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localcontext(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(c) - Set a new default context.


getcontext() - Get the current default context.


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


create_decimal(x) - Create a new Decimal instance from x, using self as the
context. Unlike the Decimal constructor, this function observes the context
limits.


copy() - Return a duplicate of the context with all flags cleared.


clear_traps() - Set all traps to False.


clear_flags() - Reset all flags to False.


shift(x, y) - Return a copy of x, shifted by y places.


scaleb(x, y) - Return the first operand after adding the second value
to its exp.


same_quantum(x, y) - Return True if the two operands have the same exponent.


rotate(x, y) - Return a copy of x, rotated by y places.


logical_xor(x, y) - Digit-wise xor of x and y.


logical_or(x, y) - Digit-wise or of x and y.


logical_and(x, y) - Digit-wise and of x and y.


copy_sign(x, y) - Copy the sign from y to x.


compare_total_mag(x, y) - Compare x and y using their abstract representation,
ignoring sign.


compare_total(x, y) - Compare x and y using their abstract representation.


to_eng_string(x) - Convert a number to a string, using engineering notation.


to_sci_string(x) - Convert a number to a string using scientific notation.


number_class(x) - Return an indication of the class of x.


logical_invert(x) - Invert all digits of x.


logb(x) - Return the exponent of the magnitude of the operand's MSD.


copy_negate(x) - Return a copy of x with the sign inverted.


copy_decimal(x) - Return a copy of Decimal x.


copy_abs(x) - Return a copy of x with the sign set to 0.


canonical(x) - Return a new instance of x.


is_zero(x) - Return True if x is a zero, False otherwise.


is_subnormal(x) - Return True if x is subnormal, False otherwise.


is_snan() - Return True if x is a signaling NaN, False otherwise.


is_signed(x) - Return True if x is negative, False otherwise.


is_qnan(x) - Return True if x is a quiet NaN, False otherwise.


is_normal(x) - Return True if x is a normal number, False otherwise.


is_nan(x) - Return True if x is a qNaN or sNaN, False otherwise.


is_infinite(x) - Return True if x is infinite, False otherwise.


is_finite(x) - Return True if x is finite, False otherwise.


is_canonical(x) - Return True if x is canonical, False otherwise.


radix() - Return 10.


Etop() - 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() - 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.


fma(x, y, z) - Return x multiplied by y, plus z.


power(x, y) - 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. In the Python version
the result is always correctly rounded, in the C version the result is
almost always correctly rounded.

power(x, y, m) - Compute (x**y) % m. The following restrictions hold:

    * all three arguments must be integral
    * y must be nonnegative
    * at least one of x or y must be nonzero
    * m must be nonzero and less than 10**prec in absolute value



subtract(x, y) - Return the difference between x and y.


remainder_near(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(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.


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


next_toward(x) - Return the number closest to x, in the direction towards y.


multiply(x, y) - Return the product of x and y.


min_mag(x, y) - Compare the values numerically with their sign ignored.


min(x, y) - Compare the values numerically and return the minimum.


max_mag(x, y) - Compare the values numerically with their sign ignored.


max(x, y) - Compare the values numerically and return the maximum.


divmod(x, y) - Return quotient and remainder of the division x / y.


divide_int(x, y) - Return x divided by y, truncated to an integer.


divide(x, y) - Return x divided by y.


compare_signal(x, y) - Compare x and y numerically. All NaNs signal.


compare(x, y) - Compare x and y numerically.


add(x, y) - Return the sum of x and y.


sqrt(x) - Square root of a non-negative number to context precision.


to_integral_value(x) - Round to an integer.


to_integral_exact(x) - Round to an integer. Signal if the result is
rounded or inexact.


to_integral(x) - Identical to to_integral_value(x).


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


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


next_plus(x) - Return the smallest representable number larger than x.


next_minus(x) - Return the largest representable number smaller than x.


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


log10(x) - Return the base 10 logarithm of x.


ln(x) - Return the natural (base e) logarithm of x.


exp(x) - Return e ** x.


abs(x) - Return the absolute value of x.


as_tuple() - Return a tuple representation of the number.


from_float(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')



shift(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(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.


rotate(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.


logical_xor(other, context=None) - Return the digit-wise exclusive or of the
two (logical) operands.


logical_or(other, context=None) - Return the digit-wise or of the two
(logical) operands.


logical_and(other, context=None) - Return the digit-wise and of the two
(logical) operands.


same_quantum(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.


copy_sign(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.


compare_total_mag(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(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.


to_eng_string(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.


number_class(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.



logical_invert(context=None) - Return the digit-wise inversion of the
(logical) operand.


logb(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.


copy_negate() - 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() - 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.


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


conjugate() - Return self.


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


adjusted() - Return the adjusted exponent of the number.

Defined as exp + digits - 1.


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


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


is_snan() - Return True if the argument is a signaling NaN and False otherwise.


is_qnan() - Return True if the argument is a quiet NaN, and False otherwise.


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


is_infinite() - Return True if the argument is either positive or negative
infinity and False otherwise.


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


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


fma(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')



remainder_near(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.


quantize(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.


next_toward(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.


min_mag(other, context=None) - Similar to the min() method, but the
comparison is done using the absolute values of the operands.


min(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(other, context=None) - Similar to the max() method, but the
comparison is done using the absolute values of the operands.


max(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.


compare_signal(other, context=None) - Identical to compare, except that
all NaNs signal.


compare(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')


sqrt(context=None) - Return the square root of the argument to full precision.
The result is correctly rounded using the ROUND_HALF_EVEN rounding mode.


to_integral_value(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(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(rounding=None, context=None) - Identical to the
to_integral_value() method. The to_integral() name has been kept
for compatibility with older versions.


normalize(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_plus(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(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.


log10(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(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.


exp(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.

C decimal arithmetic module
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=[])
    >>>



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.

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