Fix floating point issues in axes limits.

plt.plot([-.1, .2]) used to pick (in round numbers mode) [-.1, .25] as
ylims due to floating point inaccuracies; change it to pick [-.1, .2]
(up to floating point inaccuracies).

Note that this requires working around a bug in numpy's implementation
of divmod (numpy/numpy#6127).

Many test images have changed!

See matplotlib#5767.

Probably also wraps up work on matplotlib#5738, but tests are missing.

lib/matplotlib/tests/test_axes.py

@@ -21,7 +21,7 @@
 from matplotlib.testing.decorators import image_comparison, cleanup
 import matplotlib.pyplot as plt
 import matplotlib.markers as mmarkers
-from numpy.testing import assert_array_equal
+from numpy.testing import assert_allclose, assert_array_equal
 import warnings
 from matplotlib.cbook import IgnoredKeywordWarning
 
@@ -3708,8 +3708,7 @@ def test_vline_limit():
     ax.axvline(0.5)
     ax.plot([-0.1, 0, 0.2, 0.1])
     (ymin, ymax) = ax.get_ylim()
-    assert ymin == -0.1
-    assert ymax == 0.25
+    assert_allclose(ax.get_ylim(), (-.1, .2))
 
 
 @cleanup

lib/matplotlib/ticker.py

@@ -169,6 +169,15 @@
     long = int
 
 
+# Work around numpy/numpy#6127.
+def divmod(x, y):
+    if isinstance(x, np.generic):
+        x = x.item()
+    if isinstance(y, np.generic):
+        y = y.item()
+    return six.moves.builtins.divmod(x, y)
+
+
 def _mathdefault(s):
     """
     For backward compatibility, in classic mode we display
@@ -1324,7 +1333,7 @@ def view_limits(self, dmin, dmax):
 
 
 def scale_range(vmin, vmax, n=1, threshold=100):
-    dv = abs(vmax - vmin) # > 0 as nonsingular is called before.
+    dv = abs(vmax - vmin)  # > 0 as nonsingular is called before.
     meanv = (vmax + vmin) / 2
     offset = (math.copysign(10 ** (math.log10(abs(meanv)) // 1), meanv)
               if abs(meanv) / dv >= threshold
@@ -1415,7 +1424,7 @@ def set_params(self, **kwargs):
         if self._integer:
             self._steps = [n for n in self._steps if divmod(n, 1)[1] < 0.001]
 
-    def bin_boundaries(self, vmin, vmax):
+    def _raw_ticks(self, vmin, vmax):
         nbins = self._nbins
         if nbins == 'auto':
             nbins = self.axis.get_tick_space()
@@ -1438,18 +1447,19 @@ def bin_boundaries(self, vmin, vmax):
             if best_vmax >= vmax:
                 break
 
-        bounds = np.arange(nbins + 1) * step + best_vmin
-        bounds = bounds[(bounds >= vmin) & (bounds <= vmax)]
-        return bounds + offset
+        bounds = np.arange(nbins + 1) * step
+        return (bounds[(bounds >= Base(step).le(vmin - best_vmin)) &
+                       (bounds <= Base(step).ge(vmax - best_vmin))] +
+                best_vmin + offset)
 
     def __call__(self):
         vmin, vmax = self.axis.get_view_interval()
         return self.tick_values(vmin, vmax)
 
     def tick_values(self, vmin, vmax):
-        vmin, vmax = mtransforms.nonsingular(vmin, vmax, expander=1e-13,
-                                                         tiny=1e-14)
-        locs = self.bin_boundaries(vmin, vmax)
+        vmin, vmax = mtransforms.nonsingular(
+            vmin, vmax, expander=1e-13, tiny=1e-14)
+        locs = self._raw_ticks(vmin, vmax)
         prune = self._prune
         if prune == 'lower':
             locs = locs[1:]
@@ -1466,11 +1476,17 @@ def view_limits(self, dmin, dmax):
                 dmin = -maxabs
                 dmax = maxabs
 
-        dmin, dmax = mtransforms.nonsingular(dmin, dmax, expander=1e-12,
-                                                        tiny=1.e-13)
+        dmin, dmax = mtransforms.nonsingular(
+            dmin, dmax, expander=1e-12, tiny=1e-13)
 
         if rcParams['axes.autolimit_mode'] == 'round_numbers':
-            return np.take(self.bin_boundaries(dmin, dmax), [0, -1])
+            locs = self._raw_ticks(dmin, dmax)
+            step = locs[1] - locs[0]
+            low = (locs[0] if locs[0] < dmin or closeto(locs[0], dmin)
+                   else locs[0] - step)
+            high = (locs[-1] if locs[-1] > dmax or closeto(locs[-1], dmax)
+                    else locs[-1] + step)
+            return low, high
         else:
             return dmin, dmax