libs/math/include/math/TVecHelpers.h - third_party/android/platform/frameworks/native - Git at Google

 /*
  * Copyright 2013 The Android Open Source Project
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
  *
  *      http://www.apache.org/licenses/LICENSE-2.0
  *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  * See the License for the specific language governing permissions and
  * limitations under the License.
  */


 #pragma once

 #include <math.h>
 #include <stdint.h>
 #include <sys/types.h>

 #include <cmath>
 #include <limits>
 #include <iostream>

 #define PURE __attribute__((pure))

 #if __cplusplus >= 201402L
 #define CONSTEXPR constexpr
 #else
 #define CONSTEXPR
 #endif

 namespace android {
 namespace details {
 // -------------------------------------------------------------------------------------

 /*
  * No user serviceable parts here.
  *
  * Don't use this file directly, instead include ui/vec{2|3|4}.h
  */

 /*
  * TVec{Add|Product}Operators implements basic arithmetic and basic compound assignments
  * operators on a vector of type BASE<T>.
  *
  * BASE only needs to implement operator[] and size().
  * By simply inheriting from TVec{Add|Product}Operators<BASE, T> BASE will automatically
  * get all the functionality here.
  */

 template <template<typename T> class VECTOR, typename T>
 class TVecAddOperators {
 public:
     /* compound assignment from a another vector of the same size but different
      * element type.
      */
     template<typename OTHER>
     VECTOR<T>& operator +=(const VECTOR<OTHER>& v) {
         VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < lhs.size(); i++) {
             lhs[i] += v[i];
         }
         return lhs;
     }
     template<typename OTHER>
     VECTOR<T>& operator -=(const VECTOR<OTHER>& v) {
         VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < lhs.size(); i++) {
             lhs[i] -= v[i];
         }
         return lhs;
     }

     /* compound assignment from a another vector of the same type.
      * These operators can be used for implicit conversion and  handle operations
      * like "vector *= scalar" by letting the compiler implicitly convert a scalar
      * to a vector (assuming the BASE<T> allows it).
      */
     VECTOR<T>& operator +=(const VECTOR<T>& v) {
         VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < lhs.size(); i++) {
             lhs[i] += v[i];
         }
         return lhs;
     }
     VECTOR<T>& operator -=(const VECTOR<T>& v) {
         VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < lhs.size(); i++) {
             lhs[i] -= v[i];
         }
         return lhs;
     }

     /*
      * NOTE: the functions below ARE NOT member methods. They are friend functions
      * with they definition inlined with their declaration. This makes these
      * template functions available to the compiler when (and only when) this class
      * is instantiated, at which point they're only templated on the 2nd parameter
      * (the first one, BASE<T> being known).
      */

     /* The operators below handle operation between vectors of the same size
      * but of a different element type.
      */
     template<typename RT>
     friend inline constexpr VECTOR<T> PURE operator +(VECTOR<T> lv, const VECTOR<RT>& rv) {
         // don't pass lv by reference because we need a copy anyways
         return lv += rv;
     }
     template<typename RT>
     friend inline constexpr VECTOR<T> PURE operator -(VECTOR<T> lv, const VECTOR<RT>& rv) {
         // don't pass lv by reference because we need a copy anyways
         return lv -= rv;
     }

     /* The operators below (which are not templates once this class is instanced,
      * i.e.: BASE<T> is known) can be used for implicit conversion on both sides.
      * These handle operations like "vector + scalar" and "scalar + vector" by
      * letting the compiler implicitly convert a scalar to a vector (assuming
      * the BASE<T> allows it).
      */
     friend inline constexpr VECTOR<T> PURE operator +(VECTOR<T> lv, const VECTOR<T>& rv) {
         // don't pass lv by reference because we need a copy anyways
         return lv += rv;
     }
     friend inline constexpr VECTOR<T> PURE operator -(VECTOR<T> lv, const VECTOR<T>& rv) {
         // don't pass lv by reference because we need a copy anyways
         return lv -= rv;
     }
 };

 template<template<typename T> class VECTOR, typename T>
 class TVecProductOperators {
 public:
     /* compound assignment from a another vector of the same size but different
      * element type.
      */
     template<typename OTHER>
     VECTOR<T>& operator *=(const VECTOR<OTHER>& v) {
         VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < lhs.size(); i++) {
             lhs[i] *= v[i];
         }
         return lhs;
     }
     template<typename OTHER>
     VECTOR<T>& operator /=(const VECTOR<OTHER>& v) {
         VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < lhs.size(); i++) {
             lhs[i] /= v[i];
         }
         return lhs;
     }

     /* compound assignment from a another vector of the same type.
      * These operators can be used for implicit conversion and  handle operations
      * like "vector *= scalar" by letting the compiler implicitly convert a scalar
      * to a vector (assuming the BASE<T> allows it).
      */
     VECTOR<T>& operator *=(const VECTOR<T>& v) {
         VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < lhs.size(); i++) {
             lhs[i] *= v[i];
         }
         return lhs;
     }
     VECTOR<T>& operator /=(const VECTOR<T>& v) {
         VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < lhs.size(); i++) {
             lhs[i] /= v[i];
         }
         return lhs;
     }

     /*
      * NOTE: the functions below ARE NOT member methods. They are friend functions
      * with they definition inlined with their declaration. This makes these
      * template functions available to the compiler when (and only when) this class
      * is instantiated, at which point they're only templated on the 2nd parameter
      * (the first one, BASE<T> being known).
      */

     /* The operators below handle operation between vectors of the same size
      * but of a different element type.
      */
     template<typename RT>
     friend inline constexpr VECTOR<T> PURE operator *(VECTOR<T> lv, const VECTOR<RT>& rv) {
         // don't pass lv by reference because we need a copy anyways
         return lv *= rv;
     }
     template<typename RT>
     friend inline constexpr VECTOR<T> PURE operator /(VECTOR<T> lv, const VECTOR<RT>& rv) {
         // don't pass lv by reference because we need a copy anyways
         return lv /= rv;
     }

     /* The operators below (which are not templates once this class is instanced,
      * i.e.: BASE<T> is known) can be used for implicit conversion on both sides.
      * These handle operations like "vector * scalar" and "scalar * vector" by
      * letting the compiler implicitly convert a scalar to a vector (assuming
      * the BASE<T> allows it).
      */
     friend inline constexpr VECTOR<T> PURE operator *(VECTOR<T> lv, const VECTOR<T>& rv) {
         // don't pass lv by reference because we need a copy anyways
         return lv *= rv;
     }
     friend inline constexpr VECTOR<T> PURE operator /(VECTOR<T> lv, const VECTOR<T>& rv) {
         // don't pass lv by reference because we need a copy anyways
         return lv /= rv;
     }
 };

 /*
  * TVecUnaryOperators implements unary operators on a vector of type BASE<T>.
  *
  * BASE only needs to implement operator[] and size().
  * By simply inheriting from TVecUnaryOperators<BASE, T> BASE will automatically
  * get all the functionality here.
  *
  * These operators are implemented as friend functions of TVecUnaryOperators<BASE, T>
  */
 template<template<typename T> class VECTOR, typename T>
 class TVecUnaryOperators {
 public:
     VECTOR<T>& operator ++() {
         VECTOR<T>& rhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < rhs.size(); i++) {
             ++rhs[i];
         }
         return rhs;
     }

     VECTOR<T>& operator --() {
         VECTOR<T>& rhs = static_cast<VECTOR<T>&>(*this);
         for (size_t i = 0; i < rhs.size(); i++) {
             --rhs[i];
         }
         return rhs;
     }

     CONSTEXPR VECTOR<T> operator -() const {
         VECTOR<T> r(VECTOR<T>::NO_INIT);
         VECTOR<T> const& rv(static_cast<VECTOR<T> const&>(*this));
         for (size_t i = 0; i < r.size(); i++) {
             r[i] = -rv[i];
         }
         return r;
     }
 };

 /*
  * TVecComparisonOperators implements relational/comparison operators
  * on a vector of type BASE<T>.
  *
  * BASE only needs to implement operator[] and size().
  * By simply inheriting from TVecComparisonOperators<BASE, T> BASE will automatically
  * get all the functionality here.
  */
 template<template<typename T> class VECTOR, typename T>
 class TVecComparisonOperators {
 public:
     /*
      * NOTE: the functions below ARE NOT member methods. They are friend functions
      * with they definition inlined with their declaration. This makes these
      * template functions available to the compiler when (and only when) this class
      * is instantiated, at which point they're only templated on the 2nd parameter
      * (the first one, BASE<T> being known).
      */
     template<typename RT>
     friend inline
     bool PURE operator ==(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         for (size_t i = 0; i < lv.size(); i++)
             if (lv[i] != rv[i])
                 return false;
         return true;
     }

     template<typename RT>
     friend inline
     bool PURE operator !=(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         return !operator ==(lv, rv);
     }

     template<typename RT>
     friend inline
     bool PURE operator >(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         for (size_t i = 0; i < lv.size(); i++) {
             if (lv[i] == rv[i]) {
                 continue;
             }
             return lv[i] > rv[i];
         }
         return false;
     }

     template<typename RT>
     friend inline
     constexpr bool PURE operator <=(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         return !(lv > rv);
     }

     template<typename RT>
     friend inline
     bool PURE operator <(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         for (size_t i = 0; i < lv.size(); i++) {
             if (lv[i] == rv[i]) {
                 continue;
             }
             return lv[i] < rv[i];
         }
         return false;
     }

     template<typename RT>
     friend inline
     constexpr bool PURE operator >=(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         return !(lv < rv);
     }

     template<typename RT>
     friend inline
     CONSTEXPR VECTOR<bool> PURE equal(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         VECTOR<bool> r;
         for (size_t i = 0; i < lv.size(); i++) {
             r[i] = lv[i] == rv[i];
         }
         return r;
     }

     template<typename RT>
     friend inline
     CONSTEXPR VECTOR<bool> PURE notEqual(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         VECTOR<bool> r;
         for (size_t i = 0; i < lv.size(); i++) {
             r[i] = lv[i] != rv[i];
         }
         return r;
     }

     template<typename RT>
     friend inline
     CONSTEXPR VECTOR<bool> PURE lessThan(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         VECTOR<bool> r;
         for (size_t i = 0; i < lv.size(); i++) {
             r[i] = lv[i] < rv[i];
         }
         return r;
     }

     template<typename RT>
     friend inline
     CONSTEXPR VECTOR<bool> PURE lessThanEqual(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         VECTOR<bool> r;
         for (size_t i = 0; i < lv.size(); i++) {
             r[i] = lv[i] <= rv[i];
         }
         return r;
     }

     template<typename RT>
     friend inline
     CONSTEXPR VECTOR<bool> PURE greaterThan(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         VECTOR<bool> r;
         for (size_t i = 0; i < lv.size(); i++) {
             r[i] = lv[i] > rv[i];
         }
         return r;
     }

     template<typename RT>
     friend inline
     CONSTEXPR VECTOR<bool> PURE greaterThanEqual(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         VECTOR<bool> r;
         for (size_t i = 0; i < lv.size(); i++) {
             r[i] = lv[i] >= rv[i];
         }
         return r;
     }
 };

 /*
  * TVecFunctions implements functions on a vector of type BASE<T>.
  *
  * BASE only needs to implement operator[] and size().
  * By simply inheriting from TVecFunctions<BASE, T> BASE will automatically
  * get all the functionality here.
  */
 template<template<typename T> class VECTOR, typename T>
 class TVecFunctions {
 public:
     /*
      * NOTE: the functions below ARE NOT member methods. They are friend functions
      * with they definition inlined with their declaration. This makes these
      * template functions available to the compiler when (and only when) this class
      * is instantiated, at which point they're only templated on the 2nd parameter
      * (the first one, BASE<T> being known).
      */
     template<typename RT>
     friend inline CONSTEXPR T PURE dot(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         T r(0);
         for (size_t i = 0; i < lv.size(); i++) {
             //r = std::fma(lv[i], rv[i], r);
             r += lv[i] * rv[i];
         }
         return r;
     }

     friend inline constexpr T PURE norm(const VECTOR<T>& lv) {
         return std::sqrt(dot(lv, lv));
     }

     friend inline constexpr T PURE length(const VECTOR<T>& lv) {
         return norm(lv);
     }

     friend inline constexpr T PURE norm2(const VECTOR<T>& lv) {
         return dot(lv, lv);
     }

     friend inline constexpr T PURE length2(const VECTOR<T>& lv) {
         return norm2(lv);
     }

     template<typename RT>
     friend inline constexpr T PURE distance(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         return length(rv - lv);
     }

     template<typename RT>
     friend inline constexpr T PURE distance2(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
         return length2(rv - lv);
     }

     friend inline constexpr VECTOR<T> PURE normalize(const VECTOR<T>& lv) {
         return lv * (T(1) / length(lv));
     }

     friend inline constexpr VECTOR<T> PURE rcp(VECTOR<T> v) {
         return T(1) / v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE abs(VECTOR<T> v) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = std::abs(v[i]);
         }
         return v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE floor(VECTOR<T> v) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = std::floor(v[i]);
         }
         return v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE ceil(VECTOR<T> v) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = std::ceil(v[i]);
         }
         return v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE round(VECTOR<T> v) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = std::round(v[i]);
         }
         return v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE inversesqrt(VECTOR<T> v) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = T(1) / std::sqrt(v[i]);
         }
         return v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE sqrt(VECTOR<T> v) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = std::sqrt(v[i]);
         }
         return v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE pow(VECTOR<T> v, T p) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = std::pow(v[i], p);
         }
         return v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE saturate(const VECTOR<T>& lv) {
         return clamp(lv, T(0), T(1));
     }

     friend inline CONSTEXPR VECTOR<T> PURE clamp(VECTOR<T> v, T min, T max) {
         for (size_t i = 0; i< v.size(); i++) {
             v[i] = std::min(max, std::max(min, v[i]));
         }
         return v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE fma(const VECTOR<T>& lv, const VECTOR<T>& rv, VECTOR<T> a) {
         for (size_t i = 0; i<lv.size(); i++) {
             //a[i] = std::fma(lv[i], rv[i], a[i]);
             a[i] += (lv[i] * rv[i]);
         }
         return a;
     }

     friend inline CONSTEXPR VECTOR<T> PURE min(const VECTOR<T>& u, VECTOR<T> v) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = std::min(u[i], v[i]);
         }
         return v;
     }

     friend inline CONSTEXPR VECTOR<T> PURE max(const VECTOR<T>& u, VECTOR<T> v) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = std::max(u[i], v[i]);
         }
         return v;
     }

     friend inline CONSTEXPR T PURE max(const VECTOR<T>& v) {
         T r(std::numeric_limits<T>::lowest());
         for (size_t i = 0; i < v.size(); i++) {
             r = std::max(r, v[i]);
         }
         return r;
     }

     friend inline CONSTEXPR T PURE min(const VECTOR<T>& v) {
         T r(std::numeric_limits<T>::max());
         for (size_t i = 0; i < v.size(); i++) {
             r = std::min(r, v[i]);
         }
         return r;
     }

     friend inline CONSTEXPR VECTOR<T> PURE apply(VECTOR<T> v, const std::function<T(T)>& f) {
         for (size_t i = 0; i < v.size(); i++) {
             v[i] = f(v[i]);
         }
         return v;
     }

     friend inline CONSTEXPR bool PURE any(const VECTOR<T>& v) {
         for (size_t i = 0; i < v.size(); i++) {
             if (v[i] != T(0)) return true;
         }
         return false;
     }

     friend inline CONSTEXPR bool PURE all(const VECTOR<T>& v) {
         bool result = true;
         for (size_t i = 0; i < v.size(); i++) {
             result &= (v[i] != T(0));
         }
         return result;
     }

     template<typename R>
     friend inline CONSTEXPR VECTOR<R> PURE map(VECTOR<T> v, const std::function<R(T)>& f) {
         VECTOR<R> result;
         for (size_t i = 0; i < v.size(); i++) {
             result[i] = f(v[i]);
         }
         return result;
     }
 };

 /*
  * TVecDebug implements functions on a vector of type BASE<T>.
  *
  * BASE only needs to implement operator[] and size().
  * By simply inheriting from TVecDebug<BASE, T> BASE will automatically
  * get all the functionality here.
  */
 template<template<typename T> class VECTOR, typename T>
 class TVecDebug {
 public:
     /*
      * NOTE: the functions below ARE NOT member methods. They are friend functions
      * with they definition inlined with their declaration. This makes these
      * template functions available to the compiler when (and only when) this class
      * is instantiated, at which point they're only templated on the 2nd parameter
      * (the first one, BASE<T> being known).
      */
     friend std::ostream& operator<<(std::ostream& stream, const VECTOR<T>& v) {
         stream << "< ";
         for (size_t i = 0; i < v.size() - 1; i++) {
             stream << T(v[i]) << ", ";
         }
         stream << T(v[v.size() - 1]) << " >";
         return stream;
     }
 };

 #undef CONSTEXPR
 #undef PURE

 // -------------------------------------------------------------------------------------
 }  // namespace details
 }  // namespace android
	/*
	* Copyright 2013 The Android Open Source Project
	*
	* Licensed under the Apache License, Version 2.0 (the "License");
	* you may not use this file except in compliance with the License.
	* You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing, software
	* distributed under the License is distributed on an "AS IS" BASIS,
	* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	* See the License for the specific language governing permissions and
	* limitations under the License.
	*/


	#pragma once

	#include <math.h>
	#include <stdint.h>
	#include <sys/types.h>

	#include <cmath>
	#include <limits>
	#include <iostream>

	#define PURE __attribute__((pure))

	#if __cplusplus >= 201402L
	#define CONSTEXPR constexpr
	#else
	#define CONSTEXPR
	#endif

	namespace android {
	namespace details {
	// -------------------------------------------------------------------------------------

	/*
	* No user serviceable parts here.
	*
	* Don't use this file directly, instead include ui/vec{2\|3\|4}.h
	*/

	/*
	* TVec{Add\|Product}Operators implements basic arithmetic and basic compound assignments
	* operators on a vector of type BASE<T>.
	*
	* BASE only needs to implement operator[] and size().
	* By simply inheriting from TVec{Add\|Product}Operators<BASE, T> BASE will automatically
	* get all the functionality here.
	*/

	template <template<typename T> class VECTOR, typename T>
	class TVecAddOperators {
	public:
	/* compound assignment from a another vector of the same size but different
	* element type.
	*/
	template<typename OTHER>
	VECTOR<T>& operator +=(const VECTOR<OTHER>& v) {
	VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < lhs.size(); i++) {
	lhs[i] += v[i];
	}
	return lhs;
	}
	template<typename OTHER>
	VECTOR<T>& operator -=(const VECTOR<OTHER>& v) {
	VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < lhs.size(); i++) {
	lhs[i] -= v[i];
	}
	return lhs;
	}

	/* compound assignment from a another vector of the same type.
	* These operators can be used for implicit conversion and handle operations
	* like "vector *= scalar" by letting the compiler implicitly convert a scalar
	* to a vector (assuming the BASE<T> allows it).
	*/
	VECTOR<T>& operator +=(const VECTOR<T>& v) {
	VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < lhs.size(); i++) {
	lhs[i] += v[i];
	}
	return lhs;
	}
	VECTOR<T>& operator -=(const VECTOR<T>& v) {
	VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < lhs.size(); i++) {
	lhs[i] -= v[i];
	}
	return lhs;
	}

	/*
	* NOTE: the functions below ARE NOT member methods. They are friend functions
	* with they definition inlined with their declaration. This makes these
	* template functions available to the compiler when (and only when) this class
	* is instantiated, at which point they're only templated on the 2nd parameter
	* (the first one, BASE<T> being known).
	*/

	/* The operators below handle operation between vectors of the same size
	* but of a different element type.
	*/
	template<typename RT>
	friend inline constexpr VECTOR<T> PURE operator +(VECTOR<T> lv, const VECTOR<RT>& rv) {
	// don't pass lv by reference because we need a copy anyways
	return lv += rv;
	}
	template<typename RT>
	friend inline constexpr VECTOR<T> PURE operator -(VECTOR<T> lv, const VECTOR<RT>& rv) {
	// don't pass lv by reference because we need a copy anyways
	return lv -= rv;
	}

	/* The operators below (which are not templates once this class is instanced,
	* i.e.: BASE<T> is known) can be used for implicit conversion on both sides.
	* These handle operations like "vector + scalar" and "scalar + vector" by
	* letting the compiler implicitly convert a scalar to a vector (assuming
	* the BASE<T> allows it).
	*/
	friend inline constexpr VECTOR<T> PURE operator +(VECTOR<T> lv, const VECTOR<T>& rv) {
	// don't pass lv by reference because we need a copy anyways
	return lv += rv;
	}
	friend inline constexpr VECTOR<T> PURE operator -(VECTOR<T> lv, const VECTOR<T>& rv) {
	// don't pass lv by reference because we need a copy anyways
	return lv -= rv;
	}
	};

	template<template<typename T> class VECTOR, typename T>
	class TVecProductOperators {
	public:
	/* compound assignment from a another vector of the same size but different
	* element type.
	*/
	template<typename OTHER>
	VECTOR<T>& operator *=(const VECTOR<OTHER>& v) {
	VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < lhs.size(); i++) {
	lhs[i] *= v[i];
	}
	return lhs;
	}
	template<typename OTHER>
	VECTOR<T>& operator /=(const VECTOR<OTHER>& v) {
	VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < lhs.size(); i++) {
	lhs[i] /= v[i];
	}
	return lhs;
	}

	/* compound assignment from a another vector of the same type.
	* These operators can be used for implicit conversion and handle operations
	* like "vector *= scalar" by letting the compiler implicitly convert a scalar
	* to a vector (assuming the BASE<T> allows it).
	*/
	VECTOR<T>& operator *=(const VECTOR<T>& v) {
	VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < lhs.size(); i++) {
	lhs[i] *= v[i];
	}
	return lhs;
	}
	VECTOR<T>& operator /=(const VECTOR<T>& v) {
	VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < lhs.size(); i++) {
	lhs[i] /= v[i];
	}
	return lhs;
	}

	/*
	* NOTE: the functions below ARE NOT member methods. They are friend functions
	* with they definition inlined with their declaration. This makes these
	* template functions available to the compiler when (and only when) this class
	* is instantiated, at which point they're only templated on the 2nd parameter
	* (the first one, BASE<T> being known).
	*/

	/* The operators below handle operation between vectors of the same size
	* but of a different element type.
	*/
	template<typename RT>
	friend inline constexpr VECTOR<T> PURE operator *(VECTOR<T> lv, const VECTOR<RT>& rv) {
	// don't pass lv by reference because we need a copy anyways
	return lv *= rv;
	}
	template<typename RT>
	friend inline constexpr VECTOR<T> PURE operator /(VECTOR<T> lv, const VECTOR<RT>& rv) {
	// don't pass lv by reference because we need a copy anyways
	return lv /= rv;
	}

	/* The operators below (which are not templates once this class is instanced,
	* i.e.: BASE<T> is known) can be used for implicit conversion on both sides.
	* These handle operations like "vector * scalar" and "scalar * vector" by
	* letting the compiler implicitly convert a scalar to a vector (assuming
	* the BASE<T> allows it).
	*/
	friend inline constexpr VECTOR<T> PURE operator *(VECTOR<T> lv, const VECTOR<T>& rv) {
	// don't pass lv by reference because we need a copy anyways
	return lv *= rv;
	}
	friend inline constexpr VECTOR<T> PURE operator /(VECTOR<T> lv, const VECTOR<T>& rv) {
	// don't pass lv by reference because we need a copy anyways
	return lv /= rv;
	}
	};

	/*
	* TVecUnaryOperators implements unary operators on a vector of type BASE<T>.
	*
	* BASE only needs to implement operator[] and size().
	* By simply inheriting from TVecUnaryOperators<BASE, T> BASE will automatically
	* get all the functionality here.
	*
	* These operators are implemented as friend functions of TVecUnaryOperators<BASE, T>
	*/
	template<template<typename T> class VECTOR, typename T>
	class TVecUnaryOperators {
	public:
	VECTOR<T>& operator ++() {
	VECTOR<T>& rhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < rhs.size(); i++) {
	++rhs[i];
	}
	return rhs;
	}

	VECTOR<T>& operator --() {
	VECTOR<T>& rhs = static_cast<VECTOR<T>&>(*this);
	for (size_t i = 0; i < rhs.size(); i++) {
	--rhs[i];
	}
	return rhs;
	}

	CONSTEXPR VECTOR<T> operator -() const {
	VECTOR<T> r(VECTOR<T>::NO_INIT);
	VECTOR<T> const& rv(static_cast<VECTOR<T> const&>(*this));
	for (size_t i = 0; i < r.size(); i++) {
	r[i] = -rv[i];
	}
	return r;
	}
	};

	/*
	* TVecComparisonOperators implements relational/comparison operators
	* on a vector of type BASE<T>.
	*
	* BASE only needs to implement operator[] and size().
	* By simply inheriting from TVecComparisonOperators<BASE, T> BASE will automatically
	* get all the functionality here.
	*/
	template<template<typename T> class VECTOR, typename T>
	class TVecComparisonOperators {
	public:
	/*
	* NOTE: the functions below ARE NOT member methods. They are friend functions
	* with they definition inlined with their declaration. This makes these
	* template functions available to the compiler when (and only when) this class
	* is instantiated, at which point they're only templated on the 2nd parameter
	* (the first one, BASE<T> being known).
	*/
	template<typename RT>
	friend inline
	bool PURE operator ==(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	for (size_t i = 0; i < lv.size(); i++)
	if (lv[i] != rv[i])
	return false;
	return true;
	}

	template<typename RT>
	friend inline
	bool PURE operator !=(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	return !operator ==(lv, rv);
	}

	template<typename RT>
	friend inline
	bool PURE operator >(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	for (size_t i = 0; i < lv.size(); i++) {
	if (lv[i] == rv[i]) {
	continue;
	}
	return lv[i] > rv[i];
	}
	return false;
	}

	template<typename RT>
	friend inline
	constexpr bool PURE operator <=(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	return !(lv > rv);
	}

	template<typename RT>
	friend inline
	bool PURE operator <(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	for (size_t i = 0; i < lv.size(); i++) {
	if (lv[i] == rv[i]) {
	continue;
	}
	return lv[i] < rv[i];
	}
	return false;
	}

	template<typename RT>
	friend inline
	constexpr bool PURE operator >=(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	return !(lv < rv);
	}

	template<typename RT>
	friend inline
	CONSTEXPR VECTOR<bool> PURE equal(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	VECTOR<bool> r;
	for (size_t i = 0; i < lv.size(); i++) {
	r[i] = lv[i] == rv[i];
	}
	return r;
	}

	template<typename RT>
	friend inline
	CONSTEXPR VECTOR<bool> PURE notEqual(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	VECTOR<bool> r;
	for (size_t i = 0; i < lv.size(); i++) {
	r[i] = lv[i] != rv[i];
	}
	return r;
	}

	template<typename RT>
	friend inline
	CONSTEXPR VECTOR<bool> PURE lessThan(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	VECTOR<bool> r;
	for (size_t i = 0; i < lv.size(); i++) {
	r[i] = lv[i] < rv[i];
	}
	return r;
	}

	template<typename RT>
	friend inline
	CONSTEXPR VECTOR<bool> PURE lessThanEqual(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	VECTOR<bool> r;
	for (size_t i = 0; i < lv.size(); i++) {
	r[i] = lv[i] <= rv[i];
	}
	return r;
	}

	template<typename RT>
	friend inline
	CONSTEXPR VECTOR<bool> PURE greaterThan(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	VECTOR<bool> r;
	for (size_t i = 0; i < lv.size(); i++) {
	r[i] = lv[i] > rv[i];
	}
	return r;
	}

	template<typename RT>
	friend inline
	CONSTEXPR VECTOR<bool> PURE greaterThanEqual(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	VECTOR<bool> r;
	for (size_t i = 0; i < lv.size(); i++) {
	r[i] = lv[i] >= rv[i];
	}
	return r;
	}
	};

	/*
	* TVecFunctions implements functions on a vector of type BASE<T>.
	*
	* BASE only needs to implement operator[] and size().
	* By simply inheriting from TVecFunctions<BASE, T> BASE will automatically
	* get all the functionality here.
	*/
	template<template<typename T> class VECTOR, typename T>
	class TVecFunctions {
	public:
	/*
	* NOTE: the functions below ARE NOT member methods. They are friend functions
	* with they definition inlined with their declaration. This makes these
	* template functions available to the compiler when (and only when) this class
	* is instantiated, at which point they're only templated on the 2nd parameter
	* (the first one, BASE<T> being known).
	*/
	template<typename RT>
	friend inline CONSTEXPR T PURE dot(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	T r(0);
	for (size_t i = 0; i < lv.size(); i++) {
	//r = std::fma(lv[i], rv[i], r);
	r += lv[i] * rv[i];
	}
	return r;
	}

	friend inline constexpr T PURE norm(const VECTOR<T>& lv) {
	return std::sqrt(dot(lv, lv));
	}

	friend inline constexpr T PURE length(const VECTOR<T>& lv) {
	return norm(lv);
	}

	friend inline constexpr T PURE norm2(const VECTOR<T>& lv) {
	return dot(lv, lv);
	}

	friend inline constexpr T PURE length2(const VECTOR<T>& lv) {
	return norm2(lv);
	}

	template<typename RT>
	friend inline constexpr T PURE distance(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	return length(rv - lv);
	}

	template<typename RT>
	friend inline constexpr T PURE distance2(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
	return length2(rv - lv);
	}

	friend inline constexpr VECTOR<T> PURE normalize(const VECTOR<T>& lv) {
	return lv * (T(1) / length(lv));
	}

	friend inline constexpr VECTOR<T> PURE rcp(VECTOR<T> v) {
	return T(1) / v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE abs(VECTOR<T> v) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = std::abs(v[i]);
	}
	return v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE floor(VECTOR<T> v) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = std::floor(v[i]);
	}
	return v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE ceil(VECTOR<T> v) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = std::ceil(v[i]);
	}
	return v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE round(VECTOR<T> v) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = std::round(v[i]);
	}
	return v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE inversesqrt(VECTOR<T> v) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = T(1) / std::sqrt(v[i]);
	}
	return v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE sqrt(VECTOR<T> v) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = std::sqrt(v[i]);
	}
	return v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE pow(VECTOR<T> v, T p) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = std::pow(v[i], p);
	}
	return v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE saturate(const VECTOR<T>& lv) {
	return clamp(lv, T(0), T(1));
	}

	friend inline CONSTEXPR VECTOR<T> PURE clamp(VECTOR<T> v, T min, T max) {
	for (size_t i = 0; i< v.size(); i++) {
	v[i] = std::min(max, std::max(min, v[i]));
	}
	return v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE fma(const VECTOR<T>& lv, const VECTOR<T>& rv, VECTOR<T> a) {
	for (size_t i = 0; i<lv.size(); i++) {
	//a[i] = std::fma(lv[i], rv[i], a[i]);
	a[i] += (lv[i] * rv[i]);
	}
	return a;
	}

	friend inline CONSTEXPR VECTOR<T> PURE min(const VECTOR<T>& u, VECTOR<T> v) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = std::min(u[i], v[i]);
	}
	return v;
	}

	friend inline CONSTEXPR VECTOR<T> PURE max(const VECTOR<T>& u, VECTOR<T> v) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = std::max(u[i], v[i]);
	}
	return v;
	}

	friend inline CONSTEXPR T PURE max(const VECTOR<T>& v) {
	T r(std::numeric_limits<T>::lowest());
	for (size_t i = 0; i < v.size(); i++) {
	r = std::max(r, v[i]);
	}
	return r;
	}

	friend inline CONSTEXPR T PURE min(const VECTOR<T>& v) {
	T r(std::numeric_limits<T>::max());
	for (size_t i = 0; i < v.size(); i++) {
	r = std::min(r, v[i]);
	}
	return r;
	}

	friend inline CONSTEXPR VECTOR<T> PURE apply(VECTOR<T> v, const std::function<T(T)>& f) {
	for (size_t i = 0; i < v.size(); i++) {
	v[i] = f(v[i]);
	}
	return v;
	}

	friend inline CONSTEXPR bool PURE any(const VECTOR<T>& v) {
	for (size_t i = 0; i < v.size(); i++) {
	if (v[i] != T(0)) return true;
	}
	return false;
	}

	friend inline CONSTEXPR bool PURE all(const VECTOR<T>& v) {
	bool result = true;
	for (size_t i = 0; i < v.size(); i++) {
	result &= (v[i] != T(0));
	}
	return result;
	}

	template<typename R>
	friend inline CONSTEXPR VECTOR<R> PURE map(VECTOR<T> v, const std::function<R(T)>& f) {
	VECTOR<R> result;
	for (size_t i = 0; i < v.size(); i++) {
	result[i] = f(v[i]);
	}
	return result;
	}
	};

	/*
	* TVecDebug implements functions on a vector of type BASE<T>.
	*
	* BASE only needs to implement operator[] and size().
	* By simply inheriting from TVecDebug<BASE, T> BASE will automatically
	* get all the functionality here.
	*/
	template<template<typename T> class VECTOR, typename T>
	class TVecDebug {
	public:
	/*
	* NOTE: the functions below ARE NOT member methods. They are friend functions
	* with they definition inlined with their declaration. This makes these
	* template functions available to the compiler when (and only when) this class
	* is instantiated, at which point they're only templated on the 2nd parameter
	* (the first one, BASE<T> being known).
	*/
	friend std::ostream& operator<<(std::ostream& stream, const VECTOR<T>& v) {
	stream << "< ";
	for (size_t i = 0; i < v.size() - 1; i++) {
	stream << T(v[i]) << ", ";
	}
	stream << T(v[v.size() - 1]) << " >";
	return stream;
	}
	};

	#undef CONSTEXPR
	#undef PURE

	// -------------------------------------------------------------------------------------
	} // namespace details
	} // namespace android