Module: Utils

Utils module - Helper functions for the UOR Math-JS library Implements advanced mathematical utilities optimized for the Prime Framework

Source: Utils.js, line 1

Classes

PrimeMathError
PrimeMathError

Members

(inner, constant) primeCache

Export the prime cache for external use Provides access to the cache for statistics and management

Source: Utils.js, line 1195

Methods

(inner) exactDivide(dividend, divisor) → {BigInt}

Perform exact division, ensuring the result is an integer Aligns with the Prime Framework's requirement for exact arithmetic

Parameters:

Name	Type	Description
`dividend`	BigInt	The number to divide
`divisor`	BigInt	The divisor

Source: Utils.js, line 218

Throws:

If the division is not exact or if divisor is zero
Type PrimeMathError

Returns:

The result of the division

Type:: BigInt

(inner) factorial(n) → {BigInt}

Factorial function Optimized for the Prime Framework

Parameters:

Name	Type	Description
`n`	BigInt \| number	The number to calculate factorial for

Source: Utils.js, line 1171

Throws:

If n is negative
Type PrimeMathError

Returns:

Type:: BigInt

(inner) fastExp(base, exponent, modulusopt) → {BigInt}

Fast exponentiation algorithm (exponentiation by squaring) Efficiently computes base^exponent in O(log n) time Optimized for use in the Prime Framework Enhanced to handle large exponents safely

Parameters:

Name	Type	Attributes	Default	Description
`base`	BigInt			The base value
`exponent`	BigInt			The exponent value (must be non-negative)
`modulus`	BigInt	<optional>	null	Optional modulus for modular exponentiation

Source: Utils.js, line 116

Throws:

If exponent is negative
Type PrimeMathError

Returns:

base raised to the power of exponent (modulo modulus if provided)

Type:: BigInt

(inner) gcd(a, b) → {BigInt}

Calculate the greatest common divisor (GCD) of two numbers using the binary GCD algorithm Optimized version of the Euclidean algorithm for better performance in the Prime Framework

Parameters:

Name	Type	Description
`a`	BigInt	First number
`b`	BigInt	Second number

Source: Utils.js, line 238

Returns:

The GCD of a and b

Type:: BigInt

(inner) getNthPrime(n) → {BigInt}

Get the nth prime number Uses optimized caching and generation for efficiency

Parameters:

Name	Type	Description
`n`	BigInt \| number \| string	The 1-based index of the prime number to retrieve

Source: Utils.js, line 1350

Throws:

If n is not a positive integer
Type PrimeMathError

Returns:

The nth prime number

Type:: BigInt

(inner) getPrimeRange(start, end, optionsopt) → {Array.<BigInt>}

Get a range of prime numbers Efficiently generates primes within a specified range Uses segmented sieve of Eratosthenes for optimal performance Enhanced to respect configurable limits

Parameters:

Name Type Attributes Description

start

BigInt | number

The lower bound of the range (inclusive)

end

BigInt | number

The upper bound of the range (inclusive)

options

Object

Options for prime generation

Properties

Name	Type	Attributes	Description
`segmentSize`	BigInt \| number	<optional>	Size of each segment for the segmented sieve
`dynamic`	boolean	<optional>	Whether to use dynamic segment sizing (overrides config)
`maxCount`	number	<optional>	Maximum number of primes to return

Source: Utils.js, line 656

Throws:

If parameters are invalid
Type PrimeMathError

Returns:

Array of prime numbers in the specified range

Type:: Array.<BigInt>

(inner) isDivisible(num, divisor) → {boolean}

Check if a number is divisible by another

Parameters:

Name	Type	Description
`num`	BigInt	The number to check
`divisor`	BigInt	The potential divisor

Source: Utils.js, line 201

Throws:

If divisor is zero
Type PrimeMathError

Returns:

True if num is divisible by divisor, false otherwise

Type:: boolean

(inner) isMersennePrime(n) → {boolean}

Check if a number is a Mersenne prime (a prime of the form 2^n - 1) Mersenne primes have the form 2^p - 1 where p is also prime

Parameters:

Name	Type	Description
`n`	BigInt \| number \| string	The number to check

Source: Utils.js, line 1381

Returns:

True if n is a Mersenne prime, false otherwise

Type:: boolean

(inner) isPrime(n, optionsopt) → {boolean}

Parameters:

Name	Type	Attributes	Description
`n`	BigInt \| number \| string		The number to check for primality
`options`	PrimeTestOptions	<optional>	Options for primality testing

Source: Utils.js, line 474

Returns:

True if n is prime, false otherwise

Type:: boolean

(inner) lcm(a, b) → {BigInt}

Calculate the least common multiple (LCM) of two numbers Optimized for the Prime Framework using the GCD

Parameters:

Name	Type	Description
`a`	BigInt	First number
`b`	BigInt	Second number

Source: Utils.js, line 290

Returns:

The LCM of a and b

Type:: BigInt

(inner) moebiusFunction(n) → {BigInt}

Calculate the Möbius function μ(n) value for a number The Möbius function is defined as: μ(n) = 1 if n is square-free with an even number of prime factors -1 if n is square-free with an odd number of prime factors 0 if n has a squared prime factor

Parameters:

Name	Type	Description
`n`	BigInt \| number \| string	The number to compute the Möbius function for

Source: Utils.js, line 1423

Throws:

If n is not a positive integer
Type PrimeMathError

Returns:

The Möbius function value

Type:: BigInt

(inner) nextPrime(n) → {BigInt}

Get the next prime number after a given number Enhanced with prime cache for efficiency

Parameters:

Name	Type	Description
`n`	BigInt \| number	The starting number

Source: Utils.js, line 1084

Returns:

The next prime number after n

Type:: BigInt

(generator, inner) primeGenerator(options) → {Generator.<BigInt>}

Get a prime number generator/iterator that produces sequential primes Follows the Prime Framework's stream-based approach

Parameters:

Name Type Description

options

Object

Generator options

Properties

Name	Type	Attributes	Default	Description
`start`	BigInt \| number	<optional>	2	The number to start from (inclusive if prime)
`end`	BigInt \| number	<optional>		Optional end value (inclusive)
`count`	number	<optional>		Optional max count of primes to generate

Source: Utils.js, line 1133

Returns:

A generator that yields prime numbers

Type:: Generator.<BigInt>

(inner) quadraticResidue(a, p) → {boolean}

Check if a is a quadratic residue modulo p A number a is a quadratic residue modulo p if there exists an x such that x^2 ≡ a (mod p)

Parameters:

Name	Type	Description
`a`	BigInt \| number \| string	The number to check
`p`	BigInt \| number \| string	The prime modulus

Source: Utils.js, line 1475

Throws:

If p is not likely a prime
Type PrimeMathError

Returns:

True if a is a quadratic residue modulo p, false otherwise

Type:: boolean

(inner) toBigInt(value) → {BigInt}

Safely convert a value to BigInt Enhanced to handle a wider range of inputs for the Prime Framework

Parameters:

Name	Type	Description
`value`	number \| string \| BigInt	The value to convert

Source: Utils.js, line 312

Throws:

If the value cannot be converted to BigInt
Type PrimeMathError

Returns:

The value as a BigInt

Type:: BigInt

Type Definitions

PrimeTestOptions

Type:

Object

Properties

Name	Type	Description
`useCache`	boolean	Whether to use the prime cache
`updateCache`	boolean	Whether to update the cache with result

Source: Utils.js, line 463