Better choice of offset-text.

The axis offset text is chosen as follows: xlims => offsettext 123, 189 => 0 12341, 12349 => 12340 99999.5, 100010.5 => 100000 # (also a test for #5780) 99990.5, 100000.5 => 100000 1233999, 1234001 => 1234000 (and the same for negative limits). See #5755.
matplotlib · efiring · May 11, 2016 · Jan 2, 2016 · Jan 6, 2016 · Feb 18, 2016
commit 9a4ecfbdf235851a127f22152841631dadbc7558
diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
@@ -3,7 +3,7 @@
 
 from matplotlib.externals import six
 import nose.tools
-from nose.tools import assert_raises
+from nose.tools import assert_equal, assert_raises
 from numpy.testing import assert_almost_equal
 import numpy as np
 import matplotlib
@@ -159,6 +159,55 @@ def test_SymmetricalLogLocator_set_params():
     nose.tools.assert_equal(sym.numticks, 8)
 
 
+@cleanup
+def test_ScalarFormatter_offset_value():
+    fig, ax = plt.subplots()
+    formatter = ax.get_xaxis().get_major_formatter()
+
+    def update_ticks(ax):
+        return next(ax.get_xaxis().iter_ticks())
+
+    ax.set_xlim(123, 189)
+    update_ticks(ax)
+    assert_equal(formatter.offset, 0)
+
+    ax.set_xlim(-189, -123)
+    update_ticks(ax)
+    assert_equal(formatter.offset, 0)
+
+    ax.set_xlim(12341, 12349)
+    update_ticks(ax)
+    assert_equal(formatter.offset, 12340)
+
+    ax.set_xlim(-12349, -12341)
+    update_ticks(ax)
+    assert_equal(formatter.offset, -12340)
+
+    ax.set_xlim(99999.5, 100010.5)
+    update_ticks(ax)
+    assert_equal(formatter.offset, 100000)
+
+    ax.set_xlim(-100010.5, -99999.5)
+    update_ticks(ax)
+    assert_equal(formatter.offset, -100000)
+
+    ax.set_xlim(99990.5, 100000.5)
+    update_ticks(ax)
+    assert_equal(formatter.offset, 100000)
+
+    ax.set_xlim(-100000.5, -99990.5)
+    update_ticks(ax)
+    assert_equal(formatter.offset, -100000)
+
+    ax.set_xlim(1233999, 1234001)
+    update_ticks(ax)
+    assert_equal(formatter.offset, 1234000)
+
+    ax.set_xlim(-1234001, -1233999)
+    update_ticks(ax)
+    assert_equal(formatter.offset, -1234000)
+
+
 def _logfe_helper(formatter, base, locs, i, expected_result):
     vals = base**locs
     labels = [formatter(x, pos) for (x, pos) in zip(vals, i)]

diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
@@ -663,33 +663,53 @@ def set_locs(self, locs):
             vmin, vmax = self.axis.get_view_interval()
             d = abs(vmax - vmin)
             if self._useOffset:
-                self._set_offset(d)
+                self._compute_offset()
             self._set_orderOfMagnitude(d)
             self._set_format(vmin, vmax)
 
-    def _set_offset(self, range):
-        # offset of 20,001 is 20,000, for example
+    def _compute_offset(self):
         locs = self.locs
-
-        if locs is None or not len(locs) or range == 0:
+        if locs is None or not len(locs):
             self.offset = 0
             return
+        # Restrict to visible ticks.
         vmin, vmax = sorted(self.axis.get_view_interval())
         locs = np.asarray(locs)
         locs = locs[(vmin <= locs) & (locs <= vmax)]
-        ave_loc = np.mean(locs)
-        if len(locs) and ave_loc:  # dont want to take log10(0)
-            ave_oom = math.floor(math.log10(np.mean(np.absolute(locs))))
-            range_oom = math.floor(math.log10(range))
-
-            if np.absolute(ave_oom - range_oom) >= 3:  # four sig-figs
-                p10 = 10 ** range_oom
-                if ave_loc < 0:
-                    self.offset = (math.ceil(np.max(locs) / p10) * p10)
-                else:
-                    self.offset = (math.floor(np.min(locs) / p10) * p10)
-            else:
-                self.offset = 0
+        if not len(locs):
+            self.offset = 0
+            return
+        lmin, lmax = locs.min(), locs.max()
+        # min, max comparing absolute values (we want division to round towards
+        # zero so we work on absolute values).
+        abs_min, abs_max = sorted(map(abs, [lmin, lmax]))
+        # Only use offset if there are at least two ticks, every tick has the
+        # same sign, and if the span is small compared to the absolute values.
+        if (lmin == lmax or lmin <= 0 <= lmax or
+                (abs_max - abs_min) / abs_max >= 1e-2):
+            self.offset = 0
+            return
+        sign = math.copysign(1, lmin)
+        # What is the smallest power of ten such that abs_min and abs_max are
+        # equal up to that precision?
+        oom = 10 ** int(math.log10(abs_max) + 1)
+        while True:
+            if abs_min // oom != abs_max // oom:
+                oom *= 10
+                break
+            oom /= 10
+        if (abs_max - abs_min) / oom <= 1e-2:
+            # Handle the case of straddling a multiple of a large power of ten
+            # (relative to the span).
+            # What is the smallest power of ten such that abs_min and abs_max
+            # at most 1 apart?
+            oom = 10 ** int(math.log10(abs_max) + 1)
+            while True:
+                if abs_max // oom - abs_min // oom > 1:
+                    oom *= 10
+                    break
+                oom /= 10
+        self.offset = sign * (abs_max // oom) * oom
 
     def _set_orderOfMagnitude(self, range):
         # if scientific notation is to be used, find the appropriate exponent