How Can I Define and Use Very Small Numbers in Fortran 90?

[TheIsingGuy]

how do I define and use small numbers for computations? on the scale of 10^-30?

e.g.
Program A
implicit none
double precision a,b,c,d
c = (a*b)/(a+b)
d = etc...

End program

The above has an overflow error when I give a,b the values 3.345 * 10^-27

Can anyone help?

Thanks

Ising

 

[minger]

You're going to run into problems on any computer trying to do those computations. I am from the high-accuracy CFD world. Many solvers will attempt to solve for the dimensional variables directly. Unfortunately in the equations, you get very large (and very small, O e+-8) running around. Performing computations on numbers like this results in poor accuracy.

In order to avoid this, we non-dimensionalize all the variables first. Insteady of pressure being 101,300, it becomes 0.714, instead of density being 0.0012, it becomes 1.0. This makes the speed of sound 1.0, etc, etc.

In your case, if this is unavoidable, you'll have to go to alternate algorithms for this. Try to check out some IEEE papers, you might be able to find something. I was able to find this page though:
http://docs.sun.com/app/docs/doc/801-7639/6i1ucu1ug?a=view

The first computation in that equation should give a number on the order of e-700, which is out of the range of double precision.

 

[quicknote]

a small number on the scale of 10^-30 in Fortran 90 can be done by using the scientific notation format. For example, 10^-30 can be written as 1.0E-30. This notation can be used to define and use small numbers for computations in Fortran 90 without encountering overflow errors. Additionally, using the "double precision" declaration for variables can also help with precision and avoid errors when dealing with small numbers. It is important to carefully consider the precision and range of values when defining and using small numbers in Fortran 90 to ensure accurate and reliable results in your computations.