Python rounding error with float numbers [duplicate]

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.

Answer 2

Its very well known due to the nature of floating point numbers.

If you want to do decimal arithmetic not floating point arithmatic there are libraries to do this.

E.g.,

>>> from decimal import Decimal >>> Decimal(29)/Decimal(100) Decimal('0.29') >>> Decimal('0.29')*100 Decimal('29') >>> int(Decimal('29')) 29 

In general decimal is probably going overboard and still will have rounding errors in rare cases when the number does not have a finite decimal representation (for example any fraction where the denominator is not 1 or divisible by 2 or 5 - the factors of the decimal base (10)). For example:

>>> s = Decimal(7) >>> Decimal(1)/s/s/s/s/s/s/s*s*s*s*s*s*s*s Decimal('0.9999999999999999999999999996') >>> int(Decimal('0.9999999999999999999999999996')) 0 

So its best to always just round before casting floating points to ints, unless you want a floor function.

>>> int(1.9999) 1 >>> int(round(1.999)) 2 

Another alternative is to use the Fraction class from the fractions library which doesn't approximate. (It justs keeps adding/subtracting and multiplying the integer numerators and denominators as necessary).