Reading 32,767 is too many on some versions of Windows.
The exact upper bound is unclear.

For #13697, but may not fix the problem on all systems.

Change-Id: I197021ed60cbcd33c91ca6ceed456ec3d5a6c9d6
Reviewed-on: https://go-review.googlesource.com/18433Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>