c - Why prefer start + (end - start) / 2 over (start + end) / 2 when calculating the middle of an array?

Question

I've seen programmers use the formula

mid = start + (end - start) / 2

instead of using the simpler formula

mid = (start + end) / 2

for finding the middle element in the array or list.

Why do they use the former one?

Answer 1

There are three reasons.

First of all, start + (end - start) / 2 works even if you are using pointers, as long as end - start doesn't overflow¹.

int *start = ..., *end = ...;
int *mid = start + (end - start) / 2; // works as expected
int *mid = (start + end) / 2;         // type error, won't compile

Second of all, start + (end - start) / 2 won't overflow if start and end are large positive numbers. With signed operands, overflow is undefined:

int start = 0x7ffffffe, end = 0x7fffffff;
int mid = start + (end - start) / 2; // works as expected
int mid = (start + end) / 2;         // overflow... undefined

(Note that end - start may overflow, but only if start < 0 or end < 0.)

Or with unsigned arithmetic, overflow is defined but gives you the wrong answer. However, for unsigned operands, start + (end - start) / 2 will never overflow as long as end >= start.

unsigned start = 0xfffffffeu, end = 0xffffffffu;
unsigned mid = start + (end - start) / 2; // works as expected
unsigned mid = (start + end) / 2;         // mid = 0x7ffffffe

Finally, you often want to round towards the start element.

int start = -3, end = 0;
int mid = start + (end - start) / 2; // -2, closer to start
int mid = (start + end) / 2;         // -1, surprise!

Footnotes

¹ According to the C standard, if the result of pointer subtraction is not representable as a ptrdiff_t, then the behavior is undefined. However, in practice, this requires allocating a char array using at least half the entire address space.