|
|
@@ -2,27 +2,32 @@
|
|
|
// BigNum.swift
|
|
|
// Swifter
|
|
|
//
|
|
|
-// Created by Damian Kolakowski on 08/08/16.
|
|
|
+// Copyright © 2016 Damian Kołakowski. All rights reserved.
|
|
|
//
|
|
|
|
|
|
import Foundation
|
|
|
|
|
|
-public struct BigNum {
|
|
|
+public struct BigNum: Equatable, Comparable {
|
|
|
|
|
|
- //
|
|
|
+ //
|
|
|
// Big Integer
|
|
|
//
|
|
|
// TODO/Improvments
|
|
|
// - add init(...) for string literal
|
|
|
- // - switch to 'long division'
|
|
|
+ // - add powmod operation
|
|
|
// - fix '+' and '-' operators for negative numbers
|
|
|
|
|
|
internal var digits = [UInt8]()
|
|
|
internal var signum = 0
|
|
|
|
|
|
- internal init(_ digits: [UInt8]) {
|
|
|
+ internal init(_ digits: [UInt8], _ signum: Int) {
|
|
|
+ self.digits.append(contentsOf: digits)
|
|
|
+ self.signum = signum
|
|
|
+ }
|
|
|
+
|
|
|
+ internal init(_ digits: ArraySlice<UInt8>, _ signum: Int) {
|
|
|
self.digits.append(contentsOf: digits)
|
|
|
- self.signum = digits.isEmpty ? 0 : 1
|
|
|
+ self.signum = signum
|
|
|
}
|
|
|
|
|
|
public init(_ text: String) {
|
|
|
@@ -44,16 +49,20 @@ public func == (_ left: BigNum, right: BigNum) -> Bool {
|
|
|
return (left.digits == right.digits) && (left.signum == right.signum)
|
|
|
}
|
|
|
|
|
|
+infix operator != { }
|
|
|
+public func != (_ left: BigNum, right: BigNum) -> Bool {
|
|
|
+ return !(left.digits == right.digits)
|
|
|
+}
|
|
|
+
|
|
|
infix operator + { }
|
|
|
public func + (_ left: BigNum, _ right: BigNum) -> BigNum {
|
|
|
var result = [UInt8]()
|
|
|
var carry: UInt8 = 0
|
|
|
for i in 0..<max(left.digits.count, right.digits.count) {
|
|
|
- let leftDigit = (i < left.digits.count) ? left.digits[i] : 0
|
|
|
- let rightDigit = (i < right.digits.count) ? right.digits[i] : 0
|
|
|
- let sum = (leftDigit + rightDigit) + carry
|
|
|
- if sum > 9 {
|
|
|
- carry = 1
|
|
|
+ let sum = (((i < left.digits.count) ? left.digits[i] : 0) +
|
|
|
+ ((i < right.digits.count) ? right.digits[i] : 0)) + carry
|
|
|
+ if sum >= 10 {
|
|
|
+ carry = sum / 10
|
|
|
result.append(sum - 10)
|
|
|
} else {
|
|
|
carry = 0
|
|
|
@@ -63,7 +72,7 @@ public func + (_ left: BigNum, _ right: BigNum) -> BigNum {
|
|
|
if carry != 0 {
|
|
|
result.append(carry)
|
|
|
}
|
|
|
- return BigNum(result)
|
|
|
+ return BigNum(result, 1)
|
|
|
}
|
|
|
|
|
|
infix operator - { }
|
|
|
@@ -71,23 +80,25 @@ public func - (_ left: BigNum, _ right: BigNum) -> BigNum {
|
|
|
var result = [UInt8]()
|
|
|
var carry: Int = 0
|
|
|
for i in 0..<max(left.digits.count, right.digits.count) {
|
|
|
- let leftDigit = (i < left.digits.count) ? left.digits[i] : 0
|
|
|
- let rightDigit = (i < right.digits.count) ? right.digits[i] : 0
|
|
|
- let diff = (Int(leftDigit) - Int(rightDigit)) + carry
|
|
|
- if diff < 0 {
|
|
|
+ let sub = (Int((i < left.digits.count) ? left.digits[i] : 0) -
|
|
|
+ Int((i < right.digits.count) ? right.digits[i] : 0)) + carry
|
|
|
+ if sub < 0 {
|
|
|
carry = -1
|
|
|
- result.append(UInt8(10+diff))
|
|
|
+ result.append(UInt8(10+sub))
|
|
|
} else {
|
|
|
carry = 0
|
|
|
- result.append(UInt8(diff))
|
|
|
+ result.append(UInt8(sub))
|
|
|
}
|
|
|
}
|
|
|
while let last = result.last, last == 0 { result.removeLast() }
|
|
|
- return BigNum(result)
|
|
|
+ return BigNum(result, 1)
|
|
|
}
|
|
|
|
|
|
infix operator * { }
|
|
|
public func * (_ left: BigNum, _ right: BigNum) -> BigNum {
|
|
|
+ if (left.signum == 0) || (right.signum == 0) {
|
|
|
+ return BigNum([], 0)
|
|
|
+ }
|
|
|
var mulResults = Array<[UInt8]>()
|
|
|
for i in 0..<left.digits.count {
|
|
|
var row = [UInt8](repeating: 0, count: i)
|
|
|
@@ -108,42 +119,53 @@ public func * (_ left: BigNum, _ right: BigNum) -> BigNum {
|
|
|
}
|
|
|
mulResults.append(row)
|
|
|
}
|
|
|
- var sum = mulResults.reduce(BigNum([0])) { $0.partialResult + BigNum($0.1) }
|
|
|
+ var sum = mulResults.reduce(BigNum([0], 1)) { $0.partialResult + BigNum($0.1, 1) }
|
|
|
sum.signum = left.signum * right.signum
|
|
|
return sum
|
|
|
}
|
|
|
|
|
|
infix operator / { }
|
|
|
-public func / (_ left: BigNum, _ right: BigNum) -> BigNum {
|
|
|
+public func / (_ left: BigNum, _ right: BigNum) -> (quotient: BigNum, reminder: BigNum) {
|
|
|
+
|
|
|
if left < right {
|
|
|
- return BigNum([0])
|
|
|
+ return (BigNum([0], 0), left)
|
|
|
}
|
|
|
- var quotient = BigNum([0])
|
|
|
- var remainder = left
|
|
|
|
|
|
- while remainder >= right {
|
|
|
- quotient = quotient + BigNum([1])
|
|
|
- remainder = remainder - right
|
|
|
+ if left.digits == right.digits {
|
|
|
+ return (BigNum([1], left.signum * right.signum), BigNum([0], 0))
|
|
|
}
|
|
|
|
|
|
- quotient.signum = left.signum * right.signum
|
|
|
+ var shiftIndex = left.digits.count - right.digits.count
|
|
|
+ var tmp = BigNum(left.digits[shiftIndex..<left.digits.count], 1)
|
|
|
|
|
|
- return quotient
|
|
|
+ while tmp < right {
|
|
|
+ shiftIndex = shiftIndex - 1
|
|
|
+ tmp = BigNum(left.digits[shiftIndex..<left.digits.count], 1)
|
|
|
+ }
|
|
|
+
|
|
|
+ var quotient = [UInt8]()
|
|
|
+ var rest = BigNum([0], 0)
|
|
|
+
|
|
|
+ while shiftIndex >= 0 {
|
|
|
+ var i: UInt8 = 1
|
|
|
+ while (right * BigNum([i], 1)) < tmp {
|
|
|
+ i = i + 1
|
|
|
+ }
|
|
|
+ quotient.append(i-1)
|
|
|
+ rest = tmp - (right * BigNum([i-1], 1))
|
|
|
+ shiftIndex = shiftIndex - 1
|
|
|
+ if shiftIndex < 0 {
|
|
|
+ break
|
|
|
+ }
|
|
|
+ tmp = BigNum([left.digits[shiftIndex]] + rest.digits, 1)
|
|
|
+ }
|
|
|
+
|
|
|
+ return (BigNum(quotient.reversed(), left.signum * right.signum), rest)
|
|
|
}
|
|
|
|
|
|
infix operator % { }
|
|
|
public func % (_ left: BigNum, _ right: BigNum) -> BigNum {
|
|
|
- if left < right {
|
|
|
- return left
|
|
|
- }
|
|
|
- var quotient = BigNum([0])
|
|
|
- var remainder = left
|
|
|
-
|
|
|
- while remainder >= right {
|
|
|
- quotient = quotient + BigNum([1])
|
|
|
- remainder = remainder - right
|
|
|
- }
|
|
|
- return remainder
|
|
|
+ return (left / right).reminder
|
|
|
}
|
|
|
|
|
|
infix operator > { }
|
|
|
@@ -158,17 +180,12 @@ public func > (_ left: BigNum, _ right: BigNum) -> Bool {
|
|
|
return left.digits.count > right.digits.count
|
|
|
}
|
|
|
}
|
|
|
- for i in 0..<left.digits.count {
|
|
|
- if left.digits[i] == right.digits[i] {
|
|
|
- continue
|
|
|
- }
|
|
|
- if left.signum < 0 {
|
|
|
- if left.digits[i] < right.digits[i] {
|
|
|
- return true
|
|
|
- }
|
|
|
- } else {
|
|
|
- if left.digits[i] > right.digits[i] {
|
|
|
- return true
|
|
|
+ for i in (0..<left.digits.count).reversed() {
|
|
|
+ if left.digits[i] != right.digits[i] {
|
|
|
+ if left.signum < 0 {
|
|
|
+ return left.digits[i] < right.digits[i]
|
|
|
+ } else {
|
|
|
+ return left.digits[i] > right.digits[i]
|
|
|
}
|
|
|
}
|
|
|
}
|
|
|
@@ -187,17 +204,12 @@ public func < (_ left: BigNum, _ right: BigNum) -> Bool {
|
|
|
return left.digits.count < right.digits.count
|
|
|
}
|
|
|
}
|
|
|
- for i in 0..<left.digits.count {
|
|
|
- if left.digits[i] == right.digits[i] {
|
|
|
- continue
|
|
|
- }
|
|
|
- if left.signum < 0 {
|
|
|
- if right.digits[i] < left.digits[i] {
|
|
|
- return true
|
|
|
- }
|
|
|
- } else {
|
|
|
- if right.digits[i] > left.digits[i] {
|
|
|
- return true
|
|
|
+ for i in (0..<left.digits.count).reversed() {
|
|
|
+ if left.digits[i] != right.digits[i] {
|
|
|
+ if left.signum < 0 {
|
|
|
+ return right.digits[i] < left.digits[i]
|
|
|
+ } else {
|
|
|
+ return right.digits[i] > left.digits[i]
|
|
|
}
|
|
|
}
|
|
|
}
|
Damian Kołakowski