[Tut] Python divmod() — A Simple Guide with Video

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Python divmod() — A Simple Guide with Video

Python’s built-in

Code:

divmod(a, b)

function takes two integer or float numbers

Code:

a

and

Code:

b

as input arguments and returns a tuple

Code:

(a // b, a % b)

. The first tuple value is the result of theinteger division

Code:

a//b

. The second tuple is the result of the remainder, also called modulo operation

Code:

a % b

. In case of float inputs,

Code:

divmod()

still returns the division without remainder by rounding down to the next round number.



Usage

Learn by example! Here are some examples of how to use the

Code:

divmod()

built-in function with integer arguments:

Code:

# divmod() with integers >>> divmod(10, 2) (5, 0) >>> divmod(10, 3) (3, 1) >>> divmod(10, 4) (2, 2) >>> divmod(10, 5) (2, 0) >>> divmod(10, 10) (1, 0)

You can also use float arguments as follows:

Code:

# divmod() with floats >>> divmod(10.0, 2.0) (5.0, 0.0) >>> divmod(10.0, 3.0) (3.0, 1.0) >>> divmod(10.0, 4.0) (2.0, 2.0) >>> divmod(10.0, 5.0) (2.0, 0.0) >>> divmod(10.0, 10.0) (1.0, 0.0)

Video divmod()



Syntax divmod()

Code:

Syntax: divmod(a, b) -> returns a tuple of two numbers. The first is the result of the division without remainder a/b. The second is the remainder (modulo) a%b.

Arguments |

Code:

integer

|
The dividend of the division operation.

|

Code:

integer

|
The divisor of the division operation.

Return Value |

Code:

tuple

|
Returns a tupleof two numbers. The first is the result of the division without remainder. The second is the remainder (modulo).

Interactive Shell Exercise: Understanding divmod()

Consider the following interactive code:

https://trinket.io/embed/python/4b2905866a

Exercise: Guess the output before running the code.

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Exact Mathematical Definition divmod()

You can generally use the

Code:

divmod(a, b)

function with two integers, one integer and one float, or two floats.

Two integers. Say you call

Code:

divmod(a, b)

with two integers

Code:

a

and

Code:

b

. In this case, the exact mathematical definition of the return value is

Code:

(a // b, a % b)

.

Code:

a = 5 b = 2 print((a // b, a % b)) print(divmod(a, b)) # OUTPUT: # (2, 1) # (2, 1)

One integer and one float. Say you call

Code:

divmod(a, b)

with an integer

Code:

a

and a float

Code:

b

. In this case, the exact mathematical definition of the return value is the return value of converting the integer to a float and calling

Code:

divmod(a, float(b))

.

Code:

a = 5.0 b = 2 print((a // b, a % b)) print(divmod(a, b)) # OUTPUT: # (2.0, 1.0) # (2.0, 1.0)

Two floats. Say you call

Code:

divmod(a, b)

with two floats

Code:

a

and

Code:

b

. In this case, the exact mathematical definition of the return value is

Code:

(float(math.floor(a / b)), a % b)

.

Code:

import math a = 5.0 b = 2.0 print((float(math.floor(a / b)), a % b)) print(divmod(a, b)) # OUTPUT: # (2.0, 1.0) # (2.0, 1.0)

Note that because of the imprecision of floating point arithmetic, the result may have a small floating point error in one of the lower decimal positions. You can read more about the floating point trap on the Finxter blog.

Related Tutorial: Floating Point Error Explained

Python divmod() Negative Numbers

Can you use the

Code:

divmod()

method on negative numbers for the dividend or the divisor?

You can use

Code:

divmod(a, b)

for negative input arguments

Code:

a

,

Code:

b

, or both. In any case, if both arguments are integers, Python performs integer division

Code:

a // b

to obtain the first element and modulo division

Code:

a % b

to obtain the second element of the returned tuple. Both operations allow negative inputs

Code:

a

or

Code:

b

. The returned tuple

Code:

(x, y)

is calculated so that

Code:

x * b + y = a

.

Here’s an example of all three cases:

Code:

>>> divmod(-10, -3) (3, -1) >>> divmod(-10, 3) (-4, 2) >>> divmod(10, -3) (-4, -2)

Python divmod() Performance — Is It Faster Than Integer Division // and Modulo % Operators?

There are two semantically identical ways to create a tuple where the first element is the result of the integer division and the second is the result of the modulo operation:

• Use the
  Code:

  divmod(a, b)
  function.
  
  
• Use the
  Code:

  (a // b, a % b)
  explicit operation with Python built-in operators.
  

Next, we measure the performance of calculating the elapsed runtime in milliseconds when performing 10 million computations for relatively small integers. Let’s start with

Code:

divmod()

:

Code:

import time import random # Small Operands operands = zip([random.randint(1, 100) for i in range(10**7)], [random.randint(1, 100) for i in range(10**7)]) start = time.time() for i, j in operands: divmod(i, j) stop = time.time() print('divmod() elapsed time: ', (stop-start), 'milliseconds') # divmod() elapsed time: 1.7654337882995605 milliseconds

Compare this to integer division and modulo:

Code:

import time import random # Small Operands operands = zip([random.randint(1, 100) for i in range(10**7)], [random.randint(1, 100) for i in range(10**7)]) start = time.time() for i, j in operands: (i // j, i % j) stop = time.time() print('(i // j, i % j) elapsed time: ', (stop-start), 'milliseconds') # (i // j, i % j) elapsed time: 1.9048900604248047 milliseconds

The result of this performance benchmark is that

Code:

divmod()

requires 1.76 milliseconds and the explicit way of using integer division and modulo requires 1.90 milliseconds for 10,000,000 operations. Thus,

Code:

divmod()

is 8% faster. The reason is that the explicit way performs many duplicate operations to calculate the result of the integer division and the modulo operation which internally uses integer division again. This effect becomes even more pronounced if you use larger integers.



Python divmod() Implementation

For integer input arguments, here’s a semantically equivalent

Code:

divmod()

implementation:

Code:

>>> def divmod_own(x, y): return (x // y, x % y) >>> divmod_own(10, 3) (3, 1) >>> divmod(10, 3) (3, 1)

But note that this implementation still performs redundant computations (e.g., integer division) and, therefore, is less efficient than

Code:

divmod()

.

Summary

Python’s built-in

Code:

divmod(a, b)

function takes two integer or float numbers

Code:

a

and

Code:

b

as input arguments and returns a tuple

Code:

(a // b, a % b)

.

• The first tuple value is the result of theinteger division
  Code:

  a//b
  .
  
  
• The second tuple is the result of the remainder, also called modulo operation
  Code:

  a % b
  .
  

In case of float inputs,

Code:

divmod()

still returns the division without remainder by rounding down to the next round number.

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