[TVM] Rewrite simplification rule to eliminate unnecessary conditionals. (#4076)

The current bounds checking infrastructure inserts checks like:

```
for (i, 0, bounds[n]) {
  if (likely(i < bounds[n]) {
     ...
  }
}
```

into the TVM IR which is currently not removed by simplification infrastructure.
This is a little unclean, as these are trivially true since for a loop var `i`
with a given min and extent, we are guaranteed that `i >= min` and `i < min +
extent`. Thus, we can insert these checks into the IR and use them to eliminate
trivial bounds checks early on.

include/tvm/arithmetic.h

@@ -245,6 +245,8 @@ class RewriteSimplifier {
               const Expr& new_expr,
               bool override = false);
 
+  std::function<void()> EnterConstraint(const Expr& constraint);
+
  private:
   friend class Analyzer;
   friend class ConstraintContext;

src/arithmetic/analyzer.cc

@@ -67,8 +67,10 @@ void ConstraintContext::EnterWithScope() {
   // entering the scope.
   auto f0 = analyzer_->const_int_bound.EnterConstraint(constraint_);
   auto f1 = analyzer_->modular_set.EnterConstraint(constraint_);
+  auto f2 = analyzer_->rewrite_simplify.EnterConstraint(constraint_);
   // recovery function.
-  exit_ = [f0, f1]() {
+  exit_ = [f0, f1, f2]() {
+    if (f2 != nullptr) f2();
     if (f1 != nullptr) f1();
     if (f0 != nullptr) f0();
   };

src/arithmetic/rewrite_simplify.cc

@@ -220,6 +220,17 @@ Mutate_(const Add* op, const Expr& self) {
   return ret;
 }
 
+std::function<void()> RewriteSimplifier::Impl::EnterConstraint(const Expr& constraint) {
+  size_t old_literal_size = literal_constraints_.size();
+  literal_constraints_.push_back(constraint);
+  size_t new_literal_size = literal_constraints_.size();
+  auto frecover = [old_literal_size, new_literal_size, this]() {
+    CHECK_EQ(literal_constraints_.size(), new_literal_size);
+    literal_constraints_.resize(old_literal_size);
+  };
+  return frecover;
+}
+
 Expr RewriteSimplifier::Impl::
 Mutate_(const Sub* op, const Expr& self) {
   Expr ret = IRMutator::Mutate_(op, self);
@@ -1705,6 +1716,14 @@ Mutate_(const Call* op, const Expr& self) {
       return op->args[0] & op->args[1];
     }
   }
+  if (op->is_intrinsic(Call::likely)) {
+    for (const auto& constraint : literal_constraints_) {
+      // Cases such as for (i, 0, bound) {if (likely(iter_var < bound)) { .. } }
+      if (Equal(constraint, op->args[0])) {
+        return make_const(op->type, true);
+      }
+    }
+  }
   return ret;
 }
 
@@ -1761,6 +1780,10 @@ void RewriteSimplifier::Update(const Var& var,
   impl_->Update(var, info, override);
 }
 
+std::function<void()> RewriteSimplifier::EnterConstraint(const Expr& constraint) {
+  return impl_->EnterConstraint(constraint);
+}
+
 RewriteSimplifier::RewriteSimplifier(Analyzer* parent)
     : impl_(new Impl(parent)) {
 }

src/arithmetic/rewrite_simplify.h

@@ -28,6 +28,7 @@
 #include <tvm/expr_operator.h>
 #include <tvm/ir_mutator.h>
 #include <unordered_map>
+#include <vector>
 #include "const_fold.h"
 #include "pattern_match.h"
 #include "ir_mutator_with_analyzer.h"
@@ -74,6 +75,8 @@ class RewriteSimplifier::Impl : public IRMutatorWithAnalyzer {
   Expr Mutate_(const Cast* op, const Expr& self) override;
   Expr Mutate_(const Let* op, const Expr& self) override;
 
+  std::function<void()> EnterConstraint(const Expr& constraint);
+
  protected:
   /*! \brief internal structure for comparison. */
   enum CompareResult {
@@ -89,6 +92,9 @@ class RewriteSimplifier::Impl : public IRMutatorWithAnalyzer {
   int recur_depth_{0};
   // internal variable map
   std::unordered_map<Var, Expr, ExprHash, ExprEqual> var_map_;
+
+  std::vector<Expr> literal_constraints_;
+
   // maximum number of recursion allowed during a single pass.
   static const constexpr int kMaxRecurDepth = 5;
 

src/arithmetic/stmt_simplify.cc

@@ -51,6 +51,13 @@ class StmtSimplifier : public IRMutatorWithAnalyzer {
     return Mutate(stmt);
   }
 
+  Stmt Mutate_(const For* op, const Stmt& s) final {
+    analyzer_->Bind(op->loop_var, Range::make_by_min_extent(op->min, op->extent));
+    With<ConstraintContext> ctx1(analyzer_, op->loop_var >= op->min);
+    With<ConstraintContext> ctx2(analyzer_, op->loop_var < op->min + op->extent);
+    return IRMutator::Mutate_(op, s);
+  }
+
   Stmt Mutate_(const LetStmt* op, const Stmt& s) {
     Expr value = this->Mutate(op->value);
     if (!ir::HasSideEffect(value)) {

tests/python/unittest/test_arith_stmt_simplify.py

@@ -47,6 +47,62 @@ def test_thread_extent_simplify():
     assert isinstance(body.body.body.body, tvm.stmt.Store)
 
 
+def test_basic_likely_elimination():
+    n = tvm.var('n')
+    X = tvm.placeholder(shape=(n,), name="x")
+    W = tvm.placeholder(shape=(n + 1,), dtype="int32", name="w")
+
+    def f(i):
+        start = W[i]
+        extent = W[i+1] - W[i]
+        rv = tvm.reduce_axis((0, extent))
+        return tvm.sum(X[rv + start], axis=rv)
+    Y = tvm.compute(X.shape, f, name="y")
+    s = tvm.create_schedule([Y.op])
+    stmt = tvm.lower(s, [X, W, Y], simple_mode=True)
+    assert('if' not in str(stmt))
+
+def test_complex_likely_elimination():
+    def cumsum(X):
+        """
+        Y[i] = sum(X[:i])
+        """
+        (m, ) = X.shape
+        s_state = tvm.placeholder((m + 1, ), dtype="int32", name="state")
+        s_init = tvm.compute((1, ), lambda _: tvm.const(0, "int32"))
+        s_update = tvm.compute((m + 1, ), lambda l: s_state[l - 1] + X[l - 1])
+        return tvm.scan(s_init, s_update, s_state, inputs=[X], name="cumsum")
+
+    def sparse_lengths_sum(data, indices, lengths):
+        oshape = list(data.shape)
+        oshape[0] = lengths.shape[0]
+        length_offsets = cumsum(lengths)
+
+        def sls(n, d):
+            gg = tvm.reduce_axis((0, lengths[n]))
+            indices_idx = length_offsets[n] + gg
+            data_idx = indices[indices_idx]
+            data_val = data[data_idx, d]
+            return tvm.sum(data_val, axis=gg)
+
+        return tvm.compute(oshape, sls)
+
+    m, n, d, i, l = tvm.var('m'), tvm.var('n'), tvm.var('d'), tvm.var('i'), tvm.var('l')
+    data_ph = tvm.placeholder((m, d * 32), name="data")
+    indices_ph = tvm.placeholder((i,), name="indices", dtype="int32")
+    lengths_ph = tvm.placeholder((n,), name="lengths", dtype="int32")
+    Y = sparse_lengths_sum(data_ph, indices_ph, lengths_ph)
+    s = tvm.create_schedule([Y.op])
+    (n, d) = s[Y].op.axis
+    (do, di) = s[Y].split(d, factor=32)
+    (gg,) = s[Y].op.reduce_axis
+    s[Y].reorder(n, do, gg, di)
+    s[Y].vectorize(di)
+    stmt = tvm.lower(s, [data_ph, indices_ph, lengths_ph, Y], simple_mode=True)
+    assert('if' not in str(stmt))
+
 if __name__ == "__main__":
     test_stmt_simplify()
     test_thread_extent_simplify()
+    test_basic_likely_elimination()
+    test_complex_likely_elimination()