diff --git a/sprout/functional/bind/bind.hpp b/sprout/functional/bind/bind.hpp
index 94b552b4..54230baa 100644
--- a/sprout/functional/bind/bind.hpp
+++ b/sprout/functional/bind/bind.hpp
@@ -11,6 +11,7 @@
 #include <sprout/utility/lvalue_forward.hpp>
 #include <sprout/tuple/tuple/tuple.hpp>
 #include <sprout/tuple/tuple/get.hpp>
+#include <sprout/tuple/tuple/make_tuple.hpp>
 #include <sprout/functional/ref.hpp>
 #include <sprout/functional/mem_fn.hpp>
 #include <sprout/functional/type_traits/weak_result_type.hpp>
diff --git a/sprout/functional/hash/detail/hash_float.hpp b/sprout/functional/hash/detail/hash_float.hpp
index 1ea49585..2f62d2e9 100644
--- a/sprout/functional/hash/detail/hash_float.hpp
+++ b/sprout/functional/hash/detail/hash_float.hpp
@@ -6,8 +6,8 @@
 #include <sprout/config.hpp>
 #include <sprout/functional/hash/hash_fwd.hpp>
 #include <sprout/math/fpclassify.hpp>
-#include <sprout/math/scalbn.hpp>
-#include <sprout/math/float_pair.hpp>
+#include <sprout/math/ldexp.hpp>
+#include <sprout/math/float2_sig_exp.hpp>
 #include <sprout/detail/integer/static_log2.hpp>
 
 namespace sprout {
@@ -21,7 +21,7 @@ namespace sprout {
 		inline SPROUT_CONSTEXPR std::size_t
 		float_hash_value_impl_4(T v, int exp, std::size_t seed, std::size_t length, std::size_t i = 0) {
 			return i != length ? sprout::detail::float_hash_value_impl_4(
-					sprout::math::scalbn(v - static_cast<T>(static_cast<std::size_t>(v)), std::numeric_limits<std::size_t>::digits),
+					sprout::math::ldexp(v - static_cast<T>(static_cast<std::size_t>(v)), std::numeric_limits<std::size_t>::digits),
 					exp, sprout::detail::hash_float_combine(seed, static_cast<std::size_t>(v)),
 					length, i + 1
 					)
@@ -32,7 +32,7 @@ namespace sprout {
 		inline SPROUT_CONSTEXPR std::size_t
 		float_hash_value_impl_3(T v, int exp) {
 			return sprout::detail::float_hash_value_impl_4(
-				sprout::math::scalbn(v - static_cast<T>(static_cast<std::size_t>(v)), std::numeric_limits<std::size_t>::digits),
+				sprout::math::ldexp(v - static_cast<T>(static_cast<std::size_t>(v)), std::numeric_limits<std::size_t>::digits),
 				exp, static_cast<std::size_t>(v),
 				(std::numeric_limits<T>::digits * sprout::detail::static_log2<std::numeric_limits<T>::radix>::value + std::numeric_limits<std::size_t>::digits - 1)
 					/ std::numeric_limits<std::size_t>::digits
@@ -41,7 +41,7 @@ namespace sprout {
 		template<typename T>
 		inline SPROUT_CONSTEXPR std::size_t
 		float_hash_value_impl_2(T v, int exp) {
-			return sprout::detail::float_hash_value_impl_3(sprout::math::scalbn(v, std::numeric_limits<std::size_t>::digits), exp);
+			return sprout::detail::float_hash_value_impl_3(sprout::math::ldexp(v, std::numeric_limits<std::size_t>::digits), exp);
 		}
 		template<typename T, typename P>
 		inline SPROUT_CONSTEXPR std::size_t
@@ -55,7 +55,7 @@ namespace sprout {
 		template<typename T>
 		inline SPROUT_CONSTEXPR std::size_t
 		float_hash_value_impl(T v) {
-			return sprout::detail::float_hash_value_impl_1<T>(sprout::math::float_pair(v));
+			return sprout::detail::float_hash_value_impl_1<T>(sprout::math::float2_sig_exp(v));
 		}
 
 		template<typename T>
diff --git a/sprout/math/detail/config.hpp b/sprout/math/detail/config.hpp
index ad6be8c1..e5363435 100644
--- a/sprout/math/detail/config.hpp
+++ b/sprout/math/detail/config.hpp
@@ -1,6 +1,7 @@
 #ifndef SPROUT_MATH_DETAIL_CONFIG_HPP
 #define SPROUT_MATH_DETAIL_CONFIG_HPP
 
+#include <cfloat>
 #include <sprout/config.hpp>
 #if SPROUT_USE_BUILTIN_CMATH_FUNCTION
 #	include <cmath>
@@ -12,6 +13,12 @@
 #	define NS_SPROUT_MATH_DETAIL sprout::math::detail
 #endif	// #ifndef SPROUT_USE_BUILTIN_CMATH_FUNCTION
 
+#if (FLT_RADIX == 2)
+#	define SPROUT_FLT_RADIX_IS_2 1
+#else
+#	define SPROUT_FLT_RADIX_IS_2 0
+#endif
+
 #if SPROUT_NOERROR_LARGE_FLOAT_ROUNDING
 #	define SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(e, x) (x)
 #else
diff --git a/sprout/math/float2_exponent.hpp b/sprout/math/float2_exponent.hpp
new file mode 100644
index 00000000..9e84c3a8
--- /dev/null
+++ b/sprout/math/float2_exponent.hpp
@@ -0,0 +1,38 @@
+#ifndef SPROUT_MATH_FLOAT2_EXPONENT_HPP
+#define SPROUT_MATH_FLOAT2_EXPONENT_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/math/ilogb2.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR int
+			float2_exponent(FloatType x) {
+				return sprout::math::ilogb2(x) + 1;
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR int
+			float2_exponent(IntType x) {
+				return sprout::math::detail::float2_exponent(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::float2_exponent;
+	}	// namespace math
+
+	using sprout::math::float2_exponent;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_FLOAT2_EXPONENT_HPP
diff --git a/sprout/math/float2_sig_exp.hpp b/sprout/math/float2_sig_exp.hpp
new file mode 100644
index 00000000..a79a16a4
--- /dev/null
+++ b/sprout/math/float2_sig_exp.hpp
@@ -0,0 +1,46 @@
+#ifndef SPROUT_MATH_FLOAT2_SIG_EXP_HPP
+#define SPROUT_MATH_FLOAT2_SIG_EXP_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/detail/pow.hpp>
+#include <sprout/math/float2_exponent.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/utility/pair/pair.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR sprout::pair<T, int>
+			float2_sig_exp_impl(T x, int exp) {
+				return sprout::pair<T, int>(x / sprout::detail::pow_n(T(2), exp), exp);
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR sprout::pair<FloatType, int>
+			float2_sig_exp(FloatType x) {
+				return sprout::math::detail::float2_sig_exp_impl(x, sprout::math::float2_exponent(x));
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR sprout::pair<double, int>
+			float2_sig_exp(IntType x) {
+				return sprout::math::detail::float2_sig_exp(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::float2_sig_exp;
+	}	// namespace math
+
+	using sprout::math::float2_sig_exp;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_FLOAT2_SIG_EXP_HPP
diff --git a/sprout/math/float2_significand.hpp b/sprout/math/float2_significand.hpp
new file mode 100644
index 00000000..5ae3ce77
--- /dev/null
+++ b/sprout/math/float2_significand.hpp
@@ -0,0 +1,39 @@
+#ifndef SPROUT_MATH_FLOAT2_SIGNIFICAND_HPP
+#define SPROUT_MATH_FLOAT2_SIGNIFICAND_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/detail/pow.hpp>
+#include <sprout/math/float2_exponent.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			float2_significand(FloatType x) {
+				return x / sprout::detail::pow_n(FloatType(2), sprout::math::float2_exponent(x));
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			float2_significand(IntType x) {
+				return sprout::math::detail::float_significand(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::float2_significand;
+	}	// namespace math
+
+	using sprout::math::float2_significand;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_FLOAT2_SIGNIFICAND_HPP
diff --git a/sprout/math/float_frac_int.hpp b/sprout/math/float_frac_int.hpp
new file mode 100644
index 00000000..6e0d23f8
--- /dev/null
+++ b/sprout/math/float_frac_int.hpp
@@ -0,0 +1,45 @@
+#ifndef SPROUT_MATH_FLOAT_FRAC_INT_HPP
+#define SPROUT_MATH_FLOAT_FRAC_INT_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/math/float_integer_part.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/utility/pair/pair.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR sprout::pair<T, T>
+			float_frac_int_impl(T x, T ipart) {
+				return sprout::pair<T, T>(x - ipart, ipart);
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR sprout::pair<FloatType, FloatType>
+			float_frac_int(FloatType x) {
+				return sprout::math::detail::float_frac_int_impl(x, sprout::math::float_integer_part(x));
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR sprout::pair<double, double>
+			float_frac_int(IntType x) {
+				return sprout::math::detail::float_frac_int(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::float_frac_int;
+	}	// namespace math
+
+	using sprout::math::float_frac_int;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_FLOAT_FRAC_INT_HPP
diff --git a/sprout/math/float_fractional_part.hpp b/sprout/math/float_fractional_part.hpp
new file mode 100644
index 00000000..f1596cd7
--- /dev/null
+++ b/sprout/math/float_fractional_part.hpp
@@ -0,0 +1,38 @@
+#ifndef SPROUT_MATH_FLOAT_FRACTIONAL_PART_HPP
+#define SPROUT_MATH_FLOAT_FRACTIONAL_PART_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/math/float_integer_part.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			float_fractional_part(FloatType x) {
+				return x - sprout::math::float_integer_part(x);
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			float_fractional_part(IntType x) {
+				return sprout::math::detail::float_fractional_part(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::float_fractional_part;
+	}	// namespace math
+
+	using sprout::math::float_fractional_part;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_FLOAT_FRACTIONAL_PART_HPP
diff --git a/sprout/math/float_integer_part.hpp b/sprout/math/float_integer_part.hpp
new file mode 100644
index 00000000..efd08471
--- /dev/null
+++ b/sprout/math/float_integer_part.hpp
@@ -0,0 +1,38 @@
+#ifndef SPROUT_MATH_FLOAT_INTEGER_PART_HPP
+#define SPROUT_MATH_FLOAT_INTEGER_PART_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/math/floor.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			float_integer_part(FloatType x) {
+				return sprout::math::floor(x);
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			float_integer_part(IntType x) {
+				return sprout::math::detail::float_integer_part(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::float_integer_part;
+	}	// namespace math
+
+	using sprout::math::float_integer_part;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_FLOAT_INTEGER_PART_HPP
diff --git a/sprout/math/float_pair.hpp b/sprout/math/float_sig_exp.hpp
similarity index 65%
rename from sprout/math/float_pair.hpp
rename to sprout/math/float_sig_exp.hpp
index 386e57b8..425e5484 100644
--- a/sprout/math/float_pair.hpp
+++ b/sprout/math/float_sig_exp.hpp
@@ -1,5 +1,5 @@
-#ifndef SPROUT_MATH_FLOAT_PAIR_HPP
-#define SPROUT_MATH_FLOAT_PAIR_HPP
+#ifndef SPROUT_MATH_FLOAT_SIG_EXP_HPP
+#define SPROUT_MATH_FLOAT_SIG_EXP_HPP
 
 #include <limits>
 #include <type_traits>
@@ -15,7 +15,7 @@ namespace sprout {
 		namespace detail {
 			template<typename T>
 			inline SPROUT_CONSTEXPR sprout::pair<T, int>
-			float_pair_impl(T x, int exp) {
+			float_sig_exp_impl(T x, int exp) {
 				return sprout::pair<T, int>(x / sprout::detail::pow_n(T(std::numeric_limits<T>::radix), exp), exp);
 			}
 
@@ -24,8 +24,8 @@ namespace sprout {
 				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR sprout::pair<FloatType, int>
-			float_pair(FloatType x) {
-				return sprout::math::detail::float_pair_impl(x, sprout::math::float_exponent(x));
+			float_sig_exp(FloatType x) {
+				return sprout::math::detail::float_sig_exp_impl(x, sprout::math::float_exponent(x));
 			}
 
 			template<
@@ -33,15 +33,15 @@ namespace sprout {
 				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR sprout::pair<double, int>
-			float_pair(IntType x) {
-				return sprout::math::detail::float_pair(static_cast<double>(x));
+			float_sig_exp(IntType x) {
+				return sprout::math::detail::float_sig_exp(static_cast<double>(x));
 			}
 		}	// namespace detail
 
-		using sprout::math::detail::float_pair;
+		using sprout::math::detail::float_sig_exp;
 	}	// namespace math
 
-	using sprout::math::float_pair;
+	using sprout::math::float_sig_exp;
 }	// namespace sprout
 
-#endif	// #ifndef SPROUT_MATH_FLOAT_PAIR_HPP
+#endif	// #ifndef SPROUT_MATH_FLOAT_SIG_EXP_HPP
diff --git a/sprout/math/float_mantissa.hpp b/sprout/math/float_significand.hpp
similarity index 66%
rename from sprout/math/float_mantissa.hpp
rename to sprout/math/float_significand.hpp
index 0d66f7be..c582b5b1 100644
--- a/sprout/math/float_mantissa.hpp
+++ b/sprout/math/float_significand.hpp
@@ -1,5 +1,5 @@
-#ifndef SPROUT_MATH_FLOAT_MANTISSA_HPP
-#define SPROUT_MATH_FLOAT_MANTISSA_HPP
+#ifndef SPROUT_MATH_FLOAT_SIGNIFICAND_HPP
+#define SPROUT_MATH_FLOAT_SIGNIFICAND_HPP
 
 #include <limits>
 #include <type_traits>
@@ -17,7 +17,7 @@ namespace sprout {
 				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR FloatType
-			float_mantissa(FloatType x) {
+			float_significand(FloatType x) {
 				return x / sprout::detail::pow_n(FloatType(std::numeric_limits<FloatType>::radix), sprout::math::float_exponent(x));
 			}
 
@@ -26,15 +26,15 @@ namespace sprout {
 				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR double
-			float_mantissa(IntType x) {
-				return sprout::math::detail::float_mantissa(static_cast<double>(x));
+			float_significand(IntType x) {
+				return sprout::math::detail::float_significand(static_cast<double>(x));
 			}
 		}	// namespace detail
 
-		using sprout::math::detail::float_mantissa;
+		using sprout::math::detail::float_significand;
 	}	// namespace math
 
-	using sprout::math::float_mantissa;
+	using sprout::math::float_significand;
 }	// namespace sprout
 
-#endif	// #ifndef SPROUT_MATH_FLOAT_MANTISSA_HPP
+#endif	// #ifndef SPROUT_MATH_FLOAT_SIGNIFICAND_HPP
diff --git a/sprout/math/floating_point.hpp b/sprout/math/floating_point.hpp
index 524e7552..b0c30602 100644
--- a/sprout/math/floating_point.hpp
+++ b/sprout/math/floating_point.hpp
@@ -7,8 +7,16 @@
 #include <sprout/math/scalbln.hpp>
 #include <sprout/math/ilogb.hpp>
 #include <sprout/math/logb.hpp>
+#include <sprout/math/ilogb2.hpp>
+#include <sprout/math/logb2.hpp>
+#include <sprout/math/float_significand.hpp>
 #include <sprout/math/float_exponent.hpp>
-#include <sprout/math/float_mantissa.hpp>
-#include <sprout/math/float_pair.hpp>
+#include <sprout/math/float_sig_exp.hpp>
+#include <sprout/math/float2_significand.hpp>
+#include <sprout/math/float2_exponent.hpp>
+#include <sprout/math/float2_sig_exp.hpp>
+#include <sprout/math/float_fractional_part.hpp>
+#include <sprout/math/float_integer_part.hpp>
+#include <sprout/math/float_frac_int.hpp>
 
 #endif	// #ifndef SPROUT_MATH_FLOATING_POINT_HPP
diff --git a/sprout/math/iceil.hpp b/sprout/math/iceil.hpp
new file mode 100644
index 00000000..4ad04ef9
--- /dev/null
+++ b/sprout/math/iceil.hpp
@@ -0,0 +1,75 @@
+#ifndef SPROUT_MATH_ICEIL_HPP
+#define SPROUT_MATH_ICEIL_HPP
+
+#include <limits>
+#include <type_traits>
+#include <stdexcept>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+#	include <sprout/math/ceil.hpp>
+#else
+#	include <sprout/math/equal_to.hpp>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+			template<typename To, typename FloatType>
+			inline SPROUT_CONSTEXPR To
+			iceil_impl(FloatType x) {
+				return std::numeric_limits<To>::max() < x || std::numeric_limits<To>::min() > x
+						? SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(std::domain_error("iceil: large float rounding."), static_cast<To>(x))
+					: static_cast<To>(x)
+					;
+			}
+			template<
+				typename To = int,
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			iceil(FloatType x) {
+				return sprout::math::detail::iceil_impl<To>(sprout::math::ceil(x));
+			}
+#else
+			template<typename To, typename FloatType>
+			inline SPROUT_CONSTEXPR To
+			iceil_impl(FloatType x, To x0) {
+				return sprout::math::equal_to(x, x0) ? x0
+					: x0 + 1
+					;
+			}
+			template<
+				typename To = int,
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			iceil(FloatType x) {
+				return std::numeric_limits<To>::max() < x || std::numeric_limits<To>::min() > x
+						? SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(std::domain_error("iceil: large float rounding."), static_cast<To>(x))
+					: sprout::math::detail::iceil_impl(x, static_cast<To>(x))
+					;
+			}
+#endif
+			template<
+				typename To = int,
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			iceil(IntType x) {
+				return sprout::math::detail::iceil<To>(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::iceil;
+	}	// namespace math
+
+	using sprout::math::iceil;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_ICEIL_HPP
diff --git a/sprout/math/ifloor.hpp b/sprout/math/ifloor.hpp
new file mode 100644
index 00000000..964e6b06
--- /dev/null
+++ b/sprout/math/ifloor.hpp
@@ -0,0 +1,75 @@
+#ifndef SPROUT_MATH_IFLOOR_HPP
+#define SPROUT_MATH_IFLOOR_HPP
+
+#include <limits>
+#include <type_traits>
+#include <stdexcept>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+#	include <sprout/math/floor.hpp>
+#else
+#	include <sprout/math/equal_to.hpp>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+			template<typename To, typename FloatType>
+			inline SPROUT_CONSTEXPR To
+			ifloor_impl(FloatType x) {
+				return std::numeric_limits<To>::max() < x || std::numeric_limits<To>::min() > x
+						? SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(std::domain_error("ifloor: large float rounding."), static_cast<To>(x))
+					: static_cast<To>(x)
+					;
+			}
+			template<
+				typename To = int,
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			ifloor(FloatType x) {
+				return sprout::math::detail::ifloor_impl<To>(sprout::math::floor(x));
+			}
+#else
+			template<typename To, typename FloatType>
+			inline SPROUT_CONSTEXPR To
+			ifloor_impl(FloatType x, To x0) {
+				return sprout::math::equal_to(x, x0) ? x0
+					: x0 - 1
+					;
+			}
+			template<
+				typename To = int,
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			ifloor(FloatType x) {
+				return std::numeric_limits<To>::max() < x || std::numeric_limits<To>::min() > x
+						? SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(std::domain_error("ifloor: large float rounding."), static_cast<To>(x))
+					: sprout::math::detail::ifloor_impl(x, static_cast<To>(x))
+					;
+			}
+#endif
+			template<
+				typename To = int,
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			ifloor(IntType x) {
+				return sprout::math::detail::ifloor<To>(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::ifloor;
+	}	// namespace math
+
+	using sprout::math::ifloor;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_IFLOOR_HPP
diff --git a/sprout/math/ilogb2.hpp b/sprout/math/ilogb2.hpp
new file mode 100644
index 00000000..bad2eafc
--- /dev/null
+++ b/sprout/math/ilogb2.hpp
@@ -0,0 +1,71 @@
+#ifndef SPROUT_MATH_ILOGB2_HPP
+#define SPROUT_MATH_ILOGB2_HPP
+
+#include <climits>
+#include <cfloat>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#if SPROUT_FLT_RADIX_IS_2
+#	include <sprout/math/ilogb.hpp>
+#else
+#	include <sprout/math/logb2.hpp>
+#	include <sprout/math/isnan.hpp>
+#	include <sprout/math/isinf.hpp>
+#	include <sprout/math/iszero.hpp>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+#if SPROUT_FLT_RADIX_IS_2
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR int
+			ilogb2(FloatType x) {
+				return sprout::math::ilogb(x);
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR int
+			ilogb2(IntType x) {
+				return sprout::math::ilogb(x);
+			}
+#else
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR int
+			ilogb2(FloatType x) {
+				return sprout::math::iszero(x) ? FP_ILOGB0
+					: sprout::math::isinf(x) ? INT_MAX
+					: sprout::math::isnan(x) ? FP_ILOGBNAN
+					: static_cast<int>(sprout::math::logb2(x))
+					;
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR int
+			ilogb2(IntType x) {
+				return sprout::math::detail::ilogb2(static_cast<double>(x));
+			}
+#endif
+		}	// namespace detail
+
+		using sprout::math::detail::ilogb2;
+	}	// namespace math
+
+	using sprout::math::ilogb2;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_ILOGB2_HPP
diff --git a/sprout/math/iround.hpp b/sprout/math/iround.hpp
new file mode 100644
index 00000000..c7920da8
--- /dev/null
+++ b/sprout/math/iround.hpp
@@ -0,0 +1,83 @@
+#ifndef SPROUT_MATH_IROUND_HPP
+#define SPROUT_MATH_IROUND_HPP
+
+#include <limits>
+#include <type_traits>
+#include <stdexcept>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+#	include <sprout/math/round.hpp>
+#else
+#	include <sprout/math/equal_to.hpp>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+			template<typename To, typename FloatType>
+			inline SPROUT_CONSTEXPR To
+			iround_impl(FloatType x) {
+				return std::numeric_limits<To>::max() < x || std::numeric_limits<To>::min() > x
+						? SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(std::domain_error("iround: large float rounding."), static_cast<To>(x))
+					: static_cast<To>(x)
+					;
+			}
+			template<
+				typename To = int,
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			iround(FloatType x) {
+				return sprout::math::detail::iround_impl<To>(sprout::math::round(x));
+			}
+#else
+			template<typename To, typename FloatType>
+			inline SPROUT_CONSTEXPR To
+			iround_impl_positive(FloatType x, To x0) {
+				return x - x0 < FloatType(0.5) ? x0
+					: x0 + 1
+					;
+			}
+			template<typename To, typename FloatType>
+			inline SPROUT_CONSTEXPR To
+			iround_impl_nagative(FloatType x, To x0) {
+				return x0 - x < FloatType(0.5) ? x0
+					: x0 - 1
+					;
+			}
+			template<
+				typename To = int,
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			iround(FloatType x) {
+				return std::numeric_limits<To>::max() < x || std::numeric_limits<To>::min() > x
+						? SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(std::domain_error("iround: large float irounding."), x)
+					: x < 0 ? sprout::math::detail::iround_impl_nagative(x, static_cast<To>(x))
+					: sprout::math::detail::iround_impl_positive(x, static_cast<To>(x))
+					;
+			}
+#endif
+			template<
+				typename To = int,
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			iround(IntType x) {
+				return sprout::math::detail::iround(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::iround;
+	}	// namespace math
+
+	using sprout::math::iround;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_IROUND_HPP
diff --git a/sprout/math/itrunc.hpp b/sprout/math/itrunc.hpp
new file mode 100644
index 00000000..d1f2ff30
--- /dev/null
+++ b/sprout/math/itrunc.hpp
@@ -0,0 +1,66 @@
+#ifndef SPROUT_MATH_ITRUNC_HPP
+#define SPROUT_MATH_ITRUNC_HPP
+
+#include <limits>
+#include <type_traits>
+#include <stdexcept>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+#	include <sprout/math/trunc.hpp>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+			template<typename To, typename FloatType>
+			inline SPROUT_CONSTEXPR To
+			itrunc_impl(FloatType x) {
+				return std::numeric_limits<To>::max() < x || std::numeric_limits<To>::min() > x
+						? SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(std::domain_error("itrunc: large float rounding."), static_cast<To>(x))
+					: static_cast<To>(x)
+					;
+			}
+			template<
+				typename To = int,
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			itrunc(FloatType x) {
+				return sprout::math::detail::itrunc_impl<To>(sprout::math::trunc(x));
+			}
+#else
+			template<
+				typename To = int,
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			itrunc(FloatType x) {
+				return std::numeric_limits<To>::max() < x || std::numeric_limits<To>::min() > x
+						? SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(std::domain_error("itrunc: large float rounding."), static_cast<To>(x))
+					: static_cast<To>(x)
+					;
+			}
+#endif
+			template<
+				typename To = int,
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value && std::is_integral<To>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR To
+			itrunc(IntType x) {
+				return sprout::math::detail::itrunc<To>(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using sprout::math::detail::itrunc;
+	}	// namespace math
+
+	using sprout::math::itrunc;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_ITRUNC_HPP
diff --git a/sprout/math/llround.hpp b/sprout/math/llround.hpp
index a890ea29..294be32b 100644
--- a/sprout/math/llround.hpp
+++ b/sprout/math/llround.hpp
@@ -1,39 +1,22 @@
 #ifndef SPROUT_MATH_LLROUND_HPP
 #define SPROUT_MATH_LLROUND_HPP
 
-#include <limits>
 #include <type_traits>
-#include <stdexcept>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
+#include <sprout/math/iround.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
 
 namespace sprout {
 	namespace math {
 		namespace detail {
-			template<typename FloatType>
-			inline SPROUT_CONSTEXPR long long
-			llround_impl_positive(FloatType x, long long x0) {
-				return x - x0 < FloatType(0.5) ? x0
-					: x0 + 1
-					;
-			}
-			template<typename FloatType>
-			inline SPROUT_CONSTEXPR long long
-			llround_impl_nagative(FloatType x, long long x0) {
-				return x0 - x < FloatType(0.5) ? x0
-					: x0 - 1
-					;
-			}
 			template<
 				typename FloatType,
 				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR long long
 			llround(FloatType x) {
-				return x < 0 ? sprout::math::detail::llround_impl_nagative(x, static_cast<long long>(x))
-					: sprout::math::detail::llround_impl_positive(x, static_cast<long long>(x))
-					;
+				return sprout::math::iround<long long>(x);
 			}
 
 			template<
@@ -42,7 +25,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR long long
 			llround(IntType x) {
-				return static_cast<long long>(x);
+				return sprout::math::iround<long long>(x);
 			}
 		}	// namespace detail
 
diff --git a/sprout/math/logb.hpp b/sprout/math/logb.hpp
index f6404431..6d59d515 100644
--- a/sprout/math/logb.hpp
+++ b/sprout/math/logb.hpp
@@ -4,12 +4,12 @@
 #include <cstdint>
 #include <limits>
 #include <type_traits>
-#include <stdexcept>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
 #include <sprout/detail/pow.hpp>
 #include <sprout/math/log_a.hpp>
 #include <sprout/math/trunc.hpp>
+#include <sprout/math/itrunc.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
 
 namespace sprout {
@@ -79,13 +79,9 @@ namespace sprout {
 			template<typename T>
 			inline SPROUT_CONSTEXPR T
 			logb_impl(T x, T exp) {
-				return std::numeric_limits<std::intmax_t>::max() < exp || std::numeric_limits<std::intmax_t>::min() > exp
-					? SPROUT_MATH_THROW_LARGE_FLOAT_ROUNDING(std::domain_error("trunc: large float rounding."), exp)
-					: sprout::math::detail::logb_impl_1(
-						x, sprout::detail::pow_n(T(std::numeric_limits<T>::radix), static_cast<std::intmax_t>(exp)),
-						static_cast<T>(static_cast<std::intmax_t>(exp))
-						)
-					;
+				return sprout::math::detail::logb_impl_1(
+					x, sprout::detail::pow_n(T(std::numeric_limits<T>::radix), sprout::math::itrunc<std::intmax_t>(exp)), exp
+					);
 			}
 
 			template<
diff --git a/sprout/math/logb2.hpp b/sprout/math/logb2.hpp
new file mode 100644
index 00000000..3f5ba26a
--- /dev/null
+++ b/sprout/math/logb2.hpp
@@ -0,0 +1,142 @@
+#ifndef SPROUT_MATH_LOGB2_HPP
+#define SPROUT_MATH_LOGB2_HPP
+
+#include <cstdint>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+#if SPROUT_FLT_RADIX_IS_2
+#	include <sprout/math/logb.hpp>
+#else
+#	include <cstdint>
+#	include <sprout/detail/pow.hpp>
+#	include <sprout/math/log_a.hpp>
+#	include <sprout/math/trunc.hpp>
+#	include <sprout/math/itrunc.hpp>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+#if SPROUT_FLT_RADIX_IS_2
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			logb2(FloatType x) {
+				return sprout::math::logb(x);
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			logb2(IntType x) {
+				return sprout::math::logb(x);
+			}
+#else
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			logb2_impl_2_neg_lo(T x, T x0, T base, T exp) {
+				return base < 1 ? sprout::math::detail::logb2_impl_2_neg_lo(
+						x, x0 * 2, x / (x0 / 2), exp - 1
+						)
+					: exp
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			logb2_impl_2_neg_hi(T x, T x0, T base, T exp) {
+				return !(base < 2) ? sprout::math::detail::logb2_impl_2_neg_hi(
+						x, x0 / 2, x / (x0 * 2), exp + 1
+						)
+					: exp
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			logb2_impl_2_pos_lo(T x, T x0, T base, T exp) {
+				return base < 1 ? sprout::math::detail::logb2_impl_2_pos_lo(
+						x, x0 * 2, x / (x0 / 2), exp + 1
+						)
+					: exp
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			logb2_impl_2_pos_hi(T x, T x0, T base, T exp) {
+				return !(base < 2) ? sprout::math::detail::logb2_impl_2_pos_hi(
+						x, x0 / 2, x / (x0 * 2), exp - 1
+						)
+					: exp
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			logb2_impl_2(T x, T x0, T base, T exp) {
+				return exp < 0
+					? base < 1 ? sprout::math::detail::logb2_impl_2_neg_lo(
+							x, x0 * 2, x / (x0 / 2), exp - 1
+							)
+						: !(base < 2) ? sprout::math::detail::logb2_impl_2_neg_hi(
+							x, x0 / 2, x / (x0 * 2), exp + 1
+							)
+						: exp
+					: base < 1 ? sprout::math::detail::logb2_impl_2_pos_lo(
+							x, x0 * 2, x / (x0 / 2), exp + 1
+							)
+						: !(base < 2) ? sprout::math::detail::logb2_impl_2_pos_hi(
+							x, x0 / 2, x / (x0 * 2), exp - 1
+							)
+						: exp
+						;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			logb2_impl_1(T x, T x0, T exp) {
+				return sprout::math::detail::logb2_impl_2(x, x0, x / x0, exp);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			logb2_impl(T x, T exp) {
+				return sprout::math::detail::logb2_impl_1(
+					x, sprout::detail::pow_n(T(2), sprout::math::itrunc<std::intmax_t>(exp)), exp
+					);
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			logb2(FloatType x) {
+				return x < 0 ? sprout::math::detail::logb2_impl(
+						-x, sprout::math::trunc(sprout::math::log_a(FloatType(2), -x))
+						)
+					: sprout::math::detail::logb2_impl(
+						x, sprout::math::trunc(sprout::math::log_a(FloatType(2), x))
+						)
+					;
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			logb2(IntType x) {
+				return sprout::math::detail::logb2(static_cast<double>(x));
+			}
+#endif
+		}	// namespace detail
+
+		using sprout::math::detail::logb2;
+	}	// namespace math
+
+	using sprout::math::logb2;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_LOGB2_HPP
diff --git a/sprout/math/lround.hpp b/sprout/math/lround.hpp
index c073d584..8cfb020c 100644
--- a/sprout/math/lround.hpp
+++ b/sprout/math/lround.hpp
@@ -1,39 +1,22 @@
 #ifndef SPROUT_MATH_LROUND_HPP
 #define SPROUT_MATH_LROUND_HPP
 
-#include <limits>
 #include <type_traits>
-#include <stdexcept>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
+#include <sprout/math/iround.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
 
 namespace sprout {
 	namespace math {
 		namespace detail {
-			template<typename FloatType>
-			inline SPROUT_CONSTEXPR long
-			lround_impl_positive(FloatType x, long x0) {
-				return x - x0 < FloatType(0.5) ? x0
-					: x0 + 1
-					;
-			}
-			template<typename FloatType>
-			inline SPROUT_CONSTEXPR long
-			lround_impl_nagative(FloatType x, long x0) {
-				return x0 - x < FloatType(0.5) ? x0
-					: x0 - 1
-					;
-			}
 			template<
 				typename FloatType,
 				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR long
 			lround(FloatType x) {
-				return x < 0 ? sprout::math::detail::lround_impl_nagative(x, static_cast<long>(x))
-					: sprout::math::detail::lround_impl_positive(x, static_cast<long>(x))
-					;
+				return sprout::math::iround<long>(x);
 			}
 
 			template<
@@ -42,7 +25,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR long
 			lround(IntType x) {
-				return static_cast<long>(x);
+				return sprout::math::iround<long>(x);
 			}
 		}	// namespace detail
 
diff --git a/sprout/math/nearest.hpp b/sprout/math/nearest.hpp
index 15dffcd9..176b4b55 100644
--- a/sprout/math/nearest.hpp
+++ b/sprout/math/nearest.hpp
@@ -6,6 +6,10 @@
 #include <sprout/math/floor.hpp>
 #include <sprout/math/trunc.hpp>
 #include <sprout/math/round.hpp>
+#include <sprout/math/iceil.hpp>
+#include <sprout/math/ifloor.hpp>
+#include <sprout/math/itrunc.hpp>
+#include <sprout/math/iround.hpp>
 #include <sprout/math/lround.hpp>
 #include <sprout/math/llround.hpp>