aritmetic operation about

[ciccioriccio]

The code:

#include <iostream>
using namespace std;
int main() {
double a, b, c, d;
a = 1.38371e-20;
b = 4.12551e-19;
c = 1;
d = c - (a + b);
cout << scientific;
cout.precision(7);
cout << d << "\n";
if ( d == c )
cout << "(buuuu) d = c \n";
else
cout << "wow\n";
return 0;
}


returns

1.0000000e+00
(buuuu) d = c

How can I obtain the exact value for d (the result is different from 1). It should be:

0.xxxxxxxe-xxx.

Thanks in advance.

[Stewbond]

You can increase the precision in your cout.precision() function. However, note that you may not be able to display all of those digits. The reason is that a double only has 64 bits of precision. Some of those are dedicated to the exponent, and the rest are dedicated to the mantissa (the coeffeicent in front of the exponent).

1 2 3 4 5 6 7

#include <iostream> #include <limits> using namespace std; int main() { cout << numeric_limits<double>::epsilon() << endl; }

2.22045e-016 Press any key to continue . . .

You can see the smallest number that can be shown by a double with the limits library. Epsilon is a number representing the value of the smallest bit in a floating point number of 1.0. Since c is coincidently 1.0, we can see that the smallest amount that can be displayed by 1 bit is 2.22e-16. That means that any operations with smaller numbers will have no effect on it!

So, due to limits in computer science, there is no EXACT value.