diff --git a/lib/fizzy/execute.cpp b/lib/fizzy/execute.cpp
index b3c97eeec..b9441f2a3 100644
--- a/lib/fizzy/execute.cpp
+++ b/lib/fizzy/execute.cpp
@@ -214,8 +214,8 @@ std::tuple<bytes_ptr, Limits> allocate_memory(const std::vector<Memory>& module_
     }
 }
 
-uint64_t eval_constant_expression(ConstantExpression expr,
-    const std::vector<ExternalGlobal>& imported_globals, const std::vector<uint64_t>& globals)
+Value eval_constant_expression(ConstantExpression expr,
+    const std::vector<ExternalGlobal>& imported_globals, const std::vector<Value>& globals)
 {
     if (expr.kind == ConstantExpression::Kind::Constant)
         return expr.value.constant;
@@ -486,7 +486,7 @@ std::unique_ptr<Instance> instantiate(Module module,
     match_imported_globals(module.imported_global_types, imported_globals);
 
     // Init globals
-    std::vector<uint64_t> globals;
+    std::vector<Value> globals;
     globals.reserve(module.globalsec.size());
     for (auto const& global : module.globalsec)
     {
diff --git a/lib/fizzy/execute.hpp b/lib/fizzy/execute.hpp
index 2d41e3b10..065846e53 100644
--- a/lib/fizzy/execute.hpp
+++ b/lib/fizzy/execute.hpp
@@ -58,7 +58,7 @@ struct ExternalMemory
 
 struct ExternalGlobal
 {
-    uint64_t* value = nullptr;
+    Value* value = nullptr;
     bool is_mutable = false;
 };
 
@@ -77,12 +77,12 @@ struct Instance
     // For these cases unique_ptr would either have a normal deleter or noop deleter respectively.
     table_ptr table = {nullptr, [](table_elements*) {}};
     Limits table_limits;
-    std::vector<uint64_t> globals;
+    std::vector<Value> globals;
     std::vector<ExternalFunction> imported_functions;
     std::vector<ExternalGlobal> imported_globals;
 
     Instance(Module _module, bytes_ptr _memory, Limits _memory_limits, table_ptr _table,
-        Limits _table_limits, std::vector<uint64_t> _globals,
+        Limits _table_limits, std::vector<Value> _globals,
         std::vector<ExternalFunction> _imported_functions,
         std::vector<ExternalGlobal> _imported_globals)
       : module(std::move(_module)),
diff --git a/lib/fizzy/parser.cpp b/lib/fizzy/parser.cpp
index cd6dd1bd9..c89d5e6e5 100644
--- a/lib/fizzy/parser.cpp
+++ b/lib/fizzy/parser.cpp
@@ -126,6 +126,15 @@ inline parser_result<GlobalType> parse_global_type(const uint8_t* pos, const uin
     return {type, pos};
 }
 
+template <class T>
+inline parser_result<T> parse_floating_point(const uint8_t* pos, const uint8_t* end)
+{
+    if ((pos + sizeof(T)) > end)
+        throw parser_error{"unexpected EOF"};
+
+    return {*reinterpret_cast<const T*>(pos), pos + sizeof(T)};
+}
+
 inline parser_result<ConstantExpression> parse_constant_expression(
     ValType expected_type, const uint8_t* pos, const uint8_t* end)
 {
@@ -174,17 +183,14 @@ inline parser_result<ConstantExpression> parse_constant_expression(
         break;
     }
     case Instr::f32_const:
-        // TODO: support this once floating points are implemented
         result.kind = ConstantExpression::Kind::Constant;
-        result.value.constant = 0;
-        pos = skip(4, pos, end);
+        std::tie(result.value.constant, pos) = parse_floating_point<uint32_t>(pos, end);
         constant_actual_type = ValType::f32;
         break;
     case Instr::f64_const:
-        // TODO: support this once floating points are implemented
         result.kind = ConstantExpression::Kind::Constant;
         result.value.constant = 0;
-        pos = skip(8, pos, end);
+        std::tie(result.value.constant, pos) = parse_floating_point<uint64_t>(pos, end);
         constant_actual_type = ValType::f64;
         break;
     }