/*! \file pimathbase.h
 * \ingroup Math
 * \~\brief
 * \~english Basic mathematical functions and defines
 * \~russian Базовые математические функции и дефайны
 */
/*
    PIP - Platform Independent Primitives
    Basic mathematical functions and defines
    Ivan Pelipenko peri4ko@yandex.ru, Andrey Bychkov work.a.b@yandex.ru

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU Lesser General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/

#ifndef PIMATHBASE_H
#define PIMATHBASE_H

#include "piinit.h"
#include "pipair.h"
#include "pivector.h"
#ifdef QNX
#  undef PIP_MATH_J0
#  undef PIP_MATH_J1
#  undef PIP_MATH_JN
#  undef PIP_MATH_Y0
#  undef PIP_MATH_Y1
#  undef PIP_MATH_YN
#  include <math.h>
#else
#  include <cmath>
#endif

#ifndef M_LN2
#  define M_LN2 0.69314718055994530942
#endif
#ifndef M_LN10
#  define M_LN10 2.30258509299404568402
#endif
#ifndef M_SQRT2
#  define M_SQRT2 1.41421356237309514547
#endif
#ifndef M_SQRT3
#  define M_SQRT3 1.73205080756887719318
#endif
#ifndef M_1_SQRT2
#  define M_1_SQRT2 0.70710678118654746172
#endif
#ifndef M_1_SQRT3
#  define M_1_SQRT3 0.57735026918962584208
#endif
#ifndef M_PI
#  define M_PI 3.141592653589793238462643383280
#endif
#ifndef M_2PI
#  define M_2PI 6.283185307179586476925286766559
#endif
#ifndef M_PI_3
#  define M_PI_3 1.04719755119659774615
#endif
#ifndef M_2PI_3
#  define M_2PI_3 2.0943951023931954923
#endif
#ifndef M_180_PI
#  define M_180_PI 57.2957795130823208768
#endif
#ifndef M_PI_180
#  define M_PI_180 1.74532925199432957692e-2
#endif
#ifndef M_SQRT_PI
#  define M_SQRT_PI 1.772453850905516027298167483341
#endif
#ifndef M_E
#  define M_E 2.7182818284590452353602874713527
#endif
#ifndef M_LIGHT_SPEED
#  define M_LIGHT_SPEED 2.99792458e+8
#endif
#ifndef M_RELATIVE_CONST
#  define M_RELATIVE_CONST -4.442807633e-10;
#endif
#ifndef M_GRAVITY_CONST
#  define M_GRAVITY_CONST 398600.4418e9;
#endif


const double deg2rad = M_PI_180;
const double rad2deg = M_180_PI;

// clang-format off
inline int sign(const float   & x) {return (x < 0.f) ? -1 : (x > 0.f ? 1 : 0);}
inline int sign(const double  & x) {return (x < 0. ) ? -1 : (x > 0.  ? 1 : 0);}
inline int sign(const ldouble & x) {return (x < 0.L) ? -1 : (x > 0.L ? 1 : 0);}

inline int     pow2 (const int p      ) {return 1 << p;}
inline float   pow10(const float &   e) {return powf(10.f, e);}
inline double  pow10(const double &  e) {return pow (10. , e);}
inline ldouble pow10(const ldouble & e) {return powl(10.L, e);}
// clang-format on

inline double sinc(const double & v) {
	if (v == 0.) return 1.;
	double t = M_PI * v;
	return sin(t) / t;
}

PIP_EXPORT double piJ0(const double & v);
PIP_EXPORT double piJ1(const double & v);
PIP_EXPORT double piJn(int n, const double & v);
PIP_EXPORT double piY0(const double & v);
PIP_EXPORT double piY1(const double & v);
PIP_EXPORT double piYn(int n, const double & v);

// clang-format off
inline constexpr float   toRad(float   deg) {return deg * M_PI_180;}
inline constexpr double  toRad(double  deg) {return deg * M_PI_180;}
inline constexpr ldouble toRad(ldouble deg) {return deg * M_PI_180;}
inline constexpr float   toDeg(float   rad) {return rad * M_180_PI;}
inline constexpr double  toDeg(double  rad) {return rad * M_180_PI;}
inline constexpr ldouble toDeg(ldouble rad) {return rad * M_180_PI;}
// clang-format on
template<typename T>
inline constexpr T sqr(const T & v) {
	return v * v;
}
template<typename T>
inline constexpr T toDb(T val) {
	return T(10.) * std::log10(val);
}
template<typename T>
inline constexpr T fromDb(T val) {
	return std::pow(T(10.), val / T(10.));
}

// [-1 ; 1]
PIP_EXPORT double randomd();
// [-1 ; 1] normal
PIP_EXPORT double randomn(double dv = 0., double sv = 1.);

template<typename T>
inline PIVector<T> piAbs(const PIVector<T> & v) {
	PIVector<T> result;
	result.resize(v.size());
	for (uint i = 0; i < v.size(); i++)
		result[i] = piAbs<T>(v[i]);
	return result;
}


template<typename T>
void normalizeAngleDeg360(T & a) {
	while (a < 0.)
		a += 360.;
	while (a > 360.)
		a -= 360.;
}
template<typename T>
double normalizedAngleDeg360(T a) {
	normalizeAngleDeg360(a);
	return a;
}


template<typename T>
void normalizeAngleDeg180(T & a) {
	while (a < -180.)
		a += 360.;
	while (a > 180.)
		a -= 360.;
}
template<typename T>
double normalizedAngleDeg180(T a) {
	normalizeAngleDeg180(a);
	return a;
}


template<typename T>
bool OLS_Linear(const PIVector<PIPair<T, T>> & input, T * out_a, T * out_b) {
	static_assert(std::is_arithmetic<T>::value, "Type must be arithmetic");
	if (input.size_s() < 2) return false;
	int n  = input.size_s();
	T a_t0 = T(), a_t1 = T(), a_t2 = T(), a_t3 = T(), a_t4 = T(), a = T(), b = T();
	for (int i = 0; i < n; ++i) {
		const PIPair<T, T> & cv(input[i]);
		a_t0 += cv.first * cv.second;
		a_t1 += cv.first;
		a_t2 += cv.second;
		a_t3 += cv.first * cv.first;
	}
	a_t4 = n * a_t3 - a_t1 * a_t1;
	if (a_t4 != T()) a = (n * a_t0 - a_t1 * a_t2) / a_t4;
	b = (a_t2 - a * a_t1) / n;
	if (out_a != 0) *out_a = a;
	if (out_b != 0) *out_b = b;
	return true;
}


template<typename T>
bool WLS_Linear(const PIVector<PIPair<T, T>> & input, const PIVector<T> & weights, T * out_a, T * out_b) {
	static_assert(std::is_arithmetic<T>::value, "Type must be arithmetic");
	if (input.size_s() < 2) return false;
	if (input.size_s() != weights.size_s()) return false;
	int n  = input.size_s();
	T a_t0 = T(), a_t1 = T(), a_t2 = T(), a_t3 = T(), a_t4 = T(), a_n = T(), a = T(), b = T();
	for (int i = 0; i < n; ++i) {
		T cp = weights[i];
		const PIPair<T, T> & cv(input[i]);
		a_t0 += cv.first * cv.second * cp;
		a_t1 += cv.first * cp;
		a_t2 += cv.second * cp;
		a_t3 += cv.first * cv.first * cp;
		a_n += cp;
	}
	a_t4 = a_n * a_t3 - a_t1 * a_t1;
	if (a_t4 != T()) a = (a_n * a_t0 - a_t1 * a_t2) / a_t4;
	b = (a_t2 - a * a_t1) / a_n;
	if (out_a != 0) *out_a = a;
	if (out_b != 0) *out_b = b;
	return true;
}

#endif // PIMATHBASE_H