Why Doesn't My MATLAB While Loop Output the Expected Number?

[ver_mathstats]

Homework Statement

Here is some Matlab code:
x = 1;
while (x+1)-x == 1
x = 2*x;
end
x
Explain why it terminates and explain why it outputs: 9.007199254740992e+15.

Relevant Equations

matlab, loops

I am confused why this is the case, why would it output that number? When I go through the code, there is (x+1)-1 which does equal 1, then x = 2*x is 2? So why is the output not 2? How should I proceed in coming up with a solution? Does this have something to do with cancellation errors somewhere?

 

[Mark44]

Homework Statement:: Here is some Matlab code:
x = 1;
while (x+1)-x == 1
x = 2*x;
end
x
Explain why it terminates and explain why it outputs: 9.007199254740992e+15.
Relevant Equations:: matlab, loops

I am confused why this is the case, why would it output that number? When I go through the code, there is (x+1)-1 which does equal 1, then x = 2*x is 2? So why is the output not 2? How should I proceed in coming up with a solution? Does this have something to do with cancellation errors somewhere?

In your code, x is evidently a double. What's the largest double-precision number that can be represented? What would that number + 1 be?

 

[Baluncore]

(x+1)-x will be equal to 1, until the addition of one to x fails to make a change.
The mantissa of a double has 52 bits plus one implied set bit.
2^(52+1) = ?

 

[ver_mathstats]

(x+1)-x will be equal to 1, until the addition of one to x fails to make a change.
The mantissa of a double has 52 bits plus one implied set bit.
2^(52+1) = ?

Okay, I see, I think I'm understanding much better

 

[ver_mathstats]

In your code, x is evidently a double. What's the largest double-precision number that can be represented? What would that number + 1 be?

Because 2^53=9.007199254740992e+15 and (2^53)+1=9.007199254740992e+15

 

[Baluncore]

Addition and subtraction of floating point numbers requires the exponents first be made equal. The smaller number may become zero during the justification shift of the mantissa, before the arithmetic step. The arithmetic will then make no change to the bigger number.