Modulo operator in Python

What does modulo in the following piece of code do?

from math import *
3.14 % 2 * pi

How do we calculate modulo on a floating point number?

Solution 1:

When you have the expression:

a % b = c

It really means there exists an integer n that makes c as small as possible, but non-negative.

a - n*b = c

By hand, you can just subtract 2 (or add 2 if your number is negative) over and over until the end result is the smallest positive number possible:

  3.14 % 2
= 3.14 - 1 * 2
= 1.14

Also, 3.14 % 2 * pi is interpreted as (3.14 % 2) * pi. I'm not sure if you meant to write 3.14 % (2 * pi) (in either case, the algorithm is the same. Just subtract/add until the number is as small as possible).

Solution 2:

In addition to the other answers, the fmod documentation has some interesting things to say on the subject:

math.fmod(x, y)

Return fmod(x, y), as defined by the platform C library. Note that the Python expression x % y may not return the same result. The intent of the C standard is that fmod(x, y) be exactly (mathematically; to infinite precision) equal to x - n*y for some integer n such that the result has the same sign as x and magnitude less than abs(y). Python’s x % y returns a result with the sign of y instead, and may not be exactly computable for float arguments. For example, fmod(-1e-100, 1e100) is -1e-100, but the result of Python’s -1e-100 % 1e100 is 1e100-1e-100, which cannot be represented exactly as a float, and rounds to the surprising 1e100. For this reason, function fmod() is generally preferred when working with floats, while Python’s x % y is preferred when working with integers.

Solution 3:

Same thing you'd expect from normal modulo .. e.g. 7 % 4 = 3, 7.3 % 4.0 = 3.3

Beware of floating point accuracy issues.

Solution 4:

same as a normal modulo 3.14 % 6.28 = 3.14, just like 3.14%4 =3.14 3.14%2 = 1.14 (the remainder...)

Solution 5:

you should use fmod(a,b)

While abs(x%y) < abs(y) is true mathematically, for floats it may not be true numerically due to roundoff.

For example, and assuming a platform on which a Python float is an IEEE 754 double-precision number, in order that -1e-100 % 1e100 have the same sign as 1e100, the computed result is -1e-100 + 1e100, which is numerically exactly equal to 1e100.

Function fmod() in the math module returns a result whose sign matches the sign of the first argument instead, and so returns -1e-100 in this case. Which approach is more appropriate depends on the application.

where x = a%b is used for integer modulo