decimal.po

# SOME DESCRIPTIVE TITLE.
# Copyright (C) 2001-2025, Python Software Foundation
# This file is distributed under the same license as the Python package.
# FIRST AUTHOR <EMAIL@ADDRESS>, YEAR.
#
# Translators:
# Michał Biliński <m.bilinskimichal@gmail.com>, 2021
# Stefan Ocetkiewicz <stefan.ocetkiewicz@gmail.com>, 2024
# Stan Ulbrych, 2025
#
#, fuzzy
msgid ""
msgstr ""
"Project-Id-Version: Python 3.13\n"
"Report-Msgid-Bugs-To: \n"
"POT-Creation-Date: 2025-03-14 14:17+0000\n"
"PO-Revision-Date: 2021-06-28 01:04+0000\n"
"Last-Translator: Stan Ulbrych, 2025\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 ":mod:`!decimal` --- Decimal fixed-point and floating-point arithmetic"
msgstr ""

msgid "**Source code:** :source:`Lib/decimal.py`"
msgstr ""

msgid ""
"The :mod:`decimal` module provides support for fast correctly rounded "
"decimal floating-point arithmetic. It offers several advantages over the :"
"class:`float` datatype:"
msgstr ""

msgid ""
"Decimal \"is based on a floating-point model which was designed with people "
"in mind, and necessarily has a paramount guiding principle -- computers must "
"provide an arithmetic that works in the same way as the arithmetic that "
"people learn at school.\" -- excerpt from the decimal arithmetic "
"specification."
msgstr ""

msgid ""
"Decimal numbers can be represented exactly.  In contrast, numbers like "
"``1.1`` and ``2.2`` do not have exact representations in binary floating "
"point. End users typically would not expect ``1.1 + 2.2`` to display as "
"``3.3000000000000003`` as it does with binary floating point."
msgstr ""

msgid ""
"The exactness carries over into arithmetic.  In decimal floating point, "
"``0.1 + 0.1 + 0.1 - 0.3`` is exactly equal to zero.  In binary floating "
"point, the result is ``5.5511151231257827e-017``.  While near to zero, the "
"differences prevent reliable equality testing and differences can "
"accumulate. For this reason, decimal is preferred in accounting applications "
"which have strict equality invariants."
msgstr ""

msgid ""
"The decimal module incorporates a notion of significant places so that "
"``1.30 + 1.20`` is ``2.50``.  The trailing zero is kept to indicate "
"significance. This is the customary presentation for monetary applications. "
"For multiplication, the \"schoolbook\" approach uses all the figures in the "
"multiplicands.  For instance, ``1.3 * 1.2`` gives ``1.56`` while ``1.30 * "
"1.20`` gives ``1.5600``."
msgstr ""

msgid ""
"Unlike hardware based binary floating point, the decimal module has a user "
"alterable precision (defaulting to 28 places) which can be as large as "
"needed for a given problem:"
msgstr ""

msgid ""
"Both binary and decimal floating point are implemented in terms of published "
"standards.  While the built-in float type exposes only a modest portion of "
"its capabilities, the decimal module exposes all required parts of the "
"standard. When needed, the programmer has full control over rounding and "
"signal handling. This includes an option to enforce exact arithmetic by "
"using exceptions to block any inexact operations."
msgstr ""

msgid ""
"The decimal module was designed to support \"without prejudice, both exact "
"unrounded decimal arithmetic (sometimes called fixed-point arithmetic) and "
"rounded floating-point arithmetic.\"  -- excerpt from the decimal arithmetic "
"specification."
msgstr ""

msgid ""
"The module design is centered around three concepts:  the decimal number, "
"the context for arithmetic, and signals."
msgstr ""

msgid ""
"A decimal number is immutable.  It has a sign, coefficient digits, and an "
"exponent.  To preserve significance, the coefficient digits do not truncate "
"trailing zeros.  Decimals also include special values such as ``Infinity``, "
"``-Infinity``, and ``NaN``.  The standard also differentiates ``-0`` from "
"``+0``."
msgstr ""

msgid ""
"The context for arithmetic is an environment specifying precision, rounding "
"rules, limits on exponents, flags indicating the results of operations, and "
"trap enablers which determine whether signals are treated as exceptions.  "
"Rounding options include :const:`ROUND_CEILING`, :const:`ROUND_DOWN`, :const:"
"`ROUND_FLOOR`, :const:`ROUND_HALF_DOWN`, :const:`ROUND_HALF_EVEN`, :const:"
"`ROUND_HALF_UP`, :const:`ROUND_UP`, and :const:`ROUND_05UP`."
msgstr ""

msgid ""
"Signals are groups of exceptional conditions arising during the course of "
"computation.  Depending on the needs of the application, signals may be "
"ignored, considered as informational, or treated as exceptions. The signals "
"in the decimal module are: :const:`Clamped`, :const:`InvalidOperation`, :"
"const:`DivisionByZero`, :const:`Inexact`, :const:`Rounded`, :const:"
"`Subnormal`, :const:`Overflow`, :const:`Underflow` and :const:"
"`FloatOperation`."
msgstr ""

msgid ""
"For each signal there is a flag and a trap enabler.  When a signal is "
"encountered, its flag is set to one, then, if the trap enabler is set to "
"one, an exception is raised.  Flags are sticky, so the user needs to reset "
"them before monitoring a calculation."
msgstr ""

msgid ""
"IBM's General Decimal Arithmetic Specification, `The General Decimal "
"Arithmetic Specification <https://speleotrove.com/decimal/decarith.html>`_."
msgstr ""

msgid "Quick-start Tutorial"
msgstr ""

msgid ""
"The usual start to using decimals is importing the module, viewing the "
"current context with :func:`getcontext` and, if necessary, setting new "
"values for precision, rounding, or enabled traps::"
msgstr ""

msgid ""
">>> from decimal import *\n"
">>> getcontext()\n"
"Context(prec=28, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,\n"
"        capitals=1, clamp=0, flags=[], traps=[Overflow, DivisionByZero,\n"
"        InvalidOperation])\n"
"\n"
">>> getcontext().prec = 7       # Set a new precision"
msgstr ""

msgid ""
"Decimal instances can be constructed from integers, strings, floats, or "
"tuples. Construction from an integer or a float performs an exact conversion "
"of the value of that integer or float.  Decimal numbers include special "
"values such as ``NaN`` which stands for \"Not a number\", positive and "
"negative ``Infinity``, and ``-0``::"
msgstr ""

msgid ""
">>> getcontext().prec = 28\n"
">>> Decimal(10)\n"
"Decimal('10')\n"
">>> Decimal('3.14')\n"
"Decimal('3.14')\n"
">>> Decimal(3.14)\n"
"Decimal('3.140000000000000124344978758017532527446746826171875')\n"
">>> Decimal((0, (3, 1, 4), -2))\n"
"Decimal('3.14')\n"
">>> Decimal(str(2.0 ** 0.5))\n"
"Decimal('1.4142135623730951')\n"
">>> Decimal(2) ** Decimal('0.5')\n"
"Decimal('1.414213562373095048801688724')\n"
">>> Decimal('NaN')\n"
"Decimal('NaN')\n"
">>> Decimal('-Infinity')\n"
"Decimal('-Infinity')"
msgstr ""

msgid ""
"If the :exc:`FloatOperation` signal is trapped, accidental mixing of "
"decimals and floats in constructors or ordering comparisons raises an "
"exception::"
msgstr ""

msgid ""
">>> c = getcontext()\n"
">>> c.traps[FloatOperation] = True\n"
">>> Decimal(3.14)\n"
"Traceback (most recent call last):\n"
"  File \"<stdin>\", line 1, in <module>\n"
"decimal.FloatOperation: [<class 'decimal.FloatOperation'>]\n"
">>> Decimal('3.5') < 3.7\n"
"Traceback (most recent call last):\n"
"  File \"<stdin>\", line 1, in <module>\n"
"decimal.FloatOperation: [<class 'decimal.FloatOperation'>]\n"
">>> Decimal('3.5') == 3.5\n"
"True"
msgstr ""

msgid ""
"The significance of a new Decimal is determined solely by the number of "
"digits input.  Context precision and rounding only come into play during "
"arithmetic operations."
msgstr ""

msgid ""
">>> getcontext().prec = 6\n"
">>> Decimal('3.0')\n"
"Decimal('3.0')\n"
">>> Decimal('3.1415926535')\n"
"Decimal('3.1415926535')\n"
">>> Decimal('3.1415926535') + Decimal('2.7182818285')\n"
"Decimal('5.85987')\n"
">>> getcontext().rounding = ROUND_UP\n"
">>> Decimal('3.1415926535') + Decimal('2.7182818285')\n"
"Decimal('5.85988')"
msgstr ""

msgid ""
"If the internal limits of the C version are exceeded, constructing a decimal "
"raises :class:`InvalidOperation`::"
msgstr ""

msgid ""
">>> Decimal(\"1e9999999999999999999\")\n"
"Traceback (most recent call last):\n"
"  File \"<stdin>\", line 1, in <module>\n"
"decimal.InvalidOperation: [<class 'decimal.InvalidOperation'>]"
msgstr ""

msgid ""
"Decimals interact well with much of the rest of Python.  Here is a small "
"decimal floating-point flying circus:"
msgstr ""

msgid ""
">>> data = list(map(Decimal, '1.34 1.87 3.45 2.35 1.00 0.03 9.25'.split()))\n"
">>> max(data)\n"
"Decimal('9.25')\n"
">>> min(data)\n"
"Decimal('0.03')\n"
">>> sorted(data)\n"
"[Decimal('0.03'), Decimal('1.00'), Decimal('1.34'), Decimal('1.87'),\n"
" Decimal('2.35'), Decimal('3.45'), Decimal('9.25')]\n"
">>> sum(data)\n"
"Decimal('19.29')\n"
">>> a,b,c = data[:3]\n"
">>> str(a)\n"
"'1.34'\n"
">>> float(a)\n"
"1.34\n"
">>> round(a, 1)\n"
"Decimal('1.3')\n"
">>> int(a)\n"
"1\n"
">>> a * 5\n"
"Decimal('6.70')\n"
">>> a * b\n"
"Decimal('2.5058')\n"
">>> c % a\n"
"Decimal('0.77')"
msgstr ""

msgid "And some mathematical functions are also available to Decimal:"
msgstr ""

msgid ""
"The :meth:`~Decimal.quantize` method rounds a number to a fixed exponent.  "
"This method is useful for monetary applications that often round results to "
"a fixed number of places:"
msgstr ""

msgid ""
"As shown above, the :func:`getcontext` function accesses the current context "
"and allows the settings to be changed.  This approach meets the needs of "
"most applications."
msgstr ""

msgid ""
"For more advanced work, it may be useful to create alternate contexts using "
"the Context() constructor.  To make an alternate active, use the :func:"
"`setcontext` function."
msgstr ""

msgid ""
"In accordance with the standard, the :mod:`decimal` module provides two "
"ready to use standard contexts, :const:`BasicContext` and :const:"
"`ExtendedContext`. The former is especially useful for debugging because "
"many of the traps are enabled:"
msgstr ""

msgid ""
">>> myothercontext = Context(prec=60, rounding=ROUND_HALF_DOWN)\n"
">>> setcontext(myothercontext)\n"
">>> Decimal(1) / Decimal(7)\n"
"Decimal('0.142857142857142857142857142857142857142857142857142857142857')\n"
"\n"
">>> ExtendedContext\n"
"Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,\n"
"        capitals=1, clamp=0, flags=[], traps=[])\n"
">>> setcontext(ExtendedContext)\n"
">>> Decimal(1) / Decimal(7)\n"
"Decimal('0.142857143')\n"
">>> Decimal(42) / Decimal(0)\n"
"Decimal('Infinity')\n"
"\n"
">>> setcontext(BasicContext)\n"
">>> Decimal(42) / Decimal(0)\n"
"Traceback (most recent call last):\n"
"  File \"<pyshell#143>\", line 1, in -toplevel-\n"
"    Decimal(42) / Decimal(0)\n"
"DivisionByZero: x / 0"
msgstr ""

msgid ""
"Contexts also have signal flags for monitoring exceptional conditions "
"encountered during computations.  The flags remain set until explicitly "
"cleared, so it is best to clear the flags before each set of monitored "
"computations by using the :meth:`~Context.clear_flags` method. ::"
msgstr ""

msgid ""
">>> setcontext(ExtendedContext)\n"
">>> getcontext().clear_flags()\n"
">>> Decimal(355) / Decimal(113)\n"
"Decimal('3.14159292')\n"
">>> getcontext()\n"
"Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,\n"
"        capitals=1, clamp=0, flags=[Inexact, Rounded], traps=[])"
msgstr ""

msgid ""
"The *flags* entry shows that the rational approximation to pi was rounded "
"(digits beyond the context precision were thrown away) and that the result "
"is inexact (some of the discarded digits were non-zero)."
msgstr ""

msgid ""
"Individual traps are set using the dictionary in the :attr:`~Context.traps` "
"attribute of a context:"
msgstr ""

msgid ""
">>> setcontext(ExtendedContext)\n"
">>> Decimal(1) / Decimal(0)\n"
"Decimal('Infinity')\n"
">>> getcontext().traps[DivisionByZero] = 1\n"
">>> Decimal(1) / Decimal(0)\n"
"Traceback (most recent call last):\n"
"  File \"<pyshell#112>\", line 1, in -toplevel-\n"
"    Decimal(1) / Decimal(0)\n"
"DivisionByZero: x / 0"
msgstr ""

msgid ""
"Most programs adjust the current context only once, at the beginning of the "
"program.  And, in many applications, data is converted to :class:`Decimal` "
"with a single cast inside a loop.  With context set and decimals created, "
"the bulk of the program manipulates the data no differently than with other "
"Python numeric types."
msgstr ""

msgid "Decimal objects"
msgstr ""

msgid "Construct a new :class:`Decimal` object based from *value*."
msgstr ""

msgid ""
"*value* can be an integer, string, tuple, :class:`float`, or another :class:"
"`Decimal` object. If no *value* is given, returns ``Decimal('0')``.  If "
"*value* is a string, it should conform to the decimal numeric string syntax "
"after leading and trailing whitespace characters, as well as underscores "
"throughout, are removed::"
msgstr ""

msgid ""
"sign           ::=  '+' | '-'\n"
"digit          ::=  '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | "
"'9'\n"
"indicator      ::=  'e' | 'E'\n"
"digits         ::=  digit [digit]...\n"
"decimal-part   ::=  digits '.' [digits] | ['.'] digits\n"
"exponent-part  ::=  indicator [sign] digits\n"
"infinity       ::=  'Infinity' | 'Inf'\n"
"nan            ::=  'NaN' [digits] | 'sNaN' [digits]\n"
"numeric-value  ::=  decimal-part [exponent-part] | infinity\n"
"numeric-string ::=  [sign] numeric-value | [sign] nan"
msgstr ""

msgid ""
"Other Unicode decimal digits are also permitted where ``digit`` appears "
"above.  These include decimal digits from various other alphabets (for "
"example, Arabic-Indic and Devanāgarī digits) along with the fullwidth digits "
"``'\\uff10'`` through ``'\\uff19'``."
msgstr ""

msgid ""
"If *value* is a :class:`tuple`, it should have three components, a sign "
"(``0`` for positive or ``1`` for negative), a :class:`tuple` of digits, and "
"an integer exponent. For example, ``Decimal((0, (1, 4, 1, 4), -3))`` returns "
"``Decimal('1.414')``."
msgstr ""

msgid ""
"If *value* is a :class:`float`, the binary floating-point value is "
"losslessly converted to its exact decimal equivalent.  This conversion can "
"often require 53 or more digits of precision.  For example, "
"``Decimal(float('1.1'))`` converts to "
"``Decimal('1.100000000000000088817841970012523233890533447265625')``."
msgstr ""

msgid ""
"The *context* precision does not affect how many digits are stored. That is "
"determined exclusively by the number of digits in *value*. For example, "
"``Decimal('3.00000')`` records all five zeros even if the context precision "
"is only three."
msgstr ""

msgid ""
"The purpose of the *context* argument is determining what to do if *value* "
"is a malformed string.  If the context traps :const:`InvalidOperation`, an "
"exception is raised; otherwise, the constructor returns a new Decimal with "
"the value of ``NaN``."
msgstr ""

msgid "Once constructed, :class:`Decimal` objects are immutable."
msgstr ""

msgid ""
"The argument to the constructor is now permitted to be a :class:`float` "
"instance."
msgstr ""

msgid ""
":class:`float` arguments raise an exception if the :exc:`FloatOperation` "
"trap is set. By default the trap is off."
msgstr ""

msgid ""
"Underscores are allowed for grouping, as with integral and floating-point "
"literals in code."
msgstr ""

msgid ""
"Decimal floating-point objects share many properties with the other built-in "
"numeric types such as :class:`float` and :class:`int`.  All of the usual "
"math operations and special methods apply.  Likewise, decimal objects can be "
"copied, pickled, printed, used as dictionary keys, used as set elements, "
"compared, sorted, and coerced to another type (such as :class:`float` or :"
"class:`int`)."
msgstr ""

msgid ""
"There are some small differences between arithmetic on Decimal objects and "
"arithmetic on integers and floats.  When the remainder operator ``%`` is "
"applied to Decimal objects, the sign of the result is the sign of the "
"*dividend* rather than the sign of the divisor::"
msgstr ""

msgid ""
">>> (-7) % 4\n"
"1\n"
">>> Decimal(-7) % Decimal(4)\n"
"Decimal('-3')"
msgstr ""
">>> (-7) % 4\n"
"1\n"
">>> Decimal(-7) % Decimal(4)\n"
"Decimal('-3')"

msgid ""
"The integer division operator ``//`` behaves analogously, returning the "
"integer part of the true quotient (truncating towards zero) rather than its "
"floor, so as to preserve the usual identity ``x == (x // y) * y + x % y``::"
msgstr ""

msgid ""
">>> -7 // 4\n"
"-2\n"
">>> Decimal(-7) // Decimal(4)\n"
"Decimal('-1')"
msgstr ""
">>> -7 // 4\n"
"-2\n"
">>> Decimal(-7) // Decimal(4)\n"
"Decimal('-1')"

msgid ""
"The ``%`` and ``//`` operators implement the ``remainder`` and ``divide-"
"integer`` operations (respectively) as described in the specification."
msgstr ""

msgid ""
"Decimal objects cannot generally be combined with floats or instances of :"
"class:`fractions.Fraction` in arithmetic operations: an attempt to add a :"
"class:`Decimal` to a :class:`float`, for example, will raise a :exc:"
"`TypeError`.  However, it is possible to use Python's comparison operators "
"to compare a :class:`Decimal` instance ``x`` with another number ``y``.  "
"This avoids confusing results when doing equality comparisons between "
"numbers of different types."
msgstr ""

msgid ""
"Mixed-type comparisons between :class:`Decimal` instances and other numeric "
"types are now fully supported."
msgstr ""

msgid ""
"In addition to the standard numeric properties, decimal floating-point "
"objects also have a number of specialized methods:"
msgstr ""

msgid ""
"Return the adjusted exponent after shifting out the coefficient's rightmost "
"digits until only the lead digit remains: ``Decimal('321e+5').adjusted()`` "
"returns seven.  Used for determining the position of the most significant "
"digit with respect to the decimal point."
msgstr ""

msgid ""
"Return a pair ``(n, d)`` of integers that represent the given :class:"
"`Decimal` instance as a fraction, in lowest terms and with a positive "
"denominator::"
msgstr ""

msgid ""
">>> Decimal('-3.14').as_integer_ratio()\n"
"(-157, 50)"
msgstr ""
">>> Decimal('-3.14').as_integer_ratio()\n"
"(-157, 50)"

msgid ""
"The conversion is exact.  Raise OverflowError on infinities and ValueError "
"on NaNs."
msgstr ""

msgid ""
"Return a :term:`named tuple` representation of the number: "
"``DecimalTuple(sign, digits, exponent)``."
msgstr ""

msgid ""
"Return the canonical encoding of the argument.  Currently, the encoding of "
"a :class:`Decimal` instance is always canonical, so this operation returns "
"its argument unchanged."
msgstr ""

msgid ""
"Compare the values of two Decimal instances.  :meth:`compare` returns a "
"Decimal instance, and if either operand is a NaN then the result is a NaN::"
msgstr ""

msgid ""
"a or b is a NaN  ==> Decimal('NaN')\n"
"a < b            ==> Decimal('-1')\n"
"a == b           ==> Decimal('0')\n"
"a > b            ==> Decimal('1')"
msgstr ""

msgid ""
"This operation is identical to the :meth:`compare` method, except that all "
"NaNs signal.  That is, if neither operand is a signaling NaN then any quiet "
"NaN operand is treated as though it were a signaling NaN."
msgstr ""

msgid ""
"Compare two operands using their abstract representation rather than their "
"numerical value.  Similar to the :meth:`compare` method, but the result "
"gives a total ordering on :class:`Decimal` instances.  Two :class:`Decimal` "
"instances with the same numeric value but different representations compare "
"unequal in this ordering:"
msgstr ""

msgid ""
"Quiet and signaling NaNs are also included in the total ordering.  The "
"result of this function is ``Decimal('0')`` if both operands have the same "
"representation, ``Decimal('-1')`` if the first operand is lower in the total "
"order than the second, and ``Decimal('1')`` if the first operand is higher "
"in the total order than the second operand.  See the specification for "
"details of the total order."
msgstr ""

msgid ""
"This operation is unaffected by context and is quiet: no flags are changed "
"and no rounding is performed.  As an exception, the C version may raise "
"InvalidOperation if the second operand cannot be converted exactly."
msgstr ""

msgid ""
"Compare two operands using their abstract representation rather than their "
"value as in :meth:`compare_total`, but ignoring the sign of each operand. "
"``x.compare_total_mag(y)`` is equivalent to ``x.copy_abs().compare_total(y."
"copy_abs())``."
msgstr ""

msgid ""
"Just returns self, this method is only to comply with the Decimal "
"Specification."
msgstr ""

msgid ""
"Return the absolute value of the argument.  This operation is unaffected by "
"the context and is quiet: no flags are changed and no rounding is performed."
msgstr ""

msgid ""
"Return the negation of the argument.  This operation is unaffected by the "
"context and is quiet: no flags are changed and no rounding is performed."
msgstr ""

msgid ""
"Return a copy of the first operand with the sign set to be the same as the "
"sign of the second operand.  For example:"
msgstr ""

msgid ""
"Return the value of the (natural) exponential function ``e**x`` at the given "
"number.  The result is correctly rounded using the :const:`ROUND_HALF_EVEN` "
"rounding mode."
msgstr ""

msgid ""
"Alternative constructor that only accepts instances of :class:`float` or :"
"class:`int`."
msgstr ""

msgid ""
"Note ``Decimal.from_float(0.1)`` is not the same as ``Decimal('0.1')``. "
"Since 0.1 is not exactly representable in binary floating point, the value "
"is stored as the nearest representable value which is "
"``0x1.999999999999ap-4``.  That equivalent value in decimal is "
"``0.1000000000000000055511151231257827021181583404541015625``."
msgstr ""

msgid ""
"From Python 3.2 onwards, a :class:`Decimal` instance can also be constructed "
"directly from a :class:`float`."
msgstr ""

msgid ""
">>> Decimal.from_float(0.1)\n"
"Decimal('0.1000000000000000055511151231257827021181583404541015625')\n"
">>> Decimal.from_float(float('nan'))\n"
"Decimal('NaN')\n"
">>> Decimal.from_float(float('inf'))\n"
"Decimal('Infinity')\n"
">>> Decimal.from_float(float('-inf'))\n"
"Decimal('-Infinity')"
msgstr ""
">>> Decimal.from_float(0.1)\n"
"Decimal('0.1000000000000000055511151231257827021181583404541015625')\n"
">>> Decimal.from_float(float('nan'))\n"
"Decimal('NaN')\n"
">>> Decimal.from_float(float('inf'))\n"
"Decimal('Infinity')\n"
">>> Decimal.from_float(float('-inf'))\n"
"Decimal('-Infinity')"

msgid ""
"Fused multiply-add.  Return self*other+third with no rounding of the "
"intermediate product self*other."
msgstr ""

msgid ""
"Return :const:`True` if the argument is canonical and :const:`False` "
"otherwise.  Currently, a :class:`Decimal` instance is always canonical, so "
"this operation always returns :const:`True`."
msgstr ""

msgid ""
"Return :const:`True` if the argument is a finite number, and :const:`False` "
"if the argument is an infinity or a NaN."
msgstr ""

msgid ""
"Return :const:`True` if the argument is either positive or negative infinity "
"and :const:`False` otherwise."
msgstr ""

msgid ""
"Return :const:`True` if the argument is a (quiet or signaling) NaN and :"
"const:`False` otherwise."
msgstr ""

msgid ""
"Return :const:`True` if the argument is a *normal* finite number.  Return :"
"const:`False` if the argument is zero, subnormal, infinite or a NaN."
msgstr ""

msgid ""
"Return :const:`True` if the argument is a quiet NaN, and :const:`False` "
"otherwise."
msgstr ""

msgid ""
"Return :const:`True` if the argument has a negative sign and :const:`False` "
"otherwise.  Note that zeros and NaNs can both carry signs."
msgstr ""

msgid ""
"Return :const:`True` if the argument is a signaling NaN and :const:`False` "
"otherwise."
msgstr ""

msgid ""
"Return :const:`True` if the argument is subnormal, and :const:`False` "
"otherwise."
msgstr ""

msgid ""
"Return :const:`True` if the argument is a (positive or negative) zero and :"
"const:`False` otherwise."
msgstr ""

msgid ""
"Return the natural (base e) logarithm of the operand.  The result is "
"correctly rounded using the :const:`ROUND_HALF_EVEN` rounding mode."
msgstr ""

msgid ""
"Return the base ten logarithm of the operand.  The result is correctly "
"rounded using the :const:`ROUND_HALF_EVEN` rounding mode."
msgstr ""

msgid ""
"For a nonzero number, return the adjusted exponent of its operand as a :"
"class:`Decimal` instance.  If the operand is a zero then ``Decimal('-"
"Infinity')`` is returned and the :const:`DivisionByZero` flag is raised.  If "
"the operand is an infinity then ``Decimal('Infinity')`` is returned."
msgstr ""

msgid ""
":meth:`logical_and` is a logical operation which takes two *logical "
"operands* (see :ref:`logical_operands_label`).  The result is the digit-wise "
"``and`` of the two operands."
msgstr ""

msgid ""
":meth:`logical_invert` is a logical operation.  The result is the digit-wise "
"inversion of the operand."
msgstr ""

msgid ""
":meth:`logical_or` is a logical operation which takes two *logical operands* "
"(see :ref:`logical_operands_label`).  The result is the digit-wise ``or`` of "
"the two operands."
msgstr ""

msgid ""
":meth:`logical_xor` is a logical operation which takes two *logical "
"operands* (see :ref:`logical_operands_label`).  The result is the digit-wise "
"exclusive or of the two operands."
msgstr ""

msgid ""
"Like ``max(self, other)`` except that the context rounding rule is applied "
"before returning and that ``NaN`` values are either signaled or ignored "
"(depending on the context and whether they are signaling or quiet)."
msgstr ""

msgid ""
"Similar to the :meth:`.max` method, but the comparison is done using the "
"absolute values of the operands."
msgstr ""

msgid ""
"Like ``min(self, other)`` except that the context rounding rule is applied "
"before returning and that ``NaN`` values are either signaled or ignored "
"(depending on the context and whether they are signaling or quiet)."
msgstr ""

msgid ""
"Similar to the :meth:`.min` method, but the comparison is done using the "
"absolute values of the operands."
msgstr ""

msgid ""
"Return the largest number representable in the given context (or in the "
"current thread's context if no context is given) that is smaller than the "
"given operand."
msgstr ""

msgid ""
"Return the smallest number representable in the given context (or in the "
"current thread's context if no context is given) that is larger than the "
"given operand."
msgstr ""

msgid ""
"If the two operands are unequal, return the number closest to the first "
"operand in the direction of the second operand.  If both operands are "
"numerically equal, return a copy of the first operand with the sign set to "
"be the same as the sign of the second operand."
msgstr ""

msgid ""
"Used for producing canonical values of an equivalence class within either "
"the current context or the specified context."
msgstr ""

msgid ""
"This has the same semantics as the unary plus operation, except that if the "
"final result is finite it is reduced to its simplest form, with all trailing "
"zeros removed and its sign preserved. That is, while the coefficient is non-"
"zero and a multiple of ten the coefficient is divided by ten and the "
"exponent is incremented by 1. Otherwise (the coefficient is zero) the "
"exponent is set to 0. In all cases the sign is unchanged."
msgstr ""

msgid ""
"For example, ``Decimal('32.100')`` and ``Decimal('0.321000e+2')`` both "
"normalize to the equivalent value ``Decimal('32.1')``."
msgstr ""

msgid "Note that rounding is applied *before* reducing to simplest form."
msgstr ""

msgid ""
"In the latest versions of the specification, this operation is also known as "
"``reduce``."
msgstr ""

msgid ""
"Return a string describing the *class* of the operand.  The returned value "
"is one of the following ten strings."
msgstr ""

msgid "``\"-Infinity\"``, indicating that the operand is negative infinity."
msgstr ""

msgid ""
"``\"-Normal\"``, indicating that the operand is a negative normal number."
msgstr ""

msgid ""
"``\"-Subnormal\"``, indicating that the operand is negative and subnormal."
msgstr ""

msgid "``\"-Zero\"``, indicating that the operand is a negative zero."
msgstr ""

msgid "``\"+Zero\"``, indicating that the operand is a positive zero."
msgstr ""

msgid ""
"``\"+Subnormal\"``, indicating that the operand is positive and subnormal."
msgstr ""

msgid ""
"``\"+Normal\"``, indicating that the operand is a positive normal number."
msgstr ""

msgid "``\"+Infinity\"``, indicating that the operand is positive infinity."
msgstr ""

msgid "``\"NaN\"``, indicating that the operand is a quiet NaN (Not a Number)."
msgstr ""

msgid "``\"sNaN\"``, indicating that the operand is a signaling NaN."
msgstr ""

msgid ""
"Return a value equal to the first operand after rounding and having the "
"exponent of the second operand."
msgstr ""

msgid ""
"Unlike other operations, if the length of the coefficient after the quantize "
"operation would be greater than precision, then an :const:`InvalidOperation` "
"is signaled. This guarantees that, unless there is an error condition, the "
"quantized exponent is always equal to that of the right-hand operand."
msgstr ""

msgid ""
"Also unlike other operations, quantize never signals Underflow, even if the "
"result is subnormal and inexact."
msgstr ""

msgid ""
"If the exponent of the second operand is larger than that of the first then "
"rounding may be necessary.  In this case, the rounding mode is determined by "
"the ``rounding`` argument if given, else by the given ``context`` argument; "
"if neither argument is given the rounding mode of the current thread's "
"context is used."
msgstr ""

msgid ""
"An error is returned whenever the resulting exponent is greater than :attr:"
"`~Context.Emax` or less than :meth:`~Context.Etiny`."
msgstr ""

msgid ""
"Return ``Decimal(10)``, the radix (base) in which the :class:`Decimal` class "
"does all its arithmetic.  Included for compatibility with the specification."
msgstr ""

msgid ""
"Return the remainder from dividing *self* by *other*.  This differs from "
"``self % other`` in that the sign of the remainder is chosen so as to "
"minimize its absolute value.  More precisely, the return value is ``self - n "
"* other`` where ``n`` is the integer nearest to the exact value of ``self / "
"other``, and if two integers are equally near then the even one is chosen."
msgstr ""

msgid "If the result is zero then its sign will be the sign of *self*."
msgstr ""

msgid ""
"Return the result of rotating the digits of the first operand by an amount "
"specified by the second operand.  The second operand must be an integer in "
"the range -precision through precision.  The absolute value of the second "
"operand gives the number of places to rotate.  If the second operand is "
"positive then rotation is to the left; otherwise rotation is to the right. "
"The coefficient of the first operand is padded on the left with zeros to "
"length precision if necessary.  The sign and exponent of the first operand "
"are unchanged."
msgstr ""

msgid ""
"Test whether self and other have the same exponent or whether both are "
"``NaN``."
msgstr ""

msgid ""
"Return the first operand with exponent adjusted by the second. Equivalently, "
"return the first operand multiplied by ``10**other``.  The second operand "
"must be an integer."
msgstr ""

msgid ""
"Return the result of shifting the digits of the first operand by an amount "
"specified by the second operand.  The second operand must be an integer in "
"the range -precision through precision.  The absolute value of the second "
"operand gives the number of places to shift.  If the second operand is "
"positive then the shift is to the left; otherwise the shift is to the "
"right.  Digits shifted into the coefficient are zeros.  The sign and "
"exponent of the first operand are unchanged."
msgstr ""

msgid "Return the square root of the argument to full precision."
msgstr ""

msgid ""
"Convert to a string, using engineering notation if an exponent is needed."
msgstr ""

msgid ""
"Engineering notation has an exponent which is a multiple of 3.  This can "
"leave up to 3 digits to the left of the decimal place and may require the "
"addition of either one or two trailing zeros."
msgstr ""

msgid ""
"For example, this converts ``Decimal('123E+1')`` to ``Decimal('1.23E+3')``."
msgstr ""

msgid ""
"Identical to the :meth:`to_integral_value` method.  The ``to_integral`` name "
"has been kept for compatibility with older versions."
msgstr ""

msgid ""
"Round to the nearest integer, signaling :const:`Inexact` or :const:`Rounded` "
"as appropriate if rounding occurs.  The rounding mode is determined by the "
"``rounding`` parameter if given, else by the given ``context``.  If neither "
"parameter is given then the rounding mode of the current context is used."
msgstr ""

msgid ""
"Round to the nearest integer without signaling :const:`Inexact` or :const:"
"`Rounded`.  If given, applies *rounding*; otherwise, uses the rounding "
"method in either the supplied *context* or the current context."
msgstr ""

msgid "Decimal numbers can be rounded using the :func:`.round` function:"
msgstr ""

msgid ""
"If *ndigits* is not given or ``None``, returns the nearest :class:`int` to "
"*number*, rounding ties to even, and ignoring the rounding mode of the :"
"class:`Decimal` context.  Raises :exc:`OverflowError` if *number* is an "
"infinity or :exc:`ValueError` if it is a (quiet or signaling) NaN."
msgstr ""

msgid ""
"If *ndigits* is an :class:`int`, the context's rounding mode is respected "
"and a :class:`Decimal` representing *number* rounded to the nearest multiple "
"of ``Decimal('1E-ndigits')`` is returned; in this case, ``round(number, "
"ndigits)`` is equivalent to ``self.quantize(Decimal('1E-ndigits'))``.  "
"Returns ``Decimal('NaN')`` if *number* is a quiet NaN.  Raises :class:"
"`InvalidOperation` if *number* is an infinity, a signaling NaN, or if the "
"length of the coefficient after the quantize operation would be greater than "
"the current context's precision.  In other words, for the non-corner cases:"
msgstr ""

msgid ""
"if *ndigits* is positive, return *number* rounded to *ndigits* decimal "
"places;"
msgstr ""

msgid "if *ndigits* is zero, return *number* rounded to the nearest integer;"
msgstr ""

msgid ""
"if *ndigits* is negative, return *number* rounded to the nearest multiple of "
"``10**abs(ndigits)``."
msgstr ""

msgid "For example::"
msgstr "Na przykład::"

msgid ""
">>> from decimal import Decimal, getcontext, ROUND_DOWN\n"
">>> getcontext().rounding = ROUND_DOWN\n"
">>> round(Decimal('3.75'))     # context rounding ignored\n"
"4\n"
">>> round(Decimal('3.5'))      # round-ties-to-even\n"
"4\n"
">>> round(Decimal('3.75'), 0)  # uses the context rounding\n"
"Decimal('3')\n"
">>> round(Decimal('3.75'), 1)\n"
"Decimal('3.7')\n"
">>> round(Decimal('3.75'), -1)\n"
"Decimal('0E+1')"
msgstr ""

msgid "Logical operands"
msgstr ""

msgid ""
"The :meth:`~Decimal.logical_and`, :meth:`~Decimal.logical_invert`, :meth:"
"`~Decimal.logical_or`, and :meth:`~Decimal.logical_xor` methods expect their "
"arguments to be *logical operands*.  A *logical operand* is a :class:"
"`Decimal` instance whose exponent and sign are both zero, and whose digits "
"are all either ``0`` or ``1``."
msgstr ""

msgid "Context objects"
msgstr ""

msgid ""
"Contexts are environments for arithmetic operations.  They govern precision, "
"set rules for rounding, determine which signals are treated as exceptions, "
"and limit the range for exponents."
msgstr ""

msgid ""
"Each thread has its own current context which is accessed or changed using "
"the :func:`getcontext` and :func:`setcontext` functions:"
msgstr ""

msgid "Return the current context for the active thread."
msgstr ""

msgid "Set the current context for the active thread to *c*."
msgstr ""

msgid ""
"You can also use the :keyword:`with` statement and the :func:`localcontext` "
"function to temporarily change the active context."
msgstr ""

msgid ""
"Return a context manager that will set the current context for the active "
"thread to a copy of *ctx* on entry to the with-statement and restore the "
"previous context when exiting the with-statement. If no context is "
"specified, a copy of the current context is used.  The *kwargs* argument is "
"used to set the attributes of the new context."
msgstr ""

msgid ""
"For example, the following code sets the current decimal precision to 42 "
"places, performs a calculation, and then automatically restores the previous "
"context::"
msgstr ""

msgid ""
"from decimal import localcontext\n"
"\n"
"with localcontext() as ctx:\n"
"    ctx.prec = 42   # Perform a high precision calculation\n"
"    s = calculate_something()\n"
"s = +s  # Round the final result back to the default precision"
msgstr ""

msgid "Using keyword arguments, the code would be the following::"
msgstr ""

msgid ""
"from decimal import localcontext\n"
"\n"
"with localcontext(prec=42) as ctx:\n"
"    s = calculate_something()\n"
"s = +s"
msgstr ""

msgid ""
"Raises :exc:`TypeError` if *kwargs* supplies an attribute that :class:"
"`Context` doesn't support.  Raises either :exc:`TypeError` or :exc:"
"`ValueError` if *kwargs* supplies an invalid value for an attribute."
msgstr ""

msgid ""
":meth:`localcontext` now supports setting context attributes through the use "
"of keyword arguments."
msgstr ""

msgid ""
"New contexts can also be created using the :class:`Context` constructor "
"described below. In addition, the module provides three pre-made contexts:"
msgstr ""

msgid ""
"This is a standard context defined by the General Decimal Arithmetic "
"Specification.  Precision is set to nine.  Rounding is set to :const:"
"`ROUND_HALF_UP`.  All flags are cleared.  All traps are enabled (treated as "
"exceptions) except :const:`Inexact`, :const:`Rounded`, and :const:"
"`Subnormal`."
msgstr ""

msgid ""
"Because many of the traps are enabled, this context is useful for debugging."
msgstr ""

msgid ""
"This is a standard context defined by the General Decimal Arithmetic "
"Specification.  Precision is set to nine.  Rounding is set to :const:"
"`ROUND_HALF_EVEN`.  All flags are cleared.  No traps are enabled (so that "
"exceptions are not raised during computations)."
msgstr ""

msgid ""
"Because the traps are disabled, this context is useful for applications that "
"prefer to have result value of ``NaN`` or ``Infinity`` instead of raising "
"exceptions.  This allows an application to complete a run in the presence of "
"conditions that would otherwise halt the program."
msgstr ""

msgid ""
"This context is used by the :class:`Context` constructor as a prototype for "
"new contexts.  Changing a field (such a precision) has the effect of "
"changing the default for new contexts created by the :class:`Context` "
"constructor."
msgstr ""

msgid ""
"This context is most useful in multi-threaded environments.  Changing one of "
"the fields before threads are started has the effect of setting system-wide "
"defaults.  Changing the fields after threads have started is not recommended "
"as it would require thread synchronization to prevent race conditions."
msgstr ""

msgid ""
"In single threaded environments, it is preferable to not use this context at "
"all.  Instead, simply create contexts explicitly as described below."
msgstr ""

msgid ""
"The default values are :attr:`Context.prec`\\ =\\ ``28``, :attr:`Context."
"rounding`\\ =\\ :const:`ROUND_HALF_EVEN`, and enabled traps for :class:"
"`Overflow`, :class:`InvalidOperation`, and :class:`DivisionByZero`."
msgstr ""

msgid ""
"In addition to the three supplied contexts, new contexts can be created with "
"the :class:`Context` constructor."
msgstr ""

msgid ""
"Creates a new context.  If a field is not specified or is :const:`None`, the "
"default values are copied from the :const:`DefaultContext`.  If the *flags* "
"field is not specified or is :const:`None`, all flags are cleared."
msgstr ""

msgid ""
"*prec* is an integer in the range [``1``, :const:`MAX_PREC`] that sets the "
"precision for arithmetic operations in the context."
msgstr ""

msgid ""
"The *rounding* option is one of the constants listed in the section "
"`Rounding Modes`_."
msgstr ""

msgid ""
"The *traps* and *flags* fields list any signals to be set. Generally, new "
"contexts should only set traps and leave the flags clear."
msgstr ""

msgid ""
"The *Emin* and *Emax* fields are integers specifying the outer limits "
"allowable for exponents. *Emin* must be in the range [:const:`MIN_EMIN`, "
"``0``], *Emax* in the range [``0``, :const:`MAX_EMAX`]."
msgstr ""

msgid ""
"The *capitals* field is either ``0`` or ``1`` (the default). If set to "
"``1``, exponents are printed with a capital ``E``; otherwise, a lowercase "
"``e`` is used: ``Decimal('6.02e+23')``."
msgstr ""

msgid ""
"The *clamp* field is either ``0`` (the default) or ``1``. If set to ``1``, "
"the exponent ``e`` of a :class:`Decimal` instance representable in this "
"context is strictly limited to the range ``Emin - prec + 1 <= e <= Emax - "
"prec + 1``.  If *clamp* is ``0`` then a weaker condition holds: the adjusted "
"exponent of the :class:`Decimal` instance is at most :attr:`~Context.Emax`.  "
"When *clamp* is ``1``, a large normal number will, where possible, have its "
"exponent reduced and a corresponding number of zeros added to its "
"coefficient, in order to fit the exponent constraints; this preserves the "
"value of the number but loses information about significant trailing zeros.  "
"For example::"
msgstr ""

msgid ""
">>> Context(prec=6, Emax=999, clamp=1).create_decimal('1.23e999')\n"
"Decimal('1.23000E+999')"
msgstr ""
">>> Context(prec=6, Emax=999, clamp=1).create_decimal('1.23e999')\n"
"Decimal('1.23000E+999')"

msgid ""
"A *clamp* value of ``1`` allows compatibility with the fixed-width decimal "
"interchange formats specified in IEEE 754."
msgstr ""

msgid ""
"The :class:`Context` class defines several general purpose methods as well "
"as a large number of methods for doing arithmetic directly in a given "
"context. In addition, for each of the :class:`Decimal` methods described "
"above (with the exception of the :meth:`~Decimal.adjusted` and :meth:"
"`~Decimal.as_tuple` methods) there is a corresponding :class:`Context` "
"method.  For example, for a :class:`Context` instance ``C`` and :class:"
"`Decimal` instance ``x``, ``C.exp(x)`` is equivalent to ``x."
"exp(context=C)``.  Each :class:`Context` method accepts a Python integer (an "
"instance of :class:`int`) anywhere that a Decimal instance is accepted."
msgstr ""

msgid "Resets all of the flags to ``0``."
msgstr ""

msgid "Resets all of the traps to ``0``."
msgstr ""

msgid "Return a duplicate of the context."
msgstr ""

msgid "Return a copy of the Decimal instance num."
msgstr ""

msgid ""
"Creates a new Decimal instance from *num* but using *self* as context. "
"Unlike the :class:`Decimal` constructor, the context precision, rounding "
"method, flags, and traps are applied to the conversion."
msgstr ""

msgid ""
"This is useful because constants are often given to a greater precision than "
"is needed by the application.  Another benefit is that rounding immediately "
"eliminates unintended effects from digits beyond the current precision. In "
"the following example, using unrounded inputs means that adding zero to a "
"sum can change the result:"
msgstr ""

msgid ""
">>> getcontext().prec = 3\n"
">>> Decimal('3.4445') + Decimal('1.0023')\n"
"Decimal('4.45')\n"
">>> Decimal('3.4445') + Decimal(0) + Decimal('1.0023')\n"
"Decimal('4.44')"
msgstr ""

msgid ""
"This method implements the to-number operation of the IBM specification. If "
"the argument is a string, no leading or trailing whitespace or underscores "
"are permitted."
msgstr ""

msgid ""
"Creates a new Decimal instance from a float *f* but rounding using *self* as "
"the context.  Unlike the :meth:`Decimal.from_float` class method, the "
"context precision, rounding method, flags, and traps are applied to the "
"conversion."
msgstr ""

msgid ""
">>> context = Context(prec=5, rounding=ROUND_DOWN)\n"
">>> context.create_decimal_from_float(math.pi)\n"
"Decimal('3.1415')\n"
">>> context = Context(prec=5, traps=[Inexact])\n"
">>> context.create_decimal_from_float(math.pi)\n"
"Traceback (most recent call last):\n"
"    ...\n"
"decimal.Inexact: None"
msgstr ""

msgid ""
"Returns a value equal to ``Emin - prec + 1`` which is the minimum exponent "
"value for subnormal results.  When underflow occurs, the exponent is set to :"
"const:`Etiny`."
msgstr ""

msgid "Returns a value equal to ``Emax - prec + 1``."
msgstr ""

msgid ""
"The usual approach to working with decimals is to create :class:`Decimal` "
"instances and then apply arithmetic operations which take place within the "
"current context for the active thread.  An alternative approach is to use "
"context methods for calculating within a specific context.  The methods are "
"similar to those for the :class:`Decimal` class and are only briefly "
"recounted here."
msgstr ""

msgid "Returns the absolute value of *x*."
msgstr ""

msgid "Return the sum of *x* and *y*."
msgstr ""

msgid "Returns the same Decimal object *x*."
msgstr ""

msgid "Compares *x* and *y* numerically."
msgstr ""

msgid "Compares the values of the two operands numerically."
msgstr ""

msgid "Compares two operands using their abstract representation."
msgstr ""

msgid ""
"Compares two operands using their abstract representation, ignoring sign."
msgstr ""

msgid "Returns a copy of *x* with the sign set to 0."
msgstr ""

msgid "Returns a copy of *x* with the sign inverted."
msgstr ""

msgid "Copies the sign from *y* to *x*."
msgstr ""

msgid "Return *x* divided by *y*."
msgstr ""

msgid "Return *x* divided by *y*, truncated to an integer."
msgstr ""

msgid "Divides two numbers and returns the integer part of the result."
msgstr ""

msgid "Returns ``e ** x``."
msgstr ""

msgid "Returns *x* multiplied by *y*, plus *z*."
msgstr ""

msgid "Returns ``True`` if *x* is canonical; otherwise returns ``False``."
msgstr ""

msgid "Returns ``True`` if *x* is finite; otherwise returns ``False``."
msgstr ""

msgid "Returns ``True`` if *x* is infinite; otherwise returns ``False``."
msgstr ""

msgid "Returns ``True`` if *x* is a qNaN or sNaN; otherwise returns ``False``."
msgstr ""

msgid ""
"Returns ``True`` if *x* is a normal number; otherwise returns ``False``."
msgstr ""

msgid "Returns ``True`` if *x* is a quiet NaN; otherwise returns ``False``."
msgstr ""

msgid "Returns ``True`` if *x* is negative; otherwise returns ``False``."
msgstr ""

msgid ""
"Returns ``True`` if *x* is a signaling NaN; otherwise returns ``False``."
msgstr ""

msgid "Returns ``True`` if *x* is subnormal; otherwise returns ``False``."
msgstr ""

msgid "Returns ``True`` if *x* is a zero; otherwise returns ``False``."
msgstr ""

msgid "Returns the natural (base e) logarithm of *x*."
msgstr ""

msgid "Returns the base 10 logarithm of *x*."
msgstr ""

msgid "Returns the exponent of the magnitude of the operand's MSD."
msgstr ""

msgid "Applies the logical operation *and* between each operand's digits."
msgstr ""

msgid "Invert all the digits in *x*."
msgstr ""

msgid "Applies the logical operation *or* between each operand's digits."
msgstr ""

msgid "Applies the logical operation *xor* between each operand's digits."
msgstr ""

msgid "Compares two values numerically and returns the maximum."
msgstr ""

msgid "Compares the values numerically with their sign ignored."
msgstr ""

msgid "Compares two values numerically and returns the minimum."
msgstr ""

msgid "Minus corresponds to the unary prefix minus operator in Python."
msgstr ""

msgid "Return the product of *x* and *y*."
msgstr ""

msgid "Returns the largest representable number smaller than *x*."
msgstr ""

msgid "Returns the smallest representable number larger than *x*."
msgstr ""

msgid "Returns the number closest to *x*, in direction towards *y*."
msgstr ""

msgid "Reduces *x* to its simplest form."
msgstr ""

msgid "Returns an indication of the class of *x*."
msgstr ""

msgid ""
"Plus corresponds to the unary prefix plus operator in Python.  This "
"operation applies the context precision and rounding, so it is *not* an "
"identity operation."
msgstr ""

msgid "Return ``x`` to the power of ``y``, reduced modulo ``modulo`` if given."
msgstr ""

msgid ""
"With two arguments, compute ``x**y``.  If ``x`` is negative then ``y`` must "
"be integral.  The result will be inexact unless ``y`` is integral and the "
"result is finite and can be expressed exactly in 'precision' digits. The "
"rounding mode of the context is used. Results are always correctly rounded "
"in the Python version."
msgstr ""

msgid ""
"``Decimal(0) ** Decimal(0)`` results in ``InvalidOperation``, and if "
"``InvalidOperation`` is not trapped, then results in ``Decimal('NaN')``."
msgstr ""

msgid ""
"The C module computes :meth:`power` in terms of the correctly rounded :meth:"
"`exp` and :meth:`ln` functions. The result is well-defined but only \"almost "
"always correctly rounded\"."
msgstr ""

msgid ""
"With three arguments, compute ``(x**y) % modulo``.  For the three argument "
"form, the following restrictions on the arguments hold:"
msgstr ""

msgid "all three arguments must be integral"
msgstr ""

msgid "``y`` must be nonnegative"
msgstr ""

msgid "at least one of ``x`` or ``y`` must be nonzero"
msgstr ""

msgid "``modulo`` must be nonzero and have at most 'precision' digits"
msgstr ""

msgid ""
"The value resulting from ``Context.power(x, y, modulo)`` is equal to the "
"value that would be obtained by computing ``(x**y) % modulo`` with unbounded "
"precision, but is computed more efficiently.  The exponent of the result is "
"zero, regardless of the exponents of ``x``, ``y`` and ``modulo``.  The "
"result is always exact."
msgstr ""

msgid "Returns a value equal to *x* (rounded), having the exponent of *y*."
msgstr ""

msgid "Just returns 10, as this is Decimal, :)"
msgstr ""

msgid "Returns the remainder from integer division."
msgstr ""

msgid ""
"The sign of the result, if non-zero, is the same as that of the original "
"dividend."
msgstr ""

msgid ""
"Returns ``x - y * n``, where *n* is the integer nearest the exact value of "
"``x / y`` (if the result is 0 then its sign will be the sign of *x*)."
msgstr ""

msgid "Returns a rotated copy of *x*, *y* times."
msgstr ""

msgid "Returns ``True`` if the two operands have the same exponent."
msgstr ""

msgid "Returns the first operand after adding the second value its exp."
msgstr ""

msgid "Returns a shifted copy of *x*, *y* times."
msgstr ""

msgid "Square root of a non-negative number to context precision."
msgstr ""

msgid "Return the difference between *x* and *y*."
msgstr ""

msgid "Rounds to an integer."
msgstr ""

msgid "Converts a number to a string using scientific notation."
msgstr ""

msgid "Constants"
msgstr "Stały"

msgid ""
"The constants in this section are only relevant for the C module. They are "
"also included in the pure Python version for compatibility."
msgstr ""

msgid "32-bit"
msgstr ""

msgid "64-bit"
msgstr ""

msgid "``425000000``"
msgstr "``425000000``"

msgid "``999999999999999999``"
msgstr "``999999999999999999``"

msgid "``-425000000``"
msgstr "``-425000000``"

msgid "``-999999999999999999``"
msgstr "``-999999999999999999``"

msgid "``-849999999``"
msgstr "``-849999999``"

msgid "``-1999999999999999997``"
msgstr "``-1999999999999999997``"

msgid ""
"The value is ``True``.  Deprecated, because Python now always has threads."
msgstr ""

msgid ""
"The default value is ``True``. If Python is :option:`configured using the --"
"without-decimal-contextvar option <--without-decimal-contextvar>`, the C "
"version uses a thread-local rather than a coroutine-local context and the "
"value is ``False``.  This is slightly faster in some nested context "
"scenarios."
msgstr ""

msgid "Rounding modes"
msgstr ""

msgid "Round towards ``Infinity``."
msgstr ""

msgid "Round towards zero."
msgstr ""

msgid "Round towards ``-Infinity``."
msgstr ""

msgid "Round to nearest with ties going towards zero."
msgstr ""

msgid "Round to nearest with ties going to nearest even integer."
msgstr ""

msgid "Round to nearest with ties going away from zero."
msgstr ""

msgid "Round away from zero."
msgstr ""

msgid ""
"Round away from zero if last digit after rounding towards zero would have "
"been 0 or 5; otherwise round towards zero."
msgstr ""

msgid "Signals"
msgstr ""

msgid ""
"Signals represent conditions that arise during computation. Each corresponds "
"to one context flag and one context trap enabler."
msgstr ""

msgid ""
"The context flag is set whenever the condition is encountered. After the "
"computation, flags may be checked for informational purposes (for instance, "
"to determine whether a computation was exact). After checking the flags, be "
"sure to clear all flags before starting the next computation."
msgstr ""

msgid ""
"If the context's trap enabler is set for the signal, then the condition "
"causes a Python exception to be raised.  For example, if the :class:"
"`DivisionByZero` trap is set, then a :exc:`DivisionByZero` exception is "
"raised upon encountering the condition."
msgstr ""

msgid "Altered an exponent to fit representation constraints."
msgstr ""

msgid ""
"Typically, clamping occurs when an exponent falls outside the context's :"
"attr:`~Context.Emin` and :attr:`~Context.Emax` limits.  If possible, the "
"exponent is reduced to fit by adding zeros to the coefficient."
msgstr ""

msgid "Base class for other signals and a subclass of :exc:`ArithmeticError`."
msgstr ""

msgid "Signals the division of a non-infinite number by zero."
msgstr ""

msgid ""
"Can occur with division, modulo division, or when raising a number to a "
"negative power.  If this signal is not trapped, returns ``Infinity`` or ``-"
"Infinity`` with the sign determined by the inputs to the calculation."
msgstr ""

msgid "Indicates that rounding occurred and the result is not exact."
msgstr ""

msgid ""
"Signals when non-zero digits were discarded during rounding. The rounded "
"result is returned.  The signal flag or trap is used to detect when results "
"are inexact."
msgstr ""

msgid "An invalid operation was performed."
msgstr ""

msgid ""
"Indicates that an operation was requested that does not make sense. If not "
"trapped, returns ``NaN``.  Possible causes include::"
msgstr ""

msgid ""
"Infinity - Infinity\n"
"0 * Infinity\n"
"Infinity / Infinity\n"
"x % 0\n"
"Infinity % x\n"
"sqrt(-x) and x > 0\n"
"0 ** 0\n"
"x ** (non-integer)\n"
"x ** Infinity"
msgstr ""

msgid "Numerical overflow."
msgstr ""

msgid ""
"Indicates the exponent is larger than :attr:`Context.Emax` after rounding "
"has occurred.  If not trapped, the result depends on the rounding mode, "
"either pulling inward to the largest representable finite number or rounding "
"outward to ``Infinity``.  In either case, :class:`Inexact` and :class:"
"`Rounded` are also signaled."
msgstr ""

msgid "Rounding occurred though possibly no information was lost."
msgstr ""

msgid ""
"Signaled whenever rounding discards digits; even if those digits are zero "
"(such as rounding ``5.00`` to ``5.0``).  If not trapped, returns the result "
"unchanged.  This signal is used to detect loss of significant digits."
msgstr ""

msgid "Exponent was lower than :attr:`~Context.Emin` prior to rounding."
msgstr ""

msgid ""
"Occurs when an operation result is subnormal (the exponent is too small). If "
"not trapped, returns the result unchanged."
msgstr ""

msgid "Numerical underflow with result rounded to zero."
msgstr ""

msgid ""
"Occurs when a subnormal result is pushed to zero by rounding. :class:"
"`Inexact` and :class:`Subnormal` are also signaled."
msgstr ""

msgid "Enable stricter semantics for mixing floats and Decimals."
msgstr ""

msgid ""
"If the signal is not trapped (default), mixing floats and Decimals is "
"permitted in the :class:`~decimal.Decimal` constructor, :meth:`~decimal."
"Context.create_decimal` and all comparison operators. Both conversion and "
"comparisons are exact. Any occurrence of a mixed operation is silently "
"recorded by setting :exc:`FloatOperation` in the context flags. Explicit "
"conversions with :meth:`~decimal.Decimal.from_float` or :meth:`~decimal."
"Context.create_decimal_from_float` do not set the flag."
msgstr ""

msgid ""
"Otherwise (the signal is trapped), only equality comparisons and explicit "
"conversions are silent. All other mixed operations raise :exc:"
"`FloatOperation`."
msgstr ""

msgid "The following table summarizes the hierarchy of signals::"
msgstr ""

msgid ""
"exceptions.ArithmeticError(exceptions.Exception)\n"
"    DecimalException\n"
"        Clamped\n"
"        DivisionByZero(DecimalException, exceptions.ZeroDivisionError)\n"
"        Inexact\n"
"            Overflow(Inexact, Rounded)\n"
"            Underflow(Inexact, Rounded, Subnormal)\n"
"        InvalidOperation\n"
"        Rounded\n"
"        Subnormal\n"
"        FloatOperation(DecimalException, exceptions.TypeError)"
msgstr ""

msgid "Floating-Point Notes"
msgstr ""

msgid "Mitigating round-off error with increased precision"
msgstr ""

msgid ""
"The use of decimal floating point eliminates decimal representation error "
"(making it possible to represent ``0.1`` exactly); however, some operations "
"can still incur round-off error when non-zero digits exceed the fixed "
"precision."
msgstr ""

msgid ""
"The effects of round-off error can be amplified by the addition or "
"subtraction of nearly offsetting quantities resulting in loss of "
"significance.  Knuth provides two instructive examples where rounded "
"floating-point arithmetic with insufficient precision causes the breakdown "
"of the associative and distributive properties of addition:"
msgstr ""

msgid ""
"# Examples from Seminumerical Algorithms, Section 4.2.2.\n"
">>> from decimal import Decimal, getcontext\n"
">>> getcontext().prec = 8\n"
"\n"
">>> u, v, w = Decimal(11111113), Decimal(-11111111), Decimal('7.51111111')\n"
">>> (u + v) + w\n"
"Decimal('9.5111111')\n"
">>> u + (v + w)\n"
"Decimal('10')\n"
"\n"
">>> u, v, w = Decimal(20000), Decimal(-6), Decimal('6.0000003')\n"
">>> (u*v) + (u*w)\n"
"Decimal('0.01')\n"
">>> u * (v+w)\n"
"Decimal('0.0060000')"
msgstr ""

msgid ""
"The :mod:`decimal` module makes it possible to restore the identities by "
"expanding the precision sufficiently to avoid loss of significance:"
msgstr ""

msgid ""
">>> getcontext().prec = 20\n"
">>> u, v, w = Decimal(11111113), Decimal(-11111111), Decimal('7.51111111')\n"
">>> (u + v) + w\n"
"Decimal('9.51111111')\n"
">>> u + (v + w)\n"
"Decimal('9.51111111')\n"
">>>\n"
">>> u, v, w = Decimal(20000), Decimal(-6), Decimal('6.0000003')\n"
">>> (u*v) + (u*w)\n"
"Decimal('0.0060000')\n"
">>> u * (v+w)\n"
"Decimal('0.0060000')"
msgstr ""

msgid "Special values"
msgstr ""

msgid ""
"The number system for the :mod:`decimal` module provides special values "
"including ``NaN``, ``sNaN``, ``-Infinity``, ``Infinity``, and two zeros, "
"``+0`` and ``-0``."
msgstr ""

msgid ""
"Infinities can be constructed directly with:  ``Decimal('Infinity')``. Also, "
"they can arise from dividing by zero when the :exc:`DivisionByZero` signal "
"is not trapped.  Likewise, when the :exc:`Overflow` signal is not trapped, "
"infinity can result from rounding beyond the limits of the largest "
"representable number."
msgstr ""

msgid ""
"The infinities are signed (affine) and can be used in arithmetic operations "
"where they get treated as very large, indeterminate numbers.  For instance, "
"adding a constant to infinity gives another infinite result."
msgstr ""

msgid ""
"Some operations are indeterminate and return ``NaN``, or if the :exc:"
"`InvalidOperation` signal is trapped, raise an exception.  For example, "
"``0/0`` returns ``NaN`` which means \"not a number\".  This variety of "
"``NaN`` is quiet and, once created, will flow through other computations "
"always resulting in another ``NaN``.  This behavior can be useful for a "
"series of computations that occasionally have missing inputs --- it allows "
"the calculation to proceed while flagging specific results as invalid."
msgstr ""

msgid ""
"A variant is ``sNaN`` which signals rather than remaining quiet after every "
"operation.  This is a useful return value when an invalid result needs to "
"interrupt a calculation for special handling."
msgstr ""

msgid ""
"The behavior of Python's comparison operators can be a little surprising "
"where a ``NaN`` is involved.  A test for equality where one of the operands "
"is a quiet or signaling ``NaN`` always returns :const:`False` (even when "
"doing ``Decimal('NaN')==Decimal('NaN')``), while a test for inequality "
"always returns :const:`True`.  An attempt to compare two Decimals using any "
"of the ``<``, ``<=``, ``>`` or ``>=`` operators will raise the :exc:"
"`InvalidOperation` signal if either operand is a ``NaN``, and return :const:"
"`False` if this signal is not trapped.  Note that the General Decimal "
"Arithmetic specification does not specify the behavior of direct "
"comparisons; these rules for comparisons involving a ``NaN`` were taken from "
"the IEEE 854 standard (see Table 3 in section 5.7).  To ensure strict "
"standards-compliance, use the :meth:`~Decimal.compare` and :meth:`~Decimal."
"compare_signal` methods instead."
msgstr ""

msgid ""
"The signed zeros can result from calculations that underflow. They keep the "
"sign that would have resulted if the calculation had been carried out to "
"greater precision.  Since their magnitude is zero, both positive and "
"negative zeros are treated as equal and their sign is informational."
msgstr ""

msgid ""
"In addition to the two signed zeros which are distinct yet equal, there are "
"various representations of zero with differing precisions yet equivalent in "
"value.  This takes a bit of getting used to.  For an eye accustomed to "
"normalized floating-point representations, it is not immediately obvious "
"that the following calculation returns a value equal to zero:"
msgstr ""

msgid "Working with threads"
msgstr ""

msgid ""
"The :func:`getcontext` function accesses a different :class:`Context` object "
"for each thread.  Having separate thread contexts means that threads may "
"make changes (such as ``getcontext().prec=10``) without interfering with "
"other threads."
msgstr ""

msgid ""
"Likewise, the :func:`setcontext` function automatically assigns its target "
"to the current thread."
msgstr ""

msgid ""
"If :func:`setcontext` has not been called before :func:`getcontext`, then :"
"func:`getcontext` will automatically create a new context for use in the "
"current thread."
msgstr ""

msgid ""
"The new context is copied from a prototype context called *DefaultContext*. "
"To control the defaults so that each thread will use the same values "
"throughout the application, directly modify the *DefaultContext* object. "
"This should be done *before* any threads are started so that there won't be "
"a race condition between threads calling :func:`getcontext`. For example::"
msgstr ""

msgid ""
"# Set applicationwide defaults for all threads about to be launched\n"
"DefaultContext.prec = 12\n"
"DefaultContext.rounding = ROUND_DOWN\n"
"DefaultContext.traps = ExtendedContext.traps.copy()\n"
"DefaultContext.traps[InvalidOperation] = 1\n"
"setcontext(DefaultContext)\n"
"\n"
"# Afterwards, the threads can be started\n"
"t1.start()\n"
"t2.start()\n"
"t3.start()\n"
" . . ."
msgstr ""

msgid "Recipes"
msgstr ""

msgid ""
"Here are a few recipes that serve as utility functions and that demonstrate "
"ways to work with the :class:`Decimal` class::"
msgstr ""

msgid ""
"def moneyfmt(value, places=2, curr='', sep=',', dp='.',\n"
"             pos='', neg='-', trailneg=''):\n"
"    \"\"\"Convert Decimal to a money formatted string.\n"
"\n"
"    places:  required number of places after the decimal point\n"
"    curr:    optional currency symbol before the sign (may be blank)\n"
"    sep:     optional grouping separator (comma, period, space, or blank)\n"
"    dp:      decimal point indicator (comma or period)\n"
"             only specify as blank when places is zero\n"
"    pos:     optional sign for positive numbers: '+', space or blank\n"
"    neg:     optional sign for negative numbers: '-', '(', space or blank\n"
"    trailneg:optional trailing minus indicator:  '-', ')', space or blank\n"
"\n"
"    >>> d = Decimal('-1234567.8901')\n"
"    >>> moneyfmt(d, curr='$')\n"
"    '-$1,234,567.89'\n"
"    >>> moneyfmt(d, places=0, sep='.', dp='', neg='', trailneg='-')\n"
"    '1.234.568-'\n"
"    >>> moneyfmt(d, curr='$', neg='(', trailneg=')')\n"
"    '($1,234,567.89)'\n"
"    >>> moneyfmt(Decimal(123456789), sep=' ')\n"
"    '123 456 789.00'\n"
"    >>> moneyfmt(Decimal('-0.02'), neg='<', trailneg='>')\n"
"    '<0.02>'\n"
"\n"
"    \"\"\"\n"
"    q = Decimal(10) ** -places      # 2 places --> '0.01'\n"
"    sign, digits, exp = value.quantize(q).as_tuple()\n"
"    result = []\n"
"    digits = list(map(str, digits))\n"
"    build, next = result.append, digits.pop\n"
"    if sign:\n"
"        build(trailneg)\n"
"    for i in range(places):\n"
"        build(next() if digits else '0')\n"
"    if places:\n"
"        build(dp)\n"
"    if not digits:\n"
"        build('0')\n"
"    i = 0\n"
"    while digits:\n"
"        build(next())\n"
"        i += 1\n"
"        if i == 3 and digits:\n"
"            i = 0\n"
"            build(sep)\n"
"    build(curr)\n"
"    build(neg if sign else pos)\n"
"    return ''.join(reversed(result))\n"
"\n"
"def pi():\n"
"    \"\"\"Compute Pi to the current precision.\n"
"\n"
"    >>> print(pi())\n"
"    3.141592653589793238462643383\n"
"\n"
"    \"\"\"\n"
"    getcontext().prec += 2  # extra digits for intermediate steps\n"
"    three = Decimal(3)      # substitute \"three=3.0\" for regular floats\n"
"    lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24\n"
"    while s != lasts:\n"
"        lasts = s\n"
"        n, na = n+na, na+8\n"
"        d, da = d+da, da+32\n"
"        t = (t * n) / d\n"
"        s += t\n"
"    getcontext().prec -= 2\n"
"    return +s               # unary plus applies the new precision\n"
"\n"
"def exp(x):\n"
"    \"\"\"Return e raised to the power of x.  Result type matches input "
"type.\n"
"\n"
"    >>> print(exp(Decimal(1)))\n"
"    2.718281828459045235360287471\n"
"    >>> print(exp(Decimal(2)))\n"
"    7.389056098930650227230427461\n"
"    >>> print(exp(2.0))\n"
"    7.38905609893\n"
"    >>> print(exp(2+0j))\n"
"    (7.38905609893+0j)\n"
"\n"
"    \"\"\"\n"
"    getcontext().prec += 2\n"
"    i, lasts, s, fact, num = 0, 0, 1, 1, 1\n"
"    while s != lasts:\n"
"        lasts = s\n"
"        i += 1\n"
"        fact *= i\n"
"        num *= x\n"
"        s += num / fact\n"
"    getcontext().prec -= 2\n"
"    return +s\n"
"\n"
"def cos(x):\n"
"    \"\"\"Return the cosine of x as measured in radians.\n"
"\n"
"    The Taylor series approximation works best for a small value of x.\n"
"    For larger values, first compute x = x % (2 * pi).\n"
"\n"
"    >>> print(cos(Decimal('0.5')))\n"
"    0.8775825618903727161162815826\n"
"    >>> print(cos(0.5))\n"
"    0.87758256189\n"
"    >>> print(cos(0.5+0j))\n"
"    (0.87758256189+0j)\n"
"\n"
"    \"\"\"\n"
"    getcontext().prec += 2\n"
"    i, lasts, s, fact, num, sign = 0, 0, 1, 1, 1, 1\n"
"    while s != lasts:\n"
"        lasts = s\n"
"        i += 2\n"
"        fact *= i * (i-1)\n"
"        num *= x * x\n"
"        sign *= -1\n"
"        s += num / fact * sign\n"
"    getcontext().prec -= 2\n"
"    return +s\n"
"\n"
"def sin(x):\n"
"    \"\"\"Return the sine of x as measured in radians.\n"
"\n"
"    The Taylor series approximation works best for a small value of x.\n"
"    For larger values, first compute x = x % (2 * pi).\n"
"\n"
"    >>> print(sin(Decimal('0.5')))\n"
"    0.4794255386042030002732879352\n"
"    >>> print(sin(0.5))\n"
"    0.479425538604\n"
"    >>> print(sin(0.5+0j))\n"
"    (0.479425538604+0j)\n"
"\n"
"    \"\"\"\n"
"    getcontext().prec += 2\n"
"    i, lasts, s, fact, num, sign = 1, 0, x, 1, x, 1\n"
"    while s != lasts:\n"
"        lasts = s\n"
"        i += 2\n"
"        fact *= i * (i-1)\n"
"        num *= x * x\n"
"        sign *= -1\n"
"        s += num / fact * sign\n"
"    getcontext().prec -= 2\n"
"    return +s"
msgstr ""

msgid "Decimal FAQ"
msgstr ""

msgid ""
"Q. It is cumbersome to type ``decimal.Decimal('1234.5')``.  Is there a way "
"to minimize typing when using the interactive interpreter?"
msgstr ""

msgid "A. Some users abbreviate the constructor to just a single letter:"
msgstr ""

msgid ""
"Q. In a fixed-point application with two decimal places, some inputs have "
"many places and need to be rounded.  Others are not supposed to have excess "
"digits and need to be validated.  What methods should be used?"
msgstr ""

msgid ""
"A. The :meth:`~Decimal.quantize` method rounds to a fixed number of decimal "
"places. If the :const:`Inexact` trap is set, it is also useful for "
"validation:"
msgstr ""

msgid ""
"Q. Once I have valid two place inputs, how do I maintain that invariant "
"throughout an application?"
msgstr ""

msgid ""
"A. Some operations like addition, subtraction, and multiplication by an "
"integer will automatically preserve fixed point.  Others operations, like "
"division and non-integer multiplication, will change the number of decimal "
"places and need to be followed-up with a :meth:`~Decimal.quantize` step:"
msgstr ""

msgid ""
"In developing fixed-point applications, it is convenient to define functions "
"to handle the :meth:`~Decimal.quantize` step:"
msgstr ""

msgid ""
"Q. There are many ways to express the same value.  The numbers ``200``, "
"``200.000``, ``2E2``, and ``.02E+4`` all have the same value at various "
"precisions. Is there a way to transform them to a single recognizable "
"canonical value?"
msgstr ""

msgid ""
"A. The :meth:`~Decimal.normalize` method maps all equivalent values to a "
"single representative:"
msgstr ""

msgid "Q. When does rounding occur in a computation?"
msgstr ""

msgid ""
"A. It occurs *after* the computation.  The philosophy of the decimal "
"specification is that numbers are considered exact and are created "
"independent of the current context.  They can even have greater precision "
"than current context.  Computations process with those exact inputs and then "
"rounding (or other context operations) is applied to the *result* of the "
"computation::"
msgstr ""

msgid ""
">>> getcontext().prec = 5\n"
">>> pi = Decimal('3.1415926535')   # More than 5 digits\n"
">>> pi                             # All digits are retained\n"
"Decimal('3.1415926535')\n"
">>> pi + 0                         # Rounded after an addition\n"
"Decimal('3.1416')\n"
">>> pi - Decimal('0.00005')        # Subtract unrounded numbers, then round\n"
"Decimal('3.1415')\n"
">>> pi + 0 - Decimal('0.00005').   # Intermediate values are rounded\n"
"Decimal('3.1416')"
msgstr ""

msgid ""
"Q. Some decimal values always print with exponential notation.  Is there a "
"way to get a non-exponential representation?"
msgstr ""

msgid ""
"A. For some values, exponential notation is the only way to express the "
"number of significant places in the coefficient.  For example, expressing "
"``5.0E+3`` as ``5000`` keeps the value constant but cannot show the "
"original's two-place significance."
msgstr ""

msgid ""
"If an application does not care about tracking significance, it is easy to "
"remove the exponent and trailing zeroes, losing significance, but keeping "
"the value unchanged:"
msgstr ""

msgid "Q. Is there a way to convert a regular float to a :class:`Decimal`?"
msgstr ""

msgid ""
"A. Yes, any binary floating-point number can be exactly expressed as a "
"Decimal though an exact conversion may take more precision than intuition "
"would suggest:"
msgstr ""

msgid ""
">>> Decimal(math.pi)\n"
"Decimal('3.141592653589793115997963468544185161590576171875')"
msgstr ""
">>> Decimal(math.pi)\n"
"Decimal('3.141592653589793115997963468544185161590576171875')"

msgid ""
"Q. Within a complex calculation, how can I make sure that I haven't gotten a "
"spurious result because of insufficient precision or rounding anomalies."
msgstr ""

msgid ""
"A. The decimal module makes it easy to test results.  A best practice is to "
"re-run calculations using greater precision and with various rounding modes. "
"Widely differing results indicate insufficient precision, rounding mode "
"issues, ill-conditioned inputs, or a numerically unstable algorithm."
msgstr ""

msgid ""
"Q. I noticed that context precision is applied to the results of operations "
"but not to the inputs.  Is there anything to watch out for when mixing "
"values of different precisions?"
msgstr ""

msgid ""
"A. Yes.  The principle is that all values are considered to be exact and so "
"is the arithmetic on those values.  Only the results are rounded.  The "
"advantage for inputs is that \"what you type is what you get\".  A "
"disadvantage is that the results can look odd if you forget that the inputs "
"haven't been rounded:"
msgstr ""

msgid ""
">>> getcontext().prec = 3\n"
">>> Decimal('3.104') + Decimal('2.104')\n"
"Decimal('5.21')\n"
">>> Decimal('3.104') + Decimal('0.000') + Decimal('2.104')\n"
"Decimal('5.20')"
msgstr ""

msgid ""
"The solution is either to increase precision or to force rounding of inputs "
"using the unary plus operation:"
msgstr ""

msgid ""
">>> getcontext().prec = 3\n"
">>> +Decimal('1.23456789')      # unary plus triggers rounding\n"
"Decimal('1.23')"
msgstr ""
">>> getcontext().prec = 3\n"
">>> +Decimal('1.23456789')      # unary plus triggers rounding\n"
"Decimal('1.23')"

msgid ""
"Alternatively, inputs can be rounded upon creation using the :meth:`Context."
"create_decimal` method:"
msgstr ""

msgid "Q. Is the CPython implementation fast for large numbers?"
msgstr ""

msgid ""
"A. Yes.  In the CPython and PyPy3 implementations, the C/CFFI versions of "
"the decimal module integrate the high speed `libmpdec <https://www.bytereef."
"org/mpdecimal/doc/libmpdec/index.html>`_ library for arbitrary precision "
"correctly rounded decimal floating-point arithmetic [#]_. ``libmpdec`` uses "
"`Karatsuba multiplication <https://en.wikipedia.org/wiki/"
"Karatsuba_algorithm>`_ for medium-sized numbers and the `Number Theoretic "
"Transform <https://en.wikipedia.org/wiki/"
"Discrete_Fourier_transform_(general)#Number-theoretic_transform>`_ for very "
"large numbers."
msgstr ""

msgid ""
"The context must be adapted for exact arbitrary precision arithmetic. :attr:"
"`~Context.Emin` and :attr:`~Context.Emax` should always be set to the "
"maximum values, :attr:`~Context.clamp` should always be 0 (the default).  "
"Setting :attr:`~Context.prec` requires some care."
msgstr ""

msgid ""
"The easiest approach for trying out bignum arithmetic is to use the maximum "
"value for :attr:`~Context.prec` as well [#]_::"
msgstr ""

msgid ""
">>> setcontext(Context(prec=MAX_PREC, Emax=MAX_EMAX, Emin=MIN_EMIN))\n"
">>> x = Decimal(2) ** 256\n"
">>> x / 128\n"
"Decimal('904625697166532776746648320380374280103671755200316906558262375061821325312')"
msgstr ""

msgid ""
"For inexact results, :const:`MAX_PREC` is far too large on 64-bit platforms "
"and the available memory will be insufficient::"
msgstr ""

msgid ""
">>> Decimal(1) / 3\n"
"Traceback (most recent call last):\n"
"  File \"<stdin>\", line 1, in <module>\n"
"MemoryError"
msgstr ""

msgid ""
"On systems with overallocation (e.g. Linux), a more sophisticated approach "
"is to adjust :attr:`~Context.prec` to the amount of available RAM.  Suppose "
"that you have 8GB of RAM and expect 10 simultaneous operands using a maximum "
"of 500MB each::"
msgstr ""

msgid ""
">>> import sys\n"
">>>\n"
">>> # Maximum number of digits for a single operand using 500MB in 8-byte "
"words\n"
">>> # with 19 digits per word (4-byte and 9 digits for the 32-bit build):\n"
">>> maxdigits = 19 * ((500 * 1024**2) // 8)\n"
">>>\n"
">>> # Check that this works:\n"
">>> c = Context(prec=maxdigits, Emax=MAX_EMAX, Emin=MIN_EMIN)\n"
">>> c.traps[Inexact] = True\n"
">>> setcontext(c)\n"
">>>\n"
">>> # Fill the available precision with nines:\n"
">>> x = Decimal(0).logical_invert() * 9\n"
">>> sys.getsizeof(x)\n"
"524288112\n"
">>> x + 2\n"
"Traceback (most recent call last):\n"
"  File \"<stdin>\", line 1, in <module>\n"
"  decimal.Inexact: [<class 'decimal.Inexact'>]"
msgstr ""

msgid ""
"In general (and especially on systems without overallocation), it is "
"recommended to estimate even tighter bounds and set the :attr:`Inexact` trap "
"if all calculations are expected to be exact."
msgstr ""

msgid ""
"This approach now works for all exact results except for non-integer powers."
msgstr ""