diff --git a/examples/python/tensorflow/dot.cpp b/examples/python/tensorflow/dot.cpp
index 9b52020f6..0a8e1e948 100644
--- a/examples/python/tensorflow/dot.cpp
+++ b/examples/python/tensorflow/dot.cpp
@@ -30,7 +30,7 @@ void matmul(restrict read_only align(4) fp16 *A,
             restrict read_only align(4) fp16 *B,
             align(4) fp32 *C,
             int32 M, int32 N, int32 K,
-            int32 lda, int32 ldb, int32 ldc,
+            multiple_of(4) int32 lda, multiple_of(4) int32 ldb, multiple_of(4) int32 ldc,
             int32 *locks, int32 grid0, int32 grid1) {
   int32 rxa[TM] = get_global_range[TM](0);
   int32 ryb[TN] = get_global_range[TN](1);
diff --git a/include/triton/codegen/axis_info.h b/include/triton/codegen/axis_info.h
new file mode 100644
index 000000000..bfc4ef322
--- /dev/null
+++ b/include/triton/codegen/axis_info.h
@@ -0,0 +1,39 @@
+#ifndef TDL_INCLUDE_CODEGEN_AXIS_INFO_PASS_H
+#define TDL_INCLUDE_CODEGEN_AXIS_INFO_PASS_H
+
+#include <set>
+#include <map>
+
+namespace triton {
+
+namespace ir {
+  class value;
+  class module;
+}
+
+namespace codegen{
+
+class axis_info {
+private:
+  // helpers
+  bool is_first_axis_unit(ir::value *x);
+
+  // populate maps
+  bool populate_is_constant(ir::value *i);
+  unsigned populate_max_contiguous(ir::value *i);
+  unsigned populate_multiple_of(ir::value *i);
+
+public:
+  void run(ir::module &mod);
+
+private:
+  std::map<ir::value*, bool> is_constant_;
+  std::map<ir::value*, unsigned> max_contiguous_;
+  std::map<ir::value*, unsigned> multiple_of_;
+};
+
+
+}
+}
+
+#endif
diff --git a/include/triton/ir/function.h b/include/triton/ir/function.h
index cb1ab1f6d..c5f5f0605 100644
--- a/include/triton/ir/function.h
+++ b/include/triton/ir/function.h
@@ -5,6 +5,7 @@
 #include <map>
 #include "value.h"
 #include "constant.h"
+#include <iostream>
 
 namespace triton{
 namespace ir{
@@ -21,6 +22,8 @@ class argument: public value{
 public:
   static argument* create(type *ty, const std::string &name,
                           function *parent = nullptr, unsigned arg_no = 0);
+  function* get_parent() const;
+  unsigned get_arg_no() const;
 
 private:
   function *parent_;
@@ -53,6 +56,10 @@ public:
     return value_;
   }
 
+  bool is_llvm_attr() const {
+    return kind_ != multiple_of;
+  }
+
 private:
   attribute_kind_t kind_;
   unsigned value_;
@@ -89,6 +96,7 @@ public:
   // attributes
   void add_attr(unsigned arg_id, attribute attr) { attrs_[arg_id].insert(attr); }
   const attr_map_t &attrs() { return attrs_; }
+  std::set<attribute> get_attributes(argument* arg) { return attrs_[arg->get_arg_no() + 1]; }
 
 private:
   module *parent_;
diff --git a/include/triton/ir/instructions.h b/include/triton/ir/instructions.h
index 8e1da57ae..397be9d9d 100644
--- a/include/triton/ir/instructions.h
+++ b/include/triton/ir/instructions.h
@@ -122,6 +122,12 @@ public:
   bool is_int_div_rem() const;
   bool is_shift()       const;
   bool is_cast()        const;
+  bool is_int_mult()    const;
+  bool is_int_add_sub() const;
+  bool is_int_div()     const;
+  bool is_int_rem()     const;
+  bool is_shl()         const;
+  bool is_shr()         const;
 
   // Wraps
   void set_has_no_unsigned_wrap(bool b = true) { has_no_unsigned_wrap_ = b; }
diff --git a/include/triton/runtime/jit.h b/include/triton/runtime/jit.h
index a9bea664b..c12bb6b23 100644
--- a/include/triton/runtime/jit.h
+++ b/include/triton/runtime/jit.h
@@ -17,6 +17,7 @@
 #include "triton/codegen/shmem_liveness.h"
 #include "triton/codegen/shmem_info.h"
 #include "triton/codegen/shmem_barriers.h"
+#include "triton/codegen/axis_info.h"
 #include "triton/codegen/target.h"
 #include "triton/codegen/vectorize.h"
 #include <functional>
@@ -60,11 +61,13 @@ public:
                       optimize_dot(&tune),
                       optimize_cse(),
                       optimize_trans(),
+                      axis_info(),
                       target_(target) { }
 
     void target_independent(ir::module &module) {
         optimize_dot.run(module);
         optimize_trans.run(module);
+        axis_info.run(module);
 //        ir::print(module, std::cout);
     }
 
@@ -88,6 +91,7 @@ public:
     codegen::optimize_dot optimize_dot;
     codegen::optimize_cse optimize_cse;
     codegen::optimize_trans optimize_trans;
+    codegen::axis_info axis_info;
     codegen::target* target_;
   };
 
diff --git a/lib/codegen/axis_info.cpp b/lib/codegen/axis_info.cpp
new file mode 100644
index 000000000..38e2fcd9b
--- /dev/null
+++ b/lib/codegen/axis_info.cpp
@@ -0,0 +1,129 @@
+#include "triton/codegen/axis_info.h"
+#include "triton/ir/module.h"
+#include "triton/ir/function.h"
+#include "triton/ir/basic_block.h"
+#include "triton/ir/instructions.h"
+#include "triton/ir/type.h"
+
+namespace triton {
+namespace codegen{
+
+
+template<class T>
+inline T add_to_cache(ir::value *i, T value, std::map<ir::value*, T> &map) {
+  return map.insert(std::make_pair(i, value)).first->second;
+}
+
+
+bool axis_info::is_first_axis_unit(ir::value *x){
+  if(x->get_type()->is_tile_ty())
+    return x->get_type()->get_tile_shapes()[0]->get_value() == 1;
+  else
+    return true;
+}
+
+bool axis_info::populate_is_constant(ir::value *v) {
+  // helper for the cache
+  auto cache = [this,v](bool value){ return add_to_cache(v, value, is_constant_); };
+  // populate
+  if(v->get_type()->is_tile_ty()){
+    if(auto *x = dynamic_cast<ir::retile_inst*>(v)){
+      bool value = populate_is_constant(x->get_operand(0));
+      // check if broadcast (i.e., constant) along contiguous dimension
+      if(is_first_axis_unit(x->get_operand(0))
+         && !is_first_axis_unit(x))
+        return cache(value);
+    }
+    // otherwise the tile is not constant in the contiguous dimension
+    return cache(false);
+  }
+  // scalars are always constant in the contiguous dimension
+  return cache(true);
+}
+
+unsigned axis_info::populate_max_contiguous(ir::value *v){
+  // helper for the cache
+  auto cache = [this,v](unsigned value){ return add_to_cache(v, value, max_contiguous_); };
+  // populate
+  if(v->get_type()->is_tile_ty()){
+    auto shapes = v->get_type()->get_tile_shapes();
+    if(dynamic_cast<ir::get_global_range_inst*>(v))
+      return cache(shapes[0]->get_value());
+    if(auto *x = dynamic_cast<ir::binary_operator*>(v)){
+      ir::value* lhs = x->get_operand(0);
+      ir::value* rhs = x->get_operand(1);
+      unsigned lhs_max_contiguous = populate_max_contiguous(lhs);
+      bool lhs_has_cst = populate_is_constant(lhs);
+      unsigned rhs_max_contiguous = populate_max_contiguous(rhs);
+      bool rhs_has_cst = populate_is_constant(rhs);
+      if(x->is_int_add_sub()){
+        if(lhs_has_cst)
+          return cache(rhs_max_contiguous);
+        if(rhs_has_cst)
+          return cache(lhs_max_contiguous);
+      }
+    }
+  }
+  return cache(1);
+}
+
+unsigned axis_info::populate_multiple_of(ir::value *v){
+  auto cache = [this,v](unsigned value){ return add_to_cache(v, value, max_contiguous_); };
+
+  if(auto *x = dynamic_cast<ir::argument*>(v)){
+    std::set<ir::attribute> attributes = x->get_parent()->get_attributes(x);
+    for(auto attr: attributes){
+      if(attr.get_kind() == ir::multiple_of)
+        return cache(attr.get_value());
+    }
+  }
+  if(auto *x = dynamic_cast<ir::binary_operator*>(v)){
+    int lhs = populate_multiple_of(x->get_operand(0));
+    int rhs = populate_multiple_of(x->get_operand(1));
+    if(x->is_int_mult())
+      return cache(lhs * rhs);
+    if(x->is_int_add_sub())
+      return cache(std::min(lhs, rhs));
+    if(x->is_int_div())
+      return cache(std::max(lhs / rhs, 1));
+    if(x->is_int_rem())
+      return cache(std::max(lhs % rhs, 1));
+    if(x->is_shl())
+      return cache(lhs << rhs);
+    if(x->is_shr())
+      return cache(std::max(lhs >> rhs, 1));
+  }
+  if(auto *x = dynamic_cast<ir::retile_inst*>(v)){
+    return cache(populate_multiple_of(x->get_operand(0)));
+  }
+  return cache(1);
+}
+
+
+
+void axis_info::run(ir::module &mod) {
+  // populate constant
+  for(ir::function *fn: mod.get_function_list())
+  for(ir::basic_block *block: fn->blocks())
+  for(ir::instruction *i: block->get_inst_list()){
+    populate_is_constant(i);
+  }
+
+  // populate multiple_of
+  for(ir::function *fn: mod.get_function_list())
+  for(ir::basic_block *block: fn->blocks())
+  for(ir::instruction *i: block->get_inst_list()){
+    populate_multiple_of(i);
+  }
+
+  // populate maximum contiguous
+  for(ir::function *fn: mod.get_function_list())
+  for(ir::basic_block *block: fn->blocks())
+  for(ir::instruction *i: block->get_inst_list()){
+    populate_max_contiguous(i);
+  }
+}
+
+
+}
+}
diff --git a/lib/codegen/selection.cpp b/lib/codegen/selection.cpp
index fed49407f..ae2a3f1c1 100644
--- a/lib/codegen/selection.cpp
+++ b/lib/codegen/selection.cpp
@@ -1125,6 +1125,7 @@ void selection::run(ir::module &src, Module &dst) {
     for(auto attr_pair: fn->attrs()){
       unsigned id = attr_pair.first;
       for(ir::attribute attr: attr_pair.second)
+      if(attr.is_llvm_attr())
         dst_fn->addAttribute(id, llvm_attr(dst_ctx, attr));
     }
     tgt_->set_kernel(dst_builder, dst_ctx, &dst, dst_fn);
diff --git a/lib/ir/function.cpp b/lib/ir/function.cpp
index 758fd8bc3..5c7ca1e2a 100644
--- a/lib/ir/function.cpp
+++ b/lib/ir/function.cpp
@@ -16,6 +16,15 @@ argument *argument::create(type *ty, const std::string &name,
   return new argument(ty, name, parent, arg_no);
 }
 
+function* argument::get_parent() const {
+  return parent_;
+}
+
+unsigned argument::get_arg_no() const {
+  return arg_no_;
+}
+
+
 /* function */
 function::function(function_type *ty, linkage_types_t linkage,
                    const std::string &name, module *parent)
diff --git a/lib/ir/instructions.cpp b/lib/ir/instructions.cpp
index 79c951f6d..9b5d37094 100644
--- a/lib/ir/instructions.cpp
+++ b/lib/ir/instructions.cpp
@@ -109,6 +109,31 @@ std::string binary_operator::repr_impl() const {
   }
 }
 
+bool binary_operator::is_int_div() const {
+  return op_ == llop::UDiv || op_ == llop::SDiv;
+}
+
+bool binary_operator::is_int_rem() const {
+  return op_ == llop::URem || op_ == llop::SRem;
+}
+
+bool binary_operator::is_shl() const {
+  return op_ == llop::Shl;
+}
+
+bool binary_operator::is_shr() const {
+  return op_ == llop::LShr || op_ == llop::AShr;
+}
+
+bool binary_operator::is_int_mult()    const {
+  return op_ == llop::Mul;
+}
+
+bool binary_operator::is_int_add_sub() const {
+  return op_ == llop::Add || llop::Sub;
+}
+
+
 binary_operator::binary_operator(op_t op, value *lhs, value *rhs, type *ty, const std::string &name, instruction *next)
     : instruction(ty, 2, 1, name, next), op_(op){
   set_operand(0, lhs);