From 1716b7f5d1d871610961419fd425c49730ea1a2f Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Mon, 10 May 2021 17:57:49 +0300
Subject: [PATCH 01/14] Fast power is added

---
 .../kscience/kmath/benchmarks/BigIntBenchmark.kt  |  6 ++----
 .../space/kscience/kmath/operations/Algebra.kt    | 15 +++++++++++++++
 .../kmath/operations/BigIntAlgebraTest.kt         | 14 ++++++++++++++
 3 files changed, 31 insertions(+), 4 deletions(-)

diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
index b9a10c774..33c659fca 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
@@ -15,15 +15,13 @@ import space.kscience.kmath.operations.BigIntField
 import space.kscience.kmath.operations.JBigIntegerField
 import space.kscience.kmath.operations.invoke
 
-private fun BigInt.pow(power: Int): BigInt = modPow(BigIntField.number(power), BigInt.ONE)
-
 
 @State(Scope.Benchmark)
 internal class BigIntBenchmark {
 
     val kmNumber = BigIntField.number(Int.MAX_VALUE)
     val jvmNumber = JBigIntegerField.number(Int.MAX_VALUE)
-    val largeKmNumber = BigIntField { number(11).pow(100_000) }
+    val largeKmNumber = BigIntField { number(11).pow(100_000UL) }
     val largeJvmNumber = JBigIntegerField { number(11).pow(100_000) }
     val bigExponent = 50_000
 
@@ -59,7 +57,7 @@ internal class BigIntBenchmark {
 
     @Benchmark
     fun kmPower(blackhole: Blackhole) = BigIntField {
-        blackhole.consume(kmNumber.pow(bigExponent))
+        blackhole.consume(kmNumber.pow(bigExponent.toULong()))
     }
 
     @Benchmark
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index 0334e0466..49861b543 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -250,6 +250,21 @@ public interface Ring<T> : Group<T>, RingOperations<T> {
      * neutral operation for multiplication
      */
     public val one: T
+
+    public fun T.pow(exponent: ULong): T = when {
+        this == zero && exponent > 0UL -> zero
+        this == one -> this
+        else -> powWithoutOptimization(exponent)
+    }
+
+    private fun T.powWithoutOptimization(exponent: ULong): T = when (exponent) {
+        0UL -> one
+        1UL -> this
+        else -> {
+            val pre = powWithoutOptimization(exponent shr 1).let { it * it }
+            if (exponent and 1UL == 0UL) pre else pre * this
+        }
+    }
 }
 
 /**
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
index 5df89a385..05b73b49d 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
@@ -6,6 +6,7 @@
 package space.kscience.kmath.operations
 
 import space.kscience.kmath.testutils.RingVerifier
+import kotlin.math.pow
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
@@ -21,6 +22,19 @@ internal class BigIntAlgebraTest {
         assertEquals(res, 1_000_000.toBigInt())
     }
 
+    @Test
+    fun testKBigIntegerRingPow() {
+        BigIntField {
+            for (num in 0..5)
+                for (exponent in 0UL..10UL)
+                    assertEquals(
+                        num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
+                        num.toBigInt().pow(exponent),
+                        "$num ^ $exponent"
+                    )
+        }
+    }
+
     @Test
     fun testKBigIntegerRingSum_100_000_000__100_000_000() {
         BigIntField {

From d17a3ac6eff3d6c62e99af7e030010846afd413b Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Mon, 10 May 2021 18:24:13 +0300
Subject: [PATCH 02/14] Further optimization of power is added

---
 .../kotlin/space/kscience/kmath/operations/Algebra.kt           | 1 +
 .../kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt | 2 +-
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index 49861b543..f7c021998 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -254,6 +254,7 @@ public interface Ring<T> : Group<T>, RingOperations<T> {
     public fun T.pow(exponent: ULong): T = when {
         this == zero && exponent > 0UL -> zero
         this == one -> this
+        this == -one -> powWithoutOptimization(exponent % 2UL)
         else -> powWithoutOptimization(exponent)
     }
 
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
index 05b73b49d..90cd29758 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
@@ -25,7 +25,7 @@ internal class BigIntAlgebraTest {
     @Test
     fun testKBigIntegerRingPow() {
         BigIntField {
-            for (num in 0..5)
+            for (num in -5..5)
                 for (exponent in 0UL..10UL)
                     assertEquals(
                         num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),

From 3ad7f32ada115b279e00edc49f5e9ba7e63a834d Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Mon, 10 May 2021 18:41:40 +0300
Subject: [PATCH 03/14] Incorrect BigInt equality fixed

---
 .../kotlin/space/kscience/kmath/operations/BigInt.kt           | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index e74efa9ca..e81f1686d 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -56,8 +56,7 @@ public class BigInt internal constructor(
         else -> sign * compareMagnitudes(magnitude, other.magnitude)
     }
 
-    public override fun equals(other: Any?): Boolean =
-        if (other is BigInt) compareTo(other) == 0 else error("Can't compare KBigInteger to a different type")
+    public override fun equals(other: Any?): Boolean = other is BigInt && compareTo(other) == 0
 
     public override fun hashCode(): Int = magnitude.hashCode() + sign
 

From 2da0648d73829396777066f970bf861e75410f01 Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Tue, 11 May 2021 01:40:45 +0300
Subject: [PATCH 04/14] Karatsuba added Incorrect equals fix test Incorrect
 overflow handling support

---
 .../space/kscience/kmath/operations/BigInt.kt | 46 +++++++++++++++----
 .../kmath/operations/BigIntOperationsTest.kt  | 25 +++++++++-
 2 files changed, 61 insertions(+), 10 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index e81f1686d..c7079902b 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -86,20 +86,23 @@ public class BigInt internal constructor(
     public operator fun times(b: BigInt): BigInt = when {
         this.sign == 0.toByte() -> ZERO
         b.sign == 0.toByte() -> ZERO
-//          TODO: Karatsuba
+        b.magnitude.size == 1 -> this * b.magnitude[0] * b.sign.toInt()
+        this.magnitude.size == 1 -> b * this.magnitude[0] * this.sign.toInt()
         else -> BigInt((this.sign * b.sign).toByte(), multiplyMagnitudes(this.magnitude, b.magnitude))
     }
 
     public operator fun times(other: UInt): BigInt = when {
         sign == 0.toByte() -> ZERO
         other == 0U -> ZERO
+        other == 1U -> this
         else -> BigInt(sign, multiplyMagnitudeByUInt(magnitude, other))
     }
 
-    public operator fun times(other: Int): BigInt = if (other > 0)
-        this * kotlin.math.abs(other).toUInt()
-    else
-        -this * kotlin.math.abs(other).toUInt()
+    public operator fun times(other: Int): BigInt = when {
+        other > 0 -> this * kotlin.math.abs(other).toUInt()
+        other != Int.MIN_VALUE -> -this * kotlin.math.abs(other).toUInt()
+        else -> times(other.toBigInt())
+    }
 
     public operator fun div(other: UInt): BigInt = BigInt(this.sign, divideMagnitudeByUInt(this.magnitude, other))
 
@@ -237,6 +240,7 @@ public class BigInt internal constructor(
         public const val BASE_SIZE: Int = 32
         public val ZERO: BigInt = BigInt(0, uintArrayOf())
         public val ONE: BigInt = BigInt(1, uintArrayOf(1u))
+        private const val KARATSUBA_THRESHOLD = 80
 
         private val hexMapping: HashMap<UInt, String> = hashMapOf(
             0U to "0", 1U to "1", 2U to "2", 3U to "3",
@@ -317,7 +321,16 @@ public class BigInt internal constructor(
             return stripLeadingZeros(result)
         }
 
-        private fun multiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
+        internal fun multiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude = when {
+            mag1.size + mag2.size < KARATSUBA_THRESHOLD || mag1.isEmpty() || mag2.isEmpty() -> naiveMultiplyMagnitudes(
+                mag1,
+                mag2
+            )
+            // TODO implement Fourier
+            else -> karatsubaMultiplyMagnitudes(mag1, mag2)
+        }
+
+        internal fun naiveMultiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
             val resultLength = mag1.size + mag2.size
             val result = Magnitude(resultLength)
 
@@ -336,6 +349,21 @@ public class BigInt internal constructor(
             return stripLeadingZeros(result)
         }
 
+        internal fun karatsubaMultiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
+            //https://en.wikipedia.org/wiki/Karatsuba_algorithm
+            val halfSize = min(mag1.size, mag2.size) / 2
+            val x0 = mag1.sliceArray(0 until halfSize).toBigInt(1)
+            val x1 = mag1.sliceArray(halfSize until mag1.size).toBigInt(1)
+            val y0 = mag2.sliceArray(0 until halfSize).toBigInt(1)
+            val y1 = mag2.sliceArray(halfSize until mag2.size).toBigInt(1)
+
+            val z0 = x0 * y0
+            val z2 = x1 * y1
+            val z1 = (x0 + x1) * (y1 + y0) - z0 - z2
+
+            return (z2.shl(2 * halfSize * BASE_SIZE) + z1.shl(halfSize * BASE_SIZE) + z0).magnitude
+        }
+
         private fun divideMagnitudeByUInt(mag: Magnitude, x: UInt): Magnitude {
             val resultLength = mag.size
             val result = Magnitude(resultLength)
@@ -426,7 +454,7 @@ private val hexChToInt: MutableMap<Char, Int> = hashMapOf(
 public fun String.parseBigInteger(): BigInt? {
     val sign: Int
     val sPositive: String
-
+    //TODO substring = O(n). Can be replaced by some drop that is O(1)
     when {
         this[0] == '+' -> {
             sign = +1
@@ -446,8 +474,10 @@ public fun String.parseBigInteger(): BigInt? {
     var digitValue = BigInt.ONE
     val sPositiveUpper = sPositive.uppercase()
 
-    if (sPositiveUpper.startsWith("0X")) {  // hex representation
+    if (sPositiveUpper.startsWith("0X")) {
+        // hex representation
         val sHex = sPositiveUpper.substring(2)
+        // TODO optimize O(n2) -> O(n)
 
         for (ch in sHex.reversed()) {
             if (ch == '_') continue
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntOperationsTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntOperationsTest.kt
index ae34dbc04..9f35f7a69 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntOperationsTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntOperationsTest.kt
@@ -5,8 +5,9 @@
 
 package space.kscience.kmath.operations
 
-import kotlin.test.Test
-import kotlin.test.assertEquals
+import kotlin.random.Random
+import kotlin.random.nextUInt
+import kotlin.test.*
 
 @kotlin.ExperimentalUnsignedTypes
 class BigIntOperationsTest {
@@ -150,6 +151,18 @@ class BigIntOperationsTest {
         assertEquals(prod, res)
     }
 
+    @Test
+    fun testKaratsuba() {
+        val x = uintArrayOf(12U, 345U)
+        val y = uintArrayOf(6U, 789U)
+        assertContentEquals(BigInt.naiveMultiplyMagnitudes(x, y), BigInt.karatsubaMultiplyMagnitudes(x, y))
+        repeat(1000) {
+            val x1 = UIntArray(Random.nextInt(100, 1000)) { Random.nextUInt() }
+            val y1 = UIntArray(Random.nextInt(100, 1000)) { Random.nextUInt() }
+            assertContentEquals(BigInt.naiveMultiplyMagnitudes(x1, y1), BigInt.karatsubaMultiplyMagnitudes(x1, y1))
+        }
+    }
+
     @Test
     fun test_shr_20() {
         val x = 20.toBigInt()
@@ -383,4 +396,12 @@ class BigIntOperationsTest {
 
         return assertEquals(res, x % mod)
     }
+
+    @Test
+    fun testNotEqualsOtherTypeInstanceButButNotFails() = assertFalse(0.toBigInt().equals(""))
+
+    @Test
+    fun testIntAbsOverflow() {
+        assertEquals((-Int.MAX_VALUE.toLong().toBigInt() - 1.toBigInt()) * 2, 2.toBigInt() * Int.MIN_VALUE)
+    }
 }

From 74d14970b9e50e808c8901b8d2850ecd29f79ba1 Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Wed, 12 May 2021 00:58:27 +0300
Subject: [PATCH 05/14] empty string parsing fixed

---
 .../space/kscience/kmath/operations/BigInt.kt |  7 +++++-
 .../kmath/operations/BigIntConversionsTest.kt | 22 +++++++++++++++++++
 2 files changed, 28 insertions(+), 1 deletion(-)

diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index c7079902b..00b9f9fc2 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -452,6 +452,7 @@ private val hexChToInt: MutableMap<Char, Int> = hashMapOf(
  * Returns null if a valid number can not be read from a string
  */
 public fun String.parseBigInteger(): BigInt? {
+    if (this.isEmpty()) return null
     val sign: Int
     val sPositive: String
     //TODO substring = O(n). Can be replaced by some drop that is O(1)
@@ -473,15 +474,18 @@ public fun String.parseBigInteger(): BigInt? {
     var res = BigInt.ZERO
     var digitValue = BigInt.ONE
     val sPositiveUpper = sPositive.uppercase()
+    var isEmpty = true
 
     if (sPositiveUpper.startsWith("0X")) {
         // hex representation
         val sHex = sPositiveUpper.substring(2)
+        if (this.isEmpty()) return null
         // TODO optimize O(n2) -> O(n)
 
         for (ch in sHex.reversed()) {
             if (ch == '_') continue
             res += digitValue * (hexChToInt[ch] ?: return null)
+            isEmpty = false
             digitValue *= 16.toBigInt()
         }
     } else for (ch in sPositiveUpper.reversed()) {
@@ -491,10 +495,11 @@ public fun String.parseBigInteger(): BigInt? {
             return null
         }
         res += digitValue * (ch.code - '0'.code)
+        isEmpty = false
         digitValue *= 10.toBigInt()
     }
 
-    return res * sign
+    return if (isEmpty) null else res * sign
 }
 
 public inline fun Buffer.Companion.bigInt(size: Int, initializer: (Int) -> BigInt): Buffer<BigInt> =
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntConversionsTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntConversionsTest.kt
index a2832e531..1feaae808 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntConversionsTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntConversionsTest.kt
@@ -7,9 +7,31 @@ package space.kscience.kmath.operations
 
 import kotlin.test.Test
 import kotlin.test.assertEquals
+import kotlin.test.assertNull
 
 @kotlin.ExperimentalUnsignedTypes
 class BigIntConversionsTest {
+
+    @Test
+    fun emptyString() {
+        assertNull("".parseBigInteger())
+        assertNull("+".parseBigInteger())
+        assertNull("-".parseBigInteger())
+
+        assertNull("0x".parseBigInteger())
+        assertNull("+0x".parseBigInteger())
+        assertNull("-0x".parseBigInteger())
+
+
+        assertNull("_".parseBigInteger())
+        assertNull("+_".parseBigInteger())
+        assertNull("-_".parseBigInteger())
+
+        assertNull("0x_".parseBigInteger())
+        assertNull("+0x_".parseBigInteger())
+        assertNull("-0x_".parseBigInteger())
+    }
+
     @Test
     fun testToString0x10() {
         val x = 0x10.toBigInt()

From 9184bd55de46bcb16a5c33b8a02f604b592aff4a Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Wed, 12 May 2021 02:01:49 +0300
Subject: [PATCH 06/14] Parser optimization

---
 .../space/kscience/kmath/operations/BigInt.kt | 90 +++++++++++--------
 1 file changed, 55 insertions(+), 35 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 00b9f9fc2..ab05d079f 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -441,11 +441,11 @@ public fun UIntArray.toBigInt(sign: Byte): BigInt {
     return BigInt(sign, copyOf())
 }
 
-private val hexChToInt: MutableMap<Char, Int> = 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
+private val hexChToInt: MutableMap<Char, UInt> = hashMapOf(
+    '0' to 0U, '1' to 1U, '2' to 2U, '3' to 3U,
+    '4' to 4U, '5' to 5U, '6' to 6U, '7' to 7U,
+    '8' to 8U, '9' to 9U, 'A' to 10U, 'B' to 11U,
+    'C' to 12U, 'D' to 13U, 'E' to 14U, 'F' to 15U
 )
 
 /**
@@ -454,52 +454,72 @@ private val hexChToInt: MutableMap<Char, Int> = hashMapOf(
 public fun String.parseBigInteger(): BigInt? {
     if (this.isEmpty()) return null
     val sign: Int
-    val sPositive: String
-    //TODO substring = O(n). Can be replaced by some drop that is O(1)
-    when {
-        this[0] == '+' -> {
+
+    val positivePartIndex = when (this[0]) {
+        '+' -> {
             sign = +1
-            sPositive = this.substring(1)
+            1
         }
-        this[0] == '-' -> {
+        '-' -> {
             sign = -1
-            sPositive = this.substring(1)
+            1
         }
         else -> {
-            sPositive = this
             sign = +1
+            0
         }
     }
 
-    var res = BigInt.ZERO
-    var digitValue = BigInt.ONE
-    val sPositiveUpper = sPositive.uppercase()
     var isEmpty = true
 
-    if (sPositiveUpper.startsWith("0X")) {
+    return if (this.startsWith("0X", startIndex = positivePartIndex, ignoreCase = true)) {
         // hex representation
-        val sHex = sPositiveUpper.substring(2)
-        if (this.isEmpty()) return null
-        // TODO optimize O(n2) -> O(n)
 
-        for (ch in sHex.reversed()) {
-            if (ch == '_') continue
-            res += digitValue * (hexChToInt[ch] ?: return null)
+        val uInts = mutableListOf(0U)
+        var offset = 0
+        fun addDigit(value: UInt) {
+            uInts[uInts.lastIndex] += value shl offset
+            offset += 4
+            if (offset == 32) {
+                uInts.add(0U)
+                offset = 0
+            }
+        }
+
+        for (index in lastIndex downTo positivePartIndex + 2) {
+            when (val ch = this[index]) {
+                '_' -> continue
+                in '0'..'9' -> addDigit((ch - '0').toUInt())
+                in 'A'..'F' -> addDigit((ch - 'A').toUInt() + 10U)
+                in 'a'..'f' -> addDigit((ch - 'a').toUInt() + 10U)
+                else -> return null
+            }
             isEmpty = false
-            digitValue *= 16.toBigInt()
         }
-    } else for (ch in sPositiveUpper.reversed()) {
-        // decimal representation
-        if (ch == '_') continue
-        if (ch !in '0'..'9') {
-            return null
-        }
-        res += digitValue * (ch.code - '0'.code)
-        isEmpty = false
-        digitValue *= 10.toBigInt()
-    }
 
-    return if (isEmpty) null else res * sign
+        while (uInts.isNotEmpty() && uInts.last() == 0U)
+            uInts.removeLast()
+
+        if (isEmpty) null else BigInt(sign.toByte(), uInts.toUIntArray())
+    } else {
+        // hex representation
+        var res = BigInt.ZERO
+        var digitValue = BigInt.ONE
+        for (index in lastIndex downTo positivePartIndex) {
+            val ch = this[index]
+            // decimal representation
+            if (ch == '_') continue
+            if (ch !in '0'..'9') {
+                return null
+            }
+            res += digitValue * (ch.code - '0'.code)
+            isEmpty = false
+            digitValue *= 10.toBigInt()
+
+        }
+
+        if (isEmpty) null else res * sign
+    }
 }
 
 public inline fun Buffer.Companion.bigInt(size: Int, initializer: (Int) -> BigInt): Buffer<BigInt> =

From b4e47494fcf6683d14d523aaaba34e33da592c3c Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Wed, 12 May 2021 04:42:17 +0300
Subject: [PATCH 07/14] Parsing of decimal values takes 9 immediately digits
 but not 1.

---
 .../kmath/benchmarks/BigIntBenchmark.kt       | 25 ++++++++--
 .../space/kscience/kmath/operations/BigInt.kt | 47 ++++++++++---------
 .../kmath/operations/BigIntConversionsTest.kt |  8 +++-
 3 files changed, 54 insertions(+), 26 deletions(-)

diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
index 33c659fca..639eaacf3 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
@@ -10,10 +10,7 @@ import kotlinx.benchmark.Blackhole
 import org.openjdk.jmh.annotations.Benchmark
 import org.openjdk.jmh.annotations.Scope
 import org.openjdk.jmh.annotations.State
-import space.kscience.kmath.operations.BigInt
-import space.kscience.kmath.operations.BigIntField
-import space.kscience.kmath.operations.JBigIntegerField
-import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.operations.*
 
 
 @State(Scope.Benchmark)
@@ -64,4 +61,24 @@ internal class BigIntBenchmark {
     fun jvmPower(blackhole: Blackhole) = JBigIntegerField {
         blackhole.consume(jvmNumber.pow(bigExponent))
     }
+
+    @Benchmark
+    fun kmParsing16(blackhole: Blackhole) = JBigIntegerField {
+        blackhole.consume("0x7f57ed8b89c29a3b9a85c7a5b84ca3929c7b7488593".parseBigInteger())
+    }
+
+    @Benchmark
+    fun kmParsing10(blackhole: Blackhole) = JBigIntegerField {
+        blackhole.consume("236656783929183747565738292847574838922010".parseBigInteger())
+    }
+
+    @Benchmark
+    fun jvmParsing10(blackhole: Blackhole) = JBigIntegerField {
+        blackhole.consume("236656783929183747565738292847574838922010".toBigInteger(10))
+    }
+
+    @Benchmark
+    fun jvmParsing16(blackhole: Blackhole) = JBigIntegerField {
+        blackhole.consume("7f57ed8b89c29a3b9a85c7a5b84ca3929c7b7488593".toBigInteger(16))
+    }
 }
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index ab05d079f..780a4591d 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -441,13 +441,6 @@ public fun UIntArray.toBigInt(sign: Byte): BigInt {
     return BigInt(sign, copyOf())
 }
 
-private val hexChToInt: MutableMap<Char, UInt> = hashMapOf(
-    '0' to 0U, '1' to 1U, '2' to 2U, '3' to 3U,
-    '4' to 4U, '5' to 5U, '6' to 6U, '7' to 7U,
-    '8' to 8U, '9' to 9U, 'A' to 10U, 'B' to 11U,
-    'C' to 12U, 'D' to 13U, 'E' to 14U, 'F' to 15U
-)
-
 /**
  * Returns null if a valid number can not be read from a string
  */
@@ -475,7 +468,7 @@ public fun String.parseBigInteger(): BigInt? {
     return if (this.startsWith("0X", startIndex = positivePartIndex, ignoreCase = true)) {
         // hex representation
 
-        val uInts = mutableListOf(0U)
+        val uInts = ArrayList<UInt>(length).apply { add(0U) }
         var offset = 0
         fun addDigit(value: UInt) {
             uInts[uInts.lastIndex] += value shl offset
@@ -502,22 +495,34 @@ public fun String.parseBigInteger(): BigInt? {
 
         if (isEmpty) null else BigInt(sign.toByte(), uInts.toUIntArray())
     } else {
-        // hex representation
-        var res = BigInt.ZERO
-        var digitValue = BigInt.ONE
-        for (index in lastIndex downTo positivePartIndex) {
-            val ch = this[index]
-            // decimal representation
-            if (ch == '_') continue
-            if (ch !in '0'..'9') {
-                return null
-            }
-            res += digitValue * (ch.code - '0'.code)
-            isEmpty = false
-            digitValue *= 10.toBigInt()
+        // decimal representation
 
+        val positivePart = buildList(length) {
+            for (index in positivePartIndex until length)
+                when (val a = this@parseBigInteger[index]) {
+                    '_' -> continue
+                    in '0'..'9' -> add(a)
+                    else -> return null
+                }
         }
 
+        val offset = positivePart.size % 9
+        isEmpty = offset == 0
+
+        fun parseUInt(fromIndex: Int, toIndex: Int): UInt? {
+            var res = 0U
+            for (i in fromIndex until toIndex) {
+                res = res * 10U + (positivePart[i].digitToIntOrNull()?.toUInt() ?: return null)
+            }
+            return res
+        }
+
+        var res = parseUInt(0, offset)?.toBigInt() ?: return null
+
+        for (index in offset..positivePart.lastIndex step 9) {
+            isEmpty = false
+            res = res * 1_000_000_000U + (parseUInt(index, index + 9) ?: return null).toBigInt()
+        }
         if (isEmpty) null else res * sign
     }
 }
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntConversionsTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntConversionsTest.kt
index 1feaae808..85f368f3e 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntConversionsTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntConversionsTest.kt
@@ -13,7 +13,7 @@ import kotlin.test.assertNull
 class BigIntConversionsTest {
 
     @Test
-    fun emptyString() {
+    fun testEmptyString() {
         assertNull("".parseBigInteger())
         assertNull("+".parseBigInteger())
         assertNull("-".parseBigInteger())
@@ -38,6 +38,12 @@ class BigIntConversionsTest {
         assertEquals("0x10", x.toString())
     }
 
+    @Test
+    fun testUnderscores() {
+        assertEquals("0x10", "0x_1_0_".parseBigInteger().toString())
+        assertEquals("0xa", "_1_0_".parseBigInteger().toString())
+    }
+
     @Test
     fun testToString0x17ffffffd() {
         val x = 0x17ffffffdL.toBigInt()

From ed86a31c50d7d6b3890342fb2652ffdba4630fb0 Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Wed, 12 May 2021 04:58:48 +0300
Subject: [PATCH 08/14] Placing pow outside the Ring interface.

---
 .../kscience/kmath/operations/Algebra.kt      | 26 +++++++++----------
 .../space/kscience/kmath/operations/BigInt.kt |  2 ++
 2 files changed, 15 insertions(+), 13 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index f7c021998..645e60c29 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -250,21 +250,21 @@ public interface Ring<T> : Group<T>, RingOperations<T> {
      * neutral operation for multiplication
      */
     public val one: T
+}
 
-    public fun T.pow(exponent: ULong): T = when {
-        this == zero && exponent > 0UL -> zero
-        this == one -> this
-        this == -one -> powWithoutOptimization(exponent % 2UL)
-        else -> powWithoutOptimization(exponent)
-    }
+public fun <T> Ring<T>.pow(base: T, exponent: ULong): T = when {
+    this == zero && exponent > 0UL -> zero
+    this == one -> base
+    this == -one -> powWithoutOptimization(base, exponent % 2UL)
+    else -> powWithoutOptimization(base, exponent)
+}
 
-    private fun T.powWithoutOptimization(exponent: ULong): T = when (exponent) {
-        0UL -> one
-        1UL -> this
-        else -> {
-            val pre = powWithoutOptimization(exponent shr 1).let { it * it }
-            if (exponent and 1UL == 0UL) pre else pre * this
-        }
+private fun <T> Ring<T>.powWithoutOptimization(base: T, exponent: ULong): T = when (exponent) {
+    0UL -> one
+    1UL -> base
+    else -> {
+        val pre = powWithoutOptimization(base, exponent shr 1).let { it * it }
+        if (exponent and 1UL == 0UL) pre else pre * base
     }
 }
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 780a4591d..88c952928 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -98,6 +98,8 @@ public class BigInt internal constructor(
         else -> BigInt(sign, multiplyMagnitudeByUInt(magnitude, other))
     }
 
+    public fun pow(other: ULong): BigInt = BigIntField { pow(this@BigInt, other) }
+
     public operator fun times(other: Int): BigInt = when {
         other > 0 -> this * kotlin.math.abs(other).toUInt()
         other != Int.MIN_VALUE -> -this * kotlin.math.abs(other).toUInt()

From ded01251d1e94af4edf315c3d5ad70dce6b06ee0 Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Wed, 12 May 2021 11:05:42 +0300
Subject: [PATCH 09/14] Karatsuba enhancement

---
 .../kotlin/space/kscience/kmath/operations/BigInt.kt      | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 88c952928..be73e274a 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -324,10 +324,8 @@ public class BigInt internal constructor(
         }
 
         internal fun multiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude = when {
-            mag1.size + mag2.size < KARATSUBA_THRESHOLD || mag1.isEmpty() || mag2.isEmpty() -> naiveMultiplyMagnitudes(
-                mag1,
-                mag2
-            )
+            mag1.size + mag2.size < KARATSUBA_THRESHOLD || mag1.isEmpty() || mag2.isEmpty() ->
+                naiveMultiplyMagnitudes(mag1, mag2)
             // TODO implement Fourier
             else -> karatsubaMultiplyMagnitudes(mag1, mag2)
         }
@@ -361,7 +359,7 @@ public class BigInt internal constructor(
 
             val z0 = x0 * y0
             val z2 = x1 * y1
-            val z1 = (x0 + x1) * (y1 + y0) - z0 - z2
+            val z1 = (x0 - x1) * (y1 - y0) + z0 + z2
 
             return (z2.shl(2 * halfSize * BASE_SIZE) + z1.shl(halfSize * BASE_SIZE) + z0).magnitude
         }

From 1e71f29d5e64a5c933630f892fab29cdfbd36e63 Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Wed, 12 May 2021 13:59:41 +0300
Subject: [PATCH 10/14] Large addition tests added

---
 .../space/kscience/kmath/benchmarks/BigIntBenchmark.kt | 10 ++++++++++
 .../kotlin/space/kscience/kmath/operations/BigInt.kt   |  2 +-
 2 files changed, 11 insertions(+), 1 deletion(-)

diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
index 639eaacf3..d3262379f 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
@@ -32,6 +32,16 @@ internal class BigIntBenchmark {
         blackhole.consume(jvmNumber + jvmNumber + jvmNumber)
     }
 
+    @Benchmark
+    fun kmAddLarge(blackhole: Blackhole) = BigIntField {
+        blackhole.consume(largeKmNumber + largeKmNumber + largeKmNumber)
+    }
+
+    @Benchmark
+    fun jvmAddLarge(blackhole: Blackhole) = JBigIntegerField {
+        blackhole.consume(largeJvmNumber + largeJvmNumber + largeJvmNumber)
+    }
+
     @Benchmark
     fun kmMultiply(blackhole: Blackhole) = BigIntField {
         blackhole.consume(kmNumber * kmNumber * kmNumber)
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index be73e274a..605dfd265 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -281,7 +281,7 @@ public class BigInt internal constructor(
                 }
 
                 result[i] = (res and BASE).toUInt()
-                carry = (res shr BASE_SIZE)
+                carry = res shr BASE_SIZE
             }
 
             result[resultLength - 1] = carry.toUInt()

From 8443fac4ae4df746f26a1dd444be1ef194d7baa5 Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Wed, 12 May 2021 14:10:32 +0300
Subject: [PATCH 11/14] UInt can be used in exponent (in pow) now.

---
 .../kotlin/space/kscience/kmath/operations/Algebra.kt     | 2 ++
 .../kotlin/space/kscience/kmath/operations/BigInt.kt      | 1 +
 .../space/kscience/kmath/operations/BigIntAlgebraTest.kt  | 8 +++++++-
 3 files changed, 10 insertions(+), 1 deletion(-)

diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index 645e60c29..a23dc427c 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -259,6 +259,8 @@ public fun <T> Ring<T>.pow(base: T, exponent: ULong): T = when {
     else -> powWithoutOptimization(base, exponent)
 }
 
+public fun <T> Ring<T>.pow(base: T, exponent: UInt): T = pow(base, exponent.toULong())
+
 private fun <T> Ring<T>.powWithoutOptimization(base: T, exponent: ULong): T = when (exponent) {
     0UL -> one
     1UL -> base
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 605dfd265..45161149c 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -99,6 +99,7 @@ public class BigInt internal constructor(
     }
 
     public fun pow(other: ULong): BigInt = BigIntField { pow(this@BigInt, other) }
+    public fun pow(other: UInt): BigInt = BigIntField { pow(this@BigInt, other) }
 
     public operator fun times(other: Int): BigInt = when {
         other > 0 -> this * kotlin.math.abs(other).toUInt()
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
index 90cd29758..abc88934c 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
@@ -26,12 +26,18 @@ internal class BigIntAlgebraTest {
     fun testKBigIntegerRingPow() {
         BigIntField {
             for (num in -5..5)
-                for (exponent in 0UL..10UL)
+                for (exponent in 0U..10U) {
+                    assertEquals(
+                        num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
+                        num.toBigInt().pow(exponent.toULong()),
+                        "$num ^ $exponent"
+                    )
                     assertEquals(
                         num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
                         num.toBigInt().pow(exponent),
                         "$num ^ $exponent"
                     )
+                }
         }
     }
 

From 1e945389314cf8d3072f919f5c18afd9a4dcca4d Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Thu, 13 May 2021 13:11:20 +0300
Subject: [PATCH 12/14] Unstable API annotation added + inconsistent docs fix +
 unnecessary BigIntField usage removed

---
 .../kmath/benchmarks/BigIntBenchmark.kt       |  5 +++-
 .../kscience/kmath/operations/Algebra.kt      |  5 +++-
 .../space/kscience/kmath/operations/BigInt.kt |  3 ++
 .../kmath/operations/OptionalOperations.kt    |  2 +-
 .../kmath/operations/BigIntAlgebraTest.kt     | 30 +++++++++----------
 5 files changed, 27 insertions(+), 18 deletions(-)

diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
index d3262379f..21b097609 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
@@ -10,16 +10,19 @@ import kotlinx.benchmark.Blackhole
 import org.openjdk.jmh.annotations.Benchmark
 import org.openjdk.jmh.annotations.Scope
 import org.openjdk.jmh.annotations.State
+import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.*
+import java.math.BigInteger
 
 
+@UnstableKMathAPI
 @State(Scope.Benchmark)
 internal class BigIntBenchmark {
 
     val kmNumber = BigIntField.number(Int.MAX_VALUE)
     val jvmNumber = JBigIntegerField.number(Int.MAX_VALUE)
     val largeKmNumber = BigIntField { number(11).pow(100_000UL) }
-    val largeJvmNumber = JBigIntegerField { number(11).pow(100_000) }
+    val largeJvmNumber: BigInteger = JBigIntegerField { number(11).pow(100_000) }
     val bigExponent = 50_000
 
     @Benchmark
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index a23dc427c..8881ae93c 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -6,6 +6,7 @@
 package space.kscience.kmath.operations
 
 import space.kscience.kmath.misc.Symbol
+import space.kscience.kmath.misc.UnstableKMathAPI
 
 /**
  * Stub for DSL the [Algebra] is.
@@ -247,11 +248,12 @@ public interface RingOperations<T> : GroupOperations<T> {
  */
 public interface Ring<T> : Group<T>, RingOperations<T> {
     /**
-     * neutral operation for multiplication
+     * The neutral element of multiplication
      */
     public val one: T
 }
 
+@UnstableKMathAPI
 public fun <T> Ring<T>.pow(base: T, exponent: ULong): T = when {
     this == zero && exponent > 0UL -> zero
     this == one -> base
@@ -259,6 +261,7 @@ public fun <T> Ring<T>.pow(base: T, exponent: ULong): T = when {
     else -> powWithoutOptimization(base, exponent)
 }
 
+@UnstableKMathAPI
 public fun <T> Ring<T>.pow(base: T, exponent: UInt): T = pow(base, exponent.toULong())
 
 private fun <T> Ring<T>.powWithoutOptimization(base: T, exponent: ULong): T = when (exponent) {
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 45161149c..0dcbbe567 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -98,7 +98,10 @@ public class BigInt internal constructor(
         else -> BigInt(sign, multiplyMagnitudeByUInt(magnitude, other))
     }
 
+    @UnstableKMathAPI
     public fun pow(other: ULong): BigInt = BigIntField { pow(this@BigInt, other) }
+
+    @UnstableKMathAPI
     public fun pow(other: UInt): BigInt = BigIntField { pow(this@BigInt, other) }
 
     public operator fun times(other: Int): BigInt = when {
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/OptionalOperations.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/OptionalOperations.kt
index 8e3e6c777..7045c874e 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/OptionalOperations.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/OptionalOperations.kt
@@ -147,7 +147,7 @@ public interface PowerOperations<T> : Algebra<T> {
 }
 
 /**
- * Raises this element to the power [pow].
+ * Raises this element to the power [power].
  *
  * @receiver the base.
  * @param power the exponent.
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
index abc88934c..d3fca4351 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.operations
 
+import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.testutils.RingVerifier
 import kotlin.math.pow
 import kotlin.test.Test
@@ -22,23 +23,22 @@ internal class BigIntAlgebraTest {
         assertEquals(res, 1_000_000.toBigInt())
     }
 
+    @UnstableKMathAPI
     @Test
     fun testKBigIntegerRingPow() {
-        BigIntField {
-            for (num in -5..5)
-                for (exponent in 0U..10U) {
-                    assertEquals(
-                        num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
-                        num.toBigInt().pow(exponent.toULong()),
-                        "$num ^ $exponent"
-                    )
-                    assertEquals(
-                        num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
-                        num.toBigInt().pow(exponent),
-                        "$num ^ $exponent"
-                    )
-                }
-        }
+        for (num in -5..5)
+            for (exponent in 0U..10U) {
+                assertEquals(
+                    num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
+                    num.toBigInt().pow(exponent.toULong()),
+                    "$num ^ $exponent"
+                )
+                assertEquals(
+                    num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
+                    num.toBigInt().pow(exponent),
+                    "$num ^ $exponent"
+                )
+            }
     }
 
     @Test

From c2047474016f8c7de92b83f741c7bb00630cc1a9 Mon Sep 17 00:00:00 2001
From: zhelenskiy <zhelenskiy2000@yandex.ru>
Date: Thu, 13 May 2021 22:44:33 +0300
Subject: [PATCH 13/14] Reusing of existing power function

---
 .../kmath/benchmarks/BigIntBenchmark.kt       |  4 +-
 .../kscience/kmath/operations/Algebra.kt      | 20 ----------
 .../space/kscience/kmath/operations/BigInt.kt |  6 +--
 .../kmath/operations/algebraExtensions.kt     | 39 ++++++++++++-------
 .../kmath/operations/BigIntAlgebraTest.kt     |  8 +---
 .../kmath/operations/DoubleFieldTest.kt       | 12 ++++++
 6 files changed, 41 insertions(+), 48 deletions(-)

diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
index 21b097609..749cd5e75 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
@@ -21,7 +21,7 @@ internal class BigIntBenchmark {
 
     val kmNumber = BigIntField.number(Int.MAX_VALUE)
     val jvmNumber = JBigIntegerField.number(Int.MAX_VALUE)
-    val largeKmNumber = BigIntField { number(11).pow(100_000UL) }
+    val largeKmNumber = BigIntField { number(11).pow(100_000U) }
     val largeJvmNumber: BigInteger = JBigIntegerField { number(11).pow(100_000) }
     val bigExponent = 50_000
 
@@ -67,7 +67,7 @@ internal class BigIntBenchmark {
 
     @Benchmark
     fun kmPower(blackhole: Blackhole) = BigIntField {
-        blackhole.consume(kmNumber.pow(bigExponent.toULong()))
+        blackhole.consume(kmNumber.pow(bigExponent.toUInt()))
     }
 
     @Benchmark
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index 8881ae93c..b444ed964 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -253,26 +253,6 @@ public interface Ring<T> : Group<T>, RingOperations<T> {
     public val one: T
 }
 
-@UnstableKMathAPI
-public fun <T> Ring<T>.pow(base: T, exponent: ULong): T = when {
-    this == zero && exponent > 0UL -> zero
-    this == one -> base
-    this == -one -> powWithoutOptimization(base, exponent % 2UL)
-    else -> powWithoutOptimization(base, exponent)
-}
-
-@UnstableKMathAPI
-public fun <T> Ring<T>.pow(base: T, exponent: UInt): T = pow(base, exponent.toULong())
-
-private fun <T> Ring<T>.powWithoutOptimization(base: T, exponent: ULong): T = when (exponent) {
-    0UL -> one
-    1UL -> base
-    else -> {
-        val pre = powWithoutOptimization(base, exponent shr 1).let { it * it }
-        if (exponent and 1UL == 0UL) pre else pre * base
-    }
-}
-
 /**
  * Represents field without without multiplicative and additive identities, i.e. algebraic structure with associative, binary, commutative operations
  * [add] and [multiply]; binary operation [divide] as multiplication of left operand by reciprocal of right one.
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 0dcbbe567..924ef07f4 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -98,11 +98,7 @@ public class BigInt internal constructor(
         else -> BigInt(sign, multiplyMagnitudeByUInt(magnitude, other))
     }
 
-    @UnstableKMathAPI
-    public fun pow(other: ULong): BigInt = BigIntField { pow(this@BigInt, other) }
-
-    @UnstableKMathAPI
-    public fun pow(other: UInt): BigInt = BigIntField { pow(this@BigInt, other) }
+    public fun pow(exponent: UInt): BigInt = BigIntField.power(this@BigInt, exponent)
 
     public operator fun times(other: Int): BigInt = when {
         other > 0 -> this * kotlin.math.abs(other).toUInt()
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt
index b8670553d..9691c9d17 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt
@@ -97,34 +97,45 @@ public fun <T, S> Sequence<T>.averageWith(space: S): T where S : Ring<T>, S : Sc
 //TODO optimized power operation
 
 /**
- * Raises [arg] to the natural power [power].
+ * Raises [arg] to the non-negative integer power [power].
+ *
+ * Special case: 0 ^ 0 is 1.
  *
  * @receiver the algebra to provide multiplication.
  * @param arg the base.
  * @param power the exponent.
  * @return the base raised to the power.
+ * @author Evgeniy Zhelenskiy
  */
-public fun <T> Ring<T>.power(arg: T, power: Int): T {
-    require(power >= 0) { "The power can't be negative." }
-    require(power != 0 || arg != zero) { "The $zero raised to $power is not defined." }
-    if (power == 0) return one
-    var res = arg
-    repeat(power - 1) { res *= arg }
-    return res
+public fun <T> Ring<T>.power(arg: T, power: UInt): T = when {
+    this == zero && power > 0U -> zero
+    this == one -> arg
+    this == -one -> powWithoutOptimization(arg, power % 2U)
+    else -> powWithoutOptimization(arg, power)
 }
 
+private fun <T> Ring<T>.powWithoutOptimization(base: T, exponent: UInt): T = when (exponent) {
+    0U -> one
+    1U -> base
+    else -> {
+        val pre = powWithoutOptimization(base, exponent shr 1).let { it * it }
+        if (exponent and 1U == 0U) pre else pre * base
+    }
+}
+
+
 /**
  * Raises [arg] to the integer power [power].
  *
+ * Special case: 0 ^ 0 is 1.
+ *
  * @receiver the algebra to provide multiplication and division.
  * @param arg the base.
  * @param power the exponent.
  * @return the base raised to the power.
- * @author Iaroslav Postovalov
+ * @author Iaroslav Postovalov, Evgeniy Zhelenskiy
  */
-public fun <T> Field<T>.power(arg: T, power: Int): T {
-    require(power != 0 || arg != zero) { "The $zero raised to $power is not defined." }
-    if (power == 0) return one
-    if (power < 0) return one / (this as Ring<T>).power(arg, -power)
-    return (this as Ring<T>).power(arg, power)
+public fun <T> Field<T>.power(arg: T, power: Int): T = when {
+    power < 0 -> one / (this as Ring<T>).power(arg, if (power == Int.MIN_VALUE) Int.MAX_VALUE.toUInt().inc() else (-power).toUInt())
+    else -> (this as Ring<T>).power(arg, power.toUInt())
 }
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
index d3fca4351..0527f5252 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
@@ -27,18 +27,12 @@ internal class BigIntAlgebraTest {
     @Test
     fun testKBigIntegerRingPow() {
         for (num in -5..5)
-            for (exponent in 0U..10U) {
-                assertEquals(
-                    num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
-                    num.toBigInt().pow(exponent.toULong()),
-                    "$num ^ $exponent"
-                )
+            for (exponent in 0U..10U)
                 assertEquals(
                     num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
                     num.toBigInt().pow(exponent),
                     "$num ^ $exponent"
                 )
-            }
     }
 
     @Test
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/DoubleFieldTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/DoubleFieldTest.kt
index c482dc978..7e689d079 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/DoubleFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/DoubleFieldTest.kt
@@ -18,4 +18,16 @@ internal class DoubleFieldTest {
         val sqrt = DoubleField { sqrt(25 * one) }
         assertEquals(5.0, sqrt)
     }
+
+    @Test
+    fun testPow() = DoubleField {
+        val num = 5 * one
+        assertEquals(5.0, power(num, 1))
+        assertEquals(25.0, power(num, 2))
+        assertEquals(1.0, power(num, 0))
+        assertEquals(0.2, power(num, -1))
+        assertEquals(0.04, power(num, -2))
+        assertEquals(0.0, power(num, Int.MIN_VALUE))
+        assertEquals(1.0, power(zero, 0))
+    }
 }

From bdb9ce6a59bf34b4ff21945f42a05c070752fcf7 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@users.noreply.github.com>
Date: Fri, 14 May 2021 09:10:05 +0300
Subject: [PATCH 14/14] fixes to power

---
 .../kscience/kmath/operations/algebraExtensions.kt   | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt
index 9691c9d17..338dc6a5c 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt
@@ -108,9 +108,9 @@ public fun <T, S> Sequence<T>.averageWith(space: S): T where S : Ring<T>, S : Sc
  * @author Evgeniy Zhelenskiy
  */
 public fun <T> Ring<T>.power(arg: T, power: UInt): T = when {
-    this == zero && power > 0U -> zero
-    this == one -> arg
-    this == -one -> powWithoutOptimization(arg, power % 2U)
+    arg == zero && power > 0U -> zero
+    arg == one -> arg
+    arg == -one -> powWithoutOptimization(arg, power % 2U)
     else -> powWithoutOptimization(arg, power)
 }
 
@@ -135,7 +135,7 @@ private fun <T> Ring<T>.powWithoutOptimization(base: T, exponent: UInt): T = whe
  * @return the base raised to the power.
  * @author Iaroslav Postovalov, Evgeniy Zhelenskiy
  */
-public fun <T> Field<T>.power(arg: T, power: Int): T = when {
-    power < 0 -> one / (this as Ring<T>).power(arg, if (power == Int.MIN_VALUE) Int.MAX_VALUE.toUInt().inc() else (-power).toUInt())
-    else -> (this as Ring<T>).power(arg, power.toUInt())
+public fun <T> Field<T>.power(arg: T, power: UInt): T = when {
+    power < 0 -> one / (this as Ring<T>).power(arg, power)
+    else -> (this as Ring<T>).power(arg, power)
 }