Question

I encountered a strange thing when I was programming under c++. It’s about a simple multiplication.

Code:

unsigned __int64 a1 = 255*256*256*256;
unsigned __int64 a2= 255 << 24; // same as the above

cerr()<<"a1 is:"<<a1;
cerr()<<"a2 is:"<<a2;

interestingly the result is:

a1 is: 18446744073692774400 
a2 is: 18446744073692774400 

whereas it should be:(using calculator confirms)

4278190080

Can anybody tell me how could it be possible?

Answer 1

 255*256*256*256

all operands are int you are overflowing int. The overflow of a signed integer is undefined behavior in C and C++.

EDIT:

note that the expression 255 << 24 in your second declaration also invokes undefined behavior if your int type is 32-bit. 255 x (2^24) is 4278190080 which cannot be represented in a 32-bit int (the maximum value is usually 2147483647 on a 32-bit int in two’s complement representation).

C and C++ both say for E1 << E2 that if E1 is of a signed type and positive and that E1 x (2^E2) cannot be represented in the type of E1, the program invokes undefined behavior. Here ^ is the mathematical power operator.