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 calculat ...

to perform gravitational computations. Integrated with

Beowulf ''Beowulf'' (; ang, Bēowulf ) is an Old English epic poem in the tradition of Germanic heroic legend consisting of 3,182 alliterative lines. It is one of the most important and most often translated works of Old English literature. The ...

-style commodity computers, the GRAPE system calculates the

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...

of gravity that a given

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementa ...

, such as a

star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth ma ...

, exerts on others. The project resides at

Tokyo University , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project b ...

. 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. Its shortened name, GRAPE, was chosen as an intentional reference to the

Apple Inc. Apple Inc. is an American multinational technology company headquartered in Cupertino, California, United States. Apple is the largest technology company by revenue (totaling in 2021) and, as of June 2022, is the world's biggest company b ...

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 In an LNS, a number, X, is represented by the logarithm, x, of its ...

(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 that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be r ...

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 processing in Flynn's taxonomy. SIMD can be internal (part of the hardware design) and it can be directly accessible through an instruction set architecture (ISA), but it should ...

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 said, Astrophysics "seeks to ascertain the nature of the he ...

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 between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbi ...

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, 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 System. ...

(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 natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties, ...

and

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...

, 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 The Gordon Bell Prize, commonly referred to as the Nobel Prize of Supercomputing, is an award presented by the Association for Computing Machinery each year in conjunction with the SC Conference series (formerly known as the Supercomputing Conferen ...

in 1999, at about $7 per

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

. 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

{{Webarchive, url=https://web.archive.org/web/20150926185006/http://www.sc2000.org/bell/pastawrd.htm , date=2015-09-26
The Top 500 List

Supercomputers Supercomputing in Japan

Method

Application

Prizes

See also

References

External links