FNV-1a thirty-two-bit string hash

Read the equation

The algorithm starts from a fixed offset, XORs each input byte into the state, and multiplies by a fixed prime with reduction modulo 2³². Processing bytes in order yields a deterministic 32-bit integer. It is a noncryptographic hash with finitely many outputs, so different strings can collide and the hash does not retain their linguistic meaning.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

## 13.1 FNV-1a Hash

```
hash ← 2166136261
for each byte b in string:
    hash ← hash XOR b
    hash ← hash × 16777619 (mod 2³²)
return hash
```

**Explanation**: Fast, non-cryptographic hash function for converting strings to integers. Used for deterministic item encoding.

## 13.2 Hash to Unit Interval

```
h(s) = FNV1a(s) / (2³² - 1)
```

**Range**: [0, 1]

**Explanation**: Normalizes hash to unit interval for use with golden basis functions.

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# Summary Table

| Category | Equation Count |
|----------|----------------|

hash ← 2166136261
for each byte b in string:
    hash ← hash XOR b
    hash ← hash × 16777619 (mod 2³²)
return hash

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