diff --git a/slither/core/declarations/__init__.py b/slither/core/declarations/__init__.py
index d3fe3dd22..3b619c1d1 100644
--- a/slither/core/declarations/__init__.py
+++ b/slither/core/declarations/__init__.py
@@ -13,3 +13,4 @@ from .solidity_variables import (
 from .structure import Structure
 from .enum_contract import EnumContract
 from .structure_contract import StructureContract
+from .function_contract import FunctionContract
diff --git a/slither/core/declarations/contract.py b/slither/core/declarations/contract.py
index f16b0e70c..8c91fde28 100644
--- a/slither/core/declarations/contract.py
+++ b/slither/core/declarations/contract.py
@@ -25,7 +25,14 @@ from slither.utils.tests_pattern import is_test_contract
 # pylint: disable=too-many-lines,too-many-instance-attributes,import-outside-toplevel,too-many-nested-blocks
 if TYPE_CHECKING:
     from slither.utils.type_helpers import LibraryCallType, HighLevelCallType, InternalCallType
-    from slither.core.declarations import Enum, Event, Modifier, EnumContract, StructureContract
+    from slither.core.declarations import (
+        Enum,
+        Event,
+        Modifier,
+        EnumContract,
+        StructureContract,
+        FunctionContract,
+    )
     from slither.slithir.variables.variable import SlithIRVariable
     from slither.core.variables.variable import Variable
     from slither.core.variables.state_variable import StateVariable
@@ -56,7 +63,7 @@ class Contract(ChildSlither, SourceMapping):  # pylint: disable=too-many-public-
         self._variables: Dict[str, "StateVariable"] = {}
         self._variables_ordered: List["StateVariable"] = []
         self._modifiers: Dict[str, "Modifier"] = {}
-        self._functions: Dict[str, "Function"] = {}
+        self._functions: Dict[str, "FunctionContract"] = {}
         self._linearizedBaseContracts = List[int]
 
         # The only str is "*"
@@ -387,23 +394,23 @@ class Contract(ChildSlither, SourceMapping):  # pylint: disable=too-many-public-
         return self._signatures_declared
 
     @property
-    def functions(self) -> List["Function"]:
+    def functions(self) -> List["FunctionContract"]:
         """
         list(Function): List of the functions
         """
         return list(self._functions.values())
 
-    def available_functions_as_dict(self) -> Dict[str, "Function"]:
+    def available_functions_as_dict(self) -> Dict[str, "FunctionContract"]:
         if self._available_functions_as_dict is None:
             self._available_functions_as_dict = {
                 f.full_name: f for f in self._functions.values() if not f.is_shadowed
             }
         return self._available_functions_as_dict
 
-    def add_function(self, func: "Function"):
+    def add_function(self, func: "FunctionContract"):
         self._functions[func.canonical_name] = func
 
-    def set_functions(self, functions: Dict[str, "Function"]):
+    def set_functions(self, functions: Dict[str, "FunctionContract"]):
         """
         Set the functions
 
@@ -413,21 +420,21 @@ class Contract(ChildSlither, SourceMapping):  # pylint: disable=too-many-public-
         self._functions = functions
 
     @property
-    def functions_inherited(self) -> List["Function"]:
+    def functions_inherited(self) -> List["FunctionContract"]:
         """
         list(Function): List of the inherited functions
         """
         return [f for f in self.functions if f.contract_declarer != self]
 
     @property
-    def functions_declared(self) -> List["Function"]:
+    def functions_declared(self) -> List["FunctionContract"]:
         """
         list(Function): List of the functions defined within the contract (not inherited)
         """
         return [f for f in self.functions if f.contract_declarer == self]
 
     @property
-    def functions_entry_points(self) -> List["Function"]:
+    def functions_entry_points(self) -> List["FunctionContract"]:
         """
         list(Functions): List of public and external functions
         """
diff --git a/slither/core/solidity_types/elementary_type.py b/slither/core/solidity_types/elementary_type.py
index abb7852d9..dd4d3db75 100644
--- a/slither/core/solidity_types/elementary_type.py
+++ b/slither/core/solidity_types/elementary_type.py
@@ -85,8 +85,6 @@ Uint = [
 Max_Uint = {k: 2 ** (8 * i) - 1 if i > 0 else 2 ** 256 - 1 for i, k in enumerate(Uint)}
 Min_Uint = {k: 0 for k in Uint}
 
-MaxValues = dict(Max_Int, **Max_Uint)
-MinValues = dict(Min_Int, **Min_Uint)
 
 Byte = [
     "byte",
@@ -125,6 +123,16 @@ Byte = [
     "bytes32",
 ]
 
+Max_Byte = {k: 2 ** (8 * (i + 1)) - 1 for i, k in enumerate(Byte[2:])}
+Max_Byte["bytes"] = None
+Max_Byte["byte"] = 255
+Min_Byte = {k: 1 << (4 + 8 * i) for i, k in enumerate(Byte[2:])}
+Min_Byte["bytes"] = 0x0
+Min_Byte["byte"] = 0x10
+
+MaxValues = dict(dict(Max_Int, **Max_Uint), **Max_Byte)
+MinValues = dict(dict(Min_Int, **Min_Uint), **Min_Byte)
+
 # https://solidity.readthedocs.io/en/v0.4.24/types.html#fixed-point-numbers
 M = list(range(8, 257, 8))
 N = list(range(0, 81))
diff --git a/slither/slithir/convert.py b/slither/slithir/convert.py
index f9fdc79cf..97c6134e6 100644
--- a/slither/slithir/convert.py
+++ b/slither/slithir/convert.py
@@ -1,5 +1,5 @@
 import logging
-from typing import List, TYPE_CHECKING
+from typing import List, TYPE_CHECKING, Union, Optional
 
 # pylint: disable= too-many-lines,import-outside-toplevel,too-many-branches,too-many-statements,too-many-nested-blocks
 from slither.core.declarations import (
@@ -22,7 +22,12 @@ from slither.core.solidity_types import (
     UserDefinedType,
     TypeInformation,
 )
-from slither.core.solidity_types.elementary_type import Int as ElementaryTypeInt
+from slither.core.solidity_types.elementary_type import (
+    Int as ElementaryTypeInt,
+    Uint,
+    Byte,
+    MaxValues,
+)
 from slither.core.solidity_types.type import Type
 from slither.core.variables.function_type_variable import FunctionTypeVariable
 from slither.core.variables.state_variable import StateVariable
@@ -60,6 +65,7 @@ from slither.slithir.operations import (
     Unary,
     Unpack,
     Nop,
+    Operation,
 )
 from slither.slithir.operations.codesize import CodeSize
 from slither.slithir.tmp_operations.argument import Argument, ArgumentType
@@ -148,64 +154,111 @@ def is_gas(ins):
     return False
 
 
-def get_sig(ir, name):
-    """
-        Return a list of potential signature
-        It is a list, as Constant variables can be converted to int256
-    Args:
-        ir (slithIR.operation)
-    Returns:
-        list(str)
+def _fits_under_integer(val: int, can_be_int: bool, can_be_uint) -> List[str]:
     """
-    sig = "{}({})"
+    Return the list of uint/int that can contain val
 
-    # list of list of arguments
-    argss = convert_arguments(ir.arguments)
-    return [sig.format(name, ",".join(args)) for args in argss]
+    :param val:
+    :return:
+    """
+    ret: List[str] = []
+    n = 8
+    assert can_be_int | can_be_uint
+    while n <= 256:
+        if can_be_uint:
+            if val <= 2 ** n - 1:
+                ret.append(f"uint{n}")
+        if can_be_int:
+            if val <= (2 ** n) / 2 - 1:
+                ret.append(f"int{n}")
+        n = n + 8
+    return ret
 
 
-def get_canonical_names(ir, function_name, contract_name):
+def _fits_under_byte(val: Union[int, str]) -> List[str]:
     """
-        Return a list of potential signature
-        It is a list, as Constant variables can be converted to int256
-    Args:
-        ir (slithIR.operation)
-    Returns:
-        list(str)
+    Return the list of byte that can contain val
+
+    :param val:
+    :return:
     """
-    sig = "{}({})"
 
-    # list of list of arguments
-    argss = convert_arguments(ir.arguments)
-    return [sig.format(f"{contract_name}.{function_name}", ",".join(args)) for args in argss]
+    # If the value is written as an int, it can only be saved in one byte size
+    # If its a string, it can be fitted under multiple values
+
+    if isinstance(val, int):
+        hex_val = hex(val)[2:]
+        size = len(hex_val) // 2
+        return [f"byte{size}"]
+    # val is a str
+    length = len(val.encode("utf-8"))
+    return [f"byte{f}" for f in range(length, 32)]
+
 
+def _find_function_from_parameter(ir: Call, candidates: List[Function]) -> Optional[Function]:
+    """
+    Look for a function in candidates that can be the target of the ir's call
+
+    Try the implicit type conversion for uint/int/bytes. Constant values can be both uint/int
+    While variables stick to their base type, but can changed the size
 
-def convert_arguments(arguments):
-    argss = [[]]
-    for arg in arguments:
+    :param ir:
+    :param candidates:
+    :return:
+    """
+    arguments = ir.arguments
+    type_args: List[str]
+    for idx, arg in enumerate(arguments):
         if isinstance(arg, (list,)):
-            type_arg = "{}[{}]".format(get_type(arg[0].type), len(arg))
+            type_args = ["{}[{}]".format(get_type(arg[0].type), len(arg))]
         elif isinstance(arg, Function):
-            type_arg = arg.signature_str
-        else:
-            type_arg = get_type(arg.type)
-        if isinstance(arg, Constant) and arg.type == ElementaryType("uint256"):
-            # If it is a constant
-            # We dupplicate the existing list
-            # And we add uint256 and int256 cases
-            # There is no potential collision, as the compiler
-            # Prevent it with a
-            # "not unique after argument-dependent loopkup" issue
-            argss_new = [list(args) for args in argss]
-            for args in argss:
-                args.append(str(ElementaryType("uint256")))
-            for args in argss_new:
-                args.append(str(ElementaryType("int256")))
-            argss = argss + argss_new
+            type_args = [arg.signature_str]
         else:
-            for args in argss:
-                args.append(type_arg)
-    return argss
+            type_args = [get_type(arg.type)]
+
+        if (
+            isinstance(arg.type, ElementaryType)
+            and arg.type.type in ElementaryTypeInt + Uint + Byte
+        ):
+            if isinstance(arg, Constant):
+                value = arg.value
+                can_be_uint = True
+                can_be_int = True
+            else:
+                value = MaxValues[arg.type.type]
+                can_be_uint = False
+                can_be_int = False
+                if arg.type.type in ElementaryTypeInt:
+                    can_be_int = True
+                elif arg.type.type in Uint:
+                    can_be_uint = True
+
+            if arg.type.type in ElementaryTypeInt + Uint:
+                type_args = _fits_under_integer(value, can_be_int, can_be_uint)
+            else:
+                print(value)
+                type_args = _fits_under_byte(value)
+
+        not_found = True
+        candidates_kept = []
+        for type_arg in type_args:
+            if not not_found:
+                break
+            candidates_kept = []
+            for candidate in candidates:
+                param = str(candidate.parameters[idx].type)
+
+                if param == type_arg:
+                    not_found = False
+                    candidates_kept.append(candidate)
+
+            if len(candidates_kept) == 1:
+                return candidates_kept[0]
+        candidates = candidates_kept
+
+    if len(candidates) == 1:
+        return candidates[0]
+    return None
 
 
 def is_temporary(ins):
@@ -1205,17 +1258,34 @@ def get_type(t):
     return str(t)
 
 
-def convert_type_library_call(ir, lib_contract):
-    sigs = get_sig(ir, ir.function_name)
+def _can_be_implicitly_converted(source: str, target: str) -> bool:
+    if source in ElementaryTypeInt and target in ElementaryTypeInt:
+        return int(source[3:]) <= int(target[3:])
+    if source in Uint and target in Uint:
+        return int(source[4:]) <= int(target[4:])
+    return source == target
+
+
+def convert_type_library_call(ir: HighLevelCall, lib_contract: Contract):
     func = None
-    for sig in sigs:
-        func = lib_contract.get_function_from_signature(sig)
-        if not func:
-            func = lib_contract.get_state_variable_from_name(ir.function_name)
-        if func:
-            # stop to explore if func is found (prevent dupplicate issue)
-            break
+    candidates = [
+        f
+        for f in lib_contract.functions
+        if f.name == ir.function_name
+        and not f.is_shadowed
+        and len(f.parameters) == len(ir.arguments)
+    ]
+
+    if len(candidates) == 1:
+        func = candidates[0]
+    if func is None:
+        # TODO: handle collision with multiple state variables/functions
+        func = lib_contract.get_state_variable_from_name(ir.function_name)
+    if func is None and candidates:
+        func = _find_function_from_parameter(ir, candidates)
+
     # In case of multiple binding to the same type
+    # TODO: this part might not be needed with _find_function_from_parameter
     if not func:
         # specific lookup when the compiler does implicit conversion
         # for example
@@ -1282,36 +1352,39 @@ def _convert_to_structure_to_list(return_type: Type) -> List[Type]:
     return [return_type.type]
 
 
-def convert_type_of_high_and_internal_level_call(ir, contract):
+def convert_type_of_high_and_internal_level_call(ir: Operation, contract: Contract):
     func = None
     if isinstance(ir, InternalCall):
-        sigs = get_canonical_names(ir, ir.function_name, ir.contract_name)
-        for sig in sigs:
-            func = contract.get_function_from_canonical_name(sig)
-            if func:
-                # stop to explore if func is found (prevent dupplicate issue)
-                break
+        candidates = [
+            f
+            for f in contract.functions
+            if f.name == ir.function_name
+            and f.contract_declarer.name == ir.contract_name
+            and len(f.parameters) == len(ir.arguments)
+        ]
+        func = _find_function_from_parameter(ir, candidates)
+
         if not func:
             func = contract.get_state_variable_from_name(ir.function_name)
     else:
         assert isinstance(ir, HighLevelCall)
-        sigs = get_sig(ir, ir.function_name)
-        for sig in sigs:
-            func = contract.get_function_from_signature(sig)
-            if func:
-                # stop to explore if func is found (prevent dupplicate issue)
-                break
-        if not func:
+
+        candidates = [
+            f
+            for f in contract.functions
+            if f.name == ir.function_name
+            and not f.is_shadowed
+            and len(f.parameters) == len(ir.arguments)
+        ]
+
+        if len(candidates) == 1:
+            func = candidates[0]
+        if func is None:
+            # TODO: handle collision with multiple state variables/functions
             func = contract.get_state_variable_from_name(ir.function_name)
-    if not func:
-        # specific lookup when the compiler does implicit conversion
-        # for example
-        # myFunc(uint)
-        # can be called with an uint8
-        for function in contract.functions:
-            if function.name == ir.function_name and len(function.parameters) == len(ir.arguments):
-                func = function
-                break
+        if func is None and candidates:
+            func = _find_function_from_parameter(ir, candidates)
+
     # lowlelvel lookup needs to be done at last step
     if not func:
         if can_be_low_level(ir):
@@ -1319,7 +1392,7 @@ def convert_type_of_high_and_internal_level_call(ir, contract):
         if can_be_solidity_func(ir):
             return convert_to_solidity_func(ir)
     if not func:
-        to_log = "Function not found {}".format(sig)
+        to_log = "Function not found {}".format(ir.function_name)
         logger.error(to_log)
     ir.function = func
     if isinstance(func, Function):
diff --git a/slither/slithir/operations/library_call.py b/slither/slithir/operations/library_call.py
index d7c89a4de..45187b290 100644
--- a/slither/slithir/operations/library_call.py
+++ b/slither/slithir/operations/library_call.py
@@ -1,3 +1,4 @@
+from slither.core.declarations import Function
 from slither.slithir.operations.high_level_call import HighLevelCall
 from slither.core.declarations.contract import Contract
 
@@ -37,10 +38,15 @@ class LibraryCall(HighLevelCall):
         else:
             lvalue = "{}({}) = ".format(self.lvalue, self.lvalue.type)
         txt = "{}LIBRARY_CALL, dest:{}, function:{}, arguments:{} {}"
+
+        function_name = self.function_name
+        if self.function:
+            if isinstance(self.function, Function):
+                function_name = self.function.canonical_name
         return txt.format(
             lvalue,
             self.destination,
-            self.function_name,
+            function_name,
             [str(x) for x in arguments],
             gas,
         )
diff --git a/tests/ast-parsing/library_implicit_conversion-0.4.0.sol b/tests/ast-parsing/library_implicit_conversion-0.4.0.sol
new file mode 100644
index 000000000..97764c2c8
--- /dev/null
+++ b/tests/ast-parsing/library_implicit_conversion-0.4.0.sol
@@ -0,0 +1,4 @@
+// test only above 0.5
+contract C{
+
+}
diff --git a/tests/ast-parsing/library_implicit_conversion-0.5.0.sol b/tests/ast-parsing/library_implicit_conversion-0.5.0.sol
new file mode 100644
index 000000000..462615e19
--- /dev/null
+++ b/tests/ast-parsing/library_implicit_conversion-0.5.0.sol
@@ -0,0 +1,57 @@
+library LibByte{
+    function t(uint, bytes1) internal returns(uint){
+        return 0x1;
+    }
+    function t(uint, bytes32) internal returns(uint){
+        return 0x32;
+    }
+
+}
+
+
+contract TestByte{
+    using LibByte for uint;
+    function test() public returns(uint){
+        uint a;
+        return a.t(0x10); // for byte, this will match only bytes1
+    }
+}
+
+library LibUint{
+    function t(uint, uint8) internal returns(uint){
+        return 0x1;
+    }
+    function t(uint, uint256) internal returns(uint){
+        return 0x32;
+    }
+
+}
+
+contract TestUint{
+
+    using LibUint for uint;
+    function test() public returns(uint){
+        uint a;
+        return a.t(2**8); // above uint8
+    }
+}
+
+library LibInt{
+    function t(uint, int8) internal returns(uint){
+        return 0x1;
+    }
+    function t(uint, int256) internal returns(uint){
+        return 0x32;
+    }
+
+}
+
+contract TestUintWithVariableiAndConversion{
+
+    using LibInt for uint;
+    function test() public returns(uint){
+        uint a;
+        int16 v;
+        return a.t(v); // above uint8
+    }
+}