ratio.h

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/******************************************************************************
The MIT License(MIT)
 
Embedded Template Library.
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https://www.etlcpp.com
 
Copyright(c) 2016 John Wellbelove
 
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#ifndef ETL_RATIO_INCLUDED
#define ETL_RATIO_INCLUDED
 
#include "platform.h"
#include "gcd.h"
#include "static_assert.h"
 
#include "type_traits.h"
 
#include <stdint.h>

 
namespace etl
{
  //***********************************************************************
  //***********************************************************************
  template <intmax_t Num, intmax_t Den = 1UL>
  struct ratio
  {
    ETL_STATIC_ASSERT(Num != 0, "Numerator cannot be zero");
    ETL_STATIC_ASSERT(Den != 0, "Denominator cannot be zero");
 
    static ETL_CONSTANT intmax_t num = Num / etl::gcd_const<Num, Den>::value;
    static ETL_CONSTANT intmax_t den = Den / etl::gcd_const<Num, Den>::value;
 
    typedef etl::ratio<num, den> type;
  };
 
  template <intmax_t Num, intmax_t Den>
  ETL_CONSTANT intmax_t ratio<Num, Den>::num;
 
  template <intmax_t Num, intmax_t Den>
  ETL_CONSTANT intmax_t ratio<Num, Den>::den;
 
#if ETL_USING_CPP11
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  using ratio_add = etl::ratio<(TRatio1::num * TRatio2::den) + (TRatio2::num * TRatio1::den), TRatio1::den * TRatio2::den>;
 
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  using ratio_subtract = etl::ratio<(TRatio1::num * TRatio2::den) - (TRatio2::num * TRatio1::den), TRatio1::den * TRatio2::den>;
 
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  using ratio_multiply = etl::ratio<TRatio1::num * TRatio2::num, TRatio1::den * TRatio2::den>;
 
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  using ratio_divide = etl::ratio<TRatio1::num * TRatio2::den, TRatio1::den * TRatio2::num>;
#endif
 
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  struct ratio_equal : etl::bool_constant<(TRatio1::num == TRatio2::num) && (TRatio1::den == TRatio2::den)>
  {
  };
 
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  struct ratio_not_equal : etl::bool_constant<!etl::ratio_equal<TRatio1, TRatio2>::value>
  {
  };
 
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  struct ratio_less : etl::bool_constant<(TRatio1::num * TRatio2::den) < (TRatio2::num * TRatio1::den)>
  {
  };
 
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  struct ratio_less_equal : etl::bool_constant<!etl::ratio_less<TRatio2, TRatio1>::value>
  {
  };
 
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  struct ratio_greater : etl::bool_constant<etl::ratio_less<TRatio2, TRatio1>::value>
  {
  };
 
  //***********************************************************************
  //***********************************************************************
  template <typename TRatio1, typename TRatio2>
  struct ratio_greater_equal : etl::bool_constant<!etl::ratio_less<TRatio1, TRatio2>::value>
  {
  };
 
#if ETL_USING_CPP17
  template <typename R1, typename R2>
  inline constexpr bool ratio_equal_v = ratio_equal<R1, R2>::value;
 
  template <typename R1, typename R2>
  inline constexpr bool ratio_not_equal_v = ratio_not_equal<R1, R2>::value;
 
  template <typename R1, typename R2>
  inline constexpr bool ratio_less_v = ratio_less<R1, R2>::value;
 
  template <typename R1, typename R2>
  inline constexpr bool ratio_less_equal_v = ratio_less_equal<R1, R2>::value;
 
  template <typename R1, typename R2>
  inline constexpr bool ratio_greater_v = ratio_greater<R1, R2>::value;
 
  template <typename R1, typename R2>
  inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<R1, R2>::value;
#endif
 
//***********************************************************************
//***********************************************************************
#if INT_MAX > INT32_MAX
  // 2022 SI prefix (10^-30)
  typedef ratio<1, 1000000000000000000LL * 1000000000000LL> quecto;
  // 2022 SI prefix (10^-27)
  typedef ratio<1, 1000000000000000000LL * 1000000000LL> ronto;
  // 10^-24
  typedef ratio<1, 1000000000000000000LL * 1000000LL> yocto;
  // 10^-21
  typedef ratio<1, 1000000000000000000LL * 1000LL> zepto;
  typedef ratio<1, 1000000000000000000>            atto;
  typedef ratio<1, 1000000000000000>               femto;
  typedef ratio<1, 1000000000000>                  pico;
#endif
 
#if (INT_MAX >= INT32_MAX)
  typedef ratio<1, 1000000000> nano;
  typedef ratio<1, 1000000>    micro;
#endif
 
#if (INT_MAX >= INT16_MAX)
  typedef ratio<1, 1000> milli;
  typedef ratio<1, 100>  centi;
  typedef ratio<1, 10>   deci;
  typedef ratio<10, 1>   deca;
  typedef ratio<100, 1>  hecto;
  typedef ratio<1000, 1> kilo;
#endif
 
#if (INT_MAX >= INT32_MAX)
  typedef ratio<1000000, 1>    mega;
  typedef ratio<1000000000, 1> giga;
#endif
 
#if INT_MAX > INT32_MAX
  typedef ratio<1000000000000, 1>       tera;
  typedef ratio<1000000000000000, 1>    peta;
  typedef ratio<1000000000000000000, 1> exa;
  // 10^21
  typedef ratio<1000000000000000000LL * 1000LL, 1> zetta;
  // 10^24
  typedef ratio<1000000000000000000LL * 1000000LL, 1> yotta;
  // 2022 SI prefix (10^27)
  typedef ratio<1000000000000000000LL * 1000000000LL, 1> ronna;
  // 2022 SI prefix (10^30)
  typedef ratio<1000000000000000000LL * 1000000000000LL, 1> quetta;
#endif

  typedef ratio<355, 113> ratio_pi;

  typedef ratio<239, 169> ratio_root2;

  typedef ratio<169, 239> ratio_1_over_root2;

  typedef ratio<326, 120> ratio_e;
 
#if ETL_USING_CPP11
  namespace private_ratio
  {
    // Primary template for GCD calculation
    template <typename T, T Value1, T Value2, bool = (Value2 == 0)>
    struct ratio_gcd;
 
    // Specialisation for the case when Value2 is not zero
    template <typename T, T Value1, T Value2>
    struct ratio_gcd<T, Value1, Value2, false>
    {
      static constexpr T value = ratio_gcd<T, Value2, Value1 % Value2>::value;
    };
 
    // Specialisation for the case when Value2 is zero
    template <typename T, T Value1, T Value2>
    struct ratio_gcd<T, Value1, Value2, true>
    {
      static constexpr T value = (Value1 < 0) ? -Value1 : Value1;
    };
 
    // Primary template for LCM calculation
    template <typename T, T Value1, T Value2>
    struct ratio_lcm
    {
    private:
 
      static constexpr T product = ((Value1 * Value2) < 0) ? -(Value1 * Value2) : Value1 * Value2;
 
    public:
 
      static constexpr T value = product / ratio_gcd<T, Value1, Value2>::value;
    };
 
    template <typename R1>
    struct ratio_reduce
    {
    private:
 
      static ETL_CONSTEXPR11 intmax_t gcd = etl::private_ratio::ratio_gcd<intmax_t, R1::num, R1::den>::value;
 
    public:
 
      using type = ratio<R1::num / gcd, R1::den / gcd>;
    };
 
    template <typename R1, typename R2>
    struct ratio_add
    {
    private:
 
      static ETL_CONSTEXPR11 intmax_t lcm = etl::private_ratio::ratio_lcm<intmax_t, R1::den, R2::den>::value;
 
    public:
 
      using type = typename ratio_reduce< ratio<R1::num * lcm / R1::den + R2::num * lcm / R2::den, lcm>>::type;
    };
 
    template <typename R1, typename R2>
    struct ratio_subtract
    {
    public:
 
      using type = typename ratio_add<R1, ratio<-R2::num, R2::den>>::type;
    };
 
    template <typename R1, typename R2>
    struct ratio_multiply
    {
    private:
 
      static ETL_CONSTEXPR11 intmax_t gcd1 = etl::private_ratio::ratio_gcd<intmax_t, R1::num, R2::den>::value;
      static ETL_CONSTEXPR11 intmax_t gcd2 = etl::private_ratio::ratio_gcd<intmax_t, R2::num, R1::den>::value;
 
    public:
 
      using type = ratio<(R1::num / gcd1) * (R2::num / gcd2), (R1::den / gcd2) * (R2::den / gcd1)>;
    };
 
    template <typename R1, typename R2>
    struct ratio_divide
    {
    public:
 
      using type = typename ratio_multiply<R1, ratio<R2::den, R2::num>>::type;
    };
  } // namespace private_ratio
 
#endif
} // namespace etl
 
#endif