Ada 9 X Project Report The Fixed - Point Facility in Ada

This report addresses a number of issues involving fixed-point arithmetic in Ada. A number of possible Ada 9X requirements are suggested for consideration. Ada includes a facility for declaration of and arithmetic on fixed-point values. The model is deliberately intended to be as close as possible to the Ada floating-point model, including the notion of model numbers and model intervals. The major difference is that the error is absolute, rather than relative; in other words, the model numbers are spaced evenly in the fixed-point case. This fixed-point facility is intended for a variety of uses: • ‘‘Poor man’s floating-point.’’ On machines where floating-point hardware is either non-existent, or very inefficient, the use of Ada floating-point may be impractical. Ada requires that floating-point arithmetic be present on all Ada implementations, but if this is achieved by software simulation, there will be cases where the use of floatingpoint is impractical for efficiency reasons. On such machines, the use of fixed-point provides a capability for carrying out calculations with fractional quantities more efficiently. Even when reasonably efficient hardware floating-point is available, fixed-point arithmetic is often faster, and in some real-time applications which are computation-bound at critical points, this difference may be significant. • Increased accuracy. In a situation where the absolute error control of fixed-point is acceptable, e.g., a case where the range of values to be dealt with is limited, fixedpoint provides more accuracy than floating point for a given word length, since no space is wasted for the exponent. • Mapping data from specialized hardware and other external data. There are a number of situations in which data from external devices is naturally in fixed-point format, -8 for instance a volt-meter may return a voltage in units of 2 volts. In such cases it is both efficient and convenient to deal with the data directly in fixed-point format. • A special, but important, case of external world fixed-point data arises in fiscal calculations, where quantities of money are typically decimal scaled fixed-point values (e.g., $56.34). In commercial programs which deal with money, it is much more convenient to deal with such quantities directly in fixed-point form. The use of floatingpoint here is not practical because the decimal values encountered are not floatingpoint model numbers, and hence unexpected rounding and truncation errors can occur (e.g., 0.10 10 is not necessarily equal to 1.00). *