Livermore loops (also known as the Livermore Fortran kernels or LFK) is a
benchmark for
parallel computers. It was created by Francis H. McMahon from scientific
source code
In computing, source code, or simply code or source, is a plain text computer program written in a programming language. A programmer writes the human readable source code to control the behavior of a computer.
Since a computer, at base, only ...
run on computers at
Lawrence Livermore National Laboratory
Lawrence Livermore National Laboratory (LLNL) is a Federally funded research and development centers, federally funded research and development center in Livermore, California, United States. Originally established in 1952, the laboratory now i ...
. It consists of 24
do loops, some of which can be vectorized, and some of which cannot.
The benchmark was published in 1986 in ''Livermore fortran kernels: A computer test of numerical performance range''.
The Livermore loops were originally written in
Fortran, but have since been ported to many programming languages.
Each loop carries out a different mathematical kernel
.
Those kernels
[Xingfu Wu. Performance Evaluation, Prediction and Visualization of Parallel Systems. Springer, 1999. {{ISBN, 0-7923-8462-8. Page 144.]
are:
*
hydrodynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in ...
fragment
* incomplete
Cholesky conjugate gradient
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite. The conjugate gradient method is often implemented as an it ...
*
inner product
In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, ofte ...
* banded
linear system
In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator.
Linear systems typically exhibit features and properties that are much simpler than the nonlinear case.
As a mathematical abstractio ...
s solution
* tridiagonal linear systems solution
* general
linear recurrence
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear ...
equations
*
equation of state
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most mo ...
fragment
* alternating direction
implicit integration
*
integrate predictors
*
difference predictors
* first sum
*
first difference
* 2-D particle in a cell
* 1-D particle in a cell
* casual Fortran
*
Monte Carlo
Monte Carlo ( ; ; or colloquially ; , ; ) is an official administrative area of Monaco, specifically the Ward (country subdivision), ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is located. Informally, the name also refers to ...
search
* implicit
conditional computation
* 2-D explicit hydrodynamics fragment
* general linear recurrence equations
* discrete
ordinates transport
*
matrix-matrix transport
*
Planckian distribution
* 2-D implicit hydrodynamics fragment
* location of a first array minimum.
References
External links
Livermore Loops, Fortran versionLivermore Loops, C version
Parallel computing
Supercomputer benchmarks