%load_ext cythonmagic
%%cython -a
cimport cython
cdef float mod_exp(int a, int b, int m):
cdef int bb, p
cdef long aa
aa = a
bb = b
p = 1
while bb > 0:
p = cython.cmod(p * (aa**(bb & 1 == 1)) , m)
aa = cython.cmod(aa * aa,m)
bb = bb >> 1
return p
@cython.cdivision(True)
cdef float s1part(int n, int k, int j):
cdef float nu, de
nu = mod_exp(16, n - 1 - k, 8*k + j)
de = (k * 8.0 + j)
return nu / de
@cython.cdivision(True)
cdef float s2part(int n, int k, int j):
cdef float de
de = (((k << 3) + j) << ((k + 1 - n) << 2))
return 1.0 / de
cdef float s1(int n):
cdef float s
cdef int k
s = 0.0
for k from 0 <= k < n:
s = s + 4.0*s1part(n,k,1) - 2.0*s1part(n,k,4) - 1.0*s1part(n,k,5) - 1.0*s1part(n,k,6)
return s
cdef float s2(int n):
cdef float s
cdef int k
s = 0.0
for k from n <= k < n + 5:
s = s + 4.0*s2part(n,k,1) - 2.0*s2part(n,k,4) - 1.0*s2part(n,k,5) - 1.0*s2part(n,k,6)
return s
cdef extern from "math.h":
float floor(float r)
cdef float prem_hexa(float r):
cdef float x
x = r - floor(r)
return floor(16*x)
def pi_plouffe(int n):
cdef float s
s = s1(n) + s2(n)
return hex(int(prem_hexa(s)))[2:]
Generated by Cython 0.20.1 on Tue Jun 9 11:58:43 2015
1:
2: cimport cython
3:
4: cdef float mod_exp(int a, int b, int m):
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5: cdef int bb, p
6: cdef long aa
7: aa = a
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8: bb = b
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9: p = 1
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10: while bb > 0:
while (1) {
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11: p = cython.cmod(p * (aa**(bb & 1 == 1)) , m)
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13: bb = bb >> 1
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14: return p
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15:
16: @cython.cdivision(True)
17: cdef float s1part(int n, int k, int j):
static float __pyx_f_46_cython_magic_733eaafe87e911db7c0421e91c548109_s1part(int __pyx_v_n, int __pyx_v_k, int __pyx_v_j) {
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18: cdef float nu, de
19: nu = mod_exp(16, n - 1 - k, 8*k + j)
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20: de = (k * 8.0 + j)
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21: return nu / de
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22:
23: @cython.cdivision(True)
24: cdef float s2part(int n, int k, int j):
static float __pyx_f_46_cython_magic_733eaafe87e911db7c0421e91c548109_s2part(int __pyx_v_n, int __pyx_v_k, int __pyx_v_j) {
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25: cdef float de
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27: return 1.0 / de
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28:
29: cdef float s1(int n):
static float __pyx_f_46_cython_magic_733eaafe87e911db7c0421e91c548109_s1(int __pyx_v_n) {
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30: cdef float s
31: cdef int k
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34: s = s + 4.0*s1part(n,k,1) - 2.0*s1part(n,k,4) - 1.0*s1part(n,k,5) - 1.0*s1part(n,k,6)
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35: return s
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36:
37: cdef float s2(int n):
static float __pyx_f_46_cython_magic_733eaafe87e911db7c0421e91c548109_s2(int __pyx_v_n) {
float __pyx_v_s;
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38: cdef float s
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43: return s
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44:
45: cdef extern from "math.h":
46: float floor(float r)
47:
48: cdef float prem_hexa(float r):
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51: return floor(16*x)
__pyx_r = floor((16.0 * __pyx_v_x)); goto __pyx_L0;
52:
53:
54: def pi_plouffe(int n):
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__Pyx_XDECREF(__pyx_r); __pyx_t_1 = PyFloat_FromDouble(__pyx_f_46_cython_magic_733eaafe87e911db7c0421e91c548109_prem_hexa(__pyx_v_s)); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 57; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __pyx_t_2 = PyTuple_New(1); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 57; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); PyTuple_SET_ITEM(__pyx_t_2, 0, __pyx_t_1); __Pyx_GIVEREF(__pyx_t_1); __pyx_t_1 = 0; __pyx_t_1 = __Pyx_PyObject_Call(((PyObject *)((PyObject*)(&PyInt_Type))), __pyx_t_2, NULL); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 57; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0; __pyx_t_2 = PyTuple_New(1); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 57; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); PyTuple_SET_ITEM(__pyx_t_2, 0, __pyx_t_1); __Pyx_GIVEREF(__pyx_t_1); __pyx_t_1 = 0; __pyx_t_1 = __Pyx_PyObject_Call(__pyx_builtin_hex, __pyx_t_2, NULL); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 57; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0; __pyx_t_2 = __Pyx_PyObject_GetSlice(__pyx_t_1, 2, 0, NULL, NULL, &__pyx_slice_, 1, 0, 1); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 57; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; __pyx_r = __pyx_t_2; __pyx_t_2 = 0; goto __pyx_L0; /* … */ __pyx_slice_ = PySlice_New(__pyx_int_2, Py_None, Py_None); if (unlikely(!__pyx_slice_)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 57; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_slice_); __Pyx_GIVEREF(__pyx_slice_);
''.join([pi_plouffe(k) for k in range(10000)])
'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c'
%timeit(pi_plouffe(10000000))
1 loops, best of 3: 18.5 s per loop
pi_plouffe(10000000)
'8'