diff --git a/sprout/math/float2_exponent.hpp b/sprout/math/float2_exponent.hpp
index 2398cefe..493830df 100644
--- a/sprout/math/float2_exponent.hpp
+++ b/sprout/math/float2_exponent.hpp
@@ -1,7 +1,6 @@
 #ifndef SPROUT_MATH_FLOAT2_EXPONENT_HPP
 #define SPROUT_MATH_FLOAT2_EXPONENT_HPP
 
-#include <climits>
 #include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
diff --git a/sprout/math/float2_sig_exp.hpp b/sprout/math/float2_sig_exp.hpp
index d633ef9f..bf011377 100644
--- a/sprout/math/float2_sig_exp.hpp
+++ b/sprout/math/float2_sig_exp.hpp
@@ -1,7 +1,6 @@
 #ifndef SPROUT_MATH_FLOAT2_SIG_EXP_HPP
 #define SPROUT_MATH_FLOAT2_SIG_EXP_HPP
 
-#include <climits>
 #include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
diff --git a/sprout/math/is_even.hpp b/sprout/math/is_even.hpp
index c4705c75..26534a67 100644
--- a/sprout/math/is_even.hpp
+++ b/sprout/math/is_even.hpp
@@ -4,18 +4,27 @@
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/math/isfinite.hpp>
 #include <sprout/math/fmod.hpp>
 
 namespace sprout {
 	namespace math {
 		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR bool
+			is_even_unchecked(T x) {
+				return sprout::math::fmod(x, T(2)) == T(0);
+			}
+
 			template<
 				typename FloatType,
 				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR bool
 			is_even(FloatType x) {
-				return sprout::math::fmod(x, FloatType(2)) == FloatType(0);
+				return sprout::math::isfinite(x)
+					&& sprout::math::detail::is_even_unchecked(x)
+					;
 			}
 		}	// namespace detail
 
diff --git a/sprout/math/is_integer.hpp b/sprout/math/is_integer.hpp
index 2ce00093..7011329d 100644
--- a/sprout/math/is_integer.hpp
+++ b/sprout/math/is_integer.hpp
@@ -4,18 +4,27 @@
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/math/isfinite.hpp>
 #include <sprout/math/trunc.hpp>
 
 namespace sprout {
 	namespace math {
 		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR bool
+			is_integer_unchecked(T x) {
+				return x == sprout::math::trunc(x);
+			}
+
 			template<
 				typename FloatType,
 				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR bool
 			is_integer(FloatType x) {
-				return x == sprout::math::trunc(x);
+				return sprout::math::isfinite(x)
+					&& sprout::math::detail::is_integer_unchecked(x)
+					;
 			}
 		}	// namespace detail
 
diff --git a/sprout/math/is_odd.hpp b/sprout/math/is_odd.hpp
index 23596757..6c5909fa 100644
--- a/sprout/math/is_odd.hpp
+++ b/sprout/math/is_odd.hpp
@@ -4,18 +4,27 @@
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/math/isfinite.hpp>
 #include <sprout/math/fmod.hpp>
 
 namespace sprout {
 	namespace math {
 		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR bool
+			is_odd_unchecked(T x) {
+				return sprout::math::fmod(x, T(2)) == T(1);
+			}
+
 			template<
 				typename FloatType,
 				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR bool
 			is_odd(FloatType x) {
-				return sprout::math::fmod(x, FloatType(2)) == FloatType(1);
+				return sprout::math::isfinite(x)
+					&& sprout::math::detail::is_odd_unchecked(x)
+					;
 			}
 		}	// namespace detail
 
diff --git a/sprout/optional/optional.hpp b/sprout/optional/optional.hpp
index d2b061af..ee61baa4 100644
--- a/sprout/optional/optional.hpp
+++ b/sprout/optional/optional.hpp
@@ -38,6 +38,7 @@ namespace sprout {
 			init = false;
 		}
 	public:
+		// 20.5.4.1, constructors
 		SPROUT_CONSTEXPR optional() SPROUT_NOEXCEPT
 			: init(false)
 		{}
@@ -61,7 +62,7 @@ namespace sprout {
 			: init(v.is_initialized())
 			, val(v.is_initialized() ? holder_type(*v) : holder_type())
 		{}
-
+		// 20.5.4.3, assignment
 		optional& operator=(sprout::nullopt_t v) SPROUT_NOEXCEPT {
 			assign(v);
 			return *this;
@@ -106,14 +107,14 @@ namespace sprout {
 		void reset(argument_type v) {
 			assign(v);
 		}
-
+		// 20.5.4.4, swap
 		void swap(optional& other)
 		SPROUT_NOEXCEPT_EXPR(SPROUT_NOEXCEPT_EXPR(sprout::swap(val, other.val)))
 		{
 			sprout::swap(init, other.init);
 			sprout::swap(val, other.val);
 		}
-
+		// 20.5.4.5, observers
 		SPROUT_CONSTEXPR reference_const_type operator*() const {
 			return (SPROUT_ASSERT(is_initialized()), true) ? val.get()
 				: val.get()