Given a program
#include <iostream>
using namespace std;
int main()
{
const size_t DoW = 7;
const unsigned int DAYS_OF_WEEK = static_cast<unsigned int> (DoW);
unsigned int dayOfFirstDay = 0;
unsigned int _firstDayOfWeek = 1;
unsigned int diff = (DAYS_OF_WEEK+ (dayOfFirstDay - _firstDayOfWeek) ) % DAYS_OF_WEEK;
cout << "diff = (" << DAYS_OF_WEEK << " + (" << dayOfFirstDay << " - " << _firstDayOfWeek << ")) %" << DAYS_OF_WEEK
<< " = " << diff << endl;
return 0;
}
The output of that program is
diff = (7 + (0 - 1)) %7 = 6
which is expected. But a modified program without static_cast
#include <iostream>
using namespace std;
int main()
{
const size_t DAYS_OF_WEEK = 7;
unsigned int dayOfFirstDay = 0;
unsigned int _firstDayOfWeek = 1;
unsigned int diff = (DAYS_OF_WEEK+ (dayOfFirstDay - _firstDayOfWeek) ) % DAYS_OF_WEEK;
cout << "diff = (" << DAYS_OF_WEEK << " + (" << dayOfFirstDay << " - " << _firstDayOfWeek << ")) %" << DAYS_OF_WEEK
<< " = " << diff << endl;
return 0;
}
outputs
diff = (7 + (0 - 1)) %7 = 3
which is not expected. Why?
(Both programs are compiled with g++
9.3.0 on Ubuntu 64 Bit)
It seems on your platform size_t
is 64-bit, and unsigned int
is 32-bit.
There is no integral promotion to 64-bits 1 . This is the danger of mixing 64-bit operands in expressions.
So a 32-bit wraparound of -1 remains as 4294967295 when converted to 64 bits.
And we get 7 + 4294967295 (performed in 64 bits) = 4294967302 (no wraparound).
4294967302 % 7 = 3
1 Except for systems where ( unsigned
) int
itself is 64 bits, which is currently unlikely.
Such result can happen when size_t
has more width than unsigned int
.
The subtraction of unsigned int
and unsigned int
wraps around and results in unsigned int
. 0 - 1
results in -1
, and it may become 0xffffffff
when unsigned int
is 4-byte long.
Then, adding that with another unsigned int
will result in unsigned int
, so the result looks like normal subtraction and addition.
On the other hand, adding with size_t
will have it calculate in size_t
domain, so truncation doesn't happen and the value 7 + 0xffffffff
will be divided instead of 7 - 1
.
Here is an example code to check the values before division:
#include <iostream>
#include <ios>
int main()
{
const size_t DoW = 7;
const unsigned int DAYS_OF_WEEK = static_cast<unsigned int> (DoW);
unsigned int dayOfFirstDay = 0;
unsigned int _firstDayOfWeek = 1;
size_t to_add = dayOfFirstDay - _firstDayOfWeek;
size_t diff_uint = DAYS_OF_WEEK+ (dayOfFirstDay - _firstDayOfWeek);
size_t diff_sizet = DoW+ (dayOfFirstDay - _firstDayOfWeek);
std::cout << "sizeof(unsigned int) = " << sizeof(unsigned int) << '\n';
std::cout << "sizeof(size_t) = " << sizeof(size_t) << '\n';
std::cout << std::hex;
std::cout << "to add : 0x" << to_add << '\n';
std::cout << "diff_uint : 0x" << diff_uint << '\n';
std::cout << "diff_sizet : 0x" << diff_sizet << '\n';
return 0;
}
Here is an example of output :
sizeof(unsigned int) = 4
sizeof(size_t) = 8
to add : 0xffffffff
diff_uint : 0x6
diff_sizet : 0x100000006
dayOfFirstDay - _firstDayOfWeek
is an unsigned int
. As _firstDayOfWeek
is greater than dayOfFirstDay
the value is an underflow and wrap around and becomes max value of unsigned int
. Let's call this value max_uint
.
On the other hand DAYS_OF_WEEK
is a size_t
which is probably a wider type than unsigned int
. This means that DAYS_OF_WEEK + max_uint
is not overflowing. So you end-up computing max_uint % 7
. But max_uint % 7
is not equal to -1
...
Try it with less obfuscation:
#include <stdio.h>
#include <stddef.h>
int main() {
printf("0u - 1u = %u\n", 0u - 1u);
printf("7u + (0u - 1u) = %u\n", 7u + (0u - 1u));
printf("7zu + (0u - 1u) = %zu\n", size_t{7} + (0u - 1u));
}
The output I get:
0u - 1u = 4294967295
7u + (0u - 1u) = 6
7zu + (0u - 1u) = 4294967302
As you can see, 0u - 1u
results in a wraparound. Adding this huge number to an unsigned int
results in another wraparound. Adding it to a size_t
doesn't as the entire value is representable. For that reason, you get different results after the modulus operator.
In the initializer expression of this declaration
unsigned int diff = (DAYS_OF_WEEK+ (dayOfFirstDay - _firstDayOfWeek) ) % DAYS_OF_WEEK;
the sub-expression (dayOfFirstDay - _firstDayOfWeek)
is equal to the maximum value of the type unsigned int
.
Thus in this sub-expression when DAYS_OF_WEEK
has the type unsigned int
(DAYS_OF_WEEK+ (dayOfFirstDay - _firstDayOfWeek) )
an overflow occurs.
When DAYS_OF_WEEK
has the type size_t
when neither overflow occurs.
This is the reason of different results.
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