Commercial rounding in Python

As it turns out, Python does not do commercial rounding.

What is commercial rounding?

For most digits, the direction of rounding is clear. There are some special cases though: Do I round $0.5$ to $0$ or to $1$?

In commercial rounding, this “$0.5$” problem is solved by “rounding away from zero”, meaning: For positive numbers, round up; for negative numbers, round down.

This makes perfect sense for a mathematician, but others might need examples, so here are some¹:

• $0.5$ goes to $1$.
• $-0.5$ goes to $-1$ (away from zero).

The same obviously goes in other positions too: $0.05$ goes to $0.1$, etc.

What does Python do?

Here, actually mathematical rounding happens: Round to the next even possibility. Meaning:

• $0.5$ goes to $0$ (!).
• $1.5$ goes to $2$.
• $2.5$ goes to $2$ (!).

This also makes sense in some settings, which I will discuss in a later post.

How do I implement commercial rounding in Python?

I just wrote my own function,which does exactly that and is (in the cases I need) a drop-in replacement for Python’s builtin round function:

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def round(val, ndigits=0):

    # Keep the sign extra, else we need more
    # cases below
    sign = 1 if val >= 0 else -1

    factor = 10**ndigits

    scaled = int(val * sign * factor * 10)
    last_digit = scaled % 10

    scaled = scaled // 10

    # Rounding: Round up if the
    # last digit is larger or equal to 5
    if last_digit >= 5:
        scaled += 1

    # Return an integer if rounding to integer
    if ndigits == 0:
        return int(scaled * sign)

    # Return the correct float
    return scaled * sign / factor

Just define this at the beginning of your module, and then use the round function as usual.

Note!

I am not fully sure about this approach: In the end, we again return a floating point number. Why will this not be approximated?