Python modulo for negative numbers

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Description

  • When negative numbers are involved, the modulo operator % does not have the same behavior in Python and in C/C++.
  • Both variants are correct, but Python’s modulo is most commonly used in mathematics (number theory in particular). However C’s modulo might be more intuitive for programming…
  • Python has a “true” modulo operation, while C has a remainder operation. It has a direct relation with how the negative integer division is handled, i.e. rounded towards 0 or minus infinite. Python rounds towards minus infinite and C(99) towards 0.
  • In this post, we only consider the case where the numerator (分子, numérateurs) can be negative, the denominator (分母, dénominateurs) is always positive.

In Python (version 3.8.9)

Background

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int_max = 2 ** 31 - 1
int_min = - 2 ** 31

print(int_max, int_min)
print(int_max / 10, int_min / 10)

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2147483647 -2147483648
214748364.7 -214748364.8

Python’s native // and % operators (rounds towards minus infinite)

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print(int_max // 10, int_min // 10)
print(int_max % 10, int_min % 10)

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214748364 -214748365
7 2

Using math to get similar behavior as in C (rounds towards 0)

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import math

print(int_max // 10, math.ceil(int_min / 10))
print(int_max % 10, int(math.fmod(int_min, 10)))

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214748364 -214748364
7 -8

Note that:

  • math.ceil and math.floor return integers, math.fmod returns floats.
  • math.ceil and math.floor take the sign into account, see below:
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print(math.floor(4.5))   # 4
print(math.ceil(4.5))    # 5
print(math.floor(- 4.5)) # -5
print(math.ceil(- 4.5))  # -4

References