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Mathematica Wins the More Digits Friendly Competition

Published September 12, 2006

August 9, 2006–Wolfram Research cemented its position as the leader in high-precision arithmetic with a first-place finish in the More Digits Friendly Competition during the 7th Conference on Real Numbers and Computers on July 10, 2006. Hosted by Loria, a French research lab, the competition measured various programs’ speed, accuracy, and precision at solving a series of difficult numerical problems.

The Wolfram team, using Mathematica as its computing package, was the only team to answer each problem, the only team with all solutions correct, and the fastest team overall, finishing all 32 problems in less than three minutes. In many cases, Mathematica was an order of magnitude faster than the next competitor. The full results are available online.

“With its general precision-tracking mechanism and task-oriented superfunctions, Mathematica was able to produce accurate results quickly and reliably,” said Roger Germundsson, director of research and development at Wolfram. “We were happy to get the chance to show off several crucial and completely unique features in Mathematica designed for these types of tasks.”

The competition challenged teams to use any computer program to calculate answers to math problems with up to a million digits of precision–far beyond the 16-digit limit of most everyday computer programs. Mathematica is the perfect system to handle jobs like this, because there are virtually no limits to its extended-precision computation. In fact, Mathematica is capable of arbitrary-precision arithmetic, which means the only practical limit to a result’s precision is the memory available for computation.

The most efficient method for a given calculation depends on the size of the numbers involved and the precision required in the result, so if either of these changes, a different method might be much faster. With Mathematica, changing a calculation’s precision is a simple matter of setting an option. Mathematica then selects the best method on the fly.

Accuracy was also essential. Many of the problems in the competition were examples of mathematical chaos, meaning that tiny inaccuracies in the repetitions of a calculation could result in enormous errors in the final result. Mathematica‘s numerical-precision tracking ensures that each calculation retains the appropriate precision so that the final result is always correct. With the freedom to concentrate on the math and not on error-checking, the Wolfram team was able to solve many problems with a single line of Mathematica code each.

“There’s little doubt that Mathematica is the most elegant language for high-precision computations, but most people think that elegance in code comes at the expense of speed. The results of the competition show that exactly the opposite is true,” said Germundsson. “The other teams did a terrific job, but Mathematica gave us the edge.”

To learn about more features that make calculating with Mathematica fast, easy, and accurate, please see the Wolfram Technology Guide.