diff options
| -rwxr-xr-x | Demo/classes/Rat.py | 310 | ||||
| -rw-r--r-- | Doc/library/numeric.rst | 1 | ||||
| -rw-r--r-- | Doc/library/rational.rst | 65 | ||||
| -rw-r--r-- | Lib/numbers.py | 25 | ||||
| -rwxr-xr-x | Lib/rational.py | 410 | ||||
| -rw-r--r-- | Lib/test/test_rational.py | 279 |
6 files changed, 777 insertions, 313 deletions
diff --git a/Demo/classes/Rat.py b/Demo/classes/Rat.py deleted file mode 100755 index 55543b6..0000000 --- a/Demo/classes/Rat.py +++ /dev/null @@ -1,310 +0,0 @@ -'''\ -This module implements rational numbers. - -The entry point of this module is the function - rat(numerator, denominator) -If either numerator or denominator is of an integral or rational type, -the result is a rational number, else, the result is the simplest of -the types float and complex which can hold numerator/denominator. -If denominator is omitted, it defaults to 1. -Rational numbers can be used in calculations with any other numeric -type. The result of the calculation will be rational if possible. - -There is also a test function with calling sequence - test() -The documentation string of the test function contains the expected -output. -''' - -# Contributed by Sjoerd Mullender - -from types import * - -def gcd(a, b): - '''Calculate the Greatest Common Divisor.''' - while b: - a, b = b, a%b - return a - -def rat(num, den = 1): - # must check complex before float - if isinstance(num, complex) or isinstance(den, complex): - # numerator or denominator is complex: return a complex - return complex(num) / complex(den) - if isinstance(num, float) or isinstance(den, float): - # numerator or denominator is float: return a float - return float(num) / float(den) - # otherwise return a rational - return Rat(num, den) - -class Rat: - '''This class implements rational numbers.''' - - def __init__(self, num, den = 1): - if den == 0: - raise ZeroDivisionError, 'rat(x, 0)' - - # normalize - - # must check complex before float - if (isinstance(num, complex) or - isinstance(den, complex)): - # numerator or denominator is complex: - # normalized form has denominator == 1+0j - self.__num = complex(num) / complex(den) - self.__den = complex(1) - return - if isinstance(num, float) or isinstance(den, float): - # numerator or denominator is float: - # normalized form has denominator == 1.0 - self.__num = float(num) / float(den) - self.__den = 1.0 - return - if (isinstance(num, self.__class__) or - isinstance(den, self.__class__)): - # numerator or denominator is rational - new = num / den - if not isinstance(new, self.__class__): - self.__num = new - if isinstance(new, complex): - self.__den = complex(1) - else: - self.__den = 1.0 - else: - self.__num = new.__num - self.__den = new.__den - else: - # make sure numerator and denominator don't - # have common factors - # this also makes sure that denominator > 0 - g = gcd(num, den) - self.__num = num / g - self.__den = den / g - # try making numerator and denominator of IntType if they fit - try: - numi = int(self.__num) - deni = int(self.__den) - except (OverflowError, TypeError): - pass - else: - if self.__num == numi and self.__den == deni: - self.__num = numi - self.__den = deni - - def __repr__(self): - return 'Rat(%s,%s)' % (self.__num, self.__den) - - def __str__(self): - if self.__den == 1: - return str(self.__num) - else: - return '(%s/%s)' % (str(self.__num), str(self.__den)) - - # a + b - def __add__(a, b): - try: - return rat(a.__num * b.__den + b.__num * a.__den, - a.__den * b.__den) - except OverflowError: - return rat(long(a.__num) * long(b.__den) + - long(b.__num) * long(a.__den), - long(a.__den) * long(b.__den)) - - def __radd__(b, a): - return Rat(a) + b - - # a - b - def __sub__(a, b): - try: - return rat(a.__num * b.__den - b.__num * a.__den, - a.__den * b.__den) - except OverflowError: - return rat(long(a.__num) * long(b.__den) - - long(b.__num) * long(a.__den), - long(a.__den) * long(b.__den)) - - def __rsub__(b, a): - return Rat(a) - b - - # a * b - def __mul__(a, b): - try: - return rat(a.__num * b.__num, a.__den * b.__den) - except OverflowError: - return rat(long(a.__num) * long(b.__num), - long(a.__den) * long(b.__den)) - - def __rmul__(b, a): - return Rat(a) * b - - # a / b - def __div__(a, b): - try: - return rat(a.__num * b.__den, a.__den * b.__num) - except OverflowError: - return rat(long(a.__num) * long(b.__den), - long(a.__den) * long(b.__num)) - - def __rdiv__(b, a): - return Rat(a) / b - - # a % b - def __mod__(a, b): - div = a / b - try: - div = int(div) - except OverflowError: - div = long(div) - return a - b * div - - def __rmod__(b, a): - return Rat(a) % b - - # a ** b - def __pow__(a, b): - if b.__den != 1: - if isinstance(a.__num, complex): - a = complex(a) - else: - a = float(a) - if isinstance(b.__num, complex): - b = complex(b) - else: - b = float(b) - return a ** b - try: - return rat(a.__num ** b.__num, a.__den ** b.__num) - except OverflowError: - return rat(long(a.__num) ** b.__num, - long(a.__den) ** b.__num) - - def __rpow__(b, a): - return Rat(a) ** b - - # -a - def __neg__(a): - try: - return rat(-a.__num, a.__den) - except OverflowError: - # a.__num == sys.maxint - return rat(-long(a.__num), a.__den) - - # abs(a) - def __abs__(a): - return rat(abs(a.__num), a.__den) - - # int(a) - def __int__(a): - return int(a.__num / a.__den) - - # long(a) - def __long__(a): - return long(a.__num) / long(a.__den) - - # float(a) - def __float__(a): - return float(a.__num) / float(a.__den) - - # complex(a) - def __complex__(a): - return complex(a.__num) / complex(a.__den) - - # cmp(a,b) - def __cmp__(a, b): - diff = Rat(a - b) - if diff.__num < 0: - return -1 - elif diff.__num > 0: - return 1 - else: - return 0 - - def __rcmp__(b, a): - return cmp(Rat(a), b) - - # a != 0 - def __nonzero__(a): - return a.__num != 0 - - # coercion - def __coerce__(a, b): - return a, Rat(b) - -def test(): - '''\ - Test function for rat module. - - The expected output is (module some differences in floating - precission): - -1 - -1 - 0 0L 0.1 (0.1+0j) - [Rat(1,2), Rat(-3,10), Rat(1,25), Rat(1,4)] - [Rat(-3,10), Rat(1,25), Rat(1,4), Rat(1,2)] - 0 - (11/10) - (11/10) - 1.1 - OK - 2 1.5 (3/2) (1.5+1.5j) (15707963/5000000) - 2 2 2.0 (2+0j) - - 4 0 4 1 4 0 - 3.5 0.5 3.0 1.33333333333 2.82842712475 1 - (7/2) (1/2) 3 (4/3) 2.82842712475 1 - (3.5+1.5j) (0.5-1.5j) (3+3j) (0.666666666667-0.666666666667j) (1.43248815986+2.43884761145j) 1 - 1.5 1 1.5 (1.5+0j) - - 3.5 -0.5 3.0 0.75 2.25 -1 - 3.0 0.0 2.25 1.0 1.83711730709 0 - 3.0 0.0 2.25 1.0 1.83711730709 1 - (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1 - (3/2) 1 1.5 (1.5+0j) - - (7/2) (-1/2) 3 (3/4) (9/4) -1 - 3.0 0.0 2.25 1.0 1.83711730709 -1 - 3 0 (9/4) 1 1.83711730709 0 - (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1 - (1.5+1.5j) (1.5+1.5j) - - (3.5+1.5j) (-0.5+1.5j) (3+3j) (0.75+0.75j) 4.5j -1 - (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1 - (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1 - (3+3j) 0j 4.5j (1+0j) (-0.638110484918+0.705394566962j) 0 - ''' - print rat(-1L, 1) - print rat(1, -1) - a = rat(1, 10) - print int(a), long(a), float(a), complex(a) - b = rat(2, 5) - l = [a+b, a-b, a*b, a/b] - print l - l.sort() - print l - print rat(0, 1) - print a+1 - print a+1L - print a+1.0 - try: - print rat(1, 0) - raise SystemError, 'should have been ZeroDivisionError' - except ZeroDivisionError: - print 'OK' - print rat(2), rat(1.5), rat(3, 2), rat(1.5+1.5j), rat(31415926,10000000) - list = [2, 1.5, rat(3,2), 1.5+1.5j] - for i in list: - print i, - if not isinstance(i, complex): - print int(i), float(i), - print complex(i) - print - for j in list: - print i + j, i - j, i * j, i / j, i ** j, - if not (isinstance(i, complex) or - isinstance(j, complex)): - print cmp(i, j) - print - - -if __name__ == '__main__': - test() diff --git a/Doc/library/numeric.rst b/Doc/library/numeric.rst index d2b4d8b..4c65a43 100644 --- a/Doc/library/numeric.rst +++ b/Doc/library/numeric.rst @@ -21,6 +21,7 @@ The following modules are documented in this chapter: math.rst cmath.rst decimal.rst + rational.rst random.rst itertools.rst functools.rst diff --git a/Doc/library/rational.rst b/Doc/library/rational.rst new file mode 100644 index 0000000..dd18305 --- /dev/null +++ b/Doc/library/rational.rst @@ -0,0 +1,65 @@ + +:mod:`rational` --- Rational numbers +==================================== + +.. module:: rational + :synopsis: Rational numbers. +.. moduleauthor:: Jeffrey Yasskin <jyasskin at gmail.com> +.. sectionauthor:: Jeffrey Yasskin <jyasskin at gmail.com> +.. versionadded:: 2.6 + + +The :mod:`rational` module defines an immutable, infinite-precision +Rational number class. + + +.. class:: Rational(numerator=0, denominator=1) + Rational(other_rational) + + The first version requires that *numerator* and *denominator* are + instances of :class:`numbers.Integral` and returns a new + ``Rational`` representing ``numerator/denominator``. If + *denominator* is :const:`0`, raises a :exc:`ZeroDivisionError`. The + second version requires that *other_rational* is an instance of + :class:`numbers.Rational` and returns an instance of + :class:`Rational` with the same value. + + Implements all of the methods and operations from + :class:`numbers.Rational` and is hashable. + + +.. method:: Rational.from_float(flt) + + This classmethod constructs a :class:`Rational` representing the + exact value of *flt*, which must be a :class:`float`. Beware that + ``Rational.from_float(0.3)`` is not the same value as ``Rational(3, + 10)`` + + +.. method:: Rational.__floor__() + + Returns the greatest :class:`int` ``<= self``. Will be accessible + through :func:`math.floor` in Py3k. + + +.. method:: Rational.__ceil__() + + Returns the least :class:`int` ``>= self``. Will be accessible + through :func:`math.ceil` in Py3k. + + +.. method:: Rational.__round__() + Rational.__round__(ndigits) + + The first version returns the nearest :class:`int` to ``self``, + rounding half to even. The second version rounds ``self`` to the + nearest multiple of ``Rational(1, 10**ndigits)`` (logically, if + ``ndigits`` is negative), again rounding half toward even. Will be + accessible through :func:`round` in Py3k. + + +.. seealso:: + + Module :mod:`numbers` + The abstract base classes making up the numeric tower. + diff --git a/Lib/numbers.py b/Lib/numbers.py index 3c13290..8e02203 100644 --- a/Lib/numbers.py +++ b/Lib/numbers.py @@ -5,6 +5,7 @@ TODO: Fill out more detailed documentation on the operators.""" +from __future__ import division from abc import ABCMeta, abstractmethod, abstractproperty __all__ = ["Number", "Exact", "Inexact", @@ -63,7 +64,8 @@ class Complex(Number): def __complex__(self): """Return a builtin complex instance. Called for complex(self).""" - def __bool__(self): + # Will be __bool__ in 3.0. + def __nonzero__(self): """True if self != 0. Called for bool(self).""" return self != 0 @@ -98,6 +100,7 @@ class Complex(Number): """-self""" raise NotImplementedError + @abstractmethod def __pos__(self): """+self""" raise NotImplementedError @@ -122,12 +125,28 @@ class Complex(Number): @abstractmethod def __div__(self, other): - """self / other; should promote to float or complex when necessary.""" + """self / other without __future__ division + + May promote to float. + """ raise NotImplementedError @abstractmethod def __rdiv__(self, other): - """other / self""" + """other / self without __future__ division""" + raise NotImplementedError + + @abstractmethod + def __truediv__(self, other): + """self / other with __future__ division. + + Should promote to float when necessary. + """ + raise NotImplementedError + + @abstractmethod + def __rtruediv__(self, other): + """other / self with __future__ division""" raise NotImplementedError @abstractmethod diff --git a/Lib/rational.py b/Lib/rational.py new file mode 100755 index 0000000..d455dc6 --- /dev/null +++ b/Lib/rational.py @@ -0,0 +1,410 @@ +# Originally contributed by Sjoerd Mullender. +# Significantly modified by Jeffrey Yasskin <jyasskin at gmail.com>. + +"""Rational, infinite-precision, real numbers.""" + +from __future__ import division +import math +import numbers +import operator + +__all__ = ["Rational"] + +RationalAbc = numbers.Rational + + +def _gcd(a, b): + """Calculate the Greatest Common Divisor. + + Unless b==0, the result will have the same sign as b (so that when + b is divided by it, the result comes out positive). + """ + while b: + a, b = b, a%b + return a + + +def _binary_float_to_ratio(x): + """x -> (top, bot), a pair of ints s.t. x = top/bot. + + The conversion is done exactly, without rounding. + bot > 0 guaranteed. + Some form of binary fp is assumed. + Pass NaNs or infinities at your own risk. + + >>> _binary_float_to_ratio(10.0) + (10, 1) + >>> _binary_float_to_ratio(0.0) + (0, 1) + >>> _binary_float_to_ratio(-.25) + (-1, 4) + """ + + if x == 0: + return 0, 1 + f, e = math.frexp(x) + signbit = 1 + if f < 0: + f = -f + signbit = -1 + assert 0.5 <= f < 1.0 + # x = signbit * f * 2**e exactly + + # Suck up CHUNK bits at a time; 28 is enough so that we suck + # up all bits in 2 iterations for all known binary double- + # precision formats, and small enough to fit in an int. + CHUNK = 28 + top = 0 + # invariant: x = signbit * (top + f) * 2**e exactly + while f: + f = math.ldexp(f, CHUNK) + digit = trunc(f) + assert digit >> CHUNK == 0 + top = (top << CHUNK) | digit + f = f - digit + assert 0.0 <= f < 1.0 + e = e - CHUNK + assert top + + # Add in the sign bit. + top = signbit * top + + # now x = top * 2**e exactly; fold in 2**e + if e>0: + return (top * 2**e, 1) + else: + return (top, 2 ** -e) + + +class Rational(RationalAbc): + """This class implements rational numbers. + + Rational(8, 6) will produce a rational number equivalent to + 4/3. Both arguments must be Integral. The numerator defaults to 0 + and the denominator defaults to 1 so that Rational(3) == 3 and + Rational() == 0. + + """ + + __slots__ = ('_numerator', '_denominator') + + def __init__(self, numerator=0, denominator=1): + if (not isinstance(numerator, numbers.Integral) and + isinstance(numerator, RationalAbc) and + denominator == 1): + # Handle copies from other rationals. + other_rational = numerator + numerator = other_rational.numerator + denominator = other_rational.denominator + + if (not isinstance(numerator, numbers.Integral) or + not isinstance(denominator, numbers.Integral)): + raise TypeError("Rational(%(numerator)s, %(denominator)s):" + " Both arguments must be integral." % locals()) + + if denominator == 0: + raise ZeroDivisionError('Rational(%s, 0)' % numerator) + + g = _gcd(numerator, denominator) + self._numerator = int(numerator // g) + self._denominator = int(denominator // g) + + @classmethod + def from_float(cls, f): + """Converts a float to a rational number, exactly.""" + if not isinstance(f, float): + raise TypeError("%s.from_float() only takes floats, not %r (%s)" % + (cls.__name__, f, type(f).__name__)) + if math.isnan(f) or math.isinf(f): + raise TypeError("Cannot convert %r to %s." % (f, cls.__name__)) + return cls(*_binary_float_to_ratio(f)) + + @property + def numerator(a): + return a._numerator + + @property + def denominator(a): + return a._denominator + + def __repr__(self): + """repr(self)""" + return ('rational.Rational(%r,%r)' % + (self.numerator, self.denominator)) + + def __str__(self): + """str(self)""" + if self.denominator == 1: + return str(self.numerator) + else: + return '(%s/%s)' % (self.numerator, self.denominator) + + def _operator_fallbacks(monomorphic_operator, fallback_operator): + """Generates forward and reverse operators given a purely-rational + operator and a function from the operator module. + + Use this like: + __op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op) + + """ + def forward(a, b): + if isinstance(b, RationalAbc): + # Includes ints. + return monomorphic_operator(a, b) + elif isinstance(b, float): + return fallback_operator(float(a), b) + elif isinstance(b, complex): + return fallback_operator(complex(a), b) + else: + return NotImplemented + forward.__name__ = '__' + fallback_operator.__name__ + '__' + forward.__doc__ = monomorphic_operator.__doc__ + + def reverse(b, a): + if isinstance(a, RationalAbc): + # Includes ints. + return monomorphic_operator(a, b) + elif isinstance(a, numbers.Real): + return fallback_operator(float(a), float(b)) + elif isinstance(a, numbers.Complex): + return fallback_operator(complex(a), complex(b)) + else: + return NotImplemented + reverse.__name__ = '__r' + fallback_operator.__name__ + '__' + reverse.__doc__ = monomorphic_operator.__doc__ + + return forward, reverse + + def _add(a, b): + """a + b""" + return Rational(a.numerator * b.denominator + + b.numerator * a.denominator, + a.denominator * b.denominator) + + __add__, __radd__ = _operator_fallbacks(_add, operator.add) + + def _sub(a, b): + """a - b""" + return Rational(a.numerator * b.denominator - + b.numerator * a.denominator, + a.denominator * b.denominator) + + __sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub) + + def _mul(a, b): + """a * b""" + return Rational(a.numerator * b.numerator, a.denominator * b.denominator) + + __mul__, __rmul__ = _operator_fallbacks(_mul, operator.mul) + + def _div(a, b): + """a / b""" + return Rational(a.numerator * b.denominator, + a.denominator * b.numerator) + + __truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv) + __div__, __rdiv__ = _operator_fallbacks(_div, operator.div) + + @classmethod + def _floordiv(cls, a, b): + div = a / b + if isinstance(div, RationalAbc): + # trunc(math.floor(div)) doesn't work if the rational is + # more precise than a float because the intermediate + # rounding may cross an integer boundary. + return div.numerator // div.denominator + else: + return math.floor(div) + + def __floordiv__(a, b): + """a // b""" + # Will be math.floor(a / b) in 3.0. + return a._floordiv(a, b) + + def __rfloordiv__(b, a): + """a // b""" + # Will be math.floor(a / b) in 3.0. + return b._floordiv(a, b) + + @classmethod + def _mod(cls, a, b): + div = a // b + return a - b * div + + def __mod__(a, b): + """a % b""" + return a._mod(a, b) + + def __rmod__(b, a): + """a % b""" + return b._mod(a, b) + + def __pow__(a, b): + """a ** b + + If b is not an integer, the result will be a float or complex + since roots are generally irrational. If b is an integer, the + result will be rational. + + """ + if isinstance(b, RationalAbc): + if b.denominator == 1: + power = b.numerator + if power >= 0: + return Rational(a.numerator ** power, + a.denominator ** power) + else: + return Rational(a.denominator ** -power, + a.numerator ** -power) + else: + # A fractional power will generally produce an + # irrational number. + return float(a) ** float(b) + else: + return float(a) ** b + + def __rpow__(b, a): + """a ** b""" + if b.denominator == 1 and b.numerator >= 0: + # If a is an int, keep it that way if possible. + return a ** b.numerator + + if isinstance(a, RationalAbc): + return Rational(a.numerator, a.denominator) ** b + + if b.denominator == 1: + return a ** b.numerator + + return a ** float(b) + + def __pos__(a): + """+a: Coerces a subclass instance to Rational""" + return Rational(a.numerator, a.denominator) + + def __neg__(a): + """-a""" + return Rational(-a.numerator, a.denominator) + + def __abs__(a): + """abs(a)""" + return Rational(abs(a.numerator), a.denominator) + + def __trunc__(a): + """trunc(a)""" + if a.numerator < 0: + return -(-a.numerator // a.denominator) + else: + return a.numerator // a.denominator + + def __floor__(a): + """Will be math.floor(a) in 3.0.""" + return a.numerator // a.denominator + + def __ceil__(a): + """Will be math.ceil(a) in 3.0.""" + # The negations cleverly convince floordiv to return the ceiling. + return -(-a.numerator // a.denominator) + + def __round__(self, ndigits=None): + """Will be round(self, ndigits) in 3.0. + + Rounds half toward even. + """ + if ndigits is None: + floor, remainder = divmod(self.numerator, self.denominator) + if remainder * 2 < self.denominator: + return floor + elif remainder * 2 > self.denominator: + return floor + 1 + # Deal with the half case: + elif floor % 2 == 0: + return floor + else: + return floor + 1 + shift = 10**abs(ndigits) + # See _operator_fallbacks.forward to check that the results of + # these operations will always be Rational and therefore have + # __round__(). + if ndigits > 0: + return Rational((self * shift).__round__(), shift) + else: + return Rational((self / shift).__round__() * shift) + + def __hash__(self): + """hash(self) + + Tricky because values that are exactly representable as a + float must have the same hash as that float. + + """ + if self.denominator == 1: + # Get integers right. + return hash(self.numerator) + # Expensive check, but definitely correct. + if self == float(self): + return hash(float(self)) + else: + # Use tuple's hash to avoid a high collision rate on + # simple fractions. + return hash((self.numerator, self.denominator)) + + def __eq__(a, b): + """a == b""" + if isinstance(b, RationalAbc): + return (a.numerator == b.numerator and + a.denominator == b.denominator) + if isinstance(b, numbers.Complex) and b.imag == 0: + b = b.real + if isinstance(b, float): + return a == a.from_float(b) + else: + # XXX: If b.__eq__ is implemented like this method, it may + # give the wrong answer after float(a) changes a's + # value. Better ways of doing this are welcome. + return float(a) == b + + def _subtractAndCompareToZero(a, b, op): + """Helper function for comparison operators. + + Subtracts b from a, exactly if possible, and compares the + result with 0 using op, in such a way that the comparison + won't recurse. If the difference raises a TypeError, returns + NotImplemented instead. + + """ + if isinstance(b, numbers.Complex) and b.imag == 0: + b = b.real + if isinstance(b, float): + b = a.from_float(b) + try: + # XXX: If b <: Real but not <: RationalAbc, this is likely + # to fall back to a float. If the actual values differ by + # less than MIN_FLOAT, this could falsely call them equal, + # which would make <= inconsistent with ==. Better ways of + # doing this are welcome. + diff = a - b + except TypeError: + return NotImplemented + if isinstance(diff, RationalAbc): + return op(diff.numerator, 0) + return op(diff, 0) + + def __lt__(a, b): + """a < b""" + return a._subtractAndCompareToZero(b, operator.lt) + + def __gt__(a, b): + """a > b""" + return a._subtractAndCompareToZero(b, operator.gt) + + def __le__(a, b): + """a <= b""" + return a._subtractAndCompareToZero(b, operator.le) + + def __ge__(a, b): + """a >= b""" + return a._subtractAndCompareToZero(b, operator.ge) + + def __nonzero__(a): + """a != 0""" + return a.numerator != 0 diff --git a/Lib/test/test_rational.py b/Lib/test/test_rational.py new file mode 100644 index 0000000..654c46d --- /dev/null +++ b/Lib/test/test_rational.py @@ -0,0 +1,279 @@ +"""Tests for Lib/rational.py.""" + +from decimal import Decimal +from test.test_support import run_unittest, verbose +import math +import operator +import rational +import unittest +R = rational.Rational + +def _components(r): + return (r.numerator, r.denominator) + +class RationalTest(unittest.TestCase): + + def assertTypedEquals(self, expected, actual): + """Asserts that both the types and values are the same.""" + self.assertEquals(type(expected), type(actual)) + self.assertEquals(expected, actual) + + def assertRaisesMessage(self, exc_type, message, + callable, *args, **kwargs): + """Asserts that callable(*args, **kwargs) raises exc_type(message).""" + try: + callable(*args, **kwargs) + except exc_type, e: + self.assertEquals(message, str(e)) + else: + self.fail("%s not raised" % exc_type.__name__) + + def testInit(self): + self.assertEquals((0, 1), _components(R())) + self.assertEquals((7, 1), _components(R(7))) + self.assertEquals((7, 3), _components(R(R(7, 3)))) + + self.assertEquals((-1, 1), _components(R(-1, 1))) + self.assertEquals((-1, 1), _components(R(1, -1))) + self.assertEquals((1, 1), _components(R(-2, -2))) + self.assertEquals((1, 2), _components(R(5, 10))) + self.assertEquals((7, 15), _components(R(7, 15))) + self.assertEquals((10**23, 1), _components(R(10**23))) + + self.assertRaisesMessage(ZeroDivisionError, "Rational(12, 0)", + R, 12, 0) + self.assertRaises(TypeError, R, 1.5) + self.assertRaises(TypeError, R, 1.5 + 3j) + + def testFromFloat(self): + self.assertRaisesMessage( + TypeError, "Rational.from_float() only takes floats, not 3 (int)", + R.from_float, 3) + + self.assertEquals((0, 1), _components(R.from_float(-0.0))) + self.assertEquals((10, 1), _components(R.from_float(10.0))) + self.assertEquals((-5, 2), _components(R.from_float(-2.5))) + self.assertEquals((99999999999999991611392, 1), + _components(R.from_float(1e23))) + self.assertEquals(float(10**23), float(R.from_float(1e23))) + self.assertEquals((3602879701896397, 1125899906842624), + _components(R.from_float(3.2))) + self.assertEquals(3.2, float(R.from_float(3.2))) + + inf = 1e1000 + nan = inf - inf + self.assertRaisesMessage( + TypeError, "Cannot convert inf to Rational.", + R.from_float, inf) + self.assertRaisesMessage( + TypeError, "Cannot convert -inf to Rational.", + R.from_float, -inf) + self.assertRaisesMessage( + TypeError, "Cannot convert nan to Rational.", + R.from_float, nan) + + def testConversions(self): + self.assertTypedEquals(-1, trunc(R(-11, 10))) + self.assertTypedEquals(-2, R(-11, 10).__floor__()) + self.assertTypedEquals(-1, R(-11, 10).__ceil__()) + self.assertTypedEquals(-1, R(-10, 10).__ceil__()) + + self.assertTypedEquals(0, R(-1, 10).__round__()) + self.assertTypedEquals(0, R(-5, 10).__round__()) + self.assertTypedEquals(-2, R(-15, 10).__round__()) + self.assertTypedEquals(-1, R(-7, 10).__round__()) + + self.assertEquals(False, bool(R(0, 1))) + self.assertEquals(True, bool(R(3, 2))) + self.assertTypedEquals(0.1, float(R(1, 10))) + + # Check that __float__ isn't implemented by converting the + # numerator and denominator to float before dividing. + self.assertRaises(OverflowError, float, long('2'*400+'7')) + self.assertAlmostEquals(2.0/3, + float(R(long('2'*400+'7'), long('3'*400+'1')))) + + self.assertTypedEquals(0.1+0j, complex(R(1,10))) + + def testRound(self): + self.assertTypedEquals(R(-200), R(-150).__round__(-2)) + self.assertTypedEquals(R(-200), R(-250).__round__(-2)) + self.assertTypedEquals(R(30), R(26).__round__(-1)) + self.assertTypedEquals(R(-2, 10), R(-15, 100).__round__(1)) + self.assertTypedEquals(R(-2, 10), R(-25, 100).__round__(1)) + + + def testArithmetic(self): + self.assertEquals(R(1, 2), R(1, 10) + R(2, 5)) + self.assertEquals(R(-3, 10), R(1, 10) - R(2, 5)) + self.assertEquals(R(1, 25), R(1, 10) * R(2, 5)) + self.assertEquals(R(1, 4), R(1, 10) / R(2, 5)) + self.assertTypedEquals(2, R(9, 10) // R(2, 5)) + self.assertTypedEquals(10**23, R(10**23, 1) // R(1)) + self.assertEquals(R(2, 3), R(-7, 3) % R(3, 2)) + self.assertEquals(R(8, 27), R(2, 3) ** R(3)) + self.assertEquals(R(27, 8), R(2, 3) ** R(-3)) + self.assertTypedEquals(2.0, R(4) ** R(1, 2)) + # Will return 1j in 3.0: + self.assertRaises(ValueError, pow, R(-1), R(1, 2)) + + def testMixedArithmetic(self): + self.assertTypedEquals(R(11, 10), R(1, 10) + 1) + self.assertTypedEquals(1.1, R(1, 10) + 1.0) + self.assertTypedEquals(1.1 + 0j, R(1, 10) + (1.0 + 0j)) + self.assertTypedEquals(R(11, 10), 1 + R(1, 10)) + self.assertTypedEquals(1.1, 1.0 + R(1, 10)) + self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + R(1, 10)) + + self.assertTypedEquals(R(-9, 10), R(1, 10) - 1) + self.assertTypedEquals(-0.9, R(1, 10) - 1.0) + self.assertTypedEquals(-0.9 + 0j, R(1, 10) - (1.0 + 0j)) + self.assertTypedEquals(R(9, 10), 1 - R(1, 10)) + self.assertTypedEquals(0.9, 1.0 - R(1, 10)) + self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - R(1, 10)) + + self.assertTypedEquals(R(1, 10), R(1, 10) * 1) + self.assertTypedEquals(0.1, R(1, 10) * 1.0) + self.assertTypedEquals(0.1 + 0j, R(1, 10) * (1.0 + 0j)) + self.assertTypedEquals(R(1, 10), 1 * R(1, 10)) + self.assertTypedEquals(0.1, 1.0 * R(1, 10)) + self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * R(1, 10)) + + self.assertTypedEquals(R(1, 10), R(1, 10) / 1) + self.assertTypedEquals(0.1, R(1, 10) / 1.0) + self.assertTypedEquals(0.1 + 0j, R(1, 10) / (1.0 + 0j)) + self.assertTypedEquals(R(10, 1), 1 / R(1, 10)) + self.assertTypedEquals(10.0, 1.0 / R(1, 10)) + self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / R(1, 10)) + + self.assertTypedEquals(0, R(1, 10) // 1) + self.assertTypedEquals(0.0, R(1, 10) // 1.0) + self.assertTypedEquals(10, 1 // R(1, 10)) + self.assertTypedEquals(10**23, 10**22 // R(1, 10)) + self.assertTypedEquals(10.0, 1.0 // R(1, 10)) + + self.assertTypedEquals(R(1, 10), R(1, 10) % 1) + self.assertTypedEquals(0.1, R(1, 10) % 1.0) + self.assertTypedEquals(R(0, 1), 1 % R(1, 10)) + self.assertTypedEquals(0.0, 1.0 % R(1, 10)) + + # No need for divmod since we don't override it. + + # ** has more interesting conversion rules. + self.assertTypedEquals(R(100, 1), R(1, 10) ** -2) + self.assertTypedEquals(R(100, 1), R(10, 1) ** 2) + self.assertTypedEquals(0.1, R(1, 10) ** 1.0) + self.assertTypedEquals(0.1 + 0j, R(1, 10) ** (1.0 + 0j)) + self.assertTypedEquals(4 , 2 ** R(2, 1)) + # Will return 1j in 3.0: + self.assertRaises(ValueError, pow, (-1), R(1, 2)) + self.assertTypedEquals(R(1, 4) , 2 ** R(-2, 1)) + self.assertTypedEquals(2.0 , 4 ** R(1, 2)) + self.assertTypedEquals(0.25, 2.0 ** R(-2, 1)) + self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** R(1, 10)) + + def testMixingWithDecimal(self): + """Decimal refuses mixed comparisons.""" + self.assertRaisesMessage( + TypeError, + "unsupported operand type(s) for +: 'Rational' and 'Decimal'", + operator.add, R(3,11), Decimal('3.1415926')) + self.assertNotEquals(R(5, 2), Decimal('2.5')) + + def testComparisons(self): + self.assertTrue(R(1, 2) < R(2, 3)) + self.assertFalse(R(1, 2) < R(1, 2)) + self.assertTrue(R(1, 2) <= R(2, 3)) + self.assertTrue(R(1, 2) <= R(1, 2)) + self.assertFalse(R(2, 3) <= R(1, 2)) + self.assertTrue(R(1, 2) == R(1, 2)) + self.assertFalse(R(1, 2) == R(1, 3)) + + def testMixedLess(self): + self.assertTrue(2 < R(5, 2)) + self.assertFalse(2 < R(4, 2)) + self.assertTrue(R(5, 2) < 3) + self.assertFalse(R(4, 2) < 2) + + self.assertTrue(R(1, 2) < 0.6) + self.assertFalse(R(1, 2) < 0.4) + self.assertTrue(0.4 < R(1, 2)) + self.assertFalse(0.5 < R(1, 2)) + + def testMixedLessEqual(self): + self.assertTrue(0.5 <= R(1, 2)) + self.assertFalse(0.6 <= R(1, 2)) + self.assertTrue(R(1, 2) <= 0.5) + self.assertFalse(R(1, 2) <= 0.4) + self.assertTrue(2 <= R(4, 2)) + self.assertFalse(2 <= R(3, 2)) + self.assertTrue(R(4, 2) <= 2) + self.assertFalse(R(5, 2) <= 2) + + def testBigFloatComparisons(self): + # Because 10**23 can't be represented exactly as a float: + self.assertFalse(R(10**23) == float(10**23)) + # The first test demonstrates why these are important. + self.assertFalse(1e23 < float(R(trunc(1e23) + 1))) + self.assertTrue(1e23 < R(trunc(1e23) + 1)) + self.assertFalse(1e23 <= R(trunc(1e23) - 1)) + self.assertTrue(1e23 > R(trunc(1e23) - 1)) + self.assertFalse(1e23 >= R(trunc(1e23) + 1)) + + def testBigComplexComparisons(self): + self.assertFalse(R(10**23) == complex(10**23)) + self.assertTrue(R(10**23) > complex(10**23)) + self.assertFalse(R(10**23) <= complex(10**23)) + + def testMixedEqual(self): + self.assertTrue(0.5 == R(1, 2)) + self.assertFalse(0.6 == R(1, 2)) + self.assertTrue(R(1, 2) == 0.5) + self.assertFalse(R(1, 2) == 0.4) + self.assertTrue(2 == R(4, 2)) + self.assertFalse(2 == R(3, 2)) + self.assertTrue(R(4, 2) == 2) + self.assertFalse(R(5, 2) == 2) + + def testStringification(self): + self.assertEquals("rational.Rational(7,3)", repr(R(7, 3))) + self.assertEquals("(7/3)", str(R(7, 3))) + self.assertEquals("7", str(R(7, 1))) + + def testHash(self): + self.assertEquals(hash(2.5), hash(R(5, 2))) + self.assertEquals(hash(10**50), hash(R(10**50))) + self.assertNotEquals(hash(float(10**23)), hash(R(10**23))) + + def testApproximatePi(self): + # Algorithm borrowed from + # http://docs.python.org/lib/decimal-recipes.html + three = R(3) + lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24 + while abs(s - lasts) > R(1, 10**9): + lasts = s + n, na = n+na, na+8 + d, da = d+da, da+32 + t = (t * n) / d + s += t + self.assertAlmostEquals(math.pi, s) + + def testApproximateCos1(self): + # Algorithm borrowed from + # http://docs.python.org/lib/decimal-recipes.html + x = R(1) + i, lasts, s, fact, num, sign = 0, 0, R(1), 1, 1, 1 + while abs(s - lasts) > R(1, 10**9): + lasts = s + i += 2 + fact *= i * (i-1) + num *= x * x + sign *= -1 + s += num / fact * sign + self.assertAlmostEquals(math.cos(1), s) + +def test_main(): + run_unittest(RationalTest) + +if __name__ == '__main__': + test_main() |