Machine epsilon eps returns the distance from 1.0 to the next largest floating point number. When eps is machine epsilon, the logic 1+eps>1 is TRUE

Conversion binary data to decimal data Binary 0.0000001  Decimal form Binary 0.00000001  Decimal form

If computer cannot distinguish between EPS+1 and 1, the value EPS is smaller than the machine epsilon.

>>format long e >> eps ans = 2.220446049250313e-016 >>1+eps>1 1 >> 1+eps<1 >> (1+eps/2)>1

e = 0; EPS = 1.0; while (1+EPS)>1 EPS = EPS/2 e = e+1 end machineEPS = EPS*2