diff options
Diffstat (limited to 'Lib/decimal.py')
| -rw-r--r-- | Lib/decimal.py | 337 |
1 files changed, 245 insertions, 92 deletions
diff --git a/Lib/decimal.py b/Lib/decimal.py index f5277c5..6bd655b 100644 --- a/Lib/decimal.py +++ b/Lib/decimal.py @@ -46,8 +46,8 @@ Decimal('1') Decimal('-0.0123') >>> Decimal(123456) Decimal('123456') ->>> Decimal('123.45e12345678901234567890') -Decimal('1.2345E+12345678901234567892') +>>> 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') @@ -122,13 +122,20 @@ __all__ = [ # Exceptions 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero', 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow', + 'FloatOperation', # 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' + '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' ] __version__ = '1.70' # Highest version of the spec this complies with @@ -137,6 +144,7 @@ __version__ = '1.70' # Highest version of the spec this complies with import copy as _copy import math as _math import numbers as _numbers +import sys try: from collections import namedtuple as _namedtuple @@ -154,6 +162,19 @@ 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): @@ -370,9 +391,24 @@ class Underflow(Inexact, Rounded, Subnormal): In all cases, Inexact, Rounded, and Subnormal will also be raised. """ +class FloatOperation(DecimalException, TypeError): + """Enable stricter semantics for mixing floats and Decimals. + + If the signal is not trapped (default), mixing floats and Decimals is + permitted in the Decimal() constructor, context.create_decimal() and + all comparison operators. Both conversion and comparisons are exact. + Any occurrence of a mixed operation is silently recorded by setting + FloatOperation in the context flags. Explicit conversions with + Decimal.from_float() or context.create_decimal_from_float() do not + set the flag. + + Otherwise (the signal is trapped), only equality comparisons and explicit + conversions are silent. All other mixed operations raise FloatOperation. + """ + # List of public traps and flags _signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, - Underflow, InvalidOperation, Subnormal] + Underflow, InvalidOperation, Subnormal, FloatOperation] # Map conditions (per the spec) to signals _condition_map = {ConversionSyntax:InvalidOperation, @@ -380,6 +416,10 @@ _condition_map = {ConversionSyntax:InvalidOperation, DivisionUndefined:InvalidOperation, InvalidContext:InvalidOperation} +# Valid rounding modes +_rounding_modes = (ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_CEILING, + ROUND_FLOOR, ROUND_UP, ROUND_HALF_DOWN, ROUND_05UP) + ##### Context Functions ################################################## # The getcontext() and setcontext() function manage access to a thread-local @@ -392,12 +432,11 @@ 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 + del MockThreading try: threading.local @@ -650,6 +689,11 @@ class Decimal(object): return self if isinstance(value, float): + if context is None: + context = getcontext() + context._raise_error(FloatOperation, + "strict semantics for mixing floats and Decimals are " + "enabled") value = Decimal.from_float(value) self._exp = value._exp self._sign = value._sign @@ -684,7 +728,9 @@ class Decimal(object): """ if isinstance(f, int): # handle integer inputs return cls(f) - if _math.isinf(f) or _math.isnan(f): # raises TypeError if not a float + if not isinstance(f, float): + raise TypeError("argument must be int or float.") + if _math.isinf(f) or _math.isnan(f): return cls(repr(f)) if _math.copysign(1.0, f) == 1.0: sign = 0 @@ -1871,6 +1917,7 @@ class Decimal(object): """ other = _convert_other(other, raiseit=True) + third = _convert_other(third, raiseit=True) # compute product; raise InvalidOperation if either operand is # a signaling NaN or if the product is zero times infinity. @@ -1900,17 +1947,17 @@ class Decimal(object): 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) + other = _convert_other(other) + if other is NotImplemented: + return other + modulo = _convert_other(modulo) + if modulo is NotImplemented: + return modulo if context is None: context = getcontext() @@ -2001,9 +2048,9 @@ class Decimal(object): 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. + # 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 abs(y) = yc*10**ye, with xc + # and yc positive integers not divisible by 10. # The main purpose of this method is to identify the *failure* # of x**y to be exactly representable with as little effort as @@ -2011,13 +2058,12 @@ class Decimal(object): # 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. + # Here's the main idea. Express y as a rational number 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 y 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: @@ -2089,21 +2135,43 @@ class Decimal(object): 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) + + # We now have: + # + # x = 2**e * 10**xe, e > 0, and y < 0. + # + # The exact result is: + # + # x**y = 5**(-e*y) * 10**(e*y + xe*y) + # + # provided that both e*y and xe*y are integers. Note that if + # 5**(-e*y) >= 10**p, then the result can't be expressed + # exactly with p digits of precision. + # + # Using the above, we can guard against large values of ye. + # 93/65 is an upper bound for log(10)/log(5), so if + # + # ye >= len(str(93*p//65)) + # + # then + # + # -e*y >= -y >= 10**ye > 93*p/65 > p*log(10)/log(5), + # + # so 5**(-e*y) >= 10**p, and the coefficient of the result + # can't be expressed in p digits. + + # emax >= largest e such that 5**e < 10**p. + emax = p*93//65 + if ye >= len(str(emax)): + return None + + # Find -e*y and -xe*y; both must be integers + e = _decimal_lshift_exact(e * yc, ye) + xe = _decimal_lshift_exact(xe * yc, ye) + if e is None or xe is None: + return None + + if e > emax: return None xc = 5**e @@ -2117,19 +2185,20 @@ class Decimal(object): 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) + + # Guard against large values of ye, using the same logic as in + # the 'xc is a power of 2' branch. 10/3 is an upper bound for + # log(10)/log(2). + emax = p*10//3 + if ye >= len(str(emax)): + return None + + e = _decimal_lshift_exact(e * yc, ye) + xe = _decimal_lshift_exact(xe * yc, ye) + if e is None or xe is None: + return None + + if e > emax: return None xc = 2**e else: @@ -3810,11 +3879,9 @@ class Context(object): 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=None, - _ignored_flags=None): + def __init__(self, prec=None, rounding=None, Emin=None, Emax=None, + capitals=None, clamp=None, flags=None, traps=None, + _ignored_flags=None): # Set defaults; for everything except flags and _ignored_flags, # inherit from DefaultContext. try: @@ -3837,17 +3904,78 @@ class Context(object): if traps is None: self.traps = dc.traps.copy() elif not isinstance(traps, dict): - self.traps = dict((s, int(s in traps)) for s in _signals) + self.traps = dict((s, int(s in traps)) for s in _signals + traps) else: self.traps = traps if flags is None: self.flags = dict.fromkeys(_signals, 0) elif not isinstance(flags, dict): - self.flags = dict((s, int(s in flags)) for s in _signals) + self.flags = dict((s, int(s in flags)) for s in _signals + flags) else: self.flags = flags + def _set_integer_check(self, name, value, vmin, vmax): + if not isinstance(value, int): + raise TypeError("%s must be an integer" % name) + if vmin == '-inf': + if value > vmax: + raise ValueError("%s must be in [%s, %d]. got: %s" % (name, vmin, vmax, value)) + elif vmax == 'inf': + if value < vmin: + raise ValueError("%s must be in [%d, %s]. got: %s" % (name, vmin, vmax, value)) + else: + if value < vmin or value > vmax: + raise ValueError("%s must be in [%d, %d]. got %s" % (name, vmin, vmax, value)) + return object.__setattr__(self, name, value) + + def _set_signal_dict(self, name, d): + if not isinstance(d, dict): + raise TypeError("%s must be a signal dict" % d) + for key in d: + if not key in _signals: + raise KeyError("%s is not a valid signal dict" % d) + for key in _signals: + if not key in d: + raise KeyError("%s is not a valid signal dict" % d) + return object.__setattr__(self, name, d) + + def __setattr__(self, name, value): + if name == 'prec': + return self._set_integer_check(name, value, 1, 'inf') + elif name == 'Emin': + return self._set_integer_check(name, value, '-inf', 0) + elif name == 'Emax': + return self._set_integer_check(name, value, 0, 'inf') + elif name == 'capitals': + return self._set_integer_check(name, value, 0, 1) + elif name == 'clamp': + return self._set_integer_check(name, value, 0, 1) + elif name == 'rounding': + if not value in _rounding_modes: + # raise TypeError even for strings to have consistency + # among various implementations. + raise TypeError("%s: invalid rounding mode" % value) + return object.__setattr__(self, name, value) + elif name == 'flags' or name == 'traps': + return self._set_signal_dict(name, value) + elif name == '_ignored_flags': + return object.__setattr__(self, name, value) + else: + raise AttributeError( + "'decimal.Context' object has no attribute '%s'" % name) + + def __delattr__(self, name): + raise AttributeError("%s cannot be deleted" % name) + + # Support for pickling, copy, and deepcopy + def __reduce__(self): + flags = [sig for sig, v in self.flags.items() if v] + traps = [sig for sig, v in self.traps.items() if v] + return (self.__class__, + (self.prec, self.rounding, self.Emin, self.Emax, + self.capitals, self.clamp, flags, traps)) + def __repr__(self): """Show the current context.""" s = [] @@ -3866,43 +3994,27 @@ class Context(object): for flag in self.flags: self.flags[flag] = 0 + def clear_traps(self): + """Reset all traps to zero""" + for flag in self.traps: + self.traps[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) + nc = Context(self.prec, self.rounding, self.Emin, self.Emax, + self.capitals, self.clamp, self.flags, self.traps, + 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) + nc = Context(self.prec, self.rounding, self.Emin, self.Emax, + self.capitals, self.clamp, + self.flags.copy(), self.traps.copy(), + self._ignored_flags) return nc __copy__ = copy - # _clamp is provided for backwards compatibility with third-party - # code. May be removed in Python >= 3.3. - def _get_clamp(self): - "_clamp mirrors the clamp attribute. Its use is deprecated." - import warnings - warnings.warn('Use of the _clamp attribute is deprecated. ' - 'Please use clamp instead.', - DeprecationWarning) - return self.clamp - - def _set_clamp(self, clamp): - "_clamp mirrors the clamp attribute. Its use is deprecated." - import warnings - warnings.warn('Use of the _clamp attribute is deprecated. ' - 'Please use clamp instead.', - DeprecationWarning) - self.clamp = clamp - - # don't bother with _del_clamp; no sane 3rd party code should - # be deleting the _clamp attribute - _clamp = property(_get_clamp, _set_clamp) - def _raise_error(self, condition, explanation = None, *args): """Handles an error @@ -4062,6 +4174,8 @@ class Context(object): >>> ExtendedContext.canonical(Decimal('2.50')) Decimal('2.50') """ + if not isinstance(a, Decimal): + raise TypeError("canonical requires a Decimal as an argument.") return a.canonical(context=self) def compare(self, a, b): @@ -4372,6 +4486,8 @@ class Context(object): >>> ExtendedContext.is_canonical(Decimal('2.50')) True """ + if not isinstance(a, Decimal): + raise TypeError("is_canonical requires a Decimal as an argument.") return a.is_canonical() def is_finite(self, a): @@ -4964,7 +5080,7 @@ class Context(object): +Normal +Infinity - >>> c = Context(ExtendedContext) + >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.number_class(Decimal('Infinity')) @@ -5529,6 +5645,27 @@ def _normalize(op1, op2, prec = 0): _nbits = int.bit_length +def _decimal_lshift_exact(n, e): + """ Given integers n and e, return n * 10**e if it's an integer, else None. + + The computation is designed to avoid computing large powers of 10 + unnecessarily. + + >>> _decimal_lshift_exact(3, 4) + 30000 + >>> _decimal_lshift_exact(300, -999999999) # returns None + + """ + if n == 0: + return 0 + elif e >= 0: + return n * 10**e + else: + # val_n = largest power of 10 dividing n. + str_n = str(abs(n)) + val_n = len(str_n) - len(str_n.rstrip('0')) + return None if val_n < -e else n // 10**-e + 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 @@ -5895,6 +6032,12 @@ def _convert_for_comparison(self, other, equality_op=False): if equality_op and isinstance(other, _numbers.Complex) and other.imag == 0: other = other.real if isinstance(other, float): + context = getcontext() + if equality_op: + context.flags[FloatOperation] = 1 + else: + context._raise_error(FloatOperation, + "strict semantics for mixing floats and Decimals are enabled") return self, Decimal.from_float(other) return NotImplemented, NotImplemented @@ -5908,8 +6051,8 @@ DefaultContext = Context( prec=28, rounding=ROUND_HALF_EVEN, traps=[DivisionByZero, Overflow, InvalidOperation], flags=[], - Emax=999999999, - Emin=-999999999, + Emax=999999, + Emin=-999999, capitals=1, clamp=0 ) @@ -6059,7 +6202,7 @@ def _parse_format_specifier(format_spec, _localeconv=None): # 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': + if format_dict['type'] is None or format_dict['type'] in 'gGn': format_dict['precision'] = 1 # determine thousands separator, grouping, and decimal separator, and @@ -6233,16 +6376,26 @@ _SignedInfinity = (_Infinity, _NegativeInfinity) # Constants related to the hash implementation; hash(x) is based # on the reduction of x modulo _PyHASH_MODULUS -import sys _PyHASH_MODULUS = sys.hash_info.modulus # hash values to use for positive and negative infinities, and nans _PyHASH_INF = sys.hash_info.inf _PyHASH_NAN = sys.hash_info.nan -del sys # _PyHASH_10INV is the inverse of 10 modulo the prime _PyHASH_MODULUS _PyHASH_10INV = pow(10, _PyHASH_MODULUS - 2, _PyHASH_MODULUS) +del sys +try: + import _decimal +except ImportError: + pass +else: + s1 = set(dir()) + s2 = set(dir(_decimal)) + for name in s1 - s2: + del globals()[name] + del s1, s2, name + from _decimal import * if __name__ == '__main__': import doctest, decimal |