Modular exponentiation - BInt version
func expMod(_ x: BInt, _ m: BInt) -> BInt (self^x) mod m for positive x, ((self^-x) mod m) modInverse m for negative x
import BigIntSigned integers and fractions of unbounded size
struct BIntThe BInt structure
static func ** (a: BInt, x: Int) -> BInt Exponentiation
func expMod(_ x: BInt, _ m: Int) -> Int Modular exponentiation - Int version
init?(_ d: Double) Constructs a BInt from a decimal value, nil if d is infinite or NaN
init(_ x: Int) Constructs a BInt from an Int value
init<T>(_ source: T) where T : BinaryFloatingPoint init<T>(_ source: T) where T : BinaryInteger init(_ magnitude: Limbs, _ isNegative: Bool = false) Constructs a BInt from magnitude and sign
init?(_ x: String, radix: Int = 10) Constructs a BInt from a String value and radix, nil if x does not designate an integer in the given radix
init(bitWidth: Int) Constructs a uniformly distributed random BInt in the range 0 ..< 2 ^ bitWidth
init<T>(clamping source: T) where T : BinaryInteger init?<T>(exactly source: T) where T : BinaryFloatingPoint init?<T>(exactly source: T) where T : BinaryInteger init(from decoder: any Decoder) throws init(integerLiteral value: StaticBigInt) Constructs a BInt from a StaticBigInt
init(magnitude x: Bytes) Constructs a BInt from a big-endian magnitude byte array
init(signed x: Bytes) Constructs a BInt from a big-endian 2’s complement byte array
init<T>(truncatingIfNeeded source: T) where T : BinaryInteger static let EIGHT: BIntBInt(8)
static let FIVE: BIntBInt(5)
static let FOUR: BIntBInt(4)
static let NINE: BIntBInt(9)
static let ONE: BIntBInt(1)
static let SEVEN: BIntBInt(7)
static let SIX: BIntBInt(6)
static let TEN: BIntBInt(10)
static let THREE: BIntBInt(3)
static let TWO: BIntBInt(2)
static let ZERO: BIntBInt(0)
static var isSigned: Bool { get }static func binomial(_ n: Int, _ k: Int) -> BInt Compute binomial coefficient n over k
static func factorial(_ n: Int) -> BInt Factorial function
static func fibonacci(_ n: Int) -> BInt n’th Fibonacci number
static func fibonacci2(_ n: Int) -> (BInt, BInt) Fibonacci pair, n’th and n’th + 1 Fibonacci number
static func lucas(_ n: Int) -> BInt n’th Lucas number
static func lucas2(_ n: Int) -> (BInt, BInt) Lucas pair, n’th and n’th + 1 Lucas number
static func primorial(_ n: Int) -> BInt Product of primes up to n
static func probablePrime(_ bitWidth: Int, _ p: Int = 30) -> BInt A probable prime number with a given bitwidth
var _magnitude: Limbs { get }The magnitude limb array
var abs: BInt { get }The absolute value of self
var bitWidth: Int { get }The number of bits in the binary representation of the magnitude of self. 0 if self = 0
var description: String { get }Base 10 string value of self
var isEven: Bool { get }Is true if self is even, false if self is odd
var isNegative: Bool { get }The sign, true if self < 0, false if self >= 0
var isNotZero: Bool { get }Is false if self = 0, true otherwise
var isOdd: Bool { get }Is true if self is odd, false if self is even
var isOne: Bool { get }Is true if self = 1, false otherwise
var isPositive: Bool { get }Is true if self > 0, false otherwise
var isPow2: Bool { get }Is true if self is a power of 2: 1, 2, 4, 8 …, false otherwise
var isZero: Bool { get }Is true if self = 0, false otherwise
var leadingZeroBitCount: Int { get }The number of leading zero bits in the magnitude of self. 0 if self = 0
var magnitude: BInt { get }var population: Int { get }The number of 1 bits in the magnitude of self
var signum: Int { get }Is 0 if self = 0, 1 if self > 0, and -1 if self < 0
var trailingZeroBitCount: Int { get }The number of trailing zero bits in the magnitude of self. 0 if self = 0
var words: [UInt] { get }static func != (x: BInt, y: BInt) -> Bool Not equal
static func != (x: BInt, y: Int) -> Bool Not equal
static func != (x: Int, y: BInt) -> Bool Not equal
static func % (x: BInt, y: BInt) -> BInt Remainder
static func % (x: BInt, y: Int) -> BInt Remainder
static func % (x: Int, y: BInt) -> BInt Remainder
static func %= (x: inout BInt, y: BInt) x = x % y
static func %= (x: inout BInt, y: Int) x = x % y
static func & (x: BInt, y: BInt) -> BInt Bitwise and operator - behaves as if two’s complement representation were used
static func &= (x: inout BInt, y: BInt) x = x & y
static func * (x: BInt, y: BInt) -> BInt Multiplication
static func * (x: BInt, y: Int) -> BInt Multiplication
static func * (x: Int, y: BInt) -> BInt Multiplication
static func *= (x: inout BInt, y: BInt) x = x * y
static func *= (x: inout BInt, y: Int) x = x * y
static func + (x: BInt) -> BInt Prefix plus
static func + (x: BInt, y: BInt) -> BInt Addition
static func + (x: BInt, y: Int) -> BInt Addition
static func + (x: Int, y: BInt) -> BInt Addition
static func += (x: inout BInt, y: BInt) x = x + y
static func += (x: inout BInt, y: Int) x = x + y
static func - (x: BInt) -> BInt Negation
static func - (x: BInt, y: BInt) -> BInt Subtraction
static func - (x: BInt, y: Int) -> BInt Subtraction
static func - (x: Int, y: BInt) -> BInt Subtraction
static func -= (x: inout BInt, y: BInt) x = x - y
static func -= (x: inout BInt, y: Int) x = x - y
static func / (x: BInt, y: BInt) -> BInt Division
static func / (x: BInt, y: Int) -> BInt Division
static func / (x: Int, y: BInt) -> BInt Division
static func /= (x: inout BInt, y: BInt) x = x / y
static func /= (x: inout BInt, y: Int) x = x / y
static func < (x: BInt, y: BInt) -> Bool Less than
static func < (x: BInt, y: Int) -> Bool Less than
static func < (x: Int, y: BInt) -> Bool Less than
static func << (x: BInt, n: Int) -> BInt Logical left shift
static func <<= (x: inout BInt, n: Int) x = x << n
static func <<= <RHS>(lhs: inout BInt, rhs: RHS) where RHS : BinaryInteger static func <= (x: BInt, y: BInt) -> Bool Less than or equal
static func <= (x: BInt, y: Int) -> Bool Less than or equal
static func <= (x: Int, y: BInt) -> Bool Less than or equal
static func == (x: BInt, y: BInt) -> Bool Equal
static func == (x: BInt, y: Int) -> Bool Equal
static func == (x: Int, y: BInt) -> Bool Equal
static func > (x: BInt, y: BInt) -> Bool Greater than
static func > (x: BInt, y: Int) -> Bool Greater than
static func > (x: Int, y: BInt) -> Bool Greater than
static func >= (x: BInt, y: BInt) -> Bool Greater than or equal
static func >= (x: BInt, y: Int) -> Bool Greater than or equal
static func >= (x: Int, y: BInt) -> Bool Greater than or equal
static func >> (x: BInt, n: Int) -> BInt Logical right shift
static func >>= (x: inout BInt, n: Int) x = x >> n
static func >>= <RHS>(lhs: inout BInt, rhs: RHS) where RHS : BinaryInteger static func ^ (x: BInt, y: BInt) -> BInt Bitwise xor operator - behaves as if two’s complement representation were used
static func ^= (x: inout BInt, y: BInt) x = x ^ y
static func | (x: BInt, y: BInt) -> BInt Bitwise or operator - behaves as if two’s complement representation were used
static func |= (x: inout BInt, y: BInt) x = x | y
static func ~ (x: BInt) -> BInt Bitwise not operator - behaves as if two’s complement arithmetic were used
func asDouble() -> Double self as a Double
func asInt() -> Int? self as an Int
func asMagnitudeBytes() -> Bytes Byte array representation of magnitude value
func asSignedBytes() -> Bytes Byte array representation of 2’s complement value
func asString(radix: Int = 10, uppercase: Bool = false) -> String self as a String with a given radix
mutating func clearBit(_ n: Int) Clear a specified bit - a no-op if bit number < 0
mutating func flipBit(_ n: Int) Invert a specified bit - a no-op if bit number < 0
func gcd(_ x: BInt) -> BInt Greatest common divisor - BInt version
func gcd(_ x: Int) -> BInt Greatest common divisor - Int version
func gcdExtended(_ x: BInt) -> (g: BInt, a: BInt, b: BInt) Extended greatest common divisor - BInt version
func gcdExtended(_ x: Int) -> (g: BInt, a: BInt, b: BInt) Extended greatest common divisor - Int version
func isPerfectRoot() -> Bool Check whether self is a perfect root, that is, for some integer x and n > 1 self = x^n
func isPerfectSquare() -> Bool Check whether self is a perfect square, that is, for some integer x, self = x^2
func isProbablyPrime(_ p: Int = 30) -> Bool Checks whether self is prime using the Miller-Rabin algorithm
func jacobiSymbol(_ m: Int) -> Int Jacobi symbol - Int version. If m is an odd prime, this is also the Legendre symbol
func jacobiSymbol(_ m: BInt) -> Int Jacobi symbol - BInt version. If m is an odd prime, this is also the Legendre symbol
func kroneckerSymbol(_ m: Int) -> Int Kronecker symbol - Int version. If m is positive and odd, this is also the Jacobi symbol
func kroneckerSymbol(_ m: BInt) -> Int Kronecker symbol - BInt version. If m is positive and odd, this is also the Jacobi symbol
func lcm(_ x: BInt) -> BInt Least common multiple - BInt version
func lcm(_ x: Int) -> BInt Least common multiple - Int version
func mod(_ x: BInt) -> BInt Modulus - BInt version
func mod(_ x: Int) -> Int Modulus - Int version
func modInverse(_ m: BInt) -> BInt Inverse modulus - BInt version
func modInverse(_ m: Int) -> Int Inverse modulus - Int version
mutating func negate() Negates self
func nextPrime(_ p: Int = 30) -> BInt The next probable prime greater than self
func quotientAndRemainder(dividingBy x: BInt) -> (quotient: BInt, remainder: BInt) Division
func quotientAndRemainder(dividingBy x: Int) -> (quotient: BInt, remainder: Int) Division
func quotientAndRemainder(dividingBy x: BInt, _ quotient: inout BInt, _ remainder: inout BInt) Division
func quotientAndRemainder(dividingBy x: Int, _ quotient: inout BInt, _ remainder: inout Int) Division
func quotientExact(dividingBy x: BInt) -> BInt Exact division - that is, the remainder of the division is known to be 0
func randomFrom(_ x: BInt) -> BInt Random value
func randomLessThan() -> BInt Random value
func randomTo(_ x: BInt) -> BInt Random value
func root(_ n: Int) -> BInt n’th root
func rootRemainder(_ n: Int) -> (root: BInt, rem: BInt) n’th root and remainder
mutating func setBit(_ n: Int) Set a specified bit - a no-op if bit number < 0
func sqrt() -> BInt Square root of a non-negative number
func sqrtMod(_ p: BInt) -> BInt? Square root modulo a prime number - BInt version
func sqrtMod(_ p: Int) -> Int? Square root modulo a prime number - Int version
func sqrtRemainder() -> (root: BInt, rem: BInt) Square root and remainder of a non-negative number
func testBit(_ n: Int) -> Bool Test a specified bit - false if bit number < 0