Note
Go to the end to download the full example code
Compares dot implementations (numpy, cython, c++, sse)¶
numpy has a very fast implementation of the dot product. It is difficult to be better and very easy to be slower. This example looks into a couple of slower implementations with cython. The tested functions are the following:
import numpy
import matplotlib.pyplot as plt
from pandas import DataFrame, concat
from td3a_cpp.tutorial.dot_cython import (
dot_product, ddot_cython_array,
ddot_cython_array_optim, ddot_array,
ddot_array_16, ddot_array_16_sse
)
from td3a_cpp.tutorial.dot_cython import (
sdot_cython_array,
sdot_cython_array_optim, sdot_array,
sdot_array_16, sdot_array_16_sse
)
from td3a_cpp.tools import measure_time_dim
def get_vectors(fct, n, h=100, dtype=numpy.float64):
ctxs = [dict(va=numpy.random.randn(n).astype(dtype),
vb=numpy.random.randn(n).astype(dtype),
dot=fct,
x_name=n)
for n in range(10, n, h)]
return ctxs
numpy dot¶
ctxs = get_vectors(numpy.dot, 10000)
df = DataFrame(list(measure_time_dim('dot(va, vb)', ctxs, verbose=1)))
df['fct'] = 'numpy.dot'
print(df.tail(n=3))
dfs = [df]
0%| | 0/100 [00:00<?, ?it/s]
18%|#8 | 18/100 [00:00<00:00, 179.00it/s]
36%|###6 | 36/100 [00:00<00:00, 157.39it/s]
52%|#####2 | 52/100 [00:00<00:00, 141.76it/s]
67%|######7 | 67/100 [00:00<00:00, 128.59it/s]
81%|########1 | 81/100 [00:00<00:00, 117.66it/s]
93%|#########3| 93/100 [00:00<00:00, 108.65it/s]
100%|##########| 100/100 [00:00<00:00, 118.96it/s]
average deviation min_exec ... context_size x_name fct
97 0.000021 5.178455e-07 0.000021 ... 232 9710 numpy.dot
98 0.000022 3.533129e-07 0.000021 ... 232 9810 numpy.dot
99 0.000021 3.556189e-07 0.000021 ... 232 9910 numpy.dot
[3 rows x 9 columns]
Several cython dot¶
for fct in [dot_product, ddot_cython_array,
ddot_cython_array_optim, ddot_array,
ddot_array_16, ddot_array_16_sse]:
ctxs = get_vectors(fct, 10000 if fct.__name__ != 'dot_product' else 1000)
df = DataFrame(list(measure_time_dim('dot(va, vb)', ctxs, verbose=1)))
df['fct'] = fct.__name__
dfs.append(df)
print(df.tail(n=3))
0%| | 0/10 [00:00<?, ?it/s]
30%|### | 3/10 [00:00<00:00, 18.65it/s]
50%|##### | 5/10 [00:00<00:00, 8.77it/s]
70%|####### | 7/10 [00:01<00:00, 5.52it/s]
80%|######## | 8/10 [00:01<00:00, 4.57it/s]
90%|######### | 9/10 [00:01<00:00, 3.80it/s]
100%|##########| 10/10 [00:02<00:00, 3.23it/s]
100%|##########| 10/10 [00:02<00:00, 4.42it/s]
average deviation min_exec ... context_size x_name fct
7 0.000689 0.000001 0.000687 ... 232 710 dot_product
8 0.000800 0.000009 0.000788 ... 232 810 dot_product
9 0.000883 0.000002 0.000880 ... 232 910 dot_product
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
25%|##5 | 25/100 [00:00<00:00, 241.97it/s]
50%|##### | 50/100 [00:00<00:00, 169.46it/s]
69%|######9 | 69/100 [00:00<00:00, 135.10it/s]
84%|########4 | 84/100 [00:00<00:00, 114.63it/s]
97%|#########7| 97/100 [00:00<00:00, 100.00it/s]
100%|##########| 100/100 [00:00<00:00, 116.14it/s]
average deviation min_exec ... context_size x_name fct
97 0.000028 3.700952e-07 0.000028 ... 232 9710 ddot_cython_array
98 0.000026 2.974104e-07 0.000026 ... 232 9810 ddot_cython_array
99 0.000027 3.292713e-07 0.000027 ... 232 9910 ddot_cython_array
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
25%|##5 | 25/100 [00:00<00:00, 241.98it/s]
50%|##### | 50/100 [00:00<00:00, 169.08it/s]
69%|######9 | 69/100 [00:00<00:00, 135.27it/s]
84%|########4 | 84/100 [00:00<00:00, 114.78it/s]
97%|#########7| 97/100 [00:00<00:00, 100.03it/s]
100%|##########| 100/100 [00:00<00:00, 116.18it/s]
average deviation ... x_name fct
97 0.000028 3.334358e-07 ... 9710 ddot_cython_array_optim
98 0.000026 3.291796e-07 ... 9810 ddot_cython_array_optim
99 0.000027 3.524659e-07 ... 9910 ddot_cython_array_optim
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
22%|##2 | 22/100 [00:00<00:00, 209.08it/s]
43%|####3 | 43/100 [00:00<00:00, 158.78it/s]
60%|###### | 60/100 [00:00<00:00, 130.49it/s]
74%|#######4 | 74/100 [00:00<00:00, 112.22it/s]
86%|########6 | 86/100 [00:00<00:00, 99.31it/s]
97%|#########7| 97/100 [00:00<00:00, 89.15it/s]
100%|##########| 100/100 [00:00<00:00, 105.45it/s]
average deviation min_exec ... context_size x_name fct
97 0.000030 3.052402e-07 0.000029 ... 232 9710 ddot_array
98 0.000028 3.068461e-07 0.000028 ... 232 9810 ddot_array
99 0.000028 3.308606e-07 0.000028 ... 232 9910 ddot_array
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
23%|##3 | 23/100 [00:00<00:00, 219.82it/s]
45%|####5 | 45/100 [00:00<00:00, 165.47it/s]
63%|######3 | 63/100 [00:00<00:00, 135.41it/s]
78%|#######8 | 78/100 [00:00<00:00, 116.05it/s]
91%|#########1| 91/100 [00:00<00:00, 102.19it/s]
100%|##########| 100/100 [00:00<00:00, 112.42it/s]
average deviation min_exec ... context_size x_name fct
97 0.000027 3.669000e-07 0.000027 ... 232 9710 ddot_array_16
98 0.000027 4.026772e-07 0.000026 ... 232 9810 ddot_array_16
99 0.000026 2.207400e-07 0.000026 ... 232 9910 ddot_array_16
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
24%|##4 | 24/100 [00:00<00:00, 231.74it/s]
48%|####8 | 48/100 [00:00<00:00, 179.03it/s]
67%|######7 | 67/100 [00:00<00:00, 149.39it/s]
83%|########2 | 83/100 [00:00<00:00, 129.91it/s]
97%|#########7| 97/100 [00:00<00:00, 115.31it/s]
100%|##########| 100/100 [00:00<00:00, 130.51it/s]
average deviation min_exec ... context_size x_name fct
97 0.000022 5.577991e-07 0.000022 ... 232 9710 ddot_array_16_sse
98 0.000022 3.351084e-07 0.000022 ... 232 9810 ddot_array_16_sse
99 0.000022 3.721556e-07 0.000021 ... 232 9910 ddot_array_16_sse
[3 rows x 9 columns]
Let’s display the results¶
cc = concat(dfs)
cc['N'] = cc['x_name']
fig, ax = plt.subplots(2, 2, figsize=(10, 10))
cc[cc.N <= 1100].pivot(
index='N', columns='fct', values='average').plot(
logy=True, logx=True, ax=ax[0, 0])
cc[cc.fct != 'dot_product'].pivot(
index='N', columns='fct', values='average').plot(
logy=True, ax=ax[0, 1])
cc[cc.fct != 'dot_product'].pivot(
index='N', columns='fct', values='average').plot(
logy=True, logx=True, ax=ax[1, 1])
ax[0, 0].set_title("Comparison of cython ddot implementations")
ax[0, 1].set_title("Comparison of cython ddot implementations"
"\nwithout dot_product")
###################
# :epkg:`numpy` is faster but we are able to catch up.
Text(0.5, 1.0, 'Comparison of cython ddot implementations\nwithout dot_product')
Same for floats¶
Let’s for single floats.
dfs = []
for fct in [numpy.dot, sdot_cython_array,
sdot_cython_array_optim, sdot_array,
sdot_array_16, sdot_array_16_sse]:
ctxs = get_vectors(fct, 10000 if fct.__name__ != 'dot_product' else 1000,
dtype=numpy.float32)
df = DataFrame(list(measure_time_dim('dot(va, vb)', ctxs, verbose=1)))
df['fct'] = fct.__name__
dfs.append(df)
print(df.tail(n=3))
cc = concat(dfs)
cc['N'] = cc['x_name']
fig, ax = plt.subplots(1, 2, figsize=(10, 4))
cc.pivot(index='N', columns='fct', values='average').plot(
logy=True, ax=ax[0])
cc.pivot(index='N', columns='fct', values='average').plot(
logy=True, logx=True, ax=ax[1])
ax[0].set_title("Comparison of cython sdot implementations")
ax[1].set_title("Comparison of cython sdot implementations")
plt.show()
0%| | 0/100 [00:00<?, ?it/s]
20%|## | 20/100 [00:00<00:00, 190.05it/s]
40%|#### | 40/100 [00:00<00:00, 173.93it/s]
58%|#####8 | 58/100 [00:00<00:00, 162.51it/s]
75%|#######5 | 75/100 [00:00<00:00, 152.53it/s]
91%|#########1| 91/100 [00:00<00:00, 143.92it/s]
100%|##########| 100/100 [00:00<00:00, 149.66it/s]
average deviation min_exec ... context_size x_name fct
97 0.000015 3.155293e-07 0.000014 ... 232 9710 dot
98 0.000015 1.468500e-07 0.000015 ... 232 9810 dot
99 0.000014 1.669699e-07 0.000014 ... 232 9910 dot
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
27%|##7 | 27/100 [00:00<00:00, 265.89it/s]
54%|#####4 | 54/100 [00:00<00:00, 188.59it/s]
75%|#######5 | 75/100 [00:00<00:00, 151.64it/s]
92%|#########2| 92/100 [00:00<00:00, 129.02it/s]
100%|##########| 100/100 [00:00<00:00, 138.67it/s]
average deviation min_exec ... context_size x_name fct
97 0.000021 3.340554e-07 0.000021 ... 232 9710 sdot_cython_array
98 0.000022 2.817824e-07 0.000021 ... 232 9810 sdot_cython_array
99 0.000022 2.751985e-07 0.000022 ... 232 9910 sdot_cython_array
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
27%|##7 | 27/100 [00:00<00:00, 262.34it/s]
54%|#####4 | 54/100 [00:00<00:00, 186.25it/s]
74%|#######4 | 74/100 [00:00<00:00, 151.54it/s]
91%|#########1| 91/100 [00:00<00:00, 128.38it/s]
100%|##########| 100/100 [00:00<00:00, 137.25it/s]
average deviation ... x_name fct
97 0.000021 1.909457e-07 ... 9710 sdot_cython_array_optim
98 0.000022 1.676055e-07 ... 9810 sdot_cython_array_optim
99 0.000022 2.160350e-07 ... 9910 sdot_cython_array_optim
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
23%|##3 | 23/100 [00:00<00:00, 226.99it/s]
46%|####6 | 46/100 [00:00<00:00, 173.81it/s]
65%|######5 | 65/100 [00:00<00:00, 144.37it/s]
81%|########1 | 81/100 [00:00<00:00, 124.69it/s]
95%|#########5| 95/100 [00:00<00:00, 110.33it/s]
100%|##########| 100/100 [00:00<00:00, 123.78it/s]
average deviation min_exec ... context_size x_name fct
97 0.000023 3.688558e-07 0.000023 ... 232 9710 sdot_array
98 0.000023 3.984308e-07 0.000023 ... 232 9810 sdot_array
99 0.000024 2.334309e-07 0.000023 ... 232 9910 sdot_array
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
24%|##4 | 24/100 [00:00<00:00, 227.99it/s]
47%|####6 | 47/100 [00:00<00:00, 169.32it/s]
65%|######5 | 65/100 [00:00<00:00, 139.37it/s]
80%|######## | 80/100 [00:00<00:00, 119.84it/s]
93%|#########3| 93/100 [00:00<00:00, 105.75it/s]
100%|##########| 100/100 [00:00<00:00, 118.01it/s]
average deviation min_exec ... context_size x_name fct
97 0.000025 2.212216e-07 0.000025 ... 232 9710 sdot_array_16
98 0.000025 2.703401e-07 0.000025 ... 232 9810 sdot_array_16
99 0.000025 3.103866e-07 0.000025 ... 232 9910 sdot_array_16
[3 rows x 9 columns]
0%| | 0/100 [00:00<?, ?it/s]
26%|##6 | 26/100 [00:00<00:00, 257.58it/s]
52%|#####2 | 52/100 [00:00<00:00, 206.50it/s]
74%|#######4 | 74/100 [00:00<00:00, 175.35it/s]
93%|#########3| 93/100 [00:00<00:00, 153.72it/s]
100%|##########| 100/100 [00:00<00:00, 163.23it/s]
average deviation min_exec ... context_size x_name fct
97 0.000016 3.493588e-07 0.000016 ... 232 9710 sdot_array_16_sse
98 0.000017 2.715932e-07 0.000016 ... 232 9810 sdot_array_16_sse
99 0.000016 2.943432e-07 0.000016 ... 232 9910 sdot_array_16_sse
[3 rows x 9 columns]
Total running time of the script: ( 0 minutes 20.683 seconds)
