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

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

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

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

The assembly functions have been generated using my cppasm generator.

See also macheps-128.