Why does Java's hashCode() in String use 31 as a multiplier?
According to Joshua Bloch's Effective Java (a book that can't be recommended enough, and which I bought thanks to continual mentions on stackoverflow):
The value 31 was chosen because it is an odd prime. If it were even and the multiplication overflowed, information would be lost, as multiplication by 2 is equivalent to shifting. The advantage of using a prime is less clear, but it is traditional. A nice property of 31 is that the multiplication can be replaced by a shift and a subtraction for better performance:
31 * i == (i << 5) - i. Modern VMs do this sort of optimization automatically.
(from Chapter 3, Item 9: Always override hashcode when you override equals, page 48)
Goodrich and Tamassia computed from over 50,000 English words (formed as the union of the word lists provided in two variants of Unix) that using the constants 31, 33, 37, 39, and 41 will produce fewer than 7 collisions in each case. This may be the reason that so many Java implementations choose such constants.
See section 9.2 Hash Tables (page 522) of Data Structures and Algorithms in Java.
On (mostly) old processors, multiplying by 31 can be relatively cheap. On an ARM, for instance, it is only one instruction:
RSB r1, r0, r0, ASL #5 ; r1 := - r0 + (r0<<5)
Most other processors would require a separate shift and subtract instruction. However, if your multiplier is slow this is still a win. Modern processors tend to have fast multipliers so it doesn't make much difference, so long as 32 goes on the correct side.
It's not a great hash algorithm, but it's good enough and better than the 1.0 code (and very much better than the 1.0 spec!).