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+# Summary
+[summary]: #summary
+
+- Introduce a new function, `scope_fifo`, which introduces a Rayon scope
+  that executes tasks in **per-thread FIFO** order; in this mode, at
+  least with one worker thread, the tasks that are spawned first execute
+  first. This is on contrast to the tradition Rayon `scope`, which
+  executes in **per-thread LIFO** order, such that tasks that are
+  spawned first execute last. Per-thread FIFO requires a small amount of
+  indirection to implement but is important for some use-cases.
+- Introduce a new function, `spawn_fifo`, that pushes tasks onto the
+  implicit global scope. These tasks will also execute in FIFO order,
+  in contrast to the [existing `spawn` function][spawn].
+- Deprecate the [existing `breadth_first` flag on `ThreadPool`][bf].
+  Users should migrate to creating a `scope_fifo` instead, as it is better
+  behaved.
+  - In the future, the `breadth_first` flag may be converted to a no-op.
+
+[spawn]: https://docs.rs/rayon/1.0.3/rayon/fn.spawn.html
+[bf]: https://docs.rs/rayon/1.0.2/rayon/struct.ThreadPoolBuilder.html#method.breadth_first
+
+# Motivation
+[motivation]: #motivation
+
+The prioritization order for tasks can sometimes make a big difference
+to the overall system efficiency. Currently, Rayon offers only a
+single knob for tuning this behavior, in the form of [the
+`breadth_first` option][bf] on builds. This knob is not only rather
+coarse, it can lead to quite surprising behavior when one intermingles
+`scope` and `join` (including stack overflows, see [#590]). The goal
+of this RFC is to make more options available to users while ensuring
+that these options "compose well" with the overall system.
+
+[#590]: https://github.com/rayon-rs/rayon/issues/590
+
+## Current behavior: Per-thread LIFO
+
+By default, and presuming no stealing occurs, the current behavior of
+a Rayon scope is to execute tasks in the reverse of the order that
+they are created. Therefore, in the following code, task 2 would
+execute first, and then task 1:
+
+```rust
+rayon::scope(|scope| {
+  scope.spawn(|scope| /* task 1 */ );
+  scope.spawn(|scope| /* task 2 */ );
+});
+```
+
+Thieves, in contrast, steal tasks in the order that they are created,
+so a thief would steal Task 1 before Task 2. Once a task is stolen,
+any new tasks that it spawns are processed first by the thief, again
+in reverse order (but may in turn be stolen by others, again in the
+order of creation).
+
+**Implementation notes.** This behavior corresponds very nicely with
+the general "work stealing" implementation, where each thread has a
+deque of tasks. Each new task is pushed on to the back of the
+deque. The thread pops tasks from the back of the deque when executing
+locally, but steals from the front of the deque.
+
+## Per-thread FIFO
+
+Unfortunately, for some applications, executing tasks in the reverse
+order turns out to be undesirable. One such application is stylo, the
+parallel rendering engine used in Firefox. The "basic loop" in Stylo is
+a simple tree walk that descends the DOM tree, spawning off a task for each
+element:
+
+```rust
+fn style_walk<'scope>(
+  element: &'scope Element,
+  scope: &rayon::Scope<'scope>,
+) {
+  style(element);
+  for child in element {
+    scope.spawn(|scope| style_walk(child, scope));
+  }
+}
+```
+
+For efficiency, Stylo employs a per-worker-thread cache, which enables
+it to share information between tasks. For this task to be maximally
+effective, it is best to process all of the children of a given
+element first, before processing its "grandchildren" (this is because
+sibling tasks require the same cached information, but grandchildren
+may not). However, if we use the default scheduling strategy of
+per-thread LIFO, this is not what we get: instead, for a given element
+`E`, we would process first its last child `Cn`. Processing `Cn` would
+push more tasks onto the thread-local deque (the grandchildren of `E`)
+and those would be the next to be processed. In effect, we are getting
+a depth-first search when what we wanted was a breadth-first search.
+
+To address this, we currently offer a per threadpool flag called
+[`breadth_first`][bf].  This causes us to (globally) process tasks
+from the front of the queue first.  This works well for Stylo, but
+[interacts poorly with parallel iterators][#590], as previously
+mentioned.
+
+Instead of a flag on the threadpool, this RFC proposes to allow users
+to select the scheduling when constructing a scope. So stylo would
+create its scope using `rayon::scope_fifo` instead of `rayon::scope`:
+
+```rust
+rayon::scope_fifo(|scope| {
+  ...
+});
+```
+
+Creating a FIFO scope means that, when a thread goes to process a task
+that is part of the scope, it prefers first the tasks that were
+created most recently **within the current thread**. If we assume no
+stealing, then all tasks are created by one thread, and hence this is
+simply a FIFO ordering.
+
+However, when stealing occurs, the ordering can get more complex and
+does not abide by a strict FIFO ordering. To illustrate, imagine that
+a thread T1 creates a scope S and creates three tasks, A, B and C
+within the scope. This thread T1 will begin by executing A, as it is
+the task created first. Let us imagine that processing A takes a very
+long time, and all the rest of the work proceeds before it completes.
+
+Next, imagine that a thief thread T2 steals the task B. In executing
+B, it creates two more tasks, D and E. Once T2 finishes with B, it
+will proceed to execute D and E, in that order (presuming they are not
+stolen first). Only when it completes E will it go back to T1 and
+steal the task C. So the final ordering of *task creation* is A, B, C,
+D, E, but the tasks *begin* execution in a different order: A, B, D,
+E, C. This order is influenced by what gets stolen and when.
+
+As it happens, this "per-thread FIFO" behavior is a very good fit for
+Stylo. It enables each worker thread to keep a cache in its
+thread-local data. When T2 steals the task B, its local cache is
+primed to process B's children, i.e., D and E. If T2 were to go and
+process C now, it would not benefit at all from the cache built up
+when processing B.
+
+In fact, similar logic likely applies to many other applications: if
+nothing else, the caches on the CPU itself contain the state accessed
+from B, and it is likely that the tasks spawned by B are going to
+re-use more of those cache lines than task C. (In general, this is why
+we prefer a LIFO behavior, as it offers similar benefits.)
+
+# Guide-level explanation
+
+## New functions and types
+
+We extend the rayon-core API to include two new functions, as well as two
+corresponding methods on the `ThreadPool` struct:
+
+- `scope_fifo(..)` and `ThreadPool::scope_fifo`
+- `spawn_fifo(..)` and `ThreadPool::spawn_fifo`
+
+These two functions (and methods) are analogous to the existing
+[`scope`] and [`spawn`] functions respectively, except that they
+ensure **per-thread FIFO** ordering.
+
+The `scope_fifo` function (and method) takes a closure implementing
+`FnOnce(&ScopeFifo<'scope>)` as argument. The `ScopeFifo` struct (also
+introduced by this RFC) is analogous to existing [`Scope`] struct --
+it permits one to spawn new tasks that will execute before the
+`scope_fifo` function returns. It will offer one method,
+`ScopeFifo::spawn_fifo`, that permits one to spawn a (FIFO) task into
+the scope, analogous to [`Scope::spawn`].
+
+[`scope`]: https://docs.rs/rayon/1.0.3/rayon/fn.scope.html
+[scope_method]: https://docs.rs/rayon/1.0.3/rayon/struct.ThreadPool.html#method.scope
+[`spawn`]: https://docs.rs/rayon/1.0.3/rayon/fn.spawn.html
+[`Scope`]: https://docs.rs/rayon/1.0.3/rayon/struct.Scope.html
+[`Scope::spawn`]: https://docs.rs/rayon/1.0.3/rayon/struct.Scope.html#method.spawn
+
+## Deprecations
+
+The `breadth_first` flag on thread-pools is **deprecated** but (for
+now) retains its current behavior. In some future rayon-core release,
+it may become a no-op, so users are encouraged to migrate to use
+`scope_fifo` or `spawn_fifo` instead.
+
+# Implementation notes
+
+## Implementing `scope_fifo`
+
+Rayon's core thread pool operates on the traditional work-stealing
+mechanism, where each worker thread has its own deque. New tasks are
+pushed onto the back of the deque, and to obtain a local task, the
+thread pops from the back of the deque. When stealing, jobs are taken
+from the front of the deque. So how can we extend this to accommodate
+the new scheduling modes? 
+
+In addition, we have the goal that nested scopes using these modes
+should "compose" nicely with one another (and with the `join`
+operation)[^global]. So, for example, if we have a thread nesting scopes like:
+
+[^global]: The existing "global FIFO mode" fails miserably on this criteria, which is a partial motivator for this RFC.
+
+- a per-thread LIFO scope S1 that contains a
+  - per-thread FIFO scope S2 that contains
+    - a join(A, B) of tasks A and B
+    
+then we should execute:
+
+- first, the tasks from the join (in reverse order, so A and then B)
+- then, the tasks from S2, in the order that they were created
+- then, the tasks from S1, in the reverse order from which they were created.
+
+Implementing **Per-thread LIFO** scheduling is therefore very
+easy. Each new job pushed onto the stack is simply pushed directly
+onto the back of the deque. Worker threads pop local tasks from the
+back of the deque but steal from the front (if the `breadth_first`
+flag is true, then worker threads pop local tasks from the front as
+well).
+
+Implementing **Per-thread FIFO** requires a certain amount of
+indirection. The scope creates N FIFOs, one per worker thread (as of
+this writing, the number of worker threads is fixed; if we later add
+the ability to grow or shrink the thread-pool dynamically, that will
+make this implementation somewhat more complex). When a new task is
+pushed onto a FIFO scope by the worker with index W, we actually push two items:
+
+- First, we push the task itself onto the FIFO with index W.
+  This task contains the closure that needs to execute.
+- Second, we push an "indirect" task onto the worker's thread-local
+  deque. This task contains a reference to the FIFO for the worker
+  index W that created it, but does not record the actual closure that
+  needs to execute.
+
+Like any other task, this "indirect task" may be popped locally or
+stolen. In either case, when it executes, it must first find the
+closure to execute. To do that, it will find the FIFO for the worker W
+that created it and pop the next closure from the front, which it can
+then execute. Any new tasks pushed by this task T will be pushed onto
+the *current* thread, which is not necessarily the thread W that
+created it.
+
+Note that the FIFO mode does impose some "indirection overhead"
+relative to the LIFO execution mode. This is partly what motivates the
+default, as well backwards compatibility concerns. In any case, the
+overhead does not seem to be too large: the [prototype
+implementation][] of these ideas was [evaluated experimentally by
+@bholley][experiment], who found that it performs equivalently to
+today's code.
+
+[prototype implementation]: https://github.com/rayon-rs/rayon/pull/601#issuecomment-433242023
+[experiment]: https://github.com/rayon-rs/rayon/pull/601#issuecomment-433242023
+
+## Implementing `spawn_fifo`
+
+The traditional `spawn` function used by Rayon behaves (roughly) "as
+if" there were a global scope surrounding the worker thread: presuming
+that spawn is executed from inside a worker thread, it simply pushes
+the task onto the current thread-local deque. (When executed from
+**outside** a worker thread, the task is added to the "global
+injector"; it will eventually be picked up by some worker thread and
+executed.)
+
+`spawn_fifo` can be implemented in an analogous way to `scope_fifo` by
+having each worker thread have a global FIFO, analogous to the FIFOs
+created in each `scope_fifo`. `spawn_fifo` then pushes the true task
+onto this FIFO as well as an "indirect task" onto the thread-local
+deque, exactly as described above.
+
+# Rationale and alternatives
+
+**Why change at all?** Two things are clear:
+
+- There is a need for FIFO-oriented scheduling, to accommodate Stylo.
+- The existing, global implementation -- while simple -- has serious
+  drawbacks. It works well for Stylo, but it doesn't "compose" well
+  with other code, that may wish to use parallel iterators or
+  join-based invocations.
+  
+These two facts together motivate moving to something like the
+per-thread FIFO behavior described in this RFC.
+
+**Why offer both FIFO and LIFO modes?** A serious alternative however
+would be to offer **only** this behavior, and not support per-thread
+LIFO -- this is the design which e.g. [@stjepang is advocating
+for][stjepang-1]. In general, Rayon prefers offering fewer knobs, so
+that would be a general fit. However, there are some advantages to
+offering more scheduling modes:
+
+[stjepang-1]: https://github.com/rayon-rs/rfcs/pull/1#issuecomment-437074748
+
+- Per-thread LIFO is the **current default behavior** of scopes. This
+  is "semi-documented". While not strictly part of our semver
+  guarantees, altering this behavior could negatively affect existing
+  applications.
+- Per-thread LIFO offers the **most efficient** implementation in a
+  "micro" sense, as it can build directly on the work-stealing deques
+  and does not require any indirection. It also has desirable cache
+  behavior, as threads will tend to continue the "most recent thing"
+  you were doing, which is also the thing where the caches are
+  warmest, etc. **These two cases together argue that, for cases where
+  the application doesn't otherwise care about execution order,
+  per-thread LIFO is a good choice.** This also applies to
+  applications that wish to choose another scheduling constraint (see
+  the next section).
+
+**Should we offer additional scheduling modes?** Another question
+worth considering is "why stop with these two modes"?  For example,
+the [Rayon demo application for solving the Travelling Salesman
+Problem][tsp] also [uses the "indirect task"
+trick][tsp-indirect]. However, in that case, it uses a (locked)
+priority queue to control the ordering. Similarly, earlier versions of
+this RFC considered a "global FIFO" ordering where tasks always
+executed in the order they were pushed, regardless of whether they
+were stolen or not. Rayon could conceivably offer some more flexible,
+priority-queue like mechanism as well. However, it's not clear that
+this is worth doing, since one can always achieve the same effect in
+"user space", as the TSP application does. (For this purpose,
+per-thread LIFO tasks are a great fit, as they add minimal overhead.)
+
+[tsp]: https://github.com/rayon-rs/rayon/blob/a68b05ce524f79d7e7a5065714a8d3ca40ce8d4b/rayon-demo/src/tsp/
+[tsp-indirect]: https://github.com/rayon-rs/rayon/blob/a68b05ce524f79d7e7a5065714a8d3ca40ce8d4b/rayon-demo/src/tsp/step.rs#L50-L51
+
+**Should `scope_fifo` return a [`Scope`] and not a `ScopeFifo`?** The
+[prototype implementation] shares the same `Scope` type for both
+`scope_fifo` and `scope`, and stores a boolean value to remember which
+"mode" is in use. This RFC proposes a distinct return type, which
+gives us the freedom to avoid using a dynamic boolean at runtime
+(though the implementation is not required to take advantage of that
+freedom).
+
+**What to do with the `breadth_first` flag?** Earlier drafts of this
+RFC proposed making the `breadth_first` flag a no-op immediately. It
+was decided however to simply deprecate the flag but keep its current
+behavior for the time being: users of `breadth_first` are encouraged
+to migrate to `scope_fifo`, however, since the `breadth_first` flag
+may become a no-op in the future (this would simplify the overall
+rayon-core implementation somewhat).
+
+# Unresolved questions
+
+None.