def test_init_str2(self):
x = mpc('1.5', 10)
assert x == 1.5 + 0.0j
assert x.precision == (10, 10)
y = mpc('1.5+0.5j', 0)
assert y == 1.5 + 0.5j
assert y.precision == (53, 53)
def test_init_str2(self):
x = mpc('1.5', 10)
assert x == 1.5+0.0j
assert x.precision == (10, 10)
y = mpc('1.5+0.5j', 0)
assert y == 1.5+0.5j
assert y.precision == (53, 53)
def test_sin_cos(self):
assert sin_cos(0.5) == sin_cos(mpfr(0.5)) == (sin(0.5), cos(0.5))
assert sin_cos(0) == (mpfr(0.0), mpfr(1.0))
assert sin_cos(mpq(1, 3)) == (sin(mpq(1, 3)), cos(mpq(1, 3)))
assert sin_cos(mpz(3)) == (sin(mpz(3)), cos(mpz(3)))
with pytest.raises(TypeError):
sin_cos([])
assert sin_cos(0.5+0.7j) == (
mpc('0.60176007656391672+0.66571982846862043j'),
mpc('1.1015144315669947-0.36368439983078849j'))
assert sin_cos(mpc(0.5+0.7j)) == (sin(mpc(0.5+0.7j)), cos(mpc(0.5+0.7j)))
def test_sin_cos(self):
assert sin_cos(0.5) == sin_cos(mpfr(0.5)) == (sin(0.5), cos(0.5))
assert sin_cos(0) == (mpfr(0.0), mpfr(1.0))
assert sin_cos(mpq(1, 3)) == (sin(mpq(1, 3)), cos(mpq(1, 3)))
assert sin_cos(mpz(3)) == (sin(mpz(3)), cos(mpz(3)))
with pytest.raises(TypeError):
sin_cos([])
assert sin_cos(0.5 + 0.7j) == (
mpc('0.60176007656391672+0.66571982846862043j'),
mpc('1.1015144315669947-0.36368439983078849j'))
assert sin_cos(mpc(0.5 + 0.7j)) == (sin(mpc(0.5 + 0.7j)),
cos(mpc(0.5 + 0.7j)))
def test_complex(self):
complex(mpc('1.5+0.5j')) == 1.5+0.5j
complex(mpc('1.5-0.5j')) == 1.5-0.5j
complex(mpc('nan+0.5j')) == complex('nan+0.5j')
complex(mpc('0.5+nanj')) == complex('0.5+nanj')
complex(mpc('nan+nanj')) == complex('nan+nanj')
complex(mpc('inf+0.5j')) == complex('inf+0.5j')
complex(mpc('0.5+infj')) == complex('0.5+infj')
complex(mpc('inf-infj')) == complex('inf-infj')
def test_complex(self):
complex(mpc('1.5+0.5j')) == 1.5 + 0.5j
complex(mpc('1.5-0.5j')) == 1.5 - 0.5j
complex(mpc('nan+0.5j')) == complex('nan+0.5j')
complex(mpc('0.5+nanj')) == complex('0.5+nanj')
complex(mpc('nan+nanj')) == complex('nan+nanj')
complex(mpc('inf+0.5j')) == complex('inf+0.5j')
complex(mpc('0.5+infj')) == complex('0.5+infj')
complex(mpc('inf-infj')) == complex('inf-infj')
def test_repr(self):
assert repr(mpc(1.5, 1.3)) == "mpc('1.5+1.3j')"
assert repr(mpc(1.5, 2.3)) == "mpc('1.5+2.2999999999999998j')"
assert repr(mpc(1.4, 2.3)) == "mpc('1.3999999999999999+2.2999999999999998j')"
assert repr(mpc(1.5, 2.3, 100)) == "mpc('1.5+2.299999999999999822364316059975j',(100,100))"
assert repr(mpc(1.5, 2.3, (0, 60))) == "mpc('1.5+2.2999999999999998224j',(53,60))"
assert repr(mpc(1.5, 2.3, (60, 0))) == "mpc('1.5+2.2999999999999998j',(60,53))"
assert repr(mpc(1.5, 2.3, 53)) == "mpc('1.5+2.2999999999999998j')"
def test_mpc_cache(self):
_cache(lambda i : mpc(i))
_cache(lambda i : mpc(complex(i), (0, 0)))
_cache(lambda i : mpc(complex(i), (50, 50)))
_cache(lambda i : mpc(complex(i), (0, 100)))
_cache(lambda i : mpc(complex(i), (100, 0)))
_cache(lambda i : mpc(complex(i), (50, 100)))
_cache(lambda i : mpc(complex(i), (50000, 50000)))
def test_init_i2(self, i):
assert mpc(i(2), 3) == 2 + 3j
assert mpc(2, i(3)) == 2 + 3j
assert mpc(i(2), i(3)) == 2 + 3j
# Increased Precision is required
assert mpc(i(sys.maxsize), 0, 100) == sys.maxsize
assert mpc(i(sys.maxsize + 1), 0, 100) == sys.maxsize + 1
assert mpc(i(2 * sys.maxsize), 0, 100) == 2 * sys.maxsize
assert mpc(i(3 * sys.maxsize), 0, 100) == 3 * sys.maxsize
def test_init_i2(self, i):
assert mpc(i(2), 3) == 2+3j
assert mpc(2, i(3)) == 2+3j
assert mpc(i(2), i(3)) == 2+3j
# Increased Precision is required
assert mpc(i(sys.maxsize), 0, 100) == sys.maxsize
assert mpc(i(sys.maxsize+1), 0, 100) == sys.maxsize+1
assert mpc(i(2*sys.maxsize), 0, 100) == 2*sys.maxsize
assert mpc(i(3*sys.maxsize), 0, 100) == 3*sys.maxsize
def test_c(self, c):
# Left Comparison
with pytest.raises(TypeError):
assert mpc('1.5+2.5j') > c('1.5+2.5j')
with pytest.raises(TypeError):
assert mpc('1.5+2.5j') < c('1.5+2.5j')
with pytest.raises(TypeError):
assert mpc('1.5+2.5j') >= c('1.5+2.5j')
with pytest.raises(TypeError):
assert mpc('1.5+2.5j') <= c('1.5+2.5j')
assert mpc('1.5+2.5j') == c('1.5+2.5j')
assert mpc('1.5+2.5j') != c('1.4+2.5j')
assert mpc('1.5+2.5j') != c('1.5+2.4j')
def test_repr(self):
assert repr(mpc(1.5, 1.3)) == "mpc('1.5+1.3j')"
assert repr(mpc(1.5, 2.3)) == "mpc('1.5+2.2999999999999998j')"
assert repr(mpc(
1.4, 2.3)) == "mpc('1.3999999999999999+2.2999999999999998j')"
assert repr(mpc(
1.5, 2.3,
100)) == "mpc('1.5+2.299999999999999822364316059975j',(100,100))"
assert repr(mpc(
1.5, 2.3, (0, 60))) == "mpc('1.5+2.2999999999999998224j',(53,60))"
assert repr(mpc(1.5, 2.3,
(60, 0))) == "mpc('1.5+2.2999999999999998j',(60,53))"
assert repr(mpc(1.5, 2.3, 53)) == "mpc('1.5+2.2999999999999998j')"
def test_f(self, f):
# Left Comparison
with pytest.raises(TypeError):
assert mpc('1.5') > f('1.5')
with pytest.raises(TypeError):
assert mpc('1.5') < f('1.5')
with pytest.raises(TypeError):
assert mpc('1.5') >= f('1.5')
with pytest.raises(TypeError):
assert mpc('1.5') <= f('1.5')
assert mpc('1.5') == f('1.5')
assert mpc('1.5') != f('1.4')
assert mpc('1.5+0.1j') != f('1.5')
def test_c(self, c):
# Left Comparison
with pytest.raises(TypeError):
assert mpc('1.5+2.5j') > c('1.5+2.5j')
with pytest.raises(TypeError):
assert mpc('1.5+2.5j') < c('1.5+2.5j')
with pytest.raises(TypeError):
assert mpc('1.5+2.5j') >= c('1.5+2.5j')
with pytest.raises(TypeError):
assert mpc('1.5+2.5j') <= c('1.5+2.5j')
assert mpc('1.5+2.5j') == c('1.5+2.5j')
assert mpc('1.5+2.5j') != c('1.4+2.5j')
assert mpc('1.5+2.5j') != c('1.5+2.4j')
def test_f(self, f):
# Left Comparison
with pytest.raises(TypeError):
assert mpc('1.5') > f('1.5')
with pytest.raises(TypeError):
assert mpc('1.5') < f('1.5')
with pytest.raises(TypeError):
assert mpc('1.5') >= f('1.5')
with pytest.raises(TypeError):
assert mpc('1.5') <= f('1.5')
assert mpc('1.5') == f('1.5')
assert mpc('1.5') != f('1.4')
assert mpc('1.5+0.1j') != f('1.5')
def test_init_i1(self, i):
assert mpc(i(2)) == 2
def test_rsub(self):
assert mpfr('1.5') - mpc('0.5') == mpc('1.0')
assert (1.5 + 0.5j) - mpc('0.2+0.3j') == mpc('1.3+0.2j')
assert 1.5 - mpc('0.5') == mpc('1.0')
assert mpq(3, 2) - mpc('0.5') == mpc('1.0')
assert mpz(1) - mpc('0.5') == mpc('0.5')
assert 1 - mpc('0.5') == mpc('0.5')
assert (-1) - mpc('0.5') == mpc('-1.5')
assert sys.maxsize - mpc('1.2e19') == mpc('-2.7766279631452242e+18')
assert 2 * sys.maxsize - mpc('1.2e19') == mpc('6.4467440737095516e+18')
assert 3 * sys.maxsize - mpc('1.2e19') == mpc('1.5670116110564327e+19')
with pytest.raises(TypeError):
[] - mpc('1.5+0.5j')
def test_init_f1(self, f):
assert mpc(f(1.5)) == 1.5
def test_init_q2(self):
assert mpc(mpq(1,2), mpq(1,4)) == 0.5+0.25j
assert mpc(mpq(1,2), 2) == 0.5+2j
assert mpc(1, mpq(1,4)) == 1+0.25j
def test_init_i3(self, i):
x = mpc(i(2), i(3), 120)
assert x == 2+3j
assert x.precision == (120, 120)
def test_asinh(self):
assert asinh(0.5) == mpfr('0.48121182505960347')
assert asinh(0.5+0.7j) == mpc('0.58742022866413157+0.63658730712537337j')
def test_acosh(self):
assert acosh(1.5) == mpfr('0.96242365011920694')
assert acosh(0.5+0.7j) == mpc('0.70341059318814581+1.1619717971477033j')
def test_tanh(self):
assert tanh(0.5) == mpfr('0.46211715726000974')
assert tanh(0.5+0.7j) == mpc('0.68602943183000187+0.57526108892459082j')
def test_cosh(self):
assert cosh(0.5) == mpfr('1.1276259652063807')
assert cosh(0.5+0.7j) == mpc('0.86245590966723074+0.33569881253559997j')
def test_sinh(self):
assert sinh(0.5) == mpfr('0.52109530549374738')
assert sinh(0.5+0.7j) == mpc('0.39855567323751645+0.72643659137442362j')
def test_init_q3(self):
x = mpc(mpq(1,2), mpq(1,4), 110)
assert x == 0.5+0.25j
assert x.precision == (110, 110)
def test_init_q1(self):
assert mpc(mpq(1, 2)) == 0.5
def test_pow(self):
assert mpc('1.2+3.1j')**mpc('0.7+0.3j') == mpc(
'0.58374557428865026+1.5076769261293019j')
assert mpc('1.2+3.1j')**(
0.7 + 0.3j) == mpc('0.58374557428865026+1.5076769261293019j')
assert mpc('1.3+2.7j')**mpq(
2, 3) == mpc('1.523607752011799+1.4138443176037268j')
assert mpc('1.2+2.7j')**mpfr(1.35) == mpc(
'0.063993805808622087+4.3165511702888386j')
assert mpc('1.2+2.7j')**1.35 == mpc(
'0.063993805808622087+4.3165511702888386j')
assert mpc('1.2+2.7j')**15 == mpc(
'112131.44281004601-11417890.819726286j')
assert mpc('1.2+2.7j')**mpz(15) == mpc(
'112131.44281004601-11417890.819726286j')
assert mpc('1.2+2.7j')**(
-1) == mpc('0.1374570446735395-0.30927835051546393j')
assert mpc('0.0+1.0j')**sys.maxsize == mpc('-0.0-1.0j')
assert mpc('0.0+1.0j')**(2 * sys.maxsize) == mpc('-1.0+0.0j')
assert mpc('0.0+1.0j')**(3 * sys.maxsize) == mpc('0.0+1.0j')
with pytest.raises(TypeError):
mpc('1.5+0.5j')**[]
def test_atanh(self):
assert atanh(0.5) == mpfr('0.549306144334054846')
assert atanh(0.5+0.7j) == mpc('0.32726575329597513+0.69358700031280818j')
def test_init_str3(self):
x = mpc('1.5+0.5j', 0, 10)
assert x == 1.5+0.5j
assert x.precision == (53, 53)
def test_log(self):
assert log(0.5) == mpfr('-0.69314718055994529')
assert log(0.5+0.7j) == mpc('-0.15055254639196086+0.95054684081207508j')
def test_fma(self):
assert fma(0.5, 0.7, 1.1) == mpfr('1.4500000000000002')
assert fma(3, 1, 0.5+0.1j) == mpc('3.5+0.10000000000000001j')
def test_exp(self):
assert exp(0.5) == mpfr('1.6487212707001282')
assert exp(0.5+0.7j) == mpc('1.2610115829047472+1.0621354039100237j')
def test_long(self):
with pytest.raises(TypeError):
long(mpc('1.5'))
def test_cos(self):
assert cos(0.5) == mpfr('0.87758256189037276')
assert cos(0.5+0.7j) == mpc('1.1015144315669947-0.36368439983078849j')
def test_add(self):
assert mpc('1.5+0.5j') + mpc('0.2+0.3j') == mpc('1.7+0.8j')
assert mpc('1.5+0.5j') + (0.2 + 0.3j) == mpc('1.7+0.8j')
assert mpc('1.5+0.5j') + mpfr('1.5') == mpc('3.0+0.5j')
assert mpc('1.5+0.5j') + mpq(3, 2) == mpc('3.0+0.5j')
assert mpc('1.5+0.5j') + mpz(2) == mpc('3.5+0.5j')
assert mpc('1.5+0.5j') + 1.5 == mpc('3.0+0.5j')
assert mpc('1.5+0.5j') + 1 == mpc('2.5+0.5j')
assert mpc('1.5+0.5j') + (-1) == mpc('0.5+0.5j')
assert mpc('1.2e19') + sys.maxsize == mpc('2.1223372036854776e19')
assert mpc('1.2e19') + 2 * sys.maxsize == mpc('3.0446744073709552e+19')
assert mpc('1.2e19') + 3 * sys.maxsize == mpc('3.9670116110564327e+19')
with pytest.raises(TypeError):
assert mpc('1.5+0.5j') + []
assert 1.5 + mpc('1.5+0.5j') == mpc('3.0+0.5j')
def test_sin(self):
assert sin(0.5) == mpfr('0.47942553860420301')
assert sin(0.5+0.7j) == mpc('0.60176007656391672+0.66571982846862043j')
def test_sub(self):
assert mpc('1.5+0.5j') - mpc('0.2+0.3j') == mpc('1.3+0.2j')
assert mpc('1.5+0.5j') - (0.2 + 0.3j) == mpc('1.3+0.2j')
assert mpc('1.5+0.5j') - mpfr('0.2') == mpc('1.3+0.5j')
assert mpc('1.5+0.5j') - mpq(3, 2) == mpc('0.0+0.5j')
assert mpc('1.5+0.5j') - mpz(2) == mpc('-0.5+0.5j')
assert mpc('1.5+0.5j') - 1.5 == mpc('0.0+0.5j')
assert mpc('1.5+0.5j') - 1 == mpc('0.5+0.5j')
assert mpc('1.5+0.5j') - (-1) == mpc('2.5+0.5j')
assert mpc('3.2e19') - sys.maxsize == mpc('2.2776627963145224e+19')
assert mpc('3.2e19') - 2 * sys.maxsize == mpc('1.3553255926290448e+19')
assert mpc('3.2e19') - 3 * sys.maxsize == mpc('4.3298838894356726e+18')
with pytest.raises(TypeError):
assert mpc('1.5+0.5j') - []
def test_tan(self):
assert tan(0.5) == mpfr('0.54630248984379048')
assert tan(0.5+0.7j) == mpc('0.31267491960977917+0.70760291160255884j')
def test_mul(self):
assert mpc('0.5+0.1j') * mpc('0.5+0.2j') == mpc(
'0.23+0.15000000000000002j')
assert mpc('0.5+0.1j') * (0.5 +
0.2j) == mpc('0.23+0.15000000000000002j')
assert mpc('0.5+0.3j') * mpfr('1.5') == mpc(
'0.75+0.44999999999999996j')
assert mpc('0.5+0.3j') * 1.5 == mpc('0.75+0.44999999999999996j')
assert mpc('0.5+0.3j') * mpq(3, 2) == mpc('0.75+0.44999999999999996j')
assert mpc('0.5+0.3j') * mpz(3) == mpc('1.5+0.89999999999999991j')
assert mpc('0.5+0.3j') * 3 == mpc('1.5+0.89999999999999991j')
assert mpc('1.5') * sys.maxsize == mpc('1.3835058055282164e+19')
assert mpc('1.5') * (2 * sys.maxsize) == mpc('2.7670116110564327e+19')
assert mpc('1.5') * (3 * sys.maxsize) == mpc('4.1505174165846491e+19')
with pytest.raises(TypeError):
mpc('1.5+0.5j') * []
assert 3 * mpc('1.5+0.5j') == mpc('4.5+1.5j')
def test_rpow(self):
assert 2**mpc('1.2+0.7j') == mpc(
'2.0322318210346983+1.0714781699435463j')
assert (-3)**mpc('1.2+0.7j') == mpc(
'-0.07152774910532736-0.40824064717539998j')
assert mpz(2)**mpc('1.2+0.7j') == mpc(
'2.0322318210346983+1.0714781699435463j')
assert mpq(2, 3)**mpc('1.2+0.7j') == mpc(
'0.59014364683348408-0.17214537996429355j')
assert mpfr(1.3)**mpc('1.2+0.7j') == mpc(
'1.3469959279701931+0.25020189563974787j')
assert 1.3**mpc('1.2+0.7j') == mpc(
'1.3469959279701931+0.25020189563974787j')
assert (1.1 + 0.8j)**mpc('1.2+0.7j') == mpc(
'0.52663021989956504+0.76824606795641459j')
assert sys.maxsize**mpc('1.5+0.3j') == mpc(
'2.4110001396293724e+28+1.4259928106202001e+28j')
assert (2 * sys.maxsize)**mpc('1.5+0.3j') == mpc(
'5.8397586579879863e+28+5.354272702274433e+28j')
assert (3 * sys.maxsize)**mpc('1.5+0.3j') == mpc(
'9.4555004785752363e+28+1.1065518255778351e+29j')
with pytest.raises(TypeError):
[]**mpc('1.5+0.5j')
def test_truediv(self):
assert mpc(1, 3) / mpc(
2, 5) == mpc('0.58620689655172409+0.034482758620689655j')
assert mpc('1.5+3.2j') / (2.1 + 0.4j) == mpc(
'0.96936542669584247+1.3391684901531729j')
assert mpc('1.5+1.2j') / 0.3 == mpc('5.0+4.0j')
assert mpc('1.5+1.2j') / mpfr('0.3') == mpc('5.0+4.0j')
assert mpc('1.5+3.0j') / 3 == mpc('0.5+1.0j')
assert mpc('1.5+3.0j') / mpz(3) == mpc('0.5+1.0j')
assert mpc('1.5+0.6j') / mpq(
7, 5) == mpc('1.0714285714285714+0.4285714285714286j')
assert mpc('4.4+1.7j') / (-2) == mpc(
'-2.2000000000000002-0.84999999999999998j')
assert mpc(1.4e+19 - 1.2e+19j) / sys.maxsize == mpc(
'1.5178830414797062-1.3010426069826053j')
assert mpc(1.4e+19 - 1.2e+19j) / (2 * sys.maxsize) == mpc(
'0.7589415207398531-0.65052130349130266j')
assert mpc(1.4e+19 - 1.2e+19j) / (3 * sys.maxsize) == mpc(
'0.50596101382656877-0.43368086899420177j')
with pytest.raises(TypeError):
mpc('1.5+0.5j') / []
def test_pos(self):
assert +mpc('1.4+0.3j') == mpc('1.4+0.3j')
assert +mpc('1.4-0.3j') == mpc('1.4-0.3j')
def test_rtruediv(self):
assert (2.1 + 0.4j) / mpc('1.5+3.2j') == mpc(
'0.35468374699759808-0.48999199359487589j')
assert 0.3 / mpc('1.2+3.1j') == mpc(
'0.032579185520361986-0.084162895927601802j')
assert mpq(2, 3) / mpc('1.4+0.4j') == mpc(
'0.44025157232704404-0.12578616352201258j')
assert mpfr('0.3') / mpc('1.2+3.1j') == mpc(
'0.032579185520361986-0.084162895927601802j')
assert 3 / mpc('1.3+0.7j') == mpc(
'1.7889908256880733-0.96330275229357787j')
assert mpz(3) / mpc('1.3+0.7j') == mpc(
'1.7889908256880733-0.96330275229357787j')
assert (-1) / mpc(0.4 + 0.6j) == mpc(
'-0.76923076923076927+1.1538461538461537j')
assert sys.maxsize / mpc(1.3e19 + 1.6e19j) == mpc(
'0.28212667406849901-0.34723282962276802j')
assert (2 * sys.maxsize) / mpc(1.3e19 + 1.6e19j) == mpc(
'0.56425334813699801-0.69446565924553605j')
assert (3 * sys.maxsize) / mpc(1.3e19 + 1.6e19j) == mpc(
'0.84638002220549713-1.0416984888683041j')
with pytest.raises(TypeError):
[] / mpc('1.5+0.5j')
def test_init_c2(self, c):
assert mpc(c('1.0+0.5j'), 10) == 1.0 + 0.5j
assert mpc(c('1.0+0.5j'), 10).precision == (10, 10)
def test_init_str3(self):
x = mpc('1.5+0.5j', 0, 10)
assert x == 1.5 + 0.5j
assert x.precision == (53, 53)
def test_init_f3(self, f):
x = mpc(f(1.5), f(0.5), 100)
assert x == 1.5+0.5j
assert x.precision == (100, 100)
def test_neg(self):
assert -mpc('1.4+0.3j') == mpc('-1.4-0.3j')
assert -mpc('1.4-0.3j') == mpc('-1.4+0.3j')
def test_init_i3(self, i):
x = mpc(i(2), i(3), 120)
assert x == 2 + 3j
assert x.precision == (120, 120)
def test_abs(self):
assert abs(mpc('1.5+0.3j')) == mpfr('1.5297058540778354')
def test_init_c2(self, c):
assert mpc(c('1.0+0.5j'), 10) == 1.0+0.5j
assert mpc(c('1.0+0.5j'), 10).precision == (10, 10)
def test_init_f2(self, f):
assert mpc(f(1.5), 0.5) == 1.5 + 0.5j
assert mpc(1.5, f(0.5)) == 1.5 + 0.5j
assert mpc(f(1.5), f(0.5)) == 1.5 + 0.5j
def test_atan(self):
assert atan(0.5) == mpfr('0.46364760900080609')
assert atan(0.5+0.7j) == mpc('0.65821413412081531+0.55575811532302299j')
def test_init_q2(self):
assert mpc(mpq(1, 2), mpq(1, 4)) == 0.5 + 0.25j
assert mpc(mpq(1, 2), 2) == 0.5 + 2j
assert mpc(1, mpq(1, 4)) == 1 + 0.25j
def test_init_f2(self, f):
assert mpc(f(1.5), 0.5) == 1.5+0.5j
assert mpc(1.5, f(0.5)) == 1.5+0.5j
assert mpc(f(1.5), f(0.5)) == 1.5+0.5j
def test_init_f3(self, f):
x = mpc(f(1.5), f(0.5), 100)
assert x == 1.5 + 0.5j
assert x.precision == (100, 100)
def test_acos(self):
assert acos(0.5) == mpfr('1.0471975511965979')
assert acos(0.5+0.7j) == mpc('1.1619717971477033-0.70341059318814581j')
def test_init_q3(self):
x = mpc(mpq(1, 2), mpq(1, 4), 110)
assert x == 0.5 + 0.25j
assert x.precision == (110, 110)
def test_asin(self):
assert asin(0.5) == mpfr('0.52359877559829893')
assert asin(0.5+0.7j) == mpc('0.40882452964719346+0.70341059318814581j')