diff --git a/lib/matplotlib/colors.py b/lib/matplotlib/colors.py
index 511f46d18710..73e0c8570794 100644
--- a/lib/matplotlib/colors.py
+++ b/lib/matplotlib/colors.py
@@ -880,22 +880,13 @@ def process_value(value):
         Experimental; we may want to add an option to force the
         use of float32.
         """
-        if cbook.iterable(value):
-            is_scalar = False
-            result = np.ma.asarray(value)
-            if result.dtype.kind == 'f':
-                # this is overkill for lists of floats, but required
-                # to support pd.Series as input until we can reliable
-                # determine if result and value share memory in all cases
-                # (list, tuple, deque, ndarray, Series, ...)
-                result = result.copy()
-            elif result.dtype.itemsize > 2:
-                result = result.astype(float)
-            else:
-                result = result.astype(np.float32)
-        else:
-            is_scalar = True
-            result = np.ma.array([value]).astype(float)
+        is_scalar = not cbook.iterable(value)
+        if is_scalar:
+            value = [value]
+        dtype = np.min_scalar_type(value)
+        dtype = (np.float32 if dtype.itemsize <= 2
+                 else np.promote_types(dtype, float))
+        result = np.ma.array(value, dtype=dtype, copy=True)
         return result, is_scalar
 
     def __call__(self, value, clip=None):
@@ -918,8 +909,6 @@ def __call__(self, value, clip=None):
         elif vmin > vmax:
             raise ValueError("minvalue must be less than or equal to maxvalue")
         else:
-            vmin = float(vmin)
-            vmax = float(vmax)
             if clip:
                 mask = np.ma.getmask(result)
                 result = np.ma.array(np.clip(result.filled(vmax), vmin, vmax),
@@ -938,8 +927,7 @@ def __call__(self, value, clip=None):
     def inverse(self, value):
         if not self.scaled():
             raise ValueError("Not invertible until scaled")
-        vmin = float(self.vmin)
-        vmax = float(self.vmax)
+        vmin, vmax = self.vmin, self.vmax
 
         if cbook.iterable(value):
             val = np.ma.asarray(value)
diff --git a/lib/matplotlib/tests/test_colors.py b/lib/matplotlib/tests/test_colors.py
index 072959eb8ff7..986a5c9ca5cb 100644
--- a/lib/matplotlib/tests/test_colors.py
+++ b/lib/matplotlib/tests/test_colors.py
@@ -194,6 +194,16 @@ def test_Normalize():
     _scalar_tester(norm, vals)
     _mask_tester(norm, vals)
 
+    # Don't lose precision on longdoubles (float128 on Linux):
+    # for array inputs...
+    vals = np.array([1.2345678901, 9.8765432109], dtype=np.longdouble)
+    norm = mcolors.Normalize(vals.min(), vals.max())
+    assert_array_equal(np.asarray(norm(vals)), [0, 1])
+    # and for scalar ones.
+    eps = np.finfo(np.longdouble).resolution
+    norm = plt.Normalize(1, 1 + 100 * eps)
+    assert_equal(norm(1 + 50 * eps), .5)
+
 
 def test_SymLogNorm():
     """