Floating point types (`float`

, `double`

and `long double`

) cannot precisely represent some numbers because they have finite precision and represent the values in a binary format. Just like we have repeating decimals in base 10 for fractions such as 1/3, there are fractions that cannot be represented finitely in binary too (such as 1/3, but also, more importantly, 1/10). Do not directly compare floating point values; use a delta instead.

```
#include <float.h> // for DBL_EPSILON and FLT_EPSILON
#include <math.h> // for fabs()
int main(void)
{
double a = 0.1; // imprecise: (binary) 0.000110...
// may be false or true
if (a + a + a + a + a + a + a + a + a + a == 1.0) {
printf("10 * 0.1 is indeed 1.0. This is not guaranteed in the general case.\n");
}
// Using a small delta value.
if (fabs(a + a + a + a + a + a + a + a + a + a - 1.0) < 0.000001) {
// C99 5.2.4.2.2p8 guarantees at least 10 decimal digits
// of precision for the double type.
printf("10 * 0.1 is almost 1.0.\n");
}
return 0;
}
```

Another example:

```
gcc -O3 -g -I./inc -std=c11 -Wall -Wextra -Werror -Wmissing-prototypes -Wstrict-prototypes -Wold-style-definition rd11.c -o rd11 -L./lib -lsoq
#include <stdio.h>
#include <math.h>
static inline double rel_diff(double a, double b)
{
return fabs(a - b) / fmax(fabs(a), fabs(b));
}
int main(void)
{
double d1 = 3.14159265358979;
double d2 = 355.0 / 113.0;
double epsilon = 1.0;
for (int i = 0; i < 10; i++)
{
if (rel_diff(d1, d2) < epsilon)
printf("%d:%.10f <=> %.10f within tolerance %.10f (rel diff %.4E)\n",
i, d1, d2, epsilon, rel_diff(d1, d2));
else
printf("%d:%.10f <=> %.10f out of tolerance %.10f (rel diff %.4E)\n",
i, d1, d2, epsilon, rel_diff(d1, d2));
epsilon /= 10.0;
}
return 0;
}
```

Output:

```
0:3.1415926536 <=> 3.1415929204 within tolerance 1.0000000000 (rel diff 8.4914E-08)
1:3.1415926536 <=> 3.1415929204 within tolerance 0.1000000000 (rel diff 8.4914E-08)
2:3.1415926536 <=> 3.1415929204 within tolerance 0.0100000000 (rel diff 8.4914E-08)
3:3.1415926536 <=> 3.1415929204 within tolerance 0.0010000000 (rel diff 8.4914E-08)
4:3.1415926536 <=> 3.1415929204 within tolerance 0.0001000000 (rel diff 8.4914E-08)
5:3.1415926536 <=> 3.1415929204 within tolerance 0.0000100000 (rel diff 8.4914E-08)
6:3.1415926536 <=> 3.1415929204 within tolerance 0.0000010000 (rel diff 8.4914E-08)
7:3.1415926536 <=> 3.1415929204 within tolerance 0.0000001000 (rel diff 8.4914E-08)
8:3.1415926536 <=> 3.1415929204 out of tolerance 0.0000000100 (rel diff 8.4914E-08)
9:3.1415926536 <=> 3.1415929204 out of tolerance 0.0000000010 (rel diff 8.4914E-08)
```