sol/math/ratio.hpp

   1 #if !defined(sol_math_ratio_hpp_included)
   2 #define sol_math_ratio_hpp_included
   3 /// \addtogroup sol_math
   4 /// \{
   5
   6
   7 /**
   8  * \file sol/math/ratio.hpp
   9  * \brief Compute rational values at compile time
  10  *
  11  * \see http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2661.htm#ratio
  12  *
  13  * \todo ratio comparison
  14  */
  15
  16
  17 #include <sol/cstdint.hpp>
  18 #include <sol/math/abs.hpp>
  19 #include <sol/math/gcd.hpp>
  20 #include <sol/math/sign.hpp>
  21 #include <sol/static_assert.hpp>
  22
  23
  24 namespace sol { namespace math {
  25
  26
  27 /// Rational value representation (calculated during compile-time)
  28 template <intmax_t N, intmax_t D=1>
  29 class ratio
  30 {
  31 private:
  32
  33     static_assert(D != 0, "D != 0");
  34
  35 public:
  36
  37     /// numerator
  38     static intmax_t const num = N * sign<D>::value / gcd<N, D>::value;
  39
  40     /// denominator
  41     static intmax_t const den = abs<D>::value / gcd<N, D>::value;
  42 };
  43
  44
  45 /// rational arithmetic: addition
  46 template <typename R1, typename R2>
  47 struct ratio_add
  48 {
  49     /// resulting type
  50     typedef ratio<
  51         R1::num * R2::den + R2::num * R1::den
  52         , R1::den * R2::den
  53     > type;
  54 };
  55
  56
  57 /// rational arithmetic: subtraction
  58 template <typename R1, typename R2>
  59 struct ratio_subtract
  60 {
  61     /// resulting type
  62     typedef ratio<
  63         R1::num * R2::den - R2::num * R1::den
  64         , R1::den * R2::den
  65     > type;
  66 };
  67
  68
  69 /// rational arithmetic: multiplication
  70 template <typename R1, typename R2>
  71 struct ratio_multiply
  72 {
  73     /// resulting type
  74     typedef ratio<
  75         R1::num * R2::num
  76         , R1::den * R2::den
  77     > type;
  78 };
  79
  80
  81 /// rational arithmetic: division
  82 template <typename R1, typename R2>
  83 struct ratio_divide
  84 {
  85     /// resulting type
  86     typedef ratio<
  87         R1::num * R2::den
  88         , R1::den * R2::num
  89     > type;
  90 };
  91
  92
  93 /// Convenience SI units
  94 /// \{
  95 typedef ratio<1, 1000000000000000000> atto;
  96 typedef ratio<1,    1000000000000000> femto;
  97 typedef ratio<1,       1000000000000> pico;
  98 typedef ratio<1,          1000000000> nano;
  99 typedef ratio<1,             1000000> micro;
 100 typedef ratio<1,                1000> milli;
 101 typedef ratio<1,                 100> centi;
 102 typedef ratio<1,                  10> deci;
 103 typedef ratio<                 10, 1> deca;
 104 typedef ratio<                100, 1> hecto;
 105 typedef ratio<               1000, 1> kilo;
 106 typedef ratio<            1000000, 1> mega;
 107 typedef ratio<         1000000000, 1> giga;
 108 typedef ratio<      1000000000000, 1> tera;
 109 typedef ratio<   1000000000000000, 1> peta;
 110 typedef ratio<1000000000000000000, 1> exa;
 111 /// \}
 112
 113
 114 }}  // namespace sol::math
 115
 116
 117 /// \}
 118 #endif  // sol_math_ratio_hpp_included