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Commit 59c5884b authored by Facundo Batista's avatar Facundo Batista
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General clean-up. Lot of margin corrections, comments, some typos. 

Exceptions now are raised in the new style. And a mockup class is
now also new style. Thanks Santiago Pereson.
parent 8341aac1
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Lib/decimal.py
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...@@ -29,8 +29,8 @@ and IEEE standard 854-1987: ...@@ -29,8 +29,8 @@ and IEEE standard 854-1987:
Decimal floating point has finite precision with arbitrarily large bounds. Decimal floating point has finite precision with arbitrarily large bounds.
The purpose of the module is to support arithmetic using familiar The purpose of this module is to support arithmetic using familiar
"schoolhouse" rules and to avoid the some of tricky representation "schoolhouse" rules and to avoid some of the tricky representation
issues associated with binary floating point. The package is especially issues associated with binary floating point. The package is especially
useful for financial applications or for contexts where users have useful for financial applications or for contexts where users have
expectations that are at odds with binary floating point (for instance, expectations that are at odds with binary floating point (for instance,
...@@ -136,7 +136,7 @@ __all__ = [ ...@@ -136,7 +136,7 @@ __all__ = [
import copy as _copy import copy as _copy
#Rounding # Rounding
ROUND_DOWN = 'ROUND_DOWN' ROUND_DOWN = 'ROUND_DOWN'
ROUND_HALF_UP = 'ROUND_HALF_UP' ROUND_HALF_UP = 'ROUND_HALF_UP'
ROUND_HALF_EVEN = 'ROUND_HALF_EVEN' ROUND_HALF_EVEN = 'ROUND_HALF_EVEN'
...@@ -145,11 +145,11 @@ ROUND_FLOOR = 'ROUND_FLOOR' ...@@ -145,11 +145,11 @@ ROUND_FLOOR = 'ROUND_FLOOR'
ROUND_UP = 'ROUND_UP' ROUND_UP = 'ROUND_UP'
ROUND_HALF_DOWN = 'ROUND_HALF_DOWN' 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 NEVER_ROUND = 'NEVER_ROUND' # Round in division (non-divmod), sqrt ONLY
ALWAYS_ROUND = 'ALWAYS_ROUND' # Every operation rounds at end. ALWAYS_ROUND = 'ALWAYS_ROUND' # Every operation rounds at end.
#Errors # Errors
class DecimalException(ArithmeticError): class DecimalException(ArithmeticError):
"""Base exception class. """Base exception class.
...@@ -179,9 +179,9 @@ class Clamped(DecimalException): ...@@ -179,9 +179,9 @@ class Clamped(DecimalException):
This occurs and signals clamped if the exponent of a result has been This occurs and signals clamped if the exponent of a result has been
altered in order to fit the constraints of a specific concrete altered in order to fit the constraints of a specific concrete
representation. This may occur when the exponent of a zero result would representation. This may occur when the exponent of a zero result would
be outside the bounds of a representation, or when a large normal be outside the bounds of a representation, or when a large normal
number would have an encoded exponent that cannot be represented. In number would have an encoded exponent that cannot be represented. In
this latter case, the exponent is reduced to fit and the corresponding this latter case, the exponent is reduced to fit and the corresponding
number of zero digits are appended to the coefficient ("fold-down"). number of zero digits are appended to the coefficient ("fold-down").
""" """
...@@ -194,8 +194,8 @@ class InvalidOperation(DecimalException): ...@@ -194,8 +194,8 @@ class InvalidOperation(DecimalException):
Something creates a signaling NaN Something creates a signaling NaN
-INF + INF -INF + INF
0 * (+-)INF 0 * (+-)INF
(+-)INF / (+-)INF (+-)INF / (+-)INF
x % 0 x % 0
(+-)INF % x (+-)INF % x
x._rescale( non-integer ) x._rescale( non-integer )
...@@ -207,7 +207,7 @@ class InvalidOperation(DecimalException): ...@@ -207,7 +207,7 @@ class InvalidOperation(DecimalException):
""" """
def handle(self, context, *args): def handle(self, context, *args):
if 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 Decimal( (args[1]._sign, args[1]._int, 'n') )
return NaN return NaN
...@@ -216,11 +216,11 @@ class ConversionSyntax(InvalidOperation): ...@@ -216,11 +216,11 @@ class ConversionSyntax(InvalidOperation):
This occurs and signals invalid-operation if an string is being This occurs and signals invalid-operation if an string is being
converted to a number and it does not conform to the numeric string 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): 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): class DivisionByZero(DecimalException, ZeroDivisionError):
"""Division by 0. """Division by 0.
...@@ -245,7 +245,7 @@ class DivisionImpossible(InvalidOperation): ...@@ -245,7 +245,7 @@ class DivisionImpossible(InvalidOperation):
This occurs and signals invalid-operation if the integer result of a This occurs and signals invalid-operation if the integer result of a
divide-integer or remainder operation had too many digits (would be 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): def handle(self, context, *args):
...@@ -256,12 +256,12 @@ class DivisionUndefined(InvalidOperation, ZeroDivisionError): ...@@ -256,12 +256,12 @@ class DivisionUndefined(InvalidOperation, ZeroDivisionError):
This occurs and signals invalid-operation if division by zero was This occurs and signals invalid-operation if division by zero was
attempted (during a divide-integer, divide, or remainder operation), and 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): def handle(self, context, tup=None, *args):
if tup is not None: if tup is not None:
return (NaN, NaN) #for 0 %0, 0 // 0 return (NaN, NaN) # for 0 %0, 0 // 0
return NaN return NaN
class Inexact(DecimalException): class Inexact(DecimalException):
...@@ -269,7 +269,7 @@ class Inexact(DecimalException): ...@@ -269,7 +269,7 @@ class Inexact(DecimalException):
This occurs and signals inexact whenever the result of an operation is 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 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. result in all cases is unchanged.
The inexact signal may be tested (or trapped) to determine if a given The inexact signal may be tested (or trapped) to determine if a given
...@@ -281,11 +281,11 @@ class InvalidContext(InvalidOperation): ...@@ -281,11 +281,11 @@ class InvalidContext(InvalidOperation):
"""Invalid context. Unknown rounding, for example. """Invalid context. Unknown rounding, for example.
This occurs and signals invalid-operation if an invalid context was 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 on creation and either the precision exceeds the capability of the
underlying concrete representation or an unknown or unsupported rounding underlying concrete representation or an unknown or unsupported rounding
was specified. These aspects of the context need only be checked when was specified. These aspects of the context need only be checked when
the values are required to be used. The result is [0,qNaN]. the values are required to be used. The result is [0,qNaN].
""" """
def handle(self, context, *args): def handle(self, context, *args):
...@@ -296,7 +296,7 @@ class Rounded(DecimalException): ...@@ -296,7 +296,7 @@ class Rounded(DecimalException):
This occurs and signals rounded whenever the result of an operation is 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 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. result in all cases is unchanged.
The rounded signal may be tested (or trapped) to determine if a given The rounded signal may be tested (or trapped) to determine if a given
...@@ -309,7 +309,7 @@ class Subnormal(DecimalException): ...@@ -309,7 +309,7 @@ class Subnormal(DecimalException):
This occurs and signals subnormal whenever the result of a conversion or This occurs and signals subnormal whenever the result of a conversion or
operation is subnormal (that is, its adjusted exponent is less than 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 The subnormal signal may be tested (or trapped) to determine if a given
or operation (or sequence of operations) yielded a subnormal result. or operation (or sequence of operations) yielded a subnormal result.
...@@ -328,13 +328,13 @@ class Overflow(Inexact, Rounded): ...@@ -328,13 +328,13 @@ class Overflow(Inexact, Rounded):
For round-half-up and round-half-even (and for round-half-down and 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], 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 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 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 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. will also be raised.
""" """
...@@ -360,10 +360,10 @@ class Underflow(Inexact, Rounded, Subnormal): ...@@ -360,10 +360,10 @@ class Underflow(Inexact, Rounded, Subnormal):
This occurs and signals underflow if a result is inexact and the This occurs and signals underflow if a result is inexact and the
adjusted exponent of the result would be smaller (more negative) than adjusted exponent of the result would be smaller (more negative) than
the smallest value that can be handled by the implementation (the value 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 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 0 with the sign of the intermediate result and an exponent of Etiny.
In all cases, Inexact, Rounded, and Subnormal will also be raised. In all cases, Inexact, Rounded, and Subnormal will also be raised.
...@@ -379,7 +379,7 @@ _condition_map = {ConversionSyntax:InvalidOperation, ...@@ -379,7 +379,7 @@ _condition_map = {ConversionSyntax:InvalidOperation,
DivisionUndefined:InvalidOperation, DivisionUndefined:InvalidOperation,
InvalidContext:InvalidOperation} InvalidContext:InvalidOperation}
##### Context Functions ####################################### ##### Context Functions ##################################################
# The getcontext() and setcontext() function manage access to a thread-local # The getcontext() and setcontext() function manage access to a thread-local
# current context. Py2.4 offers direct support for thread locals. If that # current context. Py2.4 offers direct support for thread locals. If that
...@@ -392,7 +392,7 @@ try: ...@@ -392,7 +392,7 @@ try:
except ImportError: except ImportError:
# Python was compiled without threads; create a mock object instead # Python was compiled without threads; create a mock object instead
import sys import sys
class MockThreading: class MockThreading(object):
def local(self, sys=sys): def local(self, sys=sys):
return sys.modules[__name__] return sys.modules[__name__]
threading = MockThreading() threading = MockThreading()
...@@ -403,8 +403,8 @@ try: ...@@ -403,8 +403,8 @@ try:
except AttributeError: except AttributeError:
#To fix reloading, force it to create a new context # To fix reloading, force it to create a new context
#Old contexts have different exceptions in their dicts, making problems. # Old contexts have different exceptions in their dicts, making problems.
if hasattr(threading.currentThread(), '__decimal_context__'): if hasattr(threading.currentThread(), '__decimal_context__'):
del threading.currentThread().__decimal_context__ del threading.currentThread().__decimal_context__
...@@ -469,14 +469,14 @@ def localcontext(ctx=None): ...@@ -469,14 +469,14 @@ def localcontext(ctx=None):
ctx.prec += 2 ctx.prec += 2
# Rest of sin calculation algorithm # Rest of sin calculation algorithm
# uses a precision 2 greater than normal # uses a precision 2 greater than normal
return +s # Convert result to normal precision return +s # Convert result to normal precision
def sin(x): def sin(x):
with localcontext(ExtendedContext): with localcontext(ExtendedContext):
# Rest of sin calculation algorithm # Rest of sin calculation algorithm
# uses the Extended Context from the # uses the Extended Context from the
# General Decimal Arithmetic Specification # General Decimal Arithmetic Specification
return +s # Convert result to normal context return +s # Convert result to normal context
""" """
# The string below can't be included in the docstring until Python 2.6 # The string below can't be included in the docstring until Python 2.6
...@@ -502,7 +502,7 @@ def localcontext(ctx=None): ...@@ -502,7 +502,7 @@ def localcontext(ctx=None):
return _ContextManager(ctx) return _ContextManager(ctx)
##### Decimal class ########################################### ##### Decimal class #######################################################
class Decimal(object): class Decimal(object):
"""Floating point class for decimal arithmetic.""" """Floating point class for decimal arithmetic."""
...@@ -518,7 +518,7 @@ class Decimal(object): ...@@ -518,7 +518,7 @@ class Decimal(object):
>>> Decimal('3.14') # string input >>> Decimal('3.14') # string input
Decimal("3.14") 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("3.14")
>>> Decimal(314) # int or long >>> Decimal(314) # int or long
Decimal("314") Decimal("314")
...@@ -557,13 +557,13 @@ class Decimal(object): ...@@ -557,13 +557,13 @@ class Decimal(object):
# tuple/list conversion (possibly from as_tuple()) # tuple/list conversion (possibly from as_tuple())
if isinstance(value, (list,tuple)): if isinstance(value, (list,tuple)):
if len(value) != 3: if len(value) != 3:
raise ValueError, 'Invalid arguments' raise ValueError('Invalid arguments')
if value[0] not in (0,1): if value[0] not in (0,1):
raise ValueError, 'Invalid sign' raise ValueError('Invalid sign')
for digit in value[1]: for digit in value[1]:
if not isinstance(digit, (int,long)) or digit < 0: 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._sign = value[0]
self._int = tuple(value[1]) self._int = tuple(value[1])
if value[2] in ('F','n','N'): if value[2] in ('F','n','N'):
...@@ -596,22 +596,23 @@ class Decimal(object): ...@@ -596,22 +596,23 @@ class Decimal(object):
if _isnan(value): if _isnan(value):
sig, sign, diag = _isnan(value) sig, sign, diag = _isnan(value)
self._is_special = True 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 = \ self._sign, self._int, self._exp = \
context._raise_error(ConversionSyntax) context._raise_error(ConversionSyntax)
return self return self
if sig == 1: if sig == 1:
self._exp = 'n' #qNaN self._exp = 'n' # qNaN
else: #sig == 2 else: # sig == 2
self._exp = 'N' #sNaN self._exp = 'N' # sNaN
self._sign = sign self._sign = sign
self._int = tuple(map(int, diag)) #Diagnostic info self._int = tuple(map(int, diag)) # Diagnostic info
return self return self
try: try:
self._sign, self._int, self._exp = _string2exact(value) self._sign, self._int, self._exp = _string2exact(value)
except ValueError: except ValueError:
self._is_special = True 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 return self
raise TypeError("Cannot convert %r to Decimal" % value) raise TypeError("Cannot convert %r to Decimal" % value)
...@@ -694,15 +695,15 @@ class Decimal(object): ...@@ -694,15 +695,15 @@ class Decimal(object):
if self._is_special or other._is_special: if self._is_special or other._is_special:
ans = self._check_nans(other, context) ans = self._check_nans(other, context)
if ans: if ans:
return 1 # Comparison involving NaN's always reports self > other return 1 # Comparison involving NaN's always reports self > other
# INF = INF # INF = INF
return cmp(self._isinfinity(), other._isinfinity()) return cmp(self._isinfinity(), other._isinfinity())
if not self and not other: 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: if other._sign < self._sign:
return -1 return -1
if self._sign < other._sign: if self._sign < other._sign:
...@@ -713,7 +714,7 @@ class Decimal(object): ...@@ -713,7 +714,7 @@ class Decimal(object):
if self_adjusted == other_adjusted and \ if self_adjusted == other_adjusted and \
self._int + (0,)*(self._exp - other._exp) == \ self._int + (0,)*(self._exp - other._exp) == \
other._int + (0,)*(other._exp - self._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: elif self_adjusted > other_adjusted and self._int[0] != 0:
return (-1)**self._sign return (-1)**self._sign
elif self_adjusted < other_adjusted and other._int[0] != 0: elif self_adjusted < other_adjusted and other._int[0] != 0:
...@@ -724,7 +725,7 @@ class Decimal(object): ...@@ -724,7 +725,7 @@ class Decimal(object):
context = getcontext() context = getcontext()
context = context._shallow_copy() 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() flags = context._ignore_all_flags()
res = self.__sub__(other, context=context) res = self.__sub__(other, context=context)
...@@ -762,7 +763,7 @@ class Decimal(object): ...@@ -762,7 +763,7 @@ class Decimal(object):
if other is NotImplemented: if other is NotImplemented:
return other return other
#compare(NaN, NaN) = NaN # Compare(NaN, NaN) = NaN
if (self._is_special or other and other._is_special): if (self._is_special or other and other._is_special):
ans = self._check_nans(other, context) ans = self._check_nans(other, context)
if ans: if ans:
...@@ -823,11 +824,11 @@ class Decimal(object): ...@@ -823,11 +824,11 @@ class Decimal(object):
tmp = map(str, self._int) tmp = map(str, self._int)
numdigits = len(self._int) numdigits = len(self._int)
leftdigits = self._exp + numdigits leftdigits = self._exp + numdigits
if eng and not self: #self = 0eX wants 0[.0[0]]eY, not [[0]0]0eY 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 self._exp < 0 and self._exp >= -6: # short, no need for e/E
s = '-'*self._sign + '0.' + '0'*(abs(self._exp)) s = '-'*self._sign + '0.' + '0'*(abs(self._exp))
return s 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 exp = ((self._exp - 1)// 3 + 1) * 3
if exp != self._exp: if exp != self._exp:
s = '0.'+'0'*(exp - self._exp) s = '0.'+'0'*(exp - self._exp)
...@@ -839,7 +840,7 @@ class Decimal(object): ...@@ -839,7 +840,7 @@ class Decimal(object):
else: else:
s += 'e' s += 'e'
if exp > 0: if exp > 0:
s += '+' #0.0e+3, not 0.0e3 s += '+' # 0.0e+3, not 0.0e3
s += str(exp) s += str(exp)
s = '-'*self._sign + s s = '-'*self._sign + s
return s return s
...@@ -979,19 +980,19 @@ class Decimal(object): ...@@ -979,19 +980,19 @@ class Decimal(object):
return ans return ans
if self._isinfinity(): 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(): if self._sign != other._sign and other._isinfinity():
return context._raise_error(InvalidOperation, '-INF + INF') return context._raise_error(InvalidOperation, '-INF + INF')
return Decimal(self) return Decimal(self)
if other._isinfinity(): 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 shouldround = context._rounding_decision == ALWAYS_ROUND
exp = min(self._exp, other._exp) exp = min(self._exp, other._exp)
negativezero = 0 negativezero = 0
if context.rounding == ROUND_FLOOR and self._sign != other._sign: 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 negativezero = 1
if not self and not other: if not self and not other:
...@@ -1026,19 +1027,19 @@ class Decimal(object): ...@@ -1026,19 +1027,19 @@ class Decimal(object):
return Decimal((negativezero, (0,), exp)) return Decimal((negativezero, (0,), exp))
if op1.int < op2.int: if op1.int < op2.int:
op1, op2 = op2, op1 op1, op2 = op2, op1
#OK, now abs(op1) > abs(op2) # OK, now abs(op1) > abs(op2)
if op1.sign == 1: if op1.sign == 1:
result.sign = 1 result.sign = 1
op1.sign, op2.sign = op2.sign, op1.sign op1.sign, op2.sign = op2.sign, op1.sign
else: else:
result.sign = 0 result.sign = 0
#So we know the sign, and op1 > 0. # So we know the sign, and op1 > 0.
elif op1.sign == 1: elif op1.sign == 1:
result.sign = 1 result.sign = 1
op1.sign, op2.sign = (0, 0) op1.sign, op2.sign = (0, 0)
else: else:
result.sign = 0 result.sign = 0
#Now, op1 > abs(op2) > 0 # Now, op1 > abs(op2) > 0
if op2.sign == 0: if op2.sign == 0:
result.int = op1.int + op2.int result.int = op1.int + op2.int
...@@ -1096,7 +1097,8 @@ class Decimal(object): ...@@ -1096,7 +1097,8 @@ class Decimal(object):
if ans: if ans:
return 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 = list(self._int)
L[-1] += 1 L[-1] += 1
...@@ -1152,7 +1154,7 @@ class Decimal(object): ...@@ -1152,7 +1154,7 @@ class Decimal(object):
if not self or not other: if not self or not other:
ans = Decimal((resultsign, (0,), resultexp)) ans = Decimal((resultsign, (0,), resultexp))
if shouldround: if shouldround:
#Fixing in case the exponent is out of bounds # Fixing in case the exponent is out of bounds
ans = ans._fix(context) ans = ans._fix(context)
return ans return ans
...@@ -1171,7 +1173,7 @@ class Decimal(object): ...@@ -1171,7 +1173,7 @@ class Decimal(object):
op1 = _WorkRep(self) op1 = _WorkRep(self)
op2 = _WorkRep(other) 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: if shouldround:
ans = ans._fix(context) ans = ans._fix(context)
...@@ -1264,12 +1266,11 @@ class Decimal(object): ...@@ -1264,12 +1266,11 @@ class Decimal(object):
sign, 1) sign, 1)
return context._raise_error(DivisionByZero, 'x / 0', sign) 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 shouldround = context._rounding_decision == ALWAYS_ROUND
#If we're dividing into ints, and self < other, stop. # If we're dividing into ints, and self < other, stop.
#self.__abs__(0) does not round. # self.__abs__(0) does not round.
if divmod and (self.__abs__(0, context) < other.__abs__(0, context)): if divmod and (self.__abs__(0, context) < other.__abs__(0, context)):
if divmod == 1 or divmod == 3: if divmod == 1 or divmod == 3:
...@@ -1281,7 +1282,7 @@ class Decimal(object): ...@@ -1281,7 +1282,7 @@ class Decimal(object):
ans2) ans2)
elif divmod == 2: 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)) return (Decimal( (sign, (0,), 0) ), Decimal(self))
op1 = _WorkRep(self) op1 = _WorkRep(self)
...@@ -1330,7 +1331,7 @@ class Decimal(object): ...@@ -1330,7 +1331,7 @@ class Decimal(object):
op1.exp -= 1 op1.exp -= 1
if res.exp == 0 and divmod and op2.int > op1.int: 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: if res.int >= prec_limit and shouldround:
return context._raise_error(DivisionImpossible) return context._raise_error(DivisionImpossible)
...@@ -1416,7 +1417,7 @@ class Decimal(object): ...@@ -1416,7 +1417,7 @@ class Decimal(object):
# ignored in the calling function. # ignored in the calling function.
context = context._shallow_copy() context = context._shallow_copy()
flags = context._ignore_flags(Rounded, Inexact) flags = context._ignore_flags(Rounded, Inexact)
#keep DivisionImpossible flags # Keep DivisionImpossible flags
(side, r) = self.__divmod__(other, context=context) (side, r) = self.__divmod__(other, context=context)
if r._isnan(): if r._isnan():
...@@ -1439,7 +1440,7 @@ class Decimal(object): ...@@ -1439,7 +1440,7 @@ class Decimal(object):
if r < comparison: if r < comparison:
r._sign, comparison._sign = s1, s2 r._sign, comparison._sign = s1, s2
#Get flags now # Get flags now
self.__divmod__(other, context=context) self.__divmod__(other, context=context)
return r._fix(context) return r._fix(context)
r._sign, comparison._sign = s1, s2 r._sign, comparison._sign = s1, s2
...@@ -1461,7 +1462,8 @@ class Decimal(object): ...@@ -1461,7 +1462,8 @@ class Decimal(object):
if r > comparison or decrease and r == comparison: if r > comparison or decrease and r == comparison:
r._sign, comparison._sign = s1, s2 r._sign, comparison._sign = s1, s2
context.prec += 1 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 context.prec -= 1
return context._raise_error(DivisionImpossible)[1] return context._raise_error(DivisionImpossible)[1]
context.prec -= 1 context.prec -= 1
...@@ -1496,7 +1498,7 @@ class Decimal(object): ...@@ -1496,7 +1498,7 @@ class Decimal(object):
context = getcontext() context = getcontext()
return context._raise_error(InvalidContext) return context._raise_error(InvalidContext)
elif self._isinfinity(): elif self._isinfinity():
raise OverflowError, "Cannot convert infinity to long" raise OverflowError("Cannot convert infinity to long")
if self._exp >= 0: if self._exp >= 0:
s = ''.join(map(str, self._int)) + '0'*self._exp s = ''.join(map(str, self._int)) + '0'*self._exp
else: else:
...@@ -1550,13 +1552,13 @@ class Decimal(object): ...@@ -1550,13 +1552,13 @@ class Decimal(object):
context._raise_error(Clamped) context._raise_error(Clamped)
return ans return ans
ans = ans._rescale(Etiny, context=context) 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) context._raise_error(Subnormal)
if context.flags[Inexact]: if context.flags[Inexact]:
context._raise_error(Underflow) context._raise_error(Underflow)
else: else:
if ans: if ans:
#Only raise subnormal if non-zero. # Only raise subnormal if non-zero.
context._raise_error(Subnormal) context._raise_error(Subnormal)
else: else:
Etop = context.Etop() Etop = context.Etop()
...@@ -1573,7 +1575,8 @@ class Decimal(object): ...@@ -1573,7 +1575,8 @@ class Decimal(object):
return ans return ans
context._raise_error(Inexact) context._raise_error(Inexact)
context._raise_error(Rounded) 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 return ans
def _round(self, prec=None, rounding=None, context=None): def _round(self, prec=None, rounding=None, context=None):
...@@ -1633,18 +1636,18 @@ class Decimal(object): ...@@ -1633,18 +1636,18 @@ class Decimal(object):
ans = Decimal( (temp._sign, tmp, temp._exp - expdiff)) ans = Decimal( (temp._sign, tmp, temp._exp - expdiff))
return ans return ans
#OK, but maybe all the lost digits are 0. # OK, but maybe all the lost digits are 0.
lostdigits = self._int[expdiff:] lostdigits = self._int[expdiff:]
if lostdigits == (0,) * len(lostdigits): if lostdigits == (0,) * len(lostdigits):
ans = Decimal( (temp._sign, temp._int[:prec], temp._exp - expdiff)) ans = Decimal( (temp._sign, temp._int[:prec], temp._exp - expdiff))
#Rounded, but not Inexact # Rounded, but not Inexact
context._raise_error(Rounded) context._raise_error(Rounded)
return ans return ans
# Okay, let's round and lose data # Okay, let's round and lose data
this_function = getattr(temp, self._pick_rounding_function[rounding]) 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: if prec != context.prec:
context = context._shallow_copy() context = context._shallow_copy()
...@@ -1740,7 +1743,7 @@ class Decimal(object): ...@@ -1740,7 +1743,7 @@ class Decimal(object):
context = getcontext() context = getcontext()
if self._is_special or n._is_special or n.adjusted() > 8: 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: if n._isinfinity() or n.adjusted() > 8:
return context._raise_error(InvalidOperation, 'x ** INF') return context._raise_error(InvalidOperation, 'x ** INF')
...@@ -1770,9 +1773,10 @@ class Decimal(object): ...@@ -1770,9 +1773,10 @@ class Decimal(object):
return Infsign[sign] return Infsign[sign]
return Decimal( (sign, (0,), 0) ) return Decimal( (sign, (0,), 0) )
#with ludicrously large exponent, just raise an overflow and return inf. # With ludicrously large exponent, just raise an overflow
if not modulo and n > 0 and (self._exp + len(self._int) - 1) * n > context.Emax \ # and return inf.
and self: if not modulo and n > 0 and \
(self._exp + len(self._int) - 1) * n > context.Emax and self:
tmp = Decimal('inf') tmp = Decimal('inf')
tmp._sign = sign tmp._sign = sign
...@@ -1792,7 +1796,7 @@ class Decimal(object): ...@@ -1792,7 +1796,7 @@ class Decimal(object):
context = context._shallow_copy() context = context._shallow_copy()
context.prec = firstprec + elength + 1 context.prec = firstprec + elength + 1
if n < 0: if n < 0:
#n is a long now, not Decimal instance # n is a long now, not Decimal instance
n = -n n = -n
mul = Decimal(1).__div__(mul, context=context) mul = Decimal(1).__div__(mul, context=context)
...@@ -1801,7 +1805,7 @@ class Decimal(object): ...@@ -1801,7 +1805,7 @@ class Decimal(object):
spot <<= 1 spot <<= 1
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: while spot:
val = val.__mul__(val, context=context) val = val.__mul__(val, context=context)
if val._isinfinity(): if val._isinfinity():
...@@ -1859,7 +1863,7 @@ class Decimal(object): ...@@ -1859,7 +1863,7 @@ class Decimal(object):
if exp._isinfinity() or self._isinfinity(): if exp._isinfinity() or self._isinfinity():
if exp._isinfinity() and 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: if context is None:
context = getcontext() context = getcontext()
return context._raise_error(InvalidOperation, return context._raise_error(InvalidOperation,
...@@ -1963,13 +1967,13 @@ class Decimal(object): ...@@ -1963,13 +1967,13 @@ class Decimal(object):
return Decimal(self) return Decimal(self)
if not self: if not self:
#exponent = self._exp / 2, using round_down. # exponent = self._exp / 2, using round_down.
#if self._exp < 0: # if self._exp < 0:
# exp = (self._exp+1) // 2 # exp = (self._exp+1) // 2
#else: # else:
exp = (self._exp) // 2 exp = (self._exp) // 2
if self._sign == 1: if self._sign == 1:
#sqrt(-0) = -0 # sqrt(-0) = -0
return Decimal( (1, (0,), exp)) return Decimal( (1, (0,), exp))
else: else:
return Decimal( (0, (0,), exp)) return Decimal( (0, (0,), exp))
...@@ -2004,8 +2008,7 @@ class Decimal(object): ...@@ -2004,8 +2008,7 @@ class Decimal(object):
context=context), context=context) context=context), context=context)
ans._exp -= 1 + tmp.adjusted() // 2 ans._exp -= 1 + tmp.adjusted() // 2
#ans is now a linear approximation. # ans is now a linear approximation.
Emax, Emin = context.Emax, context.Emin Emax, Emin = context.Emax, context.Emin
context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin
...@@ -2020,12 +2023,12 @@ class Decimal(object): ...@@ -2020,12 +2023,12 @@ class Decimal(object):
if context.prec == maxp: if context.prec == maxp:
break 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 context.prec = firstprec
prevexp = ans.adjusted() prevexp = ans.adjusted()
ans = ans._round(context=context) 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 context.prec = firstprec + 1
# In case we rounded up another digit and we should actually go lower. # In case we rounded up another digit and we should actually go lower.
if prevexp != ans.adjusted(): if prevexp != ans.adjusted():
...@@ -2057,10 +2060,10 @@ class Decimal(object): ...@@ -2057,10 +2060,10 @@ class Decimal(object):
context._raise_error(Rounded) context._raise_error(Rounded)
context._raise_error(Inexact) context._raise_error(Inexact)
else: else:
#Exact answer, so let's set the exponent right. # Exact answer, so let's set the exponent right.
#if self._exp < 0: # if self._exp < 0:
# exp = (self._exp +1)// 2 # exp = (self._exp +1)// 2
#else: # else:
exp = self._exp // 2 exp = self._exp // 2
context.prec += ans._exp - exp context.prec += ans._exp - exp
ans = ans._rescale(exp, context=context) ans = ans._rescale(exp, context=context)
...@@ -2081,7 +2084,7 @@ class Decimal(object): ...@@ -2081,7 +2084,7 @@ class Decimal(object):
return other return other
if self._is_special or other._is_special: 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 # number is always returned
sn = self._isnan() sn = self._isnan()
on = other._isnan() on = other._isnan()
...@@ -2095,13 +2098,13 @@ class Decimal(object): ...@@ -2095,13 +2098,13 @@ class Decimal(object):
ans = self ans = self
c = self.__cmp__(other) c = self.__cmp__(other)
if c == 0: 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: # 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 # 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. # the result.
if self._sign != other._sign: if self._sign != other._sign:
if self._sign: if self._sign:
...@@ -2122,7 +2125,7 @@ class Decimal(object): ...@@ -2122,7 +2125,7 @@ class Decimal(object):
def min(self, other, context=None): def min(self, other, context=None):
"""Returns the smaller value. """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. NaN (and signals if one is sNaN). Also rounds.
""" """
other = _convert_other(other) other = _convert_other(other)
...@@ -2130,7 +2133,7 @@ class Decimal(object): ...@@ -2130,7 +2133,7 @@ class Decimal(object):
return other return other
if self._is_special or other._is_special: 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 # number is always returned
sn = self._isnan() sn = self._isnan()
on = other._isnan() on = other._isnan()
...@@ -2144,13 +2147,13 @@ class Decimal(object): ...@@ -2144,13 +2147,13 @@ class Decimal(object):
ans = self ans = self
c = self.__cmp__(other) c = self.__cmp__(other)
if c == 0: 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: # 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 # 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. # the result.
if self._sign != other._sign: if self._sign != other._sign:
if other._sign: if other._sign:
...@@ -2185,11 +2188,11 @@ class Decimal(object): ...@@ -2185,11 +2188,11 @@ class Decimal(object):
"""Return the adjusted exponent of self""" """Return the adjusted exponent of self"""
try: try:
return self._exp + len(self._int) - 1 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: except TypeError:
return 0 return 0
# support for pickling, copy, and deepcopy # Support for pickling, copy, and deepcopy
def __reduce__(self): def __reduce__(self):
return (self.__class__, (str(self),)) return (self.__class__, (str(self),))
...@@ -2203,13 +2206,14 @@ class Decimal(object): ...@@ -2203,13 +2206,14 @@ class Decimal(object):
return self # My components are also immutable return self # My components are also immutable
return self.__class__(str(self)) return self.__class__(str(self))
##### Context class ########################################### ##### Context class #######################################################
# get rounding method function: # get rounding method function:
rounding_functions = [name for name in Decimal.__dict__.keys() if name.startswith('_round_')] rounding_functions = [name for name in Decimal.__dict__.keys()
if name.startswith('_round_')]
for name in rounding_functions: 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() globalname = name[1:].upper()
val = globals()[globalname] val = globals()[globalname]
Decimal._pick_rounding_function[val] = name Decimal._pick_rounding_function[val] = name
...@@ -2236,7 +2240,7 @@ class Context(object): ...@@ -2236,7 +2240,7 @@ class Context(object):
Contains: Contains:
prec - precision (for use in rounding, division, square roots..) 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? _rounding_decision - ALWAYS_ROUND, NEVER_ROUND -- do you round?
traps - If traps[exception] = 1, then the exception is traps - If traps[exception] = 1, then the exception is
raised when it is caused. Otherwise, a value is raised when it is caused. Otherwise, a value is
...@@ -2277,9 +2281,13 @@ class Context(object): ...@@ -2277,9 +2281,13 @@ class Context(object):
def __repr__(self): def __repr__(self):
"""Show the current context.""" """Show the current context."""
s = [] s = []
s.append('Context(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' % vars(self)) s.append('Context(prec=%(prec)d, rounding=%(rounding)s, '
s.append('flags=[' + ', '.join([f.__name__ for f, v in self.flags.items() if v]) + ']') 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d'
s.append('traps=[' + ', '.join([t.__name__ for t, v in self.traps.items() if v]) + ']') % vars(self))
names = [f.__name__ for f, v in self.flags.items() if v]
s.append('flags=[' + ', '.join(names) + ']')
names = [t.__name__ for t, v in self.traps.items() if v]
s.append('traps=[' + ', '.join(names) + ']')
return ', '.join(s) + ')' return ', '.join(s) + ')'
def clear_flags(self): def clear_flags(self):
...@@ -2296,9 +2304,9 @@ class Context(object): ...@@ -2296,9 +2304,9 @@ class Context(object):
def copy(self): def copy(self):
"""Returns a deep copy from self.""" """Returns a deep copy from self."""
nc = Context(self.prec, self.rounding, self.traps.copy(), self.flags.copy(), nc = Context(self.prec, self.rounding, self.traps.copy(),
self._rounding_decision, self.Emin, self.Emax, self.flags.copy(), self._rounding_decision, self.Emin,
self.capitals, self._clamp, self._ignored_flags) self.Emax, self.capitals, self._clamp, self._ignored_flags)
return nc return nc
__copy__ = copy __copy__ = copy
...@@ -2312,16 +2320,16 @@ class Context(object): ...@@ -2312,16 +2320,16 @@ class Context(object):
""" """
error = _condition_map.get(condition, condition) error = _condition_map.get(condition, condition)
if error in self._ignored_flags: if error in self._ignored_flags:
#Don't touch the flag # Don't touch the flag
return error().handle(self, *args) return error().handle(self, *args)
self.flags[error] += 1 self.flags[error] += 1
if not self.traps[error]: if not self.traps[error]:
#The errors define how to handle themselves. # The errors define how to handle themselves.
return condition().handle(self, *args) return condition().handle(self, *args)
# Errors should only be risked on copies of the context # Errors should only be risked on copies of the context
#self._ignored_flags = [] # self._ignored_flags = []
raise error, explanation raise error, explanation
def _ignore_all_flags(self): def _ignore_all_flags(self):
...@@ -2345,7 +2353,7 @@ class Context(object): ...@@ -2345,7 +2353,7 @@ class Context(object):
def __hash__(self): def __hash__(self):
"""A Context cannot be hashed.""" """A Context cannot be hashed."""
# We inherit object.__hash__, so we must deny this explicitly # 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): def Etiny(self):
"""Returns Etiny (= Emin - prec + 1)""" """Returns Etiny (= Emin - prec + 1)"""
...@@ -2400,12 +2408,12 @@ class Context(object): ...@@ -2400,12 +2408,12 @@ class Context(object):
d = Decimal(num, context=self) d = Decimal(num, context=self)
return d._fix(self) return d._fix(self)
#Methods # Methods
def abs(self, a): def abs(self, a):
"""Returns the absolute value of the operand. """Returns the absolute value of the operand.
If the operand is negative, the result is the same as using the minus 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. the plus operation on the operand.
>>> ExtendedContext.abs(Decimal('2.1')) >>> ExtendedContext.abs(Decimal('2.1'))
...@@ -2507,8 +2515,8 @@ class Context(object): ...@@ -2507,8 +2515,8 @@ class Context(object):
If either operand is a NaN then the general rules apply. If either operand is a NaN then the general rules apply.
Otherwise, the operands are compared as as though by the compare Otherwise, the operands are compared as as though by the compare
operation. If they are numerically equal then the left-hand operand operation. If they are numerically equal then the left-hand operand
is chosen as the result. Otherwise the maximum (closer to positive is chosen as the result. Otherwise the maximum (closer to positive
infinity) of the two operands is chosen as the result. infinity) of the two operands is chosen as the result.
>>> ExtendedContext.max(Decimal('3'), Decimal('2')) >>> ExtendedContext.max(Decimal('3'), Decimal('2'))
...@@ -2527,8 +2535,8 @@ class Context(object): ...@@ -2527,8 +2535,8 @@ class Context(object):
If either operand is a NaN then the general rules apply. If either operand is a NaN then the general rules apply.
Otherwise, the operands are compared as as though by the compare Otherwise, the operands are compared as as though by the compare
operation. If they are numerically equal then the left-hand operand operation. If they are numerically equal then the left-hand operand
is chosen as the result. Otherwise the minimum (closer to negative is chosen as the result. Otherwise the minimum (closer to negative
infinity) of the two operands is chosen as the result. infinity) of the two operands is chosen as the result.
>>> ExtendedContext.min(Decimal('3'), Decimal('2')) >>> ExtendedContext.min(Decimal('3'), Decimal('2'))
...@@ -2617,14 +2625,14 @@ class Context(object): ...@@ -2617,14 +2625,14 @@ class Context(object):
The right-hand operand must be a whole number whose integer part (after 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 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 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 the power is used, and the left-hand operand is inverted (divided into
1) before use. 1) before use.
If the increased precision needed for the intermediate calculations If the increased precision needed for the intermediate calculations
exceeds the capabilities of the implementation then an Invalid operation exceeds the capabilities of the implementation then an Invalid
condition is raised. operation condition is raised.
If, when raising to a negative power, an underflow occurs during the If, when raising to a negative power, an underflow occurs during the
division into 1, the operation is not halted at that point but division into 1, the operation is not halted at that point but
...@@ -2662,18 +2670,18 @@ class Context(object): ...@@ -2662,18 +2670,18 @@ class Context(object):
return a.__pow__(b, modulo, context=self) return a.__pow__(b, modulo, context=self)
def quantize(self, a, b): 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 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 exponent is being increased), multiplied by a positive power of ten (if
the exponent is being decreased), or is unchanged (if the exponent is the exponent is being decreased), or is unchanged (if the exponent is
already equal to that of the right-hand operand). already equal to that of the right-hand operand).
Unlike other operations, if the length of the coefficient after the Unlike other operations, if the length of the coefficient after the
quantize operation would be greater than precision then an Invalid quantize operation would be greater than precision then an Invalid
operation condition is raised. This guarantees that, unless there is an operation condition is raised. This guarantees that, unless there is
error condition, the exponent of the result of a quantize is always an error condition, the exponent of the result of a quantize is always
equal to that of the right-hand operand. equal to that of the right-hand operand.
Also unlike other operations, quantize will never raise Underflow, even Also unlike other operations, quantize will never raise Underflow, even
...@@ -2716,9 +2724,9 @@ class Context(object): ...@@ -2716,9 +2724,9 @@ class Context(object):
"""Returns the remainder from integer division. """Returns the remainder from integer division.
The result is the residue of the dividend after the operation of The result is the residue of the dividend after the operation of
calculating integer division as described for divide-integer, rounded to calculating integer division as described for divide-integer, rounded
precision digits if necessary. The sign of the result, if non-zero, is to precision digits if necessary. The sign of the result, if
the same as that of the original dividend. non-zero, is the same as that of the original dividend.
This operation will fail under the same conditions as integer division This operation will fail under the same conditions as integer division
(that is, if integer division on the same two operands would fail, the (that is, if integer division on the same two operands would fail, the
...@@ -2742,7 +2750,7 @@ class Context(object): ...@@ -2742,7 +2750,7 @@ class Context(object):
def remainder_near(self, a, b): def remainder_near(self, a, b):
"""Returns to be "a - b * n", where n is the integer nearest the exact """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 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. sign of a.
This operation will fail under the same conditions as integer division This operation will fail under the same conditions as integer division
...@@ -2784,7 +2792,7 @@ class Context(object): ...@@ -2784,7 +2792,7 @@ class Context(object):
return a.same_quantum(b) return a.same_quantum(b)
def sqrt(self, a): 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 If the result must be inexact, it is rounded using the round-half-even
algorithm. algorithm.
...@@ -2845,7 +2853,7 @@ class Context(object): ...@@ -2845,7 +2853,7 @@ class Context(object):
as using the quantize() operation using the given operand as the as using the quantize() operation using the given operand as the
left-hand-operand, 1E+0 as the right-hand-operand, and the precision 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 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')) >>> ExtendedContext.to_integral(Decimal('2.1'))
Decimal("2") Decimal("2")
...@@ -2920,8 +2928,9 @@ def _normalize(op1, op2, shouldround = 0, prec = 0): ...@@ -2920,8 +2928,9 @@ def _normalize(op1, op2, shouldround = 0, prec = 0):
other_len = len(str(other.int)) other_len = len(str(other.int))
if numdigits > (other_len + prec + 1 - tmp_len): if numdigits > (other_len + prec + 1 - tmp_len):
# If the difference in adjusted exps is > prec+1, we know # If the difference in adjusted exps is > prec+1, we know
# other is insignificant, so might as well put a 1 after the precision. # other is insignificant, so might as well put a 1 after the
# (since this is only for addition.) Also stops use of massive longs. # precision (since this is only for addition). Also stops
# use of massive longs.
extend = prec + 2 - tmp_len extend = prec + 2 - tmp_len
if extend <= 0: if extend <= 0:
...@@ -2944,13 +2953,13 @@ def _adjust_coefficients(op1, op2): ...@@ -2944,13 +2953,13 @@ def _adjust_coefficients(op1, op2):
Used on _WorkRep instances during division. Used on _WorkRep instances during division.
""" """
adjust = 0 adjust = 0
#If op1 is smaller, make it larger # If op1 is smaller, make it larger
while op2.int > op1.int: while op2.int > op1.int:
op1.int *= 10 op1.int *= 10
op1.exp -= 1 op1.exp -= 1
adjust += 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): while op1.int >= (10 * op2.int):
op2.int *= 10 op2.int *= 10
op2.exp -= 1 op2.exp -= 1
...@@ -2958,7 +2967,7 @@ def _adjust_coefficients(op1, op2): ...@@ -2958,7 +2967,7 @@ def _adjust_coefficients(op1, op2):
return op1, op2, adjust return op1, op2, adjust
##### Helper Functions ######################################## ##### Helper Functions ####################################################
def _convert_other(other): def _convert_other(other):
"""Convert other to Decimal. """Convert other to Decimal.
...@@ -2999,16 +3008,16 @@ def _isnan(num): ...@@ -2999,16 +3008,16 @@ def _isnan(num):
if not num: if not num:
return 0 return 0
#get the sign, get rid of trailing [+-] # Get the sign, get rid of trailing [+-]
sign = 0 sign = 0
if num[0] == '+': if num[0] == '+':
num = num[1:] num = num[1:]
elif num[0] == '-': #elif avoids '+-nan' elif num[0] == '-': # elif avoids '+-nan'
num = num[1:] num = num[1:]
sign = 1 sign = 1
if num.startswith('nan'): 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 0
return (1, sign, num[3:].lstrip('0')) return (1, sign, num[3:].lstrip('0'))
if num.startswith('snan'): if num.startswith('snan'):
...@@ -3018,7 +3027,7 @@ def _isnan(num): ...@@ -3018,7 +3027,7 @@ def _isnan(num):
return 0 return 0
##### Setup Specific Contexts ################################ ##### Setup Specific Contexts ############################################
# The default context prototype used by Context() # The default context prototype used by Context()
# Is mutable, so that new contexts can have different default values # Is mutable, so that new contexts can have different default values
...@@ -3051,19 +3060,19 @@ ExtendedContext = Context( ...@@ -3051,19 +3060,19 @@ ExtendedContext = Context(
) )
##### Useful Constants (internal use only) #################### ##### Useful Constants (internal use only) ################################
#Reusable defaults # Reusable defaults
Inf = Decimal('Inf') Inf = Decimal('Inf')
negInf = Decimal('-Inf') negInf = Decimal('-Inf')
#Infsign[sign] is infinity w/ that sign # Infsign[sign] is infinity w/ that sign
Infsign = (Inf, negInf) Infsign = (Inf, negInf)
NaN = Decimal('NaN') NaN = Decimal('NaN')
##### crud for parsing strings ################################# ##### crud for parsing strings #############################################
import re import re
# There's an optional sign at the start, and an optional exponent # There's an optional sign at the start, and an optional exponent
...@@ -3083,13 +3092,15 @@ _parser = re.compile(r""" ...@@ -3083,13 +3092,15 @@ _parser = re.compile(r"""
([eE](?P<exp>[-+]? \d+))? ([eE](?P<exp>[-+]? \d+))?
# \s* # \s*
$ $
""", re.VERBOSE).match #Uncomment the \s* to allow leading or trailing spaces. """, re.VERBOSE).match # Uncomment the \s* to allow leading or trailing spaces.
del re del re
# return sign, n, p s.t. float string value == -1**sign * n * 10**p exactly
def _string2exact(s): def _string2exact(s):
"""Return sign, n, p s.t.
Float string value == -1**sign * n * 10**p exactly
"""
m = _parser(s) m = _parser(s)
if m is None: if m is None:
raise ValueError("invalid literal for Decimal: %r" % s) raise ValueError("invalid literal for Decimal: %r" % s)
......
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