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Adding large numbers

Posted on 2004-09-17
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Last Modified: 2010-04-01
I have the following c++ program:

#include <iostream>
#include <iomanip>

using namespace std;

int main()
{
    double long i=0.0000000000000000000035;
    double long j=3.24433466545467;
   
    j+=i;
   
    cout<<setprecision(100)<<j<<endl;

    return 0;
}


why does it print: 3.24433466545467
instead of: 3.2443346654546700000035
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Question by:jtk207
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4 Comments
 
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Accepted Solution

by:
drichards earned 50 total points
ID: 12089278
A double has, if I remember correctly, about 17 significant mantissa digits.  This is due to its binary representation.  You have exceeded that length so the extra 000035 is truncated off.  The value 'i' is 3.5 x 10^-21, which has only 2 significant digits in the mantissa, so it is OK.  3.24433466545467 os 15 digits, so only values in the next two places would be displayed (10^-15 and 10^-16).  'i' is beyond the representable range of 'j'.
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LVL 19

Expert Comment

by:drichards
ID: 12089284
Here's a link to how floats and doubles are represented in binary form:

    http://www.fact-index.com/i/ie/ieee_floating_point_standard.html#Double%20Precision%2064%20bit
0
 

Author Comment

by:jtk207
ID: 12089286
So how would i fix it?
0
 
LVL 19

Expert Comment

by:drichards
ID: 12089394
Directly, you can't.  You'd have to get or write an algorithm to deal with arbitrarily large/small numbers.  I've seen these for integers, but I haven't seen one for reals.  Is that amount of precision really necessary for what you're doing?
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