Information & documentation
epsilon2
#!/usr/bin/python # Start with two non-negative numbers which are definitely larger # and smaller than machine epsilon. These define an interval which # contains machine epsilon. We repeatedly calculate the mid-point # between them and determine if it is larger or smaller than machine # epsilon and change the bounds of the interval accordingly. We keep # going until the interval is short enough. # In this case, "short enough" means the smallest interval such that # when we display the bounds using print we actually see a difference # on the screen. On the PCs used for this course, this works out as an # interval of size ~1.0e-27. If the interval is any smaller then when # print displays the bounds on the screen they will appear to be the same. # (Recall that print does not necessarily display all the significant # figures of a floating point number.) Note that on other computers we # may need to use a larger or smaller interval as machine epsilon is # *machine specific*. too_large = 1.0 too_small = 0.0 tolerance = 1.0e-27 while too_large - too_small > tolerance: mid_point = (too_large + too_small) / 2.0 if 1.0 + mid_point > 1.0: too_large = mid_point else: too_small = mid_point print too_small, '< epsilon <', too_large