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cimport cython
cdef object two = 2
cdef int size_in_bits_ = sizeof(INT) * 8
cdef bint is_signed_ = not ((<INT>-1) > 0)
cdef INT max_value_ = <INT>(two ** (size_in_bits_ - is_signed_) - 1)
cdef INT min_value_ = ~max_value_
cdef INT half_ = max_value_ // <INT>2
# Python visible.
size_in_bits = size_in_bits_
is_signed = is_signed_
max_value = max_value_
min_value = min_value_
half = half_
import operator
from libc.math cimport sqrt
cpdef check(func, op, a, b):
cdef INT res = 0, op_res = 0
cdef bint func_overflow = False
cdef bint assign_overflow = False
try:
res = func(a, b)
except OverflowError:
func_overflow = True
try:
op_res = op(a, b)
except OverflowError:
assign_overflow = True
assert func_overflow == assign_overflow, "Inconsistent overflow: %s(%s, %s)" % (func, a, b)
if not func_overflow:
assert res == op_res, "Inconsistent values: %s(%s, %s) == %s != %s" % (func, a, b, res, op_res)
medium_values = (max_value_ / 2, max_value_ / 3, min_value_ / 2, <INT>sqrt(<long double>max_value_) - <INT>1, <INT>sqrt(<long double>max_value_) + 1)
def run_test(func, op):
cdef INT offset, b
check(func, op, 300, 200)
check(func, op, max_value_, max_value_)
check(func, op, max_value_, min_value_)
if not is_signed_ or not func is test_sub:
check(func, op, min_value_, min_value_)
for offset in range(5):
check(func, op, max_value_ - <INT>1, offset)
check(func, op, min_value_ + <INT>1, offset)
if is_signed_:
check(func, op, max_value_ - 1, 2 - offset)
check(func, op, min_value_ + 1, 2 - offset)
for offset in range(9):
check(func, op, max_value_ / <INT>2, offset)
check(func, op, min_value_ / <INT>3, offset)
check(func, op, max_value_ / <INT>4, offset)
check(func, op, min_value_ / <INT>5, offset)
if is_signed_:
check(func, op, max_value_ / 2, 4 - offset)
check(func, op, min_value_ / 3, 4 - offset)
check(func, op, max_value_ / -4, 3 - offset)
check(func, op, min_value_ / -5, 3 - offset)
for offset in range(-3, 4):
for a in medium_values:
for b in medium_values:
check(func, op, a, b + offset)
@cython.overflowcheck(True)
def test_add(INT a, INT b):
"""
>>> test_add(1, 2)
3
>>> test_add(max_value, max_value) #doctest: +ELLIPSIS
Traceback (most recent call last):
...
OverflowError: value too large
>>> run_test(test_add, operator.add)
"""
return int(a + b)
@cython.overflowcheck(True)
def test_sub(INT a, INT b):
"""
>>> test_sub(10, 1)
9
>>> test_sub(min_value, 1) #doctest: +ELLIPSIS
Traceback (most recent call last):
...
OverflowError: value too large
>>> run_test(test_sub, operator.sub)
"""
return int(a - b)
@cython.overflowcheck(True)
def test_mul(INT a, INT b):
"""
>>> test_mul(11, 13)
143
>>> test_mul(max_value / 2, max_value / 2) #doctest: +ELLIPSIS
Traceback (most recent call last):
...
OverflowError: value too large
>>> run_test(test_mul, operator.mul)
"""
return int(a * b)
@cython.overflowcheck(True)
def test_nested_add(INT a, INT b, INT c):
"""
>>> test_nested_add(1, 2, 3)
6
>>> expect_overflow(test_nested_add, half + 1, half + 1, half + 1)
>>> expect_overflow(test_nested_add, half - 1, half - 1, half - 1)
"""
return int(a + b + c)
def expect_overflow(func, *args):
try:
res = func(*args)
except OverflowError:
return
assert False, "Expected OverflowError, got %s" % res
cpdef format(INT value):
"""
>>> format(1)
'1'
>>> format(half - 1)
'half - 1'
>>> format(half)
'half'
>>> format(half + 2)
'half + 2'
>>> format(half + half - 3)
'half + half - 3'
>>> format(max_value)
'max_value'
"""
if value == max_value_:
return "max_value"
elif value == half_:
return "half"
elif max_value_ - value <= max_value_ // <INT>4:
return "half + half - %s" % (half_ + half_ - value)
elif max_value_ - value <= half_:
return "half + %s" % (value - half_)
elif max_value_ - value <= half_ + max_value_ // <INT>4:
return "half - %s" % (half_ - value)
else:
return "%s" % value
cdef INT called(INT value):
print("called(%s)" % format(value))
return value
@cython.overflowcheck(True)
def test_nested(INT a, INT b, INT c, INT d):
"""
>>> test_nested_func(1, 2, 3)
called(5)
6
>>> expect_overflow(test_nested, half, half, 1, 1)
>>> expect_overflow(test_nested, half, 1, half, half)
>>> expect_overflow(test_nested, half, 2, half, 2)
>>> print(format(test_nested(half, 2, 0, 1)))
half + half - 0
>>> print(format(test_nested(1, 0, half, 2)))
half + half - 0
>>> print(format(test_nested(half, 1, 1, half)))
half + half - 0
"""
return int(a * b + c * d)
@cython.overflowcheck(True)
def test_nested_func(INT a, INT b, INT c):
"""
>>> test_nested_func(1, 2, 3)
called(5)
6
>>> expect_overflow(test_nested_func, half + 1, half + 1, half + 1)
>>> expect_overflow(test_nested_func, half - 1, half - 1, half - 1)
called(half + half - 2)
>>> print(format(test_nested_func(1, half - 1, half - 1)))
called(half + half - 2)
half + half - 1
"""
return int(a + called(b + c))
@cython.overflowcheck(True)
def test_add_const(INT a):
"""
>>> test_add_const(1)
101
>>> expect_overflow(test_add_const, max_value)
>>> expect_overflow(test_add_const , max_value - 99)
>>> test_add_const(max_value - 100) == max_value
True
"""
return int(a + <INT>100)
@cython.overflowcheck(True)
def test_sub_const(INT a):
"""
>>> test_sub_const(101)
1
>>> expect_overflow(test_sub_const, min_value)
>>> expect_overflow(test_sub_const, min_value + 99)
>>> test_sub_const(min_value + 100) == min_value
True
"""
return int(a - <INT>100)
@cython.overflowcheck(True)
def test_mul_const(INT a):
"""
>>> test_mul_const(2)
200
>>> expect_overflow(test_mul_const, max_value)
>>> expect_overflow(test_mul_const, max_value // 99)
>>> test_mul_const(max_value // 100) == max_value - max_value % 100
True
"""
return int(a * <INT>100)
@cython.overflowcheck(True)
def test_lshift(INT a, int b):
"""
>>> test_lshift(1, 10)
1024
>>> test_lshift(1, size_in_bits - 2) == 1 << (size_in_bits - 2)
True
>>> test_lshift(0, size_in_bits - 1)
0
>>> test_lshift(1, size_in_bits - 1) == 1 << (size_in_bits - 1) if not is_signed else True
True
>>> if is_signed: expect_overflow(test_lshift, 1, size_in_bits - 1)
>>> expect_overflow(test_lshift, 0, size_in_bits)
>>> expect_overflow(test_lshift, 1, size_in_bits)
>>> expect_overflow(test_lshift, 0, size_in_bits + 1)
>>> expect_overflow(test_lshift, 1, size_in_bits + 1)
>>> expect_overflow(test_lshift, 1, 100)
>>> expect_overflow(test_lshift, max_value, 1)
>>> test_lshift(max_value, 0) == max_value
True
>>> check(test_lshift, operator.lshift, 10, 15)
>>> check(test_lshift, operator.lshift, 10, 30)
>>> check(test_lshift, operator.lshift, 100, 60)
"""
return int(a << b)
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