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

Testing of mpq functionality is split into multiple files.

>>> import gmpy2 as G
>>> ctx = G.get_context()
>>> from fractions import Fraction as F
>>> from gmpy2 import mpz, mpq, mpfr, mpc
>>> from supportclasses import *
>>> 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'
>>> 1
1

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'
>>> 1
1

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

>>> a//b
mpz(0)
>>> b//a
mpz(1)
>>> a/b
mpq(6,11)
>>> gmpy2.div(a, b)
mpq(6,11)
>>> ctx.div(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)
>>> mpq(355, 113) // 2
mpz(1)
>>> mpq(355, 113) // mpz(2)
mpz(1)
>>> a / z
mpq(3,22)
>>> mpq(355, 113) // z
mpz(1)
>>> mpq(3,11) / q
mpq(2,11)
>>> mpq(3,11) // q
mpz(0)
>>> a / mpc(5, 4)
mpc('0.03325942350332594-0.02660753880266075j')
>>> a / mpq(0,1)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ZeroDivisionError: division or modulo by zero
>>> a / 'str'
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unsupported operand type(s) for /: 'mpq' and 'str'
>>> 1
1

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

>>> a%b
mpq(3,11)
>>> b%a
mpq(5,22)
>>> a%z
mpq(3,11)
>>> mpq(3,1) % q
mpq(0,1)
>>> 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
>>> a % mpq(0,5)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ZeroDivisionError: division or modulo by zero
>>> ctx.mod(a, mpfr(1.5))
mpfr('0.27272727272727271')
>>> ctx.mod(a, mpc(0.5, 2))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can't take mod of complex number
>>> ctx.mod(a, mpq(0, 2))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ZeroDivisionError: 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))
>>> a % mpfr(1.5)
mpfr('0.27272727272727271')
>>> a % mpc(0.5, 2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can't take mod of complex number
>>> a % 'str'
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unsupported operand type(s) for %: 'mpq' and 'str'
>>> ctx.mod(a, 'str')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: mod() argument type not supported
>>> 1
1

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)
>>>
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'))
>>> 1
1

Test qdiv
---------

>>> gmpy2.qdiv(8,1)
mpz(8)
>>> gmpy2.qdiv(8,2)
mpz(4)
>>> gmpy2.qdiv(8,3)
mpq(8,3)
>>> gmpy2.qdiv(8,4)
mpz(2)
>>> gmpy2.qdiv(gmpy2.mpq(3,4), gmpy2.mpq(1,3))
mpq(9,4)
>>> gmpy2.qdiv(gmpy2.mpq(3,4), gmpy2.mpq(1,4))
mpz(3)
>>> args = gmpy2.mpq(2), 1/gmpy2.mpq(2)
>>> gmpy2.qdiv(*args)
mpz(4)
>>> args == (gmpy2.mpq(2), 1/gmpy2.mpq(2))
True

Test Number Protocol
--------------------

>>> a.numerator
mpz(3)
>>> a.denominator
mpz(11)
>>> a.real
mpq(3,11)
>>> a.imag
mpz(0)
>>> a.conjugate()
mpq(3,11)

Test sign function
------------------

>>> gmpy2.sign(a)
1
>>> gmpy2.sign(-a)
-1
>>> gmpy2.sign(mpq(0,5))
0
>>> gmpy2.sign('str')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: sign() argument type not supported
>>> 1
1