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The square root of a²+b² is the length of the vector (a,b). It obeys the triangle inequality and is zero only when both components are zero. Despite the local name smooth_norm, the function is not differentiable at the origin; an everywhere-smooth approximation would require an additional regularization term.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| a | First component |
| b | Second component |
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Original context
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## 12.4 Smooth Norm
```
smooth_norm(a, b) = √(a² + b²)
```
**Explanation**: L2 norm of two values, used for magnitude calculations.
---
# 13. Hash Functions
## 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.
Exact original notation
smooth_norm(a, b) = √(a² + b²)