decimal.po

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msgid ""
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"Last-Translator: Adrian Liaw <adrianliaw2000@gmail.com>\n"
"Language-Team: Chinese - TAIWAN (https://github.com/python/python-docs-zh-"
"tw)\n"
"Language: zh_TW\n"
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"Content-Transfer-Encoding: 8bit\n"
"Plural-Forms: nplurals=1; plural=0;\n"

#: ../../library/decimal.rst:2
msgid ":mod:`!decimal` --- Decimal fixed-point and floating-point arithmetic"
msgstr ":mod:`!decimal` --- 十進位固定點和浮點運算"

#: ../../library/decimal.rst:15
msgid "**Source code:** :source:`Lib/decimal.py`"
msgstr "**原始碼：**\\ :source:`Lib/decimal.py`"

#: ../../library/decimal.rst:33
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 ""

#: ../../library/decimal.rst:37
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 ""

#: ../../library/decimal.rst:42
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 ""

#: ../../library/decimal.rst:47
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 ""

#: ../../library/decimal.rst:54
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 ""

#: ../../library/decimal.rst:61
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 ""

#: ../../library/decimal.rst:73
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 ""

#: ../../library/decimal.rst:80
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 ""

#: ../../library/decimal.rst:85
msgid ""
"The module design is centered around three concepts:  the decimal number, "
"the context for arithmetic, and signals."
msgstr ""

#: ../../library/decimal.rst:88
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 ""

#: ../../library/decimal.rst:94
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 ""

#: ../../library/decimal.rst:101
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 ""

#: ../../library/decimal.rst:108
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 ""

#: ../../library/decimal.rst:116
msgid ""
"IBM's General Decimal Arithmetic Specification, `The General Decimal "
"Arithmetic Specification <https://speleotrove.com/decimal/decarith.html>`_."
msgstr ""

#: ../../library/decimal.rst:125
msgid "Quick-start Tutorial"
msgstr ""

#: ../../library/decimal.rst:127
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 ""

#: ../../library/decimal.rst:131
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 ""

#: ../../library/decimal.rst:139
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 ""

#: ../../library/decimal.rst:145
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 ""
">>> 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')"

#: ../../library/decimal.rst:163
msgid ""
"If the :exc:`FloatOperation` signal is trapped, accidental mixing of "
"decimals and floats in constructors or ordering comparisons raises an "
"exception::"
msgstr ""

#: ../../library/decimal.rst:167
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 ""
">>> 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"

#: ../../library/decimal.rst:182
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 ""

#: ../../library/decimal.rst:186
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 ""
">>> 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')"

#: ../../library/decimal.rst:199
msgid ""
"If the internal limits of the C version are exceeded, constructing a decimal "
"raises :class:`InvalidOperation`::"
msgstr ""

#: ../../library/decimal.rst:202
msgid ""
">>> Decimal(\"1e9999999999999999999\")\n"
"Traceback (most recent call last):\n"
"  File \"<stdin>\", line 1, in <module>\n"
"decimal.InvalidOperation: [<class 'decimal.InvalidOperation'>]"
msgstr ""
">>> Decimal(\"1e9999999999999999999\")\n"
"Traceback (most recent call last):\n"
"  File \"<stdin>\", line 1, in <module>\n"
"decimal.InvalidOperation: [<class 'decimal.InvalidOperation'>]"

#: ../../library/decimal.rst:209
msgid ""
"Decimals interact well with much of the rest of Python.  Here is a small "
"decimal floating-point flying circus:"
msgstr ""

#: ../../library/decimal.rst:212
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 ""
">>> 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')"

#: ../../library/decimal.rst:241
msgid "And some mathematical functions are also available to Decimal:"
msgstr ""

#: ../../library/decimal.rst:253
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 ""

#: ../../library/decimal.rst:262
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 ""

#: ../../library/decimal.rst:266
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 ""

#: ../../library/decimal.rst:270
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 ""

#: ../../library/decimal.rst:275
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 ""
">>> 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"

#: ../../library/decimal.rst:299
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 ""

#: ../../library/decimal.rst:304
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 ""
">>> 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=[])"

#: ../../library/decimal.rst:312
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 ""

#: ../../library/decimal.rst:316
msgid ""
"Individual traps are set using the dictionary in the :attr:`~Context.traps` "
"attribute of a context:"
msgstr ""

#: ../../library/decimal.rst:319
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 ""
">>> 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"

#: ../../library/decimal.rst:331
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 ""

#: ../../library/decimal.rst:343
msgid "Decimal objects"
msgstr ""

#: ../../library/decimal.rst:348
msgid "Construct a new :class:`Decimal` object based from *value*."
msgstr ""

#: ../../library/decimal.rst:350
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 ""

#: ../../library/decimal.rst:355
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 ""

#: ../../library/decimal.rst:366
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 ""

#: ../../library/decimal.rst:371
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 ""

#: ../../library/decimal.rst:376
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 ""

#: ../../library/decimal.rst:382
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 ""

#: ../../library/decimal.rst:387
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 ""

#: ../../library/decimal.rst:392
msgid "Once constructed, :class:`Decimal` objects are immutable."
msgstr ""

#: ../../library/decimal.rst:394
msgid ""
"The argument to the constructor is now permitted to be a :class:`float` "
"instance."
msgstr ""

#: ../../library/decimal.rst:398
msgid ""
":class:`float` arguments raise an exception if the :exc:`FloatOperation` "
"trap is set. By default the trap is off."
msgstr ""

#: ../../library/decimal.rst:402
msgid ""
"Underscores are allowed for grouping, as with integral and floating-point "
"literals in code."
msgstr ""

#: ../../library/decimal.rst:406
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 ""

#: ../../library/decimal.rst:413
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 ""

#: ../../library/decimal.rst:418
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')"

#: ../../library/decimal.rst:423
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 ""

#: ../../library/decimal.rst:427
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')"

#: ../../library/decimal.rst:432
msgid ""
"The ``%`` and ``//`` operators implement the ``remainder`` and ``divide-"
"integer`` operations (respectively) as described in the specification."
msgstr ""

#: ../../library/decimal.rst:436
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 ""

#: ../../library/decimal.rst:444
msgid ""
"Mixed-type comparisons between :class:`Decimal` instances and other numeric "
"types are now fully supported."
msgstr ""

#: ../../library/decimal.rst:448
msgid ""
"In addition to the standard numeric properties, decimal floating-point "
"objects also have a number of specialized methods:"
msgstr ""

#: ../../library/decimal.rst:454
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 ""

#: ../../library/decimal.rst:461
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 ""

#: ../../library/decimal.rst:465
msgid ""
">>> Decimal('-3.14').as_integer_ratio()\n"
"(-157, 50)"
msgstr ""
">>> Decimal('-3.14').as_integer_ratio()\n"
"(-157, 50)"

#: ../../library/decimal.rst:468
msgid ""
"The conversion is exact.  Raise OverflowError on infinities and ValueError "
"on NaNs."
msgstr ""

#: ../../library/decimal.rst:475
msgid ""
"Return a :term:`named tuple` representation of the number: "
"``DecimalTuple(sign, digits, exponent)``."
msgstr ""

#: ../../library/decimal.rst:481
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 ""

#: ../../library/decimal.rst:487
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 ""

#: ../../library/decimal.rst:491
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 ""
"a or b is a NaN  ==> Decimal('NaN')\n"
"a < b            ==> Decimal('-1')\n"
"a == b           ==> Decimal('0')\n"
"a > b            ==> Decimal('1')"

#: ../../library/decimal.rst:498
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 ""

#: ../../library/decimal.rst:504
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 ""

#: ../../library/decimal.rst:513
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 ""

#: ../../library/decimal.rst:520 ../../library/decimal.rst:531
#: ../../library/decimal.rst:559 ../../library/decimal.rst:846
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 ""

#: ../../library/decimal.rst:526
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 ""

#: ../../library/decimal.rst:537
msgid ""
"Just returns self, this method is only to comply with the Decimal "
"Specification."
msgstr ""

#: ../../library/decimal.rst:542
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 ""

#: ../../library/decimal.rst:548
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 ""

#: ../../library/decimal.rst:553
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 ""

#: ../../library/decimal.rst:565
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 ""

#: ../../library/decimal.rst:576
msgid ""
"Alternative constructor that only accepts instances of :class:`float` or :"
"class:`int`."
msgstr ""

#: ../../library/decimal.rst:579
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 ""

#: ../../library/decimal.rst:585
msgid ""
"From Python 3.2 onwards, a :class:`Decimal` instance can also be constructed "
"directly from a :class:`float`."
msgstr ""

#: ../../library/decimal.rst:588
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')"

#: ../../library/decimal.rst:603
msgid ""
"Fused multiply-add.  Return self*other+third with no rounding of the "
"intermediate product self*other."
msgstr ""

#: ../../library/decimal.rst:611
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 ""

#: ../../library/decimal.rst:617
msgid ""
"Return :const:`True` if the argument is a finite number, and :const:`False` "
"if the argument is an infinity or a NaN."
msgstr ""

#: ../../library/decimal.rst:622
msgid ""
"Return :const:`True` if the argument is either positive or negative infinity "
"and :const:`False` otherwise."
msgstr ""

#: ../../library/decimal.rst:627
msgid ""
"Return :const:`True` if the argument is a (quiet or signaling) NaN and :"
"const:`False` otherwise."
msgstr ""

#: ../../library/decimal.rst:632
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 ""

#: ../../library/decimal.rst:637
msgid ""
"Return :const:`True` if the argument is a quiet NaN, and :const:`False` "
"otherwise."
msgstr ""

#: ../../library/decimal.rst:642
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 ""

#: ../../library/decimal.rst:647
msgid ""
"Return :const:`True` if the argument is a signaling NaN and :const:`False` "
"otherwise."
msgstr ""

#: ../../library/decimal.rst:652
msgid ""
"Return :const:`True` if the argument is subnormal, and :const:`False` "
"otherwise."
msgstr ""

#: ../../library/decimal.rst:657
msgid ""
"Return :const:`True` if the argument is a (positive or negative) zero and :"
"const:`False` otherwise."
msgstr ""

#: ../../library/decimal.rst:662
msgid ""
"Return the natural (base e) logarithm of the operand.  The result is "
"correctly rounded using the :const:`ROUND_HALF_EVEN` rounding mode."
msgstr ""

#: ../../library/decimal.rst:667
msgid ""
"Return the base ten logarithm of the operand.  The result is correctly "
"rounded using the :const:`ROUND_HALF_EVEN` rounding mode."
msgstr ""

#: ../../library/decimal.rst:672
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 ""

#: ../../library/decimal.rst:680
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 ""

#: ../../library/decimal.rst:686
msgid ""
":meth:`logical_invert` is a logical operation.  The result is the digit-wise "
"inversion of the operand."
msgstr ""

#: ../../library/decimal.rst:691
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 ""

#: ../../library/decimal.rst:697
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 ""

#: ../../library/decimal.rst:703
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 ""

#: ../../library/decimal.rst:710
msgid ""
"Similar to the :meth:`.max` method, but the comparison is done using the "
"absolute values of the operands."
msgstr ""

#: ../../library/decimal.rst:715
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 ""

#: ../../library/decimal.rst:722
msgid ""
"Similar to the :meth:`.min` method, but the comparison is done using the "
"absolute values of the operands."
msgstr ""

#: ../../library/decimal.rst:727
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 ""

#: ../../library/decimal.rst:733
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 ""

#: ../../library/decimal.rst:739
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 ""

#: ../../library/decimal.rst:746
msgid ""
"Used for producing canonical values of an equivalence class within either "
"the current context or the specified context."
msgstr ""

#: ../../library/decimal.rst:749
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 ""

#: ../../library/decimal.rst:756
msgid ""
"For example, ``Decimal('32.100')`` and ``Decimal('0.321000e+2')`` both "
"normalize to the equivalent value ``Decimal('32.1')``."
msgstr ""

#: ../../library/decimal.rst:759
msgid "Note that rounding is applied *before* reducing to simplest form."
msgstr ""

#: ../../library/decimal.rst:761
msgid ""
"In the latest versions of the specification, this operation is also known as "
"``reduce``."
msgstr ""

#: ../../library/decimal.rst:766
msgid ""
"Return a string describing the *class* of the operand.  The returned value "
"is one of the following ten strings."
msgstr ""

#: ../../library/decimal.rst:769
msgid "``\"-Infinity\"``, indicating that the operand is negative infinity."
msgstr ""

#: ../../library/decimal.rst:770
msgid ""
"``\"-Normal\"``, indicating that the operand is a negative normal number."
msgstr ""

#: ../../library/decimal.rst:771
msgid ""
"``\"-Subnormal\"``, indicating that the operand is negative and subnormal."
msgstr ""

#: ../../library/decimal.rst:772
msgid "``\"-Zero\"``, indicating that the operand is a negative zero."
msgstr ""

#: ../../library/decimal.rst:773
msgid "``\"+Zero\"``, indicating that the operand is a positive zero."
msgstr ""

#: ../../library/decimal.rst:774
msgid ""
"``\"+Subnormal\"``, indicating that the operand is positive and subnormal."
msgstr ""

#: ../../library/decimal.rst:775
msgid ""
"``\"+Normal\"``, indicating that the operand is a positive normal number."
msgstr ""

#: ../../library/decimal.rst:776
msgid "``\"+Infinity\"``, indicating that the operand is positive infinity."
msgstr ""

#: ../../library/decimal.rst:777
msgid "``\"NaN\"``, indicating that the operand is a quiet NaN (Not a Number)."
msgstr ""

#: ../../library/decimal.rst:778
msgid "``\"sNaN\"``, indicating that the operand is a signaling NaN."
msgstr ""

#: ../../library/decimal.rst:782
msgid ""
"Return a value equal to the first operand after rounding and having the "
"exponent of the second operand."
msgstr ""

#: ../../library/decimal.rst:788
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 ""

#: ../../library/decimal.rst:794
msgid ""
"Also unlike other operations, quantize never signals Underflow, even if the "
"result is subnormal and inexact."
msgstr ""

#: ../../library/decimal.rst:797
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 ""

#: ../../library/decimal.rst:803
msgid ""
"An error is returned whenever the resulting exponent is greater than :attr:"
"`~Context.Emax` or less than :meth:`~Context.Etiny`."
msgstr ""

#: ../../library/decimal.rst:808
msgid ""
"Return ``Decimal(10)``, the radix (base) in which the :class:`Decimal` class "
"does all its arithmetic.  Included for compatibility with the specification."
msgstr ""

#: ../../library/decimal.rst:814
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 ""

#: ../../library/decimal.rst:821
msgid "If the result is zero then its sign will be the sign of *self*."
msgstr ""

#: ../../library/decimal.rst:832
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 ""

#: ../../library/decimal.rst:843
msgid ""
"Test whether self and other have the same exponent or whether both are "
"``NaN``."
msgstr ""

#: ../../library/decimal.rst:852
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 ""

#: ../../library/decimal.rst:858
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 ""

#: ../../library/decimal.rst:868
msgid "Return the square root of the argument to full precision."
msgstr ""

#: ../../library/decimal.rst:873 ../../library/decimal.rst:1510
msgid ""
"Convert to a string, using engineering notation if an exponent is needed."
msgstr ""

#: ../../library/decimal.rst:875 ../../library/decimal.rst:1512
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 ""

#: ../../library/decimal.rst:879
msgid ""
"For example, this converts ``Decimal('123E+1')`` to ``Decimal('1.23E+3')``."
msgstr ""

#: ../../library/decimal.rst:883
msgid ""
"Identical to the :meth:`to_integral_value` method.  The ``to_integral`` name "
"has been kept for compatibility with older versions."
msgstr ""

#: ../../library/decimal.rst:888
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 ""

#: ../../library/decimal.rst:896
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 ""

#: ../../library/decimal.rst:900
msgid "Decimal numbers can be rounded using the :func:`.round` function:"
msgstr ""

#: ../../library/decimal.rst:905
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 ""

#: ../../library/decimal.rst:911
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 ""

#: ../../library/decimal.rst:921
msgid ""
"if *ndigits* is positive, return *number* rounded to *ndigits* decimal "
"places;"
msgstr ""

#: ../../library/decimal.rst:923
msgid "if *ndigits* is zero, return *number* rounded to the nearest integer;"
msgstr ""

#: ../../library/decimal.rst:924
msgid ""
"if *ndigits* is negative, return *number* rounded to the nearest multiple of "
"``10**abs(ndigits)``."
msgstr ""

#: ../../library/decimal.rst:927
msgid "For example::"
msgstr ""

#: ../../library/decimal.rst:929
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 ""

#: ../../library/decimal.rst:946
msgid "Logical operands"
msgstr ""

#: ../../library/decimal.rst:948
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 ""

#: ../../library/decimal.rst:960
msgid "Context objects"
msgstr ""

#: ../../library/decimal.rst:962
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 ""

#: ../../library/decimal.rst:966
msgid ""
"Each thread has its own current context which is accessed or changed using "
"the :func:`getcontext` and :func:`setcontext` functions:"
msgstr ""

#: ../../library/decimal.rst:972
msgid "Return the current context for the active thread."
msgstr ""

#: ../../library/decimal.rst:977
msgid "Set the current context for the active thread to *c*."
msgstr ""

#: ../../library/decimal.rst:979
msgid ""
"You can also use the :keyword:`with` statement and the :func:`localcontext` "
"function to temporarily change the active context."
msgstr ""

#: ../../library/decimal.rst:984
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 ""

#: ../../library/decimal.rst:990
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 ""

#: ../../library/decimal.rst:993
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 ""

#: ../../library/decimal.rst:1000
msgid "Using keyword arguments, the code would be the following::"
msgstr ""

#: ../../library/decimal.rst:1002
msgid ""
"from decimal import localcontext\n"
"\n"
"with localcontext(prec=42) as ctx:\n"
"    s = calculate_something()\n"
"s = +s"
msgstr ""
"from decimal import localcontext\n"
"\n"
"with localcontext(prec=42) as ctx:\n"
"    s = calculate_something()\n"
"s = +s"

#: ../../library/decimal.rst:1008
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 ""

#: ../../library/decimal.rst:1012
msgid ""
":meth:`localcontext` now supports setting context attributes through the use "
"of keyword arguments."
msgstr ""

#: ../../library/decimal.rst:1015
msgid ""
"New contexts can also be created using the :class:`Context` constructor "
"described below. In addition, the module provides three pre-made contexts:"
msgstr ""

#: ../../library/decimal.rst:1021
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 ""

#: ../../library/decimal.rst:1027
msgid ""
"Because many of the traps are enabled, this context is useful for debugging."
msgstr ""

#: ../../library/decimal.rst:1032
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 ""

#: ../../library/decimal.rst:1037
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 ""

#: ../../library/decimal.rst:1045
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 ""

#: ../../library/decimal.rst:1049
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 ""

#: ../../library/decimal.rst:1054
msgid ""
"In single threaded environments, it is preferable to not use this context at "
"all.  Instead, simply create contexts explicitly as described below."
msgstr ""

#: ../../library/decimal.rst:1057
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 ""

#: ../../library/decimal.rst:1062
msgid ""
"In addition to the three supplied contexts, new contexts can be created with "
"the :class:`Context` constructor."
msgstr ""

#: ../../library/decimal.rst:1068
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 ""

#: ../../library/decimal.rst:1072
msgid ""
"*prec* is an integer in the range [``1``, :const:`MAX_PREC`] that sets the "
"precision for arithmetic operations in the context."
msgstr ""

#: ../../library/decimal.rst:1075
msgid ""
"The *rounding* option is one of the constants listed in the section "
"`Rounding Modes`_."
msgstr ""

#: ../../library/decimal.rst:1078
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 ""

#: ../../library/decimal.rst:1081
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 ""

#: ../../library/decimal.rst:1085
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 ""

#: ../../library/decimal.rst:1089
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 ""

#: ../../library/decimal.rst:1101
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')"

#: ../../library/decimal.rst:1104
msgid ""
"A *clamp* value of ``1`` allows compatibility with the fixed-width decimal "
"interchange formats specified in IEEE 754."
msgstr ""

#: ../../library/decimal.rst:1107
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 ""

#: ../../library/decimal.rst:1120
msgid "Resets all of the flags to ``0``."
msgstr ""

#: ../../library/decimal.rst:1124
msgid "Resets all of the traps to ``0``."
msgstr ""

#: ../../library/decimal.rst:1130
msgid "Return a duplicate of the context."
msgstr ""

#: ../../library/decimal.rst:1134
msgid "Return a copy of the Decimal instance num."
msgstr ""

#: ../../library/decimal.rst:1138
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 ""

#: ../../library/decimal.rst:1142
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 ""

#: ../../library/decimal.rst:1148
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 ""
">>> 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')"

#: ../../library/decimal.rst:1156
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 ""

#: ../../library/decimal.rst:1162
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 ""

#: ../../library/decimal.rst:1167
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 ""
">>> 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"

#: ../../library/decimal.rst:1182
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 ""

#: ../../library/decimal.rst:1188
msgid "Returns a value equal to ``Emax - prec + 1``."
msgstr ""

#: ../../library/decimal.rst:1190
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 ""

#: ../../library/decimal.rst:1200
msgid "Returns the absolute value of *x*."
msgstr ""

#: ../../library/decimal.rst:1205
msgid "Return the sum of *x* and *y*."
msgstr ""

#: ../../library/decimal.rst:1210
msgid "Returns the same Decimal object *x*."
msgstr ""

#: ../../library/decimal.rst:1215
msgid "Compares *x* and *y* numerically."
msgstr ""

#: ../../library/decimal.rst:1220
msgid "Compares the values of the two operands numerically."
msgstr ""

#: ../../library/decimal.rst:1225
msgid "Compares two operands using their abstract representation."
msgstr ""

#: ../../library/decimal.rst:1230
msgid ""
"Compares two operands using their abstract representation, ignoring sign."
msgstr ""

#: ../../library/decimal.rst:1235
msgid "Returns a copy of *x* with the sign set to 0."
msgstr ""

#: ../../library/decimal.rst:1240
msgid "Returns a copy of *x* with the sign inverted."
msgstr ""

#: ../../library/decimal.rst:1245
msgid "Copies the sign from *y* to *x*."
msgstr ""

#: ../../library/decimal.rst:1250
msgid "Return *x* divided by *y*."
msgstr ""

#: ../../library/decimal.rst:1255
msgid "Return *x* divided by *y*, truncated to an integer."
msgstr ""

#: ../../library/decimal.rst:1260
msgid "Divides two numbers and returns the integer part of the result."
msgstr ""

#: ../../library/decimal.rst:1265
msgid "Returns ``e ** x``."
msgstr ""

#: ../../library/decimal.rst:1270
msgid "Returns *x* multiplied by *y*, plus *z*."
msgstr ""

#: ../../library/decimal.rst:1275
msgid "Returns ``True`` if *x* is canonical; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1280
msgid "Returns ``True`` if *x* is finite; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1285
msgid "Returns ``True`` if *x* is infinite; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1290
msgid "Returns ``True`` if *x* is a qNaN or sNaN; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1295
msgid ""
"Returns ``True`` if *x* is a normal number; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1300
msgid "Returns ``True`` if *x* is a quiet NaN; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1305
msgid "Returns ``True`` if *x* is negative; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1310
msgid ""
"Returns ``True`` if *x* is a signaling NaN; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1315
msgid "Returns ``True`` if *x* is subnormal; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1320
msgid "Returns ``True`` if *x* is a zero; otherwise returns ``False``."
msgstr ""

#: ../../library/decimal.rst:1325
msgid "Returns the natural (base e) logarithm of *x*."
msgstr ""

#: ../../library/decimal.rst:1330
msgid "Returns the base 10 logarithm of *x*."
msgstr ""

#: ../../library/decimal.rst:1335
msgid "Returns the exponent of the magnitude of the operand's MSD."
msgstr ""

#: ../../library/decimal.rst:1340
msgid "Applies the logical operation *and* between each operand's digits."
msgstr ""

#: ../../library/decimal.rst:1345
msgid "Invert all the digits in *x*."
msgstr ""

#: ../../library/decimal.rst:1350
msgid "Applies the logical operation *or* between each operand's digits."
msgstr ""

#: ../../library/decimal.rst:1355
msgid "Applies the logical operation *xor* between each operand's digits."
msgstr ""

#: ../../library/decimal.rst:1360
msgid "Compares two values numerically and returns the maximum."
msgstr ""

#: ../../library/decimal.rst:1365 ../../library/decimal.rst:1375
msgid "Compares the values numerically with their sign ignored."
msgstr ""

#: ../../library/decimal.rst:1370
msgid "Compares two values numerically and returns the minimum."
msgstr ""

#: ../../library/decimal.rst:1380
msgid "Minus corresponds to the unary prefix minus operator in Python."
msgstr ""

#: ../../library/decimal.rst:1385
msgid "Return the product of *x* and *y*."
msgstr ""

#: ../../library/decimal.rst:1390
msgid "Returns the largest representable number smaller than *x*."
msgstr ""

#: ../../library/decimal.rst:1395
msgid "Returns the smallest representable number larger than *x*."
msgstr ""

#: ../../library/decimal.rst:1400
msgid "Returns the number closest to *x*, in direction towards *y*."
msgstr ""

#: ../../library/decimal.rst:1405
msgid "Reduces *x* to its simplest form."
msgstr ""

#: ../../library/decimal.rst:1410
msgid "Returns an indication of the class of *x*."
msgstr ""

#: ../../library/decimal.rst:1415
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 ""

#: ../../library/decimal.rst:1422
msgid "Return ``x`` to the power of ``y``, reduced modulo ``modulo`` if given."
msgstr ""

#: ../../library/decimal.rst:1424
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 ""

#: ../../library/decimal.rst:1430
msgid ""
"``Decimal(0) ** Decimal(0)`` results in ``InvalidOperation``, and if "
"``InvalidOperation`` is not trapped, then results in ``Decimal('NaN')``."
msgstr ""

#: ../../library/decimal.rst:1433
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 ""

#: ../../library/decimal.rst:1438
msgid ""
"With three arguments, compute ``(x**y) % modulo``.  For the three argument "
"form, the following restrictions on the arguments hold:"
msgstr ""

#: ../../library/decimal.rst:1441
msgid "all three arguments must be integral"
msgstr ""

#: ../../library/decimal.rst:1442
msgid "``y`` must be nonnegative"
msgstr ""

#: ../../library/decimal.rst:1443
msgid "at least one of ``x`` or ``y`` must be nonzero"
msgstr ""

#: ../../library/decimal.rst:1444
msgid "``modulo`` must be nonzero and have at most 'precision' digits"
msgstr ""

#: ../../library/decimal.rst:1446
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 ""

#: ../../library/decimal.rst:1456
msgid "Returns a value equal to *x* (rounded), having the exponent of *y*."
msgstr ""

#: ../../library/decimal.rst:1461
msgid "Just returns 10, as this is Decimal, :)"
msgstr ""

#: ../../library/decimal.rst:1466
msgid "Returns the remainder from integer division."
msgstr ""

#: ../../library/decimal.rst:1468
msgid ""
"The sign of the result, if non-zero, is the same as that of the original "
"dividend."
msgstr ""

#: ../../library/decimal.rst:1474
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 ""

#: ../../library/decimal.rst:1480
msgid "Returns a rotated copy of *x*, *y* times."
msgstr ""

#: ../../library/decimal.rst:1485
msgid "Returns ``True`` if the two operands have the same exponent."
msgstr ""

#: ../../library/decimal.rst:1490
msgid "Returns the first operand after adding the second value its exp."
msgstr ""

#: ../../library/decimal.rst:1495
msgid "Returns a shifted copy of *x*, *y* times."
msgstr ""

#: ../../library/decimal.rst:1500
msgid "Square root of a non-negative number to context precision."
msgstr ""

#: ../../library/decimal.rst:1505
msgid "Return the difference between *x* and *y*."
msgstr ""

#: ../../library/decimal.rst:1519
msgid "Rounds to an integer."
msgstr ""

#: ../../library/decimal.rst:1524
msgid "Converts a number to a string using scientific notation."
msgstr ""

#: ../../library/decimal.rst:1531
msgid "Constants"
msgstr "常數"

#: ../../library/decimal.rst:1533
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 ""

#: ../../library/decimal.rst:1537
msgid "32-bit"
msgstr "32 位元"

#: ../../library/decimal.rst:1537
msgid "64-bit"
msgstr "64 位元"

#: ../../library/decimal.rst:1539 ../../library/decimal.rst:1541
msgid "``425000000``"
msgstr "``425000000``"

#: ../../library/decimal.rst:1539 ../../library/decimal.rst:1541
msgid "``999999999999999999``"
msgstr "``999999999999999999``"

#: ../../library/decimal.rst:1543
msgid "``-425000000``"
msgstr "``-425000000``"

#: ../../library/decimal.rst:1543
msgid "``-999999999999999999``"
msgstr "``-999999999999999999``"

#: ../../library/decimal.rst:1545
msgid "``-849999999``"
msgstr "``-849999999``"

#: ../../library/decimal.rst:1545
msgid "``-1999999999999999997``"
msgstr "``-1999999999999999997``"

#: ../../library/decimal.rst:1551
msgid ""
"The value is ``True``.  Deprecated, because Python now always has threads."
msgstr ""

#: ../../library/decimal.rst:1557
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 ""

#: ../../library/decimal.rst:1566
msgid "Rounding modes"
msgstr ""

#: ../../library/decimal.rst:1570
msgid "Round towards ``Infinity``."
msgstr ""

#: ../../library/decimal.rst:1574
msgid "Round towards zero."
msgstr ""

#: ../../library/decimal.rst:1578
msgid "Round towards ``-Infinity``."
msgstr ""

#: ../../library/decimal.rst:1582
msgid "Round to nearest with ties going towards zero."
msgstr ""

#: ../../library/decimal.rst:1586
msgid "Round to nearest with ties going to nearest even integer."
msgstr ""

#: ../../library/decimal.rst:1590
msgid "Round to nearest with ties going away from zero."
msgstr ""

#: ../../library/decimal.rst:1594
msgid "Round away from zero."
msgstr ""

#: ../../library/decimal.rst:1598
msgid ""
"Round away from zero if last digit after rounding towards zero would have "
"been 0 or 5; otherwise round towards zero."
msgstr ""

#: ../../library/decimal.rst:1605
msgid "Signals"
msgstr ""

#: ../../library/decimal.rst:1607
msgid ""
"Signals represent conditions that arise during computation. Each corresponds "
"to one context flag and one context trap enabler."
msgstr ""

#: ../../library/decimal.rst:1610
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 ""

#: ../../library/decimal.rst:1615
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 ""

#: ../../library/decimal.rst:1623
msgid "Altered an exponent to fit representation constraints."
msgstr ""

#: ../../library/decimal.rst:1625
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 ""

#: ../../library/decimal.rst:1632
msgid "Base class for other signals and a subclass of :exc:`ArithmeticError`."
msgstr ""

#: ../../library/decimal.rst:1637
msgid "Signals the division of a non-infinite number by zero."
msgstr ""

#: ../../library/decimal.rst:1639
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 ""

#: ../../library/decimal.rst:1646
msgid "Indicates that rounding occurred and the result is not exact."
msgstr ""

#: ../../library/decimal.rst:1648
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 ""

#: ../../library/decimal.rst:1655
msgid "An invalid operation was performed."
msgstr ""

#: ../../library/decimal.rst:1657
msgid ""
"Indicates that an operation was requested that does not make sense. If not "
"trapped, returns ``NaN``.  Possible causes include::"
msgstr ""

#: ../../library/decimal.rst:1660
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 ""
"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"

#: ../../library/decimal.rst:1673
msgid "Numerical overflow."
msgstr ""

#: ../../library/decimal.rst:1675
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 ""

#: ../../library/decimal.rst:1684
msgid "Rounding occurred though possibly no information was lost."
msgstr ""

#: ../../library/decimal.rst:1686
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 ""

#: ../../library/decimal.rst:1694
msgid "Exponent was lower than :attr:`~Context.Emin` prior to rounding."
msgstr ""

#: ../../library/decimal.rst:1696
msgid ""
"Occurs when an operation result is subnormal (the exponent is too small). If "
"not trapped, returns the result unchanged."
msgstr ""

#: ../../library/decimal.rst:1702
msgid "Numerical underflow with result rounded to zero."
msgstr ""

#: ../../library/decimal.rst:1704
msgid ""
"Occurs when a subnormal result is pushed to zero by rounding. :class:"
"`Inexact` and :class:`Subnormal` are also signaled."
msgstr ""

#: ../../library/decimal.rst:1710
msgid "Enable stricter semantics for mixing floats and Decimals."
msgstr ""

#: ../../library/decimal.rst:1712
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 ""

#: ../../library/decimal.rst:1720
msgid ""
"Otherwise (the signal is trapped), only equality comparisons and explicit "
"conversions are silent. All other mixed operations raise :exc:"
"`FloatOperation`."
msgstr ""

#: ../../library/decimal.rst:1724
msgid "The following table summarizes the hierarchy of signals::"
msgstr ""

#: ../../library/decimal.rst:1726
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 ""
"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)"

#: ../../library/decimal.rst:1745
msgid "Floating-Point Notes"
msgstr ""

#: ../../library/decimal.rst:1749
msgid "Mitigating round-off error with increased precision"
msgstr ""

#: ../../library/decimal.rst:1751
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 ""

#: ../../library/decimal.rst:1755
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 ""

#: ../../library/decimal.rst:1761
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 ""

#: ../../library/decimal.rst:1779
msgid ""
"The :mod:`decimal` module makes it possible to restore the identities by "
"expanding the precision sufficiently to avoid loss of significance:"
msgstr ""

#: ../../library/decimal.rst:1782
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 ""

#: ../../library/decimal.rst:1799
msgid "Special values"
msgstr "特殊值"

#: ../../library/decimal.rst:1801
msgid ""
"The number system for the :mod:`decimal` module provides special values "
"including ``NaN``, ``sNaN``, ``-Infinity``, ``Infinity``, and two zeros, "
"``+0`` and ``-0``."
msgstr ""

#: ../../library/decimal.rst:1805
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 ""

#: ../../library/decimal.rst:1810
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 ""

#: ../../library/decimal.rst:1814
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 ""

#: ../../library/decimal.rst:1822
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 ""

#: ../../library/decimal.rst:1826
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 ""

#: ../../library/decimal.rst:1839
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 ""

#: ../../library/decimal.rst:1844
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 ""

#: ../../library/decimal.rst:1859
msgid "Working with threads"
msgstr ""

#: ../../library/decimal.rst:1861
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 ""

#: ../../library/decimal.rst:1865
msgid ""
"Likewise, the :func:`setcontext` function automatically assigns its target "
"to the current thread."
msgstr ""

#: ../../library/decimal.rst:1868
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 ""

#: ../../library/decimal.rst:1872
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 ""

#: ../../library/decimal.rst:1878
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 ""

#: ../../library/decimal.rst:1897
msgid "Recipes"
msgstr ""

#: ../../library/decimal.rst:1899
msgid ""
"Here are a few recipes that serve as utility functions and that demonstrate "
"ways to work with the :class:`Decimal` class::"
msgstr ""

#: ../../library/decimal.rst:1902
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 ""

#: ../../library/decimal.rst:2054
msgid "Decimal FAQ"
msgstr ""

#: ../../library/decimal.rst:2056
msgid ""
"Q. It is cumbersome to type ``decimal.Decimal('1234.5')``.  Is there a way "
"to minimize typing when using the interactive interpreter?"
msgstr ""

#: ../../library/decimal.rst:2059
msgid "A. Some users abbreviate the constructor to just a single letter:"
msgstr ""

#: ../../library/decimal.rst:2065
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 ""

#: ../../library/decimal.rst:2069
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 ""

#: ../../library/decimal.rst:2087
msgid ""
"Q. Once I have valid two place inputs, how do I maintain that invariant "
"throughout an application?"
msgstr ""

#: ../../library/decimal.rst:2090
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 ""

#: ../../library/decimal.rst:2108
msgid ""
"In developing fixed-point applications, it is convenient to define functions "
"to handle the :meth:`~Decimal.quantize` step:"
msgstr ""

#: ../../library/decimal.rst:2122
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 ""

#: ../../library/decimal.rst:2127
msgid ""
"A. The :meth:`~Decimal.normalize` method maps all equivalent values to a "
"single representative:"
msgstr ""

#: ../../library/decimal.rst:2134
msgid "Q. When does rounding occur in a computation?"
msgstr ""

#: ../../library/decimal.rst:2136
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 ""

#: ../../library/decimal.rst:2143
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 ""

#: ../../library/decimal.rst:2154
msgid ""
"Q. Some decimal values always print with exponential notation.  Is there a "
"way to get a non-exponential representation?"
msgstr ""

#: ../../library/decimal.rst:2157
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 ""

#: ../../library/decimal.rst:2162
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 ""

#: ../../library/decimal.rst:2172
msgid "Q. Is there a way to convert a regular float to a :class:`Decimal`?"
msgstr ""

#: ../../library/decimal.rst:2174
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 ""

#: ../../library/decimal.rst:2178
msgid ""
">>> Decimal(math.pi)\n"
"Decimal('3.141592653589793115997963468544185161590576171875')"
msgstr ""
">>> Decimal(math.pi)\n"
"Decimal('3.141592653589793115997963468544185161590576171875')"

#: ../../library/decimal.rst:2183
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 ""

#: ../../library/decimal.rst:2186
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 ""

#: ../../library/decimal.rst:2191
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 ""

#: ../../library/decimal.rst:2195
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 ""

#: ../../library/decimal.rst:2200
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 ""
">>> 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')"

#: ../../library/decimal.rst:2208
msgid ""
"The solution is either to increase precision or to force rounding of inputs "
"using the unary plus operation:"
msgstr ""

#: ../../library/decimal.rst:2211
msgid ""
">>> getcontext().prec = 3\n"
">>> +Decimal('1.23456789')      # unary plus triggers rounding\n"
"Decimal('1.23')"
msgstr ""

#: ../../library/decimal.rst:2217
msgid ""
"Alternatively, inputs can be rounded upon creation using the :meth:`Context."
"create_decimal` method:"
msgstr ""

#: ../../library/decimal.rst:2223
msgid "Q. Is the CPython implementation fast for large numbers?"
msgstr ""

#: ../../library/decimal.rst:2225
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 ""

#: ../../library/decimal.rst:2235
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 ""

#: ../../library/decimal.rst:2239
msgid ""
"The easiest approach for trying out bignum arithmetic is to use the maximum "
"value for :attr:`~Context.prec` as well [#]_::"
msgstr ""

#: ../../library/decimal.rst:2242
msgid ""
">>> setcontext(Context(prec=MAX_PREC, Emax=MAX_EMAX, Emin=MIN_EMIN))\n"
">>> x = Decimal(2) ** 256\n"
">>> x / 128\n"
"Decimal('904625697166532776746648320380374280103671755200316906558262375061821325312')"
msgstr ""
">>> setcontext(Context(prec=MAX_PREC, Emax=MAX_EMAX, Emin=MIN_EMIN))\n"
">>> x = Decimal(2) ** 256\n"
">>> x / 128\n"
"Decimal('904625697166532776746648320380374280103671755200316906558262375061821325312')"

#: ../../library/decimal.rst:2248
msgid ""
"For inexact results, :const:`MAX_PREC` is far too large on 64-bit platforms "
"and the available memory will be insufficient::"
msgstr ""

#: ../../library/decimal.rst:2251
msgid ""
">>> Decimal(1) / 3\n"
"Traceback (most recent call last):\n"
"  File \"<stdin>\", line 1, in <module>\n"
"MemoryError"
msgstr ""
">>> Decimal(1) / 3\n"
"Traceback (most recent call last):\n"
"  File \"<stdin>\", line 1, in <module>\n"
"MemoryError"

#: ../../library/decimal.rst:2256
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 ""

#: ../../library/decimal.rst:2260
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 ""

#: ../../library/decimal.rst:2280
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 ""

#: ../../library/decimal.rst:2289
msgid ""
"This approach now works for all exact results except for non-integer powers."
msgstr ""