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cppdraft/ratio/ratio.md

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