4. 內建型態

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, 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.

4.1. 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.)

4.2. Boolean Operations — and, or, not

These are the Boolean operations, ordered by ascending priority:

Operation	Result	註解
x or y	if x is false, then y, else x	(1)
x and y	if x is false, then x, else y	(2)
not x	if x is false, then True, else False	(3)

註解：

1. This is a short-circuit operator, so it only evaluates the second argument if the first one is false.
2. This is a short-circuit operator, so it only evaluates the second argument if the first one is true.
3. 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.

4.3. 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:

Operation	Meaning
<	strictly less than
<=	less than or equal
>	strictly greater than
>=	greater than or equal
==	equal
!=	not equal
is	object identity
is not	negated object identity

Objects of different types, except different numeric types, never compare equal. Furthermore, some types (for example, function objects) support only a degenerate notion of comparison where any two objects of that type are unequal. The <, <=, > and >= operators will raise a TypeError exception when comparing a complex number with another built-in numeric type, when the objects are of different types that cannot be compared, or in other cases where there is no defined ordering.

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 only by sequence types (below).

4.4. 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 additional numeric types, fractions that hold rationals, and decimal that hold 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. Comparisons between numbers of mixed type use the same rule. [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, sorted by ascending priority (all numeric operations have a higher priority than comparison operations):

Operation	Result	註解	Full documentation
x + y	sum of x and y
x - y	difference of x and y
x * y	product of x and y
x / y	quotient of x and y
x // y	floored quotient of x and y	(1)
x % y	remainder of x / y	(2)
-x	x negated
+x	x unchanged
abs(x)	absolute value or magnitude of x		abs()
int(x)	x converted to integer	(3)(6)	int()
float(x)	x converted to floating point	(4)(6)	float()
complex(re, im)	a complex number with real part re, imaginary part im. im defaults to zero.	(6)	complex()
c.conjugate()	conjugate of the complex number c
divmod(x, y)	the pair (x // y, x % y)	(2)	divmod()
pow(x, y)	x to the power y	(5)	pow()
x ** y	x to the power y	(5)

註解：

1. 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.

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

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

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

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

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

   See http://www.unicode.org/Public/10.0.0/ucd/extracted/DerivedNumericType.txt for a complete list of code points with the Nd property.

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

Operation	Result
math.trunc(x)	x truncated to Integral
round(x[, n])	x rounded to n digits, rounding half to even. If n is omitted, it defaults to 0.
math.floor(x)	the greatest Integral <= x
math.ceil(x)	the least Integral >= x

For additional numeric operations see the math and cmath modules.

4.4.1. 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:

Operation	Result	註解
x | y	bitwise or of x and y
x ^ y	bitwise exclusive or of x and y
x & y	bitwise and of x and y
x << n	x shifted left by n bits	(1)(2)
x >> n	x shifted right by n bits	(1)(3)
~x	the bits of x inverted

註解：

1. Negative shift counts are illegal and cause a ValueError to be raised.
2. A left shift by n bits is equivalent to multiplication by pow(2, n) without overflow check.
3. A right shift by n bits is equivalent to division by pow(2, n) without overflow check.
4. 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.

4.4.2. Additional Methods on Integer Types

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

int.bit_length()

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

>>> n = -37
>>> bin(n)
'-0b100101'
>>> n.bit_length()
6

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.

Equivalent to:

def bit_length(self):
    s = bin(self)       # binary representation:  bin(-37) --> '-0b100101'
    s = s.lstrip('-0b') # remove leading zeros and minus sign
    return len(s)       # len('100101') --> 6

3.1 版新加入.

int.to_bytes(length, byteorder, *, signed=False)

Return an array of bytes representing an integer.

>>> (1024).to_bytes(2, byteorder='big')
b'\x04\x00'
>>> (1024).to_bytes(10, byteorder='big')
b'\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00'
>>> (-1024).to_bytes(10, byteorder='big', signed=True)
b'\xff\xff\xff\xff\xff\xff\xff\xff\xfc\x00'
>>> x = 1000
>>> x.to_bytes((x.bit_length() + 7) // 8, byteorder='little')
b'\xe8\x03'

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.

3.2 版新加入.

classmethod int.from_bytes(bytes, byteorder, *, signed=False)

Return the integer represented by the given array of bytes.

>>> int.from_bytes(b'\x00\x10', byteorder='big')
16
>>> int.from_bytes(b'\x00\x10', byteorder='little')
4096
>>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=True)
-1024
>>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=False)
64512
>>> int.from_bytes([255, 0, 0], byteorder='big')
16711680

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.

3.2 版新加入.

4.4.3. Additional Methods on Float

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

float.as_integer_ratio()

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.

float.is_integer()

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

>>> (-2.0).is_integer()
True
>>> (3.2).is_integer()
False

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.

float.hex()

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:

[sign] ['0x'] integer ['.' fraction] ['p' exponent]

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:

>>> float.fromhex('0x3.a7p10')
3740.0

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

>>> float.hex(3740.0)
'0x1.d380000000000p+11'

4.4.4. 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, -sys.hash_info.inf and sys.hash_info.nan are used as hash values for positive infinity, negative infinity, or nans (respectively). (All hashable nans have the same hash value.)
• 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:

import sys, math

def hash_fraction(m, n):
    """Compute the hash of a rational number m / n.

    Assumes m and n are integers, with n positive.
    Equivalent to hash(fractions.Fraction(m, n)).

    """
    P = sys.hash_info.modulus
    # Remove common factors of P.  (Unnecessary if m and n already coprime.)
    while m % P == n % P == 0:
        m, n = m // P, n // P

    if n % P == 0:
        hash_value = sys.hash_info.inf
    else:
        # Fermat's Little Theorem: pow(n, P-1, P) is 1, so
        # pow(n, P-2, P) gives the inverse of n modulo P.
        hash_value = (abs(m) % P) * pow(n, P - 2, P) % P
    if m < 0:
        hash_value = -hash_value
    if hash_value == -1:
        hash_value = -2
    return hash_value

def hash_float(x):
    """Compute the hash of a float x."""

    if math.isnan(x):
        return sys.hash_info.nan
    elif math.isinf(x):
        return sys.hash_info.inf if x > 0 else -sys.hash_info.inf
    else:
        return hash_fraction(*x.as_integer_ratio())

def hash_complex(z):
    """Compute the hash of a complex number z."""

    hash_value = hash_float(z.real) + sys.hash_info.imag * hash_float(z.imag)
    # do a signed reduction modulo 2**sys.hash_info.width
    M = 2**(sys.hash_info.width - 1)
    hash_value = (hash_value & (M - 1)) - (hash_value & M)
    if hash_value == -1:
        hash_value = -2
    return hash_value

4.5. 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 iteration support:

container.__iter__()

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:

iterator.__iter__()

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.

iterator.__next__()

Return the next item from the container. 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.

4.5.1. Generator Types

Python’s generators 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.

4.6. 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.

4.6.1. 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]

Operation	Result	註解
x in s	True if an item of s is equal to x, else False	(1)
x not in s	False if an item of s is equal to x, else True	(1)
s + t	the concatenation of s and t	(6)(7)
s * n or n * s	equivalent to adding s to itself n times	(2)(7)
s[i]	ith item of s, origin 0	(3)
s[i:j]	slice of s from i to j	(3)(4)
s[i:j:k]	slice of s from i to j with step k	(3)(5)
len(s)	length of s
min(s)	smallest item of s
max(s)	largest item of s
s.index(x[,