Merge pull request #81 from mipt-npm/big-int
BigInt implementation
This commit is contained in:
Alexander Nozik
GitHub
commit
85ad44ac9b
@ -0,0 +1,459 @@
|
||||
package scientifik.kmath.operations
|
||||
|
||||
import kotlin.math.log2
|
||||
import kotlin.math.max
|
||||
import kotlin.math.min
|
||||
import kotlin.math.sign
|
||||
|
||||
/*
|
||||
* Kotlin Multiplatform implementation of Big Integer numbers (KBigInteger).
|
||||
* Initial version from https://github.com/robdrynkin/kotlin-big-integer
|
||||
*/
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
typealias Magnitude = UIntArray
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
typealias TBase = ULong
|
||||
|
||||
object KBigIntegerRing: Ring<KBigInteger> {
|
||||
override val zero: KBigInteger = KBigInteger.ZERO
|
||||
override val one: KBigInteger = KBigInteger.ONE
|
||||
|
||||
override fun add(a: KBigInteger, b: KBigInteger): KBigInteger = a.plus(b)
|
||||
|
||||
override fun multiply(a: KBigInteger, k: Number): KBigInteger = a.times(k.toLong())
|
||||
|
||||
override fun multiply(a: KBigInteger, b: KBigInteger): KBigInteger = a.times(b)
|
||||
|
||||
operator fun String.unaryPlus(): KBigInteger = this.toKBigInteger()!!
|
||||
|
||||
operator fun String.unaryMinus(): KBigInteger = -this.toKBigInteger()!!
|
||||
}
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
class KBigInteger internal constructor(
|
||||
private val sign: Byte = 0,
|
||||
private val magnitude: Magnitude = Magnitude(0)
|
||||
): Comparable<KBigInteger> {
|
||||
|
||||
constructor(x: Int) : this(x.sign.toByte(), uintArrayOf(kotlin.math.abs(x).toUInt()))
|
||||
|
||||
constructor(x: Long) : this(x.sign.toByte(), stripLeadingZeros(uintArrayOf(
|
||||
(kotlin.math.abs(x).toULong() and BASE).toUInt(),
|
||||
((kotlin.math.abs(x).toULong() shr BASE_SIZE) and BASE).toUInt())))
|
||||
|
||||
override fun compareTo(other: KBigInteger): Int {
|
||||
return when {
|
||||
(this.sign == 0.toByte()) and (other.sign == 0.toByte()) -> 0
|
||||
this.sign < other.sign -> -1
|
||||
this.sign > other.sign -> 1
|
||||
else -> this.sign * compareMagnitudes(this.magnitude, other.magnitude)
|
||||
}
|
||||
}
|
||||
|
||||
override fun equals(other: Any?): Boolean {
|
||||
if (other is KBigInteger) {
|
||||
return this.compareTo(other) == 0
|
||||
}
|
||||
else error("Can't compare KBigInteger to a different type")
|
||||
}
|
||||
|
||||
override fun hashCode(): Int {
|
||||
return magnitude.hashCode() + this.sign
|
||||
}
|
||||
|
||||
fun abs(): KBigInteger = if (sign == 0.toByte()) this else KBigInteger(1, magnitude)
|
||||
|
||||
operator fun unaryMinus(): KBigInteger {
|
||||
return if (this.sign == 0.toByte()) this else KBigInteger((-this.sign).toByte(), this.magnitude)
|
||||
}
|
||||
|
||||
operator fun plus(b: KBigInteger): KBigInteger {
|
||||
return when {
|
||||
b.sign == 0.toByte() -> this
|
||||
this.sign == 0.toByte() -> b
|
||||
this == -b -> ZERO
|
||||
this.sign == b.sign -> KBigInteger(this.sign, addMagnitudes(this.magnitude, b.magnitude))
|
||||
else -> {
|
||||
val comp: Int = compareMagnitudes(this.magnitude, b.magnitude)
|
||||
|
||||
if (comp == 1) {
|
||||
KBigInteger(this.sign, subtractMagnitudes(this.magnitude, b.magnitude))
|
||||
} else {
|
||||
KBigInteger((-this.sign).toByte(), subtractMagnitudes(b.magnitude, this.magnitude))
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
operator fun minus(b: KBigInteger): KBigInteger {
|
||||
return this + (-b)
|
||||
}
|
||||
|
||||
operator fun times(b: KBigInteger): KBigInteger {
|
||||
return when {
|
||||
this.sign == 0.toByte() -> ZERO
|
||||
b.sign == 0.toByte() -> ZERO
|
||||
// TODO: Karatsuba
|
||||
else -> KBigInteger((this.sign * b.sign).toByte(), multiplyMagnitudes(this.magnitude, b.magnitude))
|
||||
}
|
||||
}
|
||||
|
||||
operator fun times(other: UInt): KBigInteger {
|
||||
return when {
|
||||
this.sign == 0.toByte() -> ZERO
|
||||
other == 0U -> ZERO
|
||||
else -> KBigInteger(this.sign, multiplyMagnitudeByUInt(this.magnitude, other))
|
||||
}
|
||||
}
|
||||
|
||||
operator fun times(other: Int): KBigInteger {
|
||||
return if (other > 0)
|
||||
this * kotlin.math.abs(other).toUInt()
|
||||
else
|
||||
-this * kotlin.math.abs(other).toUInt()
|
||||
}
|
||||
|
||||
operator fun div(other: UInt): KBigInteger {
|
||||
return KBigInteger(this.sign, divideMagnitudeByUInt(this.magnitude, other))
|
||||
}
|
||||
|
||||
operator fun div(other: Int): KBigInteger {
|
||||
return KBigInteger((this.sign * other.sign).toByte(),
|
||||
divideMagnitudeByUInt(this.magnitude, kotlin.math.abs(other).toUInt()))
|
||||
}
|
||||
|
||||
private fun division(other: KBigInteger): Pair<KBigInteger, KBigInteger> {
|
||||
// Long division algorithm:
|
||||
// https://en.wikipedia.org/wiki/Division_algorithm#Integer_division_(unsigned)_with_remainder
|
||||
// TODO: Implement more effective algorithm
|
||||
var q: KBigInteger = ZERO
|
||||
var r: KBigInteger = ZERO
|
||||
|
||||
val bitSize = (BASE_SIZE * (this.magnitude.size - 1) + log2(this.magnitude.last().toFloat() + 1)).toInt()
|
||||
for (i in bitSize downTo 0) {
|
||||
r = r shl 1
|
||||
r = r or ((abs(this) shr i) and ONE)
|
||||
if (r >= abs(other)) {
|
||||
r -= abs(other)
|
||||
q += (ONE shl i)
|
||||
}
|
||||
}
|
||||
|
||||
return Pair(KBigInteger((this.sign * other.sign).toByte(), q.magnitude), r)
|
||||
}
|
||||
|
||||
operator fun div(other: KBigInteger): KBigInteger {
|
||||
return this.division(other).first
|
||||
}
|
||||
|
||||
infix fun shl(i: Int): KBigInteger {
|
||||
if (this == ZERO) return ZERO
|
||||
if (i == 0) return this
|
||||
|
||||
val fullShifts = i / BASE_SIZE + 1
|
||||
val relShift = i % BASE_SIZE
|
||||
val shiftLeft = {x: UInt -> if (relShift >= 32) 0U else x shl relShift}
|
||||
val shiftRight = {x: UInt -> if (BASE_SIZE - relShift >= 32) 0U else x shr (BASE_SIZE - relShift)}
|
||||
|
||||
val newMagnitude: Magnitude = Magnitude(this.magnitude.size + fullShifts)
|
||||
|
||||
for (j in this.magnitude.indices) {
|
||||
newMagnitude[j + fullShifts - 1] = shiftLeft(this.magnitude[j])
|
||||
if (j != 0) {
|
||||
newMagnitude[j + fullShifts - 1] = newMagnitude[j + fullShifts - 1] or shiftRight(this.magnitude[j - 1])
|
||||
}
|
||||
}
|
||||
|
||||
newMagnitude[this.magnitude.size + fullShifts - 1] = shiftRight(this.magnitude.last())
|
||||
|
||||
return KBigInteger(this.sign, stripLeadingZeros(newMagnitude))
|
||||
}
|
||||
|
||||
infix fun shr(i: Int): KBigInteger {
|
||||
if (this == ZERO) return ZERO
|
||||
if (i == 0) return this
|
||||
|
||||
val fullShifts = i / BASE_SIZE
|
||||
val relShift = i % BASE_SIZE
|
||||
val shiftRight = {x: UInt -> if (relShift >= 32) 0U else x shr relShift}
|
||||
val shiftLeft = {x: UInt -> if (BASE_SIZE - relShift >= 32) 0U else x shl (BASE_SIZE - relShift)}
|
||||
if (this.magnitude.size - fullShifts <= 0) {
|
||||
return ZERO
|
||||
}
|
||||
val newMagnitude: Magnitude = Magnitude(this.magnitude.size - fullShifts)
|
||||
|
||||
for (j in fullShifts until this.magnitude.size) {
|
||||
newMagnitude[j - fullShifts] = shiftRight(this.magnitude[j])
|
||||
if (j != this.magnitude.size - 1) {
|
||||
newMagnitude[j - fullShifts] = newMagnitude[j - fullShifts] or shiftLeft(this.magnitude[j + 1])
|
||||
}
|
||||
}
|
||||
|
||||
return KBigInteger(this.sign, stripLeadingZeros(newMagnitude))
|
||||
}
|
||||
|
||||
infix fun or(other: KBigInteger): KBigInteger {
|
||||
if (this == ZERO) return other;
|
||||
if (other == ZERO) return this;
|
||||
val resSize = max(this.magnitude.size, other.magnitude.size)
|
||||
val newMagnitude: Magnitude = Magnitude(resSize)
|
||||
for (i in 0 until resSize) {
|
||||
if (i < this.magnitude.size) {
|
||||
newMagnitude[i] = newMagnitude[i] or this.magnitude[i]
|
||||
}
|
||||
if (i < other.magnitude.size) {
|
||||
newMagnitude[i] = newMagnitude[i] or other.magnitude[i]
|
||||
}
|
||||
}
|
||||
return KBigInteger(1, stripLeadingZeros(newMagnitude))
|
||||
}
|
||||
|
||||
infix fun and(other: KBigInteger): KBigInteger {
|
||||
if ((this == ZERO) or (other == ZERO)) return ZERO;
|
||||
val resSize = min(this.magnitude.size, other.magnitude.size)
|
||||
val newMagnitude: Magnitude = Magnitude(resSize)
|
||||
for (i in 0 until resSize) {
|
||||
newMagnitude[i] = this.magnitude[i] and other.magnitude[i]
|
||||
}
|
||||
return KBigInteger(1, stripLeadingZeros(newMagnitude))
|
||||
}
|
||||
|
||||
operator fun rem(other: Int): Int {
|
||||
val res = this - (this / other) * other
|
||||
return if (res == ZERO) 0 else res.sign * res.magnitude[0].toInt()
|
||||
}
|
||||
|
||||
operator fun rem(other: KBigInteger): KBigInteger {
|
||||
return this - (this / other) * other
|
||||
}
|
||||
|
||||
fun modPow(exponent: KBigInteger, m: KBigInteger): KBigInteger {
|
||||
return when {
|
||||
exponent == ZERO -> ONE
|
||||
exponent % 2 == 1 -> (this * modPow(exponent - ONE, m)) % m
|
||||
else -> {
|
||||
val sqRoot = modPow(exponent / 2, m)
|
||||
(sqRoot * sqRoot) % m
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
override fun toString(): String {
|
||||
if (this.sign == 0.toByte()) {
|
||||
return "0x0"
|
||||
}
|
||||
var res: String = if (this.sign == (-1).toByte()) "-0x" else "0x"
|
||||
var numberStarted = false
|
||||
|
||||
for (i in this.magnitude.size - 1 downTo 0) {
|
||||
for (j in BASE_SIZE / 4 - 1 downTo 0) {
|
||||
val curByte = (this.magnitude[i] shr 4 * j) and 0xfU
|
||||
if (numberStarted or (curByte != 0U)) {
|
||||
numberStarted = true
|
||||
res += hexMapping[curByte]
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return res
|
||||
}
|
||||
|
||||
companion object {
|
||||
const val BASE = 0xffffffffUL
|
||||
const val BASE_SIZE: Int = 32
|
||||
val ZERO: KBigInteger = KBigInteger()
|
||||
val ONE: KBigInteger = KBigInteger(1)
|
||||
|
||||
private val hexMapping: HashMap<UInt, String> =
|
||||
hashMapOf(
|
||||
0U to "0", 1U to "1", 2U to "2", 3U to "3",
|
||||
4U to "4", 5U to "5", 6U to "6", 7U to "7",
|
||||
8U to "8", 9U to "9", 10U to "a", 11U to "b",
|
||||
12U to "c", 13U to "d", 14U to "e", 15U to "f"
|
||||
)
|
||||
|
||||
internal fun stripLeadingZeros(mag: Magnitude): Magnitude {
|
||||
if (mag.isEmpty() || mag.last() != 0U) {
|
||||
return mag
|
||||
}
|
||||
var resSize: Int = mag.size - 1
|
||||
while (mag[resSize] == 0U) {
|
||||
if (resSize == 0)
|
||||
break
|
||||
resSize -= 1
|
||||
}
|
||||
return mag.sliceArray(IntRange(0, resSize))
|
||||
}
|
||||
|
||||
private fun compareMagnitudes(mag1: Magnitude, mag2: Magnitude): Int {
|
||||
when {
|
||||
mag1.size > mag2.size -> return 1
|
||||
mag1.size < mag2.size -> return -1
|
||||
else -> {
|
||||
for (i in mag1.size - 1 downTo 0) {
|
||||
if (mag1[i] > mag2[i]) {
|
||||
return 1
|
||||
} else if (mag1[i] < mag2[i]) {
|
||||
return -1
|
||||
}
|
||||
}
|
||||
return 0
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
private fun addMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
|
||||
val resultLength: Int = max(mag1.size, mag2.size) + 1
|
||||
val result = Magnitude(resultLength)
|
||||
var carry: TBase = 0UL
|
||||
|
||||
for (i in 0 until resultLength - 1) {
|
||||
val res = when {
|
||||
i >= mag1.size -> mag2[i].toULong() + carry
|
||||
i >= mag2.size -> mag1[i].toULong() + carry
|
||||
else -> mag1[i].toULong() + mag2[i].toULong() + carry
|
||||
}
|
||||
result[i] = (res and BASE).toUInt()
|
||||
carry = (res shr BASE_SIZE)
|
||||
}
|
||||
result[resultLength - 1] = carry.toUInt()
|
||||
return stripLeadingZeros(result)
|
||||
}
|
||||
|
||||
private fun subtractMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
|
||||
val resultLength: Int = mag1.size
|
||||
val result = Magnitude(resultLength)
|
||||
var carry = 0L
|
||||
|
||||
for (i in 0 until resultLength) {
|
||||
var res: Long =
|
||||
if (i < mag2.size) mag1[i].toLong() - mag2[i].toLong() - carry
|
||||
else mag1[i].toLong() - carry
|
||||
|
||||
carry = if (res < 0) 1 else 0
|
||||
res += carry * (BASE + 1UL).toLong()
|
||||
|
||||
result[i] = res.toUInt()
|
||||
}
|
||||
|
||||
return stripLeadingZeros(result)
|
||||
}
|
||||
|
||||
private fun multiplyMagnitudeByUInt(mag: Magnitude, x: UInt): Magnitude {
|
||||
val resultLength: Int = mag.size + 1
|
||||
val result = Magnitude(resultLength)
|
||||
var carry: ULong = 0UL
|
||||
|
||||
for (i in mag.indices) {
|
||||
val cur: ULong = carry + mag[i].toULong() * x.toULong()
|
||||
result[i] = (cur and BASE.toULong()).toUInt()
|
||||
carry = cur shr BASE_SIZE
|
||||
}
|
||||
result[resultLength - 1] = (carry and BASE).toUInt()
|
||||
|
||||
return stripLeadingZeros(result)
|
||||
}
|
||||
|
||||
private fun multiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
|
||||
val resultLength: Int = mag1.size + mag2.size
|
||||
val result = Magnitude(resultLength)
|
||||
|
||||
for (i in mag1.indices) {
|
||||
var carry: ULong = 0UL
|
||||
for (j in mag2.indices) {
|
||||
val cur: ULong = result[i + j].toULong() + mag1[i].toULong() * mag2[j].toULong() + carry
|
||||
result[i + j] = (cur and BASE.toULong()).toUInt()
|
||||
carry = cur shr BASE_SIZE
|
||||
}
|
||||
result[i + mag2.size] = (carry and BASE).toUInt()
|
||||
}
|
||||
|
||||
return stripLeadingZeros(result)
|
||||
}
|
||||
|
||||
private fun divideMagnitudeByUInt(mag: Magnitude, x: UInt): Magnitude {
|
||||
val resultLength: Int = mag.size
|
||||
val result = Magnitude(resultLength)
|
||||
var carry: ULong = 0UL
|
||||
|
||||
for (i in mag.size - 1 downTo 0) {
|
||||
val cur: ULong = mag[i].toULong() + (carry shl BASE_SIZE)
|
||||
result[i] = (cur / x).toUInt()
|
||||
carry = cur % x
|
||||
}
|
||||
return stripLeadingZeros(result)
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
fun abs(x: KBigInteger): KBigInteger = x.abs()
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
// Can't put it as constructor in class due to platform declaration clash with KBigInteger(Int)
|
||||
fun KBigInteger(x: UInt): KBigInteger
|
||||
= KBigInteger(1, uintArrayOf(x))
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
// Can't put it as constructor in class due to platform declaration clash with KBigInteger(Long)
|
||||
fun KBigInteger(x: ULong): KBigInteger
|
||||
= KBigInteger(1,
|
||||
KBigInteger.stripLeadingZeros(uintArrayOf(
|
||||
(x and KBigInteger.BASE).toUInt(),
|
||||
((x shr KBigInteger.BASE_SIZE) and KBigInteger.BASE).toUInt())
|
||||
)
|
||||
)
|
||||
|
||||
val hexChToInt = hashMapOf(
|
||||
'0' to 0, '1' to 1, '2' to 2, '3' to 3,
|
||||
'4' to 4, '5' to 5, '6' to 6, '7' to 7,
|
||||
'8' to 8, '9' to 9, 'A' to 10, 'B' to 11,
|
||||
'C' to 12, 'D' to 13, 'E' to 14, 'F' to 15
|
||||
)
|
||||
|
||||
// Returns None if a valid number can not be read from a string
|
||||
fun String.toKBigInteger(): KBigInteger? {
|
||||
val sign: Int
|
||||
val sPositive: String
|
||||
when {
|
||||
this[0] == '+' -> {
|
||||
sign = +1
|
||||
sPositive = this.substring(1)
|
||||
}
|
||||
this[0] == '-' -> {
|
||||
sign = -1
|
||||
sPositive = this.substring(1)
|
||||
}
|
||||
else -> {
|
||||
sPositive = this
|
||||
sign = +1
|
||||
}
|
||||
}
|
||||
var res = KBigInteger.ZERO
|
||||
var digitValue = KBigInteger.ONE
|
||||
val sPositiveUpper = sPositive.toUpperCase()
|
||||
if (sPositiveUpper.startsWith("0X")) { // hex representation
|
||||
val sHex = sPositiveUpper.substring(2)
|
||||
for (ch in sHex.reversed()) {
|
||||
if (ch == '_') continue
|
||||
res += digitValue * (hexChToInt[ch] ?: return null)
|
||||
digitValue *= KBigInteger(16)
|
||||
}
|
||||
}
|
||||
else { // decimal representation
|
||||
val sDecimal = sPositiveUpper
|
||||
for (ch in sDecimal.reversed()) {
|
||||
if (ch == '_') continue
|
||||
if (ch !in '0'..'9') {
|
||||
return null
|
||||
}
|
||||
res += digitValue * (ch.toInt() - '0'.toInt())
|
||||
digitValue *= KBigInteger(10)
|
||||
}
|
||||
}
|
||||
return res * sign
|
||||
}
|
||||
@ -0,0 +1,543 @@
|
||||
package scientifik.kmath.operations
|
||||
|
||||
import kotlin.test.Test
|
||||
import kotlin.test.assertTrue
|
||||
import kotlin.test.assertEquals
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
class KBigIntegerConstructorTest {
|
||||
@Test
|
||||
fun testConstructorZero() {
|
||||
assertEquals(KBigInteger(0), KBigInteger(0, uintArrayOf()))
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testConstructor8() {
|
||||
assertEquals(KBigInteger(8), KBigInteger(1, uintArrayOf(8U)))
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testConstructor_0xffffffffaL() {
|
||||
val x = KBigInteger(-0xffffffffaL)
|
||||
val y = KBigInteger(-1, uintArrayOf(0xfffffffaU, 0xfU))
|
||||
assertEquals(x, y)
|
||||
}
|
||||
}
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
class KBigIntegerCompareTest {
|
||||
@Test
|
||||
fun testCompare1_2() {
|
||||
val x = KBigInteger(1)
|
||||
val y = KBigInteger(2)
|
||||
assertTrue { x < y }
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testCompare0_0() {
|
||||
val x = KBigInteger(0)
|
||||
val y = KBigInteger(0)
|
||||
assertEquals(x, y)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testCompare1__2() {
|
||||
val x = KBigInteger(1)
|
||||
val y = KBigInteger(-2)
|
||||
assertTrue { x > y }
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testCompare_1__2() {
|
||||
val x = KBigInteger(-1)
|
||||
val y = KBigInteger(-2)
|
||||
assertTrue { x > y }
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testCompare_2__1() {
|
||||
val x = KBigInteger(-2)
|
||||
val y = KBigInteger(-1)
|
||||
assertTrue { x < y }
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testCompare12345_12345() {
|
||||
val x = KBigInteger(12345)
|
||||
val y = KBigInteger(12345)
|
||||
assertEquals(x, y)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testEqualsWithLong() {
|
||||
val x = KBigInteger(12345)
|
||||
assertTrue { x == KBigInteger(12345L) }
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testEqualsWithULong() {
|
||||
val x = KBigInteger(12345)
|
||||
assertTrue { x == KBigInteger(12345UL) }
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testCompareBigNumbersGreater() {
|
||||
val x = KBigInteger(0xfffffffffL)
|
||||
val y = KBigInteger(0xffffffffaL)
|
||||
assertTrue { x > y }
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testCompareBigNumbersEqual() {
|
||||
val x = KBigInteger(0xffffffffaL)
|
||||
val y = KBigInteger(0xffffffffaL)
|
||||
assertEquals(x, y)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testCompareBigNumbersLess() {
|
||||
val x = KBigInteger(-0xffffffffaL)
|
||||
val y = KBigInteger(0xffffffffaL)
|
||||
assertTrue { x < y }
|
||||
}
|
||||
}
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
class KBigIntegerOperationsTest {
|
||||
@Test
|
||||
fun testPlus_1_1() {
|
||||
val x = KBigInteger(1)
|
||||
val y = KBigInteger(1)
|
||||
|
||||
val res = x + y
|
||||
val sum = KBigInteger(2)
|
||||
|
||||
assertEquals(sum, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testPlusBigNumbers() {
|
||||
val x = KBigInteger(0x7fffffff)
|
||||
val y = KBigInteger(0x7fffffff)
|
||||
val z = KBigInteger(0x7fffffff)
|
||||
|
||||
val res = x + y + z
|
||||
val sum = KBigInteger(1, uintArrayOf(0x7ffffffdU, 0x1U))
|
||||
|
||||
assertEquals(sum, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testUnaryMinus() {
|
||||
val x = KBigInteger(1234)
|
||||
val y = KBigInteger(-1234)
|
||||
assertEquals(-x, y)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMinus_2_1() {
|
||||
val x = KBigInteger(2)
|
||||
val y = KBigInteger(1)
|
||||
|
||||
val res = x - y
|
||||
val sum = KBigInteger(1)
|
||||
|
||||
assertEquals(sum, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMinus__2_1() {
|
||||
val x = KBigInteger(-2)
|
||||
val y = KBigInteger(1)
|
||||
|
||||
val res = x - y
|
||||
val sum = KBigInteger(-3)
|
||||
|
||||
assertEquals(sum, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMinus___2_1() {
|
||||
val x = KBigInteger(-2)
|
||||
val y = KBigInteger(1)
|
||||
|
||||
val res = -x - y
|
||||
val sum = KBigInteger(1)
|
||||
|
||||
assertEquals(sum, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMinusBigNumbers() {
|
||||
val x = KBigInteger(12345)
|
||||
val y = KBigInteger(0xffffffffaL)
|
||||
|
||||
val res = x - y
|
||||
val sum = KBigInteger(-0xfffffcfc1L)
|
||||
|
||||
assertEquals(sum, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMultiply_2_3() {
|
||||
val x = KBigInteger(2)
|
||||
val y = KBigInteger(3)
|
||||
|
||||
val res = x * y
|
||||
val prod = KBigInteger(6)
|
||||
|
||||
assertEquals(prod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMultiply__2_3() {
|
||||
val x = KBigInteger(-2)
|
||||
val y = KBigInteger(3)
|
||||
|
||||
val res = x * y
|
||||
val prod = KBigInteger(-6)
|
||||
|
||||
assertEquals(prod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMultiply_0xfff123_0xfff456() {
|
||||
val x = KBigInteger(0xfff123)
|
||||
val y = KBigInteger(0xfff456)
|
||||
|
||||
val res = x * y
|
||||
val prod = KBigInteger(0xffe579ad5dc2L)
|
||||
|
||||
assertEquals(prod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMultiplyUInt_0xfff123_0xfff456() {
|
||||
val x = KBigInteger(0xfff123)
|
||||
val y = 0xfff456U
|
||||
|
||||
val res = x * y
|
||||
val prod = KBigInteger(0xffe579ad5dc2L)
|
||||
|
||||
assertEquals(prod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMultiplyInt_0xfff123__0xfff456() {
|
||||
val x = KBigInteger(0xfff123)
|
||||
val y = -0xfff456
|
||||
|
||||
val res = x * y
|
||||
val prod = KBigInteger(-0xffe579ad5dc2L)
|
||||
|
||||
assertEquals(prod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMultiply_0xffffffff_0xffffffff() {
|
||||
val x = KBigInteger(0xffffffffL)
|
||||
val y = KBigInteger(0xffffffffL)
|
||||
|
||||
val res = x * y
|
||||
val prod = KBigInteger(0xfffffffe00000001UL)
|
||||
|
||||
assertEquals(prod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_shr_20() {
|
||||
val x = KBigInteger(20)
|
||||
assertEquals(KBigInteger(10), x shr 1)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_shl_20() {
|
||||
val x = KBigInteger(20)
|
||||
assertEquals(KBigInteger(40), x shl 1)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_shl_1_0() {
|
||||
assertEquals(KBigInteger.ONE, KBigInteger.ONE shl 0)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_shl_1_32() {
|
||||
assertEquals(KBigInteger(0x100000000UL), KBigInteger.ONE shl 32)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_shl_1_33() {
|
||||
assertEquals(KBigInteger(0x200000000UL), KBigInteger.ONE shl 33)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_shr_1_33_33() {
|
||||
assertEquals(KBigInteger.ONE, (KBigInteger.ONE shl 33) shr 33)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_shr_1_32() {
|
||||
assertEquals(KBigInteger.ZERO, KBigInteger.ONE shr 32)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_and_123_456() {
|
||||
val x = KBigInteger(123)
|
||||
val y = KBigInteger(456)
|
||||
assertEquals(KBigInteger(72), x and y)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_or_123_456() {
|
||||
val x = KBigInteger(123)
|
||||
val y = KBigInteger(456)
|
||||
assertEquals(KBigInteger(507), x or y)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_asd() {
|
||||
assertEquals(KBigInteger.ONE, KBigInteger.ZERO or ((KBigInteger(20) shr 4) and KBigInteger.ONE))
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_square_0x11223344U_0xad2ffffdU_0x17eU() {
|
||||
val num = KBigInteger(-1, uintArrayOf(0x11223344U, 0xad2ffffdU, 0x17eU ))
|
||||
println(num)
|
||||
val res = num * num
|
||||
assertEquals(res, KBigInteger(1, uintArrayOf(0xb0542a10U, 0xbbd85bc8U, 0x2a1fa515U, 0x5069e03bU, 0x23c09U)))
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testDivision_6_3() {
|
||||
val x = KBigInteger(6)
|
||||
val y = 3U
|
||||
|
||||
val res = x / y
|
||||
val div = KBigInteger(2)
|
||||
|
||||
assertEquals(div, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testBigDivision_6_3() {
|
||||
val x = KBigInteger(6)
|
||||
val y = KBigInteger(3)
|
||||
|
||||
val res = x / y
|
||||
val div = KBigInteger(2)
|
||||
|
||||
assertEquals(div, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testDivision_20__3() {
|
||||
val x = KBigInteger(20)
|
||||
val y = -3
|
||||
|
||||
val res = x / y
|
||||
val div = KBigInteger(-6)
|
||||
|
||||
assertEquals(div, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testBigDivision_20__3() {
|
||||
val x = KBigInteger(20)
|
||||
val y = KBigInteger(-3)
|
||||
|
||||
val res = x / y
|
||||
val div = KBigInteger(-6)
|
||||
|
||||
assertEquals(div, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testDivision_0xfffffffe00000001_0xffffffff() {
|
||||
val x = KBigInteger(0xfffffffe00000001UL)
|
||||
val y = 0xffffffffU
|
||||
|
||||
val res = x / y
|
||||
val div = KBigInteger(0xffffffffL)
|
||||
|
||||
assertEquals(div, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testBigDivision_0xfffffffeabcdef01UL_0xfffffffeabc() {
|
||||
val res = KBigInteger(0xfffffffeabcdef01UL) / KBigInteger(0xfffffffeabc)
|
||||
assertEquals(res, KBigInteger(0x100000))
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testBigDivision_0xfffffffe00000001_0xffffffff() {
|
||||
val x = KBigInteger(0xfffffffe00000001UL)
|
||||
val y = KBigInteger(0xffffffffU)
|
||||
|
||||
val res = x / y
|
||||
val div = KBigInteger(0xffffffffL)
|
||||
|
||||
assertEquals(div, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMod_20_3() {
|
||||
val x = KBigInteger(20)
|
||||
val y = 3
|
||||
|
||||
val res = x % y
|
||||
val mod = 2
|
||||
|
||||
assertEquals(mod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testBigMod_20_3() {
|
||||
val x = KBigInteger(20)
|
||||
val y = KBigInteger(3)
|
||||
|
||||
val res = x % y
|
||||
val mod = KBigInteger(2)
|
||||
|
||||
assertEquals(mod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testMod_0xfffffffe00000001_12345() {
|
||||
val x = KBigInteger(0xfffffffe00000001UL)
|
||||
val y = 12345
|
||||
|
||||
val res = x % y
|
||||
val mod = 1980
|
||||
|
||||
assertEquals(mod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testBigMod_0xfffffffe00000001_12345() {
|
||||
val x = KBigInteger(0xfffffffe00000001UL)
|
||||
val y = KBigInteger(12345)
|
||||
|
||||
val res = x % y
|
||||
val mod = KBigInteger(1980)
|
||||
|
||||
assertEquals(mod, res)
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testModPow_3_10_17() {
|
||||
val x = KBigInteger(3)
|
||||
val exp = KBigInteger(10)
|
||||
val mod = KBigInteger(17)
|
||||
|
||||
val res = KBigInteger(8)
|
||||
|
||||
return assertEquals(res, x.modPow(exp, mod))
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testModPowBigNumbers() {
|
||||
val x = KBigInteger(0xfffffffeabcdef01UL)
|
||||
val exp = KBigInteger(2)
|
||||
val mod = KBigInteger(0xfffffffeabcUL)
|
||||
|
||||
val res = KBigInteger(0xc2253cde01)
|
||||
|
||||
return assertEquals(res, x.modPow(exp, mod))
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testModBigNumbers() {
|
||||
val x = KBigInteger(0xfffffffeabcdef01UL)
|
||||
val mod = KBigInteger(0xfffffffeabcUL)
|
||||
|
||||
val res = KBigInteger(0xdef01)
|
||||
|
||||
return assertEquals(res, x % mod)
|
||||
}
|
||||
}
|
||||
|
||||
@kotlin.ExperimentalUnsignedTypes
|
||||
class KBigIntegerConversionsTest {
|
||||
@Test
|
||||
fun testToString0x10() {
|
||||
val x = KBigInteger(0x10)
|
||||
assertEquals("0x10", x.toString())
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testToString0x17ffffffd() {
|
||||
val x = KBigInteger(0x17ffffffdL)
|
||||
assertEquals("0x17ffffffd", x.toString())
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testToString_0x17ead2ffffd() {
|
||||
val x = KBigInteger(-0x17ead2ffffdL)
|
||||
assertEquals("-0x17ead2ffffd", x.toString())
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testToString_0x17ead2ffffd11223344() {
|
||||
val x = KBigInteger(-1, uintArrayOf(0x11223344U, 0xad2ffffdU, 0x17eU ))
|
||||
assertEquals("-0x17ead2ffffd11223344", x.toString())
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testFromString_0x17ead2ffffd11223344() {
|
||||
val x = "0x17ead2ffffd11223344".toKBigInteger()
|
||||
assertEquals( "0x17ead2ffffd11223344", x.toString())
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testFromString_7059135710711894913860() {
|
||||
val x = "-7059135710711894913860".toKBigInteger()
|
||||
assertEquals("-0x17ead2ffffd11223344", x.toString())
|
||||
}
|
||||
}
|
||||
|
||||
class KBigIntegerRingTest {
|
||||
@Test
|
||||
fun testKBigIntegerRingSum() {
|
||||
val res = KBigIntegerRing {
|
||||
KBigInteger(1_000L) * KBigInteger(1_000L)
|
||||
}
|
||||
assertEquals(res, KBigInteger(1_000_000) )
|
||||
}
|
||||
|
||||
@Test
|
||||
fun testKBigIntegerRingSum_100_000_000__100_000_000() {
|
||||
KBigIntegerRing {
|
||||
val sum = +"100_000_000" + +"100_000_000"
|
||||
assertEquals(sum, "200_000_000".toKBigInteger())
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_mul_3__4() {
|
||||
KBigIntegerRing {
|
||||
val prod = +"0x3000_0000_0000" * +"0x4000_0000_0000_0000_0000"
|
||||
assertEquals(prod, "0xc00_0000_0000_0000_0000_0000_0000_0000".toKBigInteger())
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_div_big_1() {
|
||||
KBigIntegerRing {
|
||||
val res = +"1_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000" /
|
||||
+"555_000_444_000_333_000_222_000_111_000_999_001"
|
||||
assertEquals(res, +"1801800360360432432518919022699")
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
fun test_rem_big_1() {
|
||||
KBigIntegerRing {
|
||||
val res = +"1_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000_000" %
|
||||
+"555_000_444_000_333_000_222_000_111_000_999_001"
|
||||
assertEquals(res, +"324121220440768000291647788404676301")
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user