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?
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5 Answers
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).
4 Comments
sabbahillel
I prefer the explanation x%y is x - (math.floor(x/y)*y) which is the same as what you said but looks more understandable to me
very hit
@sabbahillel And that is why
(-123) % 10 == 7 in python3, while the result is -3 in other languages like C++. Because (-123) - (math.floor(-123/10)*10) == 7
MNCODE
@veryhit Do you know any reference to the Python sourceCode where % is defined as x - (math.floor(x/y)*y) ? Is % defined differently in cPython ? I know documentation for the math.fmod method, but I want to know how the native % operator is defined.
Blender
@MNCODE: Here's how it's defined in CPython: github.com/python/cpython/blob/…
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 expressionx % ymay not return the same result. The intent of the C standard is thatfmod(x, y)be exactly (mathematically; to infinite precision) equal tox - n*yfor some integer n such that the result has the same sign asxand magnitude less thanabs(y). Python’sx % yreturns a result with the sign ofyinstead, 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 % 1e100is1e100-1e-100, which cannot be represented exactly as a float, and rounds to the surprising1e100. For this reason, functionfmod()is generally preferred when working with floats, while Python’sx % yis preferred when working with integers.
Comments
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.
Comments
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...)
4 Comments
Joran Beasley
@MadPhysicist what? the order of operations of modulo is the same as pow ... certainly less than equals ... so whats the issue?
Mad Physicist
% has the same precedence as /, which is definitely less than pow (same as times though). 3.14 % 2 * pi is the same as (3.14 % 2) * pi == 1.14 * pi rather than 3.14 % (2 * pi).Joran Beasley
I dont have any times or divides in my answer... if I did I would probably group things with parens ... Im not entirely sure what you are saying Oh I c now ... in the original question its not quite clear where the OP would like the parens
3.14 % ( 2*pi) however is still 3.14 which my example was trying to demonstrate with a number less than 3.14 ... afaik the question was not about the order of operations but mehMad Physicist
Fair enough. I can't remove the downvote now, although the answer makes sense now that you explained it.
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
