fix complex norm

sprout/complex/atanh.hpp

@@ -17,11 +17,10 @@
 #include <sprout/math/log.hpp>
 #include <sprout/math/atan2.hpp>
 #include <sprout/complex/complex.hpp>
+#include <sprout/complex/operators.hpp>
 #include <sprout/complex/log.hpp>
 #include <sprout/complex/sqrt.hpp>
 
-#include <sprout/complex/operators.hpp>
-
 namespace sprout {
 	//
 	// atanh
@@ -40,25 +39,6 @@ namespace sprout {
 	// catanh(NaN + i<>‡) returns <20>}0 + ip /2 (where the sign of the real part of the result is unspecified).
 	// catanh(NaN + iNaN) returns NaN + iNaN.
 	//
-	namespace detail {
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::complex<T>
-		atanh_impl_1(sprout::complex<T> const& x, T const& i2, T const& z, T const& num, T const& den) {
-			return sprout::complex<T>(
-				sprout::math::quarter<T>() * (sprout::math::log(i2 + num * num) - sprout::math::log(i2 + den * den)),
-				sprout::math::half<T>() * sprout::math::atan2(T(2) * x.imag(), z)
-				);
-		}
-		template<typename T>
-		inline SPROUT_CONSTEXPR sprout::complex<T>
-		atanh_impl(sprout::complex<T> const& x, T const& i2) {
-			return sprout::detail::atanh_impl_1(
-				x, i2,
-				T(1) - i2 - x.real() * x.real(),
-				T(1) + x.imag(), T(1) - x.imag()
-				);
-		}
-	}	// namespace detail
 	template<typename T>
 	inline SPROUT_CONSTEXPR sprout::complex<T>
 	atanh(sprout::complex<T> const& x) {
@@ -75,7 +55,6 @@ namespace sprout {
 				? type(sprout::math::copysign(T(0), x.real()), sprout::math::copysign(sprout::math::half_pi<T>(), x.imag()))
 			: x.real() == 0 && x.imag() == 0 ? x
 			: (x.real() == 1 || x.real() == -1) && x.imag() == 0 ? type(sprout::math::copysign(sprout::numeric_limits<T>::infinity(), x.real()), x.imag())
-//			: sprout::detail::atanh_impl(x, x.imag() * x.imag())
 			: (sprout::log(T(1) + x) - sprout::log(T(1) - x)) / T(2)
 			;
 	}

sprout/complex/norm.hpp

@@ -10,9 +10,11 @@
 
 #include <type_traits>
 #include <sprout/config.hpp>
-#include <sprout/complex/complex.hpp>
 #include <sprout/type_traits/float_promote.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
+#include <sprout/math/isnan.hpp>
+#include <sprout/math/isinf.hpp>
+#include <sprout/complex/complex.hpp>
 
 namespace sprout {
 	//
@@ -21,7 +23,11 @@ namespace sprout {
 	template<typename T>
 	inline SPROUT_CONSTEXPR T
 	norm(sprout::complex<T> const& x) {
-		return x.real() * x.real() + x.imag() * x.imag();
+		return sprout::math::isinf(x.imag()) || sprout::math::isinf(x.real()) ? sprout::numeric_limits<T>::infinity()
+			: sprout::math::isnan(x.real()) ? x.real()
+			: sprout::math::isnan(x.imag()) ? x.imag()
+			: x.real() * x.real() + x.imag() * x.imag()
+			;
 	}
 	template<
 		typename ArithmeticType,
@@ -30,7 +36,10 @@ namespace sprout {
 	inline SPROUT_CONSTEXPR typename sprout::float_promote<ArithmeticType>::type
 	norm(ArithmeticType x) {
 		typedef typename sprout::float_promote<ArithmeticType>::type type;
-		return type(x) * type(x);
+		return sprout::math::isinf(x) ? sprout::numeric_limits<type>::infinity()
+			: sprout::math::isnan(x) ? type(x)
+			: type(x) * type(x)
+			;
 	}
 }	// namespace sprout