Using double precision, find x for which exp(x) doesn't overflow.

Using double precision, find x for which exp(x) doesn't overflow.

[Steven Lord]

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the MATLAB Onramp tutorial (https://www.mathworks.com/support/learn-with-matlab-tutorials.html) to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

Assuming that you are asked to find the largest finite x with that property, as a hint: work in reverse to find a good starting point for your search.

[Rik]

Expanding on Steven's advice:

You could also carefully read the Wikipedia page for IEEE double precision floating point notation. That way you don't even have to empirically find what value is the largest x that will not overflow. Then you can test if that is true in Matlab.

[Shiksha Pandey]

This is what I have. I'm not sure if this is the best way to go though.

expn=0;
x=1:1000;
while expn < realmax
expn=(exp(x));
maxexpn = double(expn);
xx = double(log(maxexpn));
mexp = max(maxexpn(~isinf(maxexpn)));
mx = max(xx(~isinf(xx)))
abserr = abs(mexp-realmax)
relerr = (abs(mexp-realmax))/realmax
end

Is there a shorter way to go about it?

[Rik]

I don't really understand what you're attempting to do with the while loop, but yes, there is a faster way. It requires you to think a bit more.

log2(realmax)

ans = 1024

OK, so we are looking for x where e^x is at most 2^1024.

With a little bit of algebra that should not be too hard to solve. Can you see how?

Answer 1

[KALYAN ACHARJYA]

All data creates in MATLAB are douple precision (Standard /By Default)

Double

More:

e^x = 1 + (x ^ 1 / 1!) + (x ^ 2 / 2!) ......

[KALYAN ACHARJYA]

More:

https://math.stackexchange.com/questions/2988478/handling-overflow-in-matlab-with-exponential-and-imaginary-error-functions

https://in.mathworks.com/matlabcentral/answers/144445-how-to-prevent-an-exponential-function-to-return-infinity