Module solve 

Bracketed scalar root-finders for the passive kernels.

Every iterative solve on the pricing surface — an OAS from a clean price, a yield from a dirty price, a volatility from an option price — is a passive f64 problem with one unknown and a monotone objective. The two shapes here cover them: bisection when only values are available, and a bracket-safeguarded Newton when the derivative is already in hand from a forward-mode pass — and, where only values are available but the objective is smooth, Brent’s method: bisection’s bracket kept at every step, with a secant or inverse-quadratic step taken whenever one would land inside the bracket and shrink it fast enough.

All three terminate on a scale-free tolerance rather than a fixed iteration count: a residual small in the target’s own units, or a step that has stopped moving the unknown. A fixed count is either wasteful (two hundred halvings of a bracket that reached f64 resolution at fifty) or, at large notionals, unreachable (chasing the last representable digit of a ten-million-notional price). The cap is a backstop, and reaching it is a reported failure, not a silently returned midpoint.

Structs

SolveTolerance 🔒

The convergence criteria, relative to the magnitude of what they measure.

Solved 🔒

A converged solve: the root and the iterations it took.

Enums

SolveFailure 🔒

Why a solve did not produce a root.

Functions

bisect_monotone 🔒

Bisection for f(x) = target on a monotone f over [lo, hi].

brent_monotone 🔒

Brent’s method for f(x) = target on a monotone f over [lo, hi].

newton_bracketed 🔒

Newton for f(x) = target from x0, safeguarded by the bracket [lo, hi].