fix math functions

sprout/math/fdim.hpp

@@ -1,9 +1,11 @@
 #ifndef SPROUT_MATH_FDIM_HPP
 #define SPROUT_MATH_FDIM_HPP
 
+#include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
+#include <sprout/math/isnan.hpp>
 #include <sprout/type_traits/float_promote.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
 
@@ -16,9 +18,19 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			fdim(FloatType x, FloatType y) {
-				return x > y ? x - y : 0;
+				return sprout::math::isnan(y) ? y
+					: sprout::math::isnan(x) ? x
+					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
+					: x == -std::numeric_limits<FloatType>::infinity() ? FloatType(0)
+					: y == std::numeric_limits<FloatType>::infinity() ? FloatType(0)
+					: y == -std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+					: std::fdim(x, y)
+#else
+					: x > y ? x - y : FloatType(0)
+#endif
+					;
 			}
-
 			template<
 				typename ArithmeticType1,
 				typename ArithmeticType2,
@@ -33,7 +45,7 @@ namespace sprout {
 			}
 		}	// namespace detail
 
-		using NS_SPROUT_MATH_DETAIL::fdim;
+		using sprout::math::detail::fdim;
 	}	// namespace math
 
 	using sprout::math::fdim;

sprout/math/fma.hpp

@@ -1,9 +1,13 @@
 #ifndef SPROUT_MATH_FMA_HPP
 #define SPROUT_MATH_FMA_HPP
 
+#include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
+#include <sprout/math/isnan.hpp>
+#include <sprout/math/isinf.hpp>
+#include <sprout/math/signbit.hpp>
 #include <sprout/type_traits/float_promote.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
 
@@ -16,9 +20,20 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			fma(FloatType x, FloatType y, FloatType z) {
-				return x * y + z;
+				return sprout::math::isnan(x) ? x
+					: sprout::math::isnan(y) ? y
+					: sprout::math::isnan(z) ? z
+					: sprout::math::isinf(x) && y == 0 ? std::numeric_limits<FloatType>::quiet_NaN()
+					: sprout::math::isinf(y) && x == 0 ? std::numeric_limits<FloatType>::quiet_NaN()
+					: (sprout::math::isinf(x) || sprout::math::isinf(y)) && sprout::math::isinf(z) && (sprout::math::signbit(x) ^ sprout::math::signbit(y) ^ sprout::math::signbit(z))
+						? std::numeric_limits<FloatType>::quiet_NaN()
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+					: std::fma(x, y, z)
+#else
+					: x * y + z
+#endif
+					;
 			}
-
 			template<
 				typename ArithmeticType1,
 				typename ArithmeticType2,
@@ -40,7 +55,7 @@ namespace sprout {
 			}
 		}	// namespace detail
 
-		using NS_SPROUT_MATH_DETAIL::fma;
+		using sprout::math::detail::fma;
 	}	// namespace math
 
 	using sprout::math::fma;

sprout/math/fmax.hpp

@@ -1,6 +1,7 @@
 #ifndef SPROUT_MATH_FMAX_HPP
 #define SPROUT_MATH_FMAX_HPP
 
+#include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
@@ -17,7 +18,19 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			fmax(FloatType x, FloatType y) {
-				return x < y && !sprout::math::isnan(y) ? y : x;
+				return sprout::math::isnan(y) ? x
+					: sprout::math::isnan(x) ? y
+					: y == -std::numeric_limits<FloatType>::infinity() ? x
+					: x == std::numeric_limits<FloatType>::infinity() ? x
+					: x == -std::numeric_limits<FloatType>::infinity() ? y
+					: y == std::numeric_limits<FloatType>::infinity() ? y
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+					: x == 0 && y == 0 ? x
+					: std::fmax(x, y)
+#else
+					: x < y ? y : x
+#endif
+					;
 			}
 			template<
 				typename ArithmeticType1,
@@ -33,7 +46,7 @@ namespace sprout {
 			}
 		}	// namespace detail
 
-		using NS_SPROUT_MATH_DETAIL::fmax;
+		using sprout::math::detail::fmax;
 	}	// namespace math
 
 	using sprout::math::fmax;

sprout/math/fmin.hpp

@@ -1,6 +1,7 @@
 #ifndef SPROUT_MATH_FMIN_HPP
 #define SPROUT_MATH_FMIN_HPP
 
+#include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
@@ -17,7 +18,19 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			fmin(FloatType x, FloatType y) {
-				return y < x && !sprout::math::isnan(y) ? y : x;
+				return sprout::math::isnan(y) ? x
+					: sprout::math::isnan(x) ? y
+					: x == -std::numeric_limits<FloatType>::infinity() ? x
+					: y == std::numeric_limits<FloatType>::infinity() ? x
+					: y == -std::numeric_limits<FloatType>::infinity() ? y
+					: x == std::numeric_limits<FloatType>::infinity() ? y
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+					: x == 0 && y == 0 ? x
+					: std::fmin(x, y)
+#else
+					: y < x ? y : x
+#endif
+					;
 			}
 			template<
 				typename ArithmeticType1,
@@ -33,7 +46,7 @@ namespace sprout {
 			}
 		}	// namespace detail
 
-		using NS_SPROUT_MATH_DETAIL::fmin;
+		using sprout::math::detail::fmin;
 	}	// namespace math
 
 	using sprout::math::fmin;

sprout/math/fmod.hpp

@@ -77,9 +77,9 @@ namespace sprout {
 								: std::numeric_limits<FloatType>::quiet_NaN()
 							: y
 					: sprout::math::isnan(x) ? x
-					: x == 0 && y != 0 ? x
 					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity() || y == 0
 						? -std::numeric_limits<FloatType>::quiet_NaN()
+					: x == 0 ? x
 					: y == std::numeric_limits<FloatType>::infinity() || y == -std::numeric_limits<FloatType>::infinity() ? x
 					: static_cast<FloatType>(sprout::math::detail::fmod_impl(
 						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(x),

sprout/math/greater_equal.hpp

@@ -17,7 +17,7 @@ namespace sprout {
 				>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR bool
-			greater_equal_equal(FloatType1 x, FloatType2 y) {
+			greater_equal(FloatType1 x, FloatType2 y) {
 				return sprout::math::equal_to(x, y) || x > y;
 			}
 
@@ -62,7 +62,7 @@ namespace sprout {
 			}
 		}	// namespace detail
 		//
-		// greater_equal_equal
+		// greater_equal
 		//
 		template<
 			typename T, typename U,

sprout/math/iceil.hpp

@@ -12,7 +12,7 @@
 #if SPROUT_USE_BUILTIN_CMATH_FUNCTION
 #	include <sprout/math/ceil.hpp>
 #else
-#	include <sprout/math/equal_to.hpp>
+#	include <sprout/math/less_equal.hpp>
 #endif
 
 namespace sprout {
@@ -42,7 +42,7 @@ namespace sprout {
 			template<typename To, typename FloatType>
 			inline SPROUT_CONSTEXPR To
 			iceil_impl(FloatType x, To x0) {
-				return sprout::math::equal_to(x, x0) ? x0
+				return sprout::math::less_equal(x, x0) ? x0
 					: x0 + 1
 					;
 			}

sprout/math/ifloor.hpp

@@ -12,7 +12,7 @@
 #if SPROUT_USE_BUILTIN_CMATH_FUNCTION
 #	include <sprout/math/floor.hpp>
 #else
-#	include <sprout/math/equal_to.hpp>
+#	include <sprout/math/greater_equal.hpp>
 #endif
 
 namespace sprout {
@@ -42,7 +42,7 @@ namespace sprout {
 			template<typename To, typename FloatType>
 			inline SPROUT_CONSTEXPR To
 			ifloor_impl(FloatType x, To x0) {
-				return sprout::math::equal_to(x, x0) ? x0
+				return sprout::math::greater_equal(x, x0) ? x0
 					: x0 - 1
 					;
 			}

sprout/math/less_equal.hpp

@@ -18,7 +18,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR bool
 			less_equal(FloatType1 x, FloatType2 y) {
-				return sprout::math::not_equal_to(x, y) || x < y;
+				return sprout::math::equal_to(x, y) || x < y;
 			}
 
 			template<

sprout/math/minmax.hpp

@@ -2,8 +2,8 @@
 #define SPROUT_MATH_MINMAX_HPP
 
 #include <sprout/config.hpp>
+#include <sprout/math/fdim.hpp>
 #include <sprout/math/fmax.hpp>
 #include <sprout/math/fmin.hpp>
-#include <sprout/math/fdim.hpp>
 
 #endif	// #ifndef SPROUT_MATH_MINMAX_HPP

sprout/math/quotient.hpp

@@ -3,25 +3,17 @@
 
 #include <limits>
 #include <type_traits>
-#include <stdexcept>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
-#include <sprout/math/detail/float_compute.hpp>
 #include <sprout/math/isnan.hpp>
 #include <sprout/math/signbit.hpp>
-#include <sprout/math/iround.hpp>
+#include <sprout/math/rem_quo.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
 #include <sprout/type_traits/float_promote.hpp>
 
 namespace sprout {
 	namespace math {
 		namespace detail {
-			template<typename R, typename T>
-			inline SPROUT_CONSTEXPR T
-			quotient_impl(T x, T y) {
-				return sprout::math::iround<R>(x / y);
-			}
-
 			template<
 				typename R = int,
 				typename FloatType,
@@ -29,15 +21,13 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR R
 			quotient(FloatType x, FloatType y) {
-				return sprout::math::isnan(y) || sprout::math::isnan(x) ? R(0)
+				return y == 0 ? R(0)
-					: x == 0 && y != 0 ? R(0)
+					: sprout::math::isnan(y) || sprout::math::isnan(x) ? R(0)
-					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity() || y == 0
+					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity()
 						? R(0)
+					: x == 0 ? R(0)
 					: y == std::numeric_limits<FloatType>::infinity() || y == -std::numeric_limits<FloatType>::infinity() ? R(0)
-					: static_cast<FloatType>(sprout::math::detail::quotient_impl<R>(
+					: sprout::math::rem_quo<R>(x, y).second
-						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(x),
-						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(y)
-						))
 					;
 			}
 			template<

sprout/math/rem_quo.hpp

@@ -3,13 +3,14 @@
 
 #include <limits>
 #include <type_traits>
-#include <stdexcept>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
 #include <sprout/math/detail/float_compute.hpp>
 #include <sprout/math/isnan.hpp>
 #include <sprout/math/signbit.hpp>
-#include <sprout/math/quotient.hpp>
+#include <sprout/math/fabs.hpp>
+#include <sprout/math/ilogb.hpp>
+#include <sprout/math/scalbn.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
 #include <sprout/type_traits/float_promote.hpp>
 #include <sprout/utility/pair/pair.hpp>
@@ -26,9 +27,58 @@ namespace sprout {
 
 			template<typename R, typename T>
 			inline SPROUT_CONSTEXPR sprout::pair<T, R>
-			rem_quo_impl(T x, T y, R quo) {
+			rem_quo_impl_7(T x, T y, int k, R iquo, T x1, T z) {
 				typedef sprout::pair<T, R> type;
-				return type(x - quo * y, quo);
+				return (z > y) || ((z == y) && ((iquo & 1) != 0))
+					? x < 0 ? type(-(x1 - y), ((iquo + 1) & 0x7) * k) : type(x1 - y, ((iquo + 1) & 0x7) * k)
+					: x < 0 ? type(-x1, (iquo & 0x7) * k) : type(x1, (iquo & 0x7) * k)
+					;
+			}
+			template<typename R, typename T>
+			inline SPROUT_CONSTEXPR sprout::pair<T, R>
+			rem_quo_impl_6(T x, T y, int k, R iquo, T x1) {
+				return x1 >= y
+					? sprout::math::detail::rem_quo_impl_7(x, y, k, iquo + 1, x1 - y, (x1 - y) + (x1 - y))
+					: sprout::math::detail::rem_quo_impl_7(x, y, k, iquo, x1, x1 + x1)
+					;
+			}
+			template<typename R, typename T>
+			inline SPROUT_CONSTEXPR sprout::pair<T, R>
+			rem_quo_impl_5(T x, T y, int k, R iquo, T x1, T y1, T z, int iscy, int idiff, int i) {
+				return i != idiff
+					? z >= 0
+						? sprout::math::detail::rem_quo_impl_5(x, y, k, iquo + iquo + 2, z + z, y1, z + z - y1, iscy, idiff, i + 1)
+						: sprout::math::detail::rem_quo_impl_5(x, y, k, iquo + iquo, x1 + x1, y1, x1 + x1 - y1, iscy, idiff, i + 1)
+					: sprout::math::detail::rem_quo_impl_6(x, y, k, iquo, sprout::math::scalbn(x1, iscy))
+					;
+			}
+			template<typename R, typename T>
+			inline SPROUT_CONSTEXPR sprout::pair<T, R>
+			rem_quo_impl_4(T x, T y, int k, R iquo, T x1, T y1, int iscy, int idiff, int i) {
+				return sprout::math::detail::rem_quo_impl_5(x, y, k, iquo, x1, y1, x1 - y1, iscy, idiff, i);
+			}
+			template<typename R, typename T>
+			inline SPROUT_CONSTEXPR sprout::pair<T, R>
+			rem_quo_impl_3(T x, T y, int k, R iquo, T x1, int iscx, int iscy, int idiff) {
+				return idiff < 0 ? sprout::math::detail::rem_quo_impl_7(x, y, k, iquo, x1, x1 + x1)
+					: idiff ? sprout::math::detail::rem_quo_impl_4(x, y, k, iquo, sprout::math::scalbn(x1, -iscx), sprout::math::scalbn(y, -iscy), iscy, idiff, 0)
+					: sprout::math::detail::rem_quo_impl_6(x, y, k, iquo, x1)
+					;
+			}
+			template<typename R, typename T>
+			inline SPROUT_CONSTEXPR sprout::pair<T, R>
+			rem_quo_impl_2(T x, T y, int k, R iquo, T x1, int iscx, int iscy) {
+				return sprout::math::detail::rem_quo_impl_3(x, y, k, iquo, x1, iscx, iscy, iscx - iscy);
+			}
+			template<typename R, typename T>
+			inline SPROUT_CONSTEXPR sprout::pair<T, R>
+			rem_quo_impl_1(T x, T y, int k, R iquo, T x1) {
+				return sprout::math::detail::rem_quo_impl_2(x, y, k, iquo, x1, sprout::math::ilogb(x1), sprout::math::ilogb(y));
+			}
+			template<typename R, typename T>
+			inline SPROUT_CONSTEXPR sprout::pair<T, R>
+			rem_quo_impl(T x, T y, R iquo) {
+				return sprout::math::detail::rem_quo_impl_1(x, sprout::math::fabs(y), (sprout::math::signbit(x) ^ sprout::math::signbit(y) ? -1 : 1), iquo, sprout::math::fabs(x));
 			}
 
 			template<
@@ -39,19 +89,20 @@ namespace sprout {
 			inline SPROUT_CONSTEXPR sprout::pair<FloatType, R>
 			rem_quo(FloatType x, FloatType y) {
 				typedef sprout::pair<FloatType, R> type;
-				return sprout::math::isnan(y)
+				return y == 0 ? type(-std::numeric_limits<FloatType>::quiet_NaN(), R(0))
+					: sprout::math::isnan(y)
 						? sprout::math::isnan(x)
-							? sprout::math::signbit(y) || sprout::math::signbit(x) ? type(-std::numeric_limits<FloatType>::quiet_NaN(), R(0))
+							? type(sprout::math::signbit(y) && sprout::math::signbit(x) ? -std::numeric_limits<FloatType>::quiet_NaN() : std::numeric_limits<FloatType>::quiet_NaN(), R(0))
-								: type(std::numeric_limits<FloatType>::quiet_NaN(), R(0))
 							: type(y, R(0))
-					: x == 0 && y != 0 ? type(FloatType(0), R(0))
+					: sprout::math::isnan(x) ? type(x, R(0))
-					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity() || y == 0
+					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity()
-						? type(std::numeric_limits<FloatType>::quiet_NaN(), R(0))
+						? type(-std::numeric_limits<FloatType>::quiet_NaN(), R(0))
+					: x == 0 ? type(x, R(0))
 					: y == std::numeric_limits<FloatType>::infinity() || y == -std::numeric_limits<FloatType>::infinity() ? type(x, R(0))
 					: sprout::math::detail::rem_quo_ret<R, FloatType>(sprout::math::detail::rem_quo_impl(
 						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(x),
 						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(y),
-						sprout::math::quotient<R>(x, y)
+						R(0)
 						))
 					;
 			}
@@ -72,7 +123,11 @@ namespace sprout {
 				return sprout::math::detail::rem_quo(static_cast<type>(x), static_cast<type>(y));
 			}
 		}	// namespace detail
-
+		//
+		// issue:
+		//	rem_quo(-NaN, -NaN) returns {-NaN, _} .
+		//		# returns {+NaN, _} . ( same as rem_quo(+NaN, +NaN) )
+		//
 		using sprout::math::detail::rem_quo;
 	}	// namespace math
 

sprout/math/remainder.hpp

@@ -3,48 +3,38 @@
 
 #include <limits>
 #include <type_traits>
-#include <stdexcept>
 #include <sprout/config.hpp>
 #include <sprout/math/detail/config.hpp>
-#include <sprout/math/detail/float_compute.hpp>
 #include <sprout/math/isnan.hpp>
 #include <sprout/math/signbit.hpp>
-#include <sprout/math/round.hpp>
+#include <sprout/math/rem_quo.hpp>
 #include <sprout/type_traits/enabler_if.hpp>
 #include <sprout/type_traits/float_promote.hpp>
 
 namespace sprout {
 	namespace math {
 		namespace detail {
-			template<typename T>
-			inline SPROUT_CONSTEXPR T
-			remainder_impl(T x, T y) {
-				return x - sprout::math::round(x / y) * y;
-			}
-
 			template<
 				typename FloatType,
 				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			remainder(FloatType x, FloatType y) {
-				return sprout::math::isnan(y)
+				return y == 0 ? -std::numeric_limits<FloatType>::quiet_NaN()
+					: sprout::math::isnan(y)
 						? sprout::math::isnan(x)
-							? sprout::math::signbit(y) || sprout::math::signbit(x) ? -std::numeric_limits<FloatType>::quiet_NaN()
+							? sprout::math::signbit(y) && sprout::math::signbit(x) ? -std::numeric_limits<FloatType>::quiet_NaN()
 								: std::numeric_limits<FloatType>::quiet_NaN()
 							: y
 					: sprout::math::isnan(x) ? x
-					: x == 0 && y != 0 ? x
+					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity()
-					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity() || y == 0
+						? -std::numeric_limits<FloatType>::quiet_NaN()
-						? std::numeric_limits<FloatType>::quiet_NaN()
+					: x == 0 ? x
 					: y == std::numeric_limits<FloatType>::infinity() || y == -std::numeric_limits<FloatType>::infinity() ? x
 #if SPROUT_USE_BUILTIN_CMATH_FUNCTION
 					: std::remainder(x, y)
 #else
-					: static_cast<FloatType>(sprout::math::detail::remainder_impl(
+					: sprout::math::rem_quo(x, y).first
-						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(x),
-						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(y)
-						))
 #endif
 					;
 			}
@@ -61,8 +51,12 @@ namespace sprout {
 				return sprout::math::detail::remainder(static_cast<type>(x), static_cast<type>(y));
 			}
 		}	// namespace detail
-
+		//
-		using NS_SPROUT_MATH_DETAIL::remainder;
+		// issue:
+		//	remainder(-NaN, -NaN) returns -NaN .
+		//		# returns +NaN . ( same as remainder(+NaN, +NaN) )
+		//
+		using sprout::math::detail::remainder;
 	}	// namespace math
 
 	using sprout::math::remainder;