Gravity Pipe (abbreviated GRAPE) is a project which uses

hardware acceleration Hardware acceleration is the use of computer hardware designed to perform specific functions more efficiently when compared to software running on a general-purpose central processing unit (CPU). Any transformation of data that can be calcula ...

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 University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...

. 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 An application-specific integrated circuit (ASIC ) is an integrated circuit (IC) chip customized for a particular use, rather than intended for general-purpose use, such as a chip designed to run in a digital voice recorder or a high-efficien ...

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 Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. He was highly influential in the development of theoretical comput ...

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. Apple Inc. is an American multinational corporation and technology company headquartered in Cupertino, California, in Silicon Valley. It is best known for its consumer electronics, software, and services. Founded in 1976 as Apple Comput ...

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 A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing. Overview A number, X, is represented in an LNS by two components: the loga ...

(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 Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...

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 astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, which was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in ...

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 A galaxy is a system of stars, stellar remnants, interstellar gas, dust, and dark matter bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar Sys ...

(gravitation force scales as ''r''⁻²). Similar problems exist in

molecular chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and compounds made of atoms, molecules and ions: their com ...

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 Marseille Observatory () is an astronomical observatory located in Marseille, France, with a history that goes back to the early 18th century. In its 1877 incarnation, it was the discovery site of a group of galaxies known as Stephan's Quintet, ...

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 The Gordon Bell Prize is an award presented by the Association for Computing Machinery each year in conjunction with the SC Conference series (formerly known as the Supercomputing Conference). The prize recognizes outstanding achievement in hig ...

in 1999, at about $7 per

MegaFLOPS Floating point operations per second (FLOPS, flops or flop/s) is a measure of computer performance in computing, useful in fields of scientific computations that require floating-point calculations. For such cases, it is a more accurate measur ...

. 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.

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

Method

Application

Prizes

See also

References

External links