Add floordiv for the deduce bound

Author: Umang Yadav

src/arithmetic/bound_deducer.cc

@@ -150,43 +150,26 @@ class BoundDeducer: public IRVisitor {
     // always use relax bound
     bool divided = analyzer_.CanProve(floormod(result_, operand) == 0);
 
-    // TODO(tvm-team): use floordiv, which could give better bound.
-    result_ = truncdiv(result_, operand);
+    result_ = floordiv(result_, operand);   // rounding down here
 
     if (!divided) {
-      // Handle non-divisible case
-      // NOTE: this accounts for trunc div behavior.
-      bool target_is_non_neg = expr_map_[target_var].can_prove_non_negative();
-
       if (comp_op == kGreater) {
+        // System will round down in all the cases, so add one for result_ for kGreater
+        // (x >= 3/2 --> x >= 2)
+        // (x >= -3/2 --> x >= -1)
+        // (x >= 3/-2 --> x >= -1)
+        // (x >= -3/-2 --> x >= 2)
         result_ += 1;
       } else if (comp_op == kEqual) {
-        // condition unsatisfiable as with trunc div, it will change the expression
+        // condition unsatisfiable as with floor div, it will change the expression
         success_ = false;
         return;
       } else {
-        // NOTE: this is a bit sutble hack.
-        //
-        // condition:
-        // - x * operand <= result
-        // - operand > 0
-        // - x >= 0
-        //
-        // Then it is fine to deduce that x <= result / operand.
-        // - if result > 0,  this division round down
-        // - if result < 0, (result / operand) rounds up and may violate the constraint
-        //   however, given that x is always non-negative,
-        //   it is fine to have this relaxed bound, given that the user of deduce bound
-        //   will respect the bound of x
-        //
-        // TODO(tvm-team): think about a better API to incorporate constraint of x.
-        //                 e.g. specify an interval of x and return a bound
-        //                 that is in the interval and satisfies the condition.
-        if (target_is_non_neg && sign_operand == kPositive) {
-          // do nothing
-        } else {
-          result_ -= 1;
-        }
+        // System rounds down in all cases, do nothing for kLess.
+        // ( x <= 3/2 --> x <= 1)
+        // ( x <= -3/2 --> x <= -2)
+        // ( x <= 3/-2 --> x <= -2)
+        // ( x <= -3/-2 --> x <= 1)
       }
     }
     Visit(left ? op->a : op->b);