The transcendental number, e. Many applications in mathematics involve computing various powers of e. It can be proven that
ex = 1 + x/1 + x2/2! + x3/3! + ...

for all values of x. Of course, this is an infinite sum, so we can't hope to actually sum all of these values up! But the good news is that the later terms get so small that a partial sum can provide a very nice approximation for the value of ex. You are to write a single precision function (result returned in $f0) called exp with one single precision parameter (in $f12), along with a little driver program for testing your function. Your function should use the summation formula as an approximation for the value of ex, using the following guide for terminating the summation:

If the next term divided by the summation so far is less that 1.0e-15, then terminate the summation (and don't even bother to add in that next term). [One might be tempted to just stop if the next term is less that 1.0e-15, but my proposed guide is more sensitive to the relative size of the actual summation.]

Even though the summation is valid for all values of x, there is a problem with convergence when you use negative values too small such as -20. Therefore, your exp function should compute the value of e|x| instead, and then invert the result (this process should be handled by the function exp, not by your driver program).

You can expect your program to have overflow problems when tested with values of x somewhere around 90 or -90 (Why?).