Prospects for using variable precision interval software in C++ for solving some contemporary
Jeffery Stewart Ely · 1990
The floating point hardware/software used in modern scientific computing results in round-off error which can be catastrophic. Common numerical schemes for detecting catastrophic round-off are unreliable and analytic attempts to estimate it are often as difficult as (or worse than) the original problem. Interval software, in place of floating point, is capable of detecting catastrophic round-off, but variable precision is crucial to eliminating it. The author has implemented variable precision interval software in C++. The choice of C++ has permitted the construction of operators and functions operating on variable precision intervals that are as familiar and natural for scientific programmers to use as floating point is in FORTRAN. This software has been applied by the author to the solution of the Birkhoff-Rott equation, a problem in vortex dynamics, to give, for the first time, reliable data describing the equation's evolution in time toward the development of a curvature singularity. Previous researchers, having been surprised by the onset of chaos in a discrete representation of the problem, have been unable to rule out round-off error as the cause. The author's computation indicates that the chaotic behavior persists despite strict control of the round-off error. To achieve this, precisions as high as 1000 bits had to be used, requiring the dedicated services of an advanced workstation for several days. The possibilities for parallel computation have been tentatively explored with the idea that such an approach or specialized hardware will bring other such problems within range.