Weird OpenMP Reduction

Typical reductions in OpenMP* involve using a associative operator op to do local reductions, and then using a reduction clause to collect those local reductions. For example, the following code computes a dot product by computing local sums on each thread and then summing them.

// Returns dot product of two vectors
int dot( int x[], int y[], int n ) {
    int sum = 0;
#pragma omp parallel for reduction(+:sum)
    for( int i=0; i<n; ++i ) {
        sum += x[i]*y[i];
    }
    return sum;
}

The reduction clause specifies two things:

When control enters the parallel region, each thread in the region gets a thread-private copy of sum, initialized to the identity element for +.
When control leaves the parallel region, the original sum is updated by combining its value with the final values of thethread-private copies, using +. Since + is associative (or nearly so for floating-point), the final sum has the same value (or nearly so) as it would for serial execution of the code.

The reduction clause does not say specify anything more -- you are allowed to do anything with the thread-local copies of a reduction variable. The code below demonstrates this point. It computes the dot product of two integer vectors without using any addition operations inside the loop. It assumes two's complement arithmetic.

// Returns dot product of two vectors
int dot( int x[], int y[], int n ) {
    int c = 0;
    int s = 0;
#pragma omp parallel for reduction(+:c,s)
    for( int i=0; i<n; ++i ) {
        int p = x[i]*y[i];
        int q = c^p;
        c &= p|s;
        c |= p&s;
        c <<= 1;
        s ^= q;
    }
    return c+s;
}

Consider it a puzzle, not recommended practice. If you need a hint for why it works correctly, look at this datasheet for a classic TTL part.

*Other names and brands may be claimed as the property of others