Checking Python's rounding behaviour

check_float_rounding.py

# Prompted by this article about implementing "Round half away from zero" in Go
# https://www.cockroachlabs.com/blog/rounding-implementations-in-go/

# Python uses round-half-even by default to reduce statistical bias,
# but round-half-away-from-zero can be implemented more efficiently
# (since it doesn't need to examine all the bits of the number)

# I figured the folks doing computational analysis in Python would
# have made sure this was handled correctly years ago, but it never
# hurts to check that kind of assumption :)

import sys
import math

epsilon = sys.float_info.epsilon

round_half_even = {
  -0.5+epsilon: -0.0,
  -0.5: -0.0,
  -0.5-epsilon: -1,
  0.0: 0.0,
  0.5-epsilon: 0,
  0.5: 0,
  0.5+epsilon: 1,
  1.390671161567e-309: 0,
  2.2517998136852485e+15: 2.251799813685248e+15,
  4.503599627370497e+15: 4.503599627370497e+15,
  -math.inf: -math.inf,
  math.inf: math.inf,
  math.nan: math.nan,
  -0.0: -0.0,
}

as_expected = []
discrepancy = []

for original, rounded in round_half_even.items():
    actual = round(original)
    if rounded != actual:
        discrepancy.append((original, rounded, actual))
    else:
        as_expected.append((original, rounded))

if as_expected:
    print("The following cases rounded as expected:")
    for original, rounded in as_expected:
        print(f"  {original} -> {rounded}")

if discrepancy:
    print("The following cases failed to give the expected result:")
    for original, expected, actual in discrepancy:
        print(f"  {original} -> {actual}, *not* {expected}")

output.txt

The following cases rounded as expected:
  -0.4999999999999998 -> -0.0
  -0.5 -> -0.0
  -0.5000000000000002 -> -1
  0.0 -> -0.0
  0.4999999999999998 -> 0
  0.5 -> 0
  0.5000000000000002 -> 1
  1.390671161567e-309 -> 0
  2251799813685248.5 -> 2251799813685248.0
  4503599627370497.0 -> 4503599627370497.0