MPQ Functionality
=================

Testing of mpq functionality is split into multiple files.

    test_mpq.txt
        Test basic functionality and stuff not covered anywhere else.

    test_mpq_io.txt
        Test input/output and formating.

    test_mpq_comp.txt
        Test comparisons.

    >>> import gmpy2 as G
    >>> from fractions import Fraction as F
    >>> from gmpy2 import mpz, mpq, mpfr
    >>> a = mpq(3,11)
    >>> b = mpq(1,2)
    >>> c = F(5,7)

Test elementary operations
==========================

Test addition
-------------


Test subtraction
----------------

    >>> a-b
    mpq(-5,22)
    >>> b-a
    mpq(5,22)
    >>> a-1
    mpq(-8,11)
    >>> 1-a
    mpq(8,11)
    >>> a-c
    mpq(-34,77)
    >>> c-a
    mpq(34,77)
    >>> a-a
    mpq(0,1)
    >>> a-mpz(123456)
    mpq(-1358013,11)
    >>> mpz(-123456)-a
    mpq(-1358019,11)
    >>> a-'b'
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: unsupported operand type(s) for -: 'mpq' and 'str'
    >>> 'b'-a
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: unsupported operand type(s) for -: 'str' and 'mpq'

Test multiplication
-------------------

    >>> a*b
    mpq(3,22)
    >>> b*a
    mpq(3,22)
    >>> a*0
    mpq(0,1)
    >>> 0*a
    mpq(0,1)
    >>> a*-1
    mpq(-3,11)
    >>> -1*a
    mpq(-3,11)
    >>> a*mpz(17)
    mpq(51,11)
    >>> mpz(17)*a
    mpq(51,11)
    >>> a*a
    mpq(9,121)
    >>> a*'b'
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: can't multiply sequence by non-int of type 'mpq'
    >>> 'b'*a
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: can't multiply sequence by non-int of type 'mpq'

Test division
-------------

    >>> a//b
    mpz(0)
    >>> b//a
    mpz(1)
    >>> a/b
    mpq(6,11)
    >>> b/a
    mpq(11,6)
    >>> a/0
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ZeroDivisionError: division or modulo by zero
    >>> a//0
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ZeroDivisionError: division or modulo by zero
    >>> 0//a
    mpz(0)
    >>> 0/a
    mpq(0,1)

Test modulo
-----------

    >>> a%b
    mpq(3,11)
    >>> b%a
    mpq(5,22)
    >>> divmod(a,b)
    (mpz(0), mpq(3,11))
    >>> divmod(b,a)
    (mpz(1), mpq(5,22))
    >>> divmod(a,0)
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ZeroDivisionError: 'mpq' division or modulo by zero
    >>> divmod(17,a)
    (mpz(62), mpq(1,11))
    >>> divmod(mpz(17),a)
    (mpz(62), mpq(1,11))
    >>> divmod(a,c)
    (mpz(0), mpq(3,11))

Test pickle
-----------

    >>> import pickle
    >>> pickle.loads(pickle.dumps(G.mpq(1234,6789)))
    mpq(1234,6789)
    >>> pickle.loads(pickle.dumps(G.mpq(-1234,6789)))
    mpq(-1234,6789)
    >>> pickle.loads(pickle.dumps(G.mpq(0,1)))
    mpq(0,1)

Test operations involving NaN/Inf
---------------------------------

    >>> a + float('Inf')
    mpfr('inf')
    >>> float('Inf') + a
    mpfr('inf')
    >>> a + float('-Inf')
    mpfr('-inf')
    >>> float('-Inf') + a
    mpfr('-inf')
    >>> a + float('nan')
    mpfr('nan')
    >>> float('nan') + a
    mpfr('nan')
    >>> a - float('Inf')
    mpfr('-inf')
    >>> float('Inf') - a
    mpfr('inf')
    >>> a - float('-Inf')
    mpfr('inf')
    >>> float('-Inf') - a
    mpfr('-inf')
    >>> a - float('nan')
    mpfr('nan')
    >>> float('nan') - a
    mpfr('nan')
    >>> a * float('Inf')
    mpfr('inf')
    >>> float('Inf') * a
    mpfr('inf')
    >>> a * float('-Inf')
    mpfr('-inf')
    >>> float('-Inf') * a
    mpfr('-inf')
    >>> -a * float('Inf')
    mpfr('-inf')
    >>> float('Inf') * -a
    mpfr('-inf')
    >>> -a * float('-Inf')
    mpfr('inf')
    >>> float('-Inf') * -a
    mpfr('inf')
    >>> a * float('nan')
    mpfr('nan')
    >>> float('nan') * a
    mpfr('nan')
    >>> G.mpz(0) * float('Inf')
    mpfr('nan')
    >>> G.mpz(0) * float('-Inf')
    mpfr('nan')
    >>> float('Inf') * G.mpz(0)
    mpfr('nan')
    >>> float('-Inf') * G.mpz(0)
    mpfr('nan')
    >>> a / float('Inf')
    mpfr('0.0')
    >>> -a / float('Inf')
    mpfr('-0.0')
    >>> float('Inf') / a
    mpfr('inf')
    >>> float('Inf') / -a
    mpfr('-inf')
    >>> a / float('-Inf')
    mpfr('-0.0')
    >>> -a / float('-Inf')
    mpfr('0.0')
    >>> float('-Inf') / a
    mpfr('-inf')
    >>> float('-Inf') / -a
    mpfr('inf')
    >>> a / float('nan')
    mpfr('nan')
    >>> float('nan') / a
    mpfr('nan')
    >>> float('nan') / G.mpz(0)
    mpfr('nan')
    >>> float('nan') / G.mpz(0)
    mpfr('nan')

    >>> a + mpfr('Inf')
    mpfr('inf')
    >>> mpfr('Inf') + a
    mpfr('inf')
    >>> a + mpfr('-Inf')
    mpfr('-inf')
    >>> mpfr('-Inf') + a
    mpfr('-inf')
    >>> a + mpfr('nan')
    mpfr('nan')
    >>> mpfr('nan') + a
    mpfr('nan')
    >>> a - mpfr('Inf')
    mpfr('-inf')
    >>> mpfr('Inf') - a
    mpfr('inf')
    >>> a - mpfr('-Inf')
    mpfr('inf')
    >>> mpfr('-Inf') - a
    mpfr('-inf')
    >>> a - mpfr('nan')
    mpfr('nan')
    >>> mpfr('nan') - a
    mpfr('nan')
    >>> a * mpfr('Inf')
    mpfr('inf')
    >>> mpfr('Inf') * a
    mpfr('inf')
    >>> a * mpfr('-Inf')
    mpfr('-inf')
    >>> mpfr('-Inf') * a
    mpfr('-inf')
    >>> -a * mpfr('Inf')
    mpfr('-inf')
    >>> mpfr('Inf') * -a
    mpfr('-inf')
    >>> -a * mpfr('-Inf')
    mpfr('inf')
    >>> mpfr('-Inf') * -a
    mpfr('inf')
    >>> a * mpfr('nan')
    mpfr('nan')
    >>> mpfr('nan') * a
    mpfr('nan')
    >>> G.mpz(0) * mpfr('Inf')
    mpfr('nan')
    >>> G.mpz(0) * mpfr('-Inf')
    mpfr('nan')
    >>> mpfr('Inf') * G.mpz(0)
    mpfr('nan')
    >>> mpfr('-Inf') * G.mpz(0)
    mpfr('nan')
    >>> a / mpfr('Inf')
    mpfr('0.0')
    >>> -a / mpfr('Inf')
    mpfr('-0.0')
    >>> mpfr('Inf') / a
    mpfr('inf')
    >>> mpfr('Inf') / -a
    mpfr('-inf')
    >>> a / mpfr('-Inf')
    mpfr('-0.0')
    >>> -a / mpfr('-Inf')
    mpfr('0.0')
    >>> mpfr('-Inf') / a
    mpfr('-inf')
    >>> mpfr('-Inf') / -a
    mpfr('inf')
    >>> a / mpfr('nan')
    mpfr('nan')
    >>> mpfr('nan') / a
    mpfr('nan')
    >>> mpfr('nan') / G.mpz(0)
    mpfr('nan')
    >>> mpfr('nan') / G.mpz(0)
    mpfr('nan')

    >>> divmod(a, float('Inf'))
    (mpfr('0.0'), mpfr('0.27272727272727271'))
    >>> divmod(a, float('-Inf'))
    (mpfr('-1.0'), mpfr('-inf'))
    >>> divmod(-a, float('Inf'))
    (mpfr('-1.0'), mpfr('inf'))
    >>> divmod(-a, float('-Inf'))
    (mpfr('0.0'), mpfr('-0.27272727272727271'))
    >>> divmod(a, float('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(-a, float('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(G.mpz(0), float('Inf'))
    (mpfr('0.0'), mpfr('0.0'))
    >>> divmod(G.mpz(0), float('-Inf'))
    (mpfr('-0.0'), mpfr('-0.0'))
    >>> divmod(G.mpz(0), float('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('-Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('-Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('nan'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('nan'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('Inf'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('-Inf'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('nan'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))

    >>> divmod(a, mpfr('Inf'))
    (mpfr('0.0'), mpfr('0.27272727272727271'))
    >>> divmod(a, mpfr('-Inf'))
    (mpfr('-1.0'), mpfr('-inf'))
    >>> divmod(-a, mpfr('Inf'))
    (mpfr('-1.0'), mpfr('inf'))
    >>> divmod(-a, mpfr('-Inf'))
    (mpfr('0.0'), mpfr('-0.27272727272727271'))
    >>> divmod(a, mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(-a, mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(G.mpz(0), mpfr('Inf'))
    (mpfr('0.0'), mpfr('0.0'))
    >>> divmod(G.mpz(0), mpfr('-Inf'))
    (mpfr('-0.0'), mpfr('-0.0'))
    >>> divmod(G.mpz(0), mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('Inf'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))