floating point number division

vijraj · 03-06-2007, 08:38 PM

Hi all!
I am working with a problem to find the smallest floating point number that can be represented.
I am going in a loop ,stating with an initial value of 1.0 and then diving it by 10 each time thru the loop.
So the first time I am getting o.1 which I wanted.But from the next iteration I am getting 0.0099998.But this is not I want.
I want a result like this.First time I am 0.1.
Then next iteration should give me 0.01.
Next iteration should give me 0.001 and so on.
I don't know how to achieve this ..I am posting a piece of code here for u to look.
Please suggest.Thanks in advance.

Code:

for(;;)
{
        i=i*10;
        
        small=(1.0)/i; /*here I am getting 0.0099998 on the second iteration.I need 0.01 on 2nd iteration 
and 3rd iteration should be 0.001etc.*/
        
        ip=(int*)&small;
        sprintf(sztemp,"%08x",*ip);
        
         if(strcmp(sztemp,szSmall)==0) break;
        
}

PatrickNew · 03-06-2007, 09:17 PM

Floating point arithmetic inherently involves errors, so there are really two numbers you are interested in. One is how many decimal places out a floating point number can go, and the other is how many decimal places should be trusted. The first is pretty easy to find, just output 1/3 and count the decimal places. The second is rather difficult to measure, which is what you're observing with this output. Dividing by 10 should always just shift a decimal place, but it doesn't due to floating point error.

On a related note, you might get better precision by multiplying times .1. It's a weird discrete math thing, but multiplication produces less error than division.

vijraj · 03-06-2007, 09:22 PM

Thanks Patrick.But I am getting the same result.
The first time I am getting 0.1.But from next time I am not getting 0.01 but something like 0.009998.etc...

PatrickNew · 03-06-2007, 09:25 PM

Do you need to get a certain precision, or is this just curiosity? There are special arbitrary-precision libraries that let you calculate with... well, arbitrary precision. Unfortunately, you might never get more precise than that with standard floating point arithmetic.

graemef · 03-06-2007, 09:38 PM

If you are just trying to find the smallest number try division by 2 rather than 10, you should find the results are more to your liking. This is because the numbers are held internally in binary.

vijraj · 03-06-2007, 09:52 PM

Hi Patrick and graemef !
Actually I have to display the number that is >0 but the smallest number in floating point representation.
So actuallyit has the sign bit set to 1 and the exponent bit set to 00000001 and the rest 23 bits are zeroes.That is the representation of the smallest number internally.So I want to know that number that can be represented in floating point arithmetic.
so I am going in a loop and dividing 1.0 by 10 to find the smallest number >0 that can be represented by float.
any suggetions?Thanks.

v.tieubao · 03-06-2007, 10:07 PM

Quote:

Originally Posted by vijraj

Hi Patrick and graemef !
Actually I have to display the number that is >0 but the smallest number in floating point representation.
So actuallyit has the sign bit set to 1 and the exponent bit set to 00000001 and the rest 23 bits are zeroes.That is the representation of the smallest number internally.So I want to know that number that can be represented in floating point arithmetic.
so I am going in a loop and dividing 1.0 by 10 to find the smallest number >0 that can be represented by float.
any suggetions?Thanks.

Think about "Double-Precision Floating-Point Representation"

Cheers,
VTB.

vijraj · 03-06-2007, 10:12 PM

Thanks everybody!
I got it.I divided by 2 as you said and I got it.YEAHHHHHHHHHHHHHHHHHHHH!

PatrickNew · 03-06-2007, 10:14 PM

This can actually be solved on paper for languages, like C, that use IEEE floats. The lowest exponent that can be stored is -127 (because IEEE float exponents are the binary value stored - 127). The lowest mantissa is 0, corresponding to a value of 1.0. so, the lowest float value that can be stored is 1.0x2^-127, or 2^-127. Crappy MS calculator tells me this is 5.8774717541114375398436826861112e-39, so it just depends if you trust it.

makyo · 03-06-2007, 10:36 PM

Hi.

You can compare your results with the code at http://homepages.cwi.nl/~steven/enquire.html
I've been using enquire for years; very useful whenever I get to a new hardware platform ... cheers, makyo