def test_atan():
mp.dps = 15
assert atan(-2.3).ae(math.atan(-2.3))
assert atan(1e-50) == 1e-50
assert atan(1e50).ae(pi/2)
assert atan(-1e-50) == -1e-50
assert atan(-1e50).ae(-pi/2)
assert atan(10**1000).ae(pi/2)
for dps in [25, 70, 100, 300, 1000]:
mp.dps = dps
assert (4*atan(1)).ae(pi)
mp.dps = 15
pi2 = pi/2
assert atan(mpc(inf,-1)).ae(pi2)
assert atan(mpc(inf,0)).ae(pi2)
assert atan(mpc(inf,1)).ae(pi2)
assert atan(mpc(1,inf)).ae(pi2)
assert atan(mpc(0,inf)).ae(pi2)
assert atan(mpc(-1,inf)).ae(-pi2)
assert atan(mpc(-inf,1)).ae(-pi2)
assert atan(mpc(-inf,0)).ae(-pi2)
assert atan(mpc(-inf,-1)).ae(-pi2)
assert atan(mpc(-1,-inf)).ae(-pi2)
assert atan(mpc(0,-inf)).ae(-pi2)
assert atan(mpc(1,-inf)).ae(pi2)
python类atan()的实例源码
def test_atan():
mp.dps = 15
assert atan(-2.3).ae(math.atan(-2.3))
assert atan(1e-50) == 1e-50
assert atan(1e50).ae(pi/2)
assert atan(-1e-50) == -1e-50
assert atan(-1e50).ae(-pi/2)
assert atan(10**1000).ae(pi/2)
for dps in [25, 70, 100, 300, 1000]:
mp.dps = dps
assert (4*atan(1)).ae(pi)
mp.dps = 15
pi2 = pi/2
assert atan(mpc(inf,-1)).ae(pi2)
assert atan(mpc(inf,0)).ae(pi2)
assert atan(mpc(inf,1)).ae(pi2)
assert atan(mpc(1,inf)).ae(pi2)
assert atan(mpc(0,inf)).ae(pi2)
assert atan(mpc(-1,inf)).ae(-pi2)
assert atan(mpc(-inf,1)).ae(-pi2)
assert atan(mpc(-inf,0)).ae(-pi2)
assert atan(mpc(-inf,-1)).ae(-pi2)
assert atan(mpc(-1,-inf)).ae(-pi2)
assert atan(mpc(0,-inf)).ae(-pi2)
assert atan(mpc(1,-inf)).ae(pi2)
def test_atan():
mp.dps = 15
assert atan(-2.3).ae(math.atan(-2.3))
assert atan(1e-50) == 1e-50
assert atan(1e50).ae(pi/2)
assert atan(-1e-50) == -1e-50
assert atan(-1e50).ae(-pi/2)
assert atan(10**1000).ae(pi/2)
for dps in [25, 70, 100, 300, 1000]:
mp.dps = dps
assert (4*atan(1)).ae(pi)
mp.dps = 15
pi2 = pi/2
assert atan(mpc(inf,-1)).ae(pi2)
assert atan(mpc(inf,0)).ae(pi2)
assert atan(mpc(inf,1)).ae(pi2)
assert atan(mpc(1,inf)).ae(pi2)
assert atan(mpc(0,inf)).ae(pi2)
assert atan(mpc(-1,inf)).ae(-pi2)
assert atan(mpc(-inf,1)).ae(-pi2)
assert atan(mpc(-inf,0)).ae(-pi2)
assert atan(mpc(-inf,-1)).ae(-pi2)
assert atan(mpc(-1,-inf)).ae(-pi2)
assert atan(mpc(0,-inf)).ae(-pi2)
assert atan(mpc(1,-inf)).ae(pi2)
def test_atan():
mp.dps = 15
assert atan(-2.3).ae(math.atan(-2.3))
assert atan(1e-50) == 1e-50
assert atan(1e50).ae(pi/2)
assert atan(-1e-50) == -1e-50
assert atan(-1e50).ae(-pi/2)
assert atan(10**1000).ae(pi/2)
for dps in [25, 70, 100, 300, 1000]:
mp.dps = dps
assert (4*atan(1)).ae(pi)
mp.dps = 15
pi2 = pi/2
assert atan(mpc(inf,-1)).ae(pi2)
assert atan(mpc(inf,0)).ae(pi2)
assert atan(mpc(inf,1)).ae(pi2)
assert atan(mpc(1,inf)).ae(pi2)
assert atan(mpc(0,inf)).ae(pi2)
assert atan(mpc(-1,inf)).ae(-pi2)
assert atan(mpc(-inf,1)).ae(-pi2)
assert atan(mpc(-inf,0)).ae(-pi2)
assert atan(mpc(-inf,-1)).ae(-pi2)
assert atan(mpc(-1,-inf)).ae(-pi2)
assert atan(mpc(0,-inf)).ae(-pi2)
assert atan(mpc(1,-inf)).ae(pi2)
def test_atan():
mp.dps = 15
assert atan(-2.3).ae(math.atan(-2.3))
assert atan(1e-50) == 1e-50
assert atan(1e50).ae(pi/2)
assert atan(-1e-50) == -1e-50
assert atan(-1e50).ae(-pi/2)
assert atan(10**1000).ae(pi/2)
for dps in [25, 70, 100, 300, 1000]:
mp.dps = dps
assert (4*atan(1)).ae(pi)
mp.dps = 15
pi2 = pi/2
assert atan(mpc(inf,-1)).ae(pi2)
assert atan(mpc(inf,0)).ae(pi2)
assert atan(mpc(inf,1)).ae(pi2)
assert atan(mpc(1,inf)).ae(pi2)
assert atan(mpc(0,inf)).ae(pi2)
assert atan(mpc(-1,inf)).ae(-pi2)
assert atan(mpc(-inf,1)).ae(-pi2)
assert atan(mpc(-inf,0)).ae(-pi2)
assert atan(mpc(-inf,-1)).ae(-pi2)
assert atan(mpc(-1,-inf)).ae(-pi2)
assert atan(mpc(0,-inf)).ae(-pi2)
assert atan(mpc(1,-inf)).ae(pi2)
def ATAN(df, price='Close'):
"""
Arc Tangent
"""
atan_list = []
i = 0
while i < len(df[price]):
atan = cmath.atan(df[price][i]).real
atan_list.append(atan)
i += 1
return atan_list
def test_complex_inverse_functions():
mp.dps = 15
iv.dps = 15
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9*j*10**k + 0.8*one*10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2*10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9*10**k + j*0.8*one*10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def testTanhSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.tanh(z), z)
# The algorithm used for atan and atanh makes use of the system
# log1p function; If that system function doesn't respect the sign
# of zero, then atan and atanh will also have difficulties with
# the sign of complex zeros.
def test_complex_inverse_functions():
mp.dps = 15
iv.dps = 15
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9*j*10**k + 0.8*one*10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2*10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9*10**k + j*0.8*one*10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def test_complex_inverse_functions():
mp.dps = 15
iv.dps = 15
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9*j*10**k + 0.8*one*10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2*10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9*10**k + j*0.8*one*10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def testTanhSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.tanh(z), z)
# The algorithm used for atan and atanh makes use of the system
# log1p function; If that system function doesn't respect the sign
# of zero, then atan and atanh will also have difficulties with
# the sign of complex zeros.
def testAtanSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.atan(z), z)
def testTanhSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.tanh(z), z)
# The algorithm used for atan and atanh makes use of the system
# log1p function; If that system function doesn't respect the sign
# of zero, then atan and atanh will also have difficulties with
# the sign of complex zeros.
def testAtanSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.atan(z), z)
def test_complex_inverse_functions():
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9*j*10**k + 0.8*one*10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2*10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9*10**k + j*0.8*one*10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def testTanhSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.tanh(z), z)
# The algorithm used for atan and atanh makes use of the system
# log1p function; If that system function doesn't respect the sign
# of zero, then atan and atanh will also have difficulties with
# the sign of complex zeros.
def testAtanSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.atan(z), z)
def test_complex_inverse_functions():
for (z1, z2) in random_complexes(30):
# apparently cmath uses a different branch, so we
# can't use it for comparison
assert sinh(asinh(z1)).ae(z1)
#
assert acosh(z1).ae(cmath.acosh(z1))
assert atanh(z1).ae(cmath.atanh(z1))
assert atan(z1).ae(cmath.atan(z1))
# the reason we set a big eps here is that the cmath
# functions are inaccurate
assert asin(z1).ae(cmath.asin(z1), rel_eps=1e-12)
assert acos(z1).ae(cmath.acos(z1), rel_eps=1e-12)
one = mpf(1)
for i in range(-9, 10, 3):
for k in range(-9, 10, 3):
a = 0.9*j*10**k + 0.8*one*10**i
b = cos(acos(a))
assert b.ae(a)
b = sin(asin(a))
assert b.ae(a)
one = mpf(1)
err = 2*10**-15
for i in range(-9, 9, 3):
for k in range(-9, 9, 3):
a = -0.9*10**k + j*0.8*one*10**i
b = cosh(acosh(a))
assert b.ae(a, err)
b = sinh(asinh(a))
assert b.ae(a, err)
def test_perturbation_rounding():
mp.dps = 100
a = pi/10**50
b = -pi/10**50
c = 1 + a
d = 1 + b
mp.dps = 15
assert exp(a) == 1
assert exp(a, rounding='c') > 1
assert exp(b, rounding='c') == 1
assert exp(a, rounding='f') == 1
assert exp(b, rounding='f') < 1
assert cos(a) == 1
assert cos(a, rounding='c') == 1
assert cos(b, rounding='c') == 1
assert cos(a, rounding='f') < 1
assert cos(b, rounding='f') < 1
for f in [sin, atan, asinh, tanh]:
assert f(a) == +a
assert f(a, rounding='c') > a
assert f(a, rounding='f') < a
assert f(b) == +b
assert f(b, rounding='c') > b
assert f(b, rounding='f') < b
for f in [asin, tan, sinh, atanh]:
assert f(a) == +a
assert f(b) == +b
assert f(a, rounding='c') > a
assert f(b, rounding='c') > b
assert f(a, rounding='f') < a
assert f(b, rounding='f') < b
assert ln(c) == +a
assert ln(d) == +b
assert ln(c, rounding='c') > a
assert ln(c, rounding='f') < a
assert ln(d, rounding='c') > b
assert ln(d, rounding='f') < b
assert cosh(a) == 1
assert cosh(b) == 1
assert cosh(a, rounding='c') > 1
assert cosh(b, rounding='c') > 1
assert cosh(a, rounding='f') == 1
assert cosh(b, rounding='f') == 1
def test_cmath_matches_math(self):
# check that corresponding cmath and math functions are equal
# for floats in the appropriate range
# test_values in (0, 1)
test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
# test_values for functions defined on [-1., 1.]
unit_interval = test_values + [-x for x in test_values] + \
[0., 1., -1.]
# test_values for log, log10, sqrt
positive = test_values + [1.] + [1./x for x in test_values]
nonnegative = [0.] + positive
# test_values for functions defined on the whole real line
real_line = [0.] + positive + [-x for x in positive]
test_functions = {
'acos' : unit_interval,
'asin' : unit_interval,
'atan' : real_line,
'cos' : real_line,
'cosh' : real_line,
'exp' : real_line,
'log' : positive,
'log10' : positive,
'sin' : real_line,
'sinh' : real_line,
'sqrt' : nonnegative,
'tan' : real_line,
'tanh' : real_line}
for fn, values in test_functions.items():
float_fn = getattr(math, fn)
complex_fn = getattr(cmath, fn)
for v in values:
z = complex_fn(v)
self.rAssertAlmostEqual(float_fn(v), z.real)
self.assertEqual(0., z.imag)
# test two-argument version of log with various bases
for base in [0.5, 2., 10.]:
for v in positive:
z = cmath.log(v, base)
self.rAssertAlmostEqual(math.log(v, base), z.real)
self.assertEqual(0., z.imag)
def test_perturbation_rounding():
mp.dps = 100
a = pi/10**50
b = -pi/10**50
c = 1 + a
d = 1 + b
mp.dps = 15
assert exp(a) == 1
assert exp(a, rounding='c') > 1
assert exp(b, rounding='c') == 1
assert exp(a, rounding='f') == 1
assert exp(b, rounding='f') < 1
assert cos(a) == 1
assert cos(a, rounding='c') == 1
assert cos(b, rounding='c') == 1
assert cos(a, rounding='f') < 1
assert cos(b, rounding='f') < 1
for f in [sin, atan, asinh, tanh]:
assert f(a) == +a
assert f(a, rounding='c') > a
assert f(a, rounding='f') < a
assert f(b) == +b
assert f(b, rounding='c') > b
assert f(b, rounding='f') < b
for f in [asin, tan, sinh, atanh]:
assert f(a) == +a
assert f(b) == +b
assert f(a, rounding='c') > a
assert f(b, rounding='c') > b
assert f(a, rounding='f') < a
assert f(b, rounding='f') < b
assert ln(c) == +a
assert ln(d) == +b
assert ln(c, rounding='c') > a
assert ln(c, rounding='f') < a
assert ln(d, rounding='c') > b
assert ln(d, rounding='f') < b
assert cosh(a) == 1
assert cosh(b) == 1
assert cosh(a, rounding='c') > 1
assert cosh(b, rounding='c') > 1
assert cosh(a, rounding='f') == 1
assert cosh(b, rounding='f') == 1
def test_perturbation_rounding():
mp.dps = 100
a = pi/10**50
b = -pi/10**50
c = 1 + a
d = 1 + b
mp.dps = 15
assert exp(a) == 1
assert exp(a, rounding='c') > 1
assert exp(b, rounding='c') == 1
assert exp(a, rounding='f') == 1
assert exp(b, rounding='f') < 1
assert cos(a) == 1
assert cos(a, rounding='c') == 1
assert cos(b, rounding='c') == 1
assert cos(a, rounding='f') < 1
assert cos(b, rounding='f') < 1
for f in [sin, atan, asinh, tanh]:
assert f(a) == +a
assert f(a, rounding='c') > a
assert f(a, rounding='f') < a
assert f(b) == +b
assert f(b, rounding='c') > b
assert f(b, rounding='f') < b
for f in [asin, tan, sinh, atanh]:
assert f(a) == +a
assert f(b) == +b
assert f(a, rounding='c') > a
assert f(b, rounding='c') > b
assert f(a, rounding='f') < a
assert f(b, rounding='f') < b
assert ln(c) == +a
assert ln(d) == +b
assert ln(c, rounding='c') > a
assert ln(c, rounding='f') < a
assert ln(d, rounding='c') > b
assert ln(d, rounding='f') < b
assert cosh(a) == 1
assert cosh(b) == 1
assert cosh(a, rounding='c') > 1
assert cosh(b, rounding='c') > 1
assert cosh(a, rounding='f') == 1
assert cosh(b, rounding='f') == 1
def test_cmath_matches_math(self):
# check that corresponding cmath and math functions are equal
# for floats in the appropriate range
# test_values in (0, 1)
test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
# test_values for functions defined on [-1., 1.]
unit_interval = test_values + [-x for x in test_values] + \
[0., 1., -1.]
# test_values for log, log10, sqrt
positive = test_values + [1.] + [1./x for x in test_values]
nonnegative = [0.] + positive
# test_values for functions defined on the whole real line
real_line = [0.] + positive + [-x for x in positive]
test_functions = {
'acos' : unit_interval,
'asin' : unit_interval,
'atan' : real_line,
'cos' : real_line,
'cosh' : real_line,
'exp' : real_line,
'log' : positive,
'log10' : positive,
'sin' : real_line,
'sinh' : real_line,
'sqrt' : nonnegative,
'tan' : real_line,
'tanh' : real_line}
for fn, values in test_functions.items():
float_fn = getattr(math, fn)
complex_fn = getattr(cmath, fn)
for v in values:
z = complex_fn(v)
self.rAssertAlmostEqual(float_fn(v), z.real)
self.assertEqual(0., z.imag)
# test two-argument version of log with various bases
for base in [0.5, 2., 10.]:
for v in positive:
z = cmath.log(v, base)
self.rAssertAlmostEqual(math.log(v, base), z.real)
self.assertEqual(0., z.imag)
def test_cmath_matches_math(self):
# check that corresponding cmath and math functions are equal
# for floats in the appropriate range
# test_values in (0, 1)
test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
# test_values for functions defined on [-1., 1.]
unit_interval = test_values + [-x for x in test_values] + \
[0., 1., -1.]
# test_values for log, log10, sqrt
positive = test_values + [1.] + [1./x for x in test_values]
nonnegative = [0.] + positive
# test_values for functions defined on the whole real line
real_line = [0.] + positive + [-x for x in positive]
test_functions = {
'acos' : unit_interval,
'asin' : unit_interval,
'atan' : real_line,
'cos' : real_line,
'cosh' : real_line,
'exp' : real_line,
'log' : positive,
'log10' : positive,
'sin' : real_line,
'sinh' : real_line,
'sqrt' : nonnegative,
'tan' : real_line,
'tanh' : real_line}
for fn, values in test_functions.items():
float_fn = getattr(math, fn)
complex_fn = getattr(cmath, fn)
for v in values:
z = complex_fn(v)
self.rAssertAlmostEqual(float_fn(v), z.real)
self.assertEqual(0., z.imag)
# test two-argument version of log with various bases
for base in [0.5, 2., 10.]:
for v in positive:
z = cmath.log(v, base)
self.rAssertAlmostEqual(math.log(v, base), z.real)
self.assertEqual(0., z.imag)
def test_perturbation_rounding():
mp.dps = 100
a = pi/10**50
b = -pi/10**50
c = 1 + a
d = 1 + b
mp.dps = 15
assert exp(a) == 1
assert exp(a, rounding='c') > 1
assert exp(b, rounding='c') == 1
assert exp(a, rounding='f') == 1
assert exp(b, rounding='f') < 1
assert cos(a) == 1
assert cos(a, rounding='c') == 1
assert cos(b, rounding='c') == 1
assert cos(a, rounding='f') < 1
assert cos(b, rounding='f') < 1
for f in [sin, atan, asinh, tanh]:
assert f(a) == +a
assert f(a, rounding='c') > a
assert f(a, rounding='f') < a
assert f(b) == +b
assert f(b, rounding='c') > b
assert f(b, rounding='f') < b
for f in [asin, tan, sinh, atanh]:
assert f(a) == +a
assert f(b) == +b
assert f(a, rounding='c') > a
assert f(b, rounding='c') > b
assert f(a, rounding='f') < a
assert f(b, rounding='f') < b
assert ln(c) == +a
assert ln(d) == +b
assert ln(c, rounding='c') > a
assert ln(c, rounding='f') < a
assert ln(d, rounding='c') > b
assert ln(d, rounding='f') < b
assert cosh(a) == 1
assert cosh(b) == 1
assert cosh(a, rounding='c') > 1
assert cosh(b, rounding='c') > 1
assert cosh(a, rounding='f') == 1
assert cosh(b, rounding='f') == 1
def test_cmath_matches_math(self):
# check that corresponding cmath and math functions are equal
# for floats in the appropriate range
# test_values in (0, 1)
test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
# test_values for functions defined on [-1., 1.]
unit_interval = test_values + [-x for x in test_values] + \
[0., 1., -1.]
# test_values for log, log10, sqrt
positive = test_values + [1.] + [1./x for x in test_values]
nonnegative = [0.] + positive
# test_values for functions defined on the whole real line
real_line = [0.] + positive + [-x for x in positive]
test_functions = {
'acos' : unit_interval,
'asin' : unit_interval,
'atan' : real_line,
'cos' : real_line,
'cosh' : real_line,
'exp' : real_line,
'log' : positive,
'log10' : positive,
'sin' : real_line,
'sinh' : real_line,
'sqrt' : nonnegative,
'tan' : real_line,
'tanh' : real_line}
for fn, values in test_functions.items():
float_fn = getattr(math, fn)
complex_fn = getattr(cmath, fn)
for v in values:
z = complex_fn(v)
self.rAssertAlmostEqual(float_fn(v), z.real)
self.assertEqual(0., z.imag)
# test two-argument version of log with various bases
for base in [0.5, 2., 10.]:
for v in positive:
z = cmath.log(v, base)
self.rAssertAlmostEqual(math.log(v, base), z.real)
self.assertEqual(0., z.imag)
def test_perturbation_rounding():
mp.dps = 100
a = pi/10**50
b = -pi/10**50
c = 1 + a
d = 1 + b
mp.dps = 15
assert exp(a) == 1
assert exp(a, rounding='c') > 1
assert exp(b, rounding='c') == 1
assert exp(a, rounding='f') == 1
assert exp(b, rounding='f') < 1
assert cos(a) == 1
assert cos(a, rounding='c') == 1
assert cos(b, rounding='c') == 1
assert cos(a, rounding='f') < 1
assert cos(b, rounding='f') < 1
for f in [sin, atan, asinh, tanh]:
assert f(a) == +a
assert f(a, rounding='c') > a
assert f(a, rounding='f') < a
assert f(b) == +b
assert f(b, rounding='c') > b
assert f(b, rounding='f') < b
for f in [asin, tan, sinh, atanh]:
assert f(a) == +a
assert f(b) == +b
assert f(a, rounding='c') > a
assert f(b, rounding='c') > b
assert f(a, rounding='f') < a
assert f(b, rounding='f') < b
assert ln(c) == +a
assert ln(d) == +b
assert ln(c, rounding='c') > a
assert ln(c, rounding='f') < a
assert ln(d, rounding='c') > b
assert ln(d, rounding='f') < b
assert cosh(a) == 1
assert cosh(b) == 1
assert cosh(a, rounding='c') > 1
assert cosh(b, rounding='c') > 1
assert cosh(a, rounding='f') == 1
assert cosh(b, rounding='f') == 1
