From ae7aefeb6aa58100721144dfeec0aebdbe87f878 Mon Sep 17 00:00:00 2001
From: Iaroslav <postovalovya@gmail.com>
Date: Wed, 5 Aug 2020 03:58:00 +0700
Subject: [PATCH 01/12] Specify type explicitly EVERYWHERE in kmath-core, add
 newlines at ends of files, refactor minor problems, improve documentation

---
 .../kotlin/scientifik/kmath/domains/Domain.kt |  11 +-
 .../kmath/domains/HyperSquareDomain.kt        |   5 +-
 .../scientifik/kmath/domains/RealDomain.kt    |   6 +-
 .../kmath/domains/UnconstrainedDomain.kt      |   4 +-
 .../kmath/domains/UnivariateDomain.kt         |   7 +-
 .../kmath/expressions/Expression.kt           |   9 +-
 .../FunctionalExpressionAlgebra.kt            |   2 +-
 .../scientifik/kmath/linear/BufferMatrix.kt   |  16 +-
 .../scientifik/kmath/linear/FeaturedMatrix.kt |  12 +-
 .../kmath/linear/LUPDecomposition.kt          |  24 +-
 .../scientifik/kmath/linear/LinearAlgebra.kt  |   2 +-
 .../scientifik/kmath/linear/MatrixContext.kt  |   8 +-
 .../scientifik/kmath/linear/MatrixFeatures.kt |  10 +-
 .../scientifik/kmath/linear/VectorSpace.kt    |   6 +-
 .../scientifik/kmath/linear/VirtualMatrix.kt  |   4 +-
 .../kotlin/scientifik/kmath/misc/AutoDiff.kt  |  10 +-
 .../kotlin/scientifik/kmath/misc/Grids.kt     |   2 +-
 .../scientifik/kmath/misc/cumulative.kt       |  35 +--
 .../scientifik/kmath/operations/Algebra.kt    | 225 +++++++++++++++---
 .../kmath/operations/AlgebraElements.kt       |  22 +-
 .../kmath/operations/AlgebraExtensions.kt     |   2 +-
 .../scientifik/kmath/operations/BigInt.kt     |  24 +-
 .../scientifik/kmath/operations/Complex.kt    |  14 +-
 .../kmath/operations/NumberAlgebra.kt         | 125 +++++-----
 .../kmath/operations/OptionalOperations.kt    | 186 ++++++++++++---
 .../kmath/structures/BoxingNDField.kt         |   8 +-
 .../kmath/structures/BoxingNDRing.kt          |   8 +-
 .../kmath/structures/BufferAccessor2D.kt      |   8 +-
 .../kmath/structures/BufferedNDAlgebra.kt     |   4 +-
 .../kmath/structures/BufferedNDElement.kt     |  16 +-
 .../scientifik/kmath/structures/Buffers.kt    |  21 +-
 .../kmath/structures/ComplexNDField.kt        |  37 ++-
 .../kmath/structures/ExtendedNDField.kt       |   3 -
 .../kmath/structures/FlaggedBuffer.kt         |  12 +-
 .../scientifik/kmath/structures/IntBuffer.kt  |   5 +-
 .../scientifik/kmath/structures/LongBuffer.kt |   4 +-
 .../kmath/structures/MemoryBuffer.kt          |  14 +-
 .../scientifik/kmath/structures/NDAlgebra.kt  |  26 +-
 .../scientifik/kmath/structures/NDElement.kt  |  29 ++-
 .../kmath/structures/NDStructure.kt           |  41 +++-
 .../scientifik/kmath/structures/RealBuffer.kt |   4 +-
 .../kmath/structures/RealNDField.kt           |  26 +-
 .../kmath/structures/ShortBuffer.kt           |   5 +-
 .../kmath/structures/ShortNDRing.kt           |  21 +-
 .../kmath/structures/Structure1D.kt           |   8 +-
 .../kmath/structures/Structure2D.kt           |   6 +-
 .../kmath/expressions/ExpressionFieldTest.kt  |   6 +-
 .../scientifik/kmath/linear/MatrixTest.kt     |  12 +-
 .../kmath/linear/RealLUSolverTest.kt          |   2 +-
 .../scientifik/kmath/misc/AutoDiffTest.kt     |   9 +-
 .../scientifik/kmath/misc/CumulativeKtTest.kt |   2 +-
 .../kmath/operations/BigIntAlgebraTest.kt     |   1 -
 .../kmath/operations/BigIntConstructorTest.kt |   4 +-
 .../kmath/operations/BigIntConversionsTest.kt |   4 +-
 .../kmath/operations/BigIntOperationsTest.kt  |  24 +-
 .../kmath/operations/RealFieldTest.kt         |   2 +-
 .../kmath/structures/ComplexBufferSpecTest.kt |   2 +-
 .../kmath/structures/NDFieldTest.kt           |   2 +-
 .../kmath/structures/NumberNDFieldTest.kt     |   4 +-
 59 files changed, 722 insertions(+), 429 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/Domain.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/Domain.kt
index 333b77cb4..341383bfb 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/Domain.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/Domain.kt
@@ -3,13 +3,18 @@ package scientifik.kmath.domains
 import scientifik.kmath.linear.Point
 
 /**
- * A simple geometric domain
+ * A simple geometric domain.
+ *
+ * @param T the type of element of this domain.
  */
 interface Domain<T : Any> {
+    /**
+     * Checks if the specified point is contained in this domain.
+     */
     operator fun contains(point: Point<T>): Boolean
 
     /**
-     * Number of hyperspace dimensions
+     * Number of hyperspace dimensions.
      */
     val dimension: Int
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/HyperSquareDomain.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/HyperSquareDomain.kt
index e0019c96b..66798c42f 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/HyperSquareDomain.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/HyperSquareDomain.kt
@@ -42,13 +42,14 @@ class HyperSquareDomain(private val lower: RealBuffer, private val upper: RealBu
     override fun getUpperBound(num: Int): Double? = upper[num]
 
     override fun nearestInDomain(point: Point<Double>): Point<Double> {
-        val res: DoubleArray = DoubleArray(point.size) { i ->
+        val res = DoubleArray(point.size) { i ->
             when {
                 point[i] < lower[i] -> lower[i]
                 point[i] > upper[i] -> upper[i]
                 else -> point[i]
             }
         }
+
         return RealBuffer(*res)
     }
 
@@ -64,4 +65,4 @@ class HyperSquareDomain(private val lower: RealBuffer, private val upper: RealBu
         }
         return res
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/RealDomain.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/RealDomain.kt
index 89115887e..7507ccd59 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/RealDomain.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/RealDomain.kt
@@ -22,8 +22,7 @@ import scientifik.kmath.linear.Point
  *
  * @author Alexander Nozik
  */
-interface RealDomain: Domain<Double> {
-
+interface RealDomain : Domain<Double> {
     fun nearestInDomain(point: Point<Double>): Point<Double>
 
     /**
@@ -61,5 +60,4 @@ interface RealDomain: Domain<Double> {
      * @return
      */
     fun volume(): Double
-
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnconstrainedDomain.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnconstrainedDomain.kt
index e49fd3b37..595a3dbe7 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnconstrainedDomain.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnconstrainedDomain.kt
@@ -18,7 +18,6 @@ package scientifik.kmath.domains
 import scientifik.kmath.linear.Point
 
 class UnconstrainedDomain(override val dimension: Int) : RealDomain {
-
     override operator fun contains(point: Point<Double>): Boolean = true
 
     override fun getLowerBound(num: Int, point: Point<Double>): Double? = Double.NEGATIVE_INFINITY
@@ -32,5 +31,4 @@ class UnconstrainedDomain(override val dimension: Int) : RealDomain {
     override fun nearestInDomain(point: Point<Double>): Point<Double> = point
 
     override fun volume(): Double = Double.POSITIVE_INFINITY
-
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnivariateDomain.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnivariateDomain.kt
index ef521d5ea..280dc7d66 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnivariateDomain.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnivariateDomain.kt
@@ -4,7 +4,6 @@ import scientifik.kmath.linear.Point
 import scientifik.kmath.structures.asBuffer
 
 inline class UnivariateDomain(val range: ClosedFloatingPointRange<Double>) : RealDomain {
-
     operator fun contains(d: Double): Boolean = range.contains(d)
 
     override operator fun contains(point: Point<Double>): Boolean {
@@ -15,10 +14,10 @@ inline class UnivariateDomain(val range: ClosedFloatingPointRange<Double>) : Rea
     override fun nearestInDomain(point: Point<Double>): Point<Double> {
         require(point.size == 1)
         val value = point[0]
-        return when{
+        return when {
             value in range -> point
             value >= range.endInclusive -> doubleArrayOf(range.endInclusive).asBuffer()
-            else ->  doubleArrayOf(range.start).asBuffer()
+            else -> doubleArrayOf(range.start).asBuffer()
         }
     }
 
@@ -45,4 +44,4 @@ inline class UnivariateDomain(val range: ClosedFloatingPointRange<Double>) : Rea
     override fun volume(): Double = range.endInclusive - range.start
 
     override val dimension: Int get() = 1
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt
index e512b1cd8..b21a414f5 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt
@@ -14,9 +14,10 @@ interface Expression<T> {
 /**
  * Create simple lazily evaluated expression inside given algebra
  */
-fun <T> Algebra<T>.expression(block:  Algebra<T>.(arguments: Map<String, T>) -> T): Expression<T> = object: Expression<T> {
-    override fun invoke(arguments: Map<String, T>): T = block(arguments)
-}
+fun <T> Algebra<T>.expression(block: Algebra<T>.(arguments: Map<String, T>) -> T): Expression<T> =
+    object : Expression<T> {
+        override fun invoke(arguments: Map<String, T>): T = block(arguments)
+    }
 
 operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke(mapOf(*pairs))
 
@@ -33,4 +34,4 @@ interface ExpressionAlgebra<T, E> : Algebra<E> {
      * A constant expression which does not depend on arguments
      */
     fun const(value: T): E
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressionAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressionAlgebra.kt
index a8a26aa33..5a8a10717 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressionAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressionAlgebra.kt
@@ -143,4 +143,4 @@ inline fun <T, A : Ring<T>> A.expressionInRing(block: FunctionalExpressionRing<T
     FunctionalExpressionRing(this).block()
 
 inline fun <T, A : Field<T>> A.expressionInField(block: FunctionalExpressionField<T, A>.() -> Expression<T>): Expression<T> =
-    FunctionalExpressionField(this).block()
\ No newline at end of file
+    FunctionalExpressionField(this).block()
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/BufferMatrix.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/BufferMatrix.kt
index c4c38284b..2e1f32501 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/BufferMatrix.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/BufferMatrix.kt
@@ -19,22 +19,20 @@ class BufferMatrixContext<T : Any, R : Ring<T>>(
 
     override fun point(size: Int, initializer: (Int) -> T): Point<T> = bufferFactory(size, initializer)
 
-    companion object {
-
-    }
+    companion object
 }
 
 @Suppress("OVERRIDE_BY_INLINE")
 object RealMatrixContext : GenericMatrixContext<Double, RealField> {
 
-    override val elementContext get() = RealField
+    override val elementContext: RealField get() = RealField
 
     override inline fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> Double): Matrix<Double> {
         val buffer = RealBuffer(rows * columns) { offset -> initializer(offset / columns, offset % columns) }
         return BufferMatrix(rows, columns, buffer)
     }
 
-    override inline fun point(size: Int, initializer: (Int) -> Double): Point<Double> = RealBuffer(size,initializer)
+    override inline fun point(size: Int, initializer: (Int) -> Double): Point<Double> = RealBuffer(size, initializer)
 }
 
 class BufferMatrix<T : Any>(
@@ -52,7 +50,7 @@ class BufferMatrix<T : Any>(
 
     override val shape: IntArray get() = intArrayOf(rowNum, colNum)
 
-    override fun suggestFeature(vararg features: MatrixFeature) =
+    override fun suggestFeature(vararg features: MatrixFeature): BufferMatrix<T> =
         BufferMatrix(rowNum, colNum, buffer, this.features + features)
 
     override fun get(index: IntArray): T = get(index[0], index[1])
@@ -84,8 +82,8 @@ class BufferMatrix<T : Any>(
     override fun toString(): String {
         return if (rowNum <= 5 && colNum <= 5) {
             "Matrix(rowsNum = $rowNum, colNum = $colNum, features=$features)\n" +
-                    rows.asSequence().joinToString(prefix = "(", postfix = ")", separator = "\n ") {
-                        it.asSequence().joinToString(separator = "\t") { it.toString() }
+                    rows.asSequence().joinToString(prefix = "(", postfix = ")", separator = "\n ") { buffer ->
+                        buffer.asSequence().joinToString(separator = "\t") { it.toString() }
                     }
         } else {
             "Matrix(rowsNum = $rowNum, colNum = $colNum, features=$features)"
@@ -121,4 +119,4 @@ infix fun BufferMatrix<Double>.dot(other: BufferMatrix<Double>): BufferMatrix<Do
 
     val buffer = RealBuffer(array)
     return BufferMatrix(rowNum, other.colNum, buffer)
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/FeaturedMatrix.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/FeaturedMatrix.kt
index 297586fc6..dd17c4fe7 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/FeaturedMatrix.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/FeaturedMatrix.kt
@@ -23,12 +23,10 @@ interface FeaturedMatrix<T : Any> : Matrix<T> {
      */
     fun suggestFeature(vararg features: MatrixFeature): FeaturedMatrix<T>
 
-    companion object {
-
-    }
+    companion object
 }
 
-fun Structure2D.Companion.real(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
+fun Structure2D.Companion.real(rows: Int, columns: Int, initializer: (Int, Int) -> Double): Matrix<Double> =
     MatrixContext.real.produce(rows, columns, initializer)
 
 /**
@@ -41,7 +39,7 @@ fun <T : Any> Structure2D.Companion.square(vararg elements: T): FeaturedMatrix<T
     return BufferMatrix(size, size, buffer)
 }
 
-val Matrix<*>.features get() = (this as? FeaturedMatrix)?.features?: emptySet()
+val Matrix<*>.features: Set<MatrixFeature> get() = (this as? FeaturedMatrix)?.features ?: emptySet()
 
 /**
  * Check if matrix has the given feature class
@@ -68,7 +66,7 @@ fun <T : Any, R : Ring<T>> GenericMatrixContext<T, R>.one(rows: Int, columns: In
  * A virtual matrix of zeroes
  */
 fun <T : Any, R : Ring<T>> GenericMatrixContext<T, R>.zero(rows: Int, columns: Int): FeaturedMatrix<T> =
-    VirtualMatrix<T>(rows, columns) { _, _ -> elementContext.zero }
+    VirtualMatrix(rows, columns) { _, _ -> elementContext.zero }
 
 class TransposedFeature<T : Any>(val original: Matrix<T>) : MatrixFeature
 
@@ -83,4 +81,4 @@ fun <T : Any> Matrix<T>.transpose(): Matrix<T> {
     ) { i, j -> get(j, i) }
 }
 
-infix fun Matrix<Double>.dot(other: Matrix<Double>): Matrix<Double> = with(MatrixContext.real) { dot(other) }
\ No newline at end of file
+infix fun Matrix<Double>.dot(other: Matrix<Double>): Matrix<Double> = with(MatrixContext.real) { dot(other) }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUPDecomposition.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUPDecomposition.kt
index 75d7da169..d04a99fbb 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUPDecomposition.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUPDecomposition.kt
@@ -18,7 +18,7 @@ class LUPDecomposition<T : Any>(
     private val even: Boolean
 ) : LUPDecompositionFeature<T>, DeterminantFeature<T> {
 
-    val elementContext get() = context.elementContext
+    val elementContext: Field<T> get() = context.elementContext
 
     /**
      * Returns the matrix L of the decomposition.
@@ -67,7 +67,7 @@ class LUPDecomposition<T : Any>(
 
 }
 
-fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.abs(value: T) =
+fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.abs(value: T): T =
     if (value > elementContext.zero) value else with(elementContext) { -value }
 
 
@@ -169,9 +169,10 @@ fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
 inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
     matrix: Matrix<T>,
     noinline checkSingular: (T) -> Boolean
-) = lup(T::class, matrix, checkSingular)
+): LUPDecomposition<T> = lup(T::class, matrix, checkSingular)
 
-fun GenericMatrixContext<Double, RealField>.lup(matrix: Matrix<Double>) = lup(Double::class, matrix) { it < 1e-11 }
+fun GenericMatrixContext<Double, RealField>.lup(matrix: Matrix<Double>): LUPDecomposition<Double> =
+    lup(Double::class, matrix) { it < 1e-11 }
 
 fun <T : Any> LUPDecomposition<T>.solve(type: KClass<T>, matrix: Matrix<T>): Matrix<T> {
 
@@ -185,7 +186,7 @@ fun <T : Any> LUPDecomposition<T>.solve(type: KClass<T>, matrix: Matrix<T>): Mat
             // Apply permutations to b
             val bp = create { _, _ -> zero }
 
-            for (row in 0 until pivot.size) {
+            for (row in pivot.indices) {
                 val bpRow = bp.row(row)
                 val pRow = pivot[row]
                 for (col in 0 until matrix.colNum) {
@@ -194,7 +195,7 @@ fun <T : Any> LUPDecomposition<T>.solve(type: KClass<T>, matrix: Matrix<T>): Mat
             }
 
             // Solve LY = b
-            for (col in 0 until pivot.size) {
+            for (col in pivot.indices) {
                 val bpCol = bp.row(col)
                 for (i in col + 1 until pivot.size) {
                     val bpI = bp.row(i)
@@ -225,7 +226,7 @@ fun <T : Any> LUPDecomposition<T>.solve(type: KClass<T>, matrix: Matrix<T>): Mat
     }
 }
 
-inline fun <reified T : Any> LUPDecomposition<T>.solve(matrix: Matrix<T>) = solve(T::class, matrix)
+inline fun <reified T : Any> LUPDecomposition<T>.solve(matrix: Matrix<T>): Matrix<T> = solve(T::class, matrix)
 
 /**
  * Solve a linear equation **a*x = b**
@@ -240,13 +241,12 @@ inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.
     return decomposition.solve(T::class, b)
 }
 
-fun RealMatrixContext.solve(a: Matrix<Double>, b: Matrix<Double>) =
-    solve(a, b) { it < 1e-11 }
+fun RealMatrixContext.solve(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> = solve(a, b) { it < 1e-11 }
 
 inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.inverse(
     matrix: Matrix<T>,
     noinline checkSingular: (T) -> Boolean
-) = solve(matrix, one(matrix.rowNum, matrix.colNum), checkSingular)
+): Matrix<T> = solve(matrix, one(matrix.rowNum, matrix.colNum), checkSingular)
 
-fun RealMatrixContext.inverse(matrix: Matrix<Double>) =
-    solve(matrix, one(matrix.rowNum, matrix.colNum)) { it < 1e-11 }
\ No newline at end of file
+fun RealMatrixContext.inverse(matrix: Matrix<Double>): Matrix<Double> =
+    solve(matrix, one(matrix.rowNum, matrix.colNum)) { it < 1e-11 }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgebra.kt
index abd8603f4..fb49d18ed 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgebra.kt
@@ -25,4 +25,4 @@ fun <T : Any> Matrix<T>.asPoint(): Point<T> =
         error("Can't convert matrix with more than one column to vector")
     }
 
-fun <T : Any> Point<T>.asMatrix() = VirtualMatrix(size, 1) { i, _ -> get(i) }
\ No newline at end of file
+fun <T : Any> Point<T>.asMatrix(): VirtualMatrix<T> = VirtualMatrix(size, 1) { i, _ -> get(i) }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixContext.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixContext.kt
index 7797fdadf..5dc86a7dd 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixContext.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixContext.kt
@@ -29,7 +29,7 @@ interface MatrixContext<T : Any> : SpaceOperations<Matrix<T>> {
         /**
          * Non-boxing double matrix
          */
-        val real = RealMatrixContext
+        val real: RealMatrixContext = RealMatrixContext
 
         /**
          * A structured matrix with custom buffer
@@ -82,12 +82,12 @@ interface GenericMatrixContext<T : Any, R : Ring<T>> : MatrixContext<T> {
         }
     }
 
-    override operator fun Matrix<T>.unaryMinus() =
+    override operator fun Matrix<T>.unaryMinus(): Matrix<T> =
         produce(rowNum, colNum) { i, j -> elementContext.run { -get(i, j) } }
 
     override fun add(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
         if (a.rowNum != b.rowNum || a.colNum != b.colNum) error("Matrix operation dimension mismatch. [${a.rowNum},${a.colNum}] + [${b.rowNum},${b.colNum}]")
-        return produce(a.rowNum, a.colNum) { i, j -> elementContext.run { a.get(i, j) + b[i, j] } }
+        return produce(a.rowNum, a.colNum) { i, j -> elementContext.run { a[i, j] + b[i, j] } }
     }
 
     override operator fun Matrix<T>.minus(b: Matrix<T>): Matrix<T> {
@@ -96,7 +96,7 @@ interface GenericMatrixContext<T : Any, R : Ring<T>> : MatrixContext<T> {
     }
 
     override fun multiply(a: Matrix<T>, k: Number): Matrix<T> =
-        produce(a.rowNum, a.colNum) { i, j -> elementContext.run { a.get(i, j) * k } }
+        produce(a.rowNum, a.colNum) { i, j -> elementContext.run { a[i, j] * k } }
 
     operator fun Number.times(matrix: FeaturedMatrix<T>): Matrix<T> = matrix * this
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixFeatures.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixFeatures.kt
index de315071f..87cfe21b0 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixFeatures.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixFeatures.kt
@@ -1,7 +1,7 @@
 package scientifik.kmath.linear
 
 /**
- * A marker interface representing some matrix feature like diagonal, sparce, zero, etc. Features used to optimize matrix
+ * A marker interface representing some matrix feature like diagonal, sparse, zero, etc. Features used to optimize matrix
  * operations performance in some cases.
  */
 interface MatrixFeature
@@ -36,19 +36,19 @@ interface DeterminantFeature<T : Any> : MatrixFeature {
 }
 
 @Suppress("FunctionName")
-fun <T: Any> DeterminantFeature(determinant: T) = object: DeterminantFeature<T>{
+fun <T : Any> DeterminantFeature(determinant: T): DeterminantFeature<T> = object : DeterminantFeature<T> {
     override val determinant: T = determinant
 }
 
 /**
  * Lower triangular matrix
  */
-object LFeature: MatrixFeature
+object LFeature : MatrixFeature
 
 /**
  * Upper triangular feature
  */
-object UFeature: MatrixFeature
+object UFeature : MatrixFeature
 
 /**
  * TODO add documentation
@@ -59,4 +59,4 @@ interface LUPDecompositionFeature<T : Any> : MatrixFeature {
     val p: FeaturedMatrix<T>
 }
 
-//TODO add sparse matrix feature
\ No newline at end of file
+//TODO add sparse matrix feature
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VectorSpace.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VectorSpace.kt
index 8e14e2882..691b464fc 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VectorSpace.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VectorSpace.kt
@@ -54,7 +54,7 @@ interface VectorSpace<T : Any, S : Space<T>> : Space<Point<T>> {
             size: Int,
             space: S,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing
-        ) = BufferVectorSpace(size, space, bufferFactory)
+        ): BufferVectorSpace<T, S> = BufferVectorSpace(size, space, bufferFactory)
 
         /**
          * Automatic buffered vector, unboxed if it is possible
@@ -70,6 +70,6 @@ class BufferVectorSpace<T : Any, S : Space<T>>(
     override val space: S,
     val bufferFactory: BufferFactory<T>
 ) : VectorSpace<T, S> {
-    override fun produce(initializer: (Int) -> T) = bufferFactory(size, initializer)
+    override fun produce(initializer: (Int) -> T): Buffer<T> = bufferFactory(size, initializer)
     //override fun produceElement(initializer: (Int) -> T): Vector<T, S> = BufferVector(this, produce(initializer))
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VirtualMatrix.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VirtualMatrix.kt
index 0806cabea..207151d57 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VirtualMatrix.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VirtualMatrix.kt
@@ -20,7 +20,7 @@ class VirtualMatrix<T : Any>(
 
     override fun get(i: Int, j: Int): T = generator(i, j)
 
-    override fun suggestFeature(vararg features: MatrixFeature) =
+    override fun suggestFeature(vararg features: MatrixFeature): VirtualMatrix<T> =
         VirtualMatrix(rowNum, colNum, this.features + features, generator)
 
     override fun equals(other: Any?): Boolean {
@@ -56,4 +56,4 @@ class VirtualMatrix<T : Any>(
             }
         }
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt
index 076701a4f..db8863ae8 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt
@@ -22,12 +22,12 @@ class DerivationResult<T : Any>(
     val deriv: Map<Variable<T>, T>,
     val context: Field<T>
 ) : Variable<T>(value) {
-    fun deriv(variable: Variable<T>) = deriv[variable] ?: context.zero
+    fun deriv(variable: Variable<T>): T = deriv[variable] ?: context.zero
 
     /**
      * compute divergence
      */
-    fun div() = context.run { sum(deriv.values) }
+    fun div(): T = context.run { sum(deriv.values) }
 
     /**
      * Compute a gradient for variables in given order
@@ -53,7 +53,7 @@ class DerivationResult<T : Any>(
  * ```
  */
 fun <T : Any, F : Field<T>> F.deriv(body: AutoDiffField<T, F>.() -> Variable<T>): DerivationResult<T> =
-    AutoDiffContext<T, F>(this).run {
+    AutoDiffContext(this).run {
         val result = body()
         result.d = context.one// computing derivative w.r.t result
         runBackwardPass()
@@ -86,7 +86,7 @@ abstract class AutoDiffField<T : Any, F : Field<T>> : Field<Variable<T>> {
 
     abstract fun variable(value: T): Variable<T>
 
-    inline fun variable(block: F.() -> T) = variable(context.block())
+    inline fun variable(block: F.() -> T): Variable<T> = variable(context.block())
 
     // Overloads for Double constants
 
@@ -236,4 +236,4 @@ fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sin(x: Variable<T>): Var
 fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cos(x: Variable<T>): Variable<T> =
     derive(variable { cos(x.value) }) { z ->
         x.d -= z.d * sin(x.value)
-    }
\ No newline at end of file
+    }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Grids.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Grids.kt
index f040fb8d4..d3bf0891f 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Grids.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Grids.kt
@@ -43,4 +43,4 @@ fun ClosedFloatingPointRange<Double>.toSequenceWithPoints(numPoints: Int): Seque
 fun ClosedFloatingPointRange<Double>.toGrid(numPoints: Int): DoubleArray {
     if (numPoints < 2) error("Can't create generic grid with less than two points")
     return DoubleArray(numPoints) { i -> start + (endInclusive - start) / (numPoints - 1) * i }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/cumulative.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/cumulative.kt
index c3cfc448a..a0f4525cc 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/cumulative.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/cumulative.kt
@@ -1,14 +1,15 @@
 package scientifik.kmath.misc
 
 import scientifik.kmath.operations.Space
+import scientifik.kmath.operations.invoke
 import kotlin.jvm.JvmName
 
-
 /**
- * Generic cumulative operation on iterator
- * @param T type of initial iterable
- * @param R type of resulting iterable
- * @param initial lazy evaluated
+ * Generic cumulative operation on iterator.
+ *
+ * @param T the type of initial iterable.
+ * @param R the type of resulting iterable.
+ * @param initial lazy evaluated.
  */
 fun <T, R> Iterator<T>.cumulative(initial: R, operation: (R, T) -> R): Iterator<R> = object : Iterator<R> {
     var state: R = initial
@@ -36,41 +37,41 @@ fun <T, R> List<T>.cumulative(initial: R, operation: (R, T) -> R): List<R> =
 /**
  * Cumulative sum with custom space
  */
-fun <T> Iterable<T>.cumulativeSum(space: Space<T>) = with(space) {
+fun <T> Iterable<T>.cumulativeSum(space: Space<T>): Iterable<T> = space {
     cumulative(zero) { element: T, sum: T -> sum + element }
 }
 
 @JvmName("cumulativeSumOfDouble")
-fun Iterable<Double>.cumulativeSum() = this.cumulative(0.0) { element, sum -> sum + element }
+fun Iterable<Double>.cumulativeSum(): Iterable<Double> = this.cumulative(0.0) { element, sum -> sum + element }
 
 @JvmName("cumulativeSumOfInt")
-fun Iterable<Int>.cumulativeSum() = this.cumulative(0) { element, sum -> sum + element }
+fun Iterable<Int>.cumulativeSum(): Iterable<Int> = this.cumulative(0) { element, sum -> sum + element }
 
 @JvmName("cumulativeSumOfLong")
-fun Iterable<Long>.cumulativeSum() = this.cumulative(0L) { element, sum -> sum + element }
+fun Iterable<Long>.cumulativeSum(): Iterable<Long> = this.cumulative(0L) { element, sum -> sum + element }
 
-fun <T> Sequence<T>.cumulativeSum(space: Space<T>) = with(space) {
+fun <T> Sequence<T>.cumulativeSum(space: Space<T>): Sequence<T> = with(space) {
     cumulative(zero) { element: T, sum: T -> sum + element }
 }
 
 @JvmName("cumulativeSumOfDouble")
-fun Sequence<Double>.cumulativeSum() = this.cumulative(0.0) { element, sum -> sum + element }
+fun Sequence<Double>.cumulativeSum(): Sequence<Double> = this.cumulative(0.0) { element, sum -> sum + element }
 
 @JvmName("cumulativeSumOfInt")
-fun Sequence<Int>.cumulativeSum() = this.cumulative(0) { element, sum -> sum + element }
+fun Sequence<Int>.cumulativeSum(): Sequence<Int> = this.cumulative(0) { element, sum -> sum + element }
 
 @JvmName("cumulativeSumOfLong")
-fun Sequence<Long>.cumulativeSum() = this.cumulative(0L) { element, sum -> sum + element }
+fun Sequence<Long>.cumulativeSum(): Sequence<Long> = this.cumulative(0L) { element, sum -> sum + element }
 
-fun <T> List<T>.cumulativeSum(space: Space<T>) = with(space) {
+fun <T> List<T>.cumulativeSum(space: Space<T>): List<T> = with(space) {
     cumulative(zero) { element: T, sum: T -> sum + element }
 }
 
 @JvmName("cumulativeSumOfDouble")
-fun List<Double>.cumulativeSum() = this.cumulative(0.0) { element, sum -> sum + element }
+fun List<Double>.cumulativeSum(): List<Double> = this.cumulative(0.0) { element, sum -> sum + element }
 
 @JvmName("cumulativeSumOfInt")
-fun List<Int>.cumulativeSum() = this.cumulative(0) { element, sum -> sum + element }
+fun List<Int>.cumulativeSum(): List<Int> = this.cumulative(0) { element, sum -> sum + element }
 
 @JvmName("cumulativeSumOfLong")
-fun List<Long>.cumulativeSum() = this.cumulative(0L) { element, sum -> sum + element }
\ No newline at end of file
+fun List<Long>.cumulativeSum(): List<Long> = this.cumulative(0L) { element, sum -> sum + element }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
index 52b6bba02..aa190b31f 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
@@ -1,10 +1,15 @@
 package scientifik.kmath.operations
 
+/**
+ * Stub for DSL the [Algebra] is.
+ */
 @DslMarker
 annotation class KMathContext
 
 /**
- * Marker interface for any algebra
+ * Represents an algebraic structure.
+ *
+ * @param T the type of element of this structure.
  */
 interface Algebra<T> {
     /**
@@ -24,50 +29,122 @@ interface Algebra<T> {
 }
 
 /**
- * An algebra with numeric representation of members
+ * An algebraic structure where elements can have numeric representation.
+ *
+ * @param T the type of element of this structure.
  */
 interface NumericAlgebra<T> : Algebra<T> {
     /**
-     * Wrap a number
+     * Wraps a number.
      */
     fun number(value: Number): T
 
+    /**
+     * Dynamic call of binary operation [operation] on [left] and [right] where left element is [Number].
+     */
     fun leftSideNumberOperation(operation: String, left: Number, right: T): T =
         binaryOperation(operation, number(left), right)
 
+    /**
+     * Dynamic call of binary operation [operation] on [left] and [right] where right element is [Number].
+     */
     fun rightSideNumberOperation(operation: String, left: T, right: Number): T =
         leftSideNumberOperation(operation, right, left)
 }
 
 /**
- * Call a block with an [Algebra] as receiver
+ * Call a block with an [Algebra] as receiver.
  */
 inline operator fun <A : Algebra<*>, R> A.invoke(block: A.() -> R): R = run(block)
 
 /**
- * Space-like operations without neutral element
+ * Represents semigroup, i.e. algebraic structure with associative binary operation called "addition".
+ *
+ * In KMath groups are called spaces, and also define multiplication of element by [Number].
+ *
+ * @param T the type of element of this semigroup.
  */
 interface SpaceOperations<T> : Algebra<T> {
     /**
-     * Addition operation for two context elements
+     * Addition of two elements.
+     *
+     * @param a the addend.
+     * @param b the augend.
+     * @return the sum.
      */
     fun add(a: T, b: T): T
 
     /**
-     * Multiplication operation for context element and real number
+     * Multiplication of element by scalar.
+     *
+     * @param a the multiplier.
+     * @param k the multiplicand.
+     * @return the produce.
      */
     fun multiply(a: T, k: Number): T
 
-    //Operation to be performed in this context. Could be moved to extensions in case of KEEP-176
+    // Operations to be performed in this context. Could be moved to extensions in case of KEEP-176
+
+    /**
+     * The negation of this element.
+     *
+     * @receiver this value.
+     * @return the additive inverse of this value.
+     */
     operator fun T.unaryMinus(): T = multiply(this, -1.0)
 
+    /**
+     * Returns this value.
+     *
+     * @receiver this value.
+     * @return this value.
+     */
     operator fun T.unaryPlus(): T = this
 
+    /**
+     * Addition of two elements.
+     *
+     * @receiver the addend.
+     * @param b the augend.
+     * @return the sum.
+     */
     operator fun T.plus(b: T): T = add(this, b)
+
+    /**
+     * Subtraction of two elements.
+     *
+     * @receiver the minuend.
+     * @param b the subtrahend.
+     * @return the difference.
+     */
     operator fun T.minus(b: T): T = add(this, -b)
-    operator fun T.times(k: Number) = multiply(this, k.toDouble())
-    operator fun T.div(k: Number) = multiply(this, 1.0 / k.toDouble())
-    operator fun Number.times(b: T) = b * this
+
+    /**
+     * Multiplication of this element by a scalar.
+     *
+     * @receiver the multiplier.
+     * @param k the multiplicand.
+     * @return the product.
+     */
+    operator fun T.times(k: Number): T = multiply(this, k.toDouble())
+
+    /**
+     * Division of this element by scalar.
+     *
+     * @receiver the dividend.
+     * @param k the divisor.
+     * @return the quotient.
+     */
+    operator fun T.div(k: Number): T = multiply(this, 1.0 / k.toDouble())
+
+    /**
+     * Multiplication of this number by element.
+     *
+     * @receiver the multiplier.
+     * @param b the multiplicand.
+     * @return the product.
+     */
+    operator fun Number.times(b: T): T = b * this
 
     override fun unaryOperation(operation: String, arg: T): T = when (operation) {
         PLUS_OPERATION -> arg
@@ -82,37 +159,56 @@ interface SpaceOperations<T> : Algebra<T> {
     }
 
     companion object {
-        const val PLUS_OPERATION = "+"
-        const val MINUS_OPERATION = "-"
-        const val NOT_OPERATION = "!"
+        /**
+         * The identifier of addition.
+         */
+        const val PLUS_OPERATION: String = "+"
+
+        /**
+         * The identifier of subtraction (and negation).
+         */
+        const val MINUS_OPERATION: String = "-"
+
+        const val NOT_OPERATION: String = "!"
     }
 }
 
-
 /**
- * A general interface representing linear context of some kind.
- * The context defines sum operation for its elements and multiplication by real value.
- * One must note that in some cases context is a singleton class, but in some cases it
- * works as a context for operations inside it.
+ * Represents group, i.e. algebraic structure with associative binary operation called "addition" and its neutral
+ * element.
  *
- * TODO do we need non-commutative context?
+ * In KMath groups are called spaces, and also define multiplication of element by [Number].
+ *
+ * @param T the type of element of this group.
  */
 interface Space<T> : SpaceOperations<T> {
     /**
-     * Neutral element for sum operation
+     * The neutral element of addition.
      */
     val zero: T
 }
 
 /**
- * Operations on ring without multiplication neutral element
+ * Represents semiring, i.e. algebraic structure with two associative binary operations called "addition" and
+ * "multiplication".
+ *
+ * @param T the type of element of this semiring.
  */
 interface RingOperations<T> : SpaceOperations<T> {
     /**
-     * Multiplication for two field elements
+     * Multiplies two elements.
+     *
+     * @param a the multiplier.
+     * @param b the multiplicand.
      */
     fun multiply(a: T, b: T): T
 
+    /**
+     * Multiplies this element by scalar.
+     *
+     * @receiver the multiplier.
+     * @param b the multiplicand.
+     */
     operator fun T.times(b: T): T = multiply(this, b)
 
     override fun binaryOperation(operation: String, left: T, right: T): T = when (operation) {
@@ -121,12 +217,18 @@ interface RingOperations<T> : SpaceOperations<T> {
     }
 
     companion object {
-        const val TIMES_OPERATION = "*"
+        /**
+         * The identifier of multiplication.
+         */
+        const val TIMES_OPERATION: String = "*"
     }
 }
 
 /**
- * The same as {@link Space} but with additional multiplication operation
+ * Represents ring, i.e. algebraic structure with two associative binary operations called "addition" and
+ * "multiplication" and their neutral elements.
+ *
+ * @param T the type of element of this ring.
  */
 interface Ring<T> : Space<T>, RingOperations<T>, NumericAlgebra<T> {
     /**
@@ -150,20 +252,64 @@ interface Ring<T> : Space<T>, RingOperations<T>, NumericAlgebra<T> {
         else -> super.rightSideNumberOperation(operation, left, right)
     }
 
+    /**
+     * Addition of element and scalar.
+     *
+     * @receiver the addend.
+     * @param b the augend.
+     */
+    operator fun T.plus(b: Number): T = this + number(b)
 
-    operator fun T.plus(b: Number) = this.plus(number(b))
-    operator fun Number.plus(b: T) = b + this
+    /**
+     * Addition of scalar and element.
+     *
+     * @receiver the addend.
+     * @param b the augend.
+     */
+    operator fun Number.plus(b: T): T = b + this
 
-    operator fun T.minus(b: Number) = this.minus(number(b))
-    operator fun Number.minus(b: T) = -b + this
+    /**
+     * Subtraction of element from number.
+     *
+     * @receiver the minuend.
+     * @param b the subtrahend.
+     * @receiver the difference.
+     */
+    operator fun T.minus(b: Number): T = this - number(b)
+
+    /**
+     * Subtraction of number from element.
+     *
+     * @receiver the minuend.
+     * @param b the subtrahend.
+     * @receiver the difference.
+     */
+    operator fun Number.minus(b: T): T = -b + this
 }
 
 /**
- * All ring operations but without neutral elements
+ * Represents semifield, i.e. algebraic structure with three operations: associative "addition" and "multiplication",
+ * and "division".
+ *
+ * @param T the type of element of this semifield.
  */
 interface FieldOperations<T> : RingOperations<T> {
+    /**
+     * Division of two elements.
+     *
+     * @param a the dividend.
+     * @param b the divisor.
+     * @return the quotient.
+     */
     fun divide(a: T, b: T): T
 
+    /**
+     * Division of two elements.
+     *
+     * @receiver the dividend.
+     * @param b the divisor.
+     * @return the quotient.
+     */
     operator fun T.div(b: T): T = divide(this, b)
 
     override fun binaryOperation(operation: String, left: T, right: T): T = when (operation) {
@@ -172,13 +318,26 @@ interface FieldOperations<T> : RingOperations<T> {
     }
 
     companion object {
-        const val DIV_OPERATION = "/"
+        /**
+         * The identifier of division.
+         */
+        const val DIV_OPERATION: String = "/"
     }
 }
 
 /**
- * Four operations algebra
+ * Represents field, i.e. algebraic structure with three operations: associative "addition" and "multiplication",
+ * and "division" and their neutral elements.
+ *
+ * @param T the type of element of this semifield.
  */
 interface Field<T> : Ring<T>, FieldOperations<T> {
-    operator fun Number.div(b: T) = this * divide(one, b)
+    /**
+     * Division of element by scalar.
+     *
+     * @receiver the dividend.
+     * @param b the divisor.
+     * @return the quotient.
+     */
+    operator fun Number.div(b: T): T = this * divide(one, b)
 }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
index 093021ae3..9b430af39 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
@@ -2,13 +2,12 @@ package scientifik.kmath.operations
 
 /**
  * The generic mathematics elements which is able to store its context
- * @param T the type of space operation results
- * @param I self type of the element. Needed for static type checking
- * @param C the type of mathematical context for this element
+ *
+ * @param C the type of mathematical context for this element.
  */
 interface MathElement<C> {
     /**
-     * The context this element belongs to
+     * The context this element belongs to.
      */
     val context: C
 }
@@ -25,18 +24,17 @@ interface MathWrapper<T, I> {
  * @param S the type of space
  */
 interface SpaceElement<T, I : SpaceElement<T, I, S>, S : Space<T>> : MathElement<S>, MathWrapper<T, I> {
-
-    operator fun plus(b: T) = context.add(unwrap(), b).wrap()
-    operator fun minus(b: T) = context.add(unwrap(), context.multiply(b, -1.0)).wrap()
-    operator fun times(k: Number) = context.multiply(unwrap(), k.toDouble()).wrap()
-    operator fun div(k: Number) = context.multiply(unwrap(), 1.0 / k.toDouble()).wrap()
+    operator fun plus(b: T): I = context.add(unwrap(), b).wrap()
+    operator fun minus(b: T): I = context.add(unwrap(), context.multiply(b, -1.0)).wrap()
+    operator fun times(k: Number): I = context.multiply(unwrap(), k.toDouble()).wrap()
+    operator fun div(k: Number): I = context.multiply(unwrap(), 1.0 / k.toDouble()).wrap()
 }
 
 /**
  * Ring element
  */
 interface RingElement<T, I : RingElement<T, I, R>, R : Ring<T>> : SpaceElement<T, I, R> {
-    operator fun times(b: T) = context.multiply(unwrap(), b).wrap()
+    operator fun times(b: T): I = context.multiply(unwrap(), b).wrap()
 }
 
 /**
@@ -44,5 +42,5 @@ interface RingElement<T, I : RingElement<T, I, R>, R : Ring<T>> : SpaceElement<T
  */
 interface FieldElement<T, I : FieldElement<T, I, F>, F : Field<T>> : RingElement<T, I, F> {
     override val context: F
-    operator fun div(b: T) = context.divide(unwrap(), b).wrap()
-}
\ No newline at end of file
+    operator fun div(b: T): I = context.divide(unwrap(), b).wrap()
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt
index bfb4199a3..a6d508ee4 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt
@@ -12,4 +12,4 @@ fun <T> RingOperations<T>.power(arg: T, power: Int): T {
         res *= arg
     }
     return res
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/BigInt.kt
index 5e7d49b1c..fd7719157 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/BigInt.kt
@@ -194,8 +194,8 @@ class BigInt internal constructor(
     }
 
     infix fun or(other: BigInt): BigInt {
-        if (this == ZERO) return other;
-        if (other == ZERO) return this;
+        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) {
@@ -210,7 +210,7 @@ class BigInt internal constructor(
     }
 
     infix fun and(other: BigInt): BigInt {
-        if ((this == ZERO) or (other == ZERO)) return ZERO;
+        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) {
@@ -260,7 +260,7 @@ class BigInt internal constructor(
     }
 
     companion object {
-        const val BASE = 0xffffffffUL
+        const val BASE: ULong = 0xffffffffUL
         const val BASE_SIZE: Int = 32
         val ZERO: BigInt = BigInt(0, uintArrayOf())
         val ONE: BigInt = BigInt(1, uintArrayOf(1u))
@@ -394,12 +394,12 @@ fun abs(x: BigInt): BigInt = x.abs()
 /**
  * Convert this [Int] to [BigInt]
  */
-fun Int.toBigInt() = BigInt(sign.toByte(), uintArrayOf(kotlin.math.abs(this).toUInt()))
+fun Int.toBigInt(): BigInt = BigInt(sign.toByte(), uintArrayOf(kotlin.math.abs(this).toUInt()))
 
 /**
  * Convert this [Long] to [BigInt]
  */
-fun Long.toBigInt() = BigInt(
+fun Long.toBigInt(): BigInt = BigInt(
     sign.toByte(), stripLeadingZeros(
         uintArrayOf(
             (kotlin.math.abs(this).toULong() and BASE).toUInt(),
@@ -411,17 +411,17 @@ fun Long.toBigInt() = BigInt(
 /**
  * Convert UInt to [BigInt]
  */
-fun UInt.toBigInt() = BigInt(1, uintArrayOf(this))
+fun UInt.toBigInt(): BigInt = BigInt(1, uintArrayOf(this))
 
 /**
  * Convert ULong to [BigInt]
  */
-fun ULong.toBigInt() = BigInt(
+fun ULong.toBigInt(): BigInt = BigInt(
     1,
     stripLeadingZeros(
         uintArrayOf(
-            (this and BigInt.BASE).toUInt(),
-            ((this shr BigInt.BASE_SIZE) and BigInt.BASE).toUInt()
+            (this and BASE).toUInt(),
+            ((this shr BASE_SIZE) and BASE).toUInt()
         )
     )
 )
@@ -434,7 +434,7 @@ fun UIntArray.toBigInt(sign: Byte): BigInt {
     return BigInt(sign, this.copyOf())
 }
 
-val hexChToInt = hashMapOf(
+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,
@@ -497,4 +497,4 @@ fun NDElement.Companion.bigInt(
     vararg shape: Int,
     initializer: BigIntField.(IntArray) -> BigInt
 ): BufferedNDRingElement<BigInt, BigIntField> =
-    NDAlgebra.bigInt(*shape).produce(initializer)
\ No newline at end of file
+    NDAlgebra.bigInt(*shape).produce(initializer)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt
index 398ea4395..ffd6c8dec 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt
@@ -18,7 +18,7 @@ object ComplexField : ExtendedField<Complex> {
 
     override val one: Complex = Complex(1.0, 0.0)
 
-    val i = Complex(0.0, 1.0)
+    val i: Complex = Complex(0.0, 1.0)
 
     override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
 
@@ -45,15 +45,15 @@ object ComplexField : ExtendedField<Complex> {
 
     override fun ln(arg: Complex): Complex = ln(arg.r) + i * atan2(arg.im, arg.re)
 
-    operator fun Double.plus(c: Complex) = add(this.toComplex(), c)
+    operator fun Double.plus(c: Complex): Complex = add(this.toComplex(), c)
 
-    operator fun Double.minus(c: Complex) = add(this.toComplex(), -c)
+    operator fun Double.minus(c: Complex): Complex = add(this.toComplex(), -c)
 
-    operator fun Complex.plus(d: Double) = d + this
+    operator fun Complex.plus(d: Double): Complex = d + this
 
-    operator fun Complex.minus(d: Double) = add(this, -d.toComplex())
+    operator fun Complex.minus(d: Double): Complex = add(this, -d.toComplex())
 
-    operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
+    operator fun Double.times(c: Complex): Complex = Complex(c.re * this, c.im * this)
 
     override fun symbol(value: String): Complex = if (value == "i") {
         i
@@ -104,7 +104,7 @@ val Complex.r: Double get() = sqrt(re * re + im * im)
  */
 val Complex.theta: Double get() = atan(im / re)
 
-fun Double.toComplex() = Complex(this, 0.0)
+fun Double.toComplex(): Complex = Complex(this, 0.0)
 
 inline fun Buffer.Companion.complex(size: Int, crossinline init: (Int) -> Complex): Buffer<Complex> {
     return MemoryBuffer.create(Complex, size, init)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt
index 2c57d0098..2145eb4b5 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt
@@ -1,6 +1,5 @@
 package scientifik.kmath.operations
 
-import scientifik.kmath.operations.RealField.pow
 import kotlin.math.abs
 import kotlin.math.pow as kpow
 
@@ -38,6 +37,8 @@ interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T> {
 /**
  * Real field element wrapping double.
  *
+ * @property value the [Double] value wrapped by this [Real].
+ *
  * TODO inline does not work due to compiler bug. Waiting for fix for KT-27586
  */
 inline class Real(val value: Double) : FieldElement<Double, Real, RealField> {
@@ -45,7 +46,7 @@ inline class Real(val value: Double) : FieldElement<Double, Real, RealField> {
 
     override fun Double.wrap(): Real = Real(value)
 
-    override val context get() = RealField
+    override val context: RealField get() = RealField
 
     companion object
 }
@@ -56,36 +57,36 @@ inline class Real(val value: Double) : FieldElement<Double, Real, RealField> {
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object RealField : ExtendedField<Double>, Norm<Double, Double> {
     override val zero: Double = 0.0
-    override inline fun add(a: Double, b: Double) = a + b
-    override inline fun multiply(a: Double, b: Double) = a * b
-    override inline fun multiply(a: Double, k: Number) = a * k.toDouble()
+    override inline fun add(a: Double, b: Double): Double = a + b
+    override inline fun multiply(a: Double, b: Double): Double = a * b
+    override inline fun multiply(a: Double, k: Number): Double = a * k.toDouble()
 
     override val one: Double = 1.0
-    override inline fun divide(a: Double, b: Double) = a / b
+    override inline fun divide(a: Double, b: Double): Double = a / b
 
-    override inline fun sin(arg: Double) = kotlin.math.sin(arg)
-    override inline fun cos(arg: Double) = kotlin.math.cos(arg)
+    override inline fun sin(arg: Double): Double = kotlin.math.sin(arg)
+    override inline fun cos(arg: Double): Double = kotlin.math.cos(arg)
     override inline fun tan(arg: Double): Double = kotlin.math.tan(arg)
     override inline fun acos(arg: Double): Double = kotlin.math.acos(arg)
     override inline fun asin(arg: Double): Double = kotlin.math.asin(arg)
     override inline fun atan(arg: Double): Double = kotlin.math.atan(arg)
 
-    override inline fun power(arg: Double, pow: Number) = arg.kpow(pow.toDouble())
+    override inline fun power(arg: Double, pow: Number): Double = arg.kpow(pow.toDouble())
 
-    override inline fun exp(arg: Double) = kotlin.math.exp(arg)
-    override inline fun ln(arg: Double) = kotlin.math.ln(arg)
+    override inline fun exp(arg: Double): Double = kotlin.math.exp(arg)
+    override inline fun ln(arg: Double): Double = kotlin.math.ln(arg)
 
-    override inline fun norm(arg: Double) = abs(arg)
+    override inline fun norm(arg: Double): Double = abs(arg)
 
-    override inline fun Double.unaryMinus() = -this
+    override inline fun Double.unaryMinus(): Double = -this
 
-    override inline fun Double.plus(b: Double) = this + b
+    override inline fun Double.plus(b: Double): Double = this + b
 
-    override inline fun Double.minus(b: Double) = this - b
+    override inline fun Double.minus(b: Double): Double = this - b
 
-    override inline fun Double.times(b: Double) = this * b
+    override inline fun Double.times(b: Double): Double = this * b
 
-    override inline fun Double.div(b: Double) = this / b
+    override inline fun Double.div(b: Double): Double = this / b
 
     override fun binaryOperation(operation: String, left: Double, right: Double): Double = when (operation) {
         PowerOperations.POW_OPERATION -> left pow right
@@ -96,36 +97,36 @@ object RealField : ExtendedField<Double>, Norm<Double, Double> {
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object FloatField : ExtendedField<Float>, Norm<Float, Float> {
     override val zero: Float = 0f
-    override inline fun add(a: Float, b: Float) = a + b
-    override inline fun multiply(a: Float, b: Float) = a * b
-    override inline fun multiply(a: Float, k: Number) = a * k.toFloat()
+    override inline fun add(a: Float, b: Float): Float = a + b
+    override inline fun multiply(a: Float, b: Float): Float = a * b
+    override inline fun multiply(a: Float, k: Number): Float = a * k.toFloat()
 
     override val one: Float = 1f
-    override inline fun divide(a: Float, b: Float) = a / b
+    override inline fun divide(a: Float, b: Float): Float = a / b
 
-    override inline fun sin(arg: Float) = kotlin.math.sin(arg)
-    override inline fun cos(arg: Float) = kotlin.math.cos(arg)
-    override inline fun tan(arg: Float) = kotlin.math.tan(arg)
-    override inline fun acos(arg: Float) = kotlin.math.acos(arg)
-    override inline fun asin(arg: Float) = kotlin.math.asin(arg)
-    override inline fun atan(arg: Float) = kotlin.math.atan(arg)
+    override inline fun sin(arg: Float): Float = kotlin.math.sin(arg)
+    override inline fun cos(arg: Float): Float = kotlin.math.cos(arg)
+    override inline fun tan(arg: Float): Float = kotlin.math.tan(arg)
+    override inline fun acos(arg: Float): Float = kotlin.math.acos(arg)
+    override inline fun asin(arg: Float): Float = kotlin.math.asin(arg)
+    override inline fun atan(arg: Float): Float = kotlin.math.atan(arg)
 
-    override inline fun power(arg: Float, pow: Number) = arg.pow(pow.toFloat())
+    override inline fun power(arg: Float, pow: Number): Float = arg.pow(pow.toFloat())
 
-    override inline fun exp(arg: Float) = kotlin.math.exp(arg)
-    override inline fun ln(arg: Float) = kotlin.math.ln(arg)
+    override inline fun exp(arg: Float): Float = kotlin.math.exp(arg)
+    override inline fun ln(arg: Float): Float = kotlin.math.ln(arg)
 
-    override inline fun norm(arg: Float) = abs(arg)
+    override inline fun norm(arg: Float): Float = abs(arg)
 
-    override inline fun Float.unaryMinus() = -this
+    override inline fun Float.unaryMinus(): Float = -this
 
-    override inline fun Float.plus(b: Float) = this + b
+    override inline fun Float.plus(b: Float): Float = this + b
 
-    override inline fun Float.minus(b: Float) = this - b
+    override inline fun Float.minus(b: Float): Float = this - b
 
-    override inline fun Float.times(b: Float) = this * b
+    override inline fun Float.times(b: Float): Float = this * b
 
-    override inline fun Float.div(b: Float) = this / b
+    override inline fun Float.div(b: Float): Float = this / b
 }
 
 /**
@@ -134,14 +135,14 @@ object FloatField : ExtendedField<Float>, Norm<Float, Float> {
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object IntRing : Ring<Int>, Norm<Int, Int> {
     override val zero: Int = 0
-    override inline fun add(a: Int, b: Int) = a + b
-    override inline fun multiply(a: Int, b: Int) = a * b
-    override inline fun multiply(a: Int, k: Number) = k.toInt() * a
+    override inline fun add(a: Int, b: Int): Int = a + b
+    override inline fun multiply(a: Int, b: Int): Int = a * b
+    override inline fun multiply(a: Int, k: Number): Int = k.toInt() * a
     override val one: Int = 1
 
-    override inline fun norm(arg: Int) = abs(arg)
+    override inline fun norm(arg: Int): Int = abs(arg)
 
-    override inline fun Int.unaryMinus() = -this
+    override inline fun Int.unaryMinus(): Int = -this
 
     override inline fun Int.plus(b: Int): Int = this + b
 
@@ -156,20 +157,20 @@ object IntRing : Ring<Int>, Norm<Int, Int> {
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object ShortRing : Ring<Short>, Norm<Short, Short> {
     override val zero: Short = 0
-    override inline fun add(a: Short, b: Short) = (a + b).toShort()
-    override inline fun multiply(a: Short, b: Short) = (a * b).toShort()
-    override inline fun multiply(a: Short, k: Number) = (a * k.toShort()).toShort()
+    override inline fun add(a: Short, b: Short): Short = (a + b).toShort()
+    override inline fun multiply(a: Short, b: Short): Short = (a * b).toShort()
+    override inline fun multiply(a: Short, k: Number): Short = (a * k.toShort()).toShort()
     override val one: Short = 1
 
     override fun norm(arg: Short): Short = if (arg > 0) arg else (-arg).toShort()
 
-    override inline fun Short.unaryMinus() = (-this).toShort()
+    override inline fun Short.unaryMinus(): Short = (-this).toShort()
 
-    override inline fun Short.plus(b: Short) = (this + b).toShort()
+    override inline fun Short.plus(b: Short): Short = (this + b).toShort()
 
-    override inline fun Short.minus(b: Short) = (this - b).toShort()
+    override inline fun Short.minus(b: Short): Short = (this - b).toShort()
 
-    override inline fun Short.times(b: Short) = (this * b).toShort()
+    override inline fun Short.times(b: Short): Short = (this * b).toShort()
 }
 
 /**
@@ -178,20 +179,20 @@ object ShortRing : Ring<Short>, Norm<Short, Short> {
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object ByteRing : Ring<Byte>, Norm<Byte, Byte> {
     override val zero: Byte = 0
-    override inline fun add(a: Byte, b: Byte) = (a + b).toByte()
-    override inline fun multiply(a: Byte, b: Byte) = (a * b).toByte()
-    override inline fun multiply(a: Byte, k: Number) = (a * k.toByte()).toByte()
+    override inline fun add(a: Byte, b: Byte): Byte = (a + b).toByte()
+    override inline fun multiply(a: Byte, b: Byte): Byte = (a * b).toByte()
+    override inline fun multiply(a: Byte, k: Number): Byte = (a * k.toByte()).toByte()
     override val one: Byte = 1
 
     override fun norm(arg: Byte): Byte = if (arg > 0) arg else (-arg).toByte()
 
-    override inline fun Byte.unaryMinus() = (-this).toByte()
+    override inline fun Byte.unaryMinus(): Byte = (-this).toByte()
 
-    override inline fun Byte.plus(b: Byte) = (this + b).toByte()
+    override inline fun Byte.plus(b: Byte): Byte = (this + b).toByte()
 
-    override inline fun Byte.minus(b: Byte) = (this - b).toByte()
+    override inline fun Byte.minus(b: Byte): Byte = (this - b).toByte()
 
-    override inline fun Byte.times(b: Byte) = (this * b).toByte()
+    override inline fun Byte.times(b: Byte): Byte = (this * b).toByte()
 }
 
 /**
@@ -200,18 +201,18 @@ object ByteRing : Ring<Byte>, Norm<Byte, Byte> {
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object LongRing : Ring<Long>, Norm<Long, Long> {
     override val zero: Long = 0
-    override inline fun add(a: Long, b: Long) = (a + b)
-    override inline fun multiply(a: Long, b: Long) = (a * b)
-    override inline fun multiply(a: Long, k: Number) = a * k.toLong()
+    override inline fun add(a: Long, b: Long): Long = (a + b)
+    override inline fun multiply(a: Long, b: Long): Long = (a * b)
+    override inline fun multiply(a: Long, k: Number): Long = a * k.toLong()
     override val one: Long = 1
 
     override fun norm(arg: Long): Long = abs(arg)
 
-    override inline fun Long.unaryMinus() = (-this)
+    override inline fun Long.unaryMinus(): Long = (-this)
 
-    override inline fun Long.plus(b: Long) = (this + b)
+    override inline fun Long.plus(b: Long): Long = (this + b)
 
-    override inline fun Long.minus(b: Long) = (this - b)
+    override inline fun Long.minus(b: Long): Long = (this - b)
 
-    override inline fun Long.times(b: Long) = (this * b)
+    override inline fun Long.times(b: Long): Long = (this * b)
 }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt
index 709f0260f..75adb1dee 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt
@@ -1,84 +1,210 @@
 package scientifik.kmath.operations
 
-
-/* Trigonometric operations */
-
 /**
- * A container for trigonometric operations for specific type. Trigonometric operations are limited to fields.
+ * A container for trigonometric operations for specific type. They are limited to semifields.
  *
  * The operations are not exposed to class directly to avoid method bloat but instead are declared in the field.
- * It also allows to override behavior for optional operations
- *
+ * It also allows to override behavior for optional operations.
  */
 interface TrigonometricOperations<T> : FieldOperations<T> {
+    /**
+     * Computes the sine of [arg].
+     */
     fun sin(arg: T): T
+
+    /**
+     * Computes the cosine of [arg].
+     */
     fun cos(arg: T): T
+
+    /**
+     * Computes the tangent of [arg].
+     */
     fun tan(arg: T): T
 
     companion object {
-        const val SIN_OPERATION = "sin"
-        const val COS_OPERATION = "cos"
-        const val TAN_OPERATION = "tan"
+        /**
+         * The identifier of sine.
+         */
+        const val SIN_OPERATION: String = "sin"
+
+        /**
+         * The identifier of cosine.
+         */
+        const val COS_OPERATION: String = "cos"
+
+        /**
+         * The identifier of tangent.
+         */
+        const val TAN_OPERATION: String = "tan"
     }
 }
 
+/**
+ * A container for inverse trigonometric operations for specific type. They are limited to semifields.
+ *
+ * The operations are not exposed to class directly to avoid method bloat but instead are declared in the field.
+ * It also allows to override behavior for optional operations.
+ */
 interface InverseTrigonometricOperations<T> : TrigonometricOperations<T> {
+    /**
+     * Computes the inverse sine of [arg].
+     */
     fun asin(arg: T): T
+
+    /**
+     * Computes the inverse cosine of [arg].
+     */
     fun acos(arg: T): T
+
+    /**
+     * Computes the inverse tangent of [arg].
+     */
     fun atan(arg: T): T
 
     companion object {
-        const val ASIN_OPERATION = "asin"
-        const val ACOS_OPERATION = "acos"
-        const val ATAN_OPERATION = "atan"
+        /**
+         * The identifier of inverse sine.
+         */
+        const val ASIN_OPERATION: String = "asin"
+
+        /**
+         * The identifier of inverse cosine.
+         */
+        const val ACOS_OPERATION: String = "acos"
+
+        /**
+         * The identifier of inverse tangent.
+         */
+        const val ATAN_OPERATION: String = "atan"
     }
 }
 
-fun <T : MathElement<out TrigonometricOperations<T>>> sin(arg: T): T = arg.context.sin(arg)
-fun <T : MathElement<out TrigonometricOperations<T>>> cos(arg: T): T = arg.context.cos(arg)
-fun <T : MathElement<out TrigonometricOperations<T>>> tan(arg: T): T = arg.context.tan(arg)
-fun <T : MathElement<out InverseTrigonometricOperations<T>>> asin(arg: T): T = arg.context.asin(arg)
-fun <T : MathElement<out InverseTrigonometricOperations<T>>> acos(arg: T): T = arg.context.acos(arg)
-fun <T : MathElement<out InverseTrigonometricOperations<T>>> atan(arg: T): T = arg.context.atan(arg)
-
-/* Power and roots */
-
 /**
- * A context extension to include power operations like square roots, etc
+ * Computes the sine of [arg].
+ */
+fun <T : MathElement<out TrigonometricOperations<T>>> sin(arg: T): T = arg.context.sin(arg)
+
+/**
+ * Computes the cosine of [arg].
+ */
+fun <T : MathElement<out TrigonometricOperations<T>>> cos(arg: T): T = arg.context.cos(arg)
+
+/**
+ * Computes the tangent of [arg].
+ */
+fun <T : MathElement<out TrigonometricOperations<T>>> tan(arg: T): T = arg.context.tan(arg)
+
+/**
+ * Computes the inverse sine of [arg].
+ */
+fun <T : MathElement<out InverseTrigonometricOperations<T>>> asin(arg: T): T = arg.context.asin(arg)
+
+/**
+ * Computes the inverse cosine of [arg].
+ */
+fun <T : MathElement<out InverseTrigonometricOperations<T>>> acos(arg: T): T = arg.context.acos(arg)
+
+/**
+ * Computes the inverse tangent of [arg].
+ */
+fun <T : MathElement<out InverseTrigonometricOperations<T>>> atan(arg: T): T = arg.context.atan(arg)
+
+/**
+ * A context extension to include power operations based on exponentiation.
  */
 interface PowerOperations<T> : Algebra<T> {
+    /**
+     * Raises [arg] to the power [pow].
+     */
     fun power(arg: T, pow: Number): T
-    fun sqrt(arg: T) = power(arg, 0.5)
 
-    infix fun T.pow(pow: Number) = power(this, pow)
+    /**
+     * Computes the square root of the value [arg].
+     */
+    fun sqrt(arg: T): T = power(arg, 0.5)
+
+    /**
+     * Raises this value to the power [pow].
+     */
+    infix fun T.pow(pow: Number): T = power(this, pow)
 
     companion object {
-        const val POW_OPERATION = "pow"
-        const val SQRT_OPERATION = "sqrt"
+        /**
+         * The identifier of exponentiation.
+         */
+        const val POW_OPERATION: String = "pow"
+
+        /**
+         * The identifier of square root.
+         */
+        const val SQRT_OPERATION: String = "sqrt"
     }
 }
 
+/**
+ * Raises [arg] to the power [pow].
+ */
 infix fun <T : MathElement<out PowerOperations<T>>> T.pow(power: Double): T = context.power(this, power)
+
+/**
+ * Computes the square root of the value [arg].
+ */
 fun <T : MathElement<out PowerOperations<T>>> sqrt(arg: T): T = arg pow 0.5
+
+/**
+ * Computes the square of the value [arg].
+ */
 fun <T : MathElement<out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
 
-/* Exponential */
-
+/**
+ * A container for operations related to `exp` and `ln` functions.
+ */
 interface ExponentialOperations<T> : Algebra<T> {
+    /**
+     * Computes Euler's number `e` raised to the power of the value [arg].
+     */
     fun exp(arg: T): T
+
+    /**
+     * Computes the natural logarithm (base `e`) of the value [arg].
+     */
     fun ln(arg: T): T
 
     companion object {
-        const val EXP_OPERATION = "exp"
-        const val LN_OPERATION = "ln"
+        /**
+         * The identifier of exponential function.
+         */
+        const val EXP_OPERATION: String = "exp"
+
+        /**
+         * The identifier of natural logarithm.
+         */
+        const val LN_OPERATION: String = "ln"
     }
 }
 
+/**
+ * The identifier of exponential function.
+ */
 fun <T : MathElement<out ExponentialOperations<T>>> exp(arg: T): T = arg.context.exp(arg)
+
+/**
+ * The identifier of natural logarithm.
+ */
 fun <T : MathElement<out ExponentialOperations<T>>> ln(arg: T): T = arg.context.ln(arg)
 
+/**
+ * A container for norm functional on element.
+ */
 interface Norm<in T : Any, out R> {
+    /**
+     * Computes the norm of [arg] (i.e. absolute value or vector length).
+     */
     fun norm(arg: T): R
 }
 
+/**
+ * Computes the norm of [arg] (i.e. absolute value or vector length).
+ */
 fun <T : MathElement<out Norm<T, R>>, R> norm(arg: T): R = arg.context.norm(arg)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDField.kt
index e6d4b226d..516f9a8cd 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDField.kt
@@ -19,10 +19,10 @@ class BoxingNDField<T, F : Field<T>>(
         if (!elements.all { it.strides == this.strides }) error("Element strides are not the same as context strides")
     }
 
-    override val zero by lazy { produce { zero } }
-    override val one by lazy { produce { one } }
+    override val zero: BufferedNDFieldElement<T, F> by lazy { produce { zero } }
+    override val one: BufferedNDFieldElement<T, F> by lazy { produce { one } }
 
-    override fun produce(initializer: F.(IntArray) -> T) =
+    override fun produce(initializer: F.(IntArray) -> T): BufferedNDFieldElement<T, F> =
         BufferedNDFieldElement(
             this,
             buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) })
@@ -79,4 +79,4 @@ inline fun <T : Any, F : Field<T>, R> F.nd(
 ): R {
     val ndfield: BoxingNDField<T, F> = NDField.boxing(this, *shape, bufferFactory = bufferFactory)
     return ndfield.action()
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDRing.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDRing.kt
index 39fc555e8..f7be95736 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDRing.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDRing.kt
@@ -18,10 +18,10 @@ class BoxingNDRing<T, R : Ring<T>>(
         if (!elements.all { it.strides == this.strides }) error("Element strides are not the same as context strides")
     }
 
-    override val zero by lazy { produce { zero } }
-    override val one by lazy { produce { one } }
+    override val zero: BufferedNDRingElement<T, R> by lazy { produce { zero } }
+    override val one: BufferedNDRingElement<T, R> by lazy { produce { one } }
 
-    override fun produce(initializer: R.(IntArray) -> T) =
+    override fun produce(initializer: R.(IntArray) -> T): BufferedNDRingElement<T, R> =
         BufferedNDRingElement(
             this,
             buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) })
@@ -69,4 +69,4 @@ class BoxingNDRing<T, R : Ring<T>>(
 
     override fun NDBuffer<T>.toElement(): RingElement<NDBuffer<T>, *, out BufferedNDRing<T, R>> =
         BufferedNDRingElement(this@BoxingNDRing, buffer)
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferAccessor2D.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferAccessor2D.kt
index b14da5d99..00832b69c 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferAccessor2D.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferAccessor2D.kt
@@ -7,16 +7,16 @@ import kotlin.reflect.KClass
  */
 class BufferAccessor2D<T : Any>(val type: KClass<T>, val rowNum: Int, val colNum: Int) {
 
-    operator fun Buffer<T>.get(i: Int, j: Int) = get(i + colNum * j)
+    operator fun Buffer<T>.get(i: Int, j: Int): T = get(i + colNum * j)
 
     operator fun MutableBuffer<T>.set(i: Int, j: Int, value: T) {
         set(i + colNum * j, value)
     }
 
-    inline fun create(init: (i: Int, j: Int) -> T) =
+    inline fun create(init: (i: Int, j: Int) -> T): MutableBuffer<T> =
         MutableBuffer.auto(type, rowNum * colNum) { offset -> init(offset / colNum, offset % colNum) }
 
-    fun create(mat: Structure2D<T>) = create { i, j -> mat[i, j] }
+    fun create(mat: Structure2D<T>): MutableBuffer<T> = create { i, j -> mat[i, j] }
 
     //TODO optimize wrapper
     fun MutableBuffer<T>.collect(): Structure2D<T> =
@@ -41,5 +41,5 @@ class BufferAccessor2D<T : Any>(val type: KClass<T>, val rowNum: Int, val colNum
     /**
      * Get row
      */
-    fun MutableBuffer<T>.row(i: Int) = Row(this, i)
+    fun MutableBuffer<T>.row(i: Int): Row = Row(this, i)
 }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDAlgebra.kt
index 9742f3662..baf1a05a6 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDAlgebra.kt
@@ -2,7 +2,7 @@ package scientifik.kmath.structures
 
 import scientifik.kmath.operations.*
 
-interface BufferedNDAlgebra<T, C>: NDAlgebra<T, C, NDBuffer<T>>{
+interface BufferedNDAlgebra<T, C> : NDAlgebra<T, C, NDBuffer<T>> {
     val strides: Strides
 
     override fun check(vararg elements: NDBuffer<T>) {
@@ -30,7 +30,7 @@ interface BufferedNDAlgebra<T, C>: NDAlgebra<T, C, NDBuffer<T>>{
 }
 
 
-interface BufferedNDSpace<T, S : Space<T>> : NDSpace<T, S, NDBuffer<T>>, BufferedNDAlgebra<T,S>  {
+interface BufferedNDSpace<T, S : Space<T>> : NDSpace<T, S, NDBuffer<T>>, BufferedNDAlgebra<T, S> {
     override fun NDBuffer<T>.toElement(): SpaceElement<NDBuffer<T>, *, out BufferedNDSpace<T, S>>
 }
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDElement.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDElement.kt
index be80f66bf..d1d622b23 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDElement.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDElement.kt
@@ -8,7 +8,7 @@ import scientifik.kmath.operations.*
 abstract class BufferedNDElement<T, C> : NDBuffer<T>(), NDElement<T, C, NDBuffer<T>> {
     abstract override val context: BufferedNDAlgebra<T, C>
 
-    override val strides get() = context.strides
+    override val strides: Strides get() = context.strides
 
     override val shape: IntArray get() = context.shape
 }
@@ -54,9 +54,9 @@ class BufferedNDFieldElement<T, F : Field<T>>(
 
 
 /**
- * Element by element application of any operation on elements to the whole array. Just like in numpy
+ * Element by element application of any operation on elements to the whole array. Just like in numpy.
  */
-operator fun <T : Any, F : Field<T>> Function1<T, T>.invoke(ndElement: BufferedNDElement<T, F>) =
+operator fun <T : Any, F : Field<T>> Function1<T, T>.invoke(ndElement: BufferedNDElement<T, F>): MathElement<out BufferedNDAlgebra<T, F>> =
     ndElement.context.run { map(ndElement) { invoke(it) }.toElement() }
 
 /* plus and minus */
@@ -64,13 +64,13 @@ operator fun <T : Any, F : Field<T>> Function1<T, T>.invoke(ndElement: BufferedN
 /**
  * Summation operation for [BufferedNDElement] and single element
  */
-operator fun <T : Any, F : Space<T>> BufferedNDElement<T, F>.plus(arg: T) =
+operator fun <T : Any, F : Space<T>> BufferedNDElement<T, F>.plus(arg: T): NDElement<T, F, NDBuffer<T>> =
     context.map(this) { it + arg }.wrap()
 
 /**
  * Subtraction operation between [BufferedNDElement] and single element
  */
-operator fun <T : Any, F : Space<T>> BufferedNDElement<T, F>.minus(arg: T) =
+operator fun <T : Any, F : Space<T>> BufferedNDElement<T, F>.minus(arg: T): NDElement<T, F, NDBuffer<T>> =
     context.map(this) { it - arg }.wrap()
 
 /* prod and div */
@@ -78,11 +78,11 @@ operator fun <T : Any, F : Space<T>> BufferedNDElement<T, F>.minus(arg: T) =
 /**
  * Product operation for [BufferedNDElement] and single element
  */
-operator fun <T : Any, F : Ring<T>> BufferedNDElement<T, F>.times(arg: T) =
+operator fun <T : Any, F : Ring<T>> BufferedNDElement<T, F>.times(arg: T): NDElement<T, F, NDBuffer<T>> =
     context.map(this) { it * arg }.wrap()
 
 /**
  * Division operation between [BufferedNDElement] and single element
  */
-operator fun <T : Any, F : Field<T>> BufferedNDElement<T, F>.div(arg: T) =
-    context.map(this) { it / arg }.wrap()
\ No newline at end of file
+operator fun <T : Any, F : Field<T>> BufferedNDElement<T, F>.div(arg: T): NDElement<T, F, NDBuffer<T>> =
+    context.map(this) { it / arg }.wrap()
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
index 5789de9ee..723348e3f 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
@@ -15,22 +15,22 @@ typealias MutableBufferFactory<T> = (Int, (Int) -> T) -> MutableBuffer<T>
 interface Buffer<T> {
 
     /**
-     * The size of the buffer
+     * The size of this buffer.
      */
     val size: Int
 
     /**
-     * Get element at given index
+     * Gets element at given index.
      */
     operator fun get(index: Int): T
 
     /**
-     * Iterate over all elements
+     * Iterates over all elements.
      */
     operator fun iterator(): Iterator<T>
 
     /**
-     * Check content eqiality with another buffer
+     * Checks content equality with another buffer.
      */
     fun contentEquals(other: Buffer<*>): Boolean =
         asSequence().mapIndexed { index, value -> value == other[index] }.all { it }
@@ -124,10 +124,9 @@ inline class ListBuffer<T>(val list: List<T>) : Buffer<T> {
     override fun iterator(): Iterator<T> = list.iterator()
 }
 
-fun <T> List<T>.asBuffer() = ListBuffer<T>(this)
+fun <T> List<T>.asBuffer(): ListBuffer<T> = ListBuffer(this)
 
-@Suppress("FunctionName")
-inline fun <T> ListBuffer(size: Int, init: (Int) -> T) = List(size, init).asBuffer()
+inline fun <T> ListBuffer(size: Int, init: (Int) -> T): ListBuffer<T> = List(size, init).asBuffer()
 
 inline class MutableListBuffer<T>(val list: MutableList<T>) : MutableBuffer<T> {
 
@@ -165,13 +164,13 @@ fun <T> Array<T>.asBuffer(): ArrayBuffer<T> = ArrayBuffer(this)
 inline class ReadOnlyBuffer<T>(val buffer: MutableBuffer<T>) : Buffer<T> {
     override val size: Int get() = buffer.size
 
-    override fun get(index: Int): T = buffer.get(index)
+    override fun get(index: Int): T = buffer[index]
 
-    override fun iterator() = buffer.iterator()
+    override fun iterator(): Iterator<T> = buffer.iterator()
 }
 
 /**
- * A buffer with content calculated on-demand. The calculated contect is not stored, so it is recalculated on each call.
+ * A buffer with content calculated on-demand. The calculated content is not stored, so it is recalculated on each call.
  * Useful when one needs single element from the buffer.
  */
 class VirtualBuffer<T>(override val size: Int, private val generator: (Int) -> T) : Buffer<T> {
@@ -205,4 +204,4 @@ fun <T> Buffer<T>.asReadOnly(): Buffer<T> = if (this is MutableBuffer) {
  */
 typealias BufferTransform<T, R> = (Buffer<T>) -> Buffer<R>
 
-typealias SuspendBufferTransform<T, R> = suspend (Buffer<T>) -> Buffer<R>
\ No newline at end of file
+typealias SuspendBufferTransform<T, R> = suspend (Buffer<T>) -> Buffer<R>
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ComplexNDField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ComplexNDField.kt
index c7e672c28..2f7d20b6d 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ComplexNDField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ComplexNDField.kt
@@ -17,8 +17,8 @@ class ComplexNDField(override val shape: IntArray) :
     override val strides: Strides = DefaultStrides(shape)
 
     override val elementContext: ComplexField get() = ComplexField
-    override val zero by lazy { produce { zero } }
-    override val one by lazy { produce { one } }
+    override val zero: ComplexNDElement by lazy { produce { zero } }
+    override val one: ComplexNDElement by lazy { produce { one } }
 
     inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Complex): Buffer<Complex> =
         Buffer.complex(size) { initializer(it) }
@@ -69,23 +69,23 @@ class ComplexNDField(override val shape: IntArray) :
     override fun NDBuffer<Complex>.toElement(): FieldElement<NDBuffer<Complex>, *, out BufferedNDField<Complex, ComplexField>> =
         BufferedNDFieldElement(this@ComplexNDField, buffer)
 
-    override fun power(arg: NDBuffer<Complex>, pow: Number) = map(arg) { power(it, pow) }
+    override fun power(arg: NDBuffer<Complex>, pow: Number): ComplexNDElement = map(arg) { power(it, pow) }
 
-    override fun exp(arg: NDBuffer<Complex>) = map(arg) { exp(it) }
+    override fun exp(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { exp(it) }
 
-    override fun ln(arg: NDBuffer<Complex>) = map(arg) { ln(it) }
+    override fun ln(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { ln(it) }
 
-    override fun sin(arg: NDBuffer<Complex>) = map(arg) { sin(it) }
+    override fun sin(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { sin(it) }
 
-    override fun cos(arg: NDBuffer<Complex>) = map(arg) { cos(it) }
+    override fun cos(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { cos(it) }
 
-    override fun tan(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) { tan(it) }
+    override fun tan(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { tan(it) }
 
-    override fun asin(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) { asin(it) }
+    override fun asin(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { asin(it) }
 
-    override fun acos(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) {acos(it)}
+    override fun acos(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { acos(it) }
 
-    override fun atan(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) {atan(it)}
+    override fun atan(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { atan(it) }
 }
 
 
@@ -100,7 +100,7 @@ inline fun BufferedNDField<Complex, ComplexField>.produceInline(crossinline init
 /**
  * Map one [ComplexNDElement] using function with indexes
  */
-inline fun ComplexNDElement.mapIndexed(crossinline transform: ComplexField.(index: IntArray, Complex) -> Complex) =
+inline fun ComplexNDElement.mapIndexed(crossinline transform: ComplexField.(index: IntArray, Complex) -> Complex): ComplexNDElement =
     context.produceInline { offset -> transform(strides.index(offset), buffer[offset]) }
 
 /**
@@ -114,7 +114,7 @@ inline fun ComplexNDElement.map(crossinline transform: ComplexField.(Complex) ->
 /**
  * Element by element application of any operation on elements to the whole array. Just like in numpy
  */
-operator fun Function1<Complex, Complex>.invoke(ndElement: ComplexNDElement) =
+operator fun Function1<Complex, Complex>.invoke(ndElement: ComplexNDElement): ComplexNDElement =
     ndElement.map { this@invoke(it) }
 
 
@@ -123,19 +123,18 @@ operator fun Function1<Complex, Complex>.invoke(ndElement: ComplexNDElement) =
 /**
  * Summation operation for [BufferedNDElement] and single element
  */
-operator fun ComplexNDElement.plus(arg: Complex) =
-    map { it + arg }
+operator fun ComplexNDElement.plus(arg: Complex): ComplexNDElement = map { it + arg }
 
 /**
  * Subtraction operation between [BufferedNDElement] and single element
  */
-operator fun ComplexNDElement.minus(arg: Complex) =
+operator fun ComplexNDElement.minus(arg: Complex): ComplexNDElement =
     map { it - arg }
 
-operator fun ComplexNDElement.plus(arg: Double) =
+operator fun ComplexNDElement.plus(arg: Double): ComplexNDElement =
     map { it + arg }
 
-operator fun ComplexNDElement.minus(arg: Double) =
+operator fun ComplexNDElement.minus(arg: Double): ComplexNDElement =
     map { it - arg }
 
 fun NDField.Companion.complex(vararg shape: Int): ComplexNDField = ComplexNDField(shape)
@@ -148,4 +147,4 @@ fun NDElement.Companion.complex(vararg shape: Int, initializer: ComplexField.(In
  */
 inline fun <R> ComplexField.nd(vararg shape: Int, action: ComplexNDField.() -> R): R {
     return NDField.complex(*shape).run(action)
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ExtendedNDField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ExtendedNDField.kt
index 776cff880..1fe449632 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ExtendedNDField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ExtendedNDField.kt
@@ -4,7 +4,6 @@ import scientifik.kmath.operations.ExtendedField
 
 interface ExtendedNDField<T : Any, F : ExtendedField<T>, N : NDStructure<T>> : NDField<T, F, N>, ExtendedField<N>
 
-
 ///**
 // * NDField that supports [ExtendedField] operations on its elements
 // */
@@ -36,5 +35,3 @@ interface ExtendedNDField<T : Any, F : ExtendedField<T>, N : NDStructure<T>> : N
 //        return produce { with(elementContext) { cos(arg[it]) } }
 //    }
 //}
-
-
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FlaggedBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FlaggedBuffer.kt
index 749e4eeec..2382e2c57 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FlaggedBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FlaggedBuffer.kt
@@ -19,11 +19,11 @@ interface FlaggedBuffer<T> : Buffer<T> {
 /**
  * The value is valid if all flags are down
  */
-fun FlaggedBuffer<*>.isValid(index: Int) = getFlag(index) != 0.toByte()
+fun FlaggedBuffer<*>.isValid(index: Int): Boolean = getFlag(index) != 0.toByte()
 
-fun FlaggedBuffer<*>.hasFlag(index: Int, flag: ValueFlag) = (getFlag(index) and flag.mask) != 0.toByte()
+fun FlaggedBuffer<*>.hasFlag(index: Int, flag: ValueFlag): Boolean = (getFlag(index) and flag.mask) != 0.toByte()
 
-fun FlaggedBuffer<*>.isMissing(index: Int) = hasFlag(index, ValueFlag.MISSING)
+fun FlaggedBuffer<*>.isMissing(index: Int): Boolean = hasFlag(index, ValueFlag.MISSING)
 
 /**
  * A real buffer which supports flags for each value like NaN or Missing
@@ -45,9 +45,9 @@ class FlaggedRealBuffer(val values: DoubleArray, val flags: ByteArray) : Flagged
 }
 
 inline fun FlaggedRealBuffer.forEachValid(block: (Double) -> Unit) {
-    for(i in indices){
-        if(isValid(i)){
+    for (i in indices) {
+        if (isValid(i)) {
             block(values[i])
         }
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
index a354c5de0..b277374ab 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
@@ -9,12 +9,11 @@ inline class IntBuffer(val array: IntArray) : MutableBuffer<Int> {
         array[index] = value
     }
 
-    override fun iterator() = array.iterator()
+    override fun iterator(): IntIterator = array.iterator()
 
     override fun copy(): MutableBuffer<Int> =
         IntBuffer(array.copyOf())
 
 }
 
-
-fun IntArray.asBuffer() = IntBuffer(this)
\ No newline at end of file
+fun IntArray.asBuffer(): IntBuffer = IntBuffer(this)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LongBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LongBuffer.kt
index fa6229a71..3ee2e75a2 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LongBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LongBuffer.kt
@@ -9,11 +9,11 @@ inline class LongBuffer(val array: LongArray) : MutableBuffer<Long> {
         array[index] = value
     }
 
-    override fun iterator() = array.iterator()
+    override fun iterator(): LongIterator = array.iterator()
 
     override fun copy(): MutableBuffer<Long> =
         LongBuffer(array.copyOf())
 
 }
 
-fun LongArray.asBuffer() = LongBuffer(this)
\ No newline at end of file
+fun LongArray.asBuffer(): LongBuffer = LongBuffer(this)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt
index a09f09165..b15487114 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt
@@ -3,7 +3,7 @@ package scientifik.kmath.structures
 import scientifik.memory.*
 
 /**
- * A non-boxing buffer based on [ByteBuffer] storage
+ * A non-boxing buffer over [Memory] object.
  */
 open class MemoryBuffer<T : Any>(protected val memory: Memory, protected val spec: MemorySpec<T>) : Buffer<T> {
 
@@ -17,7 +17,7 @@ open class MemoryBuffer<T : Any>(protected val memory: Memory, protected val spe
 
 
     companion object {
-        fun <T : Any> create(spec: MemorySpec<T>, size: Int) =
+        fun <T : Any> create(spec: MemorySpec<T>, size: Int): MemoryBuffer<T> =
             MemoryBuffer(Memory.allocate(size * spec.objectSize), spec)
 
         inline fun <T : Any> create(
@@ -36,25 +36,25 @@ open class MemoryBuffer<T : Any>(protected val memory: Memory, protected val spe
 class MutableMemoryBuffer<T : Any>(memory: Memory, spec: MemorySpec<T>) : MemoryBuffer<T>(memory, spec),
     MutableBuffer<T> {
 
-    private val writer = memory.writer()
+    private val writer: MemoryWriter = memory.writer()
 
-    override fun set(index: Int, value: T) = writer.write(spec, spec.objectSize * index, value)
+    override fun set(index: Int, value: T): Unit = writer.write(spec, spec.objectSize * index, value)
 
     override fun copy(): MutableBuffer<T> = MutableMemoryBuffer(memory.copy(), spec)
 
     companion object {
-        fun <T : Any> create(spec: MemorySpec<T>, size: Int) =
+        fun <T : Any> create(spec: MemorySpec<T>, size: Int): MutableMemoryBuffer<T> =
             MutableMemoryBuffer(Memory.allocate(size * spec.objectSize), spec)
 
         inline fun <T : Any> create(
             spec: MemorySpec<T>,
             size: Int,
             crossinline initializer: (Int) -> T
-        ) =
+        ): MutableMemoryBuffer<T> =
             MutableMemoryBuffer(Memory.allocate(size * spec.objectSize), spec).also { buffer ->
                 (0 until size).forEach {
                     buffer[it] = initializer(it)
                 }
             }
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt
index c826565cf..750133351 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt
@@ -56,7 +56,7 @@ interface NDAlgebra<T, C, N : NDStructure<T>> {
     /**
      * element-by-element invoke a function working on [T] on a [NDStructure]
      */
-    operator fun Function1<T, T>.invoke(structure: N) = map(structure) { value -> this@invoke(value) }
+    operator fun Function1<T, T>.invoke(structure: N): N = map(structure) { value -> this@invoke(value) }
 
     companion object
 }
@@ -76,12 +76,12 @@ interface NDSpace<T, S : Space<T>, N : NDStructure<T>> : Space<N>, NDAlgebra<T,
     override fun multiply(a: N, k: Number): N = map(a) { multiply(it, k) }
 
     //TODO move to extensions after KEEP-176
-    operator fun N.plus(arg: T) = map(this) { value -> add(arg, value) }
+    operator fun N.plus(arg: T): N = map(this) { value -> add(arg, value) }
 
-    operator fun N.minus(arg: T) = map(this) { value -> add(arg, -value) }
+    operator fun N.minus(arg: T): N = map(this) { value -> add(arg, -value) }
 
-    operator fun T.plus(arg: N) = map(arg) { value -> add(this@plus, value) }
-    operator fun T.minus(arg: N) = map(arg) { value -> add(-this@minus, value) }
+    operator fun T.plus(arg: N): N = map(arg) { value -> add(this@plus, value) }
+    operator fun T.minus(arg: N): N = map(arg) { value -> add(-this@minus, value) }
 
     companion object
 }
@@ -97,20 +97,18 @@ interface NDRing<T, R : Ring<T>, N : NDStructure<T>> : Ring<N>, NDSpace<T, R, N>
     override fun multiply(a: N, b: N): N = combine(a, b) { aValue, bValue -> multiply(aValue, bValue) }
 
     //TODO move to extensions after KEEP-176
-    operator fun N.times(arg: T) = map(this) { value -> multiply(arg, value) }
+    operator fun N.times(arg: T): N = map(this) { value -> multiply(arg, value) }
 
-    operator fun T.times(arg: N) = map(arg) { value -> multiply(this@times, value) }
+    operator fun T.times(arg: N): N = map(arg) { value -> multiply(this@times, value) }
 
     companion object
 }
 
 /**
  * Field for n-dimensional structures.
- * @param shape - the list of dimensions of the array
- * @param elementField - operations field defined on individual array element
+ *
  * @param T - the type of the element contained in ND structure
  * @param F - field of structure elements
- * @param R - actual nd-element type of this field
  */
 interface NDField<T, F : Field<T>, N : NDStructure<T>> : Field<N>, NDRing<T, F, N> {
 
@@ -120,9 +118,9 @@ interface NDField<T, F : Field<T>, N : NDStructure<T>> : Field<N>, NDRing<T, F,
     override fun divide(a: N, b: N): N = combine(a, b) { aValue, bValue -> divide(aValue, bValue) }
 
     //TODO move to extensions after KEEP-176
-    operator fun N.div(arg: T) = map(this) { value -> divide(arg, value) }
+    operator fun N.div(arg: T): N = map(this) { value -> divide(arg, value) }
 
-    operator fun T.div(arg: N) = map(arg) { divide(it, this@div) }
+    operator fun T.div(arg: N): N = map(arg) { divide(it, this@div) }
 
     companion object {
 
@@ -131,7 +129,7 @@ interface NDField<T, F : Field<T>, N : NDStructure<T>> : Field<N>, NDRing<T, F,
         /**
          * Create a nd-field for [Double] values or pull it from cache if it was created previously
          */
-        fun real(vararg shape: Int) = realNDFieldCache.getOrPut(shape) { RealNDField(shape) }
+        fun real(vararg shape: Int): RealNDField = realNDFieldCache.getOrPut(shape) { RealNDField(shape) }
 
         /**
          * Create a nd-field with boxing generic buffer
@@ -140,7 +138,7 @@ interface NDField<T, F : Field<T>, N : NDStructure<T>> : Field<N>, NDRing<T, F,
             field: F,
             vararg shape: Int,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing
-        ) = BoxingNDField(shape, field, bufferFactory)
+        ): BoxingNDField<T, F> = BoxingNDField(shape, field, bufferFactory)
 
         /**
          * Create a most suitable implementation for nd-field using reified class.
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDElement.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDElement.kt
index a18a03364..9dfe2b5a8 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDElement.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDElement.kt
@@ -23,19 +23,23 @@ interface NDElement<T, C, N : NDStructure<T>> : NDStructure<T> {
         /**
          * Create a optimized NDArray of doubles
          */
-        fun real(shape: IntArray, initializer: RealField.(IntArray) -> Double = { 0.0 }) =
+        fun real(shape: IntArray, initializer: RealField.(IntArray) -> Double = { 0.0 }): RealNDElement =
             NDField.real(*shape).produce(initializer)
 
 
-        fun real1D(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }) =
+        fun real1D(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): RealNDElement =
             real(intArrayOf(dim)) { initializer(it[0]) }
 
 
-        fun real2D(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }) =
+        fun real2D(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): RealNDElement =
             real(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
 
-        fun real3D(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }) =
-            real(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
+        fun real3D(
+            dim1: Int,
+            dim2: Int,
+            dim3: Int,
+            initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }
+        ): RealNDElement = real(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
 
 
         /**
@@ -62,16 +66,17 @@ interface NDElement<T, C, N : NDStructure<T>> : NDStructure<T> {
 }
 
 
-fun <T, C, N : NDStructure<T>> NDElement<T, C, N>.mapIndexed(transform: C.(index: IntArray, T) -> T) =
+fun <T, C, N : NDStructure<T>> NDElement<T, C, N>.mapIndexed(transform: C.(index: IntArray, T) -> T): NDElement<T, C, N> =
     context.mapIndexed(unwrap(), transform).wrap()
 
-fun <T, C, N : NDStructure<T>> NDElement<T, C, N>.map(transform: C.(T) -> T) = context.map(unwrap(), transform).wrap()
+fun <T, C, N : NDStructure<T>> NDElement<T, C, N>.map(transform: C.(T) -> T): NDElement<T, C, N> =
+    context.map(unwrap(), transform).wrap()
 
 
 /**
  * Element by element application of any operation on elements to the whole [NDElement]
  */
-operator fun <T, C, N : NDStructure<T>> Function1<T, T>.invoke(ndElement: NDElement<T, C, N>) =
+operator fun <T, C, N : NDStructure<T>> Function1<T, T>.invoke(ndElement: NDElement<T, C, N>): NDElement<T, C, N> =
     ndElement.map { value -> this@invoke(value) }
 
 /* plus and minus */
@@ -79,13 +84,13 @@ operator fun <T, C, N : NDStructure<T>> Function1<T, T>.invoke(ndElement: NDElem
 /**
  * Summation operation for [NDElement] and single element
  */
-operator fun <T, S : Space<T>, N : NDStructure<T>> NDElement<T, S, N>.plus(arg: T) =
+operator fun <T, S : Space<T>, N : NDStructure<T>> NDElement<T, S, N>.plus(arg: T): NDElement<T, S, N> =
     map { value -> arg + value }
 
 /**
  * Subtraction operation between [NDElement] and single element
  */
-operator fun <T, S : Space<T>, N : NDStructure<T>> NDElement<T, S, N>.minus(arg: T) =
+operator fun <T, S : Space<T>, N : NDStructure<T>> NDElement<T, S, N>.minus(arg: T): NDElement<T, S, N> =
     map { value -> arg - value }
 
 /* prod and div */
@@ -93,13 +98,13 @@ operator fun <T, S : Space<T>, N : NDStructure<T>> NDElement<T, S, N>.minus(arg:
 /**
  * Product operation for [NDElement] and single element
  */
-operator fun <T, R : Ring<T>, N : NDStructure<T>> NDElement<T, R, N>.times(arg: T) =
+operator fun <T, R : Ring<T>, N : NDStructure<T>> NDElement<T, R, N>.times(arg: T): NDElement<T, R, N> =
     map { value -> arg * value }
 
 /**
  * Division operation between [NDElement] and single element
  */
-operator fun <T, F : Field<T>, N : NDStructure<T>> NDElement<T, F, N>.div(arg: T) =
+operator fun <T, F : Field<T>, N : NDStructure<T>> NDElement<T, F, N>.div(arg: T): NDElement<T, F, N> =
     map { value -> arg / value }
 
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt
index 236a6f366..bcd74ed2a 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt
@@ -8,7 +8,7 @@ interface NDStructure<T> {
 
     val shape: IntArray
 
-    val dimension get() = shape.size
+    val dimension: Int get() = shape.size
 
     operator fun get(index: IntArray): T
 
@@ -44,32 +44,49 @@ interface NDStructure<T> {
             strides: Strides,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
             initializer: (IntArray) -> T
-        ) =
+        ): BufferNDStructure<T> =
             BufferNDStructure(strides, bufferFactory(strides.linearSize) { i -> initializer(strides.index(i)) })
 
         /**
          * Inline create NDStructure with non-boxing buffer implementation if it is possible
          */
-        inline fun <reified T : Any> auto(strides: Strides, crossinline initializer: (IntArray) -> T) =
+        inline fun <reified T : Any> auto(
+            strides: Strides,
+            crossinline initializer: (IntArray) -> T
+        ): BufferNDStructure<T> =
             BufferNDStructure(strides, Buffer.auto(strides.linearSize) { i -> initializer(strides.index(i)) })
 
-        inline fun <T : Any> auto(type: KClass<T>, strides: Strides, crossinline initializer: (IntArray) -> T) =
+        inline fun <T : Any> auto(
+            type: KClass<T>,
+            strides: Strides,
+            crossinline initializer: (IntArray) -> T
+        ): BufferNDStructure<T> =
             BufferNDStructure(strides, Buffer.auto(type, strides.linearSize) { i -> initializer(strides.index(i)) })
 
         fun <T> build(
             shape: IntArray,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
             initializer: (IntArray) -> T
-        ) = build(DefaultStrides(shape), bufferFactory, initializer)
+        ): BufferNDStructure<T> = build(DefaultStrides(shape), bufferFactory, initializer)
 
-        inline fun <reified T : Any> auto(shape: IntArray, crossinline initializer: (IntArray) -> T) =
+        inline fun <reified T : Any> auto(
+            shape: IntArray,
+            crossinline initializer: (IntArray) -> T
+        ): BufferNDStructure<T> =
             auto(DefaultStrides(shape), initializer)
 
         @JvmName("autoVarArg")
-        inline fun <reified T : Any> auto(vararg shape: Int, crossinline initializer: (IntArray) -> T) =
+        inline fun <reified T : Any> auto(
+            vararg shape: Int,
+            crossinline initializer: (IntArray) -> T
+        ): BufferNDStructure<T> =
             auto(DefaultStrides(shape), initializer)
 
-        inline fun <T : Any> auto(type: KClass<T>, vararg shape: Int, crossinline initializer: (IntArray) -> T) =
+        inline fun <T : Any> auto(
+            type: KClass<T>,
+            vararg shape: Int,
+            crossinline initializer: (IntArray) -> T
+        ): BufferNDStructure<T> =
             auto(type, DefaultStrides(shape), initializer)
     }
 }
@@ -128,7 +145,7 @@ class DefaultStrides private constructor(override val shape: IntArray) : Strides
     /**
      * Strides for memory access
      */
-    override val strides by lazy {
+    override val strides: List<Int> by lazy {
         sequence {
             var current = 1
             yield(1)
@@ -238,7 +255,7 @@ inline fun <T, reified R : Any> NDStructure<T>.mapToBuffer(
 }
 
 /**
- * Mutable ND buffer based on linear [autoBuffer]
+ * Mutable ND buffer based on linear [MutableBuffer].
  */
 class MutableBufferNDStructure<T>(
     override val strides: Strides,
@@ -251,7 +268,7 @@ class MutableBufferNDStructure<T>(
         }
     }
 
-    override fun set(index: IntArray, value: T) = buffer.set(strides.offset(index), value)
+    override fun set(index: IntArray, value: T): Unit = buffer.set(strides.offset(index), value)
 }
 
 inline fun <reified T : Any> NDStructure<T>.combine(
@@ -260,4 +277,4 @@ inline fun <reified T : Any> NDStructure<T>.combine(
 ): NDStructure<T> {
     if (!this.shape.contentEquals(struct.shape)) error("Shape mismatch in structure combination")
     return NDStructure.auto(shape) { block(this[it], struct[it]) }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt
index f48ace3a9..20187fe19 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt
@@ -9,7 +9,7 @@ inline class RealBuffer(val array: DoubleArray) : MutableBuffer<Double> {
         array[index] = value
     }
 
-    override fun iterator() = array.iterator()
+    override fun iterator(): DoubleIterator = array.iterator()
 
     override fun copy(): MutableBuffer<Double> =
         RealBuffer(array.copyOf())
@@ -31,4 +31,4 @@ val MutableBuffer<out Double>.array: DoubleArray
         DoubleArray(size) { get(it) }
     }
 
-fun DoubleArray.asBuffer() = RealBuffer(this)
\ No newline at end of file
+fun DoubleArray.asBuffer(): RealBuffer = RealBuffer(this)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt
index 8c90f90c7..b89f28233 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt
@@ -12,8 +12,8 @@ class RealNDField(override val shape: IntArray) :
     override val strides: Strides = DefaultStrides(shape)
 
     override val elementContext: RealField get() = RealField
-    override val zero by lazy { produce { zero } }
-    override val one by lazy { produce { one } }
+    override val zero: RealNDElement by lazy { produce { zero } }
+    override val one: RealNDElement by lazy { produce { one } }
 
     inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Double): Buffer<Double> =
         RealBuffer(DoubleArray(size) { initializer(it) })
@@ -64,15 +64,15 @@ class RealNDField(override val shape: IntArray) :
     override fun NDBuffer<Double>.toElement(): FieldElement<NDBuffer<Double>, *, out BufferedNDField<Double, RealField>> =
         BufferedNDFieldElement(this@RealNDField, buffer)
 
-    override fun power(arg: NDBuffer<Double>, pow: Number) = map(arg) { power(it, pow) }
+    override fun power(arg: NDBuffer<Double>, pow: Number): RealNDElement = map(arg) { power(it, pow) }
 
-    override fun exp(arg: NDBuffer<Double>) = map(arg) { exp(it) }
+    override fun exp(arg: NDBuffer<Double>): RealNDElement = map(arg) { exp(it) }
 
-    override fun ln(arg: NDBuffer<Double>) = map(arg) { ln(it) }
+    override fun ln(arg: NDBuffer<Double>): RealNDElement = map(arg) { ln(it) }
 
-    override fun sin(arg: NDBuffer<Double>) = map(arg) { sin(it) }
+    override fun sin(arg: NDBuffer<Double>): RealNDElement = map(arg) { sin(it) }
 
-    override fun cos(arg: NDBuffer<Double>) = map(arg) { cos(it) }
+    override fun cos(arg: NDBuffer<Double>): RealNDElement = map(arg) { cos(it) }
 
     override fun tan(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { tan(it) }
 
@@ -95,7 +95,7 @@ inline fun BufferedNDField<Double, RealField>.produceInline(crossinline initiali
 /**
  * Map one [RealNDElement] using function with indexes
  */
-inline fun RealNDElement.mapIndexed(crossinline transform: RealField.(index: IntArray, Double) -> Double) =
+inline fun RealNDElement.mapIndexed(crossinline transform: RealField.(index: IntArray, Double) -> Double): RealNDElement =
     context.produceInline { offset -> transform(strides.index(offset), buffer[offset]) }
 
 /**
@@ -107,9 +107,9 @@ inline fun RealNDElement.map(crossinline transform: RealField.(Double) -> Double
 }
 
 /**
- * Element by element application of any operation on elements to the whole array. Just like in numpy
+ * Element by element application of any operation on elements to the whole array. Just like in numpy.
  */
-operator fun Function1<Double, Double>.invoke(ndElement: RealNDElement) =
+operator fun Function1<Double, Double>.invoke(ndElement: RealNDElement): RealNDElement =
     ndElement.map { this@invoke(it) }
 
 
@@ -118,13 +118,13 @@ operator fun Function1<Double, Double>.invoke(ndElement: RealNDElement) =
 /**
  * Summation operation for [BufferedNDElement] and single element
  */
-operator fun RealNDElement.plus(arg: Double) =
+operator fun RealNDElement.plus(arg: Double): RealNDElement =
     map { it + arg }
 
 /**
  * Subtraction operation between [BufferedNDElement] and single element
  */
-operator fun RealNDElement.minus(arg: Double) =
+operator fun RealNDElement.minus(arg: Double): RealNDElement =
     map { it - arg }
 
 /**
@@ -132,4 +132,4 @@ operator fun RealNDElement.minus(arg: Double) =
  */
 inline fun <R> RealField.nd(vararg shape: Int, action: RealNDField.() -> R): R {
     return NDField.real(*shape).run(action)
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortBuffer.kt
index f4b2f7d13..24c94a885 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortBuffer.kt
@@ -9,12 +9,11 @@ inline class ShortBuffer(val array: ShortArray) : MutableBuffer<Short> {
         array[index] = value
     }
 
-    override fun iterator() = array.iterator()
+    override fun iterator(): ShortIterator = array.iterator()
 
     override fun copy(): MutableBuffer<Short> =
         ShortBuffer(array.copyOf())
 
 }
 
-
-fun ShortArray.asBuffer() = ShortBuffer(this)
\ No newline at end of file
+fun ShortArray.asBuffer(): ShortBuffer = ShortBuffer(this)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortNDRing.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortNDRing.kt
index 6b09c91de..f404a2a27 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortNDRing.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortNDRing.kt
@@ -12,8 +12,8 @@ class ShortNDRing(override val shape: IntArray) :
     override val strides: Strides = DefaultStrides(shape)
 
     override val elementContext: ShortRing get() = ShortRing
-    override val zero by lazy { produce { ShortRing.zero } }
-    override val one by lazy { produce { ShortRing.one } }
+    override val zero: ShortNDElement by lazy { produce { zero } }
+    override val one: ShortNDElement by lazy { produce { one } }
 
     inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Short): Buffer<Short> =
         ShortBuffer(ShortArray(size) { initializer(it) })
@@ -40,6 +40,7 @@ class ShortNDRing(override val shape: IntArray) :
         transform: ShortRing.(index: IntArray, Short) -> Short
     ): ShortNDElement {
         check(arg)
+
         return BufferedNDRingElement(
             this,
             buildBuffer(arg.strides.linearSize) { offset ->
@@ -67,7 +68,7 @@ class ShortNDRing(override val shape: IntArray) :
 
 
 /**
- * Fast element production using function inlining
+ * Fast element production using function inlining.
  */
 inline fun BufferedNDRing<Short, ShortRing>.produceInline(crossinline initializer: ShortRing.(Int) -> Short): ShortNDElement {
     val array = ShortArray(strides.linearSize) { offset -> ShortRing.initializer(offset) }
@@ -75,22 +76,22 @@ inline fun BufferedNDRing<Short, ShortRing>.produceInline(crossinline initialize
 }
 
 /**
- * Element by element application of any operation on elements to the whole array. Just like in numpy
+ * Element by element application of any operation on elements to the whole array.
  */
-operator fun Function1<Short, Short>.invoke(ndElement: ShortNDElement) =
+operator fun Function1<Short, Short>.invoke(ndElement: ShortNDElement): ShortNDElement =
     ndElement.context.produceInline { i -> invoke(ndElement.buffer[i]) }
 
 
 /* plus and minus */
 
 /**
- * Summation operation for [StridedNDFieldElement] and single element
+ * Summation operation for [ShortNDElement] and single element.
  */
-operator fun ShortNDElement.plus(arg: Short) =
+operator fun ShortNDElement.plus(arg: Short): ShortNDElement =
     context.produceInline { i -> (buffer[i] + arg).toShort() }
 
 /**
- * Subtraction operation between [StridedNDFieldElement] and single element
+ * Subtraction operation between [ShortNDElement] and single element.
  */
-operator fun ShortNDElement.minus(arg: Short) =
-    context.produceInline { i -> (buffer[i] - arg).toShort() }
\ No newline at end of file
+operator fun ShortNDElement.minus(arg: Short): ShortNDElement =
+    context.produceInline { i -> (buffer[i] - arg).toShort() }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure1D.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure1D.kt
index 9974538ec..faf022367 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure1D.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure1D.kt
@@ -17,7 +17,7 @@ interface Structure1D<T> : NDStructure<T>, Buffer<T> {
 /**
  * A 1D wrapper for nd-structure
  */
-private inline class Structure1DWrapper<T>(val structure: NDStructure<T>) : Structure1D<T>{
+private inline class Structure1DWrapper<T>(val structure: NDStructure<T>) : Structure1D<T> {
 
     override val shape: IntArray get() = structure.shape
     override val size: Int get() = structure.shape[0]
@@ -39,14 +39,14 @@ private inline class Buffer1DWrapper<T>(val buffer: Buffer<T>) : Structure1D<T>
     override fun elements(): Sequence<Pair<IntArray, T>> =
         asSequence().mapIndexed { index, value -> intArrayOf(index) to value }
 
-    override fun get(index: Int): T = buffer.get(index)
+    override fun get(index: Int): T = buffer[index]
 }
 
 /**
  * Represent a [NDStructure] as [Structure1D]. Throw error in case of dimension mismatch
  */
 fun <T> NDStructure<T>.as1D(): Structure1D<T> = if (shape.size == 1) {
-    if( this is NDBuffer){
+    if (this is NDBuffer) {
         Buffer1DWrapper(this.buffer)
     } else {
         Structure1DWrapper(this)
@@ -59,4 +59,4 @@ fun <T> NDStructure<T>.as1D(): Structure1D<T> = if (shape.size == 1) {
 /**
  * Represent this buffer as 1D structure
  */
-fun <T> Buffer<T>.asND(): Structure1D<T> = Buffer1DWrapper(this)
\ No newline at end of file
+fun <T> Buffer<T>.asND(): Structure1D<T> = Buffer1DWrapper(this)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure2D.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure2D.kt
index bfaf8338d..30fd556d3 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure2D.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure2D.kt
@@ -32,9 +32,7 @@ interface Structure2D<T> : NDStructure<T> {
         }
     }
 
-    companion object {
-
-    }
+    companion object
 }
 
 /**
@@ -57,4 +55,4 @@ fun <T> NDStructure<T>.as2D(): Structure2D<T> = if (shape.size == 2) {
     error("Can't create 2d-structure from ${shape.size}d-structure")
 }
 
-typealias Matrix<T> = Structure2D<T>
\ No newline at end of file
+typealias Matrix<T> = Structure2D<T>
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/expressions/ExpressionFieldTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/expressions/ExpressionFieldTest.kt
index 9eae60efc..22b924ef9 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/expressions/ExpressionFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/expressions/ExpressionFieldTest.kt
@@ -31,7 +31,7 @@ class ExpressionFieldTest {
 
     @Test
     fun separateContext() {
-        fun <T> FunctionalExpressionField<T,*>.expression(): Expression<T> {
+        fun <T> FunctionalExpressionField<T, *>.expression(): Expression<T> {
             val x = variable("x")
             return x * x + 2 * x + one
         }
@@ -42,7 +42,7 @@ class ExpressionFieldTest {
 
     @Test
     fun valueExpression() {
-        val expressionBuilder: FunctionalExpressionField<Double,*>.() -> Expression<Double> = {
+        val expressionBuilder: FunctionalExpressionField<Double, *>.() -> Expression<Double> = {
             val x = variable("x")
             x * x + 2 * x + one
         }
@@ -50,4 +50,4 @@ class ExpressionFieldTest {
         val expression = FunctionalExpressionField(RealField).expressionBuilder()
         assertEquals(expression("x" to 1.0), 4.0)
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/MatrixTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/MatrixTest.kt
index dcd510e32..987426250 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/MatrixTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/MatrixTest.kt
@@ -49,17 +49,17 @@ class MatrixTest {
 
     @Test
     fun test2DDot() {
-        val firstMatrix = NDStructure.auto(2,3){ (i, j) -> (i + j).toDouble() }.as2D()
-        val secondMatrix = NDStructure.auto(3,2){ (i, j) -> (i + j).toDouble() }.as2D()
+        val firstMatrix = NDStructure.auto(2, 3) { (i, j) -> (i + j).toDouble() }.as2D()
+        val secondMatrix = NDStructure.auto(3, 2) { (i, j) -> (i + j).toDouble() }.as2D()
         MatrixContext.real.run {
 //            val firstMatrix = produce(2, 3) { i, j -> (i + j).toDouble() }
 //            val secondMatrix = produce(3, 2) { i, j -> (i + j).toDouble() }
             val result = firstMatrix dot secondMatrix
             assertEquals(2, result.rowNum)
             assertEquals(2, result.colNum)
-            assertEquals(8.0, result[0,1])
-            assertEquals(8.0, result[1,0])
-            assertEquals(14.0, result[1,1])
+            assertEquals(8.0, result[0, 1])
+            assertEquals(8.0, result[1, 0])
+            assertEquals(14.0, result[1, 1])
         }
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt
index 56a0b7aad..34bd8a0e3 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt
@@ -48,4 +48,4 @@ class RealLUSolverTest {
 
         assertEquals(expected, inverted)
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt
index 9dc8f5ef7..c08a63ccb 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt
@@ -8,10 +8,10 @@ import kotlin.test.assertEquals
 import kotlin.test.assertTrue
 
 class AutoDiffTest {
+    fun Variable(int: Int): Variable<Double> = Variable(int.toDouble())
 
-    fun Variable(int: Int) = Variable(int.toDouble())
-
-    fun deriv(body: AutoDiffField<Double, RealField>.() -> Variable<Double>) = RealField.deriv(body)
+    fun deriv(body: AutoDiffField<Double, RealField>.() -> Variable<Double>): DerivationResult<Double> =
+        RealField.deriv(body)
 
     @Test
     fun testPlusX2() {
@@ -178,5 +178,4 @@ class AutoDiffTest {
     private fun assertApprox(a: Double, b: Double) {
         if ((a - b) > 1e-10) assertEquals(a, b)
     }
-
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/CumulativeKtTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/CumulativeKtTest.kt
index e7c99e7d0..82ea5318f 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/CumulativeKtTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/CumulativeKtTest.kt
@@ -10,4 +10,4 @@ class CumulativeKtTest {
         val cumulative = initial.cumulativeSum()
         assertEquals(listOf(-1.0, 1.0, 2.0, 3.0), cumulative)
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntAlgebraTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntAlgebraTest.kt
index 5ae977196..c22d2f27b 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntAlgebraTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntAlgebraTest.kt
@@ -47,4 +47,3 @@ class BigIntAlgebraTest {
     }
 
 }
-
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntConstructorTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntConstructorTest.kt
index 2af1b7e50..5e3f6d1b0 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntConstructorTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntConstructorTest.kt
@@ -19,8 +19,8 @@ class BigIntConstructorTest {
 
     @Test
     fun testConstructor_0xffffffffaL() {
-        val x = -0xffffffffaL.toBigInt()
+        val x = (-0xffffffffaL).toBigInt()
         val y = uintArrayOf(0xfffffffaU, 0xfU).toBigInt(-1)
         assertEquals(x, y)
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntConversionsTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntConversionsTest.kt
index 51b9509e0..41df1968d 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntConversionsTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntConversionsTest.kt
@@ -19,7 +19,7 @@ class BigIntConversionsTest {
 
     @Test
     fun testToString_0x17ead2ffffd() {
-        val x = -0x17ead2ffffdL.toBigInt()
+        val x = (-0x17ead2ffffdL).toBigInt()
         assertEquals("-0x17ead2ffffd", x.toString())
     }
 
@@ -40,4 +40,4 @@ class BigIntConversionsTest {
         val x = "-7059135710711894913860".parseBigInteger()
         assertEquals("-0x17ead2ffffd11223344", x.toString())
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntOperationsTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntOperationsTest.kt
index 72ac9f229..b7f4cf43b 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntOperationsTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/BigIntOperationsTest.kt
@@ -31,7 +31,7 @@ class BigIntOperationsTest {
     @Test
     fun testUnaryMinus() {
         val x = 1234.toBigInt()
-        val y = -1234.toBigInt()
+        val y = (-1234).toBigInt()
         assertEquals(-x, y)
     }
 
@@ -48,18 +48,18 @@ class BigIntOperationsTest {
 
     @Test
     fun testMinus__2_1() {
-        val x = -2.toBigInt()
+        val x = (-2).toBigInt()
         val y = 1.toBigInt()
 
         val res = x - y
-        val sum = -3.toBigInt()
+        val sum = (-3).toBigInt()
 
         assertEquals(sum, res)
     }
 
     @Test
     fun testMinus___2_1() {
-        val x = -2.toBigInt()
+        val x = (-2).toBigInt()
         val y = 1.toBigInt()
 
         val res = -x - y
@@ -74,7 +74,7 @@ class BigIntOperationsTest {
         val y = 0xffffffffaL.toBigInt()
 
         val res = x - y
-        val sum = -0xfffffcfc1L.toBigInt()
+        val sum = (-0xfffffcfc1L).toBigInt()
 
         assertEquals(sum, res)
     }
@@ -92,11 +92,11 @@ class BigIntOperationsTest {
 
     @Test
     fun testMultiply__2_3() {
-        val x = -2.toBigInt()
+        val x = (-2).toBigInt()
         val y = 3.toBigInt()
 
         val res = x * y
-        val prod = -6.toBigInt()
+        val prod = (-6).toBigInt()
 
         assertEquals(prod, res)
     }
@@ -129,7 +129,7 @@ class BigIntOperationsTest {
         val y = -0xfff456
 
         val res = x * y
-        val prod = -0xffe579ad5dc2L.toBigInt()
+        val prod = (-0xffe579ad5dc2L).toBigInt()
 
         assertEquals(prod, res)
     }
@@ -259,7 +259,7 @@ class BigIntOperationsTest {
         val y = -3
 
         val res = x / y
-        val div = -6.toBigInt()
+        val div = (-6).toBigInt()
 
         assertEquals(div, res)
     }
@@ -267,10 +267,10 @@ class BigIntOperationsTest {
     @Test
     fun testBigDivision_20__3() {
         val x = 20.toBigInt()
-        val y = -3.toBigInt()
+        val y = (-3).toBigInt()
 
         val res = x / y
-        val div = -6.toBigInt()
+        val div = (-6).toBigInt()
 
         assertEquals(div, res)
     }
@@ -378,4 +378,4 @@ class BigIntOperationsTest {
 
         return assertEquals(res, x % mod)
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/RealFieldTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/RealFieldTest.kt
index 779cfc4b8..9dfa3bdd1 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/RealFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/RealFieldTest.kt
@@ -11,4 +11,4 @@ class RealFieldTest {
         }
         assertEquals(5.0, sqrt)
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/ComplexBufferSpecTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/ComplexBufferSpecTest.kt
index 454683dac..cbbe6f0f4 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/ComplexBufferSpecTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/ComplexBufferSpecTest.kt
@@ -11,4 +11,4 @@ class ComplexBufferSpecTest {
         val buffer = Buffer.complex(20) { Complex(it.toDouble(), -it.toDouble()) }
         assertEquals(Complex(5.0, -5.0), buffer[5])
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NDFieldTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NDFieldTest.kt
index 39cce5c67..7abeefca6 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NDFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NDFieldTest.kt
@@ -10,4 +10,4 @@ class NDFieldTest {
         val ndArray = NDElement.real(intArrayOf(10, 10)) { (it[0] + it[1]).toDouble() }
         assertEquals(ndArray[5, 5], 10.0)
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NumberNDFieldTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NumberNDFieldTest.kt
index 60f1f9979..d48aabfd0 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NumberNDFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/NumberNDFieldTest.kt
@@ -8,8 +8,8 @@ import kotlin.test.Test
 import kotlin.test.assertEquals
 
 class NumberNDFieldTest {
-    val array1 = real2D(3, 3) { i, j -> (i + j).toDouble() }
-    val array2 = real2D(3, 3) { i, j -> (i - j).toDouble() }
+    val array1: RealNDElement = real2D(3, 3) { i, j -> (i + j).toDouble() }
+    val array2: RealNDElement = real2D(3, 3) { i, j -> (i - j).toDouble() }
 
     @Test
     fun testSum() {
-- 
2.34.1


From 8debed704873df4bf9af77151bbce81dbb920057 Mon Sep 17 00:00:00 2001
From: Iaroslav Postovalov <postovalovya@gmail.com>
Date: Wed, 5 Aug 2020 17:25:56 +0700
Subject: [PATCH 02/12] Improve documentation

---
 .../kmath/operations/AlgebraElements.kt       | 40 +++++++++++++++++++
 1 file changed, 40 insertions(+)

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
index 9b430af39..0de2109c4 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
@@ -24,9 +24,36 @@ interface MathWrapper<T, I> {
  * @param S the type of space
  */
 interface SpaceElement<T, I : SpaceElement<T, I, S>, S : Space<T>> : MathElement<S>, MathWrapper<T, I> {
+    /**
+     * Adds element to this one.
+     *
+     * @param b the augend.
+     * @return the sum.
+     */
     operator fun plus(b: T): I = context.add(unwrap(), b).wrap()
+
+    /**
+     * Subtracts element from this one.
+     *
+     * @param b the subtrahend.
+     * @return the difference.
+     */
     operator fun minus(b: T): I = context.add(unwrap(), context.multiply(b, -1.0)).wrap()
+
+    /**
+     * Multiplies this element by number.
+     *
+     * @param k the multiplicand.
+     * @return the product.
+     */
     operator fun times(k: Number): I = context.multiply(unwrap(), k.toDouble()).wrap()
+
+    /**
+     * Divides this element by number.
+     *
+     * @param k the divisor.
+     * @return the quotient.
+     */
     operator fun div(k: Number): I = context.multiply(unwrap(), 1.0 / k.toDouble()).wrap()
 }
 
@@ -34,6 +61,12 @@ interface SpaceElement<T, I : SpaceElement<T, I, S>, S : Space<T>> : MathElement
  * Ring element
  */
 interface RingElement<T, I : RingElement<T, I, R>, R : Ring<T>> : SpaceElement<T, I, R> {
+    /**
+     * Multiplies this element by another one.
+     *
+     * @param b the multiplicand.
+     * @return the product.
+     */
     operator fun times(b: T): I = context.multiply(unwrap(), b).wrap()
 }
 
@@ -42,5 +75,12 @@ interface RingElement<T, I : RingElement<T, I, R>, R : Ring<T>> : SpaceElement<T
  */
 interface FieldElement<T, I : FieldElement<T, I, F>, F : Field<T>> : RingElement<T, I, F> {
     override val context: F
+
+    /**
+     * Divides this element by another one.
+     *
+     * @param b the divisor.
+     * @return the quotient.
+     */
     operator fun div(b: T): I = context.divide(unwrap(), b).wrap()
 }
-- 
2.34.1


From aed10329ebb6ea7bdedad469fbaa161ee41fba6a Mon Sep 17 00:00:00 2001
From: Iaroslav Postovalov <postovalovya@gmail.com>
Date: Wed, 5 Aug 2020 17:30:11 +0700
Subject: [PATCH 03/12] Improve documentation of elements

---
 .../kmath/operations/AlgebraElements.kt       | 21 +++++++++++++------
 1 file changed, 15 insertions(+), 6 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
index 0de2109c4..534f56e0d 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
@@ -18,10 +18,11 @@ interface MathWrapper<T, I> {
 }
 
 /**
- * The element of linear context
- * @param T the type of space operation results
- * @param I self type of the element. Needed for static type checking
- * @param S the type of space
+ * The element of [Space].
+ *
+ * @param T the type of space operation results.
+ * @param I self type of the element. Needed for static type checking.
+ * @param S the type of space.
  */
 interface SpaceElement<T, I : SpaceElement<T, I, S>, S : Space<T>> : MathElement<S>, MathWrapper<T, I> {
     /**
@@ -58,7 +59,11 @@ interface SpaceElement<T, I : SpaceElement<T, I, S>, S : Space<T>> : MathElement
 }
 
 /**
- * Ring element
+ * The element of [Ring].
+ *
+ * @param T the type of space operation results.
+ * @param I self type of the element. Needed for static type checking.
+ * @param R the type of space.
  */
 interface RingElement<T, I : RingElement<T, I, R>, R : Ring<T>> : SpaceElement<T, I, R> {
     /**
@@ -71,7 +76,11 @@ interface RingElement<T, I : RingElement<T, I, R>, R : Ring<T>> : SpaceElement<T
 }
 
 /**
- * Field element
+ * The element of [Field].
+ *
+ * @param T the type of space operation results.
+ * @param I self type of the element. Needed for static type checking.
+ * @param F the type of field.
  */
 interface FieldElement<T, I : FieldElement<T, I, F>, F : Field<T>> : RingElement<T, I, F> {
     override val context: F
-- 
2.34.1


From 8367e13057fb19df3b6c356f6d5846bb92ffc6bd Mon Sep 17 00:00:00 2001
From: Iaroslav Postovalov <postovalovya@gmail.com>
Date: Wed, 5 Aug 2020 18:41:58 +0700
Subject: [PATCH 04/12] Improve documentation of complex and memoryspec

---
 .../scientifik/kmath/operations/Complex.kt    | 57 ++++++++++++++++---
 .../kotlin/scientifik/memory/MemorySpec.kt    | 29 ++++++----
 2 files changed, 67 insertions(+), 19 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt
index ffd6c8dec..0ce144a33 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt
@@ -11,13 +11,16 @@ import kotlin.math.*
 private val PI_DIV_2 = Complex(PI / 2, 0)
 
 /**
- * A field for complex numbers
+ * A field of [Complex].
  */
 object ComplexField : ExtendedField<Complex> {
     override val zero: Complex = Complex(0.0, 0.0)
 
     override val one: Complex = Complex(1.0, 0.0)
 
+    /**
+     * The imaginary unit.
+     */
     val i: Complex = Complex(0.0, 1.0)
 
     override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
@@ -45,25 +48,59 @@ object ComplexField : ExtendedField<Complex> {
 
     override fun ln(arg: Complex): Complex = ln(arg.r) + i * atan2(arg.im, arg.re)
 
+    /**
+     * Adds complex number to real one.
+     *
+     * @receiver the addend.
+     * @param c the augend.
+     * @return the sum.
+     */
     operator fun Double.plus(c: Complex): Complex = add(this.toComplex(), c)
 
+    /**
+     * Subtracts complex number from real one.
+     *
+     * @receiver the minuend.
+     * @param c the subtrahend.
+     * @return the difference.
+     */
     operator fun Double.minus(c: Complex): Complex = add(this.toComplex(), -c)
 
+    /**
+     * Adds real number to complex one.
+     *
+     * @receiver the addend.
+     * @param d the augend.
+     * @return the sum.
+     */
     operator fun Complex.plus(d: Double): Complex = d + this
 
+    /**
+     * Subtracts real number from complex one.
+     *
+     * @receiver the minuend.
+     * @param d the subtrahend.
+     * @return the difference.
+     */
     operator fun Complex.minus(d: Double): Complex = add(this, -d.toComplex())
 
+    /**
+     * Multiplies real number by complex one.
+     *
+     * @receiver the multiplier.
+     * @param c the multiplicand.
+     * @receiver the product.
+     */
     operator fun Double.times(c: Complex): Complex = Complex(c.re * this, c.im * this)
 
-    override fun symbol(value: String): Complex = if (value == "i") {
-        i
-    } else {
-        super.symbol(value)
-    }
+    override fun symbol(value: String): Complex = if (value == "i") i else super.symbol(value)
 }
 
 /**
- * Complex number class
+ * Represents complex number.
+ *
+ * @property re The real part.
+ * @property im The imaginary part.
  */
 data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Complex, ComplexField>, Comparable<Complex> {
     constructor(re: Number, im: Number) : this(re.toDouble(), im.toDouble())
@@ -104,6 +141,12 @@ val Complex.r: Double get() = sqrt(re * re + im * im)
  */
 val Complex.theta: Double get() = atan(im / re)
 
+/**
+ * Creates a complex number with real part equal to this real.
+ *
+ * @receiver the real part.
+ * @return the new complex number.
+ */
 fun Double.toComplex(): Complex = Complex(this, 0.0)
 
 inline fun Buffer.Companion.complex(size: Int, crossinline init: (Int) -> Complex): Buffer<Complex> {
diff --git a/kmath-memory/src/commonMain/kotlin/scientifik/memory/MemorySpec.kt b/kmath-memory/src/commonMain/kotlin/scientifik/memory/MemorySpec.kt
index 7999aa2ab..4d0035d09 100644
--- a/kmath-memory/src/commonMain/kotlin/scientifik/memory/MemorySpec.kt
+++ b/kmath-memory/src/commonMain/kotlin/scientifik/memory/MemorySpec.kt
@@ -1,7 +1,9 @@
 package scientifik.memory
 
 /**
- * A specification to read or write custom objects with fixed size in bytes
+ * A specification to read or write custom objects with fixed size in bytes.
+ *
+ * @param T the type of object this spec manages.
  */
 interface MemorySpec<T : Any> {
     /**
@@ -9,27 +11,30 @@ interface MemorySpec<T : Any> {
      */
     val objectSize: Int
 
+    /**
+     * Reads the object starting from [offset].
+     */
     fun MemoryReader.read(offset: Int): T
-    //TODO consider thread safety
+
+    // TODO consider thread safety
+
+    /**
+     * Writes the object [value] starting from [offset].
+     */
     fun MemoryWriter.write(offset: Int, value: T)
 }
 
-fun <T : Any> MemoryReader.read(spec: MemorySpec<T>, offset: Int): T = spec.run { read(offset) }
-fun <T : Any> MemoryWriter.write(spec: MemorySpec<T>, offset: Int, value: T) = spec.run { write(offset, value) }
+fun <T : Any> MemoryReader.read(spec: MemorySpec<T>, offset: Int): T = with(spec) { read(offset) }
+fun <T : Any> MemoryWriter.write(spec: MemorySpec<T>, offset: Int, value: T): Unit = with(spec) { write(offset, value) }
 
-inline fun <reified T : Any> MemoryReader.readArray(spec: MemorySpec<T>, offset: Int, size: Int) =
+inline fun <reified T : Any> MemoryReader.readArray(spec: MemorySpec<T>, offset: Int, size: Int): Array<T> =
     Array(size) { i ->
         spec.run {
             read(offset + i * objectSize)
         }
     }
 
-fun <T : Any> MemoryWriter.writeArray(spec: MemorySpec<T>, offset: Int, array: Array<T>) {
-    spec.run {
-        for (i in array.indices) {
-            write(offset + i * objectSize, array[i])
-        }
-    }
-}
+fun <T : Any> MemoryWriter.writeArray(spec: MemorySpec<T>, offset: Int, array: Array<T>): Unit =
+    with(spec) { array.indices.forEach { i -> write(offset + i * objectSize, array[i]) } }
 
 //TODO It is possible to add elastic MemorySpec with unknown object size
\ No newline at end of file
-- 
2.34.1


From 7d32fe0af82c4133b8173ff0f6228d417104760c Mon Sep 17 00:00:00 2001
From: Iaroslav Postovalov <postovalovya@gmail.com>
Date: Wed, 5 Aug 2020 18:43:20 +0700
Subject: [PATCH 05/12] Update documentation of NumberAlgebra

---
 .../kotlin/scientifik/kmath/operations/NumberAlgebra.kt      | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt
index 2145eb4b5..f99a6bc0f 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt
@@ -52,7 +52,7 @@ inline class Real(val value: Double) : FieldElement<Double, Real, RealField> {
 }
 
 /**
- * A field for double without boxing. Does not produce appropriate field element
+ * A field for [Double] without boxing. Does not produce appropriate field element.
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object RealField : ExtendedField<Double>, Norm<Double, Double> {
@@ -94,6 +94,9 @@ object RealField : ExtendedField<Double>, Norm<Double, Double> {
     }
 }
 
+/**
+ * A field for [Float] without boxing. Does not produce appropriate field element.
+ */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object FloatField : ExtendedField<Float>, Norm<Float, Float> {
     override val zero: Float = 0f
-- 
2.34.1


From 4c39b9801747d5016e0e1e04414ce868d6fdce43 Mon Sep 17 00:00:00 2001
From: Iaroslav Postovalov <postovalovya@gmail.com>
Date: Wed, 5 Aug 2020 18:44:28 +0700
Subject: [PATCH 06/12] Update documentation of NumberAlgebra

---
 .../kotlin/scientifik/kmath/operations/NumberAlgebra.kt     | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt
index f99a6bc0f..b113e07a1 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt
@@ -4,7 +4,7 @@ import kotlin.math.abs
 import kotlin.math.pow as kpow
 
 /**
- * Advanced Number-like field that implements basic operations
+ * Advanced Number-like semifield that implements basic operations.
  */
 interface ExtendedFieldOperations<T> :
     InverseTrigonometricOperations<T>,
@@ -27,6 +27,10 @@ interface ExtendedFieldOperations<T> :
     }
 }
 
+
+/**
+ * Advanced Number-like field that implements basic operations.
+ */
 interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T> {
     override fun rightSideNumberOperation(operation: String, left: T, right: Number): T = when (operation) {
         PowerOperations.POW_OPERATION -> power(left, right)
-- 
2.34.1


From eae218ff5f0c46bbab8a0d425f54467944a0d71b Mon Sep 17 00:00:00 2001
From: Iaroslav Postovalov <postovalovya@gmail.com>
Date: Wed, 5 Aug 2020 20:55:50 +0700
Subject: [PATCH 07/12] Update algebra extensions, improve docs

---
 .../kmath/operations/AlgebraExtensions.kt     | 55 +++++++++++++++++--
 .../kmath/operations/OptionalOperations.kt    |  6 +-
 .../scientifik/kmath/structures/Buffers.kt    | 31 +++++++++--
 .../scientifik/kmath/structures/IntBuffer.kt  | 11 ++++
 .../scientifik/kmath/operations/BigNumbers.kt |  9 ++-
 5 files changed, 100 insertions(+), 12 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt
index a6d508ee4..6712d3baa 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt
@@ -1,15 +1,62 @@
 package scientifik.kmath.operations
 
+/**
+ * Returns the sum of all elements in the iterable in this [Space].
+ *
+ * @receiver the algebra that provides addition.
+ * @param data the collection to sum up.
+ * @return the sum.
+ */
 fun <T> Space<T>.sum(data: Iterable<T>): T = data.fold(zero) { left, right -> add(left, right) }
+
+/**
+ * Returns the sum of all elements in the sequence in this [Space].
+ *
+ * @receiver the algebra that provides addition.
+ * @param data the collection to sum up.
+ * @return the sum.
+ */
 fun <T> Space<T>.sum(data: Sequence<T>): T = data.fold(zero) { left, right -> add(left, right) }
 
+/**
+ * Returns the sum of all elements in the iterable in provided space.
+ *
+ * @receiver the collection to sum up.
+ * @param space the algebra that provides addition.
+ * @return the sum.
+ */
 fun <T : Any, S : Space<T>> Iterable<T>.sumWith(space: S): T = space.sum(this)
 
 //TODO optimized power operation
-fun <T> RingOperations<T>.power(arg: T, power: Int): T {
+
+/**
+ * Raises [arg] to the natural power [power].
+ *
+ * @receiver the algebra to provide multiplication.
+ * @param arg the base.
+ * @param power the exponent.
+ * @return the base raised to the power.
+ */
+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
-    }
+    repeat(power - 1) { res *= arg }
     return res
 }
+
+/**
+ * Raises [arg] to the integer power [power].
+ *
+ * @receiver the algebra to provide multiplication and division.
+ * @param arg the base.
+ * @param power the exponent.
+ * @return the base raised to the power.
+ */
+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)
+}
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt
index 75adb1dee..dea45a145 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt
@@ -143,7 +143,11 @@ interface PowerOperations<T> : Algebra<T> {
 }
 
 /**
- * Raises [arg] to the power [pow].
+ * Raises this element to the power [pow].
+ *
+ * @receiver the base.
+ * @param power the exponent.
+ * @return the base raised to the power.
  */
 infix fun <T : MathElement<out PowerOperations<T>>> T.pow(power: Double): T = context.power(this, power)
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
index 723348e3f..294549c31 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
@@ -4,13 +4,22 @@ import scientifik.kmath.operations.Complex
 import scientifik.kmath.operations.complex
 import kotlin.reflect.KClass
 
-
+/**
+ * Function that produces [Buffer] from its size and function that supplies values.
+ *
+ * @param T the type of buffer.
+ */
 typealias BufferFactory<T> = (Int, (Int) -> T) -> Buffer<T>
-typealias MutableBufferFactory<T> = (Int, (Int) -> T) -> MutableBuffer<T>
-
 
 /**
- * A generic random access structure for both primitives and objects
+ * Function that produces [MutableBuffer] from its size and function that supplies values.
+ *
+ * @param T the type of buffer.
+ */
+typealias MutableBufferFactory<T> = (Int, (Int) -> T) -> MutableBuffer<T>
+
+/**
+ * A generic random-access structure for both primitives and objects.
  */
 interface Buffer<T> {
 
@@ -69,12 +78,24 @@ interface Buffer<T> {
     }
 }
 
+/**
+ * Creates a sequence that returns all elements from this [Buffer].
+ */
 fun <T> Buffer<T>.asSequence(): Sequence<T> = Sequence(::iterator)
 
+/**
+ * Creates an iterable that returns all elements from this [Buffer].
+ */
 fun <T> Buffer<T>.asIterable(): Iterable<T> = Iterable(::iterator)
 
-val Buffer<*>.indices: IntRange get() = IntRange(0, size - 1)
+/**
+ * Returns an [IntRange] of the valid indices for this [Buffer].
+ */
+val Buffer<*>.indices: IntRange get() = 0 until size
 
+/**
+ * A generic mutable random-access structure for both primitives and objects.
+ */
 interface MutableBuffer<T> : Buffer<T> {
     operator fun set(index: Int, value: T)
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
index b277374ab..99fd052aa 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
@@ -1,5 +1,10 @@
 package scientifik.kmath.structures
 
+/**
+ * Specialized [MutableBuffer] implementation over [IntArray].
+ *
+ * @property array the underlying array.
+ */
 inline class IntBuffer(val array: IntArray) : MutableBuffer<Int> {
     override val size: Int get() = array.size
 
@@ -16,4 +21,10 @@ inline class IntBuffer(val array: IntArray) : MutableBuffer<Int> {
 
 }
 
+/**
+ * Returns [IntBuffer] over this array.
+ *
+ * @receiver the array.
+ * @return the new buffer.
+ */
 fun IntArray.asBuffer(): IntBuffer = IntBuffer(this)
diff --git a/kmath-core/src/jvmMain/kotlin/scientifik/kmath/operations/BigNumbers.kt b/kmath-core/src/jvmMain/kotlin/scientifik/kmath/operations/BigNumbers.kt
index eb268bb5e..06f2b31ad 100644
--- a/kmath-core/src/jvmMain/kotlin/scientifik/kmath/operations/BigNumbers.kt
+++ b/kmath-core/src/jvmMain/kotlin/scientifik/kmath/operations/BigNumbers.kt
@@ -5,7 +5,7 @@ import java.math.BigInteger
 import java.math.MathContext
 
 /**
- * A field wrapper for Java [BigInteger]
+ * A field over [BigInteger].
  */
 object JBigIntegerField : Field<BigInteger> {
     override val zero: BigInteger
@@ -24,7 +24,9 @@ object JBigIntegerField : Field<BigInteger> {
 }
 
 /**
- * A Field wrapper for Java [BigDecimal]
+ * An abstract field over [BigDecimal].
+ *
+ * @property mathContext the [MathContext] to use.
  */
 abstract class JBigDecimalFieldBase internal constructor(val mathContext: MathContext = MathContext.DECIMAL64) :
     Field<BigDecimal>,
@@ -50,6 +52,9 @@ abstract class JBigDecimalFieldBase internal constructor(val mathContext: MathCo
 
 }
 
+/**
+ * A field over [BigDecimal].
+ */
 class JBigDecimalField(mathContext: MathContext = MathContext.DECIMAL64) : JBigDecimalFieldBase(mathContext) {
     companion object : JBigDecimalFieldBase()
 }
-- 
2.34.1


From 9f6bd116f660003c36d6655c2930a8a62a4e8770 Mon Sep 17 00:00:00 2001
From: Iaroslav Postovalov <postovalovya@gmail.com>
Date: Thu, 6 Aug 2020 12:39:50 +0700
Subject: [PATCH 08/12] Document and make more consistent buffers API

---
 .../scientifik/kmath/structures/Buffers.kt    |  5 +++-
 .../scientifik/kmath/structures/IntBuffer.kt  | 22 +++++++++++++++++
 .../scientifik/kmath/structures/RealBuffer.kt | 24 ++++++++++++++-----
 3 files changed, 44 insertions(+), 7 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
index 294549c31..73c3f96f4 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
@@ -97,10 +97,13 @@ val Buffer<*>.indices: IntRange get() = 0 until size
  * A generic mutable random-access structure for both primitives and objects.
  */
 interface MutableBuffer<T> : Buffer<T> {
+    /**
+     * Sets the array element at the specified [index] to the specified [value].
+     */
     operator fun set(index: Int, value: T)
 
     /**
-     * A shallow copy of the buffer
+     * Returns a shallow copy of the buffer.
      */
     fun copy(): MutableBuffer<T>
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
index 99fd052aa..3bf8ef6ab 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
@@ -21,6 +21,28 @@ inline class IntBuffer(val array: IntArray) : MutableBuffer<Int> {
 
 }
 
+/**
+ * Creates a new [IntBuffer] with the specified [size], where each element is calculated by calling the specified
+ * [init] function.
+ *
+ * The function [init] is called for each array element sequentially starting from the first one.
+ * It should return the value for an array element given its index.
+ */
+@Suppress("FunctionName")
+inline fun IntBuffer(size: Int, init: (Int) -> Int): IntBuffer = IntBuffer(IntArray(size) { init(it) })
+
+/**
+ * Returns a new [IntBuffer] of given elements.
+ */
+@Suppress("FunctionName")
+fun IntBuffer(vararg ints: Int): IntBuffer = IntBuffer(ints)
+
+/**
+ * Returns a [IntArray] containing all of the elements of this [MutableBuffer].
+ */
+val MutableBuffer<out Int>.array: IntArray
+    get() = (if (this is IntBuffer) array else IntArray(size) { get(it) })
+
 /**
  * Returns [IntBuffer] over this array.
  *
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt
index 20187fe19..715f3a017 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt
@@ -15,20 +15,32 @@ inline class RealBuffer(val array: DoubleArray) : MutableBuffer<Double> {
         RealBuffer(array.copyOf())
 }
 
+/**
+ * Creates a new array with the specified [size], where each element is calculated by calling the specified
+ * [init] function.
+ *
+ * The function [init] is called for each array element sequentially starting from the first one.
+ * It should return the value for an array element given its index.
+ */
 @Suppress("FunctionName")
 inline fun RealBuffer(size: Int, init: (Int) -> Double): RealBuffer = RealBuffer(DoubleArray(size) { init(it) })
 
+/**
+ * Returns a new [RealBuffer] of given elements.
+ */
 @Suppress("FunctionName")
 fun RealBuffer(vararg doubles: Double): RealBuffer = RealBuffer(doubles)
 
 /**
- * Transform buffer of doubles into array for high performance operations
+ * Returns a [DoubleArray] containing all of the elements of this [MutableBuffer].
  */
 val MutableBuffer<out Double>.array: DoubleArray
-    get() = if (this is RealBuffer) {
-        array
-    } else {
-        DoubleArray(size) { get(it) }
-    }
+    get() = (if (this is RealBuffer) array else DoubleArray(size) { get(it) })
 
+/**
+ * Returns [RealBuffer] over this array.
+ *
+ * @receiver the array.
+ * @return the new buffer.
+ */
 fun DoubleArray.asBuffer(): RealBuffer = RealBuffer(this)
-- 
2.34.1


From 0a8044ddb3cf4fd6fc38431106daea4aa4ff5302 Mon Sep 17 00:00:00 2001
From: Iaroslav <postovalovya@gmail.com>
Date: Fri, 7 Aug 2020 15:20:26 +0700
Subject: [PATCH 09/12] Update buffers documentation, make API more consistent,
 minor changes

---
 .../scientifik/kmath/expressions/Builders.kt  |  6 +-
 .../kmath/operations/AlgebraElements.kt       | 13 ++++
 .../scientifik/kmath/structures/Buffers.kt    | 63 +++++++++++++++----
 .../kmath/structures/FlaggedBuffer.kt         | 22 ++++++-
 .../kmath/structures/FloatBuffer.kt           | 49 +++++++++++++++
 .../scientifik/kmath/structures/IntBuffer.kt  |  4 +-
 .../scientifik/kmath/structures/LongBuffer.kt | 31 +++++++++
 .../kmath/structures/MemoryBuffer.kt          | 13 +++-
 .../scientifik/kmath/structures/NDAlgebra.kt  |  4 +-
 .../scientifik/kmath/structures/RealBuffer.kt | 11 ++--
 .../kmath/structures/RealBufferField.kt       |  7 ++-
 .../kmath/structures/ShortBuffer.kt           | 31 +++++++++
 12 files changed, 227 insertions(+), 27 deletions(-)
 create mode 100644 kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FloatBuffer.kt

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Builders.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Builders.kt
index 9f1503285..834ef9e24 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Builders.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Builders.kt
@@ -5,19 +5,19 @@ import scientifik.kmath.operations.Ring
 import scientifik.kmath.operations.Space
 
 /**
- * Create a functional expression on this [Space]
+ * Creates a functional expression with this [Space].
  */
 fun <T> Space<T>.spaceExpression(block: FunctionalExpressionSpace<T, Space<T>>.() -> Expression<T>): Expression<T> =
     FunctionalExpressionSpace(this).run(block)
 
 /**
- * Create a functional expression on this [Ring]
+ * Creates a functional expression with this [Ring].
  */
 fun <T> Ring<T>.ringExpression(block: FunctionalExpressionRing<T, Ring<T>>.() -> Expression<T>): Expression<T> =
     FunctionalExpressionRing(this).run(block)
 
 /**
- * Create a functional expression on this [Field]
+ * Creates a functional expression with this [Field].
  */
 fun <T> Field<T>.fieldExpression(block: FunctionalExpressionField<T, Field<T>>.() -> Expression<T>): Expression<T> =
     FunctionalExpressionField(this).run(block)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
index 534f56e0d..197897c14 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt
@@ -12,8 +12,21 @@ interface MathElement<C> {
     val context: C
 }
 
+/**
+ * Represents element that can be wrapped to its "primitive" value.
+ *
+ * @param T the type wrapped by this wrapper.
+ * @param I the type of this wrapper.
+ */
 interface MathWrapper<T, I> {
+    /**
+     * Unwraps [I] to [T].
+     */
     fun unwrap(): T
+
+    /**
+     * Wraps [T] to [I].
+     */
     fun T.wrap(): I
 }
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
index 73c3f96f4..5fdf79e88 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
@@ -19,10 +19,11 @@ typealias BufferFactory<T> = (Int, (Int) -> T) -> Buffer<T>
 typealias MutableBufferFactory<T> = (Int, (Int) -> T) -> MutableBuffer<T>
 
 /**
- * A generic random-access structure for both primitives and objects.
+ * A generic immutable random-access structure for both primitives and objects.
+ *
+ * @param T the type of elements contained in the buffer.
  */
 interface Buffer<T> {
-
     /**
      * The size of this buffer.
      */
@@ -45,7 +46,6 @@ interface Buffer<T> {
         asSequence().mapIndexed { index, value -> value == other[index] }.all { it }
 
     companion object {
-
         inline fun real(size: Int, initializer: (Int) -> Double): RealBuffer {
             val array = DoubleArray(size) { initializer(it) }
             return RealBuffer(array)
@@ -95,6 +95,8 @@ val Buffer<*>.indices: IntRange get() = 0 until size
 
 /**
  * A generic mutable random-access structure for both primitives and objects.
+ *
+ * @param T the type of elements contained in the buffer.
  */
 interface MutableBuffer<T> : Buffer<T> {
     /**
@@ -138,8 +140,13 @@ interface MutableBuffer<T> : Buffer<T> {
     }
 }
 
+/**
+ * [Buffer] implementation over [List].
+ *
+ * @param T the type of elements contained in the buffer.
+ * @property list The underlying list.
+ */
 inline class ListBuffer<T>(val list: List<T>) : Buffer<T> {
-
     override val size: Int
         get() = list.size
 
@@ -148,10 +155,26 @@ inline class ListBuffer<T>(val list: List<T>) : Buffer<T> {
     override fun iterator(): Iterator<T> = list.iterator()
 }
 
+/**
+ * Returns an [ListBuffer] that wraps the original list.
+ */
 fun <T> List<T>.asBuffer(): ListBuffer<T> = ListBuffer(this)
 
+/**
+ * Creates a new [ListBuffer] with the specified [size], where each element is calculated by calling the specified
+ * [init] function.
+ *
+ * The function [init] is called for each array element sequentially starting from the first one.
+ * It should return the value for an array element given its index.
+ */
 inline fun <T> ListBuffer(size: Int, init: (Int) -> T): ListBuffer<T> = List(size, init).asBuffer()
 
+/**
+ * [MutableBuffer] implementation over [MutableList].
+ *
+ * @param T the type of elements contained in the buffer.
+ * @property list The underlying list.
+ */
 inline class MutableListBuffer<T>(val list: MutableList<T>) : MutableBuffer<T> {
 
     override val size: Int
@@ -167,8 +190,14 @@ inline class MutableListBuffer<T>(val list: MutableList<T>) : MutableBuffer<T> {
     override fun copy(): MutableBuffer<T> = MutableListBuffer(ArrayList(list))
 }
 
+/**
+ * [MutableBuffer] implementation over [Array].
+ *
+ * @param T the type of elements contained in the buffer.
+ * @property array The underlying array.
+ */
 class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
-    //Can't inline because array is invariant
+    // Can't inline because array is invariant
     override val size: Int
         get() = array.size
 
@@ -183,8 +212,17 @@ class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
     override fun copy(): MutableBuffer<T> = ArrayBuffer(array.copyOf())
 }
 
+/**
+ * Returns an [ArrayBuffer] that wraps the original array.
+ */
 fun <T> Array<T>.asBuffer(): ArrayBuffer<T> = ArrayBuffer(this)
 
+/**
+ * Immutable wrapper for [MutableBuffer].
+ *
+ * @param T the type of elements contained in the buffer.
+ * @property buffer The underlying buffer.
+ */
 inline class ReadOnlyBuffer<T>(val buffer: MutableBuffer<T>) : Buffer<T> {
     override val size: Int get() = buffer.size
 
@@ -196,6 +234,8 @@ inline class ReadOnlyBuffer<T>(val buffer: MutableBuffer<T>) : Buffer<T> {
 /**
  * A buffer with content calculated on-demand. The calculated content is not stored, so it is recalculated on each call.
  * Useful when one needs single element from the buffer.
+ *
+ * @param T the type of elements provided by the buffer.
  */
 class VirtualBuffer<T>(override val size: Int, private val generator: (Int) -> T) : Buffer<T> {
     override fun get(index: Int): T {
@@ -215,17 +255,16 @@ class VirtualBuffer<T>(override val size: Int, private val generator: (Int) -> T
 }
 
 /**
- * Convert this buffer to read-only buffer
+ * Convert this buffer to read-only buffer.
  */
-fun <T> Buffer<T>.asReadOnly(): Buffer<T> = if (this is MutableBuffer) {
-    ReadOnlyBuffer(this)
-} else {
-    this
-}
+fun <T> Buffer<T>.asReadOnly(): Buffer<T> = if (this is MutableBuffer) ReadOnlyBuffer(this) else this
 
 /**
- * Typealias for buffer transformations
+ * Typealias for buffer transformations.
  */
 typealias BufferTransform<T, R> = (Buffer<T>) -> Buffer<R>
 
+/**
+ * Typealias for buffer transformations with suspend function.
+ */
 typealias SuspendBufferTransform<T, R> = suspend (Buffer<T>) -> Buffer<R>
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FlaggedBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FlaggedBuffer.kt
index 2382e2c57..a2d0a71b3 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FlaggedBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FlaggedBuffer.kt
@@ -2,15 +2,35 @@ package scientifik.kmath.structures
 
 import kotlin.experimental.and
 
+/**
+ * Represents flags to supply additional info about values of buffer.
+ *
+ * @property mask bit mask value of this flag.
+ */
 enum class ValueFlag(val mask: Byte) {
+    /**
+     * Reports the value is NaN.
+     */
     NAN(0b0000_0001),
+
+    /**
+     * Reports the value doesn't present in the buffer (when the type of value doesn't support `null`).
+     */
     MISSING(0b0000_0010),
+
+    /**
+     * Reports the value is negative infinity.
+     */
     NEGATIVE_INFINITY(0b0000_0100),
+
+    /**
+     * Reports the value is positive infinity
+     */
     POSITIVE_INFINITY(0b0000_1000)
 }
 
 /**
- * A buffer with flagged values
+ * A buffer with flagged values.
  */
 interface FlaggedBuffer<T> : Buffer<T> {
     fun getFlag(index: Int): Byte
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FloatBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FloatBuffer.kt
new file mode 100644
index 000000000..e42df8c14
--- /dev/null
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FloatBuffer.kt
@@ -0,0 +1,49 @@
+package scientifik.kmath.structures
+
+/**
+ * Specialized [MutableBuffer] implementation over [FloatArray].
+ *
+ * @property array the underlying array.
+ */
+inline class FloatBuffer(val array: FloatArray) : MutableBuffer<Float> {
+    override val size: Int get() = array.size
+
+    override fun get(index: Int): Float = array[index]
+
+    override fun set(index: Int, value: Float) {
+        array[index] = value
+    }
+
+    override fun iterator(): FloatIterator = array.iterator()
+
+    override fun copy(): MutableBuffer<Float> =
+        FloatBuffer(array.copyOf())
+}
+
+/**
+ * Creates a new [FloatBuffer] with the specified [size], where each element is calculated by calling the specified
+ * [init] function.
+ *
+ * The function [init] is called for each array element sequentially starting from the first one.
+ * It should return the value for an buffer element given its index.
+ */
+inline fun FloatBuffer(size: Int, init: (Int) -> Float): FloatBuffer = FloatBuffer(FloatArray(size) { init(it) })
+
+/**
+ * Returns a new [FloatBuffer] of given elements.
+ */
+fun FloatBuffer(vararg floats: Float): FloatBuffer = FloatBuffer(floats)
+
+/**
+ * Returns a [FloatArray] containing all of the elements of this [MutableBuffer].
+ */
+val MutableBuffer<out Float>.array: FloatArray
+    get() = (if (this is FloatBuffer) array else FloatArray(size) { get(it) })
+
+/**
+ * Returns [FloatBuffer] over this array.
+ *
+ * @receiver the array.
+ * @return the new buffer.
+ */
+fun FloatArray.asBuffer(): FloatBuffer = FloatBuffer(this)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
index 3bf8ef6ab..a3f0f3c3e 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt
@@ -26,15 +26,13 @@ inline class IntBuffer(val array: IntArray) : MutableBuffer<Int> {
  * [init] function.
  *
  * The function [init] is called for each array element sequentially starting from the first one.
- * It should return the value for an array element given its index.
+ * It should return the value for an buffer element given its index.
  */
-@Suppress("FunctionName")
 inline fun IntBuffer(size: Int, init: (Int) -> Int): IntBuffer = IntBuffer(IntArray(size) { init(it) })
 
 /**
  * Returns a new [IntBuffer] of given elements.
  */
-@Suppress("FunctionName")
 fun IntBuffer(vararg ints: Int): IntBuffer = IntBuffer(ints)
 
 /**
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LongBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LongBuffer.kt
index 3ee2e75a2..912656c68 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LongBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LongBuffer.kt
@@ -1,5 +1,10 @@
 package scientifik.kmath.structures
 
+/**
+ * Specialized [MutableBuffer] implementation over [LongArray].
+ *
+ * @property array the underlying array.
+ */
 inline class LongBuffer(val array: LongArray) : MutableBuffer<Long> {
     override val size: Int get() = array.size
 
@@ -16,4 +21,30 @@ inline class LongBuffer(val array: LongArray) : MutableBuffer<Long> {
 
 }
 
+/**
+ * Creates a new [LongBuffer] with the specified [size], where each element is calculated by calling the specified
+ * [init] function.
+ *
+ * The function [init] is called for each array element sequentially starting from the first one.
+ * It should return the value for an buffer element given its index.
+ */
+inline fun LongBuffer(size: Int, init: (Int) -> Long): LongBuffer = LongBuffer(LongArray(size) { init(it) })
+
+/**
+ * Returns a new [LongBuffer] of given elements.
+ */
+fun LongBuffer(vararg longs: Long): LongBuffer = LongBuffer(longs)
+
+/**
+ * Returns a [IntArray] containing all of the elements of this [MutableBuffer].
+ */
+val MutableBuffer<out Long>.array: LongArray
+    get() = (if (this is LongBuffer) array else LongArray(size) { get(it) })
+
+/**
+ * Returns [LongBuffer] over this array.
+ *
+ * @receiver the array.
+ * @return the new buffer.
+ */
 fun LongArray.asBuffer(): LongBuffer = LongBuffer(this)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt
index b15487114..70e4a8f0f 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt
@@ -4,12 +4,16 @@ import scientifik.memory.*
 
 /**
  * A non-boxing buffer over [Memory] object.
+ *
+ * @param T the type of elements contained in the buffer.
+ * @property memory the underlying memory segment.
+ * @property spec the spec of [T] type.
  */
 open class MemoryBuffer<T : Any>(protected val memory: Memory, protected val spec: MemorySpec<T>) : Buffer<T> {
 
     override val size: Int get() = memory.size / spec.objectSize
 
-    private val reader = memory.reader()
+    private val reader: MemoryReader = memory.reader()
 
     override fun get(index: Int): T = reader.read(spec, spec.objectSize * index)
 
@@ -33,6 +37,13 @@ open class MemoryBuffer<T : Any>(protected val memory: Memory, protected val spe
     }
 }
 
+/**
+ * A mutable non-boxing buffer over [Memory] object.
+ *
+ * @param T the type of elements contained in the buffer.
+ * @property memory the underlying memory segment.
+ * @property spec the spec of [T] type.
+ */
 class MutableMemoryBuffer<T : Any>(memory: Memory, spec: MemorySpec<T>) : MemoryBuffer<T>(memory, spec),
     MutableBuffer<T> {
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt
index 750133351..f2805529c 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt
@@ -107,8 +107,8 @@ interface NDRing<T, R : Ring<T>, N : NDStructure<T>> : Ring<N>, NDSpace<T, R, N>
 /**
  * Field for n-dimensional structures.
  *
- * @param T - the type of the element contained in ND structure
- * @param F - field of structure elements
+ * @param T the type of the element contained in ND structure
+ * @param F field of structure elements
  */
 interface NDField<T, F : Field<T>, N : NDStructure<T>> : Field<N>, NDRing<T, F, N> {
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt
index 715f3a017..e999e12b2 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt
@@ -1,5 +1,10 @@
 package scientifik.kmath.structures
 
+/**
+ * Specialized [MutableBuffer] implementation over [DoubleArray].
+ *
+ * @property array the underlying array.
+ */
 inline class RealBuffer(val array: DoubleArray) : MutableBuffer<Double> {
     override val size: Int get() = array.size
 
@@ -16,19 +21,17 @@ inline class RealBuffer(val array: DoubleArray) : MutableBuffer<Double> {
 }
 
 /**
- * Creates a new array with the specified [size], where each element is calculated by calling the specified
+ * Creates a new [RealBuffer] with the specified [size], where each element is calculated by calling the specified
  * [init] function.
  *
  * The function [init] is called for each array element sequentially starting from the first one.
- * It should return the value for an array element given its index.
+ * It should return the value for an buffer element given its index.
  */
-@Suppress("FunctionName")
 inline fun RealBuffer(size: Int, init: (Int) -> Double): RealBuffer = RealBuffer(DoubleArray(size) { init(it) })
 
 /**
  * Returns a new [RealBuffer] of given elements.
  */
-@Suppress("FunctionName")
 fun RealBuffer(vararg doubles: Double): RealBuffer = RealBuffer(doubles)
 
 /**
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt
index 826203d1f..33198aac1 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt
@@ -6,7 +6,7 @@ import kotlin.math.*
 
 
 /**
- * A simple field over linear buffers of [Double]
+ * [ExtendedFieldOperations] over [RealBuffer].
  */
 object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
     override fun add(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
@@ -109,6 +109,11 @@ object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
         RealBuffer(DoubleArray(arg.size) { ln(arg[it]) })
 }
 
+/**
+ * [ExtendedField] over [RealBuffer].
+ *
+ * @property size the size of buffers to operate on.
+ */
 class RealBufferField(val size: Int) : ExtendedField<Buffer<Double>> {
     override val zero: Buffer<Double> by lazy { RealBuffer(size) { 0.0 } }
     override val one: Buffer<Double> by lazy { RealBuffer(size) { 1.0 } }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortBuffer.kt
index 24c94a885..a67cbec62 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortBuffer.kt
@@ -1,5 +1,10 @@
 package scientifik.kmath.structures
 
+/**
+ * Specialized [MutableBuffer] implementation over [ShortBuffer].
+ *
+ * @property array the underlying array.
+ */
 inline class ShortBuffer(val array: ShortArray) : MutableBuffer<Short> {
     override val size: Int get() = array.size
 
@@ -16,4 +21,30 @@ inline class ShortBuffer(val array: ShortArray) : MutableBuffer<Short> {
 
 }
 
+/**
+ * Creates a new [ShortBuffer] with the specified [size], where each element is calculated by calling the specified
+ * [init] function.
+ *
+ * The function [init] is called for each array element sequentially starting from the first one.
+ * It should return the value for an buffer element given its index.
+ */
+inline fun ShortBuffer(size: Int, init: (Int) -> Short): ShortBuffer = ShortBuffer(ShortArray(size) { init(it) })
+
+/**
+ * Returns a new [ShortBuffer] of given elements.
+ */
+fun ShortBuffer(vararg shorts: Short): ShortBuffer = ShortBuffer(shorts)
+
+/**
+ * Returns a [ShortArray] containing all of the elements of this [MutableBuffer].
+ */
+val MutableBuffer<out Short>.array: ShortArray
+    get() = (if (this is ShortBuffer) array else ShortArray(size) { get(it) })
+
+/**
+ * Returns [ShortBuffer] over this array.
+ *
+ * @receiver the array.
+ * @return the new buffer.
+ */
 fun ShortArray.asBuffer(): ShortBuffer = ShortBuffer(this)
-- 
2.34.1


From c8cd6cd28857b14199ee99683f789eb11a28794e Mon Sep 17 00:00:00 2001
From: Iaroslav <postovalovya@gmail.com>
Date: Sat, 8 Aug 2020 04:21:59 +0700
Subject: [PATCH 10/12] Document memory module and several ND objects

---
 .../kmath/structures/BoxingNDField.kt         |  1 -
 .../kmath/structures/BufferedNDAlgebra.kt     |  3 +-
 .../kmath/structures/ComplexNDField.kt        |  4 +-
 .../kmath/structures/ExtendedNDField.kt       |  7 ++
 .../kmath/structures/MemoryBuffer.kt          |  1 -
 .../scientifik/kmath/structures/NDAlgebra.kt  |  7 +-
 .../kmath/structures/NDStructure.kt           | 77 ++++++++++++---
 .../kmath/structures/RealNDField.kt           |  4 +-
 .../kotlin/scientifik/memory/Memory.kt        | 97 ++++++++++++++++---
 .../kotlin/scientifik/memory/MemorySpec.kt    | 17 +++-
 .../scientifik/memory/DataViewMemory.kt       | 18 ++--
 .../scientifik/memory/ByteBufferMemory.kt     | 48 ++++-----
 12 files changed, 217 insertions(+), 67 deletions(-)

diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDField.kt
index 516f9a8cd..4cbb565c1 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BoxingNDField.kt
@@ -3,7 +3,6 @@ package scientifik.kmath.structures
 import scientifik.kmath.operations.Field
 import scientifik.kmath.operations.FieldElement
 
-
 class BoxingNDField<T, F : Field<T>>(
     override val shape: IntArray,
     override val elementContext: F,
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDAlgebra.kt
index baf1a05a6..06922c56f 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDAlgebra.kt
@@ -11,7 +11,8 @@ interface BufferedNDAlgebra<T, C> : NDAlgebra<T, C, NDBuffer<T>> {
 
     /**
      * Convert any [NDStructure] to buffered structure using strides from this context.
-     * If the structure is already [NDBuffer], conversion is free. If not, it could be expensive because iteration over indexes
+     * If the structure is already [NDBuffer], conversion is free. If not, it could be expensive because iteration over
+     * indices.
      *
      * If the argument is [NDBuffer] with different strides structure, the new element will be produced.
      */
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ComplexNDField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ComplexNDField.kt
index 2f7d20b6d..be0b9e5c6 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ComplexNDField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ComplexNDField.kt
@@ -98,13 +98,13 @@ inline fun BufferedNDField<Complex, ComplexField>.produceInline(crossinline init
 }
 
 /**
- * Map one [ComplexNDElement] using function with indexes
+ * Map one [ComplexNDElement] using function with indices.
  */
 inline fun ComplexNDElement.mapIndexed(crossinline transform: ComplexField.(index: IntArray, Complex) -> Complex): ComplexNDElement =
     context.produceInline { offset -> transform(strides.index(offset), buffer[offset]) }
 
 /**
- * Map one [ComplexNDElement] using function without indexes
+ * Map one [ComplexNDElement] using function without indices.
  */
 inline fun ComplexNDElement.map(crossinline transform: ComplexField.(Complex) -> Complex): ComplexNDElement {
     val buffer = Buffer.complex(strides.linearSize) { offset -> ComplexField.transform(buffer[offset]) }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ExtendedNDField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ExtendedNDField.kt
index 1fe449632..24aa48c6b 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ExtendedNDField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ExtendedNDField.kt
@@ -2,6 +2,13 @@ package scientifik.kmath.structures
 
 import scientifik.kmath.operations.ExtendedField
 
+/**
+ * [ExtendedField] over [NDStructure].
+ *
+ * @param T the type of the element contained in ND structure.
+ * @param N the type of ND structure.
+ * @param F the extended field of structure elements.
+ */
 interface ExtendedNDField<T : Any, F : ExtendedField<T>, N : NDStructure<T>> : NDField<T, F, N>, ExtendedField<N>
 
 ///**
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt
index 70e4a8f0f..1d0c87580 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt
@@ -10,7 +10,6 @@ import scientifik.memory.*
  * @property spec the spec of [T] type.
  */
 open class MemoryBuffer<T : Any>(protected val memory: Memory, protected val spec: MemorySpec<T>) : Buffer<T> {
-
     override val size: Int get() = memory.size / spec.objectSize
 
     private val reader: MemoryReader = memory.reader()
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt
index f2805529c..f09db3c72 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDAlgebra.kt
@@ -105,10 +105,11 @@ interface NDRing<T, R : Ring<T>, N : NDStructure<T>> : Ring<N>, NDSpace<T, R, N>
 }
 
 /**
- * Field for n-dimensional structures.
+ * Field of [NDStructure].
  *
- * @param T the type of the element contained in ND structure
- * @param F field of structure elements
+ * @param T the type of the element contained in ND structure.
+ * @param N the type of ND structure.
+ * @param F field of structure elements.
  */
 interface NDField<T, F : Field<T>, N : NDStructure<T>> : Field<N>, NDRing<T, F, N> {
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt
index bcd74ed2a..9d7735053 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt
@@ -3,15 +3,38 @@ package scientifik.kmath.structures
 import kotlin.jvm.JvmName
 import kotlin.reflect.KClass
 
-
+/**
+ * Represents n-dimensional structure, i.e. multidimensional container of items of the same type and size. The number
+ * of dimensions and items in an array is defined by its shape, which is a sequence of non-negative integers that
+ * specify the sizes of each dimension.
+ *
+ * @param T the type of items.
+ */
 interface NDStructure<T> {
-
+    /**
+     * The shape of structure, i.e. non-empty sequence of non-negative integers that specify sizes of dimensions of
+     * this structure.
+     */
     val shape: IntArray
 
+    /**
+     * The count of dimensions in this structure. It should be equal to size of [shape].
+     */
     val dimension: Int get() = shape.size
 
+    /**
+     * Returns the value at the specified indices.
+     *
+     * @param index the indices.
+     * @return the value.
+     */
     operator fun get(index: IntArray): T
 
+    /**
+     * Returns the sequence of all the elements associated by their indices.
+     *
+     * @return the lazy sequence of pairs of indices to values.
+     */
     fun elements(): Sequence<Pair<IntArray, T>>
 
     override fun equals(other: Any?): Boolean
@@ -19,6 +42,9 @@ interface NDStructure<T> {
     override fun hashCode(): Int
 
     companion object {
+        /**
+         * Indicates whether some [NDStructure] is equal to another one.
+         */
         fun equals(st1: NDStructure<*>, st2: NDStructure<*>): Boolean {
             if (st1 === st2) return true
 
@@ -36,9 +62,9 @@ interface NDStructure<T> {
         }
 
         /**
-         * Create a NDStructure with explicit buffer factory
+         * Creates a NDStructure with explicit buffer factory.
          *
-         * Strides should be reused if possible
+         * Strides should be reused if possible.
          */
         fun <T> build(
             strides: Strides,
@@ -91,9 +117,24 @@ interface NDStructure<T> {
     }
 }
 
+/**
+ * Returns the value at the specified indices.
+ *
+ * @param index the indices.
+ * @return the value.
+ */
 operator fun <T> NDStructure<T>.get(vararg index: Int): T = get(index)
 
+/**
+ * Represents mutable [NDStructure].
+ */
 interface MutableNDStructure<T> : NDStructure<T> {
+    /**
+     * Inserts an item at the specified indices.
+     *
+     * @param index the indices.
+     * @param value the value.
+     */
     operator fun set(index: IntArray, value: T)
 }
 
@@ -104,7 +145,7 @@ inline fun <T> MutableNDStructure<T>.mapInPlace(action: (IntArray, T) -> T) {
 }
 
 /**
- * A way to convert ND index to linear one and back
+ * A way to convert ND index to linear one and back.
  */
 interface Strides {
     /**
@@ -141,6 +182,9 @@ interface Strides {
     }
 }
 
+/**
+ * Simple implementation of [Strides].
+ */
 class DefaultStrides private constructor(override val shape: IntArray) : Strides {
     /**
      * Strides for memory access
@@ -180,19 +224,14 @@ class DefaultStrides private constructor(override val shape: IntArray) : Strides
     override val linearSize: Int
         get() = strides[shape.size]
 
-
     override fun equals(other: Any?): Boolean {
         if (this === other) return true
         if (other !is DefaultStrides) return false
-
         if (!shape.contentEquals(other.shape)) return false
-
         return true
     }
 
-    override fun hashCode(): Int {
-        return shape.contentHashCode()
-    }
+    override fun hashCode(): Int = shape.contentHashCode()
 
     companion object {
         private val defaultStridesCache = HashMap<IntArray, Strides>()
@@ -204,8 +243,20 @@ class DefaultStrides private constructor(override val shape: IntArray) : Strides
     }
 }
 
+/**
+ * Represents [NDStructure] over [Buffer].
+ *
+ * @param T the type of items.
+ */
 abstract class NDBuffer<T> : NDStructure<T> {
+    /**
+     * The underlying buffer.
+     */
     abstract val buffer: Buffer<T>
+
+    /**
+     * The strides to access elements of [Buffer] by linear indices.
+     */
     abstract val strides: Strides
 
     override fun get(index: IntArray): T = buffer[strides.offset(index)]
@@ -263,8 +314,8 @@ class MutableBufferNDStructure<T>(
 ) : NDBuffer<T>(), MutableNDStructure<T> {
 
     init {
-        if (strides.linearSize != buffer.size) {
-            error("Expected buffer side of ${strides.linearSize}, but found ${buffer.size}")
+        require(strides.linearSize == buffer.size) {
+            "Expected buffer side of ${strides.linearSize}, but found ${buffer.size}"
         }
     }
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt
index b89f28233..e2a1a33df 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt
@@ -93,13 +93,13 @@ inline fun BufferedNDField<Double, RealField>.produceInline(crossinline initiali
 }
 
 /**
- * Map one [RealNDElement] using function with indexes
+ * Map one [RealNDElement] using function with indices.
  */
 inline fun RealNDElement.mapIndexed(crossinline transform: RealField.(index: IntArray, Double) -> Double): RealNDElement =
     context.produceInline { offset -> transform(strides.index(offset), buffer[offset]) }
 
 /**
- * Map one [RealNDElement] using function without indexes
+ * Map one [RealNDElement] using function without indices.
  */
 inline fun RealNDElement.map(crossinline transform: RealField.(Double) -> Double): RealNDElement {
     val array = DoubleArray(strides.linearSize) { offset -> RealField.transform(buffer[offset]) }
diff --git a/kmath-memory/src/commonMain/kotlin/scientifik/memory/Memory.kt b/kmath-memory/src/commonMain/kotlin/scientifik/memory/Memory.kt
index 7c6886202..a749a7074 100644
--- a/kmath-memory/src/commonMain/kotlin/scientifik/memory/Memory.kt
+++ b/kmath-memory/src/commonMain/kotlin/scientifik/memory/Memory.kt
@@ -1,77 +1,148 @@
 package scientifik.memory
 
+/**
+ * Represents a display of certain memory structure.
+ */
 interface Memory {
+    /**
+     * The length of this memory in bytes.
+     */
     val size: Int
 
     /**
-     * Get a projection of this memory (it reflects the changes in the parent memory block)
+     * Get a projection of this memory (it reflects the changes in the parent memory block).
      */
     fun view(offset: Int, length: Int): Memory
 
     /**
-     * Create a copy of this memory, which does not know anything about this memory
+     * Creates an independent copy of this memory.
      */
     fun copy(): Memory
 
     /**
-     * Create and possibly register a new reader
+     * Gets or creates a reader of this memory.
      */
     fun reader(): MemoryReader
 
+    /**
+     * Gets or creates a writer of this memory.
+     */
     fun writer(): MemoryWriter
 
-    companion object {
-
-    }
+    companion object
 }
 
+/**
+ * The interface to read primitive types in this memory.
+ */
 interface MemoryReader {
+    /**
+     * The underlying memory.
+     */
     val memory: Memory
 
+    /**
+     * Reads [Double] at certain [offset].
+     */
     fun readDouble(offset: Int): Double
+
+    /**
+     * Reads [Float] at certain [offset].
+     */
     fun readFloat(offset: Int): Float
+
+    /**
+     * Reads [Byte] at certain [offset].
+     */
     fun readByte(offset: Int): Byte
+
+    /**
+     * Reads [Short] at certain [offset].
+     */
     fun readShort(offset: Int): Short
+
+    /**
+     * Reads [Int] at certain [offset].
+     */
     fun readInt(offset: Int): Int
+
+    /**
+     * Reads [Long] at certain [offset].
+     */
     fun readLong(offset: Int): Long
 
+    /**
+     * Disposes this reader if needed.
+     */
     fun release()
 }
 
 /**
- * Use the memory for read then release the reader
+ * Uses the memory for read then releases the reader.
  */
 inline fun Memory.read(block: MemoryReader.() -> Unit) {
-    reader().apply(block).apply { release() }
+    reader().apply(block).release()
 }
 
+/**
+ * The interface to write primitive types into this memory.
+ */
 interface MemoryWriter {
+    /**
+     * The underlying memory.
+     */
     val memory: Memory
 
+    /**
+     * Writes [Double] at certain [offset].
+     */
     fun writeDouble(offset: Int, value: Double)
+
+    /**
+     * Writes [Float] at certain [offset].
+     */
     fun writeFloat(offset: Int, value: Float)
+
+    /**
+     * Writes [Byte] at certain [offset].
+     */
     fun writeByte(offset: Int, value: Byte)
+
+    /**
+     * Writes [Short] at certain [offset].
+     */
     fun writeShort(offset: Int, value: Short)
+
+    /**
+     * Writes [Int] at certain [offset].
+     */
     fun writeInt(offset: Int, value: Int)
+
+    /**
+     * Writes [Long] at certain [offset].
+     */
     fun writeLong(offset: Int, value: Long)
 
+    /**
+     * Disposes this writer if needed.
+     */
     fun release()
 }
 
 /**
- * Use the memory for write then release the writer
+ * Uses the memory for write then releases the writer.
  */
 inline fun Memory.write(block: MemoryWriter.() -> Unit) {
-    writer().apply(block).apply { release() }
+    writer().apply(block).release()
 }
 
 /**
- * Allocate the most effective platform-specific memory
+ * Allocates the most effective platform-specific memory.
  */
 expect fun Memory.Companion.allocate(length: Int): Memory
 
 /**
- * Wrap a [Memory] around existing [ByteArray]. This operation is unsafe since the array is not copied
- * and could be mutated independently from the resulting [Memory]
+ * Wraps a [Memory] around existing [ByteArray]. This operation is unsafe since the array is not copied
+ * and could be mutated independently from the resulting [Memory].
  */
 expect fun Memory.Companion.wrap(array: ByteArray): Memory
diff --git a/kmath-memory/src/commonMain/kotlin/scientifik/memory/MemorySpec.kt b/kmath-memory/src/commonMain/kotlin/scientifik/memory/MemorySpec.kt
index 4d0035d09..59a93f290 100644
--- a/kmath-memory/src/commonMain/kotlin/scientifik/memory/MemorySpec.kt
+++ b/kmath-memory/src/commonMain/kotlin/scientifik/memory/MemorySpec.kt
@@ -7,7 +7,7 @@ package scientifik.memory
  */
 interface MemorySpec<T : Any> {
     /**
-     * Size of [T] in bytes after serialization
+     * Size of [T] in bytes after serialization.
      */
     val objectSize: Int
 
@@ -24,9 +24,19 @@ interface MemorySpec<T : Any> {
     fun MemoryWriter.write(offset: Int, value: T)
 }
 
+/**
+ * Reads the object with [spec] starting from [offset].
+ */
 fun <T : Any> MemoryReader.read(spec: MemorySpec<T>, offset: Int): T = with(spec) { read(offset) }
+
+/**
+ * Writes the object [value] with [spec] starting from [offset].
+ */
 fun <T : Any> MemoryWriter.write(spec: MemorySpec<T>, offset: Int, value: T): Unit = with(spec) { write(offset, value) }
 
+/**
+ * Reads array of [size] objects mapped by [spec] at certain [offset].
+ */
 inline fun <reified T : Any> MemoryReader.readArray(spec: MemorySpec<T>, offset: Int, size: Int): Array<T> =
     Array(size) { i ->
         spec.run {
@@ -34,7 +44,10 @@ inline fun <reified T : Any> MemoryReader.readArray(spec: MemorySpec<T>, offset:
         }
     }
 
+/**
+ * Writes [array] of objects mapped by [spec] at certain [offset].
+ */
 fun <T : Any> MemoryWriter.writeArray(spec: MemorySpec<T>, offset: Int, array: Array<T>): Unit =
     with(spec) { array.indices.forEach { i -> write(offset + i * objectSize, array[i]) } }
 
-//TODO It is possible to add elastic MemorySpec with unknown object size
\ No newline at end of file
+// TODO It is possible to add elastic MemorySpec with unknown object size
diff --git a/kmath-memory/src/jsMain/kotlin/scientifik/memory/DataViewMemory.kt b/kmath-memory/src/jsMain/kotlin/scientifik/memory/DataViewMemory.kt
index 38ec14824..974750502 100644
--- a/kmath-memory/src/jsMain/kotlin/scientifik/memory/DataViewMemory.kt
+++ b/kmath-memory/src/jsMain/kotlin/scientifik/memory/DataViewMemory.kt
@@ -4,13 +4,13 @@ import org.khronos.webgl.ArrayBuffer
 import org.khronos.webgl.DataView
 import org.khronos.webgl.Int8Array
 
-class DataViewMemory(val view: DataView) : Memory {
-
+private class DataViewMemory(val view: DataView) : Memory {
     override val size: Int get() = view.byteLength
 
     override fun view(offset: Int, length: Int): Memory {
         require(offset >= 0) { "offset shouldn't be negative: $offset" }
         require(length >= 0) { "length shouldn't be negative: $length" }
+        require(offset + length <= size) { "Can't view memory outside the parent region." }
 
         if (offset + length > size)
             throw IndexOutOfBoundsException("offset + length > size: $offset + $length > $size")
@@ -33,11 +33,11 @@ class DataViewMemory(val view: DataView) : Memory {
 
         override fun readInt(offset: Int): Int = view.getInt32(offset, false)
 
-        override fun readLong(offset: Int): Long = (view.getInt32(offset, false).toLong() shl 32) or
-                view.getInt32(offset + 4, false).toLong()
+        override fun readLong(offset: Int): Long =
+            view.getInt32(offset, false).toLong() shl 32 or view.getInt32(offset + 4, false).toLong()
 
         override fun release() {
-            // does nothing on JS because of GC
+            // does nothing on JS
         }
     }
 
@@ -72,7 +72,7 @@ class DataViewMemory(val view: DataView) : Memory {
         }
 
         override fun release() {
-            //does nothing on JS
+            // does nothing on JS
         }
     }
 
@@ -81,13 +81,17 @@ class DataViewMemory(val view: DataView) : Memory {
 }
 
 /**
- * Allocate the most effective platform-specific memory
+ * Allocates memory based on a [DataView].
  */
 actual fun Memory.Companion.allocate(length: Int): Memory {
     val buffer = ArrayBuffer(length)
     return DataViewMemory(DataView(buffer, 0, length))
 }
 
+/**
+ * Wraps a [Memory] around existing [ByteArray]. This operation is unsafe since the array is not copied
+ * and could be mutated independently from the resulting [Memory].
+ */
 actual fun Memory.Companion.wrap(array: ByteArray): Memory {
     @Suppress("CAST_NEVER_SUCCEEDS") val int8Array = array as Int8Array
     return DataViewMemory(DataView(int8Array.buffer, int8Array.byteOffset, int8Array.length))
diff --git a/kmath-memory/src/jvmMain/kotlin/scientifik/memory/ByteBufferMemory.kt b/kmath-memory/src/jvmMain/kotlin/scientifik/memory/ByteBufferMemory.kt
index 9ec2b3a09..b5a0dd51b 100644
--- a/kmath-memory/src/jvmMain/kotlin/scientifik/memory/ByteBufferMemory.kt
+++ b/kmath-memory/src/jvmMain/kotlin/scientifik/memory/ByteBufferMemory.kt
@@ -6,19 +6,18 @@ import java.nio.file.Files
 import java.nio.file.Path
 import java.nio.file.StandardOpenOption
 
-
 private class ByteBufferMemory(
     val buffer: ByteBuffer,
     val startOffset: Int = 0,
     override val size: Int = buffer.limit()
 ) : Memory {
-
-
     @Suppress("NOTHING_TO_INLINE")
     private inline fun position(o: Int): Int = startOffset + o
 
     override fun view(offset: Int, length: Int): Memory {
-        if (offset + length > size) error("Selecting a Memory view outside of memory range")
+        require(offset >= 0) { "offset shouldn't be negative: $offset" }
+        require(length >= 0) { "length shouldn't be negative: $length" }
+        require(offset + length <= size) { "Can't view memory outside the parent region." }
         return ByteBufferMemory(buffer, position(offset), length)
     }
 
@@ -28,10 +27,9 @@ private class ByteBufferMemory(
         copy.put(buffer)
         copy.flip()
         return ByteBufferMemory(copy)
-
     }
 
-    private val reader = object : MemoryReader {
+    private val reader: MemoryReader = object : MemoryReader {
         override val memory: Memory get() = this@ByteBufferMemory
 
         override fun readDouble(offset: Int) = buffer.getDouble(position(offset))
@@ -47,13 +45,13 @@ private class ByteBufferMemory(
         override fun readLong(offset: Int) = buffer.getLong(position(offset))
 
         override fun release() {
-            //does nothing on JVM
+            // does nothing on JVM
         }
     }
 
     override fun reader(): MemoryReader = reader
 
-    private val writer = object : MemoryWriter {
+    private val writer: MemoryWriter = object : MemoryWriter {
         override val memory: Memory get() = this@ByteBufferMemory
 
         override fun writeDouble(offset: Int, value: Double) {
@@ -81,7 +79,7 @@ private class ByteBufferMemory(
         }
 
         override fun release() {
-            //does nothing on JVM
+            // does nothing on JVM
         }
     }
 
@@ -89,26 +87,32 @@ private class ByteBufferMemory(
 }
 
 /**
- * Allocate the most effective platform-specific memory
+ * Allocates memory based on a [ByteBuffer].
  */
-actual fun Memory.Companion.allocate(length: Int): Memory {
-    val buffer = ByteBuffer.allocate(length)
-    return ByteBufferMemory(buffer)
-}
+actual fun Memory.Companion.allocate(length: Int): Memory =
+    ByteBufferMemory(checkNotNull(ByteBuffer.allocate(length)))
 
-actual fun Memory.Companion.wrap(array: ByteArray): Memory {
-    val buffer = ByteBuffer.wrap(array)
-    return ByteBufferMemory(buffer)
-}
+/**
+ * Wraps a [Memory] around existing [ByteArray]. This operation is unsafe since the array is not copied
+ * and could be mutated independently from the resulting [Memory].
+ */
+actual fun Memory.Companion.wrap(array: ByteArray): Memory = ByteBufferMemory(checkNotNull(ByteBuffer.wrap(array)))
 
+/**
+ * Wraps this [ByteBuffer] to [Memory] object.
+ *
+ * @receiver the byte buffer.
+ * @param startOffset the start offset.
+ * @param size the size of memory to map.
+ * @return the [Memory] object.
+ */
 fun ByteBuffer.asMemory(startOffset: Int = 0, size: Int = limit()): Memory =
     ByteBufferMemory(this, startOffset, size)
 
 /**
- * Use direct memory-mapped buffer from file to read something and close it afterwards.
+ * Uses direct memory-mapped buffer from file to read something and close it afterwards.
  */
-fun <R> Path.readAsMemory(position: Long = 0, size: Long = Files.size(this), block: Memory.() -> R): R {
-    return FileChannel.open(this, StandardOpenOption.READ).use {
+fun <R> Path.readAsMemory(position: Long = 0, size: Long = Files.size(this), block: Memory.() -> R): R =
+    FileChannel.open(this, StandardOpenOption.READ).use {
         ByteBufferMemory(it.map(FileChannel.MapMode.READ_ONLY, position, size)).block()
     }
-}
\ No newline at end of file
-- 
2.34.1


From cb5234a334d2ffe07403d6ac3b553fd388f54619 Mon Sep 17 00:00:00 2001
From: Iaroslav <postovalovya@gmail.com>
Date: Sat, 8 Aug 2020 04:57:20 +0700
Subject: [PATCH 11/12] Document AST and expressions API, implement
 ExtendedField over MST and Expression<T>

---
 .../kotlin/scientifik/kmath/ast/MST.kt        | 47 ++++++++----
 .../kotlin/scientifik/kmath/ast/MstAlgebra.kt | 74 +++++++++++++------
 .../scientifik/kmath/ast/MstExpression.kt     | 65 ++++++++++++----
 .../kotlin/scientifik/kmath/ast/parser.kt     | 13 ++++
 .../scientifik/kmath/expressions/Builders.kt  |  8 ++
 .../kmath/expressions/Expression.kt           | 12 +++
 .../FunctionalExpressionAlgebra.kt            | 39 ++++++++--
 .../scientifik/kmath/streaming/RingBuffer.kt  |  2 +-
 8 files changed, 202 insertions(+), 58 deletions(-)

diff --git a/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MST.kt b/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MST.kt
index 46558cbfb..0e8151c04 100644
--- a/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MST.kt
+++ b/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MST.kt
@@ -5,42 +5,54 @@ import scientifik.kmath.operations.NumericAlgebra
 import scientifik.kmath.operations.RealField
 
 /**
- * A Mathematical Syntax Tree node for mathematical expressions
+ * A Mathematical Syntax Tree node for mathematical expressions.
  */
 sealed class MST {
-
     /**
-     * A node containing unparsed string
+     * A node containing raw string.
+     *
+     * @property value the value of this node.
      */
     data class Symbolic(val value: String) : MST()
 
     /**
-     * A node containing a number
+     * A node containing a numeric value or scalar.
+     *
+     * @property value the value of this number.
      */
     data class Numeric(val value: Number) : MST()
 
     /**
-     * A node containing an unary operation
+     * A node containing an unary operation.
+     *
+     * @property operation the identifier of operation.
+     * @property value the argument of this operation.
      */
     data class Unary(val operation: String, val value: MST) : MST() {
-        companion object {
-            const val ABS_OPERATION = "abs"
-            //TODO add operations
-        }
+        companion object
     }
 
     /**
-     * A node containing binary operation
+     * A node containing binary operation.
+     *
+     * @property operation the identifier operation.
+     * @property left the left operand.
+     * @property right the right operand.
      */
     data class Binary(val operation: String, val left: MST, val right: MST) : MST() {
         companion object
     }
 }
 
-//TODO add a function with positional arguments
-
-//TODO add a function with named arguments
+// TODO add a function with named arguments
 
+/**
+ * Interprets the [MST] node with this [Algebra].
+ *
+ * @receiver the algebra that provides operations.
+ * @param node the node to evaluate.
+ * @return the value of expression.
+ */
 fun <T> Algebra<T>.evaluate(node: MST): T = when (node) {
     is MST.Numeric -> (this as? NumericAlgebra<T>)?.number(node.value)
         ?: error("Numeric nodes are not supported by $this")
@@ -65,4 +77,11 @@ fun <T> Algebra<T>.evaluate(node: MST): T = when (node) {
     }
 }
 
-fun <T> MST.compile(algebra: Algebra<T>): T = algebra.evaluate(this)
+/**
+ * Interprets the [MST] node with this [Algebra].
+ *
+ * @receiver the node to evaluate.
+ * @param algebra the algebra that provides operations.
+ * @return the value of expression.
+ */
+fun <T> MST.interpret(algebra: Algebra<T>): T = algebra.evaluate(this)
diff --git a/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstAlgebra.kt b/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstAlgebra.kt
index 007cf57c4..b47c7cae8 100644
--- a/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstAlgebra.kt
+++ b/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstAlgebra.kt
@@ -2,6 +2,9 @@ package scientifik.kmath.ast
 
 import scientifik.kmath.operations.*
 
+/**
+ * [Algebra] over [MST] nodes.
+ */
 object MstAlgebra : NumericAlgebra<MST> {
     override fun number(value: Number): MST = MST.Numeric(value)
 
@@ -14,17 +17,16 @@ object MstAlgebra : NumericAlgebra<MST> {
         MST.Binary(operation, left, right)
 }
 
+/**
+ * [Space] over [MST] nodes.
+ */
 object MstSpace : Space<MST>, NumericAlgebra<MST> {
     override val zero: MST = number(0.0)
 
     override fun number(value: Number): MST = MstAlgebra.number(value)
     override fun symbol(value: String): MST = MstAlgebra.symbol(value)
-
-    override fun add(a: MST, b: MST): MST =
-        binaryOperation(SpaceOperations.PLUS_OPERATION, a, b)
-
-    override fun multiply(a: MST, k: Number): MST =
-        binaryOperation(RingOperations.TIMES_OPERATION, a, number(k))
+    override fun add(a: MST, b: MST): MST = binaryOperation(SpaceOperations.PLUS_OPERATION, a, b)
+    override fun multiply(a: MST, k: Number): MST = binaryOperation(RingOperations.TIMES_OPERATION, a, number(k))
 
     override fun binaryOperation(operation: String, left: MST, right: MST): MST =
         MstAlgebra.binaryOperation(operation, left, right)
@@ -32,41 +34,69 @@ object MstSpace : Space<MST>, NumericAlgebra<MST> {
     override fun unaryOperation(operation: String, arg: MST): MST = MstAlgebra.unaryOperation(operation, arg)
 }
 
+/**
+ * [Ring] over [MST] nodes.
+ */
 object MstRing : Ring<MST>, NumericAlgebra<MST> {
     override val zero: MST = number(0.0)
     override val one: MST = number(1.0)
 
-    override fun number(value: Number): MST = MstAlgebra.number(value)
-    override fun symbol(value: String): MST = MstAlgebra.symbol(value)
-    override fun add(a: MST, b: MST): MST = binaryOperation(SpaceOperations.PLUS_OPERATION, a, b)
+    override fun number(value: Number): MST = MstSpace.number(value)
+    override fun symbol(value: String): MST = MstSpace.symbol(value)
+    override fun add(a: MST, b: MST): MST = MstSpace.add(a, b)
 
-    override fun multiply(a: MST, k: Number): MST =
-        binaryOperation(RingOperations.TIMES_OPERATION, a, MstSpace.number(k))
+    override fun multiply(a: MST, k: Number): MST = MstSpace.multiply(a, k)
 
     override fun multiply(a: MST, b: MST): MST = binaryOperation(RingOperations.TIMES_OPERATION, a, b)
 
     override fun binaryOperation(operation: String, left: MST, right: MST): MST =
-        MstAlgebra.binaryOperation(operation, left, right)
+        MstSpace.binaryOperation(operation, left, right)
 
     override fun unaryOperation(operation: String, arg: MST): MST = MstAlgebra.unaryOperation(operation, arg)
 }
 
+/**
+ * [Field] over [MST] nodes.
+ */
 object MstField : Field<MST> {
     override val zero: MST = number(0.0)
     override val one: MST = number(1.0)
 
-    override fun symbol(value: String): MST = MstAlgebra.symbol(value)
-    override fun number(value: Number): MST = MstAlgebra.number(value)
-    override fun add(a: MST, b: MST): MST = binaryOperation(SpaceOperations.PLUS_OPERATION, a, b)
-
-    override fun multiply(a: MST, k: Number): MST =
-        binaryOperation(RingOperations.TIMES_OPERATION, a, MstSpace.number(k))
-
-    override fun multiply(a: MST, b: MST): MST = binaryOperation(RingOperations.TIMES_OPERATION, a, b)
+    override fun symbol(value: String): MST = MstRing.symbol(value)
+    override fun number(value: Number): MST = MstRing.number(value)
+    override fun add(a: MST, b: MST): MST = MstRing.add(a, b)
+    override fun multiply(a: MST, k: Number): MST = MstRing.multiply(a, k)
+    override fun multiply(a: MST, b: MST): MST = MstRing.multiply(a, b)
     override fun divide(a: MST, b: MST): MST = binaryOperation(FieldOperations.DIV_OPERATION, a, b)
 
     override fun binaryOperation(operation: String, left: MST, right: MST): MST =
-        MstAlgebra.binaryOperation(operation, left, right)
+        MstRing.binaryOperation(operation, left, right)
 
-    override fun unaryOperation(operation: String, arg: MST): MST = MstAlgebra.unaryOperation(operation, arg)
+    override fun unaryOperation(operation: String, arg: MST): MST = MstRing.unaryOperation(operation, arg)
+}
+
+/**
+ * [ExtendedField] over [MST] nodes.
+ */
+object MstExtendedField : ExtendedField<MST> {
+    override val zero: MST = number(0.0)
+    override val one: MST = number(1.0)
+
+    override fun sin(arg: MST): MST = unaryOperation(TrigonometricOperations.SIN_OPERATION, arg)
+    override fun cos(arg: MST): MST = unaryOperation(TrigonometricOperations.COS_OPERATION, arg)
+    override fun asin(arg: MST): MST = unaryOperation(InverseTrigonometricOperations.ASIN_OPERATION, arg)
+    override fun acos(arg: MST): MST = unaryOperation(InverseTrigonometricOperations.ACOS_OPERATION, arg)
+    override fun atan(arg: MST): MST = unaryOperation(InverseTrigonometricOperations.ATAN_OPERATION, arg)
+    override fun add(a: MST, b: MST): MST = MstField.add(a, b)
+    override fun multiply(a: MST, k: Number): MST = MstField.multiply(a, k)
+    override fun multiply(a: MST, b: MST): MST = MstField.multiply(a, b)
+    override fun divide(a: MST, b: MST): MST = MstField.divide(a, b)
+    override fun power(arg: MST, pow: Number): MST = binaryOperation(PowerOperations.POW_OPERATION, arg, number(pow))
+    override fun exp(arg: MST): MST = unaryOperation(ExponentialOperations.EXP_OPERATION, arg)
+    override fun ln(arg: MST): MST = unaryOperation(ExponentialOperations.LN_OPERATION, arg)
+
+    override fun binaryOperation(operation: String, left: MST, right: MST): MST =
+        MstField.binaryOperation(operation, left, right)
+
+    override fun unaryOperation(operation: String, arg: MST): MST = MstField.unaryOperation(operation, arg)
 }
diff --git a/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstExpression.kt b/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstExpression.kt
index 1468c3ad4..59f3f15d8 100644
--- a/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstExpression.kt
+++ b/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstExpression.kt
@@ -1,19 +1,16 @@
 package scientifik.kmath.ast
 
-import scientifik.kmath.expressions.Expression
-import scientifik.kmath.expressions.FunctionalExpressionField
-import scientifik.kmath.expressions.FunctionalExpressionRing
-import scientifik.kmath.expressions.FunctionalExpressionSpace
+import scientifik.kmath.expressions.*
 import scientifik.kmath.operations.*
 
 /**
- * The expression evaluates MST on-flight. Should be much faster than functional expression, but slower than ASM-generated expressions.
+ * The expression evaluates MST on-flight. Should be much faster than functional expression, but slower than
+ * ASM-generated expressions.
+ *
+ * @property algebra the algebra that provides operations.
+ * @property mst the [MST] node.
  */
 class MstExpression<T>(val algebra: Algebra<T>, val mst: MST) : Expression<T> {
-
-    /**
-     * Substitute algebra raw value
-     */
     private inner class InnerAlgebra(val arguments: Map<String, T>) : NumericAlgebra<T> {
         override fun symbol(value: String): T = arguments[value] ?: algebra.symbol(value)
         override fun unaryOperation(operation: String, arg: T): T = algebra.unaryOperation(operation, arg)
@@ -30,26 +27,62 @@ class MstExpression<T>(val algebra: Algebra<T>, val mst: MST) : Expression<T> {
     override fun invoke(arguments: Map<String, T>): T = InnerAlgebra(arguments).evaluate(mst)
 }
 
-
+/**
+ * Builds [MstExpression] over [Algebra].
+ */
 inline fun <reified T : Any, A : Algebra<T>, E : Algebra<MST>> A.mst(
     mstAlgebra: E,
     block: E.() -> MST
 ): MstExpression<T> = MstExpression(this, mstAlgebra.block())
 
+/**
+ * Builds [MstExpression] over [Space].
+ */
 inline fun <reified T : Any> Space<T>.mstInSpace(block: MstSpace.() -> MST): MstExpression<T> =
     MstExpression(this, MstSpace.block())
 
+/**
+ * Builds [MstExpression] over [Ring].
+ */
 inline fun <reified T : Any> Ring<T>.mstInRing(block: MstRing.() -> MST): MstExpression<T> =
     MstExpression(this, MstRing.block())
 
+/**
+ * Builds [MstExpression] over [Field].
+ */
 inline fun <reified T : Any> Field<T>.mstInField(block: MstField.() -> MST): MstExpression<T> =
     MstExpression(this, MstField.block())
 
-inline fun <reified T : Any, A : Space<T>> FunctionalExpressionSpace<T, A>.mstInSpace(block: MstSpace.() -> MST): MstExpression<T> =
-    algebra.mstInSpace(block)
+/**
+ * Builds [MstExpression] over [ExtendedField].
+ */
+inline fun <reified T : Any> Field<T>.mstInExtendedField(block: MstExtendedField.() -> MST): MstExpression<T> =
+    MstExpression(this, MstExtendedField.block())
 
-inline fun <reified T : Any, A : Ring<T>> FunctionalExpressionRing<T, A>.mstInRing(block: MstRing.() -> MST): MstExpression<T> =
-    algebra.mstInRing(block)
+/**
+ * Builds [MstExpression] over [FunctionalExpressionSpace].
+ */
+inline fun <reified T : Any, A : Space<T>> FunctionalExpressionSpace<T, A>.mstInSpace(
+    block: MstSpace.() -> MST
+): MstExpression<T> = algebra.mstInSpace(block)
 
-inline fun <reified T : Any, A : Field<T>> FunctionalExpressionField<T, A>.mstInField(block: MstField.() -> MST): MstExpression<T> =
-    algebra.mstInField(block)
\ No newline at end of file
+/**
+ * Builds [MstExpression] over [FunctionalExpressionRing].
+ */
+inline fun <reified T : Any, A : Ring<T>> FunctionalExpressionRing<T, A>.mstInRing(
+    block: MstRing.() -> MST
+): MstExpression<T> = algebra.mstInRing(block)
+
+/**
+ * Builds [MstExpression] over [FunctionalExpressionField].
+ */
+inline fun <reified T : Any, A : Field<T>> FunctionalExpressionField<T, A>.mstInField(
+    block: MstField.() -> MST
+): MstExpression<T> = algebra.mstInField(block)
+
+/**
+ * Builds [MstExpression] over [FunctionalExpressionExtendedField].
+ */
+inline fun <reified T : Any, A : ExtendedField<T>> FunctionalExpressionExtendedField<T, A>.mstInExtendedField(
+    block: MstExtendedField.() -> MST
+): MstExpression<T> = algebra.mstInExtendedField(block)
diff --git a/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/parser.kt b/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/parser.kt
index 11797d79f..cba335a8d 100644
--- a/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/parser.kt
+++ b/kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/parser.kt
@@ -80,5 +80,18 @@ object ArithmeticsEvaluator : Grammar<MST>() {
     override val rootParser: Parser<MST> by subSumChain
 }
 
+/**
+ * Tries to parse the string into [MST].
+ *
+ * @receiver the string to parse.
+ * @return the [MST] node.
+ */
 fun String.tryParseMath(): ParseResult<MST> = ArithmeticsEvaluator.tryParseToEnd(this)
+
+/**
+ * Parses the string into [MST].
+ *
+ * @receiver the string to parse.
+ * @return the [MST] node.
+ */
 fun String.parseMath(): MST = ArithmeticsEvaluator.parseToEnd(this)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Builders.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Builders.kt
index 834ef9e24..8cd6e28f8 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Builders.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Builders.kt
@@ -1,5 +1,6 @@
 package scientifik.kmath.expressions
 
+import scientifik.kmath.operations.ExtendedField
 import scientifik.kmath.operations.Field
 import scientifik.kmath.operations.Ring
 import scientifik.kmath.operations.Space
@@ -21,3 +22,10 @@ fun <T> Ring<T>.ringExpression(block: FunctionalExpressionRing<T, Ring<T>>.() ->
  */
 fun <T> Field<T>.fieldExpression(block: FunctionalExpressionField<T, Field<T>>.() -> Expression<T>): Expression<T> =
     FunctionalExpressionField(this).run(block)
+
+/**
+ * Creates a functional expression with this [ExtendedField].
+ */
+fun <T> ExtendedField<T>.fieldExpression(
+    block: FunctionalExpressionExtendedField<T, ExtendedField<T>>.() -> Expression<T>
+): Expression<T> = FunctionalExpressionExtendedField(this).run(block)
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt
index b21a414f5..380822f78 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt
@@ -6,6 +6,12 @@ import scientifik.kmath.operations.Algebra
  * An elementary function that could be invoked on a map of arguments
  */
 interface Expression<T> {
+    /**
+     * Calls this expression from arguments.
+     *
+     * @param arguments the map of arguments.
+     * @return the value.
+     */
     operator fun invoke(arguments: Map<String, T>): T
 
     companion object
@@ -19,6 +25,12 @@ fun <T> Algebra<T>.expression(block: Algebra<T>.(arguments: Map<String, T>) -> T
         override fun invoke(arguments: Map<String, T>): T = block(arguments)
     }
 
+/**
+ * Calls this expression from arguments.
+ *
+ * @param pairs the pair of arguments' names to values.
+ * @return the value.
+ */
 operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke(mapOf(*pairs))
 
 /**
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressionAlgebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressionAlgebra.kt
index 5a8a10717..dd5fb572a 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressionAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressionAlgebra.kt
@@ -40,7 +40,6 @@ internal class FunctionalConstProductExpression<T>(
  * @param algebra The algebra to provide for Expressions built.
  */
 abstract class FunctionalExpressionAlgebra<T, A : Algebra<T>>(val algebra: A) : ExpressionAlgebra<T, Expression<T>> {
-
     /**
      * Builds an Expression of constant expression which does not depend on arguments.
      */
@@ -69,14 +68,13 @@ abstract class FunctionalExpressionAlgebra<T, A : Algebra<T>>(val algebra: A) :
  */
 open class FunctionalExpressionSpace<T, A : Space<T>>(algebra: A) :
     FunctionalExpressionAlgebra<T, A>(algebra), Space<Expression<T>> {
-
     override val zero: Expression<T> get() = const(algebra.zero)
 
     /**
      * Builds an Expression of addition of two another expressions.
      */
     override fun add(a: Expression<T>, b: Expression<T>): Expression<T> =
-        FunctionalBinaryOperation(algebra, SpaceOperations.PLUS_OPERATION, a, b)
+        binaryOperation(SpaceOperations.PLUS_OPERATION, a, b)
 
     /**
      * Builds an Expression of multiplication of expression by number.
@@ -105,7 +103,7 @@ open class FunctionalExpressionRing<T, A>(algebra: A) : FunctionalExpressionSpac
      * Builds an Expression of multiplication of two expressions.
      */
     override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> =
-        FunctionalBinaryOperation(algebra, RingOperations.TIMES_OPERATION, a, b)
+        binaryOperation(RingOperations.TIMES_OPERATION, a, b)
 
     operator fun Expression<T>.times(arg: T): Expression<T> = this * const(arg)
     operator fun T.times(arg: Expression<T>): Expression<T> = arg * this
@@ -124,7 +122,7 @@ open class FunctionalExpressionField<T, A>(algebra: A) :
      * Builds an Expression of division an expression by another one.
      */
     override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> =
-        FunctionalBinaryOperation(algebra, FieldOperations.DIV_OPERATION, a, b)
+        binaryOperation(FieldOperations.DIV_OPERATION, a, b)
 
     operator fun Expression<T>.div(arg: T): Expression<T> = this / const(arg)
     operator fun T.div(arg: Expression<T>): Expression<T> = arg / this
@@ -136,6 +134,34 @@ open class FunctionalExpressionField<T, A>(algebra: A) :
         super<FunctionalExpressionRing>.binaryOperation(operation, left, right)
 }
 
+open class FunctionalExpressionExtendedField<T, A>(algebra: A) :
+    FunctionalExpressionField<T, A>(algebra),
+    ExtendedField<Expression<T>> where A : ExtendedField<T>, A : NumericAlgebra<T> {
+    override fun sin(arg: Expression<T>): Expression<T> = unaryOperation(TrigonometricOperations.SIN_OPERATION, arg)
+    override fun cos(arg: Expression<T>): Expression<T> = unaryOperation(TrigonometricOperations.COS_OPERATION, arg)
+
+    override fun asin(arg: Expression<T>): Expression<T> =
+        unaryOperation(InverseTrigonometricOperations.ASIN_OPERATION, arg)
+
+    override fun acos(arg: Expression<T>): Expression<T> =
+        unaryOperation(InverseTrigonometricOperations.ACOS_OPERATION, arg)
+
+    override fun atan(arg: Expression<T>): Expression<T> =
+        unaryOperation(InverseTrigonometricOperations.ATAN_OPERATION, arg)
+
+    override fun power(arg: Expression<T>, pow: Number): Expression<T> =
+        binaryOperation(PowerOperations.POW_OPERATION, arg, number(pow))
+
+    override fun exp(arg: Expression<T>): Expression<T> = unaryOperation(ExponentialOperations.EXP_OPERATION, arg)
+    override fun ln(arg: Expression<T>): Expression<T> = unaryOperation(ExponentialOperations.LN_OPERATION, arg)
+
+    override fun unaryOperation(operation: String, arg: Expression<T>): Expression<T> =
+        super<FunctionalExpressionField>.unaryOperation(operation, arg)
+
+    override fun binaryOperation(operation: String, left: Expression<T>, right: Expression<T>): Expression<T> =
+        super<FunctionalExpressionField>.binaryOperation(operation, left, right)
+}
+
 inline fun <T, A : Space<T>> A.expressionInSpace(block: FunctionalExpressionSpace<T, A>.() -> Expression<T>): Expression<T> =
     FunctionalExpressionSpace(this).block()
 
@@ -144,3 +170,6 @@ inline fun <T, A : Ring<T>> A.expressionInRing(block: FunctionalExpressionRing<T
 
 inline fun <T, A : Field<T>> A.expressionInField(block: FunctionalExpressionField<T, A>.() -> Expression<T>): Expression<T> =
     FunctionalExpressionField(this).block()
+
+inline fun <T, A : ExtendedField<T>> A.expressionInExtendedField(block: FunctionalExpressionExtendedField<T, A>.() -> Expression<T>): Expression<T> =
+    FunctionalExpressionExtendedField(this).block()
diff --git a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/RingBuffer.kt b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/RingBuffer.kt
index 6b99e34ff..fca9ffb9f 100644
--- a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/RingBuffer.kt
+++ b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/RingBuffer.kt
@@ -11,7 +11,7 @@ import kotlin.reflect.KClass
  * Thread-safe ring buffer
  */
 @Suppress("UNCHECKED_CAST")
-internal class RingBuffer<T>(
+class RingBuffer<T>(
     private val buffer: MutableBuffer<T?>,
     private var startIndex: Int = 0,
     size: Int = 0
-- 
2.34.1


From 6114099e68fad71e169ec86ce4dac8925fe9e6da Mon Sep 17 00:00:00 2001
From: Iaroslav <postovalovya@gmail.com>
Date: Sat, 8 Aug 2020 15:51:04 +0700
Subject: [PATCH 12/12] Edit doc files, update readmes, document coroutines API

---
 doc/algebra.md                                | 124 ++++++++++--------
 doc/buffers.md                                |   4 +-
 doc/codestyle.md                              |  34 +++--
 doc/linear.md                                 |   2 +-
 doc/nd-structure.md                           |   2 +-
 kmath-ast/README.md                           |   8 +-
 kmath-core/README.md                          |  40 ++++++
 kmath-core/build.gradle.kts                   |   8 +-
 .../scientifik/kmath/operations/Algebra.kt    |   9 +-
 .../kmath/chains/BlockingIntChain.kt          |   2 +-
 .../kmath/chains/BlockingRealChain.kt         |   2 +-
 .../kotlin/scientifik/kmath/chains/Chain.kt   |  21 ++-
 .../scientifik/kmath/chains/flowExtra.kt      |   2 +-
 .../kmath/coroutines/coroutinesExtra.kt       |  13 +-
 .../scientifik/kmath/streaming/BufferFlow.kt  |   4 +-
 .../scientifik/kmath/streaming/RingBuffer.kt  |   8 +-
 .../scientifik/kmath/chains/ChainExt.kt       |   2 +-
 .../kmath/structures/LazyNDStructure.kt       |  21 ++-
 .../kmath/streaming/BufferFlowTest.kt         |   5 +-
 .../kmath/streaming/RingBufferTest.kt         |  12 +-
 20 files changed, 189 insertions(+), 134 deletions(-)
 create mode 100644 kmath-core/README.md

diff --git a/doc/algebra.md b/doc/algebra.md
index 015f4fc82..b1b77a31f 100644
--- a/doc/algebra.md
+++ b/doc/algebra.md
@@ -1,110 +1,124 @@
-# Algebra and algebra elements
+# Algebraic Structures and Algebraic Elements
 
-The mathematical operations in `kmath` are generally separated from mathematical objects.
-This means that in order to perform an operation, say `+`, one needs two objects of a type `T` and
-and algebra context which defines appropriate operation, say `Space<T>`. Next one needs to run actual operation
-in the context:
+The mathematical operations in KMath are generally separated from mathematical objects. This means that to perform an 
+operation, say `+`, one needs two objects of a type `T` and an algebra context, which draws appropriate operation up, 
+say `Space<T>`. Next one needs to run the actual operation in the context:
 
 ```kotlin
-val a: T
-val b: T
-val space: Space<T>
+import scientifik.kmath.operations.*
 
-val c = space.run{a + b}
+val a: T = ...
+val b: T = ...
+val space: Space<T> = ...
+
+val c = space { a + b }
 ```
 
-From the first glance, this distinction seems to be a needless complication, but in fact one needs
-to remember that in mathematics, one could define different operations on the same objects. For example,
-one could use different types of geometry for vectors.
+At first glance, this distinction seems to be a needless complication, but in fact one needs to remember that in 
+mathematics, one could draw up different operations on same objects. For example, one could use different types of 
+geometry for vectors.
 
-## Algebra hierarchy
+## Algebraic Structures
 
 Mathematical contexts have the following hierarchy:
 
-**Space** <- **Ring** <- **Field**
+**Algebra** ← **Space** ← **Ring** ← **Field**
 
-All classes follow abstract mathematical constructs.
-[Space](http://mathworld.wolfram.com/Space.html) defines `zero` element, addition operation and multiplication by constant,
-[Ring](http://mathworld.wolfram.com/Ring.html) adds multiplication and unit `one` element,
-[Field](http://mathworld.wolfram.com/Field.html) adds division operation.
+These interfaces follow real algebraic structures:
 
-Typical case of `Field` is the `RealField` which works on doubles. And typical case of `Space` is a `VectorSpace`.
+- [Space](https://mathworld.wolfram.com/VectorSpace.html) defines addition, its neutral element (i.e. 0) and scalar 
+multiplication;
+- [Ring](http://mathworld.wolfram.com/Ring.html) adds multiplication and its neutral element (i.e. 1);
+- [Field](http://mathworld.wolfram.com/Field.html) adds division operation.
 
-In some cases algebra context could hold additional operation like `exp` or `sin`, in this case it inherits appropriate
-interface. Also a context could have an operation which produces an element outside of its context. For example
-`Matrix` `dot` operation produces a matrix with new dimensions which can be incompatible with initial matrix in
-terms of linear operations.
+A typical implementation of `Field<T>` is the `RealField` which works on doubles, and `VectorSpace` for `Space<T>`.
 
-## Algebra element
+In some cases algebra context can hold additional operations like `exp` or `sin`, and then it inherits appropriate
+interface. Also, contexts may have operations, which produce elements outside of the context. For example, `Matrix.dot` 
+operation produces a matrix with new dimensions, which can be incompatible with initial matrix in terms of linear 
+operations.
 
-In order to achieve more familiar behavior (where you apply operations directly to mathematical objects), without involving contexts
-`kmath` introduces special type objects called `MathElement`. A `MathElement` is basically some object coupled to
+## Algebraic Element
+
+To achieve more familiar behavior (where you apply operations directly to mathematical objects), without involving 
+contexts KMath submits special type objects called `MathElement`. A `MathElement` is basically some object coupled to
 a mathematical context. For example `Complex` is the pair of real numbers representing real and imaginary parts,
-but it also holds reference to the `ComplexField` singleton which allows to perform direct operations on `Complex`
+but it also holds reference to the `ComplexField` singleton, which allows performing direct operations on `Complex`
 numbers without explicit involving the context like:
 
 ```kotlin
-    val c1 = Complex(1.0, 1.0)
-    val c2 = Complex(1.0, -1.0)
-    val c3 = c1 + c2 + 3.0.toComplex()
-    //or with field notation:
-    val c4 = ComplexField.run{c1 + i - 2.0}
+import scientifik.kmath.operations.*
+
+// Using elements
+val c1 = Complex(1.0, 1.0)
+val c2 = Complex(1.0, -1.0)
+val c3 = c1 + c2 + 3.0.toComplex()
+
+// Using context
+val c4 = ComplexField { c1 + i - 2.0 }
 ```
 
 Both notations have their pros and cons.
 
-The hierarchy for algebra elements follows the hierarchy for the corresponding algebra.
+The hierarchy for algebraic elements follows the hierarchy for the corresponding algebraic structures.
 
-**MathElement** <- **SpaceElement** <- **RingElement** <- **FieldElement**
+**MathElement** ← **SpaceElement** ← **RingElement** ← **FieldElement**
 
-**MathElement** is the generic common ancestor of the class with context.
+`MathElement<C>` is the generic common ancestor of the class with context.
 
-One important distinction between algebra elements and algebra contexts is that algebra element has three type parameters:
+One major distinction between algebraic elements and algebraic contexts is that elements have three type 
+parameters:
 
-1. The type of elements, field operates on.
-2. The self-type of the element returned from operation (must be algebra element).
+1. The type of elements, the field operates on.
+2. The self-type of the element returned from operation (which has to be an algebraic element).
 3. The type of the algebra over first type-parameter.
 
-The middle type is needed in case algebra members do not store context. For example, it is not possible to add
-a context to regular `Double`. The element performs automatic conversions from context types and back.
-One should used context operations in all important places. The performance of element operations is not guaranteed.
+The middle type is needed for of algebra members do not store context. For example, it is impossible to add a context 
+to regular `Double`. The element performs automatic conversions from context types and back. One should use context 
+operations in all performance-critical places. The performance of element operations is not guaranteed.
 
-## Spaces and fields
+## Spaces and Fields
 
-An obvious first choice of mathematical objects to implement in a context-oriented style are algebraic elements like spaces,
-rings and fields. Those are located in the `scientifik.kmath.operations.Algebra.kt` file. Alongside common contexts, the file includes definitions for algebra elements like `FieldElement`. A `FieldElement` object
-stores a reference to the `Field` which contains additive and multiplicative operations, meaning
-it has one fixed context attached and does not require explicit external context. So those `MathElements` can be operated without context:
+KMath submits both contexts and elements for builtin algebraic structures:
 
 ```kotlin
+import scientifik.kmath.operations.*
+
 val c1 = Complex(1.0, 2.0)
 val c2 = ComplexField.i
+
 val c3 = c1 + c2
+// or
+val c3 = ComplexField { c1 + c2 }
 ```
 
-`ComplexField` also features special operations to mix complex and real numbers, for example:
+Also, `ComplexField` features special operations to mix complex and real numbers, for example:
 
 ```kotlin
+import scientifik.kmath.operations.*
+
 val c1 = Complex(1.0, 2.0)
-val c2 = ComplexField.run{ c1 - 1.0} // Returns: [re:0.0, im: 2.0]
-val c3 = ComplexField.run{ c1 - i*2.0}
+val c2 = ComplexField { c1 - 1.0 } // Returns: Complex(re=0.0, im=2.0)
+val c3 = ComplexField { c1 - i * 2.0 }
 ```
 
-**Note**: In theory it is possible to add behaviors directly to the context, but currently kotlin syntax does not support
-that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) and [KEEP-176](https://github.com/Kotlin/KEEP/pull/176) for updates.
+**Note**: In theory it is possible to add behaviors directly to the context, but as for now Kotlin does not support 
+that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) and 
+[KEEP-176](https://github.com/Kotlin/KEEP/pull/176) for updates.
 
 ## Nested fields
 
-Contexts allow one to build more complex structures. For example, it is possible to create a `Matrix` from complex elements like so:
+Contexts allow one to build more complex structures. For example, it is possible to create a `Matrix` from complex 
+elements like so:
 
 ```kotlin
-val element = NDElement.complex(shape = intArrayOf(2,2)){ index: IntArray ->
+val element = NDElement.complex(shape = intArrayOf(2, 2)) { index: IntArray ->
     Complex(index[0].toDouble() - index[1].toDouble(), index[0].toDouble() + index[1].toDouble())
 }
 ```
 
-The `element` in this example is a member of the `Field` of 2-d structures, each element of which is a member of its own
-`ComplexField`. The important thing is one does not need to create a special n-d class to hold complex
+The `element` in this example is a member of the `Field` of 2D structures, each element of which is a member of its own
+`ComplexField`. It is important one does not need to create a special n-d class to hold complex
 numbers and implement operations on it, one just needs to provide a field for its elements.
 
 **Note**: Fields themselves do not solve the problem of JVM boxing, but it is possible to solve with special contexts like
diff --git a/doc/buffers.md b/doc/buffers.md
index 52a9df86e..679bd4e78 100644
--- a/doc/buffers.md
+++ b/doc/buffers.md
@@ -1,4 +1,5 @@
 # Buffers
+
 Buffer is one of main building blocks of kmath. It is a basic interface allowing random-access read and write (with `MutableBuffer`).
 There are different types of buffers:
 
@@ -12,4 +13,5 @@ Some kmath features require a `BufferFactory` class to operate properly. A gener
 buffer for given reified type (for types with custom memory buffer it still better to use their own `MemoryBuffer.create()` factory).
 
 ## Buffer performance
-One should avoid using default boxing buffer wherever it is possible. Try to use primitive buffers or memory buffers instead  
\ No newline at end of file
+
+One should avoid using default boxing buffer wherever it is possible. Try to use primitive buffers or memory buffers instead  
diff --git a/doc/codestyle.md b/doc/codestyle.md
index 53789f7b2..541dc4973 100644
--- a/doc/codestyle.md
+++ b/doc/codestyle.md
@@ -1,22 +1,34 @@
-# Local coding conventions
+# Coding Conventions
 
-Kmath and other `scientifik` projects use general [kotlin code conventions](https://kotlinlang.org/docs/reference/coding-conventions.html), but with a number of small changes and clarifications.
+KMath code follows general [Kotlin conventions](https://kotlinlang.org/docs/reference/coding-conventions.html), but 
+with a number of small changes and clarifications.
 
-## Utility class names
-File name should coincide with a name of one of the classes contained in the file or start with small letter and describe its contents.
+## Utility Class Naming
 
-The code convention [here](https://kotlinlang.org/docs/reference/coding-conventions.html#source-file-names) says that file names should start with capital letter even if file does not contain classes. Yet starting utility classes and aggregators with a small letter seems to be a good way to clearly visually separate those files.
+Filename should coincide with a name of one of the classes contained in the file or start with small letter and 
+describe its contents.
+
+The code convention [here](https://kotlinlang.org/docs/reference/coding-conventions.html#source-file-names) says that 
+file names should start with a capital letter even if file does not contain classes. Yet starting utility classes and 
+aggregators with a small letter seems to be a good way to visually separate those files.
 
 This convention could be changed in future in a non-breaking way.
 
-## Private variable names
-Private variable names could start with underscore `_` in case the private mutable variable is shadowed by the public read-only value with the same meaning.
+## Private Variable Naming
 
-Code convention do not permit underscores in names, but is is sometimes useful to "underscore" the fact that public and private versions define the same entity. It is allowed only for private variables.
+Private variables' names may start with underscore `_` for of the private mutable variable is shadowed by the public 
+read-only value with the same meaning.
+
+This rule does not permit underscores in names, but it is sometimes useful to "underscore" the fact that public and 
+private versions draw up the same entity. It is allowed only for private variables.
 
 This convention could be changed in future in a non-breaking way.
 
-## Functions and properties one-liners
-Use one-liners when they occupy single code window line both for functions and properties with getters like `val b: String get() = "fff"`. The same should be done with multiline expressions when they could be cleanly separated.
+## Functions and Properties One-liners
 
-There is not general consensus whenever use `fun a() = {}` or `fun a(){return}`. Yet from reader perspective one-lines seem to better show that the property or function is easily calculated.
\ No newline at end of file
+Use one-liners when they occupy single code window line both for functions and properties with getters like 
+`val b: String get() = "fff"`. The same should be performed with multiline expressions when they could be 
+cleanly separated.
+
+There is no universal consensus whenever use `fun a() = ...` or `fun a() { return ... }`. Yet from reader outlook 
+one-lines seem to better show that the property or function is easily calculated.
diff --git a/doc/linear.md b/doc/linear.md
index bbcc435ba..883df275e 100644
--- a/doc/linear.md
+++ b/doc/linear.md
@@ -1,6 +1,6 @@
 ## Basic linear algebra layout
 
-Kmath support for linear algebra organized in a context-oriented way. Meaning that operations are in most cases declared 
+KMath support for linear algebra organized in a context-oriented way. Meaning that operations are in most cases declared 
 in context classes, and are not the members of classes that store data. This allows more flexible approach to maintain multiple 
 back-ends. The new operations added as extensions to contexts instead of being member functions of data structures.
 
diff --git a/doc/nd-structure.md b/doc/nd-structure.md
index cf13c6a29..835304b9f 100644
--- a/doc/nd-structure.md
+++ b/doc/nd-structure.md
@@ -1,4 +1,4 @@
-# Nd-structure generation and operations
+# ND-structure generation and operations
 
 **TODO**
 
diff --git a/kmath-ast/README.md b/kmath-ast/README.md
index a59688c8e..2339d0426 100644
--- a/kmath-ast/README.md
+++ b/kmath-ast/README.md
@@ -1,4 +1,4 @@
-# Abstract syntax tree expression representation and operations (`kmath-ast`)
+# Abstract Syntax Tree Expression Representation and Operations (`kmath-ast`)
 
 This subproject implements the following features:
 
@@ -38,7 +38,7 @@ This subproject implements the following features:
 > ```
 >
 
-## Dynamic expression code generation with ObjectWeb ASM
+## Dynamic Expression Code Generation with ObjectWeb ASM
 
 `kmath-ast` JVM module supports runtime code generation to eliminate overhead of tree traversal. Code generator builds 
 a special implementation of `Expression<T>` with implemented `invoke` function. 
@@ -46,7 +46,7 @@ a special implementation of `Expression<T>` with implemented `invoke` function.
 For example, the following builder: 
 
 ```kotlin
-    RealField.mstInField { symbol("x") + 2 }.compile()
+RealField.mstInField { symbol("x") + 2 }.compile()
 ``` 
 
 … leads to generation of bytecode, which can be decompiled to the following Java class: 
@@ -75,7 +75,7 @@ public final class AsmCompiledExpression_1073786867_0 implements Expression<Doub
 
 ### Example Usage
 
-This API is an extension to MST and MstExpression, so you may optimize as both of them: 
+This API extends MST and MstExpression, so you may optimize as both of them: 
 
 ```kotlin
 RealField.mstInField { symbol("x") + 2 }.compile()
diff --git a/kmath-core/README.md b/kmath-core/README.md
new file mode 100644
index 000000000..24e2c57d3
--- /dev/null
+++ b/kmath-core/README.md
@@ -0,0 +1,40 @@
+# The Core Module (`kmath-ast`)
+
+The core features of KMath:
+
+- Algebraic structures: contexts and elements.
+- ND structures.
+- Buffers.
+- Functional Expressions.
+- Domains.
+- Automatic differentiation.
+
+> #### Artifact:
+> This module is distributed in the artifact `scientifik:kmath-core:0.1.4-dev-8`.
+> 
+> **Gradle:**
+>
+> ```gradle
+> repositories {
+>     maven { url 'https://dl.bintray.com/mipt-npm/scientifik' }
+>     maven { url 'https://dl.bintray.com/mipt-npm/dev' }
+>     maven { url https://dl.bintray.com/hotkeytlt/maven' }
+> }
+> 
+> dependencies {
+>     implementation 'scientifik:kmath-core:0.1.4-dev-8'
+> }
+> ```
+> **Gradle Kotlin DSL:**
+>
+> ```kotlin
+> repositories {
+>     maven("https://dl.bintray.com/mipt-npm/scientifik")
+>     maven("https://dl.bintray.com/mipt-npm/dev")
+>     maven("https://dl.bintray.com/hotkeytlt/maven")
+> }
+> 
+> dependencies {``
+>     implementation("scientifik:kmath-core:0.1.4-dev-8")
+> }
+> ```
diff --git a/kmath-core/build.gradle.kts b/kmath-core/build.gradle.kts
index 18c0cc771..bea0fbf42 100644
--- a/kmath-core/build.gradle.kts
+++ b/kmath-core/build.gradle.kts
@@ -1,11 +1,7 @@
-plugins {
-    id("scientifik.mpp")
-}
+plugins { id("scientifik.mpp") }
 
 kotlin.sourceSets {
     commonMain {
-        dependencies {
-            api(project(":kmath-memory"))
-        }
+        dependencies { api(project(":kmath-memory")) }
     }
 }
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
index aa190b31f..eb44cf7a7 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
@@ -58,7 +58,8 @@ interface NumericAlgebra<T> : Algebra<T> {
 inline operator fun <A : Algebra<*>, R> A.invoke(block: A.() -> R): R = run(block)
 
 /**
- * Represents semigroup, i.e. algebraic structure with associative binary operation called "addition".
+ * Represents semispace, i.e. algebraic structure with associative binary operation called "addition" as well as
+ * multiplication by scalars.
  *
  * In KMath groups are called spaces, and also define multiplication of element by [Number].
  *
@@ -174,10 +175,8 @@ interface SpaceOperations<T> : Algebra<T> {
 }
 
 /**
- * Represents group, i.e. algebraic structure with associative binary operation called "addition" and its neutral
- * element.
- *
- * In KMath groups are called spaces, and also define multiplication of element by [Number].
+ * Represents linear space, i.e. algebraic structure with associative binary operation called "addition" and its neutral
+ * element as well as multiplication by scalars.
  *
  * @param T the type of element of this group.
  */
diff --git a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/BlockingIntChain.kt b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/BlockingIntChain.kt
index 6ec84d5c7..e9b499d71 100644
--- a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/BlockingIntChain.kt
+++ b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/BlockingIntChain.kt
@@ -9,4 +9,4 @@ abstract class BlockingIntChain : Chain<Int> {
     override suspend fun next(): Int = nextInt()
 
     fun nextBlock(size: Int): IntArray = IntArray(size) { nextInt() }
-}
\ No newline at end of file
+}
diff --git a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/BlockingRealChain.kt b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/BlockingRealChain.kt
index 6b69d2734..ab819d327 100644
--- a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/BlockingRealChain.kt
+++ b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/BlockingRealChain.kt
@@ -9,4 +9,4 @@ abstract class BlockingRealChain : Chain<Double> {
     override suspend fun next(): Double = nextDouble()
 
     fun nextBlock(size: Int): DoubleArray = DoubleArray(size) { nextDouble() }
-}
\ No newline at end of file
+}
diff --git a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/Chain.kt b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/Chain.kt
index 5635499e5..6cc9770af 100644
--- a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/Chain.kt
+++ b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/Chain.kt
@@ -22,12 +22,11 @@ import kotlinx.coroutines.flow.FlowCollector
 import kotlinx.coroutines.sync.Mutex
 import kotlinx.coroutines.sync.withLock
 
-
 /**
  * A not-necessary-Markov chain of some type
  * @param R - the chain element type
  */
-interface Chain<out R>: Flow<R> {
+interface Chain<out R> : Flow<R> {
     /**
      * Generate next value, changing state if needed
      */
@@ -41,7 +40,7 @@ interface Chain<out R>: Flow<R> {
     @OptIn(InternalCoroutinesApi::class)
     override suspend fun collect(collector: FlowCollector<R>) {
         kotlinx.coroutines.flow.flow {
-            while (true){
+            while (true) {
                 emit(next())
             }
         }.collect(collector)
@@ -71,7 +70,7 @@ class MarkovChain<out R : Any>(private val seed: suspend () -> R, private val ge
 
     private var value: R? = null
 
-    fun value() = value
+    fun value(): R? = value
 
     override suspend fun next(): R {
         mutex.withLock {
@@ -97,12 +96,11 @@ class StatefulChain<S, out R>(
     private val forkState: ((S) -> S),
     private val gen: suspend S.(R) -> R
 ) : Chain<R> {
-
-    private val mutex = Mutex()
+    private val mutex: Mutex = Mutex()
 
     private var value: R? = null
 
-    fun value() = value
+    fun value(): R? = value
 
     override suspend fun next(): R {
         mutex.withLock {
@@ -112,9 +110,7 @@ class StatefulChain<S, out R>(
         }
     }
 
-    override fun fork(): Chain<R> {
-        return StatefulChain(forkState(state), seed, forkState, gen)
-    }
+    override fun fork(): Chain<R> = StatefulChain(forkState(state), seed, forkState, gen)
 }
 
 /**
@@ -163,7 +159,8 @@ fun <T, R> Chain<T>.collect(mapper: suspend (Chain<T>) -> R): Chain<R> = object
 fun <T, S, R> Chain<T>.collectWithState(state: S, stateFork: (S) -> S, mapper: suspend S.(Chain<T>) -> R): Chain<R> =
     object : Chain<R> {
         override suspend fun next(): R = state.mapper(this@collectWithState)
-        override fun fork(): Chain<R> = this@collectWithState.fork().collectWithState(stateFork(state), stateFork, mapper)
+        override fun fork(): Chain<R> =
+            this@collectWithState.fork().collectWithState(stateFork(state), stateFork, mapper)
     }
 
 /**
@@ -173,4 +170,4 @@ fun <T, U, R> Chain<T>.zip(other: Chain<U>, block: suspend (T, U) -> R): Chain<R
     override suspend fun next(): R = block(this@zip.next(), other.next())
 
     override fun fork(): Chain<R> = this@zip.fork().zip(other.fork(), block)
-}
\ No newline at end of file
+}
diff --git a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/flowExtra.kt b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/flowExtra.kt
index bfd16d763..e8537304c 100644
--- a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/flowExtra.kt
+++ b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/flowExtra.kt
@@ -24,4 +24,4 @@ fun <T> Flow<T>.mean(space: Space<T>): Flow<T> = with(space) {
             this.num += 1
         }
     }.map { it.sum / it.num }
-}
\ No newline at end of file
+}
diff --git a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/coroutines/coroutinesExtra.kt b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/coroutines/coroutinesExtra.kt
index fdde62304..7e00b30a1 100644
--- a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/coroutines/coroutinesExtra.kt
+++ b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/coroutines/coroutinesExtra.kt
@@ -4,7 +4,8 @@ import kotlinx.coroutines.*
 import kotlinx.coroutines.channels.produce
 import kotlinx.coroutines.flow.*
 
-val Dispatchers.Math: CoroutineDispatcher get() = Dispatchers.Default
+val Dispatchers.Math: CoroutineDispatcher
+    get() = Default
 
 /**
  * An imitator of [Deferred] which holds a suspended function block and dispatcher
@@ -42,7 +43,7 @@ fun <T, R> Flow<T>.async(
 }
 
 @FlowPreview
-fun <T, R> AsyncFlow<T>.map(action: (T) -> R) =
+fun <T, R> AsyncFlow<T>.map(action: (T) -> R): AsyncFlow<R> =
     AsyncFlow(deferredFlow.map { input ->
         //TODO add function composition
         LazyDeferred(input.dispatcher) {
@@ -82,9 +83,9 @@ suspend fun <T> AsyncFlow<T>.collect(concurrency: Int, collector: FlowCollector<
 
 @ExperimentalCoroutinesApi
 @FlowPreview
-suspend fun <T> AsyncFlow<T>.collect(concurrency: Int, action: suspend (value: T) -> Unit): Unit {
+suspend fun <T> AsyncFlow<T>.collect(concurrency: Int, action: suspend (value: T) -> Unit) {
     collect(concurrency, object : FlowCollector<T> {
-        override suspend fun emit(value: T) = action(value)
+        override suspend fun emit(value: T): Unit = action(value)
     })
 }
 
@@ -94,9 +95,7 @@ fun <T, R> Flow<T>.mapParallel(
     dispatcher: CoroutineDispatcher = Dispatchers.Default,
     transform: suspend (T) -> R
 ): Flow<R> {
-    return flatMapMerge{ value ->
+    return flatMapMerge { value ->
         flow { emit(transform(value)) }
     }.flowOn(dispatcher)
 }
-
-
diff --git a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/BufferFlow.kt b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/BufferFlow.kt
index 54da66bb7..9b7e82da5 100644
--- a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/BufferFlow.kt
+++ b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/BufferFlow.kt
@@ -11,7 +11,7 @@ import scientifik.kmath.structures.asBuffer
 /**
  * Create a [Flow] from buffer
  */
-fun <T> Buffer<T>.asFlow() = iterator().asFlow()
+fun <T> Buffer<T>.asFlow(): Flow<T> = iterator().asFlow()
 
 /**
  * Flat map a [Flow] of [Buffer] into continuous [Flow] of elements
@@ -83,4 +83,4 @@ fun <T> Flow<T>.windowed(window: Int): Flow<Buffer<T>> = flow {
         ringBuffer.push(element)
         emit(ringBuffer.snapshot())
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/RingBuffer.kt b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/RingBuffer.kt
index fca9ffb9f..245d003b3 100644
--- a/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/RingBuffer.kt
+++ b/kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/RingBuffer.kt
@@ -5,7 +5,6 @@ import kotlinx.coroutines.sync.withLock
 import scientifik.kmath.structures.Buffer
 import scientifik.kmath.structures.MutableBuffer
 import scientifik.kmath.structures.VirtualBuffer
-import kotlin.reflect.KClass
 
 /**
  * Thread-safe ring buffer
@@ -16,8 +15,7 @@ class RingBuffer<T>(
     private var startIndex: Int = 0,
     size: Int = 0
 ) : Buffer<T> {
-
-    private val mutex = Mutex()
+    private val mutex: Mutex = Mutex()
 
     override var size: Int = size
         private set
@@ -28,7 +26,7 @@ class RingBuffer<T>(
         return buffer[startIndex.forward(index)] as T
     }
 
-    fun isFull() = size == buffer.size
+    fun isFull(): Boolean = size == buffer.size
 
     /**
      * Iterator could provide wrong results if buffer is changed in initialization (iteration is safe)
@@ -90,4 +88,4 @@ class RingBuffer<T>(
             return RingBuffer(buffer)
         }
     }
-}
\ No newline at end of file
+}
diff --git a/kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/chains/ChainExt.kt b/kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/chains/ChainExt.kt
index 013ea2922..0a3c67e00 100644
--- a/kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/chains/ChainExt.kt
+++ b/kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/chains/ChainExt.kt
@@ -6,7 +6,7 @@ import kotlin.sequences.Sequence
 /**
  * Represent a chain as regular iterator (uses blocking calls)
  */
-operator fun <R> Chain<R>.iterator() = object : Iterator<R> {
+operator fun <R> Chain<R>.iterator(): Iterator<R> = object : Iterator<R> {
     override fun hasNext(): Boolean = true
 
     override fun next(): R = runBlocking { next() }
diff --git a/kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/structures/LazyNDStructure.kt b/kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/structures/LazyNDStructure.kt
index e65940739..8d5145976 100644
--- a/kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/structures/LazyNDStructure.kt
+++ b/kmath-coroutines/src/jvmMain/kotlin/scientifik/kmath/structures/LazyNDStructure.kt
@@ -8,10 +8,9 @@ class LazyNDStructure<T>(
     override val shape: IntArray,
     val function: suspend (IntArray) -> T
 ) : NDStructure<T> {
+    private val cache: MutableMap<IntArray, Deferred<T>> = hashMapOf()
 
-    private val cache = HashMap<IntArray, Deferred<T>>()
-
-    fun deferred(index: IntArray) = cache.getOrPut(index) {
+    fun deferred(index: IntArray): Deferred<T> = cache.getOrPut(index) {
         scope.async(context = Dispatchers.Math) {
             function(index)
         }
@@ -42,21 +41,21 @@ class LazyNDStructure<T>(
         result = 31 * result + cache.hashCode()
         return result
     }
-
-
 }
 
-fun <T> NDStructure<T>.deferred(index: IntArray) =
+fun <T> NDStructure<T>.deferred(index: IntArray): Deferred<T> =
     if (this is LazyNDStructure<T>) this.deferred(index) else CompletableDeferred(get(index))
 
-suspend fun <T> NDStructure<T>.await(index: IntArray) =
+suspend fun <T> NDStructure<T>.await(index: IntArray): T =
     if (this is LazyNDStructure<T>) this.await(index) else get(index)
 
 /**
- * PENDING would benifit from KEEP-176
+ * PENDING would benefit from KEEP-176
  */
-fun <T, R> NDStructure<T>.mapAsyncIndexed(scope: CoroutineScope, function: suspend (T, index: IntArray) -> R) =
-    LazyNDStructure(scope, shape) { index -> function(get(index), index) }
+fun <T, R> NDStructure<T>.mapAsyncIndexed(
+    scope: CoroutineScope,
+    function: suspend (T, index: IntArray) -> R
+): LazyNDStructure<R> = LazyNDStructure(scope, shape) { index -> function(get(index), index) }
 
-fun <T, R> NDStructure<T>.mapAsync(scope: CoroutineScope, function: suspend (T) -> R) =
+fun <T, R> NDStructure<T>.mapAsync(scope: CoroutineScope, function: suspend (T) -> R): LazyNDStructure<R> =
     LazyNDStructure(scope, shape) { index -> function(get(index)) }
\ No newline at end of file
diff --git a/kmath-coroutines/src/jvmTest/kotlin/scientifik/kmath/streaming/BufferFlowTest.kt b/kmath-coroutines/src/jvmTest/kotlin/scientifik/kmath/streaming/BufferFlowTest.kt
index 147f687f0..427349072 100644
--- a/kmath-coroutines/src/jvmTest/kotlin/scientifik/kmath/streaming/BufferFlowTest.kt
+++ b/kmath-coroutines/src/jvmTest/kotlin/scientifik/kmath/streaming/BufferFlowTest.kt
@@ -15,14 +15,13 @@ import kotlin.test.Test
 @InternalCoroutinesApi
 @FlowPreview
 class BufferFlowTest {
-
-    val dispatcher = Executors.newFixedThreadPool(4).asCoroutineDispatcher()
+    val dispatcher: CoroutineDispatcher = Executors.newFixedThreadPool(4).asCoroutineDispatcher()
 
     @Test
     @Timeout(2000)
     fun map() {
         runBlocking {
-            (1..20).asFlow().mapParallel( dispatcher) {
+            (1..20).asFlow().mapParallel(dispatcher) {
                 println("Started $it on ${Thread.currentThread().name}")
                 @Suppress("BlockingMethodInNonBlockingContext")
                 Thread.sleep(200)
diff --git a/kmath-coroutines/src/jvmTest/kotlin/scientifik/kmath/streaming/RingBufferTest.kt b/kmath-coroutines/src/jvmTest/kotlin/scientifik/kmath/streaming/RingBufferTest.kt
index c14d1a26c..c84ef89ef 100644
--- a/kmath-coroutines/src/jvmTest/kotlin/scientifik/kmath/streaming/RingBufferTest.kt
+++ b/kmath-coroutines/src/jvmTest/kotlin/scientifik/kmath/streaming/RingBufferTest.kt
@@ -19,17 +19,17 @@ class RingBufferTest {
     }
 
     @Test
-    fun windowed(){
-        val flow = flow{
+    fun windowed() {
+        val flow = flow {
             var i = 0
-            while(true){
-                emit(i++)
-            }
+            while (true) emit(i++)
         }
+
         val windowed = flow.windowed(10)
+
         runBlocking {
             val first = windowed.take(1).single()
-            val res = windowed.take(15).map { it -> it.asSequence().average() }.toList()
+            val res = windowed.take(15).map { it.asSequence().average() }.toList()
             assertEquals(0.0, res[0])
             assertEquals(4.5, res[9])
             assertEquals(9.5, res[14])
-- 
2.34.1