C++ – Algorithm for finding the smallest power of two that’s greater or equal to a given value

This is because of padding added to satisfy alignment constraints. Data structure alignment impacts both performance and correctness of programs:

• Mis-aligned access might be a hard error (often SIGBUS).
• Mis-aligned access might be a soft error.
  • Either corrected in hardware, for a modest performance-degradation.
  • Or corrected by emulation in software, for a severe performance-degradation.
  • In addition, atomicity and other concurrency-guarantees might be broken, leading to subtle errors.

Here's an example using typical settings for an x86 processor (all used 32 and 64 bit modes):

struct X
{
    short s; /* 2 bytes */
             /* 2 padding bytes */
    int   i; /* 4 bytes */
    char  c; /* 1 byte */
             /* 3 padding bytes */
};

struct Y
{
    int   i; /* 4 bytes */
    char  c; /* 1 byte */
             /* 1 padding byte */
    short s; /* 2 bytes */
};

struct Z
{
    int   i; /* 4 bytes */
    short s; /* 2 bytes */
    char  c; /* 1 byte */
             /* 1 padding byte */
};

const int sizeX = sizeof(struct X); /* = 12 */
const int sizeY = sizeof(struct Y); /* = 8 */
const int sizeZ = sizeof(struct Z); /* = 8 */

One can minimize the size of structures by sorting members by alignment (sorting by size suffices for that in basic types) (like structure Z in the example above).

IMPORTANT NOTE: Both the C and C++ standards state that structure alignment is implementation-defined. Therefore each compiler may choose to align data differently, resulting in different and incompatible data layouts. For this reason, when dealing with libraries that will be used by different compilers, it is important to understand how the compilers align data. Some compilers have command-line settings and/or special #pragma statements to change the structure alignment settings.

I usually go with something like the implementation given in Josh Bloch's fabulous Effective Java. It's fast and creates a pretty good hash which is unlikely to cause collisions. Pick two different prime numbers, e.g. 17 and 23, and do:

public override int GetHashCode()
{
    unchecked // Overflow is fine, just wrap
    {
        int hash = 17;
        // Suitable nullity checks etc, of course :)
        hash = hash * 23 + field1.GetHashCode();
        hash = hash * 23 + field2.GetHashCode();
        hash = hash * 23 + field3.GetHashCode();
        return hash;
    }
}

As noted in comments, you may find it's better to pick a large prime to multiply by instead. Apparently 486187739 is good... and although most examples I've seen with small numbers tend to use primes, there are at least similar algorithms where non-prime numbers are often used. In the not-quite-FNV example later, for example, I've used numbers which apparently work well - but the initial value isn't a prime. (The multiplication constant is prime though. I don't know quite how important that is.)

This is better than the common practice of XORing hashcodes for two main reasons. Suppose we have a type with two int fields:

XorHash(x, x) == XorHash(y, y) == 0 for all x, y
XorHash(x, y) == XorHash(y, x) for all x, y

By the way, the earlier algorithm is the one currently used by the C# compiler for anonymous types.

This page gives quite a few options. I think for most cases the above is "good enough" and it's incredibly easy to remember and get right. The FNV alternative is similarly simple, but uses different constants and XOR instead of ADD as a combining operation. It looks something like the code below, but the normal FNV algorithm operates on individual bytes, so this would require modifying to perform one iteration per byte, instead of per 32-bit hash value. FNV is also designed for variable lengths of data, whereas the way we're using it here is always for the same number of field values. Comments on this answer suggest that the code here doesn't actually work as well (in the sample case tested) as the addition approach above.

// Note: Not quite FNV!
public override int GetHashCode()
{
    unchecked // Overflow is fine, just wrap
    {
        int hash = (int) 2166136261;
        // Suitable nullity checks etc, of course :)
        hash = (hash * 16777619) ^ field1.GetHashCode();
        hash = (hash * 16777619) ^ field2.GetHashCode();
        hash = (hash * 16777619) ^ field3.GetHashCode();
        return hash;
    }
}

Note that one thing to be aware of is that ideally you should prevent your equality-sensitive (and thus hashcode-sensitive) state from changing after adding it to a collection that depends on the hash code.

As per the documentation:

You can override GetHashCode for immutable reference types. In general, for mutable reference types, you should override GetHashCode only if:

• You can compute the hash code from fields that are not mutable; or
• You can ensure that the hash code of a mutable object does not change while the object is contained in a collection that relies on its hash code.

The link to the FNV article is broken but here is a copy in the Internet Archive: Eternally Confuzzled - The Art of Hashing