Mathematica Wins the More Digits Friendly Competition
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.
| 
