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# mode: run
cdef extern from *:
ctypedef long long int128_t "__int128_t"
ctypedef unsigned long long uint128_t "__uint128_t"
def bigint(x):
print(str(x).rstrip('L'))
def unsigned_conversion(x):
"""
>>> bigint(unsigned_conversion(0))
0
>>> bigint(unsigned_conversion(2))
2
>>> unsigned_conversion(-2) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: can't convert negative value to ...uint128_t
>>> unsigned_conversion(-2**120) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: can't convert negative value to ...uint128_t
>>> unsigned_conversion(-2**127) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: can't convert negative value to ...uint128_t
>>> unsigned_conversion(-2**128) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: can't convert negative value to ...uint128_t
>>> bigint(unsigned_conversion(2**20))
1048576
>>> bigint(unsigned_conversion(2**30-1))
1073741823
>>> bigint(unsigned_conversion(2**30))
1073741824
>>> bigint(unsigned_conversion(2**30+1))
1073741825
>>> bigint(2**60)
1152921504606846976
>>> bigint(unsigned_conversion(2**60-1))
1152921504606846975
>>> bigint(unsigned_conversion(2**60))
1152921504606846976
>>> bigint(unsigned_conversion(2**60+1))
1152921504606846977
>>> bigint(2**64)
18446744073709551616
>>> bigint(unsigned_conversion(2**64))
18446744073709551616
>>> bigint(2**120)
1329227995784915872903807060280344576
>>> bigint(unsigned_conversion(2**120))
1329227995784915872903807060280344576
>>> bigint(2**128-1)
340282366920938463463374607431768211455
>>> bigint(unsigned_conversion(2**128-1))
340282366920938463463374607431768211455
>>> bigint(unsigned_conversion(2**128)) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: ... to convert...
>>> bigint(unsigned_conversion(2**128+1)) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: ... to convert...
>>> bigint(unsigned_conversion(2**129-1)) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: ... to convert...
>>> bigint(unsigned_conversion(2**129)) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: ... to convert...
"""
cdef uint128_t n = x
return n
def signed_conversion(x):
"""
>>> bigint(signed_conversion(0))
0
>>> bigint(signed_conversion(2))
2
>>> bigint(signed_conversion(-2))
-2
>>> bigint(signed_conversion(2**20))
1048576
>>> bigint(signed_conversion(2**32))
4294967296
>>> bigint(2**64)
18446744073709551616
>>> bigint(signed_conversion(2**64))
18446744073709551616
>>> bigint(signed_conversion(-2**64))
-18446744073709551616
>>> bigint(2**118)
332306998946228968225951765070086144
>>> bigint(signed_conversion(2**118))
332306998946228968225951765070086144
>>> bigint(signed_conversion(-2**118))
-332306998946228968225951765070086144
>>> bigint(2**120)
1329227995784915872903807060280344576
>>> bigint(signed_conversion(2**120))
1329227995784915872903807060280344576
>>> bigint(signed_conversion(-2**120))
-1329227995784915872903807060280344576
>>> bigint(2**127-1)
170141183460469231731687303715884105727
>>> bigint(signed_conversion(2**127-2))
170141183460469231731687303715884105726
>>> bigint(signed_conversion(2**127-1))
170141183460469231731687303715884105727
>>> bigint(signed_conversion(2**127)) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: ... to convert...
>>> bigint(signed_conversion(-2**127+1))
-170141183460469231731687303715884105727
>>> bigint(signed_conversion(-2**127))
-170141183460469231731687303715884105728
>>> bigint(signed_conversion(-2**127-1)) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: ... to convert...
>>> bigint(signed_conversion(-2**127-2)) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: ... to convert...
>>> bigint(signed_conversion(-2**128+1)) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: ... to convert...
>>> bigint(signed_conversion(-2**128)) # doctest: +ELLIPSIS
Traceback (most recent call last):
OverflowError: ... to convert...
"""
cdef int128_t n = x
return n
def get_int_distribution(shuffle=True):
"""
>>> L = get_int_distribution()
>>> bigint(L[0])
682
>>> bigint(L[ len(L) // 2 ])
5617771410183435
>>> bigint(L[-1])
52818775009509558395695966805
>>> len(L)
66510
"""
# Large integers that cover 1-4 (30 bits) or 1-7 (15 bits) PyLong digits.
# Uses only integer calculations to avoid rounding issues.
pow2 = [2**exp for exp in range(98)]
ints = [
n // 3
for i in range(11, len(pow2) - 1)
# Take a low but growing number of integers from each power-of-2 range.
for n in range(pow2[i], pow2[i+1], pow2[i - 8] - 1)
]
return ints * 3 # longer list, but keeps median in the middle
def intsum(L):
"""
>>> L = get_int_distribution()
>>> bigint(intsum(L))
61084913298497804284622382871263
>>> bigint(sum(L))
61084913298497804284622382871263
>>> from random import shuffle
>>> shuffle(L)
>>> bigint(intsum(L))
61084913298497804284622382871263
"""
cdef uint128_t i, x = 0
for i in L:
x += i
return x
def intxor(L):
"""
>>> L = get_int_distribution()
>>> bigint(intxor(L))
31773794341658093722410838161
>>> bigint(intxor(L * 2))
0
>>> import operator
>>> from functools import reduce
>>> bigint(reduce(operator.xor, L))
31773794341658093722410838161
>>> bigint(reduce(operator.xor, L * 2))
0
>>> from random import shuffle
>>> shuffle(L)
>>> bigint(intxor(L))
31773794341658093722410838161
>>> bigint(intxor(L * 2))
0
"""
cdef uint128_t i, x = 0
for i in L:
x ^= i
return x
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