bad alloc on large (but not too large) image

For this example, I've created an entirely white png (attached to the bug report) with size 2400 x 36000. I saved it at compression level 9 (or whatever gimp means by that) and in 8-bit RGB. I would expect eog to be able to display this because 2400 * 36000 * 4 colours is 330 MB, which is vastly less than the available RAM on my machine. While X represents window dimensions with 16 bit values, which may perhaps be signed (I didn't check my host's type definitions), I don't expect eog to allocate a pixel-to-pixel window for the image. My screen's size is ample.

This arose because of a real image of the same dimensions, but which I can't attach here. The behaviour is the same.

jeff@starshine:data_2016-09-01 $ eog /tmp/2400x36000.png

** (eog:26198): WARNING **: Couldn't connect to accessibility bus: Failed to connect to socket /tmp/dbus-3UXmMLd2Wv: Connection refused

(eog:26198): Gdk-ERROR **: The program 'eog' received an X Window System error.
This probably reflects a bug in the program.
The error was 'BadAlloc (insufficient resources for operation)'.
  (Details: serial 415 error_code 11 request_code 130 (MIT-SHM) minor_code 5)
  (Note to programmers: normally, X errors are reported asynchronously;
   that is, you will receive the error a while after causing it.
   To debug your program, run it with the GDK_SYNCHRONIZE environment
   variable to change this behavior. You can then get a meaningful
   backtrace from your debugger if you break on the gdk_x_error() function.)
Trace/breakpoint trap (core dumped)
133, jeff@starshine:data_2016-09-01 $ ubuntu-bug eog

** (apport-gtk:27057): WARNING **: Couldn't connect to accessibility bus: Failed to connect to socket /tmp/dbus-3UXmMLd2Wv: Connection refused
/usr/share/apport/apport-gtk:16: PyGIWarning: Wnck was imported without specifying a version first. Use gi.require_version('Wnck', '3.0') before import to ensure that the right version gets loaded.
  from gi.repository import GLib, Wnck, GdkX11, Gdk
jeff@starshine:data_2016-09-01 $

ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: eog 3.18.2-1ubuntu2.1
ProcVersionSignature: Ubuntu 4.4.0-36.55-generic 4.4.16
Uname: Linux 4.4.0-36-generic x86_64
NonfreeKernelModules: wl
ApportVersion: 2.20.1-0ubuntu2.1
Architecture: amd64
CurrentDesktop: i3
Date: Mon Sep 26 10:24:34 2016
EcryptfsInUse: Yes
InstallationDate: Installed on 2015-12-17 (283 days ago)
InstallationMedia: Ubuntu 15.04 "Vivid Vervet" - Release amd64 (20150422)
SourcePackage: eog
UpgradeStatus: Upgraded to xenial on 2016-05-15 (133 days ago)