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Fix division and add tests

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This commit is contained in:
Peter Klimai 2020-04-01 23:56:39 +03:00
parent 9500ee0924
commit 19d1459a55
2 changed files with 179 additions and 60 deletions
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136
kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/KBigInteger.kt
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@ -1,6 +1,8 @@
package scientifik.kmath.operations
import kotlin.math.log2
import kotlin.math.max
import kotlin.math.min
import kotlin.math.sign
/*
@ -27,7 +29,6 @@ object KBigIntegerRing: Ring<KBigInteger> {
operator fun String.unaryPlus(): KBigInteger = KBigInteger(this)!!
operator fun String.unaryMinus(): KBigInteger = -KBigInteger(this)!!
}
@ -161,7 +162,7 @@ class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)):
return result
}
internal fun divideMagnitudeByUInt(mag: Magnitude, x: UInt): Magnitude {
private fun divideMagnitudeByUInt(mag: Magnitude, x: UInt): Magnitude {
val resultLength: Int = mag.size
val result = Magnitude(resultLength)
var carry: ULong = 0UL
@ -174,39 +175,6 @@ class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)):
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 {
@ -287,14 +255,102 @@ class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)):
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))
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, 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, 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, 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, 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, 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()

103
kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/KBigIntegerTest.kt
View File

@ -244,6 +244,62 @@ class KBigIntegerOperationsTest {
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 ))
@ -307,6 +363,12 @@ class KBigIntegerOperationsTest {
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)
@ -379,7 +441,7 @@ class KBigIntegerOperationsTest {
val exp = KBigInteger(2)
val mod = KBigInteger(0xfffffffeabcUL)
val res = KBigInteger(0x6deec7895faUL)
val res = KBigInteger(0xc2253cde01)
return assertEquals(res, x.modPow(exp, mod))
}
@ -434,26 +496,9 @@ class KBigIntegerConversionsTest {
}
}
@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() {
fun testKBigIntegerRingSum() {
val res = KBigIntegerRing {
KBigInteger(1_000L) * KBigInteger(1_000L)
}
@ -461,7 +506,7 @@ class KBigIntegerRingTest {
}
@Test
fun test_sum_100_000_000__100_000_000() {
fun testKBigIntegerRingSum_100_000_000__100_000_000() {
KBigIntegerRing {
val sum = +"100_000_000" + +"100_000_000"
assertEquals(sum, KBigInteger("200_000_000"))
@ -476,5 +521,23 @@ class KBigIntegerRingTest {
}
}
@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")
}
}
}