C Language Common pitfalls Comparing floating point numbers


Example

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)