Index: CPythonLib.includes =================================================================== --- CPythonLib.includes (revision 3707) +++ CPythonLib.includes (working copy) @@ -33,6 +33,7 @@ copy.py copy_reg.py Cookie.py +decimal.py difflib.py dircache.py dircmp.py Index: CPythonLib/decimal.py =================================================================== --- CPythonLib/decimal.py (revision 0) +++ CPythonLib/decimal.py (revision 0) @@ -0,0 +1,3079 @@ +# Copyright (c) 2004 Python Software Foundation. +# All rights reserved. + +# Written by Eric Price +# and Facundo Batista +# and Raymond Hettinger +# and Aahz +# and Tim Peters + +# This module is currently Py2.3 compatible and should be kept that way +# unless a major compelling advantage arises. IOW, 2.3 compatibility is +# strongly preferred, but not guaranteed. + +# Also, this module should be kept in sync with the latest updates of +# the IBM specification as it evolves. Those updates will be treated +# as bug fixes (deviation from the spec is a compatibility, usability +# bug) and will be backported. At this point the spec is stabilizing +# and the updates are becoming fewer, smaller, and less significant. + +""" +This is a Py2.3 implementation of decimal floating point arithmetic based on +the General Decimal Arithmetic Specification: + + www2.hursley.ibm.com/decimal/decarith.html + +and IEEE standard 854-1987: + + www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html + +Decimal floating point has finite precision with arbitrarily large bounds. + +The purpose of the module is to support arithmetic using familiar +"schoolhouse" rules and to avoid the some of tricky representation +issues associated with binary floating point. The package is especially +useful for financial applications or for contexts where users have +expectations that are at odds with binary floating point (for instance, +in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead +of the expected Decimal("0.00") returned by decimal floating point). + +Here are some examples of using the decimal module: + +>>> from decimal import * +>>> setcontext(ExtendedContext) +>>> Decimal(0) +Decimal("0") +>>> Decimal("1") +Decimal("1") +>>> Decimal("-.0123") +Decimal("-0.0123") +>>> Decimal(123456) +Decimal("123456") +>>> Decimal("123.45e12345678901234567890") +Decimal("1.2345E+12345678901234567892") +>>> Decimal("1.33") + Decimal("1.27") +Decimal("2.60") +>>> Decimal("12.34") + Decimal("3.87") - Decimal("18.41") +Decimal("-2.20") +>>> dig = Decimal(1) +>>> print dig / Decimal(3) +0.333333333 +>>> getcontext().prec = 18 +>>> print dig / Decimal(3) +0.333333333333333333 +>>> print dig.sqrt() +1 +>>> print Decimal(3).sqrt() +1.73205080756887729 +>>> print Decimal(3) ** 123 +4.85192780976896427E+58 +>>> inf = Decimal(1) / Decimal(0) +>>> print inf +Infinity +>>> neginf = Decimal(-1) / Decimal(0) +>>> print neginf +-Infinity +>>> print neginf + inf +NaN +>>> print neginf * inf +-Infinity +>>> print dig / 0 +Infinity +>>> getcontext().traps[DivisionByZero] = 1 +>>> print dig / 0 +Traceback (most recent call last): + ... + ... + ... +DivisionByZero: x / 0 +>>> c = Context() +>>> c.traps[InvalidOperation] = 0 +>>> print c.flags[InvalidOperation] +0 +>>> c.divide(Decimal(0), Decimal(0)) +Decimal("NaN") +>>> c.traps[InvalidOperation] = 1 +>>> print c.flags[InvalidOperation] +1 +>>> c.flags[InvalidOperation] = 0 +>>> print c.flags[InvalidOperation] +0 +>>> print c.divide(Decimal(0), Decimal(0)) +Traceback (most recent call last): + ... + ... + ... +InvalidOperation: 0 / 0 +>>> print c.flags[InvalidOperation] +1 +>>> c.flags[InvalidOperation] = 0 +>>> c.traps[InvalidOperation] = 0 +>>> print c.divide(Decimal(0), Decimal(0)) +NaN +>>> print c.flags[InvalidOperation] +1 +>>> +""" + +__all__ = [ + # Two major classes + 'Decimal', 'Context', + + # Contexts + 'DefaultContext', 'BasicContext', 'ExtendedContext', + + # Exceptions + 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero', + 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow', + + # Constants for use in setting up contexts + 'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING', + 'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', + + # Functions for manipulating contexts + 'setcontext', 'getcontext' +] + +import copy as _copy + +#Rounding +ROUND_DOWN = 'ROUND_DOWN' +ROUND_HALF_UP = 'ROUND_HALF_UP' +ROUND_HALF_EVEN = 'ROUND_HALF_EVEN' +ROUND_CEILING = 'ROUND_CEILING' +ROUND_FLOOR = 'ROUND_FLOOR' +ROUND_UP = 'ROUND_UP' +ROUND_HALF_DOWN = 'ROUND_HALF_DOWN' + +#Rounding decision (not part of the public API) +NEVER_ROUND = 'NEVER_ROUND' # Round in division (non-divmod), sqrt ONLY +ALWAYS_ROUND = 'ALWAYS_ROUND' # Every operation rounds at end. + +#Errors + +class DecimalException(ArithmeticError): + """Base exception class. + + Used exceptions derive from this. + If an exception derives from another exception besides this (such as + Underflow (Inexact, Rounded, Subnormal) that indicates that it is only + called if the others are present. This isn't actually used for + anything, though. + + handle -- Called when context._raise_error is called and the + trap_enabler is 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): + pass + + +class Clamped(DecimalException): + """Exponent of a 0 changed to fit bounds. + + This occurs and signals clamped if the exponent of a result has been + altered in order to fit the constraints of a specific concrete + representation. This may occur when the exponent of a zero result would + be outside the bounds of a representation, or when a large normal + number would have an encoded exponent that cannot be represented. In + this latter case, the exponent is reduced to fit and the corresponding + number of zero digits are appended to the coefficient ("fold-down"). + """ + + +class InvalidOperation(DecimalException): + """An invalid operation was performed. + + Various bad things cause this: + + Something creates a signaling NaN + -INF + INF + 0 * (+-)INF + (+-)INF / (+-)INF + x % 0 + (+-)INF % x + x._rescale( non-integer ) + sqrt(-x) , x > 0 + 0 ** 0 + x ** (non-integer) + x ** (+-)INF + An operand is invalid + """ + def handle(self, context, *args): + if args: + 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]. + """ + + def handle(self, context, *args): + return (0, (0,), 'n') #Passed to something which uses a tuple. + +class DivisionByZero(DecimalException, ZeroDivisionError): + """Division by 0. + + This occurs and signals division-by-zero if division of a finite number + by zero was attempted (during a divide-integer or divide operation, or a + power operation with negative right-hand operand), and the dividend was + not zero. + + The result of the operation is [sign,inf], where sign is the exclusive + or of the signs of the operands for divide, or is 1 for an odd power of + -0, for power. + """ + + 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]. + """ + + 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]. + """ + + def handle(self, context, tup=None, *args): + if tup is not None: + 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 + result in all cases is unchanged. + + The inexact signal may be tested (or trapped) to determine if a given + operation (or sequence of operations) was inexact. + """ + 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 + on creation and either the precision exceeds the capability of the + underlying concrete representation or an unknown or unsupported rounding + was specified. These aspects of the context need only be checked when + the values are required to be used. The result is [0,qNaN]. + """ + + def handle(self, context, *args): + 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 + result in all cases is unchanged. + + The rounded signal may be tested (or trapped) to determine if a given + operation (or sequence of operations) caused a loss of precision. + """ + 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. + + 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. + + This occurs and signals overflow if the adjusted exponent of a result + (from a conversion or from an operation that is not an attempt to divide + by zero), after rounding, would be greater than the largest value that + can be handled by the implementation (the value Emax). + + The result depends on the rounding mode: + + For round-half-up and round-half-even (and for round-half-down and + round-up, if implemented), the result of the operation is [sign,inf], + where sign is the sign of the intermediate result. For round-down, the + result is the largest finite number that can be represented in the + current precision, with the sign of the intermediate result. For + round-ceiling, the result is the same as for round-down if the sign of + the intermediate result is 1, or is [0,inf] otherwise. For round-floor, + the result is the same as for round-down if the sign of the intermediate + result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded + will also be raised. + """ + + def handle(self, context, sign, *args): + if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, + ROUND_HALF_DOWN, ROUND_UP): + return Infsign[sign] + if sign == 0: + if context.rounding == ROUND_CEILING: + return Infsign[sign] + return Decimal((sign, (9,)*context.prec, + context.Emax-context.prec+1)) + if sign == 1: + if context.rounding == ROUND_FLOOR: + return Infsign[sign] + return Decimal( (sign, (9,)*context.prec, + context.Emax-context.prec+1)) + + +class Underflow(Inexact, Rounded, Subnormal): + """Numerical underflow with result rounded to 0. + + This occurs and signals underflow if a result is inexact and the + adjusted exponent of the result would be smaller (more negative) than + the smallest value that can be handled by the implementation (the value + Emin). That is, the result is both inexact and subnormal. + + The result after an underflow will be a subnormal number rounded, if + necessary, so that its exponent is not less than Etiny. This may result + in 0 with the sign of the intermediate result and an exponent of Etiny. + + In all cases, Inexact, Rounded, and Subnormal will also be raised. + """ + +# List of public traps and flags +_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, + Underflow, InvalidOperation, Subnormal] + +# Map conditions (per the spec) to signals +_condition_map = {ConversionSyntax:InvalidOperation, + DivisionImpossible:InvalidOperation, + DivisionUndefined:InvalidOperation, + InvalidContext:InvalidOperation} + +##### Context Functions ####################################### + +# The getcontext() and setcontext() function manage access to a thread-local +# current context. Py2.4 offers direct support for thread locals. If that +# is not available, use threading.currentThread() which is slower but will +# work for older Pythons. If threads are not part of the build, create a +# mock threading object with threading.local() returning the module namespace. + +try: + import threading +except ImportError: + # Python was compiled without threads; create a mock object instead + import sys + class MockThreading: + 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. + if hasattr(threading.currentThread(), '__decimal_context__'): + del threading.currentThread().__decimal_context__ + + def setcontext(context): + """Set this thread's context to context.""" + if context in (DefaultContext, BasicContext, ExtendedContext): + context = context.copy() + context.clear_flags() + threading.currentThread().__decimal_context__ = context + + def getcontext(): + """Returns this thread's context. + + If this thread does not yet have a context, returns + a new context and sets this thread's context. + New contexts are copies of DefaultContext. + """ + try: + return threading.currentThread().__decimal_context__ + except AttributeError: + context = Context() + threading.currentThread().__decimal_context__ = context + return context + +else: + + local = threading.local() + if hasattr(local, '__decimal_context__'): + del local.__decimal_context__ + + def getcontext(_local=local): + """Returns this thread's context. + + If this thread does not yet have a context, returns + a new context and sets this thread's context. + New contexts are copies of DefaultContext. + """ + try: + return _local.__decimal_context__ + except AttributeError: + context = Context() + _local.__decimal_context__ = context + return context + + def setcontext(context, _local=local): + """Set this thread's context to context.""" + if context in (DefaultContext, BasicContext, ExtendedContext): + context = context.copy() + context.clear_flags() + _local.__decimal_context__ = context + + del threading, local # Don't contaminate the namespace + + +##### Decimal class ########################################### + +class Decimal(object): + """Floating point class for decimal arithmetic.""" + + __slots__ = ('_exp','_int','_sign', '_is_special') + # Generally, the value of the Decimal instance is given by + # (-1)**_sign * _int * 10**_exp + # Special values are signified by _is_special == True + + # We're immutable, so use __new__ not __init__ + def __new__(cls, value="0", context=None): + """Create a decimal point instance. + + >>> Decimal('3.14') # string input + Decimal("3.14") + >>> Decimal((0, (3, 1, 4), -2)) # tuple input (sign, digit_tuple, exponent) + Decimal("3.14") + >>> Decimal(314) # int or long + Decimal("314") + >>> Decimal(Decimal(314)) # another decimal instance + Decimal("314") + """ + + self = object.__new__(cls) + self._is_special = False + + # From an internal working value + if isinstance(value, _WorkRep): + self._sign = value.sign + self._int = tuple(map(int, str(value.int))) + self._exp = int(value.exp) + return self + + # From another decimal + if isinstance(value, Decimal): + self._exp = value._exp + self._sign = value._sign + self._int = value._int + self._is_special = value._is_special + return self + + # From an integer + if isinstance(value, (int,long)): + if value >= 0: + self._sign = 0 + else: + self._sign = 1 + self._exp = 0 + self._int = tuple(map(int, str(abs(value)))) + return self + + # tuple/list conversion (possibly from as_tuple()) + if isinstance(value, (list,tuple)): + if len(value) != 3: + raise ValueError, 'Invalid arguments' + if value[0] not in (0,1): + 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." + + self._sign = value[0] + self._int = tuple(value[1]) + if value[2] in ('F','n','N'): + self._exp = value[2] + self._is_special = True + else: + self._exp = int(value[2]) + return self + + if isinstance(value, float): + raise TypeError("Cannot convert float to Decimal. " + + "First convert the float to a string") + + # Other argument types may require the context during interpretation + if context is None: + context = getcontext() + + # From a string + # REs insist on real strings, so we can too. + if isinstance(value, basestring): + if _isinfinity(value): + self._exp = 'F' + self._int = (0,) + self._is_special = True + if _isinfinity(value) == 1: + self._sign = 0 + else: + self._sign = 1 + return self + if _isnan(value): + sig, sign, diag = _isnan(value) + self._is_special = True + 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 + self._exp = 'N' #sNaN + self._sign = sign + 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) + return self + + raise TypeError("Cannot convert %r to Decimal" % value) + + def _isnan(self): + """Returns whether the number is not actually one. + + 0 if a number + 1 if NaN + 2 if sNaN + """ + if self._is_special: + exp = self._exp + if exp == 'n': + return 1 + elif exp == 'N': + return 2 + return 0 + + def _isinfinity(self): + """Returns whether the number is infinite + + 0 if finite or not a number + 1 if +INF + -1 if -INF + """ + if self._exp == 'F': + if self._sign: + return -1 + return 1 + return 0 + + def _check_nans(self, other = None, context=None): + """Returns whether the number is not actually one. + + if self, other are sNaN, signal + if self, other are NaN return nan + return 0 + + Done before operations. + """ + + self_is_nan = self._isnan() + if other is None: + other_is_nan = False + else: + other_is_nan = other._isnan() + + if self_is_nan or other_is_nan: + if context is None: + context = getcontext() + + if self_is_nan == 2: + return context._raise_error(InvalidOperation, 'sNaN', + 1, self) + if other_is_nan == 2: + return context._raise_error(InvalidOperation, 'sNaN', + 1, other) + if self_is_nan: + return self + + return other + return 0 + + def __nonzero__(self): + """Is the number non-zero? + + 0 if self == 0 + 1 if self != 0 + """ + if self._is_special: + return 1 + return sum(self._int) != 0 + + def __cmp__(self, other, context=None): + other = _convert_other(other) + if other is NotImplemented: + return -2 + + 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 + + # INF = INF + return cmp(self._isinfinity(), other._isinfinity()) + + if not self and not other: + return 0 #If both 0, sign comparison isn't certain. + + #If different signs, neg one is less + if other._sign < self._sign: + return -1 + if self._sign < other._sign: + return 1 + + self_adjusted = self.adjusted() + other_adjusted = other.adjusted() + if self_adjusted == other_adjusted and \ + self._int + (0,)*(self._exp - other._exp) == \ + other._int + (0,)*(other._exp - self._exp): + return 0 #equal, except in precision. ([0]*(-x) = []) + elif self_adjusted > other_adjusted and self._int[0] != 0: + return (-1)**self._sign + elif self_adjusted < other_adjusted and other._int[0] != 0: + return -((-1)**self._sign) + + # Need to round, so make sure we have a valid context + if context is None: + context = getcontext() + + context = context._shallow_copy() + rounding = context._set_rounding(ROUND_UP) #round away from 0 + + flags = context._ignore_all_flags() + res = self.__sub__(other, context=context) + + context._regard_flags(*flags) + + context.rounding = rounding + + if not res: + return 0 + elif res._sign: + return -1 + return 1 + + def __eq__(self, other): + if not isinstance(other, (Decimal, int, long)): + return NotImplemented + return self.__cmp__(other) == 0 + + def __ne__(self, other): + if not isinstance(other, (Decimal, int, long)): + return NotImplemented + return self.__cmp__(other) != 0 + + def compare(self, other, context=None): + """Compares one to another. + + -1 => a < b + 0 => a = b + 1 => a > b + NaN => one is NaN + Like __cmp__, but returns Decimal instances. + """ + other = _convert_other(other) + if other is NotImplemented: + return other + + #compare(NaN, NaN) = NaN + if (self._is_special or other and other._is_special): + ans = self._check_nans(other, context) + if ans: + return ans + + return Decimal(self.__cmp__(other, context)) + + def __hash__(self): + """x.__hash__() <==> hash(x)""" + # Decimal integers must hash the same as the ints + # Non-integer decimals are normalized and hashed as strings + # Normalization assures that hast(100E-1) == hash(10) + if self._is_special: + if self._isnan(): + raise TypeError('Cannot hash a NaN value.') + return hash(str(self)) + i = int(self) + if self == Decimal(i): + return hash(i) + assert self.__nonzero__() # '-0' handled by integer case + return hash(str(self.normalize())) + + def as_tuple(self): + """Represents the number as a triple tuple. + + To show the internals exactly as they are. + """ + return (self._sign, self._int, self._exp) + + def __repr__(self): + """Represents the number as an instance of Decimal.""" + # Invariant: eval(repr(d)) == d + return 'Decimal("%s")' % str(self) + + def __str__(self, eng = 0, context=None): + """Return string representation of the number in scientific notation. + + Captures all of the information in the underlying representation. + """ + + if self._is_special: + if self._isnan(): + minus = '-'*self._sign + if self._int == (0,): + info = '' + else: + info = ''.join(map(str, self._int)) + if self._isnan() == 2: + return minus + 'sNaN' + info + return minus + 'NaN' + info + if self._isinfinity(): + minus = '-'*self._sign + return minus + 'Infinity' + + if context is None: + context = getcontext() + + tmp = map(str, self._int) + numdigits = len(self._int) + leftdigits = self._exp + numdigits + if eng and not self: #self = 0eX wants 0[.0[0]]eY, not [[0]0]0eY + if self._exp < 0 and self._exp >= -6: #short, no need for e/E + s = '-'*self._sign + '0.' + '0'*(abs(self._exp)) + return s + #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) + else: + s = '0' + if exp != 0: + if context.capitals: + s += 'E' + else: + s += 'e' + if exp > 0: + s += '+' #0.0e+3, not 0.0e3 + s += str(exp) + s = '-'*self._sign + s + return s + if eng: + dotplace = (leftdigits-1)%3+1 + adjexp = leftdigits -1 - (leftdigits-1)%3 + else: + adjexp = leftdigits-1 + dotplace = 1 + if self._exp == 0: + pass + elif self._exp < 0 and adjexp >= 0: + tmp.insert(leftdigits, '.') + elif self._exp < 0 and adjexp >= -6: + tmp[0:0] = ['0'] * int(-leftdigits) + tmp.insert(0, '0.') + else: + if numdigits > dotplace: + tmp.insert(dotplace, '.') + elif numdigits < dotplace: + tmp.extend(['0']*(dotplace-numdigits)) + if adjexp: + if not context.capitals: + tmp.append('e') + else: + tmp.append('E') + if adjexp > 0: + tmp.append('+') + tmp.append(str(adjexp)) + if eng: + while tmp[0:1] == ['0']: + tmp[0:1] = [] + if len(tmp) == 0 or tmp[0] == '.' or tmp[0].lower() == 'e': + tmp[0:0] = ['0'] + if self._sign: + tmp.insert(0, '-') + + return ''.join(tmp) + + def to_eng_string(self, context=None): + """Convert to engineering-type string. + + Engineering notation has an exponent which is a multiple of 3, so there + are up to 3 digits left of the decimal place. + + Same rules for when in exponential and when as a value as in __str__. + """ + return self.__str__(eng=1, context=context) + + def __neg__(self, context=None): + """Returns a copy with the sign switched. + + Rounds, if it has reason. + """ + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + + if not self: + # -Decimal('0') is Decimal('0'), not Decimal('-0') + sign = 0 + elif self._sign: + sign = 0 + else: + sign = 1 + + if context is None: + context = getcontext() + if context._rounding_decision == ALWAYS_ROUND: + return Decimal((sign, self._int, self._exp))._fix(context) + return Decimal( (sign, self._int, self._exp)) + + def __pos__(self, context=None): + """Returns a copy, unless it is a sNaN. + + Rounds the number (if more then precision digits) + """ + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + + sign = self._sign + if not self: + # + (-0) = 0 + sign = 0 + + if context is None: + context = getcontext() + + if context._rounding_decision == ALWAYS_ROUND: + ans = self._fix(context) + else: + ans = Decimal(self) + ans._sign = sign + return ans + + def __abs__(self, round=1, context=None): + """Returns the absolute value of self. + + If the second argument is 0, do not round. + """ + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + + if not round: + if context is None: + context = getcontext() + context = context._shallow_copy() + context._set_rounding_decision(NEVER_ROUND) + + if self._sign: + ans = self.__neg__(context=context) + else: + ans = self.__pos__(context=context) + + return ans + + def __add__(self, other, context=None): + """Returns self + other. + + -INF + INF (or the reverse) cause InvalidOperation errors. + """ + other = _convert_other(other) + if other is NotImplemented: + return other + + if context is None: + context = getcontext() + + if self._is_special or other._is_special: + ans = self._check_nans(other, context) + if ans: + return ans + + if self._isinfinity(): + #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 + + 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. + negativezero = 1 + + if not self and not other: + sign = min(self._sign, other._sign) + if negativezero: + sign = 1 + return Decimal( (sign, (0,), exp)) + if not self: + exp = max(exp, other._exp - context.prec-1) + ans = other._rescale(exp, watchexp=0, context=context) + if shouldround: + ans = ans._fix(context) + return ans + if not other: + exp = max(exp, self._exp - context.prec-1) + ans = self._rescale(exp, watchexp=0, context=context) + if shouldround: + ans = ans._fix(context) + return ans + + op1 = _WorkRep(self) + op2 = _WorkRep(other) + op1, op2 = _normalize(op1, op2, shouldround, context.prec) + + result = _WorkRep() + if op1.sign != op2.sign: + # Equal and opposite + if op1.int == op2.int: + if exp < context.Etiny(): + exp = context.Etiny() + context._raise_error(Clamped) + return Decimal((negativezero, (0,), exp)) + if op1.int < op2.int: + op1, op2 = op2, op1 + #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. + elif op1.sign == 1: + result.sign = 1 + op1.sign, op2.sign = (0, 0) + else: + result.sign = 0 + #Now, op1 > abs(op2) > 0 + + if op2.sign == 0: + result.int = op1.int + op2.int + else: + result.int = op1.int - op2.int + + result.exp = op1.exp + ans = Decimal(result) + if shouldround: + ans = ans._fix(context) + return ans + + __radd__ = __add__ + + def __sub__(self, other, context=None): + """Return self + (-other)""" + other = _convert_other(other) + if other is NotImplemented: + return other + + if self._is_special or other._is_special: + ans = self._check_nans(other, context=context) + if ans: + return ans + + # -Decimal(0) = Decimal(0), which we don't want since + # (-0 - 0 = -0 + (-0) = -0, but -0 + 0 = 0.) + # so we change the sign directly to a copy + tmp = Decimal(other) + tmp._sign = 1-tmp._sign + + return self.__add__(tmp, context=context) + + def __rsub__(self, other, context=None): + """Return other + (-self)""" + other = _convert_other(other) + if other is NotImplemented: + return other + + tmp = Decimal(self) + tmp._sign = 1 - tmp._sign + return other.__add__(tmp, context=context) + + def _increment(self, round=1, context=None): + """Special case of add, adding 1eExponent + + Since it is common, (rounding, for example) this adds + (sign)*one E self._exp to the number more efficiently than add. + + For example: + Decimal('5.624e10')._increment() == Decimal('5.625e10') + """ + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + + return Decimal(self) # Must be infinite, and incrementing makes no difference + + L = list(self._int) + L[-1] += 1 + spot = len(L)-1 + while L[spot] == 10: + L[spot] = 0 + if spot == 0: + L[0:0] = [1] + break + L[spot-1] += 1 + spot -= 1 + ans = Decimal((self._sign, L, self._exp)) + + if context is None: + context = getcontext() + if round and context._rounding_decision == ALWAYS_ROUND: + ans = ans._fix(context) + return ans + + def __mul__(self, other, context=None): + """Return self * other. + + (+-) INF * 0 (or its reverse) raise InvalidOperation. + """ + other = _convert_other(other) + if other is NotImplemented: + return other + + if context is None: + context = getcontext() + + resultsign = self._sign ^ other._sign + + if self._is_special or other._is_special: + ans = self._check_nans(other, context) + if ans: + return ans + + if self._isinfinity(): + if not other: + return context._raise_error(InvalidOperation, '(+-)INF * 0') + return Infsign[resultsign] + + if other._isinfinity(): + if not self: + return context._raise_error(InvalidOperation, '0 * (+-)INF') + return Infsign[resultsign] + + resultexp = self._exp + other._exp + shouldround = context._rounding_decision == ALWAYS_ROUND + + # Special case for multiplying by zero + if not self or not other: + ans = Decimal((resultsign, (0,), resultexp)) + if shouldround: + #Fixing in case the exponent is out of bounds + ans = ans._fix(context) + return ans + + # Special case for multiplying by power of 10 + if self._int == (1,): + ans = Decimal((resultsign, other._int, resultexp)) + if shouldround: + ans = ans._fix(context) + return ans + if other._int == (1,): + ans = Decimal((resultsign, self._int, resultexp)) + if shouldround: + ans = ans._fix(context) + return ans + + op1 = _WorkRep(self) + op2 = _WorkRep(other) + + ans = Decimal( (resultsign, map(int, str(op1.int * op2.int)), resultexp)) + if shouldround: + ans = ans._fix(context) + + return ans + __rmul__ = __mul__ + + def __div__(self, other, context=None): + """Return self / other.""" + return self._divide(other, context=context) + __truediv__ = __div__ + + def _divide(self, other, divmod = 0, context=None): + """Return a / b, to context.prec precision. + + divmod: + 0 => true division + 1 => (a //b, a%b) + 2 => a //b + 3 => a%b + + Actually, if divmod is 2 or 3 a tuple is returned, but errors for + computing the other value are not raised. + """ + other = _convert_other(other) + if other is NotImplemented: + if divmod in (0, 1): + return NotImplemented + return (NotImplemented, NotImplemented) + + if context is None: + context = getcontext() + + sign = self._sign ^ other._sign + + if self._is_special or other._is_special: + ans = self._check_nans(other, context) + if ans: + if divmod: + return (ans, ans) + return ans + + if self._isinfinity() and other._isinfinity(): + if divmod: + return (context._raise_error(InvalidOperation, + '(+-)INF // (+-)INF'), + context._raise_error(InvalidOperation, + '(+-)INF % (+-)INF')) + return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') + + if self._isinfinity(): + if divmod == 1: + return (Infsign[sign], + context._raise_error(InvalidOperation, 'INF % x')) + elif divmod == 2: + return (Infsign[sign], NaN) + elif divmod == 3: + return (Infsign[sign], + context._raise_error(InvalidOperation, 'INF % x')) + return Infsign[sign] + + if other._isinfinity(): + if divmod: + return (Decimal((sign, (0,), 0)), Decimal(self)) + context._raise_error(Clamped, 'Division by infinity') + return Decimal((sign, (0,), context.Etiny())) + + # Special cases for zeroes + if not self and not other: + if divmod: + return context._raise_error(DivisionUndefined, '0 / 0', 1) + return context._raise_error(DivisionUndefined, '0 / 0') + + if not self: + if divmod: + otherside = Decimal(self) + otherside._exp = min(self._exp, other._exp) + return (Decimal((sign, (0,), 0)), otherside) + exp = self._exp - other._exp + if exp < context.Etiny(): + exp = context.Etiny() + context._raise_error(Clamped, '0e-x / y') + if exp > context.Emax: + exp = context.Emax + context._raise_error(Clamped, '0e+x / y') + return Decimal( (sign, (0,), exp) ) + + if not other: + if divmod: + return context._raise_error(DivisionByZero, 'divmod(x,0)', + sign, 1) + return context._raise_error(DivisionByZero, 'x / 0', sign) + + #OK, so neither = 0, INF or NaN + + shouldround = context._rounding_decision == ALWAYS_ROUND + + #If we're dividing into ints, and self < other, stop. + #self.__abs__(0) does not round. + if divmod and (self.__abs__(0, context) < other.__abs__(0, context)): + + if divmod == 1 or divmod == 3: + exp = min(self._exp, other._exp) + ans2 = self._rescale(exp, context=context, watchexp=0) + if shouldround: + ans2 = ans2._fix(context) + return (Decimal( (sign, (0,), 0) ), + ans2) + + elif divmod == 2: + #Don't round the mod part, if we don't need it. + return (Decimal( (sign, (0,), 0) ), Decimal(self)) + + op1 = _WorkRep(self) + op2 = _WorkRep(other) + op1, op2, adjust = _adjust_coefficients(op1, op2) + res = _WorkRep( (sign, 0, (op1.exp - op2.exp)) ) + if divmod and res.exp > context.prec + 1: + return context._raise_error(DivisionImpossible) + + prec_limit = 10 ** context.prec + while 1: + while op2.int <= op1.int: + res.int += 1 + op1.int -= op2.int + if res.exp == 0 and divmod: + if res.int >= prec_limit and shouldround: + return context._raise_error(DivisionImpossible) + otherside = Decimal(op1) + frozen = context._ignore_all_flags() + + exp = min(self._exp, other._exp) + otherside = otherside._rescale(exp, context=context, watchexp=0) + context._regard_flags(*frozen) + if shouldround: + otherside = otherside._fix(context) + return (Decimal(res), otherside) + + if op1.int == 0 and adjust >= 0 and not divmod: + break + if res.int >= prec_limit and shouldround: + if divmod: + return context._raise_error(DivisionImpossible) + shouldround=1 + # Really, the answer is a bit higher, so adding a one to + # the end will make sure the rounding is right. + if op1.int != 0: + res.int *= 10 + res.int += 1 + res.exp -= 1 + + break + res.int *= 10 + res.exp -= 1 + adjust += 1 + op1.int *= 10 + op1.exp -= 1 + + if res.exp == 0 and divmod and op2.int > op1.int: + #Solves an error in precision. Same as a previous block. + + if res.int >= prec_limit and shouldround: + return context._raise_error(DivisionImpossible) + otherside = Decimal(op1) + frozen = context._ignore_all_flags() + + exp = min(self._exp, other._exp) + otherside = otherside._rescale(exp, context=context) + + context._regard_flags(*frozen) + + return (Decimal(res), otherside) + + ans = Decimal(res) + if shouldround: + ans = ans._fix(context) + return ans + + def __rdiv__(self, other, context=None): + """Swaps self/other and returns __div__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__div__(self, context=context) + __rtruediv__ = __rdiv__ + + def __divmod__(self, other, context=None): + """ + (self // other, self % other) + """ + return self._divide(other, 1, context) + + def __rdivmod__(self, other, context=None): + """Swaps self/other and returns __divmod__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__divmod__(self, context=context) + + def __mod__(self, other, context=None): + """ + self % other + """ + other = _convert_other(other) + if other is NotImplemented: + return other + + if self._is_special or other._is_special: + ans = self._check_nans(other, context) + if ans: + return ans + + if self and not other: + return context._raise_error(InvalidOperation, 'x % 0') + + return self._divide(other, 3, context)[1] + + def __rmod__(self, other, context=None): + """Swaps self/other and returns __mod__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__mod__(self, context=context) + + def remainder_near(self, other, context=None): + """ + Remainder nearest to 0- abs(remainder-near) <= other/2 + """ + other = _convert_other(other) + if other is NotImplemented: + return other + + if self._is_special or other._is_special: + ans = self._check_nans(other, context) + if ans: + return ans + if self and not other: + return context._raise_error(InvalidOperation, 'x % 0') + + if context is None: + context = getcontext() + # If DivisionImpossible causes an error, do not leave Rounded/Inexact + # ignored in the calling function. + context = context._shallow_copy() + flags = context._ignore_flags(Rounded, Inexact) + #keep DivisionImpossible flags + (side, r) = self.__divmod__(other, context=context) + + if r._isnan(): + context._regard_flags(*flags) + return r + + context = context._shallow_copy() + rounding = context._set_rounding_decision(NEVER_ROUND) + + if other._sign: + comparison = other.__div__(Decimal(-2), context=context) + else: + comparison = other.__div__(Decimal(2), context=context) + + context._set_rounding_decision(rounding) + context._regard_flags(*flags) + + s1, s2 = r._sign, comparison._sign + r._sign, comparison._sign = 0, 0 + + if r < comparison: + r._sign, comparison._sign = s1, s2 + #Get flags now + self.__divmod__(other, context=context) + return r._fix(context) + r._sign, comparison._sign = s1, s2 + + rounding = context._set_rounding_decision(NEVER_ROUND) + + (side, r) = self.__divmod__(other, context=context) + context._set_rounding_decision(rounding) + if r._isnan(): + return r + + decrease = not side._iseven() + rounding = context._set_rounding_decision(NEVER_ROUND) + side = side.__abs__(context=context) + context._set_rounding_decision(rounding) + + s1, s2 = r._sign, comparison._sign + r._sign, comparison._sign = 0, 0 + if r > comparison or decrease and r == comparison: + r._sign, comparison._sign = s1, s2 + context.prec += 1 + if len(side.__add__(Decimal(1), context=context)._int) >= context.prec: + context.prec -= 1 + return context._raise_error(DivisionImpossible)[1] + context.prec -= 1 + if self._sign == other._sign: + r = r.__sub__(other, context=context) + else: + r = r.__add__(other, context=context) + else: + r._sign, comparison._sign = s1, s2 + + return r._fix(context) + + def __floordiv__(self, other, context=None): + """self // other""" + return self._divide(other, 2, context)[0] + + def __rfloordiv__(self, other, context=None): + """Swaps self/other and returns __floordiv__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__floordiv__(self, context=context) + + def __float__(self): + """Float representation.""" + return float(str(self)) + + def __int__(self): + """Converts self to an int, truncating if necessary.""" + if self._is_special: + if self._isnan(): + context = getcontext() + return context._raise_error(InvalidContext) + elif self._isinfinity(): + raise OverflowError, "Cannot convert infinity to long" + if self._exp >= 0: + s = ''.join(map(str, self._int)) + '0'*self._exp + else: + s = ''.join(map(str, self._int))[:self._exp] + if s == '': + s = '0' + sign = '-'*self._sign + return int(sign + s) + + def __long__(self): + """Converts to a long. + + Equivalent to long(int(self)) + """ + return long(self.__int__()) + + def _fix(self, context): + """Round if it is necessary to keep self within prec precision. + + Rounds and fixes the exponent. Does not raise on a sNaN. + + Arguments: + self - Decimal instance + context - context used. + """ + if self._is_special: + return self + if context is None: + context = getcontext() + prec = context.prec + ans = self._fixexponents(context) + if len(ans._int) > prec: + ans = ans._round(prec, context=context) + ans = ans._fixexponents(context) + return ans + + def _fixexponents(self, context): + """Fix the exponents and return a copy with the exponent in bounds. + Only call if known to not be a special value. + """ + folddown = context._clamp + Emin = context.Emin + ans = self + ans_adjusted = ans.adjusted() + if ans_adjusted < Emin: + Etiny = context.Etiny() + if ans._exp < Etiny: + if not ans: + ans = Decimal(self) + ans._exp = Etiny + context._raise_error(Clamped) + return ans + ans = ans._rescale(Etiny, context=context) + #It isn't zero, and exp < Emin => subnormal + context._raise_error(Subnormal) + if context.flags[Inexact]: + context._raise_error(Underflow) + else: + if ans: + #Only raise subnormal if non-zero. + context._raise_error(Subnormal) + else: + Etop = context.Etop() + if folddown and ans._exp > Etop: + context._raise_error(Clamped) + ans = ans._rescale(Etop, context=context) + else: + Emax = context.Emax + if ans_adjusted > Emax: + if not ans: + ans = Decimal(self) + ans._exp = Emax + context._raise_error(Clamped) + return ans + context._raise_error(Inexact) + context._raise_error(Rounded) + return context._raise_error(Overflow, 'above Emax', ans._sign) + return ans + + def _round(self, prec=None, rounding=None, context=None): + """Returns a rounded version of self. + + You can specify the precision or rounding method. Otherwise, the + context determines it. + """ + + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + + if self._isinfinity(): + return Decimal(self) + + if context is None: + context = getcontext() + + if rounding is None: + rounding = context.rounding + if prec is None: + prec = context.prec + + if not self: + if prec <= 0: + dig = (0,) + exp = len(self._int) - prec + self._exp + else: + dig = (0,) * prec + exp = len(self._int) + self._exp - prec + ans = Decimal((self._sign, dig, exp)) + context._raise_error(Rounded) + return ans + + if prec == 0: + temp = Decimal(self) + temp._int = (0,)+temp._int + prec = 1 + elif prec < 0: + exp = self._exp + len(self._int) - prec - 1 + temp = Decimal( (self._sign, (0, 1), exp)) + prec = 1 + else: + temp = Decimal(self) + + numdigits = len(temp._int) + if prec == numdigits: + return temp + + # See if we need to extend precision + expdiff = prec - numdigits + if expdiff > 0: + tmp = list(temp._int) + tmp.extend([0] * expdiff) + ans = Decimal( (temp._sign, tmp, temp._exp - expdiff)) + return ans + + #OK, but maybe all the lost digits are 0. + lostdigits = self._int[expdiff:] + if lostdigits == (0,) * len(lostdigits): + ans = Decimal( (temp._sign, temp._int[:prec], temp._exp - expdiff)) + #Rounded, but not Inexact + context._raise_error(Rounded) + 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 + + if prec != context.prec: + context = context._shallow_copy() + context.prec = prec + ans = this_function(prec, expdiff, context) + context._raise_error(Rounded) + context._raise_error(Inexact, 'Changed in rounding') + + return ans + + _pick_rounding_function = {} + + def _round_down(self, prec, expdiff, context): + """Also known as round-towards-0, truncate.""" + return Decimal( (self._sign, self._int[:prec], self._exp - expdiff) ) + + def _round_half_up(self, prec, expdiff, context, tmp = None): + """Rounds 5 up (away from 0)""" + + if tmp is None: + tmp = Decimal( (self._sign,self._int[:prec], self._exp - expdiff)) + if self._int[prec] >= 5: + tmp = tmp._increment(round=0, context=context) + if len(tmp._int) > prec: + return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1)) + return tmp + + def _round_half_even(self, prec, expdiff, context): + """Round 5 to even, rest to nearest.""" + + tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff)) + half = (self._int[prec] == 5) + if half: + for digit in self._int[prec+1:]: + if digit != 0: + half = 0 + break + if half: + if self._int[prec-1] & 1 == 0: + return tmp + return self._round_half_up(prec, expdiff, context, tmp) + + def _round_half_down(self, prec, expdiff, context): + """Round 5 down""" + + tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff)) + half = (self._int[prec] == 5) + if half: + for digit in self._int[prec+1:]: + if digit != 0: + half = 0 + break + if half: + return tmp + return self._round_half_up(prec, expdiff, context, tmp) + + def _round_up(self, prec, expdiff, context): + """Rounds away from 0.""" + tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff) ) + for digit in self._int[prec:]: + if digit != 0: + tmp = tmp._increment(round=1, context=context) + if len(tmp._int) > prec: + return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1)) + else: + return tmp + return tmp + + def _round_ceiling(self, prec, expdiff, context): + """Rounds up (not away from 0 if negative.)""" + if self._sign: + return self._round_down(prec, expdiff, context) + else: + return self._round_up(prec, expdiff, context) + + def _round_floor(self, prec, expdiff, context): + """Rounds down (not towards 0 if negative)""" + if not self._sign: + return self._round_down(prec, expdiff, context) + else: + return self._round_up(prec, expdiff, context) + + def __pow__(self, n, modulo = None, context=None): + """Return self ** n (mod modulo) + + If modulo is None (default), don't take it mod modulo. + """ + n = _convert_other(n) + if n is NotImplemented: + return n + + if context is None: + context = getcontext() + + if self._is_special or n._is_special or n.adjusted() > 8: + #Because the spot << doesn't work with really big exponents + if n._isinfinity() or n.adjusted() > 8: + return context._raise_error(InvalidOperation, 'x ** INF') + + ans = self._check_nans(n, context) + if ans: + return ans + + if not n._isinteger(): + return context._raise_error(InvalidOperation, 'x ** (non-integer)') + + if not self and not n: + return context._raise_error(InvalidOperation, '0 ** 0') + + if not n: + return Decimal(1) + + if self == Decimal(1): + return Decimal(1) + + sign = self._sign and not n._iseven() + n = int(n) + + if self._isinfinity(): + if modulo: + return context._raise_error(InvalidOperation, 'INF % x') + if n > 0: + 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: + + tmp = Decimal('inf') + tmp._sign = sign + context._raise_error(Rounded) + context._raise_error(Inexact) + context._raise_error(Overflow, 'Big power', sign) + return tmp + + elength = len(str(abs(n))) + firstprec = context.prec + + if not modulo and firstprec + elength + 1 > DefaultContext.Emax: + return context._raise_error(Overflow, 'Too much precision.', sign) + + mul = Decimal(self) + val = Decimal(1) + context = context._shallow_copy() + context.prec = firstprec + elength + 1 + if n < 0: + #n is a long now, not Decimal instance + n = -n + mul = Decimal(1).__div__(mul, context=context) + + spot = 1 + while spot <= n: + spot <<= 1 + + spot >>= 1 + #Spot is the highest power of 2 less than n + while spot: + val = val.__mul__(val, context=context) + if val._isinfinity(): + val = Infsign[sign] + break + if spot & n: + val = val.__mul__(mul, context=context) + if modulo is not None: + val = val.__mod__(modulo, context=context) + spot >>= 1 + context.prec = firstprec + + if context._rounding_decision == ALWAYS_ROUND: + return val._fix(context) + return val + + def __rpow__(self, other, context=None): + """Swaps self/other and returns __pow__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__pow__(self, context=context) + + def normalize(self, context=None): + """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" + + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + + dup = self._fix(context) + if dup._isinfinity(): + return dup + + if not dup: + return Decimal( (dup._sign, (0,), 0) ) + end = len(dup._int) + exp = dup._exp + while dup._int[end-1] == 0: + exp += 1 + end -= 1 + return Decimal( (dup._sign, dup._int[:end], exp) ) + + + def quantize(self, exp, rounding=None, context=None, watchexp=1): + """Quantize self so its exponent is the same as that of exp. + + Similar to self._rescale(exp._exp) but with error checking. + """ + if self._is_special or exp._is_special: + ans = self._check_nans(exp, context) + if ans: + return ans + + if exp._isinfinity() or self._isinfinity(): + if exp._isinfinity() and self._isinfinity(): + return self #if both are inf, it is OK + if context is None: + context = getcontext() + return context._raise_error(InvalidOperation, + 'quantize with one INF') + return self._rescale(exp._exp, rounding, context, watchexp) + + def same_quantum(self, other): + """Test whether self and other have the same exponent. + + same as self._exp == other._exp, except NaN == sNaN + """ + if self._is_special or other._is_special: + if self._isnan() or other._isnan(): + return self._isnan() and other._isnan() and True + if self._isinfinity() or other._isinfinity(): + return self._isinfinity() and other._isinfinity() and True + return self._exp == other._exp + + def _rescale(self, exp, rounding=None, context=None, watchexp=1): + """Rescales so that the exponent is exp. + + exp = exp to scale to (an integer) + rounding = rounding version + watchexp: if set (default) an error is returned if exp is greater + than Emax or less than Etiny. + """ + if context is None: + context = getcontext() + + if self._is_special: + if self._isinfinity(): + return context._raise_error(InvalidOperation, 'rescale with an INF') + + ans = self._check_nans(context=context) + if ans: + return ans + + if watchexp and (context.Emax < exp or context.Etiny() > exp): + return context._raise_error(InvalidOperation, 'rescale(a, INF)') + + if not self: + ans = Decimal(self) + ans._int = (0,) + ans._exp = exp + return ans + + diff = self._exp - exp + digits = len(self._int) + diff + + if watchexp and digits > context.prec: + return context._raise_error(InvalidOperation, 'Rescale > prec') + + tmp = Decimal(self) + tmp._int = (0,) + tmp._int + digits += 1 + + if digits < 0: + tmp._exp = -digits + tmp._exp + tmp._int = (0,1) + digits = 1 + tmp = tmp._round(digits, rounding, context=context) + + if tmp._int[0] == 0 and len(tmp._int) > 1: + tmp._int = tmp._int[1:] + tmp._exp = exp + + tmp_adjusted = tmp.adjusted() + if tmp and tmp_adjusted < context.Emin: + context._raise_error(Subnormal) + elif tmp and tmp_adjusted > context.Emax: + return context._raise_error(InvalidOperation, 'rescale(a, INF)') + return tmp + + def to_integral(self, rounding=None, context=None): + """Rounds to the nearest integer, without raising inexact, rounded.""" + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + if self._exp >= 0: + return self + if context is None: + context = getcontext() + flags = context._ignore_flags(Rounded, Inexact) + ans = self._rescale(0, rounding, context=context) + context._regard_flags(flags) + return ans + + def sqrt(self, context=None): + """Return the square root of self. + + Uses a converging algorithm (Xn+1 = 0.5*(Xn + self / Xn)) + Should quadratically approach the right answer. + """ + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + + if self._isinfinity() and self._sign == 0: + return Decimal(self) + + if not self: + #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 + return Decimal( (1, (0,), exp)) + else: + return Decimal( (0, (0,), exp)) + + if context is None: + context = getcontext() + + if self._sign == 1: + return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') + + tmp = Decimal(self) + + expadd = tmp._exp // 2 + if tmp._exp & 1: + tmp._int += (0,) + tmp._exp = 0 + else: + tmp._exp = 0 + + context = context._shallow_copy() + flags = context._ignore_all_flags() + firstprec = context.prec + context.prec = 3 + if tmp.adjusted() & 1 == 0: + ans = Decimal( (0, (8,1,9), tmp.adjusted() - 2) ) + ans = ans.__add__(tmp.__mul__(Decimal((0, (2,5,9), -2)), + context=context), context=context) + ans._exp -= 1 + tmp.adjusted() // 2 + else: + ans = Decimal( (0, (2,5,9), tmp._exp + len(tmp._int)- 3) ) + ans = ans.__add__(tmp.__mul__(Decimal((0, (8,1,9), -3)), + context=context), context=context) + ans._exp -= 1 + tmp.adjusted() // 2 + + #ans is now a linear approximation. + + Emax, Emin = context.Emax, context.Emin + context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin + + half = Decimal('0.5') + + maxp = firstprec + 2 + rounding = context._set_rounding(ROUND_HALF_EVEN) + while 1: + context.prec = min(2*context.prec - 2, maxp) + ans = half.__mul__(ans.__add__(tmp.__div__(ans, context=context), + context=context), context=context) + if context.prec == maxp: + break + + #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. + context.prec = firstprec + 1 + # In case we rounded up another digit and we should actually go lower. + if prevexp != ans.adjusted(): + ans._int += (0,) + ans._exp -= 1 + + + lower = ans.__sub__(Decimal((0, (5,), ans._exp-1)), context=context) + context._set_rounding(ROUND_UP) + if lower.__mul__(lower, context=context) > (tmp): + ans = ans.__sub__(Decimal((0, (1,), ans._exp)), context=context) + + else: + upper = ans.__add__(Decimal((0, (5,), ans._exp-1)),context=context) + context._set_rounding(ROUND_DOWN) + if upper.__mul__(upper, context=context) < tmp: + ans = ans.__add__(Decimal((0, (1,), ans._exp)),context=context) + + ans._exp += expadd + + context.prec = firstprec + context.rounding = rounding + ans = ans._fix(context) + + rounding = context._set_rounding_decision(NEVER_ROUND) + if not ans.__mul__(ans, context=context) == self: + # Only rounded/inexact if here. + context._regard_flags(flags) + context._raise_error(Rounded) + context._raise_error(Inexact) + 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) + context.prec = firstprec + context._regard_flags(flags) + context.Emax, context.Emin = Emax, Emin + + return ans._fix(context) + + def max(self, other, context=None): + """Returns the larger value. + + like max(self, other) except if one is not a number, returns + NaN (and signals if one is sNaN). Also rounds. + """ + other = _convert_other(other) + if other is NotImplemented: + return other + + if self._is_special or other._is_special: + # if one operand is a quiet NaN and the other is number, then the + # number is always returned + sn = self._isnan() + on = other._isnan() + if sn or on: + if on == 1 and sn != 2: + return self + if sn == 1 and on != 2: + return other + return self._check_nans(other, context) + + ans = self + c = self.__cmp__(other) + if c == 0: + # if both operands are finite and equal in numerical value + # then an ordering is applied: + # + # if the signs differ then max returns the operand with the + # positive sign and min returns the operand with the negative sign + # + # if the signs are the same then the exponent is used to select + # the result. + if self._sign != other._sign: + if self._sign: + ans = other + elif self._exp < other._exp and not self._sign: + ans = other + elif self._exp > other._exp and self._sign: + ans = other + elif c == -1: + ans = other + + if context is None: + context = getcontext() + if context._rounding_decision == ALWAYS_ROUND: + return ans._fix(context) + return ans + + def min(self, other, context=None): + """Returns the smaller value. + + like min(self, other) except if one is not a number, returns + NaN (and signals if one is sNaN). Also rounds. + """ + other = _convert_other(other) + if other is NotImplemented: + return other + + if self._is_special or other._is_special: + # if one operand is a quiet NaN and the other is number, then the + # number is always returned + sn = self._isnan() + on = other._isnan() + if sn or on: + if on == 1 and sn != 2: + return self + if sn == 1 and on != 2: + return other + return self._check_nans(other, context) + + ans = self + c = self.__cmp__(other) + if c == 0: + # if both operands are finite and equal in numerical value + # then an ordering is applied: + # + # if the signs differ then max returns the operand with the + # positive sign and min returns the operand with the negative sign + # + # if the signs are the same then the exponent is used to select + # the result. + if self._sign != other._sign: + if other._sign: + ans = other + elif self._exp > other._exp and not self._sign: + ans = other + elif self._exp < other._exp and self._sign: + ans = other + elif c == 1: + ans = other + + if context is None: + context = getcontext() + if context._rounding_decision == ALWAYS_ROUND: + return ans._fix(context) + return ans + + def _isinteger(self): + """Returns whether self is an integer""" + if self._exp >= 0: + return True + rest = self._int[self._exp:] + return rest == (0,)*len(rest) + + def _iseven(self): + """Returns 1 if self is even. Assumes self is an integer.""" + if self._exp > 0: + return 1 + return self._int[-1+self._exp] & 1 == 0 + + def adjusted(self): + """Return the adjusted exponent of self""" + try: + return self._exp + len(self._int) - 1 + #If NaN or Infinity, self._exp is string + except TypeError: + return 0 + + # 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.__class__(str(self)) + + def __deepcopy__(self, memo): + if type(self) == Decimal: + return self # My components are also immutable + return self.__class__(str(self)) + +##### Context class ########################################### + + +# get rounding method function: +rounding_functions = [name for name in Decimal.__dict__.keys() if name.startswith('_round_')] +for name in rounding_functions: + #name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. + globalname = name[1:].upper() + val = globals()[globalname] + Decimal._pick_rounding_function[val] = name + +del name, val, globalname, rounding_functions + +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_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 + substituted in. + flags - When an exception is caused, flags[exception] is incremented. + (Whether or not the trap_enabler is set) + Should be reset by user of Decimal instance. + Emin - Minimum exponent + Emax - Maximum exponent + capitals - If 1, 1*10^1 is printed as 1E+1. + If 0, printed as 1e1 + _clamp - If 1, change exponents if too high (Default 0) + """ + + def __init__(self, prec=None, rounding=None, + traps=None, flags=None, + _rounding_decision=None, + Emin=None, Emax=None, + capitals=None, _clamp=0, + _ignored_flags=None): + if flags is None: + flags = [] + if _ignored_flags is None: + _ignored_flags = [] + if not isinstance(flags, dict): + flags = dict([(s,s in flags) for s in _signals]) + del s + if traps is not None and not isinstance(traps, dict): + traps = dict([(s,s in traps) for s in _signals]) + del s + for name, val in locals().items(): + if val is None: + setattr(self, name, _copy.copy(getattr(DefaultContext, name))) + else: + setattr(self, name, val) + del self.self + + 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]) + ']') + return ', '.join(s) + ')' + + def clear_flags(self): + """Reset all flags to zero""" + for flag in self.flags: + self.flags[flag] = 0 + + def _shallow_copy(self): + """Returns a shallow copy from self.""" + nc = Context(self.prec, self.rounding, self.traps, self.flags, + self._rounding_decision, self.Emin, self.Emax, + self.capitals, self._clamp, self._ignored_flags) + return nc + + 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) + return nc + __copy__ = copy + + def _raise_error(self, condition, explanation = None, *args): + """Handles an error + + If the flag is in _ignored_flags, returns the default response. + Otherwise, it increments the flag, then, if the corresponding + trap_enabler is set, it reaises the exception. Otherwise, it returns + the default value after incrementing the flag. + """ + error = _condition_map.get(condition, condition) + if error in self._ignored_flags: + #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. + return condition().handle(self, *args) + + # Errors should only be risked on copies of the context + #self._ignored_flags = [] + raise error, explanation + + def _ignore_all_flags(self): + """Ignore all flags, if they are raised""" + return self._ignore_flags(*_signals) + + def _ignore_flags(self, *flags): + """Ignore the flags, if they are raised""" + # Do not mutate-- This way, copies of a context leave the original + # alone. + self._ignored_flags = (self._ignored_flags + list(flags)) + return list(flags) + + def _regard_flags(self, *flags): + """Stop ignoring the flags, if they are raised""" + if flags and isinstance(flags[0], (tuple,list)): + flags = flags[0] + for flag in flags: + self._ignored_flags.remove(flag) + + def __hash__(self): + """A Context cannot be hashed.""" + # We inherit object.__hash__, so we must deny this explicitly + raise TypeError, "Cannot hash a Context." + + def Etiny(self): + """Returns Etiny (= Emin - prec + 1)""" + return int(self.Emin - self.prec + 1) + + def Etop(self): + """Returns maximum exponent (= Emax - prec + 1)""" + return int(self.Emax - self.prec + 1) + + def _set_rounding_decision(self, type): + """Sets the rounding decision. + + Sets the rounding decision, and returns the current (previous) + rounding decision. Often used like: + + context = context._shallow_copy() + # That so you don't change the calling context + # if an error occurs in the middle (say DivisionImpossible is raised). + + rounding = context._set_rounding_decision(NEVER_ROUND) + instance = instance / Decimal(2) + context._set_rounding_decision(rounding) + + This will make it not round for that operation. + """ + + rounding = self._rounding_decision + self._rounding_decision = type + return rounding + + def _set_rounding(self, type): + """Sets the rounding type. + + Sets the rounding type, and returns the current (previous) + rounding type. Often used like: + + context = context.copy() + # so you don't change the calling context + # if an error occurs in the middle. + rounding = context._set_rounding(ROUND_UP) + val = self.__sub__(other, context=context) + context._set_rounding(rounding) + + This will make it round up for that operation. + """ + rounding = self.rounding + self.rounding= type + return rounding + + def create_decimal(self, num='0'): + """Creates a new Decimal instance but using self as context.""" + d = Decimal(num, context=self) + return d._fix(self) + + #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 + the plus operation on the operand. + + >>> ExtendedContext.abs(Decimal('2.1')) + Decimal("2.1") + >>> ExtendedContext.abs(Decimal('-100')) + Decimal("100") + >>> ExtendedContext.abs(Decimal('101.5')) + Decimal("101.5") + >>> ExtendedContext.abs(Decimal('-101.5')) + Decimal("101.5") + """ + return a.__abs__(context=self) + + def add(self, a, b): + """Return the sum of the two operands. + + >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) + Decimal("19.00") + >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) + Decimal("1.02E+4") + """ + return a.__add__(b, context=self) + + def _apply(self, a): + return str(a._fix(self)) + + def compare(self, a, b): + """Compares values numerically. + + If the signs of the operands differ, a value representing each operand + ('-1' if the operand is less than zero, '0' if the operand is zero or + negative zero, or '1' if the operand is greater than zero) is used in + place of that operand for the comparison instead of the actual + operand. + + The comparison is then effected by subtracting the second operand from + the first and then returning a value according to the result of the + subtraction: '-1' if the result is less than zero, '0' if the result is + zero or negative zero, or '1' if the result is greater than zero. + + >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) + Decimal("-1") + >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) + Decimal("0") + >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) + Decimal("0") + >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) + Decimal("1") + >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) + Decimal("1") + >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) + Decimal("-1") + """ + return a.compare(b, context=self) + + def divide(self, a, b): + """Decimal division in a specified context. + + >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) + Decimal("0.333333333") + >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) + Decimal("0.666666667") + >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) + Decimal("2.5") + >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) + Decimal("0.1") + >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) + Decimal("1") + >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) + Decimal("4.00") + >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) + Decimal("1.20") + >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) + Decimal("10") + >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) + Decimal("1000") + >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) + Decimal("1.20E+6") + """ + return a.__div__(b, context=self) + + def divide_int(self, a, b): + """Divides two numbers and returns the integer part of the result. + + >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) + Decimal("0") + >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) + Decimal("3") + >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) + Decimal("3") + """ + return a.__floordiv__(b, context=self) + + def divmod(self, a, b): + return a.__divmod__(b, context=self) + + def max(self, a,b): + """max compares two values numerically and returns the maximum. + + If either operand is a NaN then the general rules apply. + Otherwise, the operands are compared as as though by the compare + operation. If they are numerically equal then the left-hand operand + is chosen as the result. Otherwise the maximum (closer to positive + infinity) of the two operands is chosen as the result. + + >>> ExtendedContext.max(Decimal('3'), Decimal('2')) + Decimal("3") + >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) + Decimal("3") + >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) + Decimal("1") + >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) + Decimal("7") + """ + return a.max(b, context=self) + + def min(self, a,b): + """min compares two values numerically and returns the minimum. + + If either operand is a NaN then the general rules apply. + Otherwise, the operands are compared as as though by the compare + operation. If they are numerically equal then the left-hand operand + is chosen as the result. Otherwise the minimum (closer to negative + infinity) of the two operands is chosen as the result. + + >>> ExtendedContext.min(Decimal('3'), Decimal('2')) + Decimal("2") + >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) + Decimal("-10") + >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) + Decimal("1.0") + >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) + Decimal("7") + """ + return a.min(b, context=self) + + def minus(self, a): + """Minus corresponds to unary prefix minus in Python. + + The operation is evaluated using the same rules as subtract; the + operation minus(a) is calculated as subtract('0', a) where the '0' + has the same exponent as the operand. + + >>> ExtendedContext.minus(Decimal('1.3')) + Decimal("-1.3") + >>> ExtendedContext.minus(Decimal('-1.3')) + Decimal("1.3") + """ + return a.__neg__(context=self) + + def multiply(self, a, b): + """multiply multiplies two operands. + + If either operand is a special value then the general rules apply. + Otherwise, the operands are multiplied together ('long multiplication'), + resulting in a number which may be as long as the sum of the lengths + of the two operands. + + >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) + Decimal("3.60") + >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) + Decimal("21") + >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) + Decimal("0.72") + >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) + Decimal("-0.0") + >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) + Decimal("4.28135971E+11") + """ + return a.__mul__(b, context=self) + + def normalize(self, a): + """normalize reduces an operand to its simplest form. + + Essentially a plus operation with all trailing zeros removed from the + result. + + >>> ExtendedContext.normalize(Decimal('2.1')) + Decimal("2.1") + >>> ExtendedContext.normalize(Decimal('-2.0')) + Decimal("-2") + >>> ExtendedContext.normalize(Decimal('1.200')) + Decimal("1.2") + >>> ExtendedContext.normalize(Decimal('-120')) + Decimal("-1.2E+2") + >>> ExtendedContext.normalize(Decimal('120.00')) + Decimal("1.2E+2") + >>> ExtendedContext.normalize(Decimal('0.00')) + Decimal("0") + """ + return a.normalize(context=self) + + def plus(self, a): + """Plus corresponds to unary prefix plus in Python. + + The operation is evaluated using the same rules as add; the + operation plus(a) is calculated as add('0', a) where the '0' + has the same exponent as the operand. + + >>> ExtendedContext.plus(Decimal('1.3')) + Decimal("1.3") + >>> ExtendedContext.plus(Decimal('-1.3')) + Decimal("-1.3") + """ + return a.__pos__(context=self) + + def power(self, a, b, modulo=None): + """Raises a to the power of b, to modulo if given. + + The right-hand operand must be a whole number whose integer part (after + any exponent has been applied) has no more than 9 digits and whose + fractional part (if any) is all zeros before any rounding. The operand + may be positive, negative, or zero; if negative, the absolute value of + the power is used, and the left-hand operand is inverted (divided into + 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. + + If, when raising to a negative power, an underflow occurs during the + division into 1, the operation is not halted at that point but + continues. + + >>> ExtendedContext.power(Decimal('2'), Decimal('3')) + Decimal("8") + >>> ExtendedContext.power(Decimal('2'), Decimal('-3')) + Decimal("0.125") + >>> ExtendedContext.power(Decimal('1.7'), Decimal('8')) + Decimal("69.7575744") + >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-2')) + Decimal("0") + >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-1')) + Decimal("0") + >>> ExtendedContext.power(Decimal('Infinity'), Decimal('0')) + Decimal("1") + >>> ExtendedContext.power(Decimal('Infinity'), Decimal('1')) + Decimal("Infinity") + >>> ExtendedContext.power(Decimal('Infinity'), Decimal('2')) + Decimal("Infinity") + >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-2')) + Decimal("0") + >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-1')) + Decimal("-0") + >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('0')) + Decimal("1") + >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('1')) + Decimal("-Infinity") + >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('2')) + Decimal("Infinity") + >>> ExtendedContext.power(Decimal('0'), Decimal('0')) + Decimal("NaN") + """ + return a.__pow__(b, modulo, context=self) + + def quantize(self, a, b): + """Returns a value equal to 'a' (rounded) and having the exponent of 'b'. + + The coefficient of the result is derived from that of the left-hand + operand. It may be rounded using the current rounding setting (if the + exponent is being increased), multiplied by a positive power of ten (if + the exponent is being decreased), or is unchanged (if the exponent is + already equal to that of the right-hand operand). + + Unlike other operations, if the length of the coefficient after the + quantize operation would be greater than precision then an Invalid + operation condition is raised. This guarantees that, unless there is an + error condition, the exponent of the result of a quantize is always + equal to that of the right-hand operand. + + Also unlike other operations, quantize will never raise Underflow, even + if the result is subnormal and inexact. + + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) + Decimal("2.170") + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) + Decimal("2.17") + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) + Decimal("2.2") + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) + Decimal("2") + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) + Decimal("0E+1") + >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) + Decimal("-Infinity") + >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) + Decimal("NaN") + >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) + Decimal("-0") + >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) + Decimal("-0E+5") + >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) + Decimal("NaN") + >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) + Decimal("NaN") + >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) + Decimal("217.0") + >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) + Decimal("217") + >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) + Decimal("2.2E+2") + >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) + Decimal("2E+2") + """ + return a.quantize(b, context=self) + + def remainder(self, a, b): + """Returns the remainder from integer division. + + The result is the residue of the dividend after the operation of + calculating integer division as described for divide-integer, rounded to + precision digits if necessary. The sign of the result, if non-zero, is + the same as that of the original dividend. + + This operation will fail under the same conditions as integer division + (that is, if integer division on the same two operands would fail, the + remainder cannot be calculated). + + >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) + Decimal("2.1") + >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) + Decimal("1") + >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) + Decimal("-1") + >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) + Decimal("0.2") + >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) + Decimal("0.1") + >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) + Decimal("1.0") + """ + return a.__mod__(b, context=self) + + def remainder_near(self, a, b): + """Returns to be "a - b * n", where n is the integer nearest the exact + value of "x / b" (if two integers are equally near then the even one + is chosen). If the result is equal to 0 then its sign will be the + sign of a. + + This operation will fail under the same conditions as integer division + (that is, if integer division on the same two operands would fail, the + remainder cannot be calculated). + + >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) + Decimal("-0.9") + >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) + Decimal("-2") + >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) + Decimal("1") + >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) + Decimal("-1") + >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) + Decimal("0.2") + >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) + Decimal("0.1") + >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) + Decimal("-0.3") + """ + return a.remainder_near(b, context=self) + + def same_quantum(self, a, b): + """Returns True if the two operands have the same exponent. + + The result is never affected by either the sign or the coefficient of + either operand. + + >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) + False + >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) + True + >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) + False + >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) + True + """ + return a.same_quantum(b) + + def sqrt(self, a): + """Returns the square root of a non-negative number to context precision. + + If the result must be inexact, it is rounded using the round-half-even + algorithm. + + >>> ExtendedContext.sqrt(Decimal('0')) + Decimal("0") + >>> ExtendedContext.sqrt(Decimal('-0')) + Decimal("-0") + >>> ExtendedContext.sqrt(Decimal('0.39')) + Decimal("0.624499800") + >>> ExtendedContext.sqrt(Decimal('100')) + Decimal("10") + >>> ExtendedContext.sqrt(Decimal('1')) + Decimal("1") + >>> ExtendedContext.sqrt(Decimal('1.0')) + Decimal("1.0") + >>> ExtendedContext.sqrt(Decimal('1.00')) + Decimal("1.0") + >>> ExtendedContext.sqrt(Decimal('7')) + Decimal("2.64575131") + >>> ExtendedContext.sqrt(Decimal('10')) + Decimal("3.16227766") + >>> ExtendedContext.prec + 9 + """ + return a.sqrt(context=self) + + def subtract(self, a, b): + """Return the difference between the two operands. + + >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) + Decimal("0.23") + >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) + Decimal("0.00") + >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) + Decimal("-0.77") + """ + return a.__sub__(b, context=self) + + def to_eng_string(self, a): + """Converts a number to a string, using scientific notation. + + The operation is not affected by the context. + """ + return a.to_eng_string(context=self) + + def to_sci_string(self, a): + """Converts a number to a string, using scientific notation. + + The operation is not affected by the context. + """ + return a.__str__(context=self) + + def to_integral(self, a): + """Rounds to an integer. + + When the operand has a negative exponent, the result is the same + as using the quantize() operation using the given operand as the + left-hand-operand, 1E+0 as the right-hand-operand, and the precision + of the operand as the precision setting, except that no flags will + be set. The rounding mode is taken from the context. + + >>> ExtendedContext.to_integral(Decimal('2.1')) + Decimal("2") + >>> ExtendedContext.to_integral(Decimal('100')) + Decimal("100") + >>> ExtendedContext.to_integral(Decimal('100.0')) + Decimal("100") + >>> ExtendedContext.to_integral(Decimal('101.5')) + Decimal("102") + >>> ExtendedContext.to_integral(Decimal('-101.5')) + Decimal("-102") + >>> ExtendedContext.to_integral(Decimal('10E+5')) + Decimal("1.0E+6") + >>> ExtendedContext.to_integral(Decimal('7.89E+77')) + Decimal("7.89E+77") + >>> ExtendedContext.to_integral(Decimal('-Inf')) + Decimal("-Infinity") + """ + return a.to_integral(context=self) + +class _WorkRep(object): + __slots__ = ('sign','int','exp') + # sign: 0 or 1 + # int: int or long + # exp: None, int, or string + + def __init__(self, value=None): + if value is None: + self.sign = None + self.int = 0 + self.exp = None + elif isinstance(value, Decimal): + self.sign = value._sign + cum = 0 + for digit in value._int: + cum = cum * 10 + digit + self.int = cum + self.exp = value._exp + else: + # assert isinstance(value, tuple) + self.sign = value[0] + self.int = value[1] + self.exp = value[2] + + def __repr__(self): + return "(%r, %r, %r)" % (self.sign, self.int, self.exp) + + __str__ = __repr__ + + + +def _normalize(op1, op2, shouldround = 0, prec = 0): + """Normalizes op1, op2 to have the same exp and length of coefficient. + + Done during addition. + """ + # Yes, the exponent is a long, but the difference between exponents + # must be an int-- otherwise you'd get a big memory problem. + numdigits = int(op1.exp - op2.exp) + if numdigits < 0: + numdigits = -numdigits + tmp = op2 + other = op1 + else: + tmp = op1 + other = op2 + + + if shouldround and numdigits > prec + 1: + # Big difference in exponents - check the adjusted exponents + tmp_len = len(str(tmp.int)) + other_len = len(str(other.int)) + if numdigits > (other_len + prec + 1 - tmp_len): + # If the difference in adjusted exps is > prec+1, we know + # other is insignificant, so might as well put a 1 after the precision. + # (since this is only for addition.) Also stops use of massive longs. + + extend = prec + 2 - tmp_len + if extend <= 0: + extend = 1 + tmp.int *= 10 ** extend + tmp.exp -= extend + other.int = 1 + other.exp = tmp.exp + return op1, op2 + + tmp.int *= 10 ** numdigits + tmp.exp -= numdigits + return op1, op2 + +def _adjust_coefficients(op1, op2): + """Adjust op1, op2 so that op2.int * 10 > op1.int >= op2.int. + + Returns the adjusted op1, op2 as well as the change in op1.exp-op2.exp. + + Used on _WorkRep instances during division. + """ + adjust = 0 + #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 + while op1.int >= (10 * op2.int): + op2.int *= 10 + op2.exp -= 1 + adjust -= 1 + + return op1, op2, adjust + +##### Helper Functions ######################################## + +def _convert_other(other): + """Convert other to Decimal. + + Verifies that it's ok to use in an implicit construction. + """ + if isinstance(other, Decimal): + return other + if isinstance(other, (int, long)): + return Decimal(other) + return NotImplemented + +_infinity_map = { + 'inf' : 1, + 'infinity' : 1, + '+inf' : 1, + '+infinity' : 1, + '-inf' : -1, + '-infinity' : -1 +} + +def _isinfinity(num): + """Determines whether a string or float is infinity. + + +1 for negative infinity; 0 for finite ; +1 for positive infinity + """ + num = str(num).lower() + return _infinity_map.get(num, 0) + +def _isnan(num): + """Determines whether a string or float is NaN + + (1, sign, diagnostic info as string) => NaN + (2, sign, diagnostic info as string) => sNaN + 0 => not a NaN + """ + num = str(num).lower() + if not num: + return 0 + + #get the sign, get rid of trailing [+-] + sign = 0 + if num[0] == '+': + num = num[1:] + 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 + return 0 + return (1, sign, num[3:].lstrip('0')) + if num.startswith('snan'): + if len(num) > 4 and not num[4:].isdigit(): + return 0 + return (2, sign, num[4:].lstrip('0')) + return 0 + + +##### Setup Specific Contexts ################################ + +# The default context prototype used by Context() +# Is mutable, so that new contexts can have different default values + +DefaultContext = Context( + prec=28, rounding=ROUND_HALF_EVEN, + traps=[DivisionByZero, Overflow, InvalidOperation], + flags=[], + _rounding_decision=ALWAYS_ROUND, + Emax=999999999, + Emin=-999999999, + capitals=1 +) + +# Pre-made alternate contexts offered by the specification +# Don't change these; the user should be able to select these +# contexts and be able to reproduce results from other implementations +# of the spec. + +BasicContext = Context( + prec=9, rounding=ROUND_HALF_UP, + traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], + flags=[], +) + +ExtendedContext = Context( + prec=9, rounding=ROUND_HALF_EVEN, + traps=[], + flags=[], +) + + +##### Useful Constants (internal use only) #################### + +#Reusable defaults +Inf = Decimal('Inf') +negInf = Decimal('-Inf') + +#Infsign[sign] is infinity w/ that sign +Infsign = (Inf, negInf) + +NaN = Decimal('NaN') + + +##### crud for parsing strings ################################# +import re + +# There's an optional sign at the start, and an optional exponent +# at the end. The exponent has an optional sign and at least one +# digit. In between, must have either at least one digit followed +# by an optional fraction, or a decimal point followed by at least +# one digit. Yuck. + +_parser = re.compile(r""" +# \s* + (?P[-+])? + ( + (?P\d+) (\. (?P\d*))? + | + \. (?P\d+) + ) + ([eE](?P[-+]? \d+))? +# \s* + $ +""", re.VERBOSE).match #Uncomment the \s* to allow leading or trailing spaces. + +del re + +# return sign, n, p s.t. float string value == -1**sign * n * 10**p exactly + +def _string2exact(s): + m = _parser(s) + if m is None: + raise ValueError("invalid literal for Decimal: %r" % s) + + if m.group('sign') == "-": + sign = 1 + else: + sign = 0 + + exp = m.group('exp') + if exp is None: + exp = 0 + else: + exp = int(exp) + + intpart = m.group('int') + if intpart is None: + intpart = "" + fracpart = m.group('onlyfrac') + else: + fracpart = m.group('frac') + if fracpart is None: + fracpart = "" + + exp -= len(fracpart) + + mantissa = intpart + fracpart + tmp = map(int, mantissa) + backup = tmp + while tmp and tmp[0] == 0: + del tmp[0] + + # It's a zero + if not tmp: + if backup: + return (sign, tuple(backup), exp) + return (sign, (0,), exp) + mantissa = tuple(tmp) + + return (sign, mantissa, exp) + + +if __name__ == '__main__': + import doctest, sys + doctest.testmod(sys.modules[__name__]) Index: CPythonLib/test/test_decimal.py =================================================================== --- CPythonLib/test/test_decimal.py (revision 0) +++ CPythonLib/test/test_decimal.py (revision 0) @@ -0,0 +1,1092 @@ +# Copyright (c) 2004 Python Software Foundation. +# All rights reserved. + +# Written by Eric Price +# and Facundo Batista +# and Raymond Hettinger +# and Aahz (aahz at pobox.com) +# and Tim Peters + +""" +These are the test cases for the Decimal module. + +There are two groups of tests, Arithmetic and Behaviour. The former test +the Decimal arithmetic using the tests provided by Mike Cowlishaw. The latter +test the pythonic behaviour according to PEP 327. + +Cowlishaw's tests can be downloaded from: + + www2.hursley.ibm.com/decimal/dectest.zip + +This test module can be called from command line with one parameter (Arithmetic +or Behaviour) to test each part, or without parameter to test both parts. If +you're working through IDLE, you can import this test module and call test_main() +with the corresponding argument. +""" + +import unittest +import glob +import os, sys +import pickle, copy +from decimal import * +from test.test_support import TestSkipped, run_unittest, run_doctest, is_resource_enabled +import random +try: + import threading +except ImportError: + threading = None + +# Useful Test Constant +Signals = getcontext().flags.keys() + +# Tests are built around these assumed context defaults +DefaultContext.prec=9 +DefaultContext.rounding=ROUND_HALF_EVEN +DefaultContext.traps=dict.fromkeys(Signals, 0) +setcontext(DefaultContext) + + +TESTDATADIR = 'decimaltestdata' +if __name__ == '__main__': + file = sys.argv[0] +else: + file = __file__ +testdir = os.path.dirname(file) or os.curdir +directory = testdir + os.sep + TESTDATADIR + os.sep + +skip_expected = not os.path.isdir(directory) + +# Make sure it actually raises errors when not expected and caught in flags +# Slower, since it runs some things several times. +EXTENDEDERRORTEST = False + + +#Map the test cases' error names to the actual errors + +ErrorNames = {'clamped' : Clamped, + 'conversion_syntax' : InvalidOperation, + 'division_by_zero' : DivisionByZero, + 'division_impossible' : InvalidOperation, + 'division_undefined' : InvalidOperation, + 'inexact' : Inexact, + 'invalid_context' : InvalidOperation, + 'invalid_operation' : InvalidOperation, + 'overflow' : Overflow, + 'rounded' : Rounded, + 'subnormal' : Subnormal, + 'underflow' : Underflow} + + +def Nonfunction(*args): + """Doesn't do anything.""" + return None + +RoundingDict = {'ceiling' : ROUND_CEILING, #Maps test-case names to roundings. + 'down' : ROUND_DOWN, + 'floor' : ROUND_FLOOR, + 'half_down' : ROUND_HALF_DOWN, + 'half_even' : ROUND_HALF_EVEN, + 'half_up' : ROUND_HALF_UP, + 'up' : ROUND_UP} + +# Name adapter to be able to change the Decimal and Context +# interface without changing the test files from Cowlishaw +nameAdapter = {'toeng':'to_eng_string', + 'tosci':'to_sci_string', + 'samequantum':'same_quantum', + 'tointegral':'to_integral', + 'remaindernear':'remainder_near', + 'divideint':'divide_int', + 'squareroot':'sqrt', + 'apply':'_apply', + } + +class DecimalTest(unittest.TestCase): + """Class which tests the Decimal class against the test cases. + + Changed for unittest. + """ + def setUp(self): + self.context = Context() + for key in DefaultContext.traps.keys(): + DefaultContext.traps[key] = 1 + self.ignore_list = ['#'] + # Basically, a # means return NaN InvalidOperation. + # Different from a sNaN in trim + + self.ChangeDict = {'precision' : self.change_precision, + 'rounding' : self.change_rounding_method, + 'maxexponent' : self.change_max_exponent, + 'minexponent' : self.change_min_exponent, + 'clamp' : self.change_clamp} + + def tearDown(self): + """Cleaning up enviroment.""" + # leaving context in original state + for key in DefaultContext.traps.keys(): + DefaultContext.traps[key] = 0 + return + + def eval_file(self, file): + global skip_expected + if skip_expected: + raise TestSkipped + return + for line in open(file).xreadlines(): + line = line.replace('\r\n', '').replace('\n', '') + #print line + try: + t = self.eval_line(line) + except InvalidOperation: + print 'Error in test cases:' + print line + continue + except DecimalException, exception: + #Exception raised where there shoudn't have been one. + self.fail('Exception "'+exception.__class__.__name__ + '" raised on line '+line) + + return + + def eval_line(self, s): + if s.find(' -> ') >= 0 and s[:2] != '--' and not s.startswith(' --'): + s = (s.split('->')[0] + '->' + + s.split('->')[1].split('--')[0]).strip() + else: + s = s.split('--')[0].strip() + + for ignore in self.ignore_list: + if s.find(ignore) >= 0: + #print s.split()[0], 'NotImplemented--', ignore + return + if not s: + return + elif ':' in s: + return self.eval_directive(s) + else: + return self.eval_equation(s) + + def eval_directive(self, s): + funct, value = map(lambda x: x.strip().lower(), s.split(':')) + if funct == 'rounding': + value = RoundingDict[value] + else: + try: + value = int(value) + except ValueError: + pass + + funct = self.ChangeDict.get(funct, Nonfunction) + funct(value) + + def eval_equation(self, s): + #global DEFAULT_PRECISION + #print DEFAULT_PRECISION + + if not TEST_ALL and random.random() < 0.90: + return + + try: + Sides = s.split('->') + L = Sides[0].strip().split() + id = L[0] +# print id, + funct = L[1].lower() + valstemp = L[2:] + L = Sides[1].strip().split() + ans = L[0] + exceptions = L[1:] + except (TypeError, AttributeError, IndexError): + raise InvalidOperation + def FixQuotes(val): + val = val.replace("''", 'SingleQuote').replace('""', 'DoubleQuote') + val = val.replace("'", '').replace('"', '') + val = val.replace('SingleQuote', "'").replace('DoubleQuote', '"') + return val + fname = nameAdapter.get(funct, funct) + if fname == 'rescale': + return + funct = getattr(self.context, fname) + vals = [] + conglomerate = '' + quote = 0 + theirexceptions = [ErrorNames[x.lower()] for x in exceptions] + + for exception in Signals: + self.context.traps[exception] = 1 #Catch these bugs... + for exception in theirexceptions: + self.context.traps[exception] = 0 + for i, val in enumerate(valstemp): + if val.count("'") % 2 == 1: + quote = 1 - quote + if quote: + conglomerate = conglomerate + ' ' + val + continue + else: + val = conglomerate + val + conglomerate = '' + v = FixQuotes(val) + if fname in ('to_sci_string', 'to_eng_string'): + if EXTENDEDERRORTEST: + for error in theirexceptions: + self.context.traps[error] = 1 + try: + funct(self.context.create_decimal(v)) + except error: + pass + except Signals, e: + self.fail("Raised %s in %s when %s disabled" % \ + (e, s, error)) + else: + self.fail("Did not raise %s in %s" % (error, s)) + self.context.traps[error] = 0 + v = self.context.create_decimal(v) + else: + v = Decimal(v) + vals.append(v) + + ans = FixQuotes(ans) + + if EXTENDEDERRORTEST and fname not in ('to_sci_string', 'to_eng_string'): + for error in theirexceptions: + self.context.traps[error] = 1 + try: + funct(*vals) + except error: + pass + except Signals, e: + self.fail("Raised %s in %s when %s disabled" % \ + (e, s, error)) + else: + self.fail("Did not raise %s in %s" % (error, s)) + self.context.traps[error] = 0 + try: + result = str(funct(*vals)) + if fname == 'same_quantum': + result = str(int(eval(result))) # 'True', 'False' -> '1', '0' + except Signals, error: + self.fail("Raised %s in %s" % (error, s)) + except: #Catch any error long enough to state the test case. + print "ERROR:", s + raise + + myexceptions = self.getexceptions() + self.context.clear_flags() + + myexceptions.sort() + theirexceptions.sort() + + self.assertEqual(result, ans, + 'Incorrect answer for ' + s + ' -- got ' + result) + self.assertEqual(myexceptions, theirexceptions, + 'Incorrect flags set in ' + s + ' -- got ' \ + + str(myexceptions)) + return + + def getexceptions(self): + return [e for e in Signals if self.context.flags[e]] + + def change_precision(self, prec): + self.context.prec = prec + def change_rounding_method(self, rounding): + self.context.rounding = rounding + def change_min_exponent(self, exp): + self.context.Emin = exp + def change_max_exponent(self, exp): + self.context.Emax = exp + def change_clamp(self, clamp): + self.context._clamp = clamp + +# Dynamically build custom test definition for each file in the test +# directory and add the definitions to the DecimalTest class. This +# procedure insures that new files do not get skipped. +for filename in os.listdir(directory): + if '.decTest' not in filename: + continue + head, tail = filename.split('.') + tester = lambda self, f=filename: self.eval_file(directory + f) + setattr(DecimalTest, 'test_' + head, tester) + del filename, head, tail, tester + + + +# The following classes test the behaviour of Decimal according to PEP 327 + +class DecimalExplicitConstructionTest(unittest.TestCase): + '''Unit tests for Explicit Construction cases of Decimal.''' + + def test_explicit_empty(self): + self.assertEqual(Decimal(), Decimal("0")) + + def test_explicit_from_None(self): + self.assertRaises(TypeError, Decimal, None) + + def test_explicit_from_int(self): + + #positive + d = Decimal(45) + self.assertEqual(str(d), '45') + + #very large positive + d = Decimal(500000123) + self.assertEqual(str(d), '500000123') + + #negative + d = Decimal(-45) + self.assertEqual(str(d), '-45') + + #zero + d = Decimal(0) + self.assertEqual(str(d), '0') + + def test_explicit_from_string(self): + + #empty + self.assertEqual(str(Decimal('')), 'NaN') + + #int + self.assertEqual(str(Decimal('45')), '45') + + #float + self.assertEqual(str(Decimal('45.34')), '45.34') + + #engineer notation + self.assertEqual(str(Decimal('45e2')), '4.5E+3') + + #just not a number + self.assertEqual(str(Decimal('ugly')), 'NaN') + + def test_explicit_from_tuples(self): + + #zero + d = Decimal( (0, (0,), 0) ) + self.assertEqual(str(d), '0') + + #int + d = Decimal( (1, (4, 5), 0) ) + self.assertEqual(str(d), '-45') + + #float + d = Decimal( (0, (4, 5, 3, 4), -2) ) + self.assertEqual(str(d), '45.34') + + #weird + d = Decimal( (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) ) + self.assertEqual(str(d), '-4.34913534E-17') + + #wrong number of items + self.assertRaises(ValueError, Decimal, (1, (4, 3, 4, 9, 1)) ) + + #bad sign + self.assertRaises(ValueError, Decimal, (8, (4, 3, 4, 9, 1), 2) ) + + #bad exp + self.assertRaises(ValueError, Decimal, (1, (4, 3, 4, 9, 1), 'wrong!') ) + + #bad coefficients + self.assertRaises(ValueError, Decimal, (1, (4, 3, 4, None, 1), 2) ) + self.assertRaises(ValueError, Decimal, (1, (4, -3, 4, 9, 1), 2) ) + + def test_explicit_from_Decimal(self): + + #positive + d = Decimal(45) + e = Decimal(d) + self.assertEqual(str(e), '45') + self.assertNotEqual(id(d), id(e)) + + #very large positive + d = Decimal(500000123) + e = Decimal(d) + self.assertEqual(str(e), '500000123') + self.assertNotEqual(id(d), id(e)) + + #negative + d = Decimal(-45) + e = Decimal(d) + self.assertEqual(str(e), '-45') + self.assertNotEqual(id(d), id(e)) + + #zero + d = Decimal(0) + e = Decimal(d) + self.assertEqual(str(e), '0') + self.assertNotEqual(id(d), id(e)) + + def test_explicit_context_create_decimal(self): + + nc = copy.copy(getcontext()) + nc.prec = 3 + + # empty + d = Decimal() + self.assertEqual(str(d), '0') + d = nc.create_decimal() + self.assertEqual(str(d), '0') + + # from None + self.assertRaises(TypeError, nc.create_decimal, None) + + # from int + d = nc.create_decimal(456) + self.failUnless(isinstance(d, Decimal)) + self.assertEqual(nc.create_decimal(45678), + nc.create_decimal('457E+2')) + + # from string + d = Decimal('456789') + self.assertEqual(str(d), '456789') + d = nc.create_decimal('456789') + self.assertEqual(str(d), '4.57E+5') + + # from tuples + d = Decimal( (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) ) + self.assertEqual(str(d), '-4.34913534E-17') + d = nc.create_decimal( (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) ) + self.assertEqual(str(d), '-4.35E-17') + + # from Decimal + prevdec = Decimal(500000123) + d = Decimal(prevdec) + self.assertEqual(str(d), '500000123') + d = nc.create_decimal(prevdec) + self.assertEqual(str(d), '5.00E+8') + + +class DecimalImplicitConstructionTest(unittest.TestCase): + '''Unit tests for Implicit Construction cases of Decimal.''' + + def test_implicit_from_None(self): + self.assertRaises(TypeError, eval, 'Decimal(5) + None', globals()) + + def test_implicit_from_int(self): + #normal + self.assertEqual(str(Decimal(5) + 45), '50') + #exceeding precision + self.assertEqual(Decimal(5) + 123456789000, Decimal(123456789000)) + + def test_implicit_from_string(self): + self.assertRaises(TypeError, eval, 'Decimal(5) + "3"', globals()) + + def test_implicit_from_float(self): + self.assertRaises(TypeError, eval, 'Decimal(5) + 2.2', globals()) + + def test_implicit_from_Decimal(self): + self.assertEqual(Decimal(5) + Decimal(45), Decimal(50)) + + def test_rop(self): + # Allow other classes to be trained to interact with Decimals + class E: + def __divmod__(self, other): + return 'divmod ' + str(other) + def __rdivmod__(self, other): + return str(other) + ' rdivmod' + def __lt__(self, other): + return 'lt ' + str(other) + def __gt__(self, other): + return 'gt ' + str(other) + def __le__(self, other): + return 'le ' + str(other) + def __ge__(self, other): + return 'ge ' + str(other) + def __eq__(self, other): + return 'eq ' + str(other) + def __ne__(self, other): + return 'ne ' + str(other) + + self.assertEqual(divmod(E(), Decimal(10)), 'divmod 10') + self.assertEqual(divmod(Decimal(10), E()), '10 rdivmod') + self.assertEqual(eval('Decimal(10) < E()'), 'gt 10') + self.assertEqual(eval('Decimal(10) > E()'), 'lt 10') + self.assertEqual(eval('Decimal(10) <= E()'), 'ge 10') + self.assertEqual(eval('Decimal(10) >= E()'), 'le 10') + self.assertEqual(eval('Decimal(10) == E()'), 'eq 10') + self.assertEqual(eval('Decimal(10) != E()'), 'ne 10') + + # insert operator methods and then exercise them + for sym, lop, rop in ( + ('+', '__add__', '__radd__'), + ('-', '__sub__', '__rsub__'), + ('*', '__mul__', '__rmul__'), + ('/', '__div__', '__rdiv__'), + ('%', '__mod__', '__rmod__'), + ('//', '__floordiv__', '__rfloordiv__'), + ('**', '__pow__', '__rpow__'), + ): + + setattr(E, lop, lambda self, other: 'str' + lop + str(other)) + setattr(E, rop, lambda self, other: str(other) + rop + 'str') + self.assertEqual(eval('E()' + sym + 'Decimal(10)'), + 'str' + lop + '10') + self.assertEqual(eval('Decimal(10)' + sym + 'E()'), + '10' + rop + 'str') + +class DecimalArithmeticOperatorsTest(unittest.TestCase): + '''Unit tests for all arithmetic operators, binary and unary.''' + + def test_addition(self): + + d1 = Decimal('-11.1') + d2 = Decimal('22.2') + + #two Decimals + self.assertEqual(d1+d2, Decimal('11.1')) + self.assertEqual(d2+d1, Decimal('11.1')) + + #with other type, left + c = d1 + 5 + self.assertEqual(c, Decimal('-6.1')) + self.assertEqual(type(c), type(d1)) + + #with other type, right + c = 5 + d1 + self.assertEqual(c, Decimal('-6.1')) + self.assertEqual(type(c), type(d1)) + + #inline with decimal + d1 += d2 + self.assertEqual(d1, Decimal('11.1')) + + #inline with other type + d1 += 5 + self.assertEqual(d1, Decimal('16.1')) + + def test_subtraction(self): + + d1 = Decimal('-11.1') + d2 = Decimal('22.2') + + #two Decimals + self.assertEqual(d1-d2, Decimal('-33.3')) + self.assertEqual(d2-d1, Decimal('33.3')) + + #with other type, left + c = d1 - 5 + self.assertEqual(c, Decimal('-16.1')) + self.assertEqual(type(c), type(d1)) + + #with other type, right + c = 5 - d1 + self.assertEqual(c, Decimal('16.1')) + self.assertEqual(type(c), type(d1)) + + #inline with decimal + d1 -= d2 + self.assertEqual(d1, Decimal('-33.3')) + + #inline with other type + d1 -= 5 + self.assertEqual(d1, Decimal('-38.3')) + + def test_multiplication(self): + + d1 = Decimal('-5') + d2 = Decimal('3') + + #two Decimals + self.assertEqual(d1*d2, Decimal('-15')) + self.assertEqual(d2*d1, Decimal('-15')) + + #with other type, left + c = d1 * 5 + self.assertEqual(c, Decimal('-25')) + self.assertEqual(type(c), type(d1)) + + #with other type, right + c = 5 * d1 + self.assertEqual(c, Decimal('-25')) + self.assertEqual(type(c), type(d1)) + + #inline with decimal + d1 *= d2 + self.assertEqual(d1, Decimal('-15')) + + #inline with other type + d1 *= 5 + self.assertEqual(d1, Decimal('-75')) + + def test_division(self): + + d1 = Decimal('-5') + d2 = Decimal('2') + + #two Decimals + self.assertEqual(d1/d2, Decimal('-2.5')) + self.assertEqual(d2/d1, Decimal('-0.4')) + + #with other type, left + c = d1 / 4 + self.assertEqual(c, Decimal('-1.25')) + self.assertEqual(type(c), type(d1)) + + #with other type, right + c = 4 / d1 + self.assertEqual(c, Decimal('-0.8')) + self.assertEqual(type(c), type(d1)) + + #inline with decimal + d1 /= d2 + self.assertEqual(d1, Decimal('-2.5')) + + #inline with other type + d1 /= 4 + self.assertEqual(d1, Decimal('-0.625')) + + def test_floor_division(self): + + d1 = Decimal('5') + d2 = Decimal('2') + + #two Decimals + self.assertEqual(d1//d2, Decimal('2')) + self.assertEqual(d2//d1, Decimal('0')) + + #with other type, left + c = d1 // 4 + self.assertEqual(c, Decimal('1')) + self.assertEqual(type(c), type(d1)) + + #with other type, right + c = 7 // d1 + self.assertEqual(c, Decimal('1')) + self.assertEqual(type(c), type(d1)) + + #inline with decimal + d1 //= d2 + self.assertEqual(d1, Decimal('2')) + + #inline with other type + d1 //= 2 + self.assertEqual(d1, Decimal('1')) + + def test_powering(self): + + d1 = Decimal('5') + d2 = Decimal('2') + + #two Decimals + self.assertEqual(d1**d2, Decimal('25')) + self.assertEqual(d2**d1, Decimal('32')) + + #with other type, left + c = d1 ** 4 + self.assertEqual(c, Decimal('625')) + self.assertEqual(type(c), type(d1)) + + #with other type, right + c = 7 ** d1 + self.assertEqual(c, Decimal('16807')) + self.assertEqual(type(c), type(d1)) + + #inline with decimal + d1 **= d2 + self.assertEqual(d1, Decimal('25')) + + #inline with other type + d1 **= 4 + self.assertEqual(d1, Decimal('390625')) + + def test_module(self): + + d1 = Decimal('5') + d2 = Decimal('2') + + #two Decimals + self.assertEqual(d1%d2, Decimal('1')) + self.assertEqual(d2%d1, Decimal('2')) + + #with other type, left + c = d1 % 4 + self.assertEqual(c, Decimal('1')) + self.assertEqual(type(c), type(d1)) + + #with other type, right + c = 7 % d1 + self.assertEqual(c, Decimal('2')) + self.assertEqual(type(c), type(d1)) + + #inline with decimal + d1 %= d2 + self.assertEqual(d1, Decimal('1')) + + #inline with other type + d1 %= 4 + self.assertEqual(d1, Decimal('1')) + + def test_floor_div_module(self): + + d1 = Decimal('5') + d2 = Decimal('2') + + #two Decimals + (p, q) = divmod(d1, d2) + self.assertEqual(p, Decimal('2')) + self.assertEqual(q, Decimal('1')) + self.assertEqual(type(p), type(d1)) + self.assertEqual(type(q), type(d1)) + + #with other type, left + (p, q) = divmod(d1, 4) + self.assertEqual(p, Decimal('1')) + self.assertEqual(q, Decimal('1')) + self.assertEqual(type(p), type(d1)) + self.assertEqual(type(q), type(d1)) + + #with other type, right + (p, q) = divmod(7, d1) + self.assertEqual(p, Decimal('1')) + self.assertEqual(q, Decimal('2')) + self.assertEqual(type(p), type(d1)) + self.assertEqual(type(q), type(d1)) + + def test_unary_operators(self): + self.assertEqual(+Decimal(45), Decimal(+45)) # + + self.assertEqual(-Decimal(45), Decimal(-45)) # - + self.assertEqual(abs(Decimal(45)), abs(Decimal(-45))) # abs + + +# The following are two functions used to test threading in the next class + +def thfunc1(cls): + d1 = Decimal(1) + d3 = Decimal(3) + cls.assertEqual(d1/d3, Decimal('0.333333333')) + cls.synchro.wait() + cls.assertEqual(d1/d3, Decimal('0.333333333')) + cls.finish1.set() + return + +def thfunc2(cls): + d1 = Decimal(1) + d3 = Decimal(3) + cls.assertEqual(d1/d3, Decimal('0.333333333')) + thiscontext = getcontext() + thiscontext.prec = 18 + cls.assertEqual(d1/d3, Decimal('0.333333333333333333')) + cls.synchro.set() + cls.finish2.set() + return + + +class DecimalUseOfContextTest(unittest.TestCase): + '''Unit tests for Use of Context cases in Decimal.''' + + try: + import threading + except ImportError: + threading = None + + # Take care executing this test from IDLE, there's an issue in threading + # that hangs IDLE and I couldn't find it + + def test_threading(self): + #Test the "threading isolation" of a Context. + + self.synchro = threading.Event() + self.finish1 = threading.Event() + self.finish2 = threading.Event() + + th1 = threading.Thread(target=thfunc1, args=(self,)) + th2 = threading.Thread(target=thfunc2, args=(self,)) + + th1.start() + th2.start() + + self.finish1.wait() + self.finish1.wait() + return + + if threading is None: + del test_threading + + +class DecimalUsabilityTest(unittest.TestCase): + '''Unit tests for Usability cases of Decimal.''' + + def test_comparison_operators(self): + + da = Decimal('23.42') + db = Decimal('23.42') + dc = Decimal('45') + + #two Decimals + self.failUnless(dc > da) + self.failUnless(dc >= da) + self.failUnless(da < dc) + self.failUnless(da <= dc) + self.failUnless(da == db) + self.failUnless(da != dc) + self.failUnless(da <= db) + self.failUnless(da >= db) + self.assertEqual(cmp(dc,da), 1) + self.assertEqual(cmp(da,dc), -1) + self.assertEqual(cmp(da,db), 0) + + #a Decimal and an int + self.failUnless(dc > 23) + self.failUnless(23 < dc) + self.failUnless(dc == 45) + self.assertEqual(cmp(dc,23), 1) + self.assertEqual(cmp(23,dc), -1) + self.assertEqual(cmp(dc,45), 0) + + #a Decimal and uncomparable + self.assertNotEqual(da, 'ugly') + self.assertNotEqual(da, 32.7) + self.assertNotEqual(da, object()) + self.assertNotEqual(da, object) + + # sortable + a = map(Decimal, xrange(100)) + b = a[:] + random.shuffle(a) + a.sort() + self.assertEqual(a, b) + + def test_copy_and_deepcopy_methods(self): + d = Decimal('43.24') + c = copy.copy(d) + self.assertEqual(id(c), id(d)) + dc = copy.deepcopy(d) + self.assertEqual(id(dc), id(d)) + + def test_hash_method(self): + #just that it's hashable + hash(Decimal(23)) + #the same hash that to an int + self.assertEqual(hash(Decimal(23)), hash(23)) + self.assertRaises(TypeError, hash, Decimal('NaN')) + self.assert_(hash(Decimal('Inf'))) + self.assert_(hash(Decimal('-Inf'))) + + def test_min_and_max_methods(self): + + d1 = Decimal('15.32') + d2 = Decimal('28.5') + l1 = 15 + l2 = 28 + + #between Decimals + self.failUnless(min(d1,d2) is d1) + self.failUnless(min(d2,d1) is d1) + self.failUnless(max(d1,d2) is d2) + self.failUnless(max(d2,d1) is d2) + + #between Decimal and long + self.failUnless(min(d1,l2) is d1) + self.failUnless(min(l2,d1) is d1) + self.failUnless(max(l1,d2) is d2) + self.failUnless(max(d2,l1) is d2) + + def test_as_nonzero(self): + #as false + self.failIf(Decimal(0)) + #as true + self.failUnless(Decimal('0.372')) + + def test_tostring_methods(self): + #Test str and repr methods. + + d = Decimal('15.32') + self.assertEqual(str(d), '15.32') # str + self.assertEqual(repr(d), 'Decimal("15.32")') # repr + + def test_tonum_methods(self): + #Test float, int and long methods. + + d1 = Decimal('66') + d2 = Decimal('15.32') + + #int + self.assertEqual(int(d1), 66) + self.assertEqual(int(d2), 15) + + #long + self.assertEqual(long(d1), 66) + self.assertEqual(long(d2), 15) + + #float + self.assertEqual(float(d1), 66) + self.assertEqual(float(d2), 15.32) + + def test_eval_round_trip(self): + + #with zero + d = Decimal( (0, (0,), 0) ) + self.assertEqual(d, eval(repr(d))) + + #int + d = Decimal( (1, (4, 5), 0) ) + self.assertEqual(d, eval(repr(d))) + + #float + d = Decimal( (0, (4, 5, 3, 4), -2) ) + self.assertEqual(d, eval(repr(d))) + + #weird + d = Decimal( (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) ) + self.assertEqual(d, eval(repr(d))) + + def test_as_tuple(self): + + #with zero + d = Decimal(0) + self.assertEqual(d.as_tuple(), (0, (0,), 0) ) + + #int + d = Decimal(-45) + self.assertEqual(d.as_tuple(), (1, (4, 5), 0) ) + + #complicated string + d = Decimal("-4.34913534E-17") + self.assertEqual(d.as_tuple(), (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) ) + + #inf + d = Decimal("Infinity") + self.assertEqual(d.as_tuple(), (0, (0,), 'F') ) + + def test_immutability_operations(self): + # Do operations and check that it didn't change change internal objects. + + d1 = Decimal('-25e55') + b1 = Decimal('-25e55') + d2 = Decimal('33e-33') + b2 = Decimal('33e-33') + + def checkSameDec(operation, useOther=False): + if useOther: + eval("d1." + operation + "(d2)") + self.assertEqual(d1._sign, b1._sign) + self.assertEqual(d1._int, b1._int) + self.assertEqual(d1._exp, b1._exp) + self.assertEqual(d2._sign, b2._sign) + self.assertEqual(d2._int, b2._int) + self.assertEqual(d2._exp, b2._exp) + else: + eval("d1." + operation + "()") + self.assertEqual(d1._sign, b1._sign) + self.assertEqual(d1._int, b1._int) + self.assertEqual(d1._exp, b1._exp) + return + + Decimal(d1) + self.assertEqual(d1._sign, b1._sign) + self.assertEqual(d1._int, b1._int) + self.assertEqual(d1._exp, b1._exp) + + checkSameDec("__abs__") + checkSameDec("__add__", True) + checkSameDec("__div__", True) + checkSameDec("__divmod__", True) + checkSameDec("__cmp__", True) + checkSameDec("__float__") + checkSameDec("__floordiv__", True) + checkSameDec("__hash__") + checkSameDec("__int__") + checkSameDec("__long__") + checkSameDec("__mod__", True) + checkSameDec("__mul__", True) + checkSameDec("__neg__") + checkSameDec("__nonzero__") + checkSameDec("__pos__") + checkSameDec("__pow__", True) + checkSameDec("__radd__", True) + checkSameDec("__rdiv__", True) + checkSameDec("__rdivmod__", True) + checkSameDec("__repr__") + checkSameDec("__rfloordiv__", True) + checkSameDec("__rmod__", True) + checkSameDec("__rmul__", True) + checkSameDec("__rpow__", True) + checkSameDec("__rsub__", True) + checkSameDec("__str__") + checkSameDec("__sub__", True) + checkSameDec("__truediv__", True) + checkSameDec("adjusted") + checkSameDec("as_tuple") + checkSameDec("compare", True) + checkSameDec("max", True) + checkSameDec("min", True) + checkSameDec("normalize") + checkSameDec("quantize", True) + checkSameDec("remainder_near", True) + checkSameDec("same_quantum", True) + checkSameDec("sqrt") + checkSameDec("to_eng_string") + checkSameDec("to_integral") + +class DecimalPythonAPItests(unittest.TestCase): + + def test_pickle(self): + d = Decimal('-3.141590000') + p = pickle.dumps(d) + e = pickle.loads(p) + self.assertEqual(d, e) + + def test_int(self): + for x in range(-250, 250): + s = '%0.2f' % (x / 100.0) + # should work the same as for floats + self.assertEqual(int(Decimal(s)), int(float(s))) + # should work the same as to_integral in the ROUND_DOWN mode + d = Decimal(s) + r = d.to_integral(ROUND_DOWN) + self.assertEqual(Decimal(int(d)), r) + +class ContextAPItests(unittest.TestCase): + + def test_pickle(self): + c = Context() + e = pickle.loads(pickle.dumps(c)) + for k in vars(c): + v1 = vars(c)[k] + v2 = vars(e)[k] + self.assertEqual(v1, v2) + + def test_equality_with_other_types(self): + self.assert_(Decimal(10) in ['a', 1.0, Decimal(10), (1,2), {}]) + self.assert_(Decimal(10) not in ['a', 1.0, (1,2), {}]) + + def test_copy(self): + # All copies should be deep + c = Context() + d = c.copy() + self.assertNotEqual(id(c), id(d)) + self.assertNotEqual(id(c.flags), id(d.flags)) + self.assertNotEqual(id(c.traps), id(d.traps)) + +def test_main(arith=False, verbose=None): + """ Execute the tests. + + Runs all arithmetic tests if arith is True or if the "decimal" resource + is enabled in regrtest.py + """ + + global TEST_ALL + TEST_ALL = arith or is_resource_enabled('decimal') + + test_classes = [ + DecimalExplicitConstructionTest, + DecimalImplicitConstructionTest, + DecimalArithmeticOperatorsTest, + DecimalUseOfContextTest, + DecimalUsabilityTest, + DecimalPythonAPItests, + ContextAPItests, + DecimalTest, + ] + + run_unittest(*test_classes) + import decimal as DecimalModule + run_doctest(DecimalModule, verbose) + + +if __name__ == '__main__': + # Calling with no arguments runs all tests. + # Calling with "Skip" will skip over 90% of the arithmetic tests. + if len(sys.argv) == 1: + test_main(arith=True, verbose=True) + elif len(sys.argv) == 2: + arith = sys.argv[1].lower() != 'skip' + test_main(arith=arith, verbose=True) + else: + raise ValueError("test called with wrong arguments, use test_Decimal [Skip]")