Gravity Pipe, otherwise known as GRAPE, is a project which uses
hardware accelerationIn computing, hardware acceleration is the use of hardware to perform some function faster than is possible in software running on the general purpose CPU...
to perform gravitational computations. Integrated with
BeowulfOriginally referring to a specific computer built in 1994, Beowulf is a class of computer clusters similar to the original NASA system. They are high-performance parallel computing clusters of inexpensive personal computer hardware...
-style commodity computers, the GRAPE system calculates the
forceIn physics, a force is any agent that causes a change in the motion of a free body, or that causes stress in a fixed body. It can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a...
of gravity that a given
massIn physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass...
, such as a star, exerts on others. The project resides at Tokyo University.
The acronym GRAPE derives from "GRAvity PipE", the capitalization used by the authors of the system on their websites.
Gravity Pipe, otherwise known as GRAPE, is a project which uses
hardware accelerationIn computing, hardware acceleration is the use of hardware to perform some function faster than is possible in software running on the general purpose CPU...
to perform gravitational computations. Integrated with
BeowulfOriginally referring to a specific computer built in 1994, Beowulf is a class of computer clusters similar to the original NASA system. They are high-performance parallel computing clusters of inexpensive personal computer hardware...
-style commodity computers, the GRAPE system calculates the
forceIn physics, a force is any agent that causes a change in the motion of a free body, or that causes stress in a fixed body. It can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a...
of gravity that a given
massIn physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass...
, such as a star, exerts on others. The project resides at Tokyo University.
Nomenclature
The acronym GRAPE derives from "GRAvity PipE", the capitalization used by the authors of the system on their websites. The GRAPE hardware acceleration component "pipes" the force computation to the general-purpose computer serving as a node in a
parallelized clusterParallel computing is a form of computation in which many calculations are carried out simultaneously, operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently . There are several different forms of parallel computing: bit-level,...
as the innermost loop of the gravitational model.
Its shortened name, GRAPE, was chosen as an intentional reference to the Apple Inc. line of computers.
Method
The primary calculation in GRAPE hardware is a summation of the forces between a particular star and every other star in the simulation. Several versions (GRAPE-1, GRAPE-3 and GRAPE-5) use the
Logarithmic Number SystemA logarithmic number system is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing.-Theory:...
(LNS) in the pipeline to calculate the approximate force between two stars, and take the antilogarithms of the x, y and z components before adding them to their corresponding total. The GRAPE-2, GRAPE-4 and GRAPE-6 use
floating pointIn computing, floating point describes a system for numerical representation in which a string of digits represents a rational number....
arithmetic for more accurate calculation of such forces. The advantage of the logarithmic-arithmetic versions is they allow more and faster parallel pipes for a given hardware cost because all but the sum portion of the GRAPE algorithm (1.5 power of the sum of the squares of the input data divided by the input data) is easy to perform with LNS.
Application
GRAPE computes approximate solutions to the historically intractable
n-body problemTo understand the motion of celestial bodies, the sun, planets and the visible stars has been the main motivation for the -body problem. The first complete mathematical formulation of this problem appeared in Newton's Principia...
, which is of interest in
astrophysicsAstrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects such as galaxies, stars, planets, exoplanets, and the interstellar medium, as well as their...
and celestial mechanics.
n refers to the number of celestial bodies in a given problem. While the 2-body problem was solved by Kepler's Laws in the 17th century, any calculation where n > 2 has historically been a nigh-impossible challenge. An analytical solution exists for n = 3 although the resulting series converges too slowly to be of practical use. For n > 2 solutions are generally calculated numerically by determining the interaction between all particles. Thus, the calculation scales as n².
GRAPE assists in calculations of interactions between particles where the interaction scales as x
-2. This dependence is hardwired, drastically improving calculation times. These problems include the evolution of galaxies (gravitation force scales as r
-2). Similar problems exist in molecular chemistry and
biologyBiology is the natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy...
, where the force considered would be electrical rather than gravitational.
Prizes
The LNS-based GRAPE-3 architecture won the Price Performance category of the
Gordon Bell PrizeThe Gordon Bell Prizes are a set of awards awarded by the Association for Computing Machinery in conjunction with the Institute of Electrical and Electronics Engineers each year at to recognize outstanding achievement in high-performance computing applications. The main purpose of the award is to...
in 1999, at about $7 per
MegaFLOPSIn computing, FLOPS is an acronym meaning FLoating point Operations Per Second. The FLOPS is a measure of a computer's performance, especially in fields of scientific calculations that make heavy use of floating point calculations, similar to the older, simpler, instructions per second...
. This category measures the price efficiency of a particular machine in terms of the price in dollars per megaFLOPS. The particular implemenation "Grape-6" also won prizes in 2000 and 2001 (see external links).
See also
- The Gordon Bell Prize
The Gordon Bell Prizes are a set of awards awarded by the Association for Computing Machinery in conjunction with the Institute of Electrical and Electronics Engineers each year at to recognize outstanding achievement in high-performance computing applications. The main purpose of the award is to...
, named in honor of Gordon BellC. Gordon Bell is a computer engineer and manager. An early employee of Digital Equipment Corporation 1960–1966, Bell designed several of their PDP machines and later became Vice President of Engineering 1972-1983, overseeing the development of the VAX...
, is administered by the Association for Computing MachineryThe Association for Computing Machinery, or ACM, is a learned society for computing. It was founded in 1947 as the world's first scientific and educational computing society. Its membership is more than 92,000 as of 2009...
.
- Supercomputer
A supercomputer is a computer that is at the frontline of current processing capacity, particularly speed of calculation. Supercomputers were introduced in the 1960s and were designed primarily by Seymour Cray at Control Data Corporation , and led the market into the 1970s until Cray left to form...
and High-performance computingHigh-performance computing uses supercomputers and computer clusters to solve advanced computation problems. Today, computer systems approaching the teraflops-region are counted as HPC-computers.-Overview:...
are main articles on the general subject.
- gravitySimulator
gravitySimulator is a novel supercomputer that incorporates special-purpose GRAPE hardware to solve the gravitational N-body problem. It was designed by Rainer Spurzem and David Merritt and funded via grants from the National Science Foundation, NASA, and the Space Telescope Science...
is a cluster containing 32 GRAPEs.
External links