MATLAB: Dlmread adds low precision digits

dlmreadMATLAB

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 ?

Best Answer

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.
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