# Uniform binary search

Jump to navigation Jump to 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-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 i, a[N] = {1,3,5,6,7,9,14,15,17,19};
make_delta(N);
for (i=0; i < 20; ++i)
printf("%d is at index %d\n", i, unisearch(a, i));
return 0;
}
```