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- #pragma once
- #include <Mathematics/Logger.h>
- #include <Mathematics/Math.h>
- #include <array>
- #define GTE_THROW_ON_INVALID_INTERVAL
- namespace WwiseGTE
- {
-
- template <typename FPType>
- class FPInterval
- {
- public:
-
-
-
- FPInterval()
- :
- mEndpoints{ static_cast<FPType>(0), static_cast<FPType>(0) }
- {
- static_assert(std::is_floating_point<FPType>::value, "Invalid type.");
- }
- FPInterval(FPInterval const& other)
- :
- mEndpoints(other.mEndpoints)
- {
- static_assert(std::is_floating_point<FPType>::value, "Invalid type.");
- }
- explicit FPInterval(FPType e)
- :
- mEndpoints{ e, e }
- {
- static_assert(std::is_floating_point<FPType>::value, "Invalid type.");
- }
- FPInterval(FPType e0, FPType e1)
- :
- mEndpoints{ e0, e1 }
- {
- static_assert(std::is_floating_point<FPType>::value, "Invalid type.");
- #if defined(GTE_THROW_ON_INVALID_INTERVAL)
- LogAssert(mEndpoints[0] <= mEndpoints[1], "Invalid FPInterval.");
- #endif
- }
- FPInterval(std::array<FPType, 2> const& endpoint)
- :
- mEndpoints(endpoint)
- {
- static_assert(std::is_floating_point<FPType>::value, "Invalid type.");
- #if defined(GTE_THROW_ON_INVALID_INTERVAL)
- LogAssert(mEndpoints[0] <= mEndpoints[1], "Invalid FPInterval.");
- #endif
- }
- FPInterval& operator=(FPInterval const& other)
- {
- static_assert(std::is_floating_point<FPType>::value, "Invalid type.");
- mEndpoints = other.mEndpoints;
- return *this;
- }
-
-
- inline FPType operator[](size_t i) const
- {
- return mEndpoints[i];
- }
- inline std::array<FPType, 2> GetEndpoints() const
- {
- return mEndpoints;
- }
-
-
-
-
-
- inline static FPInterval Add(FPType u, FPType v)
- {
- FPInterval w;
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- w.mEndpoints[0] = u + v;
- std::fesetround(FE_UPWARD);
- w.mEndpoints[1] = u + v;
- std::fesetround(saveMode);
- return w;
- }
- inline static FPInterval Sub(FPType u, FPType v)
- {
- FPInterval w;
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- w.mEndpoints[0] = u - v;
- std::fesetround(FE_UPWARD);
- w.mEndpoints[1] = u - v;
- std::fesetround(saveMode);
- return w;
- }
- inline static FPInterval Mul(FPType u, FPType v)
- {
- FPInterval w;
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- w.mEndpoints[0] = u * v;
- std::fesetround(FE_UPWARD);
- w.mEndpoints[1] = u * v;
- std::fesetround(saveMode);
- return w;
- }
- inline static FPInterval Div(FPType u, FPType v)
- {
- FPType const zero = static_cast<FPType>(0);
- if (v != zero)
- {
- FPInterval w;
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- w.mEndpoints[0] = u / v;
- std::fesetround(FE_UPWARD);
- w.mEndpoints[1] = u / v;
- std::fesetround(saveMode);
- return w;
- }
- else
- {
-
-
- return Reals();
- }
- }
- private:
- std::array<FPType, 2> mEndpoints;
- public:
-
-
- inline static FPInterval Add(FPType u0, FPType u1, FPType v0, FPType v1)
- {
- FPInterval w;
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- w.mEndpoints[0] = u0 + v0;
- std::fesetround(FE_UPWARD);
- w.mEndpoints[1] = u1 + v1;
- std::fesetround(saveMode);
- return w;
- }
- inline static FPInterval Sub(FPType u0, FPType u1, FPType v0, FPType v1)
- {
- FPInterval w;
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- w.mEndpoints[0] = u0 - v1;
- std::fesetround(FE_UPWARD);
- w.mEndpoints[1] = u1 - v0;
- std::fesetround(saveMode);
- return w;
- }
- inline static FPInterval Mul(FPType u0, FPType u1, FPType v0, FPType v1)
- {
- FPInterval w;
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- w.mEndpoints[0] = u0 * v0;
- std::fesetround(FE_UPWARD);
- w.mEndpoints[1] = u1 * v1;
- std::fesetround(saveMode);
- return w;
- }
- inline static FPInterval Mul2(FPType u0, FPType u1, FPType v0, FPType v1)
- {
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- FPType u0mv1 = u0 * v1;
- FPType u1mv0 = u1 * v0;
- std::fesetround(FE_UPWARD);
- FPType u0mv0 = u0 * v0;
- FPType u1mv1 = u1 * v1;
- std::fesetround(saveMode);
- return FPInterval<FPType>(std::min(u0mv1, u1mv0), std::max(u0mv0, u1mv1));
- }
- inline static FPInterval Div(FPType u0, FPType u1, FPType v0, FPType v1)
- {
- FPInterval w;
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- w.mEndpoints[0] = u0 / v1;
- std::fesetround(FE_UPWARD);
- w.mEndpoints[1] = u1 / v0;
- std::fesetround(saveMode);
- return w;
- }
- inline static FPInterval Reciprocal(FPType v0, FPType v1)
- {
- FPType const one = static_cast<FPType>(1);
- FPInterval w;
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- w.mEndpoints[0] = one / v1;
- std::fesetround(FE_UPWARD);
- w.mEndpoints[1] = one / v0;
- std::fesetround(saveMode);
- return w;
- }
- inline static FPInterval ReciprocalDown(FPType v)
- {
- auto saveMode = std::fegetround();
- std::fesetround(FE_DOWNWARD);
- FPType recpv = static_cast<FPType>(1) / v;
- std::fesetround(saveMode);
- FPType const inf = std::numeric_limits<FPType>::infinity();
- return FPInterval<FPType>(recpv, +inf);
- }
- inline static FPInterval ReciprocalUp(FPType v)
- {
- auto saveMode = std::fegetround();
- std::fesetround(FE_UPWARD);
- FPType recpv = static_cast<FPType>(1) / v;
- std::fesetround(saveMode);
- FPType const inf = std::numeric_limits<FPType>::infinity();
- return FPInterval<FPType>(-inf, recpv);
- }
- inline static FPInterval Reals()
- {
- FPType const inf = std::numeric_limits<FPType>::infinity();
- return FPInterval(-inf, +inf);
- }
- };
-
-
-
- template <typename FPType>
- FPInterval<FPType> operator+(FPInterval<FPType> const& u)
- {
- return u;
- }
- template <typename FPType>
- FPInterval<FPType> operator-(FPInterval<FPType> const& u)
- {
- return FPInterval<FPType>(-u[1], -u[0]);
- }
-
- template <typename FPType>
- FPInterval<FPType> operator+(FPType u, FPInterval<FPType> const& v)
- {
- return FPInterval<FPType>::Add(u, u, v[0], v[1]);
- }
- template <typename FPType>
- FPInterval<FPType> operator+(FPInterval<FPType> const& u, FPType v)
- {
- return FPInterval<FPType>::Add(u[0], u[1], v, v);
- }
- template <typename FPType>
- FPInterval<FPType> operator+(FPInterval<FPType> const& u, FPInterval<FPType> const& v)
- {
- return FPInterval<FPType>::Add(u[0], u[1], v[0], v[1]);
- }
-
- template <typename FPType>
- FPInterval<FPType> operator-(FPType u, FPInterval<FPType> const& v)
- {
- return FPInterval<FPType>::Sub(u, u, v[0], v[1]);
- }
- template <typename FPType>
- FPInterval<FPType> operator-(FPInterval<FPType> const& u, FPType v)
- {
- return FPInterval<FPType>::Sub(u[0], u[1], v, v);
- }
- template <typename FPType>
- FPInterval<FPType> operator-(FPInterval<FPType> const& u, FPInterval<FPType> const& v)
- {
- return FPInterval<FPType>::Sub(u[0], u[1], v[0], v[1]);
- }
-
- template <typename FPType>
- FPInterval<FPType> operator*(FPType u, FPInterval<FPType> const& v)
- {
- FPType const zero = static_cast<FPType>(0);
- if (u >= zero)
- {
- return FPInterval<FPType>::Mul(u, u, v[0], v[1]);
- }
- else
- {
- return FPInterval<FPType>::Mul(u, u, v[1], v[0]);
- }
- }
- template <typename FPType>
- FPInterval<FPType> operator*(FPInterval<FPType> const& u, FPType v)
- {
- FPType const zero = static_cast<FPType>(0);
- if (v >= zero)
- {
- return FPInterval<FPType>::Mul(u[0], u[1], v, v);
- }
- else
- {
- return FPInterval<FPType>::Mul(u[1], u[0], v, v);
- }
- }
- template <typename FPType>
- FPInterval<FPType> operator*(FPInterval<FPType> const& u, FPInterval<FPType> const& v)
- {
- FPType const zero = static_cast<FPType>(0);
- if (u[0] >= zero)
- {
- if (v[0] >= zero)
- {
- return FPInterval<FPType>::Mul(u[0], u[1], v[0], v[1]);
- }
- else if (v[1] <= zero)
- {
- return FPInterval<FPType>::Mul(u[1], u[0], v[0], v[1]);
- }
- else
- {
- return FPInterval<FPType>::Mul(u[1], u[1], v[0], v[1]);
- }
- }
- else if (u[1] <= zero)
- {
- if (v[0] >= zero)
- {
- return FPInterval<FPType>::Mul(u[0], u[1], v[1], v[0]);
- }
- else if (v[1] <= zero)
- {
- return FPInterval<FPType>::Mul(u[1], u[0], v[1], v[0]);
- }
- else
- {
- return FPInterval<FPType>::Mul(u[0], u[0], v[1], v[0]);
- }
- }
- else
- {
- if (v[0] >= zero)
- {
- return FPInterval<FPType>::Mul(u[0], u[1], v[1], v[1]);
- }
- else if (v[1] <= zero)
- {
- return FPInterval<FPType>::Mul(u[1], u[0], v[0], v[0]);
- }
- else
- {
- return FPInterval<FPType>::Mul2(u[0], u[1], v[0], v[1]);
- }
- }
- }
-
-
-
-
- template <typename FPType>
- FPInterval<FPType> operator/(FPType u, FPInterval<FPType> const& v)
- {
- FPType const zero = static_cast<FPType>(0);
- if (v[0] > zero || v[1] < zero)
- {
- return u * FPInterval<FPType>::Reciprocal(v[0], v[1]);
- }
- else
- {
- if (v[0] == zero)
- {
- return u * FPInterval<FPType>::ReciprocalDown(v[1]);
- }
- else if (v[1] == zero)
- {
- return u * FPInterval<FPType>::ReciprocalUp(v[0]);
- }
- else
- {
- return FPInterval<FPType>::Reals();
- }
- }
- }
- template <typename FPType>
- FPInterval<FPType> operator/(FPInterval<FPType> const& u, FPType v)
- {
- FPType const zero = static_cast<FPType>(0);
- if (v > zero)
- {
- return FPInterval<FPType>::Div(u[0], u[1], v, v);
- }
- else if (v < zero)
- {
- return FPInterval<FPType>::Div(u[1], u[0], v, v);
- }
- else
- {
- return FPInterval<FPType>::Reals();
- }
- }
- template <typename FPType>
- FPInterval<FPType> operator/(FPInterval<FPType> const& u, FPInterval<FPType> const& v)
- {
- FPType const zero = static_cast<FPType>(0);
- if (v[0] > zero || v[1] < zero)
- {
- return u * FPInterval<FPType>::Reciprocal(v[0], v[1]);
- }
- else
- {
- if (v[0] == zero)
- {
- return u * FPInterval<FPType>::ReciprocalDown(v[1]);
- }
- else if (v[1] == zero)
- {
- return u * FPInterval<FPType>::ReciprocalUp(v[0]);
- }
- else
- {
- return FPInterval<FPType>::Reals();
- }
- }
- }
- }
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