std::filesystem::path::lexically_normal, std::filesystem::path::lexically_relative, std::filesystem::path::lexically_proximate

path lexically_normal() const;	(1)	(since C++17)
path lexically_relative(const path& base) const;	(2)	(since C++17)
path lexically_proximate(const path& base) const;	(3)	(since C++17)

1) Returns *this converted to normal form in its generic format

2) Returns *this made relative to base.

First, if root_name() != base.root_name() is true or is_absolute() != base.is_absolute() is true or (!has_root_directory() && base.has_root_directory()) is true or any filename in relative_path() or base.relative_path() can be interpreted as a root-name, returns a default-constructed path.
Otherwise, first determines the first mismatched element of *this and base as if by auto [a, b] = mismatch(begin(), end(), base.begin(), base.end()), then

if a == end() and b == base.end(), returns path(".");
otherwise, define $N$ as the number of nonempty filename elements that are neither dot nor dot-dot in [b, base.end()), minus the number of dot-dot filename elements, If $N < 0$ , returns a default-constructed path.
otherwise, if $N = 0$ and a == end() || a->empty(), returns path(".").
otherwise returns an object composed from

a default-constructed path() followed by
$N$ applications of operator/=(path("..")), followed by
one application of operator/= for each element in the half-open range [a, end())

3) If the value of lexically_relative(base) is not an empty path, return it. Otherwise return *this.

Parameters

(none)

Return value

1) The normal form of the path

2) The relative form of the path

3) The proximate form of the path

Exceptions

May throw implementation-defined exceptions.

Notes

These conversions are purely lexical. They do not check that the paths exist, do not follow symlinks, and do not access the filesystem at all. For symlink-following counterparts of lexically_relative and lexically_proximate, see relative and proximate.

On Windows, the returned path has backslashes (the preferred separators).

On POSIX, no filename in a relative path is acceptable as a root-name.

Example

Run this code

#include <iostream>
#include <filesystem>
#include <cassert>
namespace fs = std::filesystem;
 
int main()
{
    assert(fs::path("a/./b/..").lexically_normal() == "a/");
    assert(fs::path("a/.///b/../").lexically_normal() == "a/");
    assert(fs::path("/a/d").lexically_relative("/a/b/c") == "../../d");
    assert(fs::path("/a/b/c").lexically_relative("/a/d") == "../b/c");
    assert(fs::path("a/b/c").lexically_relative("a") == "b/c");
    assert(fs::path("a/b/c").lexically_relative("a/b/c/x/y") == "../..");
    assert(fs::path("a/b/c").lexically_relative("a/b/c") == ".");
    assert(fs::path("a/b").lexically_relative("c/d") == "../../a/b");
    assert(fs::path("a/b").lexically_relative("/a/b") == "");
    assert(fs::path("a/b").lexically_proximate("/a/b") == "a/b");
}

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR	Applied to	Behavior as published	Correct behavior
LWG 3070	C++17	a filename that can also be a root-name may cause surprising result	treated as error case
LWG 3096	C++17	trailing "/" and "/." are handled incorrectly	corrected

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