import { TwoF64, f64, int } from "../base/common.js";
import { twoSquare } from "../base/eft.js";
//#region src/math/exp-impl.d.ts
/**
 * Compute `x²`, the square of `x`, using extended-precision arithmetic.
 *
 * Error-free transform.
 *
 * @param x A `f64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `x²`
 */
export declare const square_1: typeof twoSquare;
/**
 * Compute `x²`, the square of `x`, using extended-precision arithmetic.
 *
 * Relative error bound: `5u²`.
 *
 * @param x A `TwoF64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `x²`
 */
export declare function square_2(x: TwoF64): TwoF64;
/**
 * Compute `x³`, the cube of `x`, using extended-precision arithmetic.
 *
 * Relative error bound: `1.5u² + 4u³`.
 *
 * @param x A `f64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `x³`
 */
export declare function cube_1(x: f64): TwoF64;
/**
 * Compute `x³`, the cube of `x`, using extended-precision arithmetic.
 *
 * Relative error bound: `10u² + 25u⁴`.
 *
 * @param x A `TwoF64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `x³`
 */
export declare function cube_2(x: TwoF64): TwoF64;
/**
 * Integer power of `x` - Compute `xⁿ` using extended-precision arithmetic.
 * `n` must be an integer.
 *
 * @param x A `f64` number representing the base
 * @param n A `f64` integer representing the exponent
 * @returns The {@link TwoF64|`TwoF64`} representation of `xⁿ`
 */
export declare function powint_1(x: f64, n: int): TwoF64;
/**
 * Integer power using compensated linear product (Horner scheme applied to the
 * polynomial `p(x) = xⁿ`).
 *
 * **Assumes `n` is a {@link int | safe integer} such that `n ≥ 3`.**
 *
 * The result `[hi, lo]` is such that `f64([hi, lo])` is a faithful rounding
 * of `xⁿ` as long as `n < 2^25`.
 */
export declare function _linpow_1(x: f64, n: int): TwoF64;
/**
 * Integer power using compensated logarithmic product, based on successive
 * squarings (RTL binary exponentiation).
 * Faster than {@link _linpow_1 | `_linpow_1(x,n)`} for (roughly) `n > 30`.
 *
 * **Assumes `n` is a {@link int | safe integer} such that `n ≥ 3`.**
 *
 * The result `[hi, lo]` is such that `f64([hi, lo])` is a faithful rounding
 * of `xⁿ` as long as `n ≤ 2^49`.
 */
export declare function _logpow_1(x: f64, n: int): TwoF64;
/**
 * Integer power using compensated logarithmic product, based on successive
 * squarings (LTR binary exponentiation).
 * Faster than {@link _linpow_1 | `_linpow_1(x,n)`} for (roughly) `n > 30`.
 *
 * **Assumes `n` is an integer (supports unsafe int) such that `n ≥ 2`.**
 *
 * The result `[hi, lo]` is such that `f64([hi, lo])` is a faithful rounding
 * of `xⁿ` as long as `n ≤ 2^49`.
 */
export declare function _logpowltr(x: f64, n: int): TwoF64;
/**
 * Integer power of `x` - Compute `xⁿ` using extended-precision arithmetic.
 * `n` must be an integer.
 *
 * @param x A `TwoF64` number representing the base
 * @param n A `f64` integer representing the exponent
 * @returns The {@link TwoF64|`TwoF64`} representation of `xⁿ`
 */
export declare function powint_2(x: TwoF64, n: int): TwoF64;
/**
 * Integer power using linear product.
 *
 * **Assumes `n` is a {@link int | safe integer} such that `n ≥ 3`.**
 */
export declare function _linpow_2(x: TwoF64, n: int): TwoF64;
/**
 * Integer power using compensated logarithmic product, based on successive
 * squarings (RTL binary exponentiation).
 * Faster than {@link _linpow_2 | `_linpow_2(x,n)`} for (roughly) `n > 30`.
 *
 * **Assumes `n` is a {@link int | safe integer} such that `n ≥ 3`.**
 */
export declare function _logpow_2(x: TwoF64, n: int): TwoF64;
/**
 * Compute `eˣ`, the natural base exponential of `x`, using extended-precision
 * arithmetic.
 *
 * @param x A `f64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `eˣ`
 */
export declare function exp_1(x: f64): TwoF64;
/**
 * Compute `eˣ`, the natural base exponential of `x`, using extended-precision
 * arithmetic.
 *
 * @param x A `TwoF64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `eˣ`
 */
export declare function exp_2(x: TwoF64): TwoF64;
/**
 * Compute `eˣ - 1`, the natural base exponential of `x` subtracted by `1`,
 * using extended-precision arithmetic.
 *
 * @param x A `f64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `eˣ - 1`
 */
export declare function expm1_1(x: f64): TwoF64;
/**
 * Compute `eˣ - 1`, the natural base exponential of `x` subtracted by `1`,
 * using extended-precision arithmetic.
 *
 * @param x A `TwoF64` number
 * @returns The {@link TwoF64|`TwoF64`} representation of `eˣ - 1`
 */
export declare function expm1_2(x: TwoF64): TwoF64;
//#endregion