[PASS]LoopPartition (#56)

* loop_partition draft

* divide loop variable into constant domain and variable domain & consider multiple partitions

* process doubt interval

* fix and refactor, add relax_map arg in BoundDeduce

* fix testcase and comment

* rebase to zero, convert to SSA

* change the logic of generating loop code & fix issues

* add a testcase for relax map in deducebound && fix issues

* clean code

* const auto&

* add test_multi_if

include/tvm/expr.h

@@ -35,6 +35,8 @@ using Halide::Internal::make_const;
 using Halide::Internal::make_zero;
 using Halide::Internal::as_const_int;
 using Halide::Internal::as_const_uint;
+using Halide::Internal::const_true;
+using Halide::Internal::const_false;
 
 inline Type TVMType2Type(TVMType t) {
   return Type(static_cast<halide_type_code_t>(t.code), t.bits, t.lanes);
@@ -53,8 +55,8 @@ class Var : public Halide::VarExpr {
  public:
   explicit Var(const std::string& name_hint = "v",
                Type t = Int(32)) : VarExpr(name_hint, t) {}
-
   explicit Var(std::shared_ptr<Node> n) : VarExpr(n) {}
+  explicit Var(VarExpr v) : VarExpr(v) {}
 
   /*! \brief type indicate the container type */
   using ContainerType = Variable;

include/tvm/ir_mutator.h

@@ -62,12 +62,12 @@ class IRMutator {
   virtual Stmt Mutate_(const Allocate* op, const Stmt& s);
   virtual Stmt Mutate_(const Store* op, const Stmt& s);
   virtual Stmt Mutate_(const Free* op, const Stmt& s);
-  virtual Stmt Mutate_(const AssertStmt* op, const Stmt& e);
-  virtual Stmt Mutate_(const ProducerConsumer* op, const Stmt& e);
-  virtual Stmt Mutate_(const Provide* op, const Stmt& e);
+  virtual Stmt Mutate_(const AssertStmt* op, const Stmt& s);
+  virtual Stmt Mutate_(const ProducerConsumer* op, const Stmt& s);
+  virtual Stmt Mutate_(const Provide* op, const Stmt& s);
   virtual Stmt Mutate_(const Realize* op, const Stmt& s);
   virtual Stmt Mutate_(const Block* op, const Stmt& s);
-  virtual Stmt Mutate_(const Evaluate* op, const Stmt& e);
+  virtual Stmt Mutate_(const Evaluate* op, const Stmt& s);
 
   virtual Expr Mutate_(const Variable* op, const Expr& e);
   virtual Expr Mutate_(const Load* op, const Expr& e);

include/tvm/ir_pass.h

@@ -138,6 +138,13 @@ Stmt InjectVirtualThread(Stmt stmt);
 Stmt LiftAllocate(Stmt stmt);
 
 /*!
+ * \brief partition loops in the stmt
+ * \param stmt The stmt to do loop partition
+ * \return Transformed stmt.
+ */
+Stmt LoopPartition(Stmt stmt);
+
+/*!
  * \brief Make an user callable API LoweredFunc.
  *
  *  The main task of this function is to create code to :

src/api/api_arith.cc

@@ -29,7 +29,9 @@ TVM_REGISTER_API(_arith_EvalModular)
 
 TVM_REGISTER_API(_arith_DeduceBound)
 .set_body([](TVMArgs args, TVMRetValue *ret) {
-    *ret = DeduceBound(args[0], args[1], args[2]);
+    *ret = DeduceBound(args[0], args[1],
+        args[2].operator Map<Var, IntSet>(),
+        args[3].operator Map<Var, IntSet>());
   });
 
 TVM_REGISTER_API(_IntervalSetGetMin)

src/api/api_pass.cc

@@ -69,6 +69,7 @@ REGISTER_PASS4(MakeAPI);
 REGISTER_PASS1(SplitHostDevice);
 REGISTER_PASS1(LiftAllocate);
 REGISTER_PASS1(InjectVirtualThread);
+REGISTER_PASS1(LoopPartition);
 
 }  // namespace ir
 }  // namespace tvm

src/arithmetic/bound_deducer.cc

@@ -21,7 +21,7 @@ using Halide::Internal::Interval;
 // from a expression.
 class VariablePathFinder: public IRVisitor {
  public:
-  explicit VariablePathFinder(Var target) : target_(target) {}
+  explicit VariablePathFinder(Expr target) : target_(target) {}
 
   void Visit(const NodeRef& node) final {
     if (visited_.count(node.get()) != 0) return;
@@ -37,13 +37,13 @@ class VariablePathFinder: public IRVisitor {
 
  private:
   bool found_{false};
-  Var target_;
+  Expr target_;
   std::unordered_set<const Node*> visited_;
 };
 
 // get the path to the variable,
 // return empty vector to represent failure
-std::vector<const Node*> GetPath(Var target, Expr expr) {
+std::vector<const Node*> GetPath(Expr target, Expr expr) {
   VariablePathFinder v(target);
   v.Visit(expr);
   return v.path_;
@@ -56,11 +56,11 @@ class BoundDeducer: public IRVisitor {
  public:
   friend class BoundDeduceInputChecker;
   friend class Converter;
-  BoundDeducer(Var target, Expr expr,
-               const std::unordered_map<const Variable*, IntSet>& dom_map)
-  : target_(target), expr_(expr), dom_map_(dom_map) {}
+  BoundDeducer(Expr target, Expr expr,
+               const std::unordered_map<const Variable*, IntSet>& hint_map,
+               const std::unordered_map<const Variable*, IntSet>& relax_map)
+  : target_(target), expr_(expr), hint_map_(hint_map), relax_map_(relax_map) {}
 
-  bool Init();
   void Deduce();
 
   void Visit(const NodeRef& e) final {
@@ -137,9 +137,14 @@ class BoundDeducer: public IRVisitor {
   bool success{true};
 
  private:
-  Var  target_;
+  void Init();
+  void Transform();
+  void Relax();
+
+  Expr target_;
   Expr expr_;
-  const std::unordered_map<const Variable*, IntSet>& dom_map_;
+  const std::unordered_map<const Variable*, IntSet>& hint_map_;
+  const std::unordered_map<const Variable*, IntSet>& relax_map_;
   ExprIntSetMap expr_map_;
   std::vector<const Node*> path_;
   size_t iter_{0};
@@ -163,10 +168,13 @@ class BoundDeduceInputChecker: public IRVisitor {
   size_t target_count{0};
 };
 
-bool BoundDeducer::Init() {
+void BoundDeducer::Init() {
   BoundDeduceInputChecker checker;
   if (!checker.Check(this)) success = false;
+  Transform();
+}
 
+void BoundDeducer::Transform() {
   if (const LT* op = expr_.as<LT>()) {
     is_greater = false;
     is_equal   = false;
@@ -190,30 +198,35 @@ bool BoundDeducer::Init() {
   } else {
     success = false;
   }
-  return success;
 }
 
 void BoundDeducer::Deduce() {
   Init();
   if (!success) return;
 
+  Relax();
   // get the path
   path_ = GetPath(target_, expr_);
   // get the sign of every subexpr
-  expr_map_ = EvalSetForEachSubExpr(expr_, dom_map_);
+  expr_map_ = EvalSetForEachSubExpr(expr_, hint_map_);
 
   Visit(expr_);
 }
 
-// assuming e >= 0, deduce the bound of variable from it.
-// return empty set to represent deduce failure.
-IntSet DeduceBound(Var v, Expr e,
-                   const Map<Var, IntSet>& dom_map) {
-  std::unordered_map<const Variable*, IntSet> dmap;
-  for (auto kv : dom_map) {
-    dmap[kv.first.get()] = kv.second;
+void BoundDeducer::Relax() {
+  if (is_greater) {
+    expr_  = EvalSet(expr_ , relax_map_).min();
+    result = EvalSet(result, relax_map_).max();
+  } else {
+    expr_  = EvalSet(expr_ , relax_map_).max();
+    result = EvalSet(result, relax_map_).min();
   }
-  BoundDeducer d(v, e, dmap);
+}
+
+IntSet DeduceBound(Expr v, Expr e,
+  const std::unordered_map<const Variable*, IntSet>& hint_map,
+  const std::unordered_map<const Variable*, IntSet>& relax_map) {
+  BoundDeducer d(v, e, hint_map, relax_map);
   d.Deduce();
   if (!d.success) return IntSet::nothing();
   Expr min = Interval::neg_inf, max = Interval::pos_inf;
@@ -225,5 +238,21 @@ IntSet DeduceBound(Var v, Expr e,
   return IntSet::interval(min, max);
 }
 
+// assuming e >= 0, deduce the bound of variable from it.
+// return empty set to represent deduce failure.
+IntSet DeduceBound(Expr v, Expr e,
+                   const Map<Var, IntSet>& hint_map,
+                   const Map<Var, IntSet>& relax_map) {
+  std::unordered_map<const Variable*, IntSet> hmap;
+  for (auto kv : hint_map) {
+    hmap[kv.first.get()] = kv.second;
+  }
+  std::unordered_map<const Variable*, IntSet> rmap;
+  for (auto kv : relax_map) {
+    rmap[kv.first.get()] = kv.second;
+  }
+  return DeduceBound(v, e, hmap, rmap);
+}
+
 }  // namespace arith
 }  // namespace tvm

src/arithmetic/int_set.cc

@@ -162,11 +162,11 @@ inline bool MatchPoint(const IntSet& a,
   return i.is_single_point() && i.min.same_as(b);
 }
 
-IntSet Union(const Array<IntSet>& set) {
-  if (set.size() == 1) return set[0];
-  Interval x = set[0].cover_interval().as<IntervalSet>()->i;
-  for (size_t i = 1; i < set.size(); ++i) {
-    IntSet s = set[i].cover_interval();
+IntSet Union(const Array<IntSet>& sets) {
+  if (sets.size() == 1) return sets[0];
+  Interval x = sets[0].cover_interval().as<IntervalSet>()->i;
+  for (size_t i = 1; i < sets.size(); ++i) {
+    IntSet s = sets[i].cover_interval();
     const Interval& y = s.as<IntervalSet>()->i;
     if (can_prove(x.max + 1 >= y.min)) {
       x.max = y.max;
@@ -179,6 +179,15 @@ IntSet Union(const Array<IntSet>& set) {
   return IntervalSet::make(x);
 }
 
+IntSet Intersect(const Array<IntSet>& sets) {
+  Interval x = sets[0].cover_interval().as<IntervalSet>()->i;
+  for (size_t i = 1; i < sets.size(); ++i) {
+    Interval y = sets[i].cover_interval().as<IntervalSet>()->i;
+    x = Interval::make_intersection(x, y);
+  }
+  return IntervalSet::make(x);
+}
+
 // type traits
 template<typename OP>
 struct is_logical_op {

src/arithmetic/int_set.h

@@ -8,6 +8,7 @@
 
 #include <tvm/expr.h>
 #include <tvm/schedule.h>
+#include <vector>
 
 namespace tvm {
 namespace arith {
@@ -157,6 +158,13 @@ ExprIntSetMap EvalSetForEachSubExpr(Expr r,
  */
 IntSet Union(const Array<IntSet>& sets);
 
+/*!
+ * \brief Create an union set of all sets
+ * \param sets The sets to be intersected
+ * \return the set after intersected
+ */
+IntSet Intersect(const Array<IntSet>& sets);
+
 // implementation
 inline const IntSetNode* IntSet::operator->() const {
   return static_cast<const IntSetNode*>(node_.get());
@@ -169,11 +177,17 @@ inline const IntSetNode* IntSet::operator->() const {
  *
  * \param v The target variable to be deduced.
  * \param cond The conditional expression.
- * \param dom_map The domain of each variable.
+ * \param hint_map The domain of variable, used to help deduce.
+ * \param relax The domain of each variable, used to relax the domain.
  * \return An integer set that can cover all the possible values.
  */
-IntSet DeduceBound(Var v, Expr cond,
-                   const Map<Var, IntSet>& dom_map);
+IntSet DeduceBound(Expr v, Expr cond,
+                   const Map<Var, IntSet>& hint_map,
+                   const Map<Var, IntSet>& relax_map);
+IntSet DeduceBound(Expr v, Expr e,
+  const std::unordered_map<const Variable*, IntSet>& hint_map,
+  const std::unordered_map<const Variable*, IntSet>& relax_map);
+
 
 }  // namespace arith
 }  // namespace tvm

src/pass/ir_mutator.cc

@@ -128,7 +128,7 @@ Stmt IRMutator::Mutate_(const IfThenElse *op, const Stmt& s) {
   Expr condition = this->Mutate(op->condition);
   Stmt then_case = this->Mutate(op->then_case);
   Stmt else_case;
-  if (else_case.defined()) {
+  if (op->else_case.defined()) {
     else_case = this->Mutate(op->else_case);
   }
   if (condition.same_as(op->condition) &&

src/pass/loop_partition.cc

+/*!
+ *  Copyright (c) 2017 by Contributors
+ * \file loop_partition.cc
+ */
+#include <tvm/ir.h>
+#include <tvm/ir_visitor.h>
+#include <tvm/ir_mutator.h>
+#include <tvm/ir_pass.h>
+#include <unordered_map>
+#include <unordered_set>
+#include "../arithmetic/int_set.h"
+#include "../arithmetic/int_set_internal.h"
+
+namespace tvm {
+namespace ir {
+
+using arith::IntSet;
+
+// a partition means the expr is equal to true in the interval
+struct Partition {
+  Expr expr;
+  IntSet interval;
+};
+
+bool ExprUseVars(Expr expr, const std::unordered_set<const Variable*>& vars) {
+  bool success = false;
+  PostOrderVisit(expr, [&vars, &success](const NodeRef& node) {
+    if (const Variable* v = node.as<Variable>()) {
+      if (vars.count(v)) {
+        success = true;
+        return;
+      }
+    }
+  });
+  return success;
+}
+
+class PartitionFinder : public IRVisitor {
+ public:
+  explicit PartitionFinder(VarExpr loop_var,
+    const std::unordered_map<const Variable*, IntSet>& dom_map)
+      : target_var_(loop_var), out_vars_(dom_map.size()), hint_map_(dom_map) {
+        for (const auto& kv : dom_map) out_vars_.insert(kv.first);
+      }
+
+  void Visit_(const For* op) {
+    if (ExprUseVars(op->min, out_vars_) || ExprUseVars(op->extent, out_vars_)) return;
+
+    hint_map_.insert({op->loop_var.get(),
+      IntSet::interval(op->min, op->min + op->extent - 1)});
+    relax_map_.insert({op->loop_var.get(),
+      IntSet::interval(op->min, op->min + op->extent - 1)});
+    IRVisitor::Visit_(op);
+    relax_map_.erase(op->loop_var.get());
+    hint_map_.erase(op->loop_var.get());
+  }
+
+  void Visit_(const IfThenElse* op) {
+    if (ExprUseVars(op->condition, std::unordered_set<const Variable*>({target_var_.get()}))) {
+      IntSet interval = DeduceBound(target_var_, op->condition, hint_map_, relax_map_);
+      partitions[op->condition.get()] = Partition{op->condition, interval};
+    } else {
+      IRVisitor::Visit_(op);
+    }
+  }
+
+  std::unordered_map<const Node*, Partition> partitions;
+
+ private:
+  VarExpr target_var_;
+  std::unordered_set<const Variable*> out_vars_;
+  std::unordered_map<const Variable*, IntSet> hint_map_;
+  std::unordered_map<const Variable*, IntSet> relax_map_;
+};
+
+class PartitionReplacer : public IRMutator {
+ public:
+  explicit PartitionReplacer(const std::unordered_map<const Node*, Partition>& ps)
+    : ps_(ps) {}
+
+  Expr Mutate(Expr e) override {
+    if (ps_.count(e.get())) {
+      return Mutate(const_true());
+    }
+    return IRMutator::Mutate(e);
+  }
+  using IRMutator::Mutate;
+
+ private:
+  const std::unordered_map<const Node*, Partition>& ps_;
+};
+
+class LoopPartitioner : public IRMutator {
+ public:
+  LoopPartitioner() {}
+
+  Stmt Mutate_(const For* op, const Stmt& stmt) {
+    if (!is_const(op->min) || !is_const(op->extent)) {
+      Stmt s = DoPartition(op, stmt);
+      if (s.defined()) return s;
+    }
+    dom_map_.insert({op->loop_var.get(),
+      IntSet::interval(op->min, op->min + op->extent - 1)});
+    Stmt res = IRMutator::Mutate_(op, stmt);
+    dom_map_.erase(op->loop_var.get());
+    return res;
+  }
+
+ private:
+  Stmt DoPartition(const For* op, const Stmt& stmt);
+
+  std::unordered_map<const Variable*, IntSet> dom_map_;
+};
+
+Stmt LoopPartitioner::DoPartition(const For* op, const Stmt& stmt) {
+  PartitionFinder finder(op->loop_var, dom_map_);
+  finder.Visit(op->body);
+  const auto& partitions = finder.partitions;
+
+  if (partitions.empty()) return Stmt();
+
+  Expr min = op->min;
+  Expr max = op->min + op->extent - 1;
+  Array<IntSet> sets;
+  // merge partitions (take their intersect)
+  for (const auto& kv : partitions) {
+    sets.push_back(kv.second.interval);
+  }
+  IntSet true_itrv  = Intersect(sets);
+
+  Stmt pre_stmt;
+  Expr body_begin;
+  if (true_itrv.as<arith::IntervalSet>()->i.has_lower_bound()) {
+    body_begin = true_itrv.min();
+    if (!can_prove(body_begin == min)) {
+      if (!can_prove(body_begin - min >= 0)) {
+        LOG(WARNING) << "cannot prove: " << (body_begin - min >= 0)
+                     << ", when generating the pre doubt loop";
+        body_begin = Max::make(body_begin, min);
+      }
+      // [min, body_begin)
+      Stmt body = Substitute(op->body,
+        {{Var{op->loop_var}, op->loop_var + min}});
+      pre_stmt = For::make(op->loop_var, 0,
+        body_begin - min, op->for_type, op->device_api, body);
+    }
+  } else {
+    body_begin = min;
+  }
+
+  Stmt post_stmt;
+  Expr post_doubt_begin;
+  if (true_itrv.as<arith::IntervalSet>()->i.has_upper_bound()) {
+    post_doubt_begin = true_itrv.max() + 1;
+    if (!can_prove(true_itrv.max() == max)) {
+      if (!can_prove(max - post_doubt_begin >= 0)) {
+        LOG(WARNING) << "Cannot prove: " << (max - post_doubt_begin >= 0)
+                     << ", when generating the post doubt loop";
+        post_doubt_begin = Min::make(post_doubt_begin, max);
+      }
+      // [post_doubt_begin, max]
+      Stmt body = Substitute(op->body,
+        {{Var{op->loop_var}, op->loop_var + post_doubt_begin}});
+      post_stmt = For::make(op->loop_var, 0,
+        max - post_doubt_begin + 1, op->for_type, op->device_api, body);
+    }
+  } else {
+    post_doubt_begin = max + 1;
+  }
+
+  // [body_begin, post_doubt_begin)
+  Stmt simplified_body = PartitionReplacer(partitions).Mutate(op->body);
+  Stmt body = Substitute(simplified_body, {{Var{op->loop_var}, op->loop_var + body_begin}});
+  Stmt simplified_stmt = For::make(op->loop_var, 0,
+    post_doubt_begin - body_begin, op->for_type, op->device_api, body);
+  Stmt s = simplified_stmt;
+  if (pre_stmt.defined()) {
+    s = Block::make(pre_stmt, s);
+  }
+  if (post_stmt.defined()) {
+    s = Block::make(s, post_stmt);
+  }
+
+  return Simplify(ConvertSSA(s));
+}
+
+Stmt LoopPartition(Stmt stmt) {
+  stmt = LoopPartitioner().Mutate(stmt);
+  return stmt;
+}
+
+}  // namespace ir
+}  // namespace tvm

tests/python/unittest/test_arith_intset.py

@@ -16,20 +16,25 @@ def test_deduce():
     d_s = tvm.arith.intset_interval(-3, -1)
 
     e0 = (-b)*a+c-d
-    res0 = tvm.arith.DeduceBound(a, e0>=0, {b: b_s, c: c_s, d: d_s})
+    res0 = tvm.arith.DeduceBound(a, e0>=0, {b: b_s, c: c_s, d: d_s}, {})
     ans0 = (d-c)/(-b)+(-1)
     assert str(tvm.ir_pass.Simplify(res0.max())) == str(ans0)
 
     e1 = (a*4+b < c)
-    res1 = tvm.arith.DeduceBound(a, e1, {b: b_s, c: c_s, d: d_s})
+    res1 = tvm.arith.DeduceBound(a, e1, {b: b_s, c: c_s, d: d_s}, {})
     ans1 = (c-b)/4+(-2)
     assert str(tvm.ir_pass.Simplify(res1.max())) == str(ans1)
 
     e2 = (tvm.max(5, a * 4) < 0)
-    res2 = tvm.arith.DeduceBound(a, e2, {b: b_s, c: c_s, d: d_s})
+    res2 = tvm.arith.DeduceBound(a, e2, {b: b_s, c: c_s, d: d_s}, {})
     assert str(res2.max()) == "neg_inf"
     assert str(res2.min()) == "pos_inf"
 
+    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 = 2/c+1
+    assert str(tvm.ir_pass.Simplify(res3.min())) == str(ans3)
+
 def test_check():
     a = tvm.Var('a')
     b = tvm.Var('b')
@@ -41,15 +46,15 @@ def test_check():
     d_s = tvm.arith.intset_interval(-3, -1)
 
     # no compare operator
-    res1 = tvm.arith.DeduceBound(a, a+b, {b: b_s})
+    res1 = tvm.arith.DeduceBound(a, a+b, {b: b_s}, {})
     assert res1.is_nothing()
 
     # multiple compare operators
-    res2 = tvm.arith.DeduceBound(a, a+b>3>c , {b: b_s, c: c_s})
+    res2 = tvm.arith.DeduceBound(a, a+b>3>c , {b: b_s, c: c_s}, {})
     assert res1.is_nothing()
 
     # multiple target variable
-    res2 = tvm.arith.DeduceBound(a, a*2-a>b, {b: b_s})
+    res2 = tvm.arith.DeduceBound(a, a*2-a>b, {b: b_s}, {})
     assert res1.is_nothing()
 
 if __name__ == "__main__":

tests/python/unittest/test_pass_loop_partition.py

+import tvm
+
+def test_basic():
+    n = tvm.Var('n')
+    A = tvm.placeholder((n, ), name='A')
+    B = tvm.placeholder((n, ), name='B')
+
+    T = tvm.compute((n, ), lambda i: A[i]+B[i])
+    s = tvm.Schedule(T.op)
+    xo, xi = s[T].split(T.op.axis[0], factor=4)
+
+    bounds = tvm.schedule.InferBound(s)
+    stmt = tvm.schedule.ScheduleOps(s, bounds)
+    stmt = tvm.ir_pass.LoopPartition(stmt)
+    assert('if' not in str(stmt.body.body.body.first))
+    print(stmt)
+
+def test_multi_loop():
+    i = tvm.Var('i')
+    j = tvm.Var('j')
+    k = tvm.Var('k')
+    m = tvm.Var('m')
+    n = tvm.Var('n')
+    stmt = tvm.make.For(
+        i, 0, 4, 0, 0,
+        tvm.make.For(
+            j, 0, n, 0, 0,
+            tvm.make.For(
+                k, 0, m, 0, 0,
+                tvm.make.IfThenElse(
+                    (i*m+j+k < n), tvm.make.Evaluate(m), tvm.make.Evaluate(n)))))
+    stmt = tvm.ir_pass.LoopPartition(stmt)
+    assert('if' not in str(stmt.body.first))
+    print(stmt)
+
+def test_multi_if():
+    i = tvm.Var('i')
+    j = tvm.Var('j')
+    k = tvm.Var('k')
+    m = tvm.Var('m')
+    n = tvm.Var('n')
+    stmt = tvm.make.For(
+        i, 0, 4, 0, 0,
+        tvm.make.For(
+            j, 0, n, 0, 0,
+            tvm.make.For(
+                k, 0, m, 0, 0,
+                tvm.make.Block(
+                    tvm.make.IfThenElse((i*m+j+k < n), tvm.make.Evaluate(m), tvm.make.Evaluate(n)),
+                    tvm.make.IfThenElse((i*m+j-k < n), tvm.make.Evaluate(m), tvm.make.Evaluate(n))
+                    ))))
+    stmt = tvm.ir_pass.LoopPartition(stmt)
+    assert('if' not in str(stmt.body.first))
+    print(stmt)
+
+
+if __name__ == "__main__":
+    test_basic()
+    test_multi_loop()
+    test_multi_if()