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PCG64DXSM(seed=None)
BitGenerator for the PCG-64 DXSM 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.
Notes
-----
PCG-64 DXSM is a 128-bit implementation of O'Neill's permutation congruential
generator ([1]_, [2]_). PCG-64 DXSM has a period of :math:`2^{128}` and supports
advancing an arbitrary number of steps as well as :math:`2^{127}` streams.
The specific member of the PCG family that we use is PCG CM DXSM 128/64. It
differs from ``PCG64`` in that it uses the stronger DXSM output function,
a 64-bit "cheap multiplier" in the LCG, and outputs from the state before
advancing it rather than advance-then-output.
``PCG64DXSM`` 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.
Supports the method :meth:`advance` to advance the RNG an arbitrary number of
steps. The state of the PCG-64 DXSM RNG is represented by 2 128-bit unsigned
integers.
**State and Seeding**
The ``PCG64DXSM`` state vector consists of 2 unsigned 128-bit values,
which are represented externally as Python ints. One is the state of the
PRNG, which is advanced by a linear congruential generator (LCG). The
second is a fixed odd increment used in the LCG.
The input seed is processed by `SeedSequence` to generate both values. The
increment is not independently settable.
**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, PCG64DXSM, SeedSequence
>>> sg = SeedSequence(1234)
>>> rg = [Generator(PCG64DXSM(s)) for s in sg.spawn(10)]
**Compatibility Guarantee**
``PCG64DXSM`` makes a guarantee that a fixed seed will always produce
the same random integer stream.
References
----------
.. [1] `"PCG, A Family of Better Random Number Generators"
`_
.. [2] O'Neill, Melissa E. `"PCG: A Family of Simple Fast Space-Efficient
Statistically Good Algorithms for Random Number Generation"
`_
Get or set the PRNG state
Returns
-------
state : dict
Dictionary containing the information required to describe the
state of the PRNG
PCG64(seed=None)
BitGenerator for the PCG-64 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.
Notes
-----
PCG-64 is a 128-bit implementation of O'Neill's permutation congruential
generator ([1]_, [2]_). PCG-64 has a period of :math:`2^{128}` and supports
advancing an arbitrary number of steps as well as :math:`2^{127}` streams.
The specific member of the PCG family that we use is PCG XSL RR 128/64
as described in the paper ([2]_).
``PCG64`` 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.
Supports the method :meth:`advance` to advance the RNG an arbitrary number of
steps. The state of the PCG-64 RNG is represented by 2 128-bit unsigned
integers.
**State and Seeding**
The ``PCG64`` state vector consists of 2 unsigned 128-bit values,
which are represented externally as Python ints. One is the state of the
PRNG, which is advanced by a linear congruential generator (LCG). The
second is a fixed odd increment used in the LCG.
The input seed is processed by `SeedSequence` to generate both values. The
increment is not independently settable.
**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, PCG64, SeedSequence
>>> sg = SeedSequence(1234)
>>> rg = [Generator(PCG64(s)) for s in sg.spawn(10)]
**Compatibility Guarantee**
``PCG64`` makes a guarantee that a fixed seed will always produce
the same random integer stream.
References
----------
.. [1] `"PCG, A Family of Better Random Number Generators"
`_
.. [2] O'Neill, Melissa E. `"PCG: A Family of Simple Fast Space-Efficient
Statistically Good Algorithms for Random Number Generation"
`_
__pyx_capi__ name __loader__ loader __file__ origin __package__ parent __path__ submodule_search_locations an integer is required __reduce_cython__ name '%U' is not defined %s (%s:%d) builtins cython_runtime __builtins__ %d.%d 0x10000000000000000 numpy.core._multiarray_umath _ARRAY_API _ARRAY_API not found _ARRAY_API is NULL pointer numpy.random.bit_generator BitGenerator numpy dtype flatiter broadcast ndarray generic number unsignedinteger inexact complexfloating flexible character ufunc SeedSequence SeedlessSequence numpy.random._common double LEGACY_POISSON_LAM_MAX uint64_t MAXSIZE wrap_int _pcg64.pyx init numpy.random._pcg64 at least at most jumped Missing type object __setstate_cython__ exactly advance __init__ __del__ numpy.random._pcg64.PCG64DXSM state numpy.random._pcg64.PCG64
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 : PCG64
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.
Jumps the state as-if jumps * 210306068529402873165736369884012333109
random numbers have been generated.
Parameters
----------
jumps : integer, positive
Number of times to jump the state of the bit generator returned
Returns
-------
bit_generator : PCG64DXSM
New instance of generator jumped iter times
Notes
-----
The step size is phi-1 when multiplied by 2**128 where phi is the
golden ratio.
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 : PCG64
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.
Jumps the state as-if jumps * 210306068529402873165736369884012333109
random numbers have been generated.
Parameters
----------
jumps : integer, positive
Number of times to jump the state of the bit generator returned
Returns
-------
bit_generator : PCG64
New instance of generator jumped iter times
Notes
-----
The step size is phi-1 when multiplied by 2**128 where phi is the
golden ratio.
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