import { TwoF64, f64, int } from "../base/common.js";
//#region src/math/roots.d.ts
/**
 * Compute `√(x)`, the square root of `x`, using extended-precision arithmetic.
 *
 * Relative error bound (for `x ≥ 2^-968`): `3.125u²`, with `u = 2^-53`.
 *
 * @param x A `f64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `√(x)`
 */
export declare function sqrt_1(x: f64): TwoF64;
/**
 * Compute `√(x)`, the square root of `x`, using extended-precision arithmetic.
 *
 * Relative error bound (for `x ≥ 2^-968`): `3.125u²`, with `u = 2^-53`.
 *
 * @param x A `TwoF64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `√(x)`
 */
export declare function sqrt_2(x: TwoF64): TwoF64;
/**
 * Compute `∛(x)`, the cube root of `x`, using extended-precision arithmetic.
 *
 * @param x A `f64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `∛(x)`
 */
export declare function cbrt_1(x: f64): TwoF64;
/**
 * Compute `∛(x)`, the cube root of `x`, using extended-precision arithmetic.
 *
 * @param x A `TwoF64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `∛(x)`
 */
export declare function cbrt_2(x: TwoF64): TwoF64;
/**
 * Compute `ⁿ√(x)`, the nth root of `x`, using extended-precision arithmetic.
 *
 * @param x A `f64` number representing the radicand
 * @param n A `f64` integer representing the root degree
 * @returns The {@link TwoF64|`TwoF64`} representation of `ⁿ√(x)`
 */
export declare function nthroot_1(x: f64, n: int): TwoF64;
/**
 * Compute `ⁿ√(x)`, the nth root of `x`, using extended-precision arithmetic.
 *
 * @param x A `TwoF64` number representing the radicand
 * @param n A `f64` integer representing the root degree
 * @returns The {@link TwoF64|`TwoF64`} representation of `ⁿ√(x)`
 */
export declare function nthroot_2(x: TwoF64, n: int): TwoF64;
/**
 * Compute `√(x)`, the square root of `x`, using extended-precision arithmetic.
 *
 * Relative error bound (for `x ≥ 2^-968`): `3.125u²`, with `u = 2^-53`.
 *
 * @param x A `f64` or `TwoF64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `√(x)`
 */
export declare function sqrt(x: f64 | TwoF64): TwoF64;
/**
 * Compute `∛(x)`, the cube root of `x`, using extended-precision arithmetic.
 *
 * @param x A `f64` or `TwoF64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `∛(x)`
 */
export declare function cbrt(x: f64 | TwoF64): TwoF64;
/**
 * Compute `ⁿ√(x)`, the nth root of `x`, using extended-precision arithmetic.
 *
 * @param x A `f64` or `TwoF64` number representing the radicand
 * @param n A `f64` integer representing the root degree
 * @returns The {@link TwoF64|`TwoF64`} representation of `ⁿ√(x)`
 */
export declare function nthRoot(x: f64 | TwoF64, n: int): TwoF64;
//#endregion