Smallest positive number in MATLAB

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Dyuman Joshi
Dyuman Joshi on 27 Apr 2021
Commented: Dyuman Joshi on 30 Apr 2021
I recently stumbled upon a question on Cody (#1874), which asked the user to input the smallest in MATLAB.
As per my knowledge, realmin was supposed to return the smallest number in MATLAB, however that number is the smallest normalized floating point number. According to this thread of Stack overflow, it says eps(0) returns the smallest denormal number available in MATLAB.
However, my question is how eps(0) is denormal?
> realmin returns 2.2251e-308, where as eps(0) returns 4.9407e-324

Accepted Answer

Stephen
Stephen on 27 Apr 2021
Edited: Stephen on 27 Apr 2021
eps(0) returns the smallest positive non-zero floating point number, which is denormal:
format hex
eps(0)
ans =
0000000000000001
Normal and denormal floating point numbers are explained here:
From the main architect of IEEE 754 (the term "gradual underflow" refers to denormal numbers):
  2 Comments
Dyuman Joshi
Dyuman Joshi on 30 Apr 2021
Apparently I misunderstood the definition of a denormal (base 10 instead of base 2). Thank you for your answer and the links!

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