fixing the to coarser index conversion for negative integer values

Author: UCaromel

src/amr/data/field/refine/electric_field_refiner.hpp

@@ -43,11 +43,8 @@ class ElectricFieldRefiner
     {
         TBOX_ASSERT(coarseField.physicalQuantity() == fineField.physicalQuantity());
 
-        auto const locFineIdx          = AMRToLocal(fineIndex, fineBox_);
-        auto constexpr refinementRatio = 2;
-        auto coarseIdx{fineIndex};
-        for (auto& idx : coarseIdx)
-            idx = idx / refinementRatio;
+        auto const locFineIdx   = AMRToLocal(fineIndex, fineBox_);
+        auto const coarseIdx    = toCoarseIndex(fineIndex);
         auto const locCoarseIdx = AMRToLocal(coarseIdx, coarseBox_);
 
         if constexpr (dimension == 1)

src/amr/data/field/refine/magnetic_field_refiner.hpp

@@ -54,10 +54,8 @@ class MagneticFieldRefiner
     {
         TBOX_ASSERT(coarseField.physicalQuantity() == fineField.physicalQuantity());
 
-        auto locFineIdx = AMRToLocal(fineIndex, fineBox_);
-        auto coarseIdx{fineIndex};
-        for (auto& idx : coarseIdx)
-            idx = idx / 2;
+        auto locFineIdx   = AMRToLocal(fineIndex, fineBox_);
+        auto coarseIdx    = toCoarseIndex(fineIndex);
         auto locCoarseIdx = AMRToLocal(coarseIdx, coarseBox_);
 
 

src/amr/resources_manager/amr_utils.hpp

@@ -109,6 +109,26 @@ namespace amr
         return index;
     }
 
+    /**
+     * @brief toCoarseIndex returns a coarse index from a fine index assuming a ratio of 2 in AMR
+     * index
+     *
+     * For positive indices, it is simply index / 2. For negative indices, index / 2 doesnt work
+     * because of integer division. For example, -3 / 2 = -1, but we want it to be -2, while for
+     * even negative integers e.g. -2 / 2 = -1, this is correct. We thus end up with the following
+     * formula for negative indices: index / 2 + index % 2 (remember that in C++ the % is signed)
+     * For example, -3 % 2 = -1, so we have -3 / 2 + -1 = -2.
+     *
+     */
+    template<std::size_t dimension, template<typename, std::size_t> typename Index>
+    NO_DISCARD Index<int, dimension> toCoarseIndex(Index<int, dimension> fineIndex)
+    {
+        auto coarseIdx{fineIndex};
+        for (auto& idx : coarseIdx)
+            idx = (idx >= 0) ? idx / 2 : idx / 2 + idx % 2;
+        return coarseIdx;
+    }
+
     /**
      * @brief refinedPosition returns an index refined index with the given ratio
      * bound