[ratio] - C++17 → C++20

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@@ -1,18 +1,18 @@
 ## Compile-time rational arithmetic <a id="ratio">[[ratio]]</a>
 ### In general <a id="ratio.general">[[ratio.general]]</a>
-This subclause describes the ratio library. It provides a class template
-`ratio` which exactly represents any finite rational number with a
-numerator and denominator representable by compile-time constants of
-type `intmax_t`.
-Throughout this subclause, the names of template parameters are used to
-express type requirements. If a template parameter is named `R1` or
-`R2`, and the template argument is not a specialization of the `ratio`
-template, the program is ill-formed.
 ### Header `<ratio>` synopsis <a id="ratio.syn">[[ratio.syn]]</a>
 ``` cpp
 namespace std {
@@ -72,12 +72,11 @@ namespace std {
 ### Class template `ratio` <a id="ratio.ratio">[[ratio.ratio]]</a>
 ``` cpp
 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>;
   };
@@ -88,12 +87,12 @@ If the template argument `D` is zero or the absolute values of either of
 the template arguments `N` and `D` is not representable by type
 `intmax_t`, the program is ill-formed.
 [*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. In a two’s complement representation,
-this excludes the most negative value. — *end note*]
 The static data members `num` and `den` shall have the following values,
 where `gcd` represents the greatest common divisor of the absolute
 values of `N` and `D`:
@@ -103,22 +102,22 @@ values of `N` and `D`:
 ### Arithmetic on `ratio`s <a id="ratio.arithmetic">[[ratio.arithmetic]]</a>
 Each of the alias templates `ratio_add`, `ratio_subtract`,
 `ratio_multiply`, and `ratio_divide` denotes the result of an arithmetic
 computation on two `ratio`s `R1` and `R2`. With `X` and `Y` computed (in
-the absence of arithmetic overflow) as specified by Table
-[[tab:ratio.arithmetic]], each alias denotes a `ratio<U, V>` such that
-`U` is the same as `ratio<X, Y>::num` and `V` is the same as
 `ratio<X, Y>::den`.
 If it is not possible to represent `U` or `V` with `intmax_t`, the
 program is ill-formed. Otherwise, an implementation should yield correct
 values of `U` and `V`. If it is not possible to represent `X` or `Y`
 with `intmax_t`, the program is ill-formed unless the implementation
 yields correct values of `U` and `V`.
-**Table: Expressions used to perform ratio arithmetic** <a id="tab:ratio.arithmetic">[tab:ratio.arithmetic]</a>
 | Type                     | Value of `X`          | Value of `Y`        |
 | ------------------------ | --------------------- | ------------------- |
 | `ratio_add<R1, R2>`      | `R1::num * R2::den +` | `R1::den * R2::den` |
 |                          | `R2::num * R1::den`   |                     |
@@ -189,8 +188,8 @@ template <class R1, class R2>
 ### SI types for `ratio` <a id="ratio.si">[[ratio.si]]</a>
 For each of the *typedef-name*s `yocto`, `zepto`, `zetta`, and `yotta`,
 if both of the constants used in its specification are representable by
-`intmax_t`, the typedef shall be defined; if either of the constants is
-not representable by `intmax_t`, the typedef shall not be defined.

 ## Compile-time rational arithmetic <a id="ratio">[[ratio]]</a>
 ### In general <a id="ratio.general">[[ratio.general]]</a>
+Subclause  [[ratio]] describes the ratio library. It provides a class
+template `ratio` which exactly represents any finite rational number
+with a numerator and denominator representable by compile-time constants
+of type `intmax_t`.
+Throughout subclause  [[ratio]], the names of template parameters are
+used to express type requirements. If a template parameter is named `R1`
+or `R2`, and the template argument is not a specialization of the
+`ratio` template, the program is ill-formed.
 ### Header `<ratio>` synopsis <a id="ratio.syn">[[ratio.syn]]</a>
 ``` cpp
 namespace std {
 ### Class template `ratio` <a id="ratio.ratio">[[ratio.ratio]]</a>
 ``` cpp
 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>;
   };
 the template arguments `N` and `D` is not representable by type
 `intmax_t`, the program is ill-formed.
 [*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. This excludes the most negative
+value. — *end note*]
 The static data members `num` and `den` shall have the following values,
 where `gcd` represents the greatest common divisor of the absolute
 values of `N` and `D`:
 ### Arithmetic on `ratio`s <a id="ratio.arithmetic">[[ratio.arithmetic]]</a>
 Each of the alias templates `ratio_add`, `ratio_subtract`,
 `ratio_multiply`, and `ratio_divide` denotes the result of an arithmetic
 computation on two `ratio`s `R1` and `R2`. With `X` and `Y` computed (in
+the absence of arithmetic overflow) as specified by
+[[ratio.arithmetic]], each alias denotes a `ratio<U, V>` such that `U`
+is the same as `ratio<X, Y>::num` and `V` is the same as
 `ratio<X, Y>::den`.
 If it is not possible to represent `U` or `V` with `intmax_t`, the
 program is ill-formed. Otherwise, an implementation should yield correct
 values of `U` and `V`. If it is not possible to represent `X` or `Y`
 with `intmax_t`, the program is ill-formed unless the implementation
 yields correct values of `U` and `V`.
+**Table: Expressions used to perform ratio arithmetic** <a id="ratio.arithmetic">[ratio.arithmetic]</a>
 | Type                     | Value of `X`          | Value of `Y`        |
 | ------------------------ | --------------------- | ------------------- |
 | `ratio_add<R1, R2>`      | `R1::num * R2::den +` | `R1::den * R2::den` |
 |                          | `R2::num * R1::den`   |                     |
 ### SI types for `ratio` <a id="ratio.si">[[ratio.si]]</a>
 For each of the *typedef-name*s `yocto`, `zepto`, `zetta`, and `yotta`,
 if both of the constants used in its specification are representable by
+`intmax_t`, the typedef is defined; if either of the constants is not
+representable by `intmax_t`, the typedef is not defined.

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