Rounding.

Previously: 211018-1510 Python rounding behaviour with TL;DR that python uses banker’s rounding, with .5th rounding towards the even number.

• Rounding - Wikipedia

• Nearest Integer Function – from Wolfram MathWorld

• Floor/ceil have their usual latex notation as \rceil, \rfloor (see LaTeX/Mathematics - Wikibooks, open books for an open world at ‘delimiters’)

• “Normal” rounding (towards nearest integer) has no standard notation: ceiling and floor functions - What is the mathematical notation for rounding a given number to the nearest integer? - Mathematics Stack Exchange

  • $\lfloor3.54\rceil$ is one notation people mention
  • Some suggest $[3.54]$ but most hate this because overused
  • $nint(3.45)$ (’nearest integer function’) works
  • let XXX denote the standard rounding function

• Bankers’ rounding (that python and everyone else use for tie-breaking for normal rounding and .5) has no standard notation as well

  • Let $\lfloor x \rceil$ denote "round half to even" rounding (a.k.a. "Banker's rounding"), consistent with Python's built-in round() and NumPy's np.round() functions.