Simplified graphs generated for canonical slices

theano/tensor/basic.py

@@ -510,7 +510,7 @@ def get_scalar_constant_value(v):
     if isinstance(v, (numpy.integer, int, float)):
         return numpy.asarray(v)
 
-    def numpy_scalar(n):
+    def numpy_scalar(data):
         """ Return a scalar stored in a numpy ndarray, or raise
         NotScalarConstantError if the numpy ndarray is not a scalar
         """
@@ -526,7 +526,7 @@ def get_scalar_constant_value(v):
         except Exception:
             raise NotScalarConstantError(
                 'v.data is non-numeric, non-scalar, or has more than one'
-                ' unique value', n)
+                ' unique value', data)
 
     if isinstance(v, numpy.ndarray):
         return numpy_scalar(v)
@@ -4250,27 +4250,113 @@ def get_canonical_form_slice(theslice, length):
     that respects the conventions imposed by python and numpy.
 
     In a canonical form a slice is represented by a canonical form slice,
-    in which the start <= stop and step >0 and a flag which says if the
-    resulting set of numbers needs to be reversed or not.
+    in which 0 <= start <= stop <= length and step > 0, and a flag which says if
+    the resulting set of numbers needs to be reversed or not.
     '''
 
     if isinstance(theslice, slice):
 
-        start = extract_constant(theslice.start)
-        stop = extract_constant(theslice.stop)
-        step = extract_constant(theslice.step)
+        def analyze(x):
+            try:
+                x_constant = get_scalar_constant_value(x)
+                is_constant = True
+            except NotScalarConstantError:
+                x_constant = extract_constant(x)
+                is_constant = False
+            return x_constant, is_constant
+
+        start, is_start_constant = analyze(theslice.start)
+        stop, is_stop_constant = analyze(theslice.stop)
+        step, is_step_constant = analyze(theslice.step)
+        length, is_length_constant = analyze(length)
+
         if step is None:
             step = 1
 
-        defstart = switch(lt(step, 0), (length - 1), 0)
-        defstop = switch(lt(step, 0), -1, length)
+        # First handle the easier and common case where `step` is 1 and
+        # either `start` or `stop` is a range boundary. More specializations
+        # could be added later. This makes the resulting graph smaller than
+        # in the generic case below.
+        if step == 1:
+            is_start_0 = (
+                    start in [None, 0] or
+                    (is_start_constant and is_length_constant and
+                     start < 0 and start + length <= 0))
+            is_stop_length = (
+                    stop in [None, length, maxsize] or
+                    (is_stop_constant and is_length_constant and
+                     stop >= length))
+            if is_start_0:
+                # 0:stop:1
+                if is_stop_length:
+                    # Full slice.
+                    return slice(0, length, 1), 1
+                if is_stop_constant and stop >= 0:
+                    return (slice(0, switch(lt(stop, length), stop, length), 1),
+                            1)
+                stop_plus_len = stop + length
+                stop = switch(
+                        lt(stop, 0),
+                        # stop < 0
+                        switch(
+                            lt(stop_plus_len, 0),
+                            # stop + len < 0
+                            0,
+                            # stop + len >= 0
+                            stop_plus_len),
+                        # stop >= 0: use min(stop, length)
+                        switch(lt(stop, length), stop, length))
+                return slice(0, stop, 1), 1
+            elif is_stop_length:
+                # start:length:1
+                if is_start_constant and start >= 0:
+                    return slice(switch(lt(start, length), start, length),
+                                 length, 1), 1
+                start_plus_len = start + length
+                start = switch(
+                        lt(start, 0),
+                        # start < 0
+                        switch(
+                            lt(start_plus_len, 0),
+                            # start + len < 0
+                            0,
+                            # start + len >= 0
+                            start_plus_len),
+                        # start >= 0: use min(start, length)
+                        switch(lt(start, length), start, length))
+                return slice(start, length, 1), 1
+
+        # This is the generic case.
+
+        if is_step_constant:
+            # When we know the sign of `step`, the graph can be made simpler.
+            assert step != 0
+            if step > 0:
+                def switch_neg_step(a, b):
+                    return b
+                abs_step = step
+                sgn_step = 1
+            else:
+                def switch_neg_step(a, b):
+                    return a
+                abs_step = -step
+                sgn_step = -1
+        else:
+            is_step_neg = lt(step, 0)
+            def switch_neg_step(a, b):
+                return switch(is_step_neg, a, b)
+            abs_step = abs(step)
+            sgn_step = sgn(step)
+
+        defstart = switch_neg_step(length - 1, 0)
+        defstop = switch_neg_step(-1, length)
         if start is None:
             start = defstart
         else:
             start = switch(lt(start, 0), start + length, start)
-            start = switch(lt(start, 0), switch(lt(step, 0), -1, 0), start)
+            start = switch(lt(start, 0), switch_neg_step(-1, 0), start)
             start = switch(ge(start, length),
-                           switch(lt(step, 0), (length - 1), length),
+                           switch_neg_step(length - 1, length),
                            start)
         if stop in [None, maxsize]:
             # The special "maxsize" case is probably not needed here,
@@ -4282,18 +4368,20 @@ def get_canonical_form_slice(theslice, length):
             stop = switch(lt(stop, 0), -1, stop)
             stop = switch(ge(stop, length), length, stop)
 
-        nw_stop = switch(lt(step, 0), (start + 1), stop)
-        slice_len = (start - stop - 1) // abs(step) + 1
+        nw_stop = switch_neg_step(start + 1, stop)
+        slice_len = (start - stop - 1) // abs_step + 1
         slice_len = switch(lt(slice_len, 0), 0, slice_len)
-        neg_start = nw_stop - (slice_len - 1) * abs(step) - 1
+        neg_start = nw_stop - (slice_len - 1) * abs_step - 1
         neg_start = switch(lt(neg_start, 0), (nw_stop - 1), neg_start)
-        nw_start = switch(lt(step, 0), neg_start, start)
+        nw_start = switch_neg_step(neg_start, start)
         nw_start = switch(lt(nw_start, 0), 0, nw_start)
         nw_stop = switch(lt(nw_stop, 0), 0, nw_stop)
+        # Ensure start <= stop.
+        nw_start = switch(lt(nw_start, nw_stop), nw_start, nw_stop)
 
-        nw_step = abs(step)
+        nw_step = abs_step
         if step != 1:
-            reverse = sgn(step)
+            reverse = sgn_step
             return slice(nw_start, nw_stop, nw_step), reverse
         else:
             return slice(nw_start, nw_stop, nw_step), 1
@@ -4554,10 +4642,11 @@ class Subtensor(Op):
                     and (idx.step is None or idx.step == 1)):
                     outshp.append(xl)
                 else:
-                    cnf = get_canonical_form_slice(idx, xl)
-                    length = ((cnf[0].stop - cnf[0].start - 1) // cnf[0].step
-                            + 1)
-                    length = switch(lt(length, 0), 0, length)
+                    cnf = get_canonical_form_slice(idx, xl)[0]
+                    if cnf.step == 1:
+                        length = cnf.stop - cnf.start
+                    else:
+                        length = (cnf.stop - cnf.start - 1) // cnf.step + 1
                     outshp.append(length)
                 i += 1
             else: