As shown earlier, the nb.jit decorator works by compiling a specialized version of the function once it encounters a new argument type. To better understand how this works, we can inspect the decorated function in the sum_sq example.

Numba exposes the specialized types using the signatures attribute. Right after the sum_sq definition, we can inspect the available specialization by accessing the sum_sq.signatures, as follows:

    sum_sq.signatures
    # Output:
    # []

If we call this function with a specific argument, for instance, an array of float64 numbers, we can see how Numba compiles a specialized version on the fly. If we also apply the function on an array of float32, we can see how a new entry is added to the sum_sq.signatures list:

    x = np.random.rand(1000).astype('float64')
    sum_sq(x)
    sum_sq.signatures
    # Result:
    # [(array(float64, 1d, C),)]

    x = np.random.rand(1000).astype('float32')
    sum_sq(x)
    sum_sq.signatures
    # Result:
    # [(array(float64, 1d, C),), (array(float32, 1d, C),)]

It is possible to explicitly compile the function for certain types by passing a signature to the nb.jit function.

An individual signature can be passed as a tuple that contains the type we would like to accept. Numba provides a great variety of types that can be found in the nb.types module, and they are also available in the top-level nb namespace. If we want to specify an array of a specific type, we can use the slicing operator, [:], on the type itself. In the following example, we demonstrate how to declare a function that takes an array of float64 as its only argument:

    @nb.jit((nb.float64[:],))
    def sum_sq(a):

Note that when we explicitly declare a signature, we are prevented from using other types, as demonstrated in the following example. If we try to pass an array, x, as float32, Numba will raise a TypeError:

    sum_sq(x.astype('float32'))
    # TypeError: No matching definition for argument type(s) 
    array(float32, 1d, C)

Another way to declare signatures is through type strings. For example, a function that takes a float64 as input and returns a float64 as output can be declared with the float64(float64) string. Array types can be declared using a [:] suffix. To put this together, we can declare a signature for our sum_sq function, as follows:

    @nb.jit("float64(float64[:])")
    def sum_sq(a):

You can also pass multiple signatures by passing a list:

    @nb.jit(["float64(float64[:])",
             "float64(float32[:])"])
    def sum_sq(a):