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This is an implementation of decimal floating point arithmetic based on
the General Decimal Arithmetic Specification:
http://speleotrove.com/decimal/decarith.html
and IEEE standard 854-1987:
www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html
Decimal floating point has finite precision with arbitrarily large bounds.
The purpose of this module is to support arithmetic using familiar
"schoolhouse" rules and to avoid some of the tricky representation
issues associated with binary floating point. The package is especially
useful for financial applications or for contexts where users have
expectations that are at odds with binary floating point (for instance,
in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead
of 0.0; Decimal('1.00') % Decimal('0.1') returns the expected
Decimal('0.00')).
Here are some examples of using the decimal module:
>>> from decimal import *
>>> setcontext(ExtendedContext)
>>> Decimal(0)
Decimal('0')
>>> Decimal('1')
Decimal('1')
>>> Decimal('-.0123')
Decimal('-0.0123')
>>> Decimal(123456)
Decimal('123456')
>>> Decimal('123.45e12345678901234567890')
Decimal('1.2345E+12345678901234567892')
>>> Decimal('1.33') + Decimal('1.27')
Decimal('2.60')
>>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41')
Decimal('-2.20')
>>> dig = Decimal(1)
>>> print(dig / Decimal(3))
0.333333333
>>> getcontext().prec = 18
>>> print(dig / Decimal(3))
0.333333333333333333
>>> print(dig.sqrt())
1
>>> print(Decimal(3).sqrt())
1.73205080756887729
>>> print(Decimal(3) ** 123)
4.85192780976896427E+58
>>> inf = Decimal(1) / Decimal(0)
>>> print(inf)
Infinity
>>> neginf = Decimal(-1) / Decimal(0)
>>> print(neginf)
-Infinity
>>> print(neginf + inf)
NaN
>>> print(neginf * inf)
-Infinity
>>> print(dig / 0)
Infinity
>>> getcontext().traps[DivisionByZero] = 1
>>> print(dig / 0)
Traceback (most recent call last):
...
...
...
decimal.DivisionByZero: x / 0
>>> c = Context()
>>> c.traps[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> c.divide(Decimal(0), Decimal(0))
Decimal('NaN')
>>> c.traps[InvalidOperation] = 1
>>> print(c.flags[InvalidOperation])
1
>>> c.flags[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> print(c.divide(Decimal(0), Decimal(0)))
Traceback (most recent call last):
...
...
...
decimal.InvalidOperation: 0 / 0
>>> print(c.flags[InvalidOperation])
1
>>> c.flags[InvalidOperation] = 0
>>> c.traps[InvalidOperation] = 0
>>> print(c.divide(Decimal(0), Decimal(0)))
NaN
>>> print(c.flags[InvalidOperation])
1
>>>
u Decimalu Contextu DefaultContextu BasicContextu ExtendedContextu DecimalExceptionu Clampedu InvalidOperationu DivisionByZerou Inexactu Roundedu Subnormalu Overflowu Underflowu
ROUND_DOWNu
ROUND_HALF_UPu ROUND_HALF_EVENu
ROUND_CEILINGu ROUND_FLOORu ROUND_UPu ROUND_HALF_DOWNu
ROUND_05UPu
setcontextu
getcontextu localcontextu 1.70i N( u
namedtupleu DecimalTupleu sign digits exponentc G s | S( N( ( u args( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu <lambda>� s c B s | Ee Z d Z d � Z d S( u1 Base exception class.
Used exceptions derive from this.
If an exception derives from another exception besides this (such as
Underflow (Inexact, Rounded, Subnormal) that indicates that it is only
called if the others are present. This isn't actually used for
anything, though.
handle -- Called when context._raise_error is called and the
trap_enabler is not set. First argument is self, second is the
context. More arguments can be given, those being after
the explanation in _raise_error (For example,
context._raise_error(NewError, '(-x)!', self._sign) would
call NewError().handle(context, self._sign).)
To define a new exception, it should be sufficient to have it derive
from DecimalException.
c G s d S( N( ( u selfu contextu args( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu handle� s N( u __name__u
__module__u __doc__u handle( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu DecimalException� s
c B s | Ee Z d Z d S( u) Exponent of a 0 changed to fit bounds.
This occurs and signals clamped if the exponent of a result has been
altered in order to fit the constraints of a specific concrete
representation. This may occur when the exponent of a zero result would
be outside the bounds of a representation, or when a large normal
number would have an encoded exponent that cannot be represented. In
this latter case, the exponent is reduced to fit and the corresponding
number of zero digits are appended to the coefficient ("fold-down").
N( u __name__u
__module__u __doc__( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu Clamped� s
c B s | Ee Z d Z d � Z d S( u0 An invalid operation was performed.
Various bad things cause this:
Something creates a signaling NaN
-INF + INF
0 * (+-)INF
(+-)INF / (+-)INF
x % 0
(+-)INF % x
x._rescale( non-integer )
sqrt(-x) , x > 0
0 ** 0
x ** (non-integer)
x ** (+-)INF
An operand is invalid
The result of the operation after these is a quiet positive NaN,
except when the cause is a signaling NaN, in which case the result is
also a quiet NaN, but with the original sign, and an optional
diagnostic information.
c G s: | r6 t | d j | d j d d � } | j | � St S( Ni u nT( u _dec_from_tripleu _signu _intu Trueu _fix_nanu _NaN( u selfu contextu argsu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu handle� s #
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c B s | Ee Z d Z d � Z d S( u� Trying to convert badly formed string.
This occurs and signals invalid-operation if an string is being
converted to a number and it does not conform to the numeric string
syntax. The result is [0,qNaN].
c G s t S( N( u _NaN( u selfu contextu args( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu handle� s N( u __name__u
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u ConversionSyntaxc B s | Ee Z d Z d � Z d S( u� Division by 0.
This occurs and signals division-by-zero if division of a finite number
by zero was attempted (during a divide-integer or divide operation, or a
power operation with negative right-hand operand), and the dividend was
not zero.
The result of the operation is [sign,inf], where sign is the exclusive
or of the signs of the operands for divide, or is 1 for an odd power of
-0, for power.
c G s t | S( N( u _SignedInfinity( u selfu contextu signu args( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu handle� s N( u __name__u
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c B s | Ee Z d Z d � Z d S( u� Cannot perform the division adequately.
This occurs and signals invalid-operation if the integer result of a
divide-integer or remainder operation had too many digits (would be
longer than precision). The result is [0,qNaN].
c G s t S( N( u _NaN( u selfu contextu args( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu handle s N( u __name__u
__module__u __doc__u handle( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu DivisionImpossible� s
u DivisionImpossiblec B s | Ee Z d Z d � Z d S( u� Undefined result of division.
This occurs and signals invalid-operation if division by zero was
attempted (during a divide-integer, divide, or remainder operation), and
the dividend is also zero. The result is [0,qNaN].
c G s t S( N( u _NaN( u selfu contextu args( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu handle s N( u __name__u
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u DivisionUndefinedc B s | Ee Z d Z d S( u� Had to round, losing information.
This occurs and signals inexact whenever the result of an operation is
not exact (that is, it needed to be rounded and any discarded digits
were non-zero), or if an overflow or underflow condition occurs. The
result in all cases is unchanged.
The inexact signal may be tested (or trapped) to determine if a given
operation (or sequence of operations) was inexact.
N( u __name__u
__module__u __doc__( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu Inexact s
c B s | Ee Z d Z d � Z d S( u� Invalid context. Unknown rounding, for example.
This occurs and signals invalid-operation if an invalid context was
detected during an operation. This can occur if contexts are not checked
on creation and either the precision exceeds the capability of the
underlying concrete representation or an unknown or unsupported rounding
was specified. These aspects of the context need only be checked when
the values are required to be used. The result is [0,qNaN].
c G s t S( N( u _NaN( u selfu contextu args( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu handle& s N( u __name__u
__module__u __doc__u handle( u
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u InvalidContextc B s | Ee Z d Z d S( u� Number got rounded (not necessarily changed during rounding).
This occurs and signals rounded whenever the result of an operation is
rounded (that is, some zero or non-zero digits were discarded from the
coefficient), or if an overflow or underflow condition occurs. The
result in all cases is unchanged.
The rounded signal may be tested (or trapped) to determine if a given
operation (or sequence of operations) caused a loss of precision.
N( u __name__u
__module__u __doc__( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu Rounded) s
c B s | Ee Z d Z d S( u� Exponent < Emin before rounding.
This occurs and signals subnormal whenever the result of a conversion or
operation is subnormal (that is, its adjusted exponent is less than
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The subnormal signal may be tested (or trapped) to determine if a given
or operation (or sequence of operations) yielded a subnormal result.
N( u __name__u
__module__u __doc__( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu Subnormal5 s
c B s | Ee Z d Z d � Z d S( u Numerical overflow.
This occurs and signals overflow if the adjusted exponent of a result
(from a conversion or from an operation that is not an attempt to divide
by zero), after rounding, would be greater than the largest value that
can be handled by the implementation (the value Emax).
The result depends on the rounding mode:
For round-half-up and round-half-even (and for round-half-down and
round-up, if implemented), the result of the operation is [sign,inf],
where sign is the sign of the intermediate result. For round-down, the
result is the largest finite number that can be represented in the
current precision, with the sign of the intermediate result. For
round-ceiling, the result is the same as for round-down if the sign of
the intermediate result is 1, or is [0,inf] otherwise. For round-floor,
the result is the same as for round-down if the sign of the intermediate
result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded
will also be raised.
c G s� | j t t t t f k r# t | S| d k rk | j t k rF t | St | d | j | j | j d � S| d k r� | j t
k r� t | St | d | j | j | j d � Sd S( Ni u 9i ( u roundingu
ROUND_HALF_UPu ROUND_HALF_EVENu ROUND_HALF_DOWNu ROUND_UPu _SignedInfinityu
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c B s | Ee Z d Z d S( ux Numerical underflow with result rounded to 0.
This occurs and signals underflow if a result is inexact and the
adjusted exponent of the result would be smaller (more negative) than
the smallest value that can be handled by the implementation (the value
Emin). That is, the result is both inexact and subnormal.
The result after an underflow will be a subnormal number rounded, if
necessary, so that its exponent is not less than Etiny. This may result
in 0 with the sign of the intermediate result and an exponent of Etiny.
In all cases, Inexact, Rounded, and Subnormal will also be raised.
N( u __name__u
__module__u __doc__( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu Underflowf s
c B s | Ee Z e d � Z d S( c C s | j t S( N( u modulesu __name__( u selfu sys( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu local� s N( u __name__u
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setcontext� s
c C sF y t j � j SWn. t k
rA t � } | t j � _ | SYn Xd S( u� Returns this thread's context.
If this thread does not yet have a context, returns
a new context and sets this thread's context.
New contexts are copies of DefaultContext.
N( u threadingu current_threadu __decimal_context__u AttributeErroru Context( u context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
getcontext� s
c C s: y | j SWn( t k
r5 t � } | | _ | SYn Xd S( u� Returns this thread's context.
If this thread does not yet have a context, returns
a new context and sets this thread's context.
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getcontext� s
c C s; | t t t f k r. | j � } | j � n | | _ d S( u% Set this thread's context to context.N( u DefaultContextu BasicContextu ExtendedContextu copyu clear_flagsu __decimal_context__( u contextu _local( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
setcontext� s
c C s" | d k r t � } n t | � S( ub Return a context manager for a copy of the supplied context
Uses a copy of the current context if no context is specified
The returned context manager creates a local decimal context
in a with statement:
def sin(x):
with localcontext() as ctx:
ctx.prec += 2
# Rest of sin calculation algorithm
# uses a precision 2 greater than normal
return +s # Convert result to normal precision
def sin(x):
with localcontext(ExtendedContext):
# Rest of sin calculation algorithm
# uses the Extended Context from the
# General Decimal Arithmetic Specification
return +s # Convert result to normal context
>>> setcontext(DefaultContext)
>>> print(getcontext().prec)
28
>>> with localcontext():
... ctx = getcontext()
... ctx.prec += 2
... print(ctx.prec)
...
30
>>> with localcontext(ExtendedContext):
... print(getcontext().prec)
...
9
>>> print(getcontext().prec)
28
N( u Noneu
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t | j � | _ d | _ | St | t t f � rFt | � d k r�t d � � n t | d t � o�| d d k s�t d � � n | d | _ | d d k r+d
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>>> Decimal('3.14') # string input
Decimal('3.14')
>>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent)
Decimal('3.14')
>>> Decimal(314) # int
Decimal('314')
>>> Decimal(Decimal(314)) # another decimal instance
Decimal('314')
>>> Decimal(' 3.14 \n') # leading and trailing whitespace okay
Decimal('3.14')
u Invalid literal for Decimal: %ru signu -i i u intu fracu u expu 0u diagu signalu Nu nu Fi ut Invalid tuple size in creation of Decimal from list or tuple. The list or tuple should have exactly three elements.u| Invalid sign. The first value in the tuple should be an integer; either 0 for a positive number or 1 for a negative number.i i uT The second value in the tuple must be composed of integers in the range 0 through 9.uU The third value in the tuple must be an integer, or one of the strings 'F', 'n', 'N'.u Cannot convert %r to DecimalNFT( i i ( u nu N(" u objectu __new__u
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+
$
c C s� t | t � r | | � St j | � s7 t j | � rG | t | � � St j d | � d k rh d } n d } t | � j � \ } } | j � d } t
| t | d | � | � } | t k r� | S| | � Sd S( u. Converts a float to a decimal number, exactly.
Note that 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. The exact equivalent of the value in decimal
is 0.1000000000000000055511151231257827021181583404541015625.
>>> 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')
>>> Decimal.from_float(-0.0)
Decimal('-0')
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u
isinstanceu intu _mathu isinfu isnanu repru copysignu absu as_integer_ratiou
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from_float� s
! c C s9 | j r5 | j } | d k r" d S| d k r5 d Sn d S( ur Returns whether the number is not actually one.
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c C s� | j � } | d k r! d } n | j � } | s9 | r� | d k rQ t � } n | d k rp | j t d | � S| d k r� | j t d | � S| r� | j | � S| j | � Sd S( u� Returns whether the number is not actually one.
if self, other are sNaN, signal
if self, other are NaN return nan
return 0
Done before operations.
i u sNaNi NF( u _isnanu Noneu Falseu
getcontextu _raise_erroru InvalidOperationu _fix_nan( u selfu otheru contextu self_is_nanu other_is_nan( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _check_nans� s"
c C s� | d k r t � } n | j s* | j r� | j � rI | j t d | � S| j � rh | j t d | � S| j � r� | j t d | � S| j � r� | j t d | � Sn d S( uC Version of _check_nans used for the signaling comparisons
compare_signal, __le__, __lt__, __ge__, __gt__.
Signal InvalidOperation if either self or other is a (quiet
or signaling) NaN. Signaling NaNs take precedence over quiet
NaNs.
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u comparison involving sNaNu comparison involving NaNi N( u Noneu
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c C s | j p | j d k S( uu Return True if self is nonzero; otherwise return False.
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u� Compare the two non-NaN decimal instances self and other.
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self_adjustedu other_adjustedu self_paddedu other_padded( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _cmp" s> c C sT t | | d d �\ } } | t k r+ | S| j | | � rA d S| j | � d k S( Nu equality_opi TF( u _convert_for_comparisonu Trueu NotImplementedu _check_nansu Falseu _cmp( u selfu otheru context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __eq__b s c C sT t | | d d �\ } } | t k r+ | S| j | | � rA d S| j | � d k S( Nu equality_opi T( u _convert_for_comparisonu Trueu NotImplementedu _check_nansu _cmp( u selfu otheru context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __ne__j s c C sT t | | � \ } } | t k r% | S| j | | � } | rA d S| j | � d k S( Ni F( u _convert_for_comparisonu NotImplementedu _compare_check_nansu Falseu _cmp( u selfu otheru contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __lt__s s c C sT t | | � \ } } | t k r% | S| j | | � } | rA d S| j | � d k S( Ni F( u _convert_for_comparisonu NotImplementedu _compare_check_nansu Falseu _cmp( u selfu otheru contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __le__| s c C sT t | | � \ } } | t k r% | S| j | | � } | rA d S| j | � d k S( Ni F( u _convert_for_comparisonu NotImplementedu _compare_check_nansu Falseu _cmp( u selfu otheru contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __gt__� s c C sT t | | � \ } } | t k r% | S| j | | � } | rA d S| j | � d k S( Ni F( u _convert_for_comparisonu NotImplementedu _compare_check_nansu Falseu _cmp( u selfu otheru contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __ge__� s c C s\ t | d d �} | j s* | rI | j rI | j | | � } | rI | Sn t | j | � � S( u� Compares one to another.
-1 => a < b
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1 => a > b
NaN => one is NaN
Like __cmp__, but returns Decimal instances.
u raiseitT( u _convert_otheru Trueu _is_specialu _check_nansu Decimalu _cmp( u selfu otheru contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu compare� s c C s� | j rI | j � r$ t d � � qI | j � r4 t S| j rB t St Sn | j d k rp t d | j t � } n t t
| j t � } t | j � | t } | d k r� | n | } | d k r� d S| S( u x.__hash__() <==> hash(x)u" Cannot hash a signaling NaN value.i i
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u _is_specialu is_snanu TypeErroru is_nanu _PyHASH_NANu _signu _PyHASH_INFu _expu powu _PyHASH_MODULUSu
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( u DecimalTupleu _signu tupleu mapu intu _intu _exp( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu as_tuple� s c C s d t | � S( u0 Represents the number as an instance of Decimal.u
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| j | d � } | | k r�d } n7 | d k r�t � } n d d g | j d | | } | | | | S( u� Return string representation of the number in scientific notation.
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u u -u Fu Infinityu nu NaNu sNaNi i i u 0i u .Nu eu Eu %+di����( u _signu _is_specialu _expu _intu lenu Noneu
getcontextu capitals( u selfu engu contextu signu
leftdigitsu dotplaceu intpartu fracpartu exp( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __str__� s: c C s | j d d d | � S( u Convert to engineering-type string.
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u engu contextT( u __str__u True( u selfu context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
to_eng_string s c C s~ | j r( | j d | � } | r( | Sn | d k r@ t � } n | re | j t k re | j � } n | j � } | j | � S( uR Returns a copy with the sign switched.
Rounds, if it has reason.
u contextN( u _is_specialu _check_nansu Noneu
getcontextu roundingu ROUND_FLOORu copy_absu copy_negateu _fix( u selfu contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __neg__ s c C s~ | j r( | j d | � } | r( | Sn | d k r@ t � } n | re | j t k re | j � } n t | � } | j | � S( uh Returns a copy, unless it is a sNaN.
Rounds the number (if more then precision digits)
u contextN( u _is_specialu _check_nansu Noneu
getcontextu roundingu ROUND_FLOORu copy_absu Decimalu _fix( u selfu contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __pos__$ s c C sl | s | j � S| j r8 | j d | � } | r8 | Sn | j rV | j d | � } n | j d | � } | S( u� Returns the absolute value of self.
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expression self.__abs__(round=False) is equivalent to
self.copy_abs().
u context( u copy_absu _is_specialu _check_nansu _signu __neg__u __pos__( u selfu roundu contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __abs__9 s
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� } | j | � } | St | � } t | � } t | | | j � \ } } t � } | j | j k r�| j | j k rvt | d | � } | j | � } | S| j | j k r�| | } } n | j d k r�d | _ | j | j | _ | _ qd | _ n6 | j d k rd | _ d \ | _ | _ n d | _ | j d k r3| j | j | _ n | j | j | _ | j | _ t
| � } | j | � } | S( ub Returns self + other.
-INF + INF (or the reverse) cause InvalidOperation errors.
u
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! c C si t | � } | t k r | S| j s. | j rP | j | d | �} | rP | Sn | j | j � d | �S( u Return self - otheru context( u _convert_otheru NotImplementedu _is_specialu _check_nansu __add__u copy_negate( u selfu otheru contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __sub__� s c C s/ t | � } | t k r | S| j | d | �S( u Return other - selfu context( u _convert_otheru NotImplementedu __sub__( u selfu otheru context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __rsub__� s c C s� t | � } | t k r | S| d k r4 t � } n | j | j A} | j sV | j r� | j | | � } | rr | S| j � r� | s� | j t d � St
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| � } | S( u\ Return self * other.
(+-) INF * 0 (or its reverse) raise InvalidOperation.
u (+-)INF * 0u 0 * (+-)INFu 0u 1N( u _convert_otheru NotImplementedu Noneu
getcontextu _signu _is_specialu _check_nansu _isinfinityu _raise_erroru InvalidOperationu _SignedInfinityu _expu _dec_from_tripleu _fixu _intu _WorkRepu stru int( u selfu otheru contextu
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| S| j � r� | j t d � t | d | j
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n$ t | j | j d | � \ } }
|
r | d d k rG| d 7} qGnG | j | j } x4 | | k rF| d d k rF| d } | d 7} qWt | t | � | � } | j | � S( u Return self / other.u (+-)INF/(+-)INFu Division by infinityu 0u 0 / 0u x / 0i i i
i N( u _convert_otheru NotImplementedu Noneu
getcontextu _signu _is_specialu _check_nansu _isinfinityu _raise_erroru InvalidOperationu _SignedInfinityu Clampedu _dec_from_tripleu Etinyu DivisionUndefinedu DivisionByZerou _expu lenu _intu precu _WorkRepu divmodu intu stru _fix( u selfu otheru contextu signu ansu expu coeffu shiftu op1u op2u remainderu ideal_exp( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __truediv__� sP ' &$
c C s� | j | j A} | j � r( | j } n t | j | j � } | j � | j � } | sr | j � sr | d k r� t | d d � | j | | j � f S| | j k rot | � } t | � } | j
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f S( u� Return (self // other, self % other), to context.prec precision.
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infinite and that other is nonzero.
i u 0i i
u% quotient too large in //, % or divmodi����( u _signu _isinfinityu _expu minu adjustedu _dec_from_tripleu _rescaleu roundingu precu _WorkRepu expu intu divmodu stru _raise_erroru DivisionImpossible( u selfu otheru contextu signu ideal_expu expdiffu op1u op2u qu ru ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _divide1 s* c C s/ t | � } | t k r | S| j | d | �S( u) Swaps self/other and returns __truediv__.u context( u _convert_otheru NotImplementedu __truediv__( u selfu otheru context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __rtruediv__R s c C s8 t | � } | t k r | S| d k r4 t � } n | j | | � } | rV | | f S| j | j A} | j � r� | j � r� | j t d � } | | f St | | j t d � f Sn | s| s� | j t
d � } | | f S| j t d | � | j t d � f Sn | j | | � \ } } | j
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u divmod(INF, INF)u INF % xu divmod(0, 0)u x // 0u x % 0N( u _convert_otheru NotImplementedu Noneu
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__divmod__Y s0
c C s/ t | � } | t k r | S| j | d | �S( u( Swaps self/other and returns __divmod__.u context( u _convert_otheru NotImplementedu
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| � St | j | j � } | s� t
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| � St | � } t | � } | j | j k r�| j d | j | j 9_ n | j d | j | j 9_ t | j | j � \ } } d | | d @| j k r| | j 8} | d 7} n | d | j k r.| j t � S| j }
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c C s� t | � } | t k r | S| d k r4 t � } n | j | | � } | rP | S| j � r� | j � rx | j t d � St | j | j ASn | s� | r� | j t
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__rfloordiv__
s c C sU | j � r? | j � r' t d � � n | j r6 d n d } n t | � } t | � S( u Float representation.u% Cannot convert signaling NaN to floatu -nanu nan( u _isnanu is_snanu
ValueErroru _signu stru float( u selfu s( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __float__ s c C s� | j rB | j � r$ t d � � qB | j � rB t d � � qB n d | j } | j d k rz | t | j � d | j S| t | j d | j � p� d � Sd S( u1 Converts self to an int, truncating if necessary.u Cannot convert NaN to integeru" Cannot convert infinity to integeri i i
Nu 0i����( u _is_specialu _isnanu
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c C s | S( N( ( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu real- s c C s
t d � S( Ni ( u Decimal( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu imag1 s c C s | S( N( ( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu conjugate5 s c C s t t | � � S( N( u complexu float( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __complex__8 s c C sq | j } | j | j } t | � | k rg | t | � | d � j d � } t | j | | j d � St | � S( u2 Decapitate the payload of a NaN to fit the contextNu 0T(
u _intu precu clampu lenu lstripu _dec_from_tripleu _signu _expu Trueu Decimal( u selfu contextu payloadu max_payload_len( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _fix_nan; s #c C s; | j r/ | j � r" | j | � St | � Sn | j � } | j � } | s� | j | g | j } t t | j
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| | � } | j d | � p�d } | d k rt t | � d � } t | � | j k r| d d � } | d 7} qn | | k rA| j t d | j � } n t
| j | | � } | rr| rr| j t � n | r�| j t � n | r�| j t � n | j t � | s�| j t � n | S| r�| j t � n | j d k r1| j
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| � St | � S( u� Round if it is necessary to keep self within prec precision.
Rounds and fixes the exponent. Does not raise on a sNaN.
Arguments:
self - Decimal instance
context - context used.
u 0u
above Emaxi u 1i Ni����( u _is_specialu _isnanu _fix_nanu Decimalu Etinyu Etopu Emaxu clampu minu maxu _expu _raise_erroru Clampedu _dec_from_tripleu _signu lenu _intu precu Overflowu Inexactu Roundedu _pick_rounding_functionu roundingu stru intu Underflowu Subnormal( u selfu contextu Etinyu Etopu exp_maxu new_expu exp_minu ansu self_is_subnormalu digitsu rounding_methodu changedu coeffu self_padded( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _fixG sn
c C s t | j | � r d Sd Sd S( u( Also known as round-towards-0, truncate.i i Ni����( u
_all_zerosu _int( u selfu prec( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _round_down� s c C s | j | � S( u Rounds away from 0.( u _round_down( u selfu prec( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _round_up� s c C s5 | j | d k r d St | j | � r- d Sd Sd S( u Rounds 5 up (away from 0)u 56789i i Ni����( u _intu
_all_zeros( u selfu prec( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _round_half_up� s
c C s' t | j | � r d S| j | � Sd S( u Round 5 downi Ni����( u _exact_halfu _intu _round_half_up( u selfu prec( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _round_half_down� s c C sJ t | j | � r9 | d k s5 | j | d d k r9 d S| j | � Sd S( u! Round 5 to even, rest to nearest.i i u 02468Ni����( u _exact_halfu _intu _round_half_up( u selfu prec( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _round_half_even� s #c C s( | j r | j | � S| j | � Sd S( u( Rounds up (not away from 0 if negative.)N( u _signu _round_down( u selfu prec( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _round_ceiling� s
c C s( | j s | j | � S| j | � Sd S( u' Rounds down (not towards 0 if negative)N( u _signu _round_down( u selfu prec( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _round_floor� s
c C s< | r* | j | d d k r* | j | � S| j | � Sd S( u) Round down unless digit prec-1 is 0 or 5.i u 05N( u _intu _round_down( u selfu prec( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _round_05up� s
u
ROUND_DOWNu ROUND_UPu
ROUND_HALF_UPu ROUND_HALF_DOWNu ROUND_HALF_EVENu
ROUND_CEILINGu ROUND_FLOORu
ROUND_05UPc C s� | d k rJ t | t � s* t d � � n t d d | � } | j | � S| j r} | j � rn t d � � q} t d � � n t | j
d t � � S( u� Round self to the nearest integer, or to a given precision.
If only one argument is supplied, round a finite Decimal
instance self to the nearest integer. If self is infinite or
a NaN then a Python exception is raised. If self is finite
and lies exactly halfway between two integers then it is
rounded to the integer with even last digit.
>>> round(Decimal('123.456'))
123
>>> round(Decimal('-456.789'))
-457
>>> round(Decimal('-3.0'))
-3
>>> round(Decimal('2.5'))
2
>>> round(Decimal('3.5'))
4
>>> round(Decimal('Inf'))
Traceback (most recent call last):
...
OverflowError: cannot round an infinity
>>> round(Decimal('NaN'))
Traceback (most recent call last):
...
ValueError: cannot round a NaN
If a second argument n is supplied, self is rounded to n
decimal places using the rounding mode for the current
context.
For an integer n, round(self, -n) is exactly equivalent to
self.quantize(Decimal('1En')).
>>> round(Decimal('123.456'), 0)
Decimal('123')
>>> round(Decimal('123.456'), 2)
Decimal('123.46')
>>> round(Decimal('123.456'), -2)
Decimal('1E+2')
>>> round(Decimal('-Infinity'), 37)
Decimal('NaN')
>>> round(Decimal('sNaN123'), 0)
Decimal('NaN123')
u+ Second argument to round should be integrali u 1u cannot round a NaNu cannot round an infinityN( u Noneu
isinstanceu intu TypeErroru _dec_from_tripleu quantizeu _is_specialu is_nanu
ValueErroru
OverflowErroru _rescaleu ROUND_HALF_EVEN( u selfu nu exp( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __round__� s /
c C sI | j r3 | j � r$ t d � � q3 t d � � n t | j d t � � S( u� Return the floor of self, as an integer.
For a finite Decimal instance self, return the greatest
integer n such that n <= self. If self is infinite or a NaN
then a Python exception is raised.
u cannot round a NaNu cannot round an infinityi ( u _is_specialu is_nanu
ValueErroru
OverflowErroru intu _rescaleu ROUND_FLOOR( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __floor__. s
c C sI | j r3 | j � r$ t d � � q3 t d � � n t | j d t � � S( u� Return the ceiling of self, as an integer.
For a finite Decimal instance self, return the least integer n
such that n >= self. If self is infinite or a NaN then a
Python exception is raised.
u cannot round a NaNu cannot round an infinityi ( u _is_specialu is_nanu
ValueErroru
OverflowErroru intu _rescaleu
ROUND_CEILING( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __ceil__= s
c C s� t | d d �} | j s$ | j r+| d k r< t � } n | j d k r^ | j t d | � S| j d k r� | j t d | � S| j d k r� | } qm| j d k r� | } qm| j d k r� | s� | j t d � St | j | j A} qm| j d k rm| s| j t d � St | j | j A} qmnB t
| j | j At t | j
� t | j
� � | j | j � } t | d d �} | j | | � S(
u: Fused multiply-add.
Returns self*other+third with no rounding of the intermediate
product self*other.
self and other are multiplied together, with no rounding of
the result. The third operand is then added to the result,
and a single final rounding is performed.
u raiseitu Nu sNaNu nu Fu INF * 0 in fmau 0 * INF in fmaTN( u _convert_otheru Trueu _is_specialu Noneu
getcontextu _expu _raise_erroru InvalidOperationu _SignedInfinityu _signu _dec_from_tripleu stru intu _intu __add__( u selfu otheru thirdu contextu product( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu fmaL s6 c
C sz t | d d �} t | d d �} | d k r< t � } n | j � } | j � } | j � } | sr | sr | r| d k r� | j t d | � S| d k r� | j t d | � S| d k r� | j t d | � S| r� | j | � S| r� | j | � S| j | � S| j � o#| j � o#| j � s6| j t d � S| d k rR| j t d � S| sh| j t d � S| j � | j
k r�| j t d � S| r�| r�| j t d � S| j � r�d } n | j } t
t | � � } t | j � � } t | j � � } | j | t d
| j | � | } x) t | j � D] }
t | d
| � } q3Wt | | j | � } t | t | � d � S(
u! Three argument version of __pow__u raiseiti u sNaNu@ pow() 3rd argument not allowed unless all arguments are integersi uA pow() 2nd argument cannot be negative when 3rd argument specifiedu pow() 3rd argument cannot be 0uS insufficient precision: pow() 3rd argument must not have more than precision digitsuX at least one of pow() 1st argument and 2nd argument must be nonzero ;0**0 is not definedi
TN( u _convert_otheru Trueu Noneu
getcontextu _isnanu _raise_erroru InvalidOperationu _fix_nanu
_isintegeru adjustedu precu _isevenu _signu absu intu _WorkRepu to_integral_valueu powu expu rangeu _dec_from_tripleu str( u selfu otheru modulou contextu self_is_nanu other_is_nanu
modulo_is_nanu signu baseu exponentu i( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_power_modulox sd
$c C sz t | � } | j | j } } x( | d d k rI | d } | d 7} q" Wt | � } | j | j } } x( | d d k r� | d } | d 7} ql W| d k rv| | 9} x( | d d k r� | d } | d 7} q� W| d k r� d S| d | } | j d k r | } n | j � rT| j d k rT| j t | � }
t | |
| d � } n d } t d d d | | | � S| j d k r�| d } | d k rg| | @| k r�d St
| � d }
| d k r�| d | } |
| }
| | } nQ d | } t |
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} | r d St | | | � \ } } | rBd S|
d
| d k rZd Sd |
} n| d k r|t
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d
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t d |
| � \ } } | r�d Sx( | d d k r�| d } |
d 8}
q�W| d k r| d | } |
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| | } nQ d | } t |
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} | r4d St | | | � \ } } | rWd S|
d | d k rod Sd |
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| } t d t | � | � S| d k r�| d | d } } n| d k r t
t t | | � � � | k r d St
| � } | d k rKt
t t | � | � � | k rKd S| d | } } x< | d | d k od k n r�| d } | d } q`Wx< | d | d k o�d k n r�| d } | d } q�W| d k r�| d k r| | k rd St | | � \ } } | d k r(d Sd t
| � | >} xF t | | | d � \ } } | | k rnPqA| | d | | } qA| | k o�| d k s�d S| } n | d k r�| | d t | � k r�d S| | } | | 9} | d | k r�d St | � } | j � rX| j d k rX| j t | � }
t | |
| t
| � � } n d } t d | d | | | � S( uh Attempt to compute self**other exactly.
Given Decimals self and other and an integer p, attempt to
compute an exact result for the power self**other, with p
digits of precision. Return None if self**other is not
exactly representable in p digits.
Assumes that elimination of special cases has already been
performed: self and other must both be nonspecial; self must
be positive and not numerically equal to 1; other must be
nonzero. For efficiency, other._exp should not be too large,
so that 10**abs(other._exp) is a feasible calculation.i
i i u 1u 0i i i i iA i] i i i id N( i i i i ( u _WorkRepu intu expu Noneu signu
_isintegeru _signu _expu minu _dec_from_tripleu _nbitsu divmodu stru lenu absu _log10_lb( u selfu otheru pu xu xcu xeu yu ycu yeu exponentu ideal_exponentu zerosu
last_digitu eu y_as_intu ten_powu remainderu y_as_integeru mu nu xc_bitsu remu au qu ru str_xc( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _power_exact� s� ;
/ /'
'
&
c C s� | d k r | j | | | � St | � } | t k r; | S| d k rS t � } n | j | | � } | ro | S| s� | s� | j t d � St Sn d } | j d k r� | j
� r� | j � s� d } q� n | r� | j t d � S| j � } n | s | j d k rt
| d d � St | Sn | j � rV| j d k rCt | St
| d d � Sn | t k r-| j
� r�| j d k r�d } n' | | j k r�| j } n t | � } | j | } | d | j k rd | j } | j t � qn' | j t � | j t � d | j } t
| d d | | � S| j � } | j � r{| j d k | d k k rpt
| d d � St | Sn d } d } | j � | j � }
| d k | j d k k r�|
t t | j � � k r0t
| d | j d � } q0n> | j � } |
t t | � � k r0t
| d | d � } n | d k r�| j | | j d � } | d k r�| d k r�t
d | j | j � } n d
} q�n | d k r}| j } t | � }
|
j |
j } } t | � } | j | j } } | j! d k r | } n d } xY t" | | | | | | � \ } } | d d t t | � � | d rUPn | d 7} q t
| t | � | � } n | r�| j
� r�t | j � | j k r�| j d t | j � } t
| j | j d | | j | � } n | j# � } | j$ � x t% D] } d | j& | <q W| j' | � } | j t � | j( t) rY| j t* � n | j( t+ r| j t+ d
| j � n xL t* t) t t t, f D]# } | j( | r�| j | � q�q�Wn | j' | � } | S( uH Return self ** other [ % modulo].
With two arguments, compute self**other.
With three arguments, compute (self**other) % modulo. For the
three argument form, the following restrictions on the
arguments hold:
- all three arguments must be integral
- other must be nonnegative
- either self or other (or both) must be nonzero
- modulo must be nonzero and must have at most p digits,
where p is the context precision.
If any of these restrictions is violated the InvalidOperation
flag is raised.
The result of pow(self, other, modulo) is identical to the
result that would be obtained by computing (self**other) %
modulo with unbounded precision, but is computed more
efficiently. It is always exact.
u 0 ** 0i i u+ x ** y with x negative and y not an integeru 0u 1i i i
u
above EmaxNFT(- u Noneu
_power_modulou _convert_otheru NotImplementedu
getcontextu _check_nansu _raise_erroru InvalidOperationu _Oneu _signu
_isintegeru _isevenu copy_negateu _dec_from_tripleu _SignedInfinityu _isinfinityu precu intu _expu Roundedu Inexactu adjustedu Falseu _log10_exp_boundu lenu stru Emaxu Etinyu _power_exactu _intu Trueu _WorkRepu expu signu _dpoweru copyu clear_flagsu _signalsu trapsu _fixu flagsu Subnormalu Underflowu Overflowu Clamped( u selfu otheru modulou contextu ansu result_signu
multiplieru expu self_adju exactu boundu Etinyu pu xu xcu xeu yu ycu yeu extrau coeffu expdiffu
newcontextu exception( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __pow__� s�
"&
c C s/ t | � } | t k r | S| j | d | �S( u% Swaps self/other and returns __pow__.u context( u _convert_otheru NotImplementedu __pow__( u selfu otheru context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __rpow__{ s c C s
| d k r t � } n | j r@ | j d | � } | r@ | Sn | j | � } | j � r_ | S| sx t | j d d � S| j | j � g | j
} t | j � } | j
} x; | j | d d k r� | | k r� | d 7} | d 8} q� Wt | j | j d | � | � S( u? Normalize- strip trailing 0s, change anything equal to 0 to 0e0u contextu 0i i N( u Noneu
getcontextu _is_specialu _check_nansu _fixu _isinfinityu _dec_from_tripleu _signu Emaxu Etopu clampu lenu _intu _exp( u selfu contextu ansu dupu exp_maxu endu exp( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu normalize� s$ &
c C s� t | d d �} | d k r* t � } n | d k rB | j } n | j sT | j r� | j | | � } | rp | S| j � s� | j � r� | j � r� | j � r� t | � S| j t
d � Sn | s| j | j | � } | j | j k r| j t
� | | k r| j t � qn | S| j � | j k o=| j k n sR| j t
d � S| s}t | j d | j � } | j | � S| j � } | | j k r�| j t
d � S| | j d | j k r�| j t
d � S| j | j | � } | j � | j k r | j t
d � St | j � | j k r4| j t
d � S| r_| j � | j k r_| j t � n | j | j k r�| | k r�| j t � n | j t
� n | j | � } | S(
u� Quantize self so its exponent is the same as that of exp.
Similar to self._rescale(exp._exp) but with error checking.
u raiseitu quantize with one INFu) target exponent out of bounds in quantizeu 0u9 exponent of quantize result too large for current contexti u7 quantize result has too many digits for current contextTN( u _convert_otheru Trueu Noneu
getcontextu roundingu _is_specialu _check_nansu _isinfinityu Decimalu _raise_erroru InvalidOperationu _rescaleu _expu Roundedu Inexactu Etinyu Emaxu _dec_from_tripleu _signu _fixu adjustedu precu lenu _intu Eminu Subnormal( u selfu expu roundingu contextu watchexpu ansu
self_adjusted( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu quantize� sb
(
c C sb t | d d �} | j s$ | j rR | j � r< | j � pQ | j � oQ | j � S| j | j k S( u= Return True if self and other have the same exponent; otherwise
return False.
If either operand is a special value, the following rules are used:
* return True if both operands are infinities
* return True if both operands are NaNs
* otherwise, return False.
u raiseitT( u _convert_otheru Trueu _is_specialu is_nanu is_infiniteu _exp( u selfu other( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu same_quantum� s
c C s | j r t | � S| s, t | j d | � S| j | k r` t | j | j d | j | | � St | j � | j | } | d k r� t | j d | d � } d } n | j | } | | | � } | j d | � p� d } | d k rt t | � d � } n t | j | | � S( us Rescale self so that the exponent is exp, either by padding with zeros
or by truncating digits, using the given rounding mode.
Specials are returned without change. This operation is
quiet: it raises no flags, and uses no information from the
context.
exp = exp to scale to (an integer)
rounding = rounding mode
u 0i u 1i N(
u _is_specialu Decimalu _dec_from_tripleu _signu _expu _intu lenu _pick_rounding_functionu stru int( u selfu expu roundingu digitsu
this_functionu changedu coeff( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _rescale� s"
c C s� | d k r t d � � n | j s+ | r5 t | � S| j | j � d | | � } | j � | j � k r� | j | j � d | | � } n | S( u" Round a nonzero, nonspecial Decimal to a fixed number of
significant figures, using the given rounding mode.
Infinities, NaNs and zeros are returned unaltered.
This operation is quiet: it raises no flags, and uses no
information from the context.
i u' argument should be at least 1 in _roundi ( u
ValueErroru _is_specialu Decimalu _rescaleu adjusted( u selfu placesu roundingu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _round
s
#c C s� | j r/ | j d | � } | r% | St | � S| j d k rH t | � S| sa t | j d d � S| d k ry t � } n | d k r� | j } n | j d | � } | | k r� | j
t � n | j
t � | S( uV Rounds to a nearby integer.
If no rounding mode is specified, take the rounding mode from
the context. This method raises the Rounded and Inexact flags
when appropriate.
See also: to_integral_value, which does exactly the same as
this method except that it doesn't raise Inexact or Rounded.
u contexti u 0N(
u _is_specialu _check_nansu Decimalu _expu _dec_from_tripleu _signu Noneu
getcontextu roundingu _rescaleu _raise_erroru Inexactu Rounded( u selfu roundingu contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu to_integral_exact*
s$
c C s� | d k r t � } n | d k r0 | j } n | j r_ | j d | � } | rU | St | � S| j d k rx t | � S| j d | � Sd S( u@ Rounds to the nearest integer, without raising inexact, rounded.u contexti N( u Noneu
getcontextu roundingu _is_specialu _check_nansu Decimalu _expu _rescale( u selfu roundingu contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu to_integral_valueG
s
c C s~ | d
k r t � } n | j re | j d | � } | r= | S| j � re | j d k re t | � Sn | s� t | j d | j d � } | j | � S| j d k r� | j
t d � S| j d } t
| � } | j d ?} | j d @r
| j d } t | j � d ?d } n | j } t | j � d d ?} | | } | d k rZ| d | 9} d } n! t | d | � \ } }
|
} | | 8} d | } x+ | | } | | k r�Pq�| | d ?} q�| o�| | | k } | r| d k r�| d | } n | d | 9} | | 7} n | d d k r/| d 7} n t d t | � | � } | j � } | j t � }
| j | � } |
| _ | S( u Return the square root of self.u contexti u 0i i u sqrt(-x), x > 0i
id i NT( u Noneu
getcontextu _is_specialu _check_nansu _isinfinityu _signu Decimalu _dec_from_tripleu _expu _fixu _raise_erroru InvalidOperationu precu _WorkRepu expu intu lenu _intu Trueu divmodu stru
_shallow_copyu
_set_roundingu ROUND_HALF_EVENu rounding( u selfu contextu ansu precu opu eu cu lu shiftu exactu remainderu nu qu rounding( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu sqrtZ
s`
c C s t | d d �} | d k r* t � } n | j s< | j r� | j � } | j � } | s` | r� | d k r� | d k r� | j | � S| d k r� | d k r� | j | � S| j | | � Sn | j | � } | d k r� | j | � } n | d k r� | } n | } | j | � S( u� Returns the larger value.
Like max(self, other) except if one is not a number, returns
NaN (and signals if one is sNaN). Also rounds.
u raiseiti i TNi����(
u _convert_otheru Trueu Noneu
getcontextu _is_specialu _isnanu _fixu _check_nansu _cmpu
compare_total( u selfu otheru contextu snu onu cu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu max�
s&
c C s t | d d �} | d k r* t � } n | j s< | j r� | j � } | j � } | s` | r� | d k r� | d k r� | j | � S| d k r� | d k r� | j | � S| j | | � Sn | j | � } | d k r� | j | � } n | d k r� | } n | } | j | � S( u� Returns the smaller value.
Like min(self, other) except if one is not a number, returns
NaN (and signals if one is sNaN). Also rounds.
u raiseiti i TNi����(
u _convert_otheru Trueu Noneu
getcontextu _is_specialu _isnanu _fixu _check_nansu _cmpu
compare_total( u selfu otheru contextu snu onu cu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu min�
s&
c C sJ | j r
d S| j d k r d S| j | j d � } | d t | � k S( u" Returns whether self is an integeri Nu 0FT( u _is_specialu Falseu _expu Trueu _intu len( u selfu rest( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_isinteger s c C s2 | s | j d k r d S| j d | j d k S( u: Returns True if self is even. Assumes self is an integer.i i u 02468Ti����( u _expu Trueu _int( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _iseven s c C s9 y | j t | j � d SWn t k
r4 d SYn Xd S( u$ Return the adjusted exponent of selfi i N( u _expu lenu _intu TypeError( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu adjusted s
c C s | S( u� Returns the same Decimal object.
As we do not have different encodings for the same number, the
received object already is in its canonical form.
( ( u selfu context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu canonical s c C sA t | d d �} | j | | � } | r. | S| j | d | �S( u� Compares self to the other operand numerically.
It's pretty much like compare(), but all NaNs signal, with signaling
NaNs taking precedence over quiet NaNs.
u raiseitu contextT( u _convert_otheru Trueu _compare_check_nansu compare( u selfu otheru contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu compare_signal( s
c C s� t | d d �} | j r) | j r) t S| j r@ | j r@ t S| j } | j � } | j � } | sm | rs| | k r� t | j � | j f } t | j � | j f } | | k r� | r� t St Sn | | k r� | r� t St Sn t S| r0| d k r� t S| d k r
t S| d k r t S| d k rpt Sqs| d k r@t S| d k rPt S| d k r`t S| d k rst Sn | | k r�t S| | k r�t S| j | j k r�| r�t St Sn | j | j k r�| r�t St Sn t S( u� Compares self to other using the abstract representations.
This is not like the standard compare, which use their numerical
value. Note that a total ordering is defined for all possible abstract
representations.
u raiseiti i T(
u _convert_otheru Trueu _signu _NegativeOneu _Oneu _isnanu lenu _intu _Zerou _exp( u selfu otheru signu self_nanu other_nanu self_keyu other_key( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
compare_total4 sf c C s7 t | d d �} | j � } | j � } | j | � S( u� Compares self to other using abstract repr., ignoring sign.
Like compare_total, but with operand's sign ignored and assumed to be 0.
u raiseitT( u _convert_otheru Trueu copy_absu
compare_total( u selfu otheru su o( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu compare_total_mag} s c C s t d | j | j | j � S( u' Returns a copy with the sign set to 0. i ( u _dec_from_tripleu _intu _expu _is_special( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu copy_abs� s c C sE | j r% t d | j | j | j � St d | j | j | j � Sd S( u& Returns a copy with the sign inverted.i i N( u _signu _dec_from_tripleu _intu _expu _is_special( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu copy_negate� s c C s1 t | d d �} t | j | j | j | j � S( u$ Returns self with the sign of other.u raiseitT( u _convert_otheru Trueu _dec_from_tripleu _signu _intu _expu _is_special( u selfu other( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu copy_sign� s c
C s� | d
k r t � } n | j d | � } | r4 | S| j � d k rJ t S| sT t S| j � d k rp t | � S| j } | j � } | j d k r� | t
t | j d d � � k r� t
d d | j d � } n�| j d k r(| t
t | j � d d � � k r(t
d d | j � d � } n0| j d k rj| | k rjt
d d d | d d | � } n� | j d k r�| | d k r�t
d d | d | d � } n� t | � } | j | j } } | j d k r�| } n d } xS t | | | | � \ } }
| d d t
t | � � | d r3Pn | d 7} q�t
d t | � |
� } | j � } | j t � } | j | � } | | _ | S( u Returns e ** self.u contexti i i u 1u 0u 9i i
Ni����( u Noneu
getcontextu _check_nansu _isinfinityu _Zerou _Oneu Decimalu precu adjustedu _signu lenu stru Emaxu _dec_from_tripleu Etinyu _WorkRepu intu expu signu _dexpu
_shallow_copyu
_set_roundingu ROUND_HALF_EVENu _fixu rounding( u selfu contextu ansu pu adju opu cu eu extrau coeffu expu rounding( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu exp� sJ
2 6 & "
&
c C s d S( u� Return True if self is canonical; otherwise return False.
Currently, the encoding of a Decimal instance is always
canonical, so this method returns True for any Decimal.
T( u True( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_canonical� s c C s | j S( u� Return True if self is finite; otherwise return False.
A Decimal instance is considered finite if it is neither
infinite nor a NaN.
( u _is_special( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_finite� s c C s
| j d k S( u8 Return True if self is infinite; otherwise return False.u F( u _exp( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_infinite� s c C s
| j d k S( u> Return True if self is a qNaN or sNaN; otherwise return False.u nu N( u nu N( u _exp( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_nan� s c C s? | j s | r d S| d k r, t � } n | j | j � k S( u? Return True if self is a normal number; otherwise return False.FN( u _is_specialu Falseu Noneu
getcontextu Eminu adjusted( u selfu context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_normal� s
c C s
| j d k S( u; Return True if self is a quiet NaN; otherwise return False.u n( u _exp( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_qnan s c C s
| j d k S( u8 Return True if self is negative; otherwise return False.i ( u _sign( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_signed s c C s
| j d k S( u? Return True if self is a signaling NaN; otherwise return False.u N( u _exp( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_snan s c C s? | j s | r d S| d k r, t � } n | j � | j k S( u9 Return True if self is subnormal; otherwise return False.FN( u _is_specialu Falseu Noneu
getcontextu adjustedu Emin( u selfu context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_subnormal s
c C s | j o | j d k S( u6 Return True if self is a zero; otherwise return False.u 0( u _is_specialu _int( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_zero s c C s� | j t | j � d } | d k rB t t | d d � � d S| d k rn t t d | d d � � d St | � } | j | j } } | d k r� t | d | � } t | � } t | � t | � | | k S| t t d | | � � d S( u� Compute a lower bound for the adjusted exponent of self.ln().
In other words, compute r such that self.ln() >= 10**r. Assumes
that self is finite and positive and that self != 1.
i i i
i i i����i����( u _expu lenu _intu stru _WorkRepu intu exp( u selfu adju opu cu eu numu den( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_ln_exp_bound s c
C ss | d k r t � } n | j d | � } | r4 | S| s> t S| j � d k rT t S| t k rd t S| j d k r� | j t
d � St | � } | j | j
} } | j } | | j � d } xO t | | | � } | d d t t t | � � � | d rPn | d 7} q� t t | d k � t t | � � | � } | j � } | j t � } | j | � } | | _ | S(
u/ Returns the natural (base e) logarithm of self.u contexti u ln of a negative valuei i i
i i N( u Noneu
getcontextu _check_nansu _NegativeInfinityu _isinfinityu _Infinityu _Oneu _Zerou _signu _raise_erroru InvalidOperationu _WorkRepu intu expu precu
_ln_exp_boundu _dlogu lenu stru absu _dec_from_tripleu
_shallow_copyu
_set_roundingu ROUND_HALF_EVENu _fixu rounding(
u selfu contextu ansu opu cu eu pu placesu coeffu rounding( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu ln5 s: ,
+ c C s | j t | j � d } | d k r: t t | � � d S| d k r^ t t d | � � d St | � } | j | j } } | d k r� t | d | � } t d | � } t | � t | � | | k d St d | | � } t | � | | d k d S( u� Compute a lower bound for the adjusted exponent of self.log10().
In other words, find r such that self.log10() >= 10**r.
Assumes that self is finite and positive and that self != 1.
i i i i
i� u 231i����i����( u _expu lenu _intu stru _WorkRepu intu exp( u selfu adju opu cu eu numu den( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _log10_exp_boundg s "c
C s� | d k r t � } n | j d | � } | r4 | S| s> t S| j � d k rT t S| j d k rs | j t d � S| j d d k r� | j d d � d t
| j � d k r� t | j t
| j � d � } n� t
| � } | j | j } } | j } | | j � d } xO t | | | � } | d d
t
t t | � � � | d rTPn | d 7} qt t | d k � t t | � � | � } | j � } | j t � } | j | � } | | _ | S( u& Returns the base 10 logarithm of self.u contexti u log10 of a negative valuei u 1Nu 0i i i
i ( u Noneu
getcontextu _check_nansu _NegativeInfinityu _isinfinityu _Infinityu _signu _raise_erroru InvalidOperationu _intu lenu Decimalu _expu _WorkRepu intu expu precu _log10_exp_boundu _dlog10u stru absu _dec_from_tripleu
_shallow_copyu
_set_roundingu ROUND_HALF_EVENu _fixu rounding(
u selfu contextu ansu opu cu eu pu placesu coeffu rounding( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu log10� s: =# ,
+ c C s| | j d | � } | r | S| d k r4 t � } n | j � rD t S| s] | j t d d � St | j � � } | j | � S( uM Returns the exponent of the magnitude of self's MSD.
The result is the integer which is the exponent of the magnitude
of the most significant digit of self (as though it were truncated
to a single digit while maintaining the value of that digit and
without limiting the resulting exponent).
u contextu logb(0)i N(
u _check_nansu Noneu
getcontextu _isinfinityu _Infinityu _raise_erroru DivisionByZerou Decimalu adjustedu _fix( u selfu contextu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu logb� s c C sJ | j d k s | j d k r" d Sx! | j D] } | d k r, d Sq, Wd S( u� Return True if self is a logical operand.
For being logical, it must be a finite number with a sign of 0,
an exponent of 0, and a coefficient whose digits must all be
either 0 or 1.
i u 01FT( u _signu _expu Falseu _intu True( u selfu dig( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_islogical� s c C s� | j t | � } | d k r0 d | | } n# | d k rS | | j d � } n | j t | � } | d k r� d | | } n# | d k r� | | j d � } n | | f S( Ni u 0( u precu len( u selfu contextu opau opbu dif( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_fill_logical� s c C s� | d k r t � } n t | d d �} | j � sD | j � rQ | j t � S| j | | j | j � \ } } d j d � t
| | � D� � } t d | j d � p� d d � S( u; Applies an 'and' operation between self and other's digits.u raiseitu c S s2 g | ]( \ } } t t | � t | � @� � q S( ( u stru int( u .0u au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
<listcomp>� s i u 0NT(
u Noneu
getcontextu _convert_otheru Trueu
_islogicalu _raise_erroru InvalidOperationu
_fill_logicalu _intu joinu zipu _dec_from_tripleu lstrip( u selfu otheru contextu opau opbu result( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu logical_and� s
!"c C s; | d k r t � } n | j t d d | j d � | � S( u Invert all its digits.i u 1N( u Noneu
getcontextu logical_xoru _dec_from_tripleu prec( u selfu context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu logical_invert
s c C s� | d k r t � } n t | d d �} | j � sD | j � rQ | j t � S| j | | j | j � \ } } d j d � t
| | � D� � } t d | j d � p� d d � S( u: Applies an 'or' operation between self and other's digits.u raiseitu c S s2 g | ]( \ } } t t | � t | � B� � q S( ( u stru int( u .0u au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
<listcomp>
s i u 0NT(
u Noneu
getcontextu _convert_otheru Trueu
_islogicalu _raise_erroru InvalidOperationu
_fill_logicalu _intu joinu zipu _dec_from_tripleu lstrip( u selfu otheru contextu opau opbu result( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
logical_or
s
!"c C s� | d k r t � } n t | d d �} | j � sD | j � rQ | j t � S| j | | j | j � \ } } d j d � t
| | � D� � } t d | j d � p� d d � S( u; Applies an 'xor' operation between self and other's digits.u raiseitu c S s2 g | ]( \ } } t t | � t | � A� � q S( ( u stru int( u .0u au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
<listcomp>(
s i u 0NT(
u Noneu
getcontextu _convert_otheru Trueu
_islogicalu _raise_erroru InvalidOperationu
_fill_logicalu _intu joinu zipu _dec_from_tripleu lstrip( u selfu otheru contextu opau opbu result( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu logical_xor
s
!"c C s t | d d �} | d k r* t � } n | j s< | j r� | j � } | j � } | s` | r� | d k r� | d k r� | j | � S| d k r� | d k r� | j | � S| j | | � Sn | j � j | j � � } | d k r� | j
| � } n | d k r | } n | } | j | � S( u8 Compares the values numerically with their sign ignored.u raiseiti i TNi����( u _convert_otheru Trueu Noneu
getcontextu _is_specialu _isnanu _fixu _check_nansu copy_absu _cmpu
compare_total( u selfu otheru contextu snu onu cu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu max_mag+
s&
c C s t | d d �} | d k r* t � } n | j s< | j r� | j � } | j � } | s` | r� | d k r� | d k r� | j | � S| d k r� | d k r� | j | � S| j | | � Sn | j � j | j � � } | d k r� | j
| � } n | d k r | } n | } | j | � S( u8 Compares the values numerically with their sign ignored.u raiseiti i TNi����( u _convert_otheru Trueu Noneu
getcontextu _is_specialu _isnanu _fixu _check_nansu copy_absu _cmpu
compare_total( u selfu otheru contextu snu onu cu ans( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu min_magI
s&
c C s� | d k r t � } n | j d | � } | r4 | S| j � d k rJ t S| j � d k ry t d d | j | j � � S| j � } | j t
� | j � | j | � } | | k r� | S| j
t d d | j � d � | � S( u= Returns the largest representable number smaller than itself.u contexti i u 9u 1Ni����( u Noneu
getcontextu _check_nansu _isinfinityu _NegativeInfinityu _dec_from_tripleu precu Etopu copyu
_set_roundingu ROUND_FLOORu _ignore_all_flagsu _fixu __sub__u Etiny( u selfu contextu ansu new_self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
next_minusg
s"
c C s� | d k r t � } n | j d | � } | r4 | S| j � d k rJ t S| j � d k ry t d d | j | j � � S| j � } | j t
� | j � | j | � } | | k r� | S| j
t d d | j � d � | � S( u= Returns the smallest representable number larger than itself.u contexti u 9i u 1Ni����( u Noneu
getcontextu _check_nansu _isinfinityu _Infinityu _dec_from_tripleu precu Etopu copyu
_set_roundingu
ROUND_CEILINGu _ignore_all_flagsu _fixu __add__u Etiny( u selfu contextu ansu new_self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu next_plus~
s"
c C s@ t | d d �} | d k r* t � } n | j | | � } | rF | S| j | � } | d k rn | j | � S| d k r� | j | � } n | j | � } | j � r� | j
t d | j � | j
t
� | j
t � nb | j � | j k r<| j
t � | j
t � | j
t
� | j
t � | s<| j
t � q<n | S( u� Returns the number closest to self, in the direction towards other.
The result is the closest representable number to self
(excluding self) that is in the direction towards other,
unless both have the same value. If the two operands are
numerically equal, then the result is a copy of self with the
sign set to be the same as the sign of other.
u raiseiti i u Infinite result from next_towardTNi����( u _convert_otheru Trueu Noneu
getcontextu _check_nansu _cmpu copy_signu next_plusu
next_minusu _isinfinityu _raise_erroru Overflowu _signu Inexactu Roundedu adjustedu Eminu Underflowu Subnormalu Clamped( u selfu otheru contextu ansu
comparison( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu next_toward�
s4
c C s� | j � r d S| j � r d S| j � } | d k r< d S| d k rL d S| j � rl | j re d Sd Sn | d
k r� t � } n | j d | � r� | j r� d Sd
Sn | j r� d Sd Sd
S( u Returns an indication of the class of self.
The class is one of the following strings:
sNaN
NaN
-Infinity
-Normal
-Subnormal
-Zero
+Zero
+Subnormal
+Normal
+Infinity
u sNaNu NaNi u +Infinityu -Infinityu -Zerou +Zerou contextu
-Subnormalu
+Subnormalu -Normalu +NormalNi����( u is_snanu is_qnanu _isinfinityu is_zerou _signu Noneu
getcontextu is_subnormal( u selfu contextu inf( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu number_class�
s, c C s
t d � S( u' Just returns 10, as this is Decimal, :)i
( u Decimal( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu radix�
s c C sV | d k r t � } n t | d d �} | j | | � } | rF | S| j d k rb | j t � S| j t | � k o� | j k n s� | j t � S| j
� r� t | � St | � } | j } | j t
| � } | d k r� d | | } n | d k r| | d � } n | | d � | d | � } t | j | j d � pLd | j � S( u5 Returns a rotated copy of self, value-of-other times.u raiseiti u 0NT( u Noneu
getcontextu _convert_otheru Trueu _check_nansu _expu _raise_erroru InvalidOperationu precu intu _isinfinityu Decimalu _intu lenu _dec_from_tripleu _signu lstrip( u selfu otheru contextu ansu torotu rotdigu topadu rotated( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu rotate�
s,
)
c C s | d k r t � } n t | d d �} | j | | � } | rF | S| j d k rb | j t � Sd | j | j } d | j | j } | t
| � k o� | k n s� | j t � S| j � r� t | � St
| j | j | j t
| � � } | j | � } | S( u> Returns self operand after adding the second value to its exp.u raiseiti i NTi����( u Noneu
getcontextu _convert_otheru Trueu _check_nansu _expu _raise_erroru InvalidOperationu Emaxu precu intu _isinfinityu Decimalu _dec_from_tripleu _signu _intu _fix( u selfu otheru contextu ansu liminfu limsupu d( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu scaleb s"
"
%c C sy | d k r t � } n t | d d �} | j | | � } | rF | S| j d k rb | j t � S| j t | � k o� | j k n s� | j t � S| j
� r� t | � St | � } | j } | j t
| � } | d k r� d | | } n | d k r| | d � } n | d k r2| d | � } n" | d | } | | j d � } t | j | j d � pod | j � S( u5 Returns a shifted copy of self, value-of-other times.u raiseiti u 0NT( u Noneu
getcontextu _convert_otheru Trueu _check_nansu _expu _raise_erroru InvalidOperationu precu intu _isinfinityu Decimalu _intu lenu _dec_from_tripleu _signu lstrip( u selfu otheru contextu ansu torotu rotdigu topadu shifted( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu shift+ s2
)
c C s | j t | � f f S( N( u __class__u str( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
__reduce__R s c C s) t | � t k r | S| j t | � � S( N( u typeu Decimalu __class__u str( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __copy__U s c C s) t | � t k r | S| j t | � � S( N( u typeu Decimalu __class__u str( u selfu memo( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __deepcopy__Z s c C s | d k r t � } n t | d | �} | j rg t | j | � } t | j � � } t | | | � S| d d k r� d d g | j | d <n | d d k r� t
| j | j | j d � } n | j
} | d } | d k rn| d d k r | j | d | � } qn| d d
k r1| j | | � } qn| d d k rnt | j � | k rn| j | | � } qnn | r�| j d k r�| d d
k r�| j d | � } n | j t | j � } | d d k r�| r�| d k r�d | }
qNd }
nV | d d
k r| }
n= | d d k rN| j d k rE| d k rE| }
qNd }
n |
d k rud } d |
| j } nh |
t | j � k r�| j d |
t | j � } d } n, | j d |
� p�d } | j |
d � } | |
}
t | j | | |
| � S( u| Format a Decimal instance according to the given specifier.
The specifier should be a standard format specifier, with the
form described in PEP 3101. Formatting types 'e', 'E', 'f',
'F', 'g', 'G', 'n' and '%' are supported. If the formatting
type is omitted it defaults to 'g' or 'G', depending on the
value of context.capitals.
u _localeconvu typeu gu Gu %i u precisionu eEi u fF%u gGi i u 0u Ni����( u Noneu
getcontextu _parse_format_specifieru _is_specialu _format_signu _signu stru copy_absu
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leftdigitsu dotplaceu intpartu fracpartu exp( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
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to_eng_stringu __neg__u __pos__u Trueu __abs__u __add__u __radd__u __sub__u __rsub__u __mul__u __rmul__u __truediv__u _divideu __rtruediv__u
__divmod__u __rdivmod__u __mod__u __rmod__u remainder_nearu __floordiv__u
__rfloordiv__u __float__u __int__u __trunc__u realu propertyu imagu conjugateu __complex__u _fix_nanu _fixu _round_downu _round_upu _round_half_upu _round_half_downu _round_half_evenu _round_ceilingu _round_flooru _round_05upu dictu _pick_rounding_functionu __round__u __floor__u __ceil__u fmau
_power_modulou _power_exactu __pow__u __rpow__u normalizeu quantizeu same_quantumu _rescaleu _roundu to_integral_exactu to_integral_valueu to_integralu sqrtu maxu minu
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__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu Decimal� s
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f > , T �� G " c * " I K 2 3
. * ! ' c C s7 t j t � } | | _ | | _ | | _ | | _ | S( u� Create a decimal instance directly, without any validation,
normalization (e.g. removal of leading zeros) or argument
conversion.
This function is for *internal use only*.
( u objectu __new__u Decimalu _signu _intu _expu _is_special( u signu coefficientu exponentu specialu self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _dec_from_triple� s c B s/ | Ee Z d Z d � Z d � Z d � Z d S( u� Context manager class to support localcontext().
Sets a copy of the supplied context in __enter__() and restores
the previous decimal context in __exit__()
c C s | j � | _ d S( N( u copyu new_context( u selfu new_context( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __init__� s c C s t � | _ t | j � | j S( N( u
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c C s t | j � d S( N( u
setcontextu
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__module__u __doc__u __init__u __enter__u __exit__( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _ContextManager� s
u _ContextManagerc
B s | Ee Z d Z dO dO dO dO dO dO dO dO dO d � Z d � Z d � Z d � Z d � Z e Z d � Z
d � Z e e
e � Z
dO d � Z d � Z d
� Z d � Z dO Z d � Z d
� Z d � Z d d � Z d � Z d � Z d � Z d � Z d � Z d � Z d � Z d � Z d � Z d � Z d � Z! d � Z" d � Z# d � Z$ d � Z% d � Z& d! � Z' d" � Z( d# � Z) d$ � Z* d% � Z+ d& � Z, d' � Z- d( � Z. d) � Z/ d* � Z0 d+ � Z1 d, � Z2 d- � Z3 d. � Z4 d/ � Z5 d0 � Z6 d1 � Z7 d2 � Z8 d3 � Z9 d4 � Z: d5 � Z; d6 � Z< d7 � Z= d8 � Z> d9 � Z? d: � Z@ d; � ZA d< � ZB d= � ZC d> � ZD d? � ZE dO d@ � ZF dA � ZG dB � ZH dC � ZI dD � ZJ dE � ZK dF � ZL dG � ZM dH � ZN dI � ZO dJ � ZP dK � ZQ dL � ZR dM � ZS dN � ZT eT ZU dO S(P u� Contains the context for a Decimal instance.
Contains:
prec - precision (for use in rounding, division, square roots..)
rounding - rounding type (how you round)
traps - If traps[exception] = 1, then the exception is
raised when it is caused. Otherwise, a value is
substituted in.
flags - When an exception is caused, flags[exception] is set.
(Whether or not the trap_enabler is set)
Should be reset by user of Decimal instance.
Emin - Minimum exponent
Emax - Maximum exponent
capitals - If 1, 1*10^1 is printed as 1E+1.
If 0, printed as 1e1
clamp - If 1, change exponents if too high (Default 0)
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� f d � t D� � | _ n � | _ d S( Nc 3 s' | ] } | t | � k � f Vq d S( N( u int( u .0u s( u traps( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu <genexpr> s i c 3 s' | ] } | t | � k � f Vq d S( N( u int( u .0u s( u flags( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu <genexpr>
s ( u DefaultContextu NameErroru Noneu precu roundingu Eminu Emaxu capitalsu clampu _ignored_flagsu trapsu copyu
isinstanceu dictu _signalsu fromkeysu flags( u selfu precu roundingu trapsu flagsu Eminu Emaxu capitalsu clampu _ignored_flagsu dc( ( u flagsu trapsu. /usr/local/python-3.2/lib/python3.2/decimal.pyu __init__� s.
" "c C s� g } | j d t | � � d � | j j � D� } | j d d j | � d � d � | j j � D� } | j d d j | � d � d j | � d S( u Show the current context.ur Context(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dc S s% g | ] \ } } | r | j � q S( ( u __name__( u .0u fu v( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
<listcomp> s u flags=[u , u ]c S s% g | ] \ } } | r | j � q S( ( u __name__( u .0u tu v( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
<listcomp> s u traps=[u )( u appendu varsu flagsu itemsu joinu traps( u selfu su names( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __repr__ s c C s% x | j D] } d | j | <q
Wd S( u Reset all flags to zeroi N( u flags( u selfu flag( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu clear_flags s c
C sC t | j | j | j | j | j | j | j | j | j � } | S( u! Returns a shallow copy from self.(
u Contextu precu roundingu trapsu flagsu Eminu Emaxu capitalsu clampu _ignored_flags( u selfu nc( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_shallow_copy# s c
C sO t | j | j | j j � | j j � | j | j | j | j | j
� } | S( u Returns a deep copy from self.( u Contextu precu roundingu trapsu copyu flagsu Eminu Emaxu capitalsu clampu _ignored_flags( u selfu nc( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu copy* s c C s# d d l } | j d t � | j S( u; _clamp mirrors the clamp attribute. Its use is deprecated.i NuD Use of the _clamp attribute is deprecated. Please use clamp instead.( u warningsu warnu DeprecationWarningu clamp( u selfu warnings( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_get_clamp4 s c C s) d d l } | j d t � | | _ d S( u; _clamp mirrors the clamp attribute. Its use is deprecated.i NuD Use of the _clamp attribute is deprecated. Please use clamp instead.( u warningsu warnu DeprecationWarningu clamp( u selfu clampu warnings( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_set_clamp< s c G sq t j | | � } | | j k r4 | � j | | � Sd | j | <| j | sa | � j | | � S| | � � d S( u# Handles an error
If the flag is in _ignored_flags, returns the default response.
Otherwise, it sets the flag, then, if the corresponding
trap_enabler is set, it reraises the exception. Otherwise, it returns
the default value after setting the flag.
i N( u _condition_mapu getu _ignored_flagsu handleu flagsu traps( u selfu conditionu explanationu argsu error( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _raise_errorH s
c C s
| j t � S( u$ Ignore all flags, if they are raised( u
_ignore_flagsu _signals( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _ignore_all_flags^ s c G s | j t | � | _ t | � S( u$ Ignore the flags, if they are raised( u _ignored_flagsu list( u selfu flags( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_ignore_flagsb s c G sQ | r, t | d t t f � r, | d } n x | D] } | j j | � q3 Wd S( u+ Stop ignoring the flags, if they are raisedi N( u
isinstanceu tupleu listu _ignored_flagsu remove( u selfu flagsu flag( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_regard_flagsi s
c C s t | j | j d � S( u! Returns Etiny (= Emin - prec + 1)i ( u intu Eminu prec( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu Etinys s c C s t | j | j d � S( u, Returns maximum exponent (= Emax - prec + 1)i ( u intu Emaxu prec( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu Etopw s c C s | j } | | _ | S( u� Sets the rounding type.
Sets the rounding type, and returns the current (previous)
rounding type. Often used like:
context = context.copy()
# so you don't change the calling context
# if an error occurs in the middle.
rounding = context._set_rounding(ROUND_UP)
val = self.__sub__(other, context=context)
context._set_rounding(rounding)
This will make it round up for that operation.
( u rounding( u selfu typeu rounding( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_set_rounding{ s u 0c C s� t | t � r1 | | j � k r1 | j t d � St | d | �} | j � r~ t | j � | j | j
k r~ | j t d � S| j | � S( u� Creates a new Decimal instance but using self as context.
This method implements the to-number operation of the
IBM Decimal specification.u/ no trailing or leading whitespace is permitted.u contextu diagnostic info too long in NaN( u
isinstanceu stru stripu _raise_erroru ConversionSyntaxu Decimalu _isnanu lenu _intu precu clampu _fix( u selfu numu d( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu create_decimal� s ! + c C s t j | � } | j | � S( u� Creates a new Decimal instance from a float but rounding using self
as the context.
>>> context = Context(prec=5, rounding=ROUND_DOWN)
>>> context.create_decimal_from_float(3.1415926535897932)
Decimal('3.1415')
>>> context = Context(prec=5, traps=[Inexact])
>>> context.create_decimal_from_float(3.1415926535897932)
Traceback (most recent call last):
...
decimal.Inexact: None
( u Decimalu
from_floatu _fix( u selfu fu d( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu create_decimal_from_float� s c C s" t | d d �} | j d | � S( u[ Returns the absolute value of the operand.
If the operand is negative, the result is the same as using the minus
operation on the operand. Otherwise, the result is the same as using
the plus operation on the operand.
>>> ExtendedContext.abs(Decimal('2.1'))
Decimal('2.1')
>>> ExtendedContext.abs(Decimal('-100'))
Decimal('100')
>>> ExtendedContext.abs(Decimal('101.5'))
Decimal('101.5')
>>> ExtendedContext.abs(Decimal('-101.5'))
Decimal('101.5')
>>> ExtendedContext.abs(-1)
Decimal('1')
u raiseitu contextT( u _convert_otheru Trueu __abs__( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu abs� s c C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S( u� Return the sum of the two operands.
>>> ExtendedContext.add(Decimal('12'), Decimal('7.00'))
Decimal('19.00')
>>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4'))
Decimal('1.02E+4')
>>> ExtendedContext.add(1, Decimal(2))
Decimal('3')
>>> ExtendedContext.add(Decimal(8), 5)
Decimal('13')
>>> ExtendedContext.add(5, 5)
Decimal('10')
u raiseitu contextu Unable to convert %s to DecimalNT( u _convert_otheru Trueu __add__u NotImplementedu TypeError( u selfu au bu r( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu add� s
c C s t | j | � � S( N( u stru _fix( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _apply� s c C s | j d | � S( u� Returns the same Decimal object.
As we do not have different encodings for the same number, the
received object already is in its canonical form.
>>> ExtendedContext.canonical(Decimal('2.50'))
Decimal('2.50')
u context( u canonical( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu canonical� s c C s% t | d d �} | j | d | �S( u� Compares values numerically.
If the signs of the operands differ, a value representing each operand
('-1' if the operand is less than zero, '0' if the operand is zero or
negative zero, or '1' if the operand is greater than zero) is used in
place of that operand for the comparison instead of the actual
operand.
The comparison is then effected by subtracting the second operand from
the first and then returning a value according to the result of the
subtraction: '-1' if the result is less than zero, '0' if the result is
zero or negative zero, or '1' if the result is greater than zero.
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('3'))
Decimal('-1')
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1'))
Decimal('0')
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10'))
Decimal('0')
>>> ExtendedContext.compare(Decimal('3'), Decimal('2.1'))
Decimal('1')
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3'))
Decimal('1')
>>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1'))
Decimal('-1')
>>> ExtendedContext.compare(1, 2)
Decimal('-1')
>>> ExtendedContext.compare(Decimal(1), 2)
Decimal('-1')
>>> ExtendedContext.compare(1, Decimal(2))
Decimal('-1')
u raiseitu contextT( u _convert_otheru Trueu compare( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu compare� s !c C s% t | d d �} | j | d | �S( u Compares the values of the two operands numerically.
It's pretty much like compare(), but all NaNs signal, with signaling
NaNs taking precedence over quiet NaNs.
>>> c = ExtendedContext
>>> c.compare_signal(Decimal('2.1'), Decimal('3'))
Decimal('-1')
>>> c.compare_signal(Decimal('2.1'), Decimal('2.1'))
Decimal('0')
>>> c.flags[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> c.compare_signal(Decimal('NaN'), Decimal('2.1'))
Decimal('NaN')
>>> print(c.flags[InvalidOperation])
1
>>> c.flags[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> c.compare_signal(Decimal('sNaN'), Decimal('2.1'))
Decimal('NaN')
>>> print(c.flags[InvalidOperation])
1
>>> c.compare_signal(-1, 2)
Decimal('-1')
>>> c.compare_signal(Decimal(-1), 2)
Decimal('-1')
>>> c.compare_signal(-1, Decimal(2))
Decimal('-1')
u raiseitu contextT( u _convert_otheru Trueu compare_signal( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu compare_signal
s c C s t | d d �} | j | � S( u+ Compares two operands using their abstract representation.
This is not like the standard compare, which use their numerical
value. Note that a total ordering is defined for all possible abstract
representations.
>>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9'))
Decimal('-1')
>>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12'))
Decimal('-1')
>>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3'))
Decimal('-1')
>>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30'))
Decimal('0')
>>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300'))
Decimal('1')
>>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN'))
Decimal('-1')
>>> ExtendedContext.compare_total(1, 2)
Decimal('-1')
>>> ExtendedContext.compare_total(Decimal(1), 2)
Decimal('-1')
>>> ExtendedContext.compare_total(1, Decimal(2))
Decimal('-1')
u raiseitT( u _convert_otheru Trueu
compare_total( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
compare_total0 s c C s t | d d �} | j | � S( u� Compares two operands using their abstract representation ignoring sign.
Like compare_total, but with operand's sign ignored and assumed to be 0.
u raiseitT( u _convert_otheru Trueu compare_total_mag( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu compare_total_magM s c C s t | d d �} | j � S( u Returns a copy of the operand with the sign set to 0.
>>> ExtendedContext.copy_abs(Decimal('2.1'))
Decimal('2.1')
>>> ExtendedContext.copy_abs(Decimal('-100'))
Decimal('100')
>>> ExtendedContext.copy_abs(-1)
Decimal('1')
u raiseitT( u _convert_otheru Trueu copy_abs( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu copy_absU s
c C s t | d d �} t | � S( u Returns a copy of the decimal object.
>>> ExtendedContext.copy_decimal(Decimal('2.1'))
Decimal('2.1')
>>> ExtendedContext.copy_decimal(Decimal('-1.00'))
Decimal('-1.00')
>>> ExtendedContext.copy_decimal(1)
Decimal('1')
u raiseitT( u _convert_otheru Trueu Decimal( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu copy_decimalb s
c C s t | d d �} | j � S( u( Returns a copy of the operand with the sign inverted.
>>> ExtendedContext.copy_negate(Decimal('101.5'))
Decimal('-101.5')
>>> ExtendedContext.copy_negate(Decimal('-101.5'))
Decimal('101.5')
>>> ExtendedContext.copy_negate(1)
Decimal('-1')
u raiseitT( u _convert_otheru Trueu copy_negate( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu copy_negateo s
c C s t | d d �} | j | � S( u Copies the second operand's sign to the first one.
In detail, it returns a copy of the first operand with the sign
equal to the sign of the second operand.
>>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33'))
Decimal('1.50')
>>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33'))
Decimal('1.50')
>>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33'))
Decimal('-1.50')
>>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33'))
Decimal('-1.50')
>>> ExtendedContext.copy_sign(1, -2)
Decimal('-1')
>>> ExtendedContext.copy_sign(Decimal(1), -2)
Decimal('-1')
>>> ExtendedContext.copy_sign(1, Decimal(-2))
Decimal('-1')
u raiseitT( u _convert_otheru Trueu copy_sign( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu copy_sign| s c C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S( u� Decimal division in a specified context.
>>> ExtendedContext.divide(Decimal('1'), Decimal('3'))
Decimal('0.333333333')
>>> ExtendedContext.divide(Decimal('2'), Decimal('3'))
Decimal('0.666666667')
>>> ExtendedContext.divide(Decimal('5'), Decimal('2'))
Decimal('2.5')
>>> ExtendedContext.divide(Decimal('1'), Decimal('10'))
Decimal('0.1')
>>> ExtendedContext.divide(Decimal('12'), Decimal('12'))
Decimal('1')
>>> ExtendedContext.divide(Decimal('8.00'), Decimal('2'))
Decimal('4.00')
>>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0'))
Decimal('1.20')
>>> ExtendedContext.divide(Decimal('1000'), Decimal('100'))
Decimal('10')
>>> ExtendedContext.divide(Decimal('1000'), Decimal('1'))
Decimal('1000')
>>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2'))
Decimal('1.20E+6')
>>> ExtendedContext.divide(5, 5)
Decimal('1')
>>> ExtendedContext.divide(Decimal(5), 5)
Decimal('1')
>>> ExtendedContext.divide(5, Decimal(5))
Decimal('1')
u raiseitu contextu Unable to convert %s to DecimalNT( u _convert_otheru Trueu __truediv__u NotImplementedu TypeError( u selfu au bu r( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu divide� s
c C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S( u/ Divides two numbers and returns the integer part of the result.
>>> ExtendedContext.divide_int(Decimal('2'), Decimal('3'))
Decimal('0')
>>> ExtendedContext.divide_int(Decimal('10'), Decimal('3'))
Decimal('3')
>>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3'))
Decimal('3')
>>> ExtendedContext.divide_int(10, 3)
Decimal('3')
>>> ExtendedContext.divide_int(Decimal(10), 3)
Decimal('3')
>>> ExtendedContext.divide_int(10, Decimal(3))
Decimal('3')
u raiseitu contextu Unable to convert %s to DecimalNT( u _convert_otheru Trueu __floordiv__u NotImplementedu TypeError( u selfu au bu r( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
divide_int� s
c C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S( u� Return (a // b, a % b).
>>> ExtendedContext.divmod(Decimal(8), Decimal(3))
(Decimal('2'), Decimal('2'))
>>> ExtendedContext.divmod(Decimal(8), Decimal(4))
(Decimal('2'), Decimal('0'))
>>> ExtendedContext.divmod(8, 4)
(Decimal('2'), Decimal('0'))
>>> ExtendedContext.divmod(Decimal(8), 4)
(Decimal('2'), Decimal('0'))
>>> ExtendedContext.divmod(8, Decimal(4))
(Decimal('2'), Decimal('0'))
u raiseitu contextu Unable to convert %s to DecimalNT( u _convert_otheru Trueu
__divmod__u NotImplementedu TypeError( u selfu au bu r( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu divmod� s
c C s" t | d d �} | j d | � S( u# Returns e ** a.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.exp(Decimal('-Infinity'))
Decimal('0')
>>> c.exp(Decimal('-1'))
Decimal('0.367879441')
>>> c.exp(Decimal('0'))
Decimal('1')
>>> c.exp(Decimal('1'))
Decimal('2.71828183')
>>> c.exp(Decimal('0.693147181'))
Decimal('2.00000000')
>>> c.exp(Decimal('+Infinity'))
Decimal('Infinity')
>>> c.exp(10)
Decimal('22026.4658')
u raiseitu contextT( u _convert_otheru Trueu exp( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu exp� s c C s( t | d d �} | j | | d | �S( u Returns a multiplied by b, plus c.
The first two operands are multiplied together, using multiply,
the third operand is then added to the result of that
multiplication, using add, all with only one final rounding.
>>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7'))
Decimal('22')
>>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7'))
Decimal('-8')
>>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578'))
Decimal('1.38435736E+12')
>>> ExtendedContext.fma(1, 3, 4)
Decimal('7')
>>> ExtendedContext.fma(1, Decimal(3), 4)
Decimal('7')
>>> ExtendedContext.fma(1, 3, Decimal(4))
Decimal('7')
u raiseitu contextT( u _convert_otheru Trueu fma( u selfu au bu c( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu fma� s c C s
| j � S( u Return True if the operand is canonical; otherwise return False.
Currently, the encoding of a Decimal instance is always
canonical, so this method returns True for any Decimal.
>>> ExtendedContext.is_canonical(Decimal('2.50'))
True
( u is_canonical( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_canonical s c C s t | d d �} | j � S( u, Return True if the operand is finite; otherwise return False.
A Decimal instance is considered finite if it is neither
infinite nor a NaN.
>>> ExtendedContext.is_finite(Decimal('2.50'))
True
>>> ExtendedContext.is_finite(Decimal('-0.3'))
True
>>> ExtendedContext.is_finite(Decimal('0'))
True
>>> ExtendedContext.is_finite(Decimal('Inf'))
False
>>> ExtendedContext.is_finite(Decimal('NaN'))
False
>>> ExtendedContext.is_finite(1)
True
u raiseitT( u _convert_otheru Trueu is_finite( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_finite s c C s t | d d �} | j � S( uU Return True if the operand is infinite; otherwise return False.
>>> ExtendedContext.is_infinite(Decimal('2.50'))
False
>>> ExtendedContext.is_infinite(Decimal('-Inf'))
True
>>> ExtendedContext.is_infinite(Decimal('NaN'))
False
>>> ExtendedContext.is_infinite(1)
False
u raiseitT( u _convert_otheru Trueu is_infinite( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_infinite5 s c C s t | d d �} | j � S( uO Return True if the operand is a qNaN or sNaN;
otherwise return False.
>>> ExtendedContext.is_nan(Decimal('2.50'))
False
>>> ExtendedContext.is_nan(Decimal('NaN'))
True
>>> ExtendedContext.is_nan(Decimal('-sNaN'))
True
>>> ExtendedContext.is_nan(1)
False
u raiseitT( u _convert_otheru Trueu is_nan( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_nanD s
c C s" t | d d �} | j d | � S( u� Return True if the operand is a normal number;
otherwise return False.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.is_normal(Decimal('2.50'))
True
>>> c.is_normal(Decimal('0.1E-999'))
False
>>> c.is_normal(Decimal('0.00'))
False
>>> c.is_normal(Decimal('-Inf'))
False
>>> c.is_normal(Decimal('NaN'))
False
>>> c.is_normal(1)
True
u raiseitu contextT( u _convert_otheru Trueu is_normal( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_normalT s c C s t | d d �} | j � S( uH Return True if the operand is a quiet NaN; otherwise return False.
>>> ExtendedContext.is_qnan(Decimal('2.50'))
False
>>> ExtendedContext.is_qnan(Decimal('NaN'))
True
>>> ExtendedContext.is_qnan(Decimal('sNaN'))
False
>>> ExtendedContext.is_qnan(1)
False
u raiseitT( u _convert_otheru Trueu is_qnan( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_qnank s c C s t | d d �} | j � S( u� Return True if the operand is negative; otherwise return False.
>>> ExtendedContext.is_signed(Decimal('2.50'))
False
>>> ExtendedContext.is_signed(Decimal('-12'))
True
>>> ExtendedContext.is_signed(Decimal('-0'))
True
>>> ExtendedContext.is_signed(8)
False
>>> ExtendedContext.is_signed(-8)
True
u raiseitT( u _convert_otheru Trueu is_signed( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_signedz s c C s t | d d �} | j � S( uT Return True if the operand is a signaling NaN;
otherwise return False.
>>> ExtendedContext.is_snan(Decimal('2.50'))
False
>>> ExtendedContext.is_snan(Decimal('NaN'))
False
>>> ExtendedContext.is_snan(Decimal('sNaN'))
True
>>> ExtendedContext.is_snan(1)
False
u raiseitT( u _convert_otheru Trueu is_snan( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_snan� s
c C s" t | d d �} | j d | � S( u� Return True if the operand is subnormal; otherwise return False.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.is_subnormal(Decimal('2.50'))
False
>>> c.is_subnormal(Decimal('0.1E-999'))
True
>>> c.is_subnormal(Decimal('0.00'))
False
>>> c.is_subnormal(Decimal('-Inf'))
False
>>> c.is_subnormal(Decimal('NaN'))
False
>>> c.is_subnormal(1)
False
u raiseitu contextT( u _convert_otheru Trueu is_subnormal( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_subnormal� s c C s t | d d �} | j � S( uu Return True if the operand is a zero; otherwise return False.
>>> ExtendedContext.is_zero(Decimal('0'))
True
>>> ExtendedContext.is_zero(Decimal('2.50'))
False
>>> ExtendedContext.is_zero(Decimal('-0E+2'))
True
>>> ExtendedContext.is_zero(1)
False
>>> ExtendedContext.is_zero(0)
True
u raiseitT( u _convert_otheru Trueu is_zero( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu is_zero� s c C s" t | d d �} | j d | � S( u� Returns the natural (base e) logarithm of the operand.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.ln(Decimal('0'))
Decimal('-Infinity')
>>> c.ln(Decimal('1.000'))
Decimal('0')
>>> c.ln(Decimal('2.71828183'))
Decimal('1.00000000')
>>> c.ln(Decimal('10'))
Decimal('2.30258509')
>>> c.ln(Decimal('+Infinity'))
Decimal('Infinity')
>>> c.ln(1)
Decimal('0')
u raiseitu contextT( u _convert_otheru Trueu ln( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu ln� s c C s" t | d d �} | j d | � S( u� Returns the base 10 logarithm of the operand.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.log10(Decimal('0'))
Decimal('-Infinity')
>>> c.log10(Decimal('0.001'))
Decimal('-3')
>>> c.log10(Decimal('1.000'))
Decimal('0')
>>> c.log10(Decimal('2'))
Decimal('0.301029996')
>>> c.log10(Decimal('10'))
Decimal('1')
>>> c.log10(Decimal('70'))
Decimal('1.84509804')
>>> c.log10(Decimal('+Infinity'))
Decimal('Infinity')
>>> c.log10(0)
Decimal('-Infinity')
>>> c.log10(1)
Decimal('0')
u raiseitu contextT( u _convert_otheru Trueu log10( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu log10� s c C s" t | d d �} | j d | � S( u4 Returns the exponent of the magnitude of the operand's MSD.
The result is the integer which is the exponent of the magnitude
of the most significant digit of the operand (as though the
operand were truncated to a single digit while maintaining the
value of that digit and without limiting the resulting exponent).
>>> ExtendedContext.logb(Decimal('250'))
Decimal('2')
>>> ExtendedContext.logb(Decimal('2.50'))
Decimal('0')
>>> ExtendedContext.logb(Decimal('0.03'))
Decimal('-2')
>>> ExtendedContext.logb(Decimal('0'))
Decimal('-Infinity')
>>> ExtendedContext.logb(1)
Decimal('0')
>>> ExtendedContext.logb(10)
Decimal('1')
>>> ExtendedContext.logb(100)
Decimal('2')
u raiseitu contextT( u _convert_otheru Trueu logb( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu logb� s c C s% t | d d �} | j | d | �S( u� Applies the logical operation 'and' between each operand's digits.
The operands must be both logical numbers.
>>> ExtendedContext.logical_and(Decimal('0'), Decimal('0'))
Decimal('0')
>>> ExtendedContext.logical_and(Decimal('0'), Decimal('1'))
Decimal('0')
>>> ExtendedContext.logical_and(Decimal('1'), Decimal('0'))
Decimal('0')
>>> ExtendedContext.logical_and(Decimal('1'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010'))
Decimal('1000')
>>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10'))
Decimal('10')
>>> ExtendedContext.logical_and(110, 1101)
Decimal('100')
>>> ExtendedContext.logical_and(Decimal(110), 1101)
Decimal('100')
>>> ExtendedContext.logical_and(110, Decimal(1101))
Decimal('100')
u raiseitu contextT( u _convert_otheru Trueu logical_and( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu logical_and s c C s" t | d d �} | j d | � S( u Invert all the digits in the operand.
The operand must be a logical number.
>>> ExtendedContext.logical_invert(Decimal('0'))
Decimal('111111111')
>>> ExtendedContext.logical_invert(Decimal('1'))
Decimal('111111110')
>>> ExtendedContext.logical_invert(Decimal('111111111'))
Decimal('0')
>>> ExtendedContext.logical_invert(Decimal('101010101'))
Decimal('10101010')
>>> ExtendedContext.logical_invert(1101)
Decimal('111110010')
u raiseitu contextT( u _convert_otheru Trueu logical_invert( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu logical_invert) s c C s% t | d d �} | j | d | �S( u� Applies the logical operation 'or' between each operand's digits.
The operands must be both logical numbers.
>>> ExtendedContext.logical_or(Decimal('0'), Decimal('0'))
Decimal('0')
>>> ExtendedContext.logical_or(Decimal('0'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.logical_or(Decimal('1'), Decimal('0'))
Decimal('1')
>>> ExtendedContext.logical_or(Decimal('1'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010'))
Decimal('1110')
>>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10'))
Decimal('1110')
>>> ExtendedContext.logical_or(110, 1101)
Decimal('1111')
>>> ExtendedContext.logical_or(Decimal(110), 1101)
Decimal('1111')
>>> ExtendedContext.logical_or(110, Decimal(1101))
Decimal('1111')
u raiseitu contextT( u _convert_otheru Trueu
logical_or( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
logical_or< s c C s% t | d d �} | j | d | �S( u� Applies the logical operation 'xor' between each operand's digits.
The operands must be both logical numbers.
>>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0'))
Decimal('0')
>>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0'))
Decimal('1')
>>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1'))
Decimal('0')
>>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010'))
Decimal('110')
>>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10'))
Decimal('1101')
>>> ExtendedContext.logical_xor(110, 1101)
Decimal('1011')
>>> ExtendedContext.logical_xor(Decimal(110), 1101)
Decimal('1011')
>>> ExtendedContext.logical_xor(110, Decimal(1101))
Decimal('1011')
u raiseitu contextT( u _convert_otheru Trueu logical_xor( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu logical_xorW s c C s% t | d d �} | j | d | �S( u� max compares two values numerically and returns the maximum.
If either operand is a NaN then the general rules apply.
Otherwise, the operands are compared as though by the compare
operation. If they are numerically equal then the left-hand operand
is chosen as the result. Otherwise the maximum (closer to positive
infinity) of the two operands is chosen as the result.
>>> ExtendedContext.max(Decimal('3'), Decimal('2'))
Decimal('3')
>>> ExtendedContext.max(Decimal('-10'), Decimal('3'))
Decimal('3')
>>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))
Decimal('1')
>>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))
Decimal('7')
>>> ExtendedContext.max(1, 2)
Decimal('2')
>>> ExtendedContext.max(Decimal(1), 2)
Decimal('2')
>>> ExtendedContext.max(1, Decimal(2))
Decimal('2')
u raiseitu contextT( u _convert_otheru Trueu max( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu maxr s c C s% t | d d �} | j | d | �S( u� Compares the values numerically with their sign ignored.
>>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN'))
Decimal('7')
>>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10'))
Decimal('-10')
>>> ExtendedContext.max_mag(1, -2)
Decimal('-2')
>>> ExtendedContext.max_mag(Decimal(1), -2)
Decimal('-2')
>>> ExtendedContext.max_mag(1, Decimal(-2))
Decimal('-2')
u raiseitu contextT( u _convert_otheru Trueu max_mag( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu max_mag� s c C s% t | d d �} | j | d | �S( u� min compares two values numerically and returns the minimum.
If either operand is a NaN then the general rules apply.
Otherwise, the operands are compared as though by the compare
operation. If they are numerically equal then the left-hand operand
is chosen as the result. Otherwise the minimum (closer to negative
infinity) of the two operands is chosen as the result.
>>> ExtendedContext.min(Decimal('3'), Decimal('2'))
Decimal('2')
>>> ExtendedContext.min(Decimal('-10'), Decimal('3'))
Decimal('-10')
>>> ExtendedContext.min(Decimal('1.0'), Decimal('1'))
Decimal('1.0')
>>> ExtendedContext.min(Decimal('7'), Decimal('NaN'))
Decimal('7')
>>> ExtendedContext.min(1, 2)
Decimal('1')
>>> ExtendedContext.min(Decimal(1), 2)
Decimal('1')
>>> ExtendedContext.min(1, Decimal(29))
Decimal('1')
u raiseitu contextT( u _convert_otheru Trueu min( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu min� s c C s% t | d d �} | j | d | �S( u� Compares the values numerically with their sign ignored.
>>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2'))
Decimal('-2')
>>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN'))
Decimal('-3')
>>> ExtendedContext.min_mag(1, -2)
Decimal('1')
>>> ExtendedContext.min_mag(Decimal(1), -2)
Decimal('1')
>>> ExtendedContext.min_mag(1, Decimal(-2))
Decimal('1')
u raiseitu contextT( u _convert_otheru Trueu min_mag( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu min_mag� s c C s" t | d d �} | j d | � S( u� Minus corresponds to unary prefix minus in Python.
The operation is evaluated using the same rules as subtract; the
operation minus(a) is calculated as subtract('0', a) where the '0'
has the same exponent as the operand.
>>> ExtendedContext.minus(Decimal('1.3'))
Decimal('-1.3')
>>> ExtendedContext.minus(Decimal('-1.3'))
Decimal('1.3')
>>> ExtendedContext.minus(1)
Decimal('-1')
u raiseitu contextT( u _convert_otheru Trueu __neg__( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu minus� s c C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S( u� multiply multiplies two operands.
If either operand is a special value then the general rules apply.
Otherwise, the operands are multiplied together
('long multiplication'), resulting in a number which may be as long as
the sum of the lengths of the two operands.
>>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))
Decimal('3.60')
>>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))
Decimal('21')
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))
Decimal('0.72')
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))
Decimal('-0.0')
>>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))
Decimal('4.28135971E+11')
>>> ExtendedContext.multiply(7, 7)
Decimal('49')
>>> ExtendedContext.multiply(Decimal(7), 7)
Decimal('49')
>>> ExtendedContext.multiply(7, Decimal(7))
Decimal('49')
u raiseitu contextu Unable to convert %s to DecimalNT( u _convert_otheru Trueu __mul__u NotImplementedu TypeError( u selfu au bu r( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu multiply� s
c C s" t | d d �} | j d | � S( u" Returns the largest representable number smaller than a.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> ExtendedContext.next_minus(Decimal('1'))
Decimal('0.999999999')
>>> c.next_minus(Decimal('1E-1007'))
Decimal('0E-1007')
>>> ExtendedContext.next_minus(Decimal('-1.00000003'))
Decimal('-1.00000004')
>>> c.next_minus(Decimal('Infinity'))
Decimal('9.99999999E+999')
>>> c.next_minus(1)
Decimal('0.999999999')
u raiseitu contextT( u _convert_otheru Trueu
next_minus( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
next_minus� s c C s" t | d d �} | j d | � S( u Returns the smallest representable number larger than a.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> ExtendedContext.next_plus(Decimal('1'))
Decimal('1.00000001')
>>> c.next_plus(Decimal('-1E-1007'))
Decimal('-0E-1007')
>>> ExtendedContext.next_plus(Decimal('-1.00000003'))
Decimal('-1.00000002')
>>> c.next_plus(Decimal('-Infinity'))
Decimal('-9.99999999E+999')
>>> c.next_plus(1)
Decimal('1.00000001')
u raiseitu contextT( u _convert_otheru Trueu next_plus( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu next_plus s c C s% t | d d �} | j | d | �S( u� Returns the number closest to a, in direction towards b.
The result is the closest representable number from the first
operand (but not the first operand) that is in the direction
towards the second operand, unless the operands have the same
value.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.next_toward(Decimal('1'), Decimal('2'))
Decimal('1.00000001')
>>> c.next_toward(Decimal('-1E-1007'), Decimal('1'))
Decimal('-0E-1007')
>>> c.next_toward(Decimal('-1.00000003'), Decimal('0'))
Decimal('-1.00000002')
>>> c.next_toward(Decimal('1'), Decimal('0'))
Decimal('0.999999999')
>>> c.next_toward(Decimal('1E-1007'), Decimal('-100'))
Decimal('0E-1007')
>>> c.next_toward(Decimal('-1.00000003'), Decimal('-10'))
Decimal('-1.00000004')
>>> c.next_toward(Decimal('0.00'), Decimal('-0.0000'))
Decimal('-0.00')
>>> c.next_toward(0, 1)
Decimal('1E-1007')
>>> c.next_toward(Decimal(0), 1)
Decimal('1E-1007')
>>> c.next_toward(0, Decimal(1))
Decimal('1E-1007')
u raiseitu contextT( u _convert_otheru Trueu next_toward( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu next_toward# s c C s" t | d d �} | j d | � S( u� normalize reduces an operand to its simplest form.
Essentially a plus operation with all trailing zeros removed from the
result.
>>> ExtendedContext.normalize(Decimal('2.1'))
Decimal('2.1')
>>> ExtendedContext.normalize(Decimal('-2.0'))
Decimal('-2')
>>> ExtendedContext.normalize(Decimal('1.200'))
Decimal('1.2')
>>> ExtendedContext.normalize(Decimal('-120'))
Decimal('-1.2E+2')
>>> ExtendedContext.normalize(Decimal('120.00'))
Decimal('1.2E+2')
>>> ExtendedContext.normalize(Decimal('0.00'))
Decimal('0')
>>> ExtendedContext.normalize(6)
Decimal('6')
u raiseitu contextT( u _convert_otheru Trueu normalize( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu normalizeF s c C s" t | d d �} | j d | � S( u� Returns an indication of the class of the operand.
The class is one of the following strings:
-sNaN
-NaN
-Infinity
-Normal
-Subnormal
-Zero
+Zero
+Subnormal
+Normal
+Infinity
>>> c = Context(ExtendedContext)
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.number_class(Decimal('Infinity'))
'+Infinity'
>>> c.number_class(Decimal('1E-10'))
'+Normal'
>>> c.number_class(Decimal('2.50'))
'+Normal'
>>> c.number_class(Decimal('0.1E-999'))
'+Subnormal'
>>> c.number_class(Decimal('0'))
'+Zero'
>>> c.number_class(Decimal('-0'))
'-Zero'
>>> c.number_class(Decimal('-0.1E-999'))
'-Subnormal'
>>> c.number_class(Decimal('-1E-10'))
'-Normal'
>>> c.number_class(Decimal('-2.50'))
'-Normal'
>>> c.number_class(Decimal('-Infinity'))
'-Infinity'
>>> c.number_class(Decimal('NaN'))
'NaN'
>>> c.number_class(Decimal('-NaN'))
'NaN'
>>> c.number_class(Decimal('sNaN'))
'sNaN'
>>> c.number_class(123)
'+Normal'
u raiseitu contextT( u _convert_otheru Trueu number_class( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu number_class^ s /c C s" t | d d �} | j d | � S( u� Plus corresponds to unary prefix plus in Python.
The operation is evaluated using the same rules as add; the
operation plus(a) is calculated as add('0', a) where the '0'
has the same exponent as the operand.
>>> ExtendedContext.plus(Decimal('1.3'))
Decimal('1.3')
>>> ExtendedContext.plus(Decimal('-1.3'))
Decimal('-1.3')
>>> ExtendedContext.plus(-1)
Decimal('-1')
u raiseitu contextT( u _convert_otheru Trueu __pos__( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu plus� s c C sQ t | d d �} | j | | d | �} | t k rI t d | � � n | Sd S( u Raises a to the power of b, to modulo if given.
With two arguments, compute a**b. If a is negative then b
must be integral. The result will be inexact unless b is
integral and the result is finite and can be expressed exactly
in 'precision' digits.
With three arguments, compute (a**b) % modulo. For the
three argument form, the following restrictions on the
arguments 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 have at most 'precision' digits
The result of pow(a, b, modulo) is identical to the result
that would be obtained by computing (a**b) % modulo with
unbounded precision, but is computed more efficiently. It is
always exact.
>>> c = ExtendedContext.copy()
>>> c.Emin = -999
>>> c.Emax = 999
>>> c.power(Decimal('2'), Decimal('3'))
Decimal('8')
>>> c.power(Decimal('-2'), Decimal('3'))
Decimal('-8')
>>> c.power(Decimal('2'), Decimal('-3'))
Decimal('0.125')
>>> c.power(Decimal('1.7'), Decimal('8'))
Decimal('69.7575744')
>>> c.power(Decimal('10'), Decimal('0.301029996'))
Decimal('2.00000000')
>>> c.power(Decimal('Infinity'), Decimal('-1'))
Decimal('0')
>>> c.power(Decimal('Infinity'), Decimal('0'))
Decimal('1')
>>> c.power(Decimal('Infinity'), Decimal('1'))
Decimal('Infinity')
>>> c.power(Decimal('-Infinity'), Decimal('-1'))
Decimal('-0')
>>> c.power(Decimal('-Infinity'), Decimal('0'))
Decimal('1')
>>> c.power(Decimal('-Infinity'), Decimal('1'))
Decimal('-Infinity')
>>> c.power(Decimal('-Infinity'), Decimal('2'))
Decimal('Infinity')
>>> c.power(Decimal('0'), Decimal('0'))
Decimal('NaN')
>>> c.power(Decimal('3'), Decimal('7'), Decimal('16'))
Decimal('11')
>>> c.power(Decimal('-3'), Decimal('7'), Decimal('16'))
Decimal('-11')
>>> c.power(Decimal('-3'), Decimal('8'), Decimal('16'))
Decimal('1')
>>> c.power(Decimal('3'), Decimal('7'), Decimal('-16'))
Decimal('11')
>>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789'))
Decimal('11729830')
>>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729'))
Decimal('-0')
>>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537'))
Decimal('1')
>>> ExtendedContext.power(7, 7)
Decimal('823543')
>>> ExtendedContext.power(Decimal(7), 7)
Decimal('823543')
>>> ExtendedContext.power(7, Decimal(7), 2)
Decimal('1')
u raiseitu contextu Unable to convert %s to DecimalNT( u _convert_otheru Trueu __pow__u NotImplementedu TypeError( u selfu au bu modulou r( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu power� s
I c C s% t | d d �} | j | d | �S( u
Returns a value equal to 'a' (rounded), having the exponent of 'b'.
The coefficient of the result is derived from that of the left-hand
operand. It may be rounded using the current rounding setting (if the
exponent is being increased), multiplied by a positive power of ten (if
the exponent is being decreased), or is unchanged (if the exponent is
already equal to that of the right-hand operand).
Unlike other operations, if the length of the coefficient after the
quantize operation would be greater than precision then an Invalid
operation condition is raised. This guarantees that, unless there is
an error condition, the exponent of the result of a quantize is always
equal to that of the right-hand operand.
Also unlike other operations, quantize will never raise Underflow, even
if the result is subnormal and inexact.
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001'))
Decimal('2.170')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01'))
Decimal('2.17')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1'))
Decimal('2.2')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0'))
Decimal('2')
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1'))
Decimal('0E+1')
>>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity'))
Decimal('-Infinity')
>>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity'))
Decimal('NaN')
>>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1'))
Decimal('-0')
>>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5'))
Decimal('-0E+5')
>>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))
Decimal('NaN')
>>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))
Decimal('NaN')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1'))
Decimal('217.0')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0'))
Decimal('217')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1'))
Decimal('2.2E+2')
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2'))
Decimal('2E+2')
>>> ExtendedContext.quantize(1, 2)
Decimal('1')
>>> ExtendedContext.quantize(Decimal(1), 2)
Decimal('1')
>>> ExtendedContext.quantize(1, Decimal(2))
Decimal('1')
u raiseitu contextT( u _convert_otheru Trueu quantize( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu quantize� s 7c C s
t d � S( uk Just returns 10, as this is Decimal, :)
>>> ExtendedContext.radix()
Decimal('10')
i
( u Decimal( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu radix+ s c C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S( u Returns the remainder from integer division.
The result is the residue of the dividend after the operation of
calculating integer division as described for divide-integer, rounded
to precision digits if necessary. The sign of the result, if
non-zero, is the same as that of the original dividend.
This operation will fail under the same conditions as integer division
(that is, if integer division on the same two operands would fail, the
remainder cannot be calculated).
>>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3'))
Decimal('2.1')
>>> ExtendedContext.remainder(Decimal('10'), Decimal('3'))
Decimal('1')
>>> ExtendedContext.remainder(Decimal('-10'), Decimal('3'))
Decimal('-1')
>>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1'))
Decimal('0.2')
>>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3'))
Decimal('0.1')
>>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3'))
Decimal('1.0')
>>> ExtendedContext.remainder(22, 6)
Decimal('4')
>>> ExtendedContext.remainder(Decimal(22), 6)
Decimal('4')
>>> ExtendedContext.remainder(22, Decimal(6))
Decimal('4')
u raiseitu contextu Unable to convert %s to DecimalNT( u _convert_otheru Trueu __mod__u NotImplementedu TypeError( u selfu au bu r( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu remainder3 s
c C s% t | d d �} | j | d | �S( uG Returns to be "a - b * n", where n is the integer nearest the exact
value of "x / b" (if two integers are equally near then the even one
is chosen). If the result is equal to 0 then its sign will be the
sign of a.
This operation will fail under the same conditions as integer division
(that is, if integer division on the same two operands would fail, the
remainder cannot be calculated).
>>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3'))
Decimal('-0.9')
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6'))
Decimal('-2')
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3'))
Decimal('1')
>>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3'))
Decimal('-1')
>>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1'))
Decimal('0.2')
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3'))
Decimal('0.1')
>>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3'))
Decimal('-0.3')
>>> ExtendedContext.remainder_near(3, 11)
Decimal('3')
>>> ExtendedContext.remainder_near(Decimal(3), 11)
Decimal('3')
>>> ExtendedContext.remainder_near(3, Decimal(11))
Decimal('3')
u raiseitu contextT( u _convert_otheru Trueu remainder_near( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu remainder_nearY s c C s% t | d d �} | j | d | �S( uN Returns a rotated copy of a, b times.
The coefficient of the result is a rotated copy of the digits in
the coefficient of the first operand. The number of places of
rotation is taken from the absolute value of the second operand,
with the rotation being to the left if the second operand is
positive or to the right otherwise.
>>> ExtendedContext.rotate(Decimal('34'), Decimal('8'))
Decimal('400000003')
>>> ExtendedContext.rotate(Decimal('12'), Decimal('9'))
Decimal('12')
>>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2'))
Decimal('891234567')
>>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0'))
Decimal('123456789')
>>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2'))
Decimal('345678912')
>>> ExtendedContext.rotate(1333333, 1)
Decimal('13333330')
>>> ExtendedContext.rotate(Decimal(1333333), 1)
Decimal('13333330')
>>> ExtendedContext.rotate(1333333, Decimal(1))
Decimal('13333330')
u raiseitu contextT( u _convert_otheru Trueu rotate( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu rotate{ s c C s t | d d �} | j | � S( u� Returns True if the two operands have the same exponent.
The result is never affected by either the sign or the coefficient of
either operand.
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001'))
False
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01'))
True
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1'))
False
>>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf'))
True
>>> ExtendedContext.same_quantum(10000, -1)
True
>>> ExtendedContext.same_quantum(Decimal(10000), -1)
True
>>> ExtendedContext.same_quantum(10000, Decimal(-1))
True
u raiseitT( u _convert_otheru Trueu same_quantum( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu same_quantum� s c C s% t | d d �} | j | d | �S( u3 Returns the first operand after adding the second value its exp.
>>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2'))
Decimal('0.0750')
>>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0'))
Decimal('7.50')
>>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3'))
Decimal('7.50E+3')
>>> ExtendedContext.scaleb(1, 4)
Decimal('1E+4')
>>> ExtendedContext.scaleb(Decimal(1), 4)
Decimal('1E+4')
>>> ExtendedContext.scaleb(1, Decimal(4))
Decimal('1E+4')
u raiseitu contextT( u _convert_otheru Trueu scaleb( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu scaleb� s c C s% t | d d �} | j | d | �S( u{ Returns a shifted copy of a, b times.
The coefficient of the result is a shifted copy of the digits
in the coefficient of the first operand. The number of places
to shift is taken from the absolute value of the second operand,
with the shift being to the left if the second operand is
positive or to the right otherwise. Digits shifted into the
coefficient are zeros.
>>> ExtendedContext.shift(Decimal('34'), Decimal('8'))
Decimal('400000000')
>>> ExtendedContext.shift(Decimal('12'), Decimal('9'))
Decimal('0')
>>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2'))
Decimal('1234567')
>>> ExtendedContext.shift(Decimal('123456789'), Decimal('0'))
Decimal('123456789')
>>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2'))
Decimal('345678900')
>>> ExtendedContext.shift(88888888, 2)
Decimal('888888800')
>>> ExtendedContext.shift(Decimal(88888888), 2)
Decimal('888888800')
>>> ExtendedContext.shift(88888888, Decimal(2))
Decimal('888888800')
u raiseitu contextT( u _convert_otheru Trueu shift( u selfu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu shift� s c C s" t | d d �} | j d | � S( u� Square root of a non-negative number to context precision.
If the result must be inexact, it is rounded using the round-half-even
algorithm.
>>> ExtendedContext.sqrt(Decimal('0'))
Decimal('0')
>>> ExtendedContext.sqrt(Decimal('-0'))
Decimal('-0')
>>> ExtendedContext.sqrt(Decimal('0.39'))
Decimal('0.624499800')
>>> ExtendedContext.sqrt(Decimal('100'))
Decimal('10')
>>> ExtendedContext.sqrt(Decimal('1'))
Decimal('1')
>>> ExtendedContext.sqrt(Decimal('1.0'))
Decimal('1.0')
>>> ExtendedContext.sqrt(Decimal('1.00'))
Decimal('1.0')
>>> ExtendedContext.sqrt(Decimal('7'))
Decimal('2.64575131')
>>> ExtendedContext.sqrt(Decimal('10'))
Decimal('3.16227766')
>>> ExtendedContext.sqrt(2)
Decimal('1.41421356')
>>> ExtendedContext.prec
9
u raiseitu contextT( u _convert_otheru Trueu sqrt( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu sqrt� s c C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S( u& Return the difference between the two operands.
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07'))
Decimal('0.23')
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30'))
Decimal('0.00')
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07'))
Decimal('-0.77')
>>> ExtendedContext.subtract(8, 5)
Decimal('3')
>>> ExtendedContext.subtract(Decimal(8), 5)
Decimal('3')
>>> ExtendedContext.subtract(8, Decimal(5))
Decimal('3')
u raiseitu contextu Unable to convert %s to DecimalNT( u _convert_otheru Trueu __sub__u NotImplementedu TypeError( u selfu au bu r( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu subtract s
c C s" t | d d �} | j d | � S( uy Converts a number to a string, using scientific notation.
The operation is not affected by the context.
u raiseitu contextT( u _convert_otheru Trueu
to_eng_string( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
to_eng_string s c C s" t | d d �} | j d | � S( uy Converts a number to a string, using scientific notation.
The operation is not affected by the context.
u raiseitu contextT( u _convert_otheru Trueu __str__( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
to_sci_string s c C s" t | d d �} | j d | � S( uk Rounds to an integer.
When the operand has a negative exponent, the result is the same
as using the quantize() operation using the given operand as the
left-hand-operand, 1E+0 as the right-hand-operand, and the precision
of the operand as the precision setting; Inexact and Rounded flags
are allowed in this operation. The rounding mode is taken from the
context.
>>> ExtendedContext.to_integral_exact(Decimal('2.1'))
Decimal('2')
>>> ExtendedContext.to_integral_exact(Decimal('100'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('100.0'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('101.5'))
Decimal('102')
>>> ExtendedContext.to_integral_exact(Decimal('-101.5'))
Decimal('-102')
>>> ExtendedContext.to_integral_exact(Decimal('10E+5'))
Decimal('1.0E+6')
>>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))
Decimal('7.89E+77')
>>> ExtendedContext.to_integral_exact(Decimal('-Inf'))
Decimal('-Infinity')
u raiseitu contextT( u _convert_otheru Trueu to_integral_exact( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu to_integral_exact( s c C s" t | d d �} | j d | � S( uL Rounds to an integer.
When the operand has a negative exponent, the result is the same
as using the quantize() operation using the given operand as the
left-hand-operand, 1E+0 as the right-hand-operand, and the precision
of the operand as the precision setting, except that no flags will
be set. The rounding mode is taken from the context.
>>> ExtendedContext.to_integral_value(Decimal('2.1'))
Decimal('2')
>>> ExtendedContext.to_integral_value(Decimal('100'))
Decimal('100')
>>> ExtendedContext.to_integral_value(Decimal('100.0'))
Decimal('100')
>>> ExtendedContext.to_integral_value(Decimal('101.5'))
Decimal('102')
>>> ExtendedContext.to_integral_value(Decimal('-101.5'))
Decimal('-102')
>>> ExtendedContext.to_integral_value(Decimal('10E+5'))
Decimal('1.0E+6')
>>> ExtendedContext.to_integral_value(Decimal('7.89E+77'))
Decimal('7.89E+77')
>>> ExtendedContext.to_integral_value(Decimal('-Inf'))
Decimal('-Infinity')
u raiseitu contextT( u _convert_otheru Trueu to_integral_value( u selfu a( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu to_integral_valueF s N(V u __name__u
__module__u __doc__u Noneu __init__u __repr__u clear_flagsu
_shallow_copyu copyu __copy__u
_get_clampu
_set_clampu propertyu _clampu _raise_erroru _ignore_all_flagsu
_ignore_flagsu
_regard_flagsu __hash__u Etinyu Etopu
_set_roundingu create_decimalu create_decimal_from_floatu absu addu _applyu canonicalu compareu compare_signalu
compare_totalu compare_total_magu copy_absu copy_decimalu copy_negateu copy_signu divideu
divide_intu divmodu expu fmau is_canonicalu is_finiteu is_infiniteu is_nanu is_normalu is_qnanu is_signedu is_snanu is_subnormalu is_zerou lnu log10u logbu logical_andu logical_invertu
logical_oru logical_xoru maxu max_magu minu min_magu minusu multiplyu
next_minusu next_plusu next_towardu normalizeu number_classu plusu poweru quantizeu radixu remainderu remainder_nearu rotateu same_quantumu scalebu shiftu sqrtu subtractu
to_eng_stringu
to_sci_stringu to_integral_exactu to_integral_valueu to_integral( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu Context� s�
"
$ #
% # 2 P : & " c B s/ | Ee Z d Z d d � Z d � Z e Z d S( u signu intu expc C s� | d k r* d | _ d | _ d | _ nc t | t � rf | j | _ t | j � | _ | j | _ n' | d | _ | d | _ | d | _ d S( Ni i i ( u Noneu signu intu expu
isinstanceu Decimalu _signu _intu _exp( u selfu value( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __init__l s
c C s d | j | j | j f S( Nu (%r, %r, %r)( u signu intu exp( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __repr__{ s N( u signu intu exp( u __name__u
__module__u __slots__u Noneu __init__u __repr__u __str__( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _WorkRepf s
u _WorkRepc C s� | j | j k r! | } | } n | } | } t t | j � � } t t | j � � } | j t d | | d � } | | j d | k r� d | _ | | _ n | j d | j | j 9_ | j | _ | | f S( uc Normalizes op1, op2 to have the same exp and length of coefficient.
Done during addition.
i i i
i����( u expu lenu stru intu min( u op1u op2u precu tmpu otheru tmp_lenu other_lenu exp( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_normalize� s c C s^ | d k s | d k r' t d � � n d } x* | | k rY | | | | d ?} } q0 W| S( u� Closest integer to the square root of the positive integer n. a is
an initial approximation to the square root. Any positive integer
will do for a, but the closer a is to the square root of n the
faster convergence will be.
i u3 Both arguments to _sqrt_nearest should be positive.i ( u
ValueError( u nu au b( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_sqrt_nearest� s c C s7 d | >| | ?} } | d | | d @| d @| k S( u� Given an integer x and a nonnegative integer shift, return closest
integer to x / 2**shift; use round-to-even in case of a tie.
i i ( ( u xu shiftu bu q( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _rshift_nearest� s c C s/ t | | � \ } } | d | | d @| k S( ua Closest integer to a/b, a and b positive integers; rounds to even
in the case of a tie.
i i ( u divmod( u au bu qu r( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _div_nearest� s i c C s7 | | } d } x� | | k r9 t | � | | >| k s_ | | k r� t | � | | ?| k r� t | | d >| t | | t | | � | � � } | d 7} q Wt d t t | � � d | � } t | | � } t | | � } x> t | d d d � D]& } t | | � t | | | � } q� Wt | | | � S( u� Integer approximation to M*log(x/M), with absolute error boundable
in terms only of x/M.
Given positive integers x and M, return an integer approximation to
M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference
between the approximation and the exact result is at most 22. For
L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In
both cases these are upper bounds on the error; it will usually be
much smaller.i i i
i i����i����( u absu _div_nearestu
_sqrt_nearestu _rshift_nearestu intu lenu stru range( u xu Mu Lu yu Ru Tu yshiftu wu k( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _ilog� s
)&'% $c
C s� | d 7} t t | � � } | | | | d k } | d k r� d | } | | | } | d k ru | d | 9} n t | d | � } t | | � } t | � } t | | | � } | | } n d } t | d | � } t | | d � S( u� Given integers c, e and p with c > 0, p >= 0, compute an integer
approximation to 10**p * log10(c*10**e), with an absolute error of
at most 1. Assumes that c*10**e is not exactly 1.i i i i
id ( u lenu stru _div_nearestu _ilogu
_log10_digits(
u cu eu pu lu fu Mu ku log_du log_10u log_tenpower( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _dlog10� s
c C s | d 7} t t | � � } | | | | d k } | d k r� | | | } | d k rk | d | 9} n t | d | � } t | d | � } n d } | r� t t t | � � � d } | | d k r� t | t | | � d | � } q d } n d } t | | d � S( u� Given integers c, e and p with c > 0, compute an integer
approximation to 10**p * log(c*10**e), with an absolute error of
at most 1. Assumes that c*10**e is not exactly 1.i i i i
id ( u lenu stru _div_nearestu _ilogu absu
_log10_digits( u cu eu pu lu fu ku log_du extrau f_log_ten( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _dlog s"
$ c B s& | Ee Z d Z d � Z d � Z d S( u� Class to compute, store, and allow retrieval of, digits of the
constant log(10) = 2.302585.... This constant is needed by
Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.c C s
d | _ d S( Nu/ 23025850929940456840179914546843642076011014886( u digits( u self( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu __init__C s c C s� | d k r t d � � n | t | j � k r� d } x` d | | d } t t t d | | � d � � } | | d � d | k r� Pn | d 7} q9 | j d � d d
� | _ n t | j d | d � � S( ut Given an integer p >= 0, return floor(10**p)*log(10).
For example, self.getdigits(3) returns 2302.
i u p should be nonnegativei i
i id Nu 0i i����( u
ValueErroru lenu digitsu stru _div_nearestu _ilogu rstripu int( u selfu pu extrau Mu digits( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu getdigitsF s "
N( u __name__u
__module__u __doc__u __init__u getdigits( u
__locals__( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_Log10Memoize? s
u
_Log10Memoizec C s� t | | >| � } t d t t | � � d | � } t | | � } | | >} x9 t | d d d � D]! } t | | | | | � } qi WxC t | d d d � D]+ } | | d >} t | | | | � } q� W| | S(
u� Given integers x and M, M > 0, such that x/M is small in absolute
value, compute an integer approximation to M*exp(x/M). For 0 <=
x/M <= 2.4, the absolute error in the result is bounded by 60 (and
is usually much smaller).i
i i i i i����i����i����i����( u _nbitsu intu lenu stru _div_nearestu range( u xu Mu Lu Ru Tu yu Mshiftu iu k( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _iexpd s %
c C s� | d 7} t d | t t | � � d � } | | } | | } | d k r^ | d | } n | d | } t | t | � � \ } } t | d | � } t t | d | � d � | | d f S( u� Compute an approximation to exp(c*10**e), with p decimal places of
precision.
Returns integers d, f such that:
10**(p-1) <= d <= 10**p, and
(d-1)*10**f < exp(c*10**e) < (d+1)*10**f
In other words, d*10**f is an approximation to exp(c*10**e) with p
digits of precision, and with an error in d of at most 1. This is
almost, but not quite, the same as the error being < 1ulp: when d
= 10**(p-1) the error could be up to 10 ulp.i i i i
i� i ( u maxu lenu stru divmodu
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#
c C s* t t t | � � � | } t | | | | d � } | | } | d k ra | | d | } n t | | d | � } | d k r� t t | � � | d k | d k k r� d | d d d | } }
q d | d | } }
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t | d � } |
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f S( u5 Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and
y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that:
10**(p-1) <= c <= 10**p, and
(c-1)*10**e < x**y < (c+1)*10**e
in other words, c*10**e is an approximation to x**y with p digits
of precision, and with an error in c of at most 1. (This is
almost, but not quite, the same as the error being < 1ulp: when c
== 10**(p-1) we can only guarantee error < 10ulp.)
We assume that: x is positive and not equal to 1, and y is nonzero.
i i i
( u lenu stru absu _dlogu _div_nearestu _dexp( u xcu xeu ycu yeu pu bu lxcu shiftu pcu coeffu exp( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _dpower� s
( !
id u 1iF u 2i5 u 3i( u 4i u 5i u 6i u 7i
u 8i u 9c C sA | d k r t d � � n t | � } d t | � | | d S( u@ Compute a lower bound for 100*log10(c) for a positive integer c.i u0 The argument to _log10_lb should be nonnegative.id ( u
ValueErroru stru len( u cu
correctionu str_c( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _log10_lb� s c C sk t | t � r | St | t � r, t | � S| rN t | t � rN t j | � S| rg t d | � � n t S( u� Convert other to Decimal.
Verifies that it's ok to use in an implicit construction.
If allow_float is true, allow conversion from float; this
is used in the comparison methods (__eq__ and friends).
u Unable to convert %s to Decimal( u
isinstanceu Decimalu intu floatu
from_floatu TypeErroru NotImplemented( u otheru raiseitu allow_float( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _convert_other� s
c C s� t | t � r | | f St | t j � rx | j se t | j t t | j � | j
� | j � } n | t | j � f S| r� t | t j
� r� | j d k r� | j } n t | t � r� | t j | � f St t f S( u� Given a Decimal instance self and a Python object other, return
a pair (s, o) of Decimal instances such that "s op o" is
equivalent to "self op other" for any of the 6 comparison
operators "op".
i ( u
isinstanceu Decimalu _numbersu Rationalu _is_specialu _dec_from_tripleu _signu stru intu _intu denominatoru _expu numeratoru Complexu imagu realu floatu
from_floatu NotImplemented( u selfu otheru equality_op( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _convert_for_comparison� s
' u preci u roundingu trapsu flagsu Emaxi�ɚ;u Eminu capitalsi u clampi u� # A numeric string consists of:
# \s*
(?P<sign>[-+])? # an optional sign, followed by either...
(
(?=\d|\.\d) # ...a number (with at least one digit)
(?P<int>\d*) # having a (possibly empty) integer part
(\.(?P<frac>\d*))? # followed by an optional fractional part
(E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or...
|
Inf(inity)? # ...an infinity, or...
|
(?P<signal>s)? # ...an (optionally signaling)
NaN # NaN
(?P<diag>\d*) # with (possibly empty) diagnostic info.
)
# \s*
\Z
u 0*$u 50*$u� \A
(?:
(?P<fill>.)?
(?P<align>[<>=^])
)?
(?P<sign>[-+ ])?
(?P<alt>\#)?
(?P<zeropad>0)?
(?P<minimumwidth>(?!0)\d+)?
(?P<thousands_sep>,)?
(?:\.(?P<precision>0|(?!0)\d+))?
(?P<type>[eEfFgGn%])?
\Z
c C s+ t j | � } | d k r. t d | � � n | j � } | d } | d } | d d k | d <| d r� | d k r� t d | � � n | d k r� t d | � � q� n | p� d | d <| p� d | d <| d d k r� d
| d <n t | d p� d � | d <| d
d k r+t | d
� | d
<n | d
d k rk| d d k s[| d d k rkd | d
<qkn | d d k r�d | d <| d k r�t j � } n | d d k r�t d | � � n | d | d <| d | d <| d | d <n7 | d d k r
d | d <n d d g | d <d | d <| S( u� Parse and validate a format specifier.
Turns a standard numeric format specifier into a dict, with the
following entries:
fill: fill character to pad field to minimum width
align: alignment type, either '<', '>', '=' or '^'
sign: either '+', '-' or ' '
minimumwidth: nonnegative integer giving minimum width
zeropad: boolean, indicating whether to pad with zeros
thousands_sep: string to use as thousands separator, or ''
grouping: grouping for thousands separators, in format
used by localeconv
decimal_point: string to use for decimal point
precision: nonnegative integer giving precision, or None
type: one of the characters 'eEfFgG%', or None
u Invalid format specifier: u fillu alignu zeropadu7 Fill character conflicts with '0' in format specifier: u2 Alignment conflicts with '0' in format specifier: u u >u signu -u minimumwidthu 0u precisioni u typeu gGi u nu gu
thousands_sepuJ Explicit thousands separator conflicts with 'n' type in format specifier: u groupingu
decimal_pointu i u .N( u _parse_format_specifier_regexu matchu Noneu
ValueErroru groupdictu intu _localeu
localeconv( u format_specu _localeconvu mu format_dictu fillu align( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _parse_format_specifier| sN
c C s� | d } | d } | | t | � t | � } | d } | d k rY | | | } n� | d k rv | | | } nn | d k r� | | | } nQ | d k r� t | � d } | d | � | | | | d � } n t d
� � | S( u� Given an unpadded, non-aligned numeric string 'body' and sign
string 'sign', add padding and alignment conforming to the given
format specifier dictionary 'spec' (as produced by
parse_format_specifier).
u minimumwidthu fillu alignu <u >u =u ^i Nu Unrecognised alignment field( u lenu
ValueError( u signu bodyu specu minimumwidthu fillu paddingu alignu resultu half( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu
_format_align� s
) c C s� d d l m } m } | s g S| d d k rc t | � d k rc | | d d � | | d � � S| d
t j k r� | d d � St d � � d S( uy Convert a localeconv-style grouping into a (possibly infinite)
iterable of integers representing group lengths.
i ( u chainu repeati i Nu unrecognised format for groupingi����i����i����i����i����( u itertoolsu chainu repeatu lenu _localeu CHAR_MAXu
ValueError( u groupingu chainu repeat( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _group_lengths� s
"!c C s. | d } | d } g } x� t | � D]� } | d k rH t d � � n t t t | � | d � | � } | j d | t | � | | d � � | d | � } | | 8} | r� | d k r� Pn | t | � 8} q' Wt t | � | d � } | j d | t | � | | d � � | j t | � � S( un Insert thousands separators into a digit string.
spec is a dictionary whose keys should include 'thousands_sep' and
'grouping'; typically it's the result of parsing the format
specifier using _parse_format_specifier.
The min_width keyword argument gives the minimum length of the
result, which will be padded on the left with zeros if necessary.
If necessary, the zero padding adds an extra '0' on the left to
avoid a leading thousands separator. For example, inserting
commas every three digits in '123456', with min_width=8, gives
'0,123,456', even though that has length 9.
u
thousands_sepu groupingi u group length should be positivei u 0N( u _group_lengthsu
ValueErroru minu maxu lenu appendu joinu reversed( u digitsu specu min_widthu sepu groupingu groupsu l( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _insert_thousands_sep� s
!*
*c C s* | r
d S| d d k r" | d Sd Sd S( u Determine sign character.u -u signu +u N( ( u is_negativeu spec( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _format_sign# s
c C s t | | � } | s | d r0 | d | } n | d k sL | d d k r� i d d 6d d 6d d 6d d 6| d } | d
j | | � 7} n | d d k r� | d 7} n | d r� | d
t | � t | � } n d } t | | | � } t | | | | � S( uc Format a number, given the following data:
is_negative: true if the number is negative, else false
intpart: string of digits that must appear before the decimal point
fracpart: string of digits that must come after the point
exp: exponent, as an integer
spec: dictionary resulting from parsing the format specifier
This function uses the information in spec to:
insert separators (decimal separator and thousands separators)
format the sign
format the exponent
add trailing '%' for the '%' type
zero-pad if necessary
fill and align if necessary
u altu
decimal_pointi u typeu eEu Eu eu Gu gu {0}{1:+}u %u zeropadu minimumwidth( u _format_signu formatu lenu _insert_thousands_sepu
_format_align( u is_negativeu intpartu fracpartu expu specu signu echaru min_width( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu _format_number- s *
!u Infu -Infu NaNi u __main__(w u __doc__u __all__u __version__u copyu _copyu mathu _mathu numbersu _numbersu collectionsu
namedtupleu _namedtupleu DecimalTupleu ImportErroru
ROUND_DOWNu
ROUND_HALF_UPu ROUND_HALF_EVENu
ROUND_CEILINGu ROUND_FLOORu ROUND_UPu ROUND_HALF_DOWNu
ROUND_05UPu ArithmeticErroru DecimalExceptionu Clampedu InvalidOperationu ConversionSyntaxu ZeroDivisionErroru DivisionByZerou DivisionImpossibleu DivisionUndefinedu Inexactu InvalidContextu Roundedu Subnormalu Overflowu Underflowu _signalsu _condition_mapu threadingu sysu objectu
MockThreadingu localu AttributeErroru hasattru current_threadu __decimal_context__u
setcontextu
getcontextu Noneu localcontextu Decimalu Falseu _dec_from_tripleu Numberu registeru _ContextManageru Contextu _WorkRepu
_normalizeu intu
bit_lengthu _nbitsu
_sqrt_nearestu _rshift_nearestu _div_nearestu _ilogu _dlog10u _dlogu
_Log10Memoizeu getdigitsu
_log10_digitsu _iexpu _dexpu _dpoweru _log10_lbu _convert_otheru _convert_for_comparisonu DefaultContextu BasicContextu ExtendedContextu reu compileu VERBOSEu
IGNORECASEu matchu _parseru
_all_zerosu _exact_halfu _parse_format_specifier_regexu localeu _localeu _parse_format_specifieru
_format_alignu _group_lengthsu _insert_thousands_sepu _format_signu _format_numberu _Infinityu _NegativeInfinityu _NaNu _Zerou _Oneu _NegativeOneu _SignedInfinityu hash_infou modulusu _PyHASH_MODULUSu infu _PyHASH_INFu nanu _PyHASH_NANu powu
_PyHASH_10INVu __name__u doctestu decimalu testmod( ( ( u. /usr/local/python-3.2/lib/python3.2/decimal.pyu <module>q s8
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