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{<class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s, <class '%s'>:%s}TrueFalseinternal error in flags_as_exceptionargument must be a sequence of length 3sign must be an integer with the value 0 or 1FInfNaNNsNaNstring argument in the third position must be 'F', 'n' or 'N'exponent must be an integercoefficient must be a tuple of digits%sinternal error in dec_sequence_as_str%iinternal error in context_reprContext(prec=%zd, rounding=%s, Emin=%zd, Emax=%zd, capitals=%d, clamp=%d, flags=%s, traps=%s)cannot convert NaN to integercannot convert Infinity to integer(i)argument must be a signal dictinvalid signal dictsignal keys cannot be deletedvalid values for signals are:
  [InvalidOperation, FloatOperation, DivisionByZero,
   Overflow, Underflow, Subnormal, Inexact, Rounded,
   Clamped]valid values for capitals are 0 or 1valid range for unsafe emax is [0, 1070000000]valid range for unsafe emin is [-1070000000, 0]valid range for unsafe prec is [1, 1070000000]valid range for prec is [1, MAX_PREC]valid range for Emin is [MIN_EMIN, 0]valid range for Emax is [0, MAX_EMAX]valid values for clamp are 0 or 1trapsflagsargument must be a Decimalinvalid decimal point or unsupported combination of LC_CTYPE and LC_NUMERICcontext attributes cannot be deletedinternal error in context_settraps_dictinternal error in context_setstatus_dictO(nsnniiOO)argument must be an integerconversion from %s to Decimal is not supportedOO(OO)OO|OOOOvalid values for rounding are:
  [ROUND_CEILING, ROUND_FLOOR, ROUND_UP, ROUND_DOWN,
   ROUND_HALF_UP, ROUND_HALF_DOWN, ROUND_HALF_EVEN,
   ROUND_05UP]internal error in context_setroundargument must be a contextcannot get thread stateargument must be int of float|Oargument must be a tuple or list|OOOOOOOOinternal error in context_settraps_listinternal error in context_setstatus_listoptional argument must be a context|OOO|OOinternal error in dec_mpd_qquantizeinternal error in PyDec_ToIntegralExactinternal error in PyDec_ToIntegralValueoptional arg must be an integerO|Oformat arg must be strinvalid format stringoptional argument must be a dictdecimal_pointthousands_sepgroupinginvalid override dictformat specification exceeds internal limits of _decimalcannot convert NaN to integer ratiocannot convert Infinity to integer ratioDecimal('%s')numeratordenominatorexact conversion for comparison failedCannot hash a signaling NaN valuedec_hash: internal error: please reportO(O)cannot convert signaling NaN to float-nanas_integer_ratiointernal error: could not find method %sbit_lengthdecimal__module__numbersNumber(O)registerRationalcollectionsDecimalTuple(ss)namedtuplesign digits exponentMutableMappingSignalDicts(OO){}decimal.DecimalExceptionDefaultContext___DECIMAL_CTX__HAVE_THREADSBasicContextExtendedContext1.70__version____libmpdec_version__roundingotherexpthirdabmoduloprecEminEmaxcapitalsclampctxMAX_PRECMAX_EMAXMIN_EMINMIN_ETINYgetcontextsetcontextlocalcontextabslnlog10minusnext_minusnext_plusnormalizeplusto_integralto_integral_exactto_integral_valuesqrtaddcomparecompare_signaldividedivide_intdivmodmax_magmin_magmultiplynext_towardquantizeremainderremainder_nearsubtractpowerfmaEtinyEtopradixis_canonicalis_finiteis_infiniteis_nanis_normalis_qnanis_signedis_snanis_subnormalis_zero_applycanonicalcopy_abscopy_decimalcopy_negatelogblogical_invertnumber_classto_sci_stringto_eng_stringcompare_totalcompare_total_magcopy_signlogical_andlogical_orlogical_xorrotatesame_quantumscalebshiftclear_flagsclear_traps_unsafe_setprec_unsafe_setemin_unsafe_setemax__copy____reduce__copycreate_decimalcreate_decimal_from_floatadjustedconjugatefrom_floatas_tuple__deepcopy____format____round____ceil____floor____trunc____complex____sizeof__realimag__enter____exit__decimal.SignalDictMixindecimal.InvalidOperationdecimal.ConversionSyntaxdecimal.DivisionImpossibledecimal.DivisionUndefineddecimal.InvalidContextdecimal.FloatOperationdecimal.DivisionByZerodecimal.Overflowdecimal.Underflowdecimal.Subnormaldecimal.Inexactdecimal.Roundeddecimal.Clampeddecimal.ContextManagerdecimal.Contextdecimal.DecimalqD1D
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@è¬4d Hþÿÿo$ ÿÿÿoðÿÿoNúÿÿo_? : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :ŒCto_sci_string($self, x, /)
--

Convert a number to a string using scientific notation.

to_integral_value($self, x, /)
--

Round to an integer.

to_integral_exact($self, x, /)
--

Round to an integer. Signal if the result is rounded or inexact.

to_integral($self, x, /)
--

Identical to to_integral_value(x).

to_eng_string($self, x, /)
--

Convert a number to a string, using engineering notation.

subtract($self, x, y, /)
--

Return the difference between x and y.

sqrt($self, x, /)
--

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

shift($self, x, y, /)
--

Return a copy of x, shifted by y places.

scaleb($self, x, y, /)
--

Return the first operand after adding the second value to its exp.

same_quantum($self, x, y, /)
--

Return True if the two operands have the same exponent.

rotate($self, x, y, /)
--

Return a copy of x, rotated by y places.

remainder_near($self, x, y, /)
--

Return 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).

remainder($self, x, y, /)
--

Return the remainder from integer division.  The sign of the result,
if non-zero, is the same as that of the original dividend.

radix($self, /)
--

Return 10.

quantize($self, x, y, /)
--

Return a value equal to x (rounded), having the exponent of y.

power($self, /, a, b, modulo=None)
--

Compute a**b. If 'a' is negative, then 'b' must be integral. The result
will be inexact unless 'a' is integral and the result is finite and can
be expressed exactly in 'precision' digits.  In the Python version the
result is always correctly rounded, in the C version the result is almost
always correctly rounded.

If modulo is given, compute (a**b) % modulo. The following restrictions
hold:

    * all three arguments must be integral
    * 'b' must be nonnegative
    * at least one of 'a' or 'b' must be nonzero
    * modulo must be nonzero and less than 10**prec in absolute value


plus($self, x, /)
--

Plus corresponds to the unary prefix plus operator in Python, but applies
the context to the result.

number_class($self, x, /)
--

Return an indication of the class of x.

normalize($self, x, /)
--

Reduce x to its simplest form. Alias for reduce(x).

next_toward($self, x, y, /)
--

Return the number closest to x, in the direction towards y.

next_plus($self, x, /)
--

Return the smallest representable number larger than x.

next_minus($self, x, /)
--

Return the largest representable number smaller than x.

multiply($self, x, y, /)
--

Return the product of x and y.

minus($self, x, /)
--

Minus corresponds to the unary prefix minus operator in Python, but applies
the context to the result.

min_mag($self, x, y, /)
--

Compare the values numerically with their sign ignored.

min($self, x, y, /)
--

Compare the values numerically and return the minimum.

max_mag($self, x, y, /)
--

Compare the values numerically with their sign ignored.

max($self, x, y, /)
--

Compare the values numerically and return the maximum.

logical_xor($self, x, y, /)
--

Digit-wise xor of x and y.

logical_or($self, x, y, /)
--

Digit-wise or of x and y.

logical_invert($self, x, /)
--

Invert all digits of x.

logical_and($self, x, y, /)
--

Digit-wise and of x and y.

logb($self, x, /)
--

Return the exponent of the magnitude of the operand's MSD.

log10($self, x, /)
--

Return the base 10 logarithm of x.

ln($self, x, /)
--

Return the natural (base e) logarithm of x.

is_zero($self, x, /)
--

Return True if x is a zero, False otherwise.

is_subnormal($self, x, /)
--

Return True if x is subnormal, False otherwise.

is_snan($self, x, /)
--

Return True if x is a signaling NaN, False otherwise.

is_signed($self, x, /)
--

Return True if x is negative, False otherwise.

is_qnan($self, x, /)
--

Return True if x is a quiet NaN, False otherwise.

is_normal($self, x, /)
--

Return True if x is a normal number, False otherwise.

is_nan($self, x, /)
--

Return True if x is a qNaN or sNaN, False otherwise.

is_infinite($self, x, /)
--

Return True if x is infinite, False otherwise.

is_finite($self, x, /)
--

Return True if x is finite, False otherwise.

is_canonical($self, x, /)
--

Return True if x is canonical, False otherwise.

fma($self, x, y, z, /)
--

Return x multiplied by y, plus z.

exp($self, x, /)
--

Return e ** x.

divmod($self, x, y, /)
--

Return quotient and remainder of the division x / y.

divide_int($self, x, y, /)
--

Return x divided by y, truncated to an integer.

divide($self, x, y, /)
--

Return x divided by y.

copy_sign($self, x, y, /)
--

Copy the sign from y to x.

copy_negate($self, x, /)
--

Return a copy of x with the sign inverted.

copy_abs($self, x, /)
--

Return a copy of x with the sign set to 0.

compare_total_mag($self, x, y, /)
--

Compare x and y using their abstract representation, ignoring sign.

compare_total($self, x, y, /)
--

Compare x and y using their abstract representation.

compare_signal($self, x, y, /)
--

Compare x and y numerically.  All NaNs signal.

compare($self, x, y, /)
--

Compare x and y numerically.

canonical($self, x, /)
--

Return a new instance of x.

add($self, x, y, /)
--

Return the sum of x and y.

abs($self, x, /)
--

Return the absolute value of x.

Etop($self, /)
--

Return a value equal to Emax - prec + 1.  This is the maximum exponent
if the _clamp field of the context is set to 1 (IEEE clamp mode).  Etop()
must not be negative.

Etiny($self, /)
--

Return a value equal to Emin - prec + 1, which is the minimum exponent value
for subnormal results.  When underflow occurs, the exponent is set to Etiny.

create_decimal_from_float($self, f, /)
--

Create a new Decimal instance from float f.  Unlike the Decimal.from_float()
class method, this function observes the context limits.

create_decimal($self, num="0", /)
--

Create a new Decimal instance from num, using self as the context. Unlike the
Decimal constructor, this function observes the context limits.

copy_decimal($self, x, /)
--

Return a copy of Decimal x.

copy($self, /)
--

Return a duplicate of the context with all flags cleared.

clear_traps($self, /)
--

Set all traps to False.

clear_flags($self, /)
--

Reset all flags to False.

Context(prec=None, rounding=None, Emin=None, Emax=None, capitals=None, clamp=None, flags=None, traps=None)
--

The context affects almost all operations and controls rounding,
Over/Underflow, raising of exceptions and much more.  A new context
can be constructed as follows:

    >>> c = Context(prec=28, Emin=-425000000, Emax=425000000,
    ...             rounding=ROUND_HALF_EVEN, capitals=1, clamp=1,
    ...             traps=[InvalidOperation, DivisionByZero, Overflow],
    ...             flags=[])
    >>>


to_integral_value($self, /, rounding=None, context=None)
--

Round to the nearest integer without signaling Inexact or Rounded.  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 default context is used.

to_integral_exact($self, /, rounding=None, context=None)
--

Round to the nearest integer, signaling Inexact or 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 default context is used.

to_integral($self, /, rounding=None, context=None)
--

Identical to the to_integral_value() method.  The to_integral() name has been
kept for compatibility with older versions.

to_eng_string($self, /, context=None)
--

Convert to an engineering-type string.  Engineering notation has an exponent
which is a multiple of 3, so there are up to 3 digits left of the decimal
place. For example, Decimal('123E+1') is converted to Decimal('1.23E+3').

The value of context.capitals determines whether the exponent sign is lower
or upper case. Otherwise, the context does not affect the operation.

sqrt($self, /, context=None)
--

Return the square root of the argument to full precision. The result is
correctly rounded using the ROUND_HALF_EVEN rounding mode.

shift($self, /, other, context=None)
--

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.

scaleb($self, /, other, context=None)
--

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

same_quantum($self, /, other, context=None)
--

Test whether self and other have the same exponent or whether both are NaN.

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.

rotate($self, /, other, context=None)
--

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.

remainder_near($self, /, other, context=None)
--

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.

If the result is zero then its sign will be the sign of self.

radix($self, /)
--

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

quantize($self, /, exp, rounding=None, context=None)
--

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

    >>> Decimal('1.41421356').quantize(Decimal('1.000'))
    Decimal('1.414')

Unlike other operations, if the length of the coefficient after the quantize
operation would be greater than precision, then an 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.

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

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.

number_class($self, /, context=None)
--

Return a string describing the class of the operand.  The returned value
is one of the following ten strings:

    * '-Infinity', indicating that the operand is negative infinity.
    * '-Normal', indicating that the operand is a negative normal number.
    * '-Subnormal', indicating that the operand is negative and subnormal.
    * '-Zero', indicating that the operand is a negative zero.
    * '+Zero', indicating that the operand is a positive zero.
    * '+Subnormal', indicating that the operand is positive and subnormal.
    * '+Normal', indicating that the operand is a positive normal number.
    * '+Infinity', indicating that the operand is positive infinity.
    * 'NaN', indicating that the operand is a quiet NaN (Not a Number).
    * 'sNaN', indicating that the operand is a signaling NaN.


normalize($self, /, context=None)
--

Normalize the number by stripping the rightmost trailing zeros and
converting any result equal to Decimal('0') to Decimal('0e0').  Used
for producing canonical values for members of an equivalence class.
For example, Decimal('32.100') and Decimal('0.321000e+2') both normalize
to the equivalent value Decimal('32.1').

next_toward($self, /, other, context=None)
--

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.

next_plus($self, /, context=None)
--

Return the smallest number representable in the given context (or in the
current default context if no context is given) that is larger than the
given operand.

next_minus($self, /, context=None)
--

Return the largest number representable in the given context (or in the
current default context if no context is given) that is smaller than the
given operand.

min_mag($self, /, other, context=None)
--

Similar to the min() method, but the comparison is done using the absolute
values of the operands.

min($self, /, other, context=None)
--

Minimum of self and other. If one operand is a quiet NaN and the other is
numeric, the numeric operand is returned.

max_mag($self, /, other, context=None)
--

Similar to the max() method, but the comparison is done using the absolute
values of the operands.

max($self, /, other, context=None)
--

Maximum of self and other.  If one operand is a quiet NaN and the other is
numeric, the numeric operand is returned.

logical_xor($self, /, other, context=None)
--

Return the digit-wise 'exclusive or' of the two (logical) operands.

logical_or($self, /, other, context=None)
--

Return the digit-wise 'or' of the two (logical) operands.

logical_invert($self, /, context=None)
--

Return the digit-wise inversion of the (logical) operand.

logical_and($self, /, other, context=None)
--

Return the digit-wise 'and' of the two (logical) operands.

logb($self, /, context=None)
--

For a non-zero number, return the adjusted exponent of the operand as a
Decimal instance.  If the operand is a zero, then Decimal('-Infinity') is
returned and the DivisionByZero condition is raised. If the operand is
an infinity then Decimal('Infinity') is returned.

log10($self, /, context=None)
--

Return the base ten logarithm of the operand. The function always uses the
ROUND_HALF_EVEN mode and the result is correctly rounded.

ln($self, /, context=None)
--

Return the natural (base e) logarithm of the operand. The function always
uses the ROUND_HALF_EVEN mode and the result is correctly rounded.

is_zero($self, /)
--

Return True if the argument is a (positive or negative) zero and False
otherwise.

is_subnormal($self, /, context=None)
--

Return True if the argument is subnormal, and False otherwise. A number is
subnormal if it is non-zero, finite, and has an adjusted exponent less
than Emin.

is_snan($self, /)
--

Return True if the argument is a signaling NaN and False otherwise.

is_signed($self, /)
--

Return True if the argument has a negative sign and False otherwise.
Note that both zeros and NaNs can carry signs.

is_qnan($self, /)
--

Return True if the argument is a quiet NaN, and False otherwise.

is_normal($self, /, context=None)
--

Return True if the argument is a normal finite non-zero number with an
adjusted exponent greater than or equal to Emin. Return False if the
argument is zero, subnormal, infinite or a NaN.

is_nan($self, /)
--

Return True if the argument is a (quiet or signaling) NaN and False
otherwise.

is_infinite($self, /)
--

Return True if the argument is either positive or negative infinity and
False otherwise.

is_finite($self, /)
--

Return True if the argument is a finite number, and False if the argument
is infinite or a NaN.

is_canonical($self, /)
--

Return True if the argument is canonical and False otherwise.  Currently,
a Decimal instance is always canonical, so this operation always returns
True.

fma($self, /, other, third, context=None)
--

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

    >>> Decimal(2).fma(3, 5)
    Decimal('11')


from_float($type, f, /)
--

Class method that converts a float to a decimal number, exactly.
Since 0.1 is not exactly representable in binary floating point,
Decimal.from_float(0.1) is not the same as Decimal('0.1').

    >>> Decimal.from_float(0.1)
    Decimal('0.1000000000000000055511151231257827021181583404541015625')
    >>> Decimal.from_float(float('nan'))
    Decimal('NaN')
    >>> Decimal.from_float(float('inf'))
    Decimal('Infinity')
    >>> Decimal.from_float(float('-inf'))
    Decimal('-Infinity')


exp($self, /, context=None)
--

Return the value of the (natural) exponential function e**x at the given
number.  The function always uses the ROUND_HALF_EVEN mode and the result
is correctly rounded.

copy_sign($self, /, other, context=None)
--

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

    >>> Decimal('2.3').copy_sign(Decimal('-1.5'))
    Decimal('-2.3')

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.

copy_negate($self, /)
--

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

copy_abs($self, /)
--

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

conjugate($self, /)
--

Return self.

compare_total_mag($self, /, other, context=None)
--

Compare two operands using their abstract representation rather than their
value as in 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()).

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.

compare_total($self, /, other, context=None)
--

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

    >>> Decimal('12.0').compare_total(Decimal('12'))
    Decimal('-1')

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.

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.

compare_signal($self, /, other, context=None)
--

Identical to compare, except that all NaNs signal.

compare($self, /, other, context=None)
--

Compare self to other.  Return a decimal value:

    a or b is a NaN ==> Decimal('NaN')
    a < b           ==> Decimal('-1')
    a == b          ==> Decimal('0')
    a > b           ==> Decimal('1')

canonical($self, /)
--

Return the canonical encoding of the argument.  Currently, the encoding
of a Decimal instance is always canonical, so this operation returns its
argument unchanged.

as_integer_ratio($self, /)
--

Decimal.as_integer_ratio() -> (int, int)

Return a pair of integers, whose ratio is exactly equal to the original
Decimal and with a positive denominator. The ratio is in lowest terms.
Raise OverflowError on infinities and a ValueError on NaNs.

as_tuple($self, /)
--

Return a tuple representation of the number.

adjusted($self, /)
--

Return the adjusted exponent of the number.  Defined as exp + digits - 1.

Decimal(value="0", context=None)
--

Construct a new Decimal object. 'value' can be an integer, string, tuple,
or another Decimal object. If no value is given, return Decimal('0'). The
context does not affect the conversion and is only passed to determine if
the InvalidOperation trap is active.

localcontext($module, /, ctx=None)
--

Return a context manager that will set the default context to a copy of ctx
on entry to the with-statement and restore the previous default context when
exiting the with-statement. If no context is specified, a copy of the current
default context is used.

setcontext($module, context, /)
--

Set a new default context.

getcontext($module, /)
--

Get the current default context.

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