Initial implementation of multiplatform BigInteger

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/KBigInteger.kt

@@ -0,0 +1,398 @@
+package scientifik.kmath.operations
+
+import kotlin.math.max
+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 = KBigInteger(this)!!
+
+    operator fun String.unaryMinus(): KBigInteger = -KBigInteger(this)!!
+
+}
+
+
+@kotlin.ExperimentalUnsignedTypes
+class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)):
+        RingElement<KBigInteger, KBigInteger, KBigIntegerRing>, Comparable<KBigInteger> {
+
+    constructor(x: Int) : this(x.sign, uintArrayOf(kotlin.math.abs(x).toUInt()))
+    constructor(x: Long) : this(x.sign, uintArrayOf(
+            (kotlin.math.abs(x).toULong() and BASE).toUInt(),
+            ((kotlin.math.abs(x).toULong() shr BASE_SIZE) and BASE).toUInt()))
+
+    val magnitude = stripLeadingZeros(magnitude)
+    val sign = if (this.magnitude.isNotEmpty()) sign else 0
+    val sizeByte: Int = magnitude.size * BASE_SIZE / 4
+
+    override val context: KBigIntegerRing get() = KBigIntegerRing
+
+    override fun unwrap(): KBigInteger = this
+    override fun KBigInteger.wrap(): KBigInteger = this
+
+    companion object {
+        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"
+                )
+
+        private fun stripLeadingZeros(mag: Magnitude): Magnitude {
+            // TODO: optimize performance
+            if (mag.isEmpty()) {
+                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 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 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 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 result
+        }
+
+        internal 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 result
+        }
+
+        internal fun divideMagnitudes(mag1_: Magnitude, mag2: Magnitude): Magnitude {
+            val mag1 = ULongArray(mag1_.size) { mag1_[it].toULong() }
+
+            val resultLength: Int = mag1.size - mag2.size + 1
+            val result = LongArray(resultLength)
+
+            for (i in mag1.size - 1 downTo mag2.size - 1) {
+                val div: ULong = mag1[i] / mag2[mag2.size - 1]
+                result[i - mag2.size + 1] = div.toLong()
+                for (j in mag2.indices) {
+                    mag1[i - j] -= mag2[mag2.size - 1 - j] * div
+                }
+                if (i > 0) {
+                    mag1[i - 1] += (mag1[i] shl BASE_SIZE)
+                }
+            }
+
+            val normalizedResult = Magnitude(resultLength)
+            var carry = 0L
+
+            for (i in result.indices) {
+                result[i] += carry
+                if (result[i] < 0L) {
+                    normalizedResult[i] = (result[i] + (BASE + 1UL).toLong()).toUInt()
+                    carry = -1
+                } else {
+                    normalizedResult[i] = result[i].toUInt()
+                    carry = 0
+                }
+            }
+
+            return normalizedResult
+        }
+    }
+
+    override fun compareTo(other: KBigInteger): Int {
+        return when {
+            (this.sign == 0) and (other.sign == 0) -> 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
+    }
+
+    operator fun unaryMinus(): KBigInteger {
+        return if (this.sign == 0) this else KBigInteger(-this.sign, this.magnitude)
+    }
+
+    override operator fun plus(b: KBigInteger): KBigInteger {
+        return when {
+            b.sign == 0 -> this
+            this.sign == 0 -> 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, subtractMagnitudes(b.magnitude, this.magnitude))
+                }
+            }
+        }
+    }
+
+    override operator fun minus(b: KBigInteger): KBigInteger {
+        return this + (-b)
+    }
+
+    override operator fun times(b: KBigInteger): KBigInteger {
+        return when {
+            this.sign == 0 -> ZERO
+            b.sign == 0 -> ZERO
+//          TODO: Karatsuba
+            else -> KBigInteger(this.sign * b.sign, multiplyMagnitudes(this.magnitude, b.magnitude))
+        }
+    }
+
+    operator fun times(other: UInt): KBigInteger {
+        return when {
+            this.sign == 0 -> 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, divideMagnitudeByUInt(this.magnitude, kotlin.math.abs(other).toUInt()))
+    }
+
+    operator fun div(other: KBigInteger): KBigInteger {
+        return when {
+            this < other -> ZERO
+            this == other -> ONE
+            else -> KBigInteger(this.sign * other.sign, divideMagnitudes(this.magnitude, other.magnitude))
+        }
+    }
+
+    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) {
+            return "0x0"
+        }
+        var res: String = if (this.sign == -1) "-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
+    }
+}
+
+@kotlin.ExperimentalUnsignedTypes
+fun abs(x: KBigInteger): KBigInteger {
+    return if (x.sign == 0) x else KBigInteger(1, x.magnitude)
+}
+
+@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, 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 KBigInteger(s: String): KBigInteger? {
+    val sign: Int
+    val sPositive: String
+    when {
+        s[0] == '+' -> {
+            sign = +1
+            sPositive = s.substring(1)
+        }
+        s[0] == '-' -> {
+            sign = -1
+            sPositive = s.substring(1)
+        }
+        else -> {
+            sPositive = s
+            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
+}

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/KBigIntegerTest.kt

@@ -0,0 +1,480 @@
+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_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_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(0x6deec7895faUL)
+
+        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 = KBigInteger("0x17ead2ffffd11223344")!!
+        assertEquals( "0x17ead2ffffd11223344", x.toString())
+    }
+
+    @Test
+    fun testFromString_7059135710711894913860() {
+        val x = KBigInteger("-7059135710711894913860")
+        assertEquals("-0x17ead2ffffd11223344", x.toString())
+    }
+}
+
+@kotlin.ExperimentalUnsignedTypes
+class DivisionTests {
+    // TODO
+    @Test
+    fun test_0xfffffffeabcdef01UL_0xfffffffeabc() {
+        val res = KBigInteger(0xfffffffeabcdef01UL) / KBigInteger(0xfffffffeabc)
+        assertEquals(res, KBigInteger(0x100000))
+
+    }
+
+//        println(KBigInteger(+1, uintArrayOf(1000U, 1000U, 1000U)) / KBigInteger(0xfffffffeabc)  )
+        // >>> hex((1000 + 1000*2**32 + 1000*2**64)/ 0xfffffffeabc) == 0x3e800000L
+//        println(KBigInteger(+1, KBigInteger.divideMagnitudeByUInt(uintArrayOf(1000U, 1000U, 1000U),456789U)))
+        // 0x8f789719813969L
+
+}
+
+class KBigIntegerRingTest {
+    @Test
+    fun testSum() {
+        val res = KBigIntegerRing {
+            KBigInteger(1_000L) * KBigInteger(1_000L)
+        }
+        assertEquals(res, KBigInteger(1_000_000) )
+    }
+
+    @Test
+    fun test_sum_100_000_000__100_000_000() {
+        KBigIntegerRing {
+            val sum = +"100_000_000" + +"100_000_000"
+            assertEquals(sum, KBigInteger("200_000_000"))
+        }
+    }
+
+    @Test
+    fun test_mul_3__4() {
+        KBigIntegerRing {
+            val prod = +"0x3000_0000_0000" * +"0x4000_0000_0000_0000_0000"
+            assertEquals(prod, KBigInteger("0xc00_0000_0000_0000_0000_0000_0000_0000"))
+        }
+    }
+
+}
+