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Philox(seed=None, counter=None, key=None)
Container for the Philox (4x64) pseudo-random number generator.
Parameters
----------
seed : {None, int, array_like[ints], SeedSequence}, optional
A seed to initialize the `BitGenerator`. If None, then fresh,
unpredictable entropy will be pulled from the OS. If an ``int`` or
``array_like[ints]`` is passed, then it will be passed to
`SeedSequence` to derive the initial `BitGenerator` state. One may also
pass in a `SeedSequence` instance.
counter : {None, int, array_like}, optional
Counter to use in the Philox state. Can be either
a Python int (long in 2.x) in [0, 2**256) or a 4-element uint64 array.
If not provided, the RNG is initialized at 0.
key : {None, int, array_like}, optional
Key to use in the Philox state. Unlike ``seed``, the value in key is
directly set. Can be either a Python int in [0, 2**128) or a 2-element
uint64 array. `key` and ``seed`` cannot both be used.
Attributes
----------
lock: threading.Lock
Lock instance that is shared so that the same bit git generator can
be used in multiple Generators without corrupting the state. Code that
generates values from a bit generator should hold the bit generator's
lock.
Notes
-----
Philox is a 64-bit PRNG that uses a counter-based design based on weaker
(and faster) versions of cryptographic functions [1]_. Instances using
different values of the key produce independent sequences. Philox has a
period of :math:`2^{256} - 1` and supports arbitrary advancing and jumping
the sequence in increments of :math:`2^{128}`. These features allow
multiple non-overlapping sequences to be generated.
``Philox`` provides a capsule containing function pointers that produce
doubles, and unsigned 32 and 64- bit integers. These are not
directly consumable in Python and must be consumed by a ``Generator``
or similar object that supports low-level access.
**State and Seeding**
The ``Philox`` state vector consists of a 256-bit value encoded as
a 4-element uint64 array and a 128-bit value encoded as a 2-element uint64
array. The former is a counter which is incremented by 1 for every 4 64-bit
randoms produced. The second is a key which determined the sequence
produced. Using different keys produces independent sequences.
The input ``seed`` is processed by `SeedSequence` to generate the key. The
counter is set to 0.
Alternately, one can omit the ``seed`` parameter and set the ``key`` and
``counter`` directly.
**Parallel Features**
The preferred way to use a BitGenerator in parallel applications is to use
the `SeedSequence.spawn` method to obtain entropy values, and to use these
to generate new BitGenerators:
>>> from numpy.random import Generator, Philox, SeedSequence
>>> sg = SeedSequence(1234)
>>> rg = [Generator(Philox(s)) for s in sg.spawn(10)]
``Philox`` can be used in parallel applications by calling the ``jumped``
method to advances the state as-if :math:`2^{128}` random numbers have
been generated. Alternatively, ``advance`` can be used to advance the
counter for any positive step in [0, 2**256). When using ``jumped``, all
generators should be chained to ensure that the segments come from the same
sequence.
>>> from numpy.random import Generator, Philox
>>> bit_generator = Philox(1234)
>>> rg = []
>>> for _ in range(10):
... rg.append(Generator(bit_generator))
... bit_generator = bit_generator.jumped()
Alternatively, ``Philox`` can be used in parallel applications by using
a sequence of distinct keys where each instance uses different key.
>>> key = 2**96 + 2**33 + 2**17 + 2**9
>>> rg = [Generator(Philox(key=key+i)) for i in range(10)]
**Compatibility Guarantee**
``Philox`` makes a guarantee that a fixed ``seed`` will always produce
the same random integer stream.
Examples
--------
>>> from numpy.random import Generator, Philox
>>> rg = Generator(Philox(1234))
>>> rg.standard_normal()
0.123 # random
References
----------
.. [1] John K. Salmon, Mark A. Moraes, Ron O. Dror, and David E. Shaw,
"Parallel Random Numbers: As Easy as 1, 2, 3," Proceedings of
the International Conference for High Performance Computing,
Networking, Storage and Analysis (SC11), New York, NY: ACM, 2011.
Get or set the PRNG state
Returns
-------
state : dict
Dictionary containing the information required to describe the
state of the PRNG
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advance(delta)
Advance the underlying RNG as-if delta draws have occurred.
Parameters
----------
delta : integer, positive
Number of draws to advance the RNG. Must be less than the
size state variable in the underlying RNG.
Returns
-------
self : Philox
RNG advanced delta steps
Notes
-----
Advancing a RNG updates the underlying RNG state as-if a given
number of calls to the underlying RNG have been made. In general
there is not a one-to-one relationship between the number output
random values from a particular distribution and the number of
draws from the core RNG. This occurs for two reasons:
* The random values are simulated using a rejection-based method
and so, on average, more than one value from the underlying
RNG is required to generate an single draw.
* The number of bits required to generate a simulated value
differs from the number of bits generated by the underlying
RNG. For example, two 16-bit integer values can be simulated
from a single draw of a 32-bit RNG.
Advancing the RNG state resets any pre-computed random numbers.
This is required to ensure exact reproducibility.
jumped(jumps=1)
Returns a new bit generator with the state jumped
The state of the returned bit generator is jumped as-if
(2**128) * jumps random numbers have been generated.
Parameters
----------
jumps : integer, positive
Number of times to jump the state of the bit generator returned
Returns
-------
bit_generator : Philox
New instance of generator jumped iter times
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