Why Does Python Round Half-Floats to Even Numbers?

Rounding Half-Float Numbers

The round() function in Python exhibits an unusual behavior when rounding half floats that can be perplexing. Let's examine this behavior in more detail.

<code class="python">for i in range(1, 15, 2):
    n = i / 2
    print(n, "=>", round(n))</code>

This code prints:

0.5 => 0
1.5 => 2
2.5 => 2
3.5 => 4
4.5 => 4
5.5 => 6
6.5 => 6

Contrary to expectations, the floating values are not always rounded up. Instead, they are rounded to the nearest even number, even for half values. This behavior is documented in the Python documentation under "Numeric Types":

"round(x[, n])

x rounded to n digits, rounding half to even. If n is omitted, it defaults to 0."

This rounding to the nearest even number, known as "bankers rounding," aims to mitigate rounding errors by averaging out the rounding.

To gain more control over rounding behavior, the decimal module offers a more flexible approach. The following example demonstrates how to round up from half using the decimal module:

<code class="python">from decimal import localcontext, Decimal, ROUND_HALF_UP
with localcontext() as ctx:
    ctx.rounding = ROUND_HALF_UP
    for i in range(1, 15, 2):
        n = Decimal(i) / 2
        print(n, '=>', n.to_integral_value())</code>

Output:

0.5 => 1
1.5 => 2
2.5 => 3
3.5 => 4
4.5 => 5
5.5 => 6
6.5 => 7

By adjusting the rounding parameter within the localcontext(), you can customize rounding behavior as needed, ensuring accurate results for specific rounding scenarios.

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