| # 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 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 an implementation of decimal floating point arithmetic based on |
| the General Decimal Arithmetic Specification: |
| |
| http://speleotrove.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 this module is to support arithmetic using familiar |
| "schoolhouse" rules and to avoid some of the tricky representation |
| issues associated with binary floating point. The package is especially |
| useful for financial applications or for contexts where users have |
| expectations that are at odds with binary floating point (for instance, |
| 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): |
| ... |
| ... |
| ... |
| decimal.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): |
| ... |
| ... |
| ... |
| decimal.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', 'ROUND_05UP', |
| |
| # Functions for manipulating contexts |
| 'setcontext', 'getcontext', 'localcontext' |
| ] |
| |
| __version__ = '1.70' # Highest version of the spec this complies with |
| |
| import copy as _copy |
| import math as _math |
| import numbers as _numbers |
| |
| try: |
| from collections import namedtuple as _namedtuple |
| DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent') |
| except ImportError: |
| DecimalTuple = lambda *args: args |
| |
| # 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' |
| ROUND_05UP = 'ROUND_05UP' |
| |
| # 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 |
| |
| The result of the operation after these is a quiet positive NaN, |
| except when the cause is a signaling NaN, in which case the result is |
| also a quiet NaN, but with the original sign, and an optional |
| diagnostic information. |
| """ |
| def handle(self, context, *args): |
| if args: |
| ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True) |
| return ans._fix_nan(context) |
| 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 _NaN |
| |
| 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, *args): |
| return _SignedInfinity[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 |
| |
| 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, *args): |
| 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. |
| """ |
| |
| 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. |
| """ |
| |
| class Subnormal(DecimalException): |
| """Exponent < Emin before rounding. |
| |
| This occurs and signals subnormal whenever the result of a conversion or |
| operation is subnormal (that is, its adjusted exponent is less than |
| Emin, before any rounding). The result in all cases is unchanged. |
| |
| The subnormal signal may be tested (or trapped) to determine if a given |
| or operation (or sequence of operations) yielded a subnormal result. |
| """ |
| |
| class Overflow(Inexact, Rounded): |
| """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 _SignedInfinity[sign] |
| if sign == 0: |
| if context.rounding == ROUND_CEILING: |
| return _SignedInfinity[sign] |
| return _dec_from_triple(sign, '9'*context.prec, |
| context.Emax-context.prec+1) |
| if sign == 1: |
| if context.rounding == ROUND_FLOOR: |
| return _SignedInfinity[sign] |
| return _dec_from_triple(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.current_thread() 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(object): |
| def local(self, sys=sys): |
| return sys.modules[__name__] |
| threading = MockThreading() |
| del sys, MockThreading |
| |
| try: |
| threading.local |
| |
| except AttributeError: |
| |
| # To fix reloading, force it to create a new context |
| # Old contexts have different exceptions in their dicts, making problems. |
| if hasattr(threading.current_thread(), '__decimal_context__'): |
| del threading.current_thread().__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.current_thread().__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.current_thread().__decimal_context__ |
| except AttributeError: |
| context = Context() |
| threading.current_thread().__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 |
| |
| def localcontext(ctx=None): |
| """Return a context manager for a copy of the supplied context |
| |
| Uses a copy of the current context if no context is specified |
| The returned context manager creates a local decimal context |
| in a with statement: |
| def sin(x): |
| with localcontext() as ctx: |
| ctx.prec += 2 |
| # Rest of sin calculation algorithm |
| # uses a precision 2 greater than normal |
| return +s # Convert result to normal precision |
| |
| def sin(x): |
| with localcontext(ExtendedContext): |
| # Rest of sin calculation algorithm |
| # uses the Extended Context from the |
| # General Decimal Arithmetic Specification |
| return +s # Convert result to normal context |
| |
| >>> setcontext(DefaultContext) |
| >>> print(getcontext().prec) |
| 28 |
| >>> with localcontext(): |
| ... ctx = getcontext() |
| ... ctx.prec += 2 |
| ... print(ctx.prec) |
| ... |
| 30 |
| >>> with localcontext(ExtendedContext): |
| ... print(getcontext().prec) |
| ... |
| 9 |
| >>> print(getcontext().prec) |
| 28 |
| """ |
| if ctx is None: ctx = getcontext() |
| return _ContextManager(ctx) |
| |
| |
| ##### Decimal class ####################################################### |
| |
| # Do not subclass Decimal from numbers.Real and do not register it as such |
| # (because Decimals are not interoperable with floats). See the notes in |
| # numbers.py for more detail. |
| |
| 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 (sign, digit_tuple, exponent) |
| Decimal('3.14') |
| >>> Decimal(314) # int |
| Decimal('314') |
| >>> Decimal(Decimal(314)) # another decimal instance |
| Decimal('314') |
| >>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay |
| Decimal('3.14') |
| """ |
| |
| # Note that the coefficient, self._int, is actually stored as |
| # a string rather than as a tuple of digits. This speeds up |
| # the "digits to integer" and "integer to digits" conversions |
| # that are used in almost every arithmetic operation on |
| # Decimals. This is an internal detail: the as_tuple function |
| # and the Decimal constructor still deal with tuples of |
| # digits. |
| |
| self = object.__new__(cls) |
| |
| # From a string |
| # REs insist on real strings, so we can too. |
| if isinstance(value, str): |
| m = _parser(value.strip()) |
| if m is None: |
| if context is None: |
| context = getcontext() |
| return context._raise_error(ConversionSyntax, |
| "Invalid literal for Decimal: %r" % value) |
| |
| if m.group('sign') == "-": |
| self._sign = 1 |
| else: |
| self._sign = 0 |
| intpart = m.group('int') |
| if intpart is not None: |
| # finite number |
| fracpart = m.group('frac') or '' |
| exp = int(m.group('exp') or '0') |
| self._int = str(int(intpart+fracpart)) |
| self._exp = exp - len(fracpart) |
| self._is_special = False |
| else: |
| diag = m.group('diag') |
| if diag is not None: |
| # NaN |
| self._int = str(int(diag or '0')).lstrip('0') |
| if m.group('signal'): |
| self._exp = 'N' |
| else: |
| self._exp = 'n' |
| else: |
| # infinity |
| self._int = '0' |
| self._exp = 'F' |
| self._is_special = True |
| return self |
| |
| # From an integer |
| if isinstance(value, int): |
| if value >= 0: |
| self._sign = 0 |
| else: |
| self._sign = 1 |
| self._exp = 0 |
| self._int = str(abs(value)) |
| self._is_special = False |
| 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 internal working value |
| if isinstance(value, _WorkRep): |
| self._sign = value.sign |
| self._int = str(value.int) |
| self._exp = int(value.exp) |
| self._is_special = False |
| return self |
| |
| # tuple/list conversion (possibly from as_tuple()) |
| if isinstance(value, (list,tuple)): |
| if len(value) != 3: |
| raise ValueError('Invalid tuple size in creation of Decimal ' |
| 'from list or tuple. The list or tuple ' |
| 'should have exactly three elements.') |
| # process sign. The isinstance test rejects floats |
| if not (isinstance(value[0], int) and value[0] in (0,1)): |
| raise ValueError("Invalid sign. The first value in the tuple " |
| "should be an integer; either 0 for a " |
| "positive number or 1 for a negative number.") |
| self._sign = value[0] |
| if value[2] == 'F': |
| # infinity: value[1] is ignored |
| self._int = '0' |
| self._exp = value[2] |
| self._is_special = True |
| else: |
| # process and validate the digits in value[1] |
| digits = [] |
| for digit in value[1]: |
| if isinstance(digit, int) and 0 <= digit <= 9: |
| # skip leading zeros |
| if digits or digit != 0: |
| digits.append(digit) |
| else: |
| raise ValueError("The second value in the tuple must " |
| "be composed of integers in the range " |
| "0 through 9.") |
| if value[2] in ('n', 'N'): |
| # NaN: digits form the diagnostic |
| self._int = ''.join(map(str, digits)) |
| self._exp = value[2] |
| self._is_special = True |
| elif isinstance(value[2], int): |
| # finite number: digits give the coefficient |
| self._int = ''.join(map(str, digits or [0])) |
| self._exp = value[2] |
| self._is_special = False |
| else: |
| raise ValueError("The third value in the tuple must " |
| "be an integer, or one of the " |
| "strings 'F', 'n', 'N'.") |
| return self |
| |
| if isinstance(value, float): |
| raise TypeError("Cannot convert float to Decimal. " + |
| "First convert the float to a string") |
| |
| raise TypeError("Cannot convert %r to Decimal" % value) |
| |
| # @classmethod, but @decorator is not valid Python 2.3 syntax, so |
| # don't use it (see notes on Py2.3 compatibility at top of file) |
| def from_float(cls, f): |
| """Converts a float to a decimal number, exactly. |
| |
| Note that Decimal.from_float(0.1) is not the same as Decimal('0.1'). |
| Since 0.1 is not exactly representable in binary floating point, the |
| value is stored as the nearest representable value which is |
| 0x1.999999999999ap-4. The exact equivalent of the value in decimal |
| is 0.1000000000000000055511151231257827021181583404541015625. |
| |
| >>> Decimal.from_float(0.1) |
| Decimal('0.1000000000000000055511151231257827021181583404541015625') |
| >>> Decimal.from_float(float('nan')) |
| Decimal('NaN') |
| >>> Decimal.from_float(float('inf')) |
| Decimal('Infinity') |
| >>> Decimal.from_float(-float('inf')) |
| Decimal('-Infinity') |
| >>> Decimal.from_float(-0.0) |
| Decimal('-0') |
| |
| """ |
| if isinstance(f, int): # handle integer inputs |
| return cls(f) |
| if _math.isinf(f) or _math.isnan(f): # raises TypeError if not a float |
| return cls(repr(f)) |
| if _math.copysign(1.0, f) == 1.0: |
| sign = 0 |
| else: |
| sign = 1 |
| n, d = abs(f).as_integer_ratio() |
| k = d.bit_length() - 1 |
| result = _dec_from_triple(sign, str(n*5**k), -k) |
| if cls is Decimal: |
| return result |
| else: |
| return cls(result) |
| from_float = classmethod(from_float) |
| |
| 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', |
| self) |
| if other_is_nan == 2: |
| return context._raise_error(InvalidOperation, 'sNaN', |
| other) |
| if self_is_nan: |
| return self._fix_nan(context) |
| |
| return other._fix_nan(context) |
| return 0 |
| |
| def _compare_check_nans(self, other, context): |
| """Version of _check_nans used for the signaling comparisons |
| compare_signal, __le__, __lt__, __ge__, __gt__. |
| |
| Signal InvalidOperation if either self or other is a (quiet |
| or signaling) NaN. Signaling NaNs take precedence over quiet |
| NaNs. |
| |
| Return 0 if neither operand is a NaN. |
| |
| """ |
| if context is None: |
| context = getcontext() |
| |
| if self._is_special or other._is_special: |
| if self.is_snan(): |
| return context._raise_error(InvalidOperation, |
| 'comparison involving sNaN', |
| self) |
| elif other.is_snan(): |
| return context._raise_error(InvalidOperation, |
| 'comparison involving sNaN', |
| other) |
| elif self.is_qnan(): |
| return context._raise_error(InvalidOperation, |
| 'comparison involving NaN', |
| self) |
| elif other.is_qnan(): |
| return context._raise_error(InvalidOperation, |
| 'comparison involving NaN', |
| other) |
| return 0 |
| |
| def __bool__(self): |
| """Return True if self is nonzero; otherwise return False. |
| |
| NaNs and infinities are considered nonzero. |
| """ |
| return self._is_special or self._int != '0' |
| |
| def _cmp(self, other): |
| """Compare the two non-NaN decimal instances self and other. |
| |
| Returns -1 if self < other, 0 if self == other and 1 |
| if self > other. This routine is for internal use only.""" |
| |
| if self._is_special or other._is_special: |
| self_inf = self._isinfinity() |
| other_inf = other._isinfinity() |
| if self_inf == other_inf: |
| return 0 |
| elif self_inf < other_inf: |
| return -1 |
| else: |
| return 1 |
| |
| # check for zeros; Decimal('0') == Decimal('-0') |
| if not self: |
| if not other: |
| return 0 |
| else: |
| return -((-1)**other._sign) |
| if not other: |
| return (-1)**self._sign |
| |
| # 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: |
| self_padded = self._int + '0'*(self._exp - other._exp) |
| other_padded = other._int + '0'*(other._exp - self._exp) |
| if self_padded == other_padded: |
| return 0 |
| elif self_padded < other_padded: |
| return -(-1)**self._sign |
| else: |
| return (-1)**self._sign |
| elif self_adjusted > other_adjusted: |
| return (-1)**self._sign |
| else: # self_adjusted < other_adjusted |
| return -((-1)**self._sign) |
| |
| # Note: The Decimal standard doesn't cover rich comparisons for |
| # Decimals. In particular, the specification is silent on the |
| # subject of what should happen for a comparison involving a NaN. |
| # We take the following approach: |
| # |
| # == comparisons involving a NaN always return False |
| # != comparisons involving a NaN always return True |
| # <, >, <= and >= comparisons involving a (quiet or signaling) |
| # NaN signal InvalidOperation, and return False if the |
| # InvalidOperation is not trapped. |
| # |
| # This behavior is designed to conform as closely as possible to |
| # that specified by IEEE 754. |
| |
| def __eq__(self, other): |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| if self.is_nan() or other.is_nan(): |
| return False |
| return self._cmp(other) == 0 |
| |
| def __ne__(self, other): |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| if self.is_nan() or other.is_nan(): |
| return True |
| return self._cmp(other) != 0 |
| |
| |
| def __lt__(self, other, context=None): |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| ans = self._compare_check_nans(other, context) |
| if ans: |
| return False |
| return self._cmp(other) < 0 |
| |
| def __le__(self, other, context=None): |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| ans = self._compare_check_nans(other, context) |
| if ans: |
| return False |
| return self._cmp(other) <= 0 |
| |
| def __gt__(self, other, context=None): |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| ans = self._compare_check_nans(other, context) |
| if ans: |
| return False |
| return self._cmp(other) > 0 |
| |
| def __ge__(self, other, context=None): |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| ans = self._compare_check_nans(other, context) |
| if ans: |
| return False |
| 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, raiseit=True) |
| |
| # 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)) |
| |
| def __hash__(self): |
| """x.__hash__() <==> hash(x)""" |
| # Decimal integers must hash the same as the ints |
| # |
| # The hash of a nonspecial noninteger Decimal must depend only |
| # on the value of that Decimal, and not on its representation. |
| # For example: hash(Decimal('100E-1')) == hash(Decimal('10')). |
| if self._is_special: |
| if self._isnan(): |
| raise TypeError('Cannot hash a NaN value.') |
| return hash(str(self)) |
| if not self: |
| return 0 |
| if self._isinteger(): |
| op = _WorkRep(self.to_integral_value()) |
| # to make computation feasible for Decimals with large |
| # exponent, we use the fact that hash(n) == hash(m) for |
| # any two nonzero integers n and m such that (i) n and m |
| # have the same sign, and (ii) n is congruent to m modulo |
| # 2**64-1. So we can replace hash((-1)**s*c*10**e) with |
| # hash((-1)**s*c*pow(10, e, 2**64-1). |
| return hash((-1)**op.sign*op.int*pow(10, op.exp, 2**64-1)) |
| # The value of a nonzero nonspecial Decimal instance is |
| # faithfully represented by the triple consisting of its sign, |
| # its adjusted exponent, and its coefficient with trailing |
| # zeros removed. |
| return hash((self._sign, |
| self._exp+len(self._int), |
| self._int.rstrip('0'))) |
| |
| def as_tuple(self): |
| """Represents the number as a triple tuple. |
| |
| To show the internals exactly as they are. |
| """ |
| return DecimalTuple(self._sign, tuple(map(int, 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=False, context=None): |
| """Return string representation of the number in scientific notation. |
| |
| Captures all of the information in the underlying representation. |
| """ |
| |
| sign = ['', '-'][self._sign] |
| if self._is_special: |
| if self._exp == 'F': |
| return sign + 'Infinity' |
| elif self._exp == 'n': |
| return sign + 'NaN' + self._int |
| else: # self._exp == 'N' |
| return sign + 'sNaN' + self._int |
| |
| # number of digits of self._int to left of decimal point |
| leftdigits = self._exp + len(self._int) |
| |
| # dotplace is number of digits of self._int to the left of the |
| # decimal point in the mantissa of the output string (that is, |
| # after adjusting the exponent) |
| if self._exp <= 0 and leftdigits > -6: |
| # no exponent required |
| dotplace = leftdigits |
| elif not eng: |
| # usual scientific notation: 1 digit on left of the point |
| dotplace = 1 |
| elif self._int == '0': |
| # engineering notation, zero |
| dotplace = (leftdigits + 1) % 3 - 1 |
| else: |
| # engineering notation, nonzero |
| dotplace = (leftdigits - 1) % 3 + 1 |
| |
| if dotplace <= 0: |
| intpart = '0' |
| fracpart = '.' + '0'*(-dotplace) + self._int |
| elif dotplace >= len(self._int): |
| intpart = self._int+'0'*(dotplace-len(self._int)) |
| fracpart = '' |
| else: |
| intpart = self._int[:dotplace] |
| fracpart = '.' + self._int[dotplace:] |
| if leftdigits == dotplace: |
| exp = '' |
| else: |
| if context is None: |
| context = getcontext() |
| exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace) |
| |
| return sign + intpart + fracpart + exp |
| |
| 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=True, 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') |
| ans = self.copy_abs() |
| else: |
| ans = self.copy_negate() |
| |
| if context is None: |
| context = getcontext() |
| return ans._fix(context) |
| |
| 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 |
| |
| if not self: |
| # + (-0) = 0 |
| ans = self.copy_abs() |
| else: |
| ans = Decimal(self) |
| |
| if context is None: |
| context = getcontext() |
| return ans._fix(context) |
| |
| def __abs__(self, round=True, context=None): |
| """Returns the absolute value of self. |
| |
| If the keyword argument 'round' is false, do not round. The |
| expression self.__abs__(round=False) is equivalent to |
| self.copy_abs(). |
| """ |
| if not round: |
| return self.copy_abs() |
| |
| if self._is_special: |
| ans = self._check_nans(context=context) |
| if ans: |
| return ans |
| |
| 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 |
| |
| 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 |
| ans = _dec_from_triple(sign, '0', exp) |
| ans = ans._fix(context) |
| return ans |
| if not self: |
| exp = max(exp, other._exp - context.prec-1) |
| ans = other._rescale(exp, context.rounding) |
| ans = ans._fix(context) |
| return ans |
| if not other: |
| exp = max(exp, self._exp - context.prec-1) |
| ans = self._rescale(exp, context.rounding) |
| ans = ans._fix(context) |
| return ans |
| |
| op1 = _WorkRep(self) |
| op2 = _WorkRep(other) |
| op1, op2 = _normalize(op1, op2, context.prec) |
| |
| result = _WorkRep() |
| if op1.sign != op2.sign: |
| # Equal and opposite |
| if op1.int == op2.int: |
| ans = _dec_from_triple(negativezero, '0', exp) |
| ans = ans._fix(context) |
| return ans |
| 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) |
| 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 |
| |
| # self - other is computed as self + other.copy_negate() |
| return self.__add__(other.copy_negate(), context=context) |
| |
| def __rsub__(self, other, context=None): |
| """Return other - self""" |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| |
| return other.__sub__(self, context=context) |
| |
| 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 _SignedInfinity[resultsign] |
| |
| if other._isinfinity(): |
| if not self: |
| return context._raise_error(InvalidOperation, '0 * (+-)INF') |
| return _SignedInfinity[resultsign] |
| |
| resultexp = self._exp + other._exp |
| |
| # Special case for multiplying by zero |
| if not self or not other: |
| ans = _dec_from_triple(resultsign, '0', resultexp) |
| # 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 = _dec_from_triple(resultsign, other._int, resultexp) |
| ans = ans._fix(context) |
| return ans |
| if other._int == '1': |
| ans = _dec_from_triple(resultsign, self._int, resultexp) |
| ans = ans._fix(context) |
| return ans |
| |
| op1 = _WorkRep(self) |
| op2 = _WorkRep(other) |
| |
| ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp) |
| ans = ans._fix(context) |
| |
| return ans |
| __rmul__ = __mul__ |
| |
| def __truediv__(self, other, context=None): |
| """Return self / other.""" |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return 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: |
| return ans |
| |
| if self._isinfinity() and other._isinfinity(): |
| return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') |
| |
| if self._isinfinity(): |
| return _SignedInfinity[sign] |
| |
| if other._isinfinity(): |
| context._raise_error(Clamped, 'Division by infinity') |
| return _dec_from_triple(sign, '0', context.Etiny()) |
| |
| # Special cases for zeroes |
| if not other: |
| if not self: |
| return context._raise_error(DivisionUndefined, '0 / 0') |
| return context._raise_error(DivisionByZero, 'x / 0', sign) |
| |
| if not self: |
| exp = self._exp - other._exp |
| coeff = 0 |
| else: |
| # OK, so neither = 0, INF or NaN |
| shift = len(other._int) - len(self._int) + context.prec + 1 |
| exp = self._exp - other._exp - shift |
| op1 = _WorkRep(self) |
| op2 = _WorkRep(other) |
| if shift >= 0: |
| coeff, remainder = divmod(op1.int * 10**shift, op2.int) |
| else: |
| coeff, remainder = divmod(op1.int, op2.int * 10**-shift) |
| if remainder: |
| # result is not exact; adjust to ensure correct rounding |
| if coeff % 5 == 0: |
| coeff += 1 |
| else: |
| # result is exact; get as close to ideal exponent as possible |
| ideal_exp = self._exp - other._exp |
| while exp < ideal_exp and coeff % 10 == 0: |
| coeff //= 10 |
| exp += 1 |
| |
| ans = _dec_from_triple(sign, str(coeff), exp) |
| return ans._fix(context) |
| |
| def _divide(self, other, context): |
| """Return (self // other, self % other), to context.prec precision. |
| |
| Assumes that neither self nor other is a NaN, that self is not |
| infinite and that other is nonzero. |
| """ |
| sign = self._sign ^ other._sign |
| if other._isinfinity(): |
| ideal_exp = self._exp |
| else: |
| ideal_exp = min(self._exp, other._exp) |
| |
| expdiff = self.adjusted() - other.adjusted() |
| if not self or other._isinfinity() or expdiff <= -2: |
| return (_dec_from_triple(sign, '0', 0), |
| self._rescale(ideal_exp, context.rounding)) |
| if expdiff <= context.prec: |
| op1 = _WorkRep(self) |
| op2 = _WorkRep(other) |
| if op1.exp >= op2.exp: |
| op1.int *= 10**(op1.exp - op2.exp) |
| else: |
| op2.int *= 10**(op2.exp - op1.exp) |
| q, r = divmod(op1.int, op2.int) |
| if q < 10**context.prec: |
| return (_dec_from_triple(sign, str(q), 0), |
| _dec_from_triple(self._sign, str(r), ideal_exp)) |
| |
| # Here the quotient is too large to be representable |
| ans = context._raise_error(DivisionImpossible, |
| 'quotient too large in //, % or divmod') |
| return ans, ans |
| |
| def __rtruediv__(self, other, context=None): |
| """Swaps self/other and returns __truediv__.""" |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| return other.__truediv__(self, context=context) |
| |
| def __divmod__(self, other, context=None): |
| """ |
| Return (self // other, self % other) |
| """ |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| |
| if context is None: |
| context = getcontext() |
| |
| ans = self._check_nans(other, context) |
| if ans: |
| return (ans, ans) |
| |
| sign = self._sign ^ other._sign |
| if self._isinfinity(): |
| if other._isinfinity(): |
| ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)') |
| return ans, ans |
| else: |
| return (_SignedInfinity[sign], |
| context._raise_error(InvalidOperation, 'INF % x')) |
| |
| if not other: |
| if not self: |
| ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)') |
| return ans, ans |
| else: |
| return (context._raise_error(DivisionByZero, 'x // 0', sign), |
| context._raise_error(InvalidOperation, 'x % 0')) |
| |
| quotient, remainder = self._divide(other, context) |
| remainder = remainder._fix(context) |
| return quotient, remainder |
| |
| 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 context is None: |
| context = getcontext() |
| |
| ans = self._check_nans(other, context) |
| if ans: |
| return ans |
| |
| if self._isinfinity(): |
| return context._raise_error(InvalidOperation, 'INF % x') |
| elif not other: |
| if self: |
| return context._raise_error(InvalidOperation, 'x % 0') |
| else: |
| return context._raise_error(DivisionUndefined, '0 % 0') |
| |
| remainder = self._divide(other, context)[1] |
| remainder = remainder._fix(context) |
| return remainder |
| |
| 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 |
| """ |
| if context is None: |
| context = getcontext() |
| |
| other = _convert_other(other, raiseit=True) |
| |
| ans = self._check_nans(other, context) |
| if ans: |
| return ans |
| |
| # self == +/-infinity -> InvalidOperation |
| if self._isinfinity(): |
| return context._raise_error(InvalidOperation, |
| 'remainder_near(infinity, x)') |
| |
| # other == 0 -> either InvalidOperation or DivisionUndefined |
| if not other: |
| if self: |
| return context._raise_error(InvalidOperation, |
| 'remainder_near(x, 0)') |
| else: |
| return context._raise_error(DivisionUndefined, |
| 'remainder_near(0, 0)') |
| |
| # other = +/-infinity -> remainder = self |
| if other._isinfinity(): |
| ans = Decimal(self) |
| return ans._fix(context) |
| |
| # self = 0 -> remainder = self, with ideal exponent |
| ideal_exponent = min(self._exp, other._exp) |
| if not self: |
| ans = _dec_from_triple(self._sign, '0', ideal_exponent) |
| return ans._fix(context) |
| |
| # catch most cases of large or small quotient |
| expdiff = self.adjusted() - other.adjusted() |
| if expdiff >= context.prec + 1: |
| # expdiff >= prec+1 => abs(self/other) > 10**prec |
| return context._raise_error(DivisionImpossible) |
| if expdiff <= -2: |
| # expdiff <= -2 => abs(self/other) < 0.1 |
| ans = self._rescale(ideal_exponent, context.rounding) |
| return ans._fix(context) |
| |
| # adjust both arguments to have the same exponent, then divide |
| op1 = _WorkRep(self) |
| op2 = _WorkRep(other) |
| if op1.exp >= op2.exp: |
| op1.int *= 10**(op1.exp - op2.exp) |
| else: |
| op2.int *= 10**(op2.exp - op1.exp) |
| q, r = divmod(op1.int, op2.int) |
| # remainder is r*10**ideal_exponent; other is +/-op2.int * |
| # 10**ideal_exponent. Apply correction to ensure that |
| # abs(remainder) <= abs(other)/2 |
| if 2*r + (q&1) > op2.int: |
| r -= op2.int |
| q += 1 |
| |
| if q >= 10**context.prec: |
| return context._raise_error(DivisionImpossible) |
| |
| # result has same sign as self unless r is negative |
| sign = self._sign |
| if r < 0: |
| sign = 1-sign |
| r = -r |
| |
| ans = _dec_from_triple(sign, str(r), ideal_exponent) |
| return ans._fix(context) |
| |
| def __floordiv__(self, other, context=None): |
| """self // other""" |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| |
| if context is None: |
| context = getcontext() |
| |
| ans = self._check_nans(other, context) |
| if ans: |
| return ans |
| |
| if self._isinfinity(): |
| if other._isinfinity(): |
| return context._raise_error(InvalidOperation, 'INF // INF') |
| else: |
| return _SignedInfinity[self._sign ^ other._sign] |
| |
| if not other: |
| if self: |
| return context._raise_error(DivisionByZero, 'x // 0', |
| self._sign ^ other._sign) |
| else: |
| return context._raise_error(DivisionUndefined, '0 // 0') |
| |
| return self._divide(other, 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(): |
| raise ValueError("Cannot convert NaN to integer") |
| elif self._isinfinity(): |
| raise OverflowError("Cannot convert infinity to integer") |
| s = (-1)**self._sign |
| if self._exp >= 0: |
| return s*int(self._int)*10**self._exp |
| else: |
| return s*int(self._int[:self._exp] or '0') |
| |
| __trunc__ = __int__ |
| |
| def real(self): |
| return self |
| real = property(real) |
| |
| def imag(self): |
| return Decimal(0) |
| imag = property(imag) |
| |
| def conjugate(self): |
| return self |
| |
| def __complex__(self): |
| return complex(float(self)) |
| |
| def _fix_nan(self, context): |
| """Decapitate the payload of a NaN to fit the context""" |
| payload = self._int |
| |
| # maximum length of payload is precision if _clamp=0, |
| # precision-1 if _clamp=1. |
| max_payload_len = context.prec - context._clamp |
| if len(payload) > max_payload_len: |
| payload = payload[len(payload)-max_payload_len:].lstrip('0') |
| return _dec_from_triple(self._sign, payload, self._exp, True) |
| return Decimal(self) |
| |
| 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: |
| if self._isnan(): |
| # decapitate payload if necessary |
| return self._fix_nan(context) |
| else: |
| # self is +/-Infinity; return unaltered |
| return Decimal(self) |
| |
| # if self is zero then exponent should be between Etiny and |
| # Emax if _clamp==0, and between Etiny and Etop if _clamp==1. |
| Etiny = context.Etiny() |
| Etop = context.Etop() |
| if not self: |
| exp_max = [context.Emax, Etop][context._clamp] |
| new_exp = min(max(self._exp, Etiny), exp_max) |
| if new_exp != self._exp: |
| context._raise_error(Clamped) |
| return _dec_from_triple(self._sign, '0', new_exp) |
| else: |
| return Decimal(self) |
| |
| # exp_min is the smallest allowable exponent of the result, |
| # equal to max(self.adjusted()-context.prec+1, Etiny) |
| exp_min = len(self._int) + self._exp - context.prec |
| if exp_min > Etop: |
| # overflow: exp_min > Etop iff self.adjusted() > Emax |
| context._raise_error(Inexact) |
| context._raise_error(Rounded) |
| return context._raise_error(Overflow, 'above Emax', self._sign) |
| self_is_subnormal = exp_min < Etiny |
| if self_is_subnormal: |
| context._raise_error(Subnormal) |
| exp_min = Etiny |
| |
| # round if self has too many digits |
| if self._exp < exp_min: |
| context._raise_error(Rounded) |
| digits = len(self._int) + self._exp - exp_min |
| if digits < 0: |
| self = _dec_from_triple(self._sign, '1', exp_min-1) |
| digits = 0 |
| this_function = getattr(self, self._pick_rounding_function[context.rounding]) |
| changed = this_function(digits) |
| coeff = self._int[:digits] or '0' |
| if changed == 1: |
| coeff = str(int(coeff)+1) |
| ans = _dec_from_triple(self._sign, coeff, exp_min) |
| |
| if changed: |
| context._raise_error(Inexact) |
| if self_is_subnormal: |
| context._raise_error(Underflow) |
| if not ans: |
| # raise Clamped on underflow to 0 |
| context._raise_error(Clamped) |
| elif len(ans._int) == context.prec+1: |
| # we get here only if rescaling rounds the |
| # cofficient up to exactly 10**context.prec |
| if ans._exp < Etop: |
| ans = _dec_from_triple(ans._sign, |
| ans._int[:-1], ans._exp+1) |
| else: |
| # Inexact and Rounded have already been raised |
| ans = context._raise_error(Overflow, 'above Emax', |
| self._sign) |
| return ans |
| |
| # fold down if _clamp == 1 and self has too few digits |
| if context._clamp == 1 and self._exp > Etop: |
| context._raise_error(Clamped) |
| self_padded = self._int + '0'*(self._exp - Etop) |
| return _dec_from_triple(self._sign, self_padded, Etop) |
| |
| # here self was representable to begin with; return unchanged |
| return Decimal(self) |
| |
| _pick_rounding_function = {} |
| |
| # for each of the rounding functions below: |
| # self is a finite, nonzero Decimal |
| # prec is an integer satisfying 0 <= prec < len(self._int) |
| # |
| # each function returns either -1, 0, or 1, as follows: |
| # 1 indicates that self should be rounded up (away from zero) |
| # 0 indicates that self should be truncated, and that all the |
| # digits to be truncated are zeros (so the value is unchanged) |
| # -1 indicates that there are nonzero digits to be truncated |
| |
| def _round_down(self, prec): |
| """Also known as round-towards-0, truncate.""" |
| if _all_zeros(self._int, prec): |
| return 0 |
| else: |
| return -1 |
| |
| def _round_up(self, prec): |
| """Rounds away from 0.""" |
| return -self._round_down(prec) |
| |
| def _round_half_up(self, prec): |
| """Rounds 5 up (away from 0)""" |
| if self._int[prec] in '56789': |
| return 1 |
| elif _all_zeros(self._int, prec): |
| return 0 |
| else: |
| return -1 |
| |
| def _round_half_down(self, prec): |
| """Round 5 down""" |
| if _exact_half(self._int, prec): |
| return -1 |
| else: |
| return self._round_half_up(prec) |
| |
| def _round_half_even(self, prec): |
| """Round 5 to even, rest to nearest.""" |
| if _exact_half(self._int, prec) and \ |
| (prec == 0 or self._int[prec-1] in '02468'): |
| return -1 |
| else: |
| return self._round_half_up(prec) |
| |
| def _round_ceiling(self, prec): |
| """Rounds up (not away from 0 if negative.)""" |
| if self._sign: |
| return self._round_down(prec) |
| else: |
| return -self._round_down(prec) |
| |
| def _round_floor(self, prec): |
| """Rounds down (not towards 0 if negative)""" |
| if not self._sign: |
| return self._round_down(prec) |
| else: |
| return -self._round_down(prec) |
| |
| def _round_05up(self, prec): |
| """Round down unless digit prec-1 is 0 or 5.""" |
| if prec and self._int[prec-1] not in '05': |
| return self._round_down(prec) |
| else: |
| return -self._round_down(prec) |
| |
| def __round__(self, n=None): |
| """Round self to the nearest integer, or to a given precision. |
| |
| If only one argument is supplied, round a finite Decimal |
| instance self to the nearest integer. If self is infinite or |
| a NaN then a Python exception is raised. If self is finite |
| and lies exactly halfway between two integers then it is |
| rounded to the integer with even last digit. |
| |
| >>> round(Decimal('123.456')) |
| 123 |
| >>> round(Decimal('-456.789')) |
| -457 |
| >>> round(Decimal('-3.0')) |
| -3 |
| >>> round(Decimal('2.5')) |
| 2 |
| >>> round(Decimal('3.5')) |
| 4 |
| >>> round(Decimal('Inf')) |
| Traceback (most recent call last): |
| ... |
| OverflowError: cannot round an infinity |
| >>> round(Decimal('NaN')) |
| Traceback (most recent call last): |
| ... |
| ValueError: cannot round a NaN |
| |
| If a second argument n is supplied, self is rounded to n |
| decimal places using the rounding mode for the current |
| context. |
| |
| For an integer n, round(self, -n) is exactly equivalent to |
| self.quantize(Decimal('1En')). |
| |
| >>> round(Decimal('123.456'), 0) |
| Decimal('123') |
| >>> round(Decimal('123.456'), 2) |
| Decimal('123.46') |
| >>> round(Decimal('123.456'), -2) |
| Decimal('1E+2') |
| >>> round(Decimal('-Infinity'), 37) |
| Decimal('NaN') |
| >>> round(Decimal('sNaN123'), 0) |
| Decimal('NaN123') |
| |
| """ |
| if n is not None: |
| # two-argument form: use the equivalent quantize call |
| if not isinstance(n, int): |
| raise TypeError('Second argument to round should be integral') |
| exp = _dec_from_triple(0, '1', -n) |
| return self.quantize(exp) |
| |
| # one-argument form |
| if self._is_special: |
| if self.is_nan(): |
| raise ValueError("cannot round a NaN") |
| else: |
| raise OverflowError("cannot round an infinity") |
| return int(self._rescale(0, ROUND_HALF_EVEN)) |
| |
| def __floor__(self): |
| """Return the floor of self, as an integer. |
| |
| For a finite Decimal instance self, return the greatest |
| integer n such that n <= self. If self is infinite or a NaN |
| then a Python exception is raised. |
| |
| """ |
| if self._is_special: |
| if self.is_nan(): |
| raise ValueError("cannot round a NaN") |
| else: |
| raise OverflowError("cannot round an infinity") |
| return int(self._rescale(0, ROUND_FLOOR)) |
| |
| def __ceil__(self): |
| """Return the ceiling of self, as an integer. |
| |
| For a finite Decimal instance self, return the least integer n |
| such that n >= self. If self is infinite or a NaN then a |
| Python exception is raised. |
| |
| """ |
| if self._is_special: |
| if self.is_nan(): |
| raise ValueError("cannot round a NaN") |
| else: |
| raise OverflowError("cannot round an infinity") |
| return int(self._rescale(0, ROUND_CEILING)) |
| |
| def fma(self, other, third, context=None): |
| """Fused multiply-add. |
| |
| Returns self*other+third with no rounding of the intermediate |
| product self*other. |
| |
| self and other are multiplied together, with no rounding of |
| the result. The third operand is then added to the result, |
| and a single final rounding is performed. |
| """ |
| |
| other = _convert_other(other, raiseit=True) |
| |
| # compute product; raise InvalidOperation if either operand is |
| # a signaling NaN or if the product is zero times infinity. |
| if self._is_special or other._is_special: |
| if context is None: |
| context = getcontext() |
| if self._exp == 'N': |
| return context._raise_error(InvalidOperation, 'sNaN', self) |
| if other._exp == 'N': |
| return context._raise_error(InvalidOperation, 'sNaN', other) |
| if self._exp == 'n': |
| product = self |
| elif other._exp == 'n': |
| product = other |
| elif self._exp == 'F': |
| if not other: |
| return context._raise_error(InvalidOperation, |
| 'INF * 0 in fma') |
| product = _SignedInfinity[self._sign ^ other._sign] |
| elif other._exp == 'F': |
| if not self: |
| return context._raise_error(InvalidOperation, |
| '0 * INF in fma') |
| product = _SignedInfinity[self._sign ^ other._sign] |
| else: |
| product = _dec_from_triple(self._sign ^ other._sign, |
| str(int(self._int) * int(other._int)), |
| self._exp + other._exp) |
| |
| third = _convert_other(third, raiseit=True) |
| return product.__add__(third, context) |
| |
| def _power_modulo(self, other, modulo, context=None): |
| """Three argument version of __pow__""" |
| |
| # if can't convert other and modulo to Decimal, raise |
| # TypeError; there's no point returning NotImplemented (no |
| # equivalent of __rpow__ for three argument pow) |
| other = _convert_other(other, raiseit=True) |
| modulo = _convert_other(modulo, raiseit=True) |
| |
| if context is None: |
| context = getcontext() |
| |
| # deal with NaNs: if there are any sNaNs then first one wins, |
| # (i.e. behaviour for NaNs is identical to that of fma) |
| self_is_nan = self._isnan() |
| other_is_nan = other._isnan() |
| modulo_is_nan = modulo._isnan() |
| if self_is_nan or other_is_nan or modulo_is_nan: |
| if self_is_nan == 2: |
| return context._raise_error(InvalidOperation, 'sNaN', |
| self) |
| if other_is_nan == 2: |
| return context._raise_error(InvalidOperation, 'sNaN', |
| other) |
| if modulo_is_nan == 2: |
| return context._raise_error(InvalidOperation, 'sNaN', |
| modulo) |
| if self_is_nan: |
| return self._fix_nan(context) |
| if other_is_nan: |
| return other._fix_nan(context) |
| return modulo._fix_nan(context) |
| |
| # check inputs: we apply same restrictions as Python's pow() |
| if not (self._isinteger() and |
| other._isinteger() and |
| modulo._isinteger()): |
| return context._raise_error(InvalidOperation, |
| 'pow() 3rd argument not allowed ' |
| 'unless all arguments are integers') |
| if other < 0: |
| return context._raise_error(InvalidOperation, |
| 'pow() 2nd argument cannot be ' |
| 'negative when 3rd argument specified') |
| if not modulo: |
| return context._raise_error(InvalidOperation, |
| 'pow() 3rd argument cannot be 0') |
| |
| # additional restriction for decimal: the modulus must be less |
| # than 10**prec in absolute value |
| if modulo.adjusted() >= context.prec: |
| return context._raise_error(InvalidOperation, |
| 'insufficient precision: pow() 3rd ' |
| 'argument must not have more than ' |
| 'precision digits') |
| |
| # define 0**0 == NaN, for consistency with two-argument pow |
| # (even though it hurts!) |
| if not other and not self: |
| return context._raise_error(InvalidOperation, |
| 'at least one of pow() 1st argument ' |
| 'and 2nd argument must be nonzero ;' |
| '0**0 is not defined') |
| |
| # compute sign of result |
| if other._iseven(): |
| sign = 0 |
| else: |
| sign = self._sign |
| |
| # convert modulo to a Python integer, and self and other to |
| # Decimal integers (i.e. force their exponents to be >= 0) |
| modulo = abs(int(modulo)) |
| base = _WorkRep(self.to_integral_value()) |
| exponent = _WorkRep(other.to_integral_value()) |
| |
| # compute result using integer pow() |
| base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo |
| for i in range(exponent.exp): |
| base = pow(base, 10, modulo) |
| base = pow(base, exponent.int, modulo) |
| |
| return _dec_from_triple(sign, str(base), 0) |
| |
| def _power_exact(self, other, p): |
| """Attempt to compute self**other exactly. |
| |
| Given Decimals self and other and an integer p, attempt to |
| compute an exact result for the power self**other, with p |
| digits of precision. Return None if self**other is not |
| exactly representable in p digits. |
| |
| Assumes that elimination of special cases has already been |
| performed: self and other must both be nonspecial; self must |
| be positive and not numerically equal to 1; other must be |
| nonzero. For efficiency, other._exp should not be too large, |
| so that 10**abs(other._exp) is a feasible calculation.""" |
| |
| # In the comments below, we write x for the value of self and |
| # y for the value of other. Write x = xc*10**xe and y = |
| # yc*10**ye. |
| |
| # The main purpose of this method is to identify the *failure* |
| # of x**y to be exactly representable with as little effort as |
| # possible. So we look for cheap and easy tests that |
| # eliminate the possibility of x**y being exact. Only if all |
| # these tests are passed do we go on to actually compute x**y. |
| |
| # Here's the main idea. First normalize both x and y. We |
| # express y as a rational m/n, with m and n relatively prime |
| # and n>0. Then for x**y to be exactly representable (at |
| # *any* precision), xc must be the nth power of a positive |
| # integer and xe must be divisible by n. If m is negative |
| # then additionally xc must be a power of either 2 or 5, hence |
| # a power of 2**n or 5**n. |
| # |
| # There's a limit to how small |y| can be: if y=m/n as above |
| # then: |
| # |
| # (1) if xc != 1 then for the result to be representable we |
| # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So |
| # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <= |
| # 2**(1/|y|), hence xc**|y| < 2 and the result is not |
| # representable. |
| # |
| # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if |
| # |y| < 1/|xe| then the result is not representable. |
| # |
| # Note that since x is not equal to 1, at least one of (1) and |
| # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) < |
| # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye. |
| # |
| # There's also a limit to how large y can be, at least if it's |
| # positive: the normalized result will have coefficient xc**y, |
| # so if it's representable then xc**y < 10**p, and y < |
| # p/log10(xc). Hence if y*log10(xc) >= p then the result is |
| # not exactly representable. |
| |
| # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye, |
| # so |y| < 1/xe and the result is not representable. |
| # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y| |
| # < 1/nbits(xc). |
| |
| x = _WorkRep(self) |
| xc, xe = x.int, x.exp |
| while xc % 10 == 0: |
| xc //= 10 |
| xe += 1 |
| |
| y = _WorkRep(other) |
| yc, ye = y.int, y.exp |
| while yc % 10 == 0: |
| yc //= 10 |
| ye += 1 |
| |
| # case where xc == 1: result is 10**(xe*y), with xe*y |
| # required to be an integer |
| if xc == 1: |
| if ye >= 0: |
| exponent = xe*yc*10**ye |
| else: |
| exponent, remainder = divmod(xe*yc, 10**-ye) |
| if remainder: |
| return None |
| if y.sign == 1: |
| exponent = -exponent |
| # if other is a nonnegative integer, use ideal exponent |
| if other._isinteger() and other._sign == 0: |
| ideal_exponent = self._exp*int(other) |
| zeros = min(exponent-ideal_exponent, p-1) |
| else: |
| zeros = 0 |
| return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros) |
| |
| # case where y is negative: xc must be either a power |
| # of 2 or a power of 5. |
| if y.sign == 1: |
| last_digit = xc % 10 |
| if last_digit in (2,4,6,8): |
| # quick test for power of 2 |
| if xc & -xc != xc: |
| return None |
| # now xc is a power of 2; e is its exponent |
| e = _nbits(xc)-1 |
| # find e*y and xe*y; both must be integers |
| if ye >= 0: |
| y_as_int = yc*10**ye |
| e = e*y_as_int |
| xe = xe*y_as_int |
| else: |
| ten_pow = 10**-ye |
| e, remainder = divmod(e*yc, ten_pow) |
| if remainder: |
| return None |
| xe, remainder = divmod(xe*yc, ten_pow) |
| if remainder: |
| return None |
| |
| if e*65 >= p*93: # 93/65 > log(10)/log(5) |
| return None |
| xc = 5**e |
| |
| elif last_digit == 5: |
| # e >= log_5(xc) if xc is a power of 5; we have |
| # equality all the way up to xc=5**2658 |
| e = _nbits(xc)*28//65 |
| xc, remainder = divmod(5**e, xc) |
| if remainder: |
| return None |
| while xc % 5 == 0: |
| xc //= 5 |
| e -= 1 |
| if ye >= 0: |
| y_as_integer = yc*10**ye |
| e = e*y_as_integer |
| xe = xe*y_as_integer |
| else: |
| ten_pow = 10**-ye |
| e, remainder = divmod(e*yc, ten_pow) |
| if remainder: |
| return None |
| xe, remainder = divmod(xe*yc, ten_pow) |
| if remainder: |
| return None |
| if e*3 >= p*10: # 10/3 > log(10)/log(2) |
| return None |
| xc = 2**e |
| else: |
| return None |
| |
| if xc >= 10**p: |
| return None |
| xe = -e-xe |
| return _dec_from_triple(0, str(xc), xe) |
| |
| # now y is positive; find m and n such that y = m/n |
| if ye >= 0: |
| m, n = yc*10**ye, 1 |
| else: |
| if xe != 0 and len(str(abs(yc*xe))) <= -ye: |
| return None |
| xc_bits = _nbits(xc) |
| if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye: |
| return None |
| m, n = yc, 10**(-ye) |
| while m % 2 == n % 2 == 0: |
| m //= 2 |
| n //= 2 |
| while m % 5 == n % 5 == 0: |
| m //= 5 |
| n //= 5 |
| |
| # compute nth root of xc*10**xe |
| if n > 1: |
| # if 1 < xc < 2**n then xc isn't an nth power |
| if xc != 1 and xc_bits <= n: |
| return None |
| |
| xe, rem = divmod(xe, n) |
| if rem != 0: |
| return None |
| |
| # compute nth root of xc using Newton's method |
| a = 1 << -(-_nbits(xc)//n) # initial estimate |
| while True: |
| q, r = divmod(xc, a**(n-1)) |
| if a <= q: |
| break |
| else: |
| a = (a*(n-1) + q)//n |
| if not (a == q and r == 0): |
| return None |
| xc = a |
| |
| # now xc*10**xe is the nth root of the original xc*10**xe |
| # compute mth power of xc*10**xe |
| |
| # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m > |
| # 10**p and the result is not representable. |
| if xc > 1 and m > p*100//_log10_lb(xc): |
| return None |
| xc = xc**m |
| xe *= m |
| if xc > 10**p: |
| return None |
| |
| # by this point the result *is* exactly representable |
| # adjust the exponent to get as close as possible to the ideal |
| # exponent, if necessary |
| str_xc = str(xc) |
| if other._isinteger() and other._sign == 0: |
| ideal_exponent = self._exp*int(other) |
| zeros = min(xe-ideal_exponent, p-len(str_xc)) |
| else: |
| zeros = 0 |
| return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros) |
| |
| def __pow__(self, other, modulo=None, context=None): |
| """Return self ** other [ % modulo]. |
| |
| With two arguments, compute self**other. |
| |
| With three arguments, compute (self**other) % modulo. For the |
| three argument form, the following restrictions on the |
| arguments hold: |
| |
| - all three arguments must be integral |
| - other must be nonnegative |
| - either self or other (or both) must be nonzero |
| - modulo must be nonzero and must have at most p digits, |
| where p is the context precision. |
| |
| If any of these restrictions is violated the InvalidOperation |
| flag is raised. |
| |
| The result of pow(self, other, modulo) is identical to the |
| result that would be obtained by computing (self**other) % |
| modulo with unbounded precision, but is computed more |
| efficiently. It is always exact. |
| """ |
| |
| if modulo is not None: |
| return self._power_modulo(other, modulo, context) |
| |
| other = _convert_other(other) |
| if other is NotImplemented: |
| return other |
| |
| if context is None: |
| context = getcontext() |
| |
| # either argument is a NaN => result is NaN |
| ans = self._check_nans(other, context) |
| if ans: |
| return ans |
| |
| # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity) |
| if not other: |
| if not self: |
| return context._raise_error(InvalidOperation, '0 ** 0') |
| else: |
| return _One |
| |
| # result has sign 1 iff self._sign is 1 and other is an odd integer |
| result_sign = 0 |
| if self._sign == 1: |
| if other._isinteger(): |
| if not other._iseven(): |
| result_sign = 1 |
| else: |
| # -ve**noninteger = NaN |
| # (-0)**noninteger = 0**noninteger |
| if self: |
| return context._raise_error(InvalidOperation, |
| 'x ** y with x negative and y not an integer') |
| # negate self, without doing any unwanted rounding |
| self = self.copy_negate() |
| |
| # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity |
| if not self: |
| if other._sign == 0: |
| return _dec_from_triple(result_sign, '0', 0) |
| else: |
| return _SignedInfinity[result_sign] |
| |
| # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 |
| if self._isinfinity(): |
| if other._sign == 0: |
| return _SignedInfinity[result_sign] |
| else: |
| return _dec_from_triple(result_sign, '0', 0) |
| |
| # 1**other = 1, but the choice of exponent and the flags |
| # depend on the exponent of self, and on whether other is a |
| # positive integer, a negative integer, or neither |
| if self == _One: |
| if other._isinteger(): |
| # exp = max(self._exp*max(int(other), 0), |
| # 1-context.prec) but evaluating int(other) directly |
| # is dangerous until we know other is small (other |
| # could be 1e999999999) |
| if other._sign == 1: |
| multiplier = 0 |
| elif other > context.prec: |
| multiplier = context.prec |
| else: |
| multiplier = int(other) |
| |
| exp = self._exp * multiplier |
| if exp < 1-context.prec: |
| exp = 1-context.prec |
| context._raise_error(Rounded) |
| else: |
| context._raise_error(Inexact) |
| context._raise_error(Rounded) |
| exp = 1-context.prec |
| |
| return _dec_from_triple(result_sign, '1'+'0'*-exp, exp) |
| |
| # compute adjusted exponent of self |
| self_adj = self.adjusted() |
| |
| # self ** infinity is infinity if self > 1, 0 if self < 1 |
| # self ** -infinity is infinity if self < 1, 0 if self > 1 |
| if other._isinfinity(): |
| if (other._sign == 0) == (self_adj < 0): |
| return _dec_from_triple(result_sign, '0', 0) |
| else: |
| return _SignedInfinity[result_sign] |
| |
| # from here on, the result always goes through the call |
| # to _fix at the end of this function. |
| ans = None |
| |
| # crude test to catch cases of extreme overflow/underflow. If |
| # log10(self)*other >= 10**bound and bound >= len(str(Emax)) |
| # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence |
| # self**other >= 10**(Emax+1), so overflow occurs. The test |
| # for underflow is similar. |
| bound = self._log10_exp_bound() + other.adjusted() |
| if (self_adj >= 0) == (other._sign == 0): |
| # self > 1 and other +ve, or self < 1 and other -ve |
| # possibility of overflow |
| if bound >= len(str(context.Emax)): |
| ans = _dec_from_triple(result_sign, '1', context.Emax+1) |
| else: |
| # self > 1 and other -ve, or self < 1 and other +ve |
| # possibility of underflow to 0 |
| Etiny = context.Etiny() |
| if bound >= len(str(-Etiny)): |
| ans = _dec_from_triple(result_sign, '1', Etiny-1) |
| |
| # try for an exact result with precision +1 |
| if ans is None: |
| ans = self._power_exact(other, context.prec + 1) |
| if ans is not None and result_sign == 1: |
| ans = _dec_from_triple(1, ans._int, ans._exp) |
| |
| # usual case: inexact result, x**y computed directly as exp(y*log(x)) |
| if ans is None: |
| p = context.prec |
| x = _WorkRep(self) |
| xc, xe = x.int, x.exp |
| y = _WorkRep(other) |
| yc, ye = y.int, y.exp |
| if y.sign == 1: |
| yc = -yc |
| |
| # compute correctly rounded result: start with precision +3, |
| # then increase precision until result is unambiguously roundable |
| extra = 3 |
| while True: |
| coeff, exp = _dpower(xc, xe, yc, ye, p+extra) |
| if coeff % (5*10**(len(str(coeff))-p-1)): |
| break |
| extra += 3 |
| |
| ans = _dec_from_triple(result_sign, str(coeff), exp) |
| |
| # the specification says that for non-integer other we need to |
| # raise Inexact, even when the result is actually exact. In |
| # the same way, we need to raise Underflow here if the result |
| # is subnormal. (The call to _fix will take care of raising |
| # Rounded and Subnormal, as usual.) |
| if not other._isinteger(): |
| context._raise_error(Inexact) |
| # pad with zeros up to length context.prec+1 if necessary |
| if len(ans._int) <= context.prec: |
| expdiff = context.prec+1 - len(ans._int) |
| ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff, |
| ans._exp-expdiff) |
| if ans.adjusted() < context.Emin: |
| context._raise_error(Underflow) |
| |
| # unlike exp, ln and log10, the power function respects the |
| # rounding mode; no need to use ROUND_HALF_EVEN here |
| ans = ans._fix(context) |
| return ans |
| |
| 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 context is None: |
| context = getcontext() |
| |
| 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 _dec_from_triple(dup._sign, '0', 0) |
| exp_max = [context.Emax, context.Etop()][context._clamp] |
| end = len(dup._int) |
| exp = dup._exp |
| while dup._int[end-1] == '0' and exp < exp_max: |
| exp += 1 |
| end -= 1 |
| return _dec_from_triple(dup._sign, dup._int[:end], exp) |
| |
| def quantize(self, exp, rounding=None, context=None, watchexp=True): |
| """Quantize self so its exponent is the same as that of exp. |
| |
| Similar to self._rescale(exp._exp) but with error checking. |
| """ |
| exp = _convert_other(exp, raiseit=True) |
| |
| if context is None: |
| context = getcontext() |
| if rounding is None: |
| rounding = context.rounding |
| |
| 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 Decimal(self) # if both are inf, it is OK |
| return context._raise_error(InvalidOperation, |
| 'quantize with one INF') |
| |
| # if we're not watching exponents, do a simple rescale |
| if not watchexp: |
| ans = self._rescale(exp._exp, rounding) |
| # raise Inexact and Rounded where appropriate |
| if ans._exp > self._exp: |
| context._raise_error(Rounded) |
| if ans != self: |
| context._raise_error(Inexact) |
| return ans |
| |
| # exp._exp should be between Etiny and Emax |
| if not (context.Etiny() <= exp._exp <= context.Emax): |
| return context._raise_error(InvalidOperation, |
| 'target exponent out of bounds in quantize') |
| |
| if not self: |
| ans = _dec_from_triple(self._sign, '0', exp._exp) |
| return ans._fix(context) |
| |
| self_adjusted = self.adjusted() |
| if self_adjusted > context.Emax: |
| return context._raise_error(InvalidOperation, |
| 'exponent of quantize result too large for current context') |
| if self_adjusted - exp._exp + 1 > context.prec: |
| return context._raise_error(InvalidOperation, |
| 'quantize result has too many digits for current context') |
| |
| ans = self._rescale(exp._exp, rounding) |
| if ans.adjusted() > context.Emax: |
| return context._raise_error(InvalidOperation, |
| 'exponent of quantize result too large for current context') |
| if len(ans._int) > context.prec: |
| return context._raise_error(InvalidOperation, |
| 'quantize result has too many digits for current context') |
| |
| # raise appropriate flags |
| if ans._exp > self._exp: |
| context._raise_error(Rounded) |
| if ans != self: |
| context._raise_error(Inexact) |
| if ans and ans.adjusted() < context.Emin: |
| context._raise_error(Subnormal) |
| |
| # call to fix takes care of any necessary folddown |
| ans = ans._fix(context) |
| return ans |
| |
| def same_quantum(self, other): |
| """Return True if self and other have the same exponent; otherwise |
| return False. |
| |
| If either operand is a special value, the following rules are used: |
| * return True if both operands are infinities |
| * return True if both operands are NaNs |
| * otherwise, return False. |
| """ |
| other = _convert_other(other, raiseit=True) |
| if self._is_special or other._is_special: |
| return (self.is_nan() and other.is_nan() or |
| self.is_infinite() and other.is_infinite()) |
| return self._exp == other._exp |
| |
| def _rescale(self, exp, rounding): |
| """Rescale self so that the exponent is exp, either by padding with zeros |
| or by truncating digits, using the given rounding mode. |
| |
| Specials are returned without change. This operation is |
| quiet: it raises no flags, and uses no information from the |
| context. |
| |
| exp = exp to scale to (an integer) |
| rounding = rounding mode |
| """ |
| if self._is_special: |
| return Decimal(self) |
| if not self: |
| return _dec_from_triple(self._sign, '0', exp) |
| |
| if self._exp >= exp: |
| # pad answer with zeros if necessary |
| return _dec_from_triple(self._sign, |
| self._int + '0'*(self._exp - exp), exp) |
| |
| # too many digits; round and lose data. If self.adjusted() < |
| # exp-1, replace self by 10**(exp-1) before rounding |
| digits = len(self._int) + self._exp - exp |
| if digits < 0: |
| self = _dec_from_triple(self._sign, '1', exp-1) |
| digits = 0 |
| this_function = getattr(self, self._pick_rounding_function[rounding]) |
| changed = this_function(digits) |
| coeff = self._int[:digits] or '0' |
| if changed == 1: |
| coeff = str(int(coeff)+1) |
| return _dec_from_triple(self._sign, coeff, exp) |
| |
| def _round(self, places, rounding): |
| """Round a nonzero, nonspecial Decimal to a fixed number of |
| significant figures, using the given rounding mode. |
| |
| Infinities, NaNs and zeros are returned unaltered. |
| |
| This operation is quiet: it raises no flags, and uses no |
| information from the context. |
| |
| """ |
| if places <= 0: |
| raise ValueError("argument should be at least 1 in _round") |
| if self._is_special or not self: |
| return Decimal(self) |
| ans = self._rescale(self.adjusted()+1-places, rounding) |
| # it can happen that the rescale alters the adjusted exponent; |
| # for example when rounding 99.97 to 3 significant figures. |
| # When this happens we end up with an extra 0 at the end of |
| # the number; a second rescale fixes this. |
| if ans.adjusted() != self.adjusted(): |
| ans = ans._rescale(ans.adjusted()+1-places, rounding) |
| return ans |
| |
| def to_integral_exact(self, rounding=None, context=None): |
| """Rounds to a nearby integer. |
| |
| If no rounding mode is specified, take the rounding mode from |
| the context. This method raises the Rounded and Inexact flags |
| when appropriate. |
| |
| See also: to_integral_value, which does exactly the same as |
| this method except that it doesn't raise Inexact or Rounded. |
| """ |
| if self._is_special: |
| ans = self._check_nans(context=context) |
| if ans: |
| return ans |
| return Decimal(self) |
| if self._exp >= 0: |
| return Decimal(self) |
| if not self: |
| return _dec_from_triple(self._sign, '0', 0) |
| if context is None: |
| context = getcontext() |
| if rounding is None: |
| rounding = context.rounding |
| context._raise_error(Rounded) |
| ans = self._rescale(0, rounding) |
| if ans != self: |
| context._raise_error(Inexact) |
| return ans |
| |
| def to_integral_value(self, rounding=None, context=None): |
| """Rounds to the nearest integer, without raising inexact, rounded.""" |
| if context is None: |
| context = getcontext() |
| if rounding is None: |
| rounding = context.rounding |
| if self._is_special: |
| ans = self._check_nans(context=context) |
| if ans: |
| return ans |
| return Decimal(self) |
| if self._exp >= 0: |
| return Decimal(self) |
| else: |
| return self._rescale(0, rounding) |
| |
| # the method name changed, but we provide also the old one, for compatibility |
| to_integral = to_integral_value |
| |
| def sqrt(self, context=None): |
| """Return the square root of self.""" |
| if context is None: |
| context = getcontext() |
| |
| 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. sqrt(-0) = -0 |
| ans = _dec_from_triple(self._sign, '0', self._exp // 2) |
| return ans._fix(context) |
| |
| if self._sign == 1: |
| return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') |
| |
| # At this point self represents a positive number. Let p be |
| # the desired precision and express self in the form c*100**e |
| # with c a positive real number and e an integer, c and e |
| # being chosen so that 100**(p-1) <= c < 100**p. Then the |
| # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) |
| # <= sqrt(c) < 10**p, so the closest representable Decimal at |
| # precision p is n*10**e where n = round_half_even(sqrt(c)), |
| # the closest integer to sqrt(c) with the even integer chosen |
| # in the case of a tie. |
| # |
| # To ensure correct rounding in all cases, we use the |
| # following trick: we compute the square root to an extra |
| # place (precision p+1 instead of precision p), rounding down. |
| # Then, if the result is inexact and its last digit is 0 or 5, |
| # we increase the last digit to 1 or 6 respectively; if it's |
| # exact we leave the last digit alone. Now the final round to |
| # p places (or fewer in the case of underflow) will round |
| # correctly and raise the appropriate flags. |
| |
| # use an extra digit of precision |
| prec = context.prec+1 |
| |
| # write argument in the form c*100**e where e = self._exp//2 |
| # is the 'ideal' exponent, to be used if the square root is |
| # exactly representable. l is the number of 'digits' of c in |
| # base 100, so that 100**(l-1) <= c < 100**l. |
| op = _WorkRep(self) |
| e = op.exp >> 1 |
| if op.exp & 1: |
| c = op.int * 10 |
| l = (len(self._int) >> 1) + 1 |
| else: |
| c = op.int |
| l = len(self._int)+1 >> 1 |
| |
| # rescale so that c has exactly prec base 100 'digits' |
| shift = prec-l |
| if shift >= 0: |
| c *= 100**shift |
| exact = True |
| else: |
| c, remainder = divmod(c, 100**-shift) |
| exact = not remainder |
| e -= shift |
| |
| # find n = floor(sqrt(c)) using Newton's method |
| n = 10**prec |
| while True: |
| q = c//n |
| if n <= q: |
| break |
| else: |
| n = n + q >> 1 |
| exact = exact and n*n == c |
| |
| if exact: |
| # result is exact; rescale to use ideal exponent e |
| if shift >= 0: |
| # assert n % 10**shift == 0 |
| n //= 10**shift |
| else: |
| n *= 10**-shift |
| e += shift |
| else: |
| # result is not exact; fix last digit as described above |
| if n % 5 == 0: |
| n += 1 |
| |
| ans = _dec_from_triple(0, str(n), e) |
| |
| # round, and fit to current context |
| context = context._shallow_copy() |
| rounding = context._set_rounding(ROUND_HALF_EVEN) |
| ans = ans._fix(context) |
| context.rounding = rounding |
| |
| return ans |
| |
| 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, raiseit=True) |
| |
| if context is None: |
| context = getcontext() |
| |
| 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 == 0: |
| return self._fix(context) |
| if sn == 1 and on == 0: |
| return other._fix(context) |
| return self._check_nans(other, context) |
| |
| 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. This is exactly the ordering used in compare_total. |
| c = self.compare_total(other) |
| |
| if c == -1: |
| ans = other |
| else: |
| ans = self |
| |
| return ans._fix(context) |
| |
| 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, raiseit=True) |
| |
| if context is None: |
| context = getcontext() |
| |
| 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 == 0: |
| return self._fix(context) |
| if sn == 1 and on == 0: |
| return other._fix(context) |
| return self._check_nans(other, context) |
| |
| c = self._cmp(other) |
| if c == 0: |
| c = self.compare_total(other) |
| |
| if c == -1: |
| ans = self |
| else: |
| ans = other |
| |
| return ans._fix(context) |
| |
| def _isinteger(self): |
| """Returns whether self is an integer""" |
| if self._is_special: |
| return False |
| if self._exp >= 0: |
| return True |
| rest = self._int[self._exp:] |
| return rest == '0'*len(rest) |
| |
| def _iseven(self): |
| """Returns True if self is even. Assumes self is an integer.""" |
| if not self or self._exp > 0: |
| return True |
| return self._int[-1+self._exp] in '02468' |
| |
| 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 |
| |
| def canonical(self, context=None): |
| """Returns the same Decimal object. |
| |
| As we do not have different encodings for the same number, the |
| received object already is in its canonical form. |
| """ |
| return self |
| |
| def compare_signal(self, other, context=None): |
| """Compares self to the other operand numerically. |
| |
| It's pretty much like compare(), but all NaNs signal, with signaling |
| NaNs taking precedence over quiet NaNs. |
| """ |
| other = _convert_other(other, raiseit = True) |
| ans = self._compare_check_nans(other, context) |
| if ans: |
| return ans |
| return self.compare(other, context=context) |
| |
| def compare_total(self, other): |
| """Compares self to other using the abstract representations. |
| |
| This is not like the standard compare, which use their numerical |
| value. Note that a total ordering is defined for all possible abstract |
| representations. |
| """ |
| # if one is negative and the other is positive, it's easy |
| if self._sign and not other._sign: |
| return _NegativeOne |
| if not self._sign and other._sign: |
| return _One |
| sign = self._sign |
| |
| # let's handle both NaN types |
| self_nan = self._isnan() |
| other_nan = other._isnan() |
| if self_nan or other_nan: |
| if self_nan == other_nan: |
| # compare payloads as though they're integers |
| self_key = len(self._int), self._int |
| other_key = len(other._int), other._int |
| if self_key < other_key: |
| if sign: |
| return _One |
| else: |
| return _NegativeOne |
| if self_key > other_key: |
| if sign: |
| return _NegativeOne |
| else: |
| return _One |
| return _Zero |
| |
| if sign: |
| if self_nan == 1: |
| return _NegativeOne |
| if other_nan == 1: |
| return _One |
| if self_nan == 2: |
| return _NegativeOne |
| if other_nan == 2: |
| return _One |
| else: |
| if self_nan == 1: |
| return _One |
| if other_nan == 1: |
| return _NegativeOne |
| if self_nan == 2: |
| return _One |
| if other_nan == 2: |
| return _NegativeOne |
| |
| if self < other: |
| return _NegativeOne |
| if self > other: |
| return _One |
| |
| if self._exp < other._exp: |
| if sign: |
| return _One |
| else: |
| return _NegativeOne |
| if self._exp > other._exp: |
| if sign: |
| return _NegativeOne |
| else: |
| return _One |
| return _Zero |
| |
| |
| def compare_total_mag(self, other): |
| """Compares self to other using abstract repr., ignoring sign. |
| |
| Like compare_total, but with operand's sign ignored and assumed to be 0. |
| """ |
| s = self.copy_abs() |
| o = other.copy_abs() |
| return s.compare_total(o) |
| |
| def copy_abs(self): |
| """Returns a copy with the sign set to 0. """ |
| return _dec_from_triple(0, self._int, self._exp, self._is_special) |
| |
| def copy_negate(self): |
| """Returns a copy with the sign inverted.""" |
| if self._sign: |
| return _dec_from_triple(0, self._int, self._exp, self._is_special) |
| else: |
| return _dec_from_triple(1, self._int, self._exp, self._is_special) |
| |
| def copy_sign(self, other): |
| """Returns self with the sign of other.""" |
| return _dec_from_triple(other._sign, self._int, |
| self._exp, self._is_special) |
| |
| def exp(self, context=None): |
| """Returns e ** self.""" |
| |
| if context is None: |
| context = getcontext() |
| |
| # exp(NaN) = NaN |
| ans = self._check_nans(context=context) |
| if ans: |
| return ans |
| |
| # exp(-Infinity) = 0 |
| if self._isinfinity() == -1: |
| return _Zero |
| |
| # exp(0) = 1 |
| if not self: |
| return _One |
| |
| # exp(Infinity) = Infinity |
| if self._isinfinity() == 1: |
| return Decimal(self) |
| |
| # the result is now guaranteed to be inexact (the true |
| # mathematical result is transcendental). There's no need to |
| # raise Rounded and Inexact here---they'll always be raised as |
| # a result of the call to _fix. |
| p = context.prec |
| adj = self.adjusted() |
| |
| # we only need to do any computation for quite a small range |
| # of adjusted exponents---for example, -29 <= adj <= 10 for |
| # the default context. For smaller exponent the result is |
| # indistinguishable from 1 at the given precision, while for |
| # larger exponent the result either overflows or underflows. |
| if self._sign == 0 and adj > len(str((context.Emax+1)*3)): |
| # overflow |
| ans = _dec_from_triple(0, '1', context.Emax+1) |
| elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): |
| # underflow to 0 |
| ans = _dec_from_triple(0, '1', context.Etiny()-1) |
| elif self._sign == 0 and adj < -p: |
| # p+1 digits; final round will raise correct flags |
| ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) |
| elif self._sign == 1 and adj < -p-1: |
| # p+1 digits; final round will raise correct flags |
| ans = _dec_from_triple(0, '9'*(p+1), -p-1) |
| # general case |
| else: |
| op = _WorkRep(self) |
| c, e = op.int, op.exp |
| if op.sign == 1: |
| c = -c |
| |
| # compute correctly rounded result: increase precision by |
| # 3 digits at a time until we get an unambiguously |
| # roundable result |
| extra = 3 |
| while True: |
| coeff, exp = _dexp(c, e, p+extra) |
| if coeff % (5*10**(len(str(coeff))-p-1)): |
| break |
| extra += 3 |
| |
| ans = _dec_from_triple(0, str(coeff), exp) |
| |
| # at this stage, ans should round correctly with *any* |
| # rounding mode, not just with ROUND_HALF_EVEN |
| context = context._shallow_copy() |
| rounding = context._set_rounding(ROUND_HALF_EVEN) |
| ans = ans._fix(context) |
| context.rounding = rounding |
| |
| return ans |
| |
| def is_canonical(self): |
| """Return True if self is canonical; otherwise return False. |
| |
| Currently, the encoding of a Decimal instance is always |
| canonical, so this method returns True for any Decimal. |
| """ |
| return True |
| |
| def is_finite(self): |
| """Return True if self is finite; otherwise return False. |
| |
| A Decimal instance is considered finite if it is neither |
| infinite nor a NaN. |
| """ |
| return not self._is_special |
| |
| def is_infinite(self): |
| """Return True if self is infinite; otherwise return False.""" |
| return self._exp == 'F' |
| |
| def is_nan(self): |
| """Return True if self is a qNaN or sNaN; otherwise return False.""" |
| return self._exp in ('n', 'N') |
| |
| def is_normal(self, context=None): |
| """Return True if self is a normal number; otherwise return False.""" |
| if self._is_special or not self: |
| return False |
| if context is None: |
| context = getcontext() |
| return context.Emin <= self.adjusted() |
| |
| def is_qnan(self): |
| """Return True if self is a quiet NaN; otherwise return False.""" |
| return self._exp == 'n' |
| |
| def is_signed(self): |
| """Return True if self is negative; otherwise return False.""" |
| return self._sign == 1 |
| |
| def is_snan(self): |
| """Return True if self is a signaling NaN; otherwise return False.""" |
| return self._exp == 'N' |
| |
| def is_subnormal(self, context=None): |
| """Return True if self is subnormal; otherwise return False.""" |
| if self._is_special or not self: |
| return False |
| if context is None: |
| context = getcontext() |
| return self.adjusted() < context.Emin |
| |
| def is_zero(self): |
| """Return True if self is a zero; otherwise return False.""" |
| return not self._is_special and self._int == '0' |
| |
| def _ln_exp_bound(self): |
| """Compute a lower bound for the adjusted exponent of self.ln(). |
| In other words, compute r such that self.ln() >= 10**r. Assumes |
| that self is finite and positive and that self != 1. |
| """ |
| |
| # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 |
| adj = self._exp + len(self._int) - 1 |
| if adj >= 1: |
| # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) |
| return len(str(adj*23//10)) - 1 |
| if adj <= -2: |
| # argument <= 0.1 |
| return len(str((-1-adj)*23//10)) - 1 |
| op = _WorkRep(self) |
| c, e = op.int, op.exp |
| if adj == 0: |
| # 1 < self < 10 |
| num = str(c-10**-e) |
| den = str(c) |
| return len(num) - len(den) - (num < den) |
| # adj == -1, 0.1 <= self < 1 |
| return e + len(str(10**-e - c)) - 1 |
| |
| |
| def ln(self, context=None): |
| """Returns the natural (base e) logarithm of self.""" |
| |
| if context is None: |
| context = getcontext() |
| |
| # ln(NaN) = NaN |
| ans = self._check_nans(context=context) |
| if ans: |
| return ans |
| |
| # ln(0.0) == -Infinity |
| if not self: |
| return _NegativeInfinity |
| |
| # ln(Infinity) = Infinity |
| if self._isinfinity() == 1: |
| return _Infinity |
| |
| # ln(1.0) == 0.0 |
| if self == _One: |
| return _Zero |
| |
| # ln(negative) raises InvalidOperation |
| if self._sign == 1: |
| return context._raise_error(InvalidOperation, |
| 'ln of a negative value') |
| |
| # result is irrational, so necessarily inexact |
| op = _WorkRep(self) |
| c, e = op.int, op.exp |
| p = context.prec |
| |
| # correctly rounded result: repeatedly increase precision by 3 |
| # until we get an unambiguously roundable result |
| places = p - self._ln_exp_bound() + 2 # at least p+3 places |
| while True: |
| coeff = _dlog(c, e, places) |
| # assert len(str(abs(coeff)))-p >= 1 |
| if coeff % (5*10**(len(str(abs(coeff)))-p-1)): |
| break |
| places += 3 |
| ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) |
| |
| context = context._shallow_copy() |
| rounding = context._set_rounding(ROUND_HALF_EVEN) |
| ans = ans._fix(context) |
| context.rounding = rounding |
| return ans |
| |
| def _log10_exp_bound(self): |
| """Compute a lower bound for the adjusted exponent of self.log10(). |
| In other words, find r such that self.log10() >= 10**r. |
| Assumes that self is finite and positive and that self != 1. |
| """ |
| |
| # For x >= 10 or x < 0.1 we only need a bound on the integer |
| # part of log10(self), and this comes directly from the |
| # exponent of x. For 0.1 <= x <= 10 we use the inequalities |
| # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > |
| # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 |
| |
| adj = self._exp + len(self._int) - 1 |
| if adj >= 1: |
| # self >= 10 |
| return len(str(adj))-1 |
| if adj <= -2: |
| # self < 0.1 |
| return len(str(-1-adj))-1 |
| op = _WorkRep(self) |
| c, e = op.int, op.exp |
| if adj == 0: |
| # 1 < self < 10 |
| num = str(c-10**-e) |
| den = str(231*c) |
| return len(num) - len(den) - (num < den) + 2 |
| # adj == -1, 0.1 <= self < 1 |
| num = str(10**-e-c) |
| return len(num) + e - (num < "231") - 1 |
| |
| def log10(self, context=None): |
| """Returns the base 10 logarithm of self.""" |
| |
| if context is None: |
| context = getcontext() |
| |
| # log10(NaN) = NaN |
| ans = self._check_nans(context=context) |
| if ans: |
| return ans |
| |
| # log10(0.0) == -Infinity |
| if not self: |
| return _NegativeInfinity |
| |
| # log10(Infinity) = Infinity |
| if self._isinfinity() == 1: |
| return _Infinity |
| |
| # log10(negative or -Infinity) raises InvalidOperation |
| if self._sign == 1: |
| return context._raise_error(InvalidOperation, |
| 'log10 of a negative value') |
| |
| # log10(10**n) = n |
| if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): |
| # answer may need rounding |
| ans = Decimal(self._exp + len(self._int) - 1) |
| else: |
| # result is irrational, so necessarily inexact |
| op = _WorkRep(self) |
| c, e = op.int, op.exp |
| p = context.prec |
| |
| # correctly rounded result: repeatedly increase precision |
| # until result is unambiguously roundable |
| places = p-self._log10_exp_bound()+2 |
| while True: |
| coeff = _dlog10(c, e, places) |
| # assert len(str(abs(coeff)))-p >= 1 |
| if coeff % (5*10**(len(str(abs(coeff)))-p-1)): |
| break |
| places += 3 |
| ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) |
| |
| context = context._shallow_copy() |
| rounding = context._set_rounding(ROUND_HALF_EVEN) |
| ans = ans._fix(context) |
| context.rounding = rounding |
| return ans |
| |
| def logb(self, context=None): |
| """ Returns the exponent of the magnitude of self's MSD. |
| |
| The result is the integer which is the exponent of the magnitude |
| of the most significant digit of self (as though it were truncated |
| to a single digit while maintaining the value of that digit and |
| without limiting the resulting exponent). |
| """ |
| # logb(NaN) = NaN |
| ans = self._check_nans(context=context) |
| if ans: |
| return ans |
| |
| if context is None: |
| context = getcontext() |
| |
| # logb(+/-Inf) = +Inf |
| if self._isinfinity(): |
| return _Infinity |
| |
| # logb(0) = -Inf, DivisionByZero |
| if not self: |
| return context._raise_error(DivisionByZero, 'logb(0)', 1) |
| |
| # otherwise, simply return the adjusted exponent of self, as a |
| # Decimal. Note that no attempt is made to fit the result |
| # into the current context. |
| ans = Decimal(self.adjusted()) |
| return ans._fix(context) |
| |
| def _islogical(self): |
| """Return True if self is a logical operand. |
| |
| For being logical, it must be a finite number with a sign of 0, |
| an exponent of 0, and a coefficient whose digits must all be |
| either 0 or 1. |
| """ |
| if self._sign != 0 or self._exp != 0: |
| return False |
| for dig in self._int: |
| if dig not in '01': |
| return False |
| return True |
| |
| def _fill_logical(self, context, opa, opb): |
| dif = context.prec - len(opa) |
| if dif > 0: |
| opa = '0'*dif + opa |
| elif dif < 0: |
| opa = opa[-context.prec:] |
| dif = context.prec - len(opb) |
| if dif > 0: |
| opb = '0'*dif + opb |
| elif dif < 0: |
| opb = opb[-context.prec:] |
| return opa, opb |
| |
| def logical_and(self, other, context=None): |
| """Applies an 'and' operation between self and other's digits.""" |
| if context is None: |
| context = getcontext() |
| if not self._islogical() or not other._islogical(): |
| return context._raise_error(InvalidOperation) |
| |
| # fill to context.prec |
| (opa, opb) = self._fill_logical(context, self._int, other._int) |
| |
| # make the operation, and clean starting zeroes |
| result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) |
| return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
| |
| def logical_invert(self, context=None): |
| """Invert all its digits.""" |
| if context is None: |
| context = getcontext() |
| return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), |
| context) |
| |
| def logical_or(self, other, context=None): |
| """Applies an 'or' operation between self and other's digits.""" |
| if context is None: |
| context = getcontext() |
| if not self._islogical() or not other._islogical(): |
| return context._raise_error(InvalidOperation) |
| |
| # fill to context.prec |
| (opa, opb) = self._fill_logical(context, self._int, other._int) |
| |
| # make the operation, and clean starting zeroes |
| result = "".join([str(int(a)|int(b)) for a,b in zip(opa,opb)]) |
| return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
| |
| def logical_xor(self, other, context=None): |
| """Applies an 'xor' operation between self and other's digits.""" |
| if context is None: |
| context = getcontext() |
| if not self._islogical() or not other._islogical(): |
| return context._raise_error(InvalidOperation) |
| |
| # fill to context.prec |
| (opa, opb) = self._fill_logical(context, self._int, other._int) |
| |
| # make the operation, and clean starting zeroes |
| result = "".join([str(int(a)^int(b)) for a,b in zip(opa,opb)]) |
| return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
| |
| def max_mag(self, other, context=None): |
| """Compares the values numerically with their sign ignored.""" |
| other = _convert_other(other, raiseit=True) |
| |
| if context is None: |
| context = getcontext() |
| |
| 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 == 0: |
| return self._fix(context) |
| if sn == 1 and on == 0: |
| return other._fix(context) |
| return self._check_nans(other, context) |
| |
| c = self.copy_abs()._cmp(other.copy_abs()) |
| if c == 0: |
| c = self.compare_total(other) |
| |
| if c == -1: |
| ans = other |
| else: |
| ans = self |
| |
| return ans._fix(context) |
| |
| def min_mag(self, other, context=None): |
| """Compares the values numerically with their sign ignored.""" |
| other = _convert_other(other, raiseit=True) |
| |
| if context is None: |
| context = getcontext() |
| |
| 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 == 0: |
| return self._fix(context) |
| if sn == 1 and on == 0: |
| return other._fix(context) |
| return self._check_nans(other, context) |
| |
| c = self.copy_abs()._cmp(other.copy_abs()) |
| if c == 0: |
| c = self.compare_total(other) |
| |
| if c == -1: |
| ans = self |
| else: |
| ans = other |
| |
| return ans._fix(context) |
| |
| def next_minus(self, context=None): |
| """Returns the largest representable number smaller than itself.""" |
| if context is None: |
| context = getcontext() |
| |
| ans = self._check_nans(context=context) |
| if ans: |
| return ans |
| |
| if self._isinfinity() == -1: |
| return _NegativeInfinity |
| if self._isinfinity() == 1: |
| return _dec_from_triple(0, '9'*context.prec, context.Etop()) |
| |
| context = context.copy() |
| context._set_rounding(ROUND_FLOOR) |
| context._ignore_all_flags() |
| new_self = self._fix(context) |
| if new_self != self: |
| return new_self |
| return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), |
| context) |
| |
| def next_plus(self, context=None): |
| """Returns the smallest representable number larger than itself.""" |
| if context is None: |
| context = getcontext() |
| |
| ans = self._check_nans(context=context) |
| if ans: |
| return ans |
| |
| if self._isinfinity() == 1: |
| return _Infinity |
| if self._isinfinity() == -1: |
| return _dec_from_triple(1, '9'*context.prec, context.Etop()) |
| |
| context = context.copy() |
| context._set_rounding(ROUND_CEILING) |
| context._ignore_all_flags() |
| new_self = self._fix(context) |
| if new_self != self: |
| return new_self |
| return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), |
| context) |
| |
| def next_toward(self, other, context=None): |
| """Returns the number closest to self, in the direction towards other. |
| |
| The result is the closest representable number to self |
| (excluding self) that is in the direction towards other, |
| unless both have the same value. If the two operands are |
| numerically equal, then the result is a copy of self with the |
| sign set to be the same as the sign of other. |
| """ |
| other = _convert_other(other, raiseit=True) |
| |
| if context is None: |
| context = getcontext() |
| |
| ans = self._check_nans(other, context) |
| if ans: |
| return ans |
| |
| comparison = self._cmp(other) |
| if comparison == 0: |
| return self.copy_sign(other) |
| |
| if comparison == -1: |
| ans = self.next_plus(context) |
| else: # comparison == 1 |
| ans = self.next_minus(context) |
| |
| # decide which flags to raise using value of ans |
| if ans._isinfinity(): |
| context._raise_error(Overflow, |
| 'Infinite result from next_toward', |
| ans._sign) |
| context._raise_error(Rounded) |
| context._raise_error(Inexact) |
| elif ans.adjusted() < context.Emin: |
| context._raise_error(Underflow) |
| context._raise_error(Subnormal) |
| context._raise_error(Rounded) |
| context._raise_error(Inexact) |
| # if precision == 1 then we don't raise Clamped for a |
| # result 0E-Etiny. |
| if not ans: |
| context._raise_error(Clamped) |
| |
| return ans |
| |
| def number_class(self, context=None): |
| """Returns an indication of the class of self. |
| |
| The class is one of the following strings: |
| sNaN |
| NaN |
| -Infinity |
| -Normal |
| -Subnormal |
| -Zero |
| +Zero |
| +Subnormal |
| +Normal |
| +Infinity |
| """ |
| if self.is_snan(): |
| return "sNaN" |
| if self.is_qnan(): |
| return "NaN" |
| inf = self._isinfinity() |
| if inf == 1: |
| return "+Infinity" |
| if inf == -1: |
| return "-Infinity" |
| if self.is_zero(): |
| if self._sign: |
| return "-Zero" |
| else: |
| return "+Zero" |
| if context is None: |
| context = getcontext() |
| if self.is_subnormal(context=context): |
| if self._sign: |
| return "-Subnormal" |
| else: |
| return "+Subnormal" |
| # just a normal, regular, boring number, :) |
| if self._sign: |
| return "-Normal" |
| else: |
| return "+Normal" |
| |
| def radix(self): |
| """Just returns 10, as this is Decimal, :)""" |
| return Decimal(10) |
| |
| def rotate(self, other, context=None): |
| """Returns a rotated copy of self, value-of-other times.""" |
| if context is None: |
| context = getcontext() |
| |
| ans = self._check_nans(other, context) |
| if ans: |
| return ans |
| |
| if other._exp != 0: |
| return context._raise_error(InvalidOperation) |
| if not (-context.prec <= int(other) <= context.prec): |
| return context._raise_error(InvalidOperation) |
| |
| if self._isinfinity(): |
| return Decimal(self) |
| |
| # get values, pad if necessary |
| torot = int(other) |
| rotdig = self._int |
| topad = context.prec - len(rotdig) |
| if topad: |
| rotdig = '0'*topad + rotdig |
| |
| # let's rotate! |
| rotated = rotdig[torot:] + rotdig[:torot] |
| return _dec_from_triple(self._sign, |
| rotated.lstrip('0') or '0', self._exp) |
| |
| def scaleb (self, other, context=None): |
| """Returns self operand after adding the second value to its exp.""" |
| if context is None: |
| context = getcontext() |
| |
| ans = self._check_nans(other, context) |
| if ans: |
| return ans |
| |
| if other._exp != 0: |
| return context._raise_error(InvalidOperation) |
| liminf = -2 * (context.Emax + context.prec) |
| limsup = 2 * (context.Emax + context.prec) |
| if not (liminf <= int(other) <= limsup): |
| return context._raise_error(InvalidOperation) |
| |
| if self._isinfinity(): |
| return Decimal(self) |
| |
| d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) |
| d = d._fix(context) |
| return d |
| |
| def shift(self, other, context=None): |
| """Returns a shifted copy of self, value-of-other times.""" |
| if context is None: |
| context = getcontext() |
| |
| ans = self._check_nans(other, context) |
| if ans: |
| return ans |
| |
| if other._exp != 0: |
| return context._raise_error(InvalidOperation) |
| if not (-context.prec <= int(other) <= context.prec): |
| return context._raise_error(InvalidOperation) |
| |
| if self._isinfinity(): |
| return Decimal(self) |
| |
| # get values, pad if necessary |
| torot = int(other) |
| if not torot: |
| return Decimal(self) |
| rotdig = self._int |
| topad = context.prec - len(rotdig) |
| if topad: |
| rotdig = '0'*topad + rotdig |
| |
| # let's shift! |
| if torot < 0: |
| rotated = rotdig[:torot] |
| else: |
| rotated = rotdig + '0'*torot |
| rotated = rotated[-context.prec:] |
| |
| return _dec_from_triple(self._sign, |
| rotated.lstrip('0') or '0', self._exp) |
| |
| # 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)) |
| |
| # PEP 3101 support. the _localeconv keyword argument should be |
| # considered private: it's provided for ease of testing only. |
| def __format__(self, specifier, context=None, _localeconv=None): |
| """Format a Decimal instance according to the given specifier. |
| |
| The specifier should be a standard format specifier, with the |
| form described in PEP 3101. Formatting types 'e', 'E', 'f', |
| 'F', 'g', 'G', 'n' and '%' are supported. If the formatting |
| type is omitted it defaults to 'g' or 'G', depending on the |
| value of context.capitals. |
| """ |
| |
| # Note: PEP 3101 says that if the type is not present then |
| # there should be at least one digit after the decimal point. |
| # We take the liberty of ignoring this requirement for |
| # Decimal---it's presumably there to make sure that |
| # format(float, '') behaves similarly to str(float). |
| if context is None: |
| context = getcontext() |
| |
| spec = _parse_format_specifier(specifier, _localeconv=_localeconv) |
| |
| # special values don't care about the type or precision |
| if self._is_special: |
| sign = _format_sign(self._sign, spec) |
| body = str(self.copy_abs()) |
| return _format_align(sign, body, spec) |
| |
| # a type of None defaults to 'g' or 'G', depending on context |
| if spec['type'] is None: |
| spec['type'] = ['g', 'G'][context.capitals] |
| |
| # if type is '%', adjust exponent of self accordingly |
| if spec['type'] == '%': |
| self = _dec_from_triple(self._sign, self._int, self._exp+2) |
| |
| # round if necessary, taking rounding mode from the context |
| rounding = context.rounding |
| precision = spec['precision'] |
| if precision is not None: |
| if spec['type'] in 'eE': |
| self = self._round(precision+1, rounding) |
| elif spec['type'] in 'fF%': |
| self = self._rescale(-precision, rounding) |
| elif spec['type'] in 'gG' and len(self._int) > precision: |
| self = self._round(precision, rounding) |
| # special case: zeros with a positive exponent can't be |
| # represented in fixed point; rescale them to 0e0. |
| if not self and self._exp > 0 and spec['type'] in 'fF%': |
| self = self._rescale(0, rounding) |
| |
| # figure out placement of the decimal point |
| leftdigits = self._exp + len(self._int) |
| if spec['type'] in 'eE': |
| if not self and precision is not None: |
| dotplace = 1 - precision |
| else: |
| dotplace = 1 |
| elif spec['type'] in 'fF%': |
| dotplace = leftdigits |
| elif spec['type'] in 'gG': |
| if self._exp <= 0 and leftdigits > -6: |
| dotplace = leftdigits |
| else: |
| dotplace = 1 |
| |
| # find digits before and after decimal point, and get exponent |
| if dotplace < 0: |
| intpart = '0' |
| fracpart = '0'*(-dotplace) + self._int |
| elif dotplace > len(self._int): |
| intpart = self._int + '0'*(dotplace-len(self._int)) |
| fracpart = '' |
| else: |
| intpart = self._int[:dotplace] or '0' |
| fracpart = self._int[dotplace:] |
| exp = leftdigits-dotplace |
| |
| # done with the decimal-specific stuff; hand over the rest |
| # of the formatting to the _format_number function |
| return _format_number(self._sign, intpart, fracpart, exp, spec) |
| |
| def _dec_from_triple(sign, coefficient, exponent, special=False): |
| """Create a decimal instance directly, without any validation, |
| normalization (e.g. removal of leading zeros) or argument |
| conversion. |
| |
| This function is for *internal use only*. |
| """ |
| |
| self = object.__new__(Decimal) |
| self._sign = sign |
| self._int = coefficient |
| self._exp = exponent |
| self._is_special = special |
| |
| return self |
| |
| # Register Decimal as a kind of Number (an abstract base class). |
| # However, do not register it as Real (because Decimals are not |
| # interoperable with floats). |
| _numbers.Number.register(Decimal) |
| |
| |
| ##### 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 _ContextManager(object): |
| """Context manager class to support localcontext(). |
| |
| Sets a copy of the supplied context in __enter__() and restores |
| the previous decimal context in __exit__() |
| """ |
| def __init__(self, new_context): |
| self.new_context = new_context.copy() |
| def __enter__(self): |
| self.saved_context = getcontext() |
| setcontext(self.new_context) |
| return self.new_context |
| def __exit__(self, t, v, tb): |
| setcontext(self.saved_context) |
| |
| class Context(object): |
| """Contains the context for a Decimal instance. |
| |
| Contains: |
| prec - precision (for use in rounding, division, square roots..) |
| rounding - rounding type (how you round) |
| 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 set. |
| (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, |
| 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, int(s in flags)) for s in _signals]) |
| if traps is not None and not isinstance(traps, dict): |
| traps = dict([(s, int(s in traps)) for s in _signals]) |
| 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)) |
| names = [f.__name__ for f, v in self.flags.items() if v] |
| s.append('flags=[' + ', '.join(names) + ']') |
| names = [t.__name__ for t, v in self.traps.items() if v] |
| s.append('traps=[' + ', '.join(names) + ']') |
| return ', '.join(s) + ')' |
| |
| 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.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.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 sets the flag, then, if the corresponding |
| trap_enabler is set, it reaises the exception. Otherwise, it returns |
| the default value after setting 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) |
| |
| # We inherit object.__hash__, so we must deny this explicitly |
| __hash__ = None |
| |
| 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(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. |
| |
| This method implements the to-number operation of the |
| IBM Decimal specification.""" |
| |
| if isinstance(num, str) and num != num.strip(): |
| return self._raise_error(ConversionSyntax, |
| "no trailing or leading whitespace is " |
| "permitted.") |
| |
| d = Decimal(num, context=self) |
| if d._isnan() and len(d._int) > self.prec - self._clamp: |
| return self._raise_error(ConversionSyntax, |
| "diagnostic info too long in NaN") |
| return d._fix(self) |
| |
| def create_decimal_from_float(self, f): |
| """Creates a new Decimal instance from a float but rounding using self |
| as the context. |
| |
| >>> context = Context(prec=5, rounding=ROUND_DOWN) |
| >>> context.create_decimal_from_float(3.1415926535897932) |
| Decimal('3.1415') |
| >>> context = Context(prec=5, traps=[Inexact]) |
| >>> context.create_decimal_from_float(3.1415926535897932) |
| Traceback (most recent call last): |
| ... |
| decimal.Inexact: None |
| |
| """ |
| d = Decimal.from_float(f) # An exact conversion |
| return d._fix(self) # Apply the context rounding |
| |
| # 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 canonical(self, a): |
| """Returns the same Decimal object. |
| |
| As we do not have different encodings for the same number, the |
| received object already is in its canonical form. |
| |
| >>> ExtendedContext.canonical(Decimal('2.50')) |
| Decimal('2.50') |
| """ |
| return a.canonical(context=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 compare_signal(self, a, b): |
| """Compares the values of the two operands numerically. |
| |
| It's pretty much like compare(), but all NaNs signal, with signaling |
| NaNs taking precedence over quiet NaNs. |
| |
| >>> c = ExtendedContext |
| >>> c.compare_signal(Decimal('2.1'), Decimal('3')) |
| Decimal('-1') |
| >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) |
| Decimal('0') |
| >>> c.flags[InvalidOperation] = 0 |
| >>> print(c.flags[InvalidOperation]) |
| 0 |
| >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) |
| Decimal('NaN') |
| >>> print(c.flags[InvalidOperation]) |
| 1 |
| >>> c.flags[InvalidOperation] = 0 |
| >>> print(c.flags[InvalidOperation]) |
| 0 |
| >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) |
| Decimal('NaN') |
| >>> print(c.flags[InvalidOperation]) |
| 1 |
| """ |
| return a.compare_signal(b, context=self) |
| |
| def compare_total(self, a, b): |
| """Compares two operands using their abstract representation. |
| |
| This is not like the standard compare, which use their numerical |
| value. Note that a total ordering is defined for all possible abstract |
| representations. |
| |
| >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) |
| Decimal('-1') |
| >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) |
| Decimal('-1') |
| >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) |
| Decimal('-1') |
| >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) |
| Decimal('0') |
| >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) |
| Decimal('1') |
| >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) |
| Decimal('-1') |
| """ |
| return a.compare_total(b) |
| |
| def compare_total_mag(self, a, b): |
| """Compares two operands using their abstract representation ignoring sign. |
| |
| Like compare_total, but with operand's sign ignored and assumed to be 0. |
| """ |
| return a.compare_total_mag(b) |
| |
| def copy_abs(self, a): |
| """Returns a copy of the operand with the sign set to 0. |
| |
| >>> ExtendedContext.copy_abs(Decimal('2.1')) |
| Decimal('2.1') |
| >>> ExtendedContext.copy_abs(Decimal('-100')) |
| Decimal('100') |
| """ |
| return a.copy_abs() |
| |
| def copy_decimal(self, a): |
| """Returns a copy of the decimal objet. |
| |
| >>> ExtendedContext.copy_decimal(Decimal('2.1')) |
| Decimal('2.1') |
| >>> ExtendedContext.copy_decimal(Decimal('-1.00')) |
| Decimal('-1.00') |
| """ |
| return Decimal(a) |
| |
| def copy_negate(self, a): |
| """Returns a copy of the operand with the sign inverted. |
| |
| >>> ExtendedContext.copy_negate(Decimal('101.5')) |
| Decimal('-101.5') |
| >>> ExtendedContext.copy_negate(Decimal('-101.5')) |
| Decimal('101.5') |
| """ |
| return a.copy_negate() |
| |
| def copy_sign(self, a, b): |
| """Copies the second operand's sign to the first one. |
| |
| In detail, it returns a copy of the first operand with the sign |
| equal to the sign of the second operand. |
| |
| >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) |
| Decimal('1.50') |
| >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) |
| Decimal('1.50') |
| >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) |
| Decimal('-1.50') |
| >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) |
| Decimal('-1.50') |
| """ |
| return a.copy_sign(b) |
| |
| 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.__truediv__(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 exp(self, a): |
| """Returns e ** a. |
| |
| >>> c = ExtendedContext.copy() |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> c.exp(Decimal('-Infinity')) |
| Decimal('0') |
| >>> c.exp(Decimal('-1')) |
| Decimal('0.367879441') |
| >>> c.exp(Decimal('0')) |
| Decimal('1') |
| >>> c.exp(Decimal('1')) |
| Decimal('2.71828183') |
| >>> c.exp(Decimal('0.693147181')) |
| Decimal('2.00000000') |
| >>> c.exp(Decimal('+Infinity')) |
| Decimal('Infinity') |
| """ |
| return a.exp(context=self) |
| |
| def fma(self, a, b, c): |
| """Returns a multiplied by b, plus c. |
| |
| The first two operands are multiplied together, using multiply, |
| the third operand is then added to the result of that |
| multiplication, using add, all with only one final rounding. |
| |
| >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) |
| Decimal('22') |
| >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) |
| Decimal('-8') |
| >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) |
| Decimal('1.38435736E+12') |
| """ |
| return a.fma(b, c, context=self) |
| |
| def is_canonical(self, a): |
| """Return True if the operand is canonical; otherwise return False. |
| |
| Currently, the encoding of a Decimal instance is always |
| canonical, so this method returns True for any Decimal. |
| |
| >>> ExtendedContext.is_canonical(Decimal('2.50')) |
| True |
| """ |
| return a.is_canonical() |
| |
| def is_finite(self, a): |
| """Return True if the operand is finite; otherwise return False. |
| |
| A Decimal instance is considered finite if it is neither |
| infinite nor a NaN. |
| |
| >>> ExtendedContext.is_finite(Decimal('2.50')) |
| True |
| >>> ExtendedContext.is_finite(Decimal('-0.3')) |
| True |
| >>> ExtendedContext.is_finite(Decimal('0')) |
| True |
| >>> ExtendedContext.is_finite(Decimal('Inf')) |
| False |
| >>> ExtendedContext.is_finite(Decimal('NaN')) |
| False |
| """ |
| return a.is_finite() |
| |
| def is_infinite(self, a): |
| """Return True if the operand is infinite; otherwise return False. |
| |
| >>> ExtendedContext.is_infinite(Decimal('2.50')) |
| False |
| >>> ExtendedContext.is_infinite(Decimal('-Inf')) |
| True |
| >>> ExtendedContext.is_infinite(Decimal('NaN')) |
| False |
| """ |
| return a.is_infinite() |
| |
| def is_nan(self, a): |
| """Return True if the operand is a qNaN or sNaN; |
| otherwise return False. |
| |
| >>> ExtendedContext.is_nan(Decimal('2.50')) |
| False |
| >>> ExtendedContext.is_nan(Decimal('NaN')) |
| True |
| >>> ExtendedContext.is_nan(Decimal('-sNaN')) |
| True |
| """ |
| return a.is_nan() |
| |
| def is_normal(self, a): |
| """Return True if the operand is a normal number; |
| otherwise return False. |
| |
| >>> c = ExtendedContext.copy() |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> c.is_normal(Decimal('2.50')) |
| True |
| >>> c.is_normal(Decimal('0.1E-999')) |
| False |
| >>> c.is_normal(Decimal('0.00')) |
| False |
| >>> c.is_normal(Decimal('-Inf')) |
| False |
| >>> c.is_normal(Decimal('NaN')) |
| False |
| """ |
| return a.is_normal(context=self) |
| |
| def is_qnan(self, a): |
| """Return True if the operand is a quiet NaN; otherwise return False. |
| |
| >>> ExtendedContext.is_qnan(Decimal('2.50')) |
| False |
| >>> ExtendedContext.is_qnan(Decimal('NaN')) |
| True |
| >>> ExtendedContext.is_qnan(Decimal('sNaN')) |
| False |
| """ |
| return a.is_qnan() |
| |
| def is_signed(self, a): |
| """Return True if the operand is negative; otherwise return False. |
| |
| >>> ExtendedContext.is_signed(Decimal('2.50')) |
| False |
| >>> ExtendedContext.is_signed(Decimal('-12')) |
| True |
| >>> ExtendedContext.is_signed(Decimal('-0')) |
| True |
| """ |
| return a.is_signed() |
| |
| def is_snan(self, a): |
| """Return True if the operand is a signaling NaN; |
| otherwise return False. |
| |
| >>> ExtendedContext.is_snan(Decimal('2.50')) |
| False |
| >>> ExtendedContext.is_snan(Decimal('NaN')) |
| False |
| >>> ExtendedContext.is_snan(Decimal('sNaN')) |
| True |
| """ |
| return a.is_snan() |
| |
| def is_subnormal(self, a): |
| """Return True if the operand is subnormal; otherwise return False. |
| |
| >>> c = ExtendedContext.copy() |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> c.is_subnormal(Decimal('2.50')) |
| False |
| >>> c.is_subnormal(Decimal('0.1E-999')) |
| True |
| >>> c.is_subnormal(Decimal('0.00')) |
| False |
| >>> c.is_subnormal(Decimal('-Inf')) |
| False |
| >>> c.is_subnormal(Decimal('NaN')) |
| False |
| """ |
| return a.is_subnormal(context=self) |
| |
| def is_zero(self, a): |
| """Return True if the operand is a zero; otherwise return False. |
| |
| >>> ExtendedContext.is_zero(Decimal('0')) |
| True |
| >>> ExtendedContext.is_zero(Decimal('2.50')) |
| False |
| >>> ExtendedContext.is_zero(Decimal('-0E+2')) |
| True |
| """ |
| return a.is_zero() |
| |
| def ln(self, a): |
| """Returns the natural (base e) logarithm of the operand. |
| |
| >>> c = ExtendedContext.copy() |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> c.ln(Decimal('0')) |
| Decimal('-Infinity') |
| >>> c.ln(Decimal('1.000')) |
| Decimal('0') |
| >>> c.ln(Decimal('2.71828183')) |
| Decimal('1.00000000') |
| >>> c.ln(Decimal('10')) |
| Decimal('2.30258509') |
| >>> c.ln(Decimal('+Infinity')) |
| Decimal('Infinity') |
| """ |
| return a.ln(context=self) |
| |
| def log10(self, a): |
| """Returns the base 10 logarithm of the operand. |
| |
| >>> c = ExtendedContext.copy() |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> c.log10(Decimal('0')) |
| Decimal('-Infinity') |
| >>> c.log10(Decimal('0.001')) |
| Decimal('-3') |
| >>> c.log10(Decimal('1.000')) |
| Decimal('0') |
| >>> c.log10(Decimal('2')) |
| Decimal('0.301029996') |
| >>> c.log10(Decimal('10')) |
| Decimal('1') |
| >>> c.log10(Decimal('70')) |
| Decimal('1.84509804') |
| >>> c.log10(Decimal('+Infinity')) |
| Decimal('Infinity') |
| """ |
| return a.log10(context=self) |
| |
| def logb(self, a): |
| """ Returns the exponent of the magnitude of the operand's MSD. |
| |
| The result is the integer which is the exponent of the magnitude |
| of the most significant digit of the operand (as though the |
| operand were truncated to a single digit while maintaining the |
| value of that digit and without limiting the resulting exponent). |
| |
| >>> ExtendedContext.logb(Decimal('250')) |
| Decimal('2') |
| >>> ExtendedContext.logb(Decimal('2.50')) |
| Decimal('0') |
| >>> ExtendedContext.logb(Decimal('0.03')) |
| Decimal('-2') |
| >>> ExtendedContext.logb(Decimal('0')) |
| Decimal('-Infinity') |
| """ |
| return a.logb(context=self) |
| |
| def logical_and(self, a, b): |
| """Applies the logical operation 'and' between each operand's digits. |
| |
| The operands must be both logical numbers. |
| |
| >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) |
| Decimal('0') |
| >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) |
| Decimal('0') |
| >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) |
| Decimal('0') |
| >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) |
| Decimal('1') |
| >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) |
| Decimal('1000') |
| >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) |
| Decimal('10') |
| """ |
| return a.logical_and(b, context=self) |
| |
| def logical_invert(self, a): |
| """Invert all the digits in the operand. |
| |
| The operand must be a logical number. |
| |
| >>> ExtendedContext.logical_invert(Decimal('0')) |
| Decimal('111111111') |
| >>> ExtendedContext.logical_invert(Decimal('1')) |
| Decimal('111111110') |
| >>> ExtendedContext.logical_invert(Decimal('111111111')) |
| Decimal('0') |
| >>> ExtendedContext.logical_invert(Decimal('101010101')) |
| Decimal('10101010') |
| """ |
| return a.logical_invert(context=self) |
| |
| def logical_or(self, a, b): |
| """Applies the logical operation 'or' between each operand's digits. |
| |
| The operands must be both logical numbers. |
| |
| >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) |
| Decimal('0') |
| >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) |
| Decimal('1') |
| >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) |
| Decimal('1') |
| >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) |
| Decimal('1') |
| >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) |
| Decimal('1110') |
| >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) |
| Decimal('1110') |
| """ |
| return a.logical_or(b, context=self) |
| |
| def logical_xor(self, a, b): |
| """Applies the logical operation 'xor' between each operand's digits. |
| |
| The operands must be both logical numbers. |
| |
| >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) |
| Decimal('0') |
| >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) |
| Decimal('1') |
| >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) |
| Decimal('1') |
| >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) |
| Decimal('0') |
| >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) |
| Decimal('110') |
| >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) |
| Decimal('1101') |
| """ |
| return a.logical_xor(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 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 max_mag(self, a, b): |
| """Compares the values numerically with their sign ignored.""" |
| return a.max_mag(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 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 min_mag(self, a, b): |
| """Compares the values numerically with their sign ignored.""" |
| return a.min_mag(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 next_minus(self, a): |
| """Returns the largest representable number smaller than a. |
| |
| >>> c = ExtendedContext.copy() |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> ExtendedContext.next_minus(Decimal('1')) |
| Decimal('0.999999999') |
| >>> c.next_minus(Decimal('1E-1007')) |
| Decimal('0E-1007') |
| >>> ExtendedContext.next_minus(Decimal('-1.00000003')) |
| Decimal('-1.00000004') |
| >>> c.next_minus(Decimal('Infinity')) |
| Decimal('9.99999999E+999') |
| """ |
| return a.next_minus(context=self) |
| |
| def next_plus(self, a): |
| """Returns the smallest representable number larger than a. |
| |
| >>> c = ExtendedContext.copy() |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> ExtendedContext.next_plus(Decimal('1')) |
| Decimal('1.00000001') |
| >>> c.next_plus(Decimal('-1E-1007')) |
| Decimal('-0E-1007') |
| >>> ExtendedContext.next_plus(Decimal('-1.00000003')) |
| Decimal('-1.00000002') |
| >>> c.next_plus(Decimal('-Infinity')) |
| Decimal('-9.99999999E+999') |
| """ |
| return a.next_plus(context=self) |
| |
| def next_toward(self, a, b): |
| """Returns the number closest to a, in direction towards b. |
| |
| The result is the closest representable number from the first |
| operand (but not the first operand) that is in the direction |
| towards the second operand, unless the operands have the same |
| value. |
| |
| >>> c = ExtendedContext.copy() |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> c.next_toward(Decimal('1'), Decimal('2')) |
| Decimal('1.00000001') |
| >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) |
| Decimal('-0E-1007') |
| >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) |
| Decimal('-1.00000002') |
| >>> c.next_toward(Decimal('1'), Decimal('0')) |
| Decimal('0.999999999') |
| >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) |
| Decimal('0E-1007') |
| >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) |
| Decimal('-1.00000004') |
| >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) |
| Decimal('-0.00') |
| """ |
| return a.next_toward(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 number_class(self, a): |
| """Returns an indication of the class of the operand. |
| |
| The class is one of the following strings: |
| -sNaN |
| -NaN |
| -Infinity |
| -Normal |
| -Subnormal |
| -Zero |
| +Zero |
| +Subnormal |
| +Normal |
| +Infinity |
| |
| >>> c = Context(ExtendedContext) |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> c.number_class(Decimal('Infinity')) |
| '+Infinity' |
| >>> c.number_class(Decimal('1E-10')) |
| '+Normal' |
| >>> c.number_class(Decimal('2.50')) |
| '+Normal' |
| >>> c.number_class(Decimal('0.1E-999')) |
| '+Subnormal' |
| >>> c.number_class(Decimal('0')) |
| '+Zero' |
| >>> c.number_class(Decimal('-0')) |
| '-Zero' |
| >>> c.number_class(Decimal('-0.1E-999')) |
| '-Subnormal' |
| >>> c.number_class(Decimal('-1E-10')) |
| '-Normal' |
| >>> c.number_class(Decimal('-2.50')) |
| '-Normal' |
| >>> c.number_class(Decimal('-Infinity')) |
| '-Infinity' |
| >>> c.number_class(Decimal('NaN')) |
| 'NaN' |
| >>> c.number_class(Decimal('-NaN')) |
| 'NaN' |
| >>> c.number_class(Decimal('sNaN')) |
| 'sNaN' |
| """ |
| return a.number_class(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. |
| |
| With two arguments, compute a**b. If a is negative then b |
| must be integral. The result will be inexact unless b is |
| integral and the result is finite and can be expressed exactly |
| in 'precision' digits. |
| |
| With three arguments, compute (a**b) % modulo. For the |
| three argument form, the following restrictions on the |
| arguments hold: |
| |
| - all three arguments must be integral |
| - b must be nonnegative |
| - at least one of a or b must be nonzero |
| - modulo must be nonzero and have at most 'precision' digits |
| |
| The result of pow(a, b, modulo) is identical to the result |
| that would be obtained by computing (a**b) % modulo with |
| unbounded precision, but is computed more efficiently. It is |
| always exact. |
| |
| >>> c = ExtendedContext.copy() |
| >>> c.Emin = -999 |
| >>> c.Emax = 999 |
| >>> c.power(Decimal('2'), Decimal('3')) |
| Decimal('8') |
| >>> c.power(Decimal('-2'), Decimal('3')) |
| Decimal('-8') |
| >>> c.power(Decimal('2'), Decimal('-3')) |
| Decimal('0.125') |
| >>> c.power(Decimal('1.7'), Decimal('8')) |
| Decimal('69.7575744') |
| >>> c.power(Decimal('10'), Decimal('0.301029996')) |
| Decimal('2.00000000') |
| >>> c.power(Decimal('Infinity'), Decimal('-1')) |
| Decimal('0') |
| >>> c.power(Decimal('Infinity'), Decimal('0')) |
| Decimal('1') |
| >>> c.power(Decimal('Infinity'), Decimal('1')) |
| Decimal('Infinity') |
| >>> c.power(Decimal('-Infinity'), Decimal('-1')) |
| Decimal('-0') |
| >>> c.power(Decimal('-Infinity'), Decimal('0')) |
| Decimal('1') |
| >>> c.power(Decimal('-Infinity'), Decimal('1')) |
| Decimal('-Infinity') |
| >>> c.power(Decimal('-Infinity'), Decimal('2')) |
| Decimal('Infinity') |
| >>> c.power(Decimal('0'), Decimal('0')) |
| Decimal('NaN') |
| |
| >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) |
| Decimal('11') |
| >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) |
| Decimal('-11') |
| >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) |
| Decimal('1') |
| >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) |
| Decimal('11') |
| >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) |
| Decimal('11729830') |
| >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) |
| Decimal('-0') |
| >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) |
| Decimal('1') |
| """ |
| return a.__pow__(b, modulo, context=self) |
| |
| def quantize(self, a, b): |
| """Returns a value equal to 'a' (rounded), having the exponent of 'b'. |
| |
| The coefficient of the result is derived from that of the left-hand |
| operand. It may be rounded using the current rounding setting (if the |
| 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 radix(self): |
| """Just returns 10, as this is Decimal, :) |
| |
| >>> ExtendedContext.radix() |
| Decimal('10') |
| """ |
| return Decimal(10) |
| |
| 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 rotate(self, a, b): |
| """Returns a rotated copy of a, b times. |
| |
| The coefficient of the result is a rotated copy of the digits in |
| the coefficient of the first operand. The number of places of |
| rotation is taken from the absolute value of the second operand, |
| with the rotation being to the left if the second operand is |
| positive or to the right otherwise. |
| |
| >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) |
| Decimal('400000003') |
| >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) |
| Decimal('12') |
| >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) |
| Decimal('891234567') |
| >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) |
| Decimal('123456789') |
| >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) |
| Decimal('345678912') |
| """ |
| return a.rotate(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 scaleb (self, a, b): |
| """Returns the first operand after adding the second value its exp. |
| |
| >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) |
| Decimal('0.0750') |
| >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) |
| Decimal('7.50') |
| >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) |
| Decimal('7.50E+3') |
| """ |
| return a.scaleb (b, context=self) |
| |
| def shift(self, a, b): |
| """Returns a shifted copy of a, b times. |
| |
| The coefficient of the result is a shifted copy of the digits |
| in the coefficient of the first operand. The number of places |
| to shift is taken from the absolute value of the second operand, |
| with the shift being to the left if the second operand is |
| positive or to the right otherwise. Digits shifted into the |
| coefficient are zeros. |
| |
| >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) |
| Decimal('400000000') |
| >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) |
| Decimal('0') |
| >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) |
| Decimal('1234567') |
| >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) |
| Decimal('123456789') |
| >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) |
| Decimal('345678900') |
| """ |
| return a.shift(b, context=self) |
| |
| def sqrt(self, a): |
| """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_exact(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; Inexact and Rounded flags |
| are allowed in this operation. The rounding mode is taken from the |
| context. |
| |
| >>> ExtendedContext.to_integral_exact(Decimal('2.1')) |
| Decimal('2') |
| >>> ExtendedContext.to_integral_exact(Decimal('100')) |
| Decimal('100') |
| >>> ExtendedContext.to_integral_exact(Decimal('100.0')) |
| Decimal('100') |
| >>> ExtendedContext.to_integral_exact(Decimal('101.5')) |
| Decimal('102') |
| >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) |
| Decimal('-102') |
| >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) |
| Decimal('1.0E+6') |
| >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) |
| Decimal('7.89E+77') |
| >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) |
| Decimal('-Infinity') |
| """ |
| return a.to_integral_exact(context=self) |
| |
| def to_integral_value(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_value(Decimal('2.1')) |
| Decimal('2') |
| >>> ExtendedContext.to_integral_value(Decimal('100')) |
| Decimal('100') |
| >>> ExtendedContext.to_integral_value(Decimal('100.0')) |
| Decimal('100') |
| >>> ExtendedContext.to_integral_value(Decimal('101.5')) |
| Decimal('102') |
| >>> ExtendedContext.to_integral_value(Decimal('-101.5')) |
| Decimal('-102') |
| >>> ExtendedContext.to_integral_value(Decimal('10E+5')) |
| Decimal('1.0E+6') |
| >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) |
| Decimal('7.89E+77') |
| >>> ExtendedContext.to_integral_value(Decimal('-Inf')) |
| Decimal('-Infinity') |
| """ |
| return a.to_integral_value(context=self) |
| |
| # the method name changed, but we provide also the old one, for compatibility |
| to_integral = to_integral_value |
| |
| class _WorkRep(object): |
| __slots__ = ('sign','int','exp') |
| # sign: 0 or 1 |
| # int: int |
| # 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 |
| self.int = int(value._int) |
| 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, prec = 0): |
| """Normalizes op1, op2 to have the same exp and length of coefficient. |
| |
| Done during addition. |
| """ |
| if op1.exp < op2.exp: |
| tmp = op2 |
| other = op1 |
| else: |
| tmp = op1 |
| other = op2 |
| |
| # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). |
| # Then adding 10**exp to tmp has the same effect (after rounding) |
| # as adding any positive quantity smaller than 10**exp; similarly |
| # for subtraction. So if other is smaller than 10**exp we replace |
| # it with 10**exp. This avoids tmp.exp - other.exp getting too large. |
| tmp_len = len(str(tmp.int)) |
| other_len = len(str(other.int)) |
| exp = tmp.exp + min(-1, tmp_len - prec - 2) |
| if other_len + other.exp - 1 < exp: |
| other.int = 1 |
| other.exp = exp |
| |
| tmp.int *= 10 ** (tmp.exp - other.exp) |
| tmp.exp = other.exp |
| return op1, op2 |
| |
| ##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### |
| |
| # This function from Tim Peters was taken from here: |
| # http://mail.python.org/pipermail/python-list/1999-July/007758.html |
| # The correction being in the function definition is for speed, and |
| # the whole function is not resolved with math.log because of avoiding |
| # the use of floats. |
| def _nbits(n, correction = { |
| '0': 4, '1': 3, '2': 2, '3': 2, |
| '4': 1, '5': 1, '6': 1, '7': 1, |
| '8': 0, '9': 0, 'a': 0, 'b': 0, |
| 'c': 0, 'd': 0, 'e': 0, 'f': 0}): |
| """Number of bits in binary representation of the positive integer n, |
| or 0 if n == 0. |
| """ |
| if n < 0: |
| raise ValueError("The argument to _nbits should be nonnegative.") |
| hex_n = "%x" % n |
| return 4*len(hex_n) - correction[hex_n[0]] |
| |
| def _sqrt_nearest(n, a): |
| """Closest integer to the square root of the positive integer n. a is |
| an initial approximation to the square root. Any positive integer |
| will do for a, but the closer a is to the square root of n the |
| faster convergence will be. |
| |
| """ |
| if n <= 0 or a <= 0: |
| raise ValueError("Both arguments to _sqrt_nearest should be positive.") |
| |
| b=0 |
| while a != b: |
| b, a = a, a--n//a>>1 |
| return a |
| |
| def _rshift_nearest(x, shift): |
| """Given an integer x and a nonnegative integer shift, return closest |
| integer to x / 2**shift; use round-to-even in case of a tie. |
| |
| """ |
| b, q = 1 << shift, x >> shift |
| return q + (2*(x & (b-1)) + (q&1) > b) |
| |
| def _div_nearest(a, b): |
| """Closest integer to a/b, a and b positive integers; rounds to even |
| in the case of a tie. |
| |
| """ |
| q, r = divmod(a, b) |
| return q + (2*r + (q&1) > b) |
| |
| def _ilog(x, M, L = 8): |
| """Integer approximation to M*log(x/M), with absolute error boundable |
| in terms only of x/M. |
| |
| Given positive integers x and M, return an integer approximation to |
| M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference |
| between the approximation and the exact result is at most 22. For |
| L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In |
| both cases these are upper bounds on the error; it will usually be |
| much smaller.""" |
| |
| # The basic algorithm is the following: let log1p be the function |
| # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use |
| # the reduction |
| # |
| # log1p(y) = 2*log1p(y/(1+sqrt(1+y))) |
| # |
| # repeatedly until the argument to log1p is small (< 2**-L in |
| # absolute value). For small y we can use the Taylor series |
| # expansion |
| # |
| # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T |
| # |
| # truncating at T such that y**T is small enough. The whole |
| # computation is carried out in a form of fixed-point arithmetic, |
| # with a real number z being represented by an integer |
| # approximation to z*M. To avoid loss of precision, the y below |
| # is actually an integer approximation to 2**R*y*M, where R is the |
| # number of reductions performed so far. |
| |
| y = x-M |
| # argument reduction; R = number of reductions performed |
| R = 0 |
| while (R <= L and abs(y) << L-R >= M or |
| R > L and abs(y) >> R-L >= M): |
| y = _div_nearest((M*y) << 1, |
| M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M)) |
| R += 1 |
| |
| # Taylor series with T terms |
| T = -int(-10*len(str(M))//(3*L)) |
| yshift = _rshift_nearest(y, R) |
| w = _div_nearest(M, T) |
| for k in range(T-1, 0, -1): |
| w = _div_nearest(M, k) - _div_nearest(yshift*w, M) |
| |
| return _div_nearest(w*y, M) |
| |
| def _dlog10(c, e, p): |
| """Given integers c, e and p with c > 0, p >= 0, compute an integer |
| approximation to 10**p * log10(c*10**e), with an absolute error of |
| at most 1. Assumes that c*10**e is not exactly 1.""" |
| |
| # increase precision by 2; compensate for this by dividing |
| # final result by 100 |
| p += 2 |
| |
| # write c*10**e as d*10**f with either: |
| # f >= 0 and 1 <= d <= 10, or |
| # f <= 0 and 0.1 <= d <= 1. |
| # Thus for c*10**e close to 1, f = 0 |
| l = len(str(c)) |
| f = e+l - (e+l >= 1) |
| |
| if p > 0: |
| M = 10**p |
| k = e+p-f |
| if k >= 0: |
| c *= 10**k |
| else: |
| c = _div_nearest(c, 10**-k) |
| |
| log_d = _ilog(c, M) # error < 5 + 22 = 27 |
| log_10 = _log10_digits(p) # error < 1 |
| log_d = _div_nearest(log_d*M, log_10) |
| log_tenpower = f*M # exact |
| else: |
| log_d = 0 # error < 2.31 |
| log_tenpower = _div_nearest(f, 10**-p) # error < 0.5 |
| |
| return _div_nearest(log_tenpower+log_d, 100) |
| |
| def _dlog(c, e, p): |
| """Given integers c, e and p with c > 0, compute an integer |
| approximation to 10**p * log(c*10**e), with an absolute error of |
| at most 1. Assumes that c*10**e is not exactly 1.""" |
| |
| # Increase precision by 2. The precision increase is compensated |
| # for at the end with a division by 100. |
| p += 2 |
| |
| # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10, |
| # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e) |
| # as 10**p * log(d) + 10**p*f * log(10). |
| l = len(str(c)) |
| f = e+l - (e+l >= 1) |
| |
| # compute approximation to 10**p*log(d), with error < 27 |
| if p > 0: |
| k = e+p-f |
| if k >= 0: |
| c *= 10**k |
| else: |
| c = _div_nearest(c, 10**-k) # error of <= 0.5 in c |
| |
| # _ilog magnifies existing error in c by a factor of at most 10 |
| log_d = _ilog(c, 10**p) # error < 5 + 22 = 27 |
| else: |
| # p <= 0: just approximate the whole thing by 0; error < 2.31 |
| log_d = 0 |
| |
| # compute approximation to f*10**p*log(10), with error < 11. |
| if f: |
| extra = len(str(abs(f)))-1 |
| if p + extra >= 0: |
| # error in f * _log10_digits(p+extra) < |f| * 1 = |f| |
| # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11 |
| f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra) |
| else: |
| f_log_ten = 0 |
| else: |
| f_log_ten = 0 |
| |
| # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1 |
| return _div_nearest(f_log_ten + log_d, 100) |
| |
| class _Log10Memoize(object): |
| """Class to compute, store, and allow retrieval of, digits of the |
| constant log(10) = 2.302585.... This constant is needed by |
| Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.""" |
| def __init__(self): |
| self.digits = "23025850929940456840179914546843642076011014886" |
| |
| def getdigits(self, p): |
| """Given an integer p >= 0, return floor(10**p)*log(10). |
| |
| For example, self.getdigits(3) returns 2302. |
| """ |
| # digits are stored as a string, for quick conversion to |
| # integer in the case that we've already computed enough |
| # digits; the stored digits should always be correct |
| # (truncated, not rounded to nearest). |
| if p < 0: |
| raise ValueError("p should be nonnegative") |
| |
| if p >= len(self.digits): |
| # compute p+3, p+6, p+9, ... digits; continue until at |
| # least one of the extra digits is nonzero |
| extra = 3 |
| while True: |
| # compute p+extra digits, correct to within 1ulp |
| M = 10**(p+extra+2) |
| digits = str(_div_nearest(_ilog(10*M, M), 100)) |
| if digits[-extra:] != '0'*extra: |
| break |
| extra += 3 |
| # keep all reliable digits so far; remove trailing zeros |
| # and next nonzero digit |
| self.digits = digits.rstrip('0')[:-1] |
| return int(self.digits[:p+1]) |
| |
| _log10_digits = _Log10Memoize().getdigits |
| |
| def _iexp(x, M, L=8): |
| """Given integers x and M, M > 0, such that x/M is small in absolute |
| value, compute an integer approximation to M*exp(x/M). For 0 <= |
| x/M <= 2.4, the absolute error in the result is bounded by 60 (and |
| is usually much smaller).""" |
| |
| # Algorithm: to compute exp(z) for a real number z, first divide z |
| # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then |
| # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor |
| # series |
| # |
| # expm1(x) = x + x**2/2! + x**3/3! + ... |
| # |
| # Now use the identity |
| # |
| # expm1(2x) = expm1(x)*(expm1(x)+2) |
| # |
| # R times to compute the sequence expm1(z/2**R), |
| # expm1(z/2**(R-1)), ... , exp(z/2), exp(z). |
| |
| # Find R such that x/2**R/M <= 2**-L |
| R = _nbits((x<<L)//M) |
| |
| # Taylor series. (2**L)**T > M |
| T = -int(-10*len(str(M))//(3*L)) |
| y = _div_nearest(x, T) |
| Mshift = M<<R |
| for i in range(T-1, 0, -1): |
| y = _div_nearest(x*(Mshift + y), Mshift * i) |
| |
| # Expansion |
| for k in range(R-1, -1, -1): |
| Mshift = M<<(k+2) |
| y = _div_nearest(y*(y+Mshift), Mshift) |
| |
| return M+y |
| |
| def _dexp(c, e, p): |
| """Compute an approximation to exp(c*10**e), with p decimal places of |
| precision. |
| |
| Returns integers d, f such that: |
| |
| 10**(p-1) <= d <= 10**p, and |
| (d-1)*10**f < exp(c*10**e) < (d+1)*10**f |
| |
| In other words, d*10**f is an approximation to exp(c*10**e) with p |
| digits of precision, and with an error in d of at most 1. This is |
| almost, but not quite, the same as the error being < 1ulp: when d |
| = 10**(p-1) the error could be up to 10 ulp.""" |
| |
| # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision |
| p += 2 |
| |
| # compute log(10) with extra precision = adjusted exponent of c*10**e |
| extra = max(0, e + len(str(c)) - 1) |
| q = p + extra |
| |
| # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q), |
| # rounding down |
| shift = e+q |
| if shift >= 0: |
| cshift = c*10**shift |
| else: |
| cshift = c//10**-shift |
| quot, rem = divmod(cshift, _log10_digits(q)) |
| |
| # reduce remainder back to original precision |
| rem = _div_nearest(rem, 10**extra) |
| |
| # error in result of _iexp < 120; error after division < 0.62 |
| return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3 |
| |
| def _dpower(xc, xe, yc, ye, p): |
| """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and |
| y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: |
| |
| 10**(p-1) <= c <= 10**p, and |
| (c-1)*10**e < x**y < (c+1)*10**e |
| |
| in other words, c*10**e is an approximation to x**y with p digits |
| of precision, and with an error in c of at most 1. (This is |
| almost, but not quite, the same as the error being < 1ulp: when c |
| == 10**(p-1) we can only guarantee error < 10ulp.) |
| |
| We assume that: x is positive and not equal to 1, and y is nonzero. |
| """ |
| |
| # Find b such that 10**(b-1) <= |y| <= 10**b |
| b = len(str(abs(yc))) + ye |
| |
| # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point |
| lxc = _dlog(xc, xe, p+b+1) |
| |
| # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1) |
| shift = ye-b |
| if shift >= 0: |
| pc = lxc*yc*10**shift |
| else: |
| pc = _div_nearest(lxc*yc, 10**-shift) |
| |
| if pc == 0: |
| # we prefer a result that isn't exactly 1; this makes it |
| # easier to compute a correctly rounded result in __pow__ |
| if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1: |
| coeff, exp = 10**(p-1)+1, 1-p |
| else: |
| coeff, exp = 10**p-1, -p |
| else: |
| coeff, exp = _dexp(pc, -(p+1), p+1) |
| coeff = _div_nearest(coeff, 10) |
| exp += 1 |
| |
| return coeff, exp |
| |
| def _log10_lb(c, correction = { |
| '1': 100, '2': 70, '3': 53, '4': 40, '5': 31, |
| '6': 23, '7': 16, '8': 10, '9': 5}): |
| """Compute a lower bound for 100*log10(c) for a positive integer c.""" |
| if c <= 0: |
| raise ValueError("The argument to _log10_lb should be nonnegative.") |
| str_c = str(c) |
| return 100*len(str_c) - correction[str_c[0]] |
| |
| ##### Helper Functions #################################################### |
| |
| def _convert_other(other, raiseit=False): |
| """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): |
| return Decimal(other) |
| if raiseit: |
| raise TypeError("Unable to convert %s to Decimal" % other) |
| return NotImplemented |
| |
| ##### 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=[], |
| 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=[], |
| ) |
| |
| |
| ##### crud for parsing strings ############################################# |
| # |
| # Regular expression used for parsing numeric strings. Additional |
| # comments: |
| # |
| # 1. Uncomment the two '\s*' lines to allow leading and/or trailing |
| # whitespace. But note that the specification disallows whitespace in |
| # a numeric string. |
| # |
| # 2. For finite numbers (not infinities and NaNs) the body of the |
| # number between the optional sign and the optional exponent must have |
| # at least one decimal digit, possibly after the decimal point. The |
| # lookahead expression '(?=\d|\.\d)' checks this. |
| |
| import re |
| _parser = re.compile(r""" # A numeric string consists of: |
| # \s* |
| (?P<sign>[-+])? # an optional sign, followed by either... |
| ( |
| (?=\d|\.\d) # ...a number (with at least one digit) |
| (?P<int>\d*) # having a (possibly empty) integer part |
| (\.(?P<frac>\d*))? # followed by an optional fractional part |
| (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or... |
| | |
| Inf(inity)? # ...an infinity, or... |
| | |
| (?P<signal>s)? # ...an (optionally signaling) |
| NaN # NaN |
| (?P<diag>\d*) # with (possibly empty) diagnostic info. |
| ) |
| # \s* |
| \Z |
| """, re.VERBOSE | re.IGNORECASE).match |
| |
| _all_zeros = re.compile('0*$').match |
| _exact_half = re.compile('50*$').match |
| |
| ##### PEP3101 support functions ############################################## |
| # The functions in this section have little to do with the Decimal |
| # class, and could potentially be reused or adapted for other pure |
| # Python numeric classes that want to implement __format__ |
| # |
| # A format specifier for Decimal looks like: |
| # |
| # [[fill]align][sign][0][minimumwidth][,][.precision][type] |
| |
| _parse_format_specifier_regex = re.compile(r"""\A |
| (?: |
| (?P<fill>.)? |
| (?P<align>[<>=^]) |
| )? |
| (?P<sign>[-+ ])? |
| (?P<zeropad>0)? |
| (?P<minimumwidth>(?!0)\d+)? |
| (?P<thousands_sep>,)? |
| (?:\.(?P<precision>0|(?!0)\d+))? |
| (?P<type>[eEfFgGn%])? |
| \Z |
| """, re.VERBOSE) |
| |
| del re |
| |
| # The locale module is only needed for the 'n' format specifier. The |
| # rest of the PEP 3101 code functions quite happily without it, so we |
| # don't care too much if locale isn't present. |
| try: |
| import locale as _locale |
| except ImportError: |
| pass |
| |
| def _parse_format_specifier(format_spec, _localeconv=None): |
| """Parse and validate a format specifier. |
| |
| Turns a standard numeric format specifier into a dict, with the |
| following entries: |
| |
| fill: fill character to pad field to minimum width |
| align: alignment type, either '<', '>', '=' or '^' |
| sign: either '+', '-' or ' ' |
| minimumwidth: nonnegative integer giving minimum width |
| zeropad: boolean, indicating whether to pad with zeros |
| thousands_sep: string to use as thousands separator, or '' |
| grouping: grouping for thousands separators, in format |
| used by localeconv |
| decimal_point: string to use for decimal point |
| precision: nonnegative integer giving precision, or None |
| type: one of the characters 'eEfFgG%', or None |
| |
| """ |
| m = _parse_format_specifier_regex.match(format_spec) |
| if m is None: |
| raise ValueError("Invalid format specifier: " + format_spec) |
| |
| # get the dictionary |
| format_dict = m.groupdict() |
| |
| # zeropad; defaults for fill and alignment. If zero padding |
| # is requested, the fill and align fields should be absent. |
| fill = format_dict['fill'] |
| align = format_dict['align'] |
| format_dict['zeropad'] = (format_dict['zeropad'] is not None) |
| if format_dict['zeropad']: |
| if fill is not None: |
| raise ValueError("Fill character conflicts with '0'" |
| " in format specifier: " + format_spec) |
| if align is not None: |
| raise ValueError("Alignment conflicts with '0' in " |
| "format specifier: " + format_spec) |
| format_dict['fill'] = fill or ' ' |
| format_dict['align'] = align or '<' |
| |
| # default sign handling: '-' for negative, '' for positive |
| if format_dict['sign'] is None: |
| format_dict['sign'] = '-' |
| |
| # minimumwidth defaults to 0; precision remains None if not given |
| format_dict['minimumwidth'] = int(format_dict['minimumwidth'] or '0') |
| if format_dict['precision'] is not None: |
| format_dict['precision'] = int(format_dict['precision']) |
| |
| # if format type is 'g' or 'G' then a precision of 0 makes little |
| # sense; convert it to 1. Same if format type is unspecified. |
| if format_dict['precision'] == 0: |
| if format_dict['type'] is None or format_dict['type'] in 'gG': |
| format_dict['precision'] = 1 |
| |
| # determine thousands separator, grouping, and decimal separator, and |
| # add appropriate entries to format_dict |
| if format_dict['type'] == 'n': |
| # apart from separators, 'n' behaves just like 'g' |
| format_dict['type'] = 'g' |
| if _localeconv is None: |
| _localeconv = _locale.localeconv() |
| if format_dict['thousands_sep'] is not None: |
| raise ValueError("Explicit thousands separator conflicts with " |
| "'n' type in format specifier: " + format_spec) |
| format_dict['thousands_sep'] = _localeconv['thousands_sep'] |
| format_dict['grouping'] = _localeconv['grouping'] |
| format_dict['decimal_point'] = _localeconv['decimal_point'] |
| else: |
| if format_dict['thousands_sep'] is None: |
| format_dict['thousands_sep'] = '' |
| format_dict['grouping'] = [3, 0] |
| format_dict['decimal_point'] = '.' |
| |
| return format_dict |
| |
| def _format_align(sign, body, spec): |
| """Given an unpadded, non-aligned numeric string 'body' and sign |
| string 'sign', add padding and aligment conforming to the given |
| format specifier dictionary 'spec' (as produced by |
| parse_format_specifier). |
| |
| """ |
| # how much extra space do we have to play with? |
| minimumwidth = spec['minimumwidth'] |
| fill = spec['fill'] |
| padding = fill*(minimumwidth - len(sign) - len(body)) |
| |
| align = spec['align'] |
| if align == '<': |
| result = sign + body + padding |
| elif align == '>': |
| result = padding + sign + body |
| elif align == '=': |
| result = sign + padding + body |
| elif align == '^': |
| half = len(padding)//2 |
| result = padding[:half] + sign + body + padding[half:] |
| else: |
| raise ValueError('Unrecognised alignment field') |
| |
| return result |
| |
| def _group_lengths(grouping): |
| """Convert a localeconv-style grouping into a (possibly infinite) |
| iterable of integers representing group lengths. |
| |
| """ |
| # The result from localeconv()['grouping'], and the input to this |
| # function, should be a list of integers in one of the |
| # following three forms: |
| # |
| # (1) an empty list, or |
| # (2) nonempty list of positive integers + [0] |
| # (3) list of positive integers + [locale.CHAR_MAX], or |
| |
| from itertools import chain, repeat |
| if not grouping: |
| return [] |
| elif grouping[-1] == 0 and len(grouping) >= 2: |
| return chain(grouping[:-1], repeat(grouping[-2])) |
| elif grouping[-1] == _locale.CHAR_MAX: |
| return grouping[:-1] |
| else: |
| raise ValueError('unrecognised format for grouping') |
| |
| def _insert_thousands_sep(digits, spec, min_width=1): |
| """Insert thousands separators into a digit string. |
| |
| spec is a dictionary whose keys should include 'thousands_sep' and |
| 'grouping'; typically it's the result of parsing the format |
| specifier using _parse_format_specifier. |
| |
| The min_width keyword argument gives the minimum length of the |
| result, which will be padded on the left with zeros if necessary. |
| |
| If necessary, the zero padding adds an extra '0' on the left to |
| avoid a leading thousands separator. For example, inserting |
| commas every three digits in '123456', with min_width=8, gives |
| '0,123,456', even though that has length 9. |
| |
| """ |
| |
| sep = spec['thousands_sep'] |
| grouping = spec['grouping'] |
| |
| groups = [] |
| for l in _group_lengths(grouping): |
| if l <= 0: |
| raise ValueError("group length should be positive") |
| # max(..., 1) forces at least 1 digit to the left of a separator |
| l = min(max(len(digits), min_width, 1), l) |
| groups.append('0'*(l - len(digits)) + digits[-l:]) |
| digits = digits[:-l] |
| min_width -= l |
| if not digits and min_width <= 0: |
| break |
| min_width -= len(sep) |
| else: |
| l = max(len(digits), min_width, 1) |
| groups.append('0'*(l - len(digits)) + digits[-l:]) |
| return sep.join(reversed(groups)) |
| |
| def _format_sign(is_negative, spec): |
| """Determine sign character.""" |
| |
| if is_negative: |
| return '-' |
| elif spec['sign'] in ' +': |
| return spec['sign'] |
| else: |
| return '' |
| |
| def _format_number(is_negative, intpart, fracpart, exp, spec): |
| """Format a number, given the following data: |
| |
| is_negative: true if the number is negative, else false |
| intpart: string of digits that must appear before the decimal point |
| fracpart: string of digits that must come after the point |
| exp: exponent, as an integer |
| spec: dictionary resulting from parsing the format specifier |
| |
| This function uses the information in spec to: |
| insert separators (decimal separator and thousands separators) |
| format the sign |
| format the exponent |
| add trailing '%' for the '%' type |
| zero-pad if necessary |
| fill and align if necessary |
| """ |
| |
| sign = _format_sign(is_negative, spec) |
| |
| if fracpart: |
| fracpart = spec['decimal_point'] + fracpart |
| |
| if exp != 0 or spec['type'] in 'eE': |
| echar = {'E': 'E', 'e': 'e', 'G': 'E', 'g': 'e'}[spec['type']] |
| fracpart += "{0}{1:+}".format(echar, exp) |
| if spec['type'] == '%': |
| fracpart += '%' |
| |
| if spec['zeropad']: |
| min_width = spec['minimumwidth'] - len(fracpart) - len(sign) |
| else: |
| min_width = 0 |
| intpart = _insert_thousands_sep(intpart, spec, min_width) |
| |
| return _format_align(sign, intpart+fracpart, spec) |
| |
| |
| ##### Useful Constants (internal use only) ################################ |
| |
| # Reusable defaults |
| _Infinity = Decimal('Inf') |
| _NegativeInfinity = Decimal('-Inf') |
| _NaN = Decimal('NaN') |
| _Zero = Decimal(0) |
| _One = Decimal(1) |
| _NegativeOne = Decimal(-1) |
| |
| # _SignedInfinity[sign] is infinity w/ that sign |
| _SignedInfinity = (_Infinity, _NegativeInfinity) |
| |
| |
| |
| if __name__ == '__main__': |
| import doctest, sys |
| doctest.testmod(sys.modules[__name__]) |