Saturation Arithmetic

Part 1: Wikipedia

Saturation Arithmetic: all arithmetic operations are limited to a fixed range min and max value.

If result is > or < these values then it is clamped to that value. e.g.:

• $60+30 \rightarrow 90$
• $60+43 \rightarrow 100$ (not 103)
• $(60+43) - (75+25) \rightarrow 0$ , rather than 3

Modern Use

In computing it is useful for getting as close numerically to the true answer as possible, rather than the wrap around that occurs with modular arithmetic.

• also enhances algorithms in many problems.

Part 2: Rust Forum Post

Integers have finite ranges (0 to $2^n-1$) depending on the bits n they use:

• u8: 0 - $2^8$ - 1 (255) There are three options to handle an arithmetic operation that results in a value that does not fit this finite range: 1) wrap around 2) saturate at the $2^n-1$ for addition and 0 for subtraction 3) check the value and result in a panic (rust specific)

Part 3: Rust std::num Documentation

Although values for u32 should never overflow, sometimes in certain debug situations a panic may result. Thus saturation can be used. Example:

use std::num::Saturating;
let max = Saturating(u32::MAX);
let one = Saturating(1u32);
assert_eq!(u32::MAX, (max_one).0);

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