Gravity Pipe (abbreviated GRAPE) is a project which uses
hardware acceleration to perform
gravitational computations. Integrated with
Beowulf
''Beowulf'' (; ) is an Old English poetry, Old English poem, an Epic poetry, epic in the tradition of Germanic heroic legend consisting of 3,182 Alliterative verse, alliterative lines. It is one of the most important and List of translat ...
-style commodity computers, the GRAPE system calculates the
force
In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
of gravity that a given
mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
, such as a
star
A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
, exerts on others.
The project resides at
University of Tokyo.
The GRAPE hardware acceleration component "pipes" the force computation to the general-purpose computer serving as a node in a
parallelized cluster as the innermost loop of the gravitational model.
The GRAPE project designed an
ASIC component with mathematical logic and operations to generate the required computations. This means the latter generations of GRAPE supercomputers, despite not providing a
Turing complete computational processing power, are powerful for heavily mathematical super-computing usages. The MD-GRAPE 3 supercomputer was also used in
protein folding simulations.
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 system (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-point arithmetic
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that ba ...
for more accurate calculation of such forces. The advantage of the logarithmic-arithmetic versions is that 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.
GRAPE-DR consists of a large number of simple processors, all operating in the
SIMD
Single instruction, multiple data (SIMD) is a type of parallel computer, parallel processing in Flynn's taxonomy. SIMD describes computers with multiple processing elements that perform the same operation on multiple data points simultaneousl ...
fashion.
Application
GRAPE computes approximate solutions to the historically intractable
''n''-body problem, which is of interest in
astrophysics 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 ''n''
2.
GRAPE assists in calculations of interactions between particles where the interaction scales as ''r''
−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
biology
Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...
, where the force considered would be electrical rather than gravitational.
In 1999,
Marseilles Observatory published a study on simulating the formation of proto-planets and plantessimals with a large planetary body.
This simulation used the GRAPE-4 system.
Prizes
The LNS-based GRAPE-5 architecture won the Price Performance category of the
Gordon Bell Prize in 1999, at about $7 per
MegaFLOPS. This category measures the price efficiency of a particular machine in terms of the price in dollars per megaFLOPS. The particular implementation "Grape-6" also won prizes in 2000 and 2001 (see external links).
Grape-DR was ranked first in the June 2010 Little Green500 List,
a ranking of supercomputer's
performance per unit power consumption published by the Green500.org.
See also
* The
Gordon Bell Prize, named in honor of
Gordon Bell, is administered by the
Association for Computing Machinery
The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional membe ...
.
*
Supercomputer
A supercomputer is a type of computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instruc ...
and
High-performance computing
High-performance computing (HPC) is the use of supercomputers and computer clusters to solve advanced computation problems.
Overview
HPC integrates systems administration (including network and security knowledge) and parallel programming into ...
are main articles on the general subject.
*
gravitySimulator is a cluster containing 32 GRAPEs.
References
External links
The GRAPE site at the University of Tokyo
The Top 500 List{{Webarchive, url=https://web.archive.org/web/20090508054042/http://www.ids.ias.edu/~piet/act/comp/hardware/index.html , date=2009-05-08
Supercomputers
Supercomputing in Japan