## Python Modulo in Practice: How to Use the % Operator

Python supports a wide range of arithmetic operators that you can use when working with numbers in your code. One of these operators is the **modulo operator** ( % ), which returns the remainder of dividing two numbers.

**In this tutorial, you’ll learn:**

- How
**modulo**works in mathematics - How to use the Python modulo operator with different
**numeric types** - How Python calculates the results of a
**modulo operation** - How to override
**.__mod__()**in your classes to use them with the modulo operator - How to use the Python modulo operator to solve
**real-world problems**

The Python modulo operator can sometimes be overlooked. But having a good understanding of this operator will give you an invaluable tool in your Python tool belt.

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### Modulo in Mathematics

The term **modulo** comes from a branch of mathematics called modular arithmetic. Modular arithmetic deals with integer arithmetic on a circular number line that has a fixed set of numbers. All arithmetic operations performed on this number line will wrap around when they reach a certain number called the **modulus**.

A classic example of modulo in modular arithmetic is the twelve-hour clock. A twelve-hour clock has a fixed set of values, from 1 to 12. When counting on a twelve-hour clock, you count up to the modulus 12 and then wrap back to 1. A twelve-hour clock can be classified as “modulo 12,” sometimes shortened to “mod 12.”

The modulo operator is used when you want to compare a number with the modulus and get the equivalent number constrained to the range of the modulus.

For example, say you want to determine what time it would be nine hours after 8:00 a.m. On a twelve-hour clock, you can’t simply add 9 to 8 because you would get 17. You need to take the result, 17, and use mod to get its equivalent value in a twelve-hour context:

17 mod 12 returns 5 . This means that nine hours past 8:00 a.m. is 5:00 p.m. You determined this by taking the number 17 and applying it to a mod 12 context.

Now, if you think about it, 17 and 5 are equivalent in a mod 12 context. If you were to look at the hour hand at 5:00 and 17:00, it would be in the same position. Modular arithmetic has an equation to describe this relationship:

This equation reads “ a and b are congruent modulo n .” This means that a and b are equivalent in mod n as they have the same remainder when divided by n . In the above equation, n is the **modulus** for both a and b . Using the values 17 and 5 from before, the equation would look like this:

This reads “ 17 and 5 are congruent modulo 12 .” 17 and 5 have the same remainder, 5 , when divided by 12 . So in mod 12 , the numbers 17 and 5 are equivalent.

You can confirm this using division:

Both of the operations have the same remainder, 5 , so they’re equivalent modulo 12 .

Now, this may seem like a lot of math for a Python operator, but having this knowledge will prepare you to use the modulo operator in the examples later in this tutorial. In the next section, you’ll look at the basics of using the Python modulo operator with the numeric types int and float .

### Python Modulo Operator Basics

The modulo operator, like the other arithmetic operators, can be used with the numeric types int and float . As you’ll see later on, it can also be used with other types like math.fmod() , decimal.Decimal , and your own classes.

#### Modulo Operator With int

Most of the time you’ll use the modulo operator with integers. The modulo operator, when used with two positive integers, will return the remainder of standard Euclidean division:

Be careful! Just like with the division operator ( / ), Python will return a ZeroDivisionError if you try to use the modulo operator with a divisor of 0 :

Next, you’ll take a look at using the modulo operator with a float .

#### Modulo Operator With float

Similar to int , the modulo operator used with a float will return the remainder of division, but as a float value:

An alternative to using a float with the modulo operator is to use math.fmod() to perform modulo operations on float values:

The official Python docs suggest using math.fmod() over the Python modulo operator when working with float values because of the way math.fmod() calculates the result of the modulo operation. If you’re using a negative operand, then you may see different results between math.fmod(x, y) and x % y . You’ll explore using the modulo operator with negative operands in more detail in the next section.

Just like other arithmetic operators, the modulo operator and math.fmod() may encounter rounding and precision issues when dealing with floating-point arithmetic:

If maintaining floating-point precision is important to your application, then you can use the modulo operator with decimal.Decimal . You’ll look at this later in this tutorial.

#### Modulo Operator With a Negative Operand

All modulo operations you’ve seen up to this point have used two positive operands and returned predictable results. When a negative operand is introduced, things get more complicated.

As it turns out, the way that computers determine the result of a modulo operation with a negative operand leaves ambiguity as to whether the remainder should take the sign of the **dividend** (the number being divided) or the sign of the **divisor** (the number by which the dividend is divided). Different programming languages handle this differently.

For example, in JavaScript, the remainder will take the sign of the dividend:

The remainder in this example, 2 , is positive since it takes the sign of the dividend, 8 . In Python and other languages, the remainder will take the sign of the divisor instead:

Here you can see that the remainder, -1 , takes the sign of the divisor, -3 .

You may be wondering why the remainder in JavaScript is 2 and the remainder in Python is -1 . This has to do with how different languages determine the outcome of a modulo operation. Languages in which the remainder takes the sign of the dividend use the following equation to determine the remainder:

There are three variables this equation:

**r**is the remainder.**a**is the dividend.**n**is the divisor.

trunc() in this equation means that it uses **truncated division**, which will always round a negative number toward zero. For more clarification, see the steps of the modulo operation below using 8 as the dividend and -3 as the divisor:

Here you can see how a language like JavaScript gets the remainder 2 . Python and other languages in which the remainder takes the sign of the divisor use the following equation:

floor() in this equation means that it uses **floor division**. With positive numbers, floor division will return the same result as truncated division. But with a negative number, floor division will round the result down, away from zero:

Here you can see that the result is -1 .

Now that you understand where the difference in the remainder comes from, you may be wondering why this matters if you only use Python. Well, as it turns out, not all modulo operations in Python are the same. While the modulo used with the int and float types will take the sign of the divisor, other types will not.

You can see an example of this when you compare the results of 8.0 % -3.0 and math.fmod(8.0, -3.0) :

math.fmod() takes the sign of the dividend using truncated division, whereas float uses the sign of the divisor. Later in this tutorial, you’ll see another Python type that uses the sign of the dividend, decimal.Decimal .

#### Modulo Operator and divmod()

Python has the built-in function divmod() , which internally uses the modulo operator. divmod() takes two parameters and returns a tuple containing the results of floor division and modulo using the supplied parameters.

Below is an example of using divmod() with 37 and 5 :

You can see that divmod(37, 5) returns the tuple (7, 2) . The 7 is the result of the floor division of 37 and 5 . The 2 is the result of 37 modulo 5 .

Below is an example in which the second parameter is a negative number. As discussed in the previous section, when the modulo operator is used with an int , the remainder will take the sign of the divisor:

Now that you’ve had a chance to see the modulo operator used in several scenarios, it’s important to take a look at how Python determines the precedence of the modulo operator when used with other arithmetic operators.

#### Modulo Operator Precedence

Like other Python operators, there are specific rules for the modulo operator that determine its precedence when evaluating expressions. The modulo operator ( % ) shares the same level of precedence as the multiplication ( * ), division ( / ), and floor division ( // ) operators.

Take a look at an example of the modulo operator’s precedence below:

Both the multiplication and modulo operators have the same level of precedence, so Python will evaluate them from left to right. Here are the steps for the above operation:

**4 * 10**is evaluated, resulting in 40 % 12 — 9 .**40 % 12**is evaluated, resulting in 4 — 9 .**4 — 9**is evaluated, resulting in -5 .

If you want to override the precedence of other operators, then you can use parentheses to surround the operation you want to be evaluated first:

In this example, (12 — 9) is evaluated first, followed by 4 * 10 and finally 40 % 3 , which equals 1 .

### Python Modulo Operator in Practice

Now that you’ve gone through the basics of the Python modulo operator, you’ll look at some examples of using it to solve real-world programming problems. At times, it can be hard to determine when to use the modulo operator in your code. The examples below will give you an idea of the many ways it can be used.

#### How to Check if a Number Is Even or Odd

In this section, you’ll see how you can use the modulo operator to determine if a number is even or odd. Using the modulo operator with a modulus of 2 , you can check any number to see if it’s evenly divisible by 2 . If it is evenly divisible, then it’s an even number.

Take a look at is_even() which checks to see if the num parameter is even:

Here num % 2 will equal 0 if num is even and 1 if num is odd. Checking against 0 will return a Boolean of True or False based on whether or not num is even.

Checking for odd numbers is quite similar. To check for an odd number, you invert the equality check:

This function will return True if num % 2 does not equal 0 , meaning that there’s a remainder proving num is an odd number. Now, you may be wondering if you could use the following function to determine if num is an odd number:

The answer to this question is yes *and* no. Technically, this function will work with the way Python calculates modulo with integers. That said, you should avoid comparing the result of a modulo operation with 1 as not all modulo operations in Python will return the same remainder.

You can see why in the following examples:

In the second example, the remainder takes the sign of the negative divisor and returns -1 . In this case, the Boolean check 3 % -2 == 1 would return False .

However, if you compare the modulo operation with 0 , then it doesn’t matter which operand is negative. The result will always be True when it’s an even number:

If you stick to comparing a Python modulo operation with 0 , then you shouldn’t have any problems checking for even and odd numbers or any other multiples of a number in your code.

In the next section, you’ll take a look at how you can use the modulo operator with loops to control the flow of your program.

#### How to Run Code at Specific Intervals in a Loop

With the Python modulo operator, you can run code at specific intervals inside a loop. This is done by performing a modulo operation with the current index of the loop and a modulus. The modulus number determines how often the interval-specific code will run in the loop.

Here’s an example:

This code defines split_names_into_rows() , which takes two parameters. name_list is a list of names that should be split into rows. modulus sets a modulus for the operation, effectively determining how many names should be in each row. split_names_into_rows() will loop over name_list and start a new row after it hits the modulus value.

Before breaking down the function in more detail, take a look at it in action:

As you can see, the list of names has been split into three rows, with a maximum of three names in each row. modulus defaults to 3 , but you can specify any number:

Now that you’ve seen the code in action, you can break down what it’s doing. First, it uses enumerate() to iterate over name_list , assigning the current item in the list to name and a count value to index . You can see that the optional start argument for enumerate() is set to 1 . This means that the index count will start at 1 instead of 0 :

Next, inside the loop, the function calls print() to output name to the current row. The end parameter for print() is an empty string ( «» ) so it won’t output a newline at the end of the string. An f-string is passed to print() , which uses the string output formatting syntax that Python provides:

Without getting into too much detail, the :-^15 syntax tells print() to do the following:

- Output at least 15 characters, even if the string is shorter than 15 characters.
- Center align the string.
- Fill any space on the right or left of the string with the hyphen character ( — ).

Now that the name has been printed to the row, take a look at the main part of split_names_into_rows() :

This code takes the current iteration index and, using the modulo operator, compares it with modulus . If the result equals 0 , then it can run interval-specific code. In this case, the function calls print() to add a newline, which starts a new row.

The above code is only one example. Using the pattern index % modulus == 0 allows you to run different code at specific intervals in your loops. In the next section, you’ll take this concept a bit further and look at cyclic iteration.

#### How to Create Cyclic Iteration

**Cyclic iteration** describes a type of iteration that will reset once it gets to a certain point. Generally, this type of iteration is used to restrict the index of the iteration to a certain range.

You can use the modulo operator to create cyclic iteration. Take a look at an example using the turtle library to draw a shape:

The above code uses an infinite loop to draw a repeating star shape. After every six iterations, it changes the color of the pen. The pen size increases with each iteration until i is reset back to 0 . If you run the code, then you should get something similar to this:

The important parts of this code are highlighted below:

Each time through the loop, i is updated based on the results of (i + 1) % 6 . This new i value is used to increase the .pensize with each iteration. Once i reaches 5 , (i + 1) % 6 will equal 0 , and i will reset back to 0 .

You can see the steps of the iteration below for more clarification:

When i is reset back to 0 , the .pencolor changes to a new random color as seen below:

The code in this section uses 6 as the modulus, but you could set it to any number to adjust how many times the loop will iterate before resetting the value i .

#### How to Convert Units

In this section, you’ll look at how you can use the modulo operator to convert units. The following examples take smaller units and convert them into larger units without using decimals. The modulo operator is used to determine any remainder that may exist when the smaller unit isn’t evenly divisible by the larger unit.

In this first example, you’ll convert inches into feet. The modulo operator is used to get the remaining inches that don’t evenly divide into feet. The floor division operator ( // ) is used to get the total feet rounded down:

Here’s an example of the function in use:

As you can see from the output, 450 % 12 returns 6 , which is the remaining inches that weren’t evenly divided into feet. The result of 450 // 12 is 37 , which is the total number of feet by which the inches were evenly divided.

You can take this a bit further in this next example. convert_minutes_to_days() takes an integer, total_mins , representing a number of minutes and outputs the period of time in days, hours, and minutes:

Breaking this down, you can see that the function does the following:

- Determines the total number of evenly divisible days with total_mins // 1440 , where 1440 is the number of minutes in a day
- Calculates any extra_minutes left over with total_mins % 1440
- Uses the extra_minutes to get the evenly divisible hours and any extra minutes

You can see how it works below:

While the above examples only deal with converting inches to feet and minutes to days, you could use any type of units with the modulo operator to convert a smaller unit into a larger unit.

**Note**: Both of the above examples could be modified to use divmod() to make the code more succinct. If you remember, divmod() returns a tuple containing the results of floor division and modulo using the supplied parameters.

Below, the floor division and modulo operators have been replaced with divmod() :

As you can see, divmod(total_inches, 12) returns a tuple, which is unpacked into feet and inches .

If you try this updated function, then you’ll receive the same results as before:

You receive the same outcome, but now the code is more concise. You could update convert_minutes_to_days() as well:

Using divmod() , the function is easier to read than the previous version and returns the same result:

Using divmod() isn’t necessary for all situations, but it makes sense here as the unit conversion calculations use both floor division and modulo.

Now that you’ve seen how to use the modulo operator to convert units, in the next section you’ll look at how you can use the modulo operator to check for prime numbers.

#### How to Determine if a Number Is a Prime Number

In this next example, you’ll take a look at how you can use the Python modulo operator to check whether a number is a **prime number**. A prime number is any number that contains only two factors, 1 and itself. Some examples of prime numbers are 2 , 3 , 5 , 7 , 23 , 29 , 59 , 83 , and 97 .

The code below is an implementation for determining the primality of a number using the modulo operator:

This code defines check_prime_number() , which takes the parameter num and checks to see if it’s a prime number. If it is, then a message is displayed stating that num is a prime number. If it’s not a prime number, then a message is displayed with all the factors of the number.

**Note:** The above code isn’t the most efficient way to check for prime numbers. If you’re interested in digging deeper, then check out the Sieve of Eratosthenes and Sieve of Atkin for examples of more performant algorithms for finding prime numbers.

Before you look more closely at the function, here are the results using some different numbers:

Digging into the code, you can see it starts by checking if num is less than 2 . Prime numbers can only be greater than or equal to 2 . If num is less than 2 , then the function doesn’t need to continue. It will print() a message and return :

If num is greater than 2 , then the function checks if num is a prime number. To check this, the function iterates over all the numbers between 2 and the square root of num to see if any divide evenly into num . If one of the numbers divides evenly, then a factor has been found, and num can’t be a prime number.

Here’s the main part of the function:

There’s a lot to unpack here, so let’s take it step by step.

First, a factors list is created with the initial factors, (1, num) . This list will be used to store any other factors that are found:

Next, starting with 2 , the code increments i until it reaches the square root of num . At each iteration, it compares num with i to see if it’s evenly divisible. The code only needs to check up to and including the square root of num because it wouldn’t contain any factors above this:

Instead of trying to determine the square root of num , the function uses a while loop to see if i * i <= num . As long as i * i <= num , the loop hasn’t reached the square root of num .

Inside the while loop, the modulo operator checks if num is evenly divisible by i :

If num is evenly divisible by i , then i is a factor of num , and a tuple of the factors is added to the factors list.

Once the while loop is complete, the code checks to see if any additional factors were found:

If more than one tuple exists in the factors list, then num can’t be a prime number. For nonprime numbers, the factors are printed out. For prime numbers, the function prints a message stating that num is a prime number.

#### How to Implement Ciphers

The Python modulo operator can be used to create ciphers. A cipher is a type of algorithm for performing encryption and decryption on an input, usually text. In this section, you’ll look at two ciphers, the **Caesar cipher** and the **Vigenère cipher**.

##### Caesar Cipher

The first cipher that you’ll look at is the Caesar cipher, named after Julius Caesar, who used it to secretly communicate messages. It’s a substitution cipher that uses letter substitution to encrypt a string of text.

The Caesar cipher works by taking a letter to be encrypted and shifting it a certain number of positions to the left or right in the alphabet. Whichever letter is in that position is used as the encrypted character. This same shift value is applied to all characters in the string.

For example, if the shift were 5 , then A would shift up five letters to become F , B would become G , and so on. Below you can see the encryption process for the text REALPYTHON with a shift of 5 :

The resulting cipher is WJFQUDYMTS .

Decrypting the cipher is done by reversing the shift. Both the encryption and decryption processes can be described with the following expressions, where char_index is the index of the character in the alphabet:

This cipher uses the modulo operator to make sure that, when shifting a letter, the index will wrap around if the end of the alphabet is reached. Now that you know how this cipher works, take a look at an implementation:

This code defines a function called caesar_cipher() , which has two required parameters and one optional parameter:

**text**is the text to be encrypted or decrypted.**shift**is the number of positions to shift each letter.**decrypt**is a Boolean to set if text should be decrypted.

decrypt is included so that a single function can be used to handle both encryption and decryption. This implementation can handle only alphabetic characters, so the function first checks that text is an alphabetic character in the ASCII encoding:

The function then defines three variables to store the lowercase ASCII characters, the uppercase ASCII characters, and the results of the encryption or decryption:

Next, if the function is being used to decrypt text , then it multiplies shift by -1 to make it shift backward:

Finally, caesar_cipher() loops over the individual characters in text and performs the following actions for each char :

- Check if char is lowercase or uppercase.
- Get the index of the char in either the lowercase or uppercase ASCII lists.
- Add a shift to this index to determine the index of the cipher character to use.
- Use % 26 to make sure the shift will wrap back to the start of the alphabet.
- Append the cipher character to the result string.

After the loop finishes iterating over the text value, the result is returned:

Here’s the full code again:

Now run the code in the Python REPL using the text meetMeAtOurHideOutAtTwo with a shift of 10 :

The encrypted result is woodWoKdYebRsnoYedKdDgy . Using this encrypted text, you can run the decryption to get the original text:

The Caesar cipher is fun to play around with for an introduction to cryptography. While the Caesar cipher is rarely used on its own, it’s the basis for more complex substitution ciphers. In the next section, you’ll look at one of the Caesar cipher’s descendants, the Vigenère cipher.

##### Vigenère Cipher

The Vigenère cipher is a polyalphabetic substitution cipher. To perform its encryption, it employs a different Caesar cipher for each letter of the input text. The Vigenère cipher uses a keyword to determine which Caesar cipher should be used to find the cipher letter.

You can see an example of the encryption process in the following image. In this example, the input text REALPYTHON is encrypted using the keyword MODULO :

For each letter of the input text, REALPYTHON , a letter from the keyword MODULO is used to determine which Caesar cipher column should be selected. If the keyword is shorter than the input text, as is the case with MODULO , then the letters of the keyword are repeated until all letters of the input text have been encrypted.

Below is an implementation of the Vigenère cipher. As you’ll see, the modulo operator is used twice in the function:

You may have noticed that the signature for vigenere_cipher() is quite similar to caesar_cipher() from the previous section:

The main difference is that, instead of a shift parameter, vigenere_cipher() takes a key parameter, which is the keyword to be used during encryption and decryption. Another difference is the addition of text.isupper() . Based on this implementation, vigenere_cipher() can only accept input text that is all uppercase.

Like caesar_cipher() , vigenere_cipher() iterates over each letter of the input text to encrypt or decrypt it:

In the above code, you can see the function’s first use of the modulo operator:

Here, the current_key value is determined based on an index returned from i % len(key) . This index is used to select a letter from the key string, such as M from MODULO .

The modulo operator allows you to use any length keyword regardless of the length of the text to be encrypted. Once the index i , the index of the character currently being encrypted, equals the length of the keyword, it will start over from the beginning of the keyword.

For each letter of the input text, several steps determine how to encrypt or decrypt it:

- Determine the char_index based on the index of char inside uppercase .
- Determine the key_index based on the index of current_key inside uppercase .
- Use char_index and key_index to get the index for the encrypted or decrypted character.

Take a look at these steps in the code below:

You can see that the indices for decryption and encryption are calculated differently. That’s why decrypt is used in this function. This way, you can use the function for both encryption and decryption.

After the index is determined, you find the function’s second use of the modulo operator:

index % 26 ensures that the index of the character doesn’t exceed 25 , thus making sure it stays inside the alphabet. With this index, the encrypted or decrypted character is selected from uppercase and appended to results .

Here’s the full code the Vigenère cipher again:

Now go ahead and run it in the Python REPL:

Nice! You now have a working Vigenère cipher for encrypting text strings.

### Python Modulo Operator Advanced Uses

In this final section, you’ll take your modulo operator knowledge to the next level by using it with decimal.Decimal . You’ll also look at how you can add .__mod__() to your custom classes so they can be used with the modulo operator.

#### Using the Python Modulo Operator With decimal.Decimal

Earlier in this tutorial, you saw how you can use the modulo operator with numeric types like int and float as well as with math.fmod() . You can also use the modulo operator with Decimal from the decimal module. You use decimal.Decimal when you want discrete control of the precision of floating-point arithmetic operations.

Here are some examples of using whole integers with decimal.Decimal and the modulo operator:

Here are some floating-point numbers used with decimal.Decimal and the modulo operator:

All modulo operations with decimal.Decimal return the same results as other numeric types, except when one of the operands is negative. Unlike int and float , but like math.fmod() , decimal.Decimal uses the sign of the dividend for the results.

Take a look at the examples below comparing the results of using the modulo operator with standard int and float values and with decimal.Decimal :

Compared with math.fmod() , decimal.Decimal will have the same sign, but the precision will be different:

As you can see from the above examples, working with decimal.Decimal and the modulo operator is similar to working with other numeric types. You just need to keep in mind how it determines the sign of the result when working with a negative operand.

In the next section, you’ll look at how you can override the modulo operator in your classes to customize its behavior.

#### Using the Python Modulo Operator With Custom Classes

The Python data model allows to you override the built-in methods in a Python object to customize its behavior. In this section, you’ll look at how to override .__mod__() so that you can use the modulo operator with your own classes.

For this example, you’ll be working with a Student class. This class will track the amount of time a student has studied. Here’s the initial Student class:

The Student class is initialized with a name parameter and starts with an empty list, study_sessions , which will hold a list of integers representing minutes studied per session. There’s also .add_study_sessions() , which takes a sessions parameter that should be a list of study sessions to add to study_sessions .

Now, if you remember from the converting units section above, convert_minutes_to_day() used the Python modulo operator to convert total_mins into days, hours, and minutes. You’ll now implement a modified version of that method to see how you can use your custom class with the modulo operator:

You can use this function with the Student class to display the total hours a Student has studied. Combined with the Student class above, the code will look like this:

If you load this module in the Python REPL, then you can use it like this:

The above code prints out the total hours jane studied. This version of the code works, but it requires the extra step of summing study_sessions to get total_mins before calling total_study_time_in_hours() .

Here’s how you can modify the Student class to simplify the code:

By overriding .__mod__() and .__floordiv__() , you can use a Student instance with the modulo operator. Calculating the sum() of study_sessions is included in the Student class as well.

With these modifications, you can use a Student instance directly in total_study_time_in_hours() . As total_mins is no longer needed, you can remove it:

Here’s the full code after modifications:

Now, calling the code in the Python REPL, you can see it’s much more succinct:

By overriding .__mod__() , you allow your custom classes to behave more like Python’s built-in numeric types.

### Conclusion

At first glance, the Python modulo operator may not grab your attention. Yet, as you’ve seen, there’s so much to this humble operator. From checking for even numbers to encrypting text with ciphers, you’ve seen many different uses for the modulo operator.

**In this tutorial, you’ve learned how to:**

- Use the
**modulo operator**with int , float , math.fmod() , divmod() , and decimal.Decimal - Calculate the results of a
**modulo operation** - Solve
**real-world problems**using the modulo operator - Override
**.__mod__()**in your own classes to use them with the modulo operator

With the knowledge you’ve gained in this tutorial, you can now start using the modulo operator in your own code with great success. Happy Pythoning!

Watch Now This tutorial has a related video course created by the Real Python team. Watch it together with the written tutorial to deepen your understanding: **Python Modulo: Using the % Operator**

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About **Jason Van Schooneveld**

Jason is a software developer based in Taipei. When he's not tinkering with electronics or building Django web apps, you can find him hiking the mountains of Taiwan or brushing up on his Chinese.

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## Оператор модуля: modulo Python – примеры получения остатка

Как и в других языках программирования, оператор модуля Python выполняет ту же работу по нахождению модуля заданного числа. Оператор представляет собой математический символ, используемый для выполнения различных операций, таких как(+, -, * /) сложение, вычитание, умножение и деление над заданными двумя числами, чтобы вернуть результат в виде целого числа, а также числа с плавающей запятой.

Оператор указывает компилятору выполнить определенные действия на основе переданного символа оператора для данного числа.

### Оператор модуля

Оператор модуля Python – это встроенный оператор, который возвращает оставшиеся числа путем деления первого числа на второе. Он также известен как Python modulo. В Python символ модуля представлен в виде символа процента(%). И называется он оператором остатка.

Ниже приведен синтаксис для получения остатка путем деления первого числа на второе.

Здесь X и Y – два целых числа, а модуль(%) используется между ними, чтобы получить остаток, где первое число(X) делится на второе число(Y).

Например, у нас есть два числа, 24 и 5. И мы можем получить остаток, используя модуль или оператор по модулю между числами 24% 5. Здесь 24 делится на 5, что возвращает 4 в качестве остатка и 4 в качестве частного. Когда первое число полностью делится на другое число, не оставляя остатка, результатом будет 0.

### Получение остатка двух целых чисел с помощью цикла while

Давайте напишем программу для получения остатка от двух чисел, используя цикл while и оператор модуля(%) в Python.

### Остаток двух чисел с плавающей запятой

Напишем программу, чтобы найти остаток от двух целых чисел, используя оператор модуля в Python.

### Отрицательного числа

Давайте напишем программу, чтобы получить остаток от двух отрицательных чисел, используя цикл while и оператор модуля(%) в Python.

### Нахождение остатка двух чисел с помощью функции fmod()

Рассмотрим программу, как получить остаток от двух чисел с плавающей запятой, используя функцию fmod() в Python.

### n чисел с помощью функции

Давайте напишем программу на Python, чтобы найти модуль n чисел с помощью функции и цикла for.

### Заданного массива с помощью функции mod()

Напишем программу для демонстрации функции mod() в Python.

Как мы видим в приведенной выше программе, переменные x и y содержат массивы. После этого мы используем функцию mod() для передачи x и y в качестве параметра массива, который делит первый массив(x) на второй массив(y), а затем возвращает остаток чисел.

### Нахождение модуля двух чисел, используя numpy

Давайте рассмотрим программу для импорта пакета numpy из библиотеки Python, а затем воспользуемся функцией остатка для получения модуля в Python.

### Исключения в операторе модуля Python

В Python, когда число делится на ноль, возникает исключение, которое называется ZeroDivisionError. Другими словами, он возвращает исключение, когда число делится на делитель, равный нулю. Следовательно, если мы хотим удалить исключение из оператора модуля Python, делитель не должен быть равен нулю.

Напишем программу для демонстрации оператора Python Exception in Modulus.

Как видно из приведенного выше результата, он отображает: «Невозможно разделить число на ноль! Поэтому измените значение правого операнда». Следовательно, мы можем сказать, что когда мы делим первое число на ноль, оно возвращает исключение.

## Built-in Types¶

The following sections describe the standard types that are built into the interpreter.

The principal built-in types are numerics, sequences, mappings, classes, instances and exceptions.

Some collection classes are mutable. The methods that add, subtract, or rearrange their members in place, and don’t return a specific item, never return the collection instance itself but None .

Some operations are supported by several object types; in particular, practically all objects can be compared for equality, tested for truth value, and converted to a string (with the repr() function or the slightly different str() function). The latter function is implicitly used when an object is written by the print() function.

### Truth Value Testing¶

Any object can be tested for truth value, for use in an if or while condition or as operand of the Boolean operations below.

By default, an object is considered true unless its class defines either a __bool__() method that returns False or a __len__() method that returns zero, when called with the object. 1 Here are most of the built-in objects considered false:

constants defined to be false: None and False .

zero of any numeric type: 0 , 0.0 , 0j , Decimal(0) , Fraction(0, 1)

empty sequences and collections: » , () , [] , <> , set() , range(0)

Operations and built-in functions that have a Boolean result always return 0 or False for false and 1 or True for true, unless otherwise stated. (Important exception: the Boolean operations or and and always return one of their operands.)

### Boolean Operations — and , or , not ¶

These are the Boolean operations, ordered by ascending priority:

if *x* is false, then True , else False

This is a short-circuit operator, so it only evaluates the second argument if the first one is false.

This is a short-circuit operator, so it only evaluates the second argument if the first one is true.

not has a lower priority than non-Boolean operators, so not a == b is interpreted as not (a == b) , and a == not b is a syntax error.

### Comparisons¶

There are eight comparison operations in Python. They all have the same priority (which is higher than that of the Boolean operations). Comparisons can be chained arbitrarily; for example, x < y <= z is equivalent to x < y and y <= z , except that *y* is evaluated only once (but in both cases *z* is not evaluated at all when x < y is found to be false).

This table summarizes the comparison operations:

strictly less than

less than or equal

strictly greater than

greater than or equal

negated object identity

Objects of different types, except different numeric types, never compare equal. The == operator is always defined but for some object types (for example, class objects) is equivalent to is . The < , <= , > and >= operators are only defined where they make sense; for example, they raise a TypeError exception when one of the arguments is a complex number.

Non-identical instances of a class normally compare as non-equal unless the class defines the __eq__() method.

Instances of a class cannot be ordered with respect to other instances of the same class, or other types of object, unless the class defines enough of the methods __lt__() , __le__() , __gt__() , and __ge__() (in general, __lt__() and __eq__() are sufficient, if you want the conventional meanings of the comparison operators).

The behavior of the is and is not operators cannot be customized; also they can be applied to any two objects and never raise an exception.

Two more operations with the same syntactic priority, in and not in , are supported by types that are iterable or implement the __contains__() method.

### Numeric Types — int , float , complex ¶

There are three distinct numeric types: *integers*, *floating point numbers*, and *complex numbers*. In addition, Booleans are a subtype of integers. Integers have unlimited precision. Floating point numbers are usually implemented using double in C; information about the precision and internal representation of floating point numbers for the machine on which your program is running is available in sys.float_info . Complex numbers have a real and imaginary part, which are each a floating point number. To extract these parts from a complex number *z*, use z.real and z.imag . (The standard library includes the additional numeric types fractions.Fraction , for rationals, and decimal.Decimal , for floating-point numbers with user-definable precision.)

Numbers are created by numeric literals or as the result of built-in functions and operators. Unadorned integer literals (including hex, octal and binary numbers) yield integers. Numeric literals containing a decimal point or an exponent sign yield floating point numbers. Appending ‘j’ or ‘J’ to a numeric literal yields an imaginary number (a complex number with a zero real part) which you can add to an integer or float to get a complex number with real and imaginary parts.

Python fully supports mixed arithmetic: when a binary arithmetic operator has operands of different numeric types, the operand with the “narrower” type is widened to that of the other, where integer is narrower than floating point, which is narrower than complex. A comparison between numbers of different types behaves as though the exact values of those numbers were being compared. 2

The constructors int() , float() , and complex() can be used to produce numbers of a specific type.

All numeric types (except complex) support the following operations (for priorities of the operations, see Operator precedence ):

difference of *x* and *y*

floored quotient of *x* and *y*

remainder of x / y

absolute value or magnitude of *x*

*x* converted to integer

*x* converted to floating point

a complex number with real part *re*, imaginary part *im*. *im* defaults to zero.

conjugate of the complex number *c*

the pair (x // y, x % y)

Also referred to as integer division. The resultant value is a whole integer, though the result’s type is not necessarily int. The result is always rounded towards minus infinity: 1//2 is 0 , (-1)//2 is -1 , 1//(-2) is -1 , and (-1)//(-2) is 0 .

Not for complex numbers. Instead convert to floats using abs() if appropriate.

Conversion from floating point to integer may round or truncate as in C; see functions math.floor() and math.ceil() for well-defined conversions.

float also accepts the strings “nan” and “inf” with an optional prefix “+” or “-” for Not a Number (NaN) and positive or negative infinity.

Python defines pow(0, 0) and 0 ** 0 to be 1 , as is common for programming languages.

The numeric literals accepted include the digits 0 to 9 or any Unicode equivalent (code points with the Nd property).

All numbers.Real types ( int and float ) also include the following operations:

*x* rounded to *n* digits, rounding half to even. If *n* is omitted, it defaults to 0.

For additional numeric operations see the math and cmath modules.

#### Bitwise Operations on Integer Types¶

Bitwise operations only make sense for integers. The result of bitwise operations is calculated as though carried out in two’s complement with an infinite number of sign bits.

The priorities of the binary bitwise operations are all lower than the numeric operations and higher than the comparisons; the unary operation

has the same priority as the other unary numeric operations ( + and — ).

This table lists the bitwise operations sorted in ascending priority:

bitwise *exclusive or* of *x* and *y*

*x* shifted left by *n* bits

*x* shifted right by *n* bits

the bits of *x* inverted

Negative shift counts are illegal and cause a ValueError to be raised.

A left shift by *n* bits is equivalent to multiplication by pow(2, n) .

A right shift by *n* bits is equivalent to floor division by pow(2, n) .

Performing these calculations with at least one extra sign extension bit in a finite two’s complement representation (a working bit-width of 1 + max(x.bit_length(), y.bit_length()) or more) is sufficient to get the same result as if there were an infinite number of sign bits.

#### Additional Methods on Integer Types¶

The int type implements the numbers.Integral abstract base class . In addition, it provides a few more methods:

Return the number of bits necessary to represent an integer in binary, excluding the sign and leading zeros:

More precisely, if x is nonzero, then x.bit_length() is the unique positive integer k such that 2**(k-1) <= abs(x) < 2**k . Equivalently, when abs(x) is small enough to have a correctly rounded logarithm, then k = 1 + int(log(abs(x), 2)) . If x is zero, then x.bit_length() returns 0 .

New in version 3.1.

Return the number of ones in the binary representation of the absolute value of the integer. This is also known as the population count. Example:

New in version 3.10.

Return an array of bytes representing an integer.

The integer is represented using *length* bytes. An OverflowError is raised if the integer is not representable with the given number of bytes.

The *byteorder* argument determines the byte order used to represent the integer. If *byteorder* is "big" , the most significant byte is at the beginning of the byte array. If *byteorder* is "little" , the most significant byte is at the end of the byte array. To request the native byte order of the host system, use sys.byteorder as the byte order value.

The *signed* argument determines whether two’s complement is used to represent the integer. If *signed* is False and a negative integer is given, an OverflowError is raised. The default value for *signed* is False .

New in version 3.2.

Return the integer represented by the given array of bytes.

The argument *bytes* must either be a bytes-like object or an iterable producing bytes.

The *byteorder* argument determines the byte order used to represent the integer. If *byteorder* is "big" , the most significant byte is at the beginning of the byte array. If *byteorder* is "little" , the most significant byte is at the end of the byte array. To request the native byte order of the host system, use sys.byteorder as the byte order value.

The *signed* argument indicates whether two’s complement is used to represent the integer.

New in version 3.2.

Return a pair of integers whose ratio is exactly equal to the original integer and with a positive denominator. The integer ratio of integers (whole numbers) is always the integer as the numerator and 1 as the denominator.

New in version 3.8.

#### Additional Methods on Float¶

The float type implements the numbers.Real abstract base class . float also has the following additional methods.

Return a pair of integers whose ratio is exactly equal to the original float and with a positive denominator. Raises OverflowError on infinities and a ValueError on NaNs.

Return True if the float instance is finite with integral value, and False otherwise:

Two methods support conversion to and from hexadecimal strings. Since Python’s floats are stored internally as binary numbers, converting a float to or from a *decimal* string usually involves a small rounding error. In contrast, hexadecimal strings allow exact representation and specification of floating-point numbers. This can be useful when debugging, and in numerical work.

Return a representation of a floating-point number as a hexadecimal string. For finite floating-point numbers, this representation will always include a leading 0x and a trailing p and exponent.

*classmethod* float. fromhex ( *s* ) ¶

Class method to return the float represented by a hexadecimal string *s*. The string *s* may have leading and trailing whitespace.

Note that float.hex() is an instance method, while float.fromhex() is a class method.

A hexadecimal string takes the form:

where the optional sign may by either + or — , integer and fraction are strings of hexadecimal digits, and exponent is a decimal integer with an optional leading sign. Case is not significant, and there must be at least one hexadecimal digit in either the integer or the fraction. This syntax is similar to the syntax specified in section 6.4.4.2 of the C99 standard, and also to the syntax used in Java 1.5 onwards. In particular, the output of float.hex() is usable as a hexadecimal floating-point literal in C or Java code, and hexadecimal strings produced by C’s %a format character or Java’s Double.toHexString are accepted by float.fromhex() .

Note that the exponent is written in decimal rather than hexadecimal, and that it gives the power of 2 by which to multiply the coefficient. For example, the hexadecimal string 0x3.a7p10 represents the floating-point number (3 + 10./16 + 7./16**2) * 2.0**10 , or 3740.0 :

Applying the reverse conversion to 3740.0 gives a different hexadecimal string representing the same number:

#### Hashing of numeric types¶

For numbers x and y , possibly of different types, it’s a requirement that hash(x) == hash(y) whenever x == y (see the __hash__() method documentation for more details). For ease of implementation and efficiency across a variety of numeric types (including int , float , decimal.Decimal and fractions.Fraction ) Python’s hash for numeric types is based on a single mathematical function that’s defined for any rational number, and hence applies to all instances of int and fractions.Fraction , and all finite instances of float and decimal.Decimal . Essentially, this function is given by reduction modulo P for a fixed prime P . The value of P is made available to Python as the modulus attribute of sys.hash_info .

**CPython implementation detail:** Currently, the prime used is P = 2**31 — 1 on machines with 32-bit C longs and P = 2**61 — 1 on machines with 64-bit C longs.

Here are the rules in detail:

If x = m / n is a nonnegative rational number and n is not divisible by P , define hash(x) as m * invmod(n, P) % P , where invmod(n, P) gives the inverse of n modulo P .

If x = m / n is a nonnegative rational number and n is divisible by P (but m is not) then n has no inverse modulo P and the rule above doesn’t apply; in this case define hash(x) to be the constant value sys.hash_info.inf .

If x = m / n is a negative rational number define hash(x) as -hash(-x) . If the resulting hash is -1 , replace it with -2 .

The particular values sys.hash_info.inf and -sys.hash_info.inf are used as hash values for positive infinity or negative infinity (respectively).

For a complex number z , the hash values of the real and imaginary parts are combined by computing hash(z.real) + sys.hash_info.imag * hash(z.imag) , reduced modulo 2**sys.hash_info.width so that it lies in range(-2**(sys.hash_info.width — 1), 2**(sys.hash_info.width — 1)) . Again, if the result is -1 , it’s replaced with -2 .

To clarify the above rules, here’s some example Python code, equivalent to the built-in hash, for computing the hash of a rational number, float , or complex :

### Iterator Types¶

Python supports a concept of iteration over containers. This is implemented using two distinct methods; these are used to allow user-defined classes to support iteration. Sequences, described below in more detail, always support the iteration methods.

One method needs to be defined for container objects to provide iterable support:

Return an iterator object. The object is required to support the iterator protocol described below. If a container supports different types of iteration, additional methods can be provided to specifically request iterators for those iteration types. (An example of an object supporting multiple forms of iteration would be a tree structure which supports both breadth-first and depth-first traversal.) This method corresponds to the tp_iter slot of the type structure for Python objects in the Python/C API.

The iterator objects themselves are required to support the following two methods, which together form the *iterator protocol*:

Return the iterator object itself. This is required to allow both containers and iterators to be used with the for and in statements. This method corresponds to the tp_iter slot of the type structure for Python objects in the Python/C API.

Return the next item from the iterator . If there are no further items, raise the StopIteration exception. This method corresponds to the tp_iternext slot of the type structure for Python objects in the Python/C API.

Python defines several iterator objects to support iteration over general and specific sequence types, dictionaries, and other more specialized forms. The specific types are not important beyond their implementation of the iterator protocol.

Once an iterator’s __next__() method raises StopIteration , it must continue to do so on subsequent calls. Implementations that do not obey this property are deemed broken.

#### Generator Types¶

Python’s generator s provide a convenient way to implement the iterator protocol. If a container object’s __iter__() method is implemented as a generator, it will automatically return an iterator object (technically, a generator object) supplying the __iter__() and __next__() methods. More information about generators can be found in the documentation for the yield expression .

### Sequence Types — list , tuple , range ¶

There are three basic sequence types: lists, tuples, and range objects. Additional sequence types tailored for processing of binary data and text strings are described in dedicated sections.

#### Common Sequence Operations¶

The operations in the following table are supported by most sequence types, both mutable and immutable. The collections.abc.Sequence ABC is provided to make it easier to correctly implement these operations on custom sequence types.

This table lists the sequence operations sorted in ascending priority. In the table, *s* and *t* are sequences of the same type, *n*, *i*, *j* and *k* are integers and *x* is an arbitrary object that meets any type and value restrictions imposed by *s*.

The in and not in operations have the same priorities as the comparison operations. The + (concatenation) and * (repetition) operations have the same priority as the corresponding numeric operations. 3

True if an item of *s* is equal to *x*, else False

False if an item of *s* is equal to *x*, else True

the concatenation of *s* and *t*

equivalent to adding *s* to itself *n* times

*i*th item of *s*, origin 0

slice of *s* from *i* to *j* with step *k*

smallest item of *s*

largest item of *s*

index of the first occurrence of *x* in *s* (at or after index *i* and before index *j*)

total number of occurrences of *x* in *s*

Sequences of the same type also support comparisons. In particular, tuples and lists are compared lexicographically by comparing corresponding elements. This means that to compare equal, every element must compare equal and the two sequences must be of the same type and have the same length. (For full details see Comparisons in the language reference.)

Forward and reversed iterators over mutable sequences access values using an index. That index will continue to march forward (or backward) even if the underlying sequence is mutated. The iterator terminates only when an IndexError or a StopIteration is encountered (or when the index drops below zero).

While the in and not in operations are used only for simple containment testing in the general case, some specialised sequences (such as str , bytes and bytearray ) also use them for subsequence testing:

Values of *n* less than 0 are treated as 0 (which yields an empty sequence of the same type as *s*). Note that items in the sequence *s* are not copied; they are referenced multiple times. This often haunts new Python programmers; consider:

What has happened is that [[]] is a one-element list containing an empty list, so all three elements of [[]] * 3 are references to this single empty list. Modifying any of the elements of lists modifies this single list. You can create a list of different lists this way:

Further explanation is available in the FAQ entry How do I create a multidimensional list? .

If *i* or *j* is negative, the index is relative to the end of sequence *s*: len(s) + i or len(s) + j is substituted. But note that -0 is still 0 .

The slice of *s* from *i* to *j* is defined as the sequence of items with index *k* such that i <= k < j . If *i* or *j* is greater than len(s) , use len(s) . If *i* is omitted or None , use 0 . If *j* is omitted or None , use len(s) . If *i* is greater than or equal to *j*, the slice is empty.

The slice of *s* from *i* to *j* with step *k* is defined as the sequence of items with index x = i + n*k such that 0 <= n < (j-i)/k . In other words, the indices are i , i+k , i+2*k , i+3*k and so on, stopping when *j* is reached (but never including *j*). When *k* is positive, *i* and *j* are reduced to len(s) if they are greater. When *k* is negative, *i* and *j* are reduced to len(s) — 1 if they are greater. If *i* or *j* are omitted or None , they become “end” values (which end depends on the sign of *k*). Note, *k* cannot be zero. If *k* is None , it is treated like 1 .

Concatenating immutable sequences always results in a new object. This means that building up a sequence by repeated concatenation will have a quadratic runtime cost in the total sequence length. To get a linear runtime cost, you must switch to one of the alternatives below:

if concatenating str objects, you can build a list and use str.join() at the end or else write to an io.StringIO instance and retrieve its value when complete

if concatenating bytes objects, you can similarly use bytes.join() or io.BytesIO , or you can do in-place concatenation with a bytearray object. bytearray objects are mutable and have an efficient overallocation mechanism

if concatenating tuple objects, extend a list instead

for other types, investigate the relevant class documentation

Some sequence types (such as range ) only support item sequences that follow specific patterns, and hence don’t support sequence concatenation or repetition.

index raises ValueError when *x* is not found in *s*. Not all implementations support passing the additional arguments *i* and *j*. These arguments allow efficient searching of subsections of the sequence. Passing the extra arguments is roughly equivalent to using s[i:j].index(x) , only without copying any data and with the returned index being relative to the start of the sequence rather than the start of the slice.

#### Immutable Sequence Types¶

The only operation that immutable sequence types generally implement that is not also implemented by mutable sequence types is support for the hash() built-in.

This support allows immutable sequences, such as tuple instances, to be used as dict keys and stored in set and frozenset instances.

Attempting to hash an immutable sequence that contains unhashable values will result in TypeError .

#### Mutable Sequence Types¶

The operations in the following table are defined on mutable sequence types. The collections.abc.MutableSequence ABC is provided to make it easier to correctly implement these operations on custom sequence types.

In the table *s* is an instance of a mutable sequence type, *t* is any iterable object and *x* is an arbitrary object that meets any type and value restrictions imposed by *s* (for example, bytearray only accepts integers that meet the value restriction 0 <= x <= 255 ).

item *i* of *s* is replaced by *x*

slice of *s* from *i* to *j* is replaced by the contents of the iterable *t*

the elements of s[i:j:k] are replaced by those of *t*

removes the elements of s[i:j:k] from the list

appends *x* to the end of the sequence (same as s[len(s):len(s)] = [x] )

removes all items from *s* (same as del s[:] )

creates a shallow copy of *s* (same as s[:] )

s.extend(t) or s += t

extends *s* with the contents of *t* (for the most part the same as s[len(s):len(s)] = t )

updates *s* with its contents repeated *n* times

inserts *x* into *s* at the index given by *i* (same as s[i:i] = [x] )

retrieves the item at *i* and also removes it from *s*

remove the first item from *s* where s[i] is equal to *x*

reverses the items of *s* in place

*t* must have the same length as the slice it is replacing.

The optional argument *i* defaults to -1 , so that by default the last item is removed and returned.

remove() raises ValueError when *x* is not found in *s*.

The reverse() method modifies the sequence in place for economy of space when reversing a large sequence. To remind users that it operates by side effect, it does not return the reversed sequence.

clear() and copy() are included for consistency with the interfaces of mutable containers that don’t support slicing operations (such as dict and set ). copy() is not part of the collections.abc.MutableSequence ABC, but most concrete mutable sequence classes provide it.

New in version 3.3: clear() and copy() methods.

The value *n* is an integer, or an object implementing __index__() . Zero and negative values of *n* clear the sequence. Items in the sequence are not copied; they are referenced multiple times, as explained for s * n under Common Sequence Operations .

#### Lists¶

Lists are mutable sequences, typically used to store collections of homogeneous items (where the precise degree of similarity will vary by application).

Lists may be constructed in several ways:

Using a pair of square brackets to denote the empty list: []

Using square brackets, separating items with commas: [a] , [a, b, c]

Using a list comprehension: [x for x in iterable]

Using the type constructor: list() or list(iterable)

The constructor builds a list whose items are the same and in the same order as *iterable*’s items. *iterable* may be either a sequence, a container that supports iteration, or an iterator object. If *iterable* is already a list, a copy is made and returned, similar to iterable[:] . For example, list(‘abc’) returns [‘a’, ‘b’, ‘c’] and list( (1, 2, 3) ) returns [1, 2, 3] . If no argument is given, the constructor creates a new empty list, [] .

Many other operations also produce lists, including the sorted() built-in.

Lists implement all of the common and mutable sequence operations. Lists also provide the following additional method:

sort ( *** , *key = None* , *reverse = False* ) ¶

This method sorts the list in place, using only < comparisons between items. Exceptions are not suppressed — if any comparison operations fail, the entire sort operation will fail (and the list will likely be left in a partially modified state).

sort() accepts two arguments that can only be passed by keyword ( keyword-only arguments ):

*key* specifies a function of one argument that is used to extract a comparison key from each list element (for example, key=str.lower ). The key corresponding to each item in the list is calculated once and then used for the entire sorting process. The default value of None means that list items are sorted directly without calculating a separate key value.

The functools.cmp_to_key() utility is available to convert a 2.x style *cmp* function to a *key* function.

*reverse* is a boolean value. If set to True , then the list elements are sorted as if each comparison were reversed.

This method modifies the sequence in place for economy of space when sorting a large sequence. To remind users that it operates by side effect, it does not return the sorted sequence (use sorted() to explicitly request a new sorted list instance).

The sort() method is guaranteed to be stable. A sort is stable if it guarantees not to change the relative order of elements that compare equal — this is helpful for sorting in multiple passes (for example, sort by department, then by salary grade).

For sorting examples and a brief sorting tutorial, see Sorting HOW TO .

**CPython implementation detail:** While a list is being sorted, the effect of attempting to mutate, or even inspect, the list is undefined. The C implementation of Python makes the list appear empty for the duration, and raises ValueError if it can detect that the list has been mutated during a sort.

#### Tuples¶

Tuples are immutable sequences, typically used to store collections of heterogeneous data (such as the 2-tuples produced by the enumerate() built-in). Tuples are also used for cases where an immutable sequence of homogeneous data is needed (such as allowing storage in a set or dict instance).

Tuples may be constructed in a number of ways:

Using a pair of parentheses to denote the empty tuple: ()

Using a trailing comma for a singleton tuple: a, or (a,)

Separating items with commas: a, b, c or (a, b, c)

Using the tuple() built-in: tuple() or tuple(iterable)

The constructor builds a tuple whose items are the same and in the same order as *iterable*’s items. *iterable* may be either a sequence, a container that supports iteration, or an iterator object. If *iterable* is already a tuple, it is returned unchanged. For example, tuple(‘abc’) returns (‘a’, ‘b’, ‘c’) and tuple( [1, 2, 3] ) returns (1, 2, 3) . If no argument is given, the constructor creates a new empty tuple, () .

Note that it is actually the comma which makes a tuple, not the parentheses. The parentheses are optional, except in the empty tuple case, or when they are needed to avoid syntactic ambiguity. For example, f(a, b, c) is a function call with three arguments, while f((a, b, c)) is a function call with a 3-tuple as the sole argument.

Tuples implement all of the common sequence operations.

For heterogeneous collections of data where access by name is clearer than access by index, collections.namedtuple() may be a more appropriate choice than a simple tuple object.

#### Ranges¶

The range type represents an immutable sequence of numbers and is commonly used for looping a specific number of times in for loops.

The arguments to the range constructor must be integers (either built-in int or any object that implements the __index__() special method). If the *step* argument is omitted, it defaults to 1 . If the *start* argument is omitted, it defaults to 0 . If *step* is zero, ValueError is raised.

For a positive *step*, the contents of a range r are determined by the formula r[i] = start + step*i where i >= 0 and r[i] < stop .

For a negative *step*, the contents of the range are still determined by the formula r[i] = start + step*i , but the constraints are i >= 0 and r[i] > stop .

A range object will be empty if r[0] does not meet the value constraint. Ranges do support negative indices, but these are interpreted as indexing from the end of the sequence determined by the positive indices.

Ranges containing absolute values larger than sys.maxsize are permitted but some features (such as len() ) may raise OverflowError .

Ranges implement all of the common sequence operations except concatenation and repetition (due to the fact that range objects can only represent sequences that follow a strict pattern and repetition and concatenation will usually violate that pattern).

The value of the *start* parameter (or 0 if the parameter was not supplied)

The value of the *stop* parameter

The value of the *step* parameter (or 1 if the parameter was not supplied)

The advantage of the range type over a regular list or tuple is that a range object will always take the same (small) amount of memory, no matter the size of the range it represents (as it only stores the start , stop and step values, calculating individual items and subranges as needed).

Range objects implement the collections.abc.Sequence ABC, and provide features such as containment tests, element index lookup, slicing and support for negative indices (see Sequence Types — list, tuple, range ):

Testing range objects for equality with == and != compares them as sequences. That is, two range objects are considered equal if they represent the same sequence of values. (Note that two range objects that compare equal might have different start , stop and step attributes, for example range(0) == range(2, 1, 3) or range(0, 3, 2) == range(0, 4, 2) .)

Changed in version 3.2: Implement the Sequence ABC. Support slicing and negative indices. Test int objects for membership in constant time instead of iterating through all items.

Changed in version 3.3: Define ‘==’ and ‘!=’ to compare range objects based on the sequence of values they define (instead of comparing based on object identity).

New in version 3.3: The start , stop and step attributes.

The linspace recipe shows how to implement a lazy version of range suitable for floating point applications.

### Text Sequence Type — str ¶

Textual data in Python is handled with str objects, or *strings*. Strings are immutable sequences of Unicode code points. String literals are written in a variety of ways:

Single quotes: ‘allows embedded "double" quotes’

Double quotes: "allows embedded ‘single’ quotes"

Triple quoted: »’Three single quotes»’ , """Three double quotes"""

Triple quoted strings may span multiple lines — all associated whitespace will be included in the string literal.

String literals that are part of a single expression and have only whitespace between them will be implicitly converted to a single string literal. That is, ("spam " "eggs") == "spam eggs" .

See String and Bytes literals for more about the various forms of string literal, including supported escape sequences, and the r (“raw”) prefix that disables most escape sequence processing.

Strings may also be created from other objects using the str constructor.

Since there is no separate “character” type, indexing a string produces strings of length 1. That is, for a non-empty string *s*, s[0] == s[0:1] .

There is also no mutable string type, but str.join() or io.StringIO can be used to efficiently construct strings from multiple fragments.

Changed in version 3.3: For backwards compatibility with the Python 2 series, the u prefix is once again permitted on string literals. It has no effect on the meaning of string literals and cannot be combined with the r prefix.

Return a string version of *object*. If *object* is not provided, returns the empty string. Otherwise, the behavior of str() depends on whether *encoding* or *errors* is given, as follows.

If neither *encoding* nor *errors* is given, str(object) returns type(object).__str__(object) , which is the “informal” or nicely printable string representation of *object*. For string objects, this is the string itself. If *object* does not have a __str__() method, then str() falls back to returning repr(object) .

If at least one of *encoding* or *errors* is given, *object* should be a bytes-like object (e.g. bytes or bytearray ). In this case, if *object* is a bytes (or bytearray ) object, then str(bytes, encoding, errors) is equivalent to bytes.decode(encoding, errors) . Otherwise, the bytes object underlying the buffer object is obtained before calling bytes.decode() . See Binary Sequence Types — bytes, bytearray, memoryview and Buffer Protocol for information on buffer objects.

Passing a bytes object to str() without the *encoding* or *errors* arguments falls under the first case of returning the informal string representation (see also the -b command-line option to Python). For example:

For more information on the str class and its methods, see Text Sequence Type — str and the String Methods section below. To output formatted strings, see the Formatted string literals and Format String Syntax sections. In addition, see the Text Processing Services section.

#### String Methods¶

Strings implement all of the common sequence operations, along with the additional methods described below.

Strings also support two styles of string formatting, one providing a large degree of flexibility and customization (see str.format() , Format String Syntax and Custom String Formatting ) and the other based on C printf style formatting that handles a narrower range of types and is slightly harder to use correctly, but is often faster for the cases it can handle ( printf-style String Formatting ).

The Text Processing Services section of the standard library covers a number of other modules that provide various text related utilities (including regular expression support in the re module).

Return a copy of the string with its first character capitalized and the rest lowercased.

Changed in version 3.8: The first character is now put into titlecase rather than uppercase. This means that characters like digraphs will only have their first letter capitalized, instead of the full character.

Return a casefolded copy of the string. Casefolded strings may be used for caseless matching.

Casefolding is similar to lowercasing but more aggressive because it is intended to remove all case distinctions in a string. For example, the German lowercase letter ‘ß’ is equivalent to "ss" . Since it is already lowercase, lower() would do nothing to ‘ß’ ; casefold() converts it to "ss" .

The casefolding algorithm is described in section 3.13 of the Unicode Standard.

New in version 3.3.

Return centered in a string of length *width*. Padding is done using the specified *fillchar* (default is an ASCII space). The original string is returned if *width* is less than or equal to len(s) .

Return the number of non-overlapping occurrences of substring *sub* in the range [*start*, *end*]. Optional arguments *start* and *end* are interpreted as in slice notation.

str. encode ( *encoding = ‘utf-8’* , *errors = ‘strict’* ) ¶

Return an encoded version of the string as a bytes object. Default encoding is ‘utf-8’ . *errors* may be given to set a different error handling scheme. The default for *errors* is ‘strict’ , meaning that encoding errors raise a UnicodeError . Other possible values are ‘ignore’ , ‘replace’ , ‘xmlcharrefreplace’ , ‘backslashreplace’ and any other name registered via codecs.register_error() , see section Error Handlers . For a list of possible encodings, see section Standard Encodings .

By default, the *errors* argument is not checked for best performances, but only used at the first encoding error. Enable the Python Development Mode , or use a debug build to check *errors*.

Changed in version 3.1: Support for keyword arguments added.

Changed in version 3.9: The *errors* is now checked in development mode and in debug mode .

Return True if the string ends with the specified *suffix*, otherwise return False . *suffix* can also be a tuple of suffixes to look for. With optional *start*, test beginning at that position. With optional *end*, stop comparing at that position.

str. expandtabs ( *tabsize = 8* ) ¶

Return a copy of the string where all tab characters are replaced by one or more spaces, depending on the current column and the given tab size. Tab positions occur every *tabsize* characters (default is 8, giving tab positions at columns 0, 8, 16 and so on). To expand the string, the current column is set to zero and the string is examined character by character. If the character is a tab ( \t ), one or more space characters are inserted in the result until the current column is equal to the next tab position. (The tab character itself is not copied.) If the character is a newline ( \n ) or return ( \r ), it is copied and the current column is reset to zero. Any other character is copied unchanged and the current column is incremented by one regardless of how the character is represented when printed.

Return the lowest index in the string where substring *sub* is found within the slice s[start:end] . Optional arguments *start* and *end* are interpreted as in slice notation. Return -1 if *sub* is not found.

The find() method should be used only if you need to know the position of *sub*. To check if *sub* is a substring or not, use the in operator:

Perform a string formatting operation. The string on which this method is called can contain literal text or replacement fields delimited by braces <> . Each replacement field contains either the numeric index of a positional argument, or the name of a keyword argument. Returns a copy of the string where each replacement field is replaced with the string value of the corresponding argument.

See Format String Syntax for a description of the various formatting options that can be specified in format strings.

When formatting a number ( int , float , complex , decimal.Decimal and subclasses) with the n type (ex: ‘<:n>‘.format(1234) ), the function temporarily sets the LC_CTYPE locale to the LC_NUMERIC locale to decode decimal_point and thousands_sep fields of localeconv() if they are non-ASCII or longer than 1 byte, and the LC_NUMERIC locale is different than the LC_CTYPE locale. This temporary change affects other threads.

Changed in version 3.7: When formatting a number with the n type, the function sets temporarily the LC_CTYPE locale to the LC_NUMERIC locale in some cases.

Similar to str.format(**mapping) , except that mapping is used directly and not copied to a dict . This is useful if for example mapping is a dict subclass:

New in version 3.2.

Like find() , but raise ValueError when the substring is not found.

Return True if all characters in the string are alphanumeric and there is at least one character, False otherwise. A character c is alphanumeric if one of the following returns True : c.isalpha() , c.isdecimal() , c.isdigit() , or c.isnumeric() .

Return True if all characters in the string are alphabetic and there is at least one character, False otherwise. Alphabetic characters are those characters defined in the Unicode character database as “Letter”, i.e., those with general category property being one of “Lm”, “Lt”, “Lu”, “Ll”, or “Lo”. Note that this is different from the “Alphabetic” property defined in the Unicode Standard.

Return True if the string is empty or all characters in the string are ASCII, False otherwise. ASCII characters have code points in the range U+0000-U+007F.

New in version 3.7.

Return True if all characters in the string are decimal characters and there is at least one character, False otherwise. Decimal characters are those that can be used to form numbers in base 10, e.g. U+0660, ARABIC-INDIC DIGIT ZERO. Formally a decimal character is a character in the Unicode General Category “Nd”.

Return True if all characters in the string are digits and there is at least one character, False otherwise. Digits include decimal characters and digits that need special handling, such as the compatibility superscript digits. This covers digits which cannot be used to form numbers in base 10, like the Kharosthi numbers. Formally, a digit is a character that has the property value Numeric_Type=Digit or Numeric_Type=Decimal.

Return True if the string is a valid identifier according to the language definition, section Identifiers and keywords .

Call keyword.iskeyword() to test whether string s is a reserved identifier, such as def and class .

Return True if all cased characters 4 in the string are lowercase and there is at least one cased character, False otherwise.

Return True if all characters in the string are numeric characters, and there is at least one character, False otherwise. Numeric characters include digit characters, and all characters that have the Unicode numeric value property, e.g. U+2155, VULGAR FRACTION ONE FIFTH. Formally, numeric characters are those with the property value Numeric_Type=Digit, Numeric_Type=Decimal or Numeric_Type=Numeric.

Return True if all characters in the string are printable or the string is empty, False otherwise. Nonprintable characters are those characters defined in the Unicode character database as “Other” or “Separator”, excepting the ASCII space (0x20) which is considered printable. (Note that printable characters in this context are those which should not be escaped when repr() is invoked on a string. It has no bearing on the handling of strings written to sys.stdout or sys.stderr .)

Return True if there are only whitespace characters in the string and there is at least one character, False otherwise.

A character is *whitespace* if in the Unicode character database (see unicodedata ), either its general category is Zs (“Separator, space”), or its bidirectional class is one of WS , B , or S .

Return True if the string is a titlecased string and there is at least one character, for example uppercase characters may only follow uncased characters and lowercase characters only cased ones. Return False otherwise.

Return True if all cased characters 4 in the string are uppercase and there is at least one cased character, False otherwise.

Return a string which is the concatenation of the strings in *iterable*. A TypeError will be raised if there are any non-string values in *iterable*, including bytes objects. The separator between elements is the string providing this method.

str. ljust ( *width* [ , *fillchar* ] ) ¶

Return the string left justified in a string of length *width*. Padding is done using the specified *fillchar* (default is an ASCII space). The original string is returned if *width* is less than or equal to len(s) .

Return a copy of the string with all the cased characters 4 converted to lowercase.

The lowercasing algorithm used is described in section 3.13 of the Unicode Standard.

str. lstrip ( [ *chars* ] ) ¶

Return a copy of the string with leading characters removed. The *chars* argument is a string specifying the set of characters to be removed. If omitted or None , the *chars* argument defaults to removing whitespace. The *chars* argument is not a prefix; rather, all combinations of its values are stripped:

See str.removeprefix() for a method that will remove a single prefix string rather than all of a set of characters. For example:

This static method returns a translation table usable for str.translate() .

If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters (strings of length 1) to Unicode ordinals, strings (of arbitrary lengths) or None . Character keys will then be converted to ordinals.

If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to None in the result.

str. partition ( *sep* ) ¶

Split the string at the first occurrence of *sep*, and return a 3-tuple containing the part before the separator, the separator itself, and the part after the separator. If the separator is not found, return a 3-tuple containing the string itself, followed by two empty strings.

If the string starts with the *prefix* string, return string[len(prefix):] . Otherwise, return a copy of the original string:

New in version 3.9.

If the string ends with the *suffix* string and that *suffix* is not empty, return string[:-len(suffix)] . Otherwise, return a copy of the original string:

New in version 3.9.

Return a copy of the string with all occurrences of substring *old* replaced by *new*. If the optional argument *count* is given, only the first *count* occurrences are replaced.

Return the highest index in the string where substring *sub* is found, such that *sub* is contained within s[start:end] . Optional arguments *start* and *end* are interpreted as in slice notation. Return -1 on failure.

Like rfind() but raises ValueError when the substring *sub* is not found.

str. rjust ( *width* [ , *fillchar* ] ) ¶

Return the string right justified in a string of length *width*. Padding is done using the specified *fillchar* (default is an ASCII space). The original string is returned if *width* is less than or equal to len(s) .

str. rpartition ( *sep* ) ¶

Split the string at the last occurrence of *sep*, and return a 3-tuple containing the part before the separator, the separator itself, and the part after the separator. If the separator is not found, return a 3-tuple containing two empty strings, followed by the string itself.

str. rsplit ( *sep = None* , *maxsplit = — 1* ) ¶

Return a list of the words in the string, using *sep* as the delimiter string. If *maxsplit* is given, at most *maxsplit* splits are done, the *rightmost* ones. If *sep* is not specified or None , any whitespace string is a separator. Except for splitting from the right, rsplit() behaves like split() which is described in detail below.

str. rstrip ( [ *chars* ] ) ¶

Return a copy of the string with trailing characters removed. The *chars* argument is a string specifying the set of characters to be removed. If omitted or None , the *chars* argument defaults to removing whitespace. The *chars* argument is not a suffix; rather, all combinations of its values are stripped:

See str.removesuffix() for a method that will remove a single suffix string rather than all of a set of characters. For example:

Return a list of the words in the string, using *sep* as the delimiter string. If *maxsplit* is given, at most *maxsplit* splits are done (thus, the list will have at most maxsplit+1 elements). If *maxsplit* is not specified or -1 , then there is no limit on the number of splits (all possible splits are made).

If *sep* is given, consecutive delimiters are not grouped together and are deemed to delimit empty strings (for example, ‘1,,2’.split(‘,’) returns [‘1’, », ‘2’] ). The *sep* argument may consist of multiple characters (for example, ‘1<>2<>3’.split(‘<>’) returns [‘1’, ‘2’, ‘3’] ). Splitting an empty string with a specified separator returns [»] .

If *sep* is not specified or is None , a different splitting algorithm is applied: runs of consecutive whitespace are regarded as a single separator, and the result will contain no empty strings at the start or end if the string has leading or trailing whitespace. Consequently, splitting an empty string or a string consisting of just whitespace with a None separator returns [] .

Return a list of the lines in the string, breaking at line boundaries. Line breaks are not included in the resulting list unless *keepends* is given and true.

This method splits on the following line boundaries. In particular, the boundaries are a superset of universal newlines .

Carriage Return + Line Feed

Next Line (C1 Control Code)

Changed in version 3.2: \v and \f added to list of line boundaries.

Unlike split() when a delimiter string *sep* is given, this method returns an empty list for the empty string, and a terminal line break does not result in an extra line:

For comparison, split(‘\n’) gives:

Return True if string starts with the *prefix*, otherwise return False . *prefix* can also be a tuple of prefixes to look for. With optional *start*, test string beginning at that position. With optional *end*, stop comparing string at that position.

Return a copy of the string with the leading and trailing characters removed. The *chars* argument is a string specifying the set of characters to be removed. If omitted or None , the *chars* argument defaults to removing whitespace. The *chars* argument is not a prefix or suffix; rather, all combinations of its values are stripped:

The outermost leading and trailing *chars* argument values are stripped from the string. Characters are removed from the leading end until reaching a string character that is not contained in the set of characters in *chars*. A similar action takes place on the trailing end. For example:

Return a copy of the string with uppercase characters converted to lowercase and vice versa. Note that it is not necessarily true that s.swapcase().swapcase() == s .

Return a titlecased version of the string where words start with an uppercase character and the remaining characters are lowercase.

The algorithm uses a simple language-independent definition of a word as groups of consecutive letters. The definition works in many contexts but it means that apostrophes in contractions and possessives form word boundaries, which may not be the desired result:

The string.capwords() function does not have this problem, as it splits words on spaces only.

Alternatively, a workaround for apostrophes can be constructed using regular expressions:

Return a copy of the string in which each character has been mapped through the given translation table. The table must be an object that implements indexing via __getitem__() , typically a mapping or sequence . When indexed by a Unicode ordinal (an integer), the table object can do any of the following: return a Unicode ordinal or a string, to map the character to one or more other characters; return None , to delete the character from the return string; or raise a LookupError exception, to map the character to itself.

You can use str.maketrans() to create a translation map from character-to-character mappings in different formats.

See also the codecs module for a more flexible approach to custom character mappings.

Return a copy of the string with all the cased characters 4 converted to uppercase. Note that s.upper().isupper() might be False if s contains uncased characters or if the Unicode category of the resulting character(s) is not “Lu” (Letter, uppercase), but e.g. “Lt” (Letter, titlecase).

The uppercasing algorithm used is described in section 3.13 of the Unicode Standard.

Return a copy of the string left filled with ASCII ‘0’ digits to make a string of length *width*. A leading sign prefix ( ‘+’ / ‘-‘ ) is handled by inserting the padding *after* the sign character rather than before. The original string is returned if *width* is less than or equal to len(s) .

#### printf -style String Formatting¶

The formatting operations described here exhibit a variety of quirks that lead to a number of common errors (such as failing to display tuples and dictionaries correctly). Using the newer formatted string literals , the str.format() interface, or template strings may help avoid these errors. Each of these alternatives provides their own trade-offs and benefits of simplicity, flexibility, and/or extensibility.

String objects have one unique built-in operation: the % operator (modulo). This is also known as the string *formatting* or *interpolation* operator. Given format % values (where *format* is a string), % conversion specifications in *format* are replaced with zero or more elements of *values*. The effect is similar to using the sprintf() in the C language.

If *format* requires a single argument, *values* may be a single non-tuple object. 5 Otherwise, *values* must be a tuple with exactly the number of items specified by the format string, or a single mapping object (for example, a dictionary).

A conversion specifier contains two or more characters and has the following components, which must occur in this order:

The ‘%’ character, which marks the start of the specifier.

Mapping key (optional), consisting of a parenthesised sequence of characters (for example, (somename) ).

Conversion flags (optional), which affect the result of some conversion types.

Minimum field width (optional). If specified as an ‘*’ (asterisk), the actual width is read from the next element of the tuple in *values*, and the object to convert comes after the minimum field width and optional precision.

Precision (optional), given as a ‘.’ (dot) followed by the precision. If specified as ‘*’ (an asterisk), the actual precision is read from the next element of the tuple in *values*, and the value to convert comes after the precision.

Length modifier (optional).

When the right argument is a dictionary (or other mapping type), then the formats in the string *must* include a parenthesised mapping key into that dictionary inserted immediately after the ‘%’ character. The mapping key selects the value to be formatted from the mapping. For example:

In this case no * specifiers may occur in a format (since they require a sequential parameter list).

The conversion flag characters are:

The value conversion will use the “alternate form” (where defined below).

The conversion will be zero padded for numeric values.

The converted value is left adjusted (overrides the ‘0’ conversion if both are given).

(a space) A blank should be left before a positive number (or empty string) produced by a signed conversion.

A sign character ( ‘+’ or ‘-‘ ) will precede the conversion (overrides a “space” flag).

A length modifier ( h , l , or L ) may be present, but is ignored as it is not necessary for Python – so e.g. %ld is identical to %d .

The conversion types are:

Signed integer decimal.

Signed integer decimal.

Signed octal value.

Obsolete type – it is identical to ‘d’ .

Signed hexadecimal (lowercase).

Signed hexadecimal (uppercase).

Floating point exponential format (lowercase).

Floating point exponential format (uppercase).

Floating point decimal format.

Floating point decimal format.

Floating point format. Uses lowercase exponential format if exponent is less than -4 or not less than precision, decimal format otherwise.

Floating point format. Uses uppercase exponential format if exponent is less than -4 or not less than precision, decimal format otherwise.

Single character (accepts integer or single character string).

String (converts any Python object using repr() ).

String (converts any Python object using str() ).

String (converts any Python object using ascii() ).

No argument is converted, results in a ‘%’ character in the result.

The alternate form causes a leading octal specifier ( ‘0o’ ) to be inserted before the first digit.

The alternate form causes a leading ‘0x’ or ‘0X’ (depending on whether the ‘x’ or ‘X’ format was used) to be inserted before the first digit.

The alternate form causes the result to always contain a decimal point, even if no digits follow it.

The precision determines the number of digits after the decimal point and defaults to 6.

The alternate form causes the result to always contain a decimal point, and trailing zeroes are not removed as they would otherwise be.

The precision determines the number of significant digits before and after the decimal point and defaults to 6.

If precision is N , the output is truncated to N characters.

Since Python strings have an explicit length, %s conversions do not assume that ‘\0’ is the end of the string.

Changed in version 3.1: %f conversions for numbers whose absolute value is over 1e50 are no longer replaced by %g conversions.

### Binary Sequence Types — bytes , bytearray , memoryview ¶

The core built-in types for manipulating binary data are bytes and bytearray . They are supported by memoryview which uses the buffer protocol to access the memory of other binary objects without needing to make a copy.

The array module supports efficient storage of basic data types like 32-bit integers and IEEE754 double-precision floating values.

#### Bytes Objects¶

Bytes objects are immutable sequences of single bytes. Since many major binary protocols are based on the ASCII text encoding, bytes objects offer several methods that are only valid when working with ASCII compatible data and are closely related to string objects in a variety of other ways.

Firstly, the syntax for bytes literals is largely the same as that for string literals, except that a b prefix is added:

Single quotes: b’still allows embedded "double" quotes’

Double quotes: b"still allows embedded ‘single’ quotes"

Triple quoted: b»’3 single quotes»’ , b"""3 double quotes"""

Only ASCII characters are permitted in bytes literals (regardless of the declared source code encoding). Any binary values over 127 must be entered into bytes literals using the appropriate escape sequence.

As with string literals, bytes literals may also use a r prefix to disable processing of escape sequences. See String and Bytes literals for more about the various forms of bytes literal, including supported escape sequences.

While bytes literals and representations are based on ASCII text, bytes objects actually behave like immutable sequences of integers, with each value in the sequence restricted such that 0 <= x < 256 (attempts to violate this restriction will trigger ValueError ). This is done deliberately to emphasise that while many binary formats include ASCII based elements and can be usefully manipulated with some text-oriented algorithms, this is not generally the case for arbitrary binary data (blindly applying text processing algorithms to binary data formats that are not ASCII compatible will usually lead to data corruption).

In addition to the literal forms, bytes objects can be created in a number of other ways:

A zero-filled bytes object of a specified length: bytes(10)

From an iterable of integers: bytes(range(20))

Copying existing binary data via the buffer protocol: bytes(obj)

Also see the bytes built-in.

Since 2 hexadecimal digits correspond precisely to a single byte, hexadecimal numbers are a commonly used format for describing binary data. Accordingly, the bytes type has an additional class method to read data in that format:

*classmethod* fromhex ( *string* ) ¶

This bytes class method returns a bytes object, decoding the given string object. The string must contain two hexadecimal digits per byte, with ASCII whitespace being ignored.

Changed in version 3.7: bytes.fromhex() now skips all ASCII whitespace in the string, not just spaces.

A reverse conversion function exists to transform a bytes object into its hexadecimal representation.

Return a string object containing two hexadecimal digits for each byte in the instance.

If you want to make the hex string easier to read, you can specify a single character separator *sep* parameter to include in the output. By default, this separator will be included between each byte. A second optional *bytes_per_sep* parameter controls the spacing. Positive values calculate the separator position from the right, negative values from the left.

New in version 3.5.

Changed in version 3.8: bytes.hex() now supports optional *sep* and *bytes_per_sep* parameters to insert separators between bytes in the hex output.

Since bytes objects are sequences of integers (akin to a tuple), for a bytes object *b*, b[0] will be an integer, while b[0:1] will be a bytes object of length 1. (This contrasts with text strings, where both indexing and slicing will produce a string of length 1)

The representation of bytes objects uses the literal format ( b’. ‘ ) since it is often more useful than e.g. bytes([46, 46, 46]) . You can always convert a bytes object into a list of integers using list(b) .

#### Bytearray Objects¶

bytearray objects are a mutable counterpart to bytes objects.

*class* bytearray ( [ *source* [ , *encoding* [ , *errors* ] ] ] ) ¶

There is no dedicated literal syntax for bytearray objects, instead they are always created by calling the constructor:

Creating an empty instance: bytearray()

Creating a zero-filled instance with a given length: bytearray(10)

From an iterable of integers: bytearray(range(20))

Copying existing binary data via the buffer protocol: bytearray(b’Hi!’)

As bytearray objects are mutable, they support the mutable sequence operations in addition to the common bytes and bytearray operations described in Bytes and Bytearray Operations .

Also see the bytearray built-in.

Since 2 hexadecimal digits correspond precisely to a single byte, hexadecimal numbers are a commonly used format for describing binary data. Accordingly, the bytearray type has an additional class method to read data in that format:

*classmethod* fromhex ( *string* ) ¶

This bytearray class method returns bytearray object, decoding the given string object. The string must contain two hexadecimal digits per byte, with ASCII whitespace being ignored.

Changed in version 3.7: bytearray.fromhex() now skips all ASCII whitespace in the string, not just spaces.

A reverse conversion function exists to transform a bytearray object into its hexadecimal representation.

Return a string object containing two hexadecimal digits for each byte in the instance.

New in version 3.5.

Changed in version 3.8: Similar to bytes.hex() , bytearray.hex() now supports optional *sep* and *bytes_per_sep* parameters to insert separators between bytes in the hex output.

Since bytearray objects are sequences of integers (akin to a list), for a bytearray object *b*, b[0] will be an integer, while b[0:1] will be a bytearray object of length 1. (This contrasts with text strings, where both indexing and slicing will produce a string of length 1)

The representation of bytearray objects uses the bytes literal format ( bytearray(b’. ‘) ) since it is often more useful than e.g. bytearray([46, 46, 46]) . You can always convert a bytearray object into a list of integers using list(b) .

#### Bytes and Bytearray Operations¶

Both bytes and bytearray objects support the common sequence operations. They interoperate not just with operands of the same type, but with any bytes-like object . Due to this flexibility, they can be freely mixed in operations without causing errors. However, the return type of the result may depend on the order of operands.

The methods on bytes and bytearray objects don’t accept strings as their arguments, just as the methods on strings don’t accept bytes as their arguments. For example, you have to write:

Some bytes and bytearray operations assume the use of ASCII compatible binary formats, and hence should be avoided when working with arbitrary binary data. These restrictions are covered below.

Using these ASCII based operations to manipulate binary data that is not stored in an ASCII based format may lead to data corruption.

The following methods on bytes and bytearray objects can be used with arbitrary binary data.

bytes. count ( *sub* [ , *start* [ , *end* ] ] ) ¶ bytearray. count ( *sub* [ , *start* [ , *end* ] ] ) ¶

Return the number of non-overlapping occurrences of subsequence *sub* in the range [*start*, *end*]. Optional arguments *start* and *end* are interpreted as in slice notation.

The subsequence to search for may be any bytes-like object or an integer in the range 0 to 255.

Changed in version 3.3: Also accept an integer in the range 0 to 255 as the subsequence.

If the binary data starts with the *prefix* string, return bytes[len(prefix):] . Otherwise, return a copy of the original binary data:

The bytearray version of this method does *not* operate in place — it always produces a new object, even if no changes were made.

New in version 3.9.

If the binary data ends with the *suffix* string and that *suffix* is not empty, return bytes[:-len(suffix)] . Otherwise, return a copy of the original binary data:

The bytearray version of this method does *not* operate in place — it always produces a new object, even if no changes were made.

New in version 3.9.

Return a string decoded from the given bytes. Default encoding is ‘utf-8’ . *errors* may be given to set a different error handling scheme. The default for *errors* is ‘strict’ , meaning that encoding errors raise a UnicodeError . Other possible values are ‘ignore’ , ‘replace’ and any other name registered via codecs.register_error() , see section Error Handlers . For a list of possible encodings, see section Standard Encodings .

By default, the *errors* argument is not checked for best performances, but only used at the first decoding error. Enable the Python Development Mode , or use a debug build to check *errors*.

Passing the *encoding* argument to str allows decoding any bytes-like object directly, without needing to make a temporary bytes or bytearray object.

Changed in version 3.1: Added support for keyword arguments.

Changed in version 3.9: The *errors* is now checked in development mode and in debug mode .

Return True if the binary data ends with the specified *suffix*, otherwise return False . *suffix* can also be a tuple of suffixes to look for. With optional *start*, test beginning at that position. With optional *end*, stop comparing at that position.

The suffix(es) to search for may be any bytes-like object .

bytes. find ( *sub* [ , *start* [ , *end* ] ] ) ¶ bytearray. find ( *sub* [ , *start* [ , *end* ] ] ) ¶

Return the lowest index in the data where the subsequence *sub* is found, such that *sub* is contained in the slice s[start:end] . Optional arguments *start* and *end* are interpreted as in slice notation. Return -1 if *sub* is not found.

The subsequence to search for may be any bytes-like object or an integer in the range 0 to 255.

The find() method should be used only if you need to know the position of *sub*. To check if *sub* is a substring or not, use the in operator:

Changed in version 3.3: Also accept an integer in the range 0 to 255 as the subsequence.

Like find() , but raise ValueError when the subsequence is not found.

The subsequence to search for may be any bytes-like object or an integer in the range 0 to 255.

Changed in version 3.3: Also accept an integer in the range 0 to 255 as the subsequence.

Return a bytes or bytearray object which is the concatenation of the binary data sequences in *iterable*. A TypeError will be raised if there are any values in *iterable* that are not bytes-like objects , including str objects. The separator between elements is the contents of the bytes or bytearray object providing this method.

*static* bytes. maketrans ( *from*, *to* ) ¶ *static* bytearray. maketrans ( *from*, *to* ) ¶

This static method returns a translation table usable for bytes.translate() that will map each character in *from* into the character at the same position in *to*; *from* and *to* must both be bytes-like objects and have the same length.

New in version 3.1.

Split the sequence at the first occurrence of *sep*, and return a 3-tuple containing the part before the separator, the separator itself or its bytearray copy, and the part after the separator. If the separator is not found, return a 3-tuple containing a copy of the original sequence, followed by two empty bytes or bytearray objects.

The separator to search for may be any bytes-like object .

bytes. replace ( *old*, *new* [ , *count* ] ) ¶ bytearray. replace ( *old*, *new* [ , *count* ] ) ¶

Return a copy of the sequence with all occurrences of subsequence *old* replaced by *new*. If the optional argument *count* is given, only the first *count* occurrences are replaced.

The subsequence to search for and its replacement may be any bytes-like object .

The bytearray version of this method does *not* operate in place — it always produces a new object, even if no changes were made.

Return the highest index in the sequence where the subsequence *sub* is found, such that *sub* is contained within s[start:end] . Optional arguments *start* and *end* are interpreted as in slice notation. Return -1 on failure.

The subsequence to search for may be any bytes-like object or an integer in the range 0 to 255.

Changed in version 3.3: Also accept an integer in the range 0 to 255 as the subsequence.

Like rfind() but raises ValueError when the subsequence *sub* is not found.

The subsequence to search for may be any bytes-like object or an integer in the range 0 to 255.

Changed in version 3.3: Also accept an integer in the range 0 to 255 as the subsequence.

Split the sequence at the last occurrence of *sep*, and return a 3-tuple containing the part before the separator, the separator itself or its bytearray copy, and the part after the separator. If the separator is not found, return a 3-tuple containing two empty bytes or bytearray objects, followed by a copy of the original sequence.

The separator to search for may be any bytes-like object .

bytes. startswith ( *prefix* [ , *start* [ , *end* ] ] ) ¶ bytearray. startswith ( *prefix* [ , *start* [ , *end* ] ] ) ¶

Return True if the binary data starts with the specified *prefix*, otherwise return False . *prefix* can also be a tuple of prefixes to look for. With optional *start*, test beginning at that position. With optional *end*, stop comparing at that position.

The prefix(es) to search for may be any bytes-like object .

bytes. translate ( *table* , */* , *delete = b»* ) ¶ bytearray. translate ( *table* , */* , *delete = b»* ) ¶

Return a copy of the bytes or bytearray object where all bytes occurring in the optional argument *delete* are removed, and the remaining bytes have been mapped through the given translation table, which must be a bytes object of length 256.

You can use the bytes.maketrans() method to create a translation table.

Set the *table* argument to None for translations that only delete characters:

Changed in version 3.6: *delete* is now supported as a keyword argument.

The following methods on bytes and bytearray objects have default behaviours that assume the use of ASCII compatible binary formats, but can still be used with arbitrary binary data by passing appropriate arguments. Note that all of the bytearray methods in this section do *not* operate in place, and instead produce new objects.

bytes. center ( *width* [ , *fillbyte* ] ) ¶ bytearray. center ( *width* [ , *fillbyte* ] ) ¶

Return a copy of the object centered in a sequence of length *width*. Padding is done using the specified *fillbyte* (default is an ASCII space). For bytes objects, the original sequence is returned if *width* is less than or equal to len(s) .

*not* operate in place — it always produces a new object, even if no changes were made.

Return a copy of the object left justified in a sequence of length *width*. Padding is done using the specified *fillbyte* (default is an ASCII space). For bytes objects, the original sequence is returned if *width* is less than or equal to len(s) .

*not* operate in place — it always produces a new object, even if no changes were made.

Return a copy of the sequence with specified leading bytes removed. The *chars* argument is a binary sequence specifying the set of byte values to be removed — the name refers to the fact this method is usually used with ASCII characters. If omitted or None , the *chars* argument defaults to removing ASCII whitespace. The *chars* argument is not a prefix; rather, all combinations of its values are stripped:

The binary sequence of byte values to remove may be any bytes-like object . See removeprefix() for a method that will remove a single prefix string rather than all of a set of characters. For example:

*not* operate in place — it always produces a new object, even if no changes were made.

Return a copy of the object right justified in a sequence of length *width*. Padding is done using the specified *fillbyte* (default is an ASCII space). For bytes objects, the original sequence is returned if *width* is less than or equal to len(s) .

*not* operate in place — it always produces a new object, even if no changes were made.

Split the binary sequence into subsequences of the same type, using *sep* as the delimiter string. If *maxsplit* is given, at most *maxsplit* splits are done, the *rightmost* ones. If *sep* is not specified or None , any subsequence consisting solely of ASCII whitespace is a separator. Except for splitting from the right, rsplit() behaves like split() which is described in detail below.

bytes. rstrip ( [ *chars* ] ) ¶ bytearray. rstrip ( [ *chars* ] ) ¶

Return a copy of the sequence with specified trailing bytes removed. The *chars* argument is a binary sequence specifying the set of byte values to be removed — the name refers to the fact this method is usually used with ASCII characters. If omitted or None , the *chars* argument defaults to removing ASCII whitespace. The *chars* argument is not a suffix; rather, all combinations of its values are stripped:

The binary sequence of byte values to remove may be any bytes-like object . See removesuffix() for a method that will remove a single suffix string rather than all of a set of characters. For example:

*not* operate in place — it always produces a new object, even if no changes were made.

Split the binary sequence into subsequences of the same type, using *sep* as the delimiter string. If *maxsplit* is given and non-negative, at most *maxsplit* splits are done (thus, the list will have at most maxsplit+1 elements). If *maxsplit* is not specified or is -1 , then there is no limit on the number of splits (all possible splits are made).

If *sep* is given, consecutive delimiters are not grouped together and are deemed to delimit empty subsequences (for example, b’1,,2′.split(b’,’) returns [b’1′, b», b’2′] ). The *sep* argument may consist of a multibyte sequence (for example, b’1<>2<>3′.split(b'<>’) returns [b’1′, b’2′, b’3′] ). Splitting an empty sequence with a specified separator returns [b»] or [bytearray(b»)] depending on the type of object being split. The *sep* argument may be any bytes-like object .

If *sep* is not specified or is None , a different splitting algorithm is applied: runs of consecutive ASCII whitespace are regarded as a single separator, and the result will contain no empty strings at the start or end if the sequence has leading or trailing whitespace. Consequently, splitting an empty sequence or a sequence consisting solely of ASCII whitespace without a specified separator returns [] .

Return a copy of the sequence with specified leading and trailing bytes removed. The *chars* argument is a binary sequence specifying the set of byte values to be removed — the name refers to the fact this method is usually used with ASCII characters. If omitted or None , the *chars* argument defaults to removing ASCII whitespace. The *chars* argument is not a prefix or suffix; rather, all combinations of its values are stripped:

The binary sequence of byte values to remove may be any bytes-like object .

*not* operate in place — it always produces a new object, even if no changes were made.

The following methods on bytes and bytearray objects assume the use of ASCII compatible binary formats and should not be applied to arbitrary binary data. Note that all of the bytearray methods in this section do *not* operate in place, and instead produce new objects.

bytes. capitalize ( ) ¶ bytearray. capitalize ( ) ¶

Return a copy of the sequence with each byte interpreted as an ASCII character, and the first byte capitalized and the rest lowercased. Non-ASCII byte values are passed through unchanged.

*not* operate in place — it always produces a new object, even if no changes were made.

Return a copy of the sequence where all ASCII tab characters are replaced by one or more ASCII spaces, depending on the current column and the given tab size. Tab positions occur every *tabsize* bytes (default is 8, giving tab positions at columns 0, 8, 16 and so on). To expand the sequence, the current column is set to zero and the sequence is examined byte by byte. If the byte is an ASCII tab character ( b’\t’ ), one or more space characters are inserted in the result until the current column is equal to the next tab position. (The tab character itself is not copied.) If the current byte is an ASCII newline ( b’\n’ ) or carriage return ( b’\r’ ), it is copied and the current column is reset to zero. Any other byte value is copied unchanged and the current column is incremented by one regardless of how the byte value is represented when printed:

*not* operate in place — it always produces a new object, even if no changes were made.

Return True if all bytes in the sequence are alphabetical ASCII characters or ASCII decimal digits and the sequence is not empty, False otherwise. Alphabetic ASCII characters are those byte values in the sequence b’abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ’ . ASCII decimal digits are those byte values in the sequence b’0123456789′ .

Return True if all bytes in the sequence are alphabetic ASCII characters and the sequence is not empty, False otherwise. Alphabetic ASCII characters are those byte values in the sequence b’abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ’ .

Return True if the sequence is empty or all bytes in the sequence are ASCII, False otherwise. ASCII bytes are in the range 0-0x7F.

New in version 3.7.

Return True if all bytes in the sequence are ASCII decimal digits and the sequence is not empty, False otherwise. ASCII decimal digits are those byte values in the sequence b’0123456789′ .

Return True if there is at least one lowercase ASCII character in the sequence and no uppercase ASCII characters, False otherwise.

Lowercase ASCII characters are those byte values in the sequence b’abcdefghijklmnopqrstuvwxyz’ . Uppercase ASCII characters are those byte values in the sequence b’ABCDEFGHIJKLMNOPQRSTUVWXYZ’ .

bytes. isspace ( ) ¶ bytearray. isspace ( ) ¶

Return True if all bytes in the sequence are ASCII whitespace and the sequence is not empty, False otherwise. ASCII whitespace characters are those byte values in the sequence b’ \t\n\r\x0b\f’ (space, tab, newline, carriage return, vertical tab, form feed).

bytes. istitle ( ) ¶ bytearray. istitle ( ) ¶

Return True if the sequence is ASCII titlecase and the sequence is not empty, False otherwise. See bytes.title() for more details on the definition of “titlecase”.

Return True if there is at least one uppercase alphabetic ASCII character in the sequence and no lowercase ASCII characters, False otherwise.

Lowercase ASCII characters are those byte values in the sequence b’abcdefghijklmnopqrstuvwxyz’ . Uppercase ASCII characters are those byte values in the sequence b’ABCDEFGHIJKLMNOPQRSTUVWXYZ’ .

bytes. lower ( ) ¶ bytearray. lower ( ) ¶

Return a copy of the sequence with all the uppercase ASCII characters converted to their corresponding lowercase counterpart.

Lowercase ASCII characters are those byte values in the sequence b’abcdefghijklmnopqrstuvwxyz’ . Uppercase ASCII characters are those byte values in the sequence b’ABCDEFGHIJKLMNOPQRSTUVWXYZ’ .

*not* operate in place — it always produces a new object, even if no changes were made.

Return a list of the lines in the binary sequence, breaking at ASCII line boundaries. This method uses the universal newlines approach to splitting lines. Line breaks are not included in the resulting list unless *keepends* is given and true.

Unlike split() when a delimiter string *sep* is given, this method returns an empty list for the empty string, and a terminal line break does not result in an extra line:

Return a copy of the sequence with all the lowercase ASCII characters converted to their corresponding uppercase counterpart and vice-versa.

Unlike str.swapcase() , it is always the case that bin.swapcase().swapcase() == bin for the binary versions. Case conversions are symmetrical in ASCII, even though that is not generally true for arbitrary Unicode code points.

*not* operate in place — it always produces a new object, even if no changes were made.

Return a titlecased version of the binary sequence where words start with an uppercase ASCII character and the remaining characters are lowercase. Uncased byte values are left unmodified.

Lowercase ASCII characters are those byte values in the sequence b’abcdefghijklmnopqrstuvwxyz’ . Uppercase ASCII characters are those byte values in the sequence b’ABCDEFGHIJKLMNOPQRSTUVWXYZ’ . All other byte values are uncased.

The algorithm uses a simple language-independent definition of a word as groups of consecutive letters. The definition works in many contexts but it means that apostrophes in contractions and possessives form word boundaries, which may not be the desired result:

A workaround for apostrophes can be constructed using regular expressions:

*not* operate in place — it always produces a new object, even if no changes were made.

Return a copy of the sequence with all the lowercase ASCII characters converted to their corresponding uppercase counterpart.

*not* operate in place — it always produces a new object, even if no changes were made.

Return a copy of the sequence left filled with ASCII b’0′ digits to make a sequence of length *width*. A leading sign prefix ( b’+’ / b’-‘ ) is handled by inserting the padding *after* the sign character rather than before. For bytes objects, the original sequence is returned if *width* is less than or equal to len(seq) .

*not* operate in place — it always produces a new object, even if no changes were made.

#### printf -style Bytes Formatting¶

The formatting operations described here exhibit a variety of quirks that lead to a number of common errors (such as failing to display tuples and dictionaries correctly). If the value being printed may be a tuple or dictionary, wrap it in a tuple.

Bytes objects ( bytes / bytearray ) have one unique built-in operation: the % operator (modulo). This is also known as the bytes *formatting* or *interpolation* operator. Given format % values (where *format* is a bytes object), % conversion specifications in *format* are replaced with zero or more elements of *values*. The effect is similar to using the sprintf() in the C language.

If *format* requires a single argument, *values* may be a single non-tuple object. 5 Otherwise, *values* must be a tuple with exactly the number of items specified by the format bytes object, or a single mapping object (for example, a dictionary).

A conversion specifier contains two or more characters and has the following components, which must occur in this order:

The ‘%’ character, which marks the start of the specifier.

Mapping key (optional), consisting of a parenthesised sequence of characters (for example, (somename) ).

Conversion flags (optional), which affect the result of some conversion types.

Minimum field width (optional). If specified as an ‘*’ (asterisk), the actual width is read from the next element of the tuple in *values*, and the object to convert comes after the minimum field width and optional precision.

Precision (optional), given as a ‘.’ (dot) followed by the precision. If specified as ‘*’ (an asterisk), the actual precision is read from the next element of the tuple in *values*, and the value to convert comes after the precision.

Length modifier (optional).

When the right argument is a dictionary (or other mapping type), then the formats in the bytes object *must* include a parenthesised mapping key into that dictionary inserted immediately after the ‘%’ character. The mapping key selects the value to be formatted from the mapping. For example:

In this case no * specifiers may occur in a format (since they require a sequential parameter list).

The conversion flag characters are:

The value conversion will use the “alternate form” (where defined below).

The conversion will be zero padded for numeric values.

The converted value is left adjusted (overrides the ‘0’ conversion if both are given).

(a space) A blank should be left before a positive number (or empty string) produced by a signed conversion.

A sign character ( ‘+’ or ‘-‘ ) will precede the conversion (overrides a “space” flag).

A length modifier ( h , l , or L ) may be present, but is ignored as it is not necessary for Python – so e.g. %ld is identical to %d .

The conversion types are:

Signed integer decimal.

Signed integer decimal.

Signed octal value.

Obsolete type – it is identical to ‘d’ .

Signed hexadecimal (lowercase).

Signed hexadecimal (uppercase).

Floating point exponential format (lowercase).

Floating point exponential format (uppercase).

Floating point decimal format.

Floating point decimal format.

Floating point format. Uses lowercase exponential format if exponent is less than -4 or not less than precision, decimal format otherwise.

Floating point format. Uses uppercase exponential format if exponent is less than -4 or not less than precision, decimal format otherwise.

Single byte (accepts integer or single byte objects).

Bytes (any object that follows the buffer protocol or has __bytes__() ).

‘s’ is an alias for ‘b’ and should only be used for Python2/3 code bases.

Bytes (converts any Python object using repr(obj).encode(‘ascii’, ‘backslashreplace’) ).

‘r’ is an alias for ‘a’ and should only be used for Python2/3 code bases.

No argument is converted, results in a ‘%’ character in the result.

The alternate form causes a leading octal specifier ( ‘0o’ ) to be inserted before the first digit.

The alternate form causes a leading ‘0x’ or ‘0X’ (depending on whether the ‘x’ or ‘X’ format was used) to be inserted before the first digit.

The alternate form causes the result to always contain a decimal point, even if no digits follow it.

The precision determines the number of digits after the decimal point and defaults to 6.

The alternate form causes the result to always contain a decimal point, and trailing zeroes are not removed as they would otherwise be.

The precision determines the number of significant digits before and after the decimal point and defaults to 6.

If precision is N , the output is truncated to N characters.

b’%s’ is deprecated, but will not be removed during the 3.x series.

b’%r’ is deprecated, but will not be removed during the 3.x series.

*not* operate in place — it always produces a new object, even if no changes were made.

**PEP 461** — Adding % formatting to bytes and bytearray

New in version 3.5.

#### Memory Views¶

memoryview objects allow Python code to access the internal data of an object that supports the buffer protocol without copying.

Create a memoryview that references *object*. *object* must support the buffer protocol. Built-in objects that support the buffer protocol include bytes and bytearray .

A memoryview has the notion of an *element*, which is the atomic memory unit handled by the originating *object*. For many simple types such as bytes and bytearray , an element is a single byte, but other types such as array.array may have bigger elements.

len(view) is equal to the length of tolist . If view.ndim = 0 , the length is 1. If view.ndim = 1 , the length is equal to the number of elements in the view. For higher dimensions, the length is equal to the length of the nested list representation of the view. The itemsize attribute will give you the number of bytes in a single element.

A memoryview supports slicing and indexing to expose its data. One-dimensional slicing will result in a subview:

If format is one of the native format specifiers from the struct module, indexing with an integer or a tuple of integers is also supported and returns a single *element* with the correct type. One-dimensional memoryviews can be indexed with an integer or a one-integer tuple. Multi-dimensional memoryviews can be indexed with tuples of exactly *ndim* integers where *ndim* is the number of dimensions. Zero-dimensional memoryviews can be indexed with the empty tuple.

Here is an example with a non-byte format:

If the underlying object is writable, the memoryview supports one-dimensional slice assignment. Resizing is not allowed:

One-dimensional memoryviews of hashable (read-only) types with formats ‘B’, ‘b’ or ‘c’ are also hashable. The hash is defined as hash(m) == hash(m.tobytes()) :

Changed in version 3.3: One-dimensional memoryviews can now be sliced. One-dimensional memoryviews with formats ‘B’, ‘b’ or ‘c’ are now hashable.

Changed in version 3.4: memoryview is now registered automatically with collections.abc.Sequence

Changed in version 3.5: memoryviews can now be indexed with tuple of integers.

memoryview has several methods:

A memoryview and a **PEP 3118** exporter are equal if their shapes are equivalent and if all corresponding values are equal when the operands’ respective format codes are interpreted using struct syntax.

For the subset of struct format strings currently supported by tolist() , v and w are equal if v.tolist() == w.tolist() :

If either format string is not supported by the struct module, then the objects will always compare as unequal (even if the format strings and buffer contents are identical):

Note that, as with floating point numbers, v is w does *not* imply v == w for memoryview objects.

Changed in version 3.3: Previous versions compared the raw memory disregarding the item format and the logical array structure.

Return the data in the buffer as a bytestring. This is equivalent to calling the bytes constructor on the memoryview.

For non-contiguous arrays the result is equal to the flattened list representation with all elements converted to bytes. tobytes() supports all format strings, including those that are not in struct module syntax.

New in version 3.8: *order* can be <‘C’, ‘F’, ‘A’>. When *order* is ‘C’ or ‘F’, the data of the original array is converted to C or Fortran order. For contiguous views, ‘A’ returns an exact copy of the physical memory. In particular, in-memory Fortran order is preserved. For non-contiguous views, the data is converted to C first. *order=None* is the same as *order=’C’*.

Return a string object containing two hexadecimal digits for each byte in the buffer.

New in version 3.5.

Changed in version 3.8: Similar to bytes.hex() , memoryview.hex() now supports optional *sep* and *bytes_per_sep* parameters to insert separators between bytes in the hex output.

Return the data in the buffer as a list of elements.

Changed in version 3.3: tolist() now supports all single character native formats in struct module syntax as well as multi-dimensional representations.

Return a readonly version of the memoryview object. The original memoryview object is unchanged.

New in version 3.8.

Release the underlying buffer exposed by the memoryview object. Many objects take special actions when a view is held on them (for example, a bytearray would temporarily forbid resizing); therefore, calling release() is handy to remove these restrictions (and free any dangling resources) as soon as possible.

After this method has been called, any further operation on the view raises a ValueError (except release() itself which can be called multiple times):

The context management protocol can be used for a similar effect, using the with statement:

New in version 3.2.

Cast a memoryview to a new format or shape. *shape* defaults to [byte_length//new_itemsize] , which means that the result view will be one-dimensional. The return value is a new memoryview, but the buffer itself is not copied. Supported casts are 1D -> C- contiguous and C-contiguous -> 1D.

The destination format is restricted to a single element native format in struct syntax. One of the formats must be a byte format (‘B’, ‘b’ or ‘c’). The byte length of the result must be the same as the original length.

Cast 1D/long to 1D/unsigned bytes:

Cast 1D/unsigned bytes to 1D/char:

Cast 1D/bytes to 3D/ints to 1D/signed char:

Cast 1D/unsigned long to 2D/unsigned long:

New in version 3.3.

Changed in version 3.5: The source format is no longer restricted when casting to a byte view.

There are also several readonly attributes available:

The underlying object of the memoryview:

New in version 3.3.

nbytes == product(shape) * itemsize == len(m.tobytes()) . This is the amount of space in bytes that the array would use in a contiguous representation. It is not necessarily equal to len(m) :

New in version 3.3.

A bool indicating whether the memory is read only.

A string containing the format (in struct module style) for each element in the view. A memoryview can be created from exporters with arbitrary format strings, but some methods (e.g. tolist() ) are restricted to native single element formats.

Changed in version 3.3: format ‘B’ is now handled according to the struct module syntax. This means that memoryview(b’abc’)[0] == b’abc'[0] == 97 .

The size in bytes of each element of the memoryview:

An integer indicating how many dimensions of a multi-dimensional array the memory represents.

A tuple of integers the length of ndim giving the shape of the memory as an N-dimensional array.

Changed in version 3.3: An empty tuple instead of None when ndim = 0.

A tuple of integers the length of ndim giving the size in bytes to access each element for each dimension of the array.

Changed in version 3.3: An empty tuple instead of None when ndim = 0.

Used internally for PIL-style arrays. The value is informational only.

A bool indicating whether the memory is C- contiguous .

New in version 3.3.

A bool indicating whether the memory is Fortran contiguous .

New in version 3.3.

A bool indicating whether the memory is contiguous .

New in version 3.3.

### Set Types — set , frozenset ¶

A *set* object is an unordered collection of distinct hashable objects. Common uses include membership testing, removing duplicates from a sequence, and computing mathematical operations such as intersection, union, difference, and symmetric difference. (For other containers see the built-in dict , list , and tuple classes, and the collections module.)

Like other collections, sets support x in set , len(set) , and for x in set . Being an unordered collection, sets do not record element position or order of insertion. Accordingly, sets do not support indexing, slicing, or other sequence-like behavior.

There are currently two built-in set types, set and frozenset . The set type is mutable — the contents can be changed using methods like add() and remove() . Since it is mutable, it has no hash value and cannot be used as either a dictionary key or as an element of another set. The frozenset type is immutable and hashable — its contents cannot be altered after it is created; it can therefore be used as a dictionary key or as an element of another set.

Non-empty sets (not frozensets) can be created by placing a comma-separated list of elements within braces, for example: <'jack', 'sjoerd'>, in addition to the set constructor.

The constructors for both classes work the same:

*class* set ( [ *iterable* ] ) ¶ *class* frozenset ( [ *iterable* ] ) ¶

Return a new set or frozenset object whose elements are taken from *iterable*. The elements of a set must be hashable . To represent sets of sets, the inner sets must be frozenset objects. If *iterable* is not specified, a new empty set is returned.

Sets can be created by several means:

Use a comma-separated list of elements within braces:

Use a set comprehension:

Use the type constructor: set() , set(‘foobar’) , set([‘a’, ‘b’, ‘foo’])

Instances of set and frozenset provide the following operations:

Return the number of elements in set *s* (cardinality of *s*).

Test *x* for membership in *s*.

Test *x* for non-membership in *s*.

Return True if the set has no elements in common with *other*. Sets are disjoint if and only if their intersection is the empty set.

issubset ( *other* ) ¶ set <= other

Test whether every element in the set is in *other*.

Test whether the set is a proper subset of *other*, that is, set <= other and set != other .

issuperset ( *other* ) ¶ set >= other

Test whether every element in *other* is in the set.

Test whether the set is a proper superset of *other*, that is, set >= other and set != other .

union ( ** others* ) ¶ set | other | .

Return a new set with elements from the set and all others.

intersection ( ** others* ) ¶ set & other & .

Return a new set with elements common to the set and all others.

difference ( ** others* ) ¶ set — other — .

Return a new set with elements in the set that are not in the others.

symmetric_difference ( *other* ) ¶ set ^ other

Return a new set with elements in either the set or *other* but not both.

Return a shallow copy of the set.

Note, the non-operator versions of union() , intersection() , difference() , symmetric_difference() , issubset() , and issuperset() methods will accept any iterable as an argument. In contrast, their operator based counterparts require their arguments to be sets. This precludes error-prone constructions like set(‘abc’) & ‘cbs’ in favor of the more readable set(‘abc’).intersection(‘cbs’) .

Both set and frozenset support set to set comparisons. Two sets are equal if and only if every element of each set is contained in the other (each is a subset of the other). A set is less than another set if and only if the first set is a proper subset of the second set (is a subset, but is not equal). A set is greater than another set if and only if the first set is a proper superset of the second set (is a superset, but is not equal).

Instances of set are compared to instances of frozenset based on their members. For example, set(‘abc’) == frozenset(‘abc’) returns True and so does set(‘abc’) in set([frozenset(‘abc’)]) .

The subset and equality comparisons do not generalize to a total ordering function. For example, any two nonempty disjoint sets are not equal and are not subsets of each other, so *all* of the following return False : a<b , a==b , or a>b .

Since sets only define partial ordering (subset relationships), the output of the list.sort() method is undefined for lists of sets.

Set elements, like dictionary keys, must be hashable .

Binary operations that mix set instances with frozenset return the type of the first operand. For example: frozenset(‘ab’) | set(‘bc’) returns an instance of frozenset .

The following table lists operations available for set that do not apply to immutable instances of frozenset :

update ( ** others* ) ¶ set |= other | .

Update the set, adding elements from all others.

intersection_update ( ** others* ) ¶ set &= other & .

Update the set, keeping only elements found in it and all others.

difference_update ( ** others* ) ¶ set -= other | .

Update the set, removing elements found in others.

symmetric_difference_update ( *other* ) ¶ set ^= other

Update the set, keeping only elements found in either set, but not in both.

Add element *elem* to the set.

Remove element *elem* from the set. Raises KeyError if *elem* is not contained in the set.

Remove element *elem* from the set if it is present.

Remove and return an arbitrary element from the set. Raises KeyError if the set is empty.

Remove all elements from the set.

Note, the non-operator versions of the update() , intersection_update() , difference_update() , and symmetric_difference_update() methods will accept any iterable as an argument.

Note, the *elem* argument to the __contains__() , remove() , and discard() methods may be a set. To support searching for an equivalent frozenset, a temporary one is created from *elem*.

### Mapping Types — dict ¶

A mapping object maps hashable values to arbitrary objects. Mappings are mutable objects. There is currently only one standard mapping type, the *dictionary*. (For other containers see the built-in list , set , and tuple classes, and the collections module.)

A dictionary’s keys are *almost* arbitrary values. Values that are not hashable , that is, values containing lists, dictionaries or other mutable types (that are compared by value rather than by object identity) may not be used as keys. Numeric types used for keys obey the normal rules for numeric comparison: if two numbers compare equal (such as 1 and 1.0 ) then they can be used interchangeably to index the same dictionary entry. (Note however, that since computers store floating-point numbers as approximations it is usually unwise to use them as dictionary keys.)

*class* dict ( *** kwargs* ) ¶ *class* dict ( *mapping* , *** kwargs* ) *class* dict ( *iterable* , *** kwargs* )

Return a new dictionary initialized from an optional positional argument and a possibly empty set of keyword arguments.

Dictionaries can be created by several means:

Use a comma-separated list of key: value pairs within braces: <'jack': 4098, 'sjoerd': 4127>or

Use a dict comprehension: <> ,

Use the type constructor: dict() , dict([(‘foo’, 100), (‘bar’, 200)]) , dict(foo=100, bar=200)

If no positional argument is given, an empty dictionary is created. If a positional argument is given and it is a mapping object, a dictionary is created with the same key-value pairs as the mapping object. Otherwise, the positional argument must be an iterable object. Each item in the iterable must itself be an iterable with exactly two objects. The first object of each item becomes a key in the new dictionary, and the second object the corresponding value. If a key occurs more than once, the last value for that key becomes the corresponding value in the new dictionary.

If keyword arguments are given, the keyword arguments and their values are added to the dictionary created from the positional argument. If a key being added is already present, the value from the keyword argument replaces the value from the positional argument.

To illustrate, the following examples all return a dictionary equal to <"one": 1, "two": 2, "three": 3>:

Providing keyword arguments as in the first example only works for keys that are valid Python identifiers. Otherwise, any valid keys can be used.

These are the operations that dictionaries support (and therefore, custom mapping types should support too):

Return a list of all the keys used in the dictionary *d*.

Return the number of items in the dictionary *d*.

Return the item of *d* with key *key*. Raises a KeyError if *key* is not in the map.

If a subclass of dict defines a method __missing__() and *key* is not present, the d[key] operation calls that method with the key *key* as argument. The d[key] operation then returns or raises whatever is returned or raised by the __missing__(key) call. No other operations or methods invoke __missing__() . If __missing__() is not defined, KeyError is raised. __missing__() must be a method; it cannot be an instance variable:

The example above shows part of the implementation of collections.Counter . A different __missing__ method is used by collections.defaultdict .

Set d[key] to *value*.

Remove d[key] from *d*. Raises a KeyError if *key* is not in the map.

Return True if *d* has a key *key*, else False .

Equivalent to not key in d .

Return an iterator over the keys of the dictionary. This is a shortcut for iter(d.keys()) .

Remove all items from the dictionary.

Return a shallow copy of the dictionary.

*classmethod* fromkeys ( *iterable* [ , *value* ] ) ¶

Create a new dictionary with keys from *iterable* and values set to *value*.

fromkeys() is a class method that returns a new dictionary. *value* defaults to None . All of the values refer to just a single instance, so it generally doesn’t make sense for *value* to be a mutable object such as an empty list. To get distinct values, use a dict comprehension instead.

Return the value for *key* if *key* is in the dictionary, else *default*. If *default* is not given, it defaults to None , so that this method never raises a KeyError .

Return a new view of the dictionary’s items ( (key, value) pairs). See the documentation of view objects .

Return a new view of the dictionary’s keys. See the documentation of view objects .

If *key* is in the dictionary, remove it and return its value, else return *default*. If *default* is not given and *key* is not in the dictionary, a KeyError is raised.

Remove and return a (key, value) pair from the dictionary. Pairs are returned in LIFO order.

popitem() is useful to destructively iterate over a dictionary, as often used in set algorithms. If the dictionary is empty, calling popitem() raises a KeyError .

Changed in version 3.7: LIFO order is now guaranteed. In prior versions, popitem() would return an arbitrary key/value pair.

Return a reverse iterator over the keys of the dictionary. This is a shortcut for reversed(d.keys()) .

New in version 3.8.

If *key* is in the dictionary, return its value. If not, insert *key* with a value of *default* and return *default*. *default* defaults to None .

Update the dictionary with the key/value pairs from *other*, overwriting existing keys. Return None .

update() accepts either another dictionary object or an iterable of key/value pairs (as tuples or other iterables of length two). If keyword arguments are specified, the dictionary is then updated with those key/value pairs: d.update(red=1, blue=2) .

Return a new view of the dictionary’s values. See the documentation of view objects .

An equality comparison between one dict.values() view and another will always return False . This also applies when comparing dict.values() to itself:

Create a new dictionary with the merged keys and values of *d* and *other*, which must both be dictionaries. The values of *other* take priority when *d* and *other* share keys.

New in version 3.9.

Update the dictionary *d* with keys and values from *other*, which may be either a mapping or an iterable of key/value pairs. The values of *other* take priority when *d* and *other* share keys.

New in version 3.9.

Dictionaries compare equal if and only if they have the same (key, value) pairs (regardless of ordering). Order comparisons (‘<’, ‘<=’, ‘>=’, ‘>’) raise TypeError .

Dictionaries preserve insertion order. Note that updating a key does not affect the order. Keys added after deletion are inserted at the end.

Changed in version 3.7: Dictionary order is guaranteed to be insertion order. This behavior was an implementation detail of CPython from 3.6.

Dictionaries and dictionary views are reversible.

Changed in version 3.8: Dictionaries are now reversible.

types.MappingProxyType can be used to create a read-only view of a dict .

#### Dictionary view objects¶

The objects returned by dict.keys() , dict.values() and dict.items() are *view objects*. They provide a dynamic view on the dictionary’s entries, which means that when the dictionary changes, the view reflects these changes.

Dictionary views can be iterated over to yield their respective data, and support membership tests:

Return the number of entries in the dictionary.

Return an iterator over the keys, values or items (represented as tuples of (key, value) ) in the dictionary.

Keys and values are iterated over in insertion order. This allows the creation of (value, key) pairs using zip() : pairs = zip(d.values(), d.keys()) . Another way to create the same list is pairs = [(v, k) for (k, v) in d.items()] .

Iterating views while adding or deleting entries in the dictionary may raise a RuntimeError or fail to iterate over all entries.

Changed in version 3.7: Dictionary order is guaranteed to be insertion order.

Return True if *x* is in the underlying dictionary’s keys, values or items (in the latter case, *x* should be a (key, value) tuple).

Return a reverse iterator over the keys, values or items of the dictionary. The view will be iterated in reverse order of the insertion.

Changed in version 3.8: Dictionary views are now reversible.

Return a types.MappingProxyType that wraps the original dictionary to which the view refers.

New in version 3.10.

Keys views are set-like since their entries are unique and hashable. If all values are hashable, so that (key, value) pairs are unique and hashable, then the items view is also set-like. (Values views are not treated as set-like since the entries are generally not unique.) For set-like views, all of the operations defined for the abstract base class collections.abc.Set are available (for example, == , < , or ^ ).

An example of dictionary view usage:

### Context Manager Types¶

Python’s with statement supports the concept of a runtime context defined by a context manager. This is implemented using a pair of methods that allow user-defined classes to define a runtime context that is entered before the statement body is executed and exited when the statement ends:

Enter the runtime context and return either this object or another object related to the runtime context. The value returned by this method is bound to the identifier in the as clause of with statements using this context manager.

An example of a context manager that returns itself is a file object . File objects return themselves from __enter__() to allow open() to be used as the context expression in a with statement.

An example of a context manager that returns a related object is the one returned by decimal.localcontext() . These managers set the active decimal context to a copy of the original decimal context and then return the copy. This allows changes to be made to the current decimal context in the body of the with statement without affecting code outside the with statement.

contextmanager. __exit__ ( *exc_type* , *exc_val* , *exc_tb* ) ¶

Exit the runtime context and return a Boolean flag indicating if any exception that occurred should be suppressed. If an exception occurred while executing the body of the with statement, the arguments contain the exception type, value and traceback information. Otherwise, all three arguments are None .

Returning a true value from this method will cause the with statement to suppress the exception and continue execution with the statement immediately following the with statement. Otherwise the exception continues propagating after this method has finished executing. Exceptions that occur during execution of this method will replace any exception that occurred in the body of the with statement.

The exception passed in should never be reraised explicitly — instead, this method should return a false value to indicate that the method completed successfully and does not want to suppress the raised exception. This allows context management code to easily detect whether or not an __exit__() method has actually failed.

Python defines several context managers to support easy thread synchronisation, prompt closure of files or other objects, and simpler manipulation of the active decimal arithmetic context. The specific types are not treated specially beyond their implementation of the context management protocol. See the contextlib module for some examples.

Python’s generator s and the contextlib.contextmanager decorator provide a convenient way to implement these protocols. If a generator function is decorated with the contextlib.contextmanager decorator, it will return a context manager implementing the necessary __enter__() and __exit__() methods, rather than the iterator produced by an undecorated generator function.

Note that there is no specific slot for any of these methods in the type structure for Python objects in the Python/C API. Extension types wanting to define these methods must provide them as a normal Python accessible method. Compared to the overhead of setting up the runtime context, the overhead of a single class dictionary lookup is negligible.

### Type Annotation Types — Generic Alias , Union ¶

The core built-in types for type annotations are Generic Alias and Union .

#### Generic Alias Type¶

GenericAlias objects are generally created by subscripting a class. They are most often used with container classes , such as list or dict . For example, list[int] is a GenericAlias object created by subscripting the list class with the argument int . GenericAlias objects are intended primarily for use with type annotations .

It is generally only possible to subscript a class if the class implements the special method __class_getitem__() .

A GenericAlias object acts as a proxy for a generic type , implementing *parameterized generics*.

For a container class, the argument(s) supplied to a subscription of the class may indicate the type(s) of the elements an object contains. For example, set[bytes] can be used in type annotations to signify a set in which all the elements are of type bytes .

For a class which defines __class_getitem__() but is not a container, the argument(s) supplied to a subscription of the class will often indicate the return type(s) of one or more methods defined on an object. For example, regular expressions can be used on both the str data type and the bytes data type:

If x = re.search(‘foo’, ‘foo’) , x will be a re.Match object where the return values of x.group(0) and x[0] will both be of type str . We can represent this kind of object in type annotations with the GenericAlias re.Match[str] .

If y = re.search(b’bar’, b’bar’) , (note the b for bytes ), y will also be an instance of re.Match , but the return values of y.group(0) and y[0] will both be of type bytes . In type annotations, we would represent this variety of re.Match objects with re.Match[bytes] .

GenericAlias objects are instances of the class types.GenericAlias , which can also be used to create GenericAlias objects directly.

Creates a GenericAlias representing a type T parameterized by types *X*, *Y*, and more depending on the T used. For example, a function expecting a list containing float elements:

Another example for mapping objects, using a dict , which is a generic type expecting two type parameters representing the key type and the value type. In this example, the function expects a dict with keys of type str and values of type int :

The builtin functions isinstance() and issubclass() do not accept GenericAlias types for their second argument:

The Python runtime does not enforce type annotations . This extends to generic types and their type parameters. When creating a container object from a GenericAlias , the elements in the container are not checked against their type. For example, the following code is discouraged, but will run without errors:

Furthermore, parameterized generics erase type parameters during object creation:

Calling repr() or str() on a generic shows the parameterized type:

The __getitem__() method of generic containers will raise an exception to disallow mistakes like dict[str][str] :

However, such expressions are valid when type variables are used. The index must have as many elements as there are type variable items in the GenericAlias object’s __args__ .

##### Standard Generic Classes¶

The following standard library classes support parameterized generics. This list is non-exhaustive.