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BigUIntTests.swift
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BigUIntTests.swift
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//
// BigUIntTests.swift
// BigInt
//
// Created by Károly Lőrentey on 2015-12-27.
// Copyright © 2016-2017 Károly Lőrentey.
//
import XCTest
@testable import BigInt
class BigUIntTests: XCTestCase {
typealias Digit = BigUInt.Digit
func testInit() {
let b0 = BigUInt()
XCTAssertEqual(b0._digits, [])
XCTAssertEqual(b0._start, 0)
XCTAssertEqual(b0._end, 0)
let b1 = BigUInt([1, 2])
XCTAssertEqual(b1._digits, [1, 2])
XCTAssertEqual(b1._start, 0)
XCTAssertEqual(b1._end, 2)
let b2 = BigUInt([1, 2, 3, 0, 0])
XCTAssertEqual(b2._digits, [1, 2, 3, 0, 0])
XCTAssertEqual(b2._start, 0)
XCTAssertEqual(b2._end, 3)
let b3 = BigUInt(digits: [12, 34, 56], start: 1, end: 2)
XCTAssertEqual(b3._digits, [12, 34, 56])
XCTAssertEqual(b3._start, 1)
XCTAssertEqual(b3._end, 2)
let b4 = BigUInt(digits: [12, 34, 56], start: 5, end: 10)
XCTAssertEqual(b4._digits, [12, 34, 56])
XCTAssertEqual(b4._start, 3)
XCTAssertEqual(b4._end, 3)
let b5 = BigUInt(UIntMax(0x1827364554637281))
XCTAssertEqual(String(b5, radix: 16), "1827364554637281")
let b6 = BigUInt(UInt32(0x12345678))
XCTAssertEqual(String(b6, radix: 16), "12345678")
let b7 = BigUInt(IntMax(0x1827364554637281))
XCTAssertEqual(String(b7, radix: 16), "1827364554637281")
let b8 = BigUInt(Int16(0x1234))
XCTAssertEqual(String(b8, radix: 16), "1234")
let b9: BigUInt = 0x1827364554637281
XCTAssertEqual(String(b9, radix: 16), "1827364554637281")
}
func testInitFromLiterals() {
XCTAssertEqual(42 as BigUInt, BigUInt(42))
XCTAssertEqual("42" as BigUInt, BigUInt(42))
// I have no idea how to exercise these in the wild
XCTAssertEqual(BigUInt(unicodeScalarLiteral: UnicodeScalar(52)), BigUInt(4))
XCTAssertEqual(BigUInt(extendedGraphemeClusterLiteral: "4"), BigUInt(4))
}
func testCollection() {
let b0 = BigUInt()
XCTAssertEqual(b0.count, 0)
XCTAssertEqual(Array(b0), [])
let b1 = BigUInt([1])
XCTAssertEqual(b1.count, 1)
XCTAssertEqual(Array(b1), [1])
let b2 = BigUInt([0, 1])
XCTAssertEqual(b2.count, 2)
XCTAssertEqual(Array(b2), [0, 1])
let b3 = BigUInt([0, 1, 0])
XCTAssertEqual(b3.count, 2)
XCTAssertEqual(Array(b3), [0, 1])
let b4 = BigUInt([1, 0, 0, 0])
XCTAssertEqual(b4.count, 1)
XCTAssertEqual(Array(b4), [1])
let b5 = BigUInt([0, 0, 0, 0, 0, 0])
XCTAssertEqual(b5.count, 0)
XCTAssertEqual(Array(b5), [])
}
func testSubscriptingGetter() {
let b = BigUInt([1, 2])
XCTAssertEqual(b[0], 1)
XCTAssertEqual(b[1], 2)
XCTAssertEqual(b[2], 0)
XCTAssertEqual(b[3], 0)
XCTAssertEqual(b[10000], 0)
}
func testSubscriptingSetter() {
var d = BigUInt()
XCTAssertEqual(d.count, 0)
XCTAssertEqual(d[0], 0)
XCTAssertEqual(d[1], 0)
XCTAssertEqual(d[10], 0)
d[10] = 0
XCTAssertEqual(d.count, 0)
XCTAssertEqual(d[0], 0)
XCTAssertEqual(d[1], 0)
XCTAssertEqual(d[10], 0)
d[0] = 42
XCTAssertEqual(d.count, 1)
XCTAssertEqual(d[0], 42)
XCTAssertEqual(d[1], 0)
XCTAssertEqual(d[10], 0)
d[10] = 23
XCTAssertEqual(d.count, 11)
XCTAssertEqual(d[0], 42)
XCTAssertEqual(d[1], 0)
XCTAssertEqual(d[10], 23)
d[0] = 0
XCTAssertEqual(d.count, 11)
XCTAssertEqual(d[0], 0)
XCTAssertEqual(d[1], 0)
XCTAssertEqual(d[10], 23)
d[10] = 0
XCTAssertEqual(d.count, 0)
XCTAssertEqual(d[0], 0)
XCTAssertEqual(d[1], 0)
XCTAssertEqual(d[10], 0)
XCTAssertEqual(d, BigUInt())
}
func testSlice() {
let value = BigUInt([0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20])
let slice = value[3..<6]
XCTAssertEqual(slice.count, 3)
XCTAssertEqual(slice.startIndex, 0)
XCTAssertEqual(slice.endIndex, 3)
XCTAssertTrue(slice.elementsEqual([6, 8, 10]))
XCTAssertEqual(slice[0], 6)
XCTAssertEqual(slice[1], 8)
XCTAssertEqual(slice[2], 10)
}
func testIndices() {
let value = BigUInt([0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28])
XCTAssertEqual(0 ..< 15, value.indices)
XCTAssertEqual(3, value.index(after: 2))
XCTAssertEqual(1, value.index(before: 2))
var i = 2
value.formIndex(after: &i)
XCTAssertEqual(3, i)
value.formIndex(before: &i)
XCTAssertEqual(2, i)
XCTAssertEqual(5, value.index(2, offsetBy: 3))
XCTAssertEqual(1, value.index(3, offsetBy: -2))
XCTAssertEqual(10, value.index(3, offsetBy: 7, limitedBy: 11))
XCTAssertEqual(10, value.index(3, offsetBy: 7, limitedBy: 10))
XCTAssertEqual(nil, value.index(3, offsetBy: 7, limitedBy: 9))
XCTAssertEqual(3, value.index(7, offsetBy: -4, limitedBy: 2))
XCTAssertEqual(3, value.index(7, offsetBy: -4, limitedBy: 3))
XCTAssertEqual(nil, value.index(7, offsetBy: -4, limitedBy: 4))
XCTAssertEqual(2, value.distance(from: 3, to: 5))
}
func testIntegerArithmeticRequirements() {
XCTAssertEqual(0, BigUInt(0).toIntMax())
XCTAssertEqual(42, BigUInt(42).toIntMax())
XCTAssertEqual(5, BigUInt.addWithOverflow(2, 3).0)
XCTAssertFalse(BigUInt.addWithOverflow(2, 3).overflow)
XCTAssertEqual(2, BigUInt.subtractWithOverflow(5, 3).0)
XCTAssertFalse(BigUInt.subtractWithOverflow(5, 3).overflow)
XCTAssertEqual(BigUInt(Digit.max - 1), BigUInt.subtractWithOverflow(3, 5).0)
XCTAssertTrue(BigUInt.subtractWithOverflow(3, 5).overflow)
XCTAssertEqual(15, BigUInt.multiplyWithOverflow(5, 3).0)
XCTAssertFalse(BigUInt.multiplyWithOverflow(5, 3).overflow)
XCTAssertEqual(3, BigUInt.divideWithOverflow(17, 5).0)
XCTAssertFalse(BigUInt.divideWithOverflow(17, 5).overflow)
XCTAssertEqual(2, BigUInt.remainderWithOverflow(17, 5).0)
XCTAssertFalse(BigUInt.remainderWithOverflow(17, 5).overflow)
}
func testStrideableRequirements() {
XCTAssertEqual(BigUInt(10), BigUInt(4).advanced(by: BigInt(6)))
XCTAssertEqual(BigUInt(4), BigUInt(10).advanced(by: BigInt(-6)))
XCTAssertEqual(BigInt(6), BigUInt(4).distance(to: 10))
XCTAssertEqual(BigInt(-6), BigUInt(10).distance(to: 4))
}
func testConversionToString() {
let sample = BigUInt("123456789ABCDEFEDCBA98765432123456789ABCDEF", radix: 16)!
// Radix = 10
XCTAssertEqual(String(BigUInt()), "0")
XCTAssertEqual(String(BigUInt(1)), "1")
XCTAssertEqual(String(BigUInt(100)), "100")
XCTAssertEqual(String(BigUInt(12345)), "12345")
XCTAssertEqual(String(BigUInt(123456789)), "123456789")
XCTAssertEqual(String(sample), "425693205796080237694414176550132631862392541400559")
// Radix = 16
XCTAssertEqual(String(BigUInt(0x1001), radix: 16), "1001")
XCTAssertEqual(String(BigUInt(0x0102030405060708), radix: 16), "102030405060708")
XCTAssertEqual(String(sample, radix: 16), "123456789abcdefedcba98765432123456789abcdef")
XCTAssertEqual(String(sample, radix: 16, uppercase: true), "123456789ABCDEFEDCBA98765432123456789ABCDEF")
// Radix = 2
XCTAssertEqual(String(BigUInt(12), radix: 2), "1100")
XCTAssertEqual(String(BigUInt(123), radix: 2), "1111011")
XCTAssertEqual(String(BigUInt(1234), radix: 2), "10011010010")
XCTAssertEqual(String(sample, radix: 2), "1001000110100010101100111100010011010101111001101111011111110110111001011101010011000011101100101010000110010000100100011010001010110011110001001101010111100110111101111")
// Radix = 31
XCTAssertEqual(String(BigUInt(30), radix: 31), "u")
XCTAssertEqual(String(BigUInt(31), radix: 31), "10")
XCTAssertEqual(String(BigUInt("10000000000000000", radix: 16)!, radix: 31), "nd075ib45k86g")
XCTAssertEqual(String(BigUInt("2908B5129F59DB6A41", radix: 16)!, radix: 31), "100000000000000")
XCTAssertEqual(String(sample, radix: 31), "ptf96helfaqi7ogc3jbonmccrhmnc2b61s")
let quickLook = BigUInt(513).customPlaygroundQuickLook
if case PlaygroundQuickLook.text("513 (10 bits)") = quickLook {
} else {
XCTFail("Unexpected playground QuickLook representation: \(quickLook)")
}
}
func testConversionFromString() {
let sample = "123456789ABCDEFEDCBA98765432123456789ABCDEF"
XCTAssertEqual(BigUInt("1")!, 1)
XCTAssertEqual(BigUInt("123456789ABCDEF", radix: 16)!, 0x123456789ABCDEF)
XCTAssertEqual(BigUInt("1000000000000000000000"), BigUInt("3635C9ADC5DEA00000", radix: 16))
XCTAssertEqual(BigUInt("10000000000000000", radix: 16), BigUInt("18446744073709551616"))
XCTAssertEqual(BigUInt(sample, radix: 16)!, BigUInt("425693205796080237694414176550132631862392541400559")!)
XCTAssertNil(BigUInt("Not a number"))
XCTAssertNil(BigUInt("X"))
XCTAssertNil(BigUInt("12349A"))
XCTAssertNil(BigUInt("000000000000000000000000A000"))
XCTAssertNil(BigUInt("00A0000000000000000000000000"))
XCTAssertNil(BigUInt("00 0000000000000000000000000"))
XCTAssertNil(BigUInt("\u{4e00}\u{4e03}")) // Chinese numerals "1", "7"
XCTAssertEqual(BigUInt("u", radix: 31)!, 30)
XCTAssertEqual(BigUInt("10", radix: 31)!, 31)
XCTAssertEqual(BigUInt("100000000000000", radix: 31)!, BigUInt("2908B5129F59DB6A41", radix: 16)!)
XCTAssertEqual(BigUInt("nd075ib45k86g", radix: 31)!, BigUInt("10000000000000000", radix: 16)!)
XCTAssertEqual(BigUInt("ptf96helfaqi7ogc3jbonmccrhmnc2b61s", radix: 31)!, BigUInt(sample, radix: 16)!)
}
func testLowHigh() {
let a = BigUInt([0, 1, 2, 3])
XCTAssertEqual(a.low, BigUInt([0, 1]))
XCTAssertEqual(a.high, BigUInt([2, 3]))
XCTAssertEqual(a.low.low, BigUInt([0]))
XCTAssertEqual(a.low.high, BigUInt([1]))
XCTAssertEqual(a.high.low, BigUInt([2]))
XCTAssertEqual(a.high.high, BigUInt([3]))
let b = BigUInt([0, 1, 2, 3, 4, 5])
let bl = b.low
XCTAssertEqual(bl, BigUInt([0, 1, 2]))
let bh = b.high
XCTAssertEqual(bh, BigUInt([3, 4, 5]))
let bll = bl.low
XCTAssertEqual(bll, BigUInt([0, 1]))
let blh = bl.high
XCTAssertEqual(blh, BigUInt([2, 0]))
let bhl = bh.low
XCTAssertEqual(bhl, BigUInt([3, 4]))
let bhh = bh.high
XCTAssertEqual(bhh, BigUInt([5, 0]))
let blhl = bll.low
XCTAssertEqual(blhl, BigUInt([0]))
let blhh = bll.high
XCTAssertEqual(blhh, BigUInt([1]))
let bhhl = bhl.low
XCTAssertEqual(bhhl, BigUInt([3]))
let bhhh = bhl.high
XCTAssertEqual(bhhh, BigUInt([4]))
}
func testComparison() {
XCTAssertEqual(BigUInt([1, 2, 3]), BigUInt([1, 2, 3]))
XCTAssertNotEqual(BigUInt([1, 2]), BigUInt([1, 2, 3]))
XCTAssertNotEqual(BigUInt([1, 2, 3]), BigUInt([1, 3, 3]))
XCTAssertEqual(BigUInt([1, 2, 3, 4, 5, 6]).low.high, BigUInt([3]))
XCTAssertTrue(BigUInt([1, 2]) < BigUInt([1, 2, 3]))
XCTAssertTrue(BigUInt([1, 2, 2]) < BigUInt([1, 2, 3]))
XCTAssertFalse(BigUInt([1, 2, 3]) < BigUInt([1, 2, 3]))
XCTAssertTrue(BigUInt([3, 3]) < BigUInt([1, 2, 3, 4, 5, 6])[2..<4])
XCTAssertTrue(BigUInt([1, 2, 3, 4, 5, 6]).low.high < BigUInt([3, 5]))
}
func testIsZero() {
let b = BigUInt([0, 0, 0, 1])
XCTAssertFalse(b.isZero)
XCTAssertTrue(b.low.isZero)
XCTAssertTrue(b.high.low.isZero)
XCTAssertFalse(b.high.high.isZero)
}
func testHashing() {
var hashes: [Int] = []
hashes.append(BigUInt([]).hashValue)
hashes.append(BigUInt([1]).hashValue)
hashes.append(BigUInt([2]).hashValue)
hashes.append(BigUInt([0, 1]).hashValue)
hashes.append(BigUInt([1, 1]).hashValue)
hashes.append(BigUInt([1, 2]).hashValue)
hashes.append(BigUInt([2, 1]).hashValue)
hashes.append(BigUInt([2, 2]).hashValue)
hashes.append(BigUInt([1, 2, 3, 4, 5]).hashValue)
hashes.append(BigUInt([5, 4, 3, 2, 1]).hashValue)
hashes.append(BigUInt([Digit.max]).hashValue)
hashes.append(BigUInt([Digit.max, Digit.max]).hashValue)
hashes.append(BigUInt([Digit.max, Digit.max, Digit.max]).hashValue)
hashes.append(BigUInt([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]).hashValue)
XCTAssertEqual(hashes.count, Set(hashes).count)
}
func testBitwise() {
let a = BigUInt("1234567890ABCDEF13579BDF2468ACE", radix: 16)!
let b = BigUInt("ECA8642FDB97531FEDCBA0987654321", radix: 16)!
// a = 01234567890ABCDEF13579BDF2468ACE
// b = 0ECA8642FDB97531FEDCBA0987654321
XCTAssertEqual(String(~a, radix: 16), "fedcba9876f543210eca86420db97531")
XCTAssertEqual(String(a | b, radix: 16), "febc767fdbbfdfffffdfbbdf767cbef")
XCTAssertEqual(String(a & b, radix: 16), "2044289083410f014380982440200")
XCTAssertEqual(String(a ^ b, radix: 16), "fe9c32574b3c9ef0fe9c3b47523c9ef")
let ffff = BigUInt(Array(repeating: Digit.max, count: 30))
XCTAssertEqual(~ffff, 0)
XCTAssertEqual(a | ffff, ffff)
XCTAssertEqual(a | 0, a)
XCTAssertEqual(a & a, a)
XCTAssertEqual(a & 0, 0)
XCTAssertEqual(a & ffff, a)
XCTAssertEqual(~(a | b), (~a & ~b))
XCTAssertEqual(~(a & b), (~a | ~b)[0..<(a&b).count])
XCTAssertEqual(a ^ a, 0)
XCTAssertEqual((a ^ b) ^ b, a)
XCTAssertEqual((a ^ b) ^ a, b)
var z = a * b
z |= a
z &= b
z ^= ffff
XCTAssertEqual(z, (((a * b) | a) & b) ^ ffff)
}
func testAddition() {
XCTAssertEqual(BigUInt(0) + BigUInt(0), BigUInt(0))
XCTAssertEqual(BigUInt(0) + BigUInt(Digit.max), BigUInt(Digit.max))
XCTAssertEqual(BigUInt(Digit.max) + BigUInt(1), BigUInt([0, 1]))
var b = BigUInt()
XCTAssertEqual(b, 0)
b.add(BigUInt(Digit.max))
XCTAssertEqual(b, BigUInt(Digit.max))
b.add(1)
XCTAssertEqual(b, BigUInt([0, 1]))
b.add(BigUInt([3, 4]))
XCTAssertEqual(b, BigUInt([3, 5]))
b.add(BigUInt([0, Digit.max]))
XCTAssertEqual(b, BigUInt([3, 4, 1]))
b.add(BigUInt([0, Digit.max]))
XCTAssertEqual(b, BigUInt([3, 3, 2]))
b += 2
XCTAssertEqual(b, BigUInt([5, 3, 2]))
b = BigUInt([Digit.max, 2, Digit.max])
b.increment()
XCTAssertEqual(b, BigUInt([0, 3, Digit.max]))
XCTAssertEqual(BigUInt([Digit.max - 5, Digit.max, 4, Digit.max]).addingDigit(6), BigUInt([0, 0, 5, Digit.max]))
}
func testShiftedAddition() {
var b = BigUInt()
b.add(1, atPosition: 1)
XCTAssertEqual(b, BigUInt([0, 1]))
b.add(2, atPosition: 3)
XCTAssertEqual(b, BigUInt([0, 1, 0, 2]))
b.add(BigUInt(Digit.max), atPosition: 1)
XCTAssertEqual(b, BigUInt([0, 0, 1, 2]))
}
func testSubtraction() {
var a1 = BigUInt([1, 2, 3, 4])
XCTAssertFalse(a1.subtractDigitWithOverflow(3, atPosition: 1))
XCTAssertEqual(a1, BigUInt([1, Digit.max, 2, 4]))
let (diff, overflow) = BigUInt([1, 2, 3, 4]).subtractingDigitWithOverflow(2)
XCTAssertEqual(diff, BigUInt([Digit.max, 1, 3, 4]))
XCTAssertFalse(overflow)
var a2 = BigUInt([1, 2, 3, 4])
XCTAssertTrue(a2.subtractDigitWithOverflow(5, atPosition: 3))
XCTAssertEqual(a2, BigUInt([1, 2, 3, Digit.max]))
var a3 = BigUInt([1, 2, 3, 4])
a3.subtractDigit(4, atPosition: 3)
XCTAssertEqual(a3, BigUInt([1, 2, 3]))
var a4 = BigUInt([1, 2, 3, 4])
a4.decrement()
XCTAssertEqual(a4, BigUInt([0, 2, 3, 4]))
a4.decrement()
XCTAssertEqual(a4, BigUInt([Digit.max, 1, 3, 4]))
XCTAssertEqual(BigUInt([1, 2, 3, 4]).subtractingDigit(5), BigUInt([Digit.max - 3, 1, 3, 4]))
XCTAssertEqual(BigUInt(0) - BigUInt(0), BigUInt(0))
var b = BigUInt([1, 2, 3, 4])
XCTAssertFalse(b.subtractWithOverflow(BigUInt([0, 1, 1, 1])))
XCTAssertEqual(Array(b), [1, 1, 2, 3])
let b1 = BigUInt([1, 1, 2, 3]).subtractingWithOverflow(BigUInt([1, 1, 3, 3]))
XCTAssertEqual(b1.0, BigUInt([0, 0, Digit.max, Digit.max]))
XCTAssertTrue(b1.1)
let b2 = BigUInt([0, 0, 1]) - BigUInt([1])
XCTAssertEqual(Array(b2), [Digit.max, Digit.max])
var b3 = BigUInt([1, 0, 0, 1])
b3 -= 2
XCTAssertEqual(Array(b3), [Digit.max, Digit.max, Digit.max])
}
func testMultiplyByDigit() {
XCTAssertEqual(BigUInt([1, 2, 3, 4]).multiplied(byDigit: 0), BigUInt(0))
XCTAssertEqual(BigUInt([1, 2, 3, 4]).multiplied(byDigit: 2), BigUInt([2, 4, 6, 8]))
let full = Digit.max
let b = BigUInt([full, 0, full, 0, full]).multiplied(byDigit: 2)
XCTAssertEqual(b, BigUInt([full - 1, 1, full - 1, 1, full - 1, 1]))
let c = BigUInt([full, full, full]).multiplied(byDigit: 2)
XCTAssertEqual(c, BigUInt([full - 1, full, full, 1]))
let d = BigUInt([full, full, full]).multiplied(byDigit: full)
XCTAssertEqual(d, BigUInt([1, full, full, full - 1]))
let e = BigUInt("11111111111111111111111111111111", radix: 16)!.multiplied(byDigit: 15)
XCTAssertEqual(e, BigUInt("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", radix: 16)!)
let f = BigUInt("11111111111111111111111111111112", radix: 16)!.multiplied(byDigit: 15)
XCTAssertEqual(f, BigUInt("10000000000000000000000000000000E", radix: 16)!)
}
func testMultiplication() {
func test() {
XCTAssertEqual(
BigUInt([1, 2, 3, 4]) * BigUInt(),
BigUInt())
XCTAssertEqual(
BigUInt() * BigUInt([1, 2, 3, 4]),
BigUInt())
XCTAssertEqual(
BigUInt([1, 2, 3, 4]) * BigUInt([2]),
BigUInt([2, 4, 6, 8]))
XCTAssertEqual(
BigUInt([1, 2, 3, 4]).multiplied(by: BigUInt([2])),
BigUInt([2, 4, 6, 8]))
XCTAssertEqual(
BigUInt([2]) * BigUInt([1, 2, 3, 4]),
BigUInt([2, 4, 6, 8]))
XCTAssertEqual(
BigUInt([1, 2, 3, 4]) * BigUInt([0, 1]),
BigUInt([0, 1, 2, 3, 4]))
XCTAssertEqual(
BigUInt([0, 1]) * BigUInt([1, 2, 3, 4]),
BigUInt([0, 1, 2, 3, 4]))
XCTAssertEqual(
BigUInt([4, 3, 2, 1]) * BigUInt([1, 2, 3, 4]),
BigUInt([4, 11, 20, 30, 20, 11, 4]))
// 999 * 99 = 98901
XCTAssertEqual(
BigUInt([Digit.max, Digit.max, Digit.max]) * BigUInt([Digit.max, Digit.max]),
BigUInt([1, 0, Digit.max, Digit.max - 1, Digit.max]))
XCTAssertEqual(
BigUInt([1, 2]) * BigUInt([2, 1]),
BigUInt([2, 5, 2]))
var b = BigUInt("2637AB28", radix: 16)!
b *= BigUInt("164B", radix: 16)!
XCTAssertEqual(b, BigUInt("353FB0494B8", radix: 16))
XCTAssertEqual(BigUInt("16B60", radix: 16)! * BigUInt("33E28", radix: 16)!, BigUInt("49A5A0700", radix: 16)!)
}
test()
// Disable brute force multiplication.
let limit = BigUInt.directMultiplicationLimit
BigUInt.directMultiplicationLimit = 0
defer { BigUInt.directMultiplicationLimit = limit }
test()
}
func testLeftShifts() {
let sample = BigUInt("123456789ABCDEF01234567891631832727633", radix: 16)!
var a = sample
a <<= 0
XCTAssertEqual(a, sample)
a = sample
a <<= 1
XCTAssertEqual(a, 2 * sample)
a = sample
a <<= Digit.width
XCTAssertEqual(a.count, sample.count + 1)
XCTAssertEqual(a[0], 0)
XCTAssertEqual(a[1...sample.count + 1], sample)
a = sample
a <<= 100 * Digit.width
XCTAssertEqual(a.count, sample.count + 100)
XCTAssertEqual(a[0..<100], 0)
XCTAssertEqual(a[100...sample.count + 100], sample)
a = sample
a <<= 100 * Digit.width + 2
XCTAssertEqual(a.count, sample.count + 100)
XCTAssertEqual(a[0..<100], 0)
XCTAssertEqual(a[100...sample.count + 100], sample << 2)
a = sample
a <<= Digit.width - 1
XCTAssertEqual(a.count, sample.count + 1)
XCTAssertEqual(a, BigUInt([0] + Array(sample)) / 2)
XCTAssertEqual(sample << 4, 16 * sample)
XCTAssertEqual(sample << (2 * Digit.width), BigUInt([0, 0] + Array(sample)))
XCTAssertEqual(sample << (2 * Digit.width + 2), BigUInt([0, 0] + Array(4 * sample)))
}
func testRightShifts() {
let sample = BigUInt("123456789ABCDEF1234567891631832727633", radix: 16)!
var a = sample
a >>= 0
XCTAssertEqual(a, sample)
a = sample
a >>= 1
XCTAssertEqual(a, sample / 2)
a = sample
a >>= Digit.width
XCTAssertEqual(a, sample[1..<sample.count])
a = sample
a >>= Digit.width + 2
XCTAssertEqual(a, sample[1..<sample.count] / 4)
a = sample
a >>= sample.count * Digit.width
XCTAssertEqual(a, 0)
XCTAssertEqual(sample >> 0, sample)
XCTAssertEqual(sample >> 3, sample / 8)
XCTAssertEqual(sample >> Digit.width, sample[1..<sample.count])
XCTAssertEqual(sample >> (Digit.width + 3), sample[1..<sample.count] / 8)
XCTAssertEqual(sample >> (100 * Digit.width), 0)
}
func testWidth() {
XCTAssertEqual(BigUInt(0).width, 0)
XCTAssertEqual(BigUInt(1).width, 1)
XCTAssertEqual(BigUInt(Digit.max).width, Digit.width)
XCTAssertEqual(BigUInt([Digit.max, 1]).width, Digit.width + 1)
XCTAssertEqual(BigUInt([2, 12]).width, Digit.width + 4)
XCTAssertEqual(BigUInt([1, Digit.max]).width, 2 * Digit.width)
XCTAssertEqual(BigUInt(0).leadingZeroes, 0)
XCTAssertEqual(BigUInt(1).leadingZeroes, Digit.width - 1)
XCTAssertEqual(BigUInt(Digit.max).leadingZeroes, 0)
XCTAssertEqual(BigUInt([Digit.max, 1]).leadingZeroes, Digit.width - 1)
XCTAssertEqual(BigUInt([14, Digit.max]).leadingZeroes, 0)
XCTAssertEqual(BigUInt(0).trailingZeroes, 0)
XCTAssertEqual(BigUInt(1 << Digit(Digit.width - 1)).trailingZeroes, Digit.width - 1)
XCTAssertEqual(BigUInt(Digit.max).trailingZeroes, 0)
XCTAssertEqual(BigUInt([0, 1]).trailingZeroes, Digit.width)
XCTAssertEqual(BigUInt([0, 1 << Digit(Digit.width - 1)]).trailingZeroes, 2 * Digit.width - 1)
}
func testDivision() {
func test(_ a: [Digit], _ b: [Digit], file: StaticString = #file, line: UInt = #line) {
let x = BigUInt(a)
let y = BigUInt(b)
let (div, mod) = x.divided(by: y)
if mod >= y {
XCTFail("x:\(x) = div:\(div) * y:\(y) + mod:\(mod)", file: file, line: line)
}
if div * y + mod != x {
XCTFail("x:\(x) = div:\(div) * y:\(y) + mod:\(mod)", file: file, line: line)
}
}
// These cases exercise all code paths in the division when Digit is UInt8 or UInt64.
test([], [1])
test([1], [1])
test([1], [2])
test([2], [1])
test([], [0, 1])
test([1], [0, 1])
test([0, 1], [0, 1])
test([0, 0, 1], [0, 1])
test([0, 0, 1], [1, 1])
test([0, 0, 1], [3, 1])
test([0, 0, 1], [75, 1])
test([0, 0, 0, 1], [0, 1])
test([2, 4, 6, 8], [1, 2])
test([2, 3, 4, 5], [4, 5])
test([Digit.max, Digit.max - 1, Digit.max], [Digit.max, Digit.max])
test([0, Digit.max, Digit.max - 1], [Digit.max, Digit.max])
test([0, 0, 0, 0, 0, Digit.max / 2 + 1, Digit.max / 2], [1, 0, 0, Digit.max / 2 + 1])
test([0, Digit.max - 1, Digit.max / 2 + 1], [Digit.max, Digit.max / 2 + 1])
test([0, 0, 0x41 << Digit(Digit.width - 8)], [Digit.max, 1 << Digit(Digit.width - 1)])
XCTAssertEqual(BigUInt(328) / BigUInt(21), BigUInt(15))
XCTAssertEqual(BigUInt(328) % BigUInt(21), BigUInt(13))
var a = BigUInt(328)
a /= 21
XCTAssertEqual(a, 15)
a %= 7
XCTAssertEqual(a, 1)
#if false
for x0 in (0 ... Int(Digit.max)) {
for x1 in (0 ... Int(Digit.max)).reverse() {
for y0 in (0 ... Int(Digit.max)).reverse() {
for y1 in (1 ... Int(Digit.max)).reverse() {
for x2 in (1 ... y1).reverse() {
test(
[Digit(x0), Digit(x1), Digit(x2)],
[Digit(y0), Digit(y1)])
}
}
}
}
}
#endif
}
func testFactorial() {
let power = 10
var forward = BigUInt(1)
for i in 1 ..< (1 << power) {
forward *= BigUInt(i)
}
print("\(1 << power - 1)! = \(forward) [\(forward.count)]")
var backward = BigUInt(1)
for i in (1 ..< (1 << power)).reversed() {
backward *= BigUInt(i)
}
func balancedFactorial(level: Int, offset: Int) -> BigUInt {
if level == 0 {
return BigUInt(offset == 0 ? 1 : offset)
}
let a = balancedFactorial(level: level - 1, offset: 2 * offset)
let b = balancedFactorial(level: level - 1, offset: 2 * offset + 1)
return a * b
}
let balanced = balancedFactorial(level: power, offset: 0)
XCTAssertEqual(backward, forward)
XCTAssertEqual(balanced, forward)
var remaining = balanced
for i in 1 ..< (1 << power) {
let (div, mod) = remaining.divided(by: BigUInt(i))
XCTAssertEqual(mod, 0)
remaining = div
}
XCTAssertEqual(remaining, 1)
}
func testSqrt() {
let sample = BigUInt("123456789ABCDEF1234567891631832727633", radix: 16)!
XCTAssertEqual(sqrt(BigUInt(0)), 0)
XCTAssertEqual(sqrt(BigUInt(256)), 16)
func checkSqrt(_ value: BigUInt, file: StaticString = #file, line: UInt = #line) {
let root = sqrt(sample)
XCTAssertLessThanOrEqual(root * root, sample, file: file, line: line)
XCTAssertGreaterThan((root + 1) * (root + 1), sample, file: file, line: line)
}
checkSqrt(sample)
checkSqrt(sample * sample)
checkSqrt(sample * sample - 1)
checkSqrt(sample * sample + 1)
}
func testGCD() {
XCTAssertEqual(BigUInt.gcd(0, 2982891), 2982891)
XCTAssertEqual(BigUInt.gcd(2982891, 0), 2982891)
XCTAssertEqual(BigUInt.gcd(0, 0), 0)
XCTAssertEqual(BigUInt.gcd(4, 6), 2)
XCTAssertEqual(BigUInt.gcd(15, 10), 5)
XCTAssertEqual(BigUInt.gcd(8 * 3 * 25 * 7, 2 * 9 * 5 * 49), 2 * 3 * 5 * 7)
var fibo: [BigUInt] = [0, 1]
for i in 0...10000 {
fibo.append(fibo[i] + fibo[i + 1])
}
XCTAssertEqual(BigUInt.gcd(fibo[100], fibo[101]), 1)
XCTAssertEqual(BigUInt.gcd(fibo[1000], fibo[1001]), 1)
XCTAssertEqual(BigUInt.gcd(fibo[10000], fibo[10001]), 1)
XCTAssertEqual(BigUInt.gcd(3 * 5 * 7 * 9, 5 * 7 * 7), 5 * 7)
XCTAssertEqual(BigUInt.gcd(fibo[4], fibo[2]), fibo[2])
XCTAssertEqual(BigUInt.gcd(fibo[3 * 5 * 7 * 9], fibo[5 * 7 * 7 * 9]), fibo[5 * 7 * 9])
XCTAssertEqual(BigUInt.gcd(fibo[7 * 17 * 83], fibo[6 * 17 * 83]), fibo[17 * 83])
}
func testInverse() {
XCTAssertNil(BigUInt(4).inverse(8))
XCTAssertNil(BigUInt(12).inverse(15))
XCTAssertEqual(BigUInt(13).inverse(15), 7)
XCTAssertEqual(BigUInt(251).inverse(1023), 269)
XCTAssertNil(BigUInt(252).inverse(1023))
XCTAssertEqual(BigUInt(2).inverse(1023), 512)
}
func testExponentiation() {
XCTAssertEqual(BigUInt(0).power(0), BigUInt(1))
XCTAssertEqual(BigUInt(1).power(0), BigUInt(1))
XCTAssertEqual(BigUInt(0).power(1), BigUInt(0))
XCTAssertEqual(BigUInt(1).power(1), BigUInt(1))
XCTAssertEqual(BigUInt(2).power(0), BigUInt(1))
XCTAssertEqual(BigUInt(2).power(1), BigUInt(2))
XCTAssertEqual(BigUInt(2).power(2), BigUInt(4))
XCTAssertEqual(BigUInt(2).power(3), BigUInt(8))
XCTAssertEqual(BigUInt(3).power(0), BigUInt(1))
XCTAssertEqual(BigUInt(3).power(1), BigUInt(3))
XCTAssertEqual(BigUInt(3).power(2), BigUInt(9))
XCTAssertEqual(BigUInt(3).power(3), BigUInt(27))
XCTAssertEqual((BigUInt(1) << 256).power(0), BigUInt(1))
XCTAssertEqual((BigUInt(1) << 256).power(1), BigUInt(1) << 256)
XCTAssertEqual((BigUInt(1) << 256).power(2), BigUInt(1) << 512)
XCTAssertEqual(BigUInt(0).power(577), BigUInt(0))
XCTAssertEqual(BigUInt(1).power(577), BigUInt(1))
XCTAssertEqual(BigUInt(2).power(577), BigUInt(1) << 577)
}
func testModularExponentiation() {
XCTAssertEqual(BigUInt(2).power(11, modulus: 1), 0)
XCTAssertEqual(BigUInt(2).power(11, modulus: 1000), 48)
func test(a: BigUInt, p: BigUInt, file: StaticString = #file, line: UInt = #line) {
// For all primes p and integers a, a % p == a^p % p. (Fermat's Little Theorem)
let x = a % p
let y = x.power(p, modulus: p)
XCTAssertEqual(x, y, file: file, line: line)
}
// Here are some primes
let m61 = (BigUInt(1) << 61) - BigUInt(1)
let m127 = (BigUInt(1) << 127) - BigUInt(1)
let m521 = (BigUInt(1) << 521) - BigUInt(1)
test(a: 2, p: m127)
test(a: BigUInt(1) << 42, p: m127)
test(a: BigUInt(1) << 42 + BigUInt(1), p: m127)
test(a: m61, p: m127)
test(a: m61 + 1, p: m127)
test(a: m61, p: m521)
test(a: m61 + 1, p: m521)
test(a: m127, p: m521)
}
func data(_ bytes: Array<UInt8>) -> Data {
var result: Data? = nil
bytes.withUnsafeBufferPointer { p in
result = Data(bytes: UnsafePointer<UInt8>(p.baseAddress!), count: p.count)
}
return result!
}
func testConversionFromData() {
XCTAssertEqual(BigUInt(data([])), 0)
XCTAssertEqual(BigUInt(data([0])), 0)
XCTAssertEqual(BigUInt(data([0, 0, 0, 0, 0, 0, 0, 0])), 0)
XCTAssertEqual(BigUInt(data([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), 0)
XCTAssertEqual(BigUInt(data([1])), 1)
XCTAssertEqual(BigUInt(data([2])), 2)
XCTAssertEqual(BigUInt(data([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1])), 1)
XCTAssertEqual(BigUInt(data([0x01, 0x02, 0x03, 0x04, 0x05])), 0x0102030405)
XCTAssertEqual(BigUInt(data([0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08])), 0x0102030405060708)
XCTAssertEqual(
BigUInt(data([0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0A])),
BigUInt(0x0102) << 64 + BigUInt(0x030405060708090A))
XCTAssertEqual(
BigUInt(data([0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00])),
BigUInt(1) << 80)
XCTAssertEqual(
BigUInt(data([0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0A, 0x0B, 0x0C, 0x0D, 0x0E, 0x0F, 0x10])),
BigUInt(0x0102030405060708) << 64 + BigUInt(0x090A0B0C0D0E0F10))
// The following test produced "expression was too complex" error on Swift 2.2.1
let d = data([0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0A, 0x0B, 0x0C, 0x0D, 0x0E, 0x0F, 0x10, 0x11])
var b = BigUInt(1) << 128
b += BigUInt(0x0203040506070809) << 64
b += BigUInt(0x0A0B0C0D0E0F1011)
XCTAssertEqual(BigUInt(d), b)
}
func testConversionToData() {
func test(_ b: BigUInt, _ d: Array<UInt8>, file: StaticString = #file, line: UInt = #line) {
let expected = data(d)
let actual = b.serialize()
XCTAssertEqual(actual, expected, file: file, line: line)
XCTAssertEqual(BigUInt(actual), b, file: file, line: line)
}
test(BigUInt(), [])
test(BigUInt(1), [0x01])
test(BigUInt(2), [0x02])
test(BigUInt(0x0102030405060708), [0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08])
test(BigUInt(0x01) << 64 + BigUInt(0x0203040506070809), [0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 09])
}
func testRandomIntegerWithMaximumWidth() {
XCTAssertEqual(BigUInt.randomInteger(withMaximumWidth: 0), 0)
let randomByte = BigUInt.randomInteger(withMaximumWidth: 8)
XCTAssertLessThan(randomByte, 256)
for _ in 0 ..< 100 {
XCTAssertLessThanOrEqual(BigUInt.randomInteger(withMaximumWidth: 1024).width, 1024)
}
// Verify that all widths <= maximum are produced (with a tiny maximum)
var widths: Set<Int> = [0, 1, 2, 3]
var i = 0
while !widths.isEmpty {
let random = BigUInt.randomInteger(withMaximumWidth: 3)
XCTAssertLessThanOrEqual(random.width, 3)
widths.remove(random.width)
i += 1
if i > 4096 {
XCTFail("randomIntegerWithMaximumWidth doesn't seem random")
break
}
}
// Verify that all bits are sometimes zero, sometimes one.
var oneBits = Set<Int>(0..<1024)
var zeroBits = Set<Int>(0..<1024)
while !oneBits.isEmpty || !zeroBits.isEmpty {
var random = BigUInt.randomInteger(withMaximumWidth: 1024)
for i in 0..<1024 {
if random[0] & 1 == 1 { oneBits.remove(i) }
else { zeroBits.remove(i) }
random >>= 1
}
}
}
func testRandomIntegerWithExactWidth() {
XCTAssertEqual(BigUInt.randomInteger(withExactWidth: 0), 0)
XCTAssertEqual(BigUInt.randomInteger(withExactWidth: 1), 1)
for _ in 0 ..< 1024 {
let randomByte = BigUInt.randomInteger(withExactWidth: 8)
XCTAssertEqual(randomByte.width, 8)
XCTAssertLessThan(randomByte, 256)
XCTAssertGreaterThanOrEqual(randomByte, 128)
}
for _ in 0 ..< 100 {
XCTAssertEqual(BigUInt.randomInteger(withExactWidth: 1024).width, 1024)
}
// Verify that all bits except the top are sometimes zero, sometimes one.
var oneBits = Set<Int>(0..<1023)
var zeroBits = Set<Int>(0..<1023)
while !oneBits.isEmpty || !zeroBits.isEmpty {
var random = BigUInt.randomInteger(withExactWidth: 1024)
for i in 0..<1023 {
if random[0] & 1 == 1 { oneBits.remove(i) }
else { zeroBits.remove(i) }
random >>= 1
}
}
}
func testRandomIntegerLessThan() {
// Verify that all bits in random integers generated by `randomIntegerLessThan` are sometimes zero, sometimes one.
//
// The limit starts with "11" so that generated random integers may easily begin with all combos.
// Also, 25% of the time the initial random int will be rejected as higher than the
// limit -- this helps stabilize code coverage.
let limit = BigUInt(3) << 1024
var oneBits = Set<Int>(0..<limit.width)
var zeroBits = Set<Int>(0..<limit.width)
for _ in 0..<100 {
var random = BigUInt.randomInteger(lessThan: limit)
XCTAssertLessThan(random, limit)
for i in 0..<limit.width {
if random[0] & 1 == 1 { oneBits.remove(i) }
else { zeroBits.remove(i) }
random >>= 1
}
}
XCTAssertEqual(oneBits, [])
XCTAssertEqual(zeroBits, [])
}
func testStrongProbablePrimeTest() {
let primes: [BigUInt.Digit] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 79, 83, 89, 97]
let pseudoPrimes: [BigUInt] = [
/* 2 */ 2_047,
/* 3 */ 1_373_653,
/* 5 */ 25_326_001,
/* 7 */ 3_215_031_751,
/* 11 */ 2_152_302_898_747,
/* 13 */ 3_474_749_660_383,
/* 17 */ 341_550_071_728_321,
/* 19 */ 341_550_071_728_321,
/* 23 */ 3_825_123_056_546_413_051,
/* 29 */ 3_825_123_056_546_413_051,
/* 31 */ 3_825_123_056_546_413_051,
/* 37 */ "318665857834031151167461",
/* 41 */ "3317044064679887385961981",
]
for i in 0..<pseudoPrimes.count {
let candidate = pseudoPrimes[i]
print(candidate)
// SPPT should not rule out candidate's primality for primes less than prime[i + 1]
for j in 0...i {
XCTAssertTrue(candidate.isStrongProbablePrime(BigUInt(primes[j])))
}
// But the pseudoprimes aren't prime, so there is a base that disproves them.
let foo = (i + 1 ... i + 3).filter { !candidate.isStrongProbablePrime(BigUInt(primes[$0])) }
XCTAssertNotEqual(foo, [])
}
// Try the SPPT for some Mersenne numbers.