# Copyright (c) 2004 Python Software Foundation.
# Written by Eric Price <eprice at tjhsst.edu>
# and Facundo Batista <facundo at taniquetil.com.ar>
# and Raymond Hettinger <python at rcn.com>
# and Aahz <aahz at pobox.com>
# This module is currently Py2.3 compatible and should be kept that way
# unless a major compelling advantage arises. IOW, 2.3 compatibility is
# strongly preferred, but not guaranteed.
# Also, this module should be kept in sync with the latest updates of
# the IBM specification as it evolves. Those updates will be treated
# as bug fixes (deviation from the spec is a compatibility, usability
# bug) and will be backported. At this point the spec is stabilizing
# and the updates are becoming fewer, smaller, and less significant.
This is a Py2.3 implementation of decimal floating point arithmetic based on
the General Decimal Arithmetic Specification:
www2.hursley.ibm.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 the module is to support arithmetic using familiar
"schoolhouse" rules and to avoid the some of 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 the expected Decimal("0.00") returned by decimal floating point).
Here are some examples of using the decimal module:
>>> from decimal import *
>>> setcontext(ExtendedContext)
>>> Decimal("123.45e12345678901234567890")
Decimal("1.2345E+12345678901234567892")
>>> Decimal("1.33") + Decimal("1.27")
>>> Decimal("12.34") + Decimal("3.87") - Decimal("18.41")
>>> print dig / Decimal(3)
>>> getcontext().prec = 18
>>> print dig / Decimal(3)
>>> print Decimal(3).sqrt()
>>> print Decimal(3) ** 123
>>> inf = Decimal(1) / Decimal(0)
>>> neginf = Decimal(-1) / Decimal(0)
>>> getcontext().traps[DivisionByZero] = 1
Traceback (most recent call last):
>>> c.traps[InvalidOperation] = 0
>>> print c.flags[InvalidOperation]
>>> c.divide(Decimal(0), Decimal(0))
>>> c.traps[InvalidOperation] = 1
>>> print c.flags[InvalidOperation]
>>> c.flags[InvalidOperation] = 0
>>> print c.flags[InvalidOperation]
>>> print c.divide(Decimal(0), Decimal(0))
Traceback (most recent call last):
>>> print c.flags[InvalidOperation]
>>> c.flags[InvalidOperation] = 0
>>> c.traps[InvalidOperation] = 0
>>> print c.divide(Decimal(0), Decimal(0))
>>> print c.flags[InvalidOperation]
'DefaultContext', 'BasicContext', 'ExtendedContext',
'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero',
'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow',
# Constants for use in setting up contexts
'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING',
'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN',
# Functions for manipulating contexts
'setcontext', 'getcontext'
ROUND_DOWN
= 'ROUND_DOWN'
ROUND_HALF_UP
= 'ROUND_HALF_UP'
ROUND_HALF_EVEN
= 'ROUND_HALF_EVEN'
ROUND_CEILING
= 'ROUND_CEILING'
ROUND_FLOOR
= 'ROUND_FLOOR'
ROUND_HALF_DOWN
= 'ROUND_HALF_DOWN'
#Rounding decision (not part of the public API)
NEVER_ROUND
= 'NEVER_ROUND' # Round in division (non-divmod), sqrt ONLY
ALWAYS_ROUND
= 'ALWAYS_ROUND' # Every operation rounds at end.
class DecimalException(ArithmeticError):
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
handle -- Called when context._raise_error is called and the
trap_enabler is 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
def handle(self
, context
, *args
):
class Clamped(DecimalException
):
"""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").
class InvalidOperation(DecimalException
):
"""An invalid operation was performed.
Various bad things cause this:
Something creates a signaling NaN
x._rescale( non-integer )
def handle(self
, context
, *args
):
if args
[0] == 1: #sNaN, must drop 's' but keep diagnostics
return Decimal( (args
[1]._sign
, args
[1]._int
, 'n') )
class ConversionSyntax(InvalidOperation
):
"""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].
def handle(self
, context
, *args
):
return (0, (0,), 'n') #Passed to something which uses a tuple.
class DivisionByZero(DecimalException
, ZeroDivisionError):
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
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
def handle(self
, context
, sign
, double
= None, *args
):
return (Infsign
[sign
],)*2
class DivisionImpossible(InvalidOperation
):
"""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].
def handle(self
, context
, *args
):
class DivisionUndefined(InvalidOperation
, ZeroDivisionError):
"""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].
def handle(self
, context
, tup
=None, *args
):
return (NaN
, NaN
) #for 0 %0, 0 // 0
class Inexact(DecimalException
):
"""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.
class InvalidContext(InvalidOperation
):
"""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].
def handle(self
, context
, *args
):
class Rounded(DecimalException
):
"""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.
class Subnormal(DecimalException
):
"""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
Emin, before any rounding). The result in all cases is unchanged.
The subnormal signal may be tested (or trapped) to determine if a given
or operation (or sequence of operations) yielded a subnormal result.
class Overflow(Inexact
, Rounded
):
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
def handle(self
, context
, sign
, *args
):
if context
.rounding
in (ROUND_HALF_UP
, ROUND_HALF_EVEN
,
ROUND_HALF_DOWN
, ROUND_UP
):
if context
.rounding
== ROUND_CEILING
:
return Decimal((sign
, (9,)*context
.prec
,
context
.Emax
-context
.prec
+1))
if context
.rounding
== ROUND_FLOOR
:
return Decimal( (sign
, (9,)*context
.prec
,
context
.Emax
-context
.prec
+1))
class Underflow(Inexact
, Rounded
, Subnormal
):
"""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.
# List of public traps and flags
_signals
= [Clamped
, DivisionByZero
, Inexact
, Overflow
, Rounded
,
Underflow
, InvalidOperation
, Subnormal
]
# Map conditions (per the spec) to signals
_condition_map
= {ConversionSyntax
:InvalidOperation
,
DivisionImpossible
:InvalidOperation
,
DivisionUndefined
:InvalidOperation
,
InvalidContext
:InvalidOperation
}
##### Context Functions #######################################
# The getcontext() and setcontext() function manage access to a thread-local
# current context. Py2.4 offers direct support for thread locals. If that
# is not available, use threading.currentThread() which is slower but will
# work for older Pythons. If threads are not part of the build, create a
# mock threading object with threading.local() returning the module namespace.
# Python was compiled without threads; create a mock object instead
def local(self
, sys
=sys
):
return sys
.modules
[__name__
]
threading
= MockThreading()
#To fix reloading, force it to create a new context
#Old contexts have different exceptions in their dicts, making problems.
if hasattr(threading
.currentThread(), '__decimal_context__'):
del threading
.currentThread().__decimal
_context
__
"""Set this thread's context to context."""
if context
in (DefaultContext
, BasicContext
, ExtendedContext
):
threading
.currentThread().__decimal
_context
__ = context
"""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.
return threading
.currentThread().__decimal
_context
__
threading
.currentThread().__decimal
_context
__ = context
local
= threading
.local()
if hasattr(local
, '__decimal_context__'):
del local
.__decimal
_context
__
def getcontext(_local
=local
):
"""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.
return _local
.__decimal
_context
__
_local
.__decimal
_context
__ = context
def setcontext(context
, _local
=local
):
"""Set this thread's context to context."""
if context
in (DefaultContext
, BasicContext
, ExtendedContext
):
_local
.__decimal
_context
__ = context
del threading
, local
# Don't contaminate the namespace
##### Decimal class ###########################################
"""Floating point class for decimal arithmetic."""
__slots__
= ('_exp','_int','_sign', '_is_special')
# Generally, the value of the Decimal instance is given by
# (-1)**_sign * _int * 10**_exp
# Special values are signified by _is_special == True
# We're immutable, so use __new__ not __init__
def __new__(cls
, value
="0", context
=None):
"""Create a decimal point instance.
>>> Decimal('3.14') # string input
>>> Decimal((0, (3, 1, 4), -2)) # tuple input (sign, digit_tuple, exponent)
>>> Decimal(314) # int or long
>>> Decimal(Decimal(314)) # another decimal instance
self
= object.__new
__(cls
)
# From an internal working value
if isinstance(value
, _WorkRep
):
self
._int
= tuple(map(int, str(value
.int)))
self
._exp
= int(value
.exp
)
if isinstance(value
, Decimal
):
self
._is
_special
= value
._is
_special
if isinstance(value
, (int,long)):
self
._int
= tuple(map(int, str(abs(value
))))
# tuple/list conversion (possibly from as_tuple())
if isinstance(value
, (list,tuple)):
raise ValueError, 'Invalid arguments'
if value
[0] not in (0,1):
raise ValueError, 'Invalid sign'
if not isinstance(digit
, (int,long)) or digit
< 0:
raise ValueError, "The second value in the tuple must be composed of non negative integer elements."
self
._int
= tuple(value
[1])
if value
[2] in ('F','n','N'):
self
._exp
= int(value
[2])
if isinstance(value
, float):
raise TypeError("Cannot convert float to Decimal. " +
"First convert the float to a string")
# Other argument types may require the context during interpretation
# REs insist on real strings, so we can too.
if isinstance(value
, basestring
):
if _isinfinity(value
) == 1:
sig
, sign
, diag
= _isnan(value
)
if len(diag
) > context
.prec
: #Diagnostic info too long
self
._sign
, self
._int
, self
._exp
= \
context
._raise
_error
(ConversionSyntax
)
self
._int
= tuple(map(int, diag
)) #Diagnostic info
self
._sign
, self
._int
, self
._exp
= _string2exact(value
)
self
._sign
, self
._int
, self
._exp
= context
._raise
_error
(ConversionSyntax
)
raise TypeError("Cannot convert %r to Decimal" % value
)
"""Returns whether the number is not actually one.
"""Returns whether the number is infinite
0 if finite or not a number
def _check_nans(self
, other
= None, context
=None):
"""Returns whether the number is not actually one.
if self, other are sNaN, signal
if self, other are NaN return nan
self_is_nan
= self
._isnan
()
other_is_nan
= other
._isnan
()
if self_is_nan
or other_is_nan
:
return context
._raise
_error
(InvalidOperation
, 'sNaN',
return context
._raise
_error
(InvalidOperation
, 'sNaN',
"""Is the number non-zero?
return sum(self
._int
) != 0
def __cmp__(self
, other
, context
=None):
other
= _convert_other(other
)
if other
is NotImplemented:
if self
._is
_special
or other
._is
_special
:
ans
= self
._check
_nans
(other
, context
)
return 1 # Comparison involving NaN's always reports self > other
return cmp(self
._isinfinity
(), other
._isinfinity
())
if not self
and not other
:
return 0 #If both 0, sign comparison isn't certain.
#If different signs, neg one is less
if other
._sign
< self
._sign
:
if self
._sign
< other
._sign
:
self_adjusted
= self
.adjusted()
other_adjusted
= other
.adjusted()
if self_adjusted
== other_adjusted
and \
self
._int
+ (0,)*(self
._exp
- other
._exp
) == \
other
._int
+ (0,)*(other
._exp
- self
._exp
):
return 0 #equal, except in precision. ([0]*(-x) = [])
elif self_adjusted
> other_adjusted
and self
._int
[0] != 0:
elif self_adjusted
< other_adjusted
and other
._int
[0] != 0:
return -((-1)**self
._sign
)
# Need to round, so make sure we have a valid context
context
= context
._shallow
_copy
()
rounding
= context
._set
_rounding
(ROUND_UP
) #round away from 0
flags
= context
._ignore
_all
_flags
()
res
= self
.__sub
__(other
, context
=context
)
context
._regard
_flags
(*flags
)
context
.rounding
= rounding
if not isinstance(other
, (Decimal
, int, long)):
return self
.__cmp
__(other
) == 0
if not isinstance(other
, (Decimal
, int, long)):
return self
.__cmp
__(other
) != 0
def compare(self
, other
, context
=None):
"""Compares one to another.
Like __cmp__, but returns Decimal instances.
other
= _convert_other(other
)
if other
is NotImplemented:
if (self
._is
_special
or other
and other
._is
_special
):
ans
= self
._check
_nans
(other
, context
)
return Decimal(self
.__cmp
__(other
, context
))
"""x.__hash__() <==> hash(x)"""
# Decimal integers must hash the same as the ints
# Non-integer decimals are normalized and hashed as strings
# Normalization assures that hast(100E-1) == hash(10)
raise TypeError('Cannot hash a NaN value.')
assert self
.__nonzero
__() # '-0' handled by integer case
return hash(str(self
.normalize()))
"""Represents the number as a triple tuple.
To show the internals exactly as they are.
return (self
._sign
, self
._int
, self
._exp
)
"""Represents the number as an instance of Decimal."""
# Invariant: eval(repr(d)) == d
return 'Decimal("%s")' % str(self
)
def __str__(self
, eng
= 0, context
=None):
"""Return string representation of the number in scientific notation.
Captures all of the information in the underlying representation.
info
= ''.join(map(str, self
._int
))
return minus
+ 'sNaN' + info
return minus
+ 'NaN' + info
return minus
+ 'Infinity'
tmp
= map(str, self
._int
)
numdigits
= len(self
._int
)
leftdigits
= self
._exp
+ numdigits
if eng
and not self
: #self = 0eX wants 0[.0[0]]eY, not [[0]0]0eY
if self
._exp
< 0 and self
._exp
>= -6: #short, no need for e/E
s
= '-'*self
._sign
+ '0.' + '0'*(abs(self
._exp
))
#exp is closest mult. of 3 >= self._exp
exp
= ((self
._exp
- 1)// 3 + 1) * 3
s
= '0.'+'0'*(exp
- self
._exp
)
s
+= '+' #0.0e+3, not 0.0e3
dotplace
= (leftdigits
-1)%3+1
adjexp
= leftdigits
-1 - (leftdigits
-1)%3
elif self
._exp
< 0 and adjexp
>= 0:
tmp
.insert(leftdigits
, '.')
elif self
._exp
< 0 and adjexp
>= -6:
tmp
[0:0] = ['0'] * int(-leftdigits
)
tmp
.insert(dotplace
, '.')
elif numdigits
< dotplace
:
tmp
.extend(['0']*(dotplace
-numdigits
))
if len(tmp
) == 0 or tmp
[0] == '.' or tmp
[0].lower() == 'e':
def to_eng_string(self
, context
=None):
"""Convert to engineering-type string.
Engineering notation has an exponent which is a multiple of 3, so there
are up to 3 digits left of the decimal place.
Same rules for when in exponential and when as a value as in __str__.
return self
.__str
__(eng
=1, context
=context
)
def __neg__(self
, context
=None):
"""Returns a copy with the sign switched.
Rounds, if it has reason.
ans
= self
._check
_nans
(context
=context
)
# -Decimal('0') is Decimal('0'), not Decimal('-0')
if context
._rounding
_decision
== ALWAYS_ROUND
:
return Decimal((sign
, self
._int
, self
._exp
))._fix
(context
)
return Decimal( (sign
, self
._int
, self
._exp
))
def __pos__(self
, context
=None):
"""Returns a copy, unless it is a sNaN.
Rounds the number (if more then precision digits)
ans
= self
._check
_nans
(context
=context
)
if context
._rounding
_decision
== ALWAYS_ROUND
:
def __abs__(self
, round=1, context
=None):
"""Returns the absolute value of self.
If the second argument is 0, do not round.
ans
= self
._check
_nans
(context
=context
)
context
= context
._shallow
_copy
()
context
._set
_rounding
_decision
(NEVER_ROUND
)
ans
= self
.__neg
__(context
=context
)
ans
= self
.__pos
__(context
=context
)
def __add__(self
, other
, context
=None):
-INF + INF (or the reverse) cause InvalidOperation errors.
other
= _convert_other(other
)
if other
is NotImplemented:
if self
._is
_special
or other
._is
_special
:
ans
= self
._check
_nans
(other
, context
)
#If both INF, same sign => same as both, opposite => error.
if self
._sign
!= other
._sign
and other
._isinfinity
():
return context
._raise
_error
(InvalidOperation
, '-INF + INF')
return Decimal(other
) #Can't both be infinity here
shouldround
= context
._rounding
_decision
== ALWAYS_ROUND
exp
= min(self
._exp
, other
._exp
)
if context
.rounding
== ROUND_FLOOR
and self
._sign
!= other
._sign
:
#If the answer is 0, the sign should be negative, in this case.
if not self
and not other
:
sign
= min(self
._sign
, other
._sign
)
return Decimal( (sign
, (0,), exp
))
exp
= max(exp
, other
._exp
- context
.prec
-1)
ans
= other
._rescale
(exp
, watchexp
=0, context
=context
)
exp
= max(exp
, self
._exp
- context
.prec
-1)
ans
= self
._rescale
(exp
, watchexp
=0, context
=context
)
op1
, op2
= _normalize(op1
, op2
, shouldround
, context
.prec
)
if exp
< context
.Etiny():
context
._raise
_error
(Clamped
)
return Decimal((negativezero
, (0,), exp
))
#OK, now abs(op1) > abs(op2)
op1
.sign
, op2
.sign
= op2
.sign
, op1
.sign
#So we know the sign, and op1 > 0.
op1
.sign
, op2
.sign
= (0, 0)
result
.int = op1
.int + op2
.int
result
.int = op1
.int - op2
.int
def __sub__(self
, other
, context
=None):
"""Return self + (-other)"""
other
= _convert_other(other
)
if other
is NotImplemented:
if self
._is
_special
or other
._is
_special
:
ans
= self
._check
_nans
(other
, context
=context
)
# -Decimal(0) = Decimal(0), which we don't want since
# (-0 - 0 = -0 + (-0) = -0, but -0 + 0 = 0.)
# so we change the sign directly to a copy
return self
.__add
__(tmp
, context
=context
)
def __rsub__(self
, other
, context
=None):
"""Return other + (-self)"""
other
= _convert_other(other
)
if other
is NotImplemented:
tmp
._sign
= 1 - tmp
._sign
return other
.__add
__(tmp
, context
=context
)
def _increment(self
, round=1, context
=None):
"""Special case of add, adding 1eExponent
Since it is common, (rounding, for example) this adds
(sign)*one E self._exp to the number more efficiently than add.
Decimal('5.624e10')._increment() == Decimal('5.625e10')
ans
= self
._check
_nans
(context
=context
)
return Decimal(self
) # Must be infinite, and incrementing makes no difference
ans
= Decimal((self
._sign
, L
, self
._exp
))
if round and context
._rounding
_decision
== ALWAYS_ROUND
:
def __mul__(self
, other
, context
=None):
(+-) INF * 0 (or its reverse) raise InvalidOperation.
other
= _convert_other(other
)
if other
is NotImplemented:
resultsign
= self
._sign ^ other
._sign
if self
._is
_special
or other
._is
_special
:
ans
= self
._check
_nans
(other
, context
)
return context
._raise
_error
(InvalidOperation
, '(+-)INF * 0')
return Infsign
[resultsign
]
return context
._raise
_error
(InvalidOperation
, '0 * (+-)INF')
return Infsign
[resultsign
]
resultexp
= self
._exp
+ other
._exp
shouldround
= context
._rounding
_decision
== ALWAYS_ROUND
# Special case for multiplying by zero
if not self
or not other
:
ans
= Decimal((resultsign
, (0,), resultexp
))
#Fixing in case the exponent is out of bounds
# Special case for multiplying by power of 10
ans
= Decimal((resultsign
, other
._int
, resultexp
))
ans
= Decimal((resultsign
, self
._int
, resultexp
))
ans
= Decimal( (resultsign
, map(int, str(op1
.int * op2
.int)), resultexp
))
def __div__(self
, other
, context
=None):
"""Return self / other."""
return self
._divide
(other
, context
=context
)
def _divide(self
, other
, divmod = 0, context
=None):
"""Return a / b, to context.prec precision.
Actually, if divmod is 2 or 3 a tuple is returned, but errors for
computing the other value are not raised.
other
= _convert_other(other
)
if other
is NotImplemented:
return (NotImplemented, NotImplemented)
sign
= self
._sign ^ other
._sign
if self
._is
_special
or other
._is
_special
:
ans
= self
._check
_nans
(other
, context
)
if self
._isinfinity
() and other
._isinfinity
():
return (context
._raise
_error
(InvalidOperation
,
context
._raise
_error
(InvalidOperation
,
return context
._raise
_error
(InvalidOperation
, '(+-)INF/(+-)INF')
context
._raise
_error
(InvalidOperation
, 'INF % x'))
return (Infsign
[sign
], NaN
)
context
._raise
_error
(InvalidOperation
, 'INF % x'))
return (Decimal((sign
, (0,), 0)), Decimal(self
))
context
._raise
_error
(Clamped
, 'Division by infinity')
return Decimal((sign
, (0,), context
.Etiny()))
# Special cases for zeroes
if not self
and not other
:
return context
._raise
_error
(DivisionUndefined
, '0 / 0', 1)
return context
._raise
_error
(DivisionUndefined
, '0 / 0')
otherside
= Decimal(self
)
otherside
._exp
= min(self
._exp
, other
._exp
)
return (Decimal((sign
, (0,), 0)), otherside
)
exp
= self
._exp
- other
._exp
if exp
< context
.Etiny():
context
._raise
_error
(Clamped
, '0e-x / y')
context
._raise
_error
(Clamped
, '0e+x / y')
return Decimal( (sign
, (0,), exp
) )
return context
._raise
_error
(DivisionByZero
, 'divmod(x,0)',
return context
._raise
_error
(DivisionByZero
, 'x / 0', sign
)
#OK, so neither = 0, INF or NaN
shouldround
= context
._rounding
_decision
== ALWAYS_ROUND
#If we're dividing into ints, and self < other, stop.
#self.__abs__(0) does not round.
if divmod and (self
.__abs
__(0, context
) < other
.__abs
__(0, context
)):
if divmod == 1 or divmod == 3:
exp
= min(self
._exp
, other
._exp
)
ans2
= self
._rescale
(exp
, context
=context
, watchexp
=0)
ans2
= ans2
._fix(context
)
return (Decimal( (sign
, (0,), 0) ),
#Don't round the mod part, if we don't need it.
return (Decimal( (sign
, (0,), 0) ), Decimal(self
))
op1
, op2
, adjust
= _adjust_coefficients(op1
, op2
)
res
= _WorkRep( (sign
, 0, (op1
.exp
- op2
.exp
)) )
if divmod and res
.exp
> context
.prec
+ 1:
return context
._raise
_error
(DivisionImpossible
)
prec_limit
= 10 ** context
.prec
while op2
.int <= op1
.int:
if res
.exp
== 0 and divmod:
if res
.int >= prec_limit
and shouldround
:
return context
._raise
_error
(DivisionImpossible
)
frozen
= context
._ignore
_all
_flags
()
exp
= min(self
._exp
, other
._exp
)
otherside
= otherside
._rescale
(exp
, context
=context
, watchexp
=0)
context
._regard
_flags
(*frozen
)
otherside
= otherside
._fix
(context
)
return (Decimal(res
), otherside
)
if op1
.int == 0 and adjust
>= 0 and not divmod:
if res
.int >= prec_limit
and shouldround
:
return context
._raise
_error
(DivisionImpossible
)
# Really, the answer is a bit higher, so adding a one to
# the end will make sure the rounding is right.
if res
.exp
== 0 and divmod and op2
.int > op1
.int:
#Solves an error in precision. Same as a previous block.
if res
.int >= prec_limit
and shouldround
:
return context
._raise
_error
(DivisionImpossible
)
frozen
= context
._ignore
_all
_flags
()
exp
= min(self
._exp
, other
._exp
)
otherside
= otherside
._rescale
(exp
, context
=context
)
context
._regard
_flags
(*frozen
)
return (Decimal(res
), otherside
)
def __rdiv__(self
, other
, context
=None):
"""Swaps self/other and returns __div__."""
other
= _convert_other(other
)
if other
is NotImplemented:
return other
.__div
__(self
, context
=context
)
def __divmod__(self
, other
, context
=None):
(self // other, self % other)
return self
._divide
(other
, 1, context
)
def __rdivmod__(self
, other
, context
=None):
"""Swaps self/other and returns __divmod__."""
other
= _convert_other(other
)
if other
is NotImplemented:
return other
.__divmod
__(self
, context
=context
)
def __mod__(self
, other
, context
=None):
other
= _convert_other(other
)
if other
is NotImplemented:
if self
._is
_special
or other
._is
_special
:
ans
= self
._check
_nans
(other
, context
)
return context
._raise
_error
(InvalidOperation
, 'x % 0')
return self
._divide
(other
, 3, context
)[1]
def __rmod__(self
, other
, context
=None):
"""Swaps self/other and returns __mod__."""
other
= _convert_other(other
)
if other
is NotImplemented:
return other
.__mod
__(self
, context
=context
)
def remainder_near(self
, other
, context
=None):
Remainder nearest to 0- abs(remainder-near) <= other/2
other
= _convert_other(other
)
if other
is NotImplemented:
if self
._is
_special
or other
._is
_special
:
ans
= self
._check
_nans
(other
, context
)
return context
._raise
_error
(InvalidOperation
, 'x % 0')
# If DivisionImpossible causes an error, do not leave Rounded/Inexact
# ignored in the calling function.
context
= context
._shallow
_copy
()
flags
= context
._ignore
_flags
(Rounded
, Inexact
)
#keep DivisionImpossible flags
(side
, r
) = self
.__divmod
__(other
, context
=context
)
context
._regard
_flags
(*flags
)
context
= context
._shallow
_copy
()
rounding
= context
._set
_rounding
_decision
(NEVER_ROUND
)
comparison
= other
.__div
__(Decimal(-2), context
=context
)
comparison
= other
.__div
__(Decimal(2), context
=context
)
context
._set
_rounding
_decision
(rounding
)
context
._regard
_flags
(*flags
)
s1
, s2
= r
._sign
, comparison
._sign
r
._sign
, comparison
._sign
= 0, 0
r
._sign
, comparison
._sign
= s1
, s2
self
.__divmod
__(other
, context
=context
)
r
._sign
, comparison
._sign
= s1
, s2
rounding
= context
._set
_rounding
_decision
(NEVER_ROUND
)
(side
, r
) = self
.__divmod
__(other
, context
=context
)
context
._set
_rounding
_decision
(rounding
)
decrease
= not side
._iseven
()
rounding
= context
._set
_rounding
_decision
(NEVER_ROUND
)
side
= side
.__abs
__(context
=context
)
context
._set
_rounding
_decision
(rounding
)
s1
, s2
= r
._sign
, comparison
._sign
r
._sign
, comparison
._sign
= 0, 0
if r
> comparison
or decrease
and r
== comparison
:
r
._sign
, comparison
._sign
= s1
, s2
if len(side
.__add
__(Decimal(1), context
=context
)._int
) >= context
.prec
:
return context
._raise
_error
(DivisionImpossible
)[1]
if self
._sign
== other
._sign
:
r
= r
.__sub
__(other
, context
=context
)
r
= r
.__add
__(other
, context
=context
)
r
._sign
, comparison
._sign
= s1
, s2
def __floordiv__(self
, other
, context
=None):
return self
._divide
(other
, 2, context
)[0]
def __rfloordiv__(self
, other
, context
=None):
"""Swaps self/other and returns __floordiv__."""
other
= _convert_other(other
)
if other
is NotImplemented:
return other
.__floordiv
__(self
, context
=context
)
"""Float representation."""
"""Converts self to an int, truncating if necessary."""
return context
._raise
_error
(InvalidContext
)
raise OverflowError, "Cannot convert infinity to long"
s
= ''.join(map(str, self
._int
)) + '0'*self
._exp
s
= ''.join(map(str, self
._int
))[:self
._exp
]
Equivalent to long(int(self))
return long(self
.__int
__())
"""Round if it is necessary to keep self within prec precision.
Rounds and fixes the exponent. Does not raise on a sNaN.
ans
= self
._fixexponents
(context
)
ans
= ans
._round
(prec
, context
=context
)
ans
= ans
._fixexponents
(context
)
def _fixexponents(self
, context
):
"""Fix the exponents and return a copy with the exponent in bounds.
Only call if known to not be a special value.
folddown
= context
._clamp
ans_adjusted
= ans
.adjusted()
context
._raise
_error
(Clamped
)
ans
= ans
._rescale
(Etiny
, context
=context
)
#It isn't zero, and exp < Emin => subnormal
context
._raise
_error
(Subnormal
)
if context
.flags
[Inexact
]:
context
._raise
_error
(Underflow
)
#Only raise subnormal if non-zero.
context
._raise
_error
(Subnormal
)
if folddown
and ans
._exp
> Etop
:
context
._raise
_error
(Clamped
)
ans
= ans
._rescale
(Etop
, context
=context
)
context
._raise
_error
(Clamped
)
context
._raise
_error
(Inexact
)
context
._raise
_error
(Rounded
)
return context
._raise
_error
(Overflow
, 'above Emax', ans
._sign
)
def _round(self
, prec
=None, rounding
=None, context
=None):
"""Returns a rounded version of self.
You can specify the precision or rounding method. Otherwise, the
ans
= self
._check
_nans
(context
=context
)
rounding
= context
.rounding
exp
= len(self
._int
) - prec
+ self
._exp
exp
= len(self
._int
) + self
._exp
- prec
ans
= Decimal((self
._sign
, dig
, exp
))
context
._raise
_error
(Rounded
)
temp
._int
= (0,)+temp
._int
exp
= self
._exp
+ len(self
._int
) - prec
- 1
temp
= Decimal( (self
._sign
, (0, 1), exp
))
numdigits
= len(temp
._int
)
# See if we need to extend precision
expdiff
= prec
- numdigits
tmp
.extend([0] * expdiff
)
ans
= Decimal( (temp
._sign
, tmp
, temp
._exp
- expdiff
))
#OK, but maybe all the lost digits are 0.
lostdigits
= self
._int
[expdiff
:]
if lostdigits
== (0,) * len(lostdigits
):
ans
= Decimal( (temp
._sign
, temp
._int
[:prec
], temp
._exp
- expdiff
))
#Rounded, but not Inexact
context
._raise
_error
(Rounded
)
# Okay, let's round and lose data
this_function
= getattr(temp
, self
._pick
_rounding
_function
[rounding
])
#Now we've got the rounding function
context
= context
._shallow
_copy
()
ans
= this_function(prec
, expdiff
, context
)
context
._raise
_error
(Rounded
)
context
._raise
_error
(Inexact
, 'Changed in rounding')
_pick_rounding_function
= {}
def _round_down(self
, prec
, expdiff
, context
):
"""Also known as round-towards-0, truncate."""
return Decimal( (self
._sign
, self
._int
[:prec
], self
._exp
- expdiff
) )
def _round_half_up(self
, prec
, expdiff
, context
, tmp
= None):
"""Rounds 5 up (away from 0)"""
tmp
= Decimal( (self
._sign
,self
._int
[:prec
], self
._exp
- expdiff
))
tmp
= tmp
._increment
(round=0, context
=context
)
return Decimal( (tmp
._sign
, tmp
._int
[:-1], tmp
._exp
+ 1))
def _round_half_even(self
, prec
, expdiff
, context
):
"""Round 5 to even, rest to nearest."""
tmp
= Decimal( (self
._sign
, self
._int
[:prec
], self
._exp
- expdiff
))
half
= (self
._int
[prec
] == 5)
for digit
in self
._int
[prec
+1:]:
if self
._int
[prec
-1] & 1 == 0:
return self
._round
_half
_up
(prec
, expdiff
, context
, tmp
)
def _round_half_down(self
, prec
, expdiff
, context
):
tmp
= Decimal( (self
._sign
, self
._int
[:prec
], self
._exp
- expdiff
))
half
= (self
._int
[prec
] == 5)
for digit
in self
._int
[prec
+1:]:
return self
._round
_half
_up
(prec
, expdiff
, context
, tmp
)
def _round_up(self
, prec
, expdiff
, context
):
"""Rounds away from 0."""
tmp
= Decimal( (self
._sign
, self
._int
[:prec
], self
._exp
- expdiff
) )
for digit
in self
._int
[prec
:]:
tmp
= tmp
._increment
(round=1, context
=context
)
return Decimal( (tmp
._sign
, tmp
._int
[:-1], tmp
._exp
+ 1))
def _round_ceiling(self
, prec
, expdiff
, context
):
"""Rounds up (not away from 0 if negative.)"""
return self
._round
_down
(prec
, expdiff
, context
)
return self
._round
_up
(prec
, expdiff
, context
)
def _round_floor(self
, prec
, expdiff
, context
):
"""Rounds down (not towards 0 if negative)"""
return self
._round
_down
(prec
, expdiff
, context
)
return self
._round
_up
(prec
, expdiff
, context
)
def __pow__(self
, n
, modulo
= None, context
=None):
"""Return self ** n (mod modulo)
If modulo is None (default), don't take it mod modulo.
if self
._is
_special
or n
._is
_special
or n
.adjusted() > 8:
#Because the spot << doesn't work with really big exponents
if n
._isinfinity
() or n
.adjusted() > 8:
return context
._raise
_error
(InvalidOperation
, 'x ** INF')
ans
= self
._check
_nans
(n
, context
)
return context
._raise
_error
(InvalidOperation
, 'x ** (non-integer)')
return context
._raise
_error
(InvalidOperation
, '0 ** 0')
sign
= self
._sign
and not n
._iseven
()
return context
._raise
_error
(InvalidOperation
, 'INF % x')
return Decimal( (sign
, (0,), 0) )
#with ludicrously large exponent, just raise an overflow and return inf.
if not modulo
and n
> 0 and (self
._exp
+ len(self
._int
) - 1) * n
> context
.Emax \
context
._raise
_error
(Rounded
)
context
._raise
_error
(Inexact
)
context
._raise
_error
(Overflow
, 'Big power', sign
)
elength
= len(str(abs(n
)))
if not modulo
and firstprec
+ elength
+ 1 > DefaultContext
.Emax
:
return context
._raise
_error
(Overflow
, 'Too much precision.', sign
)
context
= context
._shallow
_copy
()
context
.prec
= firstprec
+ elength
+ 1
#n is a long now, not Decimal instance
mul
= Decimal(1).__div
__(mul
, context
=context
)
#Spot is the highest power of 2 less than n
val
= val
.__mul
__(val
, context
=context
)
val
= val
.__mul
__(mul
, context
=context
)
val
= val
.__mod
__(modulo
, context
=context
)
if context
._rounding
_decision
== ALWAYS_ROUND
:
def __rpow__(self
, other
, context
=None):
"""Swaps self/other and returns __pow__."""
other
= _convert_other(other
)
if other
is NotImplemented:
return other
.__pow
__(self
, context
=context
)
def normalize(self
, context
=None):
"""Normalize- strip trailing 0s, change anything equal to 0 to 0e0"""
ans
= self
._check
_nans
(context
=context
)
return Decimal( (dup
._sign
, (0,), 0) )
while dup
._int
[end
-1] == 0:
return Decimal( (dup
._sign
, dup
._int
[:end
], exp
) )
def quantize(self
, exp
, rounding
=None, context
=None, watchexp
=1):
"""Quantize self so its exponent is the same as that of exp.
Similar to self._rescale(exp._exp) but with error checking.
if self
._is
_special
or exp
._is
_special
:
ans
= self
._check
_nans
(exp
, context
)
if exp
._isinfinity
() or self
._isinfinity
():
if exp
._isinfinity
() and self
._isinfinity
():
return self
#if both are inf, it is OK
return context
._raise
_error
(InvalidOperation
,
return self
._rescale
(exp
._exp
, rounding
, context
, watchexp
)
def same_quantum(self
, other
):
"""Test whether self and other have the same exponent.
same as self._exp == other._exp, except NaN == sNaN
if self
._is
_special
or other
._is
_special
:
if self
._isnan
() or other
._isnan
():
return self
._isnan
() and other
._isnan
() and True
if self
._isinfinity
() or other
._isinfinity
():
return self
._isinfinity
() and other
._isinfinity
() and True
return self
._exp
== other
._exp
def _rescale(self
, exp
, rounding
=None, context
=None, watchexp
=1):
"""Rescales so that the exponent is exp.
exp = exp to scale to (an integer)
rounding = rounding version
watchexp: if set (default) an error is returned if exp is greater
than Emax or less than Etiny.
return context
._raise
_error
(InvalidOperation
, 'rescale with an INF')
ans
= self
._check
_nans
(context
=context
)
if watchexp
and (context
.Emax
< exp
or context
.Etiny() > exp
):
return context
._raise
_error
(InvalidOperation
, 'rescale(a, INF)')
digits
= len(self
._int
) + diff
if watchexp
and digits
> context
.prec
:
return context
._raise
_error
(InvalidOperation
, 'Rescale > prec')
tmp
._int
= (0,) + tmp
._int
tmp
._exp
= -digits
+ tmp
._exp
tmp
= tmp
._round
(digits
, rounding
, context
=context
)
if tmp
._int
[0] == 0 and len(tmp
._int
) > 1:
tmp_adjusted
= tmp
.adjusted()
if tmp
and tmp_adjusted
< context
.Emin
:
context
._raise
_error
(Subnormal
)
elif tmp
and tmp_adjusted
> context
.Emax
:
return context
._raise
_error
(InvalidOperation
, 'rescale(a, INF)')
def to_integral(self
, rounding
=None, context
=None):
"""Rounds to the nearest integer, without raising inexact, rounded."""
ans
= self
._check
_nans
(context
=context
)
flags
= context
._ignore
_flags
(Rounded
, Inexact
)
ans
= self
._rescale
(0, rounding
, context
=context
)
context
._regard
_flags
(flags
)
def sqrt(self
, context
=None):
"""Return the square root of self.
Uses a converging algorithm (Xn+1 = 0.5*(Xn + self / Xn))
Should quadratically approach the right answer.
ans
= self
._check
_nans
(context
=context
)
if self
._isinfinity
() and self
._sign
== 0:
#exponent = self._exp / 2, using round_down.
# exp = (self._exp+1) // 2
return Decimal( (1, (0,), exp
))
return Decimal( (0, (0,), exp
))
return context
._raise
_error
(InvalidOperation
, 'sqrt(-x), x > 0')
context
= context
._shallow
_copy
()
flags
= context
._ignore
_all
_flags
()
if tmp
.adjusted() & 1 == 0:
ans
= Decimal( (0, (8,1,9), tmp
.adjusted() - 2) )
ans
= ans
.__add
__(tmp
.__mul
__(Decimal((0, (2,5,9), -2)),
context
=context
), context
=context
)
ans
._exp
-= 1 + tmp
.adjusted() // 2
ans
= Decimal( (0, (2,5,9), tmp
._exp
+ len(tmp
._int
)- 3) )
ans
= ans
.__add
__(tmp
.__mul
__(Decimal((0, (8,1,9), -3)),
context
=context
), context
=context
)
ans
._exp
-= 1 + tmp
.adjusted() // 2
#ans is now a linear approximation.
Emax
, Emin
= context
.Emax
, context
.Emin
context
.Emax
, context
.Emin
= DefaultContext
.Emax
, DefaultContext
.Emin
rounding
= context
._set
_rounding
(ROUND_HALF_EVEN
)
context
.prec
= min(2*context
.prec
- 2, maxp
)
ans
= half
.__mul
__(ans
.__add
__(tmp
.__div
__(ans
, context
=context
),
context
=context
), context
=context
)
#round to the answer's precision-- the only error can be 1 ulp.
ans
= ans
._round
(context
=context
)
#Now, check if the other last digits are better.
context
.prec
= firstprec
+ 1
# In case we rounded up another digit and we should actually go lower.
if prevexp
!= ans
.adjusted():
lower
= ans
.__sub
__(Decimal((0, (5,), ans
._exp
-1)), context
=context
)
context
._set
_rounding
(ROUND_UP
)
if lower
.__mul
__(lower
, context
=context
) > (tmp
):
ans
= ans
.__sub
__(Decimal((0, (1,), ans
._exp
)), context
=context
)
upper
= ans
.__add
__(Decimal((0, (5,), ans
._exp
-1)),context
=context
)
context
._set
_rounding
(ROUND_DOWN
)
if upper
.__mul
__(upper
, context
=context
) < tmp
:
ans
= ans
.__add
__(Decimal((0, (1,), ans
._exp
)),context
=context
)
context
.rounding
= rounding
rounding
= context
._set
_rounding
_decision
(NEVER_ROUND
)
if not ans
.__mul
__(ans
, context
=context
) == self
:
# Only rounded/inexact if here.
context
._regard
_flags
(flags
)
context
._raise
_error
(Rounded
)
context
._raise
_error
(Inexact
)
#Exact answer, so let's set the exponent right.
# exp = (self._exp +1)// 2
context
.prec
+= ans
._exp
- exp
ans
= ans
._rescale
(exp
, context
=context
)
context
._regard
_flags
(flags
)
context
.Emax
, context
.Emin
= Emax
, Emin
def max(self
, other
, context
=None):
"""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.
other
= _convert_other(other
)
if other
is NotImplemented:
if self
._is
_special
or other
._is
_special
:
# if one operand is a quiet NaN and the other is number, then the
# number is always returned
return self
._check
_nans
(other
, context
)
# if both operands are finite and equal in numerical value
# then an ordering is applied:
# if the signs differ then max returns the operand with the
# positive sign and min returns the operand with the negative sign
# if the signs are the same then the exponent is used to select
if self
._sign
!= other
._sign
:
elif self
._exp
< other
._exp
and not self
._sign
:
elif self
._exp
> other
._exp
and self
._sign
:
if context
._rounding
_decision
== ALWAYS_ROUND
:
def min(self
, other
, context
=None):
"""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.
other
= _convert_other(other
)
if other
is NotImplemented:
if self
._is
_special
or other
._is
_special
:
# if one operand is a quiet NaN and the other is number, then the
# number is always returned
return self
._check
_nans
(other
, context
)
# if both operands are finite and equal in numerical value
# then an ordering is applied:
# if the signs differ then max returns the operand with the
# positive sign and min returns the operand with the negative sign
# if the signs are the same then the exponent is used to select
if self
._sign
!= other
._sign
:
elif self
._exp
> other
._exp
and not self
._sign
:
elif self
._exp
< other
._exp
and self
._sign
:
if context
._rounding
_decision
== ALWAYS_ROUND
:
"""Returns whether self is an integer"""
rest
= self
._int
[self
._exp
:]
return rest
== (0,)*len(rest
)
"""Returns 1 if self is even. Assumes self is an integer."""
return self
._int
[-1+self
._exp
] & 1 == 0
"""Return the adjusted exponent of self"""
return self
._exp
+ len(self
._int
) - 1
#If NaN or Infinity, self._exp is string
# support for pickling, copy, and deepcopy
return (self
.__class
__, (str(self
),))
if type(self
) == Decimal
:
return self
# I'm immutable; therefore I am my own clone
return self
.__class
__(str(self
))
def __deepcopy__(self
, memo
):
if type(self
) == Decimal
:
return self
# My components are also immutable
return self
.__class
__(str(self
))
##### Context class ###########################################
# get rounding method function:
rounding_functions
= [name
for name
in Decimal
.__dict
__.keys() if name
.startswith('_round_')]
for name
in rounding_functions
:
#name is like _round_half_even, goes to the global ROUND_HALF_EVEN value.
globalname
= name
[1:].upper()
val
= globals()[globalname
]
Decimal
._pick
_rounding
_function
[val
] = name
del name
, val
, globalname
, rounding_functions
"""Contains the context for a Decimal instance.
prec - precision (for use in rounding, division, square roots..)
rounding - rounding type. (how you round)
_rounding_decision - ALWAYS_ROUND, NEVER_ROUND -- do you round?
traps - If traps[exception] = 1, then the exception is
raised when it is caused. Otherwise, a value is
flags - When an exception is caused, flags[exception] is incremented.
(Whether or not the trap_enabler is set)
Should be reset by user of Decimal instance.
capitals - If 1, 1*10^1 is printed as 1E+1.
_clamp - If 1, change exponents if too high (Default 0)
def __init__(self
, prec
=None, rounding
=None,
if _ignored_flags
is None:
if not isinstance(flags
, dict):
flags
= dict([(s
,s
in flags
) for s
in _signals
])
if traps
is not None and not isinstance(traps
, dict):
traps
= dict([(s
,s
in traps
) for s
in _signals
])
for name
, val
in locals().items():
setattr(self
, name
, _copy
.copy(getattr(DefaultContext
, name
)))
"""Show the current context."""
s
.append('Context(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' % vars(self
))
s
.append('flags=[' + ', '.join([f
.__name
__ for f
, v
in self
.flags
.items() if v
]) + ']')
s
.append('traps=[' + ', '.join([t
.__name
__ for t
, v
in self
.traps
.items() if v
]) + ']')
return ', '.join(s
) + ')'
"""Reset all flags to zero"""
"""Returns a shallow copy from self."""
nc
= Context(self
.prec
, self
.rounding
, self
.traps
, self
.flags
,
self
._rounding
_decision
, self
.Emin
, self
.Emax
,
self
.capitals
, self
._clamp
, self
._ignored
_flags
)
"""Returns a deep copy from self."""
nc
= Context(self
.prec
, self
.rounding
, self
.traps
.copy(), self
.flags
.copy(),
self
._rounding
_decision
, self
.Emin
, self
.Emax
,
self
.capitals
, self
._clamp
, self
._ignored
_flags
)
def _raise_error(self
, condition
, explanation
= None, *args
):
If the flag is in _ignored_flags, returns the default response.
Otherwise, it increments the flag, then, if the corresponding
trap_enabler is set, it reaises the exception. Otherwise, it returns
the default value after incrementing the flag.
error
= _condition_map
.get(condition
, condition
)
if error
in self
._ignored
_flags
:
return error().handle(self
, *args
)
if not self
.traps
[error
]:
#The errors define how to handle themselves.
return condition().handle(self
, *args
)
# Errors should only be risked on copies of the context
#self._ignored_flags = []
def _ignore_all_flags(self
):
"""Ignore all flags, if they are raised"""
return self
._ignore
_flags
(*_signals
)
def _ignore_flags(self
, *flags
):
"""Ignore the flags, if they are raised"""
# Do not mutate-- This way, copies of a context leave the original
self
._ignored
_flags
= (self
._ignored
_flags
+ list(flags
))
def _regard_flags(self
, *flags
):
"""Stop ignoring the flags, if they are raised"""
if flags
and isinstance(flags
[0], (tuple,list)):
self
._ignored
_flags
.remove(flag
)
"""A Context cannot be hashed."""
# We inherit object.__hash__, so we must deny this explicitly
raise TypeError, "Cannot hash a Context."
"""Returns Etiny (= Emin - prec + 1)"""
return int(self
.Emin
- self
.prec
+ 1)
"""Returns maximum exponent (= Emax - prec + 1)"""
return int(self
.Emax
- self
.prec
+ 1)
def _set_rounding_decision(self
, type):
"""Sets the rounding decision.
Sets the rounding decision, and returns the current (previous)
rounding decision. Often used like:
context = context._shallow_copy()
# That so you don't change the calling context
# if an error occurs in the middle (say DivisionImpossible is raised).
rounding = context._set_rounding_decision(NEVER_ROUND)
instance = instance / Decimal(2)
context._set_rounding_decision(rounding)
This will make it not round for that operation.
rounding
= self
._rounding
_decision
self
._rounding
_decision
= type
def _set_rounding(self
, type):
"""Sets the rounding type.
Sets the rounding type, and returns the current (previous)
rounding type. Often used like:
# 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.
def create_decimal(self
, num
='0'):
"""Creates a new Decimal instance but using self as context."""
d
= Decimal(num
, context
=self
)
"""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'))
>>> ExtendedContext.abs(Decimal('-100'))
>>> ExtendedContext.abs(Decimal('101.5'))
>>> ExtendedContext.abs(Decimal('-101.5'))
return a
.__abs
__(context
=self
)
"""Return the sum of the two operands.
>>> ExtendedContext.add(Decimal('12'), Decimal('7.00'))
>>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4'))
return a
.__add
__(b
, context
=self
)
"""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
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'))
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1'))
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10'))
>>> ExtendedContext.compare(Decimal('3'), Decimal('2.1'))
>>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3'))
>>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1'))
return a
.compare(b
, context
=self
)
"""Decimal division in a specified context.
>>> ExtendedContext.divide(Decimal('1'), Decimal('3'))
>>> ExtendedContext.divide(Decimal('2'), Decimal('3'))
>>> ExtendedContext.divide(Decimal('5'), Decimal('2'))
>>> ExtendedContext.divide(Decimal('1'), Decimal('10'))
>>> ExtendedContext.divide(Decimal('12'), Decimal('12'))
>>> ExtendedContext.divide(Decimal('8.00'), Decimal('2'))
>>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0'))
>>> ExtendedContext.divide(Decimal('1000'), Decimal('100'))
>>> ExtendedContext.divide(Decimal('1000'), Decimal('1'))
>>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2'))
return a
.__div
__(b
, context
=self
)
def divide_int(self
, a
, b
):
"""Divides two numbers and returns the integer part of the result.
>>> ExtendedContext.divide_int(Decimal('2'), Decimal('3'))
>>> ExtendedContext.divide_int(Decimal('10'), Decimal('3'))
>>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3'))
return a
.__floordiv
__(b
, context
=self
)
return a
.__divmod
__(b
, context
=self
)
"""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 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'))
>>> ExtendedContext.max(Decimal('-10'), Decimal('3'))
>>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))
>>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))
return a
.max(b
, context
=self
)
"""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 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'))
>>> ExtendedContext.min(Decimal('-10'), Decimal('3'))
>>> ExtendedContext.min(Decimal('1.0'), Decimal('1'))
>>> ExtendedContext.min(Decimal('7'), Decimal('NaN'))
return a
.min(b
, context
=self
)
"""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'))
>>> ExtendedContext.minus(Decimal('-1.3'))
return a
.__neg
__(context
=self
)
def multiply(self
, a
, b
):
"""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
>>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))
>>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))
>>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))
>>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))
Decimal("4.28135971E+11")
return a
.__mul
__(b
, context
=self
)
"""normalize reduces an operand to its simplest form.
Essentially a plus operation with all trailing zeros removed from the
>>> ExtendedContext.normalize(Decimal('2.1'))
>>> ExtendedContext.normalize(Decimal('-2.0'))
>>> ExtendedContext.normalize(Decimal('1.200'))
>>> ExtendedContext.normalize(Decimal('-120'))
>>> ExtendedContext.normalize(Decimal('120.00'))
>>> ExtendedContext.normalize(Decimal('0.00'))
return a
.normalize(context
=self
)
"""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'))
>>> ExtendedContext.plus(Decimal('-1.3'))
return a
.__pos
__(context
=self
)
def power(self
, a
, b
, modulo
=None):
"""Raises a to the power of b, to modulo if given.
The right-hand operand must be a whole number whose integer part (after
any exponent has been applied) has no more than 9 digits and whose
fractional part (if any) is all zeros before any rounding. The operand
may be positive, negative, or zero; if negative, the absolute value of
the power is used, and the left-hand operand is inverted (divided into
If the increased precision needed for the intermediate calculations
exceeds the capabilities of the implementation then an Invalid operation
If, when raising to a negative power, an underflow occurs during the
division into 1, the operation is not halted at that point but
>>> ExtendedContext.power(Decimal('2'), Decimal('3'))
>>> ExtendedContext.power(Decimal('2'), Decimal('-3'))
>>> ExtendedContext.power(Decimal('1.7'), Decimal('8'))
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('-2'))
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('-1'))
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('0'))
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('1'))
>>> ExtendedContext.power(Decimal('Infinity'), Decimal('2'))
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-2'))
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-1'))
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('0'))
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('1'))
>>> ExtendedContext.power(Decimal('-Infinity'), Decimal('2'))
>>> ExtendedContext.power(Decimal('0'), Decimal('0'))
return a
.__pow
__(b
, modulo
, context
=self
)
def quantize(self
, a
, b
):
"""Returns a value equal to 'a' (rounded) and 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'))
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01'))
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1'))
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0'))
>>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1'))
>>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity'))
>>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity'))
>>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1'))
>>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5'))
>>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))
>>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1'))
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0'))
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1'))
>>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2'))
return a
.quantize(b
, context
=self
)
def remainder(self
, a
, b
):
"""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'))
>>> ExtendedContext.remainder(Decimal('10'), Decimal('3'))
>>> ExtendedContext.remainder(Decimal('-10'), Decimal('3'))
>>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1'))
>>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3'))
>>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3'))
return a
.__mod
__(b
, context
=self
)
def remainder_near(self
, a
, b
):
"""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
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'))
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6'))
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3'))
>>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3'))
>>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1'))
>>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3'))
>>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3'))
return a
.remainder_near(b
, context
=self
)
def same_quantum(self
, a
, b
):
"""Returns True if the two operands have the same exponent.
The result is never affected by either the sign or the coefficient of
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001'))
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01'))
>>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1'))
>>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf'))
"""Returns the square root of a non-negative number to context precision.
If the result must be inexact, it is rounded using the round-half-even
>>> ExtendedContext.sqrt(Decimal('0'))
>>> ExtendedContext.sqrt(Decimal('-0'))
>>> ExtendedContext.sqrt(Decimal('0.39'))
>>> ExtendedContext.sqrt(Decimal('100'))
>>> ExtendedContext.sqrt(Decimal('1'))
>>> ExtendedContext.sqrt(Decimal('1.0'))
>>> ExtendedContext.sqrt(Decimal('1.00'))
>>> ExtendedContext.sqrt(Decimal('7'))
>>> ExtendedContext.sqrt(Decimal('10'))
return a
.sqrt(context
=self
)
def subtract(self
, a
, b
):
"""Return the difference between the two operands.
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07'))
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30'))
>>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07'))
return a
.__sub
__(b
, context
=self
)
def to_eng_string(self
, a
):
"""Converts a number to a string, using scientific notation.
The operation is not affected by the context.
return a
.to_eng_string(context
=self
)
def to_sci_string(self
, a
):
"""Converts a number to a string, using scientific notation.
The operation is not affected by the context.
return a
.__str
__(context
=self
)
def to_integral(self
, a
):
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(Decimal('2.1'))
>>> ExtendedContext.to_integral(Decimal('100'))
>>> ExtendedContext.to_integral(Decimal('100.0'))
>>> ExtendedContext.to_integral(Decimal('101.5'))
>>> ExtendedContext.to_integral(Decimal('-101.5'))
>>> ExtendedContext.to_integral(Decimal('10E+5'))
>>> ExtendedContext.to_integral(Decimal('7.89E+77'))
>>> ExtendedContext.to_integral(Decimal('-Inf'))
return a
.to_integral(context
=self
)
__slots__
= ('sign','int','exp')
# exp: None, int, or string
def __init__(self
, value
=None):
elif isinstance(value
, Decimal
):
# assert isinstance(value, tuple)
return "(%r, %r, %r)" % (self
.sign
, self
.int, self
.exp
)
def _normalize(op1
, op2
, shouldround
= 0, prec
= 0):
"""Normalizes op1, op2 to have the same exp and length of coefficient.
# Yes, the exponent is a long, but the difference between exponents
# must be an int-- otherwise you'd get a big memory problem.
numdigits
= int(op1
.exp
- op2
.exp
)
if shouldround
and numdigits
> prec
+ 1:
# Big difference in exponents - check the adjusted exponents
tmp_len
= len(str(tmp
.int))
other_len
= len(str(other
.int))
if numdigits
> (other_len
+ prec
+ 1 - tmp_len
):
# If the difference in adjusted exps is > prec+1, we know
# other is insignificant, so might as well put a 1 after the precision.
# (since this is only for addition.) Also stops use of massive longs.
extend
= prec
+ 2 - tmp_len
tmp
.int *= 10 ** numdigits
def _adjust_coefficients(op1
, op2
):
"""Adjust op1, op2 so that op2.int * 10 > op1.int >= op2.int.
Returns the adjusted op1, op2 as well as the change in op1.exp-op2.exp.
Used on _WorkRep instances during division.
#If op1 is smaller, make it larger
#If op2 is too small, make it larger
while op1
.int >= (10 * op2
.int):
##### Helper Functions ########################################
def _convert_other(other
):
"""Convert other to Decimal.
Verifies that it's ok to use in an implicit construction.
if isinstance(other
, Decimal
):
if isinstance(other
, (int, long)):
"""Determines whether a string or float is infinity.
+1 for negative infinity; 0 for finite ; +1 for positive infinity
return _infinity_map
.get(num
, 0)
"""Determines whether a string or float is NaN
(1, sign, diagnostic info as string) => NaN
(2, sign, diagnostic info as string) => sNaN
#get the sign, get rid of trailing [+-]
elif num
[0] == '-': #elif avoids '+-nan'
if num
.startswith('nan'):
if len(num
) > 3 and not num
[3:].isdigit(): #diagnostic info
return (1, sign
, num
[3:].lstrip('0'))
if num
.startswith('snan'):
if len(num
) > 4 and not num
[4:].isdigit():
return (2, sign
, num
[4:].lstrip('0'))
##### Setup Specific Contexts ################################
# The default context prototype used by Context()
# Is mutable, so that new contexts can have different default values
DefaultContext
= Context(
prec
=28, rounding
=ROUND_HALF_EVEN
,
traps
=[DivisionByZero
, Overflow
, InvalidOperation
],
_rounding_decision
=ALWAYS_ROUND
,
# Pre-made alternate contexts offered by the specification
# Don't change these; the user should be able to select these
# contexts and be able to reproduce results from other implementations
prec
=9, rounding
=ROUND_HALF_UP
,
traps
=[DivisionByZero
, Overflow
, InvalidOperation
, Clamped
, Underflow
],
ExtendedContext
= Context(
prec
=9, rounding
=ROUND_HALF_EVEN
,
##### Useful Constants (internal use only) ####################
#Infsign[sign] is infinity w/ that sign
##### crud for parsing strings #################################
# There's an optional sign at the start, and an optional exponent
# at the end. The exponent has an optional sign and at least one
# digit. In between, must have either at least one digit followed
# by an optional fraction, or a decimal point followed by at least
_parser
= re
.compile(r
"""
(?P<int>\d+) (\. (?P<frac>\d*))?
([eE](?P<exp>[-+]? \d+))?
""", re
.VERBOSE
).match
#Uncomment the \s* to allow leading or trailing spaces.
# return sign, n, p s.t. float string value == -1**sign * n * 10**p exactly
raise ValueError("invalid literal for Decimal: %r" % s
)
if m
.group('sign') == "-":
fracpart
= m
.group('onlyfrac')
fracpart
= m
.group('frac')
mantissa
= intpart
+ fracpart
while tmp
and tmp
[0] == 0:
return (sign
, tuple(backup
), exp
)
return (sign
, mantissa
, exp
)
if __name__
== '__main__':
doctest
.testmod(sys
.modules
[__name__
])