NumPy

NEP 19 — Random Number Generator Policy

Author

Robert Kern <robert.kern@gmail.com>

Status

Final

Type

Standards Track

Created

2018-05-24

Updated

2019-05-21

Resolution

https://mail.python.org/pipermail/numpy-discussion/2018-July/078380.html

Abstract

For the past decade, NumPy has had a strict backwards compatibility policy for the number stream of all of its random number distributions. Unlike other numerical components in numpy, which are usually allowed to return different when results when they are modified if they remain correct, we have obligated the random number distributions to always produce the exact same numbers in every version. The objective of our stream-compatibility guarantee was to provide exact reproducibility for simulations across numpy versions in order to promote reproducible research. However, this policy has made it very difficult to enhance any of the distributions with faster or more accurate algorithms. After a decade of experience and improvements in the surrounding ecosystem of scientific software, we believe that there are now better ways to achieve these objectives. We propose relaxing our strict stream-compatibility policy to remove the obstacles that are in the way of accepting contributions to our random number generation capabilities.

The Status Quo

Our current policy, in full:

A fixed seed and a fixed series of calls to RandomState methods using the same parameters will always produce the same results up to roundoff error except when the values were incorrect. Incorrect values will be fixed and the NumPy version in which the fix was made will be noted in the relevant docstring. Extension of existing parameter ranges and the addition of new parameters is allowed as long the previous behavior remains unchanged.

This policy was first instated in Nov 2008 (in essence; the full set of weasel words grew over time) in response to a user wanting to be sure that the simulations that formed the basis of their scientific publication could be reproduced years later, exactly, with whatever version of numpy that was current at the time. We were keen to support reproducible research, and it was still early in the life of numpy.random. We had not seen much cause to change the distribution methods all that much.

We also had not thought very thoroughly about the limits of what we really could promise (and by “we” in this section, we really mean Robert Kern, let’s be honest). Despite all of the weasel words, our policy overpromises compatibility. The same version of numpy built on different platforms, or just in a different way could cause changes in the stream, with varying degrees of rarity. The biggest is that the .multivariate_normal() method relies on numpy.linalg functions. Even on the same platform, if one links numpy with a different LAPACK, .multivariate_normal() may well return completely different results. More rarely, building on a different OS or CPU can cause differences in the stream. We use C long integers internally for integer distribution (it seemed like a good idea at the time), and those can vary in size depending on the platform. Distribution methods can overflow their internal C longs at different breakpoints depending on the platform and cause all of the random variate draws that follow to be different.

And even if all of that is controlled, our policy still does not provide exact guarantees across versions. We still do apply bug fixes when correctness is at stake. And even if we didn’t do that, any nontrivial program does more than just draw random numbers. They do computations on those numbers, transform those with numerical algorithms from the rest of numpy, which is not subject to so strict a policy. Trying to maintain stream-compatibility for our random number distributions does not help reproducible research for these reasons.

The standard practice now for bit-for-bit reproducible research is to pin all of the versions of code of your software stack, possibly down to the OS itself. The landscape for accomplishing this is much easier today than it was in 2008. We now have pip. We now have virtual machines. Those who need to reproduce simulations exactly now can (and ought to) do so by using the exact same version of numpy. We do not need to maintain stream-compatibility across numpy versions to help them.

Our stream-compatibility guarantee has hindered our ability to make improvements to numpy.random. Several first-time contributors have submitted PRs to improve the distributions, usually by implementing a faster, or more accurate algorithm than the one that is currently there. Unfortunately, most of them would have required breaking the stream to do so. Blocked by our policy, and our inability to work around that policy, many of those contributors simply walked away.

Implementation

Work on a proposed new Pseudo Random Number Generator (PRNG) subsystem is already underway in the randomgen project. The specifics of the new design are out of scope for this NEP and up for much discussion, but we will discuss general policies that will guide the evolution of whatever code is adopted. We will also outline just a few of the requirements that such a new system must have to support the policy proposed in this NEP.

First, we will maintain API source compatibility just as we do with the rest of numpy. If we must make a breaking change, we will only do so with an appropriate deprecation period and warnings.

Second, breaking stream-compatibility in order to introduce new features or improve performance will be allowed with caution. Such changes will be considered features, and as such will be no faster than the standard release cadence of features (i.e. on X.Y releases, never X.Y.Z). Slowness will not be considered a bug for this purpose. Correctness bug fixes that break stream-compatibility can happen on bugfix releases, per usual, but developers should consider if they can wait until the next feature release. We encourage developers to strongly weight user’s pain from the break in stream-compatibility against the improvements. One example of a worthwhile improvement would be to change algorithms for a significant increase in performance, for example, moving from the Box-Muller transform method of Gaussian variate generation to the faster Ziggurat algorithm. An example of a discouraged improvement would be tweaking the Ziggurat tables just a little bit for a small performance improvement.

Any new design for the random subsystem will provide a choice of different core uniform PRNG algorithms. A promising design choice is to make these core uniform PRNGs their own lightweight objects with a minimal set of methods (randomgen calls them “BitGenerators”). The broader set of non-uniform distributions will be its own class that holds a reference to one of these core uniform PRNG objects and simply delegates to the core uniform PRNG object when it needs uniform random numbers (randomgen calls this the Generator). To borrow an example from randomgen, the class MT19937 is a BitGenerator that implements the classic Mersenne Twister algorithm. The class Generator wraps around the BitGenerator to provide all of the non-uniform distribution methods:

# This is not the only way to instantiate this object.
# This is just handy for demonstrating the delegation.
>>> bg = MT19937(seed)
>>> rg = Generator(bg)
>>> x = rg.standard_normal(10)

We will be more strict about a select subset of methods on these BitGenerator objects. They MUST guarantee stream-compatibility for a specified set of methods which are chosen to make it easier to compose them to build other distributions and which are needed to abstract over the implementation details of the variety of BitGenerator algorithms. Namely,

  • .bytes()

  • integers() (formerly .random_integers())

  • random() (formerly .random_sample())

The distributions class (Generator) SHOULD have all of the same distribution methods as RandomState with close-enough function signatures such that almost all code that currently works with RandomState instances will work with Generator instances (ignoring the precise stream values). Some variance will be allowed for integer distributions: in order to avoid some of the cross-platform problems described above, these SHOULD be rewritten to work with uint64 numbers on all platforms.

Supporting Unit Tests

Because we did make a strong stream-compatibility guarantee early in numpy’s life, reliance on stream-compatibility has grown beyond reproducible simulations. One use case that remains for stream-compatibility across numpy versions is to use pseudorandom streams to generate test data in unit tests. With care, many of the cross-platform instabilities can be avoided in the context of small unit tests.

The new PRNG subsystem MUST provide a second, legacy distributions class that uses the same implementations of the distribution methods as the current version of numpy.random.RandomState. The methods of this class will have strict stream-compatibility guarantees, even stricter than the current policy. It is intended that this class will no longer be modified, except to keep it working when numpy internals change. All new development should go into the primary distributions class. Bug fixes that change the stream SHALL NOT be made to RandomState; instead, buggy distributions should be made to warn when they are buggy. The purpose of RandomState will be documented as providing certain fixed functionality for backwards compatibility and stable numbers for the limited purpose of unit testing, and not making whole programs reproducible across numpy versions.

This legacy distributions class MUST be accessible under the name numpy.random.RandomState for backwards compatibility. All current ways of instantiating numpy.random.RandomState with a given state should instantiate the Mersenne Twister BitGenerator with the same state. The legacy distributions class MUST be capable of accepting other BitGenerators. The purpose here is to ensure that one can write a program with a consistent BitGenerator state with a mixture of libraries that may or may not have upgraded from RandomState. Instances of the legacy distributions class MUST respond True to isinstance(rg, numpy.random.RandomState) because there is current utility code that relies on that check. Similarly, old pickles of numpy.random.RandomState instances MUST unpickle correctly.

numpy.random.*

The preferred best practice for getting reproducible pseudorandom numbers is to instantiate a generator object with a seed and pass it around. The implicit global RandomState behind the numpy.random.* convenience functions can cause problems, especially when threads or other forms of concurrency are involved. Global state is always problematic. We categorically recommend avoiding using the convenience functions when reproducibility is involved.

That said, people do use them and use numpy.random.seed() to control the state underneath them. It can be hard to categorize and count API usages consistently and usefully, but a very common usage is in unit tests where many of the problems of global state are less likely.

This NEP does not propose removing these functions or changing them to use the less-stable Generator distribution implementations. Future NEPs might.

Specifically, the initial release of the new PRNG subsystem SHALL leave these convenience functions as aliases to the methods on a global RandomState that is initialized with a Mersenne Twister BitGenerator object. A call to numpy.random.seed() will be forwarded to that BitGenerator object. In addition, the global RandomState instance MUST be accessible in this initial release by the name numpy.random.mtrand._rand: Robert Kern long ago promised scikit-learn that this name would be stable. Whoops.

In order to allow certain workarounds, it MUST be possible to replace the BitGenerator underneath the global RandomState with any other BitGenerator object (we leave the precise API details up to the new subsystem). Calling numpy.random.seed() thereafter SHOULD just pass the given seed to the current BitGenerator object and not attempt to reset the BitGenerator to the Mersenne Twister. The set of numpy.random.* convenience functions SHALL remain the same as they currently are. They SHALL be aliases to the RandomState methods and not the new less-stable distributions class (Generator, in the examples above). Users who want to get the fastest, best distributions can follow best practices and instantiate generator objects explicitly.

This NEP does not propose that these requirements remain in perpetuity. After we have experience with the new PRNG subsystem, we can and should revisit these issues in future NEPs.

Alternatives

Versioning

For a long time, we considered that the way to allow algorithmic improvements while maintaining the stream was to apply some form of versioning. That is, every time we make a stream change in one of the distributions, we increment some version number somewhere. numpy.random would keep all past versions of the code, and there would be a way to get the old versions.

We will not be doing this. If one needs to get the exact bit-for-bit results from a given version of numpy, whether one uses random numbers or not, one should use the exact version of numpy.

Proposals of how to do RNG versioning varied widely, and we will not exhaustively list them here. We spent years going back and forth on these designs and were not able to find one that sufficed. Let that time lost, and more importantly, the contributors that we lost while we dithered, serve as evidence against the notion.

Concretely, adding in versioning makes maintenance of numpy.random difficult. Necessarily, we would be keeping lots of versions of the same code around. Adding a new algorithm safely would still be quite hard.

But most importantly, versioning is fundamentally difficult to use correctly. We want to make it easy and straightforward to get the latest, fastest, best versions of the distribution algorithms; otherwise, what’s the point? The way to make that easy is to make the latest the default. But the default will necessarily change from release to release, so the user’s code would need to be altered anyway to specify the specific version that one wants to replicate.

Adding in versioning to maintain stream-compatibility would still only provide the same level of stream-compatibility that we currently do, with all of the limitations described earlier. Given that the standard practice for such needs is to pin the release of numpy as a whole, versioning RandomState alone is superfluous.

StableRandom

A previous version of this NEP proposed to leave RandomState completely alone for a deprecation period and build the new subsystem alongside with new names. To satisfy the unit testing use case, it proposed introducing a small distributions class nominally called StableRandom. It would have provided a small subset of distribution methods that were considered most useful in unit testing, but not the full set such that it would be too likely to be used outside of the testing context.

During discussion about this proposal, it became apparent that there was no satisfactory subset. At least some projects used a fairly broad selection of the RandomState methods in unit tests.

Downstream project owners would have been forced to modify their code to accommodate the new PRNG subsystem. Some modifications might be simply mechanical, but the bulk of the work would have been tedious churn for no positive improvement to the downstream project, just avoiding being broken.

Furthermore, under this old proposal, we would have had a quite lengthy deprecation period where RandomState existed alongside the new system of BitGenerator and Generator classes. Leaving the implementation of RandomState fixed meant that it could not use the new BitGenerator state objects. Developing programs that use a mixture of libraries that have and have not upgraded would require managing two sets of PRNG states. This would notionally have been time-limited, but we intended the deprecation to be very long.

The current proposal solves all of these problems. All current usages of RandomState will continue to work in perpetuity, though some may be discouraged through documentation. Unit tests can continue to use the full complement of RandomState methods. Mixed RandomState/Generator code can safely share the common BitGenerator state. Unmodified RandomState code can make use of the new features of alternative BitGenerator-like settable streams.