HOW CAN I SOLVE THIS?
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Jan
on 7 Mar 2021
What are the possible numbers in IEEE 754 floating point values between 1.0 and 2.0?
x = 1.0 + k * 2^-52 with k = 0, 1, ... 2^52
Run a loop over k to find a value with x * (1 / x) ~= 1.
9 Comments
Jan
on 9 Mar 2021
Edited: Jan
on 9 Mar 2021
This is not an error. Computers store numbers with a limited precision. This has effects on arithmetics when using them. Famous examples:
0.1 + 0.1 + 0.1 == 0.3 % FALSE
any((0:0.1:1) == 0.3) % FALSE
1e17 + 1 - 1e17 == 1 % FALSE, it is 0
1e17 - 1e17 + 1 == 1 % TRUE
Welcome to the world of numerical maths. The first chapters of text books for this field of science explain the effects and teach methods to cope with them.
The alternativ is to use symbolic maths or numbers with unlimited precision. The later will exhaust the memory as soon as an irrational number is used, because you need an infinite amout of RAM to store it.
When I started to study, the loop took 1 day to find the first match of 1 * (1/x) ~= 1. Now Matlab takes seconds only. Running the full range over 2^52 elements will still take far too long. You can determine the concerned numbers by a formula also, but it is not trivial.
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