Question

I don’t know if this is an obvious bug, but while running a Python script for varying the parameters of a simulation, I realized the results with delta = 0.29 and delta = 0.58 were missing. On investigation, I noticed that the following Python code:

for i_delta in range(0, 101, 1):
  delta = float(i_delta) / 100

  (...)

filename = 'foo' + str(int(delta * 100)) + '.dat'

generated identical files for delta = 0.28 and 0.29, same with .57 and .58, the reason being that python returns float(29)/100 as 0.28999999999999998. But that isn’t a systematic error, not in the sense it happens to every integer. So I created the following Python script:

import sys

n = int(sys.argv[1])

for i in range(0, n + 1):
  a = int(100 * (float(i) / 100))
  if i != a: print i, a

And I can’t see any pattern in the numbers for which this rounding error happens. Why does this happen with those particular numbers?

Answer 1

Any number that can’t be built from exact powers of two can’t be represented exactly as a floating point number; it needs to be approximated. Sometimes the closest approximation will be less than the actual number.

Read What Every Computer Scientist Should Know About Floating-Point Arithmetic.