lcm.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_LCM_INCLUDED
#define ETL_LCM_INCLUDED
 
#include "platform.h"
#include "type_traits.h"
#include "absolute.h"
#include "static_assert.h"
#include "gcd.h"
 
namespace etl
{
  //***************************************************************************
  // Least Common Multiple.
  // Compile time.
  //***************************************************************************
  template <intmax_t Value1, intmax_t Value2>
  struct lcm_const
  {
    static ETL_CONSTANT intmax_t value = (Value1 / gcd_const<Value1, Value2>::value) * Value2;
  };
 
  //***************************************************************************
  // Least Common Multiple.
  // For unsigned types.
  //***************************************************************************
  template <typename T>
  ETL_NODISCARD
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_unsigned<T>::value, T>::type
    lcm(T a, T b) ETL_NOEXCEPT
  {
    ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Integral type required");
 
    // Early termination: if either number is zero, the LCM is zero.
    if (a == 0 || b == 0)
    {
      return 0;
    }
    else
    {
      return a * (b / gcd(a, b));
    }
  }
 
  //***************************************************************************
  // Least Common Multiple.
  // For signed types.
  //***************************************************************************
  template <typename T>
  ETL_NODISCARD
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_signed<T>::value, T>::type
    lcm(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>(lcm(ua, ub));
  }
 
#if ETL_USING_CPP11
  #if ETL_HAS_INITIALIZER_LIST
  //***************************************************************************
  // Least Common Multiple.
  // Non-recursive, using an initializer_list.
  // Top level variadic function.
  //***************************************************************************
  template<typename T, typename... TRest>
  ETL_NODISCARD
  ETL_CONSTEXPR14
  T lcm(T first, TRest... rest) ETL_NOEXCEPT
  {
    T result = first;
 
    for (T value : {rest...})
    {
      result = lcm(result, value);
 
      if (result == 0)
      {
        // Early termination: if the LCM is zero, it will remain zero
        // no matter what other numbers are processed.
        return 0;
      }
    }
 
    return result;
  }
  #else
  //***************************************************************************
  // Least Common Multiple.
  // Recursive
  // Top level variadic function.
  //***************************************************************************
  template<typename T, typename... TRest>
  ETL_NODISCARD
  ETL_CONSTEXPR14
  T lcm(T a, T b, TRest... rest) ETL_NOEXCEPT
  {
    T lcm_ab = lcm(a, b);
 
    if (lcm_ab == 0)
    {
      // Early termination: if the LCM is zero, it will remain zero
      // no matter what other numbers are processed.
      return 0;
    }
    else
    {
      return lcm(lcm_ab, rest...);
    }
  }
  #endif
#endif
}
 
#endif