diff --git a/lib/mathlib.cpp b/lib/mathlib.cpp
index 44f1de849..3992345b6 100644
--- a/lib/mathlib.cpp
+++ b/lib/mathlib.cpp
@@ -38,7 +38,6 @@
 #define ISNAN(x)      (std::isnan(x))
 #endif
 
-
 MathLib::value::value(const std::string &s) :
     intValue(0), doubleValue(0), isUnsigned(false)
 {
@@ -263,6 +262,24 @@ MathLib::value MathLib::value::add(int v) const
     return temp;
 }
 
+MathLib::value MathLib::value::shiftLeft(const MathLib::value &v) const
+{
+    if (!isInt() || !v.isInt())
+        throw InternalError(0, "Shift operand is not integer");
+    MathLib::value ret(*this);
+    ret.intValue <<= v.intValue;
+    return ret;
+}
+
+MathLib::value MathLib::value::shiftRight(const MathLib::value &v) const
+{
+    if (!isInt() || !v.isInt())
+        throw InternalError(0, "Shift operand is not integer");
+    MathLib::value ret(*this);
+    ret.intValue >>= v.intValue;
+    return ret;
+}
+
 
 MathLib::biguint MathLib::toULongNumber(const std::string & str)
 {
@@ -1250,3 +1267,13 @@ MathLib::value operator^(const MathLib::value &v1, const MathLib::value &v2)
 {
     return MathLib::value::calc('^',v1,v2);
 }
+
+MathLib::value operator<<(const MathLib::value &v1, const MathLib::value &v2)
+{
+    return v1.shiftLeft(v2);
+}
+
+MathLib::value operator>>(const MathLib::value &v1, const MathLib::value &v2)
+{
+    return v1.shiftRight(v2);
+}
diff --git a/lib/mathlib.h b/lib/mathlib.h
index 2639003ca..14decf4a5 100644
--- a/lib/mathlib.h
+++ b/lib/mathlib.h
@@ -59,6 +59,8 @@ public:
         static value calc(char op, const value &v1, const value &v2);
         int compare(const value &v) const;
         value add(int v) const;
+        value shiftLeft(const value &v) const;
+        value shiftRight(const value &v) const;
     };
 
     typedef long long bigint;
@@ -128,6 +130,8 @@ MathLib::value operator%(const MathLib::value &v1, const MathLib::value &v2);
 MathLib::value operator&(const MathLib::value &v1, const MathLib::value &v2);
 MathLib::value operator|(const MathLib::value &v1, const MathLib::value &v2);
 MathLib::value operator^(const MathLib::value &v1, const MathLib::value &v2);
+MathLib::value operator<<(const MathLib::value &v1, const MathLib::value &v2);
+MathLib::value operator>>(const MathLib::value &v1, const MathLib::value &v2);
 
 template<> CPPCHECKLIB std::string MathLib::toString(double value); // Declare specialization to avoid linker problems
 
diff --git a/lib/templatesimplifier.cpp b/lib/templatesimplifier.cpp
index 0d3d18852..3f0ddb373 100644
--- a/lib/templatesimplifier.cpp
+++ b/lib/templatesimplifier.cpp
@@ -891,48 +891,6 @@ static bool isLowerEqualThanMulDiv(const Token* lower)
     return isLowerThanMulDiv(lower) || Token::Match(lower, "[*/%]");
 }
 
-static std::string ShiftInt(const char cop, const Token* left, const Token* right)
-{
-    if (cop == '&' || cop == '|' || cop == '^')
-        return MathLib::calculate(left->str(), right->str(), cop);
-
-    const MathLib::bigint leftInt = MathLib::toLongNumber(left->str());
-    const MathLib::bigint rightInt = MathLib::toLongNumber(right->str());
-    const bool rightIntIsPositive = rightInt >= 0;
-
-    if (cop == '<') {
-        const bool leftOperationIsNotLeftShift = left->previous()->str() != "<<";
-        const bool operandIsLeftShift = right->previous()->str() == "<<";
-
-        // Ensure that its not a shift operator as used for streams
-        if (leftOperationIsNotLeftShift && operandIsLeftShift && rightIntIsPositive) {
-            const bool leftIntIsPositive = leftInt >= 0;
-            if (!leftIntIsPositive) { // In case the left integer is negative, e.g. -1000 << 16. Do not simplify.
-                return left->str() + " << " + right->str();
-            }
-            return MathLib::toString(leftInt << rightInt);
-        }
-    } else if (rightIntIsPositive) {
-        return MathLib::toString(leftInt >> rightInt);
-    }
-    return "";
-}
-
-static std::string ShiftUInt(const char cop, const Token* left, const Token* right)
-{
-    if (cop == '&' || cop == '|' || cop == '^')
-        return MathLib::calculate(left->str(), right->str(), cop);
-
-    const MathLib::biguint leftInt=MathLib::toULongNumber(left->str());
-    const MathLib::biguint rightInt=MathLib::toULongNumber(right->str());
-    if (cop == '<') {
-        if (left->previous()->str() != "<<") // Ensure that its not a shift operator as used for streams
-            return MathLib::toString(leftInt << rightInt);
-    } else {
-        return MathLib::toString(leftInt >> rightInt);
-    }
-    return "";
-}
 
 bool TemplateSimplifier::simplifyNumericCalculations(Token *tok)
 {
@@ -968,15 +926,34 @@ bool TemplateSimplifier::simplifyNumericCalculations(Token *tok)
             if (MathLib::isNegative(tok->str()) || MathLib::isNegative(tok->strAt(2)))
                 continue;
 
-            const char cop = op->str()[0];
-            std::string result;
-            if (tok->str().find_first_of("uU") != std::string::npos)
-                result = ShiftUInt(cop, tok, tok->tokAt(2));
-            else
-                result = ShiftInt(cop, tok, tok->tokAt(2));
-            if (result.empty())
+            const MathLib::value v1(tok->str());
+            const MathLib::value v2(tok->strAt(2));
+
+            if (!v1.isInt() || !v2.isInt())
+                continue;
+
+            switch (op->str()[0]) {
+            case '<':
+                tok->str((v1 << v2).str());
+                ret = true;
                 break;
-            tok->str(result);
+            case '>':
+                tok->str((v1 >> v2).str());
+                ret = true;
+                break;
+            case '&':
+                tok->str((v1 & v2).str());
+                ret = true;
+                break;
+            case '|':
+                tok->str((v1 | v2).str());
+                ret = true;
+                break;
+            case '^':
+                tok->str((v1 ^ v2).str());
+                ret = true;
+                break;
+            };
         }
 
         // Logical operations
diff --git a/test/testtokenize.cpp b/test/testtokenize.cpp
index 9b09eb130..20dd88230 100644
--- a/test/testtokenize.cpp
+++ b/test/testtokenize.cpp
@@ -2650,8 +2650,8 @@ private:
     }
 
     void simplifyKnownVariables57() { // #4724
-        ASSERT_EQUALS("unsigned long long x ; x = 9223372036854775808 ;", tokenizeAndStringify("unsigned long long x = 1UL << 63 ;", true));
-        ASSERT_EQUALS("long long x ; x = -9223372036854775808 ;", tokenizeAndStringify("long long x = 1L << 63 ;", true));
+        ASSERT_EQUALS("unsigned long long x ; x = 9223372036854775808UL ;", tokenizeAndStringify("unsigned long long x = 1UL << 63 ;", true));
+        ASSERT_EQUALS("long long x ; x = -9223372036854775808L ;", tokenizeAndStringify("long long x = 1L << 63 ;", true));
     }
 
     void simplifyKnownVariables58() { // #5268