Why Does Boost's hash_combine Function Use a 'Magic Constant'?

Boost's hash_combine: Enhancing Hash Quality with Magic Constants

The boost::hash_combine function, when employed with hash tables, plays a crucial role in distributing values efficiently and reducing collision scenarios. While its deterministic nature ensures consistency, the inclusion of a "magic constant" raises questions about its significance.

Unveiling the Magic Constant

The magic constant, denoted by 0x9e3779b9, holds a unique property: it consists of 32 random bits, with each bit having an equal probability of being either 0 or 1. Contrary to intuitive assumptions, this constant isn't haphazardly chosen but rather derived from an irrational number - the reciprocal of the golden ratio.

Specifically, the constant is calculated as the first 32 bits of the binary expansion of 2^32 / phi, where phi represents the golden ratio. This ensures that each bit of the seed undergoes a random transformation when combined with the constant.

Benefits of Bit Manipulation

By incorporating the constant, the function achieves two essential goals:

1. Wide Distribution: As the constant randomly alters every bit of the seed, similar values are mapped significantly apart. This reduces the likelihood of consecutive keys residing in adjacent hash table indices, enhancing the efficiency of probing operations.
2. Enhanced Dispersion: The addition of shifted versions of the old seed helps spread out differences across all the bits in situations where hash_value() produces a limited range of values. By introducing a delta to the seed, this step ensures that small deviations in input values lead to larger variations in the combined hash.

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