John Gustafson will unveil the Ubox Method, an all-new approach to parallelism as part of his upcoming keynote at the Multicore World 2014 conference next week in Auckland, New Zealand. A 36-year veteran of the computing industry, Gustafson best known for Gustafson’s Law and is currently CTO of Ceranovo Inc.
According to press reports, the Ubox Method will change peoples’ concepts of what is possible with multicore and parallel programming.
Imagine doing a nonlinear ordinary differential equation (ODE) with time stepping, like the exact equation of a pendulum swinging,” said Gustafson. “You get rounding error as you march through the time steps, and sampling error since you have to approximate variable acceleration and velocity with constants, but worst of all, you HAVE to perform the calculation sequentially. With my new method, you turn the problem sideways and compute the time spent in each region of space, since velocity and acceleration are functions of spatial position. Time is a function of position, instead of the other way around. Guess what that lets you do? Compute all the behaviour in parallel! I can solve a nonlinear ODE with a rigorous bound, no rounding error, no sampling error, and DO IT WITH A MILLION PROCESSORS for more speed and accuracy, if I have that many.”
So what is the Ubox Method? Gustafson’s abstract offers us a few clues:
It is time to overthrow a century of numerical analysis. Current methods are based on the acceptance of rounding error and sampling error using numerical representations that were invented in 1914 and algorithms designed for a time when transistors were expensive. The pursuit of exascale floating point is ridiculous, since we do not need to be making 10^18 sloppy rounding errors per second; we need instead to get provable, valid results for the first time, by turning the speed of parallel computers into higher quality answers instead of more junk per second. The ubox method, based on a new numerical format that uses metadata to store more information using fewer bits, creates a the richest source of data parallelism since the Monte Carlo method, and redefines what is meant by “high performance”. Examples are given for practical application to structural analysis, radiation transfer, the n-body problem, linear and nonlinear systems of equations, and Laplace’s equation that suggest that the ubox method is general and can replace the ‘bag of tricks’ we currently use to solve technical computing problems.”
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