MATLAB: Function rem issue with exact result

rem

sometimes the function rem does not return the exact solution. For example rem(135.01,100) does not return 35.01 but it returns 35.009999999999991 (visible when format is changed to long). Can anyone tel me why !? and how to fix it !?

Best Answer

Floating point arithmetic.

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MATLAB: Two equal numbers are not equal

You should never test equality between floating point numbers. There are any number of places you could search online to see the reasons for this. Many floating point numbers can not be represented to 100% accuracy and maths done on them will often introduce small inaccuracies so you should always test equality within a tolerance, not directly. The difference may only be 1e-16 and so basically equivalent to 0 for all sensible usage, but it will still fail an == test.

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To see what is going on you can examine the exact floating point values. Note that none of your original numbers except 0.5 can be represented in IEEE double format exactly:

>> num2strexact(.7)
ans =
0.6999999999999999555910790149937383830547332763671875
>> num2strexact(.5)
ans =
0.5
>> num2strexact(.4)
ans =
0.40000000000000002220446049250313080847263336181640625
>> num2strexact(.3)
ans =
0.299999999999999988897769753748434595763683319091796875
>> num2strexact(.1)
ans =
0.1000000000000000055511151231257827021181583404541015625
>> num2strexact(.7/.1)
ans =
6.99999999999999911182158029987476766109466552734375
>> num2strexact(.5/.1)
ans =
5
>> num2strexact(.4/.1)
ans =
4
>> num2strexact(.3/.1)
ans =
2.999999999999999555910790149937383830547332763671875

You can find num2strexact here:

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

Best Answer

Related Solutions

MATLAB: Two equal numbers are not equal

MATLAB: Rounding using ‘fix’… possibly a bug

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