# Copyright (c) 2004 Python Software Foundation.

# All rights reserved.

# Written by Eric Price <eprice at tjhsst.edu>

#    and Facundo Batista <facundo at taniquetil.com.ar>

#    and Raymond Hettinger <python at rcn.com>

#    and Aahz <aahz at pobox.com>

#    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: