為什麼 Python 中的 round() 函數會將半浮點數捨入為最接近的偶數？

Understanding Half Float Number Rounding Behavior in Python

When dealing with half float numbers in Python, the round() function can exhibit an unexpected behavior, as illustrated by the following code snippet:

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

Instead of rounding up all floating values, round() rounds them to the nearest even number. This peculiar behavior is attributed to "rounding half to even," also known as "bankers rounding."

Cause of Bankers Rounding

According to the Python documentation, round() rounds half towards even to prevent compounding rounding errors. By rounding to the nearest even number, the overall rounding effect is averaged out.

Correcting the Rounding Behavior

To obtain the desired rounding behavior, specifically rounding up from half, the decimal module can be utilized. By defining a local context and setting the rounding parameter to ROUND_HALF_UP, Python's rounding function can be customized.

Here's an example demonstrating 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, '=&gt;', n.to_integral_value())</code>

The output of this code is:

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

Conclusion

To achieve correct rounding behavior for half float numbers, the decimal module in Python provides the necessary tools for specifying the desired rounding strategy. By utilizing the ROUND_HALF_UP option, half float numbers can be rounded up consistently, as shown in the provided example.

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