In [1]:

    

%load_ext Cython


    

In [2]:

    

def f_py(x):
    return x**2 -x

def intg_py(a, b, N):
    s = 0
    dx = (b - a) / N
    for i in range(N):
        s += f_py(a + i*dx)
    return s * dx


    

In [3]:

    

%%cython

def f_c1(x):
    return x**2 -x

def intg_c1(a, b, N):
    s = 0
    dx = (b - a) / N
    for i in range(N):
        s += f_c1(a + i*dx)
    return s * dx


    

In [4]:

    

%%cython

def f_c2(double x):
    return x**2 - x

def intg_c2(double a, double b, int N):
    cdef int i
    cdef double s, dx
    s = 0
    dx = (b - a) / N
    for i in range(N):
        s += f_c2(a + i*dx)
    return s * dx


    

In [5]:

    

%%cython

cdef double f_c3(double x) except? -2:
    return x**2 - x

def intg_c3(double a, double b, int N):
    cdef int i
    cdef double s, dx
    s = 0
    dx = (b - a) / N
    for i in range(N):
        s += f_c3(a + i*dx)
    return s * dx


    

In [14]:

    

%%cython

cpdef double f_c4(double x) except? -2:
    return x**2 - x

def intg_c4(double a, double b, int N):
    cdef int i
    cdef double s, dx
    s = 0
    dx = (b - a) / N
    for i in range(N):
        s += f_c4(a + i*dx)
    return s * dx


    

In [10]:

    

%timeit -n3 -r5 intg_py(0, 10, 1000000)


    

    




317 ms ± 7.71 ms per loop (mean ± std. dev. of 5 runs, 3 loops each)

In [11]:

    

%timeit -n3 -r5 intg_c1(0, 10, 1000000)


    

    




203 ms ± 8.26 ms per loop (mean ± std. dev. of 5 runs, 3 loops each)

In [12]:

    

%timeit -n3 -r5 intg_c2(0, 10, 1000000)


    

    




63.3 ms ± 2.76 ms per loop (mean ± std. dev. of 5 runs, 3 loops each)

In [13]:

    

%timeit -n3 -r5 intg_c3(0, 10, 1000000)


    

    




1.87 ms ± 102 µs per loop (mean ± std. dev. of 5 runs, 3 loops each)

In [15]:

    

%timeit -n3 -r5 intg_c4(0, 10, 1000000)


    

    




2.1 ms ± 91.5 µs per loop (mean ± std. dev. of 5 runs, 3 loops each)