How much precision and range is needed for decimal arithmetic?
This depends, of course, on the application. Let’s consider financial applications. For these applications, values similar to the Gross National Product (GNP) of large countries give an idea of the largest values needed to represent a good range of currency values exactly. Two examples of these are the USA (in cents) and Japan (in Yen). Both of these need values up to about 1015 (a recent GDP number for the USA was $8,848,200,000,000.00, and for Japan ¥554,820,000,000,000). If stored in a fixed-point representation, these would require 15 digits. When carrying out calculations, more precision and range is needed because currency values are often multiplied by very precise numbers. For example, if a daily interest rate multiplier, R, is (say) 1.000171 (0.0171%, or roughly 6.4% per annum) then the exact calculation of the yearly rate in a non-leap year is R raised to the power of 365. To calculate this to give an exact (unrounded) result needs 2191 digits (both the Java BigDecimal class
