xen-dev-utils/dist/approximation.d.ts

Utility functions used by the Scale Workshop ecosystem

import { Fraction, FractionValue } from './fraction';
/**
 * Calculate best rational approximations to a given fraction that are
 * closer than any approximation with a smaller or equal denominator
 * unless non-monotonic approximations are requested as well.
 * @param value The fraction to simplify.
 * @param maxDenominator Maximum denominator to include.
 * @param maxLength Maximum length of the array of approximations.
 * @param includeSemiconvergents Include semiconvergents.
 * @param includeNonMonotonic Include non-monotonically improving approximations.
 * @returns An array of (semi)convergents.
 */
export declare function getConvergents(value: FractionValue, maxDenominator?: number, maxLength?: number, includeSemiconvergents?: boolean, includeNonMonotonic?: boolean): Fraction[];
/**
 * Approximate a musical interval by ratios of which neither the numerator or denominator
 * exceeds a specified limit, once all powers of 2 are removed.
 * @param cents Size of the musical interval measured in cents.
 * @param limit Maximum odd limit.
 * @returns All odd limit fractions within 600 cents of the input value sorted by closeness with cent offsets attached.
 */
export declare function approximateOddLimitWithErrors(cents: number, limit: number): [Fraction, number][];
/**
 * Approximate a musical interval by ratios of which neither the numerator or denominator
 * exceeds a specified limit, once all powers of 2 are removed.
 * @param cents Size of the musical interval measured in cents.
 * @param limit Maximum odd limit.
 * @returns All odd limit fractions within 600 cents of the input value sorted by closeness.
 */
export declare function approximateOddLimit(cents: number, limit: number): Fraction[];
/**
 * Approximate a musical interval by ratios of which are within a prime limit with
 * exponents that do not exceed the maximimum, exponent of 2 ignored.
 * @param cents Size of the musical interval measured in cents.
 * @param limitIndex The ordinal of the prime of the limit.
 * @param maxError Maximum error from the interval for inclusion in the result.
 * @param maxLength Maximum number of approximations to return.
 * @returns All valid fractions within `maxError` cents of the input value sorted by closeness with cent offsets attached.
 */
export declare function approximatePrimeLimitWithErrors(cents: number, limitIndex: number, maxExponent: number, maxError?: number, maxLength?: number): [Fraction, number][];
/**
 * Approximate a musical interval by ratios of which are within a prime limit with
 * exponents that do not exceed the maximimum, exponent of 2 ignored.
 * @param cents Size of the musical interval measured in cents.
 * @param limitIndex The ordinal of the prime of the limit.
 * @param maxError Maximum error from the interval for inclusion in the result.
 * @param maxLength Maximum number of approximations to return.
 * @returns All valid fractions within `maxError` cents of the input value sorted by closenesss.
 */
export declare function approximatePrimeLimit(cents: number, limitIndex: number, maxExponent: number, maxError?: number, maxLength?: number): Fraction[];
/**
 * Calculate an array of continued fraction elements representing the value.
 * https://en.wikipedia.org/wiki/Continued_fraction
 * @param value Value to turn into a continued fraction.
 * @returns An array of continued fraction elements.
 */
export declare function continuedFraction(value: number): number[];
/**
 * Approximate a value with a radical expression.
 * @param value Value to approximate.
 * @param maxIndex Maximum index of the radical. 2 means square root, 3 means cube root, etc.
 * @param maxHeight Maximum Benedetti height of the radicand in the approximation.
 * @returns Object with index of the radical and the radicand. Result is "index'th root or radicand".
 */
export declare function approximateRadical(value: number, maxIndex?: number, maxHeight?: number): {
    index: number;
    radicand: Fraction;
};