Interoperability with Decimal
=============================

    >>> import gmpy2 as G
    >>> from gmpy2 import mpz, mpq, mpfr
    >>> from decimal import Decimal

Test comparisons
----------------

Non-trivial comparions between mpfr and Decimal instances are only equal
when the fractional can be written at 1/2**n.

    >>> mpfr('123.456') == Decimal('123.456')
    False
    >>> mpfr('123.5') == Decimal('123.5')
    True
    >>> mpq(123456,1000) == Decimal('123.456')
    True
    >>> mpz(123) == Decimal(123)
    True
    >>> mpfr('123.456') > Decimal('123.456')
    True
    >>> mpfr('123.456') < Decimal('123.456')
    False
    >>> Decimal('123.456') > mpfr('123.456')
    False
    >>> Decimal('123.456') < mpfr('123.456')
    True

Test elementary operations
--------------------------

    >>> mpz(23) == Decimal(23)
    True
    >>> mpz(Decimal('123.456'))
    mpz(123)
    >>> mpq(Decimal('123.456'))
    mpq(15432,125)
    >>> mpfr(Decimal('123.456'))
    mpfr('123.456')

    >>> f = mpfr('123.456')
    >>> q = mpq('789123/1000')
    >>> z = mpz('234')
    >>> dd = Decimal('12.34')
    >>> fd = Decimal('123.456')
    >>> qd = Decimal('789.123')
    >>> zd = Decimal('234')

    >>> f+dd
    mpfr('135.79599999999999')
    >>> dd+f
    mpfr('135.79599999999999')
    >>> q+dd
    mpfr('801.46300000000008')
    >>> dd+q
    mpfr('801.46300000000008')
    >>> z+dd
    mpfr('246.34')
    >>> dd+z
    mpfr('246.34')
    >>> f-dd
    mpfr('111.116')
    >>> dd-f
    mpfr('-111.116')
    >>> q-dd
    mpfr('776.78300000000002')
    >>> dd-q
    mpfr('-776.78300000000002')
    >>> z-dd
    mpfr('221.66')
    >>> dd-z
    mpfr('-221.66')
    >>> f*dd
    mpfr('1523.44704')
    >>> dd*f
    mpfr('1523.44704')
    >>> q*dd
    mpfr('9737.7778200000012')
    >>> dd*q
    mpfr('9737.7778200000012')
    >>> z*dd
    mpfr('2887.5599999999999')
    >>> dd*z
    mpfr('2887.5599999999999')
    >>> f/dd
    mpfr('10.00453808752026')
    >>> dd/f
    mpfr('0.099954639709694135')
    >>> q/dd
    mpfr('63.948379254457052')
    >>> dd/q
    mpfr('0.015637612894314319')
    >>> z/dd
    mpfr('18.962722852512155')
    >>> dd/z
    mpfr('0.052735042735042738')

    >>> G.ceil(dd)
    mpfr('13.0')
    >>> G.floor(dd)
    mpfr('12.0')
    >>> G.trunc(dd)
    mpfr('12.0')
    >>> mpfr(dd).precision
    53

    >>> G.sin(Decimal("123.456"))
    mpfr('-0.80393736857282394')
    >>> G.sqrt(Decimal("123.456"))
    mpfr('11.111075555498667')
    >>> G.is_nan(Decimal("123.456"))
    False
    >>> G.is_nan(Decimal("NaN"))
    True
    >>> G.is_nan(Decimal("Inf"))
    False
    >>> G.is_inf(Decimal("Inf"))
    True
    >>> G.is_inf(Decimal("-Inf"))
    True