//
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// CS.BigInt.swift
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// CS.BigInt
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//
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// Created by Károly Lőrentey on 2015-12-27.
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// Copyright © 2016-2017 Károly Lőrentey.
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//
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//MARK: CS.BigInt
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extension CS {
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/// An arbitary precision signed integer type, also known as a "big integer".
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///
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/// Operations on big integers never overflow, but they might take a long time to execute.
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/// The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.
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///
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/// This particular big integer type uses base-2^64 digits to represent integers.
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///
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/// `BigInt` is essentially a tiny wrapper that extends `BigUInt` with a sign bit and provides signed integer
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/// operations. Both the underlying absolute value and the negative/positive flag are available as read-write
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/// properties.
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///
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/// Not all algorithms of `BigUInt` are available for `BigInt` values; for example, there is no square root or
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/// primality test for signed integers. When you need to call one of these, just extract the absolute value:
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///
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/// ```Swift
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/// CS.BigInt(255).abs.isPrime() // Returns false
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/// ```
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///
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public struct BigInt: SignedInteger {
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public enum Sign {
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case plus
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case minus
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}
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public typealias Magnitude = BigUInt
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/// The type representing a digit in `BigInt`'s underlying number system.
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public typealias Word = BigUInt.Word
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public static var isSigned: Bool {
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return true
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}
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/// The absolute value of this integer.
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public var magnitude: BigUInt
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/// True iff the value of this integer is negative.
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public var sign: Sign
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/// Initializes a new big integer with the provided absolute number and sign flag.
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public init(sign: Sign, magnitude: BigUInt) {
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self.sign = (magnitude.isZero ? .plus : sign)
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self.magnitude = magnitude
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}
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/// Return true iff this integer is zero.
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///
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/// - Complexity: O(1)
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public var isZero: Bool {
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return magnitude.isZero
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}
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/// Returns `-1` if this value is negative and `1` if it’s positive; otherwise, `0`.
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///
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/// - Returns: The sign of this number, expressed as an integer of the same type.
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public func signum() -> CS.BigInt {
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switch sign {
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case .plus:
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return isZero ? 0 : 1
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case .minus:
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return -1
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}
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}
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}
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}
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