- more work on the Unknown problems: the only

[libfirm] / ir / opt / combo.c

/*
 * Copyright (C) 1995-2008 University of Karlsruhe.  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
 * @brief   Cliff Click's Combined Analysis/Optimization
 * @author  Michael Beck
 * @version $Id$
 *
 * This is a slightly enhanced version of Cliff Clicks combo algorithm
 * - support for commutative nodes is added, Add(a,b) and Add(b,a) ARE congruent
 * - supports all Firm direct (by a data edge) identities except Mux
 *   (Mux can be a 2-input or 1-input identity, only 2-input is implemented yet)
 * - supports Confirm nodes (handle them like Copies but do NOT remove them)
 * - let Cmp nodes calculate Top like all othe data nodes: this would let
 *   Mux nodes to calculate Unknown instead of taking the true result
 * - let Cond(Top) always select FALSE/default: This is tricky. Nodes are only reavaluated
 *   IFF the predecessor changed its type. Because nodes are initialized with Top
 *   this never happens, let all Proj(Cond) be unreachable.
 *   We avoid this condition by the same way we work around Phi: whenever a Block
 *   node is placed on the list, place its Cond nodes (and because they are Tuple
 *   all its Proj-nodes either on the cprop list)
 *   Especially, this changes the meaning of Click's example:
 *
 *   int main() {
 *     int x;
 *
 *     if (x == 2)
 *       printf("x == 2\n");
 *     if (x == 3)
 *       printf("x == 3\n");
 *   }
 *
 *   Would print:
 *   x == 2
 *   x == 3
 *
 *   using Click's version while is silent with our.
 * - support for global congruences is implemented but not tested yet
 *
 * Note further that we use the terminology from Click's work here, which is different
 * in some cases from Firm terminology.  Especially, Click's type is a
 * Firm tarval/entity, nevertheless we call it type here for "maximum compatibility".
 */
#include "config.h"

#include <assert.h>

#include "iroptimize.h"
#include "archop.h"
#include "irflag.h"
#include "ircons.h"
#include "list.h"
#include "set.h"
#include "pmap.h"
#include "obstack.h"
#include "irgraph_t.h"
#include "irnode_t.h"
#include "iropt_t.h"
#include "irgwalk.h"
#include "irop.h"
#include "irouts.h"
#include "irgmod.h"
#include "iropt_dbg.h"
#include "debug.h"
#include "array_t.h"
#include "error.h"

#include "tv_t.h"

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

/* define this to check that all type translations are monotone */
#define VERIFY_MONOTONE

/* define this to check the consistency of partitions */
#define CHECK_PARTITIONS

/* allow optimization of non-strict programs */
#define WITH_UNKNOWN

typedef struct node_t            node_t;
typedef struct partition_t       partition_t;
typedef struct opcode_key_t      opcode_key_t;
typedef struct listmap_entry_t   listmap_entry_t;

/** The type of the compute function. */
typedef void (*compute_func)(node_t *node);

/**
 * An opcode map key.
 */
struct opcode_key_t {
        ir_opcode   code;   /**< The Firm opcode. */
        ir_mode     *mode;  /**< The mode of all nodes in the partition. */
        int         arity;  /**< The arity of this opcode (needed for Phi etc. */
        union {
                long      proj;   /**< For Proj nodes, its proj number */
                ir_entity *ent;   /**< For Sel Nodes, its entity */
        } u;
};

/**
 * An entry in the list_map.
 */
struct listmap_entry_t {
        void            *id;    /**< The id. */
        node_t          *list;  /**< The associated list for this id. */
        listmap_entry_t *next;  /**< Link to the next entry in the map. */
};

/** We must map id's to lists. */
typedef struct listmap_t {
        set             *map;    /**< Map id's to listmap_entry_t's */
        listmap_entry_t *values; /**< List of all values in the map. */
} listmap_t;

/**
 * A lattice element. Because we handle constants and symbolic constants different, we
 * have to use this union.
 */
typedef union {
        tarval          *tv;
        symconst_symbol sym;
} lattice_elem_t;

/**
 * A node.
 */
struct node_t {
        ir_node         *node;          /**< The IR-node itself. */
        list_head       node_list;      /**< Double-linked list of leader/follower entries. */
        list_head       cprop_list;     /**< Double-linked partition.cprop list. */
        partition_t     *part;          /**< points to the partition this node belongs to */
        node_t          *next;          /**< Next node on local list (partition.touched, fallen). */
        node_t          *race_next;     /**< Next node on race list. */
        lattice_elem_t  type;           /**< The associated lattice element "type". */
        int             max_user_input; /**< Maximum input number of Def-Use edges. */
        int             next_edge;      /**< Index of the next Def-Use edge to use. */
        int             n_followers;    /**< Number of Follower in the outs set. */
        unsigned        on_touched:1;   /**< Set, if this node is on the partition.touched set. */
        unsigned        on_cprop:1;     /**< Set, if this node is on the partition.cprop list. */
        unsigned        on_fallen:1;    /**< Set, if this node is on the fallen list. */
        unsigned        is_follower:1;  /**< Set, if this node is a follower. */
        unsigned        by_all_const:1; /**< Set, if this node was once evaluated by all constants. */
        unsigned        flagged:2;      /**< 2 Bits, set if this node was visited by race 1 or 2. */
};

/**
 * A partition containing congruent nodes.
 */
struct partition_t {
        list_head         Leader;          /**< The head of partition Leader node list. */
        list_head         Follower;        /**< The head of partition Follower node list. */
        list_head         cprop;           /**< The head of partition.cprop list. */
        list_head         cprop_X;         /**< The head of partition.cprop (Cond nodes and its Projs) list. */
        partition_t       *wl_next;        /**< Next entry in the work list if any. */
        partition_t       *touched_next;   /**< Points to the next partition in the touched set. */
        partition_t       *cprop_next;     /**< Points to the next partition in the cprop list. */
        partition_t       *split_next;     /**< Points to the next partition in the list that must be split by split_by(). */
        node_t            *touched;        /**< The partition.touched set of this partition. */
        unsigned          n_leader;        /**< Number of entries in this partition.Leader. */
        unsigned          n_touched;       /**< Number of entries in the partition.touched. */
        int               max_user_inputs; /**< Maximum number of user inputs of all entries. */
        unsigned          on_worklist:1;   /**< Set, if this partition is in the work list. */
        unsigned          on_touched:1;    /**< Set, if this partition is on the touched set. */
        unsigned          on_cprop:1;      /**< Set, if this partition is on the cprop list. */
        unsigned          type_is_T_or_C:1;/**< Set, if all nodes in this partition have type Top or Constant. */
#ifdef DEBUG_libfirm
        partition_t       *dbg_next;       /**< Link all partitions for debugging */
        unsigned          nr;              /**< A unique number for (what-)mapping, >0. */
#endif
};

typedef struct environment_t {
        struct obstack  obst;           /**< obstack to allocate data structures. */
        partition_t     *worklist;      /**< The work list. */
        partition_t     *cprop;         /**< The constant propagation list. */
        partition_t     *touched;       /**< the touched set. */
        partition_t     *initial;       /**< The initial partition. */
        set             *opcode2id_map; /**< The opcodeMode->id map. */
        pmap            *type2id_map;   /**< The type->id map. */
        int             end_idx;        /**< -1 for local and 0 for global congruences. */
        int             lambda_input;   /**< Captured argument for lambda_partition(). */
        unsigned        modified:1;     /**< Set, if the graph was modified. */
        unsigned        commutative:1;  /**< Set, if commutation nodes should be handled specially. */
        unsigned        unopt_cf:1;     /**< If set, control flow is not optimized due to Unknown. */
#ifdef DEBUG_libfirm
        partition_t     *dbg_list;      /**< List of all partitions. */
#endif
} environment_t;

/** Type of the what function. */
typedef void *(*what_func)(const node_t *node, environment_t *env);

#define get_irn_node(follower)         ((node_t *)get_irn_link(follower))
#define set_irn_node(follower, node)   set_irn_link(follower, node)

/* we do NOT use tarval_unreachable here, instead we use Top for this purpose */
#undef tarval_unreachable
#define tarval_unreachable tarval_top


/** The debug module handle. */
DEBUG_ONLY(static firm_dbg_module_t *dbg;)

/** The what reason. */
DEBUG_ONLY(static const char *what_reason;)

/** Next partition number. */
DEBUG_ONLY(static unsigned part_nr = 0);

/** The tarval returned by Unknown nodes. */
#ifdef WITH_UNKNOWN
#define tarval_UNKNOWN tarval_top
#else
#define tarval_UNKNOWN tarval_bad
#endif

/* forward */
static node_t *identity(node_t *node);

#ifdef CHECK_PARTITIONS
/**
 * Check a partition.
 */
static void check_partition(const partition_t *T) {
        node_t   *node;
        unsigned n = 0;

        list_for_each_entry(node_t, node, &T->Leader, node_list) {
                assert(node->is_follower == 0);
                assert(node->flagged == 0);
                assert(node->part == T);
                ++n;
        }
        assert(n == T->n_leader);

        list_for_each_entry(node_t, node, &T->Follower, node_list) {
                assert(node->is_follower == 1);
                assert(node->flagged == 0);
                assert(node->part == T);
        }
}  /* check_partition */

/**
 * check that all leader nodes in the partition have the same opcode.
 */
static void check_opcode(const partition_t *Z) {
        node_t       *node;
        opcode_key_t key;
        int          first = 1;

        list_for_each_entry(node_t, node, &Z->Leader, node_list) {
                ir_node *irn = node->node;

                if (first) {
                        key.code   = get_irn_opcode(irn);
                        key.mode   = get_irn_mode(irn);
                        key.arity  = get_irn_arity(irn);
                        key.u.proj = 0;
                        key.u.ent  = NULL;

                        switch (get_irn_opcode(irn)) {
                        case iro_Proj:
                                key.u.proj = get_Proj_proj(irn);
                                break;
                        case iro_Sel:
                                key.u.ent = get_Sel_entity(irn);
                                break;
                        default:
                                break;
                        }
                        first = 0;
                } else {
                        assert(key.code  == get_irn_opcode(irn));
                        assert(key.mode  == get_irn_mode(irn));
                        assert(key.arity == get_irn_arity(irn));

                        switch (get_irn_opcode(irn)) {
                        case iro_Proj:
                                assert(key.u.proj == get_Proj_proj(irn));
                                break;
                        case iro_Sel:
                                assert(key.u.ent == get_Sel_entity(irn));
                                break;
                        default:
                                break;
                        }
                }
        }
}  /* check_opcode */

static void check_all_partitions(environment_t *env) {
#ifdef DEBUG_libfirm
        partition_t *P;
        node_t      *node;

        for (P = env->dbg_list; P != NULL; P = P->dbg_next) {
                check_partition(P);
                if (! P->type_is_T_or_C)
                        check_opcode(P);
                list_for_each_entry(node_t, node, &P->Follower, node_list) {
                        node_t *leader = identity(node);

                        assert(leader != node && leader->part == node->part);
                }
        }
#endif
}

/**
 * Check list.
 */
static void do_check_list(const node_t *list, int ofs, const partition_t *Z) {
        const node_t *e;

#define NEXT(e)  *((const node_t **)((char *)(e) + (ofs)))
        for (e = list; e != NULL; e = NEXT(e)) {
                assert(e->part == Z);
        }
#undef NEXT
}  /* ido_check_list */

/**
 * Check a local list.
 */
static void check_list(const node_t *list, const partition_t *Z) {
        do_check_list(list, offsetof(node_t, next), Z);
}  /* check_list */

#else
#define check_partition(T)
#define check_list(list, Z)
#define check_all_partitions(env)
#endif /* CHECK_PARTITIONS */

#ifdef DEBUG_libfirm
static inline lattice_elem_t get_partition_type(const partition_t *X);

/**
 * Dump partition to output.
 */
static void dump_partition(const char *msg, const partition_t *part) {
        const node_t   *node;
        int            first = 1;
        lattice_elem_t type = get_partition_type(part);

        DB((dbg, LEVEL_2, "%s part%u%s (%u, %+F) {\n  ",
                msg, part->nr, part->type_is_T_or_C ? "*" : "",
                part->n_leader, type));
        list_for_each_entry(node_t, node, &part->Leader, node_list) {
                DB((dbg, LEVEL_2, "%s%+F", first ? "" : ", ", node->node));
                first = 0;
        }
        if (! list_empty(&part->Follower)) {
                DB((dbg, LEVEL_2, "\n---\n  "));
                first = 1;
                list_for_each_entry(node_t, node, &part->Follower, node_list) {
                        DB((dbg, LEVEL_2, "%s%+F", first ? "" : ", ", node->node));
                        first = 0;
                }
        }
        DB((dbg, LEVEL_2, "\n}\n"));
}  /* dump_partition */

/**
 * Dumps a list.
 */
static void do_dump_list(const char *msg, const node_t *node, int ofs) {
        const node_t *p;
        int          first = 1;

#define GET_LINK(p, ofs)  *((const node_t **)((char *)(p) + (ofs)))

        DB((dbg, LEVEL_3, "%s = {\n  ", msg));
        for (p = node; p != NULL; p = GET_LINK(p, ofs)) {
                DB((dbg, LEVEL_3, "%s%+F", first ? "" : ", ", p->node));
                first = 0;
        }
        DB((dbg, LEVEL_3, "\n}\n"));

#undef GET_LINK
}  /* do_dump_list */

/**
 * Dumps a race list.
 */
static void dump_race_list(const char *msg, const node_t *list) {
        do_dump_list(msg, list, offsetof(node_t, race_next));
}  /* dump_race_list */

/**
 * Dumps a local list.
 */
static void dump_list(const char *msg, const node_t *list) {
        do_dump_list(msg, list, offsetof(node_t, next));
}  /* dump_list */

/**
 * Dump all partitions.
 */
static void dump_all_partitions(const environment_t *env) {
        const partition_t *P;

        DB((dbg, LEVEL_2, "All partitions\n===============\n"));
        for (P = env->dbg_list; P != NULL; P = P->dbg_next)
                dump_partition("", P);
}  /* dump_all_partitions */

/**
 * Sump a split list.
 */
static void dump_split_list(const partition_t *list) {
        const partition_t *p;

        DB((dbg, LEVEL_2, "Split by %s produced = {\n", what_reason));
        for (p = list; p != NULL; p = p->split_next)
                DB((dbg, LEVEL_2, "part%u, ", p->nr));
        DB((dbg, LEVEL_2, "\n}\n"));
}  /* dump_split_list */

/**
 * Dump partition and type for a node.
 */
static int dump_partition_hook(FILE *F, ir_node *n, ir_node *local) {
        ir_node *irn = local != NULL ? local : n;
        node_t *node = get_irn_node(irn);

        ir_fprintf(F, "info2 : \"partition %u type %+F\"\n", node->part->nr, node->type);
        return 1;
}  /* dump_partition_hook */

#else
#define dump_partition(msg, part)
#define dump_race_list(msg, list)
#define dump_list(msg, list)
#define dump_all_partitions(env)
#define dump_split_list(list)
#endif

#if defined(VERIFY_MONOTONE) && defined (DEBUG_libfirm)
/**
 * Verify that a type transition is monotone
 */
static void verify_type(const lattice_elem_t old_type, node_t *node) {
        if (old_type.tv == node->type.tv) {
                /* no change */
                return;
        }
        if (old_type.tv == tarval_top) {
                /* from Top down-to is always allowed */
                return;
        }
        if (node->type.tv == tarval_bottom || node->type.tv == tarval_reachable) {
                /* bottom reached */
                return;
        }
        panic("combo: wrong translation from %+F to %+F on node %+F", old_type, node->type, node->node);
}  /* verify_type */

#else
#define verify_type(old_type, node)
#endif

/**
 * Compare two pointer values of a listmap.
 */
static int listmap_cmp_ptr(const void *elt, const void *key, size_t size) {
        const listmap_entry_t *e1 = elt;
        const listmap_entry_t *e2 = key;

        (void) size;
        return e1->id != e2->id;
}  /* listmap_cmp_ptr */

/**
 * Initializes a listmap.
 *
 * @param map  the listmap
 */
static void listmap_init(listmap_t *map) {
        map->map    = new_set(listmap_cmp_ptr, 16);
        map->values = NULL;
}  /* listmap_init */

/**
 * Terminates a listmap.
 *
 * @param map  the listmap
 */
static void listmap_term(listmap_t *map) {
        del_set(map->map);
}  /* listmap_term */

/**
 * Return the associated listmap entry for a given id.
 *
 * @param map  the listmap
 * @param id   the id to search for
 *
 * @return the associated listmap entry for the given id
 */
static listmap_entry_t *listmap_find(listmap_t *map, void *id) {
        listmap_entry_t key, *entry;

        key.id   = id;
        key.list = NULL;
        key.next = NULL;
        entry = set_insert(map->map, &key, sizeof(key), HASH_PTR(id));

        if (entry->list == NULL) {
                /* a new entry, put into the list */
                entry->next = map->values;
                map->values = entry;
        }
        return entry;
}  /* listmap_find */

/**
 * Calculate the hash value for an opcode map entry.
 *
 * @param entry  an opcode map entry
 *
 * @return a hash value for the given opcode map entry
 */
static unsigned opcode_hash(const opcode_key_t *entry) {
        return (entry->mode - (ir_mode *)0) * 9 + entry->code + entry->u.proj * 3 + HASH_PTR(entry->u.ent) + entry->arity;
}  /* opcode_hash */

/**
 * Compare two entries in the opcode map.
 */
static int cmp_opcode(const void *elt, const void *key, size_t size) {
        const opcode_key_t *o1 = elt;
        const opcode_key_t *o2 = key;

        (void) size;
        return o1->code != o2->code || o1->mode != o2->mode ||
               o1->arity != o2->arity ||
               o1->u.proj != o2->u.proj || o1->u.ent != o2->u.ent;
}  /* cmp_opcode */

/**
 * Compare two Def-Use edges for input position.
 */
static int cmp_def_use_edge(const void *a, const void *b) {
        const ir_def_use_edge *ea = a;
        const ir_def_use_edge *eb = b;

        /* no overrun, because range is [-1, MAXINT] */
        return ea->pos - eb->pos;
}  /* cmp_def_use_edge */

/**
 * We need the Def-Use edges sorted.
 */
static void sort_irn_outs(node_t *node) {
        ir_node *irn = node->node;
        int n_outs = get_irn_n_outs(irn);

        if (n_outs > 1) {
                qsort(&irn->out[1], n_outs, sizeof(irn->out[0]), cmp_def_use_edge);
        }
        node->max_user_input = irn->out[n_outs].pos;
}  /* sort_irn_outs */

/**
 * Return the type of a node.
 *
 * @param irn  an IR-node
 *
 * @return the associated type of this node
 */
static inline lattice_elem_t get_node_type(const ir_node *irn) {
        return get_irn_node(irn)->type;
}  /* get_node_type */

/**
 * Return the tarval of a node.
 *
 * @param irn  an IR-node
 *
 * @return the associated type of this node
 */
static inline tarval *get_node_tarval(const ir_node *irn) {
        lattice_elem_t type = get_node_type(irn);

        if (is_tarval(type.tv))
                return type.tv;
        return tarval_bottom;
}  /* get_node_type */

/**
 * Add a partition to the worklist.
 */
static inline void add_to_worklist(partition_t *X, environment_t *env) {
        assert(X->on_worklist == 0);
        DB((dbg, LEVEL_2, "Adding part%d to worklist\n", X->nr));
        X->wl_next     = env->worklist;
        X->on_worklist = 1;
        env->worklist  = X;
}  /* add_to_worklist */

/**
 * Create a new empty partition.
 *
 * @param env   the environment
 *
 * @return a newly allocated partition
 */
static inline partition_t *new_partition(environment_t *env) {
        partition_t *part = obstack_alloc(&env->obst, sizeof(*part));

        INIT_LIST_HEAD(&part->Leader);
        INIT_LIST_HEAD(&part->Follower);
        INIT_LIST_HEAD(&part->cprop);
        INIT_LIST_HEAD(&part->cprop_X);
        part->wl_next         = NULL;
        part->touched_next    = NULL;
        part->cprop_next      = NULL;
        part->split_next      = NULL;
        part->touched         = NULL;
        part->n_leader        = 0;
        part->n_touched       = 0;
        part->max_user_inputs = 0;
        part->on_worklist     = 0;
        part->on_touched      = 0;
        part->on_cprop        = 0;
        part->type_is_T_or_C  = 0;
#ifdef DEBUG_libfirm
        part->dbg_next        = env->dbg_list;
        env->dbg_list         = part;
        part->nr              = part_nr++;
#endif

        return part;
}  /* new_partition */

/**
 * Get the first node from a partition.
 */
static inline node_t *get_first_node(const partition_t *X) {
        return list_entry(X->Leader.next, node_t, node_list);
}  /* get_first_node */

/**
 * Return the type of a partition (assuming partition is non-empty and
 * all elements have the same type).
 *
 * @param X  a partition
 *
 * @return the type of the first element of the partition
 */
static inline lattice_elem_t get_partition_type(const partition_t *X) {
        const node_t *first = get_first_node(X);
        return first->type;
}  /* get_partition_type */

/**
 * Creates a partition node for the given IR-node and place it
 * into the given partition.
 *
 * @param irn   an IR-node
 * @param part  a partition to place the node in
 * @param env   the environment
 *
 * @return the created node
 */
static node_t *create_partition_node(ir_node *irn, partition_t *part, environment_t *env) {
        /* create a partition node and place it in the partition */
        node_t *node = obstack_alloc(&env->obst, sizeof(*node));

        INIT_LIST_HEAD(&node->node_list);
        INIT_LIST_HEAD(&node->cprop_list);
        node->node           = irn;
        node->part           = part;
        node->next           = NULL;
        node->race_next      = NULL;
        node->type.tv        = tarval_top;
        node->max_user_input = 0;
        node->next_edge      = 0;
        node->n_followers    = 0;
        node->on_touched     = 0;
        node->on_cprop       = 0;
        node->on_fallen      = 0;
        node->is_follower    = 0;
        node->by_all_const   = 0;
        node->flagged        = 0;
        set_irn_node(irn, node);

        list_add_tail(&node->node_list, &part->Leader);
        ++part->n_leader;

        return node;
}  /* create_partition_node */

/**
 * Pre-Walker, initialize all Nodes' type to U or top and place
 * all nodes into the TOP partition.
 */
static void create_initial_partitions(ir_node *irn, void *ctx) {
        environment_t *env  = ctx;
        partition_t   *part = env->initial;
        node_t        *node;

        node = create_partition_node(irn, part, env);
        sort_irn_outs(node);
        if (node->max_user_input > part->max_user_inputs)
                part->max_user_inputs = node->max_user_input;

        if (is_Block(irn)) {
                set_Block_phis(irn, NULL);
        }
}  /* create_initial_partitions */

/**
 * Post-Walker, collect  all Block-Phi lists, set Cond.
 */
static void init_block_phis(ir_node *irn, void *ctx) {
        (void) ctx;

        if (is_Phi(irn)) {
                add_Block_phi(get_nodes_block(irn), irn);
        }
}  /* init_block_phis */

/**
 * Add a node to the entry.partition.touched set and
 * node->partition to the touched set if not already there.
 *
 * @param y    a node
 * @param env  the environment
 */
static inline void add_to_touched(node_t *y, environment_t *env) {
        if (y->on_touched == 0) {
                partition_t *part = y->part;

                y->next       = part->touched;
                part->touched = y;
                y->on_touched = 1;
                ++part->n_touched;

                if (part->on_touched == 0) {
                        part->touched_next = env->touched;
                        env->touched       = part;
                        part->on_touched   = 1;
                }

                check_list(part->touched, part);
        }
}  /* add_to_touched */

/**
 * Place a node on the cprop list.
 *
 * @param y    the node
 * @param env  the environment
 */
static void add_to_cprop(node_t *y, environment_t *env) {
        ir_node *irn;

        /* Add y to y.partition.cprop. */
        if (y->on_cprop == 0) {
                partition_t *Y = y->part;
                ir_node *irn   = y->node;

                /* place Conds and all its Projs on the cprop_X list */
                if (is_Cond(skip_Proj(irn)))
                        list_add_tail(&y->cprop_list, &Y->cprop_X);
                else
                        list_add_tail(&y->cprop_list, &Y->cprop);
                y->on_cprop   = 1;

                DB((dbg, LEVEL_3, "Add %+F to part%u.cprop\n", y->node, Y->nr));

                /* place its partition on the cprop list */
                if (Y->on_cprop == 0) {
                        Y->cprop_next = env->cprop;
                        env->cprop    = Y;
                        Y->on_cprop   = 1;
                }
        }
        irn = y->node;
        if (get_irn_mode(irn) == mode_T) {
                /* mode_T nodes always produce tarval_bottom, so we must explicitly
                   add it's Proj's to get constant evaluation to work */
                int i;

                for (i = get_irn_n_outs(irn) - 1; i >= 0; --i) {
                        node_t *proj = get_irn_node(get_irn_out(irn, i));

                        add_to_cprop(proj, env);
                }
        } else if (is_Block(irn)) {
                /* Due to the way we handle Phi's, we must place all Phis of a block on the list
                 * if someone placed the block. The Block is only placed if the reachability
                 * changes, and this must be re-evaluated in compute_Phi(). */
                ir_node *phi;
                for (phi = get_Block_phis(irn); phi != NULL; phi = get_Phi_next(phi)) {
                        node_t *p = get_irn_node(phi);
                        add_to_cprop(p, env);
                }
        }
}  /* add_to_cprop */

/**
 * Update the worklist: If Z is on worklist then add Z' to worklist.
 * Else add the smaller of Z and Z' to worklist.
 *
 * @param Z        the Z partition
 * @param Z_prime  the Z' partition, a previous part of Z
 * @param env      the environment
 */
static void update_worklist(partition_t *Z, partition_t *Z_prime, environment_t *env) {
        if (Z->on_worklist || Z_prime->n_leader < Z->n_leader) {
                add_to_worklist(Z_prime, env);
        } else {
                add_to_worklist(Z, env);
        }
}  /* update_worklist */

/**
 * Make all inputs to x no longer be F.def_use edges.
 *
 * @param x  the node
 */
static void move_edges_to_leader(node_t *x) {
        ir_node     *irn = x->node;
        int         i, j, k;

        for (i = get_irn_arity(irn) - 1; i >= 0; --i) {
                node_t  *pred = get_irn_node(get_irn_n(irn, i));
                ir_node *p;
                int     n;

                p = pred->node;
                n = get_irn_n_outs(p);
                for (j = 1; j <= pred->n_followers; ++j) {
                        if (p->out[j].pos == i && p->out[j].use == irn) {
                                /* found a follower edge to x, move it to the Leader */
                                ir_def_use_edge edge = p->out[j];

                                /* remove this edge from the Follower set */
                                p->out[j] = p->out[pred->n_followers];
                                --pred->n_followers;

                                /* sort it into the leader set */
                                for (k = pred->n_followers + 2; k <= n; ++k) {
                                        if (p->out[k].pos >= edge.pos)
                                                break;
                                        p->out[k - 1] = p->out[k];
                                }
                                /* place the new edge here */
                                p->out[k - 1] = edge;

                                /* edge found and moved */
                                break;
                        }
                }
        }
}  /* move_edges_to_leader */

/**
 * Split a partition that has NO followers by a local list.
 *
 * @param Z    partition to split
 * @param g    a (non-empty) node list
 * @param env  the environment
 *
 * @return  a new partition containing the nodes of g
 */
static partition_t *split_no_followers(partition_t *Z, node_t *g, environment_t *env) {
        partition_t *Z_prime;
        node_t      *node;
        unsigned    n = 0;
        int         max_input;

        dump_partition("Splitting ", Z);
        dump_list("by list ", g);

        assert(g != NULL);

        /* Remove g from Z. */
        for (node = g; node != NULL; node = node->next) {
                assert(node->part == Z);
                list_del(&node->node_list);
                ++n;
        }
        assert(n < Z->n_leader);
        Z->n_leader -= n;

        /* Move g to a new partition, Z'. */
        Z_prime = new_partition(env);
        max_input = 0;
        for (node = g; node != NULL; node = node->next) {
                list_add_tail(&node->node_list, &Z_prime->Leader);
                node->part = Z_prime;
                if (node->max_user_input > max_input)
                        max_input = node->max_user_input;
        }
        Z_prime->max_user_inputs = max_input;
        Z_prime->n_leader        = n;

        check_partition(Z);
        check_partition(Z_prime);

        /* for now, copy the type info tag, it will be adjusted in split_by(). */
        Z_prime->type_is_T_or_C = Z->type_is_T_or_C;

        update_worklist(Z, Z_prime, env);

        dump_partition("Now ", Z);
        dump_partition("Created new ", Z_prime);
        return Z_prime;
}  /* split_no_followers */

/**
 * Make the Follower -> Leader transition for a node.
 *
 * @param n  the node
 */
static void follower_to_leader(node_t *n) {
        assert(n->is_follower == 1);

        DB((dbg, LEVEL_2, "%+F make the follower -> leader transition\n", n->node));
        n->is_follower = 0;
        move_edges_to_leader(n);
        list_del(&n->node_list);
        list_add_tail(&n->node_list, &n->part->Leader);
        ++n->part->n_leader;
}  /* follower_to_leader */

/**
 * The environment for one race step.
 */
typedef struct step_env {
        node_t   *initial;    /**< The initial node list. */
        node_t   *unwalked;   /**< The unwalked node list. */
        node_t   *walked;     /**< The walked node list. */
        int      index;       /**< Next index of Follower use_def edge. */
        unsigned side;        /**< side number. */
} step_env;

/**
 * Return non-zero, if a input is a real follower
 *
 * @param irn    the node to check
 * @param input  number of the input
 */
static int is_real_follower(const ir_node *irn, int input) {
        node_t *pred;

        switch (get_irn_opcode(irn)) {
        case iro_Confirm:
                if (input == 1) {
                        /* ignore the Confirm bound input */
                        return 0;
                }
                break;
        case iro_Mux:
                if (input == 0) {
                        /* ignore the Mux sel input */
                        return 0;
                }
                break;
        case iro_Phi: {
                /* dead inputs are not follower edges */
                ir_node *block = get_nodes_block(irn);
                node_t  *pred  = get_irn_node(get_Block_cfgpred(block, input));

                if (pred->type.tv == tarval_unreachable)
                        return 0;
                break;
        }
        case iro_Sub:
        case iro_Shr:
        case iro_Shl:
        case iro_Shrs:
        case iro_Rotl:
                if (input == 1) {
                        /* only a Sub x,0 / Shift x,0 might be a follower */
                        return 0;
                }
                break;
        case iro_Add:
        case iro_Or:
        case iro_Eor:
                pred = get_irn_node(get_irn_n(irn, input));
                if (is_tarval(pred->type.tv) && tarval_is_null(pred->type.tv))
                        return 0;
                break;
        case iro_Mul:
                pred = get_irn_node(get_irn_n(irn, input));
                if (is_tarval(pred->type.tv) && tarval_is_one(pred->type.tv))
                        return 0;
                break;
        case iro_And:
                pred = get_irn_node(get_irn_n(irn, input));
                if (is_tarval(pred->type.tv) && tarval_is_all_one(pred->type.tv))
                        return 0;
                break;
        case iro_Min:
        case iro_Max:
                /* all inputs are followers */
                return 1;
        default:
                assert(!"opcode not implemented yet");
                break;
        }
        return 1;
}  /* is_real_follower */

/**
 * Do one step in the race.
 */
static int step(step_env *env) {
        node_t *n;

        if (env->initial != NULL) {
                /* Move node from initial to unwalked */
                n             = env->initial;
                env->initial  = n->race_next;

                n->race_next  = env->unwalked;
                env->unwalked = n;

                return 0;
        }

        while (env->unwalked != NULL) {
                /* let n be the first node in unwalked */
                n = env->unwalked;
                while (env->index < n->n_followers) {
                        const ir_def_use_edge *edge = &n->node->out[1 + env->index];

                        /* let m be n.F.def_use[index] */
                        node_t *m = get_irn_node(edge->use);

                        assert(m->is_follower);
                        /*
                         * Some inputs, like the get_Confirm_bound are NOT
                         * real followers, sort them out.
                         */
                        if (! is_real_follower(m->node, edge->pos)) {
                                ++env->index;
                                continue;
                        }
                        ++env->index;

                        /* only followers from our partition */
                        if (m->part != n->part)
                                continue;

                        if ((m->flagged & env->side) == 0) {
                                m->flagged |= env->side;

                                if (m->flagged != 3) {
                                        /* visited the first time */
                                        /* add m to unwalked not as first node (we might still need to
                                           check for more follower node */
                                        m->race_next = n->race_next;
                                        n->race_next = m;
                                        return 0;
                                }
                                /* else already visited by the other side and on the other list */
                        }
                }
                /* move n to walked */
                env->unwalked = n->race_next;
                n->race_next  = env->walked;
                env->walked   = n;
                env->index    = 0;
        }
        return 1;
}  /* step */

/**
 * Clear the flags from a list and check for
 * nodes that where touched from both sides.
 *
 * @param list  the list
 */
static int clear_flags(node_t *list) {
        int    res = 0;
        node_t *n;

        for (n = list; n != NULL; n = n->race_next) {
                if (n->flagged == 3) {
                        /* we reach a follower from both sides, this will split congruent
                         * inputs and make it a leader. */
                        follower_to_leader(n);
                        res = 1;
                }
                n->flagged = 0;
        }
        return res;
}  /* clear_flags */

/**
 * Split a partition by a local list using the race.
 *
 * @param pX   pointer to the partition to split, might be changed!
 * @param gg   a (non-empty) node list
 * @param env  the environment
 *
 * @return  a new partition containing the nodes of gg
 */
static partition_t *split(partition_t **pX, node_t *gg, environment_t *env) {
        partition_t *X = *pX;
        partition_t *X_prime;
        list_head   tmp;
        step_env    senv[2];
        node_t      *g, *h, *node, *t;
        int         max_input, transitions, winner, shf;
        unsigned    n;
        DEBUG_ONLY(static int run = 0;)

        DB((dbg, LEVEL_2, "Run %d ", run++));
        if (list_empty(&X->Follower)) {
                /* if the partition has NO follower, we can use the fast
                   splitting algorithm. */
                return split_no_followers(X, gg, env);
        }
        /* else do the race */

        dump_partition("Splitting ", X);
        dump_list("by list ", gg);

        INIT_LIST_HEAD(&tmp);

        /* Remove gg from X.Leader and put into g */
        g = NULL;
        for (node = gg; node != NULL; node = node->next) {
                assert(node->part == X);
                assert(node->is_follower == 0);

                list_del(&node->node_list);
                list_add_tail(&node->node_list, &tmp);
                node->race_next = g;
                g               = node;
        }
        /* produce h */
        h = NULL;
        list_for_each_entry(node_t, node, &X->Leader, node_list) {
                node->race_next = h;
                h               = node;
        }
        /* restore X.Leader */
        list_splice(&tmp, &X->Leader);

        senv[0].initial   = g;
        senv[0].unwalked  = NULL;
        senv[0].walked    = NULL;
        senv[0].index     = 0;
        senv[0].side      = 1;

        senv[1].initial   = h;
        senv[1].unwalked  = NULL;
        senv[1].walked    = NULL;
        senv[1].index     = 0;
        senv[1].side      = 2;

        /*
         * Some informations on the race that are not stated clearly in Click's
         * thesis.
         * 1) A follower stays on the side that reach him first.
         * 2) If the other side reches a follower, if will be converted to
         *    a leader. /This must be done after the race is over, else the
         *    edges we are iterating on are renumbered./
         * 3) /New leader might end up on both sides./
         * 4) /If one side ends up with new Leaders, we must ensure that
         *    they can split out by opcode, hence we have to put _every_
         *    partition with new Leader nodes on the cprop list, as
         *    opcode splitting is done by split_by() at the end of
         *    constant propagation./
         */
        for (;;) {
                if (step(&senv[0])) {
                        winner = 0;
                        break;
                }
                if (step(&senv[1])) {
                        winner = 1;
                        break;
                }
        }
        assert(senv[winner].initial == NULL);
        assert(senv[winner].unwalked == NULL);

        /* clear flags from walked/unwalked */
        shf = winner;
        transitions  = clear_flags(senv[0].unwalked) << shf;
        transitions |= clear_flags(senv[0].walked)   << shf;
        shf ^= 1;
        transitions |= clear_flags(senv[1].unwalked) << shf;
        transitions |= clear_flags(senv[1].walked)   << shf;

        dump_race_list("winner ", senv[winner].walked);

        /* Move walked_{winner} to a new partition, X'. */
        X_prime   = new_partition(env);
        max_input = 0;
        n         = 0;
        for (node = senv[winner].walked; node != NULL; node = node->race_next) {
                list_del(&node->node_list);
                node->part = X_prime;
                if (node->is_follower) {
                        list_add_tail(&node->node_list, &X_prime->Follower);
                } else {
                        list_add_tail(&node->node_list, &X_prime->Leader);
                        ++n;
                }
                if (node->max_user_input > max_input)
                        max_input = node->max_user_input;
        }
        X_prime->n_leader        = n;
        X_prime->max_user_inputs = max_input;
        X->n_leader             -= X_prime->n_leader;

        /* for now, copy the type info tag, it will be adjusted in split_by(). */
        X_prime->type_is_T_or_C = X->type_is_T_or_C;

        /*
         * Even if a follower was not checked by both sides, it might have
         * loose its congruence, so we need to check this case for all follower.
         */
        list_for_each_entry_safe(node_t, node, t, &X_prime->Follower, node_list) {
                if (identity(node) == node) {
                        follower_to_leader(node);
                        transitions |= 1;
                }
        }

        check_partition(X);
        check_partition(X_prime);

        /* X' is the smaller part */
        add_to_worklist(X_prime, env);

        /*
         * If there where follower to leader transitions, ensure that the nodes
         * can be split out if necessary.
         */
        if (transitions & 1) {
                /* place winner partition on the cprop list */
                if (X_prime->on_cprop == 0) {
                        X_prime->cprop_next = env->cprop;
                        env->cprop          = X_prime;
                        X_prime->on_cprop   = 1;
                }
        }
        if (transitions & 2) {
                /* place other partition on the cprop list */
                if (X->on_cprop == 0) {
                        X->cprop_next = env->cprop;
                        env->cprop    = X;
                        X->on_cprop   = 1;
                }
        }

        dump_partition("Now ", X);
        dump_partition("Created new ", X_prime);

        /* we have to ensure that the partition containing g is returned */
        if (winner != 0) {
                *pX = X_prime;
                return X;
        }

        return X_prime;
}  /* split */

/**
 * Returns non-zero if the i'th input of a Phi node is live.
 *
 * @param phi  a Phi-node
 * @param i    an input number
 *
 * @return non-zero if the i'th input of the given Phi node is live
 */
static int is_live_input(ir_node *phi, int i) {
        if (i >= 0) {
                ir_node        *block = get_nodes_block(phi);
                ir_node        *pred  = get_Block_cfgpred(block, i);
                lattice_elem_t type   = get_node_type(pred);

                return type.tv != tarval_unreachable;
        }
        /* else it's the control input, always live */
        return 1;
}  /* is_live_input */

/**
 * Return non-zero if a type is a constant.
 */
static int is_constant_type(lattice_elem_t type) {
        if (type.tv != tarval_bottom && type.tv != tarval_top)
                return 1;
        return 0;
}  /* is_constant_type */

/**
 * Check whether a type is neither Top or a constant.
 * Note: U is handled like Top here, R is a constant.
 *
 * @param type  the type to check
 */
static int type_is_neither_top_nor_const(const lattice_elem_t type) {
        if (is_tarval(type.tv)) {
                if (type.tv == tarval_top)
                        return 0;
                if (tarval_is_constant(type.tv))
                        return 0;
        } else {
                /* is a symconst */
                return 0;
        }
        return 1;
}  /* type_is_neither_top_nor_const */

/**
 * Collect nodes to the touched list.
 *
 * @param list  the list which contains the nodes that must be evaluated
 * @param idx   the index of the def_use edge to evaluate
 * @param env   the environment
 */
static void collect_touched(list_head *list, int idx, environment_t *env) {
        node_t  *x, *y;
        int     end_idx = env->end_idx;

        list_for_each_entry(node_t, x, list, node_list) {
                int num_edges;

                if (idx == -1) {
                        /* leader edges start AFTER follower edges */
                        x->next_edge = x->n_followers + 1;
                }
                num_edges = get_irn_n_outs(x->node);

                /* for all edges in x.L.def_use_{idx} */
                while (x->next_edge <= num_edges) {
                        const ir_def_use_edge *edge = &x->node->out[x->next_edge];
                        ir_node               *succ;

                        /* check if we have necessary edges */
                        if (edge->pos > idx)
                                break;

                        ++x->next_edge;

                        succ = edge->use;

                        /* only non-commutative nodes */
                        if (env->commutative &&
                            (idx == 0 || idx == 1) && is_op_commutative(get_irn_op(succ)))
                                continue;

                        /* ignore the "control input" for non-pinned nodes
                        if we are running in GCSE mode */
                        if (idx < end_idx && get_irn_pinned(succ) != op_pin_state_pinned)
                                continue;

                        y = get_irn_node(succ);
                        assert(get_irn_n(succ, idx) == x->node);

                        /* ignore block edges touching followers */
                        if (idx == -1 && y->is_follower)
                                continue;

                        if (is_constant_type(y->type)) {
                                ir_opcode code = get_irn_opcode(succ);
                                if (code == iro_Sub || code == iro_Cmp)
                                        add_to_cprop(y, env);
                        }

                        /* Partitions of constants should not be split simply because their Nodes have unequal
                           functions or incongruent inputs. */
                        if (type_is_neither_top_nor_const(y->type) &&
                                (! is_Phi(y->node) || is_live_input(y->node, idx))) {
                                        add_to_touched(y, env);
                        }
                }
        }
}  /* collect_touched */

/**
 * Collect commutative nodes to the touched list.
 *
 * @param list  the list which contains the nodes that must be evaluated
 * @param env   the environment
 */
static void collect_commutative_touched(list_head *list, environment_t *env) {
        node_t  *x, *y;

        list_for_each_entry(node_t, x, list, node_list) {
                int num_edges;

                num_edges = get_irn_n_outs(x->node);

                x->next_edge = x->n_followers + 1;

                /* for all edges in x.L.def_use_{idx} */
                while (x->next_edge <= num_edges) {
                        const ir_def_use_edge *edge = &x->node->out[x->next_edge];
                        ir_node               *succ;

                        /* check if we have necessary edges */
                        if (edge->pos > 1)
                                break;

                        ++x->next_edge;
                        if (edge->pos < 0)
                                continue;

                        succ = edge->use;

                        /* only commutative nodes */
                        if (!is_op_commutative(get_irn_op(succ)))
                                continue;

                        y = get_irn_node(succ);
                        if (is_constant_type(y->type)) {
                                ir_opcode code = get_irn_opcode(succ);
                                if (code == iro_Eor)
                                        add_to_cprop(y, env);
                        }

                        /* Partitions of constants should not be split simply because their Nodes have unequal
                           functions or incongruent inputs. */
                        if (type_is_neither_top_nor_const(y->type)) {
                                add_to_touched(y, env);
                        }
                }
        }
}  /* collect_commutative_touched */

/**
 * Split the partitions if caused by the first entry on the worklist.
 *
 * @param env  the environment
 */
static void cause_splits(environment_t *env) {
        partition_t *X, *Z, *N;
        int         idx;

        /* remove the first partition from the worklist */
        X = env->worklist;
        env->worklist  = X->wl_next;
        X->on_worklist = 0;

        dump_partition("Cause_split: ", X);

        if (env->commutative) {
                /* handle commutative nodes first */

                /* empty the touched set: already done, just clear the list */
                env->touched = NULL;

                collect_commutative_touched(&X->Leader, env);
                collect_commutative_touched(&X->Follower, env);

                for (Z = env->touched; Z != NULL; Z = N) {
                        node_t   *e;
                        node_t   *touched  = Z->touched;
                        unsigned n_touched = Z->n_touched;

                        assert(Z->touched != NULL);

                        /* beware, split might change Z */
                        N = Z->touched_next;

                        /* remove it from the touched set */
                        Z->on_touched = 0;

                        /* Empty local Z.touched. */
                        for (e = touched; e != NULL; e = e->next) {
                                assert(e->is_follower == 0);
                                e->on_touched = 0;
                        }
                        Z->touched   = NULL;
                        Z->n_touched = 0;

                        if (0 < n_touched && n_touched < Z->n_leader) {
                                DB((dbg, LEVEL_2, "Split part%d by touched\n", Z->nr));
                                split(&Z, touched, env);
                        } else
                                assert(n_touched <= Z->n_leader);
                }
        }

        /* combine temporary leader and follower list */
        for (idx = -1; idx <= X->max_user_inputs; ++idx) {
                /* empty the touched set: already done, just clear the list */
                env->touched = NULL;

                collect_touched(&X->Leader, idx, env);
                collect_touched(&X->Follower, idx, env);

                for (Z = env->touched; Z != NULL; Z = N) {
                        node_t   *e;
                        node_t   *touched  = Z->touched;
                        unsigned n_touched = Z->n_touched;

                        assert(Z->touched != NULL);

                        /* beware, split might change Z */
                        N = Z->touched_next;

                        /* remove it from the touched set */
                        Z->on_touched = 0;

                        /* Empty local Z.touched. */
                        for (e = touched; e != NULL; e = e->next) {
                                assert(e->is_follower == 0);
                                e->on_touched = 0;
                        }
                        Z->touched   = NULL;
                        Z->n_touched = 0;

                        if (0 < n_touched && n_touched < Z->n_leader) {
                                DB((dbg, LEVEL_2, "Split part%d by touched\n", Z->nr));
                                split(&Z, touched, env);
                        } else
                                assert(n_touched <= Z->n_leader);
                }
        }
}  /* cause_splits */

/**
 * Implements split_by_what(): Split a partition by characteristics given
 * by the what function.
 *
 * @param X     the partition to split
 * @param What  a function returning an Id for every node of the partition X
 * @param P     a list to store the result partitions
 * @param env   the environment
 *
 * @return *P
 */
static partition_t *split_by_what(partition_t *X, what_func What,
                                  partition_t **P, environment_t *env) {
        node_t          *x, *S;
        listmap_t       map;
        listmap_entry_t *iter;
        partition_t     *R;

        /* Let map be an empty mapping from the range of What to (local) list of Nodes. */
        listmap_init(&map);
        list_for_each_entry(node_t, x, &X->Leader, node_list) {
                void            *id = What(x, env);
                listmap_entry_t *entry;

                if (id == NULL) {
                        /* input not allowed, ignore */
                        continue;
                }
                /* Add x to map[What(x)]. */
                entry = listmap_find(&map, id);
                x->next     = entry->list;
                entry->list = x;
        }
        /* Let P be a set of Partitions. */

        /* for all sets S except one in the range of map do */
        for (iter = map.values; iter != NULL; iter = iter->next) {
                if (iter->next == NULL) {
                        /* this is the last entry, ignore */
                        break;
                }
                S = iter->list;

                /* Add SPLIT( X, S ) to P. */
                DB((dbg, LEVEL_2, "Split part%d by WHAT = %s\n", X->nr, what_reason));
                R = split(&X, S, env);
                R->split_next = *P;
                *P            = R;
        }
        /* Add X to P. */
        X->split_next = *P;
        *P            = X;

        listmap_term(&map);
        return *P;
}  /* split_by_what */

/** lambda n.(n.type) */
static void *lambda_type(const node_t *node, environment_t *env) {
        (void)env;
        return node->type.tv;
}  /* lambda_type */

/** lambda n.(n.opcode) */
static void *lambda_opcode(const node_t *node, environment_t *env) {
        opcode_key_t key, *entry;
        ir_node      *irn = node->node;

        key.code   = get_irn_opcode(irn);
        key.mode   = get_irn_mode(irn);
        key.arity  = get_irn_arity(irn);
        key.u.proj = 0;
        key.u.ent  = NULL;

        switch (get_irn_opcode(irn)) {
        case iro_Proj:
                key.u.proj = get_Proj_proj(irn);
                break;
        case iro_Sel:
                key.u.ent = get_Sel_entity(irn);
                break;
        default:
                break;
        }

        entry = set_insert(env->opcode2id_map, &key, sizeof(key), opcode_hash(&key));
        return entry;
}  /* lambda_opcode */

/** lambda n.(n[i].partition) */
static void *lambda_partition(const node_t *node, environment_t *env) {
        ir_node *skipped = skip_Proj(node->node);
        ir_node *pred;
        node_t  *p;
        int     i = env->lambda_input;

        if (i >= get_irn_arity(node->node)) {
                /*
                 * We are outside the allowed range: This can happen even
                 * if we have split by opcode first: doing so might move Followers
                 * to Leaders and those will have a different opcode!
                 * Note that in this case the partition is on the cprop list and will be
                 * split again.
                 */
                return NULL;
        }

        /* ignore the "control input" for non-pinned nodes
           if we are running in GCSE mode */
        if (i < env->end_idx && get_irn_pinned(skipped) != op_pin_state_pinned)
                return NULL;

        pred = i == -1 ? get_irn_n(skipped, i) : get_irn_n(node->node, i);
        p    = get_irn_node(pred);

        return p->part;
}  /* lambda_partition */

/** lambda n.(n[i].partition) for commutative nodes */
static void *lambda_commutative_partition(const node_t *node, environment_t *env) {
        ir_node     *irn     = node->node;
        ir_node     *skipped = skip_Proj(irn);
        ir_node     *pred, *left, *right;
        node_t      *p;
        partition_t *pl, *pr;
        int         i = env->lambda_input;

        if (i >= get_irn_arity(node->node)) {
                /*
                 * We are outside the allowed range: This can happen even
                 * if we have split by opcode first: doing so might move Followers
                 * to Leaders and those will have a different opcode!
                 * Note that in this case the partition is on the cprop list and will be
                 * split again.
                 */
                return NULL;
        }

        /* ignore the "control input" for non-pinned nodes
           if we are running in GCSE mode */
        if (i < env->end_idx && get_irn_pinned(skipped) != op_pin_state_pinned)
                return NULL;

        if (i == -1) {
                pred = get_irn_n(skipped, i);
                p    = get_irn_node(pred);
                return p->part;
        }

        if (is_op_commutative(get_irn_op(irn))) {
                /* normalize partition order by returning the "smaller" on input 0,
                   the "bigger" on input 1. */
                left  = get_binop_left(irn);
                pl    = get_irn_node(left)->part;
                right = get_binop_right(irn);
                pr    = get_irn_node(right)->part;

                if (i == 0)
                        return pl < pr ? pl : pr;
                else
                return pl > pr ? pl : pr;
        } else {
                /* a not split out Follower */
                pred = get_irn_n(irn, i);
                p    = get_irn_node(pred);

                return p->part;
        }
}  /* lambda_commutative_partition */

/**
 * Returns true if a type is a constant (and NOT Top
 * or Bottom).
 */
static int is_con(const lattice_elem_t type) {
        /* be conservative */
        if (is_tarval(type.tv))
                return tarval_is_constant(type.tv);
        return is_entity(type.sym.entity_p);
}  /* is_con */

/**
 * Implements split_by().
 *
 * @param X    the partition to split
 * @param env  the environment
 */
static void split_by(partition_t *X, environment_t *env) {
        partition_t *I, *P = NULL;
        int         input;

        dump_partition("split_by", X);

        if (X->n_leader == 1) {
                /* we have only one leader, no need to split, just check it's type */
                node_t *x = get_first_node(X);
                X->type_is_T_or_C = x->type.tv == tarval_top || is_con(x->type);
                return;
        }

        DEBUG_ONLY(what_reason = "lambda n.(n.type)";)
        P = split_by_what(X, lambda_type, &P, env);
        dump_split_list(P);

        /* adjust the type tags, we have split partitions by type */
        for (I = P; I != NULL; I = I->split_next) {
                node_t *x = get_first_node(I);
                I->type_is_T_or_C = x->type.tv == tarval_top || is_con(x->type);
        }

        do {
                partition_t *Y = P;

                P = P->split_next;
                if (Y->n_leader > 1) {
                        /* we do not want split the TOP or constant partitions */
                        if (! Y->type_is_T_or_C) {
                                partition_t *Q = NULL;

                                DEBUG_ONLY(what_reason = "lambda n.(n.opcode)";)
                                Q = split_by_what(Y, lambda_opcode, &Q, env);
                                dump_split_list(Q);

                                do {
                                        partition_t *Z = Q;

                                        Q = Q->split_next;
                                        if (Z->n_leader > 1) {
                                                const node_t *first = get_first_node(Z);
                                                int          arity  = get_irn_arity(first->node);
                                                partition_t  *R, *S;
                                                what_func    what = lambda_partition;
                                                DEBUG_ONLY(char buf[64];)

                                                if (env->commutative && is_op_commutative(get_irn_op(first->node)))
                                                        what = lambda_commutative_partition;

                                                /*
                                                 * BEWARE: during splitting by input 2 for instance we might
                                                 * create new partitions which are different by input 1, so collect
                                                 * them and split further.
                                                 */
                                                Z->split_next = NULL;
                                                R             = Z;
                                                S             = NULL;
                                                for (input = arity - 1; input >= -1; --input) {
                                                        do {
                                                                partition_t *Z_prime = R;

                                                                R = R->split_next;
                                                                if (Z_prime->n_leader > 1) {
                                                                        env->lambda_input = input;
                                                                        DEBUG_ONLY(snprintf(buf, sizeof(buf), "lambda n.(n[%d].partition)", input);)
                                                                        DEBUG_ONLY(what_reason = buf;)
                                                                        S = split_by_what(Z_prime, what, &S, env);
                                                                        dump_split_list(S);
                                                                } else {
                                                                        Z_prime->split_next = S;
                                                                        S                   = Z_prime;
                                                                }
                                                        } while (R != NULL);
                                                        R = S;
                                                        S = NULL;
                                                }
                                        }
                                } while (Q != NULL);
                        }
                }
        } while (P != NULL);
}  /* split_by */

/**
 * (Re-)compute the type for a given node.
 *
 * @param node  the node
 */
static void default_compute(node_t *node) {
        int     i;
        ir_node *irn = node->node;
        node_t  *block = get_irn_node(get_nodes_block(irn));

        if (block->type.tv == tarval_unreachable) {
                node->type.tv = tarval_top;
                return;
        }

        /* if any of the data inputs have type top, the result is type top */
        for (i = get_irn_arity(irn) - 1; i >= 0; --i) {
                ir_node *pred = get_irn_n(irn, i);
                node_t  *p    = get_irn_node(pred);

                if (p->type.tv == tarval_top) {
                        node->type.tv = tarval_top;
                        return;
                }
        }

        if (get_irn_mode(node->node) == mode_X)
                node->type.tv = tarval_reachable;
        else
                node->type.tv = computed_value(irn);
}  /* default_compute */

/**
 * (Re-)compute the type for a Block node.
 *
 * @param node  the node
 */
static void compute_Block(node_t *node) {
        int     i;
        ir_node *block = node->node;

        if (block == get_irg_start_block(current_ir_graph)) {
                /* start block is always reachable */
                node->type.tv = tarval_reachable;
                return;
        }

        for (i = get_Block_n_cfgpreds(block) - 1; i >= 0; --i) {
                node_t *pred = get_irn_node(get_Block_cfgpred(block, i));

                if (pred->type.tv == tarval_reachable) {
                        /* A block is reachable, if at least of predecessor is reachable. */
                        node->type.tv = tarval_reachable;
                        return;
                }
        }
        node->type.tv = tarval_top;
}  /* compute_Block */

/**
 * (Re-)compute the type for a Bad node.
 *
 * @param node  the node
 */
static void compute_Bad(node_t *node) {
        /* Bad nodes ALWAYS compute Top */
        node->type.tv = tarval_top;
}  /* compute_Bad */

/**
 * (Re-)compute the type for an Unknown node.
 *
 * @param node  the node
 */
static void compute_Unknown(node_t *node) {
        /* While Unknown nodes should compute Top this is dangerous:
         * a Top input to a Cond would lead to BOTH control flows unreachable.
         * While this is correct in the given semantics, it would destroy the Firm
         * graph.
         *
         * It would be safe to compute Top IF it can be assured, that only Cmp
         * nodes are inputs to Conds. We check that first.
         * This is the way Frontends typically build Firm, but some optimizations
         * (cond_eval for instance) might replace them by Phib's...
         */
        node->type.tv = tarval_UNKNOWN;
}  /* compute_Unknown */

/**
 * (Re-)compute the type for a Jmp node.
 *
 * @param node  the node
 */
static void compute_Jmp(node_t *node) {
        node_t *block = get_irn_node(get_nodes_block(node->node));

        node->type = block->type;
}  /* compute_Jmp */

/**
 * (Re-)compute the type for the Return node.
 *
 * @param node  the node
 */
static void compute_Return(node_t *node) {
        /* The Return node is NOT dead if it is in a reachable block.
         * This is already checked in compute(). so we can return
         * Reachable here. */
        node->type.tv = tarval_reachable;
}  /* compute_Return */

/**
 * (Re-)compute the type for the End node.
 *
 * @param node  the node
 */
static void compute_End(node_t *node) {
        /* the End node is NOT dead of course */
        node->type.tv = tarval_reachable;
}  /* compute_End */

/**
 * (Re-)compute the type for a SymConst node.
 *
 * @param node  the node
 */
static void compute_SymConst(node_t *node) {
        ir_node *irn = node->node;
        node_t  *block = get_irn_node(get_nodes_block(irn));

        if (block->type.tv == tarval_unreachable) {
                node->type.tv = tarval_top;
                return;
        }
        switch (get_SymConst_kind(irn)) {
        case symconst_addr_ent:
        /* case symconst_addr_name: cannot handle this yet */
                node->type.sym = get_SymConst_symbol(irn);
                break;
        default:
                node->type.tv = computed_value(irn);
        }
}  /* compute_SymConst */

/**
 * (Re-)compute the type for a Phi node.
 *
 * @param node  the node
 */
static void compute_Phi(node_t *node) {
        int            i;
        ir_node        *phi = node->node;
        lattice_elem_t type;

        /* if a Phi is in a unreachable block, its type is TOP */
        node_t *block = get_irn_node(get_nodes_block(phi));

        if (block->type.tv == tarval_unreachable) {
                node->type.tv = tarval_top;
                return;
        }

        /* Phi implements the Meet operation */
        type.tv = tarval_top;
        for (i = get_Phi_n_preds(phi) - 1; i >= 0; --i) {
                node_t *pred   = get_irn_node(get_Phi_pred(phi, i));
                node_t *pred_X = get_irn_node(get_Block_cfgpred(block->node, i));

                if (pred_X->type.tv == tarval_unreachable || pred->type.tv == tarval_top) {
                        /* ignore TOP inputs: We must check here for unreachable blocks,
                           because Firm constants live in the Start Block are NEVER Top.
                           Else, a Phi (1,2) will produce Bottom, even if the 2 for instance
                           comes from a unreachable input. */
                        continue;
                }
                if (pred->type.tv == tarval_bottom) {
                        node->type.tv = tarval_bottom;
                        return;
                } else if (type.tv == tarval_top) {
                        /* first constant found */
                        type = pred->type;
                } else if (type.tv != pred->type.tv) {
                        /* different constants or tarval_bottom */
                        node->type.tv = tarval_bottom;
                        return;
                }
                /* else nothing, constants are the same */
        }
        node->type = type;
}  /* compute_Phi */

/**
 * (Re-)compute the type for an Add. Special case: one nodes is a Zero Const.
 *
 * @param node  the node
 */
static void compute_Add(node_t *node) {
        ir_node        *sub = node->node;
        node_t         *l   = get_irn_node(get_Add_left(sub));
        node_t         *r   = get_irn_node(get_Add_right(sub));
        lattice_elem_t a    = l->type;
        lattice_elem_t b    = r->type;
        ir_mode        *mode;

        if (a.tv == tarval_top || b.tv == tarval_top) {
                node->type.tv = tarval_top;
        } else if (a.tv == tarval_bottom || b.tv == tarval_bottom) {
                node->type.tv = tarval_bottom;
        } else {
                /* x + 0 = 0 + x = x, but beware of floating point +0 + -0, so we
                   must call tarval_add() first to handle this case! */
                if (is_tarval(a.tv)) {
                        if (is_tarval(b.tv)) {
                                node->type.tv = tarval_add(a.tv, b.tv);
                                return;
                        }
                        mode = get_tarval_mode(a.tv);
                        if (a.tv == get_mode_null(mode)) {
                                node->type = b;
                                return;
                        }
                } else if (is_tarval(b.tv)) {
                        mode = get_tarval_mode(b.tv);
                        if (b.tv == get_mode_null(mode)) {
                                node->type = a;
                                return;
                        }
                }
                node->type.tv = tarval_bottom;
        }
}  /* compute_Add */

/**
 * (Re-)compute the type for a Sub. Special case: both nodes are congruent.
 *
 * @param node  the node
 */
static void compute_Sub(node_t *node) {
        ir_node        *sub = node->node;
        node_t         *l   = get_irn_node(get_Sub_left(sub));
        node_t         *r   = get_irn_node(get_Sub_right(sub));
        lattice_elem_t a    = l->type;
        lattice_elem_t b    = r->type;
        tarval         *tv;

        if (a.tv == tarval_top || b.tv == tarval_top) {
                node->type.tv = tarval_top;
        } else if (is_con(a) && is_con(b)) {
                if (is_tarval(a.tv) && is_tarval(b.tv)) {
                        node->type.tv = tarval_sub(a.tv, b.tv, get_irn_mode(sub));
                } else if (is_tarval(a.tv) && tarval_is_null(a.tv)) {
                        node->type = b;
                } else if (is_tarval(b.tv) && tarval_is_null(b.tv)) {
                        node->type = a;
                } else {
                        node->type.tv = tarval_bottom;
                }
                node->by_all_const = 1;
        } else if (r->part == l->part &&
                   (!mode_is_float(get_irn_mode(l->node)))) {
                /*
                 * BEWARE: a - a is NOT always 0 for floating Point values, as
                 * NaN op NaN = NaN, so we must check this here.
                 */
                ir_mode *mode = get_irn_mode(sub);
                tv = get_mode_null(mode);

                /* if the node was ONCE evaluated by all constants, but now
                   this breaks AND we get from the argument partitions a different
                   result, switch to bottom.
                   This happens because initially all nodes are in the same partition ... */
                if (node->by_all_const && node->type.tv != tv)
                        tv = tarval_bottom;
                node->type.tv = tv;
        } else {
                node->type.tv = tarval_bottom;
        }
}  /* compute_Sub */

/**
 * (Re-)compute the type for an Eor. Special case: both nodes are congruent.
 *
 * @param node  the node
 */
static void compute_Eor(node_t *node) {
        ir_node        *eor = node->node;
        node_t         *l   = get_irn_node(get_Eor_left(eor));
        node_t         *r   = get_irn_node(get_Eor_right(eor));
        lattice_elem_t a    = l->type;
        lattice_elem_t b    = r->type;
        tarval         *tv;

        if (a.tv == tarval_top || b.tv == tarval_top) {
                node->type.tv = tarval_top;
        } else if (is_con(a) && is_con(b)) {
                if (is_tarval(a.tv) && is_tarval(b.tv)) {
                        node->type.tv = tarval_eor(a.tv, b.tv);
                } else if (is_tarval(a.tv) && tarval_is_null(a.tv)) {
                        node->type = b;
                } else if (is_tarval(b.tv) && tarval_is_null(b.tv)) {
                        node->type = a;
                } else {
                        node->type.tv = tarval_bottom;
                }
                node->by_all_const = 1;
        } else if (r->part == l->part) {
                ir_mode *mode = get_irn_mode(eor);
                tv = get_mode_null(mode);

                /* if the node was ONCE evaluated by all constants, but now
                   this breaks AND we get from the argument partitions a different
                   result, switch to bottom.
                   This happens because initially all nodes are in the same partition ... */
                if (node->by_all_const && node->type.tv != tv)
                        tv = tarval_bottom;
                node->type.tv = tv;
        } else {
                node->type.tv = tarval_bottom;
        }
}  /* compute_Eor */

/**
 * (Re-)compute the type for Cmp.
 *
 * @param node  the node
 */
static void compute_Cmp(node_t *node) {
        ir_node        *cmp  = node->node;
        node_t         *l    = get_irn_node(get_Cmp_left(cmp));
        node_t         *r    = get_irn_node(get_Cmp_right(cmp));
        lattice_elem_t a     = l->type;
        lattice_elem_t b     = r->type;

        if (a.tv == tarval_top || b.tv == tarval_top) {
                node->type.tv = tarval_top;
        } else if (r->part == l->part) {
                /* both nodes congruent, we can probably do something */
                node->type.tv = tarval_b_true;
        } else if (is_con(a) && is_con(b)) {
                /* both nodes are constants, we can probably do something */
                node->type.tv = tarval_b_true;
        } else {
                node->type.tv = tarval_bottom;
        }
}  /* compute_Cmp */

/**
 * (Re-)compute the type for a Proj(Cmp).
 *
 * @param node  the node
 * @param cond  the predecessor Cmp node
 */
static void compute_Proj_Cmp(node_t *node, ir_node *cmp) {
        ir_node        *proj = node->node;
        node_t         *l    = get_irn_node(get_Cmp_left(cmp));
        node_t         *r    = get_irn_node(get_Cmp_right(cmp));
        lattice_elem_t a     = l->type;
        lattice_elem_t b     = r->type;
        pn_Cmp         pnc   = get_Proj_proj(proj);
        tarval         *tv;

        if (a.tv == tarval_top || b.tv == tarval_top) {
                node->type.tv = tarval_undefined;
        } else if (is_con(a) && is_con(b)) {
                default_compute(node);
                node->by_all_const = 1;
        } else if (r->part == l->part &&
                   (!mode_is_float(get_irn_mode(l->node)) || pnc == pn_Cmp_Lt || pnc == pn_Cmp_Gt)) {
                /*
                 * BEWARE: a == a is NOT always True for floating Point values, as
                 * NaN != NaN is defined, so we must check this here.
                 */
                tv = pnc & pn_Cmp_Eq ? tarval_b_true: tarval_b_false;

                /* if the node was ONCE evaluated by all constants, but now
                   this breaks AND we get from the argument partitions a different
                   result, switch to bottom.
                   This happens because initially all nodes are in the same partition ... */
                if (node->by_all_const && node->type.tv != tv)
                        tv = tarval_bottom;
                node->type.tv = tv;
        } else {
                node->type.tv = tarval_bottom;
        }
}  /* compute_Proj_Cmp */

/**
 * (Re-)compute the type for a Proj(Cond).
 *
 * @param node  the node
 * @param cond  the predecessor Cond node
 */
static void compute_Proj_Cond(node_t *node, ir_node *cond) {
        ir_node *proj     = node->node;
        long    pnc       = get_Proj_proj(proj);
        ir_node *sel      = get_Cond_selector(cond);
        node_t  *selector = get_irn_node(sel);

        /*
         * Note: it is crucial for the monotony that the Proj(Cond)
         * are evaluates after all predecessors of the Cond selector are
         * processed.
         * Example
         *
         * if (x != 0)
         *
         * Due to the fact that 0 is a const, the Cmp gets immediately
         * on the cprop list. It will be evaluated before x is evaluated,
         * might leaving x as Top. When later x is evaluated, the Cmp
         * might change its value.
         * BUT if the Cond is evaluated before this happens, Proj(Cond, FALSE)
         * gets R, and later changed to F if Cmp is evaluated to True!
         *
         * We prevent this by putting Conds in an extra cprop_X queue, which
         * gets evaluated after the cprop queue is empty.
         *
         * Note that this even happens with Click's original algorithm, if
         * Cmp(x, 0) is evaluated to True first and later changed to False
         * if x was Top first and later changed to a Const ...
         * It is unclear how Click solved that problem ...
         *
         * However, in rare cases even this does not help, if a Top reaches
         * a compare  through a Phi, than Proj(Cond) is evaluated changing
         * the type of the Phi to something other.
         * So, we take the last resort and bind the type to R once
         * it is calculated.
         *
         * (This might be even the way Click works around the whole problem).
         *
         * Finally, we may miss some optimization possibilities due to this:
         *
         * x = phi(Top, y)
         * if (x == 0)
         *
         * If Top reaches the if first, than we decide for != here.
         * If y later is evaluated to 0, we cannot revert this decision
         * and must live with both outputs enabled. If this happens,
         * we get an unresolved if (true) in the code ...
         *
         * In Click's version where this decision is done at the Cmp,
         * the Cmp is NOT optimized away than (if y evaluated to 1
         * for instance) and we get a if (1 == 0) here ...
         *
         * Both solutions are suboptimal.
         * At least, we could easily detect this problem and run
         * cf_opt() (or even combo) again :-(
         */
        if (node->type.tv == tarval_reachable)
                return;

        if (get_irn_mode(sel) == mode_b) {
                /* an IF */
                if (pnc == pn_Cond_true) {
                        if (selector->type.tv == tarval_b_false) {
                                node->type.tv = tarval_unreachable;
                        } else if (selector->type.tv == tarval_b_true) {
                                node->type.tv = tarval_reachable;
                        } else if (selector->type.tv == tarval_bottom) {
                                node->type.tv = tarval_reachable;
                        } else {
                                assert(selector->type.tv == tarval_top);
#ifdef WITH_UNKNOWN
                                /* any condition based on Top is "!=" */
                                node->type.tv = tarval_unreachable;
#else
                                node->type.tv = tarval_unreachable;
#endif
                        }
                } else {
                        assert(pnc == pn_Cond_false);

                        if (selector->type.tv == tarval_b_false) {
                                node->type.tv = tarval_reachable;
                        } else if (selector->type.tv == tarval_b_true) {
                                node->type.tv = tarval_unreachable;
                        } else if (selector->type.tv == tarval_bottom) {
                                node->type.tv = tarval_reachable;
                        } else {
                                assert(selector->type.tv == tarval_top);
#ifdef WITH_UNKNOWN
                                /* any condition based on Top is "!=" */
                                node->type.tv = tarval_reachable;
#else
                                node->type.tv = tarval_unreachable;
#endif
                        }
                }
        } else {
                /* an SWITCH */
                if (selector->type.tv == tarval_bottom) {
                        node->type.tv = tarval_reachable;
                } else if (selector->type.tv == tarval_top) {
#ifdef WITH_UNKNOWN
                        if (pnc == get_Cond_defaultProj(cond)) {
                                /* a switch based of Top is always "default" */
                                node->type.tv = tarval_reachable;
                        } else
#endif
                                node->type.tv = tarval_unreachable;
                } else {
                        long value = get_tarval_long(selector->type.tv);
                        if (pnc == get_Cond_defaultProj(cond)) {
                                /* default switch, have to check ALL other cases */
                                int i;

                                for (i = get_irn_n_outs(cond) - 1; i >= 0; --i) {
                                        ir_node *succ = get_irn_out(cond, i);

                                        if (succ == proj)
                                                continue;
                                        if (value == get_Proj_proj(succ)) {
                                                /* we found a match, will NOT take the default case */
                                                node->type.tv = tarval_unreachable;
                                                return;
                                        }
                                }
                                /* all cases checked, no match, will take default case */
                                node->type.tv = tarval_reachable;
                        } else {
                                /* normal case */
                                node->type.tv = value == pnc ? tarval_reachable : tarval_unreachable;
                        }
                }
        }
}  /* compute_Proj_Cond */

/**
 * (Re-)compute the type for a Proj-Node.
 *
 * @param node  the node
 */
static void compute_Proj(node_t *node) {
        ir_node *proj = node->node;
        ir_mode *mode = get_irn_mode(proj);
        node_t  *block = get_irn_node(get_nodes_block(skip_Proj(proj)));
        ir_node *pred  = get_Proj_pred(proj);

        if (block->type.tv == tarval_unreachable) {
                /* a Proj in a unreachable Block stay Top */
                node->type.tv = tarval_top;
                return;
        }
        if (get_irn_node(pred)->type.tv == tarval_top && !is_Cond(pred)) {
                /* if the predecessor is Top, its Proj follow */
                node->type.tv = tarval_top;
                return;
        }

        if (mode == mode_M) {
                /* mode M is always bottom */
                node->type.tv = tarval_bottom;
                return;
        }
        if (mode != mode_X) {
                if (is_Cmp(pred))
                        compute_Proj_Cmp(node, pred);
                else
                        default_compute(node);
                return;
        }
        /* handle mode_X nodes */

        switch (get_irn_opcode(pred)) {
        case iro_Start:
                /* the Proj_X from the Start is always reachable.
                   However this is already handled at the top. */
                node->type.tv = tarval_reachable;
                break;
        case iro_Cond:
                compute_Proj_Cond(node, pred);
                break;
        default:
                default_compute(node);
        }
}  /* compute_Proj */

/**
 * (Re-)compute the type for a Confirm.
 *
 * @param node  the node
 */
static void compute_Confirm(node_t *node) {
        ir_node *confirm = node->node;
        node_t  *pred = get_irn_node(get_Confirm_value(confirm));

        if (get_Confirm_cmp(confirm) == pn_Cmp_Eq) {
                node_t *bound = get_irn_node(get_Confirm_bound(confirm));

                if (is_con(bound->type)) {
                        /* is equal to a constant */
                        node->type = bound->type;
                        return;
                }
        }
        /* a Confirm is a copy OR a Const */
        node->type = pred->type;
}  /* compute_Confirm */

/**
 * (Re-)compute the type for a Max.
 *
 * @param node  the node
 */
static void compute_Max(node_t *node) {
        ir_node        *op = node->node;
        node_t         *l  = get_irn_node(get_binop_left(op));
        node_t         *r  = get_irn_node(get_binop_right(op));
        lattice_elem_t a   = l->type;
        lattice_elem_t b   = r->type;

        if (a.tv == tarval_top || b.tv == tarval_top) {
                node->type.tv = tarval_top;
        } else if (is_con(a) && is_con(b)) {
                /* both nodes are constants, we can probably do something */
                if (a.tv == b.tv) {
                        /* this case handles SymConsts as well */
                        node->type = a;
                } else {
                        ir_mode *mode   = get_irn_mode(op);
                        tarval  *tv_min = get_mode_min(mode);

                        if (a.tv == tv_min)
                                node->type = b;
                        else if (b.tv == tv_min)
                                node->type = a;
                        else if (is_tarval(a.tv) && is_tarval(b.tv)) {
                                if (tarval_cmp(a.tv, b.tv) & pn_Cmp_Gt)
                                        node->type.tv = a.tv;
                                else
                                        node->type.tv = b.tv;
                        } else {
                                node->type.tv = tarval_bad;
                        }
                }
        } else if (r->part == l->part) {
                /* both nodes congruent, we can probably do something */
                node->type = a;
        } else {
                node->type.tv = tarval_bottom;
        }
}  /* compute_Max */

/**
 * (Re-)compute the type for a Min.
 *
 * @param node  the node
 */
static void compute_Min(node_t *node) {
        ir_node        *op = node->node;
        node_t         *l  = get_irn_node(get_binop_left(op));
        node_t         *r  = get_irn_node(get_binop_right(op));
        lattice_elem_t a   = l->type;
        lattice_elem_t b   = r->type;

        if (a.tv == tarval_top || b.tv == tarval_top) {
                node->type.tv = tarval_top;
        } else if (is_con(a) && is_con(b)) {
                /* both nodes are constants, we can probably do something */
                if (a.tv == b.tv) {
                        /* this case handles SymConsts as well */
                        node->type = a;
                } else {
                        ir_mode *mode   = get_irn_mode(op);
                        tarval  *tv_max = get_mode_max(mode);

                        if (a.tv == tv_max)
                                node->type = b;
                        else if (b.tv == tv_max)
                                node->type = a;
                        else if (is_tarval(a.tv) && is_tarval(b.tv)) {
                                if (tarval_cmp(a.tv, b.tv) & pn_Cmp_Gt)
                                        node->type.tv = a.tv;
                                else
                                        node->type.tv = b.tv;
                        } else {
                                node->type.tv = tarval_bad;
                        }
                }
        } else if (r->part == l->part) {
                /* both nodes congruent, we can probably do something */
                node->type = a;
        } else {
                node->type.tv = tarval_bottom;
        }
}  /* compute_Min */

/**
 * (Re-)compute the type for a given node.
 *
 * @param node  the node
 */
static void compute(node_t *node) {
        ir_node *irn = node->node;
        compute_func func;

#ifndef VERIFY_MONOTONE
        /*
         * Once a node reaches bottom, the type cannot fall further
         * in the lattice and we can stop computation.
         * Do not take this exit if the monotony verifier is
         * enabled to catch errors.
         */
        if (node->type.tv == tarval_bottom)
                return;
#endif
        if (is_no_Block(irn)) {
                /* for pinned nodes, check its control input */
                if (get_irn_pinned(skip_Proj(irn)) == op_pin_state_pinned) {
                        node_t *block = get_irn_node(get_nodes_block(irn));

                        if (block->type.tv == tarval_unreachable) {
                                node->type.tv = tarval_top;
                                return;
                        }
                }
        }

        func = (compute_func)node->node->op->ops.generic;
        if (func != NULL)
                func(node);
}  /* compute */

/*
 * Identity functions: Note that one might thing that identity() is just a
 * synonym for equivalent_node(). While this is true, we cannot use it for the algorithm
 * here, because it expects that the identity node is one of the inputs, which is NOT
 * always true for equivalent_node() which can handle (and does sometimes) DAGs.
 * So, we have our own implementation, which copies some parts of equivalent_node()
 */

/**
 * Calculates the Identity for Phi nodes
 */
static node_t *identity_Phi(node_t *node) {
        ir_node *phi    = node->node;
        ir_node *block  = get_nodes_block(phi);
        node_t  *n_part = NULL;
        int     i;

        for (i = get_Phi_n_preds(phi) - 1; i >= 0; --i) {
                node_t *pred_X = get_irn_node(get_Block_cfgpred(block, i));

                if (pred_X->type.tv == tarval_reachable) {
                        node_t *pred = get_irn_node(get_Phi_pred(phi, i));

                        if (n_part == NULL)
                                n_part = pred;
                        else if (n_part->part != pred->part) {
                                /* incongruent inputs, not a follower */
                                return node;
                        }
                }
        }
        /* if n_part is NULL here, all inputs path are dead, the Phi computes
         * tarval_top, is in the TOP partition and should NOT being split! */
        assert(n_part != NULL);
        return n_part;
}  /* identity_Phi */

/**
 * Calculates the Identity for commutative 0 neutral nodes.
 */
static node_t *identity_comm_zero_binop(node_t *node) {
        ir_node *op   = node->node;
        node_t  *a    = get_irn_node(get_binop_left(op));
        node_t  *b    = get_irn_node(get_binop_right(op));
        ir_mode *mode = get_irn_mode(op);
        tarval  *zero;

        /* for FP these optimizations are only allowed if fp_strict_algebraic is disabled */
        if (mode_is_float(mode) && (get_irg_fp_model(current_ir_graph) & fp_strict_algebraic))
                return node;

        /* node: no input should be tarval_top, else the binop would be also
         * Top and not being split. */
        zero = get_mode_null(mode);
        if (a->type.tv == zero)
                return b;
        if (b->type.tv == zero)
                return a;
        return node;
}  /* identity_comm_zero_binop */

/**
 * Calculates the Identity for Shift nodes.
 */
static node_t *identity_shift(node_t *node) {
        ir_node *op   = node->node;
        node_t  *b    = get_irn_node(get_binop_right(op));
        ir_mode *mode = get_irn_mode(b->node);
        tarval  *zero;

        /* node: no input should be tarval_top, else the binop would be also
         * Top and not being split. */
        zero = get_mode_null(mode);
        if (b->type.tv == zero)
                return get_irn_node(get_binop_left(op));
        return node;
}  /* identity_shift */

/**
 * Calculates the Identity for Mul nodes.
 */
static node_t *identity_Mul(node_t *node) {
        ir_node *op   = node->node;
        node_t  *a    = get_irn_node(get_Mul_left(op));
        node_t  *b    = get_irn_node(get_Mul_right(op));
        ir_mode *mode = get_irn_mode(op);
        tarval  *one;

        /* for FP these optimizations are only allowed if fp_strict_algebraic is disabled */
        if (mode_is_float(mode) && (get_irg_fp_model(current_ir_graph) & fp_strict_algebraic))
                return node;

        /* node: no input should be tarval_top, else the binop would be also
         * Top and not being split. */
        one = get_mode_one(mode);
        if (a->type.tv == one)
                return b;
        if (b->type.tv == one)
                return a;
        return node;
}  /* identity_Mul */

/**
 * Calculates the Identity for Sub nodes.
 */
static node_t *identity_Sub(node_t *node) {
        ir_node *sub  = node->node;
        node_t  *b    = get_irn_node(get_Sub_right(sub));
        ir_mode *mode = get_irn_mode(sub);

        /* for FP these optimizations are only allowed if fp_strict_algebraic is disabled */
        if (mode_is_float(mode) && (get_irg_fp_model(current_ir_graph) & fp_strict_algebraic))
                return node;

        /* node: no input should be tarval_top, else the binop would be also
         * Top and not being split. */
        if (b->type.tv == get_mode_null(mode))
                return get_irn_node(get_Sub_left(sub));
        return node;
}  /* identity_Sub */

/**
 * Calculates the Identity for And nodes.
 */
static node_t *identity_And(node_t *node) {
        ir_node *and = node->node;
        node_t  *a   = get_irn_node(get_And_left(and));
        node_t  *b   = get_irn_node(get_And_right(and));
        tarval  *neutral = get_mode_all_one(get_irn_mode(and));

        /* node: no input should be tarval_top, else the And would be also
         * Top and not being split. */
        if (a->type.tv == neutral)
                return b;
        if (b->type.tv == neutral)
                return a;
        return node;
}  /* identity_And */

/**
 * Calculates the Identity for Confirm nodes.
 */
static node_t *identity_Confirm(node_t *node) {
        ir_node *confirm = node->node;

        /* a Confirm is always a Copy */
        return get_irn_node(get_Confirm_value(confirm));
}  /* identity_Confirm */

/**
 * Calculates the Identity for Mux nodes.
 */
static node_t *identity_Mux(node_t *node) {
        ir_node *mux = node->node;
        node_t  *t   = get_irn_node(get_Mux_true(mux));
        node_t  *f   = get_irn_node(get_Mux_false(mux));
        /*node_t  *sel; */

        if (t->part == f->part)
                return t;

        /* for now, the 1-input identity is not supported */
#if 0
        sel = get_irn_node(get_Mux_sel(mux));

        /* Mux sel input is mode_b, so it is always a tarval */
        if (sel->type.tv == tarval_b_true)
                return t;
        if (sel->type.tv == tarval_b_false)
                return f;
#endif
        return node;
}  /* identity_Mux */

/**
 * Calculates the Identity for Min nodes.
 */
static node_t *identity_Min(node_t *node) {
        ir_node *op   = node->node;
        node_t  *a    = get_irn_node(get_binop_left(op));
        node_t  *b    = get_irn_node(get_binop_right(op));
        ir_mode *mode = get_irn_mode(op);
        tarval  *tv_max;

        if (a->part == b->part) {
                /* leader of multiple predecessors */
                return a;
        }

        /* works even with NaN */
        tv_max = get_mode_max(mode);
        if (a->type.tv == tv_max)
                return b;
        if (b->type.tv == tv_max)
                return a;
        return node;
}  /* identity_Min */

/**
 * Calculates the Identity for Max nodes.
 */
static node_t *identity_Max(node_t *node) {
        ir_node *op   = node->node;
        node_t  *a    = get_irn_node(get_binop_left(op));
        node_t  *b    = get_irn_node(get_binop_right(op));
        ir_mode *mode = get_irn_mode(op);
        tarval  *tv_min;

        if (a->part == b->part) {
                /* leader of multiple predecessors */
                return a;
        }

        /* works even with NaN */
        tv_min = get_mode_min(mode);
        if (a->type.tv == tv_min)
                return b;
        if (b->type.tv == tv_min)
                return a;
        return node;
}  /* identity_Max */

/**
 * Calculates the Identity for nodes.
 */
static node_t *identity(node_t *node) {
        ir_node *irn = node->node;

        switch (get_irn_opcode(irn)) {
        case iro_Phi:
                return identity_Phi(node);
        case iro_Mul:
                return identity_Mul(node);
        case iro_Add:
        case iro_Or:
        case iro_Eor:
                return identity_comm_zero_binop(node);
        case iro_Shr:
        case iro_Shl:
        case iro_Shrs:
        case iro_Rotl:
                return identity_shift(node);
        case iro_And:
                return identity_And(node);
        case iro_Sub:
                return identity_Sub(node);
        case iro_Confirm:
                return identity_Confirm(node);
        case iro_Mux:
                return identity_Mux(node);
        case iro_Min:
                return identity_Min(node);
        case iro_Max:
                return identity_Max(node);
        default:
                return node;
        }
}  /* identity */

/**
 * Node follower is a (new) follower of leader, segregate Leader
 * out edges.
 */
static void segregate_def_use_chain_1(const ir_node *follower, node_t *leader) {
        ir_node *l   = leader->node;
        int     j, i, n = get_irn_n_outs(l);

        DB((dbg, LEVEL_2, "%+F is a follower of %+F\n", follower, leader->node));
        /* The leader edges must remain sorted, but follower edges can
           be unsorted. */
        for (i = leader->n_followers + 1; i <= n; ++i) {
                if (l->out[i].use == follower) {
                        ir_def_use_edge t = l->out[i];

                        for (j = i - 1; j >= leader->n_followers + 1; --j)
                                l->out[j + 1] = l->out[j];
                        ++leader->n_followers;
                        l->out[leader->n_followers] = t;
                        break;
                }
        }
}  /* segregate_def_use_chain_1 */

/**
 * Node follower is a (new) follower segregate its Leader
 * out edges.
 *
 * @param follower  the follower IR node
 */
static void segregate_def_use_chain(const ir_node *follower) {
        int i;

        for (i = get_irn_arity(follower) - 1; i >= 0; --i) {
                node_t *pred = get_irn_node(get_irn_n(follower, i));

                segregate_def_use_chain_1(follower, pred);
        }
}  /* segregate_def_use_chain */

/**
 * Propagate constant evaluation.
 *
 * @param env  the environment
 */
static void propagate(environment_t *env) {
        partition_t    *X, *Y;
        node_t         *x;
        lattice_elem_t old_type;
        node_t         *fallen;
        unsigned       n_fallen, old_type_was_T_or_C;
        int            i;

        while (env->cprop != NULL) {
                void *oldopcode = NULL;

                /* remove the first partition X from cprop */
                X           = env->cprop;
                X->on_cprop = 0;
                env->cprop  = X->cprop_next;

                old_type_was_T_or_C = X->type_is_T_or_C;

                DB((dbg, LEVEL_2, "Propagate type on part%d\n", X->nr));
                fallen   = NULL;
                n_fallen = 0;
                for (;;) {
                        int cprop_empty   = list_empty(&X->cprop);
                        int cprop_X_empty = list_empty(&X->cprop_X);

                        if (cprop_empty && cprop_X_empty) {
                                /* both cprop lists are empty */
                                break;
                        }

                        /* remove the first Node x from X.cprop */
                        if (cprop_empty) {
                                /* Get a node from the cprop_X list only if
                                 * all data nodes are processed.
                                 * This ensures, that all inputs of the Cond
                                 * predecessor are processed if its type is still Top.
                                 */
                                x = list_entry(X->cprop_X.next, node_t, cprop_list);
                        } else {
                                x = list_entry(X->cprop.next, node_t, cprop_list);
                        }

                        //assert(x->part == X);
                        list_del(&x->cprop_list);
                        x->on_cprop = 0;

                        if (x->is_follower && identity(x) == x) {
                                /* check the opcode first */
                                if (oldopcode == NULL) {
                                        oldopcode = lambda_opcode(get_first_node(X), env);
                                }
                                if (oldopcode != lambda_opcode(x, env)) {
                                        if (x->on_fallen == 0) {
                                                /* different opcode -> x falls out of this partition */
                                                x->next      = fallen;
                                                x->on_fallen = 1;
                                                fallen       = x;
                                                ++n_fallen;
                                                DB((dbg, LEVEL_2, "Add node %+F to fallen\n", x->node));
                                        }
                                }

                                /* x will make the follower -> leader transition */
                                follower_to_leader(x);
                        }

                        /* compute a new type for x */
                        old_type = x->type;
                        DB((dbg, LEVEL_3, "computing type of %+F\n", x->node));
                        compute(x);
                        if (x->type.tv != old_type.tv) {
                                DB((dbg, LEVEL_2, "node %+F has changed type from %+F to %+F\n", x->node, old_type, x->type));
                                verify_type(old_type, x);

                                if (x->on_fallen == 0) {
                                        /* Add x to fallen. Nodes might fall from T -> const -> _|_, so check that they are
                                           not already on the list. */
                                        x->next      = fallen;
                                        x->on_fallen = 1;
                                        fallen       = x;
                                        ++n_fallen;
                                        DB((dbg, LEVEL_2, "Add node %+F to fallen\n", x->node));
                                }
                                for (i = get_irn_n_outs(x->node) - 1; i >= 0; --i) {
                                        ir_node *succ = get_irn_out(x->node, i);
                                        node_t  *y    = get_irn_node(succ);

                                        /* Add y to y.partition.cprop. */
                                        add_to_cprop(y, env);
                                }
                        }
                }

                if (n_fallen > 0 && n_fallen != X->n_leader) {
                        DB((dbg, LEVEL_2, "Splitting part%d by fallen\n", X->nr));
                        Y = split(&X, fallen, env);
                        /*
                         * We have split out fallen node. The type of the result
                         * partition is NOT set yet.
                         */
                        Y->type_is_T_or_C = 0;
                } else {
                        Y = X;
                }
                /* remove the flags from the fallen list */
                for (x = fallen; x != NULL; x = x->next)
                        x->on_fallen = 0;

                if (old_type_was_T_or_C) {
                        node_t *y, *tmp;

                        /* check if some nodes will make the leader -> follower transition */
                        list_for_each_entry_safe(node_t, y, tmp, &Y->Leader, node_list) {
                                if (y->type.tv != tarval_top && ! is_con(y->type)) {
                                        node_t *eq_node = identity(y);

                                        if (eq_node != y && eq_node->part == y->part) {
                                                DB((dbg, LEVEL_2, "Node %+F is a follower of %+F\n", y->node, eq_node->node));
                                                /* move to Follower */
                                                y->is_follower = 1;
                                                list_del(&y->node_list);
                                                list_add_tail(&y->node_list, &Y->Follower);
                                                --Y->n_leader;

                                                segregate_def_use_chain(y->node);
                                        }
                                }
                        }
                }
                split_by(Y, env);
        }
}  /* propagate */

/**
 * Get the leader for a given node from its congruence class.
 *
 * @param irn  the node
 */
static ir_node *get_leader(node_t *node) {
        partition_t *part = node->part;

        if (part->n_leader > 1 || node->is_follower) {
                if (node->is_follower) {
                        DB((dbg, LEVEL_2, "Replacing follower %+F\n", node->node));
                }
                else
                        DB((dbg, LEVEL_2, "Found congruence class for %+F\n", node->node));

                return get_first_node(part)->node;
        }
        return node->node;
}  /* get_leader */

/**
 * Returns non-zero if a mode_T node has only one reachable output.
 */
static int only_one_reachable_proj(ir_node *n) {
        int i, k = 0;

        for (i = get_irn_n_outs(n) - 1; i >= 0; --i) {
                ir_node *proj = get_irn_out(n, i);
                node_t  *node;

                /* skip non-control flow Proj's */
                if (get_irn_mode(proj) != mode_X)
                        continue;

                node = get_irn_node(proj);
                if (node->type.tv == tarval_reachable) {
                        if (++k > 1)
                                return 0;
                }
        }
        return 1;
}  /* only_one_reachable_proj */

/**
 * Return non-zero if the control flow predecessor node pred
 * is the only reachable control flow exit of its block.
 *
 * @param pred  the control flow exit
 */
static int can_exchange(ir_node *pred) {
        if (is_Start(pred))
                return 0;
        else if (is_Jmp(pred))
                return 1;
        else if (get_irn_mode(pred) == mode_T) {
                /* if the predecessor block has more than one
                   reachable outputs we cannot remove the block */
                return only_one_reachable_proj(pred);
        }
        return 0;
}  /* can_exchange */

/**
 * Block Post-Walker, apply the analysis results on control flow by
 * shortening Phi's and Block inputs.
 */
static void apply_cf(ir_node *block, void *ctx) {
        environment_t *env = ctx;
        node_t        *node = get_irn_node(block);
        int           i, j, k, n;
        ir_node       **ins, **in_X;
        ir_node       *phi, *next;

        n = get_Block_n_cfgpreds(block);

        if (node->type.tv == tarval_unreachable) {
                env->modified = 1;

                for (i = n - 1; i >= 0; --i) {
                        ir_node *pred = get_Block_cfgpred(block, i);

                        if (! is_Bad(pred)) {
                                node_t *pred_bl = get_irn_node(get_nodes_block(skip_Proj(pred)));

                                if (pred_bl->flagged == 0) {
                                        pred_bl->flagged = 3;

                                        if (pred_bl->type.tv == tarval_reachable) {
                                                /*
                                                 * We will remove an edge from block to its pred.
                                                 * This might leave the pred block as an endless loop
                                                 */
                                                if (! is_backedge(block, i))
                                                        keep_alive(pred_bl->node);
                                        }
                                }
                        }
                }

                /* the EndBlock is always reachable even if the analysis
                   finds out the opposite :-) */
                if (block != get_irg_end_block(current_ir_graph)) {
                        /* mark dead blocks */
                        set_Block_dead(block);
                        DB((dbg, LEVEL_1, "Removing dead %+F\n", block));
                } else {
                        /* the endblock is unreachable */
                        set_irn_in(block, 0, NULL);
                }
                return;
        }

        if (n == 1) {
                /* only one predecessor combine */
                ir_node *pred = skip_Proj(get_Block_cfgpred(block, 0));

                if (can_exchange(pred)) {
                        ir_node *new_block = get_nodes_block(pred);
                        DB((dbg, LEVEL_1, "Fuse %+F with %+F\n", block, new_block));
                        DBG_OPT_COMBO(block, new_block, FS_OPT_COMBO_CF);
                        exchange(block, new_block);
                        node->node = new_block;
                        env->modified = 1;
                }
                return;
        }

        NEW_ARR_A(ir_node *, in_X, n);
        k = 0;
        for (i = 0; i < n; ++i) {
                ir_node *pred = get_Block_cfgpred(block, i);
                node_t  *node = get_irn_node(pred);

                if (node->type.tv == tarval_reachable) {
                        in_X[k++] = pred;
                } else {
                        DB((dbg, LEVEL_1, "Removing dead input %d from %+F (%+F)\n", i, block, pred));
                        if (! is_Bad(pred)) {
                                node_t *pred_bl = get_irn_node(get_nodes_block(skip_Proj(pred)));

                                if (pred_bl->flagged == 0) {
                                        pred_bl->flagged = 3;

                                        if (pred_bl->type.tv == tarval_reachable) {
                                                /*
                                                 * We will remove an edge from block to its pred.
                                                 * This might leave the pred block as an endless loop
                                                 */
                                                if (! is_backedge(block, i))
                                                        keep_alive(pred_bl->node);
                                        }
                                }
                        }
                }
        }
        if (k >= n)
                return;

        /* fix Phi's */
        NEW_ARR_A(ir_node *, ins, n);
        for (phi = get_Block_phis(block); phi != NULL; phi = next) {
                node_t *node = get_irn_node(phi);

                next = get_Phi_next(phi);
                if (is_tarval(node->type.tv) && tarval_is_constant(node->type.tv)) {
                        /* this Phi is replaced by a constant */
                        tarval  *tv = node->type.tv;
                        ir_node *c  = new_r_Const(current_ir_graph, block, get_tarval_mode(tv), tv);

                        set_irn_node(c, node);
                        node->node = c;
                        DB((dbg, LEVEL_1, "%+F is replaced by %+F\n", phi, c));
                        DBG_OPT_COMBO(phi, c, FS_OPT_COMBO_CONST);
                        exchange(phi, c);
                        env->modified = 1;
                } else {
                        j = 0;
                        for (i = 0; i < n; ++i) {
                                node_t *pred = get_irn_node(get_Block_cfgpred(block, i));

                                if (pred->type.tv == tarval_reachable) {
                                        ins[j++] = get_Phi_pred(phi, i);
                                }
                        }
                        if (j == 1) {
                                /* this Phi is replaced by a single predecessor */
                                ir_node *s = ins[0];
                                node_t *phi_node = get_irn_node(phi);

                                node->node = s;
                                DB((dbg, LEVEL_1, "%+F is replaced by %+F because of cf change\n", phi, s));
                                DBG_OPT_COMBO(phi, s, FS_OPT_COMBO_FOLLOWER);
                                exchange(phi, s);
                                phi_node->node = s;
                                env->modified = 1;
                        } else {
                                set_irn_in(phi, j, ins);
                                env->modified = 1;
                        }
                }
        }

        /* fix block */
        if (k == 1) {
                /* this Block has only one live predecessor */
                ir_node *pred = skip_Proj(in_X[0]);

                if (can_exchange(pred)) {
                        ir_node *new_block = get_nodes_block(pred);
                        DBG_OPT_COMBO(block, new_block, FS_OPT_COMBO_CF);
                        exchange(block, new_block);
                        node->node = new_block;
                        env->modified = 1;
                        return;
                }
        }
        set_irn_in(block, k, in_X);
        env->modified = 1;
}  /* apply_cf */

/**
 * Exchange a node by its leader.
 * Beware: in rare cases the mode might be wrong here, for instance
 * AddP(x, NULL) is a follower of x, but with different mode.
 * Fix it here.
 */
static void exchange_leader(ir_node *irn, ir_node *leader) {
        ir_mode *mode = get_irn_mode(irn);
        if (mode != get_irn_mode(leader)) {
                /* The conv is a no-op, so we are fre to place in
                 * either in the block of the leader OR in irn's block.
                 * Probably placing it into leaders block might reduce
                 * the number of Conv due to CSE. */
                ir_node  *block = get_nodes_block(leader);
                dbg_info *dbg   = get_irn_dbg_info(irn);

                leader = new_rd_Conv(dbg, current_ir_graph, block, leader, mode);
        }
        exchange(irn, leader);
}

/**
 * Post-Walker, apply the analysis results;
 */
static void apply_result(ir_node *irn, void *ctx) {
        environment_t *env = ctx;
        node_t        *node = get_irn_node(irn);

        if (is_Block(irn) || is_End(irn) || is_Bad(irn)) {
                /* blocks already handled, do not touch the End node */
        } else {
                node_t *block = get_irn_node(get_nodes_block(irn));

                if (block->type.tv == tarval_unreachable) {
                        ir_node *bad = get_irg_bad(current_ir_graph);

                        /* here, bad might already have a node, but this can be safely ignored
                           as long as bad has at least ONE valid node */
                        set_irn_node(bad, node);
                        node->node = bad;
                        DB((dbg, LEVEL_1, "%+F is unreachable\n", irn));
                        exchange(irn, bad);
                        env->modified = 1;
                }
                else if (node->type.tv == tarval_top) {
                        /* don't kick away Unknown's, they might be still needed */
                        if (! is_Unknown(irn)) {
                                ir_mode *mode = get_irn_mode(irn);
                                ir_node *unk  = new_r_Unknown(current_ir_graph, mode);

                                /* control flow should already be handled at apply_cf() */
                                assert(mode != mode_X);

                                /* see comment above */
                                set_irn_node(unk, node);
                                node->node = unk;
                                DB((dbg, LEVEL_1, "%+F computes Top\n", irn));
                                exchange(irn, unk);
                                env->modified = 1;
                        }
                }
                else if (get_irn_mode(irn) == mode_X) {
                        if (is_Proj(irn)) {
                                /* leave or Jmp */
                                ir_node *cond = get_Proj_pred(irn);

                                if (is_Cond(cond)) {
                                        if (only_one_reachable_proj(cond)) {
                                                ir_node *jmp = new_r_Jmp(current_ir_graph, block->node);
                                                set_irn_node(jmp, node);
                                                node->node = jmp;
                                                DB((dbg, LEVEL_1, "%+F is replaced by %+F\n", irn, jmp));
                                                DBG_OPT_COMBO(irn, jmp, FS_OPT_COMBO_CF);
                                                exchange(irn, jmp);
                                                env->modified = 1;
                                        } else {
                                                node_t *sel = get_irn_node(get_Cond_selector(cond));
                                                tarval *tv  = sel->type.tv;

                                                if (is_tarval(tv) && tarval_is_constant(tv)) {
                                                        /* The selector is a constant, but more
                                                         * than one output is active: An unoptimized
                                                         * case found. */
                                                        env->unopt_cf = 1;
                                                }
                                        }
                                }
                        }
                } else {
                        /* normal data node */
                        if (is_tarval(node->type.tv) && tarval_is_constant(node->type.tv)) {
                                tarval *tv = node->type.tv;

                                /*
                                 * Beware: never replace mode_T nodes by constants. Currently we must mark
                                 * mode_T nodes with constants, but do NOT replace them.
                                 */
                                if (! is_Const(irn) && get_irn_mode(irn) != mode_T) {
                                        /* can be replaced by a constant */
                                        ir_node *c = new_r_Const(current_ir_graph, block->node, get_tarval_mode(tv), tv);
                                        set_irn_node(c, node);
                                        node->node = c;
                                        DB((dbg, LEVEL_1, "%+F is replaced by %+F\n", irn, c));
                                        DBG_OPT_COMBO(irn, c, FS_OPT_COMBO_CONST);
                                        exchange_leader(irn, c);
                                        env->modified = 1;
                                }
                        } else if (is_entity(node->type.sym.entity_p)) {
                                if (! is_SymConst(irn)) {
                                        /* can be replaced by a SymConst */
                                        ir_node *symc = new_r_SymConst(current_ir_graph, block->node, get_irn_mode(irn), node->type.sym, symconst_addr_ent);
                                        set_irn_node(symc, node);
                                        node->node = symc;

                                        DB((dbg, LEVEL_1, "%+F is replaced by %+F\n", irn, symc));
                                        DBG_OPT_COMBO(irn, symc, FS_OPT_COMBO_CONST);
                                        exchange_leader(irn, symc);
                                        env->modified = 1;
                                }
                        } else if (is_Confirm(irn)) {
                                /* Confirms are always follower, but do not kill them here */
                        } else {
                                ir_node *leader = get_leader(node);

                                if (leader != irn) {
                                        int non_strict_phi = 0;

                                        /*
                                         * Beware: Do not remove Phi(Unknown, ..., x, ..., Unknown)
                                         * as this might create non-strict programs.
                                         */
                                        if (node->is_follower && is_Phi(irn) && !is_Unknown(leader)) {
                                                int i;

                                                for (i = get_Phi_n_preds(irn) - 1; i >= 0; --i) {
                                                        ir_node *pred = get_Phi_pred(irn, i);

                                                        if (is_Unknown(pred)) {
                                                                non_strict_phi = 1;
                                                                break;
                                                        }
                                                }
                                        }
                                        if (! non_strict_phi) {
                                                DB((dbg, LEVEL_1, "%+F from part%d is replaced by %+F\n", irn, node->part->nr, leader));
                                                if (node->is_follower)
                                                        DBG_OPT_COMBO(irn, leader, FS_OPT_COMBO_FOLLOWER);
                                                else
                                                        DBG_OPT_COMBO(irn, leader, FS_OPT_COMBO_CONGRUENT);
                                                exchange_leader(irn, leader);
                                                env->modified = 1;
                                        }
                                }
                        }
                }
        }
}  /* apply_result */

/**
 * Fix the keep-alives by deleting unreachable ones.
 */
static void apply_end(ir_node *end, environment_t *env) {
        int i, j,  n = get_End_n_keepalives(end);
        ir_node **in;

        if (n > 0)
                NEW_ARR_A(ir_node *, in, n);

        /* fix the keep alive */
        for (i = j = 0; i < n; i++) {
                ir_node *ka   = get_End_keepalive(end, i);
                node_t  *node = get_irn_node(ka);

                if (! is_Block(ka))
                        node = get_irn_node(get_nodes_block(ka));

                if (node->type.tv != tarval_unreachable && !is_Bad(ka))
                        in[j++] = ka;
        }
        if (j != n) {
                set_End_keepalives(end, j, in);
                env->modified = 1;
        }
}  /* apply_end */

#define SET(code) op_##code->ops.generic = (op_func)compute_##code

/**
 * sets the generic functions to compute.
 */
static void set_compute_functions(void) {
        int i;

        /* set the default compute function */
        for (i = get_irp_n_opcodes() - 1; i >= 0; --i) {
                ir_op *op = get_irp_opcode(i);
                op->ops.generic = (op_func)default_compute;
        }

        /* set specific functions */
        SET(Block);
        SET(Unknown);
        SET(Bad);
        SET(Jmp);
        SET(Phi);
        SET(Add);
        SET(Sub);
        SET(Eor);
        SET(SymConst);
        SET(Cmp);
        SET(Proj);
        SET(Confirm);
        SET(Return);
        SET(End);

        if (op_Max != NULL)
                SET(Max);
        if (op_Min != NULL)
                SET(Min);

}  /* set_compute_functions */

void combo(ir_graph *irg) {
        environment_t env;
        ir_node       *initial_bl;
        node_t        *start;
        ir_graph      *rem = current_ir_graph;

        current_ir_graph = irg;

        /* register a debug mask */
        FIRM_DBG_REGISTER(dbg, "firm.opt.combo");

        DB((dbg, LEVEL_1, "Doing COMBO for %+F\n", irg));

        obstack_init(&env.obst);
        env.worklist       = NULL;
        env.cprop          = NULL;
        env.touched        = NULL;
        env.initial        = NULL;
#ifdef DEBUG_libfirm
        env.dbg_list       = NULL;
#endif
        env.opcode2id_map  = new_set(cmp_opcode, iro_Last * 4);
        env.type2id_map    = pmap_create();
        env.end_idx        = get_opt_global_cse() ? 0 : -1;
        env.lambda_input   = 0;
        env.commutative    = 1;
        env.modified       = 0;
        env.unopt_cf       = 0;

        assure_irg_outs(irg);
        assure_cf_loop(irg);

        /* we have our own value_of function */
        set_value_of_func(get_node_tarval);

        set_compute_functions();
        DEBUG_ONLY(part_nr = 0);

        ir_reserve_resources(irg, IR_RESOURCE_IRN_LINK);

        /* create the initial partition and place it on the work list */
        env.initial = new_partition(&env);
        add_to_worklist(env.initial, &env);
        irg_walk_graph(irg, create_initial_partitions, init_block_phis, &env);

        /* set the hook: from now, every node has a partition and a type */
        DEBUG_ONLY(set_dump_node_vcgattr_hook(dump_partition_hook));

        /* all nodes on the initial partition have type Top */
        env.initial->type_is_T_or_C = 1;

        /* Place the START Node's partition on cprop.
           Place the START Node on its local worklist. */
        initial_bl = get_irg_start_block(irg);
        start      = get_irn_node(initial_bl);
        add_to_cprop(start, &env);

        do {
                propagate(&env);
                if (env.worklist != NULL)
                        cause_splits(&env);
        } while (env.cprop != NULL || env.worklist != NULL);

        dump_all_partitions(&env);
        check_all_partitions(&env);

#if 0
        dump_ir_block_graph(irg, "-partition");
#endif

        /* apply the result */
        irg_block_walk_graph(irg, NULL, apply_cf, &env);
        /* Kill keep-alives of dead blocks: this speeds up apply_result()
         * and fixes assertion because dead cf to dead blocks is NOT removed by
         * apply_cf(). */
        apply_end(get_irg_end(irg), &env);
        irg_walk_graph(irg, NULL, apply_result, &env);

        if (env.unopt_cf) {
                DB((dbg, LEVEL_1, "Unoptimized Control Flow left"));
        }

        if (env.modified) {
                /* control flow might changed */
                set_irg_outs_inconsistent(irg);
                set_irg_extblk_inconsistent(irg);
                set_irg_doms_inconsistent(irg);
                set_irg_loopinfo_inconsistent(irg);
        }

        ir_free_resources(irg, IR_RESOURCE_IRN_LINK);

        /* remove the partition hook */
        DEBUG_ONLY(set_dump_node_vcgattr_hook(NULL));

        pmap_destroy(env.type2id_map);
        del_set(env.opcode2id_map);
        obstack_free(&env.obst, NULL);

        /* restore value_of() default behavior */
        set_value_of_func(NULL);
        current_ir_graph = rem;
}  /* combo */