Merge pull request #7 from YosysHQ/master

[yosys.git] / 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