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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:
# Sukhmanpreet kaur, 2026
# DARSHAN RAJPUT, 2026
# Bhuvansh Kataria, 2026
#
#, fuzzy
msgid ""
msgstr ""
"Project-Id-Version: Python 3.15\n"
"Report-Msgid-Bugs-To: \n"
"POT-Creation-Date: 2026-11-09 23:13+0000\n"
"PO-Revision-Date: 2026-09-13 17:09+0000\n"
"Last-Translator: Bhuvansh Kataria, 2026\n"
"Language-Team: Panjabi (Punjabi) (https://app.transifex.com/python-doc/teams/"
"5390/pa/)\n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\n"
"Language: pa\n"
"Plural-Forms: nplurals=2; plural=(n != 1);\n"
msgid "Built-in Types"
msgstr ""
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 ""
msgid "``x or y``"
msgstr ""
msgid "if *x* is true, then *x*, else *y*"
msgstr ""
msgid "\\(1)"
msgstr ""
msgid "``x and y``"
msgstr ""
msgid "if *x* is false, then *x*, else *y*"
msgstr ""
msgid "\\(2)"
msgstr ""
msgid "``not x``"
msgstr ""
msgid "if *x* is false, then ``True``, else ``False``"
msgstr ""
msgid "\\(3)"
msgstr ""
msgid "Notes:"
msgstr ""
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 ""
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 ""
msgid "object identity"
msgstr ""
msgid "``is not``"
msgstr ""
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 ""
msgid "sum of *x* and *y*"
msgstr ""
msgid "``x - y``"
msgstr ""
msgid "difference of *x* and *y*"
msgstr ""
msgid "``x * y``"
msgstr ""
msgid "product of *x* and *y*"
msgstr ""
msgid "``x / y``"
msgstr ""
msgid "quotient of *x* and *y*"
msgstr ""
msgid "``x // y``"
msgstr ""
msgid "floored quotient of *x* and *y*"
msgstr ""
msgid "\\(1)\\(2)"
msgstr ""
msgid "``x % y``"
msgstr ""
msgid "remainder of ``x / y``"
msgstr ""
msgid "``-x``"
msgstr ""
msgid "*x* negated"
msgstr ""
msgid "``+x``"
msgstr ""
msgid "*x* unchanged"
msgstr ""
msgid "``abs(x)``"
msgstr ""
msgid "absolute value or magnitude of *x*"
msgstr ""
msgid ":func:`abs`"
msgstr ""
msgid "``int(x)``"
msgstr ""
msgid "*x* converted to integer"
msgstr ""
msgid "\\(3)\\(6)"
msgstr ""
msgid ":func:`int`"
msgstr ""
msgid "``float(x)``"
msgstr ""
msgid "*x* converted to floating point"
msgstr ""
msgid "\\(4)\\(6)"
msgstr ""
msgid ":func:`float`"
msgstr ""
msgid "``complex(re, im)``"
msgstr ""
msgid ""
"a complex number with real part *re*, imaginary part *im*. *im* defaults to "
"zero."
msgstr ""
msgid "\\(6)"
msgstr ""
msgid ":func:`complex`"
msgstr ""
msgid "``c.conjugate()``"
msgstr ""
msgid "conjugate of the complex number *c*"
msgstr ""
msgid "``divmod(x, y)``"
msgstr ""
msgid "the pair ``(x // y, x % y)``"
msgstr ""
msgid ":func:`divmod`"
msgstr ""
msgid "``pow(x, y)``"
msgstr ""
msgid "*x* to the power *y*"
msgstr ""
msgid "\\(5)"
msgstr ""
msgid ":func:`pow`"
msgstr ""
msgid "``x ** y``"
msgstr ""
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 ""
msgid "*x* truncated to :class:`~numbers.Integral`"
msgstr ""
msgid ":func:`round(x[, n]) <round>`"
msgstr ""
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 ""
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 ""
msgid "bitwise :dfn:`or` of *x* and *y*"
msgstr ""
msgid "\\(4)"
msgstr ""
msgid "``x ^ y``"
msgstr ""
msgid "bitwise :dfn:`exclusive or` of *x* and *y*"
msgstr ""
msgid "``x & y``"
msgstr ""
msgid "bitwise :dfn:`and` of *x* and *y*"
msgstr ""
msgid "``x << n``"
msgstr ""
msgid "*x* shifted left by *n* bits"
msgstr ""
msgid "(1)(2)"
msgstr ""
msgid "``x >> n``"
msgstr ""
msgid "*x* shifted right by *n* bits"
msgstr ""
msgid "(1)(3)"
msgstr ""
msgid "``~x``"
msgstr ""
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 ""
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 ""
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 ""
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 ""
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 ""
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 ""
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 ""
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"
" # Remove common factors of P. (Unnecessary if m and n already "
"coprime.)\n"
" while m % P == n % P == 0:\n"
" m, n = m // P, n // P\n"
"\n"
" if n % P == 0:\n"
" hash_value = sys.hash_info.inf\n"
" else:\n"
" # Fermat's Little Theorem: pow(n, P-1, P) is 1, so\n"
" # pow(n, P-2, P) gives the inverse of n modulo P.\n"
" hash_value = (abs(m) % P) * pow(n, P - 2, P) % P\n"
" if m < 0:\n"
" hash_value = -hash_value\n"
" if hash_value == -1:\n"
" hash_value = -2\n"
" return hash_value\n"
"\n"
"def hash_float(x):\n"