Why Do Floating-Point Calculations in Python Lead to Unexpected Filename Generation?

Floating Point Precision in Python

When performing calculations with floating-point numbers, it is crucial to be aware of potential rounding errors. In Python, the behavior of float numbers can be unexpected, leading to missing results in simulations.

Rounding Issue Explanation

Consider the following Python code:

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

In this code, the rounding error occurs because float(29) / 100 is not exactly 0.29 but rather 0.28999999999999998. This approximation prevents the correct filename from being generated for delta = 0.29.

Pattern of Rounding Errors

The rounding errors are not consistent across all integers. To investigate the pattern, the following Python script was created:

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

However, this script does not reveal any apparent pattern in the numbers for which rounding errors occur.

Cause of the Errors

The root cause of these errors lies in the nature of floating-point representation. Numbers that cannot be expressed as exact powers of two cannot be represented precisely as floating-point numbers. In these cases, floating-point numbers provide an approximation, which can sometimes be less than the actual value.

Resolution

To avoid these rounding errors, it is recommended to use decimal numbers (e.g., Decimal or fractions modules) for calculations that require precise numeric representation.

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