Tests for functions and methods of gmpy2_math.c
===============================================

Note: tests for trigonometric operations are in
files test_mpfr_trig.txt and test_mpc_trig.txt.

>>> from gmpy2 import mpz, mpq, mpfr, mpc
>>> import gmpy2
>>> ctx = gmpy2.get_context()

>>> ctx.log(mpfr(2))
mpfr('0.69314718055994529')
>>> ctx.log(mpfr(1))
mpfr('0.0')
>>> gmpy2.log10(mpfr(10))
mpfr('1.0')
>>> ctx.exp(10.5)
mpfr('36315.502674246636')
>>> gmpy2.exp(mpfr(1))
mpfr('2.7182818284590451')

Tests sqrt
----------

>>> gmpy2.sqrt(float(25))
mpfr('5.0')
>>> 19.5 ** 2
380.25
>>> ctx.sqrt(mpfr(380.25))
mpfr('19.5')
>>> ctx.allow_complex = True
>>> ctx.sqrt(mpfr(-380.25))
mpc('0.0+19.5j')
>>> ctx.allow_complex = False
>>> ctx.sqrt(mpfr(-380.25))
mpfr('nan')
>>> ctx.sqrt(complex(16,4))
mpc('4.0306589103067649+0.4961967868047123j')
>>> ctx.sqrt(mpc(16,4))
mpc('4.0306589103067649+0.4961967868047123j')
>>> gmpy2.rec_sqrt(mpfr('380.25'))
mpfr('0.05128205128205128')

Tests root
----------

>>> ctx.rootn(5.5)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: rootn() requires 2 arguments
>>> ctx.rootn(mpc(4,1), 4)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: rootn() argument type not supported
>>> ctx.rootn(mpfr(25), 4)
mpfr('2.2360679774997898')
>>> ctx.rootn(mpfr(25), 4.0)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: rootn() argument type not supported
>>> ctx.root(mpfr(25))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: root() requires 2 arguments

Tests other binary operations
-----------------------------

>>> gmpy2.jn(43.2, 5)
mpfr('-0.11672089168206982')
>>> gmpy2.jn(43.2, 1.2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: jn() argument type not supported
>>> gmpy2.yn(43.2, 5)
mpfr('-0.034805474763124698')
>>> gmpy2.yn(43.2, 5.5)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: yn() argument type not supported
>>> gmpy2.agm(mpc(4,4), 5)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: agm() argument type not supported
>>> gmpy2.fmod(mpfr(25), mpfr(2.5))
mpfr('0.0')
>>> gmpy2.fmod(mpfr(25), 5.0)
mpfr('0.0')
>>> gmpy2.fmod(mpfr(25))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: fmod() requires 2 arguments

Tests round2
------------

>>> r = mpfr(1.65656565)
>>> gmpy2.round2(r, 2)
mpfr('1.5',2)
>>> gmpy2.round2(r, 5)
mpfr('1.69',5)
>>> gmpy2.round2(r)
mpfr('1.6565656499999999')
>>> gmpy2.round2(mpq('1/3'))
mpfr('0.33333333333333331')
>>> gmpy2.round2(mpq('1/3'), 30)
mpfr('0.33333333349',30)
>>> gmpy2.round2(r, -5)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: invalid precision
>>> gmpy2.round2(mpc(4, 4), 5)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: round2() argument type not supported
>>> gmpy2.round2(mpz(5), 5)
mpfr('5.0',5)
>>> gmpy2.round2(5, 6, 5)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: round2() requires 1 or 2 arguments
>>> gmpy2.round2()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: round2() requires 1 or 2 arguments

Tests reldiff ( abs(x-y)/x )
----------------------------

>>> gmpy2.reldiff(mpfr(2.5), mpfr(17.5))
mpfr('6.0')

Tests modf
----------

>>> r, r2 = mpfr('5.6'), mpfr(5.4)
>>> f = 0.6
>>> gmpy2.modf(r, r2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: modf() takes exactly one argument (2 given)
>>> gmpy2.modf(0.8)
(mpfr('0.0'), mpfr('0.80000000000000004'))
>>> gmpy2.modf(r)
(mpfr('5.0'), mpfr('0.59999999999999964'))
>>> gmpy2.modf(-r2)
(mpfr('-5.0'), mpfr('-0.40000000000000036'))

Tests remquo
------------

>>> gmpy2.remquo()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: remquo() requires 2 arguments
>>> gmpy2.remquo(r)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: remquo() requires 2 arguments
>>> gmpy2.remquo(r, f)
(mpfr('0.19999999999999984'), 9)
>>> gmpy2.remquo(r, r2)
(mpfr('0.19999999999999929'), 1)

Tests frexp
-----------

>>> gmpy2.frexp()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: frexp() takes exactly one argument (0 given)
>>> gmpy2.frexp(r, r2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: frexp() takes exactly one argument (2 given)
>>> gmpy2.frexp(r)
(3, mpfr('0.69999999999999996'))
>>> gmpy2.frexp(r2)
(3, mpfr('0.67500000000000004'))
>>> gmpy2.frexp(f)
(0, mpfr('0.59999999999999998'))

Tests next_toward
-----------------

>>> gmpy2.next_toward()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: next_toward() requires 2 arguments
>>> gmpy2.next_toward(r)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: next_toward() requires 2 arguments
>>> gmpy2.next_toward(r, r2)
mpfr('5.5999999999999988')
>>> gmpy2.next_toward(r, f)
mpfr('5.5999999999999988')

Tests next_above
-----------------

>>> gmpy2.next_above()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: next_above() takes exactly one argument (0 given)
>>> gmpy2.next_above(r, r2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: next_above() takes exactly one argument (2 given)
>>> gmpy2.next_above(r)
mpfr('5.6000000000000005')
>>> gmpy2.next_above(r2)
mpfr('5.4000000000000012')
>>> gmpy2.next_above(f)
mpfr('0.60000000000000009')

Tests factorial
---------------

>>> gmpy2.factorial(0)
mpfr('1.0')
>>> gmpy2.factorial(-0.0)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: factorial() requires non-negative integer argument
>>> gmpy2.factorial(2)
mpfr('2.0')
>>> gmpy2.factorial('fred')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: factorial() requires non-negative integer argument
>>> gmpy2.factorial(123)
mpfr('1.2146304367025329e+205')
>>> gmpy2.factorial(123456)
mpfr('2.6040699049291379e+574964')
>>> gmpy2.factorial(123456789)
mpfr('inf')
>>> gmpy2.factorial(1234567899999999999999)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
OverflowError: long int too large to convert
>>> gmpy2.factorial(mpz(5))
mpfr('120.0')
>>> ctx.factorial(4)
mpfr('24.0')

Tests fsum
----------

>>> gmpy2.fsum([])
mpfr('0.0')
>>> gmpy2.fsum([4, 5, 6])
mpfr('15.0')
>>> gmpy2.fsum(range(13))
mpfr('78.0')
>>> gmpy2.fsum(r)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: argument must be an iterable

Tests round, floor ceil and trunc
---------------------------------

>>> gmpy2.rint(r)
mpfr('6.0')
>>> gmpy2.rint(r2)
mpfr('5.0')
>>> gmpy2.rint_ceil(r)
mpfr('6.0')
>>> gmpy2.rint_ceil(r2)
mpfr('6.0')
>>> gmpy2.rint_ceil(f)
mpfr('1.0')
>>> gmpy2.rint_floor(r)
mpfr('5.0')
>>> gmpy2.rint_floor(r2)
mpfr('5.0')
>>> gmpy2.rint_floor(f)
mpfr('0.0')
>>> gmpy2.rint_round(r)
mpfr('6.0')
>>> gmpy2.rint_round(r2)
mpfr('5.0')
>>> gmpy2.rint_round(f)
mpfr('1.0')
>>> gmpy2.rint_trunc(r)
mpfr('5.0')
>>> gmpy2.rint_trunc(r2)
mpfr('5.0')
>>> gmpy2.rint_trunc(f)
mpfr('0.0')
>>> gmpy2.ceil(r)
mpfr('6.0')
>>> gmpy2.ceil(r2)
mpfr('6.0')
>>> gmpy2.ceil(f)
mpfr('1.0')
>>> gmpy2.floor(r)
mpfr('5.0')
>>> gmpy2.floor(r2)
mpfr('5.0')
>>> gmpy2.floor(f)
mpfr('0.0')
>>> gmpy2.trunc(r)
mpfr('5.0')
>>> gmpy2.trunc(r2)
mpfr('5.0')
>>> gmpy2.trunc(f)
mpfr('0.0')
>>> gmpy2.round_away(r)
mpfr('6.0')
>>> gmpy2.round_away(r2)
mpfr('5.0')
>>> gmpy2.round_away(f)
mpfr('1.0')



Tests exp functions
-------------------

>>> gmpy2.exp2(r)
mpfr('48.502930128332729')
>>> gmpy2.exp10(r)
mpfr('398107.17055349692')
>>> gmpy2.exp2(r2)
mpfr('42.224253144732629')
>>> gmpy2.exp10(r2)
mpfr('251188.6431509582')
>>> gmpy2.exp2(f)
mpfr('1.515716566510398')
>>> gmpy2.exp10(f)
mpfr('3.9810717055349722')
>>> gmpy2.expm1(r)
mpfr('269.42640742615254')
>>> gmpy2.expm1(r2)
mpfr('220.40641620418717')
>>> gmpy2.expm1(f)
mpfr('0.82211880039050889')
>>> gmpy2.eint(r)
mpfr('63.101785974299247')

Tests gamma functions
---------------------

>>> gmpy2.gamma(r)
mpfr('61.55391500628923')
>>> gmpy2.lngamma(r)
mpfr('4.1199134575335288')
>>> gmpy2.digamma(r)
mpfr('1.6308319195144647')
>>> gmpy2.lgamma()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: lgamma() takes exactly one argument (0 given)
>>> gmpy2.lgamma(r, r2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: lgamma() takes exactly one argument (2 given)
>>> gmpy2.lgamma(r)
(mpfr('4.1199134575335288'), 1)
>>> gmpy2.lgamma(mpfr('nan'))
(mpfr('nan'), 1)
>>> gmpy2.lgamma(mpfr('inf'))
(mpfr('inf'), 1)

Tests Bessel functions
----------------------
>>> gmpy2.j0(r)
mpfr('0.026970884685114358')
>>> gmpy2.j1(r)
mpfr('-0.33433283629100752')
>>> gmpy2.y0(r)
mpfr('-0.33544418124531583')
>>> gmpy2.y1(r)
mpfr('-0.056805614399479849')

Other tests
-----------

>>> gmpy2.frac(r)
mpfr('0.59999999999999964')
>>> gmpy2.frac(r2)
mpfr('0.40000000000000036')
>>> gmpy2.frac(f)
mpfr('0.59999999999999998')
>>> gmpy2.cbrt(r)
mpfr('1.7758080034852013')
>>> gmpy2.cbrt(r2)
mpfr('1.7544106429277198')
>>> gmpy2.cbrt(f)
mpfr('0.84343266530174921')
>>> gmpy2.log2(r)
mpfr('2.4854268271702415')
>>> gmpy2.log2(r2)
mpfr('2.4329594072761065')
>>> gmpy2.log2(f)
mpfr('-0.73696559416620622')
>>> gmpy2.log1p(r)
mpfr('1.8870696490323797')
>>> gmpy2.log1p(r2)
mpfr('1.8562979903656263')
>>> gmpy2.log1p(f)
mpfr('0.47000362924573552')
>>> gmpy2.li2(r)
mpfr('1.6186578451141254')
>>> gmpy2.zeta(r)
mpfr('1.02337547922703')
>>> gmpy2.erf(r)
mpfr('0.99999999999999767')
>>> gmpy2.erfc(r)
mpfr('2.382836284583028e-15')
>>> gmpy2.ai(r)
mpfr('2.6500613296849995e-05')
>>> gmpy2.remainder(mpfr(5), mpfr(3.2))
mpfr('-1.4000000000000004')