diff --git a/doc/api/next_api_changes/2019-03-04-AL.rst b/doc/api/next_api_changes/2019-03-04-AL.rst
new file mode 100644
index 000000000000..2688774aac59
--- /dev/null
+++ b/doc/api/next_api_changes/2019-03-04-AL.rst
@@ -0,0 +1,20 @@
+Autoscaling changes
+```````````````````
+
+Matplotlib used to recompute autoscaled limits after every plotting
+(``plot()``, ``bar()``, etc.) call.  It now only does so when actually
+rendering the canvas, or when the user queries the Axes limits.  This is a
+major performance improvement for plots with a large number of artists.
+
+In particular, this means that artists added manually with `Axes.add_line`,
+`Axes.add_patch`, etc. will be taken into account by the autoscale, even
+without an explicit call to `Axes.autoscale_view`.
+
+In some cases, this can result in different limits being reported.  If this is
+an issue, consider triggering a draw with `fig.canvas.draw`.
+
+LogLocator.nonsingular now maintains the orders of its arguments
+````````````````````````````````````````````````````````````````
+
+It no longer reorders them in increasing order.  The new behavior is consistent
+with MaxNLocator.
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index affc329f1be0..464b5f007071 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -840,7 +840,7 @@ def axhline(self, y=0, xmin=0, xmax=1, **kwargs):
         trans = self.get_yaxis_transform(which='grid')
         l = mlines.Line2D([xmin, xmax], [y, y], transform=trans, **kwargs)
         self.add_line(l)
-        self.autoscale_view(scalex=False, scaley=scaley)
+        self._request_autoscale_view(scalex=False, scaley=scaley)
         return l
 
     @docstring.dedent_interpd
@@ -909,7 +909,7 @@ def axvline(self, x=0, ymin=0, ymax=1, **kwargs):
         trans = self.get_xaxis_transform(which='grid')
         l = mlines.Line2D([x, x], [ymin, ymax], transform=trans, **kwargs)
         self.add_line(l)
-        self.autoscale_view(scalex=scalex, scaley=False)
+        self._request_autoscale_view(scalex=scalex, scaley=False)
         return l
 
     @docstring.dedent_interpd
@@ -965,7 +965,7 @@ def axhspan(self, ymin, ymax, xmin=0, xmax=1, **kwargs):
         p = mpatches.Polygon(verts, **kwargs)
         p.set_transform(trans)
         self.add_patch(p)
-        self.autoscale_view(scalex=False)
+        self._request_autoscale_view(scalex=False)
         return p
 
     def axvspan(self, xmin, xmax, ymin=0, ymax=1, **kwargs):
@@ -1030,7 +1030,7 @@ def axvspan(self, xmin, xmax, ymin=0, ymax=1, **kwargs):
         p = mpatches.Polygon(verts, **kwargs)
         p.set_transform(trans)
         self.add_patch(p)
-        self.autoscale_view(scaley=False)
+        self._request_autoscale_view(scaley=False)
         return p
 
     @_preprocess_data(replace_names=["y", "xmin", "xmax", "colors"],
@@ -1105,7 +1105,7 @@ def hlines(self, y, xmin, xmax, colors='k', linestyles='solid',
             corners = (minx, miny), (maxx, maxy)
 
             self.update_datalim(corners)
-            self.autoscale_view()
+            self._request_autoscale_view()
 
         return lines
 
@@ -1182,7 +1182,7 @@ def vlines(self, x, ymin, ymax, colors='k', linestyles='solid',
 
             corners = (minx, miny), (maxx, maxy)
             self.update_datalim(corners)
-            self.autoscale_view()
+            self._request_autoscale_view()
 
         return lines
 
@@ -1398,7 +1398,7 @@ def eventplot(self, positions, orientation='horizontal', lineoffsets=1,
                 else:  # "horizontal", None or "none" (see EventCollection)
                     corners = (minpos, minline), (maxpos, maxline)
                 self.update_datalim(corners)
-                self.autoscale_view()
+                self._request_autoscale_view()
 
         return colls
 
@@ -1642,7 +1642,7 @@ def plot(self, *args, scalex=True, scaley=True, data=None, **kwargs):
         lines = [*self._get_lines(*args, data=data, **kwargs)]
         for line in lines:
             self.add_line(line)
-        self.autoscale_view(scalex=scalex, scaley=scaley)
+        self._request_autoscale_view(scalex=scalex, scaley=scaley)
         return lines
 
     @_preprocess_data(replace_names=["x", "y"], label_namer="y")
@@ -1718,7 +1718,7 @@ def plot_date(self, x, y, fmt='o', tz=None, xdate=True, ydate=False,
 
         ret = self.plot(x, y, fmt, **kwargs)
 
-        self.autoscale_view()
+        self._request_autoscale_view()
 
         return ret
 
@@ -2422,7 +2422,7 @@ def bar(self, x, height, width=0.8, bottom=None, *, align="center",
                 ymin = ymin - np.max(yerr)
             ymin = max(ymin * 0.9, 1e-100)
             self.dataLim.intervaly = (ymin, ymax)
-        self.autoscale_view()
+        self._request_autoscale_view()
 
         bar_container = BarContainer(patches, errorbar, label=label)
         self.add_container(bar_container)
@@ -2623,7 +2623,7 @@ def broken_barh(self, xranges, yrange, **kwargs):
 
         col = mcoll.BrokenBarHCollection(xranges_conv, yrange_conv, **kwargs)
         self.add_collection(col, autolim=True)
-        self.autoscale_view()
+        self._request_autoscale_view()
 
         return col
 
@@ -3429,7 +3429,7 @@ def extract_err(err, data):
         for l in caplines:
             self.add_line(l)
 
-        self.autoscale_view()
+        self._request_autoscale_view()
         errorbar_container = ErrorbarContainer((data_line, tuple(caplines),
                                                 tuple(barcols)),
                                                has_xerr=(xerr is not None),
@@ -4101,7 +4101,7 @@ def dopatch(xs, ys, **kwargs):
                 axis.set_major_formatter(formatter)
             formatter.seq = [*formatter.seq, *datalabels]
 
-            self.autoscale_view(
+            self._request_autoscale_view(
                 scalex=self._autoscaleXon, scaley=self._autoscaleYon)
 
         return dict(whiskers=whiskers, caps=caps, boxes=boxes,
@@ -4479,7 +4479,7 @@ def scatter(self, x, y, s=None, c=None, marker=None, cmap=None, norm=None,
                 self.set_ymargin(0.05)
 
         self.add_collection(collection)
-        self.autoscale_view()
+        self._request_autoscale_view()
 
         return collection
 
@@ -4832,9 +4832,7 @@ def hexbin(self, x, y, C=None, gridsize=100, bins=None,
 
         corners = ((xmin, ymin), (xmax, ymax))
         self.update_datalim(corners)
-        collection.sticky_edges.x[:] = [xmin, xmax]
-        collection.sticky_edges.y[:] = [ymin, ymax]
-        self.autoscale_view(tight=True)
+        self._request_autoscale_view(tight=True)
 
         # add the collection last
         self.add_collection(collection, autolim=False)
@@ -5004,7 +5002,7 @@ def quiver(self, *args, **kw):
         q = mquiver.Quiver(self, *args, **kw)
 
         self.add_collection(q, autolim=True)
-        self.autoscale_view()
+        self._request_autoscale_view()
         return q
     quiver.__doc__ = mquiver.Quiver.quiver_doc
 
@@ -5020,7 +5018,7 @@ def barbs(self, *args, **kw):
 
         b = mquiver.Barbs(self, *args, **kw)
         self.add_collection(b, autolim=True)
-        self.autoscale_view()
+        self._request_autoscale_view()
         return b
 
     # Uses a custom implementation of data-kwarg handling in
@@ -5075,7 +5073,7 @@ def fill(self, *args, data=None, **kwargs):
         for poly in self._get_patches_for_fill(*args, data=data, **kwargs):
             self.add_patch(poly)
             patches.append(poly)
-        self.autoscale_view()
+        self._request_autoscale_view()
         return patches
 
     @_preprocess_data(replace_names=["x", "y1", "y2", "where"])
@@ -5257,7 +5255,7 @@ def get_interp_point(ind):
         self.dataLim.update_from_data_xy(XY2, self.ignore_existing_data_limits,
                                          updatex=False, updatey=True)
         self.add_collection(collection, autolim=False)
-        self.autoscale_view()
+        self._request_autoscale_view()
         return collection
 
     @_preprocess_data(replace_names=["y", "x1", "x2", "where"])
@@ -5438,7 +5436,7 @@ def get_interp_point(ind):
         self.dataLim.update_from_data_xy(X2Y, self.ignore_existing_data_limits,
                                          updatex=True, updatey=False)
         self.add_collection(collection, autolim=False)
-        self.autoscale_view()
+        self._request_autoscale_view()
         return collection
 
     #### plotting z(x,y): imshow, pcolor and relatives, contour
@@ -5937,7 +5935,7 @@ def pcolor(self, *args, alpha=None, norm=None, cmap=None, vmin=None,
         collection.sticky_edges.y[:] = [miny, maxy]
         corners = (minx, miny), (maxx, maxy)
         self.update_datalim(corners)
-        self.autoscale_view()
+        self._request_autoscale_view()
         return collection
 
     @_preprocess_data()
@@ -6150,7 +6148,7 @@ def pcolormesh(self, *args, alpha=None, norm=None, cmap=None, vmin=None,
         collection.sticky_edges.y[:] = [miny, maxy]
         corners = (minx, miny), (maxx, maxy)
         self.update_datalim(corners)
-        self.autoscale_view()
+        self._request_autoscale_view()
         return collection
 
     @_preprocess_data()
@@ -6320,14 +6318,14 @@ def pcolorfast(self, *args, alpha=None, norm=None, cmap=None, vmin=None,
         ret.sticky_edges.x[:] = [xl, xr]
         ret.sticky_edges.y[:] = [yb, yt]
         self.update_datalim(np.array([[xl, yb], [xr, yt]]))
-        self.autoscale_view(tight=True)
+        self._request_autoscale_view(tight=True)
         return ret
 
     @_preprocess_data()
     def contour(self, *args, **kwargs):
         kwargs['filled'] = False
         contours = mcontour.QuadContourSet(self, *args, **kwargs)
-        self.autoscale_view()
+        self._request_autoscale_view()
         return contours
     contour.__doc__ = mcontour.QuadContourSet._contour_doc
 
@@ -6335,7 +6333,7 @@ def contour(self, *args, **kwargs):
     def contourf(self, *args, **kwargs):
         kwargs['filled'] = True
         contours = mcontour.QuadContourSet(self, *args, **kwargs)
-        self.autoscale_view()
+        self._request_autoscale_view()
         return contours
     contourf.__doc__ = mcontour.QuadContourSet._contour_doc
 
@@ -6842,7 +6840,7 @@ def hist(self, x, bins=None, range=None, density=None, weights=None,
 
         self.set_autoscalex_on(_saved_autoscalex)
         self.set_autoscaley_on(_saved_autoscaley)
-        self.autoscale_view()
+        self._request_autoscale_view()
 
         if label is None:
             labels = [None]
diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 5eee450a29f9..893cdf3775e1 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -470,6 +470,8 @@ def __init__(self, fig, rect,
         self._aspect = 'auto'
         self._adjustable = 'box'
         self._anchor = 'C'
+        self._stale_viewlim_x = False
+        self._stale_viewlim_y = False
         self._sharex = sharex
         self._sharey = sharey
         if sharex is not None:
@@ -615,12 +617,41 @@ def set_figure(self, fig):
                                                 fig.transFigure)
         # these will be updated later as data is added
         self.dataLim = mtransforms.Bbox.null()
-        self.viewLim = mtransforms.Bbox.unit()
+        self._viewLim = mtransforms.Bbox.unit()
         self.transScale = mtransforms.TransformWrapper(
             mtransforms.IdentityTransform())
 
         self._set_lim_and_transforms()
 
+    def _unstale_viewLim(self):
+        # We should arrange to store this information once per share-group
+        # instead of on every axis.
+        scalex = any(ax._stale_viewlim_x
+                     for ax in self._shared_x_axes.get_siblings(self))
+        scaley = any(ax._stale_viewlim_y
+                     for ax in self._shared_y_axes.get_siblings(self))
+        if scalex or scaley:
+            for ax in self._shared_x_axes.get_siblings(self):
+                ax._stale_viewlim_x = False
+            for ax in self._shared_y_axes.get_siblings(self):
+                ax._stale_viewlim_y = False
+            self.autoscale_view(scalex=scalex, scaley=scaley)
+
+    @property
+    def viewLim(self):
+        self._unstale_viewLim()
+        return self._viewLim
+
+    # API could be better, right now this is just to match the old calls to
+    # autoscale_view() after each plotting method.
+    def _request_autoscale_view(self, tight=None, scalex=True, scaley=True):
+        if tight is not None:
+            self._tight = tight
+        if scalex:
+            self._stale_viewlim_x = True  # Else keep old state.
+        if scaley:
+            self._stale_viewlim_y = True
+
     def _set_lim_and_transforms(self):
         """
         Set the *_xaxis_transform*, *_yaxis_transform*, *transScale*,
@@ -645,7 +676,7 @@ def _set_lim_and_transforms(self):
         # An affine transformation on the data, generally to limit the
         # range of the axes
         self.transLimits = mtransforms.BboxTransformFrom(
-            mtransforms.TransformedBbox(self.viewLim, self.transScale))
+            mtransforms.TransformedBbox(self._viewLim, self.transScale))
 
         # The parentheses are important for efficiency here -- they
         # group the last two (which are usually affines) separately
@@ -1862,6 +1893,9 @@ def add_collection(self, collection, autolim=True):
             collection.set_clip_path(self.patch)
 
         if autolim:
+            # Make sure viewLim is not stale (mostly to match
+            # pre-lazy-autoscale behavior, which is not really better).
+            self._unstale_viewLim()
             self.update_datalim(collection.get_datalim(self.transData))
 
         self.stale = True
@@ -2019,7 +2053,7 @@ def _on_units_changed(self, scalex=False, scaley=False):
         Currently forces updates of data limits and view limits.
         """
         self.relim()
-        self.autoscale_view(scalex=scalex, scaley=scaley)
+        self._request_autoscale_view(scalex=scalex, scaley=scaley)
 
     def relim(self, visible_only=False):
         """
@@ -2313,7 +2347,7 @@ def margins(self, *margins, x=None, y=None, tight=True):
         if y is not None:
             self.set_ymargin(y)
 
-        self.autoscale_view(
+        self._request_autoscale_view(
             tight=tight, scalex=(x is not None), scaley=(y is not None)
         )
 
@@ -2375,7 +2409,7 @@ def autoscale(self, enable=True, axis='both', tight=None):
             self._xmargin = 0
         if tight and scaley:
             self._ymargin = 0
-        self.autoscale_view(tight=tight, scalex=scalex, scaley=scaley)
+        self._request_autoscale_view(tight=tight, scalex=scalex, scaley=scaley)
 
     def autoscale_view(self, tight=None, scalex=True, scaley=True):
         """
@@ -2556,11 +2590,12 @@ def draw(self, renderer=None, inframe=False):
         """Draw everything (plot lines, axes, labels)"""
         if renderer is None:
             renderer = self.figure._cachedRenderer
-
         if renderer is None:
             raise RuntimeError('No renderer defined')
         if not self.get_visible():
             return
+        self._unstale_viewLim()
+
         renderer.open_group('axes')
 
         # prevent triggering call backs during the draw process
@@ -2886,7 +2921,7 @@ def locator_params(self, axis='both', tight=None, **kwargs):
             self.xaxis.get_major_locator().set_params(**kwargs)
         if _y:
             self.yaxis.get_major_locator().set_params(**kwargs)
-        self.autoscale_view(tight=tight, scalex=_x, scaley=_y)
+        self._request_autoscale_view(tight=tight, scalex=_x, scaley=_y)
 
     def tick_params(self, axis='both', **kwargs):
         """Change the appearance of ticks, tick labels, and gridlines.
@@ -3122,7 +3157,6 @@ def _validate_converted_limits(self, limit, convert):
         Returns
         -------
         The limit value after call to convert(), or None if limit is None.
-
         """
         if limit is not None:
             converted_limit = convert(limit)
@@ -3214,11 +3248,14 @@ def set_xlim(self, left=None, right=None, emit=True, auto=False,
         left = self._validate_converted_limits(left, self.convert_xunits)
         right = self._validate_converted_limits(right, self.convert_xunits)
 
-        old_left, old_right = self.get_xlim()
-        if left is None:
-            left = old_left
-        if right is None:
-            right = old_right
+        if left is None or right is None:
+            # Axes init calls set_xlim(0, 1) before get_xlim() can be called,
+            # so only grab the limits if we really need them.
+            old_left, old_right = self.get_xlim()
+            if left is None:
+                left = old_left
+            if right is None:
+                right = old_right
 
         if self.get_xscale() == 'log':
             if left <= 0:
@@ -3240,7 +3277,7 @@ def set_xlim(self, left=None, right=None, emit=True, auto=False,
         left, right = self.xaxis.get_major_locator().nonsingular(left, right)
         left, right = self.xaxis.limit_range_for_scale(left, right)
 
-        self.viewLim.intervalx = (left, right)
+        self._viewLim.intervalx = (left, right)
         if auto is not None:
             self._autoscaleXon = bool(auto)
 
@@ -3297,8 +3334,7 @@ def set_xscale(self, value, **kwargs):
             ax.xaxis._set_scale(value, **kwargs)
             ax._update_transScale()
             ax.stale = True
-
-        self.autoscale_view(scaley=False)
+        self._request_autoscale_view(scaley=False)
 
     def get_xticks(self, minor=False):
         """Return the x ticks as a list of locations"""
@@ -3592,12 +3628,14 @@ def set_ylim(self, bottom=None, top=None, emit=True, auto=False,
         bottom = self._validate_converted_limits(bottom, self.convert_yunits)
         top = self._validate_converted_limits(top, self.convert_yunits)
 
-        old_bottom, old_top = self.get_ylim()
-
-        if bottom is None:
-            bottom = old_bottom
-        if top is None:
-            top = old_top
+        if bottom is None or top is None:
+            # Axes init calls set_ylim(0, 1) before get_ylim() can be called,
+            # so only grab the limits if we really need them.
+            old_bottom, old_top = self.get_ylim()
+            if bottom is None:
+                bottom = old_bottom
+            if top is None:
+                top = old_top
 
         if self.get_yscale() == 'log':
             if bottom <= 0:
@@ -3620,7 +3658,7 @@ def set_ylim(self, bottom=None, top=None, emit=True, auto=False,
         bottom, top = self.yaxis.get_major_locator().nonsingular(bottom, top)
         bottom, top = self.yaxis.limit_range_for_scale(bottom, top)
 
-        self.viewLim.intervaly = (bottom, top)
+        self._viewLim.intervaly = (bottom, top)
         if auto is not None:
             self._autoscaleYon = bool(auto)
 
@@ -3677,7 +3715,7 @@ def set_yscale(self, value, **kwargs):
             ax.yaxis._set_scale(value, **kwargs)
             ax._update_transScale()
             ax.stale = True
-        self.autoscale_view(scalex=False)
+        self._request_autoscale_view(scalex=False)
 
     def get_yticks(self, minor=False):
         """Return the y ticks as a list of locations"""
diff --git a/lib/matplotlib/collections.py b/lib/matplotlib/collections.py
index 53df43a41a45..65285bf85f48 100644
--- a/lib/matplotlib/collections.py
+++ b/lib/matplotlib/collections.py
@@ -365,6 +365,9 @@ def contains(self, mouseevent):
                self._picker is not True  # the bool, not just nonzero or 1
             else self._pickradius)
 
+        if self.axes and self.get_offset_position() == "data":
+            self.axes._unstale_viewLim()
+
         transform, transOffset, offsets, paths = self._prepare_points()
 
         ind = _path.point_in_path_collection(
diff --git a/lib/matplotlib/table.py b/lib/matplotlib/table.py
index 55eadc51b0c1..0086d88c2b34 100644
--- a/lib/matplotlib/table.py
+++ b/lib/matplotlib/table.py
@@ -320,6 +320,7 @@ def __init__(self, ax, loc=None, bbox=None, **kwargs):
         self._bbox = bbox
 
         # use axes coords
+        ax._unstale_viewLim()
         self.set_transform(ax.transAxes)
 
         self._texts = []
diff --git a/lib/matplotlib/tests/test_bbox_tight.py b/lib/matplotlib/tests/test_bbox_tight.py
index 8c99c4572f76..c4566e519dec 100644
--- a/lib/matplotlib/tests/test_bbox_tight.py
+++ b/lib/matplotlib/tests/test_bbox_tight.py
@@ -32,6 +32,7 @@ def test_bbox_inches_tight():
         yoff = yoff + data[row]
         cellText.append([''])
     plt.xticks([])
+    plt.xlim(0, 5)
     plt.legend([''] * 5, loc=(1.2, 0.2))
     # Add a table at the bottom of the axes
     cellText.reverse()
diff --git a/lib/matplotlib/tests/test_patches.py b/lib/matplotlib/tests/test_patches.py
index 13c5dd1a83eb..d32ada81a73c 100644
--- a/lib/matplotlib/tests/test_patches.py
+++ b/lib/matplotlib/tests/test_patches.py
@@ -363,6 +363,9 @@ def test_multi_color_hatch():
         rect.set_edgecolor('C{}'.format(i))
         rect.set_hatch('/')
 
+    ax.autoscale_view()
+    ax.autoscale(False)
+
     for i in range(5):
         with mstyle.context({'hatch.color': 'C{}'.format(i)}):
             r = Rectangle((i - .8 / 2, 5), .8, 1, hatch='//', fc='none')
diff --git a/lib/matplotlib/tests/test_simplification.py b/lib/matplotlib/tests/test_simplification.py
index 9818c9495e17..e91e91461b35 100644
--- a/lib/matplotlib/tests/test_simplification.py
+++ b/lib/matplotlib/tests/test_simplification.py
@@ -54,6 +54,8 @@ def test_noise():
     fig, ax = plt.subplots()
     p1 = ax.plot(x, solid_joinstyle='round', linewidth=2.0)
 
+    # Ensure that the path's transform takes the new axes limits into account.
+    fig.canvas.draw()
     path = p1[0].get_path()
     transform = p1[0].get_transform()
     path = transform.transform_path(path)
@@ -195,6 +197,8 @@ def test_sine_plus_noise():
     fig, ax = plt.subplots()
     p1 = ax.plot(x, solid_joinstyle='round', linewidth=2.0)
 
+    # Ensure that the path's transform takes the new axes limits into account.
+    fig.canvas.draw()
     path = p1[0].get_path()
     transform = p1[0].get_transform()
     path = transform.transform_path(path)
@@ -232,6 +236,8 @@ def test_fft_peaks():
     t = np.arange(65536)
     p1 = ax.plot(abs(np.fft.fft(np.sin(2*np.pi*.01*t)*np.blackman(len(t)))))
 
+    # Ensure that the path's transform takes the new axes limits into account.
+    fig.canvas.draw()
     path = p1[0].get_path()
     transform = p1[0].get_transform()
     path = transform.transform_path(path)
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index b29ddba2e0b6..4f48e5ced850 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -1670,6 +1670,15 @@ def __init__(self, numticks=None, presets=None):
         else:
             self.presets = presets
 
+    @property
+    def numticks(self):
+        # Old hard-coded default.
+        return self._numticks if self._numticks is not None else 11
+
+    @numticks.setter
+    def numticks(self, numticks):
+        self._numticks = numticks
+
     def set_params(self, numticks=None, presets=None):
         """Set parameters within this locator."""
         if presets is not None:
@@ -1690,18 +1699,12 @@ def tick_values(self, vmin, vmax):
         if (vmin, vmax) in self.presets:
             return self.presets[(vmin, vmax)]
 
-        if self.numticks is None:
-            self._set_numticks()
-
         if self.numticks == 0:
             return []
         ticklocs = np.linspace(vmin, vmax, self.numticks)
 
         return self.raise_if_exceeds(ticklocs)
 
-    def _set_numticks(self):
-        self.numticks = 11  # todo; be smart here; this is just for dev
-
     def view_limits(self, vmin, vmax):
         'Try to choose the view limits intelligently'
 
@@ -2376,25 +2379,28 @@ def view_limits(self, vmin, vmax):
         return vmin, vmax
 
     def nonsingular(self, vmin, vmax):
-        if not np.isfinite(vmin) or not np.isfinite(vmax):
-            return 1, 10  # initial range, no data plotted yet
-
+        swap_vlims = False
         if vmin > vmax:
+            swap_vlims = True
             vmin, vmax = vmax, vmin
-        if vmax <= 0:
+        if not np.isfinite(vmin) or not np.isfinite(vmax):
+            vmin, vmax = 1, 10  # Initial range, no data plotted yet.
+        elif vmax <= 0:
             cbook._warn_external(
                 "Data has no positive values, and therefore cannot be "
                 "log-scaled.")
-            return 1, 10
-
-        minpos = self.axis.get_minpos()
-        if not np.isfinite(minpos):
-            minpos = 1e-300  # This should never take effect.
-        if vmin <= 0:
-            vmin = minpos
-        if vmin == vmax:
-            vmin = _decade_less(vmin, self._base)
-            vmax = _decade_greater(vmax, self._base)
+            vmin, vmax = 1, 10
+        else:
+            minpos = self.axis.get_minpos()
+            if not np.isfinite(minpos):
+                minpos = 1e-300  # This should never take effect.
+            if vmin <= 0:
+                vmin = minpos
+            if vmin == vmax:
+                vmin = _decade_less(vmin, self._base)
+                vmax = _decade_greater(vmax, self._base)
+        if swap_vlims:
+            vmin, vmax = vmax, vmin
         return vmin, vmax