In his paper, Yasuda notes that since roundoff error should be unbiased and nearly random, the sum of N single-precision numbers
with an absolute value, s, contains the relative error of [2.sup.-23][sN.sup.-1/2] and that the error estimate will decrease as the number of terms increases.
We have assumed that the hardware supports double-precision arithmetic and that the double-precision format holds at least two digits more than in the product of two single-precision numbers, a condition met by IEEE floating point [ANSI 1985].
The result is returned as four single-precision numbers.
Figure 4 shows one way to add two numbers in the single-single format and return the leading quad-precision part of the result in four single-precision numbers. Each such addition takes 12 floating-point operations.
Numeric variables can be convened to string variables by using the MKS$, MKI$, or MKD$ functions for single-precision numbers
, integers, and double-precision numbers, respectively.