Module arithmetic

Arbitrary-length expansion arithmetic.

An expansion is a list of non-overlapping f64 components whose exact sum is the value it represents. Two f64s can hold a product exactly; a list can hold an arbitrary determinant exactly. This is what lets orient3d, incircle, and insphere certify a sign rather than guess one.

Components are ordered smallest to largest, so the sign of a non-zero expansion is the sign of its last component.

Cost and where it is paid

These operations allocate. That is deliberate and confined to the exact path, which a filtered predicate reaches only when the floating-point determinant is too close to zero to trust. The benchmark harness measures the escalation rate precisely so this cost is a number, not a hope.

Functions

expansion_product

Multiply two expansions exactly.

expansion_sign

Sign of an expansion.

expansion_sum

Sum of two expansions, exactly.

grow_expansion

Grow an expansion by one scalar: e + b, exactly.

negate_expansion

Negate every component. Exact: negation is always representable.

scale_expansion

Scale an expansion by a scalar, exactly.