Right shifting negative numbers in C

Question

I have C code in which I do the following.

int nPosVal = +0xFFFF;   // + Added for ease of understanding int nNegVal = -0xFFFF;   // - Added for valid reason 

Now when I try

printf ("%d %d", nPosVal >> 1, nNegVal >> 1); 

I get

32767 -32768 

Is this expected?

I am able to think something like

65535 >> 1 = (int) 32767.5 = 32767 -65535 >> 1 = (int) -32767.5 = -32768 

That is, -32767.5 is rounded off to -32768.

Is this understanding correct?

Answer 1

It looks like your implementation is probably doing an arithmetic bit shift with two's complement numbers. In this system, it shifts all of the bits to the right and then fills in the upper bits with a copy of whatever the last bit was. So for your example, treating int as 32-bits here:

nPosVal = 00000000000000001111111111111111 nNegVal = 11111111111111110000000000000001 

After the shift, you've got:

nPosVal = 00000000000000000111111111111111 nNegVal = 11111111111111111000000000000000 

If you convert this back to decimal, you get 32767 and -32768 respectively.

Effectively, a right shift rounds towards negative infinity.

Edit: According to the Section 6.5.7 of the latest draft standard, this behavior on negative numbers is implementation dependent:

The result of E1 >> E2 is E1 right-shifted E2 bit positions. If E1 has an unsigned type or if E1 has a signed type and a nonnegative value, the value of the result is the integral part of the quotient of E1 / 2^E2. If E1 has a signed type and a negative value, the resulting value is implementation-defined.

Their stated rational for this:

The C89 Committee affirmed the freedom in implementation granted by K&R in not requiring the signed right shift operation to sign extend, since such a requirement might slow down fast code and since the usefulness of sign extended shifts is marginal. (Shifting a negative two’s complement integer arithmetically right one place is not the same as dividing by two!)

So it's implementation dependent in theory. In practice, I've never seen an implementation not do an arithmetic shift right when the left operand is signed.

Answer 2

No, you don't get fractional numbers like 0.5 when working with integers. The results can be easily explained when you look at the binary representations of the two numbers:

      65535: 00000000000000001111111111111111      -65535: 11111111111111110000000000000001 

Bit shifting to the right one bit, and extending at the left (note that this is implementation dependant, thanks Trent):

 65535 >> 1: 00000000000000000111111111111111 -65535 >> 1: 11111111111111111000000000000000 

Convert back to decimal:

 65535 >> 1 = 32767 -65535 >> 1 = -32768