I sent a version of this patch to the list previously but I believe the
opinion was that nftw should preserve slashes as best it could, so
here's one that does that.

Using the test program from man nftw:

$ ./a.out ftw
d    0    4096   ftw                                      0 ftw
d    1    4096   ftw/a                                    4 a
f    2       0   ftw/a/f                                  6 f
d    2    4096   ftw/a/d                                  6 d
d    3    4096   ftw/a/d/e                                8 e
d    1    4096   ftw/b                                    4 b
f    2       0   ftw/b/g                                  6 g
f    1       0   ftw/c                                    4 c
$ ./a.out ftw/
d    0    4096   ftw                                      0 ftw
d    1    4096   ftw/a                                    4 a
f    2       0   ftw/a/f                                  6 f
d    2    4096   ftw/a/d                                  6 d
d    3    4096   ftw/a/d/e                                8 e
d    1    4096   ftw/b                                    4 b
f    2       0   ftw/b/g                                  6 g
f    1       0   ftw/c                                    4 c
$ ./a.out ftw//
d    0    4096   ftw                                      0 ftw
d    1    4096   ftw//a                                   5 a
f    2       0   ftw//a/f                                 7 f
d    2    4096   ftw//a/d                                 7 d
d    3    4096   ftw//a/d/e                               9 e
d    1    4096   ftw//b                                   5 b
f    2       0   ftw//b/g                                 7 g
f    1       0   ftw//c                                   5 c

And on the root

$ ./a.out / | sed 4q
d    0    4096   /                                        0 /
d    1    4096   /projects                                1 projects
d    2    4096   /projects/p9.git                         10 p9.git
d    3    4096   /projects/p9.git/hooks                   17 hooks
$ ./a.out // | sed 4q
d    0    4096   //                                       1 /
d    1    4096   //projects                               2 projects
d    2    4096   //projects/p9.git                        11 p9.git
d    3    4096   //projects/p9.git/hooks                  18 hooks

However glibc does this:

$ ./a.out / | sed 4q
d    0    4096   /                                        1
d    1    4096   /projects                                1 projects
d    2    4096   /projects/p9.git                         10 p9.git
d    3    4096   /projects/p9.git/hooks                   17 hooks

The standard just says:
 > The value of base is the offset of the object's filename in the
 > pathname passed as the first argument to fn

Which I believe should be interpreted as the root dir being called /
but I'm not sure. It's a simple change either way.