Numpy: Multiplying large arrays with dtype=int8 is SLOW

Question

Consider the following piece of code, which generates some (potentially) huge, multi-dimensional array and performs numpy.tensordot with it (whether we multiply the same or two different arrays here, does not really matter).

import time
import numpy

L, N = 6, 4

shape = (2*L)*[N,]
A = numpy.arange(numpy.prod(shape)).reshape(shape)
A = A % 256 - 128   # [-127,+127]
axes=(range(1,2*L,2), range(0,2*L,2))

def run(dtype, repeat=1):
    A_ = A.astype(dtype)
    t = time.time()
    for i in range(repeat):
        numpy.tensordot(A_, A_, axes)
    t = time.time() - t
    print(dtype, '   \t%8.2f sec\t%8.2f MB' %(t, A_.nbytes/1e6))

Now we can compare the performance for different data types, e.g.:

run(numpy.float64)
run(numpy.int64)

Since the array only consists of small integer numbers, I would like to save some memory by using dtype=int8. However, this slows down the matrix multiplication A LOT.

Here are some test cases

The first one, is the important one for my use case. The others are just for reference. Using Numpy 1.13.1 and Python 3.4.2

Large array

L, N = 6, 4; A.size = 4**12 = 16777216
<class 'numpy.float64'>        59.58 sec      134.22 MB
<class 'numpy.float32'>        44.19 sec       67.11 MB
<class 'numpy.int16'>         711.16 sec       33.55 MB
<class 'numpy.int8'>          647.40 sec       16.78 MB

Same array with different data types. Memory decreases as expected. But why the large differences in the CPU time? If anything I would expect int to be faster than float.

Large array with different shape

L, N = 1, 4**6; A.size = (4**6)**2 = 16777216
<class 'numpy.float64'>        57.95 sec      134.22 MB
<class 'numpy.float32'>        42.84 sec       67.11 MB

The shape doesn't seem to have a large effect.

Not so large array

L, N = 5, 4
<class 'numpy.float128'>       10.91 sec       16.78 MB
<class 'numpy.float64'>         0.98 sec        8.39 MB
<class 'numpy.float32'>         0.90 sec        4.19 MB
<class 'numpy.float16'>         9.80 sec        2.10 MB
<class 'numpy.int64'>           8.84 sec        8.39 MB
<class 'numpy.int32'>           5.55 sec        4.19 MB
<class 'numpy.int16'>           2.23 sec        2.10 MB
<class 'numpy.int8'>            1.82 sec        1.05 MB

Smaller values, but same weird trend.

small array, lots of repetitions

L, N = 2, 4; A.size = 4**4 = 256; repeat=1000000

<class 'numpy.float128'>       17.92 sec        4.10 KB
<class 'numpy.float64'>        14.20 sec        2.05 KB
<class 'numpy.float32'>        12.21 sec        1.02 KB
<class 'numpy.float16'>        41.72 sec        0.51 KB
<class 'numpy.int64'>          14.21 sec        2.05 KB
<class 'numpy.int32'>          14.26 sec        1.02 KB
<class 'numpy.int16'>          13.88 sec        0.51 KB
<class 'numpy.int8'>           13.03 sec        0.26 KB

Other than float16 being much slower, everything is fine here.

Question

Why is int8 for very large arrays so much slower? Is there any way around this? Saving memory becomes increasingly important for larger arrays!

Answer 1

Unfortunately,

as correctly underlined in the comments, the "engine" behind the scenes is BLAS, and it does not have native integer type. That's why The float64 or 32 will then run faster (some discussion in a related answer for a similar question for C++).

As a side note to the core of your question, a way to explore to speed up your problem while limiting the memory consumption is to go with Cython, where you can run C code directly and getting back the result in Python.