++)
				log(" %10.2e", M[(N+1)*i + j]);
			log("\n");
		}
#endif

		if (config.verbose)
			log("> Update nodes\n");

		// update node positions
		for (int i = 0; i < N; i++)
		{
			double v = M[(N+1)*i + N];
			double c = alt_mode ? alt_midpos : midpos;
			double r = alt_mode ? alt_radius : radius;

			if (std::isfinite(v)) {
				v = min(v, c+r);
				v = max(v, c-r);
			} else {
				v = c;
			}

			if (alt_mode) {
				if (!nodes[i].alt_tied)
					nodes[i].alt_pos = v;
			} else {
				if (!nodes[i].tied)
					nodes[i].pos = v;
			}
		}
	}

	void log_cell_coordinates(int indent, bool log_all_nodes = false)
	{
		for (auto &node : nodes)
		{
			if (node.cell == nullptr && !log_all_nodes)
				continue;

			for (int i = 0; i < indent; i++)
				log("  ");

			if (direction == 'x')
				log("X=%.2f, Y=%.2f", node.pos, node.alt_pos);
			else
				log("X=%.2f, Y=%.2f", node.alt_pos, node.pos);

			if (node.tied)
				log(" [%c-tied]", direction);

			if (node.alt_tied)
				log(" [%c-tied]", direction == 'x' ? 'y' : 'x');

			if (node.cell != nullptr)
				log(" %s (%s)", log_id(node.cell), log_id(node.cell->type));
			else
				log(" (none)");

			log("\n");
		}
	}

	void dump_svg(const pool<int> *green_nodes = nullptr, double median = -1)
	{
		double x_center = direction == 'x' ? midpos : alt_midpos;
		double y_center = direction == 'y' ? midpos : alt_midpos;

		double x_radius = direction == 'x' ? radius : alt_radius;
		double y_radius = direction == 'y' ? radius : alt_radius;

		config.dump_file << stringf("<svg height=\"240\" width=\"470\">\n");
		config.dump_file << stringf("<rect x=\"0\" y=\"0\" width=\"470\" height=\"240\" style=\"fill:rgb(250,250,200);\" />\n");
		config.dump_file << stringf("<rect x=\"20\" y=\"20\" width=\"200\" height=\"200\" style=\"fill:rgb(200,200,200);\" />\n");
		config.dump_file << stringf("<rect x=\"250\" y=\"20\" width=\"200\" height=\"200\" style=\"fill:rgb(200,200,200);\" />\n");

		double win_x = 250 + 200 * (direction == 'x' ? midpos - radius : alt_midpos - alt_radius);
		double win_y =  20 + 200 * (direction == 'y' ? midpos - radius : alt_midpos - alt_radius);

		double win_w = 200 * (direction == 'x' ? 2*radius : 2*alt_radius);
		double win_h = 200 * (direction == 'y' ? 2*radius : 2*alt_radius);

		config.dump_file << stringf("<rect x=\"%.2f\" y=\"%.2f\" width=\"%.2f\" height=\"%.2f\" "
				"style=\"stroke:rgb(0,0,0);stroke-width:1;fill:none\" />\n", win_x, win_y, win_w, win_h);

		if (median >= 0)
		{
			double x1 = 20.0, x2 = 220.0, y1 = 20.0, y2 = 220.0;

			if (direction == 'x')
				x1 = x2 = 120 + 100 * (median - x_center) / x_radius;
			else
				y1 = y2 = 120 + 100 * (median - y_center) / y_radius;

			config.dump_file << stringf("<line x1=\"%.2f\" y1=\"%.2f\" x2=\"%.2f\" y2=\"%.2f\" "
					"style=\"stroke:rgb(150,0,150);stroke-width:1\" />\n", x1, y1, x2, y2);
		}

		for (auto &edge : edges)
		{
			auto &node1 = nodes[edge.first.first];
			auto &node2 = nodes[edge.first.second];

			double x1 = direction == 'x' ? node1.pos : node1.alt_pos;
			double y1 = direction == 'y' ? node1.pos : node1.alt_pos;

			double x2 = direction == 'x' ? node2.pos : node2.alt_pos;
			double y2 = direction == 'y' ? node2.pos : node2.alt_pos;

			x1 = 120 + 100 * (x1 - x_center) / x_radius;
			y1 = 120 + 100 * (y1 - y_center) / y_radius;

			x2 = 120 + 100 * (x2 - x_center) / x_radius;
			y2 = 120 + 100 * (y2 - y_center) / y_radius;

			config.dump_file << stringf("<line x1=\"%.2f\" y1=\"%.2f\" x2=\"%.2f\" y2=\"%.2f\" "
					"style=\"stroke:rgb(0,0,0);stroke-width:1\" />\n", x1, y1, x2, y2);
		}

		for (int i = 0; i < GetSize(nodes); i++)
		{
			auto &node = nodes[i];

			double x = direction == 'x' ? node.pos : node.alt_pos;
			double y = direction == 'y' ? node.pos : node.alt_pos;

			x = 120 + 100 * (x - x_center) / x_radius;
			y = 120 + 100 * (y - y_center) / y_radius;

			const char *color = node.cell == nullptr ? "blue" : "red";

			if (green_nodes != nullptr && green_nodes->count(i))
				color = "green";

			config.dump_file << stringf("<circle cx=\"%.2f\" cy=\"%.2f\" r=\"3\" fill=\"%s\"/>\n", x, y, color);
		}

		config.dump_file << stringf("</svg>\n");
	}

	void run_worker(int indent)
	{
		int count_cells = 0;

		for (auto &node : nodes)
			if (node.cell != nullptr)
				count_cells++;

		for (int i = 0; i < indent; i++)
			log("  ");

		string range_str;

		if (direction == 'x')
			range_str = stringf("X=%.2f:%.2f, Y=%.2f:%.2f",
					midpos - radius, midpos + radius,
					alt_midpos - alt_radius, alt_midpos + alt_radius);
		else
			range_str = stringf("X=%.2f:%.2f, Y=%.2f:%.2f",
					alt_midpos - alt_radius, alt_midpos + alt_radius,
					midpos - radius, midpos + radius);

		log("%c-qwp on %s with %d cells, %d nodes, and %d edges.\n", direction,
				range_str.c_str(), count_cells, GetSize(nodes), GetSize(edges));

		solve();
		solve(true);

		// detect median position and check for break condition

		vector<pair<double, int>> sorted_pos;
		for (int i = 0; i < GetSize(nodes); i++)
			if (nodes[i].cell != nullptr)
				sorted_pos.push_back(pair<double, int>(nodes[i].pos, i));

		std::sort(sorted_pos.begin(), sorted_pos.end());
		int median_sidx = GetSize(sorted_pos)/2;
		double median = sorted_pos[median_sidx].first;

		double left_scale = radius / (median - (midpos - radius));
		double right_scale = radius / ((midpos + radius) - median);

		if (config.dump_file.is_open())
		{
			config.dump_file << stringf("<h4>LSQ %c-Solution for %s:</h4>\n", direction, range_str.c_str());

			pool<int> green_nodes;
			for (int i = 0; i < median_sidx; i++)
				green_nodes.insert(sorted_pos[i].second);

			dump_svg(&green_nodes, median);
		}

		for (auto &node : nodes)
		{
			double rel_pos = node.pos - median;
			if (rel_pos < 0) {
				node.pos = midpos + left_scale*rel_pos;
				if (std::isfinite(node.pos)) {
					node.pos = min(node.pos, midpos);
					node.pos = max(node.pos, midpos - radius);
				} else
					node.pos = midpos - radius/2;
			} else {
				node.pos = midpos + right_scale*rel_pos;
				if (std::isfinite(node.pos)) {
					node.pos = max(node.pos, midpos);
					node.pos = min(node.pos, midpos + radius);
				} else
					node.pos = midpos + radius/2;
			}
		}

		if (GetSize(sorted_pos) < 2 || (2*radius <= config.grid && 2*alt_radius <= config.grid)) {
			log_cell_coordinates(indent + 1);
			return;
		}

		// create child workers

		char child_direction = direction == 'x' ? 'y' : 'x';

		QwpWorker left_worker(config, module, child_direction);
		QwpWorker right_worker(config, module, child_direction);

		// duplicate nodes into child workers

		dict<int, int> left_nodes, right_nodes;

		for (int k = 0; k < GetSize(sorted_pos); k++)
		{
			int i = sorted_pos[k].second;

			if (k < median_sidx) {
				left_nodes[i] = GetSize(left_worker.nodes);
				left_worker.nodes.push_back(nodes[i]);
				if (left_worker.nodes.back().pos > midpos)
					left_worker.nodes.back().pos = midpos;
				left_worker.nodes.back().swap_alt();
			} else {
				right_nodes[i] = GetSize(right_worker.nodes);
				right_worker.nodes.push_back(nodes[i]);
				if (right_worker.nodes.back().pos < midpos)
					right_worker.nodes.back().pos = midpos;
				right_worker.nodes.back().swap_alt();
			}
		}

		// duplicate edges into child workers, project nodes as needed

		for (auto &edge : edges)
		{
			int idx1 = edge.first.first;
			int idx2 = edge.first.second;
			double weight = edge.second;

			if (nodes[idx1].cell == nullptr && nodes[idx2].cell == nullptr)
				continue;

			int left_idx1 = left_nodes.count(idx1) ? left_nodes.at(idx1) : -1;
			int left_idx2 = left_nodes.count(idx2) ? left_nodes.at(idx2) : -1;

			int right_idx1 = right_nodes.count(idx1) ? right_nodes.at(idx1) : -1;
			int right_idx2 = right_nodes.count(idx2) ? right_nodes.at(idx2) : -1;

			if (left_idx1 >= 0 && left_worker.nodes[left_idx1].cell && left_idx2 < 0) {
				left_idx2 = left_nodes[idx2] = GetSize(left_worker.nodes);
				left_worker.nodes.push_back(nodes[idx2]);
				left_worker.nodes.back().proj_left(midpos);
				left_worker.nodes.back().swap_alt();
			} else
			if (left_idx2 >= 0 && left_worker.nodes[left_idx2].cell && left_idx1 < 0) {
				left_idx1 = left_nodes[idx1] = GetSize(left_worker.nodes);
				left_worker.nodes.push_back(nodes[idx1]);
				left_worker.nodes.back().proj_left(midpos);
				left_worker.nodes.back().swap_alt();
			}

			if (right_idx1 >= 0 && right_worker.nodes[right_idx1].cell && right_idx2 < 0) {
				right_idx2 = right_nodes[idx2] = GetSize(right_worker.nodes);
				right_worker.nodes.push_back(nodes[idx2]);
				right_worker.nodes.back().proj_right(midpos);
				right_worker.nodes.back().swap_alt();
			} else
			if (right_idx2 >= 0 && right_worker.nodes[right_idx2].cell && right_idx1 < 0) {
				right_idx1 = right_nodes[idx1] = GetSize(right_worker.nodes);
				right_worker.nodes.push_back(nodes[idx1]);
				right_worker.nodes.back().proj_right(midpos);
				right_worker.nodes.back().swap_alt();
			}

			if (left_idx1 >= 0 && left_idx2 >= 0)
				left_worker.edges[pair<int, int>(left_idx1, left_idx2)] += weight;

			if (right_idx1 >= 0 && right_idx2 >= 0)
				right_worker.edges[pair<int, int>(right_idx1, right_idx2)] += weight;
		}

		// run child workers

		left_worker.midpos = right_worker.midpos = alt_midpos;
		left_worker.radius = right_worker.radius = alt_radius;

		left_worker.alt_midpos = midpos - radius/2;
		right_worker.alt_midpos = midpos + radius/2;
		left_worker.alt_radius = right_worker.alt_radius = radius/2;

		left_worker.run_worker(indent+1);
		right_worker.run_worker(indent+1);

		// re-integrate results

		for (auto &it : left_nodes)
			if (left_worker.nodes[it.second].cell != nullptr) {
				nodes[it.first].pos = left_worker.nodes[it.second].alt_pos;
				nodes[it.first].alt_pos = left_worker.nodes[it.second].pos;
			}

		for (auto &it : right_nodes)
			if (right_worker.nodes[it.second].cell != nullptr) {
				nodes[it.first].pos = right_worker.nodes[it.second].alt_pos;
				nodes[it.first].alt_pos = right_worker.nodes[it.second].pos;
			}

		if (config.dump_file.is_open()) {
			config.dump_file << stringf("<h4>Final %c-Solution for %s:</h4>\n", direction, range_str.c_str());
			dump_svg();
		}
	}

	void histogram(const vector<double> &values)
	{
		if (values.empty()) {
			log("no data\n");
			return;
		}

		double min_value = values.front();
		double max_value = values.front();

		for (auto &v : values) {
			min_value = min(min_value, v);
			max_value = max(max_value, v);
		}

		if (fabs(max_value - min_value) < 0.001) {
			log("all values in range %f .. %f\n", min_value, max_value);
			return;
		}

		vector<int> buckets(60);
		int max_bucket_val = 0;

		for (auto &v : values) {
			int idx = min(int(GetSize(buckets) * (v - min_value) / (max_value - min_value)), GetSize(buckets)-1);
			max_bucket_val = max(max_bucket_val, ++buckets.at(idx));
		}

		for (int i = 4; i >= 0; i--) {
			for (int k = 0; k < GetSize(buckets); k++) {
				int v = 10 * buckets[k] / max_bucket_val;
				if (v >= 2*i+1)
					log(v == 2*i+1 ? "." : ":");
				else
					log(i == 0 ? (buckets[k] > 0 ? "," : "_") : " ");
			}
			log("\n");
		}
		log("%-30f%30f\n", min_value, max_value);
	}

	void run()
	{
		log("\n");
		log("Running qwp on module %s..\n", log_id(module));

		if (config.dump_file.is_open())
			config.dump_file << stringf("<h3>QWP protocol for module %s:</h3>\n", log_id(module));

		load_module();

		midpos = 0.5;
		radius = 0.5;
		alt_midpos = 0.5;
		alt_radius = 0.5;
		run_worker(1);

		for (auto &node : nodes)
			if (node.cell != nullptr)
				node.cell->attributes["\\qwp_position"] = stringf("%f %f", node.pos, node.alt_pos);

		vector<double> edge_lengths;
		vector<double> weighted_edge_lengths;

		double total_edge_length = 0;
		double total_weighted_edge_length = 0;

		for (auto &edge : edges)
		{
			auto &node1 = nodes[edge.first.first];
			auto &node2 = nodes[edge.first.second];

			double distance = sqrt(pow(node1.pos - node2.pos, 2) + pow(node1.alt_pos - node2.alt_pos, 2));
			double weighted_distance = distance * edge.second;

			edge_lengths.push_back(distance);
			weighted_edge_lengths.push_back(weighted_distance);

			total_edge_length += distance;
			total_weighted_edge_length += weighted_distance;
		}

		log("\n");
		log("Summary for module %s:\n", log_id(module));
		log("Number of edges: %d\n", GetSize(edges));
		log("Total edge length: %f\n", total_edge_length);
		log("Total weighted edge length: %f\n", total_weighted_edge_length);

		log("\n");
		log("Histogram over edge lengths:\n");
		histogram(edge_lengths);

		log("\n");
		log("Histogram over weighted edge lengths:\n");
		histogram(weighted_edge_lengths);
	}
};

struct QwpPass : public Pass {
	QwpPass() : Pass("qwp", "quadratic wirelength placer") { }
	void help() YS_OVERRIDE
	{
		//   |---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|---v---|
		log("\n");
		log("    qwp [options] [selection]\n");
		log("\n");
		log("This command runs quadratic wirelength placement on the selected modules and\n");
		log("annotates the cells in the design with 'qwp_position' attributes.\n");
		log("\n");
		log("    -ltr\n");
		log("        Add left-to-right constraints: constrain all inputs on the left border\n");
		log("        outputs to the right border.\n");
		log("\n");
		log("    -alpha\n");
		log("        Add constraints for inputs/outputs to be placed in alphanumerical\n");
		log("        order along the y-axis (top-to-bottom).\n");
		log("\n");
		log("    -grid N\n");
		log("        Number of grid divisions in x- and y-direction. (default=16)\n");
		log("\n");
		log("    -dump <html_file_name>\n");
		log("        Dump a protocol of the placement algorithm to the html file.\n");
		log("\n");
		log("    -v\n");
		log("        Verbose solver output for profiling or debugging\n");
		log("\n");
		log("Note: This implementation of a quadratic wirelength placer uses exact\n");
		log("dense matrix operations. It is only a toy-placer for small circuits.\n");
		log("\n");
	}
	void execute(std::vector<std::string> args, RTLIL::Design *design) YS_OVERRIDE
	{
		QwpConfig config;
		xorshift32_state = 123456789;

		log_header(design, "Executing QWP pass (quadratic wirelength placer).\n");

		size_t argidx;
		for (argidx = 1; argidx < args.size(); argidx++) {
			if (args[argidx] == "-ltr") {
				config.ltr = true;
				continue;
			}
			if (args[argidx] == "-alpha") {
				config.alpha = true;
				continue;
			}
			if (args[argidx] == "-v") {
				config.verbose = true;
				continue;
			}
			if (args[argidx] == "-grid" && argidx+1 < args.size()) {
				config.grid = 1.0 / atoi(args[++argidx].c_str());
				continue;
			}
			if (args[argidx] == "-dump" && argidx+1 < args.size()) {
				config.dump_file.open(args[++argidx], std::ofstream::trunc);
				yosys_output_files.insert(args[argidx]);
				continue;
			}
			break;
		}
		extra_args(args, argidx, design);

		for (auto module : design->selected_modules())
		{
			QwpWorker worker(config, module);
			worker.run();

#ifdef PYPLOT_EDGES
			log("\n");
			log("plt.figure(figsize=(10, 10));\n");

			for (auto &edge : worker.edges) {
				log("plt.plot([%.2f, %.2f], [%.2f, %.2f], \"r-\");\n",
						worker.nodes[edge.first.first].pos,
						worker.nodes[edge.first.second].pos,
						worker.nodes[edge.first.first].alt_pos,
						worker.nodes[edge.first.second].alt_pos);
			}

			for (auto &node : worker.nodes) {
				const char *style = node.cell != nullptr ? "ko" : "ks";
				log("plt.plot([%.2f], [%.2f], \"%s\");\n", node.pos, node.alt_pos, style);
			}
#endif
		}
	}
} QwpPass;

PRIVATE_NAMESPACE_END