@@ -49,9 +49,9 @@ RandomState(seed=None)
4949Container for the xorshift128+ pseudo random number generator.
5050
5151xorshift128+ is a 64-bit implementation of Saito and Matsumoto's XSadd
52- generator [1]_. xorshift128+ has a period of 2**128 - 1 and supports jumping
53- the sequence in increments of 2**64, which allow multiple non-overlapping
54- sequences to be generated.
52+ generator [1]_,[2]_,[3]_,[4]_ . xorshift128+ has a period of 2**128 - 1 and
53+ supports jumping the sequence in increments of 2**64, which allow multiple
54+ non-overlapping sequences to be generated.
5555
5656``xorshift128.RandomState`` exposes a number of methods for generating random
5757numbers drawn from a variety of probability distributions. In addition to the
@@ -84,11 +84,13 @@ Notes
8484See xorshift1024 for an implementation with a larger period
8585(2**1024 - 1) and jump size.
8686
87- ** Parallel Features **
87+ **Parallel Features**
8888
8989``xorshift128.RandomState`` can be used in parallel applications by
90- invoking the ``xorshift128.RandomState.jump`` which will advance the
91- the state as-if :math:`2^64` random numbers have been generated.
90+ calling the method ``jump`` which advances the
91+ the state as-if :math:`2^{64}` random numbers have been generated. This
92+ allow the original sequence to be split so that distinct segments can be used
93+ on each worker process.
9294
9395>>> import randomstate.prng.xorshift128 as rnd
9496>>> rs = [rnd.RandomState(1234) for _ in range(10)]
@@ -100,4 +102,10 @@ References
100102----------
101103.. [1] "xorshift*/xorshift+ generators and the PRNG shootout",
102104 http://xorshift.di.unimi.it/
105+ .. [2] Marsaglia, George. "Xorshift RNGs." Journal of Statistical Software
106+ [Online], 8.14, pp. 1 - 6, .2003.
107+ .. [3] Sebastiano Vigna. "An experimental exploration of Marsaglia's xorshift
108+ generators, scrambled." CoRR, abs/1402.6246, 2014.
109+ .. [4] Sebastiano Vigna. "Further scramblings of Marsaglia's xorshift
110+ generators." CoRR, abs/1403.0930, 2014.
103111"""
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