Uniform binary search

Uniform binary search is an optimization of the classic binary search algorithm invented by Donald Knuth and given in Knuth's The Art of Computer Programming. It uses a lookup table to update a single array index, rather than taking the midpoint of an upper and a lower bound on each iteration; therefore, it is optimized for architectures (such as Knuth's MIX) on which

• a table lookup is generally faster than an addition and a shift, and
• many searches will be performed on the same array, or on several arrays of the same length

C implementation

The uniform binary search algorithm looks like this, when implemented in C.

#define LOG_N 4

static int delta[LOG_N];

void make_delta(int N)
{
    int power = 1;
    int i = 0;

    do {
        int half = power;
        power <<= 1;
        delta[i] = (N + half) / power;
    } while (delta[i++] != 0);
}

int unisearch(int *a, int key)
{
    int i = delta[0] - 1;  /* midpoint of array */
    int d = 0;

    while (1) {
        if (key == a[i]) {
            return i;
        } else if (delta[d] == 0) {
            return -1;
        } else {
            if (key < a[i]) {
                i -= delta[++d];
            } else {
                i += delta[++d];
            }
        }
    }
}

/* Example of use: */
#define N 10

int main(void)
{
    int a[N] = {1, 3, 5, 6, 7, 9, 14, 15, 17, 19};

    make_delta(N);

    for (int i = 0; i < 20; ++i)
        printf("%d is at index %d\n", i, unisearch(a, i));

    return 0;
}

References

• Knuth. The Art of Computer Programming, Volume 3. Page 412, Algorithm C.

External links

• An implementation of Knuth's algorithm in Pascal, by Han de Bruijn
• An implementation of Knuth's algorithm in Go, by Adrianus Warmenhoven