On binary search

There are many articles about the pedagogical benefits of writing a binary search algorithm. Instead of just implementing binary search, I wanted to take it one step furtuer. Is is possible to write a standards compliant, formally correct, and beautiful implementation of bsearch() in C?

// This type simplifies the 
// argument list of bsearch.
typedef int (*compare_f)(
  const void *x,
  const void *y);

void *
bsearch(
  const void *key,
  const void *base,
  size_t nel,
  size_t width,
  compare_f compar)
{
  size_t k;
  size_t lo = 0;
  size_t hi = nel - 1;
  const void *mid;

  while (lo <= hi) {
    // If we used (lo + hi)/2, then it
    // would overflow for large integers. 
    // The following formula prevents that.
    k = lo + (hi - lo)/2;
    mid = base + k*width;

    // If we used compar(mid, key), then it 
    // would violate POSIX, which specifies
    // that key must be the first argument.
    int cmp = compar(key, mid);
    if (cmp < 0) hi = k - 1;
    if (cmp > 0) lo = k + 1;
    if (cmp == 0)
      return (void *)mid;
  }

  return NULL;
}

Note that not every argument and variable have been colorized, just the ones that usually give people the hardest time when reasoning about this function. The average (k) can be reduced to (lo + hi)/2 if the array you are handling is less than 2⁶³ elements long, but since it isn't technically correct, I didn't write it that way.