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| author | Robert Kern <robert.kern@gmail.com> | 2021-05-04 17:08:45 -0400 |
|---|---|---|
| committer | Robert Kern <robert.kern@gmail.com> | 2021-05-04 17:08:45 -0400 |
| commit | 819433652f344526b36cf42b2fadf69e4af8eb45 (patch) | |
| tree | 32b23012264c60039d4e6662e730e25d863c732a /doc/source/reference | |
| parent | 771ce9d1c02f2b4fefcbfc603fd234cceba3d8fe (diff) | |
| download | numpy-819433652f344526b36cf42b2fadf69e4af8eb45.tar.gz | |
DOC: math formatting.
Diffstat (limited to 'doc/source/reference')
| -rw-r--r-- | doc/source/reference/random/upgrading-pcg64.rst | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/doc/source/reference/random/upgrading-pcg64.rst b/doc/source/reference/random/upgrading-pcg64.rst index 105d8efcb..ea7ebcb6b 100644 --- a/doc/source/reference/random/upgrading-pcg64.rst +++ b/doc/source/reference/random/upgrading-pcg64.rst @@ -68,7 +68,7 @@ too much computational cost. One of these known weaknesses is that advancing the state of the LCG by steps numbering a power of two (``bg.advance(2**N)``) will leave the lower ``N`` bits identical to the state that was just left. For a single stream drawn from -sequentially, this is of little consequence. The remaining ``128-N`` bits provide +sequentially, this is of little consequence. The remaining :math:`128-N` bits provide plenty of pseudorandomness that will be mixed in for any practical ``N`` that can be observed in a single stream, which is why one does not need to worry about this if you only use a single stream in your application. Similarly, the @@ -84,7 +84,7 @@ increment, then the pair of streams, when interleaved, will fail `PractRand <http://pracrand.sourceforge.net/>`_ in a reasonable amount of time, after drawing a few gigabytes of data. Following the standard Birthday Paradox calculations for a collision of 58 bits, we can -see that we can create ``2**29``, or about half a billion, streams which is when +see that we can create :math:`2^{29}`, or about half a billion, streams which is when the probability of such a collision becomes high. Half a billion streams is quite high, and the amount of data each stream needs to draw before the statistical correlations become apparent to even the strict ``PractRand`` tests @@ -107,7 +107,7 @@ size inside of `SeedSequence` (and 128-bit collisions are in the One of the known properties of an LCG is that different increments create *distinct* streams, but with a known relationship. Each LCG has an orbit that -traverses all ``2**128`` different 128-bit states. Two LCGs with different +traverses all :math:`2^{128}` different 128-bit states. Two LCGs with different increments are related in that one can "rotate" the orbit of the first LCG (advance it by a number of steps that we can compute from the two increments) such that then both LCGs will always then have the same state, up to an |