diff --git a/python/taichi/lang/matrix.py b/python/taichi/lang/matrix.py
index 1c7add5cd19c3..103246daeb381 100644
--- a/python/taichi/lang/matrix.py
+++ b/python/taichi/lang/matrix.py
@@ -1457,8 +1457,8 @@ def _calc_dynamic_index_stride(self):
             return
         length = len(paths[0])
         if any(
-                len(path) != length or ti_core.is_custom_type(path[length -
-                                                                   1]._dtype)
+                len(path) != length or ti_core.is_quant(path[length -
+                                                             1]._dtype)
                 for path in paths):
             return
         for i in range(length):
diff --git a/taichi/backends/metal/codegen_metal.cpp b/taichi/backends/metal/codegen_metal.cpp
index a020c4635d26a..e3c9aa95f282d 100644
--- a/taichi/backends/metal/codegen_metal.cpp
+++ b/taichi/backends/metal/codegen_metal.cpp
@@ -981,7 +981,7 @@ class KernelCodegenImpl : public IRVisitor {
       validate_cft_for_metal(cft);
       auto *digits_cit = cft->get_digits_type()->as<CustomIntType>();
       cit = digits_cit;
-      store_value_expr = construct_float_to_custom_int_expr(
+      store_value_expr = construct_quant_fixed_to_quant_int_expr(
           stmt->val, cft->get_scale(), digits_cit);
     } else {
       TI_NOT_IMPLEMENTED;
@@ -1004,10 +1004,10 @@ class KernelCodegenImpl : public IRVisitor {
     TI_ASSERT(ptr_type->is_bit_pointer());
     auto *pointee_type = ptr_type->get_pointee_type();
     if (auto *cit = pointee_type->cast<CustomIntType>()) {
-      return construct_load_as_custom_int(stmt->src, cit);
+      return construct_load_quant_int(stmt->src, cit);
     } else if (auto *cft = pointee_type->cast<CustomFloatType>()) {
       validate_cft_for_metal(cft);
-      const auto loaded = construct_load_as_custom_int(
+      const auto loaded = construct_load_quant_int(
           stmt->src, cft->get_digits_type()->as<CustomIntType>());
       // Computes `float(digits_expr) * scale`
       // See LLVM backend's reconstruct_quant_fixed()
@@ -1033,8 +1033,8 @@ class KernelCodegenImpl : public IRVisitor {
       val_expr = stmt->val->raw_name();
     } else if (auto *cft = pointee_type->cast<CustomFloatType>()) {
       cit = cft->get_digits_type()->as<CustomIntType>();
-      val_expr =
-          construct_float_to_custom_int_expr(stmt->val, cft->get_scale(), cit);
+      val_expr = construct_quant_fixed_to_quant_int_expr(stmt->val,
+                                                         cft->get_scale(), cit);
     } else {
       TI_NOT_IMPLEMENTED;
     }
@@ -1051,7 +1051,7 @@ class KernelCodegenImpl : public IRVisitor {
   }
 
   // Returns the expression of `int(val_stmt * (1.0f / scale) + 0.5f)`
-  std::string construct_float_to_custom_int_expr(
+  std::string construct_quant_fixed_to_quant_int_expr(
       const Stmt *val_stmt,
       float64 scale,
       CustomIntType *digits_cit) const {
@@ -1062,14 +1062,14 @@ class KernelCodegenImpl : public IRVisitor {
     // variables) because |val_stmt| could be used multiple times. If the
     // intermediate variables are named based on |val_stmt|, it would result in
     // symbol redefinitions.
-    return fmt::format("mtl_float_to_custom_int<{}>(/*inv_scale=*/{} * {})",
-                       metal_data_type_name(compute_dt), inv_scale,
-                       val_stmt->raw_name());
+    return fmt::format(
+        "mtl_quant_fixed_to_quant_int<{}>(/*inv_scale=*/{} * {})",
+        metal_data_type_name(compute_dt), inv_scale, val_stmt->raw_name());
   }
 
   // Returns expression of the loaded integer.
-  std::string construct_load_as_custom_int(const Stmt *bit_ptr_stmt,
-                                           CustomIntType *cit) const {
+  std::string construct_load_quant_int(const Stmt *bit_ptr_stmt,
+                                       CustomIntType *cit) const {
     DataType compute_dt(cit->get_compute_type()->as<PrimitiveType>());
     const auto num_bits = cit->get_num_bits();
     if (is_full_bits(num_bits)) {
diff --git a/taichi/backends/metal/shaders/snode_bit_pointer.metal.h b/taichi/backends/metal/shaders/snode_bit_pointer.metal.h
index 63310fe1ff39f..4b390e5ceac42 100644
--- a/taichi/backends/metal/shaders/snode_bit_pointer.metal.h
+++ b/taichi/backends/metal/shaders/snode_bit_pointer.metal.h
@@ -38,7 +38,7 @@ STR(
 
     // |f| should already be scaled. |C| is the compute type.
     template <typename C>
-    C mtl_float_to_custom_int(float f) {
+    C mtl_quant_fixed_to_quant_int(float f) {
       // Branch free implementation of `f + sign(f) * 0.5`.
       // See rounding_prepare_f* in taichi/runtime/llvm/runtime.cpp
       const int32_t delta_bits =
diff --git a/taichi/codegen/codegen_llvm.h b/taichi/codegen/codegen_llvm.h
index af7a0bf091740..662ef2d9d7199 100644
--- a/taichi/codegen/codegen_llvm.h
+++ b/taichi/codegen/codegen_llvm.h
@@ -265,9 +265,9 @@ class CodeGenLLVM : public IRVisitor, public LLVMModuleBuilder {
 
   void visit(GlobalStoreStmt *stmt) override;
 
-  llvm::Value *custom_type_to_bits(llvm::Value *val,
-                                   Type *input_type,
-                                   Type *output_type);
+  llvm::Value *quant_int_or_quant_fixed_to_bits(llvm::Value *val,
+                                                Type *input_type,
+                                                Type *output_type);
 
   void visit(BitStructStoreStmt *stmt) override;
 
@@ -399,7 +399,7 @@ class CodeGenLLVM : public IRVisitor, public LLVMModuleBuilder {
 
   llvm::Value *extract_digits_from_f32(llvm::Value *f, bool full);
 
-  llvm::Value *extract_digits_from_quant_float_with_shared_exponent(
+  llvm::Value *extract_digits_from_f32_with_shared_exponent(
       llvm::Value *f,
       llvm::Value *shared_exp);
 
diff --git a/taichi/codegen/codegen_llvm_quant.cpp b/taichi/codegen/codegen_llvm_quant.cpp
index ec3c764bfd78d..6e1aaa175ebde 100644
--- a/taichi/codegen/codegen_llvm_quant.cpp
+++ b/taichi/codegen/codegen_llvm_quant.cpp
@@ -51,9 +51,8 @@ llvm::Value *CodeGenLLVM::quant_fixed_to_quant_int(CustomFloatType *cft,
   // Compute int(real * (1.0 / scale) + 0.5)
   auto s_numeric = 1.0 / cft->get_scale();
   auto compute_type = cft->get_compute_type();
-  s = builder->CreateFPCast(
-      llvm::ConstantFP::get(*llvm_context, llvm::APFloat(s_numeric)),
-      llvm_type(compute_type));
+  s = builder->CreateFPCast(tlctx->get_constant(s_numeric),
+                            llvm_type(compute_type));
   auto input_real = builder->CreateFPCast(real, llvm_type(compute_type));
   auto scaled = builder->CreateFMul(input_real, s);
 
@@ -128,9 +127,9 @@ llvm::Value *CodeGenLLVM::get_exponent_offset(llvm::Value *exponent,
       tlctx->get_constant(0));
 }
 
-llvm::Value *CodeGenLLVM::custom_type_to_bits(llvm::Value *val,
-                                              Type *input_type,
-                                              Type *output_type) {
+llvm::Value *CodeGenLLVM::quant_int_or_quant_fixed_to_bits(llvm::Value *val,
+                                                           Type *input_type,
+                                                           Type *output_type) {
   CustomIntType *cit = nullptr;
   if (auto cft = input_type->cast<CustomFloatType>()) {
     TI_ASSERT(cft->get_exponent_type() == nullptr);
@@ -262,7 +261,8 @@ void CodeGenLLVM::visit(BitStructStoreStmt *stmt) {
       val = builder->CreateBitCast(val, llvm_type(bit_struct_physical_type));
       val = builder->CreateShl(val, digits_snode->bit_offset);
     } else {
-      val = custom_type_to_bits(val, dtype, bit_struct_physical_type);
+      val = quant_int_or_quant_fixed_to_bits(val, dtype,
+                                             bit_struct_physical_type);
       val = builder->CreateShl(val, bit_struct_snode->ch[ch_id]->bit_offset);
     }
 
@@ -374,8 +374,8 @@ void CodeGenLLVM::store_quant_floats_with_shared_exponents(
     for (int c = 0; c < (int)exp->exponent_users.size(); c++) {
       auto user = exp->exponent_users[c];
       auto ch_id = snode->child_id(user);
-      auto digits = extract_digits_from_quant_float_with_shared_exponent(
-          floats[c], max_exp_bits);
+      auto digits =
+          extract_digits_from_f32_with_shared_exponent(floats[c], max_exp_bits);
       auto digits_snode = snode->ch[ch_id].get();
       auto cft = digits_snode->dt->as<CustomFloatType>();
       auto digits_bit_offset = digits_snode->bit_offset;
@@ -435,7 +435,7 @@ llvm::Value *CodeGenLLVM::extract_digits_from_f32(llvm::Value *f, bool full) {
   return digits;
 }
 
-llvm::Value *CodeGenLLVM::extract_digits_from_quant_float_with_shared_exponent(
+llvm::Value *CodeGenLLVM::extract_digits_from_f32_with_shared_exponent(
     llvm::Value *f,
     llvm::Value *shared_exp) {
   auto exp = extract_exponent_from_f32(f);
@@ -518,13 +518,12 @@ llvm::Value *CodeGenLLVM::reconstruct_quant_fixed(llvm::Value *digits,
   // Compute float(digits) * scale
   llvm::Value *cast = nullptr;
   auto compute_type = cft->get_compute_type()->as<PrimitiveType>();
-  if (cft->get_digits_type()->cast<CustomIntType>()->get_is_signed()) {
+  if (cft->get_is_signed()) {
     cast = builder->CreateSIToFP(digits, llvm_type(compute_type));
   } else {
     cast = builder->CreateUIToFP(digits, llvm_type(compute_type));
   }
-  llvm::Value *s =
-      llvm::ConstantFP::get(*llvm_context, llvm::APFloat(cft->get_scale()));
+  llvm::Value *s = tlctx->get_constant(cft->get_scale());
   s = builder->CreateFPCast(s, llvm_type(compute_type));
   return builder->CreateFMul(cast, s);
 }
diff --git a/taichi/ir/frontend_ir.cpp b/taichi/ir/frontend_ir.cpp
index 9ded4ffae1146..6e2deabb2b734 100644
--- a/taichi/ir/frontend_ir.cpp
+++ b/taichi/ir/frontend_ir.cpp
@@ -510,10 +510,8 @@ void AtomicOpExpression::type_check(CompileConfig *) {
   };
   if (!val->ret_type->is<PrimitiveType>())
     error();
-  if (auto cit = dest->ret_type->cast<CustomIntType>()) {
-    ret_type = cit->get_compute_type();
-  } else if (auto cft = dest->ret_type->cast<CustomFloatType>()) {
-    ret_type = cft->get_compute_type();
+  if (is_quant(dest->ret_type)) {
+    ret_type = dest->ret_type->get_compute_type();
   } else if (dest->ret_type->is<PrimitiveType>()) {
     ret_type = dest->ret_type;
   } else {
diff --git a/taichi/ir/type_utils.h b/taichi/ir/type_utils.h
index b5e10ed0f29c5..da1087bc9d7e5 100644
--- a/taichi/ir/type_utils.h
+++ b/taichi/ir/type_utils.h
@@ -73,7 +73,7 @@ inline PrimitiveTypeID get_primitive_data_type() {
   }
 }
 
-inline bool is_custom_type(DataType dt) {
+inline bool is_quant(DataType dt) {
   return dt->is<CustomIntType>() || dt->is<CustomFloatType>();
 }
 
diff --git a/taichi/python/export_lang.cpp b/taichi/python/export_lang.cpp
index 228e57b67e4bc..a6a303d0f1e2b 100644
--- a/taichi/python/export_lang.cpp
+++ b/taichi/python/export_lang.cpp
@@ -859,7 +859,7 @@ void export_lang(py::module &m) {
 #undef PER_TYPE
 
   m.def("data_type_size", data_type_size);
-  m.def("is_custom_type", is_custom_type);
+  m.def("is_quant", is_quant);
   m.def("is_integral", is_integral);
   m.def("is_signed", is_signed);
   m.def("is_real", is_real);
diff --git a/taichi/transforms/type_check.cpp b/taichi/transforms/type_check.cpp
index a7cc5b60ecfb8..10132bafd3d40 100644
--- a/taichi/transforms/type_check.cpp
+++ b/taichi/transforms/type_check.cpp
@@ -23,7 +23,7 @@ class TypeCheck : public IRVisitor {
                          Stmt *&val,
                          const std::string &stmt_name) {
     auto dst_type = dst->ret_type.ptr_removed();
-    if (dst_type->is<CustomIntType>() || dst_type->is<CustomFloatType>()) {
+    if (is_quant(dst_type)) {
       // We force the value type to be the compute_type of the bit pointer.
       // Casting from compute_type to physical_type is handled in codegen.
       dst_type = dst_type->get_compute_type();