6.5.1 Avoiding Simple Underflow

Some applications actually do a lot of computation very near zero. This is common in algorithms computing residuals or differential corrections. For maximum numerically safe performance, perform the key computations in extended precision arithmetic. If the application is a single-precision application, you can perform key computations in double precision.

Example: A simple dot product computation in single precision:

      sum = 0
      DO i = 1, n
         sum = sum + a(i) * b(i)
      END DO

If a(i) and b(i) are very small, many underflows occur. By forcing the computation to double precision, you compute the dot product with greater accuracy and do not suffer underflows:

      DOUBLE PRECISION sum
      DO i = 1, n
         sum = sum + dble(a(i)) * dble(b(i))
      END DO
      result = sum

You can force a SPARC processor to behave like an older system with respect to underflow (Store Zero) by adding a call to the library routine nonstandard_arithmetic() or by compiling the application’s main program with the -fns option.