Using multiple-precision arithmetic

High-precision arithmetic is useful in many different computational problems. The most common is a numerically unstable algorithm, for which, say, 53-bit (ANSI/IEEE 754-1985 Standard) double precision would not yield a sufficiently accurate result.. For most current machines, 53-bit double precision is the highest provided in hardware, giving about 16 significant digits. (By "significant digits", I mean the number of equivalent decimal digits of precision, rather than the number with base /spl ne/ 10.) Calculating with 30 or 40 significant digits can often overcome the algorithm's instability and provide adequate accuracy. In the article, I give some examples of calculations in which multiple precision can be useful.