6.5.3 Excessive Underflow

If two very small numbers are multiplied, the result underflows.

If you know in advance that the operands in a multiplication (or subtraction) may be small and underflow is likely, run the calculation in double precision and convert the result to single precision later.

For example, a dot product loop like this:

  real sum, a(maxn), b(maxn)
  ...
  do i =1, n
      sum = sum + a(i)*b(i)
  enddo

where the a(*) and b(*) are known to have small elements, should be run in double precision to preserve numeric accuracy:

  real a(maxn), b(maxn)
  double sum
  ...
  do i =1, n
      sum = sum + a(i)*dble(b(i))
  enddo

Doing so may also improve performance due to the software resolution of excessive underflows caused by the original loop. However, there is no hard and fast rule here; experiment with your intensely computational code to determine the most profitable solutions.