[libfirm] / ir / ana / irlivechk.c

/*
 * Copyright (C) 1995-2007 Inria Rhone-Alpes.  All right reserved.
 *
 * This file is part of libFirm.
 *
 * This file may be distributed and/or modified under the terms of the
 * GNU General Public License version 2 as published by the Free Software
 * Foundation and appearing in the file LICENSE.GPL included in the
 * packaging of this file.
 *
 * Licensees holding valid libFirm Professional Edition licenses may use
 * this file in accordance with the libFirm Commercial License.
 * Agreement provided with the Software.
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE.
 */

/**
 * @file    livechk.c
 * @date    21.04.2007
 * @author  Sebastian Hack
 * @version $Id$
 * @summary
 *
 * Liveness checks as developed by Benoit Boissinot, Fabrice Rastello and myself.
 *
 * The speciality here is, that nothing has to be recomputed if new nodes are created
 * or old ones deleted.
 *
 * This algo has one core routine check_live_end_internal() which performs the liveness check.
 * It only relies on the precomputation done in the constructor, which in turn needs:
 * - out edges
 * - the dominance tree
 * - data obtained from a depth-first-search
 *
 * The precomputation remains valid as long as the CFG is not altered.
 */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <stdio.h>

#include "irgraph_t.h"
#include "irnode_t.h"
#include "irphase_t.h"
#include "iredges_t.h"

#include "irprintf.h"
#include "irdom.h"
#include "irdump.h"

#include "dfs_t.h"
#include "bitset.h"
#include "util.h"

#include "irlivechk.h"

#include "statev.h"

typedef struct _bl_info_t {
        ir_node *block;            /**< The block. */

        int be_tgt_calc : 1;
        int id : 31;               /**< a tight number for the block.
                                                                 we're just reusing the pre num from
                                                                 the DFS. */
        bitset_t *red_reachable;   /**< Holds all id's if blocks reachable
                                                                 in the CFG modulo back edges. */

        bitset_t *be_tgt_reach;    /**< target blocks of back edges whose
                                                                 sources are reachable from this block
                                                                 in the reduced graph. */
} bl_info_t;

#define get_block_info(lv, bl) ((bl_info_t *) phase_get_irn_data(&(lv)->ph, bl))

struct _lv_chk_t {
        ir_phase ph;
        const dfs_t *dfs;
        DEBUG_ONLY(firm_dbg_module_t *dbg;)
        int n_blocks;
        bitset_t *back_edge_src;
        bitset_t *back_edge_tgt;
        bl_info_t **map;
};

static void *init_block_data(ir_phase *ph, ir_node *irn, void *old)
{
        lv_chk_t *lv      = container_of(ph, lv_chk_t, ph);
        bl_info_t *bi     = phase_alloc(ph, sizeof(bi[0]));

        bi->id            = get_Block_dom_tree_pre_num(irn);
        bi->block         = irn;
        bi->red_reachable = bitset_obstack_alloc(phase_obst(ph), lv->n_blocks);
        bi->be_tgt_reach  = bitset_obstack_alloc(phase_obst(ph), lv->n_blocks);
        bi->be_tgt_calc   = 0;
        (void) old;
        return bi;
}

/**
 * Filter function to select all nodes for which liveness is computed.
 * @param irn A node.
 * @return    1 if the node shall be considered in liveness, 0 if not.
 */
static INLINE int is_liveness_node(const ir_node *irn)
{
        switch(get_irn_opcode(irn)) {
        case iro_Block:
        case iro_Bad:
        case iro_End:
                return 0;
        default:;
        }

        return 1;
}

/**
 * Compute the transitive closure on the reduced graph.
 * The reduced graph is the original graph without back edges.
 * Since that is a DAG, a reverse post order of the graph gives a toposort
 * which is ideally suited to compute the transitive closure.
 * Note also, that the DFS tree of the reduced graph is the same than the one
 * of the original graph. This saves us computing a new reverse post order.
 * We also can re-use the DFS tree of the original graph.
 */
static void red_trans_closure(lv_chk_t *lv)
{
        int i, n;

        for (i = 0, n = dfs_get_n_nodes(lv->dfs); i < n; ++i) {
                const ir_node *bl   = dfs_get_post_num_node(lv->dfs, i);
                bl_info_t *bi = get_block_info(lv, bl);

                const ir_edge_t *edge;

                bitset_set(bi->red_reachable, bi->id);
                foreach_block_succ (bl, edge) {
                        ir_node *succ = get_edge_src_irn(edge);
                        bl_info_t *si = get_block_info(lv, succ);
                        dfs_edge_kind_t kind = dfs_get_edge_kind(lv->dfs, bl, succ);

                        /*
                         * if the successor is no back edge, include all reachable
                         * blocks from there into the reachable set of the current node
                         */
                        if (kind != DFS_EDGE_BACK) {
                                assert(dfs_get_post_num(lv->dfs, bl) > dfs_get_post_num(lv->dfs, succ));
                                bitset_or(bi->red_reachable, si->red_reachable);
                        }

                        /* mark the block as a back edge src and succ as back edge tgt. */
                        else {
                                bitset_set(lv->back_edge_src, bi->id);
                                bitset_set(lv->back_edge_tgt, si->id);
                        }
                }

        }

}

static void compute_back_edge_chain(lv_chk_t *lv, ir_node *bl)
{
        bitset_t *tmp = bitset_alloca(lv->n_blocks);
        bl_info_t *bi = get_block_info(lv, bl);

        bitset_pos_t elm;

        DBG((lv->dbg, LEVEL_2, "computing T_%d\n", bi->id));

        /* put all back edge sources reachable (reduced) from here in tmp */
        bitset_copy(tmp, bi->red_reachable);
        bitset_set(tmp, bi->id);
        bitset_and(tmp, lv->back_edge_src);
        bi->be_tgt_calc = 1;

        DBG((lv->dbg, LEVEL_2, "\treachable be src: %B\n", tmp));

        /* iterate over them ... */
        bitset_foreach(tmp, elm) {
                bl_info_t *si = lv->map[elm];
                const ir_edge_t *edge;

                /* and find back edge targets which are not reduced reachable from bl */
                foreach_block_succ (si->block, edge) {
                        ir_node *tgt         = get_edge_src_irn(edge);
                        bl_info_t *ti        = get_block_info(lv, tgt);
                        dfs_edge_kind_t kind = dfs_get_edge_kind(lv->dfs, si->block, tgt);

                        if (kind == DFS_EDGE_BACK && !bitset_is_set(bi->red_reachable, ti->id)) {
                                if (!ti->be_tgt_calc)
                                        compute_back_edge_chain(lv, tgt);
                                bitset_set(bi->be_tgt_reach, ti->id);
                                bitset_or(bi->be_tgt_reach, ti->be_tgt_reach);
                        }
                }
                bitset_clear(bi->be_tgt_reach, bi->id);
        }
}


static INLINE void compute_back_edge_chains(lv_chk_t *lv)
{
        bitset_pos_t elm;
        int i, n;

        DBG((lv->dbg, LEVEL_2, "back edge sources: %B\n", lv->back_edge_src));
        bitset_foreach(lv->back_edge_src, elm) {
                compute_back_edge_chain(lv, lv->map[elm]->block);
        }

        for (i = 0, n = dfs_get_n_nodes(lv->dfs); i < n; ++i) {
                const ir_node *bl = dfs_get_post_num_node(lv->dfs, i);
                bl_info_t *bi     = get_block_info(lv, bl);

                const ir_edge_t *edge;

                if (!bitset_is_set(lv->back_edge_tgt, bi->id)) {
                        foreach_block_succ (bl, edge) {
                                ir_node *succ = get_edge_src_irn(edge);
                                bl_info_t *si = get_block_info(lv, succ);
                                dfs_edge_kind_t kind = dfs_get_edge_kind(lv->dfs, bl, succ);

                                if (kind != DFS_EDGE_BACK) {
                                        assert(dfs_get_post_num(lv->dfs, bl) > dfs_get_post_num(lv->dfs, succ));
                                        bitset_or(bi->be_tgt_reach, si->be_tgt_reach);
                                }
                        }
                }
        }

        for (i = 0, n = dfs_get_n_nodes(lv->dfs); i < n; ++i) {
                const ir_node *bl = dfs_get_post_num_node(lv->dfs, i);
                bl_info_t *bi     = get_block_info(lv, bl);
                bitset_set(bi->be_tgt_reach, bi->id);
        }
}

lv_chk_t *lv_chk_new(ir_graph *irg, const dfs_t *dfs)
{
        lv_chk_t *res = xmalloc(sizeof(res[0]));
        struct obstack *obst;
        int i;

        stat_ev_tim_push();
        phase_init(&res->ph, "liveness check", irg, PHASE_DEFAULT_GROWTH, init_block_data, NULL);
        obst = phase_obst(&res->ph);

        FIRM_DBG_REGISTER(res->dbg, "ir.ana.lvchk");

        res->dfs           = dfs;
        res->n_blocks      = dfs_get_n_nodes(res->dfs);
        res->back_edge_src = bitset_obstack_alloc(obst, res->n_blocks);
        res->back_edge_tgt = bitset_obstack_alloc(obst, res->n_blocks);
        res->map           = obstack_alloc(obst, res->n_blocks * sizeof(res->map[0]));

#if 0
        {
                char name[256];
                FILE *f;
                ir_snprintf(name, sizeof(name), "dfs_%F.dot", irg);
                if ((f = fopen(name, "wt")) != NULL) {
                        dfs_dump(res->dfs, f);
                        fclose(f);
                }
                dump_ir_block_graph(irg, "-lvchk");
        }
#endif

        /* fill the map which maps pre_num to block infos */
        for (i = res->n_blocks - 1; i >= 0; --i) {
                ir_node *irn  = (ir_node *) dfs_get_pre_num_node(res->dfs, i);
                bl_info_t *bi = phase_get_or_set_irn_data(&res->ph, irn);
                res->map[bi->id] = bi;
        }

        /* first of all, compute the transitive closure of the CFG *without* back edges */
        red_trans_closure(res);

        /* compute back edge chains */
        compute_back_edge_chains(res);

#ifndef NDEBUG
        DBG((res->dbg, LEVEL_1, "liveness chk in %+F\n", irg));
        for (i = res->n_blocks - 1; i >= 0; --i) {
                const ir_node *irn = dfs_get_pre_num_node(res->dfs, i);
                bl_info_t *bi      = get_block_info(res, irn);
                DBG((res->dbg, LEVEL_1, "lv_chk for %d -> %+F\n", i, irn));
                DBG((res->dbg, LEVEL_1, "\tred reach: %B\n", bi->red_reachable));
                DBG((res->dbg, LEVEL_1, "\ttgt reach: %B\n", bi->be_tgt_reach));
        }
#endif

        DBG((res->dbg, LEVEL_1, "back edge src: %B\n", res->back_edge_src));
        DBG((res->dbg, LEVEL_1, "back edge tgt: %B\n", res->back_edge_tgt));

        stat_ev_tim_pop("lv_chk_cons_time");
        return res;
}

void lv_chk_free(lv_chk_t *lv)
{
        obstack_free(phase_obst(&lv->ph), NULL);
        xfree(lv);
}

/**
 * Check if a node is live at the end of a block.
 * This function is for internal use as its code is shared between
 * the in/end routines below. It is almost the "live_end" routine
 * but passing in the bitset for recording the blocks where the variable
 * is used saves some effort in the "live_in" routine. See below for
 * details.
 *
 * @param lv    The liveness check environment.
 * @param what  The node to check for.
 * @param bl    The block under investigation.
 * @param uses  A bitset where this routine records all ids of blocks
 *              where this variable is used. Note that the bitset
 *              is only guaranteed to be filled if the node was not
 *              live at the end of the block.
 * @return      1, if @p what is live at the end at @p bl.
 */
unsigned lv_chk_bl_in_mask(const lv_chk_t *lv, const ir_node *bl, const ir_node *var)
{
        stat_ev_cnt_decl(uses);

        ir_node *def_bl;
        const ir_edge_t *edge;

        int res = 0;

        assert(is_Block(bl) && "can only check for liveness in a block");

        if (!is_liveness_node(var))
                return 0;

        def_bl = get_nodes_block(var);
        if (def_bl == bl || !block_dominates(def_bl, bl)) {
                goto end;
        }

        else {
                bitset_t *uses = bitset_alloca(lv->n_blocks);
                bitset_t *tmp  = bitset_alloca(lv->n_blocks);
                int min_dom    = get_Block_dom_tree_pre_num(def_bl) + 1;
                int max_dom    = get_Block_dom_max_subtree_pre_num(def_bl);
                bl_info_t *bli = get_block_info(lv, bl);
                int i;

                DBG((lv->dbg, LEVEL_2, "lv check of %+F, def=%+F,%d != q=%+F,%d\n",
                                        var, def_bl, min_dom - 1, bl, bli->id));

                foreach_out_edge (var, edge) {
                        ir_node *user = get_edge_src_irn(edge);
                        ir_node *use_bl;
                        bl_info_t *bi;

                        if (!is_liveness_node(user))
                                continue;

                        stat_ev_cnt_inc(uses);
                        use_bl = get_nodes_block(user);
                        if (is_Phi(user)) {
                                int pos = get_edge_src_pos(edge);
                                use_bl  = get_Block_cfgpred_block(use_bl, pos);
                        }

                        if (use_bl == bl) {
                                res = lv_chk_state_in;
                                DBG((lv->dbg, LEVEL_2, "\tuse directly in block %+F by %+F\n", use_bl, user));
                                goto end;
                        }

                        bi = get_block_info(lv, use_bl);
                        bitset_set(uses, bi->id);
                }

                DBG((lv->dbg, LEVEL_2, "\tuses: %B\n", uses));

                {

                        bitset_copy(tmp, bli->be_tgt_reach);
                        bitset_set(tmp, bli->id);

                        DBG((lv->dbg, LEVEL_2, "\tbe tgt reach: %B, dom span: [%d, %d]\n", tmp, min_dom, max_dom));
                        for (i = bitset_next_set(tmp, min_dom); i >= 0 && i <= max_dom; i = bitset_next_set(tmp, i + 1)) {
                                bl_info_t *ti = lv->map[i];
                                DBG((lv->dbg, LEVEL_2, "\tlooking from %d: seeing %B\n", ti->id, ti->red_reachable));
                                if (bitset_intersect(ti->red_reachable, uses)) {
                                        res = lv_chk_state_in;
                                        goto end;
                                }

                                bitset_andnot(tmp, ti->red_reachable);
                        }
                }
        }

end:
        return res;
}

unsigned lv_chk_bl_end_mask(const lv_chk_t *lv, const ir_node *bl, const ir_node *var)
{
        stat_ev_cnt_decl(uses);

        ir_node *def_bl;
        const ir_edge_t *edge;

        int res = 0;

        assert(is_Block(bl) && "can only check for liveness in a block");

        if (!is_liveness_node(var))
                return 0;

        def_bl = get_nodes_block(var);
        if (!block_dominates(def_bl, bl)) {
                goto end;
        }

        else {
                bitset_t *uses = bitset_alloca(lv->n_blocks);
                bitset_t *tmp  = bitset_alloca(lv->n_blocks);
                int min_dom    = get_Block_dom_tree_pre_num(def_bl) + 1;
                int max_dom    = get_Block_dom_max_subtree_pre_num(def_bl);
                bl_info_t *bli = get_block_info(lv, bl);
                int i;

                DBG((lv->dbg, LEVEL_2, "lv end check of %+F, def=%+F,%d != q=%+F,%d\n",
                                        var, def_bl, min_dom - 1, bl, bli->id));

                foreach_out_edge (var, edge) {
                        ir_node *user = get_edge_src_irn(edge);
                        ir_node *use_bl;
                        bl_info_t *bi;

                        if (!is_liveness_node(user))
                                continue;

                        stat_ev_cnt_inc(uses);
                        use_bl = get_nodes_block(user);
                        if (is_Phi(user)) {
                                int pos = get_edge_src_pos(edge);
                                use_bl  = get_Block_cfgpred_block(use_bl, pos);

                                if (bl == use_bl)
                                        res |= lv_chk_state_end;
                        }

                        bi = get_block_info(lv, use_bl);
                        if (use_bl != bl || bitset_is_set(lv->back_edge_tgt, bi->id))
                                bitset_set(uses, bi->id);
                }

                DBG((lv->dbg, LEVEL_2, "\tuses: %B\n", uses));

                bitset_copy(tmp, bli->be_tgt_reach);
                bitset_set(tmp, bli->id);

                DBG((lv->dbg, LEVEL_2, "\tbe tgt reach + current: %B, dom span: [%d, %d]\n", tmp, min_dom, max_dom));
                for (i = bitset_next_set(tmp, min_dom); i >= 0 && i <= max_dom; i = bitset_next_set(tmp, i + 1)) {
                        bl_info_t *ti = lv->map[i];
                        DBG((lv->dbg, LEVEL_2, "\tlooking from %d: seeing %B\n", ti->id, ti->red_reachable));
                        if (bitset_intersect(ti->red_reachable, uses)) {
                                res = lv_chk_state_out | lv_chk_state_end;
                                goto end;
                        }

                        bitset_andnot(tmp, ti->red_reachable);
                }
        }

end:
        return res;
}

/**
 * Check a nodes liveness situation of a block.
 * This routine considers both cases, the live in and end/out case.
 *
 * @param lv   The liveness check environment.
 * @param bl   The block under investigation.
 * @param var  The node to check for.
 * @return     A bitmask of lv_chk_state_XXX fields.
 */
unsigned lv_chk_bl_xxx(const lv_chk_t *lv, const ir_node *bl, const ir_node *var)
{
        stat_ev_cnt_decl(uses);
        stat_ev_cnt_decl(iter);

        int res  = 0;
        ir_node *def_bl;

        assert(is_Block(bl) && "can only check for liveness in a block");

        /* If the variable ist no liveness related var, bail out. */
        if (!is_liveness_node(var))
                return 0;

        stat_ev_ctx_push_fmt("lv_chk", "%u", get_irn_idx(var));
        stat_ev_tim_push();

        /* If there is no dominance relation, go out, too */
        def_bl = get_nodes_block(var);
        if (!block_dominates(def_bl, bl)) {
                stat_ev("lv_chk_no_dom");
                goto end;
        }

        /*
         * If the block in question is the same as the definition block,
         * the algorithm is simple. Just check for uses not inside this block.
         */
        if (def_bl == bl) {
                const ir_edge_t *edge;

                stat_ev("lv_chk_def_block");
                DBG((lv->dbg, LEVEL_2, "lv check same block %+F in %+F\n", var, bl));
                foreach_out_edge (var, edge) {
                        ir_node *use    = get_edge_src_irn(edge);
                        ir_node *use_bl;

                        if (!is_liveness_node(use))
                                continue;

                        stat_ev_cnt_inc(uses);
                        use_bl = get_nodes_block(use);
                        if (is_Phi(use)) {
                                int pos = get_edge_src_pos(edge);
                                use_bl  = get_Block_cfgpred_block(use_bl, pos);

                                if (use_bl == bl) {
                                        DBG((lv->dbg, LEVEL_2, "\tphi %+F in succ %+F,%d -> live end\n", use, use_bl, pos));
                                        res |= lv_chk_state_end;
                                }
                        }

                        if (use_bl != def_bl) {
                                res = lv_chk_state_end | lv_chk_state_out;
                                goto end;
                        }
                }

                goto end;
        }

        /*
         * this is the more complicated case.
         * We try to gather as much information as possible during looking
         * at the uses.
         *
         * Note that we know for shure that bl != def_bl. That is sometimes
         * silently exploited below.
         */
        else {
                bl_info_t *def = get_block_info(lv, def_bl);
                bl_info_t *bli = get_block_info(lv, bl);
                bitset_t *uses = bitset_alloca(lv->n_blocks);
                bitset_t *Tq;

                unsigned i, min_dom, max_dom;
                const ir_edge_t *edge;

                /* if the block has no DFS info, it cannot be reached.
                 * This can happen in functions with endless loops.
                 * we then go out, since nothing is live there.
                 *
                 * TODO: Is that right?
                 */
                if (!bli)
                        goto end;

                (void) def;
                DBG((lv->dbg, LEVEL_2, "lv check %+F (def in %+F #%d) in different block %+F #%d\n",
                                        var, def_bl, def->id, bl, bli->id));

                foreach_out_edge (var, edge) {
                        ir_node *user = get_edge_src_irn(edge);
                        int mask      = lv_chk_state_in;

                        ir_node *use_bl;
                        bl_info_t *bi;

                        /* if the user is no liveness node, the use does not count */
                        if (!is_liveness_node(user))
                                continue;

                        stat_ev_cnt_inc(uses);

                        /* if the user is a phi, the use is in the predecessor
                         * furthermore, prepare a mask so that in the case where
                         * bl (the block in question) coincides with a use, it
                         * can be marked live_end there. */
                        use_bl = get_nodes_block(user);
                        if (is_Phi(user)) {
                                int pos = get_edge_src_pos(edge);
                                use_bl  = get_Block_cfgpred_block(use_bl, pos);
                                mask   |= lv_chk_state_end;
                        }


                        /* if the use block coincides with the query block, we
                         * already gather a little liveness information.
                         * The variable is surely live there, since bl != def_bl
                         * (that case is treated above). */
                        if (use_bl == bl)
                                res |= mask;

                        bi = get_block_info(lv, use_bl);

                        if (bi)
                                bitset_set(uses, bi->id);
                }

                /* get the dominance range which really matters. all uses outside
                 * the definition's dominance range are not to consider. note,
                 * that the definition itself is also not considered. The case
                 * where bl == def_bl is considered above. */
                min_dom = get_Block_dom_tree_pre_num(def_bl) + 1;
                max_dom = get_Block_dom_max_subtree_pre_num(def_bl);

                DBG((lv->dbg, LEVEL_2, "\tuses: %B\n", uses));

                /* prepare a set with all reachable back edge targets.
                 * this will determine our "looking points" from where
                 * we will search/find the calculated uses. */
                Tq = bli->be_tgt_reach;

                /* now, visit all viewing points in the temporary bitset lying
                 * in the dominance range of the variable. Note that for reducible
                 * flow-graphs the first iteration is sufficient and the loop
                 * will be left. */
                DBG((lv->dbg, LEVEL_2, "\tbe tgt reach: %B, dom span: [%d, %d]\n", Tq, min_dom, max_dom));
                i = bitset_next_set(Tq, min_dom);
                while(i <= max_dom) {
                        bl_info_t *ti = lv->map[i];
                        int use_in_current_block = bitset_is_set(uses, ti->id);

                        stat_ev_cnt_inc(iter);

                        /*
                         * This is somehat tricky. Since this routine handles both, live in
                         * and end/out we have to handle all the border cases correctly.
                         * Each node is in its own red_reachable set (see calculation
                         * function above). That means, that in the case where bl == t, the
                         * intersection check of uses and rechability below will always
                         * find an intersection, namely t.
                         *
                         * However, if a block contains a use and the variable is dead
                         * afterwards, it is not live end/out at that block. Besides
                         * back-edge target. If a var is live-in at a back-edge target it
                         * is also live out/end there since the variable is live in the
                         * underlying loop. So in the case where t == bl and that is not
                         * a back-edge target, we have to remove that use from consideration
                         * to determine if the var is live out/end there.
                         *
                         * Note that the live in information has been calculated by the
                         * uses iteration above.
                         */
                        if (ti == bli && !bitset_is_set(lv->back_edge_tgt, ti->id)) {
                                DBG((lv->dbg, LEVEL_2, "\tlooking not from a back edge target and q == t. removing use: %d\n", ti->id));
                                bitset_clear(uses, ti->id);
                        }

                        /* If we can reach a use, the variable is live there and we say goodbye */
                        DBG((lv->dbg, LEVEL_2, "\tlooking from %d: seeing %B\n", ti->id, ti->red_reachable));
                        if (bitset_intersect(ti->red_reachable, uses)) {
                                res |= lv_chk_state_in | lv_chk_state_out | lv_chk_state_end;
                                goto end;
                        }

                        /*
                         * if we deleted a use do to the commentary above, we have to
                         * re-add it since it might be visible from further view points
                         * (we only need that in the non-reducible case).
                         */
                        if (use_in_current_block)
                                bitset_set(uses, ti->id);

                        i = bitset_next_set(Tq, get_Block_dom_max_subtree_pre_num(ti->block) + 1);
                }

        }

end:
        stat_ev_tim_pop("lv_chk_query_time");
        stat_ev_cnt_done(uses, "lv_chk_uses");
        stat_ev_cnt_done(iter, "lv_chk_iter");
        stat_ev_ctx_pop("lv_chk");

        return res;
}