44 lines
1.4 KiB
Markdown
44 lines
1.4 KiB
Markdown
[ratio.ratio]
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# 21 Metaprogramming library [[meta]](./#meta)
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## 21.5 Compile-time rational arithmetic [[ratio]](ratio#ratio)
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### 21.5.3 Class template ratio [ratio.ratio]
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[ð](#lib:ratio)
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namespace std {template<intmax_t N, intmax_t D = 1> class ratio {public:static constexpr intmax_t num; static constexpr intmax_t den; using type = ratio<num, den>; };}
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[1](#1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/meta.tex#L7127)
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If the template argument D is zero or the absolute values of either of the
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template arguments N and D is not representable by typeintmax_t, the program is ill-formed[.](#1.sentence-1)
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[*Note [1](#note-1)*:
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These rules ensure that infinite
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ratios are avoided and that for any negative input, there exists a representable value
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of its absolute value which is positive[.](#1.sentence-2)
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This excludes the most negative value[.](#1.sentence-3)
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â *end note*]
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[2](#2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/meta.tex#L7139)
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The static data members num and den shall have the following values,
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where gcd represents the greatest common divisor of the absolute values ofN and D:
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- [(2.1)](#2.1)
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num shall have the value sgn(N) * sgn(D) * abs(N) / gcd[.](#2.1.sentence-1)
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- [(2.2)](#2.2)
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den shall have the value abs(D) / gcd[.](#2.2.sentence-1)
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