Making the double type

Type’s contract

In Theano’s framework, a Type (gof.type.Type) is any object which defines the following methods. To obtain the default methods described below, the Type should be an instance of Type or should be an instance of a subclass of Type. If you will write all methods yourself, you need not use an instance of Type.

Methods with default arguments must be defined with the same signature, i.e. the same default argument names and values. If you wish to add extra arguments to any of these methods, these extra arguments must have default values.

class PureType
filter(value, strict=False, allow_downcast=None)

This casts a value to match the Type and returns the cast value. If value is incompatible with the Type, the method must raise an exception. If strict is True, filter must return a reference to value (i.e. casting prohibited). If strict is False, then casting may happen, but downcasting should only be used in two situations:

  • if allow_downcast is True
  • if allow_downcast is None and the default behavior for this type allows downcasting for the given value (this behavior is type-dependent, you may decide what your own type does by default)

We need to define filter with three arguments. The second argument must be called strict (Theano often calls it by keyword) and must have a default value of False. The third argument must be called allow_downcast and must have a default value of None.

filter_inplace(value, storage, strict=False, allow_downcast=None)

If filter_inplace is defined, it will be called instead of filter() This is to allow reusing the old allocated memory. As of this writing this is used only when we transfer new data to a shared variable on the gpu.

storage will be the old value. i.e. The old numpy array, CudaNdarray, ...

is_valid_value(value)

Returns True iff the value is compatible with the Type. If filter(value, strict = True) does not raise an exception, the value is compatible with the Type.

Default: True iff filter(value, strict=True) does not raise an exception.

values_eq(a, b)

Returns True iff a and b are equal.

Default: a == b

values_eq_approx(a, b)

Returns True iff a and b are approximately equal, for a definition of “approximately” which varies from Type to Type.

Default: values_eq(a, b)

make_variable(name=None)

Makes a Variable of this Type with the specified name, if name is not None. If name is None, then the Variable does not have a name. The Variable will have its type field set to the Type object.

Default: there is a generic definition of this in Type. The Variable’s type will be the object that defines this method (in other words, self).

__call__(name=None)

Syntactic shortcut to make_variable.

Default: make_variable

__eq__(other)

Used to compare Type instances themselves

Default: object.__eq__

__hash__()

Types should not be mutable, so it should be OK to define a hash function. Typically this function should hash all of the terms involved in __eq__.

Default: id(self)

get_shape_info(obj)

Optional. Only needed to profile the memory of this Type of object.

Return the information needed to compute the memory size of obj.

The memory size is only the data, so this excludes the container. For an ndarray, this is the data, but not the ndarray object and other data structures such as shape and strides.

get_shape_info() and get_size() work in tandem for the memory profiler.

get_shape_info() is called during the execution of the function. So it is better that it is not too slow.

get_size() will be called on the output of this function when printing the memory profile.

Parameters:obj – The object that this Type represents during execution
Returns:Python object that self.get_size() understands
get_size(shape_info)

Number of bytes taken by the object represented by shape_info.

Optional. Only needed to profile the memory of this Type of object.

Parameters:shape_info – the output of the call to get_shape_info()
Returns:the number of bytes taken by the object described by shape_info.
clone(dtype=None, broadcastable=None)

Optional, for TensorType-alikes.

Return a copy of the type with a possibly changed value for dtype and broadcastable (if they aren’t None).

Parameters:
  • dtype – New dtype for the copy.
  • broadcastable – New broadcastable tuple for the copy.
may_share_memory(a, b)

Optional to run, but mandatory for DebugMode. Return True if the Python objects a and b could share memory. Return False otherwise. It is used to debug when Ops did not declare memory aliasing between variables. Can be a static method. It is highly recommended to use and is mandatory for Type in Theano as our buildbot runs in DebugMode.

For each method, the default is what Type defines for you. So, if you create an instance of Type or an instance of a subclass of Type, you must define filter. You might want to override values_eq_approx, as well as values_eq. The other defaults generally need not be overridden.

For more details you can go see the documentation for Type.

Defining double

We are going to base Type double on Python’s float. We must define filter and shall override values_eq_approx.

filter

# Note that we shadow Python's function ``filter`` with this
# definition.
def filter(x, strict=False, allow_downcast=None):
    if strict:
        if isinstance(x, float):
            return x
        else:
            raise TypeError('Expected a float!')
    elif allow_downcast:
        return float(x)
    else:   # Covers both the False and None cases.
        x_float = float(x)
        if x_float == x:
            return x_float
        else:
             raise TypeError('The double type cannot accurately represent '
                             'value %s (of type %s): you must explicitly '
                             'allow downcasting if you want to do this.'
                             % (x, type(x)))

If strict is True we need to return x. If strict is True and x is not a float (for example, x could easily be an int) then it is incompatible with our Type and we must raise an exception.

If strict is False then we are allowed to cast x to a float, so if x is an int it we will return an equivalent float. However if this cast triggers a precision loss (x != float(x)) and allow_downcast is not True, then we also raise an exception. Note that here we decided that the default behavior of our type (when allow_downcast is set to None) would be the same as when allow_downcast is False, i.e. no precision loss is allowed.

values_eq_approx

def values_eq_approx(x, y, tolerance=1e-4):
    return abs(x - y) / (abs(x) + abs(y)) < tolerance

The second method we define is values_eq_approx. This method allows approximate comparison between two values respecting our Type’s constraints. It might happen that an optimization changes the computation graph in such a way that it produces slightly different variables, for example because of numerical instability like rounding errors at the end of the mantissa. For instance, a + a + a + a + a + a might not actually produce the exact same output as 6 * a (try with a=0.1), but with values_eq_approx we do not necessarily mind.

We added an extra tolerance argument here. Since this argument is not part of the API, it must have a default value, which we chose to be 1e-4.

Note

values_eq is never actually used by Theano, but it might be used internally in the future. Equality testing in DebugMode is done using values_eq_approx.

Putting them together

What we want is an object that respects the aforementioned contract. Recall that Type defines default implementations for all required methods of the interface, except filter. One way to make the Type is to instantiate a plain Type and set the needed fields:

from theano import gof

double = gof.Type()
double.filter = filter
double.values_eq_approx = values_eq_approx

Another way to make this Type is to make a subclass of gof.Type and define filter and values_eq_approx in the subclass:

from theano import gof

class Double(gof.Type):

    def filter(self, x, strict=False, allow_downcast=None):
        # See code above.
        ...

    def values_eq_approx(self, x, y, tolerance=1e-4):
        # See code above.
        ...

double = Double()

double is then an instance of Type Double, which in turn is a subclass of Type.

There is a small issue with defining double this way. All instances of Double are technically the same Type. However, different Double Type instances do not compare the same:

>>> double1 = Double()
>>> double2 = Double()
>>> double1 == double2
False

Theano compares Types using == to see if they are the same. This happens in DebugMode. Also, Ops can (and should) ensure that their inputs have the expected Type by checking something like if x.type == lvector.

There are several ways to make sure that equality testing works properly:

  1. Define Double.__eq__ so that instances of type Double are equal. For example:

    def __eq__(self, other):
        return type(self) is Double and type(other) is Double
    
  2. Override Double.__new__ to always return the same instance.

  3. Hide the Double class and only advertise a single instance of it.

Here we will prefer the final option, because it is the simplest. Ops in the Theano code often define the __eq__ method though.

Untangling some concepts

Initially, confusion is common on what an instance of Type is versus a subclass of Type or an instance of Variable. Some of this confusion is syntactic. A Type is any object which has fields corresponding to the functions defined above. The Type class provides sensible defaults for all of them except filter, so when defining new Types it is natural to subclass Type. Therefore, we often end up with Type subclasses and it is can be confusing what these represent semantically. Here is an attempt to clear up the confusion:

  • An instance of Type (or an instance of a subclass) is a set of constraints on real data. It is akin to a primitive type or class in C. It is a static annotation.
  • An instance of Variable symbolizes data nodes in a data flow graph. If you were to parse the C expression int x;, int would be a Type instance and x would be a Variable instance of that Type instance. If you were to parse the C expression c = a + b;, a, b and c would all be Variable instances.
  • A subclass of Type is a way of implementing a set of Type instances that share structural similarities. In the double example that we are doing, there is actually only one Type in that set, therefore the subclass does not represent anything that one of its instances does not. In this case it is a singleton, a set with one element. However, the TensorType class in Theano (which is a subclass of Type) represents a set of types of tensors parametrized by their data type or number of dimensions. We could say that subclassing Type builds a hierarchy of Types which is based upon structural similarity rather than compatibility.

Final version

from theano import gof

class Double(gof.Type):

    def filter(self, x, strict=False, allow_downcast=None):
        if strict:
            if isinstance(x, float):
                return x
            else:
                raise TypeError('Expected a float!')
        elif allow_downcast:
            return float(x)
        else:   # Covers both the False and None cases.
            x_float = float(x)
            if x_float == x:
                return x_float
            else:
                 raise TypeError('The double type cannot accurately represent '
                                 'value %s (of type %s): you must explicitly '
                                 'allow downcasting if you want to do this.'
                                 % (x, type(x)))

    def values_eq_approx(self, x, y, tolerance=1e-4):
        return abs(x - y) / (abs(x) + abs(y)) < tolerance

    def __str__(self):
        return "double"

double = Double()

We add one utility function, __str__. That way, when we print double, it will print out something intelligible.