Karatsuba added
Incorrect equals fix test Incorrect overflow handling support
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@ -86,20 +86,23 @@ public class BigInt internal constructor(
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public operator fun times(b: BigInt): BigInt = when {
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this.sign == 0.toByte() -> ZERO
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b.sign == 0.toByte() -> ZERO
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// TODO: Karatsuba
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b.magnitude.size == 1 -> this * b.magnitude[0] * b.sign.toInt()
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this.magnitude.size == 1 -> b * this.magnitude[0] * this.sign.toInt()
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else -> BigInt((this.sign * b.sign).toByte(), multiplyMagnitudes(this.magnitude, b.magnitude))
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}
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public operator fun times(other: UInt): BigInt = when {
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sign == 0.toByte() -> ZERO
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other == 0U -> ZERO
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other == 1U -> this
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else -> BigInt(sign, multiplyMagnitudeByUInt(magnitude, other))
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}
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public operator fun times(other: Int): BigInt = if (other > 0)
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this * kotlin.math.abs(other).toUInt()
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else
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-this * kotlin.math.abs(other).toUInt()
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public operator fun times(other: Int): BigInt = when {
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other > 0 -> this * kotlin.math.abs(other).toUInt()
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other != Int.MIN_VALUE -> -this * kotlin.math.abs(other).toUInt()
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else -> times(other.toBigInt())
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}
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public operator fun div(other: UInt): BigInt = BigInt(this.sign, divideMagnitudeByUInt(this.magnitude, other))
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@ -237,6 +240,7 @@ public class BigInt internal constructor(
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public const val BASE_SIZE: Int = 32
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public val ZERO: BigInt = BigInt(0, uintArrayOf())
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public val ONE: BigInt = BigInt(1, uintArrayOf(1u))
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private const val KARATSUBA_THRESHOLD = 80
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private val hexMapping: HashMap<UInt, String> = hashMapOf(
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0U to "0", 1U to "1", 2U to "2", 3U to "3",
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@ -317,7 +321,16 @@ public class BigInt internal constructor(
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return stripLeadingZeros(result)
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}
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private fun multiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
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internal fun multiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude = when {
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mag1.size + mag2.size < KARATSUBA_THRESHOLD || mag1.isEmpty() || mag2.isEmpty() -> naiveMultiplyMagnitudes(
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mag1,
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mag2
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)
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// TODO implement Fourier
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else -> karatsubaMultiplyMagnitudes(mag1, mag2)
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}
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internal fun naiveMultiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
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val resultLength = mag1.size + mag2.size
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val result = Magnitude(resultLength)
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@ -336,6 +349,21 @@ public class BigInt internal constructor(
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return stripLeadingZeros(result)
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}
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internal fun karatsubaMultiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
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//https://en.wikipedia.org/wiki/Karatsuba_algorithm
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val halfSize = min(mag1.size, mag2.size) / 2
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val x0 = mag1.sliceArray(0 until halfSize).toBigInt(1)
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val x1 = mag1.sliceArray(halfSize until mag1.size).toBigInt(1)
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val y0 = mag2.sliceArray(0 until halfSize).toBigInt(1)
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val y1 = mag2.sliceArray(halfSize until mag2.size).toBigInt(1)
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val z0 = x0 * y0
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val z2 = x1 * y1
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val z1 = (x0 + x1) * (y1 + y0) - z0 - z2
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return (z2.shl(2 * halfSize * BASE_SIZE) + z1.shl(halfSize * BASE_SIZE) + z0).magnitude
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}
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private fun divideMagnitudeByUInt(mag: Magnitude, x: UInt): Magnitude {
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val resultLength = mag.size
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val result = Magnitude(resultLength)
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@ -426,7 +454,7 @@ private val hexChToInt: MutableMap<Char, Int> = hashMapOf(
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public fun String.parseBigInteger(): BigInt? {
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val sign: Int
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val sPositive: String
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//TODO substring = O(n). Can be replaced by some drop that is O(1)
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when {
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this[0] == '+' -> {
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sign = +1
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@ -446,8 +474,10 @@ public fun String.parseBigInteger(): BigInt? {
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var digitValue = BigInt.ONE
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val sPositiveUpper = sPositive.uppercase()
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if (sPositiveUpper.startsWith("0X")) { // hex representation
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if (sPositiveUpper.startsWith("0X")) {
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// hex representation
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val sHex = sPositiveUpper.substring(2)
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// TODO optimize O(n2) -> O(n)
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for (ch in sHex.reversed()) {
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if (ch == '_') continue
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@ -5,8 +5,9 @@
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package space.kscience.kmath.operations
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.random.Random
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import kotlin.random.nextUInt
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import kotlin.test.*
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@kotlin.ExperimentalUnsignedTypes
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class BigIntOperationsTest {
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@ -150,6 +151,18 @@ class BigIntOperationsTest {
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assertEquals(prod, res)
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}
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@Test
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fun testKaratsuba() {
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val x = uintArrayOf(12U, 345U)
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val y = uintArrayOf(6U, 789U)
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assertContentEquals(BigInt.naiveMultiplyMagnitudes(x, y), BigInt.karatsubaMultiplyMagnitudes(x, y))
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repeat(1000) {
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val x1 = UIntArray(Random.nextInt(100, 1000)) { Random.nextUInt() }
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val y1 = UIntArray(Random.nextInt(100, 1000)) { Random.nextUInt() }
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assertContentEquals(BigInt.naiveMultiplyMagnitudes(x1, y1), BigInt.karatsubaMultiplyMagnitudes(x1, y1))
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}
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}
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@Test
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fun test_shr_20() {
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val x = 20.toBigInt()
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@ -383,4 +396,12 @@ class BigIntOperationsTest {
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return assertEquals(res, x % mod)
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}
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@Test
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fun testNotEqualsOtherTypeInstanceButButNotFails() = assertFalse(0.toBigInt().equals(""))
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@Test
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fun testIntAbsOverflow() {
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assertEquals((-Int.MAX_VALUE.toLong().toBigInt() - 1.toBigInt()) * 2, 2.toBigInt() * Int.MIN_VALUE)
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}
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}
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