/**
 * Adaptive Gauss-Kronrod (G7-K15) quadrature.
 *
 * QUADPACK-style adaptive numerical integration: on each subinterval, a
 * 15-point Kronrod estimate `K` is compared against the embedded 7-point
 * Gauss estimate `G` (both reuse the same 15 evaluation points, so `G` is
 * "free" once `K` is computed). `|K - G|` is the panel's error estimate; if
 * it exceeds tolerance the interval is bisected and each half is refined
 * recursively. This adapts naturally to endpoint singularities and peaked
 * integrands, unlike a fixed-order Gauss-Legendre rule (see `gaussLegendre5`
 * in `../typed/numeric.ts`, whose Richardson-extrapolation adaptivity still
 * converges slowly on e.g. `x^-1/2` near 0).
 *
 * @packageDocumentation
 */
type f64 = number;
type i32 = number;
/** Options for {@link quad}. */
export interface QuadOptions {
    /** Relative tolerance on each panel's `|K - G|` vs `|K|` (default 1e-10). */
    tol?: f64;
    /** Maximum bisection recursion depth per panel (default 50). */
    maxDepth?: i32;
}
/** Result of {@link quad}. */
export interface QuadResult {
    /** The estimated integral. */
    value: f64;
    /** Sum of the absolute per-panel `|K - G|` error estimates. */
    error: f64;
}
/**
 * Adaptive Gauss-Kronrod (G7-K15) numerical integration of `f` over `[a, b]`.
 *
 * Each subinterval is evaluated with the 15-point Kronrod rule and its
 * embedded 7-point Gauss rule; `|K - G|` is the panel's error estimate. A
 * panel whose error exceeds `tol * |K|` (or the absolute floor, for panels
 * near zero) is bisected and each half refined recursively, up to
 * `maxDepth`. This adapts naturally to endpoint singularities and sharply
 * peaked integrands.
 *
 * @param f - Function to integrate
 * @param a - Lower bound
 * @param b - Upper bound
 * @param opts - Options (tol, maxDepth)
 * @returns `{ value, error }` — the estimated integral and summed panel error
 *
 * @example
 * ```typescript
 * quad((x) => 4 / (1 + x * x), 0, 1).value; // ~pi
 * quad((x) => 1 / Math.sqrt(x), 0, 1).value; // ~2, despite the endpoint singularity
 * ```
 */
export declare function quad(f: (x: f64) => f64, a: f64, b: f64, opts?: QuadOptions): QuadResult;
export {};
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