From Jason Turner

[fs.path.decompose]

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+ ##### `path` decomposition <a id="fs.path.decompose">[[fs.path.decompose]]</a>
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+
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+ ``` cpp
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+ path root_name() const;
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+ ```
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+
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+ *Returns:* *root-name*, if the pathname in the generic format includes
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+ *root-name*, otherwise `path()`.
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+
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+ ``` cpp
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+ path root_directory() const;
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+ ```
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+
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+ *Returns:* *root-directory*, if the pathname in the generic format
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+ includes *root-directory*, otherwise `path()`.
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+
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+ ``` cpp
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+ path root_path() const;
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+ ```
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+
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+ *Returns:* `root_name() / root_directory()`.
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+
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+ ``` cpp
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+ path relative_path() const;
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+ ```
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+
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+ *Returns:* A `path` composed from the pathname in the generic format, if
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+ `!empty()`, beginning with the first *filename* after *root-path*.
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+ Otherwise, `path()`.
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+
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+ ``` cpp
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+ path parent_path() const;
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+ ```
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+
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+ *Returns:* `*this` if `!has_relative_path()`, otherwise a path whose
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+ generic format pathname is the longest prefix of the generic format
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+ pathname of `*this` that produces one fewer element in its iteration.
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+
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+ ``` cpp
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+ path filename() const;
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+ ```
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+
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+ *Returns:* `relative_path().empty() ? path() : *–end()`.
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+
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+ [*Example 6*:
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+
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+ ``` cpp
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+ path("/foo/bar.txt").filename(); // yields "bar.txt"
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+ path("/foo/bar").filename(); // yields "bar"
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+ path("/foo/bar/").filename(); // yields ""
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+ path("/").filename(); // yields ""
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+ path("//host").filename(); // yields ""
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+ path(".").filename(); // yields "."
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+ path("..").filename(); // yields ".."
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+ ```
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+
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+ — *end example*]
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+
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+ ``` cpp
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+ path stem() const;
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+ ```
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+
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+ *Returns:* Let `f` be the generic format pathname of `filename()`.
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+ Returns a path whose pathname in the generic format is
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+
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+ - `f`, if it contains no periods other than a leading period or consists
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+ solely of one or two periods;
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+ - otherwise, the prefix of `f` ending before its last period.
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+
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+ [*Example 7*:
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+
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+ ``` cpp
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+ std::cout << path("/foo/bar.txt").stem(); // outputs "bar"
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+ path p = "foo.bar.baz.tar";
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+ for (; !p.extension().empty(); p = p.stem())
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+ std::cout << p.extension() << '\n';
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+ // outputs: .tar
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+ // .baz
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+ // .bar
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+ ```
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+
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+ — *end example*]
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+
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+ ``` cpp
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+ path extension() const;
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+ ```
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+
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+ *Returns:* a path whose pathname in the generic format is the suffix of
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+ `filename()` not included in `stem()`.
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+
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+ [*Example 8*:
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+
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+ ``` cpp
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+ path("/foo/bar.txt").extension(); // yields ".txt" and stem() is "bar"
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+ path("/foo/bar").extension(); // yields "" and stem() is "bar"
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+ path("/foo/.profile").extension(); // yields "" and stem() is ".profile"
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+ path(".bar").extension(); // yields "" and stem() is ".bar"
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+ path("..bar").extension(); // yields ".bar" and stem() is "."
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+ ```
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+
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+ — *end example*]
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+
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+ [*Note 4*: The period is included in the return value so that it is
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+ possible to distinguish between no extension and an empty
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+ extension. — *end note*]
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+
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+ [*Note 5*: On non-POSIX operating systems, for a path `p`, it may not
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+ be the case that `p.stem() + p.extension() == p.filename()`, even though
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+ the generic format pathnames are the same. — *end note*]
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+