6.4. A guide to using @overload¶

6.4.1. Concrete Example¶

Let’s assume that you are working on a minimization algorithm that makes use of scipy.linalg.norm to find different vector norms and the frobenius norm for matrices. You know that only integer and real numbers will be involved. (While this may sound like an artificial example, especially because a Numba implementation of numpy.linalg.norm exists, it is largely pedagogical and serves to illustrate how and when to use @overload).

The skeleton might look something like this:

def algorithm():
    # setup
    v = ...
    while True:
        # take a step
        d = scipy.linalg.norm(v)
        if d < tolerance:
            break

Now, let’s further assume, that you have heard of Numba and you now wish to use it to accelerate your function. However, after adding the jit(nopython=True) decorator, Numba complains that scipy.linalg.norm isn’t supported. From looking at the documentation, you realize that a norm is probably fairly easy to implement using NumPy. A good starting point is the following template.

# Declare that function `myfunc` is going to be overloaded (have a
# substitutable Numba implementation)
@overload(myfunc)
# Define the overload function with formal arguments
# these arguments must be matched in the inner function implementation
def jit_myfunc(arg0, arg1, arg2, ...):
    # This scope is for typing, access is available to the *type* of all
    # arguments. This information can be used to change the behaviour of the
    # implementing function and check that the types are actually supported
    # by the implementation.

    print(arg0) # this will show the Numba type of arg0

    # This is the definition of the function that implements the `myfunc` work.
    # It does whatever algorithm is needed to implement myfunc.
    def myfunc_impl(arg0, arg1, arg2, ...): # match arguments to jit_myfunc
        # < Implementation goes here >
        return # whatever needs to be returned by the algorithm

    # return the implementation
    return myfunc_impl

After some deliberation and tinkering, you end up with the following code:

import numpy as np
from numba import njit, types
from numba.extending import overload, register_jitable
from numba.errors import TypingError

import scipy.linalg


@register_jitable
def _oneD_norm_2(a):
    # re-usable implementation of the 2-norm
    val = np.abs(a)
    return np.sqrt(np.sum(val * val))


@overload(scipy.linalg.norm)
def jit_norm(a, ord=None):
    if isinstance(ord, types.Optional):
        ord = ord.type
    # Reject non integer, floating-point or None types for ord
    if not isinstance(ord, (types.Integer, types.Float, types.NoneType)):
        raise TypingError("'ord' must be either integer or floating-point")
    # Reject non-ndarray types
    if not isinstance(a, types.Array):
        raise TypingError("Only accepts NumPy ndarray")
    # Reject ndarrays with non integer or floating-point dtype
    if not isinstance(a.dtype, (types.Integer, types.Float)):
        raise TypingError("Only integer and floating point types accepted")
    # Reject ndarrays with unsupported dimensionality
    if not (0 <= a.ndim <= 2):
        raise TypingError('3D and beyond are not allowed')
    # Implementation for scalars/0d-arrays
    elif a.ndim == 0:
        return a.item()
    # Implementation for vectors
    elif a.ndim == 1:
        def _oneD_norm_x(a, ord=None):
            if ord == 2 or ord is None:
                return _oneD_norm_2(a)
            elif ord == np.inf:
                return np.max(np.abs(a))
            elif ord == -np.inf:
                return np.min(np.abs(a))
            elif ord == 0:
                return np.sum(a != 0)
            elif ord == 1:
                return np.sum(np.abs(a))
            else:
                return np.sum(np.abs(a)**ord)**(1. / ord)
        return _oneD_norm_x
    # Implementation for matrices
    elif a.ndim == 2:
        def _two_D_norm_2(a, ord=None):
            return _oneD_norm_2(a.ravel())
        return _two_D_norm_2


if __name__ == "__main__":
    @njit
    def use(a, ord=None):
        # simple test function to check that the overload works
        return scipy.linalg.norm(a, ord)

    # spot check for vectors
    a = np.arange(10)
    print(use(a))
    print(scipy.linalg.norm(a))

    # spot check for matrices
    b = np.arange(9).reshape((3, 3))
    print(use(b))
    print(scipy.linalg.norm(b))

As you can see, the implementation only supports what you need right now:

• Only supports integer and floating-point types
• All vector norms
• Only the Frobenius norm for matrices
• Code sharing between vector and matrix implementations using @register_jitable.
• Norms are implemented using NumPy syntax. (This is possible because Numba is very aware of NumPy and many functions are supported.)

So what actually happens here? The overload decorator registers a suitable implementation for scipy.linalg.norm in case a call to this is encountered in code that is being JIT-compiled, for example when you decorate your algorithm function with @jit(nopython=True). In that case, the function jit_norm will be called with the currently encountered types and will then return either _oneD_norm_x in the vector case and _two_D_norm_2.

You can download the example code here: mynorm.py

6.4.2. Implementing @overload for NumPy functions¶

Numba supports NumPy through the provision of @jit compatible re-implementations of NumPy functions. In such cases @overload is a very convenient option for writing such implementations, however there are a few additional things to watch out for.

• The Numba implementation should match the NumPy implementation as closely as feasible with respect to accepted types, arguments, raised exceptions and algorithmic complexity (Big-O / Landau order).
• When implementing supported argument types, bear in mind that, due to duck typing, NumPy does tend to accept a multitude of argument types beyond NumPy arrays such as scalar, list, tuple, set, iterator, generator etc. You will need to account for that during type inference and subsequently as part of the tests.
• A NumPy function may return a scalar, array or a data structure which matches one of its inputs, you need to be aware of type unification problems and dispatch to appropriate implementations. For example, np.corrcoef may return an array or a scalar depending on its inputs.

• If you are implementing a new function, you should always update the documentation. The sources can be found in docs/source/reference/numpysupported.rst. Be sure to mention any limitations that your implementation has, e.g. no support for the axis keyword.

• When writing tests for the functionality itself, it’s useful to include handling of non-finite values, arrays with different shapes and layouts, complex inputs, scalar inputs, inputs with types for which support is not documented (e.g. a function which the NumPy docs say requires a float or int input might also ‘work’ if given a bool or complex input).

• When writing tests for exceptions, for example if adding tests to numba/tests/test_np_functions.py, you may encounter the following error message:

  ======================================================================
  FAIL: test_foo (numba.tests.test_np_functions.TestNPFunctions)
  ----------------------------------------------------------------------
  Traceback (most recent call last):
  File "<path>/numba/numba/tests/support.py", line 645, in tearDown
      self.memory_leak_teardown()
  File "<path>/numba/numba/tests/support.py", line 619, in memory_leak_teardown
      self.assert_no_memory_leak()
  File "<path>/numba/numba/tests/support.py", line 628, in assert_no_memory_leak
      self.assertEqual(total_alloc, total_free)
  AssertionError: 36 != 35
  

  This occurs because raising exceptions from jitted code leads to reference leaks. Ideally, you will place all exception testing in a separate test method and then add a call in each test to self.disable_leak_check() to disable the leak-check (inherit from numba.tests.support.TestCase to make that available).

• For many of the functions that are available in NumPy, there are corresponding methods defined on the NumPy ndarray type. For example, the function repeat is available as a NumPy module level function and a member function on the ndarray class.

  import numpy as np
  a = np.arange(10)
  # function
  np.repeat(a, 10)
  # method
  a.repeat(10)
  

  Once you have written the function implementation, you can easily use @overload_method and reuse it. Just be sure to check that NumPy doesn’t diverge in the implementations of its function/method.

  As an example, the repeat function/method:

  @extending.overload_method(types.Array, 'repeat')
  def array_repeat(a, repeats):
      def array_repeat_impl(a, repeat):
          # np.repeat has already been overloaded
          return np.repeat(a, repeat)
  
      return array_repeat_impl
  

• If you need to create ancillary functions, for example to re-use a small utility function or to split your implementation across functions for the sake of readability, you can make use of the @register_jitable decorator. This will make those functions available from within your @jit and @overload decorated functions.

• The Numba continuous integration (CI) set up tests a wide variety of NumPy versions, you’ll sometimes be alerted to a change in behaviour from some previous NumPy version. If you can find supporting evidence in the NumPy change log / repository, then you’ll need to decide whether to create branches and attempt to replicate the logic across versions, or use a version gate (with associated wording in the documentation) to advertise that Numba replicates NumPy from some particular version onwards.

• You can look at the Numba source code for inspiration, many of the overloaded NumPy functions and methods are in numba/targets/arrayobj.py. Below, you will find a list of implementations to look at that are well implemented in terms of accepted types and test coverage.

  • np.repeat