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127 lines
3.8 KiB
Swift
127 lines
3.8 KiB
Swift
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//
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// Addition.swift
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// BigInt
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//
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// Created by Károly Lőrentey on 2016-01-03.
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// Copyright © 2016-2017 Károly Lőrentey.
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//
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extension BigUInt {
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//MARK: Addition
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/// Add `word` to this integer in place.
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/// `word` is shifted `shift` words to the left before being added.
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///
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/// - Complexity: O(max(count, shift))
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internal mutating func addWord(_ word: Word, shiftedBy shift: Int = 0) {
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precondition(shift >= 0)
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var carry = word
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var i = shift
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while carry > 0 {
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let (d, c) = self[i].addingReportingOverflow(carry)
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self[i] = d
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carry = (c ? 1 : 0)
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i += 1
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}
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}
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/// Add the digit `d` to this integer and return the result.
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/// `d` is shifted `shift` words to the left before being added.
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///
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/// - Complexity: O(max(count, shift))
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internal func addingWord(_ word: Word, shiftedBy shift: Int = 0) -> BigUInt {
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var r = self
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r.addWord(word, shiftedBy: shift)
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return r
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}
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/// Add `b` to this integer in place.
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/// `b` is shifted `shift` words to the left before being added.
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///
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/// - Complexity: O(max(count, b.count + shift))
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internal mutating func add(_ b: BigUInt, shiftedBy shift: Int = 0) {
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precondition(shift >= 0)
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var carry = false
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var bi = 0
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let bc = b.count
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while bi < bc || carry {
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let ai = shift + bi
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let (d, c) = self[ai].addingReportingOverflow(b[bi])
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if carry {
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let (d2, c2) = d.addingReportingOverflow(1)
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self[ai] = d2
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carry = c || c2
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}
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else {
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self[ai] = d
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carry = c
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}
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bi += 1
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}
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}
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/// Add `b` to this integer and return the result.
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/// `b` is shifted `shift` words to the left before being added.
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///
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/// - Complexity: O(max(count, b.count + shift))
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internal func adding(_ b: BigUInt, shiftedBy shift: Int = 0) -> BigUInt {
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var r = self
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r.add(b, shiftedBy: shift)
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return r
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}
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/// Increment this integer by one. If `shift` is non-zero, it selects
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/// the word that is to be incremented.
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///
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/// - Complexity: O(count + shift)
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internal mutating func increment(shiftedBy shift: Int = 0) {
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self.addWord(1, shiftedBy: shift)
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}
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/// Add `a` and `b` together and return the result.
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///
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/// - Complexity: O(max(a.count, b.count))
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public static func +(a: BigUInt, b: BigUInt) -> BigUInt {
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return a.adding(b)
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}
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/// Add `a` and `b` together, and store the sum in `a`.
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///
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/// - Complexity: O(max(a.count, b.count))
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public static func +=(a: inout BigUInt, b: BigUInt) {
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a.add(b, shiftedBy: 0)
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}
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}
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extension BigInt {
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/// Add `a` to `b` and return the result.
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public static func +(a: BigInt, b: BigInt) -> BigInt {
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switch (a.sign, b.sign) {
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case (.plus, .plus):
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return BigInt(sign: .plus, magnitude: a.magnitude + b.magnitude)
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case (.minus, .minus):
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return BigInt(sign: .minus, magnitude: a.magnitude + b.magnitude)
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case (.plus, .minus):
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if a.magnitude >= b.magnitude {
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return BigInt(sign: .plus, magnitude: a.magnitude - b.magnitude)
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}
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else {
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return BigInt(sign: .minus, magnitude: b.magnitude - a.magnitude)
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}
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case (.minus, .plus):
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if b.magnitude >= a.magnitude {
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return BigInt(sign: .plus, magnitude: b.magnitude - a.magnitude)
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}
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else {
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return BigInt(sign: .minus, magnitude: a.magnitude - b.magnitude)
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}
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}
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}
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/// Add `b` to `a` in place.
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public static func +=(a: inout BigInt, b: BigInt) {
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a = a + b
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}
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}
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