macheps

Computation of the machine epsilon (macheps) on x86 using approximating algorithm like:

value = 1.0;
epsilon = 1.0;
sum = value + epsilon;

while (value != sum)
{
    epsilon = epsilon / 2.0;
    sum = value + epsilon;
}

The approach used here is:

• Computations are done by assembly functions
• Constants 1.0 and 2.0 are computed using corresponding FPU instructions
• Comparison of the value and sum is done raw with memcmp() function
• Additionally the loops are counted and printed out with the epsilon

Single precision using FPU (IEEE 754: binary32, 32-bit)

Machine epsilon (fp32):
    Loop counter: 24
    epsilon: 5.96046e-08

Double precision using FPU (IEEE 754: binary64, 64-bit)

Machine epsilon (fp64):
    Loop counter: 53
    epsilon: 1.11022e-16

Long double precision using FPU (IEEE 754: -, 80-bit)

Machine epsilon (fp80):
    Loop counter: 64
    epsilon: 5.42101e-20

Note

The assembly functions have been generated using my cppasm generator.

See also macheps-128.