Gravity Pipe
Encyclopedia
Gravity Pipe, otherwise known as GRAPE, is a project which uses hardware acceleration
to perform gravitational computations. Integrated with Beowulf
-style commodity computers, the GRAPE system calculates the force
of gravity that a given mass
, such as a star, exerts on others. The project resides at Tokyo University.
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.
(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 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. GRAPE-DR consists of a large number of simple processors, all operating in the SIMD
fashion.
, 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 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 biology
, where the force considered would be electrical rather than gravitational.
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 implemenation "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.
Hardware acceleration
In computing, Hardware acceleration is the use of computer hardware to perform some function faster than is possible in software running on the general-purpose CPU...
to perform gravitational computations. Integrated with Beowulf
Beowulf (computing)
A Beowulf cluster is a computer cluster of what are normally identical, commodity-grade computers networked into a small local area network with libraries and programs installed which allow processing to be shared among them...
-style commodity computers, the GRAPE system calculates the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
of gravity that a given mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, 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
Parallel 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 SystemLogarithmic Number System
A 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 point
Floating point
In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...
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. GRAPE-DR consists of a large number of simple processors, all operating in the SIMD
SIMD
Single instruction, multiple data , is a class of parallel computers in Flynn's taxonomy. It describes computers with multiple processing elements that perform the same operation on multiple data simultaneously...
fashion.
Application
GRAPE computes approximate solutions to the historically intractable n-body problemN-body problem
The n-body problem is the problem of predicting the motion of a group of celestial objects that interact with each other gravitationally. Solving this problem has been motivated by the need to understand the motion of the Sun, planets and the visible stars...
, which is of interest in astrophysics
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
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 biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
, where the force considered would be electrical rather than gravitational.
Prizes
The LNS-based GRAPE-5 architecture won the Price Performance category of the Gordon Bell PrizeGordon 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 the Supercomputing Conference to recognize outstanding achievement in high-performance computing applications...
in 1999, at about $7 per MegaFLOPS
FLOPS
In computing, 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).
Grape-DR was ranked first in the June 2010 Little Green500 List, a ranking of supercomputer's performance per unit power consumption
Performance per watt
In computing, performance per watt is a measure of the energy efficiency of a particular computer architecture or computer hardware. Literally, it measures the rate of computation that can be delivered by a computer for every watt of power consumed....
published by the Green500.org.
See also
- The Gordon Bell PrizeGordon 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 the Supercomputing Conference to recognize outstanding achievement in high-performance computing applications...
, named in honor of Gordon BellGordon BellC. Gordon Bell is an American 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 MachineryAssociation for Computing MachineryThe Association for Computing Machinery 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...
. - SupercomputerSupercomputerA supercomputer is a computer at the frontline of current processing capacity, particularly speed of calculation.Supercomputers are used for highly calculation-intensive tasks such as problems including quantum physics, weather forecasting, climate research, molecular modeling A supercomputer is a...
and High-performance computingHigh-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. - gravitySimulatorGravitySimulatorgravitySimulator is a novel supercomputer that incorporates special-purpose GRAPE hardware to solve the gravitational N-body problem. It is housed in the Center for Computational Relativity and Gravitation at the Rochester Institute of Technology...
is a cluster containing 32 GRAPEs.