gcd.h

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/******************************************************************************
The MIT License(MIT)
 
Embedded Template Library.
https://github.com/ETLCPP/etl
https://www.etlcpp.com
 
Copyright(c) 2024 John Wellbelove
 
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#ifndef ETL_GDC_INCLUDED
#define ETL_GDC_INCLUDED
 
#include "type_traits.h"
#include "absolute.h"
#include "static_assert.h"
 
namespace etl
{
  //***************************************************************************
  // Greatest Common Divisor.
  // Compile time.
  //***************************************************************************
  template <intmax_t A, intmax_t B>
  struct gcd_const
  {
    static ETL_CONSTANT intmax_t value = gcd_const<B, A % B>::value;
  };
 
  template <intmax_t A>
  struct gcd_const<A, 0>
  {
    static ETL_CONSTANT intmax_t value = A;
  };
 
  //***************************************************************************
  // Greatest Common Divisor.
  // For unsigned types.
  //***************************************************************************
  template <typename T>
  ETL_NODISCARD
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_unsigned<T>::value, T>::type
    gcd(T a, T b) ETL_NOEXCEPT
  {
    ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Integral type required");
 
    if ((a == 0 || b == 0))
    {
      return (a + b);
    }
 
    while (b != 0) 
    {
      T t = b;
      b = a % b;
      a = t;
    }
    
    return a;
  }
 
  //***************************************************************************
  // Greatest Common Divisor.
  // For signed types.
  //***************************************************************************
  template <typename T>
  ETL_NODISCARD
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_signed<T>::value, T>::type
    gcd(T a, T b) ETL_NOEXCEPT
  {
    ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Integral type required");
 
    typedef typename etl::make_unsigned<T>::type utype;
 
    utype ua = etl::absolute_unsigned(a);
    utype ub = etl::absolute_unsigned(b);
 
    return static_cast<T>(gcd(ua, ub));
  }
 
#if ETL_USING_CPP11
  #if ETL_HAS_INITIALIZER_LIST
  //***************************************************************************
  // Greatest Common Divisor.
  // Non-recursive, using an initializer_list.
  // Top level variadic function.
  //***************************************************************************
  template<typename T, typename... TRest>
  ETL_NODISCARD
  ETL_CONSTEXPR14
  T gcd(T first, TRest... rest) ETL_NOEXCEPT
  {
    T result = first;
 
    for (T value : {rest...})
    {
      result = gcd(result, value);
 
      if (result == 1)
      {
        // Early termination: if the GCD is one, it will remain one
        // no matter what other numbers are processed.
        return 1;
      }
    }
 
    return result;
  }
  #else
  //***************************************************************************
  // Greatest Common Divisor.
  // Recursive.
  // Top level variadic function.
  //***************************************************************************
  template<typename T, typename... TRest>
  ETL_NODISCARD
  ETL_CONSTEXPR14
  T gcd(T a, T b, TRest... rest) ETL_NOEXCEPT
  {
    T gcd_ab = gcd(a, b);
 
    if (gcd_ab == 1)
    {
      // Early termination: if the GCD is one, it will remain one
      // no matter what other numbers are processed.
      return 1;
    }
    else
    {
      return gcd(gcd_ab, rest...);
    }
  }
  #endif
#endif
}
 
#endif