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# 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: http://en.wikipedia.org/wiki/IEEE_854-1987 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 0.0; Decimal('1.00') % Decimal('0.1') returns the expected Decimal('0.00')). 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('123.45e12345678') Decimal('1.2345E+12345680') >>> 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', # Named tuple representation 'DecimalTuple', # Contexts 'DefaultContext', 'BasicContext', 'ExtendedContext', # Exceptions 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero', 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow', 'FloatOperation', # Exceptional conditions that trigger InvalidOperation 'DivisionImpossible', 'InvalidContext', 'ConversionSyntax', 'DivisionUndefined', # 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', # Limits for the C version for compatibility 'MAX_PREC', 'MAX_EMAX', 'MIN_EMIN', 'MIN_ETINY', # C version: compile time choice that enables the thread local context 'HAVE_THREADS' ] __xname__ = __name__ # sys.modules lookup (--without-threads) __name__ = 'decimal' # For pickling __version__ = '1.70' # Highest version of the spec this complies with # See http://speleotrove.com/decimal/ __libmpdec_version__ = "2.4.2" # compatible libmpdec version import math as _math import numbers as _numbers import sys 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' # Compatibility with the C version HAVE_THREADS = True if sys.maxsize == 2**63-1: MAX_PREC = 999999999999999999 MAX_EMAX = 999999999999999999 MIN_EMIN = -999999999999999999 else: MAX_PREC = 425000000 MAX_EMAX = 425000000 MIN_EMIN = -425000000 MIN_ETINY = MIN_EMIN - (MAX_PREC-1) # 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 not 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 a 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 divisio