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+---
+title: Evolving the Go Standard Library with math/rand/v2
+date: 2024-05-01
+by:
+- Russ Cox
+summary: Go 1.23 adds math/rand/v2 and charts a course for the evolution of the Go standard library.
+---
+
+Since Go 1 was [released in March 2012](/blog/go1),
+changes to the standard library have been
+constrained by Go's [compatibility promise](/doc/go1compat).
+Overall, compatibility has been a boon for Go users,
+providing a stable base for production systems,
+documentation, tutorials, books, and more.
+Over time, however, we've realized mistakes in the original APIs
+that cannot be fixed compatibly; in other cases,
+best practices and convention have changed.
+We need a plan for making important, breaking changes too.
+
+This blog post is about Go 1.22's new [`math/rand/v2`](/pkg/math/rand/v2/) package,
+the first “v2” in the standard library.
+It brings needed improvements to the [`math/rand`](/pkg/math/rand/) API,
+but more importantly it sets an example for how we can
+revise other standard library packages as the need arises.
+
+(In Go, `math/rand` and `math/rand/v2` are two different packages
+with different import paths.
+Go 1 and every release after it have included `math/rand`; Go 1.22 added `math/rand/v2`.
+A Go program can import either package, or both.)
+
+This post discusses the specific rationale for the changes in `math/rand/v2`
+and then [reflects on the general principles](#principles) that will guide
+new versions of other packages.
+
+## Pseudorandom Number Generators {#pseudo}
+
+Before we look at `math/rand`, which is an API for a pseudorandom number generator,
+let's take a moment to understand what that means.
+
+A pseudorandom number generator is a deterministic program
+that generates a long sequence of
+seemingly random numbers from a small seed input,
+although the numbers are not in fact random at all.
+In the case of `math/rand`, the seed is a single int64,
+and the algorithm produces a sequence of int64s
+using a variant of a
+[linear-feedback shift register (LFSR)](https://en.wikipedia.org/wiki/Linear-feedback_shift_register).
+The algorithm is based on an idea by George Marsaglia,
+tweaked by Don Mitchell and Jim Reeds,
+and further customized by Ken Thompson for Plan 9 and then Go.
+It has no official name, so this post calls it the Go 1 generator.
+
+The goal is for these generators to be fast,
+repeatable, and random enough to support simulations,
+shuffling, and other non-cryptographic use cases.
+Repeatability is particularly important for uses like
+numerical simulations or randomized testing.
+For example, a randomized tester might pick a seed
+(perhaps based on the current time), generate
+a large random test input, and repeat.
+When the tester finds a failure, it only needs to print the seed
+to allow repeating the test with that specific large input.
+
+Repeatability also matters over time: given a particular
+seed, a new version of Go needs to generate the same
+sequence of values that an older version did.
+We didn't realize this when we released Go 1;
+instead, we discovered it the hard way,
+when we tried to make a change in Go 1.2
+and got reports that we had broken certain tests
+and other use cases.
+At that point, we decided Go 1 compatibility included
+the specific random outputs for a given seed
+and [added a test](/change/5aca0514941ce7dd0f3cea8d8ffe627dbcd542ca).
+
+It is not a goal for these kinds of generators to produce
+random numbers suitable for deriving cryptographic keys
+or other important secrets.
+Because the seed is only 63 bits,
+any output drawn from the generator, no matter how long,
+will also only contain 63 bits of entropy.
+For example, using `math/rand` to generate a 128-bit or 256-bit AES key
+would be a serious mistake,
+since the key would be easier to brute force.
+For that kind of use, you need a cryptographically strong
+random number generator, as provided by [`crypto/rand`](/pkg/crypto/rand/).
+
+That's enough background that we can move on to what needed
+fixing in the `math/rand` package.
+
+## Problems with `math/rand` {#problems}
+
+Over time, we noticed more and more problems with `math/rand`.
+The most serious were the following.
+
+### Generator Algorithm {#problem.generator}
+
+The generator itself needed replacement.
+
+The initial implementation of Go, while production ready, was in many ways a “pencil sketch”
+of the entire system, working well enough to serve as a base for future development:
+the compiler and runtime were written in C; the garbage collector was a conservative, single-threaded,
+stop-the-world collector; and the libraries used basic implementations throughout.
+From Go 1 through around Go 1.5, we went back and drew the “fully inked”
+version of each of these: we converted the compiler and runtime to Go; we wrote a new, precise, parallel,
+concurrent garbage collection with microsecond pause times; and we replaced
+standard library implementations with more sophisticated, optimized algorithms
+as needed.
+
+Unfortunately, the repeatability requirement in `math/rand`
+meant that we couldn't replace the generator there without
+breaking compatibility.
+We were stuck with the Go 1 generator,
+which is reasonably fast (about 1.8ns per number on my M3 Mac)
+but maintains an internal state of almost 5 kilobytes.
+In contrast, Melissa O'Neill's [PCG family of generators](https://www.pcg-random.org/)
+generates better random numbers in about 2.1ns per number
+with only 16 bytes of internal state.
+We also wanted to explore using
+Daniel J. Bernstein's [ChaCha stream cipher](https://cr.yp.to/chacha.html)
+as a generator.
+A followup post will discuss that generator specifically.
+
+### Source Interface {#problem.source}
+
+The [`rand.Source` interface](/pkg/math/rand/#Source) was wrong.
+That interface defines the
+concept of a low-level random number generator that generates
+non-negative `int64` values:
+
+{{raw `
+	% go doc -src math/rand.Source
+	package rand // import "math/rand"
+
+	// A Source represents a source of uniformly-distributed
+	// pseudo-random int64 values in the range [0, 1<<63).
+	//
+	// A Source is not safe for concurrent use by multiple goroutines.
+	type Source interface {
+		Int63() int64
+		Seed(seed int64)
+	}
+
+	func NewSource(seed int64) Source
+	%
+`}}
+
+(In the doc comment, “[0, N)” denotes a
+[half-open interval](https://en.wikipedia.org/wiki/Interval_(mathematics)#Definitions_and_terminology),
+meaning the range includes 0 but ends just before 2⁶³.)
+
+The [`rand.Rand` type](/pkg/math/rand/#Rand) wraps a `Source`
+to implement a richer set of operations, such as
+generating [an integer between 0 and N](/pkg/math/rand/#Rand.Intn),
+generating [floating-point numbers](/pkg/math/rand/#Rand.Float64), and so on.
+
+We defined the `Source` interface to return a shortened 63-bit value
+instead of a uint64 because that's what the Go 1 generator and
+other widely-used generators produce,
+and it matches the convention set by the C standard library.
+But this was a mistake: more modern generators produce full-width uint64s,
+which is a more convenient interface.
+
+Another problem is the `Seed` method hard-coding an `int64` seed:
+some generators are seeded by larger values,
+and the interface provides no way to handle that.
+
+### Seeding Responsibility {#problem.seed}
+
+A bigger problem with `Seed` is that responsibility for seeding the global generator was unclear.
+Most users don't use `Source` and `Rand` directly.
+Instead, the `math/rand` package provides a global generator
+accessed by top-level functions like [`Intn`](/pkg/math/rand/#Intn).
+Following the C standard library, the global generator defaults to
+behaving as if `Seed(1)` is called at startup.
+This is good for repeatability but bad for programs that want
+their random outputs to be different from one run to the next.
+The package documentation suggests using `rand.Seed(time.Now().UnixNano())` in that case,
+to make the generator's output time-dependent,
+but what code should do this?
+
+Probably the main package should be in charge of how `math/rand` is seeded:
+it would be unfortunate for imported libraries to configure global state themselves,
+since their choices might conflict with other libraries or the main package.
+But what happens if a library needs some random data and wants to use `math/rand`?
+What if the main package doesn't even know `math/rand` is being used?
+We found that in practice many libraries add init functions
+that seed the global generator with the current time, “just to be sure”.
+
+Library packages seeding the global generator themselves causes a new problem.
+Suppose package main imports two packages that both use `math/rand`:
+package A assumes the global generator will be seeded by package main,
+but package B seeds it in an `init` func.
+And suppose that package main doesn't seed the generator itself.
+Now package A's correct operation depends on the coincidence that package B is also
+imported in the program.
+If package main stops importing package B, package A will stop getting random values.
+We observed this happening in practice in large codebases.
+
+In retrospect, it was clearly a mistake to follow the C standard library here:
+seeding the global generator automatically would remove the confusion
+about who seeds it, and users would stop being surprised by repeatable
+output when they didn't want that.
+
+### Scalability {#problem.scale}
+
+The global generator also did not scale well.
+Because top-level functions like [`rand.Intn`](/pkg/math/rand/#Intn)
+can be called simultaneously from multiple goroutines,
+the implementation needed a lock protecting the shared generator state.
+In parallel usage, acquiring and releasing this lock was more expensive
+than the actual generation.
+It would make sense instead to have a per-thread generator state,
+but doing so would break repeatability
+in programs without concurrent use of `math/rand`.
+
+### The `Rand` implementation was missing important optimizations {#problem.rand}
+
+The [`rand.Rand` type](/pkg/math/rand/#Rand) wraps a `Source`
+to implement a richer set of operations
+For example, here is the Go 1 implementation of `Int63n`, which returns
+a random integer in the range [0, `n`).
+
+{{raw `
+	func (r *Rand) Int63n(n int64) int64 {
+		if n <= 0 {
+			panic("invalid argument to Int63n")
+		}
+		max := int64((1<<63 - 1)  - (1<<63)%uint64(n))
+		v := r.src.Int63()
+		for v > max {
+			v = r.Int63()
+		}
+		return v % n
+	}
+`}}
+
+The actual conversion is easy: `v % n`.
+However, no algorithm can convert 2⁶³ equally likely values
+into `n` equally likely values unless 2⁶³ is a multiple of `n`:
+otherwise some outputs will necessarily happen more often
+than others. (As a simpler example, try converting 4 equally likely values into 3.)
+The code computes `max` such that
+`max+1` is the largest multiple of `n` less than or equal to 2⁶³,
+and then the loop rejects random values greater than or equal to `max+1`.
+Rejecting this too-large values ensures that all `n` outputs are equally likely.
+For small `n`, needing to reject any value at all is rare;
+rejection becomes more common and more important for larger values.
+Even without the rejection loop, the two (slow) modulus operations
+can make the conversion more expensive than generating the random value `v`
+in the first place.
+
+In 2018, [Daniel Lemire found an algorithm](https://arxiv.org/abs/1805.10941)
+that avoids the divisions nearly all the time
+(see also his [2019 blog post](https://lemire.me/blog/2019/06/06/nearly-divisionless-random-integer-generation-on-various-systems/)).
+In `math/rand`, adopting Lemire's algorithm would make `Intn(1000)` 20-30% faster,
+but we can't: the faster algorithm generates different values than the standard conversion,
+breaking repeatability.
+
+Other methods are also slower than they could be, constrained by repeatability.
+For example, the `Float64` method could easily be sped up by about 10%
+if we could change the generated value stream.
+(This was the change we tried to make in Go 1.2 and rolled back, mentioned earlier.)
+
+### The `Read` Mistake {#problem.read}
+
+As mentioned earlier, `math/rand` is not intended for
+and not suitable for generating cryptographic secrets.
+The `crypto/rand` package does that, and its fundamental
+primitive is its [`Read` function](/pkg/crypto/rand/#Read)
+and [`Reader`](/pkg/crypto/rand/#Reader) variable.
+
+In 2015, we accepted a proposal to make
+`rand.Rand` implement `io.Reader` as well,
+along with [adding a top-level `Read` function](/pkg/math/rand/#Read).
+This seemed reasonable at the time,
+but in retrospect we did not pay enough attention to the
+software engineering aspects of this change.
+Now if you want to read random data, now you have
+two choices: `math/rand.Read` and `crypto/rand.Read`.
+If the data is going to be used for key material,
+it is very important to use `crypto/rand`,
+but now it is possible to use `math/rand` instead,
+potentially with disastrous consequences.
+
+Tools like `goimports` and `gopls` have a special case
+to make sure they prefer to use `rand.Read` from
+`crypto/rand` instead of `math/rand`, but that's not a complete fix.
+It would be better to remove `Read` entirely.
+
+## Fixing `math/rand` directly {#fix.v1}
+
+Making a new, incompatible major version of a package is never our first choice:
+that new version only benefits programs that switch to it,
+leaving all existing usage of the old major version behind.
+In contrast, fixing a problem in the existing package has much more impact,
+since it fixes all the existing usage.
+We should never create a `v2` without doing as much as possible to fix `v1`.
+In the case of `math/rand`, we were able to partly address
+a few of the problems described above:
+
+- Go 1.8 introduced an optional [`Source64` interface](/pkg/math/rand/#Uint64) with a `Uint64` method.
+  If a `Source` also implements `Source64`, then `Rand` uses that method
+  when appropriate.
+  This “extension interface” pattern provides a compatible (if slightly awkward)
+  way to revise an interface after the fact.
+
+- Go 1.20 automatically seeded the top-level generator and
+  deprecated [`rand.Seed`](/pkg/math/rand/#Seed).
+  Although this may seem like an incompatible change
+  given our focus on repeatability of the output stream,
+  [we reasoned](/issue/56319) that any imported package that called [`rand.Int`](/pkg/math/rand/#Int)
+  at init time or inside any computation would also
+  visibly change the output stream, and surely adding or removing
+  such a call cannot be considered a breaking change.
+  And if that's true, then auto-seeding is no worse,
+  and it would eliminate this source of fragility for future programs.
+  We also added a [GODEBUG setting](/doc/godebug) to opt
+  back into the old behavior.
+  Then we marked the top-level `rand.Seed` as [deprecated](/wiki/Deprecated).
+  (Programs that need seeded repeatability can still use
+  `rand.New(rand.NewSource(seed))` to obtain a local generator
+  instead of using the global one.)
+
+- Having eliminated repeatability of the global output stream,
+  Go 1.20 was also able to make the global generator scale better
+  in programs that don't call `rand.Seed`,
+  replacing the Go 1 generator with a very cheap per-thread
+  [wyrand generator](https://github.com/wangyi-fudan/wyhash)
+  already used inside the Go runtime. This removed the global mutex
+  and made the top-level functions scale much better.
+  Programs that do call `rand.Seed` fall back to the
+  mutex-protected Go 1 generator.
+
+- We were able to adopt Lemire's optimization in the Go runtime,
+  and we also used it inside [`rand.Shuffle`](/pkg/math/rand/#Shuffle),
+  which was implemented after Lemire's paper was published.
+
+- Although we couldn't remove [`rand.Read`](/pkg/math/rand/#Read) entirely,
+  Go 1.20 marked it [deprecated](/wiki/Deprecated) in favor of
+  `crypto/rand`.
+  We have since heard from people who discovered that they were accidentally
+  using `math/rand.Read` in cryptographic contexts when their editors
+  flagged the use of the deprecated function.
+
+These fixes are imperfect and incomplete but also real improvements
+that helped all users of the existing `math/rand` package.
+For more complete fixes, we needed to turn our attention to `math/rand/v2`.
+
+## Fixing the rest in `math/rand/v2` {#fix.v2}
+
+Defining `math/rand/v2` took
+significant planning,
+then a [GitHub Discussion](/issue/60751)
+and then a [proposal discussion](/issue/61716).
+It is the same
+as `math/rand` with the following breaking changes
+addressing the problems outlined above:
+
+- We removed the Go 1 generator entirely, replacing it with two new generators,
+  [PCG](/pkg/math/rand/v2/#PCG) and [ChaCha8](/pkg/math/rand/v2/#ChaCha8).
+  The new types are named for their algorithms (avoiding the generic name `NewSource`)
+  so that if another important algorithm needs to be added, it will fit well into the
+  naming scheme.
+
+  Adopting a suggestion from the proposal discussion, the new types implement the
+  [`encoding.BinaryMarshaler`](/pkg/encoding/#BinaryMarshaler)
+  and
+  [`encoding.BinaryUnmarshaler`](/pkg/encoding/#BinaryUnmarshaler)
+  interfaces.
+
+- We changed the `Source` interface, replacing the `Int63` method with a `Uint64` method
+  and deleting the `Seed` method. Implementations that support seeding can provide
+  their own concrete methods, like [`PCG.Seed`](/pkg/math/rand/v2/#PCG.Seed) and
+  [`ChaCha8.Seed`](/pkg/math/rand/v2/#ChaCha8.Seed).
+  Note that the two take different seed types, and neither is a single `int64`.
+
+- We removed the top-level `Seed` function: the global functions like `Int` can only be used
+  in auto-seeded form now.
+
+- Removing the top-level `Seed` also let us hard-code the use of scalable,
+  per-thread generators by the top-level methods,
+  avoiding a GODEBUG check at each use.
+
+- We implemented Lemire's optimization for `Intn` and related functions.
+  The concrete `rand.Rand` API is now locked in to that value stream,
+  so we will not be able to take advantage of any optimizations yet to be discovered,
+  but at least we are up to date once again.
+  We also implemented the `Float32` and `Float64` optimizations we wanted to use back in Go 1.2.
+
+- During the proposal discussion, a contributor pointed out detectable bias in the
+  implementations of `ExpFloat64` and `NormFloat64`.
+  We fixed that bias and locked in the new value streams.
+
+- `Perm` and `Shuffle` used different shuffling algorithms and produced different value streams,
+  because `Shuffle` happened second and used a faster algorithm.
+  Deleting `Perm` entirely would have made migration harder for users.
+  Instead we implemented `Perm` in terms of `Shuffle`, which still lets us
+  delete an implementation.
+
+- We renamed `Int31`, `Int63`, `Intn`, `Int31n`, and `Int63n` to
+  `Int32`, `Int64`, `IntN`, `Int32N`, and `Int64N`.
+  The 31 and 63 in the names were unnecessarily pedantic
+  and confusing, and the capitalized N is more idiomatic for a second
+  “word” in the name in Go.
+
+- We added `Uint`, `Uint32`, `Uint64`, `UintN`, `Uint32N`, and `Uint64N`
+  top-level functions and methods.
+  We needed to add `Uint64` to provide direct access to the core `Source`
+  functionality, and it seemed inconsistent not to add the others.
+
+- Adopting another suggestion from the proposal discussion,
+  we added a new top-level, generic function `N` that is like
+  `Int64N` or `Uint64N` but works for any integer type.
+  In the old API, to create a random duration of up to 5 seconds,
+  it was necessary to write:
+
+      d := time.Duration(rand.Int63n(int64(5*time.Second)))
+
+  Using `N`, the equivalent code is:
+
+      d := rand.N(5 * time.Second)
+
+  `N` is only a top-level function; there is no `N` method on `rand.Rand`
+  because there are no generic methods in Go.
+  (Generic methods are not likely in the future, either;
+  they conflict badly with interfaces, and a complete implementation
+  would require either run-time code generation or slow execution.)
+
+- To ameliorate misuse of `math/rand` in cryptographic contexts,
+  we made `ChaCha8` the default generator used in global functions,
+  and we also changed the Go runtime to use it (replacing wyrand).
+  Programs are still strongly encouraged to use `crypto/rand`
+  to generate cryptographic secrets,
+  but accidentally using `math/rand/v2` is not as catastrophic
+  as using `math/rand` would be.
+  Even in `math/rand`, the global functions now use the `ChaCha8` generator when not explicitly seeded.
+
+## Principles for evolving the Go standard library {#principles}
+
+As mentioned at the start this post, one of the goals for this work
+was to establish principles and a pattern for how we approach all
+v2 packages in the standard library.
+There will not be a glut of v2 packages
+in the next few Go releases.
+Instead, we will handle one package
+at a time, making sure we set a quality bar that will last for another decade.
+Many packages will not need a v2 at all.
+But for those that do, our approach boils down to three principles.
+
+First, a new, incompatible version of a package will use
+`that/package/v2` as its import path,
+following
+[semantic import versioning](https://research.swtch.com/vgo-import)
+just like a v2 module outside the standard library would.
+This allows uses of the original package and the v2 package
+to coexist in a single program,
+which is critical for a
+[gradual conversion](/talks/2016/refactor.article) to the new API.
+
+Second, all changes must be rooted in
+respect for existing usage and users:
+we must not introduce needless churn,
+whether in the form of unnecessary changes to an existing package or
+an entirely new package that must be learned instead.
+In practice, that means we take the existing package
+as the starting point
+and only make changes that are well motivated
+and provide a value that justifies the cost to users of updating.
+
+Third, the v2 package must not leave v1 users behind.
+Ideally, the v2 package should be able to do everything the v1 package
+could do,
+and when v2 is released, the v1 package should be rewritten
+to be a thin wrapper around v2.
+This would ensure that existing uses of v1 continue to benefit
+from bug fixes and performance optimizations in v2.
+Of course, given that v2 is introducing breaking changes,
+this is not always possible, but it is always something to consider carefully.
+For `math/rand/v2`, we arranged for the auto-seeded v1 functions to
+call the v2 generator, but we were unable to share other code
+due to the repeatability violations.
+Ultimately `math/rand` is not a lot of code and does not require
+regular maintenance, so the duplication is manageable.
+In other contexts, more work to avoid duplication could be worthwhile.
+For example, in the
+[encoding/json/v2 design (still in progress)](/issue/63397),
+although the default semantics and the API are changed,
+the package provides configuration knobs that
+make it possible to implement the v1 API.
+When we eventually ship `encoding/json/v2`,
+`encoding/json` (v1) will become a thin wrapper around it,
+ensuring that users who don't migrate from v1 still
+benefit from optimizations and security fixes in v2.
+
+A follow-up blog post will present the `ChaCha8` generator in more detail.