Unify how atol and rtol are determined.

theano/sandbox/gpuarray/type.py

@@ -162,13 +162,7 @@ class GpuArrayType(Type):
                 return tensor.TensorType.values_eq_approx(
                     an, bn, allow_remove_inf=allow_remove_inf,
                     allow_remove_nan=allow_remove_nan, rtol=rtol, atol=atol)
-            narrow = 'float32', 'complex64'
-            if (str(a.dtype) in narrow) or (str(b.dtype) in narrow):
-                atol_ = theano.tensor.basic.float32_atol
-                rtol_ = theano.tensor.basic.float32_rtol
-            else:
-                atol_ = theano.tensor.basic.float64_atol
-                rtol_ = theano.tensor.basic.float64_rtol
+            atol_, rtol_ = theano.tensor.basic._get_atol_rtol(a, b)
             if rtol is not None:
                 rtol_ = rtol
             if atol is not None:

theano/tensor/basic.py

@@ -459,18 +459,29 @@ if int(config.tensor.cmp_sloppy) > 1:
     # When config.tensor.cmp_sloppy>1 we are even more sloppy. This is
     # useful to test the GPU as they don't use extended precision and
     # this cause some difference bigger then the normal sloppy.
+    float16_atol = 5e-3
+    float16_rtol = 1e-2
+
     float32_atol = 5e-4
     float32_rtol = 1e-3
+
     float64_rtol = 1e-4
     float64_atol = 1e-3
 elif int(config.tensor.cmp_sloppy):
+    float16_atol = 1e-3
+    float16_rtol = 5e-3
+
     float32_atol = 1e-4
     float32_rtol = 1e-3
+
     float64_rtol = 1e-4
     float64_atol = 1e-3
 else:
     # If you change those value in test don't forget to put them back
     # when the test end.  Don't forget the case when the test fail.
+    float16_atol = 5e-4
+    float16_rtol = 5e-4
+
     float32_atol = 1e-5
     float32_rtol = 1e-5
 
@@ -481,16 +492,25 @@ else:
     float64_rtol = 1.0000000000000001e-06
 
 
+def _get_atol_rtol(a, b):
+    tiny = ('float16',)
+    narrow = ('float32', 'complex64')
+    if (str(a.dtype) in tiny) or (str(b.dtype) in tiny):
+        atol = float16_atol
+        rtol = float16_rtol
+    elif (str(a.dtype) in narrow) or (str(b.dtype) in narrow):
+        atol = float32_atol
+        rtol = float32_rtol
+    else:
+        atol = float64_atol
+        rtol = float64_rtol
+    return atol, rtol
+
+
 def _allclose(a, b, rtol=None, atol=None):
     a = numpy.asarray(a)
     b = numpy.asarray(b)
-    narrow = 'float32', 'complex64'
-    if (str(a.dtype) in narrow) or (str(b.dtype) in narrow):
-        atol_ = float32_atol
-        rtol_ = float32_rtol
-    else:
-        atol_ = float64_atol
-        rtol_ = float64_rtol
+    atol_, rtol_ = _get_atol_rtol(a, b)
     if rtol is not None:
         rtol_ = rtol
     if atol is not None:

theano/tests/unittest_tools.py

@@ -309,15 +309,7 @@ def str_diagnostic(expected, value, rtol, atol):
         print(ssio.getvalue(), file=sio)
     except Exception:
         pass
-    # Use the same formula as in _allclose to find the tolerance used
-    narrow = 'float32', 'complex64'
-    if ((str(expected.dtype) in narrow) or
-        (str(value.dtype) in narrow)):
-        atol_ = T.basic.float32_atol
-        rtol_ = T.basic.float32_rtol
-    else:
-        atol_ = T.basic.float64_atol
-        rtol_ = T.basic.float64_rtol
+    atol_, rtol_ = T.basic._get_atol_rtol(expected, value)
     if rtol is not None:
         rtol_ = rtol
     if atol is not None: