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Kaydet (Commit) ac4ae4ba authored tarafından Facundo Batista's avatar Facundo Batista
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Comments and docs cleanups, and some little fixes, provided by Santiágo Peresón

üst caebe220
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Lib/decimal.py
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......@@ -29,8 +29,8 @@ and IEEE standard 854-1987:
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
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,
......@@ -136,7 +136,7 @@ __all__ = [
import copy as _copy
#Rounding
# Rounding
ROUND_DOWN = 'ROUND_DOWN'
ROUND_HALF_UP = 'ROUND_HALF_UP'
ROUND_HALF_EVEN = 'ROUND_HALF_EVEN'
......@@ -145,11 +145,11 @@ ROUND_FLOOR = 'ROUND_FLOOR'
ROUND_UP = 'ROUND_UP'
ROUND_HALF_DOWN = 'ROUND_HALF_DOWN'
#Rounding decision (not part of the public API)
# 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.
#Errors
# Errors
class DecimalException(ArithmeticError):
"""Base exception class.
......@@ -160,17 +160,17 @@ class DecimalException(ArithmeticError):
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 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.
"""
def handle(self, context, *args):
"""Called when context._raise_error is called and 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).)
"""
pass
......@@ -179,12 +179,13 @@ class Clamped(DecimalException):
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
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").
"""
pass
class InvalidOperation(DecimalException):
......@@ -194,8 +195,8 @@ class InvalidOperation(DecimalException):
Something creates a signaling NaN
-INF + INF
0 * (+-)INF
(+-)INF / (+-)INF
0 * (+-)INF
(+-)INF / (+-)INF
x % 0
(+-)INF % x
x._rescale( non-integer )
......@@ -207,20 +208,21 @@ class InvalidOperation(DecimalException):
"""
def handle(self, context, *args):
if args:
if args[0] == 1: #sNaN, must drop 's' but keep diagnostics
if args[0] == 1: # sNaN, must drop 's' but keep diagnostics
return Decimal( (args[1]._sign, args[1]._int, 'n') )
return NaN
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].
syntax. The result is [0,qNaN].
"""
def handle(self, context, *args):
return (0, (0,), 'n') #Passed to something which uses a tuple.
return (0, (0,), 'n') # Passed to something which uses a tuple.
class DivisionByZero(DecimalException, ZeroDivisionError):
"""Division by 0.
......@@ -234,42 +236,42 @@ class DivisionByZero(DecimalException, ZeroDivisionError):
or of the signs of the operands for divide, or is 1 for an odd power of
-0, for power.
"""
def handle(self, context, sign, double = None, *args):
if double is not None:
return (Infsign[sign],)*2
return Infsign[sign]
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].
longer than precision). The result is [0,qNaN].
"""
def handle(self, context, *args):
return (NaN, NaN)
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].
the dividend is also zero. The result is [0,qNaN].
"""
def handle(self, context, tup=None, *args):
if tup is not None:
return (NaN, NaN) #for 0 %0, 0 // 0
return (NaN, NaN) # For 0 %0, 0 // 0
return NaN
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
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
......@@ -277,26 +279,27 @@ class Inexact(DecimalException):
"""
pass
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
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].
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):
return NaN
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
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
......@@ -304,18 +307,20 @@ class Rounded(DecimalException):
"""
pass
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.
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.
"""
pass
class Overflow(Inexact, Rounded):
"""Numerical overflow.
......@@ -328,16 +333,15 @@ class Overflow(Inexact, Rounded):
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
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
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 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
result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded
will also be raised.
"""
"""
def handle(self, context, sign, *args):
if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN,
ROUND_HALF_DOWN, ROUND_UP):
......@@ -360,18 +364,20 @@ class Underflow(Inexact, Rounded, Subnormal):
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.
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
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.
"""
pass
# List of public traps and flags
_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded,
Underflow, InvalidOperation, Subnormal]
Underflow, InvalidOperation, Subnormal]
# Map conditions (per the spec) to signals
_condition_map = {ConversionSyntax:InvalidOperation,
......@@ -379,32 +385,34 @@ _condition_map = {ConversionSyntax:InvalidOperation,
DivisionUndefined:InvalidOperation,
InvalidContext:InvalidOperation}
##### Context Functions #######################################
##### 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.
# mock threading object with threading.local() returning the module
# namespace.
try:
import threading
except ImportError:
# Python was compiled without threads; create a mock object instead
import sys
class MockThreading:
class MockThreading(object):
def local(self, sys=sys):
return sys.modules[__name__]
threading = MockThreading()
del sys, MockThreading
try:
threading.local
except AttributeError:
#To fix reloading, force it to create a new context
#Old contexts have different exceptions in their dicts, making problems.
# 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__
......@@ -456,10 +464,10 @@ else:
context.clear_flags()
_local.__decimal_context__ = context
del threading, local # Don't contaminate the namespace
del threading, local # Don't contaminate the namespace
##### Decimal class ###########################################
##### Decimal class ##########################################################
class Decimal(object):
"""Floating point class for decimal arithmetic."""
......@@ -475,7 +483,7 @@ class Decimal(object):
>>> Decimal('3.14') # string input
Decimal("3.14")
>>> Decimal((0, (3, 1, 4), -2)) # tuple input (sign, digit_tuple, exponent)
>>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent)
Decimal("3.14")
>>> Decimal(314) # int or long
Decimal("314")
......@@ -514,12 +522,13 @@ class Decimal(object):
# tuple/list conversion (possibly from as_tuple())
if isinstance(value, (list,tuple)):
if len(value) != 3:
raise ValueError, 'Invalid arguments'
raise ValueError('Invalid arguments')
if value[0] not in (0,1):
raise ValueError, 'Invalid sign'
raise ValueError('Invalid sign')
for digit in value[1]:
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."
raise ValueError("The second value in the tuple must be "+
"composed of non negative integer elements.")
self._sign = value[0]
self._int = tuple(value[1])
......@@ -553,22 +562,23 @@ class Decimal(object):
if _isnan(value):
sig, sign, diag = _isnan(value)
self._is_special = True
if len(diag) > context.prec: #Diagnostic info too long
if len(diag) > context.prec: # Diagnostic info too long
self._sign, self._int, self._exp = \
context._raise_error(ConversionSyntax)
return self
if sig == 1:
self._exp = 'n' #qNaN
else: #sig == 2
else: # sig == 2
self._exp = 'N' #sNaN
self._sign = sign
self._int = tuple(map(int, diag)) #Diagnostic info
self._int = tuple(map(int, diag)) # Diagnostic info
return self
try:
self._sign, self._int, self._exp = _string2exact(value)
except ValueError:
self._is_special = True
self._sign, self._int, self._exp = context._raise_error(ConversionSyntax)
self._sign, self._int, self._exp = \
context._raise_error(ConversionSyntax)
return self
raise TypeError("Cannot convert %r to Decimal" % value)
......@@ -651,15 +661,15 @@ class Decimal(object):
if self._is_special or other._is_special:
ans = self._check_nans(other, context)
if ans:
return 1 # Comparison involving NaN's always reports self > other
return 1 # Comparison involving NaN's always reports self > other
# INF = INF
return cmp(self._isinfinity(), other._isinfinity())
if not self and not other:
return 0 #If both 0, sign comparison isn't certain.
return 0 # If both 0, sign comparison isn't certain.
#If different signs, neg one is less
# If different signs, neg one is less
if other._sign < self._sign:
return -1
if self._sign < other._sign:
......@@ -670,7 +680,7 @@ class Decimal(object):
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) = [])
return 0 # Equal, except in precision. ([0]*(-x) = [])
elif self_adjusted > other_adjusted and self._int[0] != 0:
return (-1)**self._sign
elif self_adjusted < other_adjusted and other._int[0] != 0:
......@@ -681,7 +691,7 @@ class Decimal(object):
context = getcontext()
context = context._shallow_copy()
rounding = context._set_rounding(ROUND_UP) #round away from 0
rounding = context._set_rounding(ROUND_UP) # Round away from 0
flags = context._ignore_all_flags()
res = self.__sub__(other, context=context)
......@@ -719,7 +729,7 @@ class Decimal(object):
if other is NotImplemented:
return other
#compare(NaN, NaN) = NaN
# Compare(NaN, NaN) = NaN
if (self._is_special or other and other._is_special):
ans = self._check_nans(other, context)
if ans:
......@@ -780,11 +790,11 @@ class Decimal(object):
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
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))
return s
#exp is closest mult. of 3 >= self._exp
# exp is closest mult. of 3 >= self._exp
exp = ((self._exp - 1)// 3 + 1) * 3
if exp != self._exp:
s = '0.'+'0'*(exp - self._exp)
......@@ -796,7 +806,7 @@ class Decimal(object):
else:
s += 'e'
if exp > 0:
s += '+' #0.0e+3, not 0.0e3
s += '+' # 0.0e+3, not 0.0e3
s += str(exp)
s = '-'*self._sign + s
return s
......@@ -936,19 +946,19 @@ class Decimal(object):
return ans
if self._isinfinity():
#If both INF, same sign => same as both, opposite => error.
# 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(self)
if other._isinfinity():
return Decimal(other) #Can't both be infinity here
return Decimal(other) # Can't both be infinity here
shouldround = context._rounding_decision == ALWAYS_ROUND
exp = min(self._exp, other._exp)
negativezero = 0
if context.rounding == ROUND_FLOOR and self._sign != other._sign:
#If the answer is 0, the sign should be negative, in this case.
# If the answer is 0, the sign should be negative, in this case.
negativezero = 1
if not self and not other:
......@@ -983,19 +993,19 @@ class Decimal(object):
return Decimal((negativezero, (0,), exp))
if op1.int < op2.int:
op1, op2 = op2, op1
#OK, now abs(op1) > abs(op2)
# OK, now abs(op1) > abs(op2)
if op1.sign == 1:
result.sign = 1
op1.sign, op2.sign = op2.sign, op1.sign
else:
result.sign = 0
#So we know the sign, and op1 > 0.
# So we know the sign, and op1 > 0.
elif op1.sign == 1:
result.sign = 1
op1.sign, op2.sign = (0, 0)
else:
result.sign = 0
#Now, op1 > abs(op2) > 0
# Now, op1 > abs(op2) > 0
if op2.sign == 0:
result.int = op1.int + op2.int
......@@ -1052,8 +1062,8 @@ class Decimal(object):
ans = self._check_nans(context=context)
if ans:
return ans
return Decimal(self) # Must be infinite, and incrementing makes no difference
# Must be infinite, and incrementing makes no difference
return Decimal(self)
L = list(self._int)
L[-1] += 1
......@@ -1109,7 +1119,7 @@ class Decimal(object):
if not self or not other:
ans = Decimal((resultsign, (0,), resultexp))
if shouldround:
#Fixing in case the exponent is out of bounds
# Fixing in case the exponent is out of bounds
ans = ans._fix(context)
return ans
......@@ -1128,7 +1138,7 @@ class Decimal(object):
op1 = _WorkRep(self)
op2 = _WorkRep(other)
ans = Decimal( (resultsign, map(int, str(op1.int * op2.int)), resultexp))
ans = Decimal((resultsign, map(int, str(op1.int * op2.int)), resultexp))
if shouldround:
ans = ans._fix(context)
......@@ -1221,12 +1231,11 @@ class Decimal(object):
sign, 1)
return context._raise_error(DivisionByZero, 'x / 0', sign)
#OK, so neither = 0, INF or NaN
# 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 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:
......@@ -1238,7 +1247,7 @@ class Decimal(object):
ans2)
elif divmod == 2:
#Don't round the mod part, if we don't need it.
# Don't round the mod part, if we don't need it.
return (Decimal( (sign, (0,), 0) ), Decimal(self))
op1 = _WorkRep(self)
......@@ -1287,7 +1296,7 @@ class Decimal(object):
op1.exp -= 1
if res.exp == 0 and divmod and op2.int > op1.int:
#Solves an error in precision. Same as a previous block.
# Solves an error in precision. Same as a previous block.
if res.int >= prec_limit and shouldround:
return context._raise_error(DivisionImpossible)
......@@ -1373,7 +1382,7 @@ class Decimal(object):
# ignored in the calling function.
context = context._shallow_copy()
flags = context._ignore_flags(Rounded, Inexact)
#keep DivisionImpossible flags
# Keep DivisionImpossible flags
(side, r) = self.__divmod__(other, context=context)
if r._isnan():
......@@ -1396,7 +1405,7 @@ class Decimal(object):
if r < comparison:
r._sign, comparison._sign = s1, s2
#Get flags now
# Get flags now
self.__divmod__(other, context=context)
return r._fix(context)
r._sign, comparison._sign = s1, s2
......@@ -1418,7 +1427,8 @@ class Decimal(object):
if r > comparison or decrease and r == comparison:
r._sign, comparison._sign = s1, s2
context.prec += 1
if len(side.__add__(Decimal(1), context=context)._int) >= context.prec:
numbsquant = len(side.__add__(Decimal(1), context=context)._int)
if numbsquant >= context.prec:
context.prec -= 1
return context._raise_error(DivisionImpossible)[1]
context.prec -= 1
......@@ -1453,7 +1463,7 @@ class Decimal(object):
context = getcontext()
return context._raise_error(InvalidContext)
elif self._isinfinity():
raise OverflowError, "Cannot convert infinity to long"
raise OverflowError("Cannot convert infinity to long")
if self._exp >= 0:
s = ''.join(map(str, self._int)) + '0'*self._exp
else:
......@@ -1507,13 +1517,13 @@ class Decimal(object):
context._raise_error(Clamped)
return ans
ans = ans._rescale(Etiny, context=context)
#It isn't zero, and exp < Emin => subnormal
# It isn't zero, and exp < Emin => subnormal
context._raise_error(Subnormal)
if context.flags[Inexact]:
context._raise_error(Underflow)
else:
if ans:
#Only raise subnormal if non-zero.
# Only raise subnormal if non-zero.
context._raise_error(Subnormal)
else:
Etop = context.Etop()
......@@ -1530,7 +1540,8 @@ class Decimal(object):
return ans
context._raise_error(Inexact)
context._raise_error(Rounded)
return context._raise_error(Overflow, 'above Emax', ans._sign)
c = context._raise_error(Overflow, 'above Emax', ans._sign)
return c
return ans
def _round(self, prec=None, rounding=None, context=None):
......@@ -1590,18 +1601,18 @@ class Decimal(object):
ans = Decimal( (temp._sign, tmp, temp._exp - expdiff))
return ans
#OK, but maybe all the lost digits are 0.
# 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
# Rounded, but not Inexact
context._raise_error(Rounded)
return ans
# Okay, let's round and lose data
this_function = getattr(temp, self._pick_rounding_function[rounding])
#Now we've got the rounding function
# Now we've got the rounding function
if prec != context.prec:
context = context._shallow_copy()
......@@ -1697,7 +1708,7 @@ class Decimal(object):
context = getcontext()
if self._is_special or n._is_special or n.adjusted() > 8:
#Because the spot << doesn't work with really big exponents
# Because the spot << doesn't work with really big exponents
if n._isinfinity() or n.adjusted() > 8:
return context._raise_error(InvalidOperation, 'x ** INF')
......@@ -1727,10 +1738,9 @@ class Decimal(object):
return Infsign[sign]
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 \
and self:
# 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 and self:
tmp = Decimal('inf')
tmp._sign = sign
context._raise_error(Rounded)
......@@ -1749,7 +1759,7 @@ class Decimal(object):
context = context._shallow_copy()
context.prec = firstprec + elength + 1
if n < 0:
#n is a long now, not Decimal instance
# n is a long now, not Decimal instance
n = -n
mul = Decimal(1).__div__(mul, context=context)
......@@ -1758,7 +1768,7 @@ class Decimal(object):
spot <<= 1
spot >>= 1
#Spot is the highest power of 2 less than n
# Spot is the highest power of 2 less than n
while spot:
val = val.__mul__(val, context=context)
if val._isinfinity():
......@@ -1816,7 +1826,7 @@ class Decimal(object):
if exp._isinfinity() or self._isinfinity():
if exp._isinfinity() and self._isinfinity():
return self #if both are inf, it is OK
return self # If both are inf, it is OK
if context is None:
context = getcontext()
return context._raise_error(InvalidOperation,
......@@ -1848,7 +1858,8 @@ class Decimal(object):
if self._is_special:
if self._isinfinity():
return context._raise_error(InvalidOperation, 'rescale with an INF')
return context._raise_error(InvalidOperation,
'rescale with an INF')
ans = self._check_nans(context=context)
if ans:
......@@ -1920,13 +1931,13 @@ class Decimal(object):
return Decimal(self)
if not self:
#exponent = self._exp / 2, using round_down.
#if self._exp < 0:
# exp = (self._exp+1) // 2
#else:
# exponent = self._exp / 2, using round_down.
# if self._exp < 0:
# exp = (self._exp+1) // 2
# else:
exp = (self._exp) // 2
if self._sign == 1:
#sqrt(-0) = -0
# sqrt(-0) = -0
return Decimal( (1, (0,), exp))
else:
return Decimal( (0, (0,), exp))
......@@ -1960,8 +1971,7 @@ class Decimal(object):
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.
# ans is now a linear approximation.
Emax, Emin = context.Emax, context.Emin
context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin
......@@ -1977,12 +1987,12 @@ class Decimal(object):
if context.prec == maxp:
break
#round to the answer's precision-- the only error can be 1 ulp.
# Round to the answer's precision-- the only error can be 1 ulp.
context.prec = firstprec
prevexp = ans.adjusted()
ans = ans._round(context=context)
#Now, check if the other last digits are better.
# 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():
......@@ -2014,10 +2024,10 @@ class Decimal(object):
context._raise_error(Rounded)
context._raise_error(Inexact)
else:
#Exact answer, so let's set the exponent right.
#if self._exp < 0:
# exp = (self._exp +1)// 2
#else:
# Exact answer, so let's set the exponent right.
# if self._exp < 0:
# exp = (self._exp +1)// 2
# else:
exp = self._exp // 2
context.prec += ans._exp - exp
ans = ans._rescale(exp, context=context)
......@@ -2052,13 +2062,13 @@ class Decimal(object):
ans = self
c = self.__cmp__(other)
if c == 0:
# if both operands are finite and equal in numerical value
# 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
# 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 the signs are the same then the exponent is used to select
# the result.
if self._sign != other._sign:
if self._sign:
......@@ -2079,7 +2089,7 @@ class Decimal(object):
def min(self, other, context=None):
"""Returns the smaller value.
like min(self, other) except if one is not a number, returns
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)
......@@ -2087,7 +2097,7 @@ class Decimal(object):
return other
if self._is_special or other._is_special:
# if one operand is a quiet NaN and the other is number, then the
# If one operand is a quiet NaN and the other is number, then the
# number is always returned
sn = self._isnan()
on = other._isnan()
......@@ -2101,13 +2111,13 @@ class Decimal(object):
ans = self
c = self.__cmp__(other)
if c == 0:
# if both operands are finite and equal in numerical value
# 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
# 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 the signs are the same then the exponent is used to select
# the result.
if self._sign != other._sign:
if other._sign:
......@@ -2142,37 +2152,38 @@ class Decimal(object):
"""Return the adjusted exponent of self"""
try:
return self._exp + len(self._int) - 1
#If NaN or Infinity, self._exp is string
# If NaN or Infinity, self._exp is string
except TypeError:
return 0
# support for pickling, copy, and deepcopy
# Support for pickling, copy, and deepcopy
def __reduce__(self):
return (self.__class__, (str(self),))
def __copy__(self):
if type(self) == Decimal:
return self # I'm immutable; therefore I am my own clone
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 # My components are also immutable
return self.__class__(str(self))
##### Context class ###########################################
##### Context class ##########################################################
# get rounding method function:
rounding_functions = [name for name in Decimal.__dict__.keys() if name.startswith('_round_')]
# 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.
# 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
class ContextManager(object):
"""Helper class to simplify Context management.
......@@ -2197,12 +2208,13 @@ class ContextManager(object):
def __exit__(self, t, v, tb):
setcontext(self.saved_context)
class Context(object):
"""Contains the context for a Decimal instance.
Contains:
prec - precision (for use in rounding, division, square roots..)
rounding - rounding type. (how you round)
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
......@@ -2243,9 +2255,13 @@ class Context(object):
def __repr__(self):
"""Show the current context."""
s = []
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]) + ']')
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) + ')'
def get_manager(self):
......@@ -2265,9 +2281,10 @@ class Context(object):
def copy(self):
"""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)
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)
return nc
__copy__ = copy
......@@ -2281,16 +2298,16 @@ class Context(object):
"""
error = _condition_map.get(condition, condition)
if error in self._ignored_flags:
#Don't touch the flag
# Don't touch the flag
return error().handle(self, *args)
self.flags[error] += 1
if not self.traps[error]:
#The errors define how to handle themselves.
# 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 = []
# self._ignored_flags = []
raise error, explanation
def _ignore_all_flags(self):
......@@ -2314,7 +2331,7 @@ class Context(object):
def __hash__(self):
"""A Context cannot be hashed."""
# We inherit object.__hash__, so we must deny this explicitly
raise TypeError, "Cannot hash a Context."
raise TypeError("Cannot hash a Context.")
def Etiny(self):
"""Returns Etiny (= Emin - prec + 1)"""
......@@ -2340,7 +2357,6 @@ class Context(object):
This will make it not round for that operation.
"""
rounding = self._rounding_decision
self._rounding_decision = type
return rounding
......@@ -2369,12 +2385,12 @@ class Context(object):
d = Decimal(num, context=self)
return d._fix(self)
#Methods
# Methods
def abs(self, a):
"""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
operation on the operand. Otherwise, the result is the same as using
the plus operation on the operand.
>>> ExtendedContext.abs(Decimal('2.1'))
......@@ -2476,8 +2492,8 @@ class Context(object):
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
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'))
......@@ -2496,8 +2512,8 @@ class Context(object):
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
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'))
......@@ -2528,10 +2544,10 @@ class Context(object):
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
of the 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")
......@@ -2586,14 +2602,14 @@ class Context(object):
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
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
1) before use.
If the increased precision needed for the intermediate calculations
exceeds the capabilities of the implementation then an Invalid operation
condition is raised.
exceeds the capabilities of the implementation then an Invalid
operation condition is raised.
If, when raising to a negative power, an underflow occurs during the
division into 1, the operation is not halted at that point but
......@@ -2631,18 +2647,18 @@ class Context(object):
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'.
"""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
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
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
......@@ -2685,9 +2701,9 @@ class Context(object):
"""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.
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
......@@ -2711,7 +2727,7 @@ class Context(object):
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
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
......@@ -2753,7 +2769,7 @@ class Context(object):
return a.same_quantum(b)
def sqrt(self, a):
"""Returns the square root of a non-negative number to context precision.
"""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.
......@@ -2814,7 +2830,7 @@ class Context(object):
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.
be set. The rounding mode is taken from the context.
>>> ExtendedContext.to_integral(Decimal('2.1'))
Decimal("2")
......@@ -2835,6 +2851,7 @@ class Context(object):
"""
return a.to_integral(context=self)
class _WorkRep(object):
__slots__ = ('sign','int','exp')
# sign: 0 or 1
......@@ -2889,9 +2906,9 @@ def _normalize(op1, op2, shouldround = 0, prec = 0):
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.
# 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
if extend <= 0:
extend = 1
......@@ -2913,13 +2930,13 @@ def _adjust_coefficients(op1, op2):
Used on _WorkRep instances during division.
"""
adjust = 0
#If op1 is smaller, make it larger
# If op1 is smaller, make it larger
while op2.int > op1.int:
op1.int *= 10
op1.exp -= 1
adjust += 1
#If op2 is too small, make it larger
# If op2 is too small, make it larger
while op1.int >= (10 * op2.int):
op2.int *= 10
op2.exp -= 1
......@@ -2927,7 +2944,8 @@ def _adjust_coefficients(op1, op2):
return op1, op2, adjust
##### Helper Functions ########################################
##### Helper Functions #######################################################
def _convert_other(other):
"""Convert other to Decimal.
......@@ -2968,16 +2986,16 @@ def _isnan(num):
if not num:
return 0
#get the sign, get rid of trailing [+-]
# get the sign, get rid of trailing [+-]
sign = 0
if num[0] == '+':
num = num[1:]
elif num[0] == '-': #elif avoids '+-nan'
elif num[0] == '-': # elif avoids '+-nan'
num = num[1:]
sign = 1
if num.startswith('nan'):
if len(num) > 3 and not num[3:].isdigit(): #diagnostic info
if len(num) > 3 and not num[3:].isdigit(): # diagnostic info
return 0
return (1, sign, num[3:].lstrip('0'))
if num.startswith('snan'):
......@@ -2987,7 +3005,7 @@ def _isnan(num):
return 0
##### Setup Specific Contexts ################################
##### Setup Specific Contexts ################################################
# The default context prototype used by Context()
# Is mutable, so that new contexts can have different default values
......@@ -3020,19 +3038,19 @@ ExtendedContext = Context(
)
##### Useful Constants (internal use only) ####################
##### Useful Constants (internal use only) ###################################
#Reusable defaults
# Reusable defaults
Inf = Decimal('Inf')
negInf = Decimal('-Inf')
#Infsign[sign] is infinity w/ that sign
# Infsign[sign] is infinity w/ that sign
Infsign = (Inf, negInf)
NaN = Decimal('NaN')
##### crud for parsing strings #################################
##### crud for parsing strings ################################################
import re
# There's an optional sign at the start, and an optional exponent
......@@ -3052,13 +3070,16 @@ _parser = re.compile(r"""
([eE](?P<exp>[-+]? \d+))?
# \s*
$
""", re.VERBOSE).match #Uncomment the \s* to allow leading or trailing spaces.
""", re.VERBOSE).match # Uncomment the \s* to allow leading/trailing spaces
del re
# return sign, n, p s.t. float string value == -1**sign * n * 10**p exactly
def _string2exact(s):
"""Return sign, n, p s.t.
Float string value == -1**sign * n * 10**p exactly
"""
m = _parser(s)
if m is None:
raise ValueError("invalid literal for Decimal: %r" % s)
......
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