#pragma once
 
#ifndef TCG_NUMERIC_OPS_H
#define TCG_NUMERIC_OPS_H
 
// tcg includes
#include "traits.h"
#include "sfinae.h"
#include "macros.h"
 
// STD includes
#include <cmath>
#include <limits>
 
/*!
  \file     tcg_numeric_ops.h
 
  \brief    This file contains small function snippets to manipulate scalars
            or numerical objects.
*/
 
//***************************************************************************
//    Numerical Operations
//***************************************************************************
 
namespace tcg
{
 
/*!
  Contains small function snippets to manipulate scalars
  or numerical objects.
*/
namespace numeric_ops
{
 
template <typename Scalar>
//inline Scalar NaN() {return (std::numeric_limits<Scalar>::quiet_NaN)();}
inline Scalar NaN()
{
	return (std::numeric_limits<Scalar>::max)();
}
 
//-------------------------------------------------------------------------------------------
 
/*!
  Calculates the sign of a scalar.
  \remark  This function returns the \a integral values \p 1 in case the input value is
           \a positive, \p -1 in case it's negative, and \p 0 in case it's \a exactly \p 0.
  \return  The sign of the input scalar.
*/
template <typename Scalar>
inline int sign(Scalar val, Scalar tol = 0)
{
	return (val > tol) ? 1 : (val < -tol) ? -1 : 0;
}
 
//-------------------------------------------------------------------------------------------
 
//! Computes the nearest integer not greater in magnitude than the given value
template <typename Scalar>
Scalar trunc(Scalar val)
{
	return (val < 0) ? std::ceil(val) : std::floor(val);
}
 
//! Computes the nearest integer \b strictly not greater in magnitude than the given value
template <typename Scalar>
Scalar truncStrict(Scalar val)
{
	return (val < 0) ? std::floor(val + 1) : std::ceil(val - 1);
}
 
//! Computes the nearest integer not lesser in magnitude than the given value
template <typename Scalar>
Scalar grow(Scalar val)
{
	return (val < 0) ? std::floor(val) : std::ceil(val);
}
 
//! Computes the nearest integer \b strictly not lesser in magnitude than the given value
template <typename Scalar>
Scalar growStrict(Scalar val)
{
	return (val < 0) ? std::ceil(val - 1) : std::floor(val + 1);
}
 
//-------------------------------------------------------------------------------------------
 
template <typename Scalar>
inline bool areNear(Scalar a, Scalar b, Scalar tolerance)
{
	return (std::abs(b - a) < tolerance);
}
 
//-------------------------------------------------------------------------------------------
 
template <typename Scalar>
inline typename tcg::disable_if<tcg::is_floating_point<Scalar>::value, Scalar>::type
mod(Scalar val, Scalar mod)
{
	Scalar m = val % mod;
	return (m >= 0) ? m : m + mod;
}
 
template <typename Scalar>
inline typename tcg::enable_if<tcg::is_floating_point<Scalar>::value, Scalar>::type
mod(Scalar val, Scalar mod)
{
	Scalar m = fmod(val, mod);
	return (m >= 0) ? m : m + mod;
}
 
//-------------------------------------------------------------------------------------------
 
template <typename Scalar>
inline Scalar mod(Scalar val, Scalar a, Scalar b)
{
	return a + mod(val - a, b - a);
}
 
//-------------------------------------------------------------------------------------------
 
//! Returns the modular shift value with minimal abs:  <TT>mod(val2, m) = mod(val1 + shift, m)</TT>
template <typename Scalar>
inline Scalar modShift(Scalar val1, Scalar val2, Scalar m)
{
	Scalar shift1 = mod(val2 - val1, m), shift2 = m - shift1;
	return (shift2 < shift1) ? -shift2 : shift1;
}
 
//-------------------------------------------------------------------------------------------
 
//! Returns the modular shift value with minimal abs:  <TT>mod(val2, a, b) = mod(val1 + shift, a, b)</TT>
template <typename Scalar>
inline Scalar modShift(Scalar val1, Scalar val2, Scalar a, Scalar b)
{
	return modShift(val1 - a, val2 - a, b - a);
}
 
//-------------------------------------------------------------------------------------------
 
/*!
  Returns the \a quotient associated to the remainder calculated with mod().
  \return  Integral quotient of the division of \p val by \p d.
*/
template <typename Scalar>
inline typename tcg::disable_if<tcg::is_floating_point<Scalar>::value, Scalar>::type
div(Scalar val, Scalar d)
{
	TCG_STATIC_ASSERT(-3 / 5 == 0);
	TCG_STATIC_ASSERT(3 / -5 == 0);
 
	return (val < 0 || d < 0) ? (val / d) - 1 : val / d;
}
 
/*!
  Returns the \a quotient associated to the remainder calculated with mod().
  \return  Integral quotient of the division of \p val by \p d.
*/
template <typename Scalar>
inline typename tcg::enable_if<tcg::is_floating_point<Scalar>::value, Scalar>::type
div(Scalar val, Scalar d)
{
	return std::floor(val / d);
}
 
//-------------------------------------------------------------------------------------------
 
/*!
  Returns the \a quotient associated to the remainder calculated with mod().
  \return  Integral quotient of the division of \p val by <TT>(b-a)</TT>.
*/
template <typename Scalar>
inline Scalar div(Scalar val, Scalar a, Scalar b)
{
	return div(val - a, b - a);
}
 
//-------------------------------------------------------------------------------------------
 
//! Linear interpolation of values \p v0 and \p v1 with parameter \p t.
template <typename T, typename Scalar>
inline T lerp(const T &v0, const T &v1, Scalar t)
{
	return (1 - t) * v0 + t * v1;
}
 
//-------------------------------------------------------------------------------------------
 
/*!
  \brief Computes the second degree Bezier curve of control points \p c0, \p c1 and \p c2
         at parameter \p t.
*/
template <typename T, typename Scalar>
inline T bezier(const T &c0, const T &c1, const T &c2, Scalar t)
{
	Scalar one_t = 1 - t, t_one_t = t * one_t;							   // 3  Scalar-Scalar products
	return (one_t * one_t) * c0 + (t_one_t + t_one_t) * c1 + (t * t) * c2; // 3  Scalar-T products
 
	// return (c0 * one_t + c1 * t) * one_t + (c1 * one_t + c2 * t) * t;              // 6 Scalar-T products
}
 
//-------------------------------------------------------------------------------------------
 
//! \deprecated
template <typename UScalar>
inline UScalar GE_2Power(UScalar val)
{
	if (!val)
		return 0;
	--val;
 
	UScalar i;
	for (i = 0; val; ++i)
		val = val >> 1;
 
	return 1 << i;
}
}
} // namespace tcg::numeric_ops
 
#endif // TCG_NUMERIC_OPS_H