1.13. Performance Tips

This is a short guide to features present in Numba that can help with obtaining the best performance from code. Two examples are used, both are entirely contrived and exist purely for pedagogical reasons to motivate discussion. The first is the computation of the trigonometric identity cos(x)^2 + sin(x)^2, the second is a simple element wise square root of a vector with reduction over summation. All performance numbers are indicative only and unless otherwise stated were taken from running on an Intel i7-4790 CPU (4 hardware threads) with an input of np.arange(1.e7).

Note

A reasonably effective approach to achieving high performance code is to profile the code running with real data and use that to guide performance tuning. The information presented here is to demonstrate features, not to act as canonical guidance!

1.13.1. No Python mode vs Object mode

A common pattern is to decorate functions with @jit as this is the most flexible decorator offered by Numba. @jit essentially encompasses two modes of compilation, first it will try and compile the decorated function in no Python mode, if this fails it will try again to compile the function using object mode. Whilst the use of looplifting in object mode can enable some performance increase, getting functions to compile under no python mode is really the key to good performance. To make it such that only no python mode is used and if compilation fails an exception is raised the decorators @njit and @jit(nopython=True) can be used (the first is an alias of the second for convenience).

1.13.2. Loops

Whilst NumPy has developed a strong idiom around the use of vector operations, Numba is perfectly happy with loops too. For users familiar with C or Fortran, writing Python in this style will work fine in Numba (after all, LLVM gets a lot of use in compiling C lineage languages). For example:

@njit
def ident_np(x):
    return np.cos(x) ** 2 + np.sin(x) ** 2

@njit
def ident_loops(x):
    r = np.empty_like(x)
    n = len(x)
    for i in range(n):
        r[i] = np.cos(x[i]) ** 2 + np.sin(x[i]) ** 2
    return r

The above run at almost identical speeds when decorated with @njit, without the decorator the vectorized function is a couple of orders of magnitude faster.

Function Name @njit Execution time
ident_np No 0.581s
ident_np Yes 0.659s
ident_loops No 25.2s
ident_loops Yes 0.670s

1.13.3. Fastmath

In certain classes of applications strict IEEE 754 compliance is less important. As a result it is possible to relax some numerical rigour with view of gaining additional performance. The way to achieve this behaviour in Numba is through the use of the fastmath keyword argument:

@njit(fastmath=False)
def do_sum(A):
    acc = 0.
    # without fastmath, this loop must accumulate in strict order
    for x in A:
        acc += np.sqrt(x)
    return acc

@njit(fastmath=True)
def do_sum_fast(A):
    acc = 0.
    # with fastmath, the reduction can be vectorized as floating point
    # reassociation is permitted.
    for x in A:
        acc += np.sqrt(x)
    return acc
Function Name Execution time
do_sum 35.2 ms
do_sum_fast 17.8 ms

In some cases you may wish to opt-in to only a subset of possible fast-math optimizations. This can be done by supplying a set of LLVM fast-math flags to fastmath.:

def add_assoc(x, y):
    return (x - y) + y

print(njit(fastmath=False)(add_assoc)(0, np.inf)) # nan
print(njit(fastmath=True) (add_assoc)(0, np.inf)) # 0.0
print(njit(fastmath={'reassoc', 'nsz'})(add_assoc)(0, np.inf)) # 0.0
print(njit(fastmath={'reassoc'})       (add_assoc)(0, np.inf)) # nan
print(njit(fastmath={'nsz'})           (add_assoc)(0, np.inf)) # nan

1.13.4. Parallel=True

If code contains operations that are parallelisable (and supported) Numba can compile a version of that will run in parallel on multiple native threads (no GIL!). This parallelisation is performed automatically and is enabled by simply adding the parallel keyword argument:

@njit(parallel=True)
def ident_parallel(A):
    return np.cos(x) ** 2 + np.sin(x) ** 2

Executions times are as follows:

Function Name Execution time
ident_parallel 112 ms

The execution speed of this function with parallel=True present is approximately 5x that of the NumPy equivalent and 6x that of standard @njit.

Numba parallel execution also has support for explicit parallel loop declaration similar to that in OpenMP. To indicate that a loop should be executed in parallel the numba.prange function should be used, this function behaves like Python range and if parallel=True is not set it acts simply as an alias of range. Loops induced with prange can be used for embarrassingly parallel computation and also reductions.

Revisiting the reduce over sum example, assuming it is safe for the sum to be accumulated out of order, the loop in n can be parallelised through the use of prange. Further, the fastmath=True keyword argument can be added without concern in this case as the assumption that out of order execution is valid has already been made through the use of parallel=True (as each thread computes a partial sum).

@njit(parallel=True)
def do_sum_parallel(A):
    # each thread can accumulate its own partial sum, and then a cross
    # thread reduction is performed to obtain the result to return
    n = len(A)
    acc = 0.
    for i in prange(n):
        acc += np.sqrt(A[i])
    return acc

@njit(parallel=True, fastmath=True)
def do_sum_parallel_fast(A):
    n = len(A)
    acc = 0.
    for i in prange(n):
        acc += np.sqrt(A[i])
    return acc

Execution times are as follows, fastmath again improves performance.

Function Name Execution time
do_sum_parallel 9.81 ms
do_sum_parallel_fast 5.37 ms

1.13.5. Intel SVML

Intel provides a short vector math library (SVML) that contains a large number of optimised transcendental functions available for use as compiler intrinsics. If the icc_rt package is present in the environment (or the SVML libraries are simply locatable!) then Numba automatically configures the LLVM back end to use the SVML intrinsic functions where ever possible. SVML provides both high and low accuracy versions of each intrinsic and the version that is used is determined through the use of the fastmath keyword. The default is to use high accuracy which is accurate to within 1 ULP, however if fastmath is set to True then the lower accuracy versions of the intrinsics are used (answers to within 4 ULP).

First obtain SVML, using conda for example:

conda install -c numba icc_rt

Rerunning the identity function example ident_np from above with various combinations of options to @njit and with/without SVML yields the following performance results (input size np.arange(1.e8)). For reference, with just NumPy the function executed in 5.84s:

@njit kwargs SVML Execution time
None No 5.95s
None Yes 2.26s
fastmath=True No 5.97s
fastmath=True Yes 1.8s
parallel=True No 1.36s
parallel=True Yes 0.624s
parallel=True, fastmath=True No 1.32s
parallel=True, fastmath=True Yes 0.576s

It is evident that SVML significantly increases the performance of this function. The impact of fastmath in the case of SVML not being present is zero, this is expected as there is nothing in the original function that would benefit from relaxing numerical strictness.

1.13.6. Linear algebra

Numba supports most of numpy.linalg in no Python mode. The internal implementation relies on a LAPACK and BLAS library to do the numerical work and it obtains the bindings for the necessary functions from SciPy. Therefore, to achieve good performance in numpy.linalg functions with Numba it is necessary to use a SciPy built against a well optimised LAPACK/BLAS library. In the case of the Anaconda distribution SciPy is built against Intel’s MKL which is highly optimised and as a result Numba makes use of this performance.