RF: check fp error in offset for offset scaling

When trying to scale integers only with inter, we need to make sure the
inter as cast to the scaling type does in fact keep the integers in the
range of the output type.  We also want to make sure that inter
generates numbers with the smallest possible absolute magnitude to
avoid floating point error in the resulting numbers.

Author: matthew-brett

nibabel/arraywriters.py

@@ -464,9 +464,25 @@ def _iu2iu(self):
         t_min, t_max = np.iinfo(out_dtype).min, np.iinfo(out_dtype).max
         type_range = as_int(t_max) - as_int(t_min)
         mn2mx = mx - mn
-        if mn2mx <= type_range: # offset enough?
-            self.inter = mn - t_min
-            return
+        if mn2mx <= type_range: # might offset be enough?
+            if t_min == 0: # uint output - take min to 0
+                # decrease offset with floor_exact, meaning mn >= t_min after
+                # subtraction.  But we may have pushed the data over t_max,
+                # which we check below
+                inter = floor_exact(mn - t_min, self.scaler_dtype)
+            else: # int output - take midpoint to 0
+                # ceil below increases inter, pushing scale up to 0.5 towards
+                # -inf, because ints have abs min == abs max + 1
+                midpoint = mn + as_int(np.ceil(mn2mx / 2.0))
+                # Floor exact decreases inter, so pulling scaled values more
+                # positive. This may make mx - inter > t_max
+                inter = floor_exact(midpoint, self.scaler_dtype)
+            # Need to check still in range after floor_exact-ing
+            int_inter = as_int(inter)
+            assert mn - int_inter >= t_min
+            if mx - int_inter <= t_max:
+                self.inter = inter
+                return
         # Try slope options (sign flip) and then range scaling
         super(SlopeInterArrayWriter, self)._iu2iu()