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# cython: language_level=3
# distutils: extra_compile_args = -O3
cimport cython
ctypedef fused INT:
int
long long
unsigned int
unsigned long long
object
ctypedef fused C_INT:
int
long long
unsigned int
unsigned long long
@cython.overflowcheck(False)
def fib(INT n):
"""
>>> [fib(k) for k in range(10)]
[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
"""
cdef INT a, b, k
a, b = 0, 1
for k in range(n):
a, b = b, a + b
return int(b)
@cython.overflowcheck(True)
def fib_overflow(INT n):
"""
>>> [fib_overflow(k) for k in range(10)]
[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
"""
cdef INT a, b, k
a, b = 0, 1
for k in range(n):
a, b = b, a + b
return int(b)
@cython.overflowcheck(False)
def collatz(INT n):
"""
>>> collatz(1)
0
>>> collatz(5)
5
>>> collatz(10)
6
"""
cdef INT k = 0
while n != 1:
if n % 2 == 0:
n //= 2
else:
n = 3*n + 1
k += 1
return int(k)
@cython.overflowcheck(True)
@cython.overflowcheck.fold(False)
def collatz_overflow(INT n):
"""
>>> collatz_overflow(1)
0
>>> collatz_overflow(5)
5
>>> collatz_overflow(10)
6
"""
cdef INT k = 0
while n != 1:
if n % 2 == 0:
n //= 2
else:
n = 3*n + 1
k += 1
return int(k)
@cython.overflowcheck(True)
@cython.overflowcheck.fold(True)
def collatz_overflow_fold(INT n):
"""
>>> collatz_overflow_fold(1)
0
>>> collatz_overflow_fold(5)
5
>>> collatz_overflow_fold(10)
6
"""
cdef INT k = 0
while n != 1:
if n % 2 == 0:
n //= 2
else:
n = 3*n + 1
k += 1
return int(k)
@cython.overflowcheck(False)
def factorial(INT n):
"""
>>> factorial(2)
2
>>> factorial(5)
120
"""
cdef INT k, res = 1
for k in range(2, n+1):
res = res * k
return int(res)
@cython.overflowcheck(True)
def factorial_overflow(INT n):
"""
>>> factorial_overflow(2)
2
>>> factorial_overflow(5)
120
"""
cdef INT k, res = 1
for k in range(2, n+1):
res = res * k
return int(res)
@cython.overflowcheck(False)
def most_orthogonal(C_INT[:,::1] vectors):
cdef C_INT n = vectors.shape[0]
cdef C_INT* a
cdef C_INT* b
cdef double min_dot = 2 # actual max is 1
for i in range(n):
for j in range(i):
a = &vectors[i, 0]
b = &vectors[j, 0]
# A highly nested arithmetic expression...
normalized_dot = (1.0 * (a[0]*b[0] + a[1]*b[1] + a[2]*b[2]) /
((a[0]*a[0] + a[1]*a[1] + a[2]*a[2]) * (b[0]*b[0] + b[1]*b[1]+b[2]*b[2])))
if normalized_dot < min_dot:
min_dot = normalized_dot
min_pair = i, j
return vectors[i], vectors[j]
@cython.overflowcheck(True)
@cython.overflowcheck.fold(False)
def most_orthogonal_overflow(C_INT[:,::1] vectors):
cdef C_INT n = vectors.shape[0]
cdef C_INT* a
cdef C_INT* b
cdef double min_dot = 2 # actual max is 1
for i in range(n):
for j in range(i):
a = &vectors[i, 0]
b = &vectors[j, 0]
# A highly nested arithmetic expression...
normalized_dot = ((a[0]*b[0] + a[1]*b[1] + a[2]*b[2]) /
(1.0 * (a[0]*a[0] + a[1]*a[1] + a[2]*a[2]) * (b[0]*b[0] + b[1]*b[1]+b[2]*b[2])))
if normalized_dot < min_dot:
min_dot = normalized_dot
min_pair = i, j
return vectors[i], vectors[j]
@cython.overflowcheck(True)
@cython.overflowcheck.fold(True)
def most_orthogonal_overflow_fold(C_INT[:,::1] vectors):
cdef C_INT n = vectors.shape[0]
cdef C_INT* a
cdef C_INT* b
cdef double min_dot = 2 # actual max is 1
for i in range(n):
for j in range(i):
a = &vectors[i, 0]
b = &vectors[j, 0]
# A highly nested arithmetic expression...
normalized_dot = ((a[0]*b[0] + a[1]*b[1] + a[2]*b[2]) /
(1.0 * (a[0]*a[0] + a[1]*a[1] + a[2]*a[2]) * (b[0]*b[0] + b[1]*b[1]+b[2]*b[2])))
if normalized_dot < min_dot:
min_dot = normalized_dot
min_pair = i, j
return vectors[i], vectors[j]