[ARITH] Add floordiv for the deduce bound (apache#4025)

Use fdiv in the tests for the deduce_bound

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);

tests/python/unittest/test_arith_deduce_bound.py

@@ -35,11 +35,11 @@ def test_deduce():
     d_s = tvm.arith.IntervalSet(-3, -1)
     zero = tvm.const(0, "int32")
 
-    tdiv = tvm.truncdiv
+    fdiv = tvm.floordiv
 
     e0 = (-b)*a+c-d
     res0 = tvm.arith.DeduceBound(a, e0>=0, {b: b_s, c: c_s, d: d_s}, {})
-    ans0 = (tdiv(d - c, b*-1) + (-1))
+    ans0 = fdiv(d - c, b*-1)
     assert_expr_equal(res0.max_value, ans0)
 
     # expression containing variable a is on rhs
@@ -48,7 +48,7 @@ def test_deduce():
 
     e0 = d*a+c-d
     res0 = tvm.arith.DeduceBound(a, e0>=0, {b: b_s, c: c_s, d: d_s}, {})
-    ans0 = (tdiv(d-c,d) - 1)
+    ans0 = fdiv(d-c, d)
     assert_expr_equal(res0.max_value, ans0)
 
     # expression containing variable a is on rhs
@@ -58,7 +58,7 @@ def test_deduce():
 
     e1 = (a*4+b < c)
     res1 = tvm.arith.DeduceBound(a, e1, {b: b_s, c: c_s, d: d_s}, {})
-    ans1 = (tdiv((c - b) + -1,4) -1)
+    ans1 = fdiv(c-1-b, 4)
     assert_expr_equal(res1.max_value, ans1)
 
 
@@ -81,7 +81,7 @@ def test_deduce():
 
     e3 = (-b)+a*c-d
     res3 = tvm.arith.DeduceBound(a, e3>=0, {b: b_s, c: c_s, d: d_s}, {b: b_s, d: d_s})
-    ans3 = tdiv(2,c)+1
+    ans3 = fdiv(2,c)+1
     assert str(tvm.ir_pass.Simplify(res3.min_value)) == str(ans3)
 
     res3 = tvm.arith.DeduceBound(a, zero <= e3, {b: b_s, c: c_s, d: d_s}, {b: b_s, d: d_s})