dlmread adds low precision digits

Hello all,

I'm using dlmread to import datas and when the datas contains integers and float numbers, dlmread sometimes makes an error on the last digit of the output precision.

I'm not sure I am clear, so here is an example :

If my text file ('test.rpt') contains only the row :

  1         10.8000             31.         10.5001

the command

A = dlmread('test.rpt')

gives back :

A =
   1.000000000000000  10.800000000000001  31.000000000000000  10.500100000000000

I don't understand why this 10e-15 is added on the second number. Ok, it's not a big error, but it prevent me from easly comparing two values...

Does anyone know how to prevent this behaviour ?

[dpb]

In short, you can't. It's fact of life with floating point numbers. See <Why-is-0-3-0-2-0-1-not-equal-to-zero?> for more explanation.

For comparison of floating point values with rounding error, see ismembertol

[Adam Danz]

I wonder if you read it in as text and then convert it to numeric values, whether the problem would persist.

[Arnaud WILHELM]

Ok, I understand the problem of floating point numbers. But I don't remember seeing this when using fscanf and specifing a number format.

@ Adam : I am not sure I understand what you mean in "read it in as text" ?

[Adam Danz]

I know 0 about rpt files so I can't recommend alternative methods to read in the data. You're currently reading in the data usling dlmread (which has been replaced by readmatrix() starting in r2019a).

Some methods allow you to read in data as text in which case 10.8000 would be read as a string (or char array) '10.8000'. Then you could convert that to numeric by using str2double() or num2str() (the prior is better).

[dpb]

> x=10.8
x =
   10.8000
>> fprintf('%.15f\n',x)
10.800000000000001
>> 

so it doesn't matter how you enter it, 10.8 is not exactly representable.

"I don't remember seeing this when using fscanf and specifing a number format."

Probably because you just didn't notice until you did try to do an exact comparison on floating point values.

>> fprintf('%.15f\n',round(x,1))
10.800000000000001
>> 

It's doing the best it can within the constraints of IEEE floating point representation.

[Adam Danz]

Ah, ok then. Thanks dpb & James Tursa .

Answer 1

[James Tursa]

Any function (dlmread, fscanf, etc) in any language (MATLAB, C, etc.) reading text numbers into floating point will have this issue. You may not have noticed it before, but it has always been there. With some exceptions (integers, etc), in general you simply can't represent many decimal numbers exactly in IEEE binary floating point format. For your numbers, here are the exact conversions:

>> sprintf('%.50f',1)
ans =
    '1.00000000000000000000000000000000000000000000000000'
>> sprintf('%.50f',10.8)
ans =
    '10.80000000000000071054273576010018587112426757812500'
>> sprintf('%.50f',31)
ans =
    '31.00000000000000000000000000000000000000000000000000'
>> sprintf('%.50f',10.5001)
ans =
    '10.50009999999999976694198267068713903427124023437500'

Integers (that are not too big) it does fine with, but your other decimal numbers cannot be represented internally exactly. Read the links that dpb has provided.

[Arnaud WILHELM]

All right, I understand now.

Thanks everyone for these anwsers !