machine precision problem in code

my function is supposed to take any rational number as an input, and it's supposed to output the number of digits after the decimal point. I keep on rechecking my code, but what am i doing wrong with my code?

function y = digits_debugged(x)

x = abs(x); %in case of negative numbers
y = 0;

while (floor(x)~=x)
    y = y+1;
    x = x*10;
end

[Azzi Abdelmalek]

what is the problem?

[Ben]

If I call this function as digits bug(-11.12345), it should output 5, but that is not the answer i am getting.

[Azzi Abdelmalek]

I am getting 5. what did you get?

[Ben]

oh i am getting 5 as well. I am confused as to why my instructor told me my function has several bugs. thank you!

Answer 1

[Jan]

Walter has mentioned, that the number of digits is not well defined, because the displayed output use the base 10 while the internal storage uses the base 2. The conversion of the bases effects the number of digits due to the limited precision of the internal representation of doubles. In consequence, there cannot be a program, which replies the "number of digits after the decimal point" for "any rational number".

It is not a question of fixing the code, the task is not possible. Therefore any program, which needs this, has a structural problem.

Remark: The efficient and smart V8 java engine uses a C-library for the stable conversion between numbers and strings, e.g. str2double. It has 8MB(!) of source code, which is a sign that this task is not trivial and therefore it cannot be implemented reliably in a few lines.

(For all cracks: Yes, I know that code size is not a 100% perfect measurement of the complexity of the task. A counter-example is writing a letter to your grandma with Windows Office 2010 Professional Plus. In this case even the name of the program is a strong indicator already.)

[Ben]

oh okay, so would I use something like

(floor(11.111*10^3))-11.111*10^3 = eps(11.111*10^3)*2

in my function instead? thanks for telling my I had to rewrite it I have been going crazy just trying to debug!

Answer 2

[Walter Roberson]

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

[Matt Fig]

Yep. I think that in general this assignment is not possible to complete as described. For example, how many digits are after the decimal for N = 1.1? Let's check:

N = 1.1;
sprintf('%17.17f',N)
% Try for N = 1.21335;

[Ben]

so I just checked with my lab instructor,and you guys are write. How would I go about fixing my code? My instructor suggested using eps() and I haven't learnt that yet/can't find anything on google on how to use it. Do either of you know how to use eps() in this situation?

Answer 3

[SB]

Hey, it should be something like this:

    % 
x = abs(x); %in case of negative numbers
y = 0;
n=0
while (floor(x*10^n)~=x*10^n)
  u=floor(x)~=x
y = y+1
n=n+1
end

By the way, could you show me how to do the decimal to binary conversion question?

Answer 4

[James Tursa]

Ben, as many others have already pointed out, this assignment is ill conceived and cannot be accomplished per the reasons others have already given. For example, you can use the num2strexact function from the FEX to see the exact decimal conversion for any single or double precision number:

http://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str

Given that conversion, what exactly is it that your instructor wants to see for an output? Sure, one could use eps in some fashion, but that is only going to give you a number that is about 1e-15 smaller than the number you started with. How is that going to be related to the "number of digits after the decimal point"? Once you start going down this path of what "number of digits after the decimal point" means you will quickly head in the direction of the code/algorithms that Jan has alluded to. I.e., is it the "minimum number of digits that will, when read in via "standard" algorithms, reproduce the input number exactly"? Or what?

[Ben]

I asked my instructor and told him about how many digits we were supposed to go to, and he said to use eps() which implies 1e-15. I just don't know how to correctly implement eps() and google isn't helping me either.