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Performance
-----------
.. py:module:: numpy.random
.. currentmodule:: numpy.random
Recommendation
**************
The recommended generator for single use is :class:`~.xoshiro256.Xoshiro256`.
The recommended generator for use in large-scale parallel applications is
:class:`~.xoshiro512.Xoshiro512` where the `jumped` method is used to advance
the state. For very large scale applications -- requiring 1,000+ independent
streams -- is the best choice. For very large scale applications -- requiring
1,000+ independent streams, :class:`~pcg64.PCG64` or :class:`~.philox.Philox`
are the best choices.
Timings
*******
The timings below are the time in ns to produce 1 random value from a
specific distribution. The original :class:`~mt19937.MT19937` generator is
much slower since it requires 2 32-bit values to equal the output of the
faster generators.
Integer performance has a similar ordering although `dSFMT` is slower since
it generates 53-bit floating point values rather than integer values.
The pattern is similar for other, more complex generators. The normal
performance of the legacy :class:`~mtrand.RandomState` generator is much
lower than the other since it uses the Box-Muller transformation rather
than the Ziggurat generator. The performance gap for Exponentials is also
large due to the cost of computing the log function to invert the CDF.
The column labeled MT19973 is used the same 32-bit generator as
:class:`~mtrand.RandomState` but produces random values using
:class:`~generator.Generator`.
.. csv-table::
:header: ,Xoshiro256**,Xoshiro512**,DSFMT,PCG64,MT19937,Philox,RandomState,ThreeFry
:widths: 14,14,14,14,14,14,14,14,14
32-bit Unsigned Ints,2.6,2.9,3.5,3.2,3.3,4.8,3.2,7.6
64-bit Unsigned Ints,3.3,4.3,5.7,4.8,5.7,6.9,5.7,12.8
Uniforms,3.4,4.0,3.2,5.0,7.3,8.0,7.3,12.8
Normals,7.9,9.0,11.8,11.3,13.0,13.7,34.4,18.1
Exponentials,4.7,5.2,7.4,6.7,7.9,8.6,40.3,14.7
Gammas,29.1,27.5,28.5,30.6,34.2,35.1,58.1,47.6
Binomials,22.7,23.1,21.1,25.7,27.7,28.4,25.9,32.1
Laplaces,38.5,38.1,36.9,41.1,44.5,45.4,46.9,50.2
Poissons,46.9,50.9,46.4,58.1,68.4,70.2,86.0,88.2
The next table presents the performance in percentage relative to values
generated by the legagy generator, `RandomState(MT19937())`. The overall
performance was computed using a geometric mean.
.. csv-table::
:header: ,Xoshiro256**,Xoshiro256**,DSFMT,PCG64,MT19937,Philox,ThreeFry
:widths: 14,14,14,14,14,14,14,14
32-bit Unsigned Ints,124,113,93,100,99,67,43
64-bit Unsigned Ints,174,133,100,118,100,83,44
Uniforms,212,181,229,147,100,91,57
Normals,438,382,291,304,264,252,190
Exponentials,851,770,547,601,512,467,275
Gammas,200,212,204,190,170,166,122
Binomials,114,112,123,101,93,91,81
Laplaces,122,123,127,114,105,103,93
Poissons,183,169,185,148,126,123,98
Overall,212,194,180,167,145,131,93
.. note::
All timings were taken using Linux on a i5-3570 processor.
Performance on different Operating Systems
******************************************
Performance differs across platforms due to compiler and hardware availability
(e.g., register width) differences. The default bit generator has been chosen
to perform well on 64-bit platforms. Performance on 32-bit operating systems
is very different.
The values reported are normalized relative to the speed of MT19937 in
each table. A value of 100 indicates that the performance matches the MT19937.
Higher values indicate improved performance. These values cannot be compared
across tables.
64-bit Linux
~~~~~~~~~~~~
=================== ======= ========= ======= ======== ========== ============
Distribution DSFMT MT19937 PCG64 Philox ThreeFry Xoshiro256
=================== ======= ========= ======= ======== ========== ============
32-bit Unsigned Int 99.3 100 113.9 72.1 48.3 117.1
64-bit Unsigned Int 105.7 100 143.3 89.7 48.1 161.7
Uniform 222.1 100 181.5 90.8 59.9 204.7
Exponential 110.8 100 145.5 92.5 55.0 177.1
Normal 113.2 100 121.4 98.3 71.9 162.0
**Overall** 123.9 100 139.3 88.2 56.0 161.9
=================== ======= ========= ======= ======== ========== ============
64-bit Windows
~~~~~~~~~~~~~~
The performance on 64-bit Linux and 64-bit Windows is broadly similar.
=================== ======= ========= ======= ======== ========== ============
Distribution DSFMT MT19937 PCG64 Philox ThreeFry Xoshiro256
=================== ======= ========= ======= ======== ========== ============
32-bit Unsigned Int 122.8 100 134.9 44.1 72.3 133.1
64-bit Unsigned Int 130.4 100 162.7 41.0 77.7 142.3
Uniform 273.2 100 200.0 44.8 84.6 175.8
Exponential 135.0 100 167.8 47.4 84.5 166.9
Normal 115.3 100 135.6 60.3 93.6 169.6
**Overall** 146.7 100 158.4 47.1 82.2 156.5
=================== ======= ========= ======= ======== ========== ============
32-bit Windows
~~~~~~~~~~~~~~
The performance of 64-bit generators on 32-bit Windows is much lower than on 64-bit
operating systems due to register width. DSFMT uses SSE2 when available, and so is less
affected by the size of the operating system's register. MT19937, the generator that has been
in NumPy since 2005, operates on 32-bit integers and so is close to DSFMT.
=================== ======= ========= ======= ======== ========== ============
Distribution DSFMT MT19937 PCG64 Philox ThreeFry Xoshiro256
=================== ======= ========= ======= ======== ========== ============
32-bit Unsigned Int 110.9 100 30.6 28.1 29.2 74.4
64-bit Unsigned Int 104.7 100 24.2 23.7 22.7 72.7
Uniform 247.0 100 26.7 28.4 27.8 78.8
Exponential 110.1 100 32.1 32.6 30.5 89.6
Normal 107.2 100 36.3 37.5 35.2 93.0
**Overall** 127.6 100 29.7 29.7 28.8 81.3
=================== ======= ========= ======= ======== ========== ============
.. note::
Linux timings used Ubuntu 18.04 and GCC 7.4. Windows timings were made on Windows 10
using Microsoft C/C++ Optimizing Compiler Version 19 (Visual Studio 2015). All timings
were produced on a i5-3570 processor.
|
