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 teachcompute.validation.cython.dot_cython import (
    dot_product,
    ddot_cython_array,
    ddot_cython_array_optim,
    ddot_array,
    ddot_array_16,
    ddot_array_16_sse,
)
from teachcompute.validation.cython.dot_cython import (
    sdot_cython_array,
    sdot_cython_array_optim,
    sdot_array,
    sdot_array_16,
    sdot_array_16_sse,
)
from teachcompute.ext_test_case 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]

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name        fct
97  0.000003  9.925625e-08  0.000002  0.000003      10      50  0.000025           184     0.000011    9710  numpy.dot
98  0.000003  9.436711e-09  0.000003  0.000003      10      50  0.000025           184     0.000012    9810  numpy.dot
99  0.000003  1.160821e-07  0.000003  0.000003      10      50  0.000026           184     0.000010    9910  numpy.dot

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))

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    average  deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name          fct
7  0.000123   0.000006  0.000118  0.000138      10      50  0.001227           184     0.000130     710  dot_product
8  0.000136   0.000002  0.000135  0.000140      10      50  0.001364           184     0.000146     810  dot_product
9  0.000179   0.000039  0.000153  0.000283      10      50  0.001787           184     0.000167     910  dot_product

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name                fct
97  0.000010  8.729575e-07  0.000008  0.000011      10      50  0.000095           184     0.000017    9710  ddot_cython_array
98  0.000013  1.537107e-06  0.000010  0.000016      10      50  0.000133           184     0.000019    9810  ddot_cython_array
99  0.000013  9.683444e-07  0.000011  0.000015      10      50  0.000126           184     0.000019    9910  ddot_cython_array

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name                      fct
97  0.000007  1.895534e-07  0.000007  0.000007      10      50  0.000069           184     0.000013    9710  ddot_cython_array_optim
98  0.000007  9.850135e-08  0.000007  0.000007      10      50  0.000069           184     0.000012    9810  ddot_cython_array_optim
99  0.000007  1.462113e-07  0.000007  0.000007      10      50  0.000070           184     0.000012    9910  ddot_cython_array_optim

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name         fct
97  0.000007  1.668467e-07  0.000007  0.000007      10      50  0.000069           184     0.000013    9710  ddot_array
98  0.000007  2.074146e-07  0.000007  0.000008      10      50  0.000070           184     0.000012    9810  ddot_array
99  0.000007  1.312301e-07  0.000007  0.000007      10      50  0.000070           184     0.000014    9910  ddot_array

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name            fct
97  0.000004  2.483395e-07  0.000004  0.000004      10      50  0.000037           184     0.000012    9710  ddot_array_16
98  0.000004  9.604787e-08  0.000004  0.000004      10      50  0.000037           184     0.000012    9810  ddot_array_16
99  0.000004  1.166749e-07  0.000004  0.000004      10      50  0.000037           184     0.000012    9910  ddot_array_16

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name                fct
97  0.000003  9.790456e-08  0.000003  0.000003      10      50  0.000027           184     0.000012    9710  ddot_array_16_sse
98  0.000003  2.841234e-07  0.000003  0.000004      10      50  0.000029           184     0.000011    9810  ddot_array_16_sse
99  0.000003  1.359109e-08  0.000003  0.000003      10      50  0.000027           184     0.000015    9910  ddot_array_16_sse

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.

Comparison of cython ddot implementations, Comparison of cython ddot implementations without dot_product

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")

Comparison of cython sdot implementations, Comparison of cython sdot implementations

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name  fct
97  0.000002  1.978880e-07  0.000002  0.000003      10      50  0.000025           184     0.000009    9710  dot
98  0.000003  1.251694e-07  0.000002  0.000003      10      50  0.000026           184     0.000008    9810  dot
99  0.000003  3.443201e-07  0.000003  0.000004      10      50  0.000030           184     0.000009    9910  dot

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name                fct
97  0.000007  1.068626e-07  0.000007  0.000007      10      50  0.000068           184     0.000012    9710  sdot_cython_array
98  0.000008  6.436713e-07  0.000007  0.000009      10      50  0.000085           184     0.000011    9810  sdot_cython_array
99  0.000010  3.937788e-07  0.000010  0.000011      10      50  0.000100           184     0.000015    9910  sdot_cython_array

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name                      fct
97  0.000007  4.399225e-07  0.000007  0.000008      10      50  0.000069           184     0.000009    9710  sdot_cython_array_optim
98  0.000007  1.615574e-07  0.000007  0.000007      10      50  0.000069           184     0.000013    9810  sdot_cython_array_optim
99  0.000007  1.686930e-07  0.000007  0.000007      10      50  0.000070           184     0.000012    9910  sdot_cython_array_optim

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name         fct
97  0.000007  2.734671e-07  0.000007  0.000008      10      50  0.000069           184     0.000011    9710  sdot_array
98  0.000007  9.951844e-07  0.000007  0.000010      10      50  0.000074           184     0.000011    9810  sdot_array
99  0.000007  2.961736e-07  0.000007  0.000008      10      50  0.000073           184     0.000014    9910  sdot_array

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name            fct
97  0.000003  1.174517e-07  0.000003  0.000004      10      50  0.000033           184     0.000008    9710  sdot_array_16
98  0.000003  1.211944e-07  0.000003  0.000004      10      50  0.000034           184     0.000009    9810  sdot_array_16
99  0.000003  2.285007e-07  0.000003  0.000004      10      50  0.000034           184     0.000009    9910  sdot_array_16

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     average     deviation  min_exec  max_exec  repeat  number     ttime  context_size  warmup_time  x_name                fct
97  0.000002  6.594129e-07  0.000002  0.000004      10      50  0.000023           184     0.000008    9710  sdot_array_16_sse
98  0.000002  1.493392e-08  0.000002  0.000002      10      50  0.000021           184     0.000009    9810  sdot_array_16_sse
99  0.000002  1.304799e-07  0.000002  0.000003      10      50  0.000021           184     0.000007    9910  sdot_array_16_sse

Text(0.5, 1.0, 'Comparison of cython sdot implementations')

Total running time of the script: (0 minutes 3.620 seconds)

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