How to Precisely Truncate Float Values Without Rounding?

How to Get Precisely Truncated Float Values?

Truncating float values, or removing digits beyond a specified number of decimal places, is a common operation in programming. However, achieving accurate truncation without rounding can be challenging due to the limitations of floating-point representation.

Understanding the Issue

Consider the example:

1.923328437452 -> 1.923

A naive approach would be to convert the float to a string and truncate it, but this can lead to errors due to the imprecise nature of floating-point representations. Different floating-point values may have the same binary representation, resulting in ambiguous truncation.

The Recommended Method

For Python versions 2.7 and above, the following function provides accurate truncation without rounding:

def truncate(f, n):
    '''Truncates/pads a float f to n decimal places without rounding'''
    s = '{}'.format(f)
    if 'e' in s or 'E' in s:
        return '{0:.{1}f}'.format(f, n)
    i, p, d = s.partition('.')
    return '.'.join([i, (d+'0'*n)[:n]])

Explanation

The core of this method is to convert the float to a string using '{}'.format(f) and truncate the string to the desired number of decimal places. For values in scientific notation ('e' or 'E'), the '{0:.{1}f}'.format(f, n) syntax is used to specify the precision.

Handling Special Cases

In rare cases, floats very close to round numbers may still be truncated incorrectly. For such cases, specify a higher precision to ensure that rounding during string conversion does not affect the result.

Alternatives for Older Python Versions

For Python versions below 2.7, a less accurate method involves rounding the float to 12 decimal places before truncation:

def truncate(f, n):
    '''Truncates/pads a float f to n decimal places without rounding'''
    s = '%.12f' % f
    i, p, d = s.partition('.')
    return '.'.join([i, (d+'0'*n)[:n]])

Conclusion

This code provides a robust solution for truncating float values without rounding, ensuring accurate truncation for a wide range of inputs.

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