From 3498e9214fabc20ad1bec9c1841a2be801c209d6 Mon Sep 17 00:00:00 2001
From: bolero-MURAKAMI <bolero.murakami@gmail.com>
Date: Tue, 7 May 2013 13:40:18 +0900
Subject: [PATCH] fix fmod

---
 sprout/math/fmod.hpp      | 57 +++++++++++++++++++++++++++++++++++----
 sprout/math/quotient.hpp  | 24 ++++++++++++-----
 sprout/math/rem_quo.hpp   | 36 +++++++++++++++++++------
 sprout/math/remainder.hpp | 29 +++++++++++++++++---
 4 files changed, 123 insertions(+), 23 deletions(-)

diff --git a/sprout/math/fmod.hpp b/sprout/math/fmod.hpp
index b5cc0842..20df9e84 100644
--- a/sprout/math/fmod.hpp
+++ b/sprout/math/fmod.hpp
@@ -3,23 +3,66 @@
 
 #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/trunc.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>
 
 namespace sprout {
 	namespace math {
 		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			fmod_impl_6(T x, T y, T x1) {
+				return x1 >= y
+					? x < 0 ? -(x1 - y) : x1 - y
+					: x < 0 ? -x1 : x1
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			fmod_impl_5(T x, T y, T x1, T y1, T z, int iscy, int idiff, int i) {
+				return i != idiff
+					? z >= 0
+						? sprout::math::detail::fmod_impl_5(x, y, z + z, y1, z + z - y1, iscy, idiff, i + 1)
+						: sprout::math::detail::fmod_impl_5(x, y, x1 + x1, y1, x1 + x1 - y1, iscy, idiff, i + 1)
+					: sprout::math::detail::fmod_impl_6(x, y, sprout::math::scalbn(x1, iscy))
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			fmod_impl_4(T x, T y, T x1, T y1, int iscy, int idiff, int i) {
+				return sprout::math::detail::fmod_impl_5(x, y, x1, y1, x1 - y1, iscy, idiff, i);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			fmod_impl_3(T x, T y, T x1, int iscx, int iscy, int idiff) {
+				return idiff ? sprout::math::detail::fmod_impl_4(x, y, sprout::math::scalbn(x1, -iscx), sprout::math::scalbn(y, -iscy), iscy, idiff, 0)
+					: sprout::math::detail::fmod_impl_6(x, y, x1)
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			fmod_impl_2(T x, T y, T x1, int iscx, int iscy) {
+				return sprout::math::detail::fmod_impl_3(x, y, x1, iscx, iscy, iscx - iscy);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			fmod_impl_1(T x, T y, T x1) {
+				return y > x1 ? x
+					: sprout::math::detail::fmod_impl_2(x, y, x1, sprout::math::ilogb(x1), sprout::math::ilogb(y))
+					;
+			}
 			template<typename T>
 			inline SPROUT_CONSTEXPR T
 			fmod_impl(T x, T y) {
-				return x - sprout::math::trunc(x / y) * y;
+				return sprout::math::detail::fmod_impl_1(x, sprout::math::fabs(y), sprout::math::fabs(x));
 			}
 
 			template<
@@ -34,9 +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),
@@ -58,7 +101,11 @@ namespace sprout {
 				return sprout::math::detail::fmod(static_cast<type>(x), static_cast<type>(y));
 			}
 		}	// namespace detail
-
+		//
+		// issue:
+		//	fmod(-NaN, -NaN) returns -NaN .
+		//		# returns +NaN . ( same as fmod(+NaN, +NaN) )
+		//
 		using sprout::math::detail::fmod;
 	}	// namespace math
 
diff --git a/sprout/math/quotient.hpp b/sprout/math/quotient.hpp
index 8fb8db54..39cb3262 100644
--- a/sprout/math/quotient.hpp
+++ b/sprout/math/quotient.hpp
@@ -6,6 +6,9 @@
 #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/type_traits/enabler_if.hpp>
 #include <sprout/type_traits/float_promote.hpp>
@@ -13,6 +16,12 @@
 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,
@@ -20,14 +29,17 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR R
 			quotient(FloatType x, FloatType y) {
-				return x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity() || y == 0
-						? 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)
+				return sprout::math::isnan(y) || sprout::math::isnan(x) ? R(0)
+					: x == 0 && y != 0 ? R(0)
+					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity() || y == 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>(
+						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(x),
+						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(y)
+						))
 					;
 			}
-
 			template<
 				typename R = int,
 				typename ArithmeticType1,
diff --git a/sprout/math/rem_quo.hpp b/sprout/math/rem_quo.hpp
index 0fee35de..c3737a44 100644
--- a/sprout/math/rem_quo.hpp
+++ b/sprout/math/rem_quo.hpp
@@ -6,6 +6,9 @@
 #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/type_traits/enabler_if.hpp>
 #include <sprout/type_traits/float_promote.hpp>
@@ -14,17 +17,20 @@
 namespace sprout {
 	namespace math {
 		namespace detail {
+			template<typename R, typename FloatType, typename Pair>
+			inline SPROUT_CONSTEXPR sprout::pair<FloatType, R>
+			rem_quo_ret(Pair const& p) {
+				typedef sprout::pair<FloatType, R> type;
+				return type(static_cast<FloatType>(p.first), p.second);
+			}
+
 			template<typename R, typename T>
 			inline SPROUT_CONSTEXPR sprout::pair<T, R>
 			rem_quo_impl(T x, T y, R quo) {
 				typedef sprout::pair<T, R> type;
-				return x == std::numeric_limits<T>::infinity() || x == -std::numeric_limits<T>::infinity() || y == 0
-						? type(std::numeric_limits<T>::quiet_NaN(), quo)
-					: x == 0 ? type(T(0), quo)
-					: y == std::numeric_limits<T>::infinity() || y == -std::numeric_limits<T>::infinity() ? type(x, quo)
-					: type(x - quo * y, quo)
-					;
+				return type(x - quo * y, quo);
 			}
+
 			template<
 				typename R = int,
 				typename FloatType,
@@ -32,9 +38,23 @@ 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::quotient(x, y));
+				typedef sprout::pair<FloatType, R> type;
+				return 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(std::numeric_limits<FloatType>::quiet_NaN(), R(0))
+							: type(y, R(0))
+					: x == 0 && y != 0 ? type(FloatType(0), R(0))
+					: x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity() || y == 0
+						? type(std::numeric_limits<FloatType>::quiet_NaN(), 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)
+						))
+					;
 			}
-
 			template<
 				typename R = int,
 				typename ArithmeticType1,
diff --git a/sprout/math/remainder.hpp b/sprout/math/remainder.hpp
index af4fd035..eca81b88 100644
--- a/sprout/math/remainder.hpp
+++ b/sprout/math/remainder.hpp
@@ -6,6 +6,9 @@
 #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/type_traits/enabler_if.hpp>
 #include <sprout/type_traits/float_promote.hpp>
@@ -13,20 +16,38 @@
 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 x == std::numeric_limits<FloatType>::infinity() || x == -std::numeric_limits<FloatType>::infinity() || y == 0
+				return sprout::math::isnan(y)
+						? sprout::math::isnan(x)
+							? 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() || y == 0
 						? 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
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+					: std::remainder(x, y)
+#else
+					: static_cast<FloatType>(sprout::math::detail::remainder_impl(
+						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(x),
+						static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(y)
+						))
+#endif
 					;
 			}
-
 			template<
 				typename ArithmeticType1,
 				typename ArithmeticType2,