C's pow() function as per header file <math.h> not working properly

Question

Hi Experts,

I see that for the following code produces the result as below, any idea on why is the output like this:-

#include < stdio.h >
#include < math.h >

int main(){

 int i=0;

 for(i=0; i<10; i++){

  printf("%d\t\t\t%d\t\t\t", i, (int)pow(10, i));

  printf("%f\n", pow(10, i));
}

 return 0;

}

/* Outputs:-

0 1 1.000000

1 10 10.000000

2 99 100.000000

3 1000 1000.000000

4 9999 10000.000000

5 100000 100000.000000

6 1000000 1000000.000000

7 9999999 10000000.000000

8 99999999 100000000.000000

9 999999999 1000000000.000000

*/

Answer 1

Use the round() function before casting to int, else the trailing digits will just get truncated.

Answer 2

As with every one of the billion other questions on SO to do with floating point :-), the answer is that not all numbers can be represented exactly.

And, even if they can be represented exacly, you may get a bad result from something like pow which may work within a loop. In other words, no matter how small the error on an operation, if you do it a lot of times, the error becomes large.

Try printing out the return from pow(10,4) with a %.50f or other floating point specifier, and I'll guarantee you'll see something like 9999.9999999237623465 instead of 10000.

For what it's worth, the correct results are produced under gcc 3.4.4 under CygWin so it's likely that you're using a less-exact implementation of pow.