Python: Fastest way of packing a 2d array of binary values into UINT64 array

Question

I have a 2D UINT8 numpy array of size (149797, 64) . Each of the elements are either 0 or 1. I want to pack these binary values in each row into a UINT64 value so that i get a UINT64 array of shape 149797 as a result. I tried the following code using numpy bitpack function.

test = np.random.randint(0, 2, (149797, 64),dtype=np.uint8)
col_pack=np.packbits(test.reshape(-1, 8, 8)[:, ::-1]).view(np.uint64)

The packbits function takes about 10 ms to execute. A simple reshaping of this array itself seems to take around 7 ms .I also tried iterating over 2d numpy array using shifting operations to achieve the same result; but there was no speed improvement.

Finally i also want to compile it using numba for CPU.

@njit
def shifting(bitlist):
    x=np.zeros(149797,dtype=np.uint64)  #54
    rows,cols=bitlist.shape
    for i in range(0,rows):             #56
      out=0
      for bit in range(0,cols):
         out = (out << 1) | bitlist[i][bit] # If i comment out bitlist, time=190 microsec
      x[i]=np.uint64(out)  # Reduces time to microseconds if line is commented in njit
    return x

It takes about 6 ms using njit .

Here is the parallel njit version

@njit(parallel=True)
def shifting(bitlist): 
    rows,cols=149797,64
    out=0
    z=np.zeros(rows,dtype=np.uint64)
    for i in prange(rows):
      for bit in range(cols):
         z[i] = (z[i] * 2) + bitlist[i,bit] # Time becomes 100 micro if i use 'out' instead of 'z[i] array'

    return z

It's slightly better wit 3.24ms execution time(google colab dual core 2.2Ghz) Currently, the python solution with swapbytes(Paul's) method seems to be the best one ie 1.74 ms .

How can we further speed up this conversion? Is there scope for using any vectorization(or parallelization), bitarrays etc, for achieving speedup?

Ref: numpy packbits pack to uint16 array

On a 12 core machine (Intel(R) Xeon(R) CPU E5-1650 v2 @ 3.50GHz),

Pauls method: 1595.0 microseconds (it does not use multicore, i suppose)

Numba code: 146.0 microseconds (aforementioned parallel-numba)

ie around 10x speedup !!!

Answer 1

You can get a sizeable speedup by using byteswap instead of reshaping etc.:

test = np.random.randint(0, 2, (149797, 64),dtype=np.uint8)

np.packbits(test.reshape(-1, 8, 8)[:, ::-1]).view(np.uint64)
# array([ 1079982015491401631,   246233595099746297, 16216705265283876830,
#        ...,  1943876987915462704, 14189483758685514703,
       12753669247696755125], dtype=uint64)
np.packbits(test).view(np.uint64).byteswap()
# array([ 1079982015491401631,   246233595099746297, 16216705265283876830,
#        ...,  1943876987915462704, 14189483758685514703,
       12753669247696755125], dtype=uint64)

timeit(lambda:np.packbits(test.reshape(-1, 8, 8)[:, ::-1]).view(np.uint64),number=100)
# 1.1054180909413844

timeit(lambda:np.packbits(test).view(np.uint64).byteswap(),number=100)
# 0.18370431219227612

Answer 2

A bit Numba solution (version 0.46/Windows).

Code

import numpy as np
import numba as nb

#with memory allocation
@nb.njit(parallel=True)
def shifting(bitlist):
    assert bitlist.shape[1]==64
    x=np.empty(bitlist.shape[0],dtype=np.uint64)

    for i in nb.prange(bitlist.shape[0]):
        out=np.uint64(0)
        for bit in range(bitlist.shape[1]):
            out = (out << 1) | bitlist[i,bit] 
        x[i]=out
    return x

#without memory allocation
@nb.njit(parallel=True)
def shifting_2(bitlist,x):
    assert bitlist.shape[1]==64

    for i in nb.prange(bitlist.shape[0]):
        out=np.uint64(0)
        for bit in range(bitlist.shape[1]):
            out = (out << 1) | bitlist[i,bit] 
        x[i]=out
    return x

Timings

test = np.random.randint(0, 2, (149797, 64),dtype=np.uint8)

#If you call this function multiple times, only allocating memory 
#once may be enough
x=np.empty(test.shape[0],dtype=np.uint64)

#Warmup first call takes significantly longer
res=shifting(test)
res=shifting_2(test,x)

%timeit res=shifting(test)
#976 µs ± 41.6 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
%timeit res=shifting_2(test,x)
#764 µs ± 63 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
%timeit np.packbits(test).view(np.uint64).byteswap()
#8.07 ms ± 52.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
%timeit np.packbits(test.reshape(-1, 8, 8)[:, ::-1]).view(np.uint64)
#17.9 ms ± 91 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)