Stream processing also exhibits the painful abstraction vs. performance trade-off. Manually written loops and state-machines offer the highest performance and the least memory overhead, but are not reusable or extensible. Libraries of freely composable stream components let programmers quickly assemble an obviously correct stream application, but suffer from the high overhead of abstractions, mainly due to the repeated creation and disposal of intermediate data structures such as closures, captured continuations, objects and collections -- let alone intermediate streams. Eliminating such intermediate structures is broadly known as stream fusion.
According to a survey of stream processing, ``Within computer science the term stream has been attributed to P.J. Landin, formulated during the development of operational constructs presented as part of his work on the correspondence between ALGOL 60 and the lambda-calculus. Indeed, we note that P.J. Landin's original use for streams was to model the histories of loop variables, but he also observed that streams could have been used as a model for I/O in ALGOL 60.''
R. Stephens: A Survey Of Stream Processing
Acta Informatica, July 1997, Volume 34, Issue 7, pp 491–541
All Things Flow: Unfolding the History of Streams
Stream Seminar
<http://www.win.tue.nl/~hzantema/strsem.html>
Stream Fusion, to Completeness
The Related Work section of the paper
The library is based on assured code generation (at present, OCaml, C and Scala/Java) and guarantees in all cases complete fusion: if each operation in a pipeline individually runs without any function calls and memory allocations, the entire streaming pipeline runs without calls and allocations. Thus strymonas per se introduces not even constant-size intermediary data structures. The main processing loop thus may run in constant memory and stack space.
In essence, strymonas is a DSL that generates high-performance single-core stream processing code from declarative descriptions of stream pipelines and user actions -- something like Yacc. Unlike (ocaml)yacc, strymonas is an embedded DSL. Therefore, it integrates as is with the existing OCaml/Scala code and tools. Any typing or pipeline mis-assembling errors are reported immediately (even during editing).
There are two flavors of the library, with the host language being OCaml and Scala 3. The C generation back-end needs no other dependencies; the OCaml back-end relies on BER MetaOCaml; the Scala backend uses Scala 3 native metaprogramming facilities.
The present strymonas is the completely re-written and the much extended and improved version of the library described in POPL 2017 paper. The main differences are:
Joint work with Aggelos Biboudis, Tomoaki Kobayashi and Nick Palladinos.
<http://strymonas.github.io/>
The official, user-facing repository repository
(not the development repository)
<https://github.com/strymonas/strymonas-ocaml/tree/main/examples/TryFirst>
Step-by-step explanation of the main facilities of the library
<https://github.com/strymonas/strymonas-ocaml/tree/main/examples>
Further, realistic examples: sliding-window, run-length-encoding
<https://github.com/strymonas/strymonas-ocaml/tree/main/benchmarks>
Extensive benchmarks, comparing strymonas with the hand-written code
and other (OCaml) libraries
Complete Stream Fusion for Software-Defined Radio
Stream Fusion, to Completeness
The earlier version of the library
zip
operator and are still an order of magnitude slower than hand-written
loops.
We present the first approach that represents the full generality of stream processing and eliminates overheads, via the use of staging. It is based on an unusually rich semantic model of stream interaction. We support any combination of zipping, nesting (or flat-mapping), sub-ranging, filtering, mapping --of finite or infinite streams. Our model captures idiosyncrasies that a programmer uses in optimizing stream pipelines, such as rate differences and the choice of a ``for'' vs. ``while'' loops. Our approach delivers hand-written--like code, but automatically. It explicitly avoids the reliance on black-box optimizers and sufficiently-smart compilers, offering highest, guaranteed and portable performance.
Our approach relies on high-level concepts that are then readily mapped into an implementation. Accordingly, we have two distinct implementations: an OCaml stream library, staged via MetaOCaml, and a Scala library for the JVM, staged via LMS. In both cases, we derive libraries richer and simultaneously many tens of times faster than past work. We greatly exceed in performance the standard stream libraries available in Java, Scala and OCaml, including the well-optimized Java 8 streams.
Joint work with Aggelos Biboudis, Nick Palladinos and Yannis Smaragdakis.
strymonas.pdf [614K]
<https://arxiv.org/abs/1612.06668>
The complete paper, whose shorter version (without Appendices)
is published in the Proceedings of POPL 2017
doi:10.1145/3009837
<http://strymonas.github.io/>
The complete code for both MetaOCaml and Scala/Java versions
of the strymonas library, and the complete code for all benchmarks.
The code received the Artifact Evaluated
badge from the POPL 2017 artifact evaluation committee.
Even Better Stream Fusion
This talk explains at the end the essence of complete fusion:
eliminating even constant-size intermediary data structures
The joint work with Aggelos Biboudis and Jeremy Gibbons.
Although the diagrams are easy to draw, they are difficult to implement with low latency and in low memory. This talk is about the key optimization: stream fusion, which is combining several simple processing steps into one complex step, reducing the amount of intermediary data and communication overhead. Specifically, we will talk about complete fusion: not just reduction but complete elimination. This is hard, especially for diagrams with "fat pipes" (flatmap) and "joins" (zip).
This talk introduces the ongoing work on strymonas, which is a high-performance code generation library (DSL) that converts a diagram-like specification into hand-written-like code -- with assured complete fusion. We describe the main ideas behind the complete fusion of diagrams with joins, and illustrate on the example of the software FM radio.
<http://www.cs.ox.ac.uk/seminars/2447.html>
The web page of the seminar talk, with the pointer to the YouTube
recording
Joint work with Tomoaki Kobayashi.
Functional stream libraries let us easily build stream processing
pipelines, by composing sequences of simple transformers such as
map or filter with producers (backed by an array, a
file, or a generating function) and consumers (reducers). The purely
applicative approach of building a complex pipeline from simple
immutable pieces simplifies programming and reasoning: the assembled
pipeline is an executable specification. To be practical, however, a
library has to be efficient: at the very least, it should avoid
creating intermediate structures -- especially structures like
files and lists whose size grows with the length of the stream. Even
the bounded-size intermediate structures significantly, up to two
orders of magnitude, slow down the processing. Eliminating the
intermediate structures is the central problem in stream processing:
so-called stream fusion.
Stream fusion has been the subject of intensive research since late 1950's. By now, the low-hanging fruit in stream processing has been all picked up -- although some of it quite recently, POPL 2017. Stream fusion made it to the front page of CACM (May 2017). Java 8 Streams and Haskell compilers, among others, have implemented some of the earlier research results. We have attained a milestone. What are the further challenges?
That was the topic of many discussions at the workshop. Several main questions have come up over and over again:
As a tangible outcome, the meeting has identified a set of problems -- challenges -- to help drive and evaluate further research: filterMax, sorted merge, multiple appends, parallel merge. The report of the meeting discusses them in detail.
The workshop is organized together with Aggelos Biboudis and Martin Odersky. The Shonan seminar series is sponsored by Japan's National Institute of Informatics (NII).
shonan-streams.pdf [280K]
The final report
A stream-wise access to a collection is an important access method, which may even be supported by hardware. For example, Pentium III floating-point extension (Internet Streaming SIMD Extension) lets programmers designate arrays as streams and provides instructions to handle such data efficiently (Internet Streaming SIMD Extensions, Shreekant (Ticky) Thakkar and Tom Huff, Computer, Vol. 32, No. 12, December 1999, pp. 26-34). Streaming is a typical memory access model of DSPs: that's why DSP almost never incorporate a data cache (See ``DSP Processors Hit the Mainstream'', Jennifer Eyre and Jeff Bier, Computer, Vol. 31, No. 8, August 1998, pp. 51-59). A memory architecture designed in the article ``Smarter Memory: Improving Bandwidth for Streamed References'' (IEEE Computer, July 1998, pp.54-63) achieves low overall latencies because the CPU is told by a compiler that a stream operation is to follow. LinAlg offers this streaming access model to an application programmer.
Matrix streams may stride a matrix by an arbitrary amount. This lets us traverse a matrix along the diagonal, by columns, by rows, etc. Streams can be constructed of a Matrix itself, or from other matrix views (MatrixColumn, MatrixRow, MatrixDiag). In the latter case, the streams are confined only to the specific portions of the matrix.
Many functions of LinAlg are written in terms of streams: for example, the computation of vector norms, the addition of a vector to the diagonal or the anti-diagonal of a matrix, Aitken-Lagrange interpolation. Singular value decomposition SVD demonstrates many applications of streams: e.g., multiplying a matrix by a rotation matrix avoids random access to matrix elements and the corresponding range checks and offset calculations. The stream code is also more lucid. One may create a stream that spans over a part of another stream. We use substreams, for example, to efficiently reflect the upper triangle of a square matrix onto the lower one, yielding a symmetric matrix. The SVD computation uses subranging extensively, e.g., for left Householder transformations.
LinAlg's streams may span an arbitrary rectangular block of a matrix, including the whole matrix, a single matrix element, a matrix row or a column, or a part thereof. Assigning a block of one matrix to a block of another takes only one line -- which, due to inlining, is just as efficient as the direct loop with pointer manipulation.
map and take
transform lists, we transform folds. We implement the range of
progressively more complex transformers -- from map,
filter, takeWhile to take, drop, dropWhile,
and finally, zip and zipWith. The standard list API
is also provided.
Emphatically we never convert a stream to a list and so we do not use recursion or recursive types. All iterative processing is driven by the fold itself. Therefore, all operations of the library are assuredly terminating. We only need higher-ranked types, because lists cannot be fully implemented in simply typed lambda-calculus.
The implementation of zip also solves the problem of ``parallel loops''. One can think of a fold as an accumulating loop and realize a nested loop as a nested fold. Representing a parallel loop as a fold is a challenge, answered at the end of the article. This becomes especially interesting in the case of general backtracking computations, or backtracking computations in direct style, with delimited continuations modeling `lists'.
Beyond Church encoding: Boehm-Berarducci isomorphism of algebraic data types and polymorphic lambda-terms
LogicT: backtracking monad transformer with fair operations and pruning
which illustrates the close connection with foldr/build
list-fusion, aka ``short-cut deforestation''.
Predecessor and lists are not representable in
simply-typed lambda calculus
Therefore, higher-rank or recursive/inductive types are necessary for lists
Parallel composition of streams: several sources to one sink
Folding over multiple streams using monad transformers