For a thorough presentation of our framework, please read our recently accepted journal article, "BLIS: A Framework for Rapidly Instantiating BLAS Functionality". For those who just want an executive summary, please see the next section.
In a follow-up article, "The BLIS Framework: Experiments in Portability", we investigate using BLIS to instantiate level-3 BLAS implementations on a variety of general-purpose, low-power, and multicore architectures.
An IPDPS'14 conference paper titled "Anatomy of High-Performance Many-Threaded Matrix Multiplication" systematically explores the opportunities for parallelism within the five loops that BLIS exposes in its matrix multiplication algorithm.
It is our belief that BLIS offers substantial benefits in productivity when compared to conventional approaches to developing BLAS libraries, as well as a much-needed refinement of the BLAS interface, and thus constitutes a major advance in dense linear algebra computation. While BLIS remains a work-in-progress, we are excited to continue its development and further cultivate its use within the community.
BLIS offers several advantages over traditional BLAS libraries:
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Portability that doesn't impede high performance. Portability was a top
priority of ours when creating BLIS. With zero additional effort on the part of
the developer, BLIS is configurable as a fully-functional reference
implementation. But more importantly, the framework identifies and isolates a
key set of computational kernels which, when optimized, immediately and
automatically optimize performance across virtually all level-2 and level-3
BLIS operations. In this way, the framework acts as a productivity multiplier.
And since the optimized (non-portable) code is compartmentalized within these
few kernels, instantiating a high-performance BLIS library on a new
architecture is a relatively straightforward endeavor.
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Generalized matrix storage. The BLIS framework exports interfaces that
allow one to specify both the row stride and column stride of a matrix. This
allows one to compute with matrices stored in column-major order, row-major
order, or by general stride. (This latter storage format is important for those
seeking to implement tensor contractions on multidimensional arrays.)
Furthermore, since BLIS tracks stride information for each matrix, operands of
different storage formats can be used within the same operation invocation. By
contrast, BLAS requires column-major storage. And while the CBLAS interface
supports row-major storage, it does not allow mixing storage formats.
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Full support for the complex domain. BLIS operations are developed and
expressed in their most general form, which is typically in the complex domain.
These formulations then simplify elegantly down to the real domain, with
conjugations becoming no-ops. Unlike the BLAS, all input operands in BLIS that
allow transposition and conjugate-transposition also support conjugation
(without transposition), which obviates the need for thread-unsafe workarounds.
Also, where applicable, both complex symmetric and complex Hermitian forms are
supported. (BLAS omits some complex symmetric operations, such as
symv,syr, andsyr2.)
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Advanced multithreading support. BLIS allows multiple levels of
symmetric multithreading for nearly all level-3 operations. (Currently, users
may choose to obtain parallelism via either OpenMP or POSIX threads). This
means that matrices may be partitioned in multiple dimensions simultaneously to
attain scalable, high-performance parallelism on multicore and many-core
architectures. The key to this innovation is a thread-specific control tree
infrastructure which encodes information about the logical thread topology and
allows threads to query and communicate data amongst one another. BLIS also
employs so-called "quadratic partitioning" when computing dimension sub-ranges
for each thread, so that arbitrary diagonal offsets of structured matrices with
unreferenced regions are taken into account to achieve proper load balance.
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Ease of use. The BLIS framework, and the library of routines it
generates, are easy to use for end users, experts, and vendors alike. An
optional BLAS compatibility layer provides application developers with
backwards compatibility to existing BLAS-dependent codes. Or, one may adjust or
write their application to take advantage of new BLIS functionality (such as
generalized storage formats or additional complex operations) by calling BLIS
directly. BLIS's interfaces will feel familiar to many veterans of BLAS since
BLIS exports APIs with BLAS-like calling sequences. And experts will find
BLIS's internal object-based APIs a delight to use when customizing or writing
their own BLIS operations. (Objects are relatively lightweight
structsand passed by address, which helps tame function calling overhead.)
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Multilayered API and exposed kernels. The BLIS framework exposes its
implementations in various layers, allowing expert developers to access exactly
the functionality desired. This layered interface includes that of the
lowest-level kernels, for those who wish to bypass the bulk of the framework.
Optimizations can occur at various levels, in part thanks to exposed packing
and unpacking facilities, which by default are highly parameterized and
flexible.
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Functionality that grows with the community's needs. As its name
suggests, the BLIS framework is not a single library or static API, but rather
a nearly-complete template for instantiating high-performance BLAS-like
libraries. Furthermore, the framework is extensible, allowing developers to
leverage existing components to support new operations as they are identified.
If such operations require new kernels for optimal efficiency, the framework
and its APIs will be adjusted and extended accordingly.
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Code re-use. Auto-generation approaches to achieving the aforementioned
goals tend to quickly lead to code bloat due to the multiple dimensions of
variation supported: operation (i.e.
gemm,herk,trmm, etc.); parameter case (i.e. side, [conjugate-]transposition, upper/lower storage, unit/non-unit diagonal); datatype (i.e. single-/double-precision real/complex); matrix storage (i.e. row-major, column-major, generalized); and algorithm (i.e. partitioning path and kernel shape). These "brute force" approaches often consider and optimize each operation or case combination in isolation, which is less than ideal when the goal is to provide entire libraries. BLIS was designed to be a complete framework for implementing basic linear algebra operations, but supporting this vast amount of functionality in a manageable way required a holistic design that employed careful abstractions, layering, and recycling of generic (highly parameterized) codes, subject to the constraint that high performance remain attainable.
- A foundation for mixed domain and/or mixed precision operations. BLIS was designed with the hope of one day allowing computation on real and complex operands within the same operation. Similarly, we wanted to allow mixing operands' floating-point precisions, or both domain and precision. Unfortunately, this feature results in a significant amount of additional code, mostly in level-2 and lower operations, thus, it is disabled by default. However, mixing domains in level-3 operations is possible, in theory, with almost no additional effort on the part of the library developer, and such operations would remain capable of high performance. (Please note that this functionality is still highly experimental and should be thought of as a feature that will be more thoroughly implemented at some future date.)
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