Why Do Floating-Point Numbers in Python Cause Rounding Errors and How Can They Be Addressed?

Python's Rounding Error with Floating-Point Numbers

When working with floating-point numbers in Python, it's crucial to be aware of the potential for rounding errors. These errors arise because floating-point numbers can only approximate real numbers, and certain values may be represented differently depending on their proximity to exact powers of two.

For instance, consider the code snippet:

for i_delta in range(0, 101, 1):
  delta = float(i_delta) / 100
  (...)
  filename = 'foo' + str(int(delta * 100)) + '.dat'

In this code, the following values of delta will result in identical files:

• delta = 0.29 and delta = 0.28999999999999998
• delta = 0.58 and delta = 0.57999999999999996

This occurs because the exact result of float(29) / 100 is 0.28999999999999998, which is rounded down to 0.28. Similarly, float(58) / 100 is rounded down to 0.57999999999999996.

It's important to note that this rounding error is not systematic and does not affect every integer. To gain further insight into these errors, consider the following code:

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

When run, this code will output pairs of numbers for which the rounding error occurs. By analyzing these pairs, it's possible to identify that the errors tend to occur for numbers that cannot be represented as exact powers of two.

To address this issue, it's recommended to use exact arithmetic where possible and to be aware of the limitations and rounding errors associated with floating-point numbers. For further reading, consult the article "What Every Computer Scientist Should Know About Floating-Point Arithmetic" for a comprehensive guide to this complex topic.

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