What is the difference between float and double?

Question

I\'ve read about the difference between double precision and single precision. However, in most cases, float and double seem to be interchangeable,

Answer 1

Given a quadratic equation: x² − 4.0000000 x + 3.9999999 = 0, the exact roots to 10 significant digits are, r₁ = 2.000316228 and r₂ = 1.999683772.

Using float and double, we can write a test program:

#include 
#include 

void dbl_solve(double a, double b, double c)
{
    double d = b*b - 4.0*a*c;
    double sd = sqrt(d);
    double r1 = (-b + sd) / (2.0*a);
    double r2 = (-b - sd) / (2.0*a);
    printf("%.5f\t%.5f\n", r1, r2);
}

void flt_solve(float a, float b, float c)
{
    float d = b*b - 4.0f*a*c;
    float sd = sqrtf(d);
    float r1 = (-b + sd) / (2.0f*a);
    float r2 = (-b - sd) / (2.0f*a);
    printf("%.5f\t%.5f\n", r1, r2);
}   

int main(void)
{
    float fa = 1.0f;
    float fb = -4.0000000f;
    float fc = 3.9999999f;
    double da = 1.0;
    double db = -4.0000000;
    double dc = 3.9999999;
    flt_solve(fa, fb, fc);
    dbl_solve(da, db, dc);
    return 0;
}  

Running the program gives me:

2.00000 2.00000
2.00032 1.99968

Note that the numbers aren't large, but still you get cancellation effects using float.

(In fact, the above is not the best way of solving quadratic equations using either single- or double-precision floating-point numbers, but the answer remains unchanged even if one uses a more stable method.)