Directory fsync

[Zhu Han]

I note below words in the manual of fsync:
       Calling  fsync()  does  not  necessarily  ensure  that  the entry in
the directory containing the file has also reached disk.  For that an
explicit fsync() on a file
       descriptor for the directory is also needed.

I am wondering is directory sync is essential after below steps if I want to
assure the file can be retrieved after system crash?

1) create file A
2) write file A
3) fsync(file A)

--------------------------------> fsync(parent directory) [Is it essential
to make the inode linked to parent directory?]
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