300 lines
9.7 KiB
C++
300 lines
9.7 KiB
C++
///\file
|
|
|
|
/******************************************************************************
|
|
The MIT License(MIT)
|
|
|
|
Embedded Template Library.
|
|
https://github.com/ETLCPP/etl
|
|
https://www.etlcpp.com
|
|
|
|
Copyright(c) 2016 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
|
|
copies of the Software, and to permit persons to whom the Software is
|
|
furnished to do so, subject to the following conditions :
|
|
|
|
The above copyright notice and this permission notice shall be included in all
|
|
copies or substantial portions of the Software.
|
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE
|
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
|
SOFTWARE.
|
|
******************************************************************************/
|
|
|
|
#ifndef ETL_RATIO_INCLUDED
|
|
#define ETL_RATIO_INCLUDED
|
|
|
|
#include "platform.h"
|
|
#include "gcd.h"
|
|
#include "static_assert.h"
|
|
|
|
#include "type_traits.h"
|
|
|
|
#include <stddef.h>
|
|
#include <stdint.h>
|
|
|
|
///\defgroup ratio ratio
|
|
///\ingroup maths
|
|
|
|
namespace etl
|
|
{
|
|
//***********************************************************************
|
|
/// ratio
|
|
//***********************************************************************
|
|
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
|
|
//***********************************************************************
|
|
/// ratio_add
|
|
//***********************************************************************
|
|
template <typename TRatio1, typename TRatio2>
|
|
using ratio_add = etl::ratio<(TRatio1::num * TRatio2::den) + (TRatio2::num * TRatio1::den), TRatio1::den * TRatio2::den>;
|
|
|
|
//***********************************************************************
|
|
/// ratio_subtract
|
|
//***********************************************************************
|
|
template <typename TRatio1, typename TRatio2>
|
|
using ratio_subtract = etl::ratio<(TRatio1::num * TRatio2::den) - (TRatio2::num * TRatio1::den), TRatio1::den * TRatio2::den>;
|
|
|
|
//***********************************************************************
|
|
/// ratio_multiply
|
|
//***********************************************************************
|
|
template <typename TRatio1, typename TRatio2>
|
|
using ratio_multiply = etl::ratio<TRatio1::num * TRatio2::num, TRatio1::den * TRatio2::den>;
|
|
|
|
//***********************************************************************
|
|
/// ratio_divide
|
|
//***********************************************************************
|
|
template <typename TRatio1, typename TRatio2>
|
|
using ratio_divide = etl::ratio<TRatio1::num * TRatio2::den, TRatio1::den * TRatio2::num>;
|
|
#endif
|
|
|
|
//***********************************************************************
|
|
/// ratio_equal
|
|
//***********************************************************************
|
|
template <typename TRatio1, typename TRatio2>
|
|
struct ratio_equal : etl::bool_constant<(TRatio1::num == TRatio2::num) && (TRatio1::den == TRatio2::den)>
|
|
{
|
|
};
|
|
|
|
//***********************************************************************
|
|
/// ratio_not_equal
|
|
//***********************************************************************
|
|
template <typename TRatio1, typename TRatio2>
|
|
struct ratio_not_equal : etl::bool_constant<!etl::ratio_equal<TRatio1, TRatio2>::value>
|
|
{
|
|
};
|
|
|
|
//***********************************************************************
|
|
/// ratio_less
|
|
//***********************************************************************
|
|
template <typename TRatio1, typename TRatio2>
|
|
struct ratio_less : etl::bool_constant<(TRatio1::num * TRatio2::den) < (TRatio2::num * TRatio1::den)>
|
|
{
|
|
};
|
|
|
|
//***********************************************************************
|
|
/// ratio_less_equal
|
|
//***********************************************************************
|
|
template <typename TRatio1, typename TRatio2>
|
|
struct ratio_less_equal : etl::bool_constant<!etl::ratio_less<TRatio2, TRatio1>::value>
|
|
{
|
|
};
|
|
|
|
//***********************************************************************
|
|
/// ratio_greater
|
|
//***********************************************************************
|
|
template <typename TRatio1, typename TRatio2>
|
|
struct ratio_greater : etl::bool_constant<etl::ratio_less<TRatio2, TRatio1>::value>
|
|
{
|
|
};
|
|
|
|
//***********************************************************************
|
|
/// ratio_greater_equal
|
|
//***********************************************************************
|
|
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
|
|
|
|
//***********************************************************************
|
|
/// Predefined ration types.
|
|
//***********************************************************************
|
|
#if INT_MAX > INT32_MAX
|
|
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;
|
|
#endif
|
|
|
|
/// An approximation of Pi.
|
|
typedef ratio<355, 113> ratio_pi;
|
|
|
|
/// An approximation of root 2.
|
|
typedef ratio<239, 169> ratio_root2;
|
|
|
|
/// An approximation of 1 over root 2.
|
|
typedef ratio<169, 239> ratio_1_over_root2;
|
|
|
|
/// An approximation of e.
|
|
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
|