A data processing system 10 comprises an arbitrary precision number C++ class program code 18, which incorporates arbitrary precision arithmetic. The arbitrary precision number program code 18 resides in a client program 14 and never lose bits of precision by maintaining an internal data structure 16, which holds the data, and by manipulating that data by operators and methods which the program code 18 defines. The program code 18, which is embedded in a client program 14, comprises a method that uses "lazy" storage allocation for transparent data management for the arbitrary precision number in the internal data array 22, a "lazy" arithmetic evaluation for avoiding more costly arithmetic operations, a width method for an optimized significant bit calculation, and a method for efficient determining the number of trailing zeros method for more efficient IEEE floating point math emulation operations.