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- #pragma once
- #include <Mathematics/Logger.h>
- #include <Mathematics/ArbitraryPrecision.h>
- #define GTE_THROW_ON_INVALID_APINTERVAL
- namespace WwiseGTE
- {
-
- template <typename APType>
- class APInterval
- {
- public:
-
-
-
- APInterval()
- :
- mEndpoints{ static_cast<APType>(0), static_cast<APType>(0) }
- {
- static_assert(WwiseGTE::is_arbitrary_precision<APType>::value, "Invalid type.");
- }
- APInterval(APInterval const& other)
- :
- mEndpoints(other.mEndpoints)
- {
- static_assert(WwiseGTE::is_arbitrary_precision<APType>::value, "Invalid type.");
- }
- explicit APInterval(APType e)
- :
- mEndpoints{ e, e }
- {
- static_assert(WwiseGTE::is_arbitrary_precision<APType>::value, "Invalid type.");
- }
- APInterval(APType e0, APType e1)
- :
- mEndpoints{ e0, e1 }
- {
- static_assert(WwiseGTE::is_arbitrary_precision<APType>::value, "Invalid type.");
- #if defined(GTE_THROW_ON_INVALID_APINTERVAL)
- LogAssert(mEndpoints[0] <= mEndpoints[1], "Invalid interval.");
- #endif
- }
- APInterval(std::array<APType, 2> const& endpoint)
- :
- mEndpoints(endpoint)
- {
- static_assert(WwiseGTE::is_arbitrary_precision<APType>::value, "Invalid type.");
- #if defined(GTE_THROW_ON_INVALID_APINTERVAL)
- LogAssert(mEndpoints[0] <= mEndpoints[1], "Invalid interval.");
- #endif
- }
- APInterval& operator=(APInterval const& other)
- {
- static_assert(WwiseGTE::is_arbitrary_precision<APType>::value, "Invalid type.");
- mEndpoints = other.mEndpoints;
- return *this;
- }
-
-
- inline APType operator[](size_t i) const
- {
- return mEndpoints[i];
- }
- inline std::array<APType, 2> GetEndpoints() const
- {
- return mEndpoints;
- }
-
-
-
-
-
- inline static APInterval Add(APType u, APType v)
- {
- APInterval w;
- w.mEndpoints[0] = u + v;
- w.mEndpoints[1] = w.mEndpoints[0];
- return w;
- }
- inline static APInterval Sub(APType u, APType v)
- {
- APInterval w;
- w.mEndpoints[0] = u - v;
- w.mEndpoints[1] = w.mEndpoints[0];
- return w;
- }
- inline static APInterval Mul(APType u, APType v)
- {
- APInterval w;
- w.mEndpoints[0] = u * v;
- w.mEndpoints[1] = w.mEndpoints[0];
- return w;
- }
- template <typename Dummy = APType>
- inline static
- typename std::enable_if<has_division_operator<Dummy>::value, APInterval>::type
- Div(APType u, APType v)
- {
- APType const zero = static_cast<APType>(0);
- if (v != zero)
- {
- APInterval w;
- w.mEndpoints[0] = u / v;
- w.mEndpoints[1] = w.mEndpoints[0];
- return w;
- }
- else
- {
-
-
- return Reals();
- }
- }
- private:
- std::array<APType, 2> mEndpoints;
- public:
-
-
- inline static APInterval Add(APType u0, APType u1, APType v0, APType v1)
- {
- APInterval w;
- w.mEndpoints[0] = u0 + v0;
- w.mEndpoints[1] = u1 + v1;
- return w;
- }
- inline static APInterval Sub(APType u0, APType u1, APType v0, APType v1)
- {
- APInterval w;
- w.mEndpoints[0] = u0 - v1;
- w.mEndpoints[1] = u1 - v0;
- return w;
- }
- inline static APInterval Mul(APType u0, APType u1, APType v0, APType v1)
- {
- APInterval w;
- w.mEndpoints[0] = u0 * v0;
- w.mEndpoints[1] = u1 * v1;
- return w;
- }
- inline static APInterval Mul2(APType u0, APType u1, APType v0, APType v1)
- {
- APType u0mv1 = u0 * v1;
- APType u1mv0 = u1 * v0;
- APType u0mv0 = u0 * v0;
- APType u1mv1 = u1 * v1;
- return APInterval<APType>(std::min(u0mv1, u1mv0), std::max(u0mv0, u1mv1));
- }
- template <typename Dummy = APType>
- inline static
- typename std::enable_if<has_division_operator<Dummy>::value, APInterval>::type
- Div(APType u0, APType u1, APType v0, APType v1)
- {
- APInterval w;
- w.mEndpoints[0] = u0 / v1;
- w.mEndpoints[1] = u1 / v0;
- return w;
- }
- template <typename Dummy = APType>
- inline static
- typename std::enable_if<has_division_operator<Dummy>::value, APInterval>::type
- Reciprocal(APType v0, APType v1)
- {
- APType const one = static_cast<APType>(1);
- APInterval w;
- w.mEndpoints[0] = one / v1;
- w.mEndpoints[1] = one / v0;
- return w;
- }
- template <typename Dummy = APType>
- inline static
- typename std::enable_if<has_division_operator<Dummy>::value, APInterval>::type
- ReciprocalDown(APType v)
- {
- APType recpv = static_cast<APType>(1) / v;
- APType posinf(0);
- posinf.SetSign(+2);
- return APInterval<APType>(recpv, posinf);
- }
- template <typename Dummy = APType>
- inline static
- typename std::enable_if<has_division_operator<Dummy>::value, APInterval>::type
- ReciprocalUp(APType v)
- {
- APType recpv = static_cast<APType>(1) / v;
- APType neginf(0);
- neginf.SetSign(-2);
- return APInterval<APType>(neginf, recpv);
- }
- inline static APInterval Reals()
- {
- APType posinf(0), neginf(0);
- posinf.SetSign(+2);
- neginf.SetSign(-2);
- return APInterval(neginf, posinf);
- }
- };
-
-
-
- template <typename APType>
- APInterval<APType> operator+(APInterval<APType> const& u)
- {
- return u;
- }
- template <typename APType>
- APInterval<APType> operator-(APInterval<APType> const& u)
- {
- return APInterval<APType>(-u[1], -u[0]);
- }
-
- template <typename APType>
- APInterval<APType> operator+(APType u, APInterval<APType> const& v)
- {
- return APInterval<APType>::Add(u, u, v[0], v[1]);
- }
- template <typename APType>
- APInterval<APType> operator+(APInterval<APType> const& u, APType v)
- {
- return APInterval<APType>::Add(u[0], u[1], v, v);
- }
- template <typename APType>
- APInterval<APType> operator+(APInterval<APType> const& u, APInterval<APType> const& v)
- {
- return APInterval<APType>::Add(u[0], u[1], v[0], v[1]);
- }
-
- template <typename APType>
- APInterval<APType> operator-(APType u, APInterval<APType> const& v)
- {
- return APInterval<APType>::Sub(u, u, v[0], v[1]);
- }
- template <typename APType>
- APInterval<APType> operator-(APInterval<APType> const& u, APType v)
- {
- return APInterval<APType>::Sub(u[0], u[1], v, v);
- }
- template <typename APType>
- APInterval<APType> operator-(APInterval<APType> const& u, APInterval<APType> const& v)
- {
- return APInterval<APType>::Sub(u[0], u[1], v[0], v[1]);
- }
-
- template <typename APType>
- APInterval<APType> operator*(APType u, APInterval<APType> const& v)
- {
- APType const zero = static_cast<APType>(0);
- if (u >= zero)
- {
- return APInterval<APType>::Mul(u, u, v[0], v[1]);
- }
- else
- {
- return APInterval<APType>::Mul(u, u, v[1], v[0]);
- }
- }
- template <typename APType>
- APInterval<APType> operator*(APInterval<APType> const& u, APType v)
- {
- APType const zero = static_cast<APType>(0);
- if (v >= zero)
- {
- return APInterval<APType>::Mul(u[0], u[1], v, v);
- }
- else
- {
- return APInterval<APType>::Mul(u[1], u[0], v, v);
- }
- }
- template <typename APType>
- APInterval<APType> operator*(APInterval<APType> const& u, APInterval<APType> const& v)
- {
- APType const zero = static_cast<APType>(0);
- if (u[0] >= zero)
- {
- if (v[0] >= zero)
- {
- return APInterval<APType>::Mul(u[0], u[1], v[0], v[1]);
- }
- else if (v[1] <= zero)
- {
- return APInterval<APType>::Mul(u[1], u[0], v[0], v[1]);
- }
- else
- {
- return APInterval<APType>::Mul(u[1], u[1], v[0], v[1]);
- }
- }
- else if (u[1] <= zero)
- {
- if (v[0] >= zero)
- {
- return APInterval<APType>::Mul(u[0], u[1], v[1], v[0]);
- }
- else if (v[1] <= zero)
- {
- return APInterval<APType>::Mul(u[1], u[0], v[1], v[0]);
- }
- else
- {
- return APInterval<APType>::Mul(u[0], u[0], v[1], v[0]);
- }
- }
- else
- {
- if (v[0] >= zero)
- {
- return APInterval<APType>::Mul(u[0], u[1], v[1], v[1]);
- }
- else if (v[1] <= zero)
- {
- return APInterval<APType>::Mul(u[1], u[0], v[0], v[0]);
- }
- else
- {
- return APInterval<APType>::Mul2(u[0], u[1], v[0], v[1]);
- }
- }
- }
-
-
-
-
- template <typename APType>
- APInterval<APType> operator/(APType u, APInterval<APType> const& v)
- {
- APType const zero = static_cast<APType>(0);
- if (v[0] > zero || v[1] < zero)
- {
- return u * APInterval<APType>::Reciprocal(v[0], v[1]);
- }
- else
- {
- if (v[0] == zero)
- {
- return u * APInterval<APType>::ReciprocalDown(v[1]);
- }
- else if (v[1] == zero)
- {
- return u * APInterval<APType>::ReciprocalUp(v[0]);
- }
- else
- {
- return APInterval<APType>::Reals();
- }
- }
- }
- template <typename APType>
- APInterval<APType> operator/(APInterval<APType> const& u, APType v)
- {
- APType const zero = static_cast<APType>(0);
- if (v > zero)
- {
- return APInterval<APType>::Div(u[0], u[1], v, v);
- }
- else if (v < zero)
- {
- return APInterval<APType>::Div(u[1], u[0], v, v);
- }
- else
- {
- return APInterval<APType>::Reals();
- }
- }
- template <typename APType>
- APInterval<APType> operator/(APInterval<APType> const& u, APInterval<APType> const& v)
- {
- APType const zero = static_cast<APType>(0);
- if (v[0] > zero || v[1] < zero)
- {
- return u * APInterval<APType>::Reciprocal(v[0], v[1]);
- }
- else
- {
- if (v[0] == zero)
- {
- return u * APInterval<APType>::ReciprocalDown(v[1]);
- }
- else if (v[1] == zero)
- {
- return u * APInterval<APType>::ReciprocalUp(v[0]);
- }
- else
- {
- return APInterval<APType>::Reals();
- }
- }
- }
- }
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