Interesting confusion in matlab - Number format

I found one interesting in matlab and actually this is causing a bug in my code. I am unable understand the behaviour/logic of matlab. It is something to do with how the number is represented. Please see the below example and could you please me help to understand what is the issue ?

j_values = [ 25.3850 25.3900 25.3950 25.4000 25.4050 25.4100];

time_interval = 0.005;

 % ' i ' can be between 1 and 6
index = ( j_values(i) / time_interval);

When i value is 3 , i get output in exponential form (5.0790e+003) where as for other values of i i get a decimal number (5078). Why is this behaviour ??

How this causes issue is when i use ceil:

 index = ceil (j_values(i) / time_interval);

So index value will be same for both i = 3 and 4.

ceil(j_values(3) / time_interval)

ans = 5080

 ceil(j_values(4) / time_interval)

ans = 5080

But if i give value directly then output is different : ceil(5.0790e+003)

ans = 5079

This is really interersting confusion :P Can someone help me to understand what is happening ?

Cheers :)

Answer 1

[per isakson]

On R2013a,64bit,Win7 I get

    >> j_values/time_interval
    ans =
            5077        5078        5079        5080        5081        5082
    >> j_values(3)/time_interval
    ans =
            5079

What you see is a consequence of how floating point arithmetic works. See: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

&nbsp

Added later:

Replace

    index = ceil(j_values(i) / time_interval);

by

    index = round(j_values(i) / time_interval);

[kk]

I tried on R2011a with windows 8. Ok is see but when does matlab convert into exponent form ? In my example it does it only for index 3. Any general guidelines to deal with these issues ? Especially when i take data from excel or other editors and then use in matlab.

[per isakson]

• Did you read Cleve's piece?
• Did you notice "We like to use the term flint to describe a floating-point number whose value is an integer. Floating point operations on flints do not introduce any round- off error, as long as the results are not too large."?
• "general guidelines" No, I don't think there are any.
• My "general guideline" is simple. Never depend on that functions return doubles, the values of which are flint. There are a few exceptions, e.g. the counter in for loops. The functions round, ceil and floor return of course flint
• See http://www.mathworks.com/matlabcentral/answers/67247#answer_78702

Answer 2

[Adam]

Use

round

rather than ceil when your result is so close to the integer you want.

I have occasionally been caught by this too, it is just an effect of the way Matlab works with numbers that are double precision unless you explicitly create them as a different data type.

On my machine the example you showed works fine and gives an integer value (still in a double though obviously) for index 3.

[kk]

Hey thanks for the reply. I too understand that it is something to do with the data type. But still for index 3 why does it display/represent in exponential form but not for others. The values are similar. In general how can i control the data presicion ?? Even there is problem when i copy data from excel. I deal with such data and precision is important or else i may loose the information in my data.

Answer 3

[Iain]

Double format numbers are only accurate to about 15 significant figures. When you do sums, you can get errors at the 15th significant figure because double format numbers are NOT exact.

Eg:

 1E30 + 1 - 1E30 == 1 will return false, because 1 is too small to add to 1E30 without using a format other than double.