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# ticket: t305
from cpython.object cimport Py_EQ, Py_NE
cimport cython
DEF C21 = 2-1j
cdef class Complex3j:
"""
>>> Complex3j() == 3j
True
>>> Complex3j() == Complex3j()
True
>>> Complex3j() != 3j
False
>>> Complex3j() != 3
True
>>> Complex3j() != Complex3j()
False
"""
def __richcmp__(a, b, int op):
if op == Py_EQ or op == Py_NE:
if isinstance(a, Complex3j):
eq = isinstance(b, Complex3j) or b == 3j
else:
eq = isinstance(b, Complex3j) and a == 3j
return eq if op == Py_EQ else not eq
return NotImplemented
def test_object_conversion(o):
"""
>>> test_object_conversion(2)
((2+0j), (2+0j))
>>> test_object_conversion(2j - 0.5)
((-0.5+2j), (-0.5+2j))
"""
cdef float complex a = o
cdef double complex b = o
return (a, b)
def test_arithmetic(double complex z, double complex w):
"""
>>> test_arithmetic(2j, 4j)
(2j, -2j, 6j, -2j, (-8+0j), (0.5+0j))
>>> test_arithmetic(6+12j, 3j)
((6+12j), (-6-12j), (6+15j), (6+9j), (-36+18j), (4-2j))
>>> test_arithmetic(5-10j, 3+4j)
((5-10j), (-5+10j), (8-6j), (2-14j), (55-10j), (-1-2j))
"""
return +z, -z+0, z+w, z-w, z*w, z/w
def test_div(double complex a, double complex b, expected):
"""
>>> big = 2.0**1023
>>> test_div(1 + 1j, 1 + big*1j, 1/big - 1j/big)
>>> test_div(1 + 1j, 1/big + 1j/big, big)
"""
# Can't count on good c99 complex division :(
if '_c99_' not in __name__:
assert a / b == expected, (a / b, expected)
def test_pow(double complex z, double complex w, tol=None):
"""
Various implementations produce slightly different results...
>>> a = complex(3, 1)
>>> test_pow(a, 1, 1e-15)
True
>>> test_pow(a, 2, 1e-15)
True
>>> test_pow(a, a, 1e-15)
True
>>> test_pow(complex(0.5, -.25), complex(3, 4), 1e-15)
True
>>> test_pow(-0.5, 1j, tol=1e-15)
True
"""
if tol is None:
return z**w
else:
return abs(z**w / <object>z ** <object>w - 1) < tol
def test_int_pow(double complex z, int n, tol=None):
"""
>>> [test_int_pow(complex(0, 1), k, 1e-15) for k in range(-4, 5)]
[True, True, True, True, True, True, True, True, True]
>>> [test_int_pow(complex(0, 2), k, 1e-15) for k in range(-4, 5)]
[True, True, True, True, True, True, True, True, True]
>>> [test_int_pow(complex(2, 0.5), k, 1e-14) for k in range(0, 10)]
[True, True, True, True, True, True, True, True, True, True]
>>> test_int_pow(-0.5, 5, tol=1e-15)
True
"""
if tol is None:
return z**n + <object>0 # add zero to normalize zero sign
else:
return abs(z**n / <object>z ** <object>n - 1) < tol
@cython.cdivision(False)
def test_div_by_zero(double complex z):
"""
>>> test_div_by_zero(4j)
-0.25j
>>> test_div_by_zero(0)
Traceback (most recent call last):
...
ZeroDivisionError: float division
"""
return 1/z
def test_coercion(int a, float b, double c, float complex d, double complex e):
"""
>>> test_coercion(1, 1.5, 2.5, 4+1j, 10j)
(1+0j)
(1.5+0j)
(2.5+0j)
(4+1j)
10j
(9+21j)
"""
cdef double complex z
z = a; print z
z = b; print z
z = c; print z
z = d; print z
z = e; print z
return z + a + b + c + d + e
def test_compare(double complex a, double complex b):
"""
>>> test_compare(3, 3)
(True, False, False, False, False, True, False)
>>> test_compare(3j, 3j)
(True, False, True, True, True, False, False)
>>> test_compare(3j, 4j)
(False, True, True, False, True, True, False)
>>> test_compare(3, 4)
(False, True, False, False, False, True, False)
>>> test_compare(2-1j, 4)
(False, True, False, False, False, True, True)
"""
return a == b, a != b, a == 3j, 3j == b, a == Complex3j(), Complex3j() != b, a == C21
def test_compare_coerce(double complex a, int b):
"""
>>> test_compare_coerce(3, 4)
(False, True, False, False, False, True)
>>> test_compare_coerce(4+1j, 4)
(False, True, False, True, False, True)
>>> test_compare_coerce(4, 4)
(True, False, False, False, False, True)
>>> test_compare_coerce(3j, 4)
(False, True, True, False, True, False)
"""
return a == b, a != b, a == 3j, 4+1j == a, a == Complex3j(), Complex3j() != a
def test_literal():
"""
>>> test_literal()
(5j, (1-2.5j), (2-1j))
"""
return 5j, 1-2.5j, C21
def test_real_imag(double complex z):
"""
>>> test_real_imag(1-3j)
(1.0, -3.0)
>>> test_real_imag(5)
(5.0, 0.0)
>>> test_real_imag(1.5j)
(0.0, 1.5)
"""
return z.real, z.imag
def test_real_imag_assignment(object a, double b):
"""
>>> test_real_imag_assignment(1, 2)
(1+2j)
>>> test_real_imag_assignment(1.5, -3.5)
(1.5-3.5j)
"""
cdef double complex z
z.real = a
z.imag = b
return z
def test_conjugate(float complex z):
"""
>>> test_conjugate(2+3j)
(2-3j)
"""
return z.conjugate()
def test_conjugate_double(double complex z):
"""
>>> test_conjugate_double(2+3j)
(2-3j)
"""
return z.conjugate()
ctypedef double complex cdouble
def test_conjugate_typedef(cdouble z):
"""
>>> test_conjugate_typedef(2+3j)
(2-3j)
"""
return z.conjugate()
cdef cdouble test_conjugate_nogil(cdouble z) nogil:
# Really just a compile test.
return z.conjugate()
test_conjugate_nogil(0) # use it
## cdef extern from "complex_numbers_T305.h":
## ctypedef double double_really_float "myfloat"
## ctypedef float float_really_double "mydouble"
## ctypedef float real_float "myfloat"
## ctypedef double real_double "mydouble"
## def test_conjugate_nosizeassumptions(double_really_float x,
## float_really_double y,
## real_float z, real_double w):
## """
## >>> test_conjugate_nosizeassumptions(1, 1, 1, 1)
## (-1j, -1j, -1j, -1j)
## >>> ["%.2f" % x.imag for x in test_conjugate_nosizeassumptions(2e300, 2e300, 2e300, 2e300)]
## ['-inf', '-2e+300', '-inf', '-2e+300']
## """
## cdef double complex I = 1j
## return ((x*I).conjugate(), (y*I).conjugate(), (z*I).conjugate(), (w*I).conjugate())
ctypedef double mydouble
def test_coerce_typedef_multiply(mydouble x, double complex z):
"""
>>> test_coerce_typedef_multiply(3, 1+1j)
(3+3j)
"""
return x * z
ctypedef int myint
def test_coerce_typedef_multiply_int(myint x, double complex z):
"""
>>> test_coerce_typedef_multiply_int(3, 1+1j)
(3+3j)
"""
return x * z
cpdef double complex complex_retval():
"""
>>> complex_retval()
1j
"""
return 1j
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