Numeric128

Numeric128<P,S> is a fixed-scale decimal backed by int128.

• P = precision (digits), 1..38
• S = scale (fraction digits), 0..P
• Stored as raw = value * 10^S (int128)

Construction

Numeric128<38,4> a("12.34005");              // default HalfUp
Numeric128<38,4> b("12.34005", Rounding::Trunc);
Numeric128<38,4> c(int64_t{42});

Error model

• No exceptions.
• Each value carries Err:
• None, Invalid, Overflow, DivByZero
• ok() / error() / operator bool()

Rounding

Parsing and division/multiplication use: - Trunc (toward zero) - HalfUp (ties round away from zero)

Operators

• + - * / between same P,S
• mixed with integers
• to_string() prints exactly S fractional digits (pads with zeros)

Precision rule

Any operation that produces a value requiring >= 10^P magnitude is Overflow.