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

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Shiksha Pandey
Shiksha Pandey el 24 de Mzo. de 2021
Comentada: Rik el 24 de Mzo. de 2021
Using double precision, find x for which exp(x) doesn't overflow.
  4 comentarios
Shiksha Pandey
Shiksha Pandey el 24 de Mzo. de 2021
Editada: Rik el 24 de Mzo. de 2021
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
Rik el 24 de Mzo. de 2021
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?

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KALYAN ACHARJYA
KALYAN ACHARJYA el 24 de Mzo. de 2021
Editada: KALYAN ACHARJYA el 24 de Mzo. de 2021
All data creates in MATLAB are douple precision (Standard /By Default)
More:
e^x = 1 + (x ^ 1 / 1!) + (x ^ 2 / 2!) ......

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