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Difference between revisions of "cpp/numeric/ratio/ratio multiply"

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< cpp‎ | numeric‎ | ratio
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{{cpp/title | ratio_multiply}}
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{{cpp/title|ratio_multiply}}
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{{cpp/numeric/ratio/sidebar}}
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{{cpp/numeric/ratio/navbar}}
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{{ddcl list begin}}
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{{ddcl|header=ratio|since=c++11|1=
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{{ddcl list header | ratio}}
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{{ddcl list item | 1=
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template< class R1, class R2 >
 
template< class R1, class R2 >
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using ratio_multiply = /* unspecified */;
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using ratio_multiply = /* see below */;
 
}}
 
}}
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{{ddcl list end}}
 
  
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The template alias {{tt|std::ratio_multiply}} denotes the result of multiplying two exact rational fractions represented by the {{c|std::ratio}} instances {{tt|R1}} and {{tt|R2}}. The result a {{c|std::ratio}} instance {{tt|std::ratio<Num, Denom>}} where {{c|1=Num == R1::num * R2::num}} and {{c|1=Denom == R1::den * R2::den}}.
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The alias template {{tt|std::ratio_multiply}} denotes the result of multiplying two exact rational fractions represented by the {{lc|std::ratio}} specializations {{tt|R1}} and {{tt|R2}}.
  
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===Member types===
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The result is a {{lc|std::ratio}} specialization {{c|std::ratio<U, V>}}, such that given  {{c|1=Num == R1::num * R2::num}} and {{c|1=Denom == R1::den * R2::den}} (computed without arithmetic overflow), {{tt|U}} is {{c|std::ratio<Num, Denom>::num}} and {{tt|V}} is {{c|std::ratio<Num, Denom>::den}}.
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{{dcl list begin}}
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{{tdcl list hitem | Member type | Definition}}
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{{tdcl list item | {{tt|type}} | {{c|std::ratio<num, den>}}}}
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{{dcl list end}}
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===Member constants===
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===Notes===
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{{dcl list begin}}
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If {{tt|U}} or {{tt|V}} is not representable in {{lc|std::intmax_t}}, the program is ill-formed. If {{tt|Num}} or {{tt|Denom}} is not representable in {{lc|std::intmax_t}}, the program is ill-formed unless the implementation yields correct values for {{tt|U}} and {{tt|V}}.
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{{dcl list mem sconst | nolink=true | num | {{c|constexpr}} value of type {{c|std::intmax_t}} equal to {{tt|sign(Num) * sign(Denom) * abs(Num) / gcd(Num, Denom)}} }}
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{{dcl list mem sconst | nolink=true | den | {{c|constexpr}} value of type {{c|std::intmax_t}} equal to {{tt|abs(Denom) / gcd(Num, Denom)}} }}
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The above definition requires that the result of {{c|std::ratio_multiply<R1, R2>}} be already reduced to lowest terms; for example, {{c|std::ratio_multiply<std::ratio<1, 6>, std::ratio<4, 5>>}} is the same type as {{c|std::ratio<2, 15>}}.
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{{dcl list end}}
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===Example===
 
===Example===
 
{{example
 
{{example
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|
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|
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| code=
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|code=
 
#include <iostream>
 
#include <iostream>
 
#include <ratio>
 
#include <ratio>
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int main()
 
int main()
 
{
 
{
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     typedef std::ratio<2, 3> two_third;
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     using two_third = std::ratio<2, 3>;
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     typedef std::ratio<1, 6> one_sixth;
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     using one_sixth = std::ratio<1, 6>;
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     typedef std::ratio_multiply<two_third, one_sixth> r;
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     using product = std::ratio_multiply<two_third, one_sixth>;
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     std::cout << "2/3 * 1/6 = " << r::num << '/' << r::den << '\n';
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    static_assert(std::ratio_equal_v<product, std::ratio<13, 117>>);
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     std::cout << "2/3 * 1/6 = " << product::num << '/' << product::den << '\n';
 
}
 
}
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| output=
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|output=
 
2/3 * 1/6 = 1/9
 
2/3 * 1/6 = 1/9
 
}}
 
}}
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===See also===
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{{dsc begin}}
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{{dsc inc|cpp/numeric/ratio/dsc ratio_divide}}
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{{dsc end}}
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{{langlinks|de|es|fr|it|ja|pt|ru|zh}}

Latest revision as of 14:46, 20 March 2023

 
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Compile-time rational arithmetic
Compile-time integer sequences
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Compile time rational arithmetic
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ratio_multiply
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(C++11)
 
Defined in header <ratio>
template< class R1, class R2 >
using ratio_multiply = /* see below */;
 (since C++11)

The alias template std::ratio_multiply denotes the result of multiplying two exact rational fractions represented by the std::ratio specializations R1 and R2.

The result is a std::ratio specialization std::ratio<U, V>, such that given Num == R1::num * R2::num and Denom == R1::den * R2::den (computed without arithmetic overflow), U is std::ratio<Num, Denom>::num and V is std::ratio<Num, Denom>::den.

[edit] Notes

If U or V is not representable in std::intmax_t, the program is ill-formed. If Num or Denom is not representable in std::intmax_t, the program is ill-formed unless the implementation yields correct values for U and V.

The above definition requires that the result of std::ratio_multiply<R1, R2> be already reduced to lowest terms; for example, std::ratio_multiply<std::ratio<1, 6>, std::ratio<4, 5>> is the same type as std::ratio<2, 15>.

[edit] Example

Run this code
#include <iostream>
#include <ratio>
 
int main()
{
    using two_third = std::ratio<2, 3>;
    using one_sixth = std::ratio<1, 6>;
    using product = std::ratio_multiply<two_third, one_sixth>;
    static_assert(std::ratio_equal_v<product, std::ratio<13, 117>>);
    std::cout << "2/3 * 1/6 = " << product::num << '/' << product::den << '\n';
}

Output: 

2/3 * 1/6 = 1/9

[edit] See also

(C++11)
 divides two ratio objects at compile-time
(alias template)[edit]
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