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
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******************************************************************************/
 
#ifndef ETL_NUMERIC_INCLUDED
#define ETL_NUMERIC_INCLUDED
 
#include "platform.h"
#include "iterator.h"
#include "limits.h"
#include "type_traits.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) / 2);
    }
    else
    {
      return a + (etl::distance(a, b) / 2);
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  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) / 2);
    }
    else
    {
      return a + (etl::distance(a, b) / 2);
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  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) / 2);
    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)));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<etl::is_integral<T>::value && etl::is_unsigned<T>::value, T>::type add_sat(T x, T y) ETL_NOEXCEPT
  {
    T result = static_cast<T>(x + y);
    // Overflow occurred if result < x
    if (result < x)
    {
      return etl::numeric_limits<T>::max();
    }
    return result;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<etl::is_integral<T>::value && etl::is_signed<T>::value, T>::type add_sat(T x, T y) ETL_NOEXCEPT
  {
    // Check for overflow: both operands have same sign and result has different sign
    if (y > T(0))
    {
      // Positive overflow check
      if (x > (etl::numeric_limits<T>::max() - y))
      {
        return etl::numeric_limits<T>::max();
      }
    }
    else
    {
      // Negative overflow check
      if (x < (etl::numeric_limits<T>::min() - y))
      {
        return etl::numeric_limits<T>::min();
      }
    }
 
    return static_cast<T>(x + y);
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<etl::is_integral<T>::value && etl::is_unsigned<T>::value, T>::type sub_sat(T x, T y) ETL_NOEXCEPT
  {
    // Underflow occurred if y > x
    if (y > x)
    {
      return T(0);
    }
    return static_cast<T>(x - y);
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<etl::is_integral<T>::value && etl::is_signed<T>::value, T>::type sub_sat(T x, T y) ETL_NOEXCEPT
  {
    // Check for overflow/underflow
    if (y > T(0))
    {
      // Subtracting positive: check for underflow
      if (x < (etl::numeric_limits<T>::min() + y))
      {
        return etl::numeric_limits<T>::min();
      }
    }
    else
    {
      // Subtracting negative (adding): check for overflow
      if (x > (etl::numeric_limits<T>::max() + y))
      {
        return etl::numeric_limits<T>::max();
      }
    }
 
    return static_cast<T>(x - y);
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<etl::is_integral<T>::value && etl::is_unsigned<T>::value, T>::type mul_sat(T x, T y) ETL_NOEXCEPT
  {
    if ((x == T(0)) || (y == T(0)))
    {
      return T(0);
    }
 
    // Check for overflow: x * y > max  =>  x > max / y
    if (x > (etl::numeric_limits<T>::max() / y))
    {
      return etl::numeric_limits<T>::max();
    }
 
    return static_cast<T>(x * y);
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<etl::is_integral<T>::value && etl::is_signed<T>::value, T>::type mul_sat(T x, T y) ETL_NOEXCEPT
  {
    if ((x == T(0)) || (y == T(0)))
    {
      return T(0);
    }
 
    // Both positive
    if ((x > T(0)) && (y > T(0)))
    {
      if (x > (etl::numeric_limits<T>::max() / y))
      {
        return etl::numeric_limits<T>::max();
      }
    }
    // Both negative
    else if ((x < T(0)) && (y < T(0)))
    {
      if (x < (etl::numeric_limits<T>::max() / y))
      {
        return etl::numeric_limits<T>::max();
      }
    }
    // Different signs (x positive, y negative)
    else if ((x > T(0)) && (y < T(0)))
    {
      if (y < (etl::numeric_limits<T>::min() / x))
      {
        return etl::numeric_limits<T>::min();
      }
    }
    // Different signs (x negative, y positive)
    else
    {
      if (x < (etl::numeric_limits<T>::min() / y))
      {
        return etl::numeric_limits<T>::min();
      }
    }
 
    return static_cast<T>(x * y);
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<etl::is_integral<T>::value && etl::is_unsigned<T>::value, T>::type div_sat(T x, T y) ETL_NOEXCEPT
  {
    return static_cast<T>(x / y);
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14 typename etl::enable_if<etl::is_integral<T>::value && etl::is_signed<T>::value, T>::type div_sat(T x, T y) ETL_NOEXCEPT
  {
    // The only overflow case: min / -1 would be max + 1
    if ((x == etl::numeric_limits<T>::min()) && (y == T(-1)))
    {
      return etl::numeric_limits<T>::max();
    }
 
    return static_cast<T>(x / y);
  }
 
  //***************************************************************************
  //***************************************************************************
 
  // Case 1: Both unsigned.
  template <typename R, typename T>
  ETL_CONSTEXPR14
    typename etl::enable_if<etl::is_integral<R>::value && etl::is_integral<T>::value && etl::is_unsigned<R>::value && etl::is_unsigned<T>::value,
                            R>::type
    saturate_cast(T value) ETL_NOEXCEPT
  {
    // If sizeof(R) >= sizeof(T), all values of T fit in R.
    // If sizeof(R) < sizeof(T), clamp to R's max. The comparison is safe
    // because R's max fits in T when T is wider.
    if ((sizeof(R) < sizeof(T)) && (value > static_cast<T>(etl::numeric_limits<R>::max())))
    {
      return etl::numeric_limits<R>::max();
    }
    return static_cast<R>(value);
  }
 
  // Case 2: Both signed.
  template <typename R, typename T>
  ETL_CONSTEXPR14
    typename etl::enable_if<etl::is_integral<R>::value && etl::is_integral<T>::value && etl::is_signed<R>::value && etl::is_signed<T>::value, R>::type
    saturate_cast(T value) ETL_NOEXCEPT
  {
    // Only need to clamp when narrowing (R is smaller than T).
    // When sizeof(R) >= sizeof(T), all values of T fit in R.
    if (sizeof(R) < sizeof(T))
    {
      if (value > static_cast<T>(etl::numeric_limits<R>::max()))
      {
        return etl::numeric_limits<R>::max();
      }
      if (value < static_cast<T>(etl::numeric_limits<R>::min()))
      {
        return etl::numeric_limits<R>::min();
      }
    }
    return static_cast<R>(value);
  }
 
  // Case 3: Signed source -> Unsigned destination.
  template <typename R, typename T>
  ETL_CONSTEXPR14
    typename etl::enable_if<etl::is_integral<R>::value && etl::is_integral<T>::value && etl::is_unsigned<R>::value && etl::is_signed<T>::value,
                            R>::type
    saturate_cast(T value) ETL_NOEXCEPT
  {
    if (value < T(0))
    {
      return R(0);
    }
 
    typedef typename etl::make_unsigned<T>::type unsigned_t;
    unsigned_t                                   uvalue = static_cast<unsigned_t>(value);
 
    // Compare in unsigned domain. R's max is always representable as unsigned_t
    // when sizeof(T) > sizeof(R), and when sizeof(R) >= sizeof(T) all positive
    // values of T fit in R.
    if ((sizeof(R) < sizeof(T)) && (uvalue > static_cast<unsigned_t>(etl::numeric_limits<R>::max())))
    {
      return etl::numeric_limits<R>::max();
    }
    return static_cast<R>(value);
  }
 
  // Case 4: Unsigned source -> Signed destination.
  template <typename R, typename T>
  ETL_CONSTEXPR14
    typename etl::enable_if<etl::is_integral<R>::value && etl::is_integral<T>::value && etl::is_signed<R>::value && etl::is_unsigned<T>::value,
                            R>::type
    saturate_cast(T value) ETL_NOEXCEPT
  {
    // R's max is positive, so we can safely represent it as T (unsigned) when
    // sizeof(T) >= sizeof(R). When sizeof(T) < sizeof(R), all values of T fit.
    typedef typename etl::make_unsigned<R>::type unsigned_r;
 
    if (value > static_cast<T>(static_cast<unsigned_r>(etl::numeric_limits<R>::max())))
    {
      return etl::numeric_limits<R>::max();
    }
    return static_cast<R>(value);
  }
} // namespace etl
 
#endif