[autoparallel] rotor solver refactor (#2813)

* [autoparallel] rotor solver refactor

* [autoparallel] rotor solver refactor

colossalai/auto_parallel/checkpoint/ckpt_solver_rotor.c

 #define PY_SSIZE_T_CLEAN
 #include <Python.h>
 
+/*
+Rotor solver for checkpointing problem in C. We follow the modeling mentioned in
+paper `Optimal checkpointing for heterogeneous chains: how to train deep neural
+networks with limited memory` https://hal.inria.fr/hal-02352969. Some lines of
+the code are adapted from https://gitlab.inria.fr/hiepacs/rotor.
+*/
 long* PySequenceToLongArray(PyObject* pylist) {
   if (!(pylist && PySequence_Check(pylist))) return NULL;
   Py_ssize_t len = PySequence_Size(pylist);
@@ -81,14 +87,16 @@ static PyObject* computeTable(PyObject* self, PyObject* args) {
       (mmax + 1) * (chainLength + 1) * (chainLength + 1), sizeof(long));
 
   for (long m = 0; m <= mmax; ++m)
-    for (long i = 0; i <= chainLength; ++i)
+    for (long i = 0; i <= chainLength; ++i) {
       if ((m >= x[i + 1] + xbar[i + 1] + btmp[i]) &&
-          (m >= x[i + 1] + xbar[i + 1] + ftmp[i]))
+          (m >= x[i + 1] + xbar[i + 1] + ftmp[i])) {
         COST_TABLE(m, i, i) = ftime[i] + btime[i];
-      else
+      } else {
         COST_TABLE(m, i, i) = INFINITY;
+      }
+    }
 
-  for (long m = 0; m <= mmax; ++m)
+  for (long m = 0; m <= mmax; ++m) {
     for (long d = 1; d <= chainLength; ++d) {
       for (long i = 0; i <= chainLength - d; ++i) {
         long idx = i + d;
@@ -116,9 +124,10 @@ static PyObject* computeTable(PyObject* self, PyObject* args) {
             }
           }
           double chainCost = INFINITY;
-          if (m >= xbar[i + 1])
+          if (m >= xbar[i + 1]) {
             chainCost =
                 COST_TABLE(m, i, i) + COST_TABLE(m - xbar[i + 1], i + 1, idx);
+          }
           if (bestLeafCost <= chainCost) {
             COST_TABLE(m, i, idx) = bestLeafCost;
             BACK_PTR(m, i, idx) = bestLeaf;
@@ -126,10 +135,12 @@ static PyObject* computeTable(PyObject* self, PyObject* args) {
             COST_TABLE(m, i, idx) = chainCost;
             BACK_PTR(m, i, idx) = -1;
           }
-        } else
+        } else {
           COST_TABLE(m, i, idx) = INFINITY;
         }
       }
+    }
+  }
 
   free(ftime);
   free(btime);
@@ -158,10 +169,11 @@ static PyObject* computeTable(PyObject* self, PyObject* args) {
         PyDict_SetItem(pyCostTable_m_i, pyVar_l, pyCostTable_m_i_l);
         Py_DECREF(pyCostTable_m_i_l);
         PyObject* pyBackPtr_m_i_l;
-        if (BACK_PTR(m, i, l) < 0)
+        if (BACK_PTR(m, i, l) < 0) {
           pyBackPtr_m_i_l = Py_BuildValue("(O)", Py_True);
-        else
+        } else {
           pyBackPtr_m_i_l = Py_BuildValue("(Ol)", Py_False, BACK_PTR(m, i, l));
+        }
         PyDict_SetItem(pyBackPtr_m_i, pyVar_l, pyBackPtr_m_i_l);
         Py_DECREF(pyBackPtr_m_i_l);
         Py_DECREF(pyVar_l);

colossalai/auto_parallel/checkpoint/ckpt_solver_rotor.py

@@ -207,11 +207,10 @@ class CheckpointSolverRotor(CheckpointSolverBase):
             mmax (int): Maximum number of memory slots.
 
         Returns:
-            cost_table (List): cost_table[m][lhs][rhs] with lhs = 0...chain.length
-                                     and rhs = lhs...chain.length (lhs is not included) and m = 0...mmax
-            back_ptr (List): back_ptr[m][lhs][rhs] is (True,) if the optimal choice
-                                     is a chain checkpoint (False, j) if the optimal choice is a leaf checkpoint
-                                     of length j
+            cost_table (List): cost_table[m][lhs][rhs] indicates the optimal cost of the subproblem from lhs to rhs
+            with m memory slots.
+            back_ptr (List): back_ptr[m][lhs][rhs] indicates the best operation at this point. It is (True,) if the optimal choice
+            is a chain checkpoint, it is (False, j) if the optimal choice is a leaf checkpoint of length j
         """
 
         ftime = chain.ftime + [0.0]
@@ -224,18 +223,17 @@ class CheckpointSolverRotor(CheckpointSolverBase):
         # Build table
         cost_table = [[{} for _ in range(len(chain) + 1)] for _ in range(mmax + 1)]
         back_ptr = [[{} for _ in range(len(chain) + 1)] for _ in range(mmax + 1)]
-        # Last one is a dict because its indices go from i to l. Renumbering will wait for C implementation
 
-        # Initialize borders of the tables for lmax-lmin = 0
+        # Initialize corner cases where length of sequence equals to 1, i.e. lhs == rhs
         for m in range(mmax + 1):
             for i in range(len(chain) + 1):
                 limit = max(x[i + 1] + xbar[i + 1] + ftmp[i], x[i + 1] + xbar[i + 1] + btmp[i])
-                if m >= limit:    # Equation (1)
+                if m >= limit:
                     cost_table[m][i][i] = ftime[i] + btime[i]
                 else:
                     cost_table[m][i][i] = float("inf")
 
-        # Compute everything
+        # Compute tables
         for m in range(mmax + 1):
             for d in range(1, len(chain) + 1):
                 for i in range(len(chain) + 1 - d):