diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/KBigInteger.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/KBigInteger.kt new file mode 100644 index 000000000..0238492d2 --- /dev/null +++ b/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 { + 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, Comparable { + + 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 = + 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 +} diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/KBigIntegerTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/KBigIntegerTest.kt new file mode 100644 index 000000000..10b89f28b --- /dev/null +++ b/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")) + } + } + +} +