What is the purpose of the div() library function?

From the C99 Rationale document:

(7.20.6.2 The div, ldiv, and lldiv functions) Because C89 had implementation-defined semantics for division of signed integers when negative operands were involved, div and ldiv, and lldiv in C99, were invented to provide well-specified semantics for signed integer division and remainder operations. The semantics were adopted to be the same as in Fortran. Since these functions return both the quotient and the remainder, they also serve as a convenient way of efficiently modeling underlying hardware that computes both results as part of the same operation. [...] Now that C99 requires similar semantics for the division operator, the main reason for new programs to use div, ldiv or lldiv is to simultaneously obtain quotient and remainder.

Quoted from C Programming: A Modern Approach, 2nd Edition, chapter 26, Q & A section.

Q: Why do the div and ldiv functions exist? Can't we just use the / and % operators?

A: div and ldiv aren't quite the same as / and %. Recall from Section 4.1 that applying / and % to negative operands doesn't give a portable result in C89. If i or j is negative, whether the value of i / j is rounded up or down is implementation defined, as is the sign of i % j. The answer computed by div and ldiv, on the other hand, don't depend on the implementation. The quotient is rounded toward zero; the remainder is computed according to the formula n = q x d + r, where n is the original number, q is the quotient, d is the divisor, and r is the remainder. Here are a few examples:

 n      |  d     |  q     |  r
--------|--------|--------|--------
 7      |  3     |  2     |  1
-7      |  3     | -2     | -1
 7      | -3     | -2     |  1
-7      | -3     |  2     | -1

In C99, the / and % operators are guaranteed to produce the same result as div and ldiv.

Efficiency is the other reason that div and ldiv exist. Many machines have an instruction that can compute both the quotient and remainder, so calling div or ldiv may be faster than using the / and % operators separately.