Fast power is added

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

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
+        }
+    }
 }
 
 /**

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 {