The data representation clause of the contract specifies the source, type of error, and format of input and output data. There are two choices for source which are ``user-supplied'' and ``computed''. User-supplied means that the data is input by user. Computed means that the value is output from the application program. This information is necessary for the computation of output error.
The term error applies to both input and output values. When an error of zero is explicitly demanded on either input or output for an numerical algorithms, the user incurs the sometimes high price of that demand. Otherwise, the error can be stated or calculated in either absolute or relative amounts. One way to calculate error is by use of interval arithmetic techniques [12,15]. Ordinarily, error is applied only to numeric values. However, the term can be generalized. For example, a misspelled word in text may be thought of as a correctable and/or measurable error.
In the next subclause, the end user specifies the format of numeric values. The end user has the option of working in the binary or decimal number system. A wide variety of non-numeric formats can also exist. For now, we are choosing to ignore the variety of choices; however, in the future the non-numeric values may need to be developed.
Finally, the range, precision, and uncertainty of numeric values are specified by the user through a length adjustable, number template which is in exponential form. Absolute error is specified by omitting the trailing percent sign; relative error is specified with the percent sign.
All of the specifications in the data representation clause are applied to one or more variables specified in a variable list. Use of the clause may be repeated any arbitrary number of times for different variable lists.