numeric.h

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/******************************************************************************
The MIT License(MIT)
 
Embedded Template Library.
https://github.com/ETLCPP/etl
https://www.etlcpp.com
 
Copyright(c) 2014 John Wellbelove
 
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files(the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and / or sell
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The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
 
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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******************************************************************************/
 
#ifndef ETL_NUMERIC_INCLUDED
#define ETL_NUMERIC_INCLUDED
 
#include "platform.h"
#include "type_traits.h"
#include "limits.h"
#include "iterator.h"
 
#if ETL_USING_STL
  #include <iterator>
#endif
 
 
namespace etl
{
  //***************************************************************************
  //***************************************************************************
  template <typename TIterator, typename T>
  ETL_CONSTEXPR14 void iota(TIterator first, TIterator last, T value)
  {
    while (first != last)
    {
      *first++ = value++;
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<!etl::is_pointer<T>::value &&
                                          !etl::is_integral<T>::value &&
                                          etl::is_floating_point<T>::value, T>::type
    midpoint(T a, T b) ETL_NOEXCEPT
  {
    T lo = etl::numeric_limits<T>::min() * T(2);
    T hi = etl::numeric_limits<T>::max() * T(2);
 
    return ((abs(a) <= hi) && (abs(b) <= hi)) ?
              (a + b) / T(2) :
              (abs(a) < lo) ?
                a + (b / T(2)) :
                (abs(b) < lo) ?
                  ((a / T(2)) + b) :
                  (a / T(2)) + (b / T(2));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<!etl::is_pointer<T>::value &&
                                          etl::is_integral<T>::value &&
                                          !etl::is_floating_point<T>::value &&
                                          etl::is_unsigned<T>::value, T>::type
    midpoint(T a, T b) ETL_NOEXCEPT
  {
    if (a > b)
    {
      return a - ((a - b) >> 1);
    }
    else
    {
      return a + ((b - a) >> 1);
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<!etl::is_pointer<T>::value&&
                                          etl::is_integral<T>::value &&
                                          !etl::is_floating_point<T>::value&&
                                          etl::is_signed<T>::value, T>::type
    midpoint(T a, T b) ETL_NOEXCEPT
  {
    typedef typename etl::make_unsigned<T>::type utype;
 
    if (a > b)
    {
      return a - T(utype(utype(a) - utype(b)) >> 1);
    }
    else
    {
      return a + T((utype(b) - utype(a)) >> 1);
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<etl::is_pointer<T>::value&&
                                          !etl::is_integral<T>::value &&
                                          !etl::is_floating_point<T>::value, T>::type
    midpoint(T a, T b) ETL_NOEXCEPT
  {
    if (a > b)
    {
      return b + (etl::distance(b, a) / 2U);
    }
    else
    {
      return a + (etl::distance(a, b) / 2U);
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 T midpoint(T a, T b, typename etl::enable_if<!etl::is_pointer<T>::value &&
    !etl::is_integral<T>::value &&
    !etl::is_floating_point<T>::value &&
    etl::is_same<typename etl::iterator_traits<T>::iterator_category, ETL_OR_STD::random_access_iterator_tag>::value , int>::type = 0)
  {
    if (a > b)
    {
      return b + (etl::distance(b, a) / 2U);
    }
    else
    {
      return a + (etl::distance(a, b) / 2U);
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 T midpoint(T a, T b, typename etl::enable_if<(!etl::is_pointer<T>::value &&
                                                                !etl::is_integral<T>::value &&
                                                                !etl::is_floating_point<T>::value &&
                                                                (etl::is_same<typename etl::iterator_traits<T>::iterator_category, ETL_OR_STD::forward_iterator_tag>::value ||
                                                                 etl::is_same<typename etl::iterator_traits<T>::iterator_category, ETL_OR_STD::bidirectional_iterator_tag>::value)),  int>::type = 0)
  {
    etl::advance(a, etl::distance(a, b) / 2U);
    return a;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR typename etl::enable_if<etl::is_floating_point<T>::value, T>::type
    lerp(T a, T b, T t) ETL_NOEXCEPT
  {
    return a + (t * (b - a));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename TArithmetic1, typename TArithmetic2, typename TArithmetic3>
  ETL_CONSTEXPR typename etl::enable_if<!etl::is_floating_point<TArithmetic1>::value ||
                                        !etl::is_floating_point<TArithmetic2>::value ||
                                        !etl::is_floating_point<TArithmetic3>::value, typename etl::conditional<etl::is_same<TArithmetic1, long double>::value ||
                                                                                                                etl::is_same<TArithmetic2, long double>::value ||
                                                                                                                etl::is_same<TArithmetic3, long double>::value, long double, double>::type>::type
    lerp(TArithmetic1 a, TArithmetic2 b, TArithmetic3 t) ETL_NOEXCEPT
  {
    typedef typename etl::conditional<etl::is_integral<TArithmetic1>::value, double, TArithmetic1>::type typecast_a;
    typedef typename etl::conditional<etl::is_integral<TArithmetic2>::value, double, TArithmetic2>::type typecast_b;
    typedef typename etl::conditional<etl::is_integral<TArithmetic3>::value, double, TArithmetic3>::type typecast_t;
 
    return typecast_a(a) + (typecast_t(t) * (typecast_b(b) - typecast_a(a)));
  }
}
 
#endif