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.
Its shortened name, GRAPE, was chosen as an intentional reference to the Apple Inc. line of computers.
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 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 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.
The LNS-based GRAPE-3 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 implemenation "Grape-6" also won prizes in 2000 and 2001 (see external links).
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