diff --git a/doc/release/upcoming_changes/18906.new_function.rst b/doc/release/upcoming_changes/18906.new_function.rst new file mode 100644 index 000000000000..38444009d3cd --- /dev/null +++ b/doc/release/upcoming_changes/18906.new_function.rst @@ -0,0 +1,17 @@ +.. currentmodule:: numpy.random + +Add `PCG64DXSM` `BitGenerator` +------------------------------ + +Uses of the `PCG64` `BitGenerator` in a massively-parallel context have been +shown to have statistical weaknesses that were not apparent at the first +release in numpy 1.17. Most users will never observe this weakness and are +safe to continue to use `PCG64`. We have introduced a new `PCG64DXSM` +`BitGenerator` that will eventually become the new default `BitGenerator` +implementation used by `default_rng` in future releases. `PCG64DXSM` solves +the statistical weakness while preserving the performance and the features of +`PCG64`. + +See :ref:`upgrading-pcg64` for more details. + +.. currentmodule:: numpy diff --git a/doc/source/reference/random/bit_generators/index.rst b/doc/source/reference/random/bit_generators/index.rst index 6f8cf02ca49d..c5c3498068bd 100644 --- a/doc/source/reference/random/bit_generators/index.rst +++ b/doc/source/reference/random/bit_generators/index.rst @@ -15,10 +15,13 @@ Supported BitGenerators The included BitGenerators are: -* PCG-64 - The default. A fast generator that supports 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. +* PCG-64 - The default. A fast generator that 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. +* PCG-64 DXSM - An upgraded version of PCG-64 with better statistical + properties in parallel contexts. See :ref:`upgrading-pcg64` for more + information on these improvements. * MT19937 - The standard Python BitGenerator. Adds a `MT19937.jumped` function that returns a new generator with state as-if :math:`2^{128}` draws have been made. @@ -43,6 +46,7 @@ The included BitGenerators are: MT19937 PCG64 + PCG64DXSM Philox SFC64 diff --git a/doc/source/reference/random/bit_generators/pcg64dxsm.rst b/doc/source/reference/random/bit_generators/pcg64dxsm.rst new file mode 100644 index 000000000000..e37efa5d39da --- /dev/null +++ b/doc/source/reference/random/bit_generators/pcg64dxsm.rst @@ -0,0 +1,32 @@ +Permuted Congruential Generator (64-bit, PCG64 DXSM) +---------------------------------------------------- + +.. currentmodule:: numpy.random + +.. autoclass:: PCG64DXSM + :members: __init__ + :exclude-members: __init__ + +State +===== + +.. autosummary:: + :toctree: generated/ + + ~PCG64DXSM.state + +Parallel generation +=================== +.. autosummary:: + :toctree: generated/ + + ~PCG64DXSM.advance + ~PCG64DXSM.jumped + +Extending +========= +.. autosummary:: + :toctree: generated/ + + ~PCG64DXSM.cffi + ~PCG64DXSM.ctypes diff --git a/doc/source/reference/random/index.rst b/doc/source/reference/random/index.rst index fc7743c64d0c..96cd47017cca 100644 --- a/doc/source/reference/random/index.rst +++ b/doc/source/reference/random/index.rst @@ -222,6 +222,9 @@ one of three ways: * :ref:`independent-streams` * :ref:`parallel-jumped` +Users with a very large amount of parallelism will want to consult +:ref:`upgrading-pcg64`. + Concepts -------- .. toctree:: @@ -230,6 +233,7 @@ Concepts generator Legacy Generator (RandomState) BitGenerators, SeedSequences + Upgrading PCG64 with PCG64DXSM Features -------- diff --git a/doc/source/reference/random/parallel.rst b/doc/source/reference/random/parallel.rst index 72158401447e..7f0207bdebb2 100644 --- a/doc/source/reference/random/parallel.rst +++ b/doc/source/reference/random/parallel.rst @@ -88,10 +88,11 @@ territory ([2]_). estimate the naive upper bound on a napkin and take comfort knowing that the probability is actually lower. -.. [2] In this calculation, we can ignore the amount of numbers drawn from each - stream. Each of the PRNGs we provide has some extra protection built in +.. [2] In this calculation, we can mostly ignore the amount of numbers drawn from each + stream. See :ref:`upgrading-pcg64` for the technical details about + `PCG64`. The other PRNGs we provide have some extra protection built in that avoids overlaps if the `~SeedSequence` pools differ in the - slightest bit. `PCG64` has :math:`2^{127}` separate cycles + slightest bit. `PCG64DXSM` has :math:`2^{127}` separate cycles determined by the seed in addition to the position in the :math:`2^{128}` long period for each cycle, so one has to both get on or near the same cycle *and* seed a nearby position in the cycle. @@ -150,12 +151,14 @@ BitGenerator, the size of the jump and the bits in the default unsigned random are listed below. +-----------------+-------------------------+-------------------------+-------------------------+ -| BitGenerator | Period | Jump Size | Bits | +| BitGenerator | Period | Jump Size | Bits per Draw | +=================+=========================+=========================+=========================+ -| MT19937 | :math:`2^{19937}` | :math:`2^{128}` | 32 | +| MT19937 | :math:`2^{19937}-1` | :math:`2^{128}` | 32 | +-----------------+-------------------------+-------------------------+-------------------------+ | PCG64 | :math:`2^{128}` | :math:`~2^{127}` ([3]_) | 64 | +-----------------+-------------------------+-------------------------+-------------------------+ +| PCG64DXSM | :math:`2^{128}` | :math:`~2^{127}` ([3]_) | 64 | ++-----------------+-------------------------+-------------------------+-------------------------+ | Philox | :math:`2^{256}` | :math:`2^{128}` | 64 | +-----------------+-------------------------+-------------------------+-------------------------+ diff --git a/doc/source/reference/random/performance.py b/doc/source/reference/random/performance.py index 3267197f53fb..794142836652 100644 --- a/doc/source/reference/random/performance.py +++ b/doc/source/reference/random/performance.py @@ -3,9 +3,9 @@ import pandas as pd import numpy as np -from numpy.random import MT19937, PCG64, Philox, SFC64 +from numpy.random import MT19937, PCG64, PCG64DXSM, Philox, SFC64 -PRNGS = [MT19937, PCG64, Philox, SFC64] +PRNGS = [MT19937, PCG64, PCG64DXSM, Philox, SFC64] funcs = {} integers = 'integers(0, 2**{bits},size=1000000, dtype="uint{bits}")' @@ -53,7 +53,7 @@ col[key] = 1000 * min(t) table['RandomState'] = pd.Series(col) -columns = ['MT19937','PCG64','Philox','SFC64', 'RandomState'] +columns = ['MT19937', 'PCG64', 'PCG64DXSM', 'Philox', 'SFC64', 'RandomState'] table = pd.DataFrame(table) order = np.log(table).mean().sort_values().index table = table.T diff --git a/doc/source/reference/random/performance.rst b/doc/source/reference/random/performance.rst index 74dad4cc37d3..812c719f8750 100644 --- a/doc/source/reference/random/performance.rst +++ b/doc/source/reference/random/performance.rst @@ -5,9 +5,12 @@ Performance Recommendation ************** -The recommended generator for general use is `PCG64`. It is -statistically high quality, full-featured, and fast on most platforms, but -somewhat slow when compiled for 32-bit processes. + +The recommended generator for general use is `PCG64` or its upgraded variant +`PCG64DXSM` for heavily-parallel use cases. They are statistically high quality, +full-featured, and fast on most platforms, but somewhat slow when compiled for +32-bit processes. See :ref:`upgrading-pcg64` for details on when heavy +parallelism would indicate using `PCG64DXSM`. `Philox` is fairly slow, but its statistical properties have very high quality, and it is easy to get assuredly-independent stream by using diff --git a/doc/source/reference/random/upgrading-pcg64.rst b/doc/source/reference/random/upgrading-pcg64.rst new file mode 100644 index 000000000000..9e540ace9331 --- /dev/null +++ b/doc/source/reference/random/upgrading-pcg64.rst @@ -0,0 +1,152 @@ +.. _upgrading-pcg64: + +.. currentmodule:: numpy.random + +Upgrading ``PCG64`` with ``PCG64DXSM`` +-------------------------------------- + +Uses of the `PCG64` `BitGenerator` in a massively-parallel context have been +shown to have statistical weaknesses that were not apparent at the first +release in numpy 1.17. Most users will never observe this weakness and are +safe to continue to use `PCG64`. We have introduced a new `PCG64DXSM` +`BitGenerator` that will eventually become the new default `BitGenerator` +implementation used by `default_rng` in future releases. `PCG64DXSM` solves +the statistical weakness while preserving the performance and the features of +`PCG64`. + +Does this affect me? +==================== + +If you + + 1. only use a single `Generator` instance, + 2. only use `RandomState` or the functions in `numpy.random`, + 3. only use the `PCG64.jumped` method to generate parallel streams, + 4. explicitly use a `BitGenerator` other than `PCG64`, + +then this weakness does not affect you at all. Carry on. + +If you use moderate numbers of parallel streams created with `default_rng` or +`SeedSequence.spawn`, in the 1000s, then the chance of observing this weakness +is negligibly small. You can continue to use `PCG64` comfortably. + +If you use very large numbers of parallel streams, in the millions, and draw +large amounts of numbers from each, then the chance of observing this weakness +can become non-negligible, if still small. An example of such a use case would +be a very large distributed reinforcement learning problem with millions of +long Monte Carlo playouts each generating billions of random number draws. Such +use cases should consider using `PCG64DXSM` explicitly or another +modern `BitGenerator` like `SFC64` or `Philox`, but it is unlikely that any +old results you may have calculated are invalid. In any case, the weakness is +a kind of `Birthday Paradox `_ +collision. That is, a single pair of parallel streams out of the millions, +considered together, might fail a stringent set of statistical tests of +randomness. The remaining millions of streams would all be perfectly fine, and +the effect of the bad pair in the whole calculation is very likely to be +swamped by the remaining streams in most applications. + +.. _upgrading-pcg64-details: + +Technical Details +================= + +Like many PRNG algorithms, `PCG64` is constructed from a transition function, +which advances a 128-bit state, and an output function, that mixes the 128-bit +state into a 64-bit integer to be output. One of the guiding design principles +of the PCG family of PRNGs is to balance the computational cost (and +pseudorandomness strength) between the transition function and the output +function. The transition function is a 128-bit linear congruential generator +(LCG), which consists of multiplying the 128-bit state with a fixed +multiplication constant and then adding a user-chosen increment, in 128-bit +modular arithmetic. LCGs are well-analyzed PRNGs with known weaknesses, though +128-bit LCGs are large enough to pass stringent statistical tests on their own, +with only the trivial output function. The output function of `PCG64` is +intended to patch up some of those known weaknesses by doing "just enough" +scrambling of the bits to assist in the statistical properties without adding +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 :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 +`PCG64.jumped` method uses a carefully chosen number of steps to avoid creating +these collisions. However, once you start creating "randomly-initialized" +parallel streams, either using OS entropy by calling `default_rng` repeatedly +or using `SeedSequence.spawn`, then we need to consider how many lower bits +need to "collide" in order to create a bad pair of streams, and then evaluate +the probability of creating such a collision. +`Empirically `_, it has been +determined that if one shares the lower 58 bits of state and shares an +increment, then the pair of streams, when interleaved, will fail +`PractRand `_ 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 :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 +is in the gigabytes. But this is on the horizon for very large applications +like distributed reinforcement learning. There are reasons to expect that even +in these applications a collision probably will not have a practical effect in +the total result, since the statistical problem is constrained to just the +colliding pair. + +Now, let us consider the case when the increment is not constrained to be the +same. Our implementation of `PCG64` seeds both the state and the increment; +that is, two calls to `default_rng` (almost certainly) have different states +and increments. Upon our first release, we believed that having the seeded +increment would provide a certain amount of extra protection, that one would +have to be "close" in both the state space and increment space in order to +observe correlations (``PractRand`` failures) in a pair of streams. If that were +true, then the "bottleneck" for collisions would be the 128-bit entropy pool +size inside of `SeedSequence` (and 128-bit collisions are in the +"preposterously unlikely" category). Unfortunately, this is not true. + +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 :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 +additive constant and maybe an inversion of the bits. If you then iterate both +streams in lockstep, then the states will *always* remain related by that same +additive constant (and the inversion, if present). Recall that `PCG64` is +constructed from both a transition function (the LCG) and an output function. +It was expected that the scrambling effect of the output function would have +been strong enough to make the distinct streams practically independent (i.e. +"passing the ``PractRand`` tests") unless the two increments were +pathologically related to each other (e.g. 1 and 3). The output function XSL-RR +of the then-standard PCG algorithm that we implemented in `PCG64` turns out to +be too weak to cover up for the 58-bit collision of the underlying LCG that we +described above. For any given pair of increments, the size of the "colliding" +space of states is the same, so for this weakness, the extra distinctness +provided by the increments does not translate into extra protection from +statistical correlations that ``PractRand`` can detect. + +Fortunately, strengthening the output function is able to correct this weakness +and *does* turn the extra distinctness provided by differing increments into +additional protection from these low-bit collisions. To the `PCG author's +credit `_, +she had developed a stronger output function in response to related discussions +during the long birth of the new `BitGenerator` system. We NumPy developers +chose to be "conservative" and use the XSL-RR variant that had undergone +a longer period of testing at that time. The DXSM output function adopts +a "xorshift-multiply" construction used in strong integer hashes that has much +better avalanche properties than the XSL-RR output function. While there are +"pathological" pairs of increments that induce "bad" additive constants that +relate the two streams, the vast majority of pairs induce "good" additive +constants that make the merely-distinct streams of LCG states into +practically-independent output streams. Indeed, now the claim we once made +about `PCG64` is actually true of `PCG64DXSM`: collisions are possible, but +both streams have to simultaneously be both "close" in the 128 bit state space +*and* "close" in the 127-bit increment space, so that would be less likely than +the negligible chance of colliding in the 128-bit internal `SeedSequence` pool. +The DXSM output function is more computationally intensive than XSL-RR, but +some optimizations in the LCG more than make up for the performance hit on most +machines, so `PCG64DXSM` is a good, safe upgrade. There are, of course, an +infinite number of stronger output functions that one could consider, but most +will have a greater computational cost, and the DXSM output function has now +received many CPU cycles of testing via ``PractRand`` at this time. diff --git a/numpy/random/__init__.py b/numpy/random/__init__.py index 7efa5c07fcfe..2e8f99fe3045 100644 --- a/numpy/random/__init__.py +++ b/numpy/random/__init__.py @@ -17,6 +17,7 @@ --------------------------------------------- --- MT19937 PCG64 +PCG64DXSM Philox SFC64 ============================================= === @@ -183,13 +184,14 @@ from ._generator import Generator, default_rng from .bit_generator import SeedSequence, BitGenerator from ._mt19937 import MT19937 -from ._pcg64 import PCG64 +from ._pcg64 import PCG64, PCG64DXSM from ._philox import Philox from ._sfc64 import SFC64 from .mtrand import * __all__ += ['Generator', 'RandomState', 'SeedSequence', 'MT19937', - 'Philox', 'PCG64', 'SFC64', 'default_rng', 'BitGenerator'] + 'Philox', 'PCG64', 'PCG64DXSM', 'SFC64', 'default_rng', + 'BitGenerator'] def __RandomState_ctor(): diff --git a/numpy/random/__init__.pyi b/numpy/random/__init__.pyi index 1187b7d8ecb0..48b620c48b92 100644 --- a/numpy/random/__init__.pyi +++ b/numpy/random/__init__.pyi @@ -3,7 +3,10 @@ from typing import List from numpy.random._generator import Generator as Generator from numpy.random._generator import default_rng as default_rng from numpy.random._mt19937 import MT19937 as MT19937 -from numpy.random._pcg64 import PCG64 as PCG64 +from numpy.random._pcg64 import ( + PCG64 as PCG64, + PCG64DXSM as PCG64DXSM, +) from numpy.random._philox import Philox as Philox from numpy.random._sfc64 import SFC64 as SFC64 from numpy.random.bit_generator import BitGenerator as BitGenerator diff --git a/numpy/random/_pcg64.pyi b/numpy/random/_pcg64.pyi index a4f6e0760bc6..25e2fdde602d 100644 --- a/numpy/random/_pcg64.pyi +++ b/numpy/random/_pcg64.pyi @@ -32,3 +32,17 @@ class PCG64(BitGenerator): value: _PCG64State, ) -> None: ... def advance(self, delta: int) -> PCG64: ... + +class PCG64DXSM(BitGenerator): + def __init__(self, seed: Union[None, _ArrayLikeInt_co, SeedSequence] = ...) -> None: ... + def jumped(self, jumps: int = ...) -> PCG64DXSM: ... + @property + def state( + self, + ) -> _PCG64State: ... + @state.setter + def state( + self, + value: _PCG64State, + ) -> None: ... + def advance(self, delta: int) -> PCG64DXSM: ... diff --git a/numpy/random/_pcg64.pyx b/numpy/random/_pcg64.pyx index 605aae4bcb21..8a00dc265f23 100644 --- a/numpy/random/_pcg64.pyx +++ b/numpy/random/_pcg64.pyx @@ -26,6 +26,10 @@ cdef extern from "src/pcg64/pcg64.h": void pcg64_get_state(pcg64_state *state, uint64_t *state_arr, int *has_uint32, uint32_t *uinteger) void pcg64_set_state(pcg64_state *state, uint64_t *state_arr, int has_uint32, uint32_t uinteger) + uint64_t pcg64_cm_next64(pcg64_state *state) nogil + uint32_t pcg64_cm_next32(pcg64_state *state) nogil + void pcg64_cm_advance(pcg64_state *state, uint64_t *step) + cdef uint64_t pcg64_uint64(void* st) nogil: return pcg64_next64(st) @@ -35,6 +39,14 @@ cdef uint32_t pcg64_uint32(void *st) nogil: cdef double pcg64_double(void* st) nogil: return uint64_to_double(pcg64_next64(st)) +cdef uint64_t pcg64_cm_uint64(void* st) nogil: + return pcg64_cm_next64(st) + +cdef uint32_t pcg64_cm_uint32(void *st) nogil: + return pcg64_cm_next32( st) + +cdef double pcg64_cm_double(void* st) nogil: + return uint64_to_double(pcg64_cm_next64(st)) cdef class PCG64(BitGenerator): """ @@ -268,3 +280,239 @@ cdef class PCG64(BitGenerator): pcg64_advance(&self.rng_state, np.PyArray_DATA(d)) self._reset_state_variables() return self + + +cdef class PCG64DXSM(BitGenerator): + """ + 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 and 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" + `_ + """ + cdef pcg64_state rng_state + cdef pcg64_random_t pcg64_random_state + + def __init__(self, seed=None): + BitGenerator.__init__(self, seed) + self.rng_state.pcg_state = &self.pcg64_random_state + + self._bitgen.state = &self.rng_state + self._bitgen.next_uint64 = &pcg64_cm_uint64 + self._bitgen.next_uint32 = &pcg64_cm_uint32 + self._bitgen.next_double = &pcg64_cm_double + self._bitgen.next_raw = &pcg64_cm_uint64 + # Seed the _bitgen + val = self._seed_seq.generate_state(4, np.uint64) + pcg64_set_seed(&self.rng_state, + np.PyArray_DATA(val), + (np.PyArray_DATA(val) + 2)) + self._reset_state_variables() + + cdef _reset_state_variables(self): + self.rng_state.has_uint32 = 0 + self.rng_state.uinteger = 0 + + cdef jump_inplace(self, jumps): + """ + Jump state in-place + Not part of public API + + Parameters + ---------- + jumps : integer, positive + Number of times to jump the state of the rng. + + Notes + ----- + The step size is phi-1 when multiplied by 2**128 where phi is the + golden ratio. + """ + step = 0x9e3779b97f4a7c15f39cc0605cedc835 + self.advance(step * int(jumps)) + + def jumped(self, jumps=1): + """ + 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. + """ + cdef PCG64DXSM bit_generator + + bit_generator = self.__class__() + bit_generator.state = self.state + bit_generator.jump_inplace(jumps) + + return bit_generator + + @property + def state(self): + """ + Get or set the PRNG state + + Returns + ------- + state : dict + Dictionary containing the information required to describe the + state of the PRNG + """ + cdef np.ndarray state_vec + cdef int has_uint32 + cdef uint32_t uinteger + + # state_vec is state.high, state.low, inc.high, inc.low + state_vec = np.empty(4, dtype=np.uint64) + pcg64_get_state(&self.rng_state, + np.PyArray_DATA(state_vec), + &has_uint32, &uinteger) + state = int(state_vec[0]) * 2**64 + int(state_vec[1]) + inc = int(state_vec[2]) * 2**64 + int(state_vec[3]) + return {'bit_generator': self.__class__.__name__, + 'state': {'state': state, 'inc': inc}, + 'has_uint32': has_uint32, + 'uinteger': uinteger} + + @state.setter + def state(self, value): + cdef np.ndarray state_vec + cdef int has_uint32 + cdef uint32_t uinteger + if not isinstance(value, dict): + raise TypeError('state must be a dict') + bitgen = value.get('bit_generator', '') + if bitgen != self.__class__.__name__: + raise ValueError('state must be for a {0} ' + 'RNG'.format(self.__class__.__name__)) + state_vec = np.empty(4, dtype=np.uint64) + state_vec[0] = value['state']['state'] // 2 ** 64 + state_vec[1] = value['state']['state'] % 2 ** 64 + state_vec[2] = value['state']['inc'] // 2 ** 64 + state_vec[3] = value['state']['inc'] % 2 ** 64 + has_uint32 = value['has_uint32'] + uinteger = value['uinteger'] + pcg64_set_state(&self.rng_state, + np.PyArray_DATA(state_vec), + has_uint32, uinteger) + + def advance(self, delta): + """ + 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. + """ + delta = wrap_int(delta, 128) + + cdef np.ndarray d = np.empty(2, dtype=np.uint64) + d[0] = delta // 2**64 + d[1] = delta % 2**64 + pcg64_cm_advance(&self.rng_state, np.PyArray_DATA(d)) + self._reset_state_variables() + return self + diff --git a/numpy/random/_pickle.py b/numpy/random/_pickle.py index 71b01d6cd1e5..a32f64f4a3d3 100644 --- a/numpy/random/_pickle.py +++ b/numpy/random/_pickle.py @@ -1,6 +1,6 @@ from .mtrand import RandomState from ._philox import Philox -from ._pcg64 import PCG64 +from ._pcg64 import PCG64, PCG64DXSM from ._sfc64 import SFC64 from ._generator import Generator @@ -8,6 +8,7 @@ BitGenerators = {'MT19937': MT19937, 'PCG64': PCG64, + 'PCG64DXSM': PCG64DXSM, 'Philox': Philox, 'SFC64': SFC64, } diff --git a/numpy/random/src/pcg64/pcg64.c b/numpy/random/src/pcg64/pcg64.c index b15973aefafc..c623c809b02e 100644 --- a/numpy/random/src/pcg64/pcg64.c +++ b/numpy/random/src/pcg64/pcg64.c @@ -61,6 +61,10 @@ pcg_setseq_128_xsl_rr_64_boundedrand_r(pcg_state_setseq_128 *rng, uint64_t bound); extern inline void pcg_setseq_128_advance_r(pcg_state_setseq_128 *rng, pcg128_t delta); +extern inline uint64_t pcg_cm_random_r(pcg_state_setseq_128 *rng); +extern inline void pcg_cm_step_r(pcg_state_setseq_128 *rng); +extern inline uint64_t pcg_output_cm_128_64(pcg128_t state); +extern inline void pcg_cm_srandom_r(pcg_state_setseq_128 *rng, pcg128_t initstate, pcg128_t initseq); /* Multi-step advance functions (jump-ahead, jump-back) * @@ -117,6 +121,9 @@ pcg128_t pcg_advance_lcg_128(pcg128_t state, pcg128_t delta, pcg128_t cur_mult, extern inline uint64_t pcg64_next64(pcg64_state *state); extern inline uint32_t pcg64_next32(pcg64_state *state); +extern inline uint64_t pcg64_cm_next64(pcg64_state *state); +extern inline uint32_t pcg64_cm_next32(pcg64_state *state); + extern void pcg64_advance(pcg64_state *state, uint64_t *step) { pcg128_t delta; #ifndef PCG_EMULATED_128BIT_MATH @@ -128,6 +135,17 @@ extern void pcg64_advance(pcg64_state *state, uint64_t *step) { pcg64_advance_r(state->pcg_state, delta); } +extern void pcg64_cm_advance(pcg64_state *state, uint64_t *step) { + pcg128_t delta; +#ifndef PCG_EMULATED_128BIT_MATH + delta = (((pcg128_t)step[0]) << 64) | step[1]; +#else + delta.high = step[0]; + delta.low = step[1]; +#endif + pcg_cm_advance_r(state->pcg_state, delta); +} + extern void pcg64_set_seed(pcg64_state *state, uint64_t *seed, uint64_t *inc) { pcg128_t s, i; #ifndef PCG_EMULATED_128BIT_MATH diff --git a/numpy/random/src/pcg64/pcg64.h b/numpy/random/src/pcg64/pcg64.h index 31899cbc1469..6691a18fcb16 100644 --- a/numpy/random/src/pcg64/pcg64.h +++ b/numpy/random/src/pcg64/pcg64.h @@ -104,6 +104,9 @@ typedef struct { , PCG_128BIT_CONSTANT(0x0000000000000001ULL, 0xda3e39cb94b95bdbULL) \ } +#define PCG_CHEAP_MULTIPLIER_128 (0xda942042e4dd58b5ULL) + + static inline uint64_t pcg_rotr_64(uint64_t value, unsigned int rot) { #ifdef _WIN32 return _rotr64(value, rot); @@ -198,6 +201,62 @@ pcg_setseq_128_xsl_rr_64_random_r(pcg_state_setseq_128 *rng) { #endif } +static inline pcg128_t pcg128_mult_64(pcg128_t a, uint64_t b) { + uint64_t h1; + pcg128_t result; + + h1 = a.high * b; + _pcg_mult64(a.low, b, &(result.high), &(result.low)); + result.high += h1; + return result; +} + +static inline void pcg_cm_step_r(pcg_state_setseq_128 *rng) { +#if defined _WIN32 && _MSC_VER >= 1900 && _M_AMD64 + uint64_t h1; + pcg128_t product; + + /* Manually inline the multiplication and addition using intrinsics */ + h1 = rng->state.high * PCG_CHEAP_MULTIPLIER_128; + product.low = + _umul128(rng->state.low, PCG_CHEAP_MULTIPLIER_128, &(product.high)); + product.high += h1; + _addcarry_u64(_addcarry_u64(0, product.low, rng->inc.low, &(rng->state.low)), + product.high, rng->inc.high, &(rng->state.high)); +#else + rng->state = pcg128_add(pcg128_mult_64(rng->state, PCG_CHEAP_MULTIPLIER_128), + rng->inc); +#endif +} + +static inline uint64_t pcg_output_cm_128_64(pcg128_t state) { + uint64_t hi = state.high; + uint64_t lo = state.low; + + lo |= 1; + hi ^= hi >> 32; + hi *= 0xda942042e4dd58b5ULL; + hi ^= hi >> 48; + hi *= lo; + return hi; +} + +static inline void pcg_cm_srandom_r(pcg_state_setseq_128 *rng, pcg128_t initstate, pcg128_t initseq) { + rng->state = PCG_128BIT_CONSTANT(0ULL, 0ULL); + rng->inc.high = initseq.high << 1u; + rng->inc.high |= initseq.low >> 63u; + rng->inc.low = (initseq.low << 1u) | 1u; + pcg_cm_step_r(rng); + rng->state = pcg128_add(rng->state, initstate); + pcg_cm_step_r(rng); +} + +static inline uint64_t pcg_cm_random_r(pcg_state_setseq_128* rng) +{ + uint64_t ret = pcg_output_cm_128_64(rng->state); + pcg_cm_step_r(rng); + return ret; +} #else /* PCG_EMULATED_128BIT_MATH */ static inline void pcg_setseq_128_step_r(pcg_state_setseq_128 *rng) { @@ -209,6 +268,37 @@ static inline uint64_t pcg_output_xsl_rr_128_64(pcg128_t state) { state >> 122u); } +static inline void pcg_cm_step_r(pcg_state_setseq_128 *rng) { + rng-> state = rng->state * PCG_CHEAP_MULTIPLIER_128 + rng->inc; +} + +static inline uint64_t pcg_output_cm_128_64(pcg128_t state) { + uint64_t hi = state >> 64; + uint64_t lo = state; + + lo |= 1; + hi ^= hi >> 32; + hi *= 0xda942042e4dd58b5ULL; + hi ^= hi >> 48; + hi *= lo; + return hi; +} + +static inline void pcg_cm_srandom_r(pcg_state_setseq_128 *rng, pcg128_t initstate, pcg128_t initseq) { + rng->state = 0U; + rng->inc = (initseq << 1u) | 1u; + pcg_cm_step_r(rng); + rng->state += initstate; + pcg_cm_step_r(rng); +} + +static inline uint64_t pcg_cm_random_r(pcg_state_setseq_128* rng) +{ + uint64_t ret = pcg_output_cm_128_64(rng->state); + pcg_cm_step_r(rng); + return ret; +} + static inline uint64_t pcg_setseq_128_xsl_rr_64_random_r(pcg_state_setseq_128* rng) { @@ -248,6 +338,12 @@ static inline void pcg_setseq_128_advance_r(pcg_state_setseq_128 *rng, PCG_DEFAULT_MULTIPLIER_128, rng->inc); } +static inline void pcg_cm_advance_r(pcg_state_setseq_128 *rng, pcg128_t delta) { + rng->state = pcg_advance_lcg_128(rng->state, delta, + PCG_128BIT_CONSTANT(0, PCG_CHEAP_MULTIPLIER_128), + rng->inc); +} + typedef pcg_state_setseq_128 pcg64_random_t; #define pcg64_random_r pcg_setseq_128_xsl_rr_64_random_r #define pcg64_boundedrand_r pcg_setseq_128_xsl_rr_64_boundedrand_r @@ -281,7 +377,24 @@ static inline uint32_t pcg64_next32(pcg64_state *state) { return (uint32_t)(next & 0xffffffff); } +static inline uint64_t pcg64_cm_next64(pcg64_state *state) { + return pcg_cm_random_r(state->pcg_state); +} + +static inline uint32_t pcg64_cm_next32(pcg64_state *state) { + uint64_t next; + if (state->has_uint32) { + state->has_uint32 = 0; + return state->uinteger; + } + next = pcg_cm_random_r(state->pcg_state); + state->has_uint32 = 1; + state->uinteger = (uint32_t)(next >> 32); + return (uint32_t)(next & 0xffffffff); +} + void pcg64_advance(pcg64_state *state, uint64_t *step); +void pcg64_cm_advance(pcg64_state *state, uint64_t *step); void pcg64_set_seed(pcg64_state *state, uint64_t *seed, uint64_t *inc); diff --git a/numpy/random/tests/data/pcg64dxsm-testset-1.csv b/numpy/random/tests/data/pcg64dxsm-testset-1.csv new file mode 100644 index 000000000000..39cef057f449 --- /dev/null +++ b/numpy/random/tests/data/pcg64dxsm-testset-1.csv @@ -0,0 +1,1001 @@ +seed, 0xdeadbeaf +0, 0xdf1ddcf1e22521fe +1, 0xc71b2f9c706cf151 +2, 0x6922a8cc24ad96b2 +3, 0x82738c549beccc30 +4, 0x5e8415cdb1f17580 +5, 0x64c54ad0c09cb43 +6, 0x361a17a607dce278 +7, 0x4346f6afb7acad68 +8, 0x6e9f14d4f6398d6b +9, 0xf818d4343f8ed822 +10, 0x6327647daf508ed6 +11, 0xe1d1dbe5496a262a +12, 0xfc081e619076b2e0 +13, 0x37126563a956ab1 +14, 0x8bb46e155db16b9 +15, 0x56449f006c9f3fb4 +16, 0x34a9273550941803 +17, 0x5b4df62660f99462 +18, 0xb8665cad532e3018 +19, 0x72fc3e5f7f84216a +20, 0x71d3c47f6fd59939 +21, 0xfd4218afa1de463b +22, 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0xc16a1b625e467ade +979, 0x1a4a320fb5e8b098 +980, 0x8819cccd8b4ab32f +981, 0x42daa88531fd0bfd +982, 0xcf732226409be17c +983, 0xfddcdb25ccbf378c +984, 0x9b15b603bf589fc1 +985, 0x2436066b95d366fe +986, 0x8d42eff2e9cbda90 +987, 0x694b2fc8a4e8303c +988, 0x8e207f98aaea3ccd +989, 0x4730d7a620f822d9 +990, 0x468dc9ca30fe2fd4 +991, 0x74b36d8a1c0f031b +992, 0x3c1aac1c488c1a94 +993, 0x19d0101042444585 +994, 0x8ec50c56d0c8adf4 +995, 0x721ec629e4d66394 +996, 0x3ca5ad93abeac4a4 +997, 0xaaebc76e71592623 +998, 0x969cc319e3ed6058 +999, 0xc0a277e3b2bfc3de diff --git a/numpy/random/tests/test_direct.py b/numpy/random/tests/test_direct.py index d602b36b4169..29054b70b95a 100644 --- a/numpy/random/tests/test_direct.py +++ b/numpy/random/tests/test_direct.py @@ -8,8 +8,8 @@ import pytest from numpy.random import ( - Generator, MT19937, PCG64, Philox, RandomState, SeedSequence, SFC64, - default_rng + Generator, MT19937, PCG64, PCG64DXSM, Philox, RandomState, SeedSequence, + SFC64, default_rng ) from numpy.random._common import interface @@ -359,6 +359,34 @@ def test_advance_symmetry(self): assert val_big == val_pos +class TestPCG64DXSM(Base): + @classmethod + def setup_class(cls): + cls.bit_generator = PCG64DXSM + cls.bits = 64 + cls.dtype = np.uint64 + cls.data1 = cls._read_csv(join(pwd, './data/pcg64dxsm-testset-1.csv')) + cls.data2 = cls._read_csv(join(pwd, './data/pcg64dxsm-testset-2.csv')) + cls.seed_error_type = (ValueError, TypeError) + cls.invalid_init_types = [(3.2,), ([None],), (1, None)] + cls.invalid_init_values = [(-1,)] + + def test_advance_symmetry(self): + rs = Generator(self.bit_generator(*self.data1['seed'])) + state = rs.bit_generator.state + step = -0x9e3779b97f4a7c150000000000000000 + rs.bit_generator.advance(step) + val_neg = rs.integers(10) + rs.bit_generator.state = state + rs.bit_generator.advance(2**128 + step) + val_pos = rs.integers(10) + rs.bit_generator.state = state + rs.bit_generator.advance(10 * 2**128 + step) + val_big = rs.integers(10) + assert val_neg == val_pos + assert val_big == val_pos + + class TestMT19937(Base): @classmethod def setup_class(cls): diff --git a/numpy/random/tests/test_smoke.py b/numpy/random/tests/test_smoke.py index 909bfaa8dab6..9becc434d0d1 100644 --- a/numpy/random/tests/test_smoke.py +++ b/numpy/random/tests/test_smoke.py @@ -4,7 +4,7 @@ import numpy as np import pytest from numpy.testing import assert_equal, assert_, assert_array_equal -from numpy.random import (Generator, MT19937, PCG64, Philox, SFC64) +from numpy.random import (Generator, MT19937, PCG64, PCG64DXSM, Philox, SFC64) @pytest.fixture(scope='module', params=(np.bool_, np.int8, np.int16, np.int32, np.int64, @@ -774,6 +774,18 @@ def setup_class(cls): cls._extra_setup() +class TestPCG64DXSM(RNG): + @classmethod + def setup_class(cls): + cls.bit_generator = PCG64DXSM + cls.advance = 2**63 + 2**31 + 2**15 + 1 + cls.seed = [12345] + cls.rg = Generator(cls.bit_generator(*cls.seed)) + cls.initial_state = cls.rg.bit_generator.state + cls.seed_vector_bits = 64 + cls._extra_setup() + + class TestDefaultRNG(RNG): @classmethod def setup_class(cls):