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#
SOME DESCRIPTIVE TITLE.
#
Copyright (C) 2001 Python Software Foundation
#
This file is distributed under the same license as the Python package.
#
FIRST AUTHOR <EMAIL@ADDRESS>, YEAR.
#
#
Translators:
#
python-doc bot, 2026
#
Maciej Olko, 2026
#
Rafael Fontenelle <rffontenelle@gmail.com>, 2026
#
#,
fuzzy
msgid ""
msgstr ""
"
Project-Id-Version
:
Python 3.15\n
"
"
Report-Msgid-Bugs-To
:
\n
"
"
POT-Creation-Date
:
2026-10-13 19:59+0000\n
"
"
PO-Revision-Date
:
2026-09-13 17:09+0000\n
"
"
Last-Translator
:
Rafael Fontenelle <rffontenelle@gmail.com>, 2026\n
"
"
Language-Team
:
Polish (https://app.transifex.com/python-doc/teams/5390/pl/)\n
"
"
MIME-Version
:
1.0\n
"
"
Content-Type
:
text/plain; charset=UTF-8\n
"
"
Content-Transfer-Encoding
:
8bit\n
"
"
Language
:
pl\n
"
"
Plural-Forms
:
nplurals=4; plural=(n==1 ? 0 : (n%10>=2 && n%10<=4) &&
"
"
(n%100<12 || n%100>14) ? 1 : n!=1 && (n%10>=0 && n%10<=1) || (n%10>=5 &&
"
"
n%10<=9) || (n%100>=12 && n%100<=14) ? 2 : 3);\n
"
msgid
"Built-in Types"
msgstr
"Wbudowane typy"
msgid
""
"The following sections describe the standard types that are built into the "
"interpreter."
msgstr
""
msgid
""
"The principal built-in types are numerics, sequences, mappings, classes, "
"instances and exceptions."
msgstr
""
msgid
""
"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``."
msgstr
""
msgid
""
"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 :func:`repr` function or the "
"slightly different :func:`str` function). The latter function is implicitly "
"used when an object is written by the :func:`print` function."
msgstr
""
msgid
"Truth Value Testing"
msgstr
""
msgid
""
"Any object can be tested for truth value, for use in an :keyword:`if` or :"
"keyword:`while` condition or as operand of the Boolean operations below."
msgstr
""
msgid
""
"By default, an object is considered true unless its class defines either a :"
"meth:`~object.__bool__` method that returns ``False`` or a :meth:`~object."
"__len__` method that returns zero, when called with the object. [1]_ If one "
"of the methods raises an exception when called, the exception is propagated "
"and the object does not have a truth value (for example, :data:"
"`NotImplemented`). Here are most of the built-in objects considered false:"
msgstr
""
msgid
"constants defined to be false: ``None`` and ``False``"
msgstr
""
msgid
""
"zero of any numeric type: ``0``, ``0.0``, ``0j``, ``Decimal(0)``, "
"``Fraction(0, 1)``"
msgstr
""
msgid
""
"empty sequences and collections: ``''``, ``()``, ``[]``, ``{}``, ``set()``, "
"``range(0)``"
msgstr
""
msgid
""
"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.)"
msgstr
""
msgid
"Boolean Operations --- :keyword:`!and`, :keyword:`!or`, :keyword:`!not`"
msgstr
""
msgid
"These are the Boolean operations, ordered by ascending priority:"
msgstr
""
msgid
"Operation"
msgstr
""
msgid
"Result"
msgstr
""
msgid
"Notes"
msgstr
"Notatki"
msgid
"``x or y``"
msgstr
"``x or y``"
msgid
"if *x* is true, then *x*, else *y*"
msgstr
""
msgid
"
\\
(1)"
msgstr
"
\\
(1)"
msgid
"``x and y``"
msgstr
"``x and y``"
msgid
"if *x* is false, then *x*, else *y*"
msgstr
""
msgid
"
\\
(2)"
msgstr
"
\\
(2)"
msgid
"``not x``"
msgstr
"``not x``"
msgid
"if *x* is false, then ``True``, else ``False``"
msgstr
""
msgid
"
\\
(3)"
msgstr
"
\\
(3)"
msgid
"Notes:"
msgstr
"Uwagi:"
msgid
""
"This is a short-circuit operator, so it only evaluates the second argument "
"if the first one is false."
msgstr
""
msgid
""
"This is a short-circuit operator, so it only evaluates the second argument "
"if the first one is true."
msgstr
""
msgid
""
"``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."
msgstr
""
msgid
"Comparisons"
msgstr
""
msgid
""
"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)."
msgstr
""
msgid
"This table summarizes the comparison operations:"
msgstr
""
msgid
"Meaning"
msgstr
"Znaczenie"
msgid
"``<``"
msgstr
"``<``"
msgid
"strictly less than"
msgstr
""
msgid
"``<=``"
msgstr
"``<=``"
msgid
"less than or equal"
msgstr
""
msgid
"``>``"
msgstr
"``>``"
msgid
"strictly greater than"
msgstr
""
msgid
"``>=``"
msgstr
"``>=``"
msgid
"greater than or equal"
msgstr
""
msgid
"``==``"
msgstr
"``==``"
msgid
"equal"
msgstr
""
msgid
"``!=``"
msgstr
"``!=``"
msgid
"not equal"
msgstr
""
msgid
"``is``"
msgstr
"``is``"
msgid
"object identity"
msgstr
""
msgid
"``is not``"
msgstr
"``is not``"
msgid
"negated object identity"
msgstr
""
msgid
""
"Unless stated otherwise, objects of different types never compare equal. The "
"``==`` operator is always defined but for some object types (for example, "
"class objects) is equivalent to :keyword:`is`. The ``<``, ``<=``, ``>`` and "
"``>=`` operators are only defined where they make sense; for example, they "
"raise a :exc:`TypeError` exception when one of the arguments is a complex "
"number."
msgstr
""
msgid
""
"Non-identical instances of a class normally compare as non-equal unless the "
"class defines the :meth:`~object.__eq__` method."
msgstr
""
msgid
""
"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 :meth:`~object.__lt__`, :meth:`~object.__le__`, :meth:`~object."
"__gt__`, and :meth:`~object.__ge__` (in general, :meth:`~object.__lt__` and :"
"meth:`~object.__eq__` are sufficient, if you want the conventional meanings "
"of the comparison operators)."
msgstr
""
msgid
""
"The behavior of the :keyword:`is` and :keyword:`is not` operators cannot be "
"customized; also they can be applied to any two objects and never raise an "
"exception."
msgstr
""
msgid
""
"Two more operations with the same syntactic priority, :keyword:`in` and :"
"keyword:`not in`, are supported by types that are :term:`iterable` or "
"implement the :meth:`~object.__contains__` method."
msgstr
""
msgid
"Numeric Types --- :class:`int`, :class:`float`, :class:`complex`"
msgstr
""
msgid
""
"There are three distinct numeric types: :dfn:`integers`, :dfn:`floating-"
"point numbers`, and :dfn:`complex numbers`. In addition, Booleans are a "
"subtype of integers. Integers have unlimited precision. Floating-point "
"numbers are usually implemented using :c:expr:`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 :data:`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 :mod:`fractions.Fraction`, for rationals, and :mod:`decimal."
"Decimal`, for floating-point numbers with user-definable precision.)"
msgstr
""
msgid
""
"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."
msgstr
""
msgid
""
"The constructors :func:`int`, :func:`float`, and :func:`complex` can be used "
"to produce numbers of a specific type."
msgstr
""
msgid
""
"Python fully supports mixed arithmetic: when a binary arithmetic operator "
"has operands of different built-in numeric types, the operand with the "
"
\"
narrower
\"
type is widened to that of the other:"
msgstr
""
msgid
"If both arguments are complex numbers, no conversion is performed;"
msgstr
""
msgid
""
"if either argument is a complex or a floating-point number, the other is "
"converted to a floating-point number;"
msgstr
""
msgid
"otherwise, both must be integers and no conversion is necessary."
msgstr
""
msgid
""
"Arithmetic with complex and real operands is defined by the usual "
"mathematical formula, for example::"
msgstr
""
msgid
""
"x + complex(u, v) = complex(x + u, v)\n"
"x * complex(u, v) = complex(x * u, x * v)"
msgstr
""
msgid
""
"A comparison between numbers of different types behaves as though the exact "
"values of those numbers were being compared. [2]_"
msgstr
""
msgid
""
"All numeric types (except complex) support the following operations (for "
"priorities of the operations, see :ref:`operator-summary`):"
msgstr
""
msgid
"Full documentation"
msgstr
""
msgid
"``x + y``"
msgstr
"``x + y``"
msgid
"sum of *x* and *y*"
msgstr
""
msgid
"``x - y``"
msgstr
"``x - y``"
msgid
"difference of *x* and *y*"
msgstr
""
msgid
"``x * y``"
msgstr
"``x * y``"
msgid
"product of *x* and *y*"
msgstr
""
msgid
"``x / y``"
msgstr
"``x / y``"
msgid
"quotient of *x* and *y*"
msgstr
""
msgid
"``x // y``"
msgstr
"``x // y``"
msgid
"floored quotient of *x* and *y*"
msgstr
""
msgid
"
\\
(1)
\\
(2)"
msgstr
""
msgid
"``x % y``"
msgstr
"``x % y``"
msgid
"remainder of ``x / y``"
msgstr
""
msgid
"``-x``"
msgstr
"``-x``"
msgid
"*x* negated"
msgstr
""
msgid
"``+x``"
msgstr
"``+x``"
msgid
"*x* unchanged"
msgstr
""
msgid
"``abs(x)``"
msgstr
"``abs(x)``"
msgid
"absolute value or magnitude of *x*"
msgstr
""
msgid
":func:`abs`"
msgstr
":func:`abs`"
msgid
"``int(x)``"
msgstr
"``int(x)``"
msgid
"*x* converted to integer"
msgstr
""
msgid
"
\\
(3)
\\
(6)"
msgstr
""
msgid
":func:`int`"
msgstr
":func:`int`"
msgid
"``float(x)``"
msgstr
"``float(x)``"
msgid
"*x* converted to floating point"
msgstr
""
msgid
"
\\
(4)
\\
(6)"
msgstr
""
msgid
":func:`float`"
msgstr
":func:`float`"
msgid
"``complex(re, im)``"
msgstr
"``complex(re, im)``"
msgid
""
"a complex number with real part *re*, imaginary part *im*. *im* defaults to "
"zero."
msgstr
""
msgid
"
\\
(6)"
msgstr
"
\\
(6)"
msgid
":func:`complex`"
msgstr
":func:`complex`"
msgid
"``c.conjugate()``"
msgstr
"``c.conjugate()``"
msgid
"conjugate of the complex number *c*"
msgstr
""
msgid
"``divmod(x, y)``"
msgstr
"``divmod(x, y)``"
msgid
"the pair ``(x // y, x % y)``"
msgstr
""
msgid
":func:`divmod`"
msgstr
":func:`divmod`"
msgid
"``pow(x, y)``"
msgstr
"``pow(x, y)``"
msgid
"*x* to the power *y*"
msgstr
""
msgid
"
\\
(5)"
msgstr
"
\\
(5)"
msgid
":func:`pow`"
msgstr
":func:`pow`"
msgid
"``x ** y``"
msgstr
"``x ** y``"
msgid
""
"Also referred to as integer division. For operands of type :class:`int`, "
"the result has type :class:`int`. For operands of type :class:`float`, the "
"result has type :class:`float`. In general, the result is a whole integer, "
"though the result's type is not necessarily :class:`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``."
msgstr
""
msgid
""
"Not for complex numbers. Instead convert to floats using :func:`abs` if "
"appropriate."
msgstr
""
msgid
""
"Conversion from :class:`float` to :class:`int` truncates, discarding the "
"fractional part. See functions :func:`math.floor` and :func:`math.ceil` for "
"alternative conversions."
msgstr
""
msgid
""
"float also accepts the strings
\"
nan
\"
and
\"
inf
\"
with an optional prefix "
"
\"
+
\"
or
\"
-
\"
for Not a Number (NaN) and positive or negative infinity."
msgstr
""
msgid
""
"Python defines ``pow(0, 0)`` and ``0 ** 0`` to be ``1``, as is common for "
"programming languages."
msgstr
""
msgid
""
"The numeric literals accepted include the digits ``0`` to ``9`` or any "
"Unicode equivalent (code points with the ``Nd`` property)."
msgstr
""
msgid
""
"See `the Unicode Standard <https://unicode.org/Public/UNIDATA/extracted/"
"DerivedNumericType.txt>`_ for a complete list of code points with the ``Nd`` "
"property."
msgstr
""
msgid
""
"All :class:`numbers.Real` types (:class:`int` and :class:`float`) also "
"include the following operations:"
msgstr
""
msgid
":func:`math.trunc(
\\
x) <math.trunc>`"
msgstr
":func:`math.trunc(
\\
x) <math.trunc>`"
msgid
"*x* truncated to :class:`~numbers.Integral`"
msgstr
""
msgid
":func:`round(x[, n]) <round>`"
msgstr
":func:`round(x[, n]) <round>`"
msgid
""
"*x* rounded to *n* digits, rounding half to even. If *n* is omitted, it "
"defaults to 0."
msgstr
""
msgid
":func:`math.floor(
\\
x) <math.floor>`"
msgstr
":func:`math.floor(
\\
x) <math.floor>`"
msgid
"the greatest :class:`~numbers.Integral` <= *x*"
msgstr
""
msgid
":func:`math.ceil(x) <math.ceil>`"
msgstr
""
msgid
"the least :class:`~numbers.Integral` >= *x*"
msgstr
""
msgid
""
"For additional numeric operations see the :mod:`math` and :mod:`cmath` "
"modules."
msgstr
""
msgid
"Bitwise Operations on Integer Types"
msgstr
""
msgid
""
"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."
msgstr
""
msgid
""
"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 "
"``-``)."
msgstr
""
msgid
"This table lists the bitwise operations sorted in ascending priority:"
msgstr
""
msgid
"``x | y``"
msgstr
"``x | y``"
msgid
"bitwise :dfn:`or` of *x* and *y*"
msgstr
""
msgid
"
\\
(4)"
msgstr
"
\\
(4)"
msgid
"``x ^ y``"
msgstr
"``x ^ y``"
msgid
"bitwise :dfn:`exclusive or` of *x* and *y*"
msgstr
""
msgid
"``x & y``"
msgstr
"``x & y``"
msgid
"bitwise :dfn:`and` of *x* and *y*"
msgstr
""
msgid
"``x << n``"
msgstr
"``x << n``"
msgid
"*x* shifted left by *n* bits"
msgstr
""
msgid
"(1)(2)"
msgstr
"(1)(2)"
msgid
"``x >> n``"
msgstr
"``x >> n``"
msgid
"*x* shifted right by *n* bits"
msgstr
""
msgid
"(1)(3)"
msgstr
""
msgid
"``~x``"
msgstr
"``~x``"
msgid
"the bits of *x* inverted"
msgstr
""
msgid
""
"Negative shift counts are illegal and cause a :exc:`ValueError` to be raised."
msgstr
""
msgid
""
"A left shift by *n* bits is equivalent to multiplication by ``pow(2, n)``."
msgstr
""
msgid
""
"A right shift by *n* bits is equivalent to floor division by ``pow(2, n)``."
msgstr
""
msgid
""
"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."
msgstr
""
msgid
"Additional Methods on Integer Types"
msgstr
""
msgid
""
"The int type implements the :class:`numbers.Integral` :term:`abstract base "
"class`. In addition, it provides a few more methods:"
msgstr
""
msgid
""
"Return the number of bits necessary to represent an integer in binary, "
"excluding the sign and leading zeros::"
msgstr
""
msgid
""
">>> n = -37\n"
">>> bin(n)\n"
"'-0b100101'\n"
">>> n.bit_length()\n"
"6"
msgstr
""
">>> n = -37\n"
">>> bin(n)\n"
"'-0b100101'\n"
">>> n.bit_length()\n"
"6"
msgid
""
"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``."
msgstr
""
msgid
"Equivalent to::"
msgstr
"Odpowiednik::"
msgid
""
"def bit_length(self):\n"
" s = bin(self) # binary representation: bin(-37) --> '-0b100101'\n"
" s = s.lstrip('-0b') # remove leading zeros and minus sign\n"
" return len(s) # len('100101') --> 6"
msgstr
""
msgid
""
"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::"
msgstr
""
msgid
""
">>> n = 19\n"
">>> bin(n)\n"
"'0b10011'\n"
">>> n.bit_count()\n"
"3\n"
">>> (-n).bit_count()\n"
"3"
msgstr
""
">>> n = 19\n"
">>> bin(n)\n"
"'0b10011'\n"
">>> n.bit_count()\n"
"3\n"
">>> (-n).bit_count()\n"
"3"
msgid
""
"def bit_count(self):\n"
" return bin(self).count(
\"
1
\"
)"
msgstr
""
msgid
"Return an array of bytes representing an integer."
msgstr
""
msgid
""
"The integer is represented using *length* bytes, and defaults to 1. An :exc:"
"`OverflowError` is raised if the integer is not representable with the given "
"number of bytes."
msgstr
""
msgid
""
"The *byteorder* argument determines the byte order used to represent the "
"integer, and defaults to ``
\"
big
\"
``. 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."
msgstr
""
msgid
""
"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 :exc:`OverflowError` is raised. The default value for *signed* is "
"``False``."
msgstr
""
msgid
""
"The default values can be used to conveniently turn an integer into a single "
"byte object::"
msgstr
""
msgid
""
">>> (65).to_bytes()\n"
"b'A'"
msgstr
""
">>> (65).to_bytes()\n"
"b'A'"
msgid
""
"However, when using the default arguments, don't try to convert a value "
"greater than 255 or you'll get an :exc:`OverflowError`."
msgstr
""
msgid
""
"def to_bytes(n, length=1, byteorder='big', signed=False):\n"
" if byteorder == 'little':\n"
" order = range(length)\n"
" elif byteorder == 'big':\n"
" order = reversed(range(length))\n"
" else:\n"
" raise ValueError(
\"
byteorder must be either 'little' or 'big'
\"
)\n"
"\n"
" return bytes((n >> i*8) & 0xff for i in order)"
msgstr
""
msgid
"Added default argument values for ``length`` and ``byteorder``."
msgstr
""
msgid
"Return the integer represented by the given array of bytes."
msgstr
""
msgid
""
"The argument *bytes* must either be a :term:`bytes-like object` or an "
"iterable producing bytes."
msgstr
""
msgid
""
"The *byteorder* argument determines the byte order used to represent the "
"integer, and defaults to ``
\"
big
\"
``. 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 :data:`sys."
"byteorder` as the byte order value."
msgstr
""
msgid
""
"The *signed* argument indicates whether two's complement is used to "
"represent the integer."
msgstr
""
msgid
""
"def from_bytes(bytes, byteorder='big', signed=False):\n"
" if byteorder == 'little':\n"
" little_ordered = list(bytes)\n"
" elif byteorder == 'big':\n"
" little_ordered = list(reversed(bytes))\n"
" else:\n"
" raise ValueError(
\"
byteorder must be either 'little' or 'big'
\"
)\n"
"\n"
" n = sum(b << i*8 for i, b in enumerate(little_ordered))\n"
" if signed and little_ordered and (little_ordered[-1] & 0x80):\n"
" n -= 1 << 8*len(little_ordered)\n"
"\n"
" return n"
msgstr
""
msgid
"Added default argument value for ``byteorder``."
msgstr
""
msgid
""
"Return a pair of integers whose ratio is equal to the original integer and "
"has a positive denominator. The integer ratio of integers (whole numbers) "
"is always the integer as the numerator and ``1`` as the denominator."
msgstr
""
msgid
""
"Returns ``True``. Exists for duck type compatibility with :meth:`float."
"is_integer`."
msgstr
""
msgid
"Additional Methods on Float"
msgstr
""
msgid
""
"The float type implements the :class:`numbers.Real` :term:`abstract base "
"class`. float also has the following additional methods."
msgstr
""
msgid
""
"Class method to return a floating-point number constructed from a number *x*."
msgstr
""
msgid
""
"If the argument is an integer or a floating-point number, a floating-point "
"number with the same value (within Python's floating-point precision) is "
"returned. If the argument is outside the range of a Python float, an :exc:"
"`OverflowError` will be raised."
msgstr
""
msgid
""
"For a general Python object ``x``, ``float.from_number(x)`` delegates to ``x."
"__float__()``. If :meth:`~object.__float__` is not defined then it falls "
"back to :meth:`~object.__index__`."
msgstr
""
msgid
""
"Return a pair of integers whose ratio is exactly equal to the original "
"float. The ratio is in lowest terms and has a positive denominator. Raises :"
"exc:`OverflowError` on infinities and a :exc:`ValueError` on NaNs."
msgstr
""
msgid
""
"Return ``True`` if the float instance is finite with integral value, and "
"``False`` otherwise::"
msgstr
""
msgid
""
">>> (-2.0).is_integer()\n"
"True\n"
">>> (3.2).is_integer()\n"
"False"
msgstr
""
">>> (-2.0).is_integer()\n"
"True\n"
">>> (3.2).is_integer()\n"
"False"
msgid
""
"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."
msgstr
""
msgid
""
"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."
msgstr
""
msgid
""
"Class method to return the float represented by a hexadecimal string *s*. "
"The string *s* may have leading and trailing whitespace."
msgstr
""
msgid
""
"Note that :meth:`float.hex` is an instance method, while :meth:`float."
"fromhex` is a class method."
msgstr
""
msgid
"A hexadecimal string takes the form::"
msgstr
""
msgid
"[sign] ['0x'] integer ['.' fraction] ['p' exponent]"
msgstr
""
msgid
""
"where the optional ``sign`` may be 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 :meth:`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 :meth:`float.fromhex`."
msgstr
""
msgid
""
"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``::"
msgstr
""
msgid
""
">>> float.fromhex('0x3.a7p10')\n"
"3740.0"
msgstr
""
">>> float.fromhex('0x3.a7p10')\n"
"3740.0"
msgid
""
"Applying the reverse conversion to ``3740.0`` gives a different hexadecimal "
"string representing the same number::"
msgstr
""
msgid
""
">>> float.hex(3740.0)\n"
"'0x1.d380000000000p+11'"
msgstr
""
">>> float.hex(3740.0)\n"
"'0x1.d380000000000p+11'"
msgid
"Additional Methods on Complex"
msgstr
""
msgid
""
"The :class:`!complex` type implements the :class:`numbers.Complex` :term:"
"`abstract base class`. :class:`!complex` also has the following additional "
"methods."
msgstr
""
msgid
"Class method to convert a number to a complex number."
msgstr
""
msgid
""
"For a general Python object ``x``, ``complex.from_number(x)`` delegates to "
"``x.__complex__()``. If :meth:`~object.__complex__` is not defined then it "
"falls back to :meth:`~object.__float__`. If :meth:`!__float__` is not "
"defined then it falls back to :meth:`~object.__index__`."
msgstr
""
msgid
"Hashing of numeric types"
msgstr
""
msgid
""
"For numbers ``x`` and ``y``, possibly of different types, it's a requirement "
"that ``hash(x) == hash(y)`` whenever ``x == y`` (see the :meth:`~object."
"__hash__` method documentation for more details). For ease of "
"implementation and efficiency across a variety of numeric types (including :"
"class:`int`, :class:`float`, :class:`decimal.Decimal` and :class:`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 :class:`int` and :class:`fractions.Fraction`, and all finite "
"instances of :class:`float` and :class:`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 :attr:`~sys.hash_info."
"modulus` attribute of :data:`sys.hash_info`."
msgstr
""
msgid
""
"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."
msgstr
""
msgid
"Here are the rules in detail:"
msgstr
""
msgid
""
"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``."
msgstr
""
msgid
""
"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``."
msgstr
""
msgid
""
"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``."
msgstr
""
msgid
""
"The particular values ``sys.hash_info.inf`` and ``-sys.hash_info.inf`` are "
"used as hash values for positive infinity or negative infinity "
"(respectively)."
msgstr
""
msgid
""
"For a :class:`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``."
msgstr
""
msgid
""
"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, :class:"
"`float`, or :class:`complex`::"
msgstr
""
msgid
""
"import sys, math\n"
"\n"
"def hash_fraction(m, n):\n"
"
\"\"\"
Compute the hash of a rational number m / n.\n"
"\n"
" Assumes m and n are integers, with n positive.\n"
" Equivalent to hash(fractions.Fraction(m, n)).\n"
"\n"
"
\"\"\"
\n"
" P = sys.hash_info.modulus\n"
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