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# cython: profile=True
# cython: linetrace=True
# distutils: define_macros=CYTHON_TRACE=1
ctypedef long double Float
def cos(Float x, int n): # Start: cos
cdef Float neg_xsq = -x * x
cdef Float last_term = 1.
cdef Float result = 0.
for n in range(2, 2 * n, 2):
result += last_term
last_term *= neg_xsq / <Float>(n * (n - 1))
return result + last_term # End: cos
cpdef sin(Float x, int n): # Start: sin
cdef Float neg_xsq = -x * x
cdef Float last_term = x
cdef Float result = 0.
for n in range(2, 2 * n, 2):
result += last_term
last_term *= neg_xsq / <Float>(n * (n + 1))
return result + last_term # End: sin
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