Karatsuba added, 2 bugs are fixed

benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt

@@ -10,21 +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.operations.BigInt
-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)
+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_000) }
-    val largeJvmNumber = JBigIntegerField { number(11).pow(100_000) }
+    val largeKmNumber = BigIntField { number(11).pow(100_000U) }
+    val largeJvmNumber: BigInteger = JBigIntegerField { number(11).pow(100_000) }
     val bigExponent = 50_000
 
     @Benchmark
@@ -37,6 +35,16 @@ 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)
@@ -59,11 +67,31 @@ internal class BigIntBenchmark {
 
     @Benchmark
     fun kmPower(blackhole: Blackhole) = BigIntField {
-        blackhole.consume(kmNumber.pow(bigExponent))
+        blackhole.consume(kmNumber.pow(bigExponent.toUInt()))
     }
 
     @Benchmark
     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))
+    }
 }

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.
@@ -247,7 +248,7 @@ 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
 }

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
 
@@ -87,20 +86,25 @@ 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 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()
+        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))
 
@@ -238,6 +242,7 @@ 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",
@@ -276,7 +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()
@@ -318,7 +323,14 @@ 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)
 
@@ -337,6 +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)
@@ -414,58 +441,90 @@ 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
-)
-
 /**
  * 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
 
-    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")) {  // hex representation
-        val sHex = sPositiveUpper.substring(2)
+    return if (this.startsWith("0X", startIndex = positivePartIndex, ignoreCase = true)) {
+        // hex representation
+
+        val uInts = ArrayList<UInt>(length).apply { add(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 (ch in sHex.reversed()) {
-            if (ch == '_') continue
-            res += digitValue * (hexChToInt[ch] ?: return null)
-            digitValue *= 16.toBigInt()
+        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
         }
-    } else for (ch in sPositiveUpper.reversed()) {
+
+        while (uInts.isNotEmpty() && uInts.last() == 0U)
+            uInts.removeLast()
+
+        if (isEmpty) null else BigInt(sign.toByte(), uInts.toUIntArray())
+    } else {
         // decimal representation
-        if (ch == '_') continue
-        if (ch !in '0'..'9') {
-            return null
+
+        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
+                }
         }
-        res += digitValue * (ch.code - '0'.code)
-        digitValue *= 10.toBigInt()
-    }
 
-    return res * sign
+        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
+    }
 }
 
 public inline fun Buffer.Companion.bigInt(size: Int, initializer: (Int) -> BigInt): Buffer<BigInt> =

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.

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())
 }