From 5f40808f75bf6cb96502fdff5e1df0896fb5354f Mon Sep 17 00:00:00 2001
From: bolero-MURAKAMI <bolero.murakami@gmail.com>
Date: Tue, 23 Apr 2013 19:03:03 +0900
Subject: [PATCH] add math::lgamma

---
 sprout/compost/effects/chorus.hpp            |   2 +-
 sprout/compost/effects/overdriven.hpp        |   4 +-
 sprout/compost/effects/vibrato.hpp           |   2 +-
 sprout/functional/hash/detail/hash_float.hpp |   8 +-
 sprout/math/acos.hpp                         |   2 +-
 sprout/math/acosh.hpp                        |   2 +-
 sprout/math/asinh.hpp                        |   2 +-
 sprout/math/atan2.hpp                        |   4 +-
 sprout/math/atanh.hpp                        |   2 +-
 sprout/math/cbrt.hpp                         |   4 +-
 sprout/math/erf.hpp                          |   2 +-
 sprout/math/erfc.hpp                         |   2 +-
 sprout/math/exp10.hpp                        |   2 +-
 sprout/math/exp2.hpp                         |   2 +-
 sprout/math/expm1.hpp                        |   2 +-
 sprout/math/float2_exponent.hpp              |   2 +-
 sprout/math/float2_significand.hpp           |   2 +-
 sprout/math/float_exponent.hpp               |   2 +-
 sprout/math/float_sig_exp.hpp                |   2 +-
 sprout/math/float_significand.hpp            |   2 +-
 sprout/math/fmod.hpp                         |   2 +-
 sprout/math/fpclassify.hpp                   |   6 +-
 sprout/math/frac_int.hpp                     |   2 +-
 sprout/math/fractional_part.hpp              |   2 +-
 sprout/math/gamma.hpp                        |   1 +
 sprout/math/gcd.hpp                          |   4 +-
 sprout/math/hypot.hpp                        |   6 +-
 sprout/math/iceil.hpp                        |   2 +-
 sprout/math/ifloor.hpp                       |   2 +-
 sprout/math/ilogb.hpp                        |   8 +-
 sprout/math/ilogb2.hpp                       |  12 +-
 sprout/math/integer_part.hpp                 |   2 +-
 sprout/math/iround.hpp                       |   2 +-
 sprout/math/isfinite.hpp                     |   4 +-
 sprout/math/isnormal.hpp                     |   4 +-
 sprout/math/issubnormal.hpp                  |   2 +-
 sprout/math/itrunc.hpp                       |   2 +-
 sprout/math/lcm.hpp                          |   4 +-
 sprout/math/lgamma.hpp                       | 210 +++++++++++++++++++
 sprout/math/llround.hpp                      |   4 +-
 sprout/math/log.hpp                          |   2 +-
 sprout/math/log10.hpp                        |   2 +-
 sprout/math/log1p.hpp                        |   2 +-
 sprout/math/log2.hpp                         |   2 +-
 sprout/math/log_a.hpp                        |   6 +-
 sprout/math/logb.hpp                         |   6 +-
 sprout/math/logb2.hpp                        |  10 +-
 sprout/math/lround.hpp                       |   4 +-
 sprout/math/pow.hpp                          |  12 +-
 sprout/math/quotient.hpp                     |   2 +-
 sprout/math/rem_quo.hpp                      |   2 +-
 sprout/math/remainder.hpp                    |   2 +-
 sprout/math/sin.hpp                          |   2 +-
 sprout/math/tan.hpp                          |   2 +-
 sprout/math/tanh.hpp                         |   2 +-
 sprout/math/tgamma.hpp                       |  14 +-
 sprout/rational/arithmetic.hpp               |  16 +-
 sprout/rational/rational.hpp                 |  18 +-
 58 files changed, 323 insertions(+), 116 deletions(-)
 create mode 100644 sprout/math/lgamma.hpp

diff --git a/sprout/compost/effects/chorus.hpp b/sprout/compost/effects/chorus.hpp
index 0746ce28..933583e2 100644
--- a/sprout/compost/effects/chorus.hpp
+++ b/sprout/compost/effects/chorus.hpp
@@ -57,7 +57,7 @@ namespace sprout {
 			template<typename Outdirected>
 			SPROUT_CONSTEXPR typename std::iterator_traits<Outdirected>::value_type
 			operator()(Outdirected const& x) const {
-				return calc(x, d_ + depth_ * sprout::math::sin(sprout::math::two_pi<Value>() * rate_ * x.index() / samples_per_sec_));
+				return calc(x, d_ + depth_ * sprout::sin(sprout::math::two_pi<Value>() * rate_ * x.index() / samples_per_sec_));
 			}
 		};
 
diff --git a/sprout/compost/effects/overdriven.hpp b/sprout/compost/effects/overdriven.hpp
index 38bf159e..c7d9ff8c 100644
--- a/sprout/compost/effects/overdriven.hpp
+++ b/sprout/compost/effects/overdriven.hpp
@@ -21,8 +21,8 @@ namespace sprout {
 		public:
 			SPROUT_CONSTEXPR T
 			operator()(T const& x) const {
-				return x >= 0 ? sprout::math::atan(x) / sprout::math::half_pi<T>()
-					: sprout::math::atan(x) / sprout::math::half_pi<T>() / 10
+				return x >= 0 ? sprout::atan(x) / sprout::math::half_pi<T>()
+					: sprout::atan(x) / sprout::math::half_pi<T>() / 10
 					;
 			}
 		};
diff --git a/sprout/compost/effects/vibrato.hpp b/sprout/compost/effects/vibrato.hpp
index 34f53d2b..414c4b4b 100644
--- a/sprout/compost/effects/vibrato.hpp
+++ b/sprout/compost/effects/vibrato.hpp
@@ -56,7 +56,7 @@ namespace sprout {
 			template<typename Outdirected>
 			SPROUT_CONSTEXPR typename std::iterator_traits<Outdirected>::value_type
 			operator()(Outdirected const& x) const {
-				return calc(x, d_ + depth_ * sprout::math::sin(sprout::math::two_pi<Value>() * rate_ * x.index() / samples_per_sec_));
+				return calc(x, d_ + depth_ * sprout::sin(sprout::math::two_pi<Value>() * rate_ * x.index() / samples_per_sec_));
 			}
 		};
 
diff --git a/sprout/functional/hash/detail/hash_float.hpp b/sprout/functional/hash/detail/hash_float.hpp
index 1d0bcc77..4c56d9f3 100644
--- a/sprout/functional/hash/detail/hash_float.hpp
+++ b/sprout/functional/hash/detail/hash_float.hpp
@@ -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::ldexp(v - static_cast<T>(static_cast<std::size_t>(v)), std::numeric_limits<std::size_t>::digits),
+					sprout::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::ldexp(v - static_cast<T>(static_cast<std::size_t>(v)), std::numeric_limits<std::size_t>::digits),
+				sprout::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::ldexp(v, std::numeric_limits<std::size_t>::digits), exp);
+			return sprout::detail::float_hash_value_impl_3(sprout::ldexp(v, std::numeric_limits<std::size_t>::digits), exp);
 		}
 		template<typename T, typename P>
 		inline SPROUT_CONSTEXPR std::size_t
@@ -70,7 +70,7 @@ namespace sprout {
 		template<typename T>
 		inline SPROUT_CONSTEXPR std::size_t
 		float_hash_value(T v) {
-			return sprout::detail::float_hash_value_1(v, sprout::math::fpclassify(v));
+			return sprout::detail::float_hash_value_1(v, sprout::fpclassify(v));
 		}
 	}	// namespace detail
 }	// namespace sprout
diff --git a/sprout/math/acos.hpp b/sprout/math/acos.hpp
index d3cd21c6..511134db 100644
--- a/sprout/math/acos.hpp
+++ b/sprout/math/acos.hpp
@@ -20,7 +20,7 @@ namespace sprout {
 			acos(FloatType x) {
 				return x == 1 ? FloatType(0)
 					: x > 1 || x < -1 ? std::numeric_limits<FloatType>::quiet_NaN()
-					: sprout::math::half_pi<FloatType>() - sprout::math::asin(x)
+					: sprout::math::half_pi<FloatType>() - sprout::asin(x)
 					;
 			}
 
diff --git a/sprout/math/acosh.hpp b/sprout/math/acosh.hpp
index 9c46c502..4eb02eae 100644
--- a/sprout/math/acosh.hpp
+++ b/sprout/math/acosh.hpp
@@ -21,7 +21,7 @@ namespace sprout {
 				return x == 1 ? FloatType(0)
 					: x < 1 ? std::numeric_limits<FloatType>::quiet_NaN()
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
-					: sprout::math::log(x + sprout::math::sqrt(x * x - 1))
+					: sprout::log(x + sprout::sqrt(x * x - 1))
 					;
 			}
 
diff --git a/sprout/math/asinh.hpp b/sprout/math/asinh.hpp
index abfb5d86..1931faef 100644
--- a/sprout/math/asinh.hpp
+++ b/sprout/math/asinh.hpp
@@ -21,7 +21,7 @@ namespace sprout {
 				return x == 0 ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
 					: x == -std::numeric_limits<FloatType>::infinity() ? -std::numeric_limits<FloatType>::infinity()
-					: sprout::math::log(x + sprout::math::sqrt(x * x + 1))
+					: sprout::log(x + sprout::sqrt(x * x + 1))
 					;
 			}
 
diff --git a/sprout/math/atan2.hpp b/sprout/math/atan2.hpp
index 94ab68e9..6a5215ff 100644
--- a/sprout/math/atan2.hpp
+++ b/sprout/math/atan2.hpp
@@ -34,8 +34,8 @@ namespace sprout {
 							: FloatType(0)
 					: y == std::numeric_limits<FloatType>::infinity() ? sprout::math::half_pi<FloatType>()
 					: y == -std::numeric_limits<FloatType>::infinity() ? -sprout::math::half_pi<FloatType>()
-					: x < 0 ? sprout::math::atan(y / x) + (y < 0 ? -1 : 1) * sprout::math::pi<FloatType>()
-					: sprout::math::atan(y / x)
+					: x < 0 ? sprout::atan(y / x) + (y < 0 ? -1 : 1) * sprout::math::pi<FloatType>()
+					: sprout::atan(y / x)
 					;
 			}
 
diff --git a/sprout/math/atanh.hpp b/sprout/math/atanh.hpp
index 8e1da4fe..254fcbaf 100644
--- a/sprout/math/atanh.hpp
+++ b/sprout/math/atanh.hpp
@@ -21,7 +21,7 @@ namespace sprout {
 					: x == 1 ? std::numeric_limits<FloatType>::infinity()
 					: x == -1 ? -std::numeric_limits<FloatType>::infinity()
 					: x > 1 || x < -1 ? std::numeric_limits<FloatType>::quiet_NaN()
-					: sprout::math::log((1 + x) / (1 - x)) / 2
+					: sprout::log((1 + x) / (1 - x)) / 2
 					;
 			}
 
diff --git a/sprout/math/cbrt.hpp b/sprout/math/cbrt.hpp
index d5493a04..f23865fd 100644
--- a/sprout/math/cbrt.hpp
+++ b/sprout/math/cbrt.hpp
@@ -21,8 +21,8 @@ namespace sprout {
 				return x == 0 ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
 					: x == -std::numeric_limits<FloatType>::infinity() ? -std::numeric_limits<FloatType>::infinity()
-					: x < 0 ? -sprout::math::pow(-x, sprout::math::third<FloatType>())
-					: sprout::math::pow(x, sprout::math::third<FloatType>())
+					: x < 0 ? -sprout::pow(-x, sprout::math::third<FloatType>())
+					: sprout::pow(x, sprout::math::third<FloatType>())
 					;
 			}
 
diff --git a/sprout/math/erf.hpp b/sprout/math/erf.hpp
index 062dbcc2..1d387cd0 100644
--- a/sprout/math/erf.hpp
+++ b/sprout/math/erf.hpp
@@ -34,7 +34,7 @@ namespace sprout {
 			template<typename T>
 			inline SPROUT_CONSTEXPR T
 			erf_impl(T x2, T a) {
-				return T(1) - sprout::math::exp(-x2 / (T(1) + a * x2) * (sprout::math::quarter_pi<T>() + a * x2));
+				return T(1) - sprout::exp(-x2 / (T(1) + a * x2) * (sprout::math::quarter_pi<T>() + a * x2));
 			}
 			template<
 				typename FloatType,
diff --git a/sprout/math/erfc.hpp b/sprout/math/erfc.hpp
index a0d2f201..ee221a0b 100644
--- a/sprout/math/erfc.hpp
+++ b/sprout/math/erfc.hpp
@@ -18,7 +18,7 @@ namespace sprout {
 			erfc(FloatType x) {
 				return x == std::numeric_limits<FloatType>::infinity() ? FloatType(0)
 					: x == -std::numeric_limits<FloatType>::infinity() ? FloatType(2)
-					: FloatType(1) - sprout::math::erf(x)
+					: FloatType(1) - sprout::erf(x)
 					;
 			}
 
diff --git a/sprout/math/exp10.hpp b/sprout/math/exp10.hpp
index ff0214d3..83ff9bf8 100644
--- a/sprout/math/exp10.hpp
+++ b/sprout/math/exp10.hpp
@@ -20,7 +20,7 @@ namespace sprout {
 				return x == 0 ? FloatType(1)
 					: x == -std::numeric_limits<FloatType>::infinity() ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
-					: sprout::math::exp(x * sprout::math::ln_ten<FloatType>())
+					: sprout::exp(x * sprout::math::ln_ten<FloatType>())
 					;
 			}
 
diff --git a/sprout/math/exp2.hpp b/sprout/math/exp2.hpp
index 794ec434..3e1a9cb4 100644
--- a/sprout/math/exp2.hpp
+++ b/sprout/math/exp2.hpp
@@ -21,7 +21,7 @@ namespace sprout {
 				return x == 0 ? FloatType(1)
 					: x == -std::numeric_limits<FloatType>::infinity() ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
-					: sprout::math::exp(x * sprout::math::ln_two<FloatType>())
+					: sprout::exp(x * sprout::math::ln_two<FloatType>())
 					;
 			}
 
diff --git a/sprout/math/expm1.hpp b/sprout/math/expm1.hpp
index b68dc124..dbfe5074 100644
--- a/sprout/math/expm1.hpp
+++ b/sprout/math/expm1.hpp
@@ -21,7 +21,7 @@ namespace sprout {
 				return x == 0 ? FloatType(0)
 					: x == -std::numeric_limits<FloatType>::infinity() ? FloatType(-1)
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
-					: sprout::math::exp(x) - FloatType(1)
+					: sprout::exp(x) - FloatType(1)
 					;
 			}
 
diff --git a/sprout/math/float2_exponent.hpp b/sprout/math/float2_exponent.hpp
index 70bbf5af..e8204aee 100644
--- a/sprout/math/float2_exponent.hpp
+++ b/sprout/math/float2_exponent.hpp
@@ -18,7 +18,7 @@ namespace sprout {
 			inline SPROUT_CONSTEXPR int
 			float2_exponent(FloatType x) {
 				return x == 0 ? 0
-					: sprout::math::ilogb2(x) + 1
+					: sprout::ilogb2(x) + 1
 					;
 			}
 
diff --git a/sprout/math/float2_significand.hpp b/sprout/math/float2_significand.hpp
index 5ca0f6ac..e21a98c0 100644
--- a/sprout/math/float2_significand.hpp
+++ b/sprout/math/float2_significand.hpp
@@ -22,7 +22,7 @@ namespace sprout {
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
 					: x == -std::numeric_limits<FloatType>::infinity() ? -std::numeric_limits<FloatType>::infinity()
 					: x == std::numeric_limits<FloatType>::quiet_NaN() ? std::numeric_limits<FloatType>::quiet_NaN()
-					: x / sprout::detail::pow_n(FloatType(2), sprout::math::float2_exponent(x))
+					: x / sprout::detail::pow_n(FloatType(2), sprout::float2_exponent(x))
 					;
 			}
 
diff --git a/sprout/math/float_exponent.hpp b/sprout/math/float_exponent.hpp
index 661dac6e..3bd46d00 100644
--- a/sprout/math/float_exponent.hpp
+++ b/sprout/math/float_exponent.hpp
@@ -18,7 +18,7 @@ namespace sprout {
 			inline SPROUT_CONSTEXPR int
 			float_exponent(FloatType x) {
 				return x == 0 ? 0
-					: sprout::math::ilogb(x) + 1
+					: sprout::ilogb(x) + 1
 					;
 			}
 
diff --git a/sprout/math/float_sig_exp.hpp b/sprout/math/float_sig_exp.hpp
index 74fc1bdf..45d65e9d 100644
--- a/sprout/math/float_sig_exp.hpp
+++ b/sprout/math/float_sig_exp.hpp
@@ -31,7 +31,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR sprout::pair<FloatType, int>
 			float_sig_exp(FloatType x) {
-				return sprout::math::detail::float_sig_exp_impl(x, sprout::math::float_exponent(x));
+				return sprout::math::detail::float_sig_exp_impl(x, sprout::float_exponent(x));
 			}
 
 			template<
diff --git a/sprout/math/float_significand.hpp b/sprout/math/float_significand.hpp
index 6cee2bca..792fdb72 100644
--- a/sprout/math/float_significand.hpp
+++ b/sprout/math/float_significand.hpp
@@ -22,7 +22,7 @@ namespace sprout {
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
 					: x == -std::numeric_limits<FloatType>::infinity() ? -std::numeric_limits<FloatType>::infinity()
 					: x == std::numeric_limits<FloatType>::quiet_NaN() ? std::numeric_limits<FloatType>::quiet_NaN()
-					: x / sprout::detail::pow_n(FloatType(std::numeric_limits<FloatType>::radix), sprout::math::float_exponent(x))
+					: x / sprout::detail::pow_n(FloatType(std::numeric_limits<FloatType>::radix), sprout::float_exponent(x))
 					;
 			}
 
diff --git a/sprout/math/fmod.hpp b/sprout/math/fmod.hpp
index 2b8fd467..e10c9f5a 100644
--- a/sprout/math/fmod.hpp
+++ b/sprout/math/fmod.hpp
@@ -22,7 +22,7 @@ namespace sprout {
 						? std::numeric_limits<FloatType>::quiet_NaN()
 					: x == 0 ? FloatType(0)
 					: y == std::numeric_limits<FloatType>::infinity() || y == -std::numeric_limits<FloatType>::infinity() ? x
-					: x - sprout::math::trunc(x / y) * y
+					: x - sprout::trunc(x / y) * y
 					;
 			}
 
diff --git a/sprout/math/fpclassify.hpp b/sprout/math/fpclassify.hpp
index 466897c7..afa3dd60 100644
--- a/sprout/math/fpclassify.hpp
+++ b/sprout/math/fpclassify.hpp
@@ -20,9 +20,9 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR int
 			fpclassify(FloatType x) {
-				return sprout::math::isnan(x) ? FP_NAN
-					: sprout::math::isinf(x) ? FP_INFINITE
-					: sprout::math::iszero(x) ? FP_ZERO
+				return sprout::isnan(x) ? FP_NAN
+					: sprout::isinf(x) ? FP_INFINITE
+					: sprout::iszero(x) ? FP_ZERO
 					: sprout::math::detail::issubnormal_or_zero(x) ? FP_SUBNORMAL
 					: FP_NORMAL
 					;
diff --git a/sprout/math/frac_int.hpp b/sprout/math/frac_int.hpp
index 151c67d8..7cb84fb0 100644
--- a/sprout/math/frac_int.hpp
+++ b/sprout/math/frac_int.hpp
@@ -28,7 +28,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR sprout::pair<FloatType, FloatType>
 			frac_int(FloatType x) {
-				return sprout::math::detail::frac_int_impl(x, sprout::math::integer_part(x));
+				return sprout::math::detail::frac_int_impl(x, sprout::integer_part(x));
 			}
 
 			template<
diff --git a/sprout/math/fractional_part.hpp b/sprout/math/fractional_part.hpp
index 7a584476..c8e53c80 100644
--- a/sprout/math/fractional_part.hpp
+++ b/sprout/math/fractional_part.hpp
@@ -19,7 +19,7 @@ namespace sprout {
 			fractional_part(FloatType x) {
 				return x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity() ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::quiet_NaN() ? std::numeric_limits<FloatType>::quiet_NaN()
-					: x - sprout::math::integer_part(x)
+					: x - sprout::integer_part(x)
 					;
 			}
 
diff --git a/sprout/math/gamma.hpp b/sprout/math/gamma.hpp
index 999c7a91..95d863f4 100644
--- a/sprout/math/gamma.hpp
+++ b/sprout/math/gamma.hpp
@@ -3,5 +3,6 @@
 
 #include <sprout/config.hpp>
 #include <sprout/math/tgamma.hpp>
+#include <sprout/math/lgamma.hpp>
 
 #endif	// #ifndef SPROUT_MATH_GAMMA_HPP
diff --git a/sprout/math/gcd.hpp b/sprout/math/gcd.hpp
index fbbf1591..4bbbddbb 100644
--- a/sprout/math/gcd.hpp
+++ b/sprout/math/gcd.hpp
@@ -246,6 +246,8 @@ namespace sprout {
 			return sprout::math::gcd_evaluator<IntType>().operator()(a, b);
 		}
 	}	// namespace math
-}	// namespace boost
+
+	using sprout::math::gcd;
+}	// namespace sprout
 
 #endif	// #ifndef SPROUT_MATH_GCD_HPP
diff --git a/sprout/math/hypot.hpp b/sprout/math/hypot.hpp
index 4334d580..a6c90c51 100644
--- a/sprout/math/hypot.hpp
+++ b/sprout/math/hypot.hpp
@@ -19,13 +19,13 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			hypot(FloatType x, FloatType y) {
-				return y == 0 ? sprout::math::fabs(x)
-					: x == 0 ? sprout::math::fabs(y)
+				return y == 0 ? sprout::fabs(x)
+					: x == 0 ? sprout::fabs(y)
 					: y == std::numeric_limits<FloatType>::infinity() || y == -std::numeric_limits<FloatType>::infinity()
 						? std::numeric_limits<FloatType>::infinity()
 					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity()
 						? std::numeric_limits<FloatType>::infinity()
-					: sprout::math::sqrt(x * x + y * y)
+					: sprout::sqrt(x * x + y * y)
 					;
 			}
 
diff --git a/sprout/math/iceil.hpp b/sprout/math/iceil.hpp
index 5e8f4f03..c01a192a 100644
--- a/sprout/math/iceil.hpp
+++ b/sprout/math/iceil.hpp
@@ -32,7 +32,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR To
 			iceil(FloatType x) {
-				return sprout::math::detail::iceil_impl<To>(sprout::math::ceil(x));
+				return sprout::math::detail::iceil_impl<To>(sprout::ceil(x));
 			}
 #else
 			template<typename To, typename FloatType>
diff --git a/sprout/math/ifloor.hpp b/sprout/math/ifloor.hpp
index a68ab205..e7e8dd74 100644
--- a/sprout/math/ifloor.hpp
+++ b/sprout/math/ifloor.hpp
@@ -32,7 +32,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR To
 			ifloor(FloatType x) {
-				return sprout::math::detail::ifloor_impl<To>(sprout::math::floor(x));
+				return sprout::math::detail::ifloor_impl<To>(sprout::floor(x));
 			}
 #else
 			template<typename To, typename FloatType>
diff --git a/sprout/math/ilogb.hpp b/sprout/math/ilogb.hpp
index a58ccc5d..55eaa9e7 100644
--- a/sprout/math/ilogb.hpp
+++ b/sprout/math/ilogb.hpp
@@ -21,10 +21,10 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR int
 			ilogb(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::logb(x))
+				return sprout::iszero(x) ? FP_ILOGB0
+					: sprout::isinf(x) ? INT_MAX
+					: sprout::isnan(x) ? FP_ILOGBNAN
+					: static_cast<int>(sprout::logb(x))
 					;
 			}
 
diff --git a/sprout/math/ilogb2.hpp b/sprout/math/ilogb2.hpp
index bad2eafc..d5e8aae3 100644
--- a/sprout/math/ilogb2.hpp
+++ b/sprout/math/ilogb2.hpp
@@ -26,7 +26,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR int
 			ilogb2(FloatType x) {
-				return sprout::math::ilogb(x);
+				return sprout::ilogb(x);
 			}
 
 			template<
@@ -35,7 +35,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR int
 			ilogb2(IntType x) {
-				return sprout::math::ilogb(x);
+				return sprout::ilogb(x);
 			}
 #else
 			template<
@@ -44,10 +44,10 @@ namespace sprout {
 			>
 			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))
+				return sprout::iszero(x) ? FP_ILOGB0
+					: sprout::isinf(x) ? INT_MAX
+					: sprout::isnan(x) ? FP_ILOGBNAN
+					: static_cast<int>(sprout::logb2(x))
 					;
 			}
 
diff --git a/sprout/math/integer_part.hpp b/sprout/math/integer_part.hpp
index 338fa39e..cec6ffd4 100644
--- a/sprout/math/integer_part.hpp
+++ b/sprout/math/integer_part.hpp
@@ -20,7 +20,7 @@ namespace sprout {
 				return x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
 					: x == -std::numeric_limits<FloatType>::infinity() ? -std::numeric_limits<FloatType>::infinity()
 					: x == std::numeric_limits<FloatType>::quiet_NaN() ? std::numeric_limits<FloatType>::quiet_NaN()
-					: sprout::math::trunc(x)
+					: sprout::trunc(x)
 					;
 			}
 
diff --git a/sprout/math/iround.hpp b/sprout/math/iround.hpp
index 9190ddea..4160a8f4 100644
--- a/sprout/math/iround.hpp
+++ b/sprout/math/iround.hpp
@@ -32,7 +32,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR To
 			iround(FloatType x) {
-				return sprout::math::detail::iround_impl<To>(sprout::math::round(x));
+				return sprout::math::detail::iround_impl<To>(sprout::round(x));
 			}
 #else
 			template<typename To, typename FloatType>
diff --git a/sprout/math/isfinite.hpp b/sprout/math/isfinite.hpp
index 0228ce8e..c8cbc70f 100644
--- a/sprout/math/isfinite.hpp
+++ b/sprout/math/isfinite.hpp
@@ -17,8 +17,8 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR int
 			isfinite(FloatType x) {
-				return !sprout::math::isnan(x)
-					&& !sprout::math::isinf(x)
+				return !sprout::isnan(x)
+					&& !sprout::isinf(x)
 					;
 			}
 		}	// namespace detail
diff --git a/sprout/math/isnormal.hpp b/sprout/math/isnormal.hpp
index 315674c7..9d1e33ee 100644
--- a/sprout/math/isnormal.hpp
+++ b/sprout/math/isnormal.hpp
@@ -18,8 +18,8 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR int
 			isnormal(FloatType x) {
-				return !sprout::math::isnan(x)
-					&& !sprout::math::isinf(x)
+				return !sprout::isnan(x)
+					&& !sprout::isinf(x)
 					&& !sprout::math::detail::issubnormal_or_zero(x)
 					;
 			}
diff --git a/sprout/math/issubnormal.hpp b/sprout/math/issubnormal.hpp
index a1bfc955..8e182194 100644
--- a/sprout/math/issubnormal.hpp
+++ b/sprout/math/issubnormal.hpp
@@ -28,7 +28,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR int
 			issubnormal(FloatType x) {
-				return !sprout::math::iszero(x)
+				return !sprout::iszero(x)
 					&& sprout::math::detail::issubnormal_or_zero(x)
 					;
 			}
diff --git a/sprout/math/itrunc.hpp b/sprout/math/itrunc.hpp
index d0e0f6a4..1857f384 100644
--- a/sprout/math/itrunc.hpp
+++ b/sprout/math/itrunc.hpp
@@ -30,7 +30,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR To
 			itrunc(FloatType x) {
-				return sprout::math::detail::itrunc_impl<To>(sprout::math::trunc(x));
+				return sprout::math::detail::itrunc_impl<To>(sprout::trunc(x));
 			}
 #else
 			template<
diff --git a/sprout/math/lcm.hpp b/sprout/math/lcm.hpp
index a421593c..f4d323fb 100644
--- a/sprout/math/lcm.hpp
+++ b/sprout/math/lcm.hpp
@@ -105,6 +105,8 @@ namespace sprout {
 			return sprout::math::lcm_evaluator<IntType>().operator()(a, b);
 		}
 	}	// namespace math
-}	// namespace boost
+
+	using sprout::math::lcm;
+}	// namespace sprout
 
 #endif	// #ifndef SPROUT_MATH_LCM_HPP
diff --git a/sprout/math/lgamma.hpp b/sprout/math/lgamma.hpp
new file mode 100644
index 00000000..ebacd50d
--- /dev/null
+++ b/sprout/math/lgamma.hpp
@@ -0,0 +1,210 @@
+#ifndef SPROUT_MATH_LGAMMA_HPP
+#define SPROUT_MATH_LGAMMA_HPP
+
+#include <limits>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/detail/config.hpp>
+#include <sprout/math/detail/float_compute.hpp>
+#include <sprout/math/constants.hpp>
+#include <sprout/math/factorial.hpp>
+#include <sprout/math/log.hpp>
+#include <sprout/math/sin.hpp>
+#include <sprout/math/abs.hpp>
+#include <sprout/math/itrunc.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_3(T x, T y) {
+				return x < 0 ? sprout::log(sprout::math::pi<T>() / sprout::abs(x * sprout::sin(x * sprout::math::pi<T>()))) - y
+					: y
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_2_d_1(T x, T w, T v, T t) {
+				return sprout::math::detail::lgamma_impl_3(
+					x,
+					(((((-0.00163312359200500807 * t + 8.3644533703385956e-4) * t + -5.9518947575728181e-4) * t
+						+ 7.9365057505415415e-4) * t + -0.00277777777735463043) * t + 0.08333333333333309869) * v + 0.91893853320467274178
+						+ ((w - T(0.5)) * sprout::log(w) - w)
+					);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_2_d(T x, T w, T v) {
+				return sprout::math::detail::lgamma_impl_2_d_1(x, w, v, v * v);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_2_c_1(T x, T w, T t, int k) {
+				return sprout::math::detail::lgamma_impl_3(
+					x,
+					k == 0 ? (((((((((((
+							1.16333640008e-8 * t + -8.33156123568e-8) * t
+							+ 3.832869977018e-7) * t + -1.5814047847688e-6) * t + 6.50106723241e-6) * t
+							+ -2.74514060128677e-5) * t + 1.209015360925566e-4) * t + -5.666333178228163e-4) * t
+							+ 0.0029294103665559733) * t + -0.0180340086069185819) * t + 0.1651788780501166204) * t
+							+ 1.1031566406452431944) * t + 1.2009736023470742248
+						: k == 1 ? (((((((((((
+							1.3842760642e-9 * t + -6.9417501176e-9) * t
+							+ 3.42976459827e-8) * t + -1.785317236779e-7) * t + 9.525947257118e-7) * t
+							+ -5.2483007560905e-6) * t + 3.02364659535708e-5) * t + -1.858396115473822e-4) * t
+							+ 0.0012634378559425382) * t + -0.0102594702201954322) * t + 0.1243625515195050218) * t
+							+ 1.3888709263595291174) * t + 2.4537365708424422209
+						: k == 2 ? (((((((((((
+							1.298977078e-10 * t + -8.02957489e-10) * t
+							+ 4.945484615e-9) * t + -3.17563534834e-8) * t + 2.092136698089e-7) * t
+							+ -1.4252023958462e-6) * t + 1.01652510114008e-5) * t + -7.74550502862323e-5) * t
+							+ 6.537746948291078e-4) * t + -0.006601491253552183) * t + 0.0996711934948138193) * t
+							+ 1.6110931485817511402) * t + 3.9578139676187162939
+						: k == 3 ? (((((((((((
+							1.83995642e-11 * t + -1.353537034e-10) * t
+							+ 9.984676809e-10) * t + -7.6346363974e-9) * t + 5.99311464148e-8) * t
+							+ -4.868554120177e-7) * t + 4.1441957716669e-6) * t + -3.77160856623282e-5) * t
+							+ 3.805693126824884e-4) * t + -0.0045979851178130194) * t + 0.0831422678749791178) * t
+							+ 1.7929113303999329439) * t + 5.6625620598571415285
+						: (((((((((((
+							3.4858778e-12 * t + -2.97587783e-11) * t
+							+ 2.557677575e-10) * t + -2.2705728282e-9) * t + 2.0702499245e-8) * t
+							+ -1.954426390917e-7) * t + 1.9343161886722e-6) * t + -2.0479024910257e-5) * t
+							+ 2.405181940241215e-4) * t + -0.0033842087561074799) * t + 0.0713079483483518997) * t
+							+ 1.9467574842460867884) * t + 7.5343642367587329552
+					);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_2_c(T x, T w, int k) {
+				return sprout::math::detail::lgamma_impl_2_c_1(x, w, w - (static_cast<T>(k) + 3.5), k);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_2_b_2(T x, T w, T t, int k) {
+				return sprout::math::detail::lgamma_impl_3(
+					x,
+					k == 0 ? ((((((((((((
+							-4.587497028e-11 * t + 1.902363396e-10) * t
+							+ 8.6377323367e-10) * t + 1.15513678861e-8) * t + -2.556403058605e-8) * t
+							+ -1.5236723372486e-7) * t + -3.1680510638574e-6) * t + 1.22903704923381e-6) * t
+							+ 2.334372474572637e-5) * t + 0.00111544038088797696) * t + 0.00344717051723468982) * t
+							+ 0.03198287045148788384) * t + -0.32705333652955399526) * t + 0.40120442440953927615
+						: k == 1 ? ((((((((((((
+							-5.184290387e-11 * t + -8.3355121068e-10) * t
+							+ -2.56167239813e-9) * t + 1.455875381397e-8) * t + 1.3512178394703e-7) * t
+							+ 2.9898826810905e-7) * t + -3.58107254612779e-6) * t + -2.445260816156224e-5) * t
+							+ -4.417127762011821e-5) * t + 0.00112859455189416567) * t + 0.00804694454346728197) * t
+							+ 0.04919775747126691372) * t + -0.24818372840948854178) * t + 0.11071780856646862561
+						: k == 2 ? ((((((((((((
+							3.0279161576e-10 * t + 1.60742167357e-9) * t
+							+ -4.05596009522e-9) * t + -5.089259920266e-8) * t + -2.029496209743e-8) * t
+							+ 1.35130272477793e-6) * t + 3.91430041115376e-6) * t + -2.871505678061895e-5) * t
+							+ -2.3052137536922035e-4) * t + 4.5534656385400747e-4) * t + 0.01153444585593040046) * t
+							+ 0.07924014651650476036) * t + -0.12152192626936502982) * t + -0.07916438300260539592
+						: k == 3 ? ((((((((((((
+							-5.091914958e-10 * t + -1.15274986907e-9) * t
+							+ 1.237873512188e-8) * t + 2.937383549209e-8) * t + -3.0621450667958e-7) * t
+							+ -7.7409414949954e-7) * t + 8.16753874325579e-6) * t + 2.412433382517375e-5) * t
+							+ -2.60612176060637e-4) * t + -9.1000087658659231e-4) * t + 0.01068093850598380797) * t
+							+ 0.11395654404408482305) * t + 0.07209569059984075595) * t + -0.10971041451764266684
+						: k == 4 ? ((((((((((((
+							4.0119897187e-10 * t + -1.3224526679e-10) * t
+							+ -1.002723190355e-8) * t + 2.569249716518e-8) * t + 2.0336011868466e-7) * t
+							+ -1.1809768272606e-6) * t + -3.00660303810663e-6) * t + 4.402212897757763e-5) * t
+							+ -1.462405876235375e-5) * t + -0.0016487379559600128) * t + 0.00513927520866443706) * t
+							+ 0.13843580753590579416) * t + 0.32730190978254056722) * t + 0.08588339725978624973
+						: k == 5 ? ((((((((((((
+							-1.5413428348e-10 * t + 6.4905779353e-10) * t
+							+ 1.60702811151e-9) * t + -2.655645793815e-8) * t + 7.619544277956e-8) * t
+							+ 4.7604380765353e-7) * t + -4.90748870866195e-6) * t + 8.21513040821212e-6) * t
+							+ 1.4804944070262948e-4) * t + -0.00122152255762163238) * t + -8.7425289205498532e-4) * t
+							+ 0.1443870369965796831) * t + 0.61315889733595543766) * t + 0.55513708159976477557
+						: ((((((((((((
+							1.049740243e-11 * t + -2.5832017855e-10) * t
+							+ 1.39591845075e-9) * t + -2.1177278325e-10) * t + -5.082950464905e-8) * t
+							+ 3.7801785193343e-7) * t + -7.3982266659145e-7) * t + -1.088918441519888e-5) * t
+							+ 1.2491810452478905e-4) * t + -4.9171790705139895e-4) * t + -0.0042570708944826646) * t
+							+ 0.13595080378472757216) * t + 0.89518356003149514744) * t + 1.31073912535196238583
+					);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_2_b_1(T x, T w, T t, int k) {
+				return sprout::math::detail::lgamma_impl_2_b_2(x, w, t - (static_cast<T>(k) - T(3.5)), k);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_2_b(T x, T w, T t) {
+				return sprout::math::detail::lgamma_impl_2_b_1(x, w, t, sprout::itrunc(t) + 4);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_2_a(T x, T w, int k) {
+				return sprout::math::detail::lgamma_impl_3(
+					x,
+					-sprout::log(
+						k == 0 ? ((((((((((
+								9.967270908702825e-5 * w + -1.9831672170162227e-4) * w
+								+ -0.00117085315349625822) * w + 0.00722012810948319552) * w + -0.0096221300936780297) * w
+								+ -0.04219772092994235254) * w + 0.16653861065243609743) * w + -0.04200263501129018037) * w
+								+ -0.65587807152061930091) * w + 0.57721566490153514421) * w + 0.99999999999999999764) * w
+							: ((((((((((
+								4.67209725901142e-5 * w + -6.812300803992063e-5) * w
+								+ -0.00132531159076610073) * w + 0.0073352117810720277) * w + -0.00968095666383935949) * w
+								+ -0.0421764281187354028) * w + 0.16653313644244428256) * w + -0.04200165481709274859) * w
+								+ -0.65587818792782740945) * w + 0.57721567315209190522) * w + 0.99999999973565236061) * w
+						)
+					);
+			}
+
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl_1(T x, T w) {
+				return w < T(0.5) ? sprout::math::detail::lgamma_impl_2_a(x, w, w < T(0.25) ? 0 : 1)
+					: w < T(3.5) ? sprout::math::detail::lgamma_impl_2_b(x, w, w - T(4.5) / (w + T(0.5)))
+					: w < T(8) ? sprout::math::detail::lgamma_impl_2_c(x, w, sprout::itrunc(w) - 3)
+					: sprout::math::detail::lgamma_impl_2_d(x, w, T(1) / w)
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			lgamma_impl(T x) {
+				return sprout::math::detail::lgamma_impl_1(x, x < 0 ? -x : x);
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			lgamma(FloatType x) {
+				typedef typename sprout::math::detail::float_compute<FloatType>::type type;
+				return x == 1 ? FloatType(0)
+					: x == 2 ? FloatType(0)
+					: x <= 0 && x == std::trunc(x) ? std::numeric_limits<FloatType>::infinity()
+					: x == -std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
+					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
+					: static_cast<FloatType>(sprout::math::detail::lgamma_impl(static_cast<type>(x)))
+					;
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			lgamma(IntType x) {
+				return sprout::math::detail::lgamma(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using NS_SPROUT_MATH_DETAIL::lgamma;
+	}	// namespace math
+
+	using sprout::math::lgamma;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_LGAMMA_HPP
diff --git a/sprout/math/llround.hpp b/sprout/math/llround.hpp
index 294be32b..4067e210 100644
--- a/sprout/math/llround.hpp
+++ b/sprout/math/llround.hpp
@@ -16,7 +16,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR long long
 			llround(FloatType x) {
-				return sprout::math::iround<long long>(x);
+				return sprout::iround<long long>(x);
 			}
 
 			template<
@@ -25,7 +25,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR long long
 			llround(IntType x) {
-				return sprout::math::iround<long long>(x);
+				return sprout::iround<long long>(x);
 			}
 		}	// namespace detail
 
diff --git a/sprout/math/log.hpp b/sprout/math/log.hpp
index 4309d08c..b9303520 100644
--- a/sprout/math/log.hpp
+++ b/sprout/math/log.hpp
@@ -30,7 +30,7 @@ namespace sprout {
 			log_impl(T x) {
 				return !(x > sprout::math::root_two<T>())
 					? sprout::math::detail::log_impl_1(x - 1, 1, sprout::math::factorial_limit<T>() + 1)
-					: 2 * sprout::math::detail::log_impl(sprout::math::sqrt(x))
+					: 2 * sprout::math::detail::log_impl(sprout::sqrt(x))
 					;
 			}
 
diff --git a/sprout/math/log10.hpp b/sprout/math/log10.hpp
index 819ab27f..4b5c4b3a 100644
--- a/sprout/math/log10.hpp
+++ b/sprout/math/log10.hpp
@@ -22,7 +22,7 @@ namespace sprout {
 					: x == 1 ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
 					: x < 0 ? std::numeric_limits<FloatType>::quiet_NaN()
-					: sprout::math::log(x) / sprout::math::ln_ten<FloatType>()
+					: sprout::log(x) / sprout::math::ln_ten<FloatType>()
 					;
 			}
 
diff --git a/sprout/math/log1p.hpp b/sprout/math/log1p.hpp
index c38525bc..0aaa29af 100644
--- a/sprout/math/log1p.hpp
+++ b/sprout/math/log1p.hpp
@@ -21,7 +21,7 @@ namespace sprout {
 					: x == -1 ? -std::numeric_limits<FloatType>::infinity()
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
 					: x < -1 ? std::numeric_limits<FloatType>::quiet_NaN()
-					: sprout::math::log(1 + x)
+					: sprout::log(1 + x)
 					;
 			}
 
diff --git a/sprout/math/log2.hpp b/sprout/math/log2.hpp
index 6524bce8..415f7080 100644
--- a/sprout/math/log2.hpp
+++ b/sprout/math/log2.hpp
@@ -22,7 +22,7 @@ namespace sprout {
 					: x == 1 ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
 					: x < 0 ? std::numeric_limits<FloatType>::quiet_NaN()
-					: sprout::math::log(x) / sprout::math::ln_two<FloatType>()
+					: sprout::log(x) / sprout::math::ln_two<FloatType>()
 					;
 			}
 
diff --git a/sprout/math/log_a.hpp b/sprout/math/log_a.hpp
index 8de92409..eb96165b 100644
--- a/sprout/math/log_a.hpp
+++ b/sprout/math/log_a.hpp
@@ -18,9 +18,9 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			log_a(FloatType x, FloatType y) {
-				return x == 2 ? sprout::math::log(y) / sprout::math::ln_two<FloatType>()
-					: x == 10 ? sprout::math::log(y) / sprout::math::ln_ten<FloatType>()
-					: sprout::math::log(y) / sprout::math::log(x)
+				return x == 2 ? sprout::log(y) / sprout::math::ln_two<FloatType>()
+					: x == 10 ? sprout::log(y) / sprout::math::ln_ten<FloatType>()
+					: sprout::log(y) / sprout::log(x)
 					;
 			}
 
diff --git a/sprout/math/logb.hpp b/sprout/math/logb.hpp
index a47619e4..0e42f30f 100644
--- a/sprout/math/logb.hpp
+++ b/sprout/math/logb.hpp
@@ -80,7 +80,7 @@ namespace sprout {
 			inline SPROUT_CONSTEXPR T
 			logb_impl(T x, 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
+					x, sprout::detail::pow_n(T(std::numeric_limits<T>::radix), sprout::itrunc<std::intmax_t>(exp)), exp
 					);
 			}
 
@@ -93,8 +93,8 @@ namespace sprout {
 				return x == 0 ? -std::numeric_limits<FloatType>::infinity()
 					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity()
 						? std::numeric_limits<FloatType>::infinity()
-					: x < 0 ? sprout::math::detail::logb_impl(-x, sprout::math::trunc(sprout::math::log_a(FloatType(std::numeric_limits<FloatType>::radix), -x)))
-					: sprout::math::detail::logb_impl(x, sprout::math::trunc(sprout::math::log_a(FloatType(std::numeric_limits<FloatType>::radix), x)))
+					: x < 0 ? sprout::math::detail::logb_impl(-x, sprout::trunc(sprout::log_a(FloatType(std::numeric_limits<FloatType>::radix), -x)))
+					: sprout::math::detail::logb_impl(x, sprout::trunc(sprout::log_a(FloatType(std::numeric_limits<FloatType>::radix), x)))
 					;
 			}
 
diff --git a/sprout/math/logb2.hpp b/sprout/math/logb2.hpp
index 2648c975..fd0f21e2 100644
--- a/sprout/math/logb2.hpp
+++ b/sprout/math/logb2.hpp
@@ -27,7 +27,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			logb2(FloatType x) {
-				return sprout::math::logb(x);
+				return sprout::logb(x);
 			}
 
 			template<
@@ -36,7 +36,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR double
 			logb2(IntType x) {
-				return sprout::math::logb(x);
+				return sprout::logb(x);
 			}
 #else
 			template<typename T>
@@ -104,7 +104,7 @@ namespace sprout {
 			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
+					x, sprout::detail::pow_n(T(2), sprout::itrunc<std::intmax_t>(exp)), exp
 					);
 			}
 
@@ -117,8 +117,8 @@ namespace sprout {
 				return x == 0 ? -std::numeric_limits<FloatType>::infinity()
 					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity()
 						? std::numeric_limits<FloatType>::infinity()
-					: 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)))
+					: x < 0 ? sprout::math::detail::logb2_impl(-x, sprout::trunc(sprout::log_a(FloatType(2), -x)))
+					: sprout::math::detail::logb2_impl(x, sprout::trunc(sprout::log_a(FloatType(2), x)))
 					;
 			}
 
diff --git a/sprout/math/lround.hpp b/sprout/math/lround.hpp
index 8cfb020c..559d3a49 100644
--- a/sprout/math/lround.hpp
+++ b/sprout/math/lround.hpp
@@ -16,7 +16,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR long
 			lround(FloatType x) {
-				return sprout::math::iround<long>(x);
+				return sprout::iround<long>(x);
 			}
 
 			template<
@@ -25,7 +25,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR long
 			lround(IntType x) {
-				return sprout::math::iround<long>(x);
+				return sprout::iround<long>(x);
 			}
 		}	// namespace detail
 
diff --git a/sprout/math/pow.hpp b/sprout/math/pow.hpp
index 415595ce..5ca85317 100644
--- a/sprout/math/pow.hpp
+++ b/sprout/math/pow.hpp
@@ -23,27 +23,27 @@ namespace sprout {
 				return x == 0
 						? y < 0 ? std::numeric_limits<FloatType>::infinity()
 						: y > 0 ? FloatType(0)
-						: sprout::math::exp(y * sprout::math::log(x))
+						: sprout::exp(y * sprout::log(x))
 					: x == -1 && (y == std::numeric_limits<FloatType>::infinity() || y == -std::numeric_limits<FloatType>::infinity()) ? FloatType(1)
 					: x == 1 ? FloatType(1)
 					: y == 0 ? FloatType(1)
 					: y == -std::numeric_limits<FloatType>::infinity()
 						? x < 1 && x > -1 ? std::numeric_limits<FloatType>::infinity()
 						: x > 1 || x < -1 ? FloatType(0)
-						: sprout::math::exp(y * sprout::math::log(x))
+						: sprout::exp(y * sprout::log(x))
 					: y == std::numeric_limits<FloatType>::infinity()
 						? x < 1 && x > -1 ? FloatType(0)
 						: x > 1 || x < -1 ? std::numeric_limits<FloatType>::infinity()
-						: sprout::math::exp(y * sprout::math::log(x))
+						: sprout::exp(y * sprout::log(x))
 					: x == -std::numeric_limits<FloatType>::infinity()
 						? y < 0 ? FloatType(0)
 						: y > 0 ? std::numeric_limits<FloatType>::infinity()
-						: sprout::math::exp(y * sprout::math::log(x))
+						: sprout::exp(y * sprout::log(x))
 					: x == std::numeric_limits<FloatType>::infinity()
 						? y < 0 ? FloatType(0)
 						: y > 0 ? std::numeric_limits<FloatType>::infinity()
-						: sprout::math::exp(y * sprout::math::log(x))
-					: sprout::math::exp(y * sprout::math::log(x))
+						: sprout::exp(y * sprout::log(x))
+					: sprout::exp(y * sprout::log(x))
 					;
 			}
 
diff --git a/sprout/math/quotient.hpp b/sprout/math/quotient.hpp
index 8fb8db54..5f2ae673 100644
--- a/sprout/math/quotient.hpp
+++ b/sprout/math/quotient.hpp
@@ -24,7 +24,7 @@ namespace sprout {
 						? std::numeric_limits<FloatType>::quiet_NaN()
 					: x == 0 ? FloatType(0)
 					: y == std::numeric_limits<FloatType>::infinity() || y == -std::numeric_limits<FloatType>::infinity() ? FloatType(0)
-					: sprout::math::iround<R>(x / y)
+					: sprout::iround<R>(x / y)
 					;
 			}
 
diff --git a/sprout/math/rem_quo.hpp b/sprout/math/rem_quo.hpp
index 37691d40..0fee35de 100644
--- a/sprout/math/rem_quo.hpp
+++ b/sprout/math/rem_quo.hpp
@@ -32,7 +32,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR sprout::pair<FloatType, R>
 			rem_quo(FloatType x, FloatType y) {
-				return sprout::math::detail::rem_quo_impl(x, y, sprout::math::quotient(x, y));
+				return sprout::math::detail::rem_quo_impl(x, y, sprout::quotient(x, y));
 			}
 
 			template<
diff --git a/sprout/math/remainder.hpp b/sprout/math/remainder.hpp
index af4fd035..9fbbd8ca 100644
--- a/sprout/math/remainder.hpp
+++ b/sprout/math/remainder.hpp
@@ -23,7 +23,7 @@ namespace sprout {
 						? std::numeric_limits<FloatType>::quiet_NaN()
 					: x == 0 ? FloatType(0)
 					: y == std::numeric_limits<FloatType>::infinity() || y == -std::numeric_limits<FloatType>::infinity() ? x
-					: x - sprout::math::round(x / y) * y
+					: x - sprout::round(x / y) * y
 					;
 			}
 
diff --git a/sprout/math/sin.hpp b/sprout/math/sin.hpp
index 9f5003ad..6bfbcdf5 100644
--- a/sprout/math/sin.hpp
+++ b/sprout/math/sin.hpp
@@ -21,7 +21,7 @@ namespace sprout {
 				return x == 0 ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity()
 						? std::numeric_limits<FloatType>::quiet_NaN()
-					: -sprout::math::cos(x + sprout::math::half_pi<FloatType>())
+					: -sprout::cos(x + sprout::math::half_pi<FloatType>())
 					;
 			}
 
diff --git a/sprout/math/tan.hpp b/sprout/math/tan.hpp
index c23bcd4a..f744e6a7 100644
--- a/sprout/math/tan.hpp
+++ b/sprout/math/tan.hpp
@@ -21,7 +21,7 @@ namespace sprout {
 				return x == 0 ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity()
 						? std::numeric_limits<FloatType>::quiet_NaN()
-					: sprout::math::sin(x) / sprout::math::cos(x)
+					: sprout::sin(x) / sprout::cos(x)
 					;
 			}
 
diff --git a/sprout/math/tanh.hpp b/sprout/math/tanh.hpp
index 007b2225..238cc3f8 100644
--- a/sprout/math/tanh.hpp
+++ b/sprout/math/tanh.hpp
@@ -21,7 +21,7 @@ namespace sprout {
 				return x == 0 ? FloatType(0)
 					: x == std::numeric_limits<FloatType>::infinity() ? FloatType(1)
 					: x == -std::numeric_limits<FloatType>::infinity() ? FloatType(-1)
-					: sprout::math::sinh(x) / sprout::math::cosh(x)
+					: sprout::sinh(x) / sprout::cosh(x)
 					;
 			}
 
diff --git a/sprout/math/tgamma.hpp b/sprout/math/tgamma.hpp
index f45274cd..7da7d0f9 100644
--- a/sprout/math/tgamma.hpp
+++ b/sprout/math/tgamma.hpp
@@ -68,27 +68,19 @@ namespace sprout {
 			}
 			template<typename T>
 			inline SPROUT_CONSTEXPR T
-			tgamma_impl_2_pos(T x, T y, T t) {
+			tgamma_impl_2_pos_rec(T x, T y, T t) {
 				return t == 0 ? std::numeric_limits<T>::infinity()
 					: (x - T(1)) / y / t
 					;
 			}
 			template<typename T>
 			inline SPROUT_CONSTEXPR T
-			tgamma_impl_2_neg(T x, T y, T t) {
-				return t == 0 ? T(0)
-					: T(1) / y * t
-					;
-			}
-			template<typename T>
-			inline SPROUT_CONSTEXPR T
 			tgamma_impl_1(T x, int n) {
 				return n == 1 ? (x - T(1)) / sprout::math::detail::tgamma_impl_y(x - (n + 2))
 					: n == 0 ? T(1) / sprout::math::detail::tgamma_impl_y(x - (n + 2))
 					: n == static_cast<int>(sprout::math::factorial_limit<T>())
-						? sprout::math::detail::tgamma_impl_2_pos(x, sprout::math::detail::tgamma_impl_y(x - (n + 2)), sprout::math::detail::tgamma_impl_t_pos_rec(x, 2, n + 1))
+						? sprout::math::detail::tgamma_impl_2_pos_rec(x, sprout::math::detail::tgamma_impl_y(x - (n + 2)), sprout::math::detail::tgamma_impl_t_pos_rec(x, 2, n + 1))
 					: n == -static_cast<int>(sprout::math::factorial_limit<T>())
-//						? sprout::math::detail::tgamma_impl_2_neg(x, sprout::math::detail::tgamma_impl_y(x - (n + 2)), sprout::math::detail::tgamma_impl_t_neg_rec(x, 0, -n))
 						? T(1) / sprout::math::detail::tgamma_impl_y(x - (n + 2)) * sprout::math::detail::tgamma_impl_t_neg_rec(x, 0, -n)
 					: n > 1 ? (x - T(1)) / sprout::math::detail::tgamma_impl_y(x - (n + 2)) * sprout::math::detail::tgamma_impl_t_pos(x, 2, n + 1)
 					: T(1) / sprout::math::detail::tgamma_impl_y(x - (n + 2)) / sprout::math::detail::tgamma_impl_t_neg(x, 0, -n)
@@ -100,7 +92,7 @@ namespace sprout {
 				return sprout::math::detail::tgamma_impl_1(
 					x,
 					sprout::clamp(
-						sprout::math::iround(x - T(2)),
+						sprout::iround(x - T(2)),
 						-static_cast<int>(sprout::math::factorial_limit<T>()),
 						static_cast<int>(sprout::math::factorial_limit<T>())
 						)
diff --git a/sprout/rational/arithmetic.hpp b/sprout/rational/arithmetic.hpp
index e03397e7..b4f84bbe 100644
--- a/sprout/rational/arithmetic.hpp
+++ b/sprout/rational/arithmetic.hpp
@@ -53,7 +53,7 @@ namespace sprout {
 		{
 			return rational_add_impl_3(
 				rhs,
-				sprout::math::gcd(num, g), den, num
+				sprout::gcd(num, g), den, num
 				);
 		}
 		template<typename IntType>
@@ -86,7 +86,7 @@ namespace sprout {
 	operator+(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
 		return sprout::detail::rational_add_impl(
 			lhs, rhs,
-			sprout::math::gcd(lhs.denominator(), rhs.denominator())
+			sprout::gcd(lhs.denominator(), rhs.denominator())
 			);
 	}
 	template<typename IntType>
@@ -122,7 +122,7 @@ namespace sprout {
 		{
 			return rational_sub_impl_3(
 				rhs,
-				sprout::math::gcd(num, g), den, num
+				sprout::gcd(num, g), den, num
 				);
 		}
 		template<typename IntType>
@@ -155,7 +155,7 @@ namespace sprout {
 	operator-(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
 		return sprout::detail::rational_sub_impl(
 			lhs, rhs,
-			sprout::math::gcd(lhs.denominator(), rhs.denominator())
+			sprout::gcd(lhs.denominator(), rhs.denominator())
 			);
 	}
 	template<typename IntType>
@@ -189,8 +189,8 @@ namespace sprout {
 	operator*(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
 		return sprout::detail::rational_mul_impl(
 			lhs, rhs,
-			sprout::math::gcd(lhs.numerator(), rhs.denominator()),
-			sprout::math::gcd(rhs.numerator(), lhs.denominator())
+			sprout::gcd(lhs.numerator(), rhs.denominator()),
+			sprout::gcd(rhs.numerator(), lhs.denominator())
 			);
 	}
 	template<typename IntType>
@@ -238,8 +238,8 @@ namespace sprout {
 			: lhs.numerator() == IntType(0) ? lhs
 			: sprout::detail::rational_div_impl(
 				lhs, rhs,
-				sprout::math::gcd(lhs.numerator(), rhs.numerator()),
-				sprout::math::gcd(rhs.denominator(), lhs.denominator())
+				sprout::gcd(lhs.numerator(), rhs.numerator()),
+				sprout::gcd(rhs.denominator(), lhs.denominator())
 				)
 			;
 	}
diff --git a/sprout/rational/rational.hpp b/sprout/rational/rational.hpp
index ddbb968f..a5e0dff1 100644
--- a/sprout/rational/rational.hpp
+++ b/sprout/rational/rational.hpp
@@ -71,7 +71,7 @@ namespace sprout {
 		static SPROUT_CONSTEXPR IntType normalize_g(IntType num, IntType den) {
 			return den == 0 ? throw sprout::bad_rational()
 				: num == 0 ? den
-				: normalize_g_1(den, sprout::math::gcd(num, den))
+				: normalize_g_1(den, sprout::gcd(num, den))
 				;
 		}
 	private:
@@ -111,26 +111,26 @@ namespace sprout {
 		}
 
 		rational& operator+=(rational const& rhs) {
-			IntType g = sprout::math::gcd(den_, rhs.den_);
+			IntType g = sprout::gcd(den_, rhs.den_);
 			den_ /= g;
 			num_ = num_ * (rhs.den_ / g) + rhs.num_ * den_;
-			g = sprout::math::gcd(num_, g);
+			g = sprout::gcd(num_, g);
 			num_ /= g;
 			den_ *= rhs.den_ / g;
 			return *this;
 		}
 		rational& operator-=(rational const& rhs) {
-			IntType g = sprout::math::gcd(den_, rhs.den_);
+			IntType g = sprout::gcd(den_, rhs.den_);
 			den_ /= g;
 			num_ = num_ * (rhs.den_ / g) - rhs.num_ * den_;
-			g = sprout::math::gcd(num_, g);
+			g = sprout::gcd(num_, g);
 			num_ /= g;
 			den_ *= rhs.den_ / g;
 			return *this;
 		}
 		rational& operator*=(rational const& rhs) {
-			IntType gcd1 = sprout::math::gcd(num_, rhs.den_);
-			IntType gcd2 = sprout::math::gcd(rhs.num_, den_);
+			IntType gcd1 = sprout::gcd(num_, rhs.den_);
+			IntType gcd2 = sprout::gcd(rhs.num_, den_);
 			num_ =(num_ / gcd1) * (rhs.num_ / gcd2);
 			den_ =(den_ / gcd2) * (rhs.den_ / gcd1);
 			return *this;
@@ -142,8 +142,8 @@ namespace sprout {
 			if (num_ == IntType(0)) {
 				return *this;
 			}
-			IntType gcd1 = sprout::math::gcd(num_, rhs.num_);
-			IntType gcd2 = sprout::math::gcd(rhs.den_, den_);
+			IntType gcd1 = sprout::gcd(num_, rhs.num_);
+			IntType gcd2 = sprout::gcd(rhs.den_, den_);
 			num_ =(num_ / gcd1) * (rhs.den_ / gcd2);
 			den_ =(den_ / gcd2) * (rhs.num_ / gcd1);
 			if (den_ < IntType(0)) {