A Partitioned Boolean Quadratic Programming (PBQP) based register allocator.
Contributed by Lang Hames.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@56959 91177308-0d34-0410-b5e6-96231b3b80d8
diff --git a/lib/CodeGen/PBQP.cpp b/lib/CodeGen/PBQP.cpp
new file mode 100644
index 0000000..ade9e7c
--- /dev/null
+++ b/lib/CodeGen/PBQP.cpp
@@ -0,0 +1,1395 @@
+//===---------------- PBQP.cpp --------- PBQP Solver ------------*- C++ -*-===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// Developed by: Bernhard Scholz
+// The Univesity of Sydney
+// http://www.it.usyd.edu.au/~scholz
+//===----------------------------------------------------------------------===//
+
+
+#include <limits>
+#include <cassert>
+
+#include "PBQP.h"
+
+namespace llvm {
+
+/**************************************************************************
+ * Data Structures
+ **************************************************************************/
+
+/* edge of PBQP graph */
+typedef struct adjnode {
+ struct adjnode *prev, /* doubly chained list */
+ *succ,
+ *reverse; /* reverse edge */
+ int adj; /* adj. node */
+ PBQPMatrix *costs; /* cost matrix of edge */
+
+ bool tc_valid; /* flag whether following fields are valid */
+ int *tc_safe_regs; /* safe registers */
+ int tc_impact; /* impact */
+} adjnode;
+
+/* bucket node */
+typedef struct bucketnode {
+ struct bucketnode *prev; /* doubly chained list */
+ struct bucketnode *succ;
+ int u; /* node */
+} bucketnode;
+
+/* data structure of partitioned boolean quadratic problem */
+struct pbqp {
+ int num_nodes; /* number of nodes */
+ int max_deg; /* maximal degree of a node */
+ bool solved; /* flag that indicates whether PBQP has been solved yet */
+ bool optimal; /* flag that indicates whether PBQP is optimal */
+ PBQPNum min;
+ bool changed; /* flag whether graph has changed in simplification */
+
+ /* node fields */
+ PBQPVector **node_costs; /* cost vectors of nodes */
+ int *node_deg; /* node degree of nodes */
+ int *solution; /* solution for node */
+ adjnode **adj_list; /* adj. list */
+ bucketnode **bucket_ptr; /* bucket pointer of a node */
+
+ /* node stack */
+ int *stack; /* stack of nodes */
+ int stack_ptr; /* stack pointer */
+
+ /* bucket fields */
+ bucketnode **bucket_list; /* bucket list */
+
+ int num_r0; /* counters for number statistics */
+ int num_ri;
+ int num_rii;
+ int num_rn;
+ int num_rn_special;
+};
+
+bool isInf(PBQPNum n) { return n == std::numeric_limits<PBQPNum>::infinity(); }
+
+/*****************************************************************************
+ * allocation/de-allocation of pbqp problem
+ ****************************************************************************/
+
+/* allocate new partitioned boolean quadratic program problem */
+pbqp *alloc_pbqp(int num_nodes)
+{
+ pbqp *this_;
+ int u;
+
+ assert(num_nodes > 0);
+
+ /* allocate memory for pbqp data structure */
+ this_ = (pbqp *)malloc(sizeof(pbqp));
+
+ /* Initialize pbqp fields */
+ this_->num_nodes = num_nodes;
+ this_->solved = false;
+ this_->optimal = true;
+ this_->min = 0.0;
+ this_->max_deg = 0;
+ this_->changed = false;
+ this_->num_r0 = 0;
+ this_->num_ri = 0;
+ this_->num_rii = 0;
+ this_->num_rn = 0;
+ this_->num_rn_special = 0;
+
+ /* initialize/allocate stack fields of pbqp */
+ this_->stack = (int *) malloc(sizeof(int)*num_nodes);
+ this_->stack_ptr = 0;
+
+ /* initialize/allocate node fields of pbqp */
+ this_->adj_list = (adjnode **) malloc(sizeof(adjnode *)*num_nodes);
+ this_->node_deg = (int *) malloc(sizeof(int)*num_nodes);
+ this_->solution = (int *) malloc(sizeof(int)*num_nodes);
+ this_->bucket_ptr = (bucketnode **) malloc(sizeof(bucketnode **)*num_nodes);
+ this_->node_costs = (PBQPVector**) malloc(sizeof(PBQPVector*) * num_nodes);
+ for(u=0;u<num_nodes;u++) {
+ this_->solution[u]=-1;
+ this_->adj_list[u]=NULL;
+ this_->node_deg[u]=0;
+ this_->bucket_ptr[u]=NULL;
+ this_->node_costs[u]=NULL;
+ }
+
+ /* initialize bucket list */
+ this_->bucket_list = NULL;
+
+ return this_;
+}
+
+/* free pbqp problem */
+void free_pbqp(pbqp *this_)
+{
+ int u;
+ int deg;
+ adjnode *adj_ptr,*adj_next;
+ bucketnode *bucket,*bucket_next;
+
+ assert(this_ != NULL);
+
+ /* free node cost fields */
+ for(u=0;u < this_->num_nodes;u++) {
+ delete this_->node_costs[u];
+ }
+ free(this_->node_costs);
+
+ /* free bucket list */
+ for(deg=0;deg<=this_->max_deg;deg++) {
+ for(bucket=this_->bucket_list[deg];bucket!=NULL;bucket=bucket_next) {
+ this_->bucket_ptr[bucket->u] = NULL;
+ bucket_next = bucket-> succ;
+ free(bucket);
+ }
+ }
+ free(this_->bucket_list);
+
+ /* free adj. list */
+ assert(this_->adj_list != NULL);
+ for(u=0;u < this_->num_nodes; u++) {
+ for(adj_ptr = this_->adj_list[u]; adj_ptr != NULL; adj_ptr = adj_next) {
+ adj_next = adj_ptr -> succ;
+ if (u < adj_ptr->adj) {
+ assert(adj_ptr != NULL);
+ delete adj_ptr->costs;
+ }
+ if (adj_ptr -> tc_safe_regs != NULL) {
+ free(adj_ptr -> tc_safe_regs);
+ }
+ free(adj_ptr);
+ }
+ }
+ free(this_->adj_list);
+
+ /* free other node fields */
+ free(this_->node_deg);
+ free(this_->solution);
+ free(this_->bucket_ptr);
+
+ /* free stack */
+ free(this_->stack);
+
+ /* free pbqp data structure itself */
+ free(this_);
+}
+
+
+/****************************************************************************
+ * adj. node routines
+ ****************************************************************************/
+
+/* find data structure of adj. node of a given node */
+static
+adjnode *find_adjnode(pbqp *this_,int u,int v)
+{
+ adjnode *adj_ptr;
+
+ assert (this_ != NULL);
+ assert (u >= 0 && u < this_->num_nodes);
+ assert (v >= 0 && v < this_->num_nodes);
+ assert(this_->adj_list != NULL);
+
+ for(adj_ptr = this_ -> adj_list[u];adj_ptr != NULL; adj_ptr = adj_ptr -> succ) {
+ if (adj_ptr->adj == v) {
+ return adj_ptr;
+ }
+ }
+ return NULL;
+}
+
+/* allocate a new data structure for adj. node */
+static
+adjnode *alloc_adjnode(pbqp *this_,int u, PBQPMatrix *costs)
+{
+ adjnode *p;
+
+ assert(this_ != NULL);
+ assert(costs != NULL);
+ assert(u >= 0 && u < this_->num_nodes);
+
+ p = (adjnode *)malloc(sizeof(adjnode));
+ assert(p != NULL);
+
+ p->adj = u;
+ p->costs = costs;
+
+ p->tc_valid= false;
+ p->tc_safe_regs = NULL;
+ p->tc_impact = 0;
+
+ return p;
+}
+
+/* insert adjacence node to adj. list */
+static
+void insert_adjnode(pbqp *this_, int u, adjnode *adj_ptr)
+{
+
+ assert(this_ != NULL);
+ assert(adj_ptr != NULL);
+ assert(u >= 0 && u < this_->num_nodes);
+
+ /* if adjacency list of node is not empty -> update
+ first node of the list */
+ if (this_ -> adj_list[u] != NULL) {
+ assert(this_->adj_list[u]->prev == NULL);
+ this_->adj_list[u] -> prev = adj_ptr;
+ }
+
+ /* update doubly chained list pointers of pointers */
+ adj_ptr -> succ = this_->adj_list[u];
+ adj_ptr -> prev = NULL;
+
+ /* update adjacency list pointer of node u */
+ this_->adj_list[u] = adj_ptr;
+}
+
+/* remove entry in an adj. list */
+static
+void remove_adjnode(pbqp *this_, int u, adjnode *adj_ptr)
+{
+ assert(this_!= NULL);
+ assert(u >= 0 && u <= this_->num_nodes);
+ assert(this_->adj_list != NULL);
+ assert(adj_ptr != NULL);
+
+ if (adj_ptr -> prev == NULL) {
+ this_->adj_list[u] = adj_ptr -> succ;
+ } else {
+ adj_ptr -> prev -> succ = adj_ptr -> succ;
+ }
+
+ if (adj_ptr -> succ != NULL) {
+ adj_ptr -> succ -> prev = adj_ptr -> prev;
+ }
+
+ if(adj_ptr->reverse != NULL) {
+ adjnode *rev = adj_ptr->reverse;
+ rev->reverse = NULL;
+ }
+
+ if (adj_ptr -> tc_safe_regs != NULL) {
+ free(adj_ptr -> tc_safe_regs);
+ }
+
+ free(adj_ptr);
+}
+
+/*****************************************************************************
+ * node functions
+ ****************************************************************************/
+
+/* get degree of a node */
+static
+int get_deg(pbqp *this_,int u)
+{
+ adjnode *adj_ptr;
+ int deg = 0;
+
+ assert(this_ != NULL);
+ assert(u >= 0 && u < this_->num_nodes);
+ assert(this_->adj_list != NULL);
+
+ for(adj_ptr = this_ -> adj_list[u];adj_ptr != NULL; adj_ptr = adj_ptr -> succ) {
+ deg ++;
+ }
+ return deg;
+}
+
+/* reinsert node */
+static
+void reinsert_node(pbqp *this_,int u)
+{
+ adjnode *adj_u,
+ *adj_v;
+
+ assert(this_!= NULL);
+ assert(u >= 0 && u <= this_->num_nodes);
+ assert(this_->adj_list != NULL);
+
+ for(adj_u = this_ -> adj_list[u]; adj_u != NULL; adj_u = adj_u -> succ) {
+ int v = adj_u -> adj;
+ adj_v = alloc_adjnode(this_,u,adj_u->costs);
+ insert_adjnode(this_,v,adj_v);
+ }
+}
+
+/* remove node */
+static
+void remove_node(pbqp *this_,int u)
+{
+ adjnode *adj_ptr;
+
+ assert(this_!= NULL);
+ assert(u >= 0 && u <= this_->num_nodes);
+ assert(this_->adj_list != NULL);
+
+ for(adj_ptr = this_ -> adj_list[u]; adj_ptr != NULL; adj_ptr = adj_ptr -> succ) {
+ remove_adjnode(this_,adj_ptr->adj,adj_ptr -> reverse);
+ }
+}
+
+/*****************************************************************************
+ * edge functions
+ ****************************************************************************/
+
+/* insert edge to graph */
+/* (does not check whether edge exists in graph */
+static
+void insert_edge(pbqp *this_, int u, int v, PBQPMatrix *costs)
+{
+ adjnode *adj_u,
+ *adj_v;
+
+ /* create adjanceny entry for u */
+ adj_u = alloc_adjnode(this_,v,costs);
+ insert_adjnode(this_,u,adj_u);
+
+
+ /* create adjanceny entry for v */
+ adj_v = alloc_adjnode(this_,u,costs);
+ insert_adjnode(this_,v,adj_v);
+
+ /* create link for reverse edge */
+ adj_u -> reverse = adj_v;
+ adj_v -> reverse = adj_u;
+}
+
+/* delete edge */
+static
+void delete_edge(pbqp *this_,int u,int v)
+{
+ adjnode *adj_ptr;
+ adjnode *rev;
+
+ assert(this_ != NULL);
+ assert( u >= 0 && u < this_->num_nodes);
+ assert( v >= 0 && v < this_->num_nodes);
+
+ adj_ptr=find_adjnode(this_,u,v);
+ assert(adj_ptr != NULL);
+ assert(adj_ptr->reverse != NULL);
+
+ delete adj_ptr -> costs;
+
+ rev = adj_ptr->reverse;
+ remove_adjnode(this_,u,adj_ptr);
+ remove_adjnode(this_,v,rev);
+}
+
+/*****************************************************************************
+ * cost functions
+ ****************************************************************************/
+
+/* Note: Since cost(u,v) = transpose(cost(v,u)), it would be necessary to store
+ two matrices for both edges (u,v) and (v,u). However, we only store the
+ matrix for the case u < v. For the other case we transpose the stored matrix
+ if required.
+*/
+
+/* add costs to cost vector of a node */
+void add_pbqp_nodecosts(pbqp *this_,int u, PBQPVector *costs)
+{
+ assert(this_ != NULL);
+ assert(costs != NULL);
+ assert(u >= 0 && u <= this_->num_nodes);
+
+ if (!this_->node_costs[u]) {
+ this_->node_costs[u] = new PBQPVector(*costs);
+ } else {
+ *this_->node_costs[u] += *costs;
+ }
+}
+
+/* get cost matrix ptr */
+static
+PBQPMatrix *get_costmatrix_ptr(pbqp *this_, int u, int v)
+{
+ adjnode *adj_ptr;
+ PBQPMatrix *m = NULL;
+
+ assert (this_ != NULL);
+ assert (u >= 0 && u < this_->num_nodes);
+ assert (v >= 0 && v < this_->num_nodes);
+
+ adj_ptr = find_adjnode(this_,u,v);
+
+ if (adj_ptr != NULL) {
+ m = adj_ptr -> costs;
+ }
+
+ return m;
+}
+
+/* get cost matrix ptr */
+/* Note: only the pointer is returned for
+ cost(u,v), if u < v.
+*/
+static
+PBQPMatrix *pbqp_get_costmatrix(pbqp *this_, int u, int v)
+{
+ adjnode *adj_ptr = find_adjnode(this_,u,v);
+
+ if (adj_ptr != NULL) {
+ if ( u < v) {
+ return new PBQPMatrix(*adj_ptr->costs);
+ } else {
+ return new PBQPMatrix(adj_ptr->costs->transpose());
+ }
+ } else {
+ return NULL;
+ }
+}
+
+/* add costs to cost matrix of an edge */
+void add_pbqp_edgecosts(pbqp *this_,int u,int v, PBQPMatrix *costs)
+{
+ PBQPMatrix *adj_costs;
+
+ assert(this_!= NULL);
+ assert(costs != NULL);
+ assert(u >= 0 && u <= this_->num_nodes);
+ assert(v >= 0 && v <= this_->num_nodes);
+
+ /* does the edge u-v exists ? */
+ if (u == v) {
+ PBQPVector *diag = new PBQPVector(costs->diagonalize());
+ add_pbqp_nodecosts(this_,v,diag);
+ delete diag;
+ } else if ((adj_costs = get_costmatrix_ptr(this_,u,v))!=NULL) {
+ if ( u < v) {
+ *adj_costs += *costs;
+ } else {
+ *adj_costs += costs->transpose();
+ }
+ } else {
+ adj_costs = new PBQPMatrix((u < v) ? *costs : costs->transpose());
+ insert_edge(this_,u,v,adj_costs);
+ }
+}
+
+/* remove bucket from bucket list */
+static
+void pbqp_remove_bucket(pbqp *this_, bucketnode *bucket)
+{
+ int u = bucket->u;
+
+ assert(this_ != NULL);
+ assert(u >= 0 && u < this_->num_nodes);
+ assert(this_->bucket_list != NULL);
+ assert(this_->bucket_ptr[u] != NULL);
+
+ /* update predecessor node in bucket list
+ (if no preceeding bucket exists, then
+ the bucket_list pointer needs to be
+ updated.)
+ */
+ if (bucket->prev != NULL) {
+ bucket->prev-> succ = bucket->succ;
+ } else {
+ this_->bucket_list[this_->node_deg[u]] = bucket -> succ;
+ }
+
+ /* update successor node in bucket list */
+ if (bucket->succ != NULL) {
+ bucket->succ-> prev = bucket->prev;
+ }
+}
+
+/**********************************************************************************
+ * pop functions
+ **********************************************************************************/
+
+/* pop node of given degree */
+static
+int pop_node(pbqp *this_,int deg)
+{
+ bucketnode *bucket;
+ int u;
+
+ assert(this_ != NULL);
+ assert(deg >= 0 && deg <= this_->max_deg);
+ assert(this_->bucket_list != NULL);
+
+ /* get first bucket of bucket list */
+ bucket = this_->bucket_list[deg];
+ assert(bucket != NULL);
+
+ /* remove bucket */
+ pbqp_remove_bucket(this_,bucket);
+ u = bucket->u;
+ free(bucket);
+ return u;
+}
+
+/**********************************************************************************
+ * reorder functions
+ **********************************************************************************/
+
+/* add bucket to bucketlist */
+static
+void add_to_bucketlist(pbqp *this_,bucketnode *bucket, int deg)
+{
+ bucketnode *old_head;
+
+ assert(bucket != NULL);
+ assert(this_ != NULL);
+ assert(deg >= 0 && deg <= this_->max_deg);
+ assert(this_->bucket_list != NULL);
+
+ /* store node degree (for re-ordering purposes)*/
+ this_->node_deg[bucket->u] = deg;
+
+ /* put bucket to front of doubly chained list */
+ old_head = this_->bucket_list[deg];
+ bucket -> prev = NULL;
+ bucket -> succ = old_head;
+ this_ -> bucket_list[deg] = bucket;
+ if (bucket -> succ != NULL ) {
+ assert ( old_head -> prev == NULL);
+ old_head -> prev = bucket;
+ }
+}
+
+
+/* reorder node in bucket list according to
+ current node degree */
+static
+void reorder_node(pbqp *this_, int u)
+{
+ int deg;
+
+ assert(this_ != NULL);
+ assert(u>= 0 && u < this_->num_nodes);
+ assert(this_->bucket_list != NULL);
+ assert(this_->bucket_ptr[u] != NULL);
+
+ /* get current node degree */
+ deg = get_deg(this_,u);
+
+ /* remove bucket from old bucket list only
+ if degree of node has changed. */
+ if (deg != this_->node_deg[u]) {
+ pbqp_remove_bucket(this_,this_->bucket_ptr[u]);
+ add_to_bucketlist(this_,this_->bucket_ptr[u],deg);
+ }
+}
+
+/* reorder adj. nodes of a node */
+static
+void reorder_adjnodes(pbqp *this_,int u)
+{
+ adjnode *adj_ptr;
+
+ assert(this_!= NULL);
+ assert(u >= 0 && u <= this_->num_nodes);
+ assert(this_->adj_list != NULL);
+
+ for(adj_ptr = this_ -> adj_list[u]; adj_ptr != NULL; adj_ptr = adj_ptr -> succ) {
+ reorder_node(this_,adj_ptr->adj);
+ }
+}
+
+/**********************************************************************************
+ * creation functions
+ **********************************************************************************/
+
+/* create new bucket entry */
+/* consistency of the bucket list is not checked! */
+static
+void create_bucket(pbqp *this_,int u,int deg)
+{
+ bucketnode *bucket;
+
+ assert(this_ != NULL);
+ assert(u >= 0 && u < this_->num_nodes);
+ assert(this_->bucket_list != NULL);
+
+ bucket = (bucketnode *)malloc(sizeof(bucketnode));
+ assert(bucket != NULL);
+
+ bucket -> u = u;
+ this_->bucket_ptr[u] = bucket;
+
+ add_to_bucketlist(this_,bucket,deg);
+}
+
+/* create bucket list */
+static
+void create_bucketlist(pbqp *this_)
+{
+ int u;
+ int max_deg;
+ int deg;
+
+ assert(this_ != NULL);
+ assert(this_->bucket_list == NULL);
+
+ /* determine max. degree of the nodes */
+ max_deg = 2; /* at least of degree two! */
+ for(u=0;u<this_->num_nodes;u++) {
+ deg = this_->node_deg[u] = get_deg(this_,u);
+ if (deg > max_deg) {
+ max_deg = deg;
+ }
+ }
+ this_->max_deg = max_deg;
+
+ /* allocate bucket list */
+ this_ -> bucket_list = (bucketnode **)malloc(sizeof(bucketnode *)*(max_deg + 1));
+ memset(this_->bucket_list,0,sizeof(bucketnode *)*(max_deg + 1));
+ assert(this_->bucket_list != NULL);
+
+ /* insert nodes to the list */
+ for(u=0;u<this_->num_nodes;u++) {
+ create_bucket(this_,u,this_->node_deg[u]);
+ }
+}
+
+/*****************************************************************************
+ * PBQP simplification for trivial nodes
+ ****************************************************************************/
+
+/* remove trivial node with cost vector length of one */
+static
+void disconnect_trivialnode(pbqp *this_,int u)
+{
+ int v;
+ adjnode *adj_ptr,
+ *next;
+ PBQPMatrix *c_uv;
+ PBQPVector *c_v;
+
+ assert(this_ != NULL);
+ assert(this_->node_costs != NULL);
+ assert(u >= 0 && u < this_ -> num_nodes);
+ assert(this_->node_costs[u]->getLength() == 1);
+
+ /* add edge costs to node costs of adj. nodes */
+ for(adj_ptr = this_->adj_list[u]; adj_ptr != NULL; adj_ptr = next){
+ next = adj_ptr -> succ;
+ v = adj_ptr -> adj;
+ assert(v >= 0 && v < this_ -> num_nodes);
+
+ /* convert matrix to cost vector offset for adj. node */
+ c_uv = pbqp_get_costmatrix(this_,u,v);
+ c_v = new PBQPVector(c_uv->getRowAsVector(0));
+ *this_->node_costs[v] += *c_v;
+
+ /* delete edge & free vec/mat */
+ delete c_v;
+ delete c_uv;
+ delete_edge(this_,u,v);
+ }
+}
+
+/* find all trivial nodes and disconnect them */
+static
+void eliminate_trivial_nodes(pbqp *this_)
+{
+ int u;
+
+ assert(this_ != NULL);
+ assert(this_ -> node_costs != NULL);
+
+ for(u=0;u < this_ -> num_nodes; u++) {
+ if (this_->node_costs[u]->getLength() == 1) {
+ disconnect_trivialnode(this_,u);
+ }
+ }
+}
+
+/*****************************************************************************
+ * Normal form for PBQP
+ ****************************************************************************/
+
+/* simplify a cost matrix. If the matrix
+ is independent, then simplify_matrix
+ returns true - otherwise false. In
+ vectors u and v the offset values of
+ the decomposition are stored.
+*/
+
+static
+bool normalize_matrix(PBQPMatrix *m, PBQPVector *u, PBQPVector *v)
+{
+ assert( m != NULL);
+ assert( u != NULL);
+ assert( v != NULL);
+ assert( u->getLength() > 0);
+ assert( v->getLength() > 0);
+
+ assert(m->getRows() == u->getLength());
+ assert(m->getCols() == v->getLength());
+
+ /* determine u vector */
+ for(unsigned r = 0; r < m->getRows(); ++r) {
+ PBQPNum min = m->getRowMin(r);
+ (*u)[r] += min;
+ if (!isInf(min)) {
+ m->subFromRow(r, min);
+ } else {
+ m->setRow(r, 0);
+ }
+ }
+
+ /* determine v vector */
+ for(unsigned c = 0; c < m->getCols(); ++c) {
+ PBQPNum min = m->getColMin(c);
+ (*v)[c] += min;
+ if (!isInf(min)) {
+ m->subFromCol(c, min);
+ } else {
+ m->setCol(c, 0);
+ }
+ }
+
+ /* determine whether matrix is
+ independent or not.
+ */
+ return m->isZero();
+}
+
+/* simplify single edge */
+static
+void simplify_edge(pbqp *this_,int u,int v)
+{
+ PBQPMatrix *costs;
+ bool is_zero;
+
+ assert (this_ != NULL);
+ assert (u >= 0 && u <this_->num_nodes);
+ assert (v >= 0 && v <this_->num_nodes);
+ assert (u != v);
+
+ /* swap u and v if u > v in order to avoid un-necessary
+ tranpositions of the cost matrix */
+
+ if (u > v) {
+ int swap = u;
+ u = v;
+ v = swap;
+ }
+
+ /* get cost matrix and simplify it */
+ costs = get_costmatrix_ptr(this_,u,v);
+ is_zero=normalize_matrix(costs,this_->node_costs[u],this_->node_costs[v]);
+
+ /* delete edge */
+ if(is_zero){
+ delete_edge(this_,u,v);
+ this_->changed = true;
+ }
+}
+
+/* normalize cost matrices and remove
+ edges in PBQP if they ary independent,
+ i.e. can be decomposed into two
+ cost vectors.
+*/
+static
+void eliminate_independent_edges(pbqp *this_)
+{
+ int u,v;
+ adjnode *adj_ptr,*next;
+
+ assert(this_ != NULL);
+ assert(this_ -> adj_list != NULL);
+
+ this_->changed = false;
+ for(u=0;u < this_->num_nodes;u++) {
+ for (adj_ptr = this_ -> adj_list[u]; adj_ptr != NULL; adj_ptr = next) {
+ next = adj_ptr -> succ;
+ v = adj_ptr -> adj;
+ assert(v >= 0 && v < this_->num_nodes);
+ if (u < v) {
+ simplify_edge(this_,u,v);
+ }
+ }
+ }
+}
+
+
+/*****************************************************************************
+ * PBQP reduction rules
+ ****************************************************************************/
+
+/* RI reduction
+ This reduction rule is applied for nodes
+ of degree one. */
+
+static
+void apply_RI(pbqp *this_,int x)
+{
+ int y;
+ unsigned xlen,
+ ylen;
+ PBQPMatrix *c_yx;
+ PBQPVector *c_x, *delta;
+
+ assert(this_ != NULL);
+ assert(x >= 0 && x < this_->num_nodes);
+ assert(this_ -> adj_list[x] != NULL);
+ assert(this_ -> adj_list[x] -> succ == NULL);
+
+ /* get adjacence matrix */
+ y = this_ -> adj_list[x] -> adj;
+ assert(y >= 0 && y < this_->num_nodes);
+
+ /* determine length of cost vectors for node x and y */
+ xlen = this_ -> node_costs[x]->getLength();
+ ylen = this_ -> node_costs[y]->getLength();
+
+ /* get cost vector c_x and matrix c_yx */
+ c_x = this_ -> node_costs[x];
+ c_yx = pbqp_get_costmatrix(this_,y,x);
+ assert (c_yx != NULL);
+
+
+ /* allocate delta vector */
+ delta = new PBQPVector(ylen);
+
+ /* compute delta vector */
+ for(unsigned i = 0; i < ylen; ++i) {
+ PBQPNum min = (*c_yx)[i][0] + (*c_x)[0];
+ for(unsigned j = 1; j < xlen; ++j) {
+ PBQPNum c = (*c_yx)[i][j] + (*c_x)[j];
+ if ( c < min )
+ min = c;
+ }
+ (*delta)[i] = min;
+ }
+
+ /* add delta vector */
+ *this_ -> node_costs[y] += *delta;
+
+ /* delete node x */
+ remove_node(this_,x);
+
+ /* reorder adj. nodes of node x */
+ reorder_adjnodes(this_,x);
+
+ /* push node x on stack */
+ assert(this_ -> stack_ptr < this_ -> num_nodes);
+ this_->stack[this_ -> stack_ptr++] = x;
+
+ /* free vec/mat */
+ delete c_yx;
+ delete delta;
+
+ /* increment counter for number statistic */
+ this_->num_ri++;
+}
+
+/* RII reduction
+ This reduction rule is applied for nodes
+ of degree two. */
+
+static
+void apply_RII(pbqp *this_,int x)
+{
+ int y,z;
+ unsigned xlen,ylen,zlen;
+ adjnode *adj_yz;
+
+ PBQPMatrix *c_yx, *c_zx;
+ PBQPVector *cx;
+ PBQPMatrix *delta;
+
+ assert(this_ != NULL);
+ assert(x >= 0 && x < this_->num_nodes);
+ assert(this_ -> adj_list[x] != NULL);
+ assert(this_ -> adj_list[x] -> succ != NULL);
+ assert(this_ -> adj_list[x] -> succ -> succ == NULL);
+
+ /* get adjacence matrix */
+ y = this_ -> adj_list[x] -> adj;
+ z = this_ -> adj_list[x] -> succ -> adj;
+ assert(y >= 0 && y < this_->num_nodes);
+ assert(z >= 0 && z < this_->num_nodes);
+
+ /* determine length of cost vectors for node x and y */
+ xlen = this_ -> node_costs[x]->getLength();
+ ylen = this_ -> node_costs[y]->getLength();
+ zlen = this_ -> node_costs[z]->getLength();
+
+ /* get cost vector c_x and matrix c_yx */
+ cx = this_ -> node_costs[x];
+ c_yx = pbqp_get_costmatrix(this_,y,x);
+ c_zx = pbqp_get_costmatrix(this_,z,x);
+ assert(c_yx != NULL);
+ assert(c_zx != NULL);
+
+ /* Colour Heuristic */
+ if ( (adj_yz = find_adjnode(this_,y,z)) != NULL) {
+ adj_yz->tc_valid = false;
+ adj_yz->reverse->tc_valid = false;
+ }
+
+ /* allocate delta matrix */
+ delta = new PBQPMatrix(ylen, zlen);
+
+ /* compute delta matrix */
+ for(unsigned i=0;i<ylen;i++) {
+ for(unsigned j=0;j<zlen;j++) {
+ PBQPNum min = (*c_yx)[i][0] + (*c_zx)[j][0] + (*cx)[0];
+ for(unsigned k=1;k<xlen;k++) {
+ PBQPNum c = (*c_yx)[i][k] + (*c_zx)[j][k] + (*cx)[k];
+ if ( c < min ) {
+ min = c;
+ }
+ }
+ (*delta)[i][j] = min;
+ }
+ }
+
+ /* add delta matrix */
+ add_pbqp_edgecosts(this_,y,z,delta);
+
+ /* delete node x */
+ remove_node(this_,x);
+
+ /* simplify cost matrix c_yz */
+ simplify_edge(this_,y,z);
+
+ /* reorder adj. nodes */
+ reorder_adjnodes(this_,x);
+
+ /* push node x on stack */
+ assert(this_ -> stack_ptr < this_ -> num_nodes);
+ this_->stack[this_ -> stack_ptr++] = x;
+
+ /* free vec/mat */
+ delete c_yx;
+ delete c_zx;
+ delete delta;
+
+ /* increment counter for number statistic */
+ this_->num_rii++;
+
+}
+
+/* RN reduction */
+static
+void apply_RN(pbqp *this_,int x)
+{
+ unsigned xlen;
+
+ assert(this_ != NULL);
+ assert(x >= 0 && x < this_->num_nodes);
+ assert(this_ -> node_costs[x] != NULL);
+
+ xlen = this_ -> node_costs[x] -> getLength();
+
+ /* after application of RN rule no optimality
+ can be guaranteed! */
+ this_ -> optimal = false;
+
+ /* push node x on stack */
+ assert(this_ -> stack_ptr < this_ -> num_nodes);
+ this_->stack[this_ -> stack_ptr++] = x;
+
+ /* delete node x */
+ remove_node(this_,x);
+
+ /* reorder adj. nodes of node x */
+ reorder_adjnodes(this_,x);
+
+ /* increment counter for number statistic */
+ this_->num_rn++;
+}
+
+
+static
+void compute_tc_info(pbqp *this_, adjnode *p)
+{
+ adjnode *r;
+ PBQPMatrix *m;
+ int x,y;
+ PBQPVector *c_x, *c_y;
+ int *row_inf_counts;
+
+ assert(p->reverse != NULL);
+
+ /* set flags */
+ r = p->reverse;
+ p->tc_valid = true;
+ r->tc_valid = true;
+
+ /* get edge */
+ x = r->adj;
+ y = p->adj;
+
+ /* get cost vectors */
+ c_x = this_ -> node_costs[x];
+ c_y = this_ -> node_costs[y];
+
+ /* get cost matrix */
+ m = pbqp_get_costmatrix(this_, x, y);
+
+
+ /* allocate allowed set for edge (x,y) and (y,x) */
+ if (p->tc_safe_regs == NULL) {
+ p->tc_safe_regs = (int *) malloc(sizeof(int) * c_x->getLength());
+ }
+
+ if (r->tc_safe_regs == NULL ) {
+ r->tc_safe_regs = (int *) malloc(sizeof(int) * c_y->getLength());
+ }
+
+ p->tc_impact = r->tc_impact = 0;
+
+ row_inf_counts = (int *) alloca(sizeof(int) * c_x->getLength());
+
+ /* init arrays */
+ p->tc_safe_regs[0] = 0;
+ row_inf_counts[0] = 0;
+ for(unsigned i = 1; i < c_x->getLength(); ++i){
+ p->tc_safe_regs[i] = 1;
+ row_inf_counts[i] = 0;
+ }
+
+ r->tc_safe_regs[0] = 0;
+ for(unsigned j = 1; j < c_y->getLength(); ++j){
+ r->tc_safe_regs[j] = 1;
+ }
+
+ for(unsigned j = 0; j < c_y->getLength(); ++j) {
+ int col_inf_counts = 0;
+ for (unsigned i = 0; i < c_x->getLength(); ++i) {
+ if (isInf((*m)[i][j])) {
+ ++col_inf_counts;
+ ++row_inf_counts[i];
+
+ p->tc_safe_regs[i] = 0;
+ r->tc_safe_regs[j] = 0;
+ }
+ }
+ if (col_inf_counts > p->tc_impact) {
+ p->tc_impact = col_inf_counts;
+ }
+ }
+
+ for(unsigned i = 0; i < c_x->getLength(); ++i){
+ if (row_inf_counts[i] > r->tc_impact)
+ {
+ r->tc_impact = row_inf_counts[i];
+ }
+ }
+
+ delete m;
+}
+
+/*
+ * Checks whether node x can be locally coloured.
+ */
+static
+int is_colorable(pbqp *this_,int x)
+{
+ adjnode *adj_ptr;
+ PBQPVector *c_x;
+ int result = 1;
+ int *allowed;
+ int num_allowed = 0;
+ unsigned total_impact = 0;
+
+ assert(this_ != NULL);
+ assert(x >= 0 && x < this_->num_nodes);
+ assert(this_ -> node_costs[x] != NULL);
+
+ c_x = this_ -> node_costs[x];
+
+ /* allocate allowed set */
+ allowed = (int *)malloc(sizeof(int) * c_x->getLength());
+ for(unsigned i = 0; i < c_x->getLength(); ++i){
+ if (!isInf((*c_x)[i]) && i > 0) {
+ allowed[i] = 1;
+ ++num_allowed;
+ } else {
+ allowed[i] = 0;
+ }
+ }
+
+ /* determine local minimum */
+ for(adj_ptr=this_->adj_list[x] ;adj_ptr != NULL; adj_ptr = adj_ptr -> succ) {
+ if (!adj_ptr -> tc_valid) {
+ compute_tc_info(this_, adj_ptr);
+ }
+
+ total_impact += adj_ptr->tc_impact;
+
+ if (num_allowed > 0) {
+ for (unsigned i = 1; i < c_x->getLength(); ++i){
+ if (allowed[i]){
+ if (!adj_ptr->tc_safe_regs[i]){
+ allowed[i] = 0;
+ --num_allowed;
+ if (num_allowed == 0)
+ break;
+ }
+ }
+ }
+ }
+
+ if ( total_impact >= c_x->getLength() - 1 && num_allowed == 0 ) {
+ result = 0;
+ break;
+ }
+ }
+ free(allowed);
+
+ return result;
+}
+
+/* use briggs heuristic
+ note: this_ is not a general heuristic. it only is useful for
+ interference graphs.
+ */
+int pop_colorablenode(pbqp *this_)
+{
+ int deg;
+ bucketnode *min_bucket=NULL;
+ PBQPNum min = std::numeric_limits<PBQPNum>::infinity();
+
+ /* select node where the number of colors is less than the node degree */
+ for(deg=this_->max_deg;deg > 2;deg--) {
+ bucketnode *bucket;
+ for(bucket=this_->bucket_list[deg];bucket!= NULL;bucket = bucket -> succ) {
+ int u = bucket->u;
+ if (is_colorable(this_,u)) {
+ pbqp_remove_bucket(this_,bucket);
+ this_->num_rn_special++;
+ free(bucket);
+ return u;
+ }
+ }
+ }
+
+ /* select node with minimal ratio between average node costs and degree of node */
+ for(deg=this_->max_deg;deg >2; deg--) {
+ bucketnode *bucket;
+ for(bucket=this_->bucket_list[deg];bucket!= NULL;bucket = bucket -> succ) {
+ PBQPNum h;
+ int u;
+
+ u = bucket->u;
+ assert(u>=0 && u < this_->num_nodes);
+ h = (*this_->node_costs[u])[0] / (PBQPNum) deg;
+ if (h < min) {
+ min_bucket = bucket;
+ min = h;
+ }
+ }
+ }
+
+ /* return node and free bucket */
+ if (min_bucket != NULL) {
+ int u;
+
+ pbqp_remove_bucket(this_,min_bucket);
+ u = min_bucket->u;
+ free(min_bucket);
+ return u;
+ } else {
+ return -1;
+ }
+}
+
+
+/*****************************************************************************
+ * PBQP graph parsing
+ ****************************************************************************/
+
+/* reduce pbqp problem (first phase) */
+static
+void reduce_pbqp(pbqp *this_)
+{
+ int u;
+
+ assert(this_ != NULL);
+ assert(this_->bucket_list != NULL);
+
+ for(;;){
+
+ if (this_->bucket_list[1] != NULL) {
+ u = pop_node(this_,1);
+ apply_RI(this_,u);
+ } else if (this_->bucket_list[2] != NULL) {
+ u = pop_node(this_,2);
+ apply_RII(this_,u);
+ } else if ((u = pop_colorablenode(this_)) != -1) {
+ apply_RN(this_,u);
+ } else {
+ break;
+ }
+ }
+}
+
+/*****************************************************************************
+ * PBQP back propagation
+ ****************************************************************************/
+
+/* determine solution of a reduced node. Either
+ RI or RII was applied for this_ node. */
+static
+void determine_solution(pbqp *this_,int x)
+{
+ PBQPVector *v = new PBQPVector(*this_ -> node_costs[x]);
+ adjnode *adj_ptr;
+
+ assert(this_ != NULL);
+ assert(x >= 0 && x < this_->num_nodes);
+ assert(this_ -> adj_list != NULL);
+ assert(this_ -> solution != NULL);
+
+ for(adj_ptr=this_->adj_list[x] ;adj_ptr != NULL; adj_ptr = adj_ptr -> succ) {
+ int y = adj_ptr -> adj;
+ int y_sol = this_ -> solution[y];
+
+ PBQPMatrix *c_yx = pbqp_get_costmatrix(this_,y,x);
+ assert(y_sol >= 0 && y_sol < (int)this_->node_costs[y]->getLength());
+ (*v) += c_yx->getRowAsVector(y_sol);
+ delete c_yx;
+ }
+ this_ -> solution[x] = v->minIndex();
+
+ delete v;
+}
+
+/* back popagation phase of PBQP */
+static
+void back_propagate(pbqp *this_)
+{
+ int i;
+
+ assert(this_ != NULL);
+ assert(this_->stack != NULL);
+ assert(this_->stack_ptr < this_->num_nodes);
+
+ for(i=this_ -> stack_ptr-1;i>=0;i--) {
+ int x = this_ -> stack[i];
+ assert( x >= 0 && x < this_ -> num_nodes);
+ reinsert_node(this_,x);
+ determine_solution(this_,x);
+ }
+}
+
+/* solve trivial nodes of degree zero */
+static
+void determine_trivialsolution(pbqp *this_)
+{
+ int u;
+ PBQPNum delta;
+
+ assert( this_ != NULL);
+ assert( this_ -> bucket_list != NULL);
+
+ /* determine trivial solution */
+ while (this_->bucket_list[0] != NULL) {
+ u = pop_node(this_,0);
+
+ assert( u >= 0 && u < this_ -> num_nodes);
+
+ this_->solution[u] = this_->node_costs[u]->minIndex();
+ delta = (*this_->node_costs[u])[this_->solution[u]];
+ this_->min = this_->min + delta;
+
+ /* increment counter for number statistic */
+ this_->num_r0++;
+ }
+}
+
+/*****************************************************************************
+ * debug facilities
+ ****************************************************************************/
+static
+void check_pbqp(pbqp *this_)
+{
+ int u,v;
+ PBQPMatrix *costs;
+ adjnode *adj_ptr;
+
+ assert( this_ != NULL);
+
+ for(u=0;u< this_->num_nodes; u++) {
+ assert (this_ -> node_costs[u] != NULL);
+ for(adj_ptr = this_ -> adj_list[u];adj_ptr != NULL; adj_ptr = adj_ptr -> succ) {
+ v = adj_ptr -> adj;
+ assert( v>= 0 && v < this_->num_nodes);
+ if (u < v ) {
+ costs = adj_ptr -> costs;
+ assert( costs->getRows() == this_->node_costs[u]->getLength() &&
+ costs->getCols() == this_->node_costs[v]->getLength());
+ }
+ }
+ }
+}
+
+/*****************************************************************************
+ * PBQP solve routines
+ ****************************************************************************/
+
+/* solve PBQP problem */
+void solve_pbqp(pbqp *this_)
+{
+ assert(this_ != NULL);
+ assert(!this_->solved);
+
+ /* check vector & matrix dimensions */
+ check_pbqp(this_);
+
+ /* simplify PBQP problem */
+
+ /* eliminate trivial nodes, i.e.
+ nodes with cost vectors of length one. */
+ eliminate_trivial_nodes(this_);
+
+ /* eliminate edges with independent
+ cost matrices and normalize matrices */
+ eliminate_independent_edges(this_);
+
+ /* create bucket list for graph parsing */
+ create_bucketlist(this_);
+
+ /* reduce phase */
+ reduce_pbqp(this_);
+
+ /* solve trivial nodes */
+ determine_trivialsolution(this_);
+
+ /* back propagation phase */
+ back_propagate(this_);
+
+ this_->solved = true;
+}
+
+/* get solution of a node */
+int get_pbqp_solution(pbqp *this_,int x)
+{
+ assert(this_ != NULL);
+ assert(this_->solution != NULL);
+ assert(this_ -> solved);
+
+ return this_->solution[x];
+}
+
+/* is solution optimal? */
+bool is_pbqp_optimal(pbqp *this_)
+{
+ assert(this_ -> solved);
+ return this_->optimal;
+}
+
+}
+
+/* end of pbqp.c */