macheps-128

Computation of the machine epsilon (macheps) with 128-bit floating point type.

The approximating algorithm looks 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:

• 128-bit floating point data type is __float128
• GCC libquadmath is used
• Comparison of the value and sum is done raw with memcmp() function
• Additionally the loops are counted and printed out with the epsilon

Output

Machine epsilon (fp128):
    Loop counter: 113
    epsilon: 9.629649721936179265279889712924636593e-35
    epsilon2: 1.925929944387235853055977942584927319e-34

Machine epsilon (libquadmath): 1.925929944387235853055977942584927319e-34

Note

See also macheps.