6. Expressões¶

Este capítulo explica o significado dos elementos das expressões em Python.

Notas de sintaxe: Neste e nos capítulos seguintes, a notação BNF estendida será usada para descrever a sintaxe, não a análise lexical. Quando (uma alternativa de) uma regra de sintaxe tem a forma

name ::=  othername

e nenhuma semântica é fornecida, a semântica desta forma de name é a mesma que para othername.

6.1. Conversões aritméticas¶

Quando uma descrição de um operador aritmético abaixo usa a frase “os argumentos numéricos são convertidos em um tipo comum”, isso significa que a implementação do operador para tipos embutidos funciona da seguinte maneira:

Se um dos argumentos for um número complexo, o outro será convertido em complexo;
caso contrário, se um dos argumentos for um número de ponto flutuante, o outro será convertido em ponto flutuante;
caso contrário, ambos devem ser inteiros e nenhuma conversão é necessária.

Algumas regras adicionais se aplicam a certos operadores (por exemplo, uma string como um argumento à esquerda para o operador ‘%’). As extensões devem definir seu próprio comportamento de conversão.

6.2. Átomos¶

Os átomos são os elementos mais básicos das expressões. Os átomos mais simples são identificadores ou literais. As formas entre parênteses, colchetes ou chaves também são categorizadas sintaticamente como átomos. A sintaxe para átomos é:

atom      ::=  identifier | literal | enclosure
enclosure ::=  parenth_form | list_display | dict_display | set_display
               | generator_expression | yield_atom

6.2.1. Identificadores (Nomes)¶

Um identificador que ocorre como um átomo é um nome. Veja a seção Identificadores e Keywords para a definição lexical e a seção Nomeação e ligação para documentação de nomenclatura e ligação.

Quando o nome está vinculado a um objeto, a avaliação do átomo produz esse objeto. Quando um nome não está vinculado, uma tentativa de avaliá-lo levanta uma exceção NameError.

Mangling de nome privado: Quando um identificador que ocorre textualmente em uma definição de classe começa com dois ou mais caracteres de sublinhado e não termina em dois ou mais sublinhados, ele é considerado um nome privado dessa classe. Os nomes privados são transformados em um formato mais longo antes que o código seja gerado para eles. A transformação insere o nome da classe, com sublinhados à esquerda removidos e um único sublinhado inserido na frente do nome. Por exemplo, o identificador __spam que ocorre em uma classe chamada Ham será transformado em _Ham__spam. Essa transformação é independente do contexto sintático em que o identificador é usado. Se o nome transformado for extremamente longo (mais de 255 caracteres), poderá ocorrer truncamento definido pela implementação. Se o nome da classe consistir apenas em sublinhados, nenhuma transformação será feita.

6.2.2. Literais¶

Python oferece suporte a strings e bytes literais e vários literais numéricos:

literal ::=  stringliteral | bytesliteral
             | integer | floatnumber | imagnumber

A avaliação de um literal produz um objeto do tipo fornecido (string, bytes, inteiro, número de ponto flutuante, número complexo) com o valor fornecido. O valor pode ser aproximado no caso de ponto flutuante e literais imaginários (complexos). Veja a seção Literais para detalhes.

Todos os literais correspondem a tipos de dados imutáveis e, portanto, a identidade do objeto é menos importante que seu valor. Múltiplas avaliações de literais com o mesmo valor (seja a mesma ocorrência no texto do programa ou uma ocorrência diferente) podem obter o mesmo objeto ou um objeto diferente com o mesmo valor.

6.2.3. Formas de parênteses¶

Um formulário entre parênteses é uma lista de expressões opcional entre parênteses:

parenth_form ::=  "(" [starred_expression] ")"

Uma lista de expressões entre parênteses produz tudo o que aquela lista de expressões produz: se a lista contiver pelo menos uma vírgula, ela produzirá uma tupla; caso contrário, produz a única expressão que compõe a lista de expressões.

Um par de parênteses vazio produz um objeto de tupla vazio. Como as tuplas são imutáveis, aplicam-se as mesmas regras dos literais (isto é, duas ocorrências da tupla vazia podem ou não produzir o mesmo objeto).

Note that tuples are not formed by the parentheses, but rather by use of the comma operator. The exception is the empty tuple, for which parentheses are required — allowing unparenthesized “nothing” in expressions would cause ambiguities and allow common typos to pass uncaught.

6.2.4. Sintaxe de criação de listas, conjuntos e dicionários¶

Para construir uma lista, um conjunto ou um dicionário, o Python fornece uma sintaxe especial chamada “sintaxes de criação” (em inglês, displays), cada uma delas em dois tipos:

o conteúdo do contêiner é listado explicitamente ou
eles são calculados por meio de um conjunto de instruções de laço e filtragem, chamado de compreensão.

Elementos de sintaxe comuns para compreensões são:

comprehension ::=  expression comp_for
comp_for      ::=  ["async"] "for" target_list "in" or_test [comp_iter]
comp_iter     ::=  comp_for | comp_if
comp_if       ::=  "if" expression_nocond [comp_iter]

A compreensão consiste em uma única expressão seguida por pelo menos uma cláusula for e zero ou mais cláusulas for ou if. Neste caso, os elementos do novo contêiner são aqueles que seriam produzidos considerando cada uma das cláusulas for ou if de um bloco, aninhando da esquerda para a direita, e avaliando a expressão para produzir um elemento cada vez que o bloco mais interno é alcançado.

No entanto, além da expressão iterável na cláusula for mais à esquerda, a compreensão é executada em um escopo aninhado implicitamente separado. Isso garante que os nomes atribuídos na lista de destino não “vazem” para o escopo delimitador.

The iterable expression in the leftmost for clause is evaluated directly in the enclosing scope and then passed as an argument to the implictly nested scope. Subsequent for clauses and any filter condition in the leftmost for clause cannot be evaluated in the enclosing scope as they may depend on the values obtained from the leftmost iterable. For example: [x*y for x in range(10) for y in range(x, x+10)].

To ensure the comprehension always results in a container of the appropriate type, yield and yield from expressions are prohibited in the implicitly nested scope (in Python 3.7, such expressions emit DeprecationWarning when compiled, in Python 3.8+ they will emit SyntaxError).

Since Python 3.6, in an async def function, an async for clause may be used to iterate over a asynchronous iterator. A comprehension in an async def function may consist of either a for or async for clause following the leading expression, may contain additional for or async for clauses, and may also use await expressions. If a comprehension contains either async for clauses or await expressions it is called an asynchronous comprehension. An asynchronous comprehension may suspend the execution of the coroutine function in which it appears. See also PEP 530.

Novo na versão 3.6: Compreensões assíncronas foram introduzidas.

Obsoleto desde a versão 3.7: yield and yield from deprecated in the implicitly nested scope.

6.2.5. Sintaxes de criação de lista¶

Uma sintaxe de criação de lista é uma série possivelmente vazia de expressões entre colchetes:

list_display ::=  "[" [starred_list | comprehension] "]"

Uma sintaxe de criação de lista produz um novo objeto de lista, sendo o conteúdo especificado por uma lista de expressões ou uma compreensão. Quando uma lista de expressões separadas por vírgulas é fornecida, seus elementos são avaliados da esquerda para a direita e colocados no objeto de lista nessa ordem. Quando uma compreensão é fornecida, a lista é construída a partir dos elementos resultantes da compreensão.

6.2.6. Sintaxes de criação de conjunto¶

Uma sintaxe de criação definida é denotada por chaves e distinguível de sintaxes de criação de dicionário pela falta de caractere de dois pontos separando chaves e valores:

set_display ::=  "{" (starred_list | comprehension) "}"

Uma sintaxe de criação de conjunto produz um novo objeto de conjunto mutável, sendo o conteúdo especificado por uma sequência de expressões ou uma compreensão. Quando uma lista de expressões separadas por vírgula é fornecida, seus elementos são avaliados da esquerda para a direita e adicionados ao objeto definido. Quando uma compreensão é fornecida, o conjunto é construído a partir dos elementos resultantes da compreensão.

Um conjunto vazio não pode ser construído com {}; este literal constrói um dicionário vazio.

6.2.7. Sintaxes de criação de dicionário¶

Uma sintaxe de criação de dicionário é uma série possivelmente vazia de pares chave/dado entre chaves:

dict_display       ::=  "{" [key_datum_list | dict_comprehension] "}"
key_datum_list     ::=  key_datum ("," key_datum)* [","]
key_datum          ::=  expression ":" expression | "**" or_expr
dict_comprehension ::=  expression ":" expression comp_for

Uma sintaxe de criação de dicionário produz um novo objeto dicionário.

Se for fornecida uma sequência separada por vírgulas de pares chave/dado, eles são avaliados da esquerda para a direita para definir as entradas do dicionário: cada objeto chave é usado como uma chave no dicionário para armazenar o dado correspondente. Isso significa que você pode especificar a mesma chave várias vezes na lista de dados/chave, e o valor final do dicionário para essa chave será o último dado.

Um asterisco duplo ** denota desempacotamento do dicionário. Seu operando deve ser um mapeamento. Cada item de mapeamento é adicionado ao novo dicionário. Os valores posteriores substituem os valores já definidos por pares de dados/chave anteriores e desempacotamentos de dicionário anteriores.

Novo na versão 3.5: Descompactando em sintaxes de criação de dicionário, originalmente proposto pela PEP 448.

Uma compreensão de dict, em contraste com as compreensões de lista e conjunto, precisa de duas expressões separadas por dois pontos, seguidas pelas cláusulas usuais “for” e “if”. Quando a compreensão é executada, os elementos chave e valor resultantes são inseridos no novo dicionário na ordem em que são produzidos.

Restrições nos tipos de valores de chave são listadas anteriormente na seção A hierarquia de tipos padrão. (Para resumir, o tipo de chave deve ser hasheável, que exclui todos os objetos mutáveis.) Não são detectadas colisões entre chaves duplicadas; o último dado (textualmente mais à direita na sintaxe de criação) armazenado para um determinado valor de chave prevalece.

6.2.8. Expressões geradoras¶

Uma expressão geradora é uma notação geradora compacta entre parênteses:

generator_expression ::=  "(" expression comp_for ")"

Uma expressão geradora produz um novo objeto gerador. Sua sintaxe é a mesma das compreensões, exceto pelo fato de estar entre parênteses em vez de colchetes ou chaves.

As variáveis usadas na expressão geradora são avaliadas lentamente quando o método __next__() é chamado para o objeto gerador (da mesma forma que os geradores normais). No entanto, a expressão iterável na cláusula for mais à esquerda é avaliada imediatamente, de modo que um erro produzido por ela será emitido no ponto em que a expressão do gerador é definida, em vez de no ponto em que o primeiro valor é recuperado. Cláusulas for subsequentes e qualquer condição de filtro na cláusula for mais à esquerda não podem ser avaliadas no escopo delimitador, pois podem depender dos valores obtidos do iterável mais à esquerda. Por exemplo: (x*y for x in range(10) for y in range(x, x+10)).

Os parênteses podem ser omitidos em chamadas com apenas um argumento. Veja a seção Chamadas para detalhes.

To avoid interfering with the expected operation of the generator expression itself, yield and yield from expressions are prohibited in the implicitly defined generator (in Python 3.7, such expressions emit DeprecationWarning when compiled, in Python 3.8+ they will emit SyntaxError).

Se uma expressão geradora contém cláusulas async for ou expressões await, ela é chamada de expressão geradora assíncrona. Uma expressão geradora assíncrona retorna um novo objeto gerador assíncrono, que é um iterador assíncrono (consulte Iteradores Assíncronos).

Novo na versão 3.6: Expressões geradoras assíncronas foram introduzidas.

Alterado na versão 3.7: Antes do Python 3.7, as expressões geradoras assíncronas só podiam aparecer em corrotinas async def. A partir da versão 3.7, qualquer função pode usar expressões geradoras assíncronas.

Obsoleto desde a versão 3.7: yield and yield from deprecated in the implicitly nested scope.

6.2.9. Expressões yield¶

yield_atom       ::=  "(" yield_expression ")"
yield_expression ::=  "yield" [expression_list | "from" expression]

The yield expression is used when defining a generator function or an asynchronous generator function and thus can only be used in the body of a function definition. Using a yield expression in a function’s body causes that function to be a generator, and using it in an async def function’s body causes that coroutine function to be an asynchronous generator. For example:

def gen():  # defines a generator function
    yield 123

async def agen(): # defines an asynchronous generator function
    yield 123

Due to their side effects on the containing scope, yield expressions are not permitted as part of the implicitly defined scopes used to implement comprehensions and generator expressions (in Python 3.7, such expressions emit DeprecationWarning when compiled, in Python 3.8+ they will emit SyntaxError)..

Obsoleto desde a versão 3.7: Yield expressions deprecated in the implicitly nested scopes used to implement comprehensions and generator expressions.

As funções geradoras são descritas abaixo, enquanto as funções geradoras assíncronas são descritas separadamente na seção Funções geradoras assíncronas

When a generator function is called, it returns an iterator known as a generator. That generator then controls the execution of the generator function. The execution starts when one of the generator’s methods is called. At that time, the execution proceeds to the first yield expression, where it is suspended again, returning the value of expression_list to the generator’s caller. By suspended, we mean that all local state is retained, including the current bindings of local variables, the instruction pointer, the internal evaluation stack, and the state of any exception handling. When the execution is resumed by calling one of the generator’s methods, the function can proceed exactly as if the yield expression were just another external call. The value of the yield expression after resuming depends on the method which resumed the execution. If __next__() is used (typically via either a for or the next() builtin) then the result is None. Otherwise, if send() is used, then the result will be the value passed in to that method.

Tudo isso torna as funções geradoras bastante semelhantes às corrotinas; cedem múltiplas vezes, possuem mais de um ponto de entrada e sua execução pode ser suspensa. A única diferença é que uma função geradora não pode controlar onde a execução deve continuar após o seu rendimento; o controle é sempre transferido para o chamador do gerador.

Expressões yield são permitidas em qualquer lugar em uma construção try. Se o gerador não for retomado antes de ser finalizado (ao atingir uma contagem de referências zero ou ao ser coletado como lixo), o método close() do iterador de gerador será chamado, permitindo que quaisquer cláusulas finally pendentes sejam executadas.

When yield from <expr> is used, it treats the supplied expression as a subiterator. All values produced by that subiterator are passed directly to the caller of the current generator’s methods. Any values passed in with send() and any exceptions passed in with throw() are passed to the underlying iterator if it has the appropriate methods. If this is not the case, then send() will raise AttributeError or TypeError, while throw() will just raise the passed in exception immediately.

Quando o iterador subjacente estiver completo, o atributo value da instância StopIteration gerada torna-se o valor da expressão yield. Ele pode ser definido explicitamente ao levantar StopIteration ou automaticamente quando o subiterador é um gerador (retornando um valor do subgerador).

Alterado na versão 3.3: Adicionado yield from <expr> para delegar o fluxo de controle a um subiterador.

Os parênteses podem ser omitidos quando a expressão yield é a única expressão no lado direito de uma instrução de atribuição.

Ver também

PEP 255 - Geradores simples: A proposta para adicionar geradores e a instrução yield ao Python.
PEP 342 - Corrotinas via Geradores Aprimorados: A proposta de aprimorar a API e a sintaxe dos geradores, tornando-os utilizáveis como simples corrotinas.
PEP 380 - Sintaxe para Delegar a um Subgerador: The proposal to introduce the yield_from syntax, making delegation to subgenerators easy.
PEP 525 - Geradores assíncronos: A proposta que se expandiu em PEP 492 adicionando recursos de gerador a funções de corrotina.

6.2.9.1. Métodos de iterador gerador¶

Esta subseção descreve os métodos de um iterador gerador. Eles podem ser usados para controlar a execução de uma função geradora.

Observe que chamar qualquer um dos métodos do gerador abaixo quando o gerador já estiver em execução levanta uma exceção ValueError.

generator.__next__()¶

Starts the execution of a generator function or resumes it at the last executed yield expression. When a generator function is resumed with a __next__() method, the current yield expression always evaluates to None. The execution then continues to the next yield expression, where the generator is suspended again, and the value of the expression_list is returned to __next__()’s caller. If the generator exits without yielding another value, a StopIteration exception is raised.

Este método é normalmente chamado implicitamente, por exemplo por um laço for, ou pela função embutida next().

generator.send(value)¶: Retoma a execução e “envia” um valor para a função geradora. O argumento value torna-se o resultado da expressão yield atual. O método send() retorna o próximo valor gerado pelo gerador, ou levanta StopIteration se o gerador sair sem produzir outro valor. Quando send() é chamado para iniciar o gerador, ele deve ser chamado com None como argumento, porque não há nenhuma expressão yield que possa receber o valor.

generator.throw(type[, value[, traceback]])¶: Raises an exception of type type at the point where the generator was paused, and returns the next value yielded by the generator function. If the generator exits without yielding another value, a StopIteration exception is raised. If the generator function does not catch the passed-in exception, or raises a different exception, then that exception propagates to the caller.

generator.close()¶: Levanta GeneratorExit no ponto onde a função geradora foi pausada. Se a função geradora sair normalmente, já estiver fechada ou levantar GeneratorExit (por não capturar a exceção), “close” retornará ao seu chamador. Se o gerador produzir um valor, um RuntimeError é levantado. Se o gerador levantar qualquer outra exceção, ela será propagada para o chamador. close() não faz nada se o gerador já saiu devido a uma exceção ou saída normal.

6.2.9.2. Exemplos¶

Aqui está um exemplo simples que demonstra o comportamento de geradores e funções geradoras:

>>> def echo(value=None):
...     print("Execution starts when 'next()' is called for the first time.")
...     try:
...         while True:
...             try:
...                 value = (yield value)
...             except Exception as e:
...                 value = e
...     finally:
...         print("Don't forget to clean up when 'close()' is called.")
...
>>> generator = echo(1)
>>> print(next(generator))
Execution starts when 'next()' is called for the first time.
1
>>> print(next(generator))
None
>>> print(generator.send(2))
2
>>> generator.throw(TypeError, "spam")
TypeError('spam',)
>>> generator.close()
Don't forget to clean up when 'close()' is called.

Para exemplos usando yield from, consulte a PEP 380: Syntax for Delegating to a Subgenerator em “O que há de novo no Python.”

6.2.9.3. Funções geradoras assíncronas¶

The presence of a yield expression in a function or method defined using async def further defines the function as an asynchronous generator function.

When an asynchronous generator function is called, it returns an asynchronous iterator known as an asynchronous generator object. That object then controls the execution of the generator function. An asynchronous generator object is typically used in an async for statement in a coroutine function analogously to how a generator object would be used in a for statement.

Calling one of the asynchronous generator’s methods returns an awaitable object, and the execution starts when this object is awaited on. At that time, the execution proceeds to the first yield expression, where it is suspended again, returning the value of expression_list to the awaiting coroutine. As with a generator, suspension means that all local state is retained, including the current bindings of local variables, the instruction pointer, the internal evaluation stack, and the state of any exception handling. When the execution is resumed by awaiting on the next object returned by the asynchronous generator’s methods, the function can proceed exactly as if the yield expression were just another external call. The value of the yield expression after resuming depends on the method which resumed the execution. If __anext__() is used then the result is None. Otherwise, if asend() is used, then the result will be the value passed in to that method.

In an asynchronous generator function, yield expressions are allowed anywhere in a try construct. However, if an asynchronous generator is not resumed before it is finalized (by reaching a zero reference count or by being garbage collected), then a yield expression within a try construct could result in a failure to execute pending finally clauses. In this case, it is the responsibility of the event loop or scheduler running the asynchronous generator to call the asynchronous generator-iterator’s aclose() method and run the resulting coroutine object, thus allowing any pending finally clauses to execute.

To take care of finalization, an event loop should define a finalizer function which takes an asynchronous generator-iterator and presumably calls aclose() and executes the coroutine. This finalizer may be registered by calling sys.set_asyncgen_hooks(). When first iterated over, an asynchronous generator-iterator will store the registered finalizer to be called upon finalization. For a reference example of a finalizer method see the implementation of asyncio.Loop.shutdown_asyncgens in Lib/asyncio/base_events.py.

The expression yield from <expr> is a syntax error when used in an asynchronous generator function.

6.2.9.4. Asynchronous generator-iterator methods¶

This subsection describes the methods of an asynchronous generator iterator, which are used to control the execution of a generator function.

coroutine agen.__anext__()¶

Returns an awaitable which when run starts to execute the asynchronous generator or resumes it at the last executed yield expression. When an asynchronous generator function is resumed with an __anext__() method, the current yield expression always evaluates to None in the returned awaitable, which when run will continue to the next yield expression. The value of the expression_list of the yield expression is the value of the StopIteration exception raised by the completing coroutine. If the asynchronous generator exits without yielding another value, the awaitable instead raises a StopAsyncIteration exception, signalling that the asynchronous iteration has completed.

This method is normally called implicitly by a async for loop.

coroutine agen.asend(value)¶: Returns an awaitable which when run resumes the execution of the asynchronous generator. As with the send() method for a generator, this “sends” a value into the asynchronous generator function, and the value argument becomes the result of the current yield expression. The awaitable returned by the asend() method will return the next value yielded by the generator as the value of the raised StopIteration, or raises StopAsyncIteration if the asynchronous generator exits without yielding another value. When asend() is called to start the asynchronous generator, it must be called with None as the argument, because there is no yield expression that could receive the value.

coroutine agen.athrow(value)¶
coroutine agen.athrow(type[, value[, traceback]]): Returns an awaitable that raises an exception of type type at the point where the asynchronous generator was paused, and returns the next value yielded by the generator function as the value of the raised StopIteration exception. If the asynchronous generator exits without yielding another value, a StopAsyncIteration exception is raised by the awaitable. If the generator function does not catch the passed-in exception, or raises a different exception, then when the awaitable is run that exception propagates to the caller of the awaitable.

coroutine agen.aclose()¶: Returns an awaitable that when run will throw a GeneratorExit into the asynchronous generator function at the point where it was paused. If the asynchronous generator function then exits gracefully, is already closed, or raises GeneratorExit (by not catching the exception), then the returned awaitable will raise a StopIteration exception. Any further awaitables returned by subsequent calls to the asynchronous generator will raise a StopAsyncIteration exception. If the asynchronous generator yields a value, a RuntimeError is raised by the awaitable. If the asynchronous generator raises any other exception, it is propagated to the caller of the awaitable. If the asynchronous generator has already exited due to an exception or normal exit, then further calls to aclose() will return an awaitable that does nothing.

6.3. Primaries¶

Primaries represent the most tightly bound operations of the language. Their syntax is:

primary ::=  atom | attributeref | subscription | slicing | call

6.3.1. Attribute references¶

An attribute reference is a primary followed by a period and a name:

attributeref ::=  primary "." identifier

The primary must evaluate to an object of a type that supports attribute references, which most objects do. This object is then asked to produce the attribute whose name is the identifier. This production can be customized by overriding the __getattr__() method. If this attribute is not available, the exception AttributeError is raised. Otherwise, the type and value of the object produced is determined by the object. Multiple evaluations of the same attribute reference may yield different objects.

6.3.2. Subscriptions¶

A subscription selects an item of a sequence (string, tuple or list) or mapping (dictionary) object:

subscription ::=  primary "[" expression_list "]"

The primary must evaluate to an object that supports subscription (lists or dictionaries for example). User-defined objects can support subscription by defining a __getitem__() method.

For built-in objects, there are two types of objects that support subscription:

If the primary is a mapping, the expression list must evaluate to an object whose value is one of the keys of the mapping, and the subscription selects the value in the mapping that corresponds to that key. (The expression list is a tuple except if it has exactly one item.)

If the primary is a sequence, the expression list must evaluate to an integer or a slice (as discussed in the following section).

The formal syntax makes no special provision for negative indices in sequences; however, built-in sequences all provide a __getitem__() method that interprets negative indices by adding the length of the sequence to the index (so that x[-1] selects the last item of x). The resulting value must be a nonnegative integer less than the number of items in the sequence, and the subscription selects the item whose index is that value (counting from zero). Since the support for negative indices and slicing occurs in the object’s __getitem__() method, subclasses overriding this method will need to explicitly add that support.

A string’s items are characters. A character is not a separate data type but a string of exactly one character.

6.3.3. Slicings¶

A slicing selects a range of items in a sequence object (e.g., a string, tuple or list). Slicings may be used as expressions or as targets in assignment or del statements. The syntax for a slicing:

slicing      ::=  primary "[" slice_list "]"
slice_list   ::=  slice_item ("," slice_item)* [","]
slice_item   ::=  expression | proper_slice
proper_slice ::=  [lower_bound] ":" [upper_bound] [ ":" [stride] ]
lower_bound  ::=  expression
upper_bound  ::=  expression
stride       ::=  expression

There is ambiguity in the formal syntax here: anything that looks like an expression list also looks like a slice list, so any subscription can be interpreted as a slicing. Rather than further complicating the syntax, this is disambiguated by defining that in this case the interpretation as a subscription takes priority over the interpretation as a slicing (this is the case if the slice list contains no proper slice).

The semantics for a slicing are as follows. The primary is indexed (using the same __getitem__() method as normal subscription) with a key that is constructed from the slice list, as follows. If the slice list contains at least one comma, the key is a tuple containing the conversion of the slice items; otherwise, the conversion of the lone slice item is the key. The conversion of a slice item that is an expression is that expression. The conversion of a proper slice is a slice object (see section A hierarquia de tipos padrão) whose start, stop and step attributes are the values of the expressions given as lower bound, upper bound and stride, respectively, substituting None for missing expressions.

6.3.4. Chamadas¶

A call calls a callable object (e.g., a function) with a possibly empty series of arguments:

call                 ::=  primary "(" [argument_list [","] | comprehension] ")"
argument_list        ::=  positional_arguments ["," starred_and_keywords]
                            ["," keywords_arguments]
                          | starred_and_keywords ["," keywords_arguments]
                          | keywords_arguments
positional_arguments ::=  ["*"] expression ("," ["*"] expression)*
starred_and_keywords ::=  ("*" expression | keyword_item)
                          ("," "*" expression | "," keyword_item)*
keywords_arguments   ::=  (keyword_item | "**" expression)
                          ("," keyword_item | "," "**" expression)*
keyword_item         ::=  identifier "=" expression

An optional trailing comma may be present after the positional and keyword arguments but does not affect the semantics.

The primary must evaluate to a callable object (user-defined functions, built-in functions, methods of built-in objects, class objects, methods of class instances, and all objects having a __call__() method are callable). All argument expressions are evaluated before the call is attempted. Please refer to section Definições de função for the syntax of formal parameter lists.

If keyword arguments are present, they are first converted to positional arguments, as follows. First, a list of unfilled slots is created for the formal parameters. If there are N positional arguments, they are placed in the first N slots. Next, for each keyword argument, the identifier is used to determine the corresponding slot (if the identifier is the same as the first formal parameter name, the first slot is used, and so on). If the slot is already filled, a TypeError exception is raised. Otherwise, the value of the argument is placed in the slot, filling it (even if the expression is None, it fills the slot). When all arguments have been processed, the slots that are still unfilled are filled with the corresponding default value from the function definition. (Default values are calculated, once, when the function is defined; thus, a mutable object such as a list or dictionary used as default value will be shared by all calls that don’t specify an argument value for the corresponding slot; this should usually be avoided.) If there are any unfilled slots for which no default value is specified, a TypeError exception is raised. Otherwise, the list of filled slots is used as the argument list for the call.

CPython implementation detail: An implementation may provide built-in functions whose positional parameters do not have names, even if they are ‘named’ for the purpose of documentation, and which therefore cannot be supplied by keyword. In CPython, this is the case for functions implemented in C that use PyArg_ParseTuple() to parse their arguments.

If there are more positional arguments than there are formal parameter slots, a TypeError exception is raised, unless a formal parameter using the syntax *identifier is present; in this case, that formal parameter receives a tuple containing the excess positional arguments (or an empty tuple if there were no excess positional arguments).

If any keyword argument does not correspond to a formal parameter name, a TypeError exception is raised, unless a formal parameter using the syntax **identifier is present; in this case, that formal parameter receives a dictionary containing the excess keyword arguments (using the keywords as keys and the argument values as corresponding values), or a (new) empty dictionary if there were no excess keyword arguments.

If the syntax *expression appears in the function call, expression must evaluate to an iterable. Elements from these iterables are treated as if they were additional positional arguments. For the call f(x1, x2, *y, x3, x4), if y evaluates to a sequence y1, …, yM, this is equivalent to a call with M+4 positional arguments x1, x2, y1, …, yM, x3, x4.

A consequence of this is that although the *expression syntax may appear after explicit keyword arguments, it is processed before the keyword arguments (and any **expression arguments – see below). So:

>>> def f(a, b):
...     print(a, b)
...
>>> f(b=1, *(2,))
2 1
>>> f(a=1, *(2,))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: f() got multiple values for keyword argument 'a'
>>> f(1, *(2,))
1 2

It is unusual for both keyword arguments and the *expression syntax to be used in the same call, so in practice this confusion does not arise.

If the syntax **expression appears in the function call, expression must evaluate to a mapping, the contents of which are treated as additional keyword arguments. If a keyword is already present (as an explicit keyword argument, or from another unpacking), a TypeError exception is raised.

Formal parameters using the syntax *identifier or **identifier cannot be used as positional argument slots or as keyword argument names.

Alterado na versão 3.5: Function calls accept any number of * and ** unpackings, positional arguments may follow iterable unpackings (*), and keyword arguments may follow dictionary unpackings (**). Originally proposed by PEP 448.

A call always returns some value, possibly None, unless it raises an exception. How this value is computed depends on the type of the callable object.

If it is—

a user-defined function:: The code block for the function is executed, passing it the argument list. The first thing the code block will do is bind the formal parameters to the arguments; this is described in section Definições de função. When the code block executes a return statement, this specifies the return value of the function call.
a built-in function or method:: The result is up to the interpreter; see Funções embutidas for the descriptions of built-in functions and methods.
um objeto classe:: A new instance of that class is returned.
a class instance method:: The corresponding user-defined function is called, with an argument list that is one longer than the argument list of the call: the instance becomes the first argument.
a class instance:: The class must define a __call__() method; the effect is then the same as if that method was called.

6.4. Await expression¶

Suspend the execution of coroutine on an awaitable object. Can only be used inside a coroutine function.

await_expr ::=  "await" primary

Novo na versão 3.5.

6.5. The power operator¶

The power operator binds more tightly than unary operators on its left; it binds less tightly than unary operators on its right. The syntax is:

power ::=  (await_expr | primary) ["**" u_expr]

Thus, in an unparenthesized sequence of power and unary operators, the operators are evaluated from right to left (this does not constrain the evaluation order for the operands): -1**2 results in -1.

The power operator has the same semantics as the built-in pow() function, when called with two arguments: it yields its left argument raised to the power of its right argument. The numeric arguments are first converted to a common type, and the result is of that type.

For int operands, the result has the same type as the operands unless the second argument is negative; in that case, all arguments are converted to float and a float result is delivered. For example, 10**2 returns 100, but 10**-2 returns 0.01.

Raising 0.0 to a negative power results in a ZeroDivisionError. Raising a negative number to a fractional power results in a complex number. (In earlier versions it raised a ValueError.)

6.6. Unary arithmetic and bitwise operations¶

All unary arithmetic and bitwise operations have the same priority:

u_expr ::=  power | "-" u_expr | "+" u_expr | "~" u_expr

The unary - (minus) operator yields the negation of its numeric argument.

The unary + (plus) operator yields its numeric argument unchanged.

The unary ~ (invert) operator yields the bitwise inversion of its integer argument. The bitwise inversion of x is defined as -(x+1). It only applies to integral numbers.

In all three cases, if the argument does not have the proper type, a TypeError exception is raised.

6.7. Binary arithmetic operations¶

The binary arithmetic operations have the conventional priority levels. Note that some of these operations also apply to certain non-numeric types. Apart from the power operator, there are only two levels, one for multiplicative operators and one for additive operators:

m_expr ::=  u_expr | m_expr "*" u_expr | m_expr "@" m_expr |
            m_expr "//" u_expr | m_expr "/" u_expr |
            m_expr "%" u_expr
a_expr ::=  m_expr | a_expr "+" m_expr | a_expr "-" m_expr

The * (multiplication) operator yields the product of its arguments. The arguments must either both be numbers, or one argument must be an integer and the other must be a sequence. In the former case, the numbers are converted to a common type and then multiplied together. In the latter case, sequence repetition is performed; a negative repetition factor yields an empty sequence.

The @ (at) operator is intended to be used for matrix multiplication. No builtin Python types implement this operator.

Novo na versão 3.5.

The / (division) and // (floor division) operators yield the quotient of their arguments. The numeric arguments are first converted to a common type. Division of integers yields a float, while floor division of integers results in an integer; the result is that of mathematical division with the ‘floor’ function applied to the result. Division by zero raises the ZeroDivisionError exception.

The % (modulo) operator yields the remainder from the division of the first argument by the second. The numeric arguments are first converted to a common type. A zero right argument raises the ZeroDivisionError exception. The arguments may be floating point numbers, e.g., 3.14%0.7 equals 0.34 (since 3.14 equals 4*0.7 + 0.34.) The modulo operator always yields a result with the same sign as its second operand (or zero); the absolute value of the result is strictly smaller than the absolute value of the second operand 1.

The floor division and modulo operators are connected by the following identity: x == (x//y)*y + (x%y). Floor division and modulo are also connected with the built-in function divmod(): divmod(x, y) == (x//y, x%y). 2.

In addition to performing the modulo operation on numbers, the % operator is also overloaded by string objects to perform old-style string formatting (also known as interpolation). The syntax for string formatting is described in the Python Library Reference, section Formatação de String no Formato printf-style.

The floor division operator, the modulo operator, and the divmod() function are not defined for complex numbers. Instead, convert to a floating point number using the abs() function if appropriate.

The + (addition) operator yields the sum of its arguments. The arguments must either both be numbers or both be sequences of the same type. In the former case, the numbers are converted to a common type and then added together. In the latter case, the sequences are concatenated.

The - (subtraction) operator yields the difference of its arguments. The numeric arguments are first converted to a common type.

6.8. Shifting operations¶

The shifting operations have lower priority than the arithmetic operations:

shift_expr ::=  a_expr | shift_expr ("<<" | ">>") a_expr

These operators accept integers as arguments. They shift the first argument to the left or right by the number of bits given by the second argument.

A right shift by n bits is defined as floor division by pow(2,n). A left shift by n bits is defined as multiplication with pow(2,n).

6.9. Binary bitwise operations¶

Each of the three bitwise operations has a different priority level:

and_expr ::=  shift_expr | and_expr "&" shift_expr
xor_expr ::=  and_expr | xor_expr "^" and_expr
or_expr  ::=  xor_expr | or_expr "|" xor_expr

The & operator yields the bitwise AND of its arguments, which must be integers.

The ^ operator yields the bitwise XOR (exclusive OR) of its arguments, which must be integers.

The | operator yields the bitwise (inclusive) OR of its arguments, which must be integers.

6.10. Comparações¶

Unlike C, all comparison operations in Python have the same priority, which is lower than that of any arithmetic, shifting or bitwise operation. Also unlike C, expressions like a < b < c have the interpretation that is conventional in mathematics:

comparison    ::=  or_expr (comp_operator or_expr)*
comp_operator ::=  "<" | ">" | "==" | ">=" | "<=" | "!="
                   | "is" ["not"] | ["not"] "in"

Comparisons yield boolean values: True or False.

Comparisons can be chained arbitrarily, e.g., 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).

Formally, if a, b, c, …, y, z are expressions and op1, op2, …, opN are comparison operators, then a op1 b op2 c ... y opN z is equivalent to a op1 b and b op2 c and ... y opN z, except that each expression is evaluated at most once.

Note that a op1 b op2 c doesn’t imply any kind of comparison between a and c, so that, e.g., x < y > z is perfectly legal (though perhaps not pretty).

6.10.1. Value comparisons¶

The operators <, >, ==, >=, <=, and != compare the values of two objects. The objects do not need to have the same type.

Chapter Objetos, valores e tipos states that objects have a value (in addition to type and identity). The value of an object is a rather abstract notion in Python: For example, there is no canonical access method for an object’s value. Also, there is no requirement that the value of an object should be constructed in a particular way, e.g. comprised of all its data attributes. Comparison operators implement a particular notion of what the value of an object is. One can think of them as defining the value of an object indirectly, by means of their comparison implementation.

Because all types are (direct or indirect) subtypes of object, they inherit the default comparison behavior from object. Types can customize their comparison behavior by implementing rich comparison methods like __lt__(), described in Customização básica.

The default behavior for equality comparison (== and !=) is based on the identity of the objects. Hence, equality comparison of instances with the same identity results in equality, and equality comparison of instances with different identities results in inequality. A motivation for this default behavior is the desire that all objects should be reflexive (i.e. x is y implies x == y).

A default order comparison (<, >, <=, and >=) is not provided; an attempt raises TypeError. A motivation for this default behavior is the lack of a similar invariant as for equality.

The behavior of the default equality comparison, that instances with different identities are always unequal, may be in contrast to what types will need that have a sensible definition of object value and value-based equality. Such types will need to customize their comparison behavior, and in fact, a number of built-in types have done that.

The following list describes the comparison behavior of the most important built-in types.

Numbers of built-in numeric types (Tipos Numéricos — int, float, complex) and of the standard library types fractions.Fraction and decimal.Decimal can be compared within and across their types, with the restriction that complex numbers do not support order comparison. Within the limits of the types involved, they compare mathematically (algorithmically) correct without loss of precision.

The not-a-number values float('NaN') and decimal.Decimal('NaN') are special. Any ordered comparison of a number to a not-a-number value is false. A counter-intuitive implication is that not-a-number values are not equal to themselves. For example, if x = float('NaN'), 3 < x, x < 3 and x == x are all false, while x != x is true. This behavior is compliant with IEEE 754.
Binary sequences (instances of bytes or bytearray) can be compared within and across their types. They compare lexicographically using the numeric values of their elements.
Strings (instances of str) compare lexicographically using the numerical Unicode code points (the result of the built-in function ord()) of their characters. 3

Strings and binary sequences cannot be directly compared.
Sequences (instances of tuple, list, or range) can be compared only within each of their types, with the restriction that ranges do not support order comparison. Equality comparison across these types results in inequality, and ordering comparison across these types raises TypeError.

Sequences compare lexicographically using comparison of corresponding elements, whereby reflexivity of the elements is enforced.

In enforcing reflexivity of elements, the comparison of collections assumes that for a collection element x, x == x is always true. Based on that assumption, element identity is compared first, and element comparison is performed only for distinct elements. This approach yields the same result as a strict element comparison would, if the compared elements are reflexive. For non-reflexive elements, the result is different than for strict element comparison, and may be surprising: The non-reflexive not-a-number values for example result in the following comparison behavior when used in a list:
```
>>> nan = float('NaN')
>>> nan is nan
True
>>> nan == nan
False                 <-- the defined non-reflexive behavior of NaN
>>> [nan] == [nan]
True                  <-- list enforces reflexivity and tests identity first
```
Lexicographical comparison between built-in collections works as follows:
- For two collections to compare equal, they must be of the same type, have the same length, and each pair of corresponding elements must compare equal (for example, [1,2] == (1,2) is false because the type is not the same).
- Collections that support order comparison are ordered the same as their first unequal elements (for example, [1,2,x] <= [1,2,y] has the same value as x <= y). If a corresponding element does not exist, the shorter collection is ordered first (for example, [1,2] < [1,2,3] is true).
Mappings (instances of dict) compare equal if and only if they have equal (key, value) pairs. Equality comparison of the keys and values enforces reflexivity.

Order comparisons (<, >, <=, and >=) raise TypeError.
Sets (instances of set or frozenset) can be compared within and across their types.

They define order comparison operators to mean subset and superset tests. Those relations do not define total orderings (for example, the two sets {1,2} and {2,3} are not equal, nor subsets of one another, nor supersets of one another). Accordingly, sets are not appropriate arguments for functions which depend on total ordering (for example, min(), max(), and sorted() produce undefined results given a list of sets as inputs).

Comparison of sets enforces reflexivity of its elements.
Most other built-in types have no comparison methods implemented, so they inherit the default comparison behavior.

User-defined classes that customize their comparison behavior should follow some consistency rules, if possible:

Equality comparison should be reflexive. In other words, identical objects should compare equal:

x is y implies x == y
Comparison should be symmetric. In other words, the following expressions should have the same result:

x == y and y == x

x != y and y != x

x < y and y > x

x <= y and y >= x
Comparison should be transitive. The following (non-exhaustive) examples illustrate that:

x > y and y > z implies x > z

x < y and y <= z implies x < z
Inverse comparison should result in the boolean negation. In other words, the following expressions should have the same result:

x == y and not x != y

x < y and not x >= y (for total ordering)

x > y and not x <= y (for total ordering)

The last two expressions apply to totally ordered collections (e.g. to sequences, but not to sets or mappings). See also the total_ordering() decorator.
The hash() result should be consistent with equality. Objects that are equal should either have the same hash value, or be marked as unhashable.

Python does not enforce these consistency rules. In fact, the not-a-number values are an example for not following these rules.

6.10.2. Membership test operations¶

The operators in and not in test for membership. x in s evaluates to True if x is a member of s, and False otherwise. x not in s returns the negation of x in s. All built-in sequences and set types support this as well as dictionary, for which in tests whether the dictionary has a given key. For container types such as list, tuple, set, frozenset, dict, or collections.deque, the expression x in y is equivalent to any(x is e or x == e for e in y).

For the string and bytes types, x in y is True if and only if x is a substring of y. An equivalent test is y.find(x) != -1. Empty strings are always considered to be a substring of any other string, so "" in "abc" will return True.

For user-defined classes which define the __contains__() method, x in y returns True if y.__contains__(x) returns a true value, and False otherwise.

For user-defined classes which do not define __contains__() but do define __iter__(), x in y is True if some value z, for which the expression x is z or x == z is true, is produced while iterating over y. If an exception is raised during the iteration, it is as if in raised that exception.

Lastly, the old-style iteration protocol is tried: if a class defines __getitem__(), x in y is True if and only if there is a non-negative integer index i such that x is y[i] or x == y[i], and no lower integer index raises the IndexError exception. (If any other exception is raised, it is as if in raised that exception).

The operator not in is defined to have the inverse truth value of in.

6.10.3. Identity comparisons¶

The operators is and is not test for an object’s identity: x is y is true if and only if x and y are the same object. An Object’s identity is determined using the id() function. x is not y yields the inverse truth value. 4

6.11. Boolean operations¶

or_test  ::=  and_test | or_test "or" and_test
and_test ::=  not_test | and_test "and" not_test
not_test ::=  comparison | "not" not_test

In the context of Boolean operations, and also when expressions are used by control flow statements, the following values are interpreted as false: False, None, numeric zero of all types, and empty strings and containers (including strings, tuples, lists, dictionaries, sets and frozensets). All other values are interpreted as true. User-defined objects can customize their truth value by providing a __bool__() method.

The operator not yields True if its argument is false, False otherwise.

The expression x and y first evaluates x; if x is false, its value is returned; otherwise, y is evaluated and the resulting value is returned.

The expression x or y first evaluates x; if x is true, its value is returned; otherwise, y is evaluated and the resulting value is returned.

Note that neither and nor or restrict the value and type they return to False and True, but rather return the last evaluated argument. This is sometimes useful, e.g., if s is a string that should be replaced by a default value if it is empty, the expression s or 'foo' yields the desired value. Because not has to create a new value, it returns a boolean value regardless of the type of its argument (for example, not 'foo' produces False rather than ''.)

6.12. Conditional expressions¶

conditional_expression ::=  or_test ["if" or_test "else" expression]
expression             ::=  conditional_expression | lambda_expr
expression_nocond      ::=  or_test | lambda_expr_nocond

Conditional expressions (sometimes called a “ternary operator”) have the lowest priority of all Python operations.

The expression x if C else y first evaluates the condition, C rather than x. If C is true, x is evaluated and its value is returned; otherwise, y is evaluated and its value is returned.

See PEP 308 for more details about conditional expressions.

6.13. Lambdas¶

lambda_expr        ::=  "lambda" [parameter_list] ":" expression
lambda_expr_nocond ::=  "lambda" [parameter_list] ":" expression_nocond

Lambda expressions (sometimes called lambda forms) are used to create anonymous functions. The expression lambda parameters: expression yields a function object. The unnamed object behaves like a function object defined with:

def <lambda>(parameters):
    return expression

See section Definições de função for the syntax of parameter lists. Note that functions created with lambda expressions cannot contain statements or annotations.

6.14. Expression lists¶

expression_list    ::=  expression ("," expression)* [","]
starred_list       ::=  starred_item ("," starred_item)* [","]
starred_expression ::=  expression | (starred_item ",")* [starred_item]
starred_item       ::=  expression | "*" or_expr

Except when part of a list or set display, an expression list containing at least one comma yields a tuple. The length of the tuple is the number of expressions in the list. The expressions are evaluated from left to right.

An asterisk * denotes iterable unpacking. Its operand must be an iterable. The iterable is expanded into a sequence of items, which are included in the new tuple, list, or set, at the site of the unpacking.

Novo na versão 3.5: Iterable unpacking in expression lists, originally proposed by PEP 448.

The trailing comma is required only to create a single tuple (a.k.a. a singleton); it is optional in all other cases. A single expression without a trailing comma doesn’t create a tuple, but rather yields the value of that expression. (To create an empty tuple, use an empty pair of parentheses: ().)

6.15. Evaluation order¶

Python evaluates expressions from left to right. Notice that while evaluating an assignment, the right-hand side is evaluated before the left-hand side.

In the following lines, expressions will be evaluated in the arithmetic order of their suffixes:

expr1, expr2, expr3, expr4
(expr1, expr2, expr3, expr4)
{expr1: expr2, expr3: expr4}
expr1 + expr2 * (expr3 - expr4)
expr1(expr2, expr3, *expr4, **expr5)
expr3, expr4 = expr1, expr2

6.16. Operator precedence¶

The following table summarizes the operator precedence in Python, from lowest precedence (least binding) to highest precedence (most binding). Operators in the same box have the same precedence. Unless the syntax is explicitly given, operators are binary. Operators in the same box group left to right (except for exponentiation, which groups from right to left).

Note that comparisons, membership tests, and identity tests, all have the same precedence and have a left-to-right chaining feature as described in the Comparações section.

Operator	Description (descrição)
`lambda`	Lambda expression
`if` – `else`	Conditional expression
`or`	Boolean OR
`and`	Boolean AND
`not` `x`	Boolean NOT
`in`, `not in`, `is`, `is not`, `<`, `<=`, `>`, `>=`, `!=`, `==`	Comparisons, including membership tests and identity tests
`\|`	Bitwise OR
`^`	Bitwise XOR
`&`	Bitwise AND
`<<`, `>>`	Shifts
`+`, `-`	Addition and subtraction
`*`, `@`, `/`, `//`, `%`	Multiplication, matrix multiplication, division, floor division, remainder 5
`+x`, `-x`, `~x`	Positive, negative, bitwise NOT
`**`	Exponentiation 6
`await` `x`	Await expression
`x[index]`, `x[index:index]`, `x(arguments...)`, `x.attribute`	Subscription, slicing, call, attribute reference
`(expressions...)`, `[expressions...]`, `{key: value...}`, `{expressions...}`	Binding or parenthesized expression, list display, dictionary display, set display

Notas de rodapé

1

While abs(x%y) < abs(y) is true mathematically, for floats it may not be true numerically due to roundoff. For example, and assuming a platform on which a Python float is an IEEE 754 double-precision number, in order that -1e-100 % 1e100 have the same sign as 1e100, the computed result is -1e-100 + 1e100, which is numerically exactly equal to 1e100. The function math.fmod() returns a result whose sign matches the sign of the first argument instead, and so returns -1e-100 in this case. Which approach is more appropriate depends on the application.

2

If x is very close to an exact integer multiple of y, it’s possible for x//y to be one larger than (x-x%y)//y due to rounding. In such cases, Python returns the latter result, in order to preserve that divmod(x,y)[0] * y + x % y be very close to x.

3

The Unicode standard distinguishes between code points (e.g. U+0041) and abstract characters (e.g. “LATIN CAPITAL LETTER A”). While most abstract characters in Unicode are only represented using one code point, there is a number of abstract characters that can in addition be represented using a sequence of more than one code point. For example, the abstract character “LATIN CAPITAL LETTER C WITH CEDILLA” can be represented as a single precomposed character at code position U+00C7, or as a sequence of a base character at code position U+0043 (LATIN CAPITAL LETTER C), followed by a combining character at code position U+0327 (COMBINING CEDILLA).

The comparison operators on strings compare at the level of Unicode code points. This may be counter-intuitive to humans. For example, "\u00C7" == "\u0043\u0327" is False, even though both strings represent the same abstract character “LATIN CAPITAL LETTER C WITH CEDILLA”.

To compare strings at the level of abstract characters (that is, in a way intuitive to humans), use unicodedata.normalize().

4

Due to automatic garbage-collection, free lists, and the dynamic nature of descriptors, you may notice seemingly unusual behaviour in certain uses of the is operator, like those involving comparisons between instance methods, or constants. Check their documentation for more info.

5

The % operator is also used for string formatting; the same precedence applies.

6

The power operator ** binds less tightly than an arithmetic or bitwise unary operator on its right, that is, 2**-1 is 0.5.