diff options
Diffstat (limited to 'doc/source/reference/random')
| -rw-r--r-- | doc/source/reference/random/bit_generators/index.rst | 25 | ||||
| -rw-r--r-- | doc/source/reference/random/index.rst | 22 | ||||
| -rw-r--r-- | doc/source/reference/random/performance.rst | 114 |
3 files changed, 80 insertions, 81 deletions
diff --git a/doc/source/reference/random/bit_generators/index.rst b/doc/source/reference/random/bit_generators/index.rst index 7f88231bd..0b3d563ec 100644 --- a/doc/source/reference/random/bit_generators/index.rst +++ b/doc/source/reference/random/bit_generators/index.rst @@ -12,6 +12,27 @@ setting the state, jumping or advancing the state, and for accessing low-level wrappers for consumption by code that can efficiently access the functions provided, e.g., `numba <https://numba.pydata.org>`_. +Supported BitGenerators +======================= + +The included BitGenerators are: + +* MT19937 - The standard Python BitGenerator. Adds a `~mt19937.MT19937.jumped` + function that returns a new generator with state as-if ``2**128`` draws have + been made. +* PCG-64 - Fast generator that support many parallel streams and + can be advanced by an arbitrary amount. See the documentation for + :meth:`~.PCG64.advance`. PCG-64 has a period of + :math:`2^{128}`. See the `PCG author's page`_ for more details about + this class of PRNG. +* Philox - a counter-based generator capable of being advanced an + arbitrary number of steps or generating independent streams. See the + `Random123`_ page for more details about this class of bit generators. + +.. _`PCG author's page`: http://www.pcg-random.org/ +.. _`Random123`: https://www.deshawresearch.com/resources_random123.html + + .. toctree:: :maxdepth: 1 @@ -32,8 +53,8 @@ generate BitGenerators that are correlated or overlap within a few samples. NumPy uses a `SeedSequence` class to mix the seed in a reproducible way that introduces the necessary entropy to produce independent and largely non- -overlapping streams. Small seeds may still be unable to reach all possible -initialization states, which can cause biases among an ensemble of small-seed +overlapping streams. Small seeds are unable to fill the complete range of +initializaiton states, and lead to biases among an ensemble of small-seed runs. For many cases, that doesn't matter. If you just want to hold things in place while you debug something, biases aren't a concern. For actual simulations whose results you care about, let ``SeedSequence(None)`` do its diff --git a/doc/source/reference/random/index.rst b/doc/source/reference/random/index.rst index 109302b7a..f32853e7c 100644 --- a/doc/source/reference/random/index.rst +++ b/doc/source/reference/random/index.rst @@ -159,28 +159,6 @@ one of two ways: * :ref:`independent-streams` * :ref:`jump-and-advance` -Supported BitGenerators ------------------------ -The included BitGenerators are: - -* MT19937 - The standard Python BitGenerator. Adds a `~mt19937.MT19937.jumped` - function that returns a new generator with state as-if ``2**128`` draws have - been made. -* PCG-64 - Fast generator that support many parallel streams and - can be advanced by an arbitrary amount. See the documentation for - :meth:`~.PCG64.advance`. PCG-64 has a period of - :math:`2^{128}`. See the `PCG author's page`_ for more details about - this class of PRNG. -* Xorshiro256** and Xorshiro512** - The most recently introduced XOR, - shift, and rotate generator. Supports ``jumped`` and so can be used in - parallel applications. See the documentation for -* ThreeFry and Philox - counter-based generators capable of being advanced an - arbitrary number of steps or generating independent streams. See the - `Random123`_ page for more details about this class of bit generators. - -.. _`PCG author's page`: http://www.pcg-random.org/ -.. _`Random123`: https://www.deshawresearch.com/resources_random123.html - Concepts -------- .. toctree:: diff --git a/doc/source/reference/random/performance.rst b/doc/source/reference/random/performance.rst index c1b501f8f..3e5c20e3a 100644 --- a/doc/source/reference/random/performance.rst +++ b/doc/source/reference/random/performance.rst @@ -29,18 +29,18 @@ The column labeled MT19973 is used the same 32-bit generator as :class:`~generator.Generator`. .. csv-table:: - :header: ,Xoshiro256**,Xoshiro512**,DSFMT,PCG64,MT19937,Philox,RandomState,ThreeFry - :widths: 14,14,14,14,14,14,14,14,14 + :header: ,PCG64,MT19937,Philox,RandomState + :widths: 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 + 32-bit Unsigned Ints,3.2,3.3,4.8,3.2 + 64-bit Unsigned Ints,4.8,5.7,6.9,5.7 + Uniforms,5.0,7.3,8.0,7.3 + Normals,11.3,13.0,13.7,34.4 + Exponentials,6.7,7.9,8.6,40.3 + Gammas,30.6,34.2,35.1,58.1 + Binomials,25.7,27.7,28.4,25.9 + Laplaces,41.1,44.5,45.4,46.9 + Poissons,58.1,68.4,70.2,86.0 The next table presents the performance in percentage relative to values @@ -48,19 +48,19 @@ 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 + :header: ,PCG64,MT19937,Philox + :widths: 14,14,14,14 + + 32-bit Unsigned Ints,100,99,67 + 64-bit Unsigned Ints,118,100,83 + Uniforms,147,100,91 + Normals,304,264,252 + Exponentials,601,512,467 + Gammas,190,170,166 + Binomials,101,93,91 + Laplaces,114,105,103 + Poissons,148,126,123 + Overall,167,145,131 .. note:: @@ -81,16 +81,16 @@ 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 -=================== ======= ========= ======= ======== ========== ============ +=================== ========= ======= ======== +Distribution MT19937 PCG64 Philox +=================== ========= ======= ======== +32-bit Unsigned Int 100 113.9 72.1 +64-bit Unsigned Int 100 143.3 89.7 +Uniform 100 181.5 90.8 +Exponential 100 145.5 92.5 +Normal 100 121.4 98.3 +**Overall** 100 139.3 88.2 +=================== ========= ======= ======== 64-bit Windows @@ -98,16 +98,16 @@ Normal 113.2 100 121.4 98.3 71.9 1 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 -=================== ======= ========= ======= ======== ========== ============ +=================== ========= ======= ======== +Distribution MT19937 PCG64 Philox +=================== ========= ======= ======== +32-bit Unsigned Int 100 134.9 44.1 +64-bit Unsigned Int 100 162.7 41.0 +Uniform 100 200.0 44.8 +Exponential 100 167.8 47.4 +Normal 100 135.6 60.3 +**Overall** 100 158.4 47.1 +=================== ========= ======= ======== 32-bit Windows ~~~~~~~~~~~~~~ @@ -116,20 +116,20 @@ The performance of 64-bit generators on 32-bit Windows is much lower than on 64- operating systems due to register width. MT19937, the generator that has been in NumPy since 2005, operates on 32-bit integers. -=================== ======= ========= ======= ======== ========== ============ -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 -=================== ======= ========= ======= ======== ========== ============ +=================== ========= ======= ======== +Distribution MT19937 PCG64 Philox +=================== ========= ======= ======== +32-bit Unsigned Int 100 30.6 28.1 +64-bit Unsigned Int 100 24.2 23.7 +Uniform 100 26.7 28.4 +Exponential 100 32.1 32.6 +Normal 100 36.3 37.5 +**Overall** 100 29.7 29.7 +=================== ========= ======= ======== .. 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. + 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. |