[MRG] Correct pointer overflow in EMD (#381)

* avoid overflow on openmp version of emd solver

* monothread version updated

* Fixed typo in readme

* added PR in releases

* typo in releases.md

* added a precision to releases.md

* added a precision to releases.md

* correct readme

* forgot to cast

* lower error

4 files changed, 26 insertions, 23 deletions

diff --git a/README.md b/README.md
index 12340d5..7c9475b 100644
--- a/README.md
+++ b/README.md
@@ -26,8 +26,8 @@ POT provides the following generic OT solvers (links to examples):
 * Debiased Sinkhorn barycenters [Sinkhorn divergence barycenter](https://pythonot.github.io/auto_examples/barycenters/plot_debiased_barycenter.html) [37]
 * [Smooth optimal transport solvers](https://pythonot.github.io/auto_examples/plot_OT_1D_smooth.html) (dual and semi-dual) for KL and squared L2 regularizations [17].
 * Weak OT solver between empirical distributions [39]
-* Non regularized [Wasserstein barycenters [16] ](https://pythonot.github.io/auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html)) with LP solver (only small scale).
-* [Gromov-Wasserstein distances](https://pythonot.github.io/auto_examples/gromov/plot_gromov.html) and [GW barycenters](https://pythonot.github.io/auto_examples/gromov/plot_gromov_barycenter.html)  (exact [13] and regularized [12]), differentiable using gradients from
+* Non regularized [Wasserstein barycenters [16] ](https://pythonot.github.io/auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html) with LP solver (only small scale).
+* [Gromov-Wasserstein distances](https://pythonot.github.io/auto_examples/gromov/plot_gromov.html) and [GW barycenters](https://pythonot.github.io/auto_examples/gromov/plot_gromov_barycenter.html)  (exact [13] and regularized [12]), differentiable using gradients from Graph Dictionary Learning [38]
  * [Fused-Gromov-Wasserstein distances solver](https://pythonot.github.io/auto_examples/gromov/plot_fgw.html#sphx-glr-auto-examples-plot-fgw-py) and [FGW barycenters](https://pythonot.github.io/auto_examples/gromov/plot_barycenter_fgw.html) [24]
 * [Stochastic
   solver](https://pythonot.github.io/auto_examples/others/plot_stochastic.html) and
diff --git a/RELEASES.md b/RELEASES.md
index fdaff59..b384617 100644
--- a/RELEASES.md
+++ b/RELEASES.md
@@ -13,7 +13,10 @@
 - Fixed an issue where Sinkhorn solver assumed a symmetric cost matrix (Issue #374, PR #375)
 - Fixed an issue where hitting iteration limits would be reported to stderr by std::cerr regardless of Python's stderr stream status (PR #377)
 - Fixed an issue where the metric argument in ot.dist did not allow a callable parameter (Issue #378, PR #379)
-- Fixed an issue where the max number of iterations in ot.emd was not allow to go beyond 2^31 (PR #380) 
+- Fixed an issue where the max number of iterations in ot.emd was not allowed to go beyond 2^31 (PR #380)
+- Fixed an issue where pointers would overflow in the EMD solver, returning an
+incomplete transport plan above a certain size (slightly above 46k, its square being
+roughly 2^31) (PR #381)
 
 
 ## 0.8.2
diff --git a/ot/lp/EMD_wrapper.cpp b/ot/lp/EMD_wrapper.cpp
index 457216b..4aa5a6e 100644
--- a/ot/lp/EMD_wrapper.cpp
+++ b/ot/lp/EMD_wrapper.cpp
@@ -24,7 +24,7 @@ int EMD_wrap(int n1, int n2, double *X, double *Y, double *D, double *G,
     // beware M and C are stored in row major C style!!!
 
     using namespace lemon;
-    int n, m, cur;
+    uint64_t n, m, cur;
 
     typedef FullBipartiteDigraph Digraph;
     DIGRAPH_TYPEDEFS(Digraph);
@@ -51,15 +51,15 @@ int EMD_wrap(int n1, int n2, double *X, double *Y, double *D, double *G,
 
     // Define the graph
 
-    std::vector<int> indI(n), indJ(m);
+    std::vector<uint64_t> indI(n), indJ(m);
     std::vector<double> weights1(n), weights2(m);
     Digraph di(n, m);
-    NetworkSimplexSimple<Digraph,double,double, node_id_type> net(di, true, n+m, ((int64_t)n)*((int64_t)m), maxIter);
+    NetworkSimplexSimple<Digraph,double,double, node_id_type> net(di, true, (int) (n + m), n * m, maxIter);
 
     // Set supply and demand, don't account for 0 values (faster)
 
     cur=0;
-    for (int i=0; i<n1; i++) {
+    for (uint64_t i=0; i<n1; i++) {
         double val=*(X+i);
         if (val>0) {
             weights1[ cur ] = val;
@@ -70,7 +70,7 @@ int EMD_wrap(int n1, int n2, double *X, double *Y, double *D, double *G,
     // Demand is actually negative supply...
 
     cur=0;
-    for (int i=0; i<n2; i++) {
+    for (uint64_t i=0; i<n2; i++) {
         double val=*(Y+i);
         if (val>0) {
             weights2[ cur ] = -val;
@@ -79,12 +79,12 @@ int EMD_wrap(int n1, int n2, double *X, double *Y, double *D, double *G,
     }
 
 
-    net.supplyMap(&weights1[0], n, &weights2[0], m);
+    net.supplyMap(&weights1[0], (int) n, &weights2[0], (int) m);
 
     // Set the cost of each edge
     int64_t idarc = 0;
-    for (int i=0; i<n; i++) {
-        for (int j=0; j<m; j++) {
+    for (uint64_t i=0; i<n; i++) {
+        for (uint64_t j=0; j<m; j++) {
             double val=*(D+indI[i]*n2+indJ[j]);
             net.setCost(di.arcFromId(idarc), val);
             ++idarc;
@@ -95,7 +95,7 @@ int EMD_wrap(int n1, int n2, double *X, double *Y, double *D, double *G,
     // Solve the problem with the network simplex algorithm
 
     int ret=net.run();
-    int i, j;
+    uint64_t i, j;
     if (ret==(int)net.OPTIMAL || ret==(int)net.MAX_ITER_REACHED) {
         *cost = 0;
         Arc a; di.first(a);
@@ -126,7 +126,7 @@ int EMD_wrap_omp(int n1, int n2, double *X, double *Y, double *D, double *G,
     // beware M and C are stored in row major C style!!!
 
     using namespace lemon_omp;
-    int n, m, cur;
+    uint64_t n, m, cur;
 
     typedef FullBipartiteDigraph Digraph;
     DIGRAPH_TYPEDEFS(Digraph);
@@ -153,15 +153,15 @@ int EMD_wrap_omp(int n1, int n2, double *X, double *Y, double *D, double *G,
 
     // Define the graph
 
-    std::vector<int> indI(n), indJ(m);
+    std::vector<uint64_t> indI(n), indJ(m);
     std::vector<double> weights1(n), weights2(m);
     Digraph di(n, m);
-    NetworkSimplexSimple<Digraph,double,double, node_id_type> net(di, true, n+m, ((int64_t)n)*((int64_t)m), maxIter, numThreads);
+    NetworkSimplexSimple<Digraph,double,double, node_id_type> net(di, true, (int) (n + m), n * m, maxIter, numThreads);
 
     // Set supply and demand, don't account for 0 values (faster)
 
     cur=0;
-    for (int i=0; i<n1; i++) {
+    for (uint64_t i=0; i<n1; i++) {
         double val=*(X+i);
         if (val>0) {
             weights1[ cur ] = val;
@@ -172,7 +172,7 @@ int EMD_wrap_omp(int n1, int n2, double *X, double *Y, double *D, double *G,
     // Demand is actually negative supply...
 
     cur=0;
-    for (int i=0; i<n2; i++) {
+    for (uint64_t i=0; i<n2; i++) {
         double val=*(Y+i);
         if (val>0) {
             weights2[ cur ] = -val;
@@ -181,12 +181,12 @@ int EMD_wrap_omp(int n1, int n2, double *X, double *Y, double *D, double *G,
     }
 
 
-    net.supplyMap(&weights1[0], n, &weights2[0], m);
+    net.supplyMap(&weights1[0], (int) n, &weights2[0], (int) m);
 
     // Set the cost of each edge
     int64_t idarc = 0;
-    for (int i=0; i<n; i++) {
-        for (int j=0; j<m; j++) {
+    for (uint64_t i=0; i<n; i++) {
+        for (uint64_t j=0; j<m; j++) {
             double val=*(D+indI[i]*n2+indJ[j]);
             net.setCost(di.arcFromId(idarc), val);
             ++idarc;
@@ -197,7 +197,7 @@ int EMD_wrap_omp(int n1, int n2, double *X, double *Y, double *D, double *G,
     // Solve the problem with the network simplex algorithm
 
     int ret=net.run();
-    int i, j;
+    uint64_t i, j;
     if (ret==(int)net.OPTIMAL || ret==(int)net.MAX_ITER_REACHED) {
         *cost = 0;
         Arc a; di.first(a);
diff --git a/ot/lp/network_simplex_simple_omp.h b/ot/lp/network_simplex_simple_omp.h
index 5f19d73..c324d4c 100644
--- a/ot/lp/network_simplex_simple_omp.h
+++ b/ot/lp/network_simplex_simple_omp.h
@@ -41,8 +41,8 @@
 #undef EPSILON
 #undef _EPSILON
 #undef MAX_DEBUG_ITER
-#define EPSILON std::numeric_limits<Cost>::epsilon()*10
-#define _EPSILON 1e-8
+#define EPSILON std::numeric_limits<Cost>::epsilon()
+#define _EPSILON 1e-14
 #define MAX_DEBUG_ITER 100000
 
 /// \ingroup min_cost_flow_algs