Why does boost::hash_combine use a "magic constant" and how does it contribute to its effectiveness?

Understanding the Magic Constant in boost::hash_combine

The boost::hash_combine function is a powerful tool for combining hash values in a way that guarantees a deterministic and evenly distributed result. However, one aspect of the function that raises questions is its use of a "magic constant," 0x9e3779b9.

The magic constant is designed to provide randomness and break correlations between bits in the seed value. It is calculated as the binary expansion of an irrational number known as the reciprocal of the golden ratio:

phi = (1 + sqrt(5)) / 2
2^32 / phi = 0x9e3779b9

By including this constant in the hash combination process, each bit of the seed is effectively modified in a random fashion. This prevents consecutive values from having a close correlation, ensuring a wider spread of hash values.

In addition, the formula used to combine the seed with the hash of the object includes shifted versions of the seed. This ensures that even if the hash function for the object has a small range of values, differences between successive seeds will be spread across all the bits of the resulting hash.

The combination of the magic constant and the shifting operations in boost::hash_combine contributes to its effectiveness in generating unique and well-distributed hash values, making it a reliable choice for hash table implementations and other applications requiring predictable and collision-resistant hashing.

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