while loop ends too early

Hi everyone,

Why is this loop not executed for t_max = 5.0000e-04 anymore? if I output t, the maximum (last) value is 5.0000e-04 instead of 5.0100e-04

delta_t = 10e-7;
t_max   = 5.0000e-04; %[s]
t       = 0;
while t <= t_max
    t = t+delta_t;
end

Answer 1

[Ameer Hamza]

Image Analyst and Sriram explained the reason as it is caused by the finite precision of floating-point representation. One way is to solve the issue with limited precision is to use variable precision arithmetic

delta_t = vpa(10e-7);
t_max   = vpa(5.0000e-04); %[s]
t       = vpa(0);
while t <= t_max
    t = t+delta_t;
end

However, note that this will be slower as compared to the numeric version. The other solution is to add a tolerance value for comparison

delta_t = 10e-7;
t_max   = 5.0000e-04; %[s]
t       = 0;
while t <= t_max + 1e-10 % small tolerance in comparison
    t = t+delta_t;
end

[Ann Gerber]

Thank you so much!

I expected this would be the problem but didn't know how to solve it the good way.

Cheers :)

Answer 2

[Image Analyst]

Take the semicolon off and format long and you'll see why

format long g;
format compact
delta_t = 10e-7;
t_max   = 5.0000e-04; %[s]
t       = 0;
while t <= t_max
    t = t+delta_t
end

t =

0.000498000000000006

t =

0.000499000000000006

t =

0.000500000000000006

You see, it ends up being slightly larger than 0.0005 so it doesn't even enter the loop that last time.

So, basically you need to see the FAQ for an explanation of digitization error: FAQ Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero?

Answer 3

[Sriram Tadavarty]

Hi Ann,

The loop runs as expected, since the floating values are represented in IEEE 754 format as described here.

To know what the value of t that end from the loop, use format long as below:

format long
>> t_max

t_max =

     5.000000000000000e-04
>> t

t =

     5.000000000000056e-04

Observe that t is lager than t_max and thus, the loop ended.

Hope this helps.

Regards,

Sriram