Livermore loops (also known as the Livermore Fortran kernels or LFK) is a

benchmark Benchmark may refer to: Business and economics * Benchmarking, evaluating performance within organizations * Benchmark price * Benchmark (crude oil), oil-specific practices Science and technology * Benchmark (surveying), a point of known elevatio ...

for

parallel computers Parallel computing is a type of computing, computation in which many calculations or Process (computing), processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. ...

. It was created by Francis H. McMahon from scientific

source code In computing, source code, or simply code, is any collection of code, with or without comments, written using a human-readable programming language, usually as plain text. The source code of a program is specially designed to facilitate the wo ...

run on computers at

Lawrence Livermore National Laboratory Lawrence Livermore National Laboratory (LLNL) is a federal research facility in Livermore, California, United States. The lab was originally established as the University of California Radiation Laboratory, Livermore Branch in 1952 in response ...

. 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 kernelsXingfu Wu. Performance Evaluation, Prediction and Visualization of Parallel Systems. Springer, 1999. {{ISBN, 0-7923-8462-8. Page 144. are: *

hydrodynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...

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-definite. The conjugate gradient method is often implemented as an iterative ...

inner product In mathematics, an inner product space (or, rarely, a Hausdorff space, Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation (mathematics), operation called an inner product. The inner product of two ve ...

* 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 abstraction o ...

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, chemistry, and thermodynamics, 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 ...

fragment * alternating direction implicit integration * integrate predictors * difference predictors * first sum *

first difference In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a paramete ...

* 2-D particle in a cell * 1-D particle in a cell * casual Fortran *

Monte Carlo Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...

search * implicit conditional computation * 2-D explicit hydrodynamics fragment * general linear recurrence equations * discrete ordinates transport * matrix-matrix transport *

Planckian distribution In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature , when there is no net flow of matter or energy between the body and its environment. At ...

* 2-D implicit hydrodynamics fragment * location of a first array minimum.

References

External links

Livermore Loops, Fortran version

Livermore Loops, C version
Parallel computing Supercomputer benchmarks