How can I perform arithmetic right shift in C in a portable way?

Question

We are writing an emulator where we need sign propagating right shift. The emulated system uses 2\'s complement numbers.

I read that the >> operat

Answer 1

int s = -((unsigned) x >> 31);
int sar = (s^x) >> n ^ s;

This requires 5 bitwise operations.

Explanation

As already mentioned, an arithmetic right shift x >> n corresponds to the division x / 2**n. In case the system supports only logical right shift, a negative number can be first converted into a positive number and then its sign is copied back afterwards sgn(x) * (abs(x)/2**n). This is equivalent to multiply with +/-1 before and after the right shift sgn(x) * ((sgn(x)*x)/2**n).

Multiplying an integer with +/-1 can be emulated with the conditional branchless negation s^(s+x) or (x^s)-s. When s is 0, nothing happens and x remains unchanged, so a multiplication with 1. When s is -1, we obtain -x, so a multiplication with -1.

The first line of the snippet, -((unsigned) x >> 31), extracts the sign bit. Here, the unsigned conversion ensures compilation into a logical right shift (SHR in assembly). Therefore, the immediate result is 0 or 1, and after the negation s is 0 or -1 as desired.

With two branchless negations before and after the shift, we arrive at ((s^s+x) >> n) + s ^ s. This performs a division with rounding the result towards zero (e.g. -5>>1 = -2). However, an arithmetic right shift (SAR in assembly) floors the result (i.e. -5>>1 = -3). To achieve this behaviour, one has to drop the +s operation.

A demo is here: https://godbolt.org/ and https://onlinegdb.com/Hymres0y8.

PS: I arrived here, because gnuplot has only logical shifts.