Why Does Boost's `hash_combine` Use the Golden Ratio as a 'Magic Constant'?

Exploring the Magic Constant in Boost's hash_combine

The hash_combine function in Boost is a critical component in hash generation. It takes a seed hash and an object to combine their hash values. Understanding the inner workings of this function is essential for effective hash generation.

One aspect of hash_combine that raises curiosity is the inclusion of a "magic constant," 0x9e3779b9. This constant is not a random number but rather a specific value derived from the irrational number known as the golden ratio (φ).

According to the Boost documentation, this constant serves a specific purpose. It randomly modifies each bit of the seed hash due to the expected randomness of irrational numbers. By doing so, it helps spread the differences between consecutive values across a wider range.

To enhance the randomization effect, hash_combine also incorporates shifted versions of the seed hash. This ensures that even if the object hash itself has a relatively limited range, the accumulated differences will eventually encompass all bits.

By understanding the role of the magic constant in Boost's hash_combine, developers can gain a deeper appreciation for the effectiveness and robustness of this hash generation function.

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