ratio

Overview

The estd::ratio provides compile-time rational arithmetic support.

This template is used to instantiate types that represent a finite rational number denoted by a numerator and a denominator, which are implemented as compile-time constants of type intmax_t.
The ratio is not represented by an object of this type but by the type itself, which uses compile-time constant members to define the ratio. Therefore, ratio can only be used to express constants and cannot contain any value.

N - Numerator. D - Denominator. Their absolute values shall be in the range of representable values of intmax_t, which is the widest signed integer type, and D shall not be zero.

The static constants num and den are not the same as the template arguments N and D if the greatest common divisor among N and D is not one, as the num and den are the results of dividing N and D by that greatest common divisor.

Usage

The usage constraints and guidelines apply for ratio:

Constraints

ratio with zero denominator cannot be created. Static assertion is thrown if attempt to create is made.

Example

The estd::ratio.h provides compile-time rational arithmetic support.

Following example shows the basic functionalities of ratio:

    // num is used to get the numerator of a ratio.
    static_assert((3 == ::estd::ratio<3, 5>::num), "");

    // den is used to get the denominator of a ratio.
    static_assert((5 == ::estd::ratio<3, 5>::den), "");

    static_assert(std::is_same<::estd::ratio<1, 5>::type, ::estd::ratio<1, 5>>::value, "");

    static_assert(std::is_same<::estd::ratio<10, 50>::type, ::estd::ratio<1, 5>>::value, "");

    static_assert(std::is_same<::estd::ratio<-1, -5>::type, ::estd::ratio<1, 5>>::value, "");

    static_assert(std::is_same<::estd::ratio<-10, 50>::type, ::estd::ratio<-1, 5>>::value, "");

Usage example of comparison operator in ratio:

    static_assert(::estd::ratio_equal<::estd::ratio<1, 5>, ::estd::ratio<2, 10>>::value, "");

    static_assert(!::estd::ratio_not_equal<::estd::ratio<1, 5>, ::estd::ratio<2, 10>>::value, "");

    static_assert(!::estd::ratio_less<::estd::ratio<1, 5>, ::estd::ratio<2, 10>>::value, "");

    static_assert(!::estd::ratio_greater<::estd::ratio<1, 5>, ::estd::ratio<2, 10>>::value, "");

    static_assert(::estd::ratio_less_equal<::estd::ratio<1, 5>, ::estd::ratio<2, 10>>::value, "");

    static_assert(
        ::estd::ratio_greater_equal<::estd::ratio<1, 5>, ::estd::ratio<2, 10>>::value, "");

Usage example of arithmetic operator in ratio:

    {
        static_assert(
            std::is_same<
                ::estd::ratio<11, 30>,
                ::estd::ratio_add<::estd::ratio<1, 5>, ::estd::ratio<1, 6>>::type>::value,
            "");

        static_assert(
            std::is_same<
                ::estd::ratio<1, 30>,
                ::estd::ratio_subtract<::estd::ratio<1, 5>, ::estd::ratio<1, 6>>::type>::value,
            "");

        static_assert(
            std::is_same<
                ::estd::ratio<7, 15>,
                ::estd::ratio_multiply<::estd::ratio<2, 5>, ::estd::ratio<7, 6>>::type>::value,
            "");

        static_assert(
            std::is_same<
                ::estd::ratio<4, 3>,
                ::estd::ratio_divide<::estd::ratio<2, 4>, ::estd::ratio<3, 8>>::type>::value,
            "");
    }

Example of some predefined types in ratio:

    static_assert(std::is_same<::estd::ratio<1000000000000000000, 1>, ::estd::exa>::value, "");

    static_assert(std::is_same<::estd::ratio<1000000000000000, 1>, ::estd::peta>::value, "");