CHANGELOG.md

@@ -0,0 +1,32 @@
+# KMath
+
+## [Unreleased]
+
+### Added
+- Functional Expressions API
+- Mathematical Syntax Tree, its interpreter and API
+- String to MST parser (https://github.com/mipt-npm/kmath/pull/120)
+- MST to JVM bytecode translator (https://github.com/mipt-npm/kmath/pull/94)
+- FloatBuffer (specialized MutableBuffer over FloatArray)
+- FlaggedBuffer to associate primitive numbers buffer with flags (to mark values infinite or missing, etc.)
+- Specialized builder functions for all primitive buffers like `IntBuffer(25) { it + 1 }` (https://github.com/mipt-npm/kmath/pull/125)
+- Interface `NumericAlgebra` where `number` operation is available to convert numbers to algebraic elements
+- Inverse trigonometric functions support in ExtendedField (`asin`, `acos`, `atan`) (https://github.com/mipt-npm/kmath/pull/114)
+- New space extensions: `average` and `averageWith`
+- Local coding conventions
+- Geometric Domains API in `kmath-core`
+- Blocking chains in `kmath-coroutines`
+
+### Changed
+- BigInteger and BigDecimal algebra: JBigDecimalField has companion object with default math context; minor optimizations
+- `power(T, Int)` extension function has preconditions and supports `Field<T>`
+- Memory objects have more preconditions (overflow checking)
+- `tg` function is renamed to `tan` (https://github.com/mipt-npm/kmath/pull/114)
+- Gradle version: 6.3 -> 6.5.1
+- Moved probability distributions to commons-rng and to `kmath-prob`.
+
+### Fixed
+- Missing copy method in Memory implementation on JS (https://github.com/mipt-npm/kmath/pull/106)
+- D3.dim value in `kmath-dimensions`
+- Multiplication in integer rings in `kmath-core` (https://github.com/mipt-npm/kmath/pull/101)
+- Commons RNG compatibility (https://github.com/mipt-npm/kmath/issues/93)

build.gradle.kts

@@ -1,8 +1,8 @@
 plugins {
-    id("scientifik.publish") version "0.4.2" apply false
+    id("scientifik.publish") apply false
 }
 
-val kmathVersion by extra("0.1.4-dev-4")
+val kmathVersion by extra("0.1.4-dev-8")
 
 val bintrayRepo by extra("scientifik")
 val githubProject by extra("kmath")
@@ -11,6 +11,7 @@ allprojects {
     repositories {
         jcenter()
         maven("https://dl.bintray.com/kotlin/kotlinx")
+        maven("https://dl.bintray.com/hotkeytlt/maven")
     }
 
     group = "scientifik"

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

doc/buffers.md

@@ -1,8 +1,9 @@
 # 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:
 
-* Primitive buffers wrapping like `DoubleBuffer` which are wrapping primitive arrays.
+* Primitive buffers wrapping like `RealBuffer` which are wrapping primitive arrays.
 * Boxing `ListBuffer` wrapping a list
 * Functionally defined `VirtualBuffer` which does not hold a state itself, but provides a function to calculate value
 * `MemoryBuffer` allows direct allocation of objects in continuous memory block.
@@ -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  

doc/codestyle.md

@@ -0,0 +1,34 @@
+# Coding Conventions
+
+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 Naming
+
+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 Naming
+
+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 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.

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.
 

doc/nd-structure.md

@@ -1,4 +1,4 @@
-# Nd-structure generation and operations
+# ND-structure generation and operations
 
 **TODO**
 

examples/build.gradle.kts

@@ -4,8 +4,8 @@ import org.jetbrains.kotlin.gradle.tasks.KotlinCompile
 plugins {
     java
     kotlin("jvm")
-    kotlin("plugin.allopen") version "1.3.71"
-    id("kotlinx.benchmark") version "0.2.0-dev-7"
+    kotlin("plugin.allopen") version "1.3.72"
+    id("kotlinx.benchmark") version "0.2.0-dev-8"
 }
 
 configure<AllOpenExtension> {
@@ -24,16 +24,18 @@ sourceSets {
 }
 
 dependencies {
+    implementation(project(":kmath-ast"))
     implementation(project(":kmath-core"))
     implementation(project(":kmath-coroutines"))
     implementation(project(":kmath-commons"))
+    implementation(project(":kmath-prob"))
     implementation(project(":kmath-koma"))
     implementation(project(":kmath-viktor"))
     implementation(project(":kmath-dimensions"))
     implementation("com.kyonifer:koma-core-ejml:0.12")
     implementation("org.jetbrains.kotlinx:kotlinx-io-jvm:0.2.0-npm-dev-6")
-    implementation("org.jetbrains.kotlinx:kotlinx.benchmark.runtime:0.2.0-dev-7")
-    "benchmarksCompile"(sourceSets.main.get().compileClasspath)
+    implementation("org.jetbrains.kotlinx:kotlinx.benchmark.runtime:0.2.0-dev-8")
+    "benchmarksCompile"(sourceSets.main.get().output + sourceSets.main.get().compileClasspath) //sourceSets.main.output + sourceSets.main.runtimeClasspath
 }
 
 // Configure benchmark
@@ -57,6 +59,6 @@ benchmark {
 
 tasks.withType<KotlinCompile> {
     kotlinOptions {
-        jvmTarget = Scientifik.JVM_VERSION
+        jvmTarget = Scientifik.JVM_TARGET.toString()
     }
 }

examples/src/benchmarks/kotlin/scientifik/kmath/structures/BufferBenchmark.kt

@@ -10,8 +10,8 @@ import scientifik.kmath.operations.complex
 class BufferBenchmark {
 
     @Benchmark
-    fun genericDoubleBufferReadWrite() {
-        val buffer = DoubleBuffer(size){it.toDouble()}
+    fun genericRealBufferReadWrite() {
+        val buffer = RealBuffer(size){it.toDouble()}
 
         (0 until size).forEach {
             buffer[it]

examples/src/benchmarks/kotlin/scientifik/kmath/structures/ViktorBenchmark.kt

@@ -20,48 +20,39 @@ class ViktorBenchmark {
     final val viktorField = ViktorNDField(intArrayOf(dim, dim))
 
     @Benchmark
-    fun `Automatic field addition`() {
+    fun automaticFieldAddition() {
         autoField.run {
             var res = one
-            repeat(n) {
-                res += 1.0
-            }
+            repeat(n) { res += one }
         }
     }
 
     @Benchmark
-    fun `Viktor field addition`() {
+    fun viktorFieldAddition() {
         viktorField.run {
             var res = one
-            repeat(n) {
-                res += one
-            }
+            repeat(n) { res += one }
         }
     }
 
     @Benchmark
-    fun `Raw Viktor`() {
+    fun rawViktor() {
         val one = F64Array.full(init = 1.0, shape = *intArrayOf(dim, dim))
         var res = one
-        repeat(n) {
-            res = res + one
-        }
+        repeat(n) { res = res + one }
     }
 
     @Benchmark
-    fun `Real field log`() {
+    fun realdFieldLog() {
         realField.run {
             val fortyTwo = produce { 42.0 }
             var res = one
-
-            repeat(n) {
-                res = ln(fortyTwo)
-            }
+            repeat(n) { res = ln(fortyTwo) }
         }
     }
 
     @Benchmark
-    fun `Raw Viktor log`() {
+    fun rawViktorLog() {
         val fortyTwo = F64Array.full(dim, dim, init = 42.0)
         var res: F64Array
         repeat(n) {

examples/src/main/kotlin/scientifik/kmath/ast/ExpressionsInterpretersBenchmark.kt

@@ -0,0 +1,70 @@
+package scientifik.kmath.ast
+
+import scientifik.kmath.asm.compile
+import scientifik.kmath.expressions.Expression
+import scientifik.kmath.expressions.expressionInField
+import scientifik.kmath.expressions.invoke
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.RealField
+import kotlin.random.Random
+import kotlin.system.measureTimeMillis
+
+class ExpressionsInterpretersBenchmark {
+    private val algebra: Field<Double> = RealField
+    fun functionalExpression() {
+        val expr = algebra.expressionInField {
+            variable("x") * const(2.0) + const(2.0) / variable("x") - const(16.0)
+        }
+
+        invokeAndSum(expr)
+    }
+
+    fun mstExpression() {
+        val expr = algebra.mstInField {
+            symbol("x") * number(2.0) + number(2.0) / symbol("x") - number(16.0)
+        }
+
+        invokeAndSum(expr)
+    }
+
+    fun asmExpression() {
+        val expr = algebra.mstInField {
+            symbol("x") * number(2.0) + number(2.0) / symbol("x") - number(16.0)
+        }.compile()
+
+        invokeAndSum(expr)
+    }
+
+    private fun invokeAndSum(expr: Expression<Double>) {
+        val random = Random(0)
+        var sum = 0.0
+
+        repeat(1000000) {
+            sum += expr("x" to random.nextDouble())
+        }
+
+        println(sum)
+    }
+}
+
+fun main() {
+    val benchmark = ExpressionsInterpretersBenchmark()
+
+    val fe = measureTimeMillis {
+        benchmark.functionalExpression()
+    }
+
+    println("fe=$fe")
+
+    val mst = measureTimeMillis {
+        benchmark.mstExpression()
+    }
+
+    println("mst=$mst")
+
+    val asm = measureTimeMillis {
+        benchmark.asmExpression()
+    }
+
+    println("asm=$asm")
+}

examples/src/main/kotlin/scientifik/kmath/commons/prob/DistributionBenchmark.kt

@@ -0,0 +1,71 @@
+package scientifik.kmath.commons.prob
+
+import kotlinx.coroutines.Dispatchers
+import kotlinx.coroutines.async
+import kotlinx.coroutines.runBlocking
+import org.apache.commons.rng.sampling.distribution.ZigguratNormalizedGaussianSampler
+import org.apache.commons.rng.simple.RandomSource
+import scientifik.kmath.chains.BlockingRealChain
+import scientifik.kmath.prob.*
+import java.time.Duration
+import java.time.Instant
+
+
+private suspend fun runChain(): Duration {
+    val generator = RandomGenerator.fromSource(RandomSource.MT, 123L)
+
+    val normal = Distribution.normal(NormalSamplerMethod.Ziggurat)
+    val chain = normal.sample(generator) as BlockingRealChain
+
+    val startTime = Instant.now()
+    var sum = 0.0
+    repeat(10000001) { counter ->
+
+        sum += chain.nextDouble()
+
+        if (counter % 100000 == 0) {
+            val duration = Duration.between(startTime, Instant.now())
+            val meanValue = sum / counter
+            println("Chain sampler completed $counter elements in $duration: $meanValue")
+        }
+    }
+    return Duration.between(startTime, Instant.now())
+}
+
+private fun runDirect(): Duration {
+    val provider = RandomSource.create(RandomSource.MT, 123L)
+    val sampler = ZigguratNormalizedGaussianSampler(provider)
+    val startTime = Instant.now()
+
+    var sum = 0.0
+    repeat(10000001) { counter ->
+
+        sum += sampler.sample()
+
+        if (counter % 100000 == 0) {
+            val duration = Duration.between(startTime, Instant.now())
+            val meanValue = sum / counter
+            println("Direct sampler completed $counter elements in $duration: $meanValue")
+        }
+    }
+    return Duration.between(startTime, Instant.now())
+}
+
+/**
+ * Comparing chain sampling performance with direct sampling performance
+ */
+fun main() {
+    runBlocking(Dispatchers.Default) {
+        val chainJob = async {
+            runChain()
+        }
+
+        val directJob = async {
+            runDirect()
+        }
+
+        println("Chain: ${chainJob.await()}")
+        println("Direct: ${directJob.await()}")
+    }
+
+}

examples/src/main/kotlin/scientifik/kmath/commons/prob/DistributionDemo.kt

@@ -5,10 +5,11 @@ import scientifik.kmath.chains.Chain
 import scientifik.kmath.chains.collectWithState
 import scientifik.kmath.prob.Distribution
 import scientifik.kmath.prob.RandomGenerator
+import scientifik.kmath.prob.normal
 
 data class AveragingChainState(var num: Int = 0, var value: Double = 0.0)
 
-fun Chain<Double>.mean(): Chain<Double> = collectWithState(AveragingChainState(),{it.copy()}){ chain->
+fun Chain<Double>.mean(): Chain<Double> = collectWithState(AveragingChainState(), { it.copy() }) { chain ->
     val next = chain.next()
     num++
     value += next

examples/src/main/kotlin/scientifik/kmath/structures/ComplexND.kt

@@ -27,7 +27,7 @@ fun main() {
 
     val complexTime = measureTimeMillis {
         complexField.run {
-            var res = one
+            var res: NDBuffer<Complex> = one
             repeat(n) {
                 res += 1.0
             }

examples/src/main/kotlin/scientifik/kmath/structures/NDField.kt

@@ -23,14 +23,14 @@ fun main() {
 
     measureAndPrint("Automatic field addition") {
         autoField.run {
-            var res = one
+            var res: NDBuffer<Double> = one
             repeat(n) {
-                res += 1.0
+                res += number(1.0)
             }
         }
     }
 
-    measureAndPrint("Element addition"){
+    measureAndPrint("Element addition") {
         var res = genericField.one
         repeat(n) {
             res += 1.0
@@ -63,7 +63,7 @@ fun main() {
         genericField.run {
             var res: NDBuffer<Double> = one
             repeat(n) {
-                res += 1.0
+                res += one // con't avoid using `one` due to resolution ambiguity
             }
         }
     }

examples/src/main/kotlin/scientifik/kmath/structures/StructureReadBenchmark.kt

@@ -6,7 +6,7 @@ fun main(args: Array<String>) {
     val n = 6000
 
     val array = DoubleArray(n * n) { 1.0 }
-    val buffer = DoubleBuffer(array)
+    val buffer = RealBuffer(array)
     val strides = DefaultStrides(intArrayOf(n, n))
 
     val structure = BufferNDStructure(strides, buffer)

examples/src/main/kotlin/scientifik/kmath/structures/StructureWriteBenchmark.kt

@@ -26,10 +26,10 @@ fun main(args: Array<String>) {
     }
     println("Array mapping finished in $time2 millis")
 
-    val buffer = DoubleBuffer(DoubleArray(n * n) { 1.0 })
+    val buffer = RealBuffer(DoubleArray(n * n) { 1.0 })
 
     val time3 = measureTimeMillis {
-        val target = DoubleBuffer(DoubleArray(n * n))
+        val target = RealBuffer(DoubleArray(n * n))
         val res = array.forEachIndexed { index, value ->
             target[index] = value + 1
         }

gradle/wrapper/gradle-wrapper.properties

@@ -1,5 +1,5 @@
 distributionBase=GRADLE_USER_HOME
 distributionPath=wrapper/dists
-distributionUrl=https\://services.gradle.org/distributions/gradle-6.3-bin.zip
+distributionUrl=https\://services.gradle.org/distributions/gradle-6.5.1-bin.zip
 zipStoreBase=GRADLE_USER_HOME
 zipStorePath=wrapper/dists

gradlew

@@ -82,6 +82,7 @@ esac
 
 CLASSPATH=$APP_HOME/gradle/wrapper/gradle-wrapper.jar
 
+
 # Determine the Java command to use to start the JVM.
 if [ -n "$JAVA_HOME" ] ; then
     if [ -x "$JAVA_HOME/jre/sh/java" ] ; then
@@ -129,6 +130,7 @@ fi
 if [ "$cygwin" = "true" -o "$msys" = "true" ] ; then
     APP_HOME=`cygpath --path --mixed "$APP_HOME"`
     CLASSPATH=`cygpath --path --mixed "$CLASSPATH"`
+    
     JAVACMD=`cygpath --unix "$JAVACMD"`
 
     # We build the pattern for arguments to be converted via cygpath

gradlew.bat

@@ -84,6 +84,7 @@ set CMD_LINE_ARGS=%*
 
 set CLASSPATH=%APP_HOME%\gradle\wrapper\gradle-wrapper.jar
 
+
 @rem Execute Gradle
 "%JAVA_EXE%" %DEFAULT_JVM_OPTS% %JAVA_OPTS% %GRADLE_OPTS% "-Dorg.gradle.appname=%APP_BASE_NAME%" -classpath "%CLASSPATH%" org.gradle.wrapper.GradleWrapperMain %CMD_LINE_ARGS%
 

kmath-ast/README.md

@@ -0,0 +1,91 @@
+# Abstract Syntax Tree Expression Representation and Operations (`kmath-ast`)
+
+This subproject implements the following features:
+
+- Expression Language and its parser.
+- MST (Mathematical Syntax Tree) as expression language's syntax intermediate representation.
+- Type-safe builder for MST.
+- Evaluating expressions by traversing MST.
+
+> #### Artifact:
+> This module is distributed in the artifact `scientifik:kmath-ast: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-ast: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-ast:0.1.4-dev-8")
+> }
+> ```
+>
+
+## 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. 
+
+For example, the following builder: 
+
+```kotlin
+RealField.mstInField { symbol("x") + 2 }.compile()
+``` 
+
+… leads to generation of bytecode, which can be decompiled to the following Java class: 
+
+```java
+package scientifik.kmath.asm.generated;
+
+import java.util.Map;
+import scientifik.kmath.asm.internal.MapIntrinsics;
+import scientifik.kmath.expressions.Expression;
+import scientifik.kmath.operations.RealField;
+
+public final class AsmCompiledExpression_1073786867_0 implements Expression<Double> {
+    private final RealField algebra;
+
+    public final Double invoke(Map<String, ? extends Double> arguments) {
+        return (Double)this.algebra.add(((Double)MapIntrinsics.getOrFail(arguments, "x")).doubleValue(), 2.0D);
+    }
+
+    public AsmCompiledExpression_1073786867_0(RealField algebra) {
+        this.algebra = algebra;
+    }
+}
+
+```
+
+### Example Usage
+
+This API extends MST and MstExpression, so you may optimize as both of them: 
+
+```kotlin
+RealField.mstInField { symbol("x") + 2 }.compile()
+RealField.expression("x+2".parseMath())
+```
+
+### Known issues
+
+- The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid
+class loading overhead. 
+- This API is not supported by non-dynamic JVM implementations (like TeaVM and GraalVM) because of using class loaders.
+
+Contributed by [Iaroslav Postovalov](https://github.com/CommanderTvis).

kmath-ast/build.gradle.kts

@@ -0,0 +1,23 @@
+plugins { id("scientifik.mpp") }
+
+kotlin.sourceSets {
+//    all {
+//       languageSettings.apply{
+//            enableLanguageFeature("NewInference")
+//       }
+//    }
+    commonMain {
+        dependencies {
+            api(project(":kmath-core"))
+            implementation("com.github.h0tk3y.betterParse:better-parse:0.4.0")
+        }
+    }
+
+    jvmMain {
+        dependencies {
+            implementation("org.ow2.asm:asm:8.0.1")
+            implementation("org.ow2.asm:asm-commons:8.0.1")
+            implementation(kotlin("reflect"))
+        }
+    }
+}

kmath-ast/reference/ArithmeticsEvaluator.g4

@@ -0,0 +1,59 @@
+grammar ArithmeticsEvaluator;
+
+fragment DIGIT: '0'..'9';
+fragment LETTER: 'a'..'z';
+fragment CAPITAL_LETTER: 'A'..'Z';
+fragment UNDERSCORE: '_';
+
+ID: (LETTER | UNDERSCORE | CAPITAL_LETTER) (LETTER | UNDERSCORE | DIGIT | CAPITAL_LETTER)*;
+NUM: (DIGIT | '.')+ ([eE] [-+]? DIGIT+)?;
+MUL: '*';
+DIV: '/';
+PLUS: '+';
+MINUS: '-';
+POW: '^';
+COMMA: ',';
+LPAR: '(';
+RPAR: ')';
+WS: [ \n\t\r]+ -> skip;
+
+num
+    : NUM
+    ;
+
+singular
+    : ID
+    ;
+
+unaryFunction
+    : ID LPAR subSumChain RPAR
+    ;
+
+binaryFunction
+    : ID LPAR subSumChain COMMA subSumChain RPAR
+    ;
+
+term
+    : num
+    | singular
+    | unaryFunction
+    | binaryFunction
+    | MINUS term
+    | LPAR subSumChain RPAR
+    ;
+
+powChain
+    : term (POW term)*
+    ;
+
+divMulChain
+    : powChain ((DIV | MUL) powChain)*
+    ;
+
+subSumChain
+    : divMulChain ((PLUS | MINUS) divMulChain)*
+    ;
+
+rootParser
+    : subSumChain EOF
+    ;

kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MST.kt

@@ -0,0 +1,87 @@
+package scientifik.kmath.ast
+
+import scientifik.kmath.operations.Algebra
+import scientifik.kmath.operations.NumericAlgebra
+import scientifik.kmath.operations.RealField
+
+/**
+ * A Mathematical Syntax Tree node for mathematical expressions.
+ */
+sealed class MST {
+    /**
+     * A node containing raw string.
+     *
+     * @property value the value of this node.
+     */
+    data class Symbolic(val value: String) : MST()
+
+    /**
+     * 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.
+     *
+     * @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
+    }
+
+    /**
+     * 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 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")
+    is MST.Symbolic -> symbol(node.value)
+    is MST.Unary -> unaryOperation(node.operation, evaluate(node.value))
+    is MST.Binary -> when {
+        this !is NumericAlgebra -> binaryOperation(node.operation, evaluate(node.left), evaluate(node.right))
+
+        node.left is MST.Numeric && node.right is MST.Numeric -> {
+            val number = RealField.binaryOperation(
+                node.operation,
+                node.left.value.toDouble(),
+                node.right.value.toDouble()
+            )
+
+            number(number)
+        }
+
+        node.left is MST.Numeric -> leftSideNumberOperation(node.operation, node.left.value, evaluate(node.right))
+        node.right is MST.Numeric -> rightSideNumberOperation(node.operation, evaluate(node.left), node.right.value)
+        else -> binaryOperation(node.operation, evaluate(node.left), evaluate(node.right))
+    }
+}
+
+/**
+ * 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)

kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstAlgebra.kt

@@ -0,0 +1,102 @@
+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)
+
+    override fun symbol(value: String): MST = MST.Symbolic(value)
+
+    override fun unaryOperation(operation: String, arg: MST): MST =
+        MST.Unary(operation, arg)
+
+    override fun binaryOperation(operation: String, left: MST, right: MST): 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 binaryOperation(operation: String, left: MST, right: MST): MST =
+        MstAlgebra.binaryOperation(operation, left, right)
+
+    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 = 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 = 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 =
+        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 = 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 =
+        MstRing.binaryOperation(operation, left, right)
+
+    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)
+}

kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MstExpression.kt

@@ -0,0 +1,88 @@
+package scientifik.kmath.ast
+
+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.
+ *
+ * @property algebra the algebra that provides operations.
+ * @property mst the [MST] node.
+ */
+class MstExpression<T>(val algebra: Algebra<T>, val mst: MST) : Expression<T> {
+    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)
+
+        override fun binaryOperation(operation: String, left: T, right: T): T =
+            algebra.binaryOperation(operation, left, right)
+
+        override fun number(value: Number): T = if (algebra is NumericAlgebra)
+            algebra.number(value)
+        else
+            error("Numeric nodes are not supported by $this")
+    }
+
+    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())
+
+/**
+ * Builds [MstExpression] over [ExtendedField].
+ */
+inline fun <reified T : Any> Field<T>.mstInExtendedField(block: MstExtendedField.() -> MST): MstExpression<T> =
+    MstExpression(this, MstExtendedField.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)
+
+/**
+ * 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)

kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/parser.kt

@@ -0,0 +1,97 @@
+package scientifik.kmath.ast
+
+import com.github.h0tk3y.betterParse.combinators.*
+import com.github.h0tk3y.betterParse.grammar.Grammar
+import com.github.h0tk3y.betterParse.grammar.parseToEnd
+import com.github.h0tk3y.betterParse.grammar.parser
+import com.github.h0tk3y.betterParse.grammar.tryParseToEnd
+import com.github.h0tk3y.betterParse.lexer.Token
+import com.github.h0tk3y.betterParse.lexer.TokenMatch
+import com.github.h0tk3y.betterParse.lexer.regexToken
+import com.github.h0tk3y.betterParse.parser.ParseResult
+import com.github.h0tk3y.betterParse.parser.Parser
+import scientifik.kmath.operations.FieldOperations
+import scientifik.kmath.operations.PowerOperations
+import scientifik.kmath.operations.RingOperations
+import scientifik.kmath.operations.SpaceOperations
+
+/**
+ * TODO move to core
+ */
+object ArithmeticsEvaluator : Grammar<MST>() {
+    // TODO replace with "...".toRegex() when better-parse 0.4.1 is released
+    private val num: Token by regexToken("[\\d.]+(?:[eE][-+]?\\d+)?")
+    private val id: Token by regexToken("[a-z_A-Z][\\da-z_A-Z]*")
+    private val lpar: Token by regexToken("\\(")
+    private val rpar: Token by regexToken("\\)")
+    private val comma: Token by regexToken(",")
+    private val mul: Token by regexToken("\\*")
+    private val pow: Token by regexToken("\\^")
+    private val div: Token by regexToken("/")
+    private val minus: Token by regexToken("-")
+    private val plus: Token by regexToken("\\+")
+    private val ws: Token by regexToken("\\s+", ignore = true)
+
+    private val number: Parser<MST> by num use { MST.Numeric(text.toDouble()) }
+    private val singular: Parser<MST> by id use { MST.Symbolic(text) }
+
+    private val unaryFunction: Parser<MST> by (id and skip(lpar) and parser(::subSumChain) and skip(rpar))
+        .map { (id, term) -> MST.Unary(id.text, term) }
+
+    private val binaryFunction: Parser<MST> by id
+        .and(skip(lpar))
+        .and(parser(::subSumChain))
+        .and(skip(comma))
+        .and(parser(::subSumChain))
+        .and(skip(rpar))
+        .map { (id, left, right) -> MST.Binary(id.text, left, right) }
+
+    private val term: Parser<MST> by number
+        .or(binaryFunction)
+        .or(unaryFunction)
+        .or(singular)
+        .or(skip(minus) and parser(::term) map { MST.Unary(SpaceOperations.MINUS_OPERATION, it) })
+        .or(skip(lpar) and parser(::subSumChain) and skip(rpar))
+
+    private val powChain: Parser<MST> by leftAssociative(term = term, operator = pow) { a, _, b ->
+        MST.Binary(PowerOperations.POW_OPERATION, a, b)
+    }
+
+    private val divMulChain: Parser<MST> by leftAssociative(
+        term = powChain,
+        operator = div or mul use TokenMatch::type
+    ) { a, op, b ->
+        if (op == div)
+            MST.Binary(FieldOperations.DIV_OPERATION, a, b)
+        else
+            MST.Binary(RingOperations.TIMES_OPERATION, a, b)
+    }
+
+    private val subSumChain: Parser<MST> by leftAssociative(
+        term = divMulChain,
+        operator = plus or minus use TokenMatch::type
+    ) { a, op, b ->
+        if (op == plus)
+            MST.Binary(SpaceOperations.PLUS_OPERATION, a, b)
+        else
+            MST.Binary(SpaceOperations.MINUS_OPERATION, a, b)
+    }
+
+    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)

kmath-ast/src/jvmMain/kotlin/scientifik/kmath/asm/asm.kt

@@ -0,0 +1,64 @@
+package scientifik.kmath.asm
+
+import scientifik.kmath.asm.internal.AsmBuilder
+import scientifik.kmath.asm.internal.MstType
+import scientifik.kmath.asm.internal.buildAlgebraOperationCall
+import scientifik.kmath.asm.internal.buildName
+import scientifik.kmath.ast.MST
+import scientifik.kmath.ast.MstExpression
+import scientifik.kmath.expressions.Expression
+import scientifik.kmath.operations.Algebra
+import kotlin.reflect.KClass
+
+/**
+ * Compile given MST to an Expression using AST compiler
+ */
+fun <T : Any> MST.compileWith(type: KClass<T>, algebra: Algebra<T>): Expression<T> {
+    fun AsmBuilder<T>.visit(node: MST) {
+        when (node) {
+            is MST.Symbolic -> {
+                val symbol = try {
+                    algebra.symbol(node.value)
+                } catch (ignored: Throwable) {
+                    null
+                }
+
+                if (symbol != null)
+                    loadTConstant(symbol)
+                else
+                    loadVariable(node.value)
+            }
+
+            is MST.Numeric -> loadNumeric(node.value)
+
+            is MST.Unary -> buildAlgebraOperationCall(
+                context = algebra,
+                name = node.operation,
+                fallbackMethodName = "unaryOperation",
+                parameterTypes = arrayOf(MstType.fromMst(node.value))
+            ) { visit(node.value) }
+
+            is MST.Binary -> buildAlgebraOperationCall(
+                context = algebra,
+                name = node.operation,
+                fallbackMethodName = "binaryOperation",
+                parameterTypes = arrayOf(MstType.fromMst(node.left), MstType.fromMst(node.right))
+            ) {
+                visit(node.left)
+                visit(node.right)
+            }
+        }
+    }
+
+    return AsmBuilder(type, algebra, buildName(this)) { visit(this@compileWith) }.getInstance()
+}
+
+/**
+ * Compile an [MST] to ASM using given algebra
+ */
+inline fun <reified T : Any> Algebra<T>.expression(mst: MST): Expression<T> = mst.compileWith(T::class, this)
+
+/**
+ * Optimize performance of an [MstExpression] using ASM codegen
+ */
+inline fun <reified T : Any> MstExpression<T>.compile(): Expression<T> = mst.compileWith(T::class, algebra)

kmath-ast/src/jvmMain/kotlin/scientifik/kmath/asm/internal/AsmBuilder.kt

@@ -0,0 +1,568 @@
+package scientifik.kmath.asm.internal
+
+import org.objectweb.asm.*
+import org.objectweb.asm.Opcodes.*
+import org.objectweb.asm.commons.InstructionAdapter
+import scientifik.kmath.asm.internal.AsmBuilder.ClassLoader
+import scientifik.kmath.ast.MST
+import scientifik.kmath.expressions.Expression
+import scientifik.kmath.operations.Algebra
+import scientifik.kmath.operations.NumericAlgebra
+import java.util.*
+import java.util.stream.Collectors
+import kotlin.reflect.KClass
+
+/**
+ * ASM Builder is a structure that abstracts building a class designated to unwrap [MST] to plain Java expression.
+ * This class uses [ClassLoader] for loading the generated class, then it is able to instantiate the new class.
+ *
+ * @property T the type of AsmExpression to unwrap.
+ * @property algebra the algebra the applied AsmExpressions use.
+ * @property className the unique class name of new loaded class.
+ * @property invokeLabel0Visitor the function to apply to this object when generating invoke method, label 0.
+ */
+internal class AsmBuilder<T> internal constructor(
+    private val classOfT: KClass<*>,
+    private val algebra: Algebra<T>,
+    private val className: String,
+    private val invokeLabel0Visitor: AsmBuilder<T>.() -> Unit
+) {
+    /**
+     * Internal classloader of [AsmBuilder] with alias to define class from byte array.
+     */
+    private class ClassLoader(parent: java.lang.ClassLoader) : java.lang.ClassLoader(parent) {
+        internal fun defineClass(name: String?, b: ByteArray): Class<*> = defineClass(name, b, 0, b.size)
+    }
+
+    /**
+     * The instance of [ClassLoader] used by this builder.
+     */
+    private val classLoader: ClassLoader = ClassLoader(javaClass.classLoader)
+
+    /**
+     * ASM Type for [algebra].
+     */
+    private val tAlgebraType: Type = algebra::class.asm
+
+    /**
+     * ASM type for [T].
+     */
+    internal val tType: Type = classOfT.asm
+
+    /**
+     * ASM type for new class.
+     */
+    private val classType: Type = Type.getObjectType(className.replace(oldChar = '.', newChar = '/'))!!
+
+    /**
+     * Index of `this` variable in invoke method of the built subclass.
+     */
+    private val invokeThisVar: Int = 0
+
+    /**
+     * Index of `arguments` variable in invoke method of the built subclass.
+     */
+    private val invokeArgumentsVar: Int = 1
+
+    /**
+     * List of constants to provide to the subclass.
+     */
+    private val constants: MutableList<Any> = mutableListOf()
+
+    /**
+     * Method visitor of `invoke` method of the subclass.
+     */
+    private lateinit var invokeMethodVisitor: InstructionAdapter
+
+    /**
+     * State if this [AsmBuilder] needs to generate constants field.
+     */
+    private var hasConstants: Boolean = true
+
+    /**
+     * State if [T] a primitive type, so [AsmBuilder] may generate direct primitive calls.
+     */
+    internal var primitiveMode: Boolean = false
+
+    /**
+     * Primitive type to apple for specific primitive calls. Use [OBJECT_TYPE], if not in [primitiveMode].
+     */
+    internal var primitiveMask: Type = OBJECT_TYPE
+
+    /**
+     * Boxed primitive type to apple for specific primitive calls. Use [OBJECT_TYPE], if not in [primitiveMode].
+     */
+    internal var primitiveMaskBoxed: Type = OBJECT_TYPE
+
+    /**
+     * Stack of useful objects types on stack to verify types.
+     */
+    private val typeStack: ArrayDeque<Type> = ArrayDeque()
+
+    /**
+     * Stack of useful objects types on stack expected by algebra calls.
+     */
+    internal val expectationStack: ArrayDeque<Type> = ArrayDeque(listOf(tType))
+
+    /**
+     * The cache for instance built by this builder.
+     */
+    private var generatedInstance: Expression<T>? = null
+
+    /**
+     * Subclasses, loads and instantiates [Expression] for given parameters.
+     *
+     * The built instance is cached.
+     */
+    @Suppress("UNCHECKED_CAST")
+    internal fun getInstance(): Expression<T> {
+        generatedInstance?.let { return it }
+
+        if (SIGNATURE_LETTERS.containsKey(classOfT)) {
+            primitiveMode = true
+            primitiveMask = SIGNATURE_LETTERS.getValue(classOfT)
+            primitiveMaskBoxed = tType
+        }
+
+        val classWriter = ClassWriter(ClassWriter.COMPUTE_FRAMES) {
+            visit(
+                V1_8,
+                ACC_PUBLIC or ACC_FINAL or ACC_SUPER,
+                classType.internalName,
+                "${OBJECT_TYPE.descriptor}L${EXPRESSION_TYPE.internalName}<${tType.descriptor}>;",
+                OBJECT_TYPE.internalName,
+                arrayOf(EXPRESSION_TYPE.internalName)
+            )
+
+            visitMethod(
+                ACC_PUBLIC or ACC_FINAL,
+                "invoke",
+                Type.getMethodDescriptor(tType, MAP_TYPE),
+                "(L${MAP_TYPE.internalName}<${STRING_TYPE.descriptor}+${tType.descriptor}>;)${tType.descriptor}",
+                null
+            ).instructionAdapter {
+                invokeMethodVisitor = this
+                visitCode()
+                val l0 = label()
+                invokeLabel0Visitor()
+                areturn(tType)
+                val l1 = label()
+
+                visitLocalVariable(
+                    "this",
+                    classType.descriptor,
+                    null,
+                    l0,
+                    l1,
+                    invokeThisVar
+                )
+
+                visitLocalVariable(
+                    "arguments",
+                    MAP_TYPE.descriptor,
+                    "L${MAP_TYPE.internalName}<${STRING_TYPE.descriptor}+${tType.descriptor}>;",
+                    l0,
+                    l1,
+                    invokeArgumentsVar
+                )
+
+                visitMaxs(0, 2)
+                visitEnd()
+            }
+
+            visitMethod(
+                ACC_PUBLIC or ACC_FINAL or ACC_BRIDGE or ACC_SYNTHETIC,
+                "invoke",
+                Type.getMethodDescriptor(OBJECT_TYPE, MAP_TYPE),
+                null,
+                null
+            ).instructionAdapter {
+                val thisVar = 0
+                val argumentsVar = 1
+                visitCode()
+                val l0 = label()
+                load(thisVar, OBJECT_TYPE)
+                load(argumentsVar, MAP_TYPE)
+                invokevirtual(classType.internalName, "invoke", Type.getMethodDescriptor(tType, MAP_TYPE), false)
+                areturn(tType)
+                val l1 = label()
+
+                visitLocalVariable(
+                    "this",
+                    classType.descriptor,
+                    null,
+                    l0,
+                    l1,
+                    thisVar
+                )
+
+                visitMaxs(0, 2)
+                visitEnd()
+            }
+
+            hasConstants = constants.isNotEmpty()
+
+            visitField(
+                access = ACC_PRIVATE or ACC_FINAL,
+                name = "algebra",
+                descriptor = tAlgebraType.descriptor,
+                signature = null,
+                value = null,
+                block = FieldVisitor::visitEnd
+            )
+
+            if (hasConstants)
+                visitField(
+                    access = ACC_PRIVATE or ACC_FINAL,
+                    name = "constants",
+                    descriptor = OBJECT_ARRAY_TYPE.descriptor,
+                    signature = null,
+                    value = null,
+                    block = FieldVisitor::visitEnd
+                )
+
+            visitMethod(
+                ACC_PUBLIC,
+                "<init>",
+
+                Type.getMethodDescriptor(
+                    Type.VOID_TYPE,
+                    tAlgebraType,
+                    *OBJECT_ARRAY_TYPE.wrapToArrayIf { hasConstants }),
+
+                null,
+                null
+            ).instructionAdapter {
+                val thisVar = 0
+                val algebraVar = 1
+                val constantsVar = 2
+                val l0 = label()
+                load(thisVar, classType)
+                invokespecial(OBJECT_TYPE.internalName, "<init>", Type.getMethodDescriptor(Type.VOID_TYPE), false)
+                label()
+                load(thisVar, classType)
+                load(algebraVar, tAlgebraType)
+                putfield(classType.internalName, "algebra", tAlgebraType.descriptor)
+
+                if (hasConstants) {
+                    label()
+                    load(thisVar, classType)
+                    load(constantsVar, OBJECT_ARRAY_TYPE)
+                    putfield(classType.internalName, "constants", OBJECT_ARRAY_TYPE.descriptor)
+                }
+
+                label()
+                visitInsn(RETURN)
+                val l4 = label()
+                visitLocalVariable("this", classType.descriptor, null, l0, l4, thisVar)
+
+                visitLocalVariable(
+                    "algebra",
+                    tAlgebraType.descriptor,
+                    null,
+                    l0,
+                    l4,
+                    algebraVar
+                )
+
+                if (hasConstants)
+                    visitLocalVariable("constants", OBJECT_ARRAY_TYPE.descriptor, null, l0, l4, constantsVar)
+
+                visitMaxs(0, 3)
+                visitEnd()
+            }
+
+            visitEnd()
+        }
+
+        val new = classLoader
+            .defineClass(className, classWriter.toByteArray())
+            .constructors
+            .first()
+            .newInstance(algebra, *(constants.toTypedArray().wrapToArrayIf { hasConstants })) as Expression<T>
+
+        generatedInstance = new
+        return new
+    }
+
+    /**
+     * Loads a [T] constant from [constants].
+     */
+    internal fun loadTConstant(value: T) {
+        if (classOfT in INLINABLE_NUMBERS) {
+            val expectedType = expectationStack.pop()
+            val mustBeBoxed = expectedType.sort == Type.OBJECT
+            loadNumberConstant(value as Number, mustBeBoxed)
+
+            if (mustBeBoxed)
+                invokeMethodVisitor.checkcast(tType)
+
+            if (mustBeBoxed) typeStack.push(tType) else typeStack.push(primitiveMask)
+            return
+        }
+
+        loadObjectConstant(value as Any, tType)
+    }
+
+    /**
+     * Boxes the current value and pushes it.
+     */
+    private fun box(primitive: Type) {
+        val r = PRIMITIVES_TO_BOXED.getValue(primitive)
+
+        invokeMethodVisitor.invokestatic(
+            r.internalName,
+            "valueOf",
+            Type.getMethodDescriptor(r, primitive),
+            false
+        )
+    }
+
+    /**
+     * Unboxes the current boxed value and pushes it.
+     */
+    private fun unboxTo(primitive: Type) = invokeMethodVisitor.invokevirtual(
+        NUMBER_TYPE.internalName,
+        NUMBER_CONVERTER_METHODS.getValue(primitive),
+        Type.getMethodDescriptor(primitive),
+        false
+    )
+
+    /**
+     * Loads [java.lang.Object] constant from constants.
+     */
+    private fun loadObjectConstant(value: Any, type: Type): Unit = invokeMethodVisitor.run {
+        val idx = if (value in constants) constants.indexOf(value) else constants.apply { add(value) }.lastIndex
+        loadThis()
+        getfield(classType.internalName, "constants", OBJECT_ARRAY_TYPE.descriptor)
+        iconst(idx)
+        visitInsn(AALOAD)
+        checkcast(type)
+    }
+
+    internal fun loadNumeric(value: Number) {
+        if (expectationStack.peek() == NUMBER_TYPE) {
+            loadNumberConstant(value, true)
+            expectationStack.pop()
+            typeStack.push(NUMBER_TYPE)
+        } else (algebra as? NumericAlgebra<T>)?.number(value)?.let { loadTConstant(it) }
+            ?: error("Cannot resolve numeric $value since target algebra is not numeric, and the current operation doesn't accept numbers.")
+    }
+
+    /**
+     * Loads this variable.
+     */
+    private fun loadThis(): Unit = invokeMethodVisitor.load(invokeThisVar, classType)
+
+    /**
+     * Either loads a numeric constant [value] from the class's constants field or boxes a primitive
+     * constant from the constant pool (some numbers with special opcodes like [Opcodes.ICONST_0] aren't even loaded
+     * from it).
+     */
+    private fun loadNumberConstant(value: Number, mustBeBoxed: Boolean) {
+        val boxed = value::class.asm
+        val primitive = BOXED_TO_PRIMITIVES[boxed]
+
+        if (primitive != null) {
+            when (primitive) {
+                Type.BYTE_TYPE -> invokeMethodVisitor.iconst(value.toInt())
+                Type.DOUBLE_TYPE -> invokeMethodVisitor.dconst(value.toDouble())
+                Type.FLOAT_TYPE -> invokeMethodVisitor.fconst(value.toFloat())
+                Type.LONG_TYPE -> invokeMethodVisitor.lconst(value.toLong())
+                Type.INT_TYPE -> invokeMethodVisitor.iconst(value.toInt())
+                Type.SHORT_TYPE -> invokeMethodVisitor.iconst(value.toInt())
+            }
+
+            if (mustBeBoxed)
+                box(primitive)
+
+            return
+        }
+
+        loadObjectConstant(value, boxed)
+
+        if (!mustBeBoxed)
+            unboxTo(primitiveMask)
+    }
+
+    /**
+     * Loads a variable [name] from arguments [Map] parameter of [Expression.invoke]. The [defaultValue] may be
+     * provided.
+     */
+    internal fun loadVariable(name: String, defaultValue: T? = null): Unit = invokeMethodVisitor.run {
+        load(invokeArgumentsVar, MAP_TYPE)
+        aconst(name)
+
+        if (defaultValue != null)
+            loadTConstant(defaultValue)
+
+        invokestatic(
+            MAP_INTRINSICS_TYPE.internalName,
+            "getOrFail",
+
+            Type.getMethodDescriptor(
+                OBJECT_TYPE,
+                MAP_TYPE,
+                OBJECT_TYPE,
+                *OBJECT_TYPE.wrapToArrayIf { defaultValue != null }),
+            false
+        )
+
+        checkcast(tType)
+        val expectedType = expectationStack.pop()
+
+        if (expectedType.sort == Type.OBJECT)
+            typeStack.push(tType)
+        else {
+            unboxTo(primitiveMask)
+            typeStack.push(primitiveMask)
+        }
+    }
+
+    /**
+     * Loads algebra from according field of the class and casts it to class of [algebra] provided.
+     */
+    internal fun loadAlgebra() {
+        loadThis()
+        invokeMethodVisitor.getfield(classType.internalName, "algebra", tAlgebraType.descriptor)
+    }
+
+    /**
+     * Writes a method instruction of opcode with its [owner], [method] and its [descriptor]. The default opcode is
+     * [Opcodes.INVOKEINTERFACE], since most Algebra functions are declared in interfaces. [loadAlgebra] should be
+     * called before the arguments and this operation.
+     *
+     * The result is casted to [T] automatically.
+     */
+    internal fun invokeAlgebraOperation(
+        owner: String,
+        method: String,
+        descriptor: String,
+        expectedArity: Int,
+        opcode: Int = INVOKEINTERFACE
+    ) {
+        run loop@{
+            repeat(expectedArity) {
+                if (typeStack.isEmpty()) return@loop
+                typeStack.pop()
+            }
+        }
+
+        invokeMethodVisitor.visitMethodInsn(
+            opcode,
+            owner,
+            method,
+            descriptor,
+            opcode == INVOKEINTERFACE
+        )
+
+        invokeMethodVisitor.checkcast(tType)
+        val isLastExpr = expectationStack.size == 1
+        val expectedType = expectationStack.pop()
+
+        if (expectedType.sort == Type.OBJECT || isLastExpr)
+            typeStack.push(tType)
+        else {
+            unboxTo(primitiveMask)
+            typeStack.push(primitiveMask)
+        }
+    }
+
+    /**
+     * Writes a LDC Instruction with string constant provided.
+     */
+    internal fun loadStringConstant(string: String): Unit = invokeMethodVisitor.aconst(string)
+
+    internal companion object {
+        /**
+         * Maps JVM primitive numbers boxed types to their primitive ASM types.
+         */
+        private val SIGNATURE_LETTERS: Map<KClass<out Any>, Type> by lazy {
+            hashMapOf(
+                java.lang.Byte::class to Type.BYTE_TYPE,
+                java.lang.Short::class to Type.SHORT_TYPE,
+                java.lang.Integer::class to Type.INT_TYPE,
+                java.lang.Long::class to Type.LONG_TYPE,
+                java.lang.Float::class to Type.FLOAT_TYPE,
+                java.lang.Double::class to Type.DOUBLE_TYPE
+            )
+        }
+
+        /**
+         * Maps JVM primitive numbers boxed ASM types to their primitive ASM types.
+         */
+        private val BOXED_TO_PRIMITIVES: Map<Type, Type> by lazy { SIGNATURE_LETTERS.mapKeys { (k, _) -> k.asm } }
+
+        /**
+         * Maps JVM primitive numbers boxed ASM types to their primitive ASM types.
+         */
+        private val PRIMITIVES_TO_BOXED: Map<Type, Type> by lazy {
+            BOXED_TO_PRIMITIVES.entries.stream().collect(
+                Collectors.toMap(
+                    Map.Entry<Type, Type>::value,
+                    Map.Entry<Type, Type>::key
+                )
+            )
+        }
+
+        /**
+         * Maps primitive ASM types to [Number] functions unboxing them.
+         */
+        private val NUMBER_CONVERTER_METHODS: Map<Type, String> by lazy {
+            hashMapOf(
+                Type.BYTE_TYPE to "byteValue",
+                Type.SHORT_TYPE to "shortValue",
+                Type.INT_TYPE to "intValue",
+                Type.LONG_TYPE to "longValue",
+                Type.FLOAT_TYPE to "floatValue",
+                Type.DOUBLE_TYPE to "doubleValue"
+            )
+        }
+
+        /**
+         * Provides boxed number types values of which can be stored in JVM bytecode constant pool.
+         */
+        private val INLINABLE_NUMBERS: Set<KClass<out Any>> by lazy { SIGNATURE_LETTERS.keys }
+
+        /**
+         * ASM type for [Expression].
+         */
+        internal val EXPRESSION_TYPE: Type by lazy { Expression::class.asm }
+
+        /**
+         * ASM type for [java.lang.Number].
+         */
+        internal val NUMBER_TYPE: Type by lazy { java.lang.Number::class.asm }
+
+        /**
+         * ASM type for [java.util.Map].
+         */
+        internal val MAP_TYPE: Type by lazy { java.util.Map::class.asm }
+
+        /**
+         * ASM type for [java.lang.Object].
+         */
+        internal val OBJECT_TYPE: Type by lazy { java.lang.Object::class.asm }
+
+        /**
+         * ASM type for array of [java.lang.Object].
+         */
+        @Suppress("PLATFORM_CLASS_MAPPED_TO_KOTLIN", "RemoveRedundantQualifierName")
+        internal val OBJECT_ARRAY_TYPE: Type by lazy { Array<java.lang.Object>::class.asm }
+
+        /**
+         * ASM type for [Algebra].
+         */
+        internal val ALGEBRA_TYPE: Type by lazy { Algebra::class.asm }
+
+        /**
+         * ASM type for [java.lang.String].
+         */
+        internal val STRING_TYPE: Type by lazy { java.lang.String::class.asm }
+
+        /**
+         * ASM type for MapIntrinsics.
+         */
+        internal val MAP_INTRINSICS_TYPE: Type by lazy { Type.getObjectType("scientifik/kmath/asm/internal/MapIntrinsics") }
+    }
+}

kmath-ast/src/jvmMain/kotlin/scientifik/kmath/asm/internal/MstType.kt

@@ -0,0 +1,17 @@
+package scientifik.kmath.asm.internal
+
+import scientifik.kmath.ast.MST
+
+internal enum class MstType {
+    GENERAL,
+    NUMBER;
+
+    companion object {
+        fun fromMst(mst: MST): MstType {
+            if (mst is MST.Numeric)
+                return NUMBER
+
+            return GENERAL
+        }
+    }
+}

kmath-ast/src/jvmMain/kotlin/scientifik/kmath/asm/internal/codegenUtils.kt

@@ -0,0 +1,178 @@
+package scientifik.kmath.asm.internal
+
+import org.objectweb.asm.*
+import org.objectweb.asm.Opcodes.INVOKEVIRTUAL
+import org.objectweb.asm.commons.InstructionAdapter
+import scientifik.kmath.ast.MST
+import scientifik.kmath.expressions.Expression
+import scientifik.kmath.operations.Algebra
+import java.lang.reflect.Method
+import kotlin.reflect.KClass
+
+private val methodNameAdapters: Map<Pair<String, Int>, String> by lazy {
+    hashMapOf(
+        "+" to 2 to "add",
+        "*" to 2 to "multiply",
+        "/" to 2 to "divide",
+        "+" to 1 to "unaryPlus",
+        "-" to 1 to "unaryMinus",
+        "-" to 2 to "minus"
+    )
+}
+
+internal val KClass<*>.asm: Type
+    get() = Type.getType(java)
+
+/**
+ * Returns singleton array with this value if the [predicate] is true, returns empty array otherwise.
+ */
+internal inline fun <reified T> T.wrapToArrayIf(predicate: (T) -> Boolean): Array<T> =
+    if (predicate(this)) arrayOf(this) else emptyArray()
+
+/**
+ * Creates an [InstructionAdapter] from this [MethodVisitor].
+ */
+private fun MethodVisitor.instructionAdapter(): InstructionAdapter = InstructionAdapter(this)
+
+/**
+ * Creates an [InstructionAdapter] from this [MethodVisitor] and applies [block] to it.
+ */
+internal fun MethodVisitor.instructionAdapter(block: InstructionAdapter.() -> Unit): InstructionAdapter =
+    instructionAdapter().apply(block)
+
+/**
+ * Constructs a [Label], then applies it to this visitor.
+ */
+internal fun MethodVisitor.label(): Label = Label().also { visitLabel(it) }
+
+/**
+ * Creates a class name for [Expression] subclassed to implement [mst] provided.
+ *
+ * This methods helps to avoid collisions of class name to prevent loading several classes with the same name. If there
+ * is a colliding class, change [collision] parameter or leave it `0` to check existing classes recursively.
+ */
+internal tailrec fun buildName(mst: MST, collision: Int = 0): String {
+    val name = "scientifik.kmath.asm.generated.AsmCompiledExpression_${mst.hashCode()}_$collision"
+
+    try {
+        Class.forName(name)
+    } catch (ignored: ClassNotFoundException) {
+        return name
+    }
+
+    return buildName(mst, collision + 1)
+}
+
+@Suppress("FunctionName")
+internal inline fun ClassWriter(flags: Int, block: ClassWriter.() -> Unit): ClassWriter =
+    ClassWriter(flags).apply(block)
+
+internal inline fun ClassWriter.visitField(
+    access: Int,
+    name: String,
+    descriptor: String,
+    signature: String?,
+    value: Any?,
+    block: FieldVisitor.() -> Unit
+): FieldVisitor = visitField(access, name, descriptor, signature, value).apply(block)
+
+private fun <T> AsmBuilder<T>.findSpecific(context: Algebra<T>, name: String, parameterTypes: Array<MstType>): Method? =
+    context.javaClass.methods.find { method ->
+        val nameValid = method.name == name
+        val arityValid = method.parameters.size == parameterTypes.size
+        val notBridgeInPrimitive = !(primitiveMode && method.isBridge)
+
+        val paramsValid = method.parameterTypes.zip(parameterTypes).all { (type, mstType) ->
+            !(mstType != MstType.NUMBER && type == java.lang.Number::class.java)
+        }
+
+        nameValid && arityValid && notBridgeInPrimitive && paramsValid
+    }
+
+/**
+ * Checks if the target [context] for code generation contains a method with needed [name] and arity, also builds
+ * type expectation stack for needed arity.
+ *
+ * @return `true` if contains, else `false`.
+ */
+private fun <T> AsmBuilder<T>.buildExpectationStack(
+    context: Algebra<T>,
+    name: String,
+    parameterTypes: Array<MstType>
+): Boolean {
+    val arity = parameterTypes.size
+    val specific = findSpecific(context, methodNameAdapters[name to arity] ?: name, parameterTypes)
+
+    if (specific != null)
+        mapTypes(specific, parameterTypes).reversed().forEach { expectationStack.push(it) }
+    else
+        repeat(arity) { expectationStack.push(tType) }
+
+    return specific != null
+}
+
+private fun <T> AsmBuilder<T>.mapTypes(method: Method, parameterTypes: Array<MstType>): List<Type> = method
+    .parameterTypes
+    .zip(parameterTypes)
+    .map { (type, mstType) ->
+        when {
+            type == java.lang.Number::class.java && mstType == MstType.NUMBER -> AsmBuilder.NUMBER_TYPE
+            else -> if (primitiveMode) primitiveMask else primitiveMaskBoxed
+        }
+    }
+
+/**
+ * Checks if the target [context] for code generation contains a method with needed [name] and arity and inserts
+ * [AsmBuilder.invokeAlgebraOperation] of this method.
+ *
+ * @return `true` if contains, else `false`.
+ */
+private fun <T> AsmBuilder<T>.tryInvokeSpecific(
+    context: Algebra<T>,
+    name: String,
+    parameterTypes: Array<MstType>
+): Boolean {
+    val arity = parameterTypes.size
+    val theName = methodNameAdapters[name to arity] ?: name
+    val spec = findSpecific(context, theName, parameterTypes) ?: return false
+    val owner = context::class.asm
+
+    invokeAlgebraOperation(
+        owner = owner.internalName,
+        method = theName,
+        descriptor = Type.getMethodDescriptor(primitiveMaskBoxed, *mapTypes(spec, parameterTypes).toTypedArray()),
+        expectedArity = arity,
+        opcode = INVOKEVIRTUAL
+    )
+
+    return true
+}
+
+/**
+ * Builds specialized algebra call with option to fallback to generic algebra operation accepting String.
+ */
+internal inline fun <T> AsmBuilder<T>.buildAlgebraOperationCall(
+    context: Algebra<T>,
+    name: String,
+    fallbackMethodName: String,
+    parameterTypes: Array<MstType>,
+    parameters: AsmBuilder<T>.() -> Unit
+) {
+    val arity = parameterTypes.size
+    loadAlgebra()
+    if (!buildExpectationStack(context, name, parameterTypes)) loadStringConstant(name)
+    parameters()
+
+    if (!tryInvokeSpecific(context, name, parameterTypes)) invokeAlgebraOperation(
+        owner = AsmBuilder.ALGEBRA_TYPE.internalName,
+        method = fallbackMethodName,
+
+        descriptor = Type.getMethodDescriptor(
+            AsmBuilder.OBJECT_TYPE,
+            AsmBuilder.STRING_TYPE,
+            *Array(arity) { AsmBuilder.OBJECT_TYPE }
+        ),
+
+        expectedArity = arity
+    )
+}

kmath-ast/src/jvmMain/kotlin/scientifik/kmath/asm/internal/mapIntrinsics.kt

@@ -0,0 +1,7 @@
+@file:JvmName("MapIntrinsics")
+
+package scientifik.kmath.asm.internal
+
+@JvmOverloads
+internal fun <K, V> Map<K, V>.getOrFail(key: K, default: V? = null): V =
+    this[key] ?: default ?: error("Parameter not found: $key")

kmath-ast/src/jvmTest/kotlin/scietifik/kmath/asm/TestAsmAlgebras.kt

@@ -0,0 +1,110 @@
+package scietifik.kmath.asm
+
+import scientifik.kmath.asm.compile
+import scientifik.kmath.ast.mstInField
+import scientifik.kmath.ast.mstInRing
+import scientifik.kmath.ast.mstInSpace
+import scientifik.kmath.expressions.invoke
+import scientifik.kmath.operations.ByteRing
+import scientifik.kmath.operations.RealField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+internal class TestAsmAlgebras {
+    @Test
+    fun space() {
+        val res1 = ByteRing.mstInSpace {
+            binaryOperation(
+                "+",
+
+                unaryOperation(
+                    "+",
+                    number(3.toByte()) - (number(2.toByte()) + (multiply(
+                        add(number(1), number(1)),
+                        2
+                    ) + number(1.toByte()) * 3.toByte() - number(1.toByte())))
+                ),
+
+                number(1)
+            ) + symbol("x") + zero
+        }("x" to 2.toByte())
+
+        val res2 = ByteRing.mstInSpace {
+            binaryOperation(
+                "+",
+
+                unaryOperation(
+                    "+",
+                    number(3.toByte()) - (number(2.toByte()) + (multiply(
+                        add(number(1), number(1)),
+                        2
+                    ) + number(1.toByte()) * 3.toByte() - number(1.toByte())))
+                ),
+
+                number(1)
+            ) + symbol("x") + zero
+        }.compile()("x" to 2.toByte())
+
+        assertEquals(res1, res2)
+    }
+
+    @Test
+    fun ring() {
+        val res1 = ByteRing.mstInRing {
+            binaryOperation(
+                "+",
+
+                unaryOperation(
+                    "+",
+                    (symbol("x") - (2.toByte() + (multiply(
+                        add(number(1), number(1)),
+                        2
+                    ) + 1.toByte()))) * 3.0 - 1.toByte()
+                ),
+
+                number(1)
+            ) * number(2)
+        }("x" to 3.toByte())
+
+        val res2 = ByteRing.mstInRing {
+            binaryOperation(
+                "+",
+
+                unaryOperation(
+                    "+",
+                    (symbol("x") - (2.toByte() + (multiply(
+                        add(number(1), number(1)),
+                        2
+                    ) + 1.toByte()))) * 3.0 - 1.toByte()
+                ),
+
+                number(1)
+            ) * number(2)
+        }.compile()("x" to 3.toByte())
+
+        assertEquals(res1, res2)
+    }
+
+    @Test
+    fun field() {
+        val res1 = RealField.mstInField {
+            +(3 - 2 + 2 * number(1) + 1.0) + binaryOperation(
+                "+",
+                (3.0 - (symbol("x") + (multiply(add(number(1.0), number(1.0)), 2) + 1.0))) * 3 - 1.0
+                        + number(1),
+                number(1) / 2 + number(2.0) * one
+            ) + zero
+        }("x" to 2.0)
+
+        val res2 = RealField.mstInField {
+            +(3 - 2 + 2 * number(1) + 1.0) + binaryOperation(
+                "+",
+                (3.0 - (symbol("x") + (multiply(add(number(1.0), number(1.0)), 2) + 1.0))) * 3 - 1.0
+                        + number(1),
+                number(1) / 2 + number(2.0) * one
+            ) + zero
+        }.compile()("x" to 2.0)
+
+        assertEquals(res1, res2)
+    }
+}

kmath-ast/src/jvmTest/kotlin/scietifik/kmath/asm/TestAsmExpressions.kt

@@ -0,0 +1,31 @@
+package scietifik.kmath.asm
+
+import scientifik.kmath.asm.compile
+import scientifik.kmath.ast.mstInField
+import scientifik.kmath.ast.mstInSpace
+import scientifik.kmath.expressions.invoke
+import scientifik.kmath.operations.RealField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+internal class TestAsmExpressions {
+    @Test
+    fun testUnaryOperationInvocation() {
+        val expression = RealField.mstInSpace { -symbol("x") }.compile()
+        val res = expression("x" to 2.0)
+        assertEquals(-2.0, res)
+    }
+
+    @Test
+    fun testBinaryOperationInvocation() {
+        val expression = RealField.mstInSpace { -symbol("x") + number(1.0) }.compile()
+        val res = expression("x" to 2.0)
+        assertEquals(-1.0, res)
+    }
+
+    @Test
+    fun testConstProductInvocation() {
+        val res = RealField.mstInField { symbol("x") * 2 }("x" to 2.0)
+        assertEquals(4.0, res)
+    }
+}

kmath-ast/src/jvmTest/kotlin/scietifik/kmath/asm/TestAsmSpecialization.kt

@@ -0,0 +1,55 @@
+package scietifik.kmath.asm
+
+import scientifik.kmath.asm.compile
+import scientifik.kmath.ast.mstInField
+import scientifik.kmath.expressions.invoke
+import scientifik.kmath.operations.RealField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+internal class TestAsmSpecialization {
+    @Test
+    fun testUnaryPlus() {
+        val expr = RealField.mstInField { unaryOperation("+", symbol("x")) }.compile()
+        assertEquals(2.0, expr("x" to 2.0))
+    }
+
+    @Test
+    fun testUnaryMinus() {
+        val expr = RealField.mstInField { unaryOperation("-", symbol("x")) }.compile()
+        assertEquals(-2.0, expr("x" to 2.0))
+    }
+
+    @Test
+    fun testAdd() {
+        val expr = RealField.mstInField { binaryOperation("+", symbol("x"), symbol("x")) }.compile()
+        assertEquals(4.0, expr("x" to 2.0))
+    }
+
+    @Test
+    fun testSine() {
+        val expr = RealField.mstInField { unaryOperation("sin", symbol("x")) }.compile()
+        assertEquals(0.0, expr("x" to 0.0))
+    }
+
+    @Test
+    fun testMinus() {
+        val expr = RealField.mstInField { binaryOperation("-", symbol("x"), symbol("x")) }.compile()
+        assertEquals(0.0, expr("x" to 2.0))
+    }
+
+    @Test
+    fun testDivide() {
+        val expr = RealField.mstInField { binaryOperation("/", symbol("x"), symbol("x")) }.compile()
+        assertEquals(1.0, expr("x" to 2.0))
+    }
+
+    @Test
+    fun testPower() {
+        val expr = RealField
+            .mstInField { binaryOperation("power", symbol("x"), number(2)) }
+            .compile()
+
+        assertEquals(4.0, expr("x" to 2.0))
+    }
+}

kmath-ast/src/jvmTest/kotlin/scietifik/kmath/asm/TestAsmVariables.kt

@@ -0,0 +1,22 @@
+package scietifik.kmath.asm
+
+import scientifik.kmath.ast.mstInRing
+import scientifik.kmath.expressions.invoke
+import scientifik.kmath.operations.ByteRing
+import kotlin.test.Test
+import kotlin.test.assertEquals
+import kotlin.test.assertFailsWith
+
+internal class TestAsmVariables {
+    @Test
+    fun testVariableWithoutDefault() {
+        val expr = ByteRing.mstInRing { symbol("x") }
+        assertEquals(1.toByte(), expr("x" to 1.toByte()))
+    }
+
+    @Test
+    fun testVariableWithoutDefaultFails() {
+        val expr = ByteRing.mstInRing { symbol("x") }
+        assertFailsWith<IllegalStateException> { expr() }
+    }
+}

kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/AsmTest.kt

@@ -0,0 +1,25 @@
+package scietifik.kmath.ast
+
+import scientifik.kmath.asm.compile
+import scientifik.kmath.asm.expression
+import scientifik.kmath.ast.mstInField
+import scientifik.kmath.ast.parseMath
+import scientifik.kmath.expressions.invoke
+import scientifik.kmath.operations.Complex
+import scientifik.kmath.operations.ComplexField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+internal class AsmTest {
+    @Test
+    fun `compile MST`() {
+        val res = ComplexField.expression("2+2*(2+2)".parseMath())()
+        assertEquals(Complex(10.0, 0.0), res)
+    }
+
+    @Test
+    fun `compile MSTExpression`() {
+        val res = ComplexField.mstInField { number(2) + number(2) * (number(2) + number(2)) }.compile()()
+        assertEquals(Complex(10.0, 0.0), res)
+    }
+}

kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/ParserPrecedenceTest.kt

@@ -0,0 +1,36 @@
+package scietifik.kmath.ast
+
+import scientifik.kmath.ast.evaluate
+import scientifik.kmath.ast.parseMath
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.RealField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+internal class ParserPrecedenceTest {
+    private val f: Field<Double> = RealField
+
+    @Test
+    fun test1(): Unit = assertEquals(6.0, f.evaluate("2*2+2".parseMath()))
+
+    @Test
+    fun test2(): Unit = assertEquals(6.0, f.evaluate("2+2*2".parseMath()))
+
+    @Test
+    fun test3(): Unit = assertEquals(10.0, f.evaluate("2^3+2".parseMath()))
+
+    @Test
+    fun test4(): Unit = assertEquals(10.0, f.evaluate("2+2^3".parseMath()))
+
+    @Test
+    fun test5(): Unit = assertEquals(16.0, f.evaluate("2^3*2".parseMath()))
+
+    @Test
+    fun test6(): Unit = assertEquals(16.0, f.evaluate("2*2^3".parseMath()))
+
+    @Test
+    fun test7(): Unit = assertEquals(18.0, f.evaluate("2+2^3*2".parseMath()))
+
+    @Test
+    fun test8(): Unit = assertEquals(18.0, f.evaluate("2*2^3+2".parseMath()))
+}

kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/ParserTest.kt

@@ -0,0 +1,60 @@
+package scietifik.kmath.ast
+
+import scientifik.kmath.ast.evaluate
+import scientifik.kmath.ast.mstInField
+import scientifik.kmath.ast.parseMath
+import scientifik.kmath.expressions.invoke
+import scientifik.kmath.operations.Algebra
+import scientifik.kmath.operations.Complex
+import scientifik.kmath.operations.ComplexField
+import scientifik.kmath.operations.RealField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+internal class ParserTest {
+    @Test
+    fun `evaluate MST`() {
+        val mst = "2+2*(2+2)".parseMath()
+        val res = ComplexField.evaluate(mst)
+        assertEquals(Complex(10.0, 0.0), res)
+    }
+
+    @Test
+    fun `evaluate MSTExpression`() {
+        val res = ComplexField.mstInField { number(2) + number(2) * (number(2) + number(2)) }()
+        assertEquals(Complex(10.0, 0.0), res)
+    }
+
+    @Test
+    fun `evaluate MST with singular`() {
+        val mst = "i".parseMath()
+        val res = ComplexField.evaluate(mst)
+        assertEquals(ComplexField.i, res)
+    }
+
+
+    @Test
+    fun `evaluate MST with unary function`() {
+        val mst = "sin(0)".parseMath()
+        val res = RealField.evaluate(mst)
+        assertEquals(0.0, res)
+    }
+
+    @Test
+    fun `evaluate MST with binary function`() {
+        val magicalAlgebra = object : Algebra<String> {
+            override fun symbol(value: String): String = value
+
+            override fun unaryOperation(operation: String, arg: String): String = throw NotImplementedError()
+
+            override fun binaryOperation(operation: String, left: String, right: String): String = when (operation) {
+                "magic" -> "$left ★ $right"
+                else -> throw NotImplementedError()
+            }
+        }
+
+        val mst = "magic(a, b)".parseMath()
+        val res = magicalAlgebra.evaluate(mst)
+        assertEquals("a ★ b", res)
+    }
+}

kmath-commons/src/main/kotlin/scientifik/kmath/commons/expressions/DiffExpression.kt

@@ -2,7 +2,7 @@ package scientifik.kmath.commons.expressions
 
 import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
 import scientifik.kmath.expressions.Expression
-import scientifik.kmath.expressions.ExpressionContext
+import scientifik.kmath.expressions.ExpressionAlgebra
 import scientifik.kmath.operations.ExtendedField
 import scientifik.kmath.operations.Field
 import kotlin.properties.ReadOnlyProperty
@@ -59,8 +59,10 @@ class DerivativeStructureField(
     override fun divide(a: DerivativeStructure, b: DerivativeStructure): DerivativeStructure = a.divide(b)
 
     override fun sin(arg: DerivativeStructure): DerivativeStructure = arg.sin()
-
     override fun cos(arg: DerivativeStructure): DerivativeStructure = arg.cos()
+    override fun asin(arg: DerivativeStructure): DerivativeStructure = arg.asin()
+    override fun acos(arg: DerivativeStructure): DerivativeStructure = arg.acos()
+    override fun atan(arg: DerivativeStructure): DerivativeStructure = arg.atan()
 
     override fun power(arg: DerivativeStructure, pow: Number): DerivativeStructure = when (pow) {
         is Double -> arg.pow(pow)
@@ -74,10 +76,10 @@ class DerivativeStructureField(
 
     override fun ln(arg: DerivativeStructure): DerivativeStructure = arg.log()
 
-    operator fun DerivativeStructure.plus(n: Number): DerivativeStructure = add(n.toDouble())
-    operator fun DerivativeStructure.minus(n: Number): DerivativeStructure = subtract(n.toDouble())
-    operator fun Number.plus(s: DerivativeStructure) = s + this
-    operator fun Number.minus(s: DerivativeStructure) = s - this
+    override operator fun DerivativeStructure.plus(b: Number): DerivativeStructure = add(b.toDouble())
+    override operator fun DerivativeStructure.minus(b: Number): DerivativeStructure = subtract(b.toDouble())
+    override operator fun Number.plus(b: DerivativeStructure) = b + this
+    override operator fun Number.minus(b: DerivativeStructure) = b - this
 }
 
 /**
@@ -113,7 +115,7 @@ fun DiffExpression.derivative(name: String) = derivative(name to 1)
 /**
  * A context for [DiffExpression] (not to be confused with [DerivativeStructure])
  */
-object DiffExpressionContext : ExpressionContext<Double>, Field<DiffExpression> {
+object DiffExpressionAlgebra : ExpressionAlgebra<Double, DiffExpression>, Field<DiffExpression> {
     override fun variable(name: String, default: Double?) =
         DiffExpression { variable(name, default?.const()) }
 
@@ -136,6 +138,3 @@ object DiffExpressionContext : ExpressionContext<Double>, Field<DiffExpression>
     override fun divide(a: DiffExpression, b: DiffExpression) =
         DiffExpression { a.function(this) / b.function(this) }
 }
-
-
-

kmath-commons/src/main/kotlin/scientifik/kmath/commons/linear/CMMatrix.kt

@@ -5,6 +5,7 @@ import org.apache.commons.math3.linear.RealMatrix
 import org.apache.commons.math3.linear.RealVector
 import scientifik.kmath.linear.*
 import scientifik.kmath.structures.Matrix
+import scientifik.kmath.structures.NDStructure
 
 class CMMatrix(val origin: RealMatrix, features: Set<MatrixFeature>? = null) :
     FeaturedMatrix<Double> {
@@ -19,6 +20,16 @@ class CMMatrix(val origin: RealMatrix, features: Set<MatrixFeature>? = null) :
         CMMatrix(origin, this.features + features)
 
     override fun get(i: Int, j: Int): Double = origin.getEntry(i, j)
+
+    override fun equals(other: Any?): Boolean {
+        return NDStructure.equals(this, other as? NDStructure<*> ?: return false)
+    }
+
+    override fun hashCode(): Int {
+        var result = origin.hashCode()
+        result = 31 * result + features.hashCode()
+        return result
+    }
 }
 
 fun Matrix<Double>.toCM(): CMMatrix = if (this is CMMatrix) {

kmath-commons/src/main/kotlin/scientifik/kmath/commons/prob/CMRandomGeneratorWrapper.kt

@@ -1,32 +0,0 @@
-package scientifik.kmath.commons.prob
-
-import org.apache.commons.math3.random.JDKRandomGenerator
-import scientifik.kmath.prob.RandomGenerator
-import org.apache.commons.math3.random.RandomGenerator as CMRandom
-
-inline class CMRandomGeneratorWrapper(val generator: CMRandom) : RandomGenerator {
-    override fun nextDouble(): Double = generator.nextDouble()
-
-    override fun nextInt(): Int = generator.nextInt()
-
-    override fun nextLong(): Long = generator.nextLong()
-
-    override fun nextBlock(size: Int): ByteArray = ByteArray(size).apply { generator.nextBytes(this) }
-
-    override fun fork(): RandomGenerator {
-        TODO("not implemented") //To change body of created functions use File | Settings | File Templates.
-    }
-}
-
-fun CMRandom.asKmathGenerator(): RandomGenerator = CMRandomGeneratorWrapper(this)
-
-fun RandomGenerator.asCMGenerator(): CMRandom =
-    (this as? CMRandomGeneratorWrapper)?.generator ?: TODO("Implement reverse CM wrapper")
-
-val RandomGenerator.Companion.default: RandomGenerator by lazy { JDKRandomGenerator().asKmathGenerator() }
-
-fun RandomGenerator.Companion.jdk(seed: Int? = null): RandomGenerator = if (seed == null) {
-    JDKRandomGenerator()
-} else {
-    JDKRandomGenerator(seed)
-}.asKmathGenerator()

kmath-commons/src/main/kotlin/scientifik/kmath/commons/prob/CommonsDistribution.kt

@@ -1,82 +0,0 @@
-package scientifik.kmath.commons.prob
-
-import org.apache.commons.math3.distribution.*
-import scientifik.kmath.prob.Distribution
-import scientifik.kmath.prob.RandomChain
-import scientifik.kmath.prob.RandomGenerator
-import scientifik.kmath.prob.UnivariateDistribution
-import org.apache.commons.math3.random.RandomGenerator as CMRandom
-
-class CMRealDistributionWrapper(val builder: (CMRandom?) -> RealDistribution) : UnivariateDistribution<Double> {
-
-    private val defaultDistribution by lazy { builder(null) }
-
-    override fun probability(arg: Double): Double = defaultDistribution.probability(arg)
-
-    override fun cumulative(arg: Double): Double = defaultDistribution.cumulativeProbability(arg)
-
-    override fun sample(generator: RandomGenerator): RandomChain<Double> {
-        val distribution = builder(generator.asCMGenerator())
-        return RandomChain(generator) { distribution.sample() }
-    }
-}
-
-class CMIntDistributionWrapper(val builder: (CMRandom?) -> IntegerDistribution) : UnivariateDistribution<Int> {
-
-    private val defaultDistribution by lazy { builder(null) }
-
-    override fun probability(arg: Int): Double = defaultDistribution.probability(arg)
-
-    override fun cumulative(arg: Int): Double = defaultDistribution.cumulativeProbability(arg)
-
-    override fun sample(generator: RandomGenerator): RandomChain<Int> {
-        val distribution = builder(generator.asCMGenerator())
-        return RandomChain(generator) { distribution.sample() }
-    }
-}
-
-
-fun Distribution.Companion.normal(mean: Double = 0.0, sigma: Double = 1.0): UnivariateDistribution<Double> =
-    CMRealDistributionWrapper { generator -> NormalDistribution(generator, mean, sigma) }
-
-fun Distribution.Companion.poisson(mean: Double): UnivariateDistribution<Int> = CMIntDistributionWrapper { generator ->
-    PoissonDistribution(
-        generator,
-        mean,
-        PoissonDistribution.DEFAULT_EPSILON,
-        PoissonDistribution.DEFAULT_MAX_ITERATIONS
-    )
-}
-
-fun Distribution.Companion.binomial(trials: Int, p: Double): UnivariateDistribution<Int> =
-    CMIntDistributionWrapper { generator ->
-        BinomialDistribution(generator, trials, p)
-    }
-
-fun Distribution.Companion.student(degreesOfFreedom: Double): UnivariateDistribution<Double> =
-    CMRealDistributionWrapper { generator ->
-        TDistribution(generator, degreesOfFreedom, TDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY)
-    }
-
-fun Distribution.Companion.chi2(degreesOfFreedom: Double): UnivariateDistribution<Double> =
-    CMRealDistributionWrapper { generator ->
-        ChiSquaredDistribution(generator, degreesOfFreedom)
-    }
-
-fun Distribution.Companion.fisher(
-    numeratorDegreesOfFreedom: Double,
-    denominatorDegreesOfFreedom: Double
-): UnivariateDistribution<Double> =
-    CMRealDistributionWrapper { generator ->
-        FDistribution(generator, numeratorDegreesOfFreedom, denominatorDegreesOfFreedom)
-    }
-
-fun Distribution.Companion.exponential(mean: Double): UnivariateDistribution<Double> =
-    CMRealDistributionWrapper { generator ->
-        ExponentialDistribution(generator, mean)
-    }
-
-fun Distribution.Companion.uniform(a: Double, b: Double): UnivariateDistribution<Double> =
-    CMRealDistributionWrapper { generator ->
-        UniformRealDistribution(generator, a, b)
-    }

kmath-commons/src/main/kotlin/scientifik/kmath/commons/random/CMRandomGeneratorWrapper.kt

@@ -0,0 +1,38 @@
+package scientifik.kmath.commons.random
+
+import scientifik.kmath.prob.RandomGenerator
+
+class CMRandomGeneratorWrapper(val factory: (IntArray) -> RandomGenerator) :
+    org.apache.commons.math3.random.RandomGenerator {
+    private var generator = factory(intArrayOf())
+
+    override fun nextBoolean(): Boolean = generator.nextBoolean()
+
+    override fun nextFloat(): Float = generator.nextDouble().toFloat()
+
+    override fun setSeed(seed: Int) {
+        generator = factory(intArrayOf(seed))
+    }
+
+    override fun setSeed(seed: IntArray) {
+        generator = factory(seed)
+    }
+
+    override fun setSeed(seed: Long) {
+        setSeed(seed.toInt())
+    }
+
+    override fun nextBytes(bytes: ByteArray) {
+        generator.fillBytes(bytes)
+    }
+
+    override fun nextInt(): Int = generator.nextInt()
+
+    override fun nextInt(n: Int): Int = generator.nextInt(n)
+
+    override fun nextGaussian(): Double = TODO()
+
+    override fun nextDouble(): Double = generator.nextDouble()
+
+    override fun nextLong(): Long = generator.nextLong()
+}

kmath-commons/src/main/kotlin/scientifik/kmath/commons/transform/Transformations.kt

@@ -18,7 +18,7 @@ object Transformations {
     private fun Buffer<Complex>.toArray(): Array<org.apache.commons.math3.complex.Complex> =
         Array(size) { org.apache.commons.math3.complex.Complex(get(it).re, get(it).im) }
 
-    private fun Buffer<Double>.asArray() = if (this is DoubleBuffer) {
+    private fun Buffer<Double>.asArray() = if (this is RealBuffer) {
         array
     } else {
         DoubleArray(size) { i -> get(i) }

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")
+> }
+> ```

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")) }
     }
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/Domain.kt

@@ -0,0 +1,20 @@
+package scientifik.kmath.domains
+
+import scientifik.kmath.linear.Point
+
+/**
+ * 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.
+     */
+    val dimension: Int
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/HyperSquareDomain.kt

@@ -0,0 +1,68 @@
+/* 
+ * Copyright 2015 Alexander Nozik.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package scientifik.kmath.domains
+
+import scientifik.kmath.linear.Point
+import scientifik.kmath.structures.RealBuffer
+import scientifik.kmath.structures.indices
+
+/**
+ *
+ * HyperSquareDomain class.
+ *
+ * @author Alexander Nozik
+ */
+class HyperSquareDomain(private val lower: RealBuffer, private val upper: RealBuffer) : RealDomain {
+
+    override operator fun contains(point: Point<Double>): Boolean = point.indices.all { i ->
+        point[i] in lower[i]..upper[i]
+    }
+
+    override val dimension: Int get() = lower.size
+
+    override fun getLowerBound(num: Int, point: Point<Double>): Double? = lower[num]
+
+    override fun getLowerBound(num: Int): Double? = lower[num]
+
+    override fun getUpperBound(num: Int, point: Point<Double>): Double? = upper[num]
+
+    override fun getUpperBound(num: Int): Double? = upper[num]
+
+    override fun nearestInDomain(point: Point<Double>): Point<Double> {
+        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)
+    }
+
+    override fun volume(): Double {
+        var res = 1.0
+        for (i in 0 until dimension) {
+            if (lower[i].isInfinite() || upper[i].isInfinite()) {
+                return Double.POSITIVE_INFINITY
+            }
+            if (upper[i] > lower[i]) {
+                res *= upper[i] - lower[i]
+            }
+        }
+        return res
+    }
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/RealDomain.kt

@@ -0,0 +1,63 @@
+/* 
+ * Copyright 2015 Alexander Nozik.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package scientifik.kmath.domains
+
+import scientifik.kmath.linear.Point
+
+/**
+ * n-dimensional volume
+ *
+ * @author Alexander Nozik
+ */
+interface RealDomain : Domain<Double> {
+    fun nearestInDomain(point: Point<Double>): Point<Double>
+
+    /**
+     * The lower edge for the domain going down from point
+     * @param num
+     * @param point
+     * @return
+     */
+    fun getLowerBound(num: Int, point: Point<Double>): Double?
+
+    /**
+     * The upper edge of the domain going up from point
+     * @param num
+     * @param point
+     * @return
+     */
+    fun getUpperBound(num: Int, point: Point<Double>): Double?
+
+    /**
+     * Global lower edge
+     * @param num
+     * @return
+     */
+    fun getLowerBound(num: Int): Double?
+
+    /**
+     * Global upper edge
+     * @param num
+     * @return
+     */
+    fun getUpperBound(num: Int): Double?
+
+    /**
+     * Hyper volume
+     * @return
+     */
+    fun volume(): Double
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnconstrainedDomain.kt

@@ -0,0 +1,34 @@
+/* 
+ * Copyright 2015 Alexander Nozik.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+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
+
+    override fun getLowerBound(num: Int): Double? = Double.NEGATIVE_INFINITY
+
+    override fun getUpperBound(num: Int, point: Point<Double>): Double? = Double.POSITIVE_INFINITY
+
+    override fun getUpperBound(num: Int): Double? = Double.POSITIVE_INFINITY
+
+    override fun nearestInDomain(point: Point<Double>): Point<Double> = point
+
+    override fun volume(): Double = Double.POSITIVE_INFINITY
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/domains/UnivariateDomain.kt

@@ -0,0 +1,47 @@
+package scientifik.kmath.domains
+
+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 {
+        require(point.size == 0)
+        return contains(point[0])
+    }
+
+    override fun nearestInDomain(point: Point<Double>): Point<Double> {
+        require(point.size == 1)
+        val value = point[0]
+        return when {
+            value in range -> point
+            value >= range.endInclusive -> doubleArrayOf(range.endInclusive).asBuffer()
+            else -> doubleArrayOf(range.start).asBuffer()
+        }
+    }
+
+    override fun getLowerBound(num: Int, point: Point<Double>): Double? {
+        require(num == 0)
+        return range.start
+    }
+
+    override fun getUpperBound(num: Int, point: Point<Double>): Double? {
+        require(num == 0)
+        return range.endInclusive
+    }
+
+    override fun getLowerBound(num: Int): Double? {
+        require(num == 0)
+        return range.start
+    }
+
+    override fun getUpperBound(num: Int): Double? {
+        require(num == 0)
+        return range.endInclusive
+    }
+
+    override fun volume(): Double = range.endInclusive - range.start
+
+    override val dimension: Int get() = 1
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Builders.kt

@@ -0,0 +1,31 @@
+package scientifik.kmath.expressions
+
+import scientifik.kmath.operations.ExtendedField
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.Ring
+import scientifik.kmath.operations.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)
+
+/**
+ * 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)
+
+/**
+ * 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)
+
+/**
+ * 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)

kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt

@@ -1,92 +1,49 @@
 package scientifik.kmath.expressions
 
-import scientifik.kmath.operations.Field
-import scientifik.kmath.operations.Ring
-import scientifik.kmath.operations.Space
+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
 }
 
+/**
+ * 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)
+    }
+
+/**
+ * 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))
 
 /**
  * A context for expression construction
  */
-interface ExpressionContext<T> {
+interface ExpressionAlgebra<T, E> : Algebra<E> {
     /**
      * Introduce a variable into expression context
      */
-    fun variable(name: String, default: T? = null): Expression<T>
+    fun variable(name: String, default: T? = null): E
 
     /**
      * A constant expression which does not depend on arguments
      */
-    fun const(value: T): Expression<T>
-}
-
-internal class VariableExpression<T>(val name: String, val default: T? = null) : Expression<T> {
-    override fun invoke(arguments: Map<String, T>): T =
-        arguments[name] ?: default ?: error("Parameter not found: $name")
-}
-
-internal class ConstantExpression<T>(val value: T) : Expression<T> {
-    override fun invoke(arguments: Map<String, T>): T = value
-}
-
-internal class SumExpression<T>(val context: Space<T>, val first: Expression<T>, val second: Expression<T>) :
-    Expression<T> {
-    override fun invoke(arguments: Map<String, T>): T = context.add(first.invoke(arguments), second.invoke(arguments))
-}
-
-internal class ProductExpression<T>(val context: Ring<T>, val first: Expression<T>, val second: Expression<T>) :
-    Expression<T> {
-    override fun invoke(arguments: Map<String, T>): T =
-        context.multiply(first.invoke(arguments), second.invoke(arguments))
-}
-
-internal class ConstProductExpession<T>(val context: Space<T>, val expr: Expression<T>, val const: Number) :
-    Expression<T> {
-    override fun invoke(arguments: Map<String, T>): T = context.multiply(expr.invoke(arguments), const)
-}
-
-internal class DivExpession<T>(val context: Field<T>, val expr: Expression<T>, val second: Expression<T>) :
-    Expression<T> {
-    override fun invoke(arguments: Map<String, T>): T = context.divide(expr.invoke(arguments), second.invoke(arguments))
-}
-
-open class ExpressionSpace<T>(val space: Space<T>) : Space<Expression<T>>, ExpressionContext<T> {
-    override val zero: Expression<T> = ConstantExpression(space.zero)
-
-    override fun const(value: T): Expression<T> = ConstantExpression(value)
-
-    override fun variable(name: String, default: T?): Expression<T> = VariableExpression(name, default)
-
-    override fun add(a: Expression<T>, b: Expression<T>): Expression<T> = SumExpression(space, a, b)
-
-    override fun multiply(a: Expression<T>, k: Number): Expression<T> = ConstProductExpession(space, a, k)
-
-
-    operator fun Expression<T>.plus(arg: T) = this + const(arg)
-    operator fun Expression<T>.minus(arg: T) = this - const(arg)
-
-    operator fun T.plus(arg: Expression<T>) = arg + this
-    operator fun T.minus(arg: Expression<T>) = arg - this
-}
-
-
-class ExpressionField<T>(val field: Field<T>) : Field<Expression<T>>, ExpressionSpace<T>(field) {
-    override val one: Expression<T> = ConstantExpression(field.one)
-    override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> = ProductExpression(field, a, b)
-
-    override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> = DivExpession(field, a, b)
-
-    operator fun Expression<T>.times(arg: T) = this * const(arg)
-    operator fun Expression<T>.div(arg: T) = this / const(arg)
-
-    operator fun T.times(arg: Expression<T>) = arg * this
-    operator fun T.div(arg: Expression<T>) = arg / this
+    fun const(value: T): E
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/FunctionalExpressionAlgebra.kt

@@ -0,0 +1,175 @@
+package scientifik.kmath.expressions
+
+import scientifik.kmath.operations.*
+
+internal class FunctionalUnaryOperation<T>(val context: Algebra<T>, val name: String, private val expr: Expression<T>) :
+    Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T = context.unaryOperation(name, expr.invoke(arguments))
+}
+
+internal class FunctionalBinaryOperation<T>(
+    val context: Algebra<T>,
+    val name: String,
+    val first: Expression<T>,
+    val second: Expression<T>
+) : Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T =
+        context.binaryOperation(name, first.invoke(arguments), second.invoke(arguments))
+}
+
+internal class FunctionalVariableExpression<T>(val name: String, val default: T? = null) : Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T =
+        arguments[name] ?: default ?: error("Parameter not found: $name")
+}
+
+internal class FunctionalConstantExpression<T>(val value: T) : Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T = value
+}
+
+internal class FunctionalConstProductExpression<T>(
+    val context: Space<T>,
+    private val expr: Expression<T>,
+    val const: Number
+) : Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T = context.multiply(expr.invoke(arguments), const)
+}
+
+/**
+ * A context class for [Expression] construction.
+ *
+ * @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.
+     */
+    override fun const(value: T): Expression<T> = FunctionalConstantExpression(value)
+
+    /**
+     * Builds an Expression to access a variable.
+     */
+    override fun variable(name: String, default: T?): Expression<T> = FunctionalVariableExpression(name, default)
+
+    /**
+     * Builds an Expression of dynamic call of binary operation [operation] on [left] and [right].
+     */
+    override fun binaryOperation(operation: String, left: Expression<T>, right: Expression<T>): Expression<T> =
+        FunctionalBinaryOperation(algebra, operation, left, right)
+
+    /**
+     * Builds an Expression of dynamic call of unary operation with name [operation] on [arg].
+     */
+    override fun unaryOperation(operation: String, arg: Expression<T>): Expression<T> =
+        FunctionalUnaryOperation(algebra, operation, arg)
+}
+
+/**
+ * A context class for [Expression] construction for [Space] algebras.
+ */
+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> =
+        binaryOperation(SpaceOperations.PLUS_OPERATION, a, b)
+
+    /**
+     * Builds an Expression of multiplication of expression by number.
+     */
+    override fun multiply(a: Expression<T>, k: Number): Expression<T> =
+        FunctionalConstProductExpression(algebra, a, k)
+
+    operator fun Expression<T>.plus(arg: T): Expression<T> = this + const(arg)
+    operator fun Expression<T>.minus(arg: T): Expression<T> = this - const(arg)
+    operator fun T.plus(arg: Expression<T>): Expression<T> = arg + this
+    operator fun T.minus(arg: Expression<T>): Expression<T> = arg - this
+
+    override fun unaryOperation(operation: String, arg: Expression<T>): Expression<T> =
+        super<FunctionalExpressionAlgebra>.unaryOperation(operation, arg)
+
+    override fun binaryOperation(operation: String, left: Expression<T>, right: Expression<T>): Expression<T> =
+        super<FunctionalExpressionAlgebra>.binaryOperation(operation, left, right)
+}
+
+open class FunctionalExpressionRing<T, A>(algebra: A) : FunctionalExpressionSpace<T, A>(algebra),
+    Ring<Expression<T>> where  A : Ring<T>, A : NumericAlgebra<T> {
+    override val one: Expression<T>
+        get() = const(algebra.one)
+
+    /**
+     * Builds an Expression of multiplication of two expressions.
+     */
+    override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> =
+        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
+
+    override fun unaryOperation(operation: String, arg: Expression<T>): Expression<T> =
+        super<FunctionalExpressionSpace>.unaryOperation(operation, arg)
+
+    override fun binaryOperation(operation: String, left: Expression<T>, right: Expression<T>): Expression<T> =
+        super<FunctionalExpressionSpace>.binaryOperation(operation, left, right)
+}
+
+open class FunctionalExpressionField<T, A>(algebra: A) :
+    FunctionalExpressionRing<T, A>(algebra),
+    Field<Expression<T>> where A : Field<T>, A : NumericAlgebra<T> {
+    /**
+     * Builds an Expression of division an expression by another one.
+     */
+    override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> =
+        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
+
+    override fun unaryOperation(operation: String, arg: Expression<T>): Expression<T> =
+        super<FunctionalExpressionRing>.unaryOperation(operation, arg)
+
+    override fun binaryOperation(operation: String, left: Expression<T>, right: Expression<T>): Expression<T> =
+        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()
+
+inline fun <T, A : Ring<T>> A.expressionInRing(block: FunctionalExpressionRing<T, A>.() -> Expression<T>): Expression<T> =
+    FunctionalExpressionRing(this).block()
+
+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()

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 = 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 = DoubleBuffer(rows * columns) { offset -> initializer(offset / columns, offset % columns) }
+        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> = DoubleBuffer(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)"
@@ -101,8 +99,15 @@ infix fun BufferMatrix<Double>.dot(other: BufferMatrix<Double>): BufferMatrix<Do
 
     val array = DoubleArray(this.rowNum * other.colNum)
 
-    val a = this.buffer.array
-    val b = other.buffer.array
+    //convert to array to insure there is not memory indirection
+    fun Buffer<out Double>.unsafeArray(): DoubleArray = if (this is RealBuffer) {
+        array
+    } else {
+        DoubleArray(size) { get(it) }
+    }
+
+    val a = this.buffer.unsafeArray()
+    val b = other.buffer.unsafeArray()
 
     for (i in (0 until rowNum)) {
         for (j in (0 until other.colNum)) {
@@ -112,6 +117,6 @@ infix fun BufferMatrix<Double>.dot(other: BufferMatrix<Double>): BufferMatrix<Do
         }
     }
 
-    val buffer = DoubleBuffer(array)
+    val buffer = RealBuffer(array)
     return BufferMatrix(rowNum, other.colNum, buffer)
 }

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
 

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 }
 
 
@@ -128,14 +128,14 @@ fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
                     luRow[col] = sum
 
                     // maintain best permutation choice
-                    if (abs(sum) > largest) {
-                        largest = abs(sum)
+                    if (this@lup.abs(sum) > largest) {
+                        largest = this@lup.abs(sum)
                         max = row
                     }
                 }
 
                 // Singularity check
-                if (checkSingular(abs(lu[max, col]))) {
+                if (checkSingular(this@lup.abs(lu[max, col]))) {
                     error("The matrix is singular")
                 }
 
@@ -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>) =
+fun RealMatrixContext.inverse(matrix: Matrix<Double>): Matrix<Double> =
     solve(matrix, one(matrix.rowNum, matrix.colNum)) { it < 1e-11 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgebra.kt

@@ -1,12 +1,8 @@
 package scientifik.kmath.linear
 
-import scientifik.kmath.operations.Field
-import scientifik.kmath.operations.Norm
-import scientifik.kmath.operations.RealField
 import scientifik.kmath.structures.Buffer
 import scientifik.kmath.structures.Matrix
 import scientifik.kmath.structures.VirtualBuffer
-import scientifik.kmath.structures.asSequence
 
 typealias Point<T> = Buffer<T>
 
@@ -19,8 +15,6 @@ interface LinearSolver<T : Any> {
     fun inverse(a: Matrix<T>): Matrix<T>
 }
 
-typealias RealMatrix = Matrix<Double>
-
 /**
  * Convert matrix to vector if it is possible
  */
@@ -31,4 +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) }
+fun <T : Any> Point<T>.asMatrix(): VirtualMatrix<T> = VirtualMatrix(size, 1) { i, _ -> get(i) }

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixBuilder.kt

@@ -1,14 +1,46 @@
 package scientifik.kmath.linear
 
+import scientifik.kmath.structures.Buffer
+import scientifik.kmath.structures.BufferFactory
 import scientifik.kmath.structures.Structure2D
 import scientifik.kmath.structures.asBuffer
 
-class MatrixBuilder<T : Any>(val rows: Int, val columns: Int) {
-    operator fun invoke(vararg elements: T): FeaturedMatrix<T> {
+class MatrixBuilder(val rows: Int, val columns: Int) {
+    operator fun <T : Any> invoke(vararg elements: T): FeaturedMatrix<T> {
         if (rows * columns != elements.size) error("The number of elements ${elements.size} is not equal $rows * $columns")
         val buffer = elements.asBuffer()
         return BufferMatrix(rows, columns, buffer)
     }
+
+    //TODO add specific matrix builder functions like diagonal, etc
 }
 
-fun <T : Any> Structure2D.Companion.build(rows: Int, columns: Int): MatrixBuilder<T> = MatrixBuilder(rows, columns)
+fun Structure2D.Companion.build(rows: Int, columns: Int): MatrixBuilder = MatrixBuilder(rows, columns)
+
+fun <T : Any> Structure2D.Companion.row(vararg values: T): FeaturedMatrix<T> {
+    val buffer = values.asBuffer()
+    return BufferMatrix(1, values.size, buffer)
+}
+
+inline fun <reified T : Any> Structure2D.Companion.row(
+    size: Int,
+    factory: BufferFactory<T> = Buffer.Companion::auto,
+    noinline builder: (Int) -> T
+): FeaturedMatrix<T> {
+    val buffer = factory(size, builder)
+    return BufferMatrix(1, size, buffer)
+}
+
+fun <T : Any> Structure2D.Companion.column(vararg values: T): FeaturedMatrix<T> {
+    val buffer = values.asBuffer()
+    return BufferMatrix(values.size, 1, buffer)
+}
+
+inline fun <reified T : Any> Structure2D.Companion.column(
+    size: Int,
+    factory: BufferFactory<T> = Buffer.Companion::auto,
+    noinline builder: (Int) -> T
+): FeaturedMatrix<T> {
+    val buffer = factory(size, builder)
+    return BufferMatrix(size, 1, buffer)
+}

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
 

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

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))
 }

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 {

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()
@@ -86,24 +86,24 @@ 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
 
-    operator fun Number.plus(that: Variable<T>): Variable<T> =
-        derive(variable { this@plus.toDouble() * one + that.value }) { z ->
-            that.d += z.d
+    override operator fun Number.plus(b: Variable<T>): Variable<T> =
+        derive(variable { this@plus.toDouble() * one + b.value }) { z ->
+            b.d += z.d
         }
 
-    operator fun Variable<T>.plus(b: Number): Variable<T> = b.plus(this)
+    override operator fun Variable<T>.plus(b: Number): Variable<T> = b.plus(this)
 
-    operator fun Number.minus(that: Variable<T>): Variable<T> =
-        derive(variable { this@minus.toDouble() * one - that.value }) { z ->
-            that.d -= z.d
+    override operator fun Number.minus(b: Variable<T>): Variable<T> =
+        derive(variable { this@minus.toDouble() * one - b.value }) { z ->
+            b.d -= z.d
         }
 
-    operator fun Variable<T>.minus(that: Number): Variable<T> =
-        derive(variable { this@minus.value - one * that.toDouble() }) { z ->
+    override operator fun Variable<T>.minus(b: Number): Variable<T> =
+        derive(variable { this@minus.value - one * b.toDouble() }) { z ->
             this@minus.d += z.d
         }
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Grids.kt

@@ -1,5 +1,7 @@
 package scientifik.kmath.misc
 
+import kotlin.math.abs
+
 /**
  * Convert double range to sequence.
  *
@@ -8,28 +10,36 @@ package scientifik.kmath.misc
  *
  * If step is negative, the same goes from upper boundary downwards
  */
-fun ClosedFloatingPointRange<Double>.toSequence(step: Double): Sequence<Double> =
-        when {
-            step == 0.0 -> error("Zero step in double progression")
-            step > 0 -> sequence {
-                var current = start
-                while (current <= endInclusive) {
-                    yield(current)
-                    current += step
-                }
-            }
-            else -> sequence {
-                var current = endInclusive
-                while (current >= start) {
-                    yield(current)
-                    current += step
-                }
-            }
+fun ClosedFloatingPointRange<Double>.toSequenceWithStep(step: Double): Sequence<Double> = when {
+    step == 0.0 -> error("Zero step in double progression")
+    step > 0 -> sequence {
+        var current = start
+        while (current <= endInclusive) {
+            yield(current)
+            current += step
         }
+    }
+    else -> sequence {
+        var current = endInclusive
+        while (current >= start) {
+            yield(current)
+            current += step
+        }
+    }
+}
+
+/**
+ * Convert double range to sequence with the fixed number of points
+ */
+fun ClosedFloatingPointRange<Double>.toSequenceWithPoints(numPoints: Int): Sequence<Double> {
+    require(numPoints > 1) { "The number of points should be more than 2" }
+    return toSequenceWithStep(abs(endInclusive - start) / (numPoints - 1))
+}
 
 /**
  * Convert double range to array of evenly spaced doubles, where the size of array equals [numPoints]
  */
+@Deprecated("Replace by 'toSequenceWithPoints'")
 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 }

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 }
+fun List<Long>.cumulativeSum(): List<Long> = this.cumulative(0L) { element, sum -> sum + element }

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt

@@ -1,95 +1,340 @@
 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>
+interface Algebra<T> {
+    /**
+     * Wrap raw string or variable
+     */
+    fun symbol(value: String): T = error("Wrapping of '$value' is not supported in $this")
 
-inline operator fun <T : Algebra<*>, R> T.invoke(block: T.() -> R): R = run(block)
+    /**
+     * Dynamic call of unary operation with name [operation] on [arg]
+     */
+    fun unaryOperation(operation: String, arg: T): T
+
+    /**
+     * Dynamic call of binary operation [operation] on [left] and [right]
+     */
+    fun binaryOperation(operation: String, left: T, right: T): T
+}
 
 /**
- * Space-like operations without neutral element
+ * An algebraic structure where elements can have numeric representation.
+ *
+ * @param T the type of element of this structure.
+ */
+interface NumericAlgebra<T> : Algebra<T> {
+    /**
+     * 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.
+ */
+inline operator fun <A : Algebra<*>, R> A.invoke(block: A.() -> R): R = run(block)
+
+/**
+ * Represents "semispace", i.e. algebraic structure with associative binary operation called "addition" as well as
+ * multiplication by scalars.
+ *
+ * @param T the type of element of this semispace.
  */
 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
+    // 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
+        MINUS_OPERATION -> -arg
+        else -> error("Unary operation $operation not defined in $this")
+    }
+
+    override fun binaryOperation(operation: String, left: T, right: T): T = when (operation) {
+        PLUS_OPERATION -> add(left, right)
+        MINUS_OPERATION -> left - right
+        else -> error("Binary operation $operation not defined in $this")
+    }
+
+    companion object {
+        /**
+         * 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 linear space, i.e. algebraic structure with associative binary operation called "addition" and its neutral
+ * element as well as multiplication by scalars.
  *
- * TODO do we need non-commutative context?
+ * @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) {
+        TIMES_OPERATION -> multiply(left, right)
+        else -> super.binaryOperation(operation, left, right)
+    }
+
+    companion object {
+        /**
+         * 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> {
+interface Ring<T> : Space<T>, RingOperations<T>, NumericAlgebra<T> {
     /**
      * neutral operation for multiplication
      */
     val one: T
 
-//    operator fun T.plus(b: Number) = this.plus(b * one)
-//    operator fun Number.plus(b: T) = b + this
-//
-//    operator fun T.minus(b: Number) = this.minus(b * one)
-//    operator fun Number.minus(b: T) = -b + this
+    override fun number(value: Number): T = one * value.toDouble()
+
+    override fun leftSideNumberOperation(operation: String, left: Number, right: T): T = when (operation) {
+        SpaceOperations.PLUS_OPERATION -> left + right
+        SpaceOperations.MINUS_OPERATION -> left - right
+        RingOperations.TIMES_OPERATION -> left * right
+        else -> super.leftSideNumberOperation(operation, left, right)
+    }
+
+    override fun rightSideNumberOperation(operation: String, left: T, right: Number): T = when (operation) {
+        SpaceOperations.PLUS_OPERATION -> left + right
+        SpaceOperations.MINUS_OPERATION -> left - right
+        RingOperations.TIMES_OPERATION -> left * right
+        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)
+
+    /**
+     * Addition of scalar and element.
+     *
+     * @receiver the addend.
+     * @param b the augend.
+     */
+    operator fun Number.plus(b: T): 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) {
+        DIV_OPERATION -> divide(left, right)
+        else -> super.binaryOperation(operation, left, right)
+    }
+
+    companion object {
+        /**
+         * 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)
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraElements.kt

@@ -2,47 +2,107 @@ 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
 }
 
+/**
+ * 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
 }
 
 /**
- * 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> {
+    /**
+     * Adds element to this one.
+     *
+     * @param b the augend.
+     * @return the sum.
+     */
+    operator fun plus(b: T): I = context.add(unwrap(), b).wrap()
 
-    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()
+    /**
+     * 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()
 }
 
 /**
- * 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> {
-    operator fun times(b: T) = context.multiply(unwrap(), b).wrap()
+    /**
+     * Multiplies this element by another one.
+     *
+     * @param b the multiplicand.
+     * @return the product.
+     */
+    operator fun times(b: T): I = context.multiply(unwrap(), b).wrap()
 }
 
 /**
- * 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
-    operator fun div(b: T) = context.divide(unwrap(), b).wrap()
+
+    /**
+     * Divides this element by another one.
+     *
+     * @param b the divisor.
+     * @return the quotient.
+     */
+    operator fun div(b: T): I = context.divide(unwrap(), b).wrap()
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt

@@ -1,15 +1,107 @@
 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 iterable 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 sequence to sum up.
+ * @return the sum.
+ */
 fun <T> Space<T>.sum(data: Sequence<T>): T = data.fold(zero) { left, right -> add(left, right) }
 
-fun <T : Any, S : Space<T>> Iterable<T>.sumWith(space: S): T = space.sum(this)
+/**
+ * Returns an average value of elements in the iterable in this [Space].
+ *
+ * @receiver the algebra that provides addition and division.
+ * @param data the iterable to find average.
+ * @return the average value.
+ */
+fun <T> Space<T>.average(data: Iterable<T>): T = sum(data) / data.count()
+
+/**
+ * Returns an average value of elements in the sequence in this [Space].
+ *
+ * @receiver the algebra that provides addition and division.
+ * @param data the sequence to find average.
+ * @return the average value.
+ */
+fun <T> Space<T>.average(data: Sequence<T>): T = sum(data) / data.count()
+
+/**
+ * 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> Iterable<T>.sumWith(space: Space<T>): T = space.sum(this)
+
+/**
+ * Returns the sum of all elements in the sequence in provided space.
+ *
+ * @receiver the collection to sum up.
+ * @param space the algebra that provides addition.
+ * @return the sum.
+ */
+fun <T> Sequence<T>.sumWith(space: Space<T>): T = space.sum(this)
+
+/**
+ * Returns an average value of elements in the iterable in this [Space].
+ *
+ * @receiver the iterable to find average.
+ * @param space the algebra that provides addition and division.
+ * @return the average value.
+ */
+fun <T> Iterable<T>.averageWith(space: Space<T>): T = space.average(this)
+
+/**
+ * Returns an average value of elements in the sequence in this [Space].
+ *
+ * @receiver the sequence to find average.
+ * @param space the algebra that provides addition and division.
+ * @return the average value.
+ */
+fun <T> Sequence<T>.averageWith(space: Space<T>): T = space.average(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)
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/BigInt.kt

@@ -2,6 +2,7 @@ package scientifik.kmath.operations
 
 import scientifik.kmath.operations.BigInt.Companion.BASE
 import scientifik.kmath.operations.BigInt.Companion.BASE_SIZE
+import scientifik.kmath.structures.*
 import kotlin.math.log2
 import kotlin.math.max
 import kotlin.math.min
@@ -193,8 +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) {
@@ -209,7 +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) {
@@ -259,7 +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))
@@ -393,12 +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(),
@@ -410,17 +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()
         )
     )
 )
@@ -433,7 +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,
@@ -482,3 +483,18 @@ fun String.parseBigInteger(): BigInt? {
     }
     return res * sign
 }
+
+inline fun Buffer.Companion.bigInt(size: Int, initializer: (Int) -> BigInt): Buffer<BigInt> =
+    boxing(size, initializer)
+
+inline fun MutableBuffer.Companion.bigInt(size: Int, initializer: (Int) -> BigInt): MutableBuffer<BigInt> =
+    boxing(size, initializer)
+
+fun NDAlgebra.Companion.bigInt(vararg shape: Int): BoxingNDRing<BigInt, BigIntField> =
+    BoxingNDRing(shape, BigIntField, Buffer.Companion::bigInt)
+
+fun NDElement.Companion.bigInt(
+    vararg shape: Int,
+    initializer: BigIntField.(IntArray) -> BigInt
+): BufferedNDRingElement<BigInt, BigIntField> =
+    NDAlgebra.bigInt(*shape).produce(initializer)

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt

@@ -8,15 +8,20 @@ import scientifik.memory.MemorySpec
 import scientifik.memory.MemoryWriter
 import kotlin.math.*
 
+private val PI_DIV_2 = Complex(PI / 2, 0)
+
 /**
- * A field for complex numbers
+ * A field of [Complex].
  */
-object ComplexField : ExtendedFieldOperations<Complex>, Field<Complex> {
+object ComplexField : ExtendedField<Complex> {
     override val zero: Complex = Complex(0.0, 0.0)
 
     override val one: Complex = Complex(1.0, 0.0)
 
-    val i = Complex(0.0, 1.0)
+    /**
+     * 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)
 
@@ -30,9 +35,11 @@ object ComplexField : ExtendedFieldOperations<Complex>, Field<Complex> {
         return Complex((a.re * b.re + a.im * b.im) / norm, (a.re * b.im - a.im * b.re) / norm)
     }
 
-    override fun sin(arg: Complex): Complex = i / 2 * (exp(-i * arg) - exp(i * arg))
-
+    override fun sin(arg: Complex): Complex = i * (exp(-i * arg) - exp(i * arg)) / 2
     override fun cos(arg: Complex): Complex = (exp(-i * arg) + exp(i * arg)) / 2
+    override fun asin(arg: Complex): Complex = -i * ln(sqrt(one - arg pow 2) + i * arg)
+    override fun acos(arg: Complex): Complex = PI_DIV_2 + i * ln(sqrt(one - arg pow 2) + i * arg)
+    override fun atan(arg: Complex): Complex = i * (ln(one - i * arg) - ln(one + i * arg)) / 2
 
     override fun power(arg: Complex, pow: Number): Complex =
         arg.r.pow(pow.toDouble()) * (cos(pow.toDouble() * arg.theta) + i * sin(pow.toDouble() * arg.theta))
@@ -41,19 +48,59 @@ object ComplexField : ExtendedFieldOperations<Complex>, Field<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)
+    /**
+     * 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)
 
-    operator fun Double.minus(c: 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)
 
-    operator fun Complex.plus(d: Double) = d + this
+    /**
+     * 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
 
-    operator fun Complex.minus(d: Double) = add(this, -d.toComplex())
+    /**
+     * 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())
 
-    operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
+    /**
+     * 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)
 }
 
 /**
- * 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())
@@ -94,7 +141,13 @@ 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)
+/**
+ * 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> {
     return MemoryBuffer.create(Complex, size, init)

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt

@@ -4,19 +4,45 @@ 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> :
-    FieldOperations<T>,
-    TrigonometricOperations<T>,
+    InverseTrigonometricOperations<T>,
     PowerOperations<T>,
-    ExponentialOperations<T>
+    ExponentialOperations<T> {
 
-interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T>
+    override fun tan(arg: T): T = sin(arg) / cos(arg)
+
+    override fun unaryOperation(operation: String, arg: T): T = when (operation) {
+        TrigonometricOperations.COS_OPERATION -> cos(arg)
+        TrigonometricOperations.SIN_OPERATION -> sin(arg)
+        TrigonometricOperations.TAN_OPERATION -> tan(arg)
+        InverseTrigonometricOperations.ACOS_OPERATION -> acos(arg)
+        InverseTrigonometricOperations.ASIN_OPERATION -> asin(arg)
+        InverseTrigonometricOperations.ATAN_OPERATION -> atan(arg)
+        PowerOperations.SQRT_OPERATION -> sqrt(arg)
+        ExponentialOperations.EXP_OPERATION -> exp(arg)
+        ExponentialOperations.LN_OPERATION -> ln(arg)
+        else -> super.unaryOperation(operation, arg)
+    }
+}
+
+
+/**
+ * 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)
+        else -> super.rightSideNumberOperation(operation, left, right)
+    }
+}
 
 /**
  * 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> {
@@ -24,74 +50,90 @@ 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
 }
 
 /**
- * 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> {
     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
+        else -> super.binaryOperation(operation, left, right)
+    }
 }
 
+/**
+ * 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
-    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 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
 }
 
 /**
@@ -100,14 +142,14 @@ 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 * 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
 
@@ -122,20 +164,20 @@ 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)
+    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()
 }
 
 /**
@@ -144,20 +186,20 @@ 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)
+    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()
 }
 
 /**
@@ -166,18 +208,18 @@ 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)
+    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)
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt

@@ -1,57 +1,214 @@
 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
 
-    fun tg(arg: T): T = sin(arg) / cos(arg)
+    /**
+     * Computes the tangent of [arg].
+     */
+    fun tan(arg: T): T
 
-    fun ctg(arg: T): T = cos(arg) / sin(arg)
+    companion object {
+        /**
+         * 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"
+    }
 }
 
-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>>> tg(arg: T): T = arg.context.tg(arg)
-fun <T : MathElement<out TrigonometricOperations<T>>> ctg(arg: T): T = arg.context.ctg(arg)
-
-/* Power and roots */
-
 /**
- * A context extension to include power operations like square roots, etc
+ * 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 {
+        /**
+         * 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"
+    }
+}
+
+/**
+ * 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 {
+        /**
+         * The identifier of exponentiation.
+         */
+        const val POW_OPERATION: String = "pow"
+
+        /**
+         * The identifier of square root.
+         */
+        const val SQRT_OPERATION: String = "sqrt"
+    }
 }
 
+/**
+ * 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)
+
+/**
+ * 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 */
-
-interface ExponentialOperations<T>: Algebra<T> {
+/**
+ * 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 {
+        /**
+         * 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)

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,
@@ -19,10 +18,10 @@ 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)) })

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)) })

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)
 }

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>) {
@@ -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.
      */
@@ -30,7 +31,7 @@ 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>>
 }
 

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferedNDElement.kt

@@ -3,12 +3,12 @@ package scientifik.kmath.structures
 import scientifik.kmath.operations.*
 
 /**
- * Base interface for an element with context, containing strides
+ * Base class for an element with context, containing strides
  */
-interface BufferedNDElement<T, C> : NDBuffer<T>, NDElement<T, C, NDBuffer<T>> {
-    override val context: BufferedNDAlgebra<T, C>
+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
 }
@@ -16,7 +16,7 @@ interface BufferedNDElement<T, C> : NDBuffer<T>, NDElement<T, C, NDBuffer<T>> {
 class BufferedNDSpaceElement<T, S : Space<T>>(
     override val context: BufferedNDSpace<T, S>,
     override val buffer: Buffer<T>
-) : BufferedNDElement<T, S>, SpaceElement<NDBuffer<T>, BufferedNDSpaceElement<T, S>, BufferedNDSpace<T, S>> {
+) : BufferedNDElement<T, S>(), SpaceElement<NDBuffer<T>, BufferedNDSpaceElement<T, S>, BufferedNDSpace<T, S>> {
 
     override fun unwrap(): NDBuffer<T> = this
 
@@ -29,7 +29,7 @@ class BufferedNDSpaceElement<T, S : Space<T>>(
 class BufferedNDRingElement<T, R : Ring<T>>(
     override val context: BufferedNDRing<T, R>,
     override val buffer: Buffer<T>
-) : BufferedNDElement<T, R>, RingElement<NDBuffer<T>, BufferedNDRingElement<T, R>, BufferedNDRing<T, R>> {
+) : BufferedNDElement<T, R>(), RingElement<NDBuffer<T>, BufferedNDRingElement<T, R>, BufferedNDRing<T, R>> {
 
     override fun unwrap(): NDBuffer<T> = this
 
@@ -42,7 +42,7 @@ class BufferedNDRingElement<T, R : Ring<T>>(
 class BufferedNDFieldElement<T, F : Field<T>>(
     override val context: BufferedNDField<T, F>,
     override val buffer: Buffer<T>
-) : BufferedNDElement<T, F>, FieldElement<NDBuffer<T>, BufferedNDFieldElement<T, F>, BufferedNDField<T, F>> {
+) : BufferedNDElement<T, F>(), FieldElement<NDBuffer<T>, BufferedNDFieldElement<T, F>, BufferedNDField<T, F>> {
 
     override fun unwrap(): NDBuffer<T> = this
 
@@ -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) =
+operator fun <T : Any, F : Field<T>> BufferedNDElement<T, F>.div(arg: T): NDElement<T, F, NDBuffer<T>> =
     context.map(this) { it / arg }.wrap()

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt

@@ -4,42 +4,51 @@ 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 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 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 }
 
     companion object {
-
-        inline fun real(size: Int, initializer: (Int) -> Double): DoubleBuffer {
+        inline fun real(size: Int, initializer: (Int) -> Double): RealBuffer {
             val array = DoubleArray(size) { initializer(it) }
-            return DoubleBuffer(array)
+            return RealBuffer(array)
         }
 
         /**
@@ -51,7 +60,7 @@ interface Buffer<T> {
         inline fun <T : Any> auto(type: KClass<T>, size: Int, crossinline initializer: (Int) -> T): Buffer<T> {
             //TODO add resolution based on Annotation or companion resolution
             return when (type) {
-                Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as Buffer<T>
+                Double::class -> RealBuffer(DoubleArray(size) { initializer(it) as Double }) as Buffer<T>
                 Short::class -> ShortBuffer(ShortArray(size) { initializer(it) as Short }) as Buffer<T>
                 Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as Buffer<T>
                 Long::class -> LongBuffer(LongArray(size) { initializer(it) as Long }) as Buffer<T>
@@ -69,17 +78,34 @@ interface Buffer<T> {
     }
 }
 
+/**
+ * Creates a sequence that returns all elements from this [Buffer].
+ */
 fun <T> Buffer<T>.asSequence(): Sequence<T> = Sequence(::iterator)
 
-fun <T> Buffer<T>.asIterable(): Iterable<T> = asSequence().asIterable()
+/**
+ * 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.
+ *
+ * @param T the type of elements contained in the buffer.
+ */
 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>
 
@@ -93,7 +119,7 @@ interface MutableBuffer<T> : Buffer<T> {
         @Suppress("UNCHECKED_CAST")
         inline fun <T : Any> auto(type: KClass<out T>, size: Int, initializer: (Int) -> T): MutableBuffer<T> {
             return when (type) {
-                Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as MutableBuffer<T>
+                Double::class -> RealBuffer(DoubleArray(size) { initializer(it) as Double }) as MutableBuffer<T>
                 Short::class -> ShortBuffer(ShortArray(size) { initializer(it) as Short }) as MutableBuffer<T>
                 Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as MutableBuffer<T>
                 Long::class -> LongBuffer(LongArray(size) { initializer(it) as Long }) as MutableBuffer<T>
@@ -109,14 +135,18 @@ interface MutableBuffer<T> : Buffer<T> {
             auto(T::class, size, initializer)
 
         val real: MutableBufferFactory<Double> = { size: Int, initializer: (Int) -> Double ->
-            DoubleBuffer(DoubleArray(size) { initializer(it) })
+            RealBuffer(DoubleArray(size) { initializer(it) })
         }
     }
 }
 
-
+/**
+ * [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
 
@@ -125,11 +155,26 @@ 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)
+/**
+ * Returns an [ListBuffer] that wraps the original list.
+ */
+fun <T> List<T>.asBuffer(): ListBuffer<T> = ListBuffer(this)
 
-@Suppress("FunctionName")
-inline fun <T> ListBuffer(size: Int, init: (Int) -> T) = List(size, init).asBuffer()
+/**
+ * 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
@@ -145,8 +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
 
@@ -161,99 +212,30 @@ class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
     override fun copy(): MutableBuffer<T> = ArrayBuffer(array.copyOf())
 }
 
-fun <T> Array<T>.asBuffer() = ArrayBuffer(this)
-
-inline class DoubleBuffer(val array: DoubleArray) : MutableBuffer<Double> {
-    override val size: Int get() = array.size
-
-    override fun get(index: Int): Double = array[index]
-
-    override fun set(index: Int, value: Double) {
-        array[index] = value
-    }
-
-    override fun iterator() = array.iterator()
-
-    override fun copy(): MutableBuffer<Double> = DoubleBuffer(array.copyOf())
-}
-
-@Suppress("FunctionName")
-inline fun DoubleBuffer(size: Int, init: (Int) -> Double) = DoubleBuffer(DoubleArray(size) { init(it) })
+/**
+ * Returns an [ArrayBuffer] that wraps the original array.
+ */
+fun <T> Array<T>.asBuffer(): ArrayBuffer<T> = ArrayBuffer(this)
 
 /**
- * Transform buffer of doubles into array for high performance operations
+ * Immutable wrapper for [MutableBuffer].
+ *
+ * @param T the type of elements contained in the buffer.
+ * @property buffer The underlying buffer.
  */
-val Buffer<out Double>.array: DoubleArray
-    get() = if (this is DoubleBuffer) {
-        array
-    } else {
-        DoubleArray(size) { get(it) }
-    }
-
-fun DoubleArray.asBuffer() = DoubleBuffer(this)
-
-inline class ShortBuffer(val array: ShortArray) : MutableBuffer<Short> {
-    override val size: Int get() = array.size
-
-    override fun get(index: Int): Short = array[index]
-
-    override fun set(index: Int, value: Short) {
-        array[index] = value
-    }
-
-    override fun iterator() = array.iterator()
-
-    override fun copy(): MutableBuffer<Short> = ShortBuffer(array.copyOf())
-
-}
-
-fun ShortArray.asBuffer() = ShortBuffer(this)
-
-inline class IntBuffer(val array: IntArray) : MutableBuffer<Int> {
-    override val size: Int get() = array.size
-
-    override fun get(index: Int): Int = array[index]
-
-    override fun set(index: Int, value: Int) {
-        array[index] = value
-    }
-
-    override fun iterator() = array.iterator()
-
-    override fun copy(): MutableBuffer<Int> = IntBuffer(array.copyOf())
-
-}
-
-fun IntArray.asBuffer() = IntBuffer(this)
-
-inline class LongBuffer(val array: LongArray) : MutableBuffer<Long> {
-    override val size: Int get() = array.size
-
-    override fun get(index: Int): Long = array[index]
-
-    override fun set(index: Int, value: Long) {
-        array[index] = value
-    }
-
-    override fun iterator() = array.iterator()
-
-    override fun copy(): MutableBuffer<Long> = LongBuffer(array.copyOf())
-
-}
-
-fun LongArray.asBuffer() = LongBuffer(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.
+ *
+ * @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 {
@@ -273,17 +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>

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) }
@@ -69,16 +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>): ComplexNDElement = map(arg) { tan(it) }
+
+    override fun asin(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { asin(it) }
+
+    override fun acos(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { acos(it) }
+
+    override fun atan(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { atan(it) }
 }
 
 
@@ -91,13 +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) =
+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]) }
@@ -107,7 +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) }
 
 
@@ -116,19 +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)

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ExtendedNDField.kt

@@ -1,14 +1,15 @@
 package scientifik.kmath.structures
 
-import scientifik.kmath.operations.*
-
-interface ExtendedNDField<T : Any, F, N : NDStructure<T>> :
-    NDField<T, F, N>,
-    TrigonometricOperations<N>,
-    PowerOperations<N>,
-    ExponentialOperations<N>
-        where F : ExtendedFieldOperations<T>, F : Field<T>
+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>
 
 ///**
 // * NDField that supports [ExtendedField] operations on its elements
@@ -41,5 +42,3 @@ interface ExtendedNDField<T : Any, F, N : NDStructure<T>> :
 //        return produce { with(elementContext) { cos(arg[it]) } }
 //    }
 //}
-
-

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/FlaggedBuffer.kt

@@ -0,0 +1,73 @@
+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.
+ */
+interface FlaggedBuffer<T> : Buffer<T> {
+    fun getFlag(index: Int): Byte
+}
+
+/**
+ * The value is valid if all flags are down
+ */
+fun FlaggedBuffer<*>.isValid(index: Int): Boolean = getFlag(index) != 0.toByte()
+
+fun FlaggedBuffer<*>.hasFlag(index: Int, flag: ValueFlag): Boolean = (getFlag(index) and flag.mask) != 0.toByte()
+
+fun FlaggedBuffer<*>.isMissing(index: Int): Boolean = hasFlag(index, ValueFlag.MISSING)
+
+/**
+ * A real buffer which supports flags for each value like NaN or Missing
+ */
+class FlaggedRealBuffer(val values: DoubleArray, val flags: ByteArray) : FlaggedBuffer<Double?>, Buffer<Double?> {
+    init {
+        require(values.size == flags.size) { "Values and flags must have the same dimensions" }
+    }
+
+    override fun getFlag(index: Int): Byte = flags[index]
+
+    override val size: Int get() = values.size
+
+    override fun get(index: Int): Double? = if (isValid(index)) values[index] else null
+
+    override fun iterator(): Iterator<Double?> = values.indices.asSequence().map {
+        if (isValid(it)) values[it] else null
+    }.iterator()
+}
+
+inline fun FlaggedRealBuffer.forEachValid(block: (Double) -> Unit) {
+    for (i in indices) {
+        if (isValid(i)) {
+            block(values[i])
+        }
+    }
+}

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)

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/IntBuffer.kt

@@ -0,0 +1,50 @@
+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
+
+    override fun get(index: Int): Int = array[index]
+
+    override fun set(index: Int, value: Int) {
+        array[index] = value
+    }
+
+    override fun iterator(): IntIterator = array.iterator()
+
+    override fun copy(): MutableBuffer<Int> =
+        IntBuffer(array.copyOf())
+
+}
+
+/**
+ * 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 buffer element given its index.
+ */
+inline fun IntBuffer(size: Int, init: (Int) -> Int): IntBuffer = IntBuffer(IntArray(size) { init(it) })
+
+/**
+ * Returns a new [IntBuffer] of given elements.
+ */
+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.
+ *
+ * @receiver the array.
+ * @return the new buffer.
+ */
+fun IntArray.asBuffer(): IntBuffer = IntBuffer(this)

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LongBuffer.kt

@@ -0,0 +1,50 @@
+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
+
+    override fun get(index: Int): Long = array[index]
+
+    override fun set(index: Int, value: Long) {
+        array[index] = value
+    }
+
+    override fun iterator(): LongIterator = array.iterator()
+
+    override fun copy(): MutableBuffer<Long> =
+        LongBuffer(array.copyOf())
+
+}
+
+/**
+ * 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)

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/MemoryBuffer.kt

@@ -3,13 +3,16 @@ package scientifik.kmath.structures
 import scientifik.memory.*
 
 /**
- * A non-boxing buffer based on [ByteBuffer] storage
+ * 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)
 
@@ -17,7 +20,7 @@ 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(
@@ -33,24 +36,31 @@ 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> {
 
-    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)

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 +97,19 @@ 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
+ * Field of [NDStructure].
+ *
+ * @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> {
 
@@ -120,9 +119,9 @@ 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 +130,7 @@ 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 +139,7 @@ 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.

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 }
 
 

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt

@@ -3,70 +3,138 @@ 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
 
-    val dimension get() = shape.size
+    /**
+     * 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
+
+    override fun hashCode(): Int
+
     companion object {
+        /**
+         * Indicates whether some [NDStructure] is equal to another one.
+         */
         fun equals(st1: NDStructure<*>, st2: NDStructure<*>): Boolean {
-            return when {
-                st1 === st2 -> true
-                st1 is BufferNDStructure<*> && st2 is BufferNDStructure<*> && st1.strides == st2.strides -> st1.buffer.contentEquals(
-                    st2.buffer
-                )
-                else -> st1.elements().all { (index, value) -> value == st2[index] }
+            if (st1 === st2) return true
+
+            // fast comparison of buffers if possible
+            if (
+                st1 is NDBuffer &&
+                st2 is NDBuffer &&
+                st1.strides == st2.strides
+            ) {
+                return st1.buffer.contentEquals(st2.buffer)
             }
+
+            //element by element comparison if it could not be avoided
+            return st1.elements().all { (index, value) -> value == st2[index] }
         }
 
         /**
-         * 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,
             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)
     }
 }
 
+/**
+ * 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)
 }
 
@@ -77,7 +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 {
     /**
@@ -114,11 +182,14 @@ interface Strides {
     }
 }
 
+/**
+ * Simple implementation of [Strides].
+ */
 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)
@@ -153,19 +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>()
@@ -177,15 +243,37 @@ class DefaultStrides private constructor(override val shape: IntArray) : Strides
     }
 }
 
-interface NDBuffer<T> : NDStructure<T> {
-    val buffer: Buffer<T>
-    val strides: 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)]
 
     override val shape: IntArray get() = strides.shape
 
-    override fun elements() = strides.indices().map { it to this[it] }
+    override fun elements(): Sequence<Pair<IntArray, T>> = strides.indices().map { it to this[it] }
+
+    override fun equals(other: Any?): Boolean {
+        return NDStructure.equals(this, other as? NDStructure<*> ?: return false)
+    }
+
+    override fun hashCode(): Int {
+        var result = strides.hashCode()
+        result = 31 * result + buffer.hashCode()
+        return result
+    }
 }
 
 /**
@@ -194,34 +282,12 @@ interface NDBuffer<T> : NDStructure<T> {
 class BufferNDStructure<T>(
     override val strides: Strides,
     override val buffer: Buffer<T>
-) : NDBuffer<T> {
-
+) : NDBuffer<T>() {
     init {
         if (strides.linearSize != buffer.size) {
             error("Expected buffer side of ${strides.linearSize}, but found ${buffer.size}")
         }
     }
-
-    override fun get(index: IntArray): T = buffer[strides.offset(index)]
-
-    override val shape: IntArray get() = strides.shape
-
-    override fun elements() = strides.indices().map { it to this[it] }
-
-    override fun equals(other: Any?): Boolean {
-        return when {
-            this === other -> true
-            other is BufferNDStructure<*> && this.strides == other.strides -> this.buffer.contentEquals(other.buffer)
-            other is NDStructure<*> -> elements().all { (index, value) -> value == other[index] }
-            else -> false
-        }
-    }
-
-    override fun hashCode(): Int {
-        var result = strides.hashCode()
-        result = 31 * result + buffer.hashCode()
-        return result
-    }
 }
 
 /**
@@ -240,20 +306,20 @@ 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,
     override val buffer: MutableBuffer<T>
-) : NDBuffer<T>, MutableNDStructure<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}"
         }
     }
 
-    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(

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBuffer.kt

@@ -0,0 +1,49 @@
+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
+
+    override fun get(index: Int): Double = array[index]
+
+    override fun set(index: Int, value: Double) {
+        array[index] = value
+    }
+
+    override fun iterator(): DoubleIterator = array.iterator()
+
+    override fun copy(): MutableBuffer<Double> =
+        RealBuffer(array.copyOf())
+}
+
+/**
+ * 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 buffer element given its index.
+ */
+inline fun RealBuffer(size: Int, init: (Int) -> Double): RealBuffer = RealBuffer(DoubleArray(size) { init(it) })
+
+/**
+ * Returns a new [RealBuffer] of given elements.
+ */
+fun RealBuffer(vararg doubles: Double): RealBuffer = RealBuffer(doubles)
+
+/**
+ * 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) })
+
+/**
+ * Returns [RealBuffer] over this array.
+ *
+ * @receiver the array.
+ * @return the new buffer.
+ */
+fun DoubleArray.asBuffer(): RealBuffer = RealBuffer(this)

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt

@@ -6,148 +6,180 @@ 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>): DoubleBuffer {
+    override fun add(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
         require(b.size == a.size) { "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} " }
-        return if (a is DoubleBuffer && b is DoubleBuffer) {
+
+        return if (a is RealBuffer && b is RealBuffer) {
             val aArray = a.array
             val bArray = b.array
-            DoubleBuffer(DoubleArray(a.size) { aArray[it] + bArray[it] })
-        } else {
-            DoubleBuffer(DoubleArray(a.size) { a[it] + b[it] })
-        }
+            RealBuffer(DoubleArray(a.size) { aArray[it] + bArray[it] })
+        } else
+            RealBuffer(DoubleArray(a.size) { a[it] + b[it] })
     }
 
-    override fun multiply(a: Buffer<Double>, k: Number): DoubleBuffer {
+    override fun multiply(a: Buffer<Double>, k: Number): RealBuffer {
         val kValue = k.toDouble()
-        return if (a is DoubleBuffer) {
+
+        return if (a is RealBuffer) {
             val aArray = a.array
-            DoubleBuffer(DoubleArray(a.size) { aArray[it] * kValue })
-        } else {
-            DoubleBuffer(DoubleArray(a.size) { a[it] * kValue })
-        }
+            RealBuffer(DoubleArray(a.size) { aArray[it] * kValue })
+        } else
+            RealBuffer(DoubleArray(a.size) { a[it] * kValue })
     }
 
-    override fun multiply(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+    override fun multiply(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
         require(b.size == a.size) { "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} " }
-        return if (a is DoubleBuffer && b is DoubleBuffer) {
+
+        return if (a is RealBuffer && b is RealBuffer) {
             val aArray = a.array
             val bArray = b.array
-            DoubleBuffer(DoubleArray(a.size) { aArray[it] * bArray[it] })
-        } else {
-            DoubleBuffer(DoubleArray(a.size) { a[it] * b[it] })
-        }
+            RealBuffer(DoubleArray(a.size) { aArray[it] * bArray[it] })
+        } else
+            RealBuffer(DoubleArray(a.size) { a[it] * b[it] })
     }
 
-    override fun divide(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+    override fun divide(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
         require(b.size == a.size) { "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} " }
-        return if (a is DoubleBuffer && b is DoubleBuffer) {
+
+        return if (a is RealBuffer && b is RealBuffer) {
             val aArray = a.array
             val bArray = b.array
-            DoubleBuffer(DoubleArray(a.size) { aArray[it] / bArray[it] })
-        } else {
-            DoubleBuffer(DoubleArray(a.size) { a[it] / b[it] })
-        }
+            RealBuffer(DoubleArray(a.size) { aArray[it] / bArray[it] })
+        } else
+            RealBuffer(DoubleArray(a.size) { a[it] / b[it] })
     }
 
-    override fun sin(arg: Buffer<Double>): DoubleBuffer {
-        return if (arg is DoubleBuffer) {
-            val array = arg.array
-            DoubleBuffer(DoubleArray(arg.size) { sin(array[it]) })
-        } else {
-            DoubleBuffer(DoubleArray(arg.size) { sin(arg[it]) })
-        }
+    override fun sin(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { sin(array[it]) })
+    } else {
+        RealBuffer(DoubleArray(arg.size) { sin(arg[it]) })
     }
 
-    override fun cos(arg: Buffer<Double>): DoubleBuffer {
-        return if (arg is DoubleBuffer) {
-            val array = arg.array
-            DoubleBuffer(DoubleArray(arg.size) { cos(array[it]) })
-        } else {
-            DoubleBuffer(DoubleArray(arg.size) { cos(arg[it]) })
-        }
+    override fun cos(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { cos(array[it]) })
+    } else
+        RealBuffer(DoubleArray(arg.size) { cos(arg[it]) })
+
+    override fun tan(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { tan(array[it]) })
+    } else
+        RealBuffer(DoubleArray(arg.size) { tan(arg[it]) })
+
+    override fun asin(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { asin(array[it]) })
+    } else {
+        RealBuffer(DoubleArray(arg.size) { asin(arg[it]) })
     }
 
-    override fun power(arg: Buffer<Double>, pow: Number): DoubleBuffer {
-        return if (arg is DoubleBuffer) {
-            val array = arg.array
-            DoubleBuffer(DoubleArray(arg.size) { array[it].pow(pow.toDouble()) })
-        } else {
-            DoubleBuffer(DoubleArray(arg.size) { arg[it].pow(pow.toDouble()) })
-        }
-    }
+    override fun acos(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { acos(array[it]) })
+    } else
+        RealBuffer(DoubleArray(arg.size) { acos(arg[it]) })
 
-    override fun exp(arg: Buffer<Double>): DoubleBuffer {
-        return if (arg is DoubleBuffer) {
-            val array = arg.array
-            DoubleBuffer(DoubleArray(arg.size) { exp(array[it]) })
-        } else {
-            DoubleBuffer(DoubleArray(arg.size) { exp(arg[it]) })
-        }
-    }
+    override fun atan(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { atan(array[it]) })
+    } else
+        RealBuffer(DoubleArray(arg.size) { atan(arg[it]) })
 
-    override fun ln(arg: Buffer<Double>): DoubleBuffer {
-        return if (arg is DoubleBuffer) {
-            val array = arg.array
-            DoubleBuffer(DoubleArray(arg.size) { ln(array[it]) })
-        } else {
-            DoubleBuffer(DoubleArray(arg.size) { ln(arg[it]) })
-        }
-    }
+    override fun power(arg: Buffer<Double>, pow: Number): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { array[it].pow(pow.toDouble()) })
+    } else
+        RealBuffer(DoubleArray(arg.size) { arg[it].pow(pow.toDouble()) })
+
+    override fun exp(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { exp(array[it]) })
+    } else
+        RealBuffer(DoubleArray(arg.size) { exp(arg[it]) })
+
+    override fun ln(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { ln(array[it]) })
+    } else
+        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 } }
 
-    override val zero: Buffer<Double> by lazy { DoubleBuffer(size) { 0.0 } }
-
-    override val one: Buffer<Double> by lazy { DoubleBuffer(size) { 1.0 } }
-
-    override fun add(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+    override fun add(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
         require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
         return RealBufferFieldOperations.add(a, b)
     }
 
-    override fun multiply(a: Buffer<Double>, k: Number): DoubleBuffer {
+    override fun multiply(a: Buffer<Double>, k: Number): RealBuffer {
         require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
         return RealBufferFieldOperations.multiply(a, k)
     }
 
-    override fun multiply(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+    override fun multiply(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
         require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
         return RealBufferFieldOperations.multiply(a, b)
     }
 
-
-    override fun divide(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
+    override fun divide(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
         require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
         return RealBufferFieldOperations.divide(a, b)
     }
 
-    override fun sin(arg: Buffer<Double>): DoubleBuffer {
+    override fun sin(arg: Buffer<Double>): RealBuffer {
         require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
         return RealBufferFieldOperations.sin(arg)
     }
 
-    override fun cos(arg: Buffer<Double>): DoubleBuffer {
+    override fun cos(arg: Buffer<Double>): RealBuffer {
         require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
         return RealBufferFieldOperations.cos(arg)
     }
 
-    override fun power(arg: Buffer<Double>, pow: Number): DoubleBuffer {
+    override fun tan(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.tan(arg)
+    }
+
+    override fun asin(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.asin(arg)
+    }
+
+    override fun acos(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.acos(arg)
+    }
+
+    override fun atan(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.atan(arg)
+    }
+
+    override fun power(arg: Buffer<Double>, pow: Number): RealBuffer {
         require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
         return RealBufferFieldOperations.power(arg, pow)
     }
 
-    override fun exp(arg: Buffer<Double>): DoubleBuffer {
+    override fun exp(arg: Buffer<Double>): RealBuffer {
         require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
         return RealBufferFieldOperations.exp(arg)
     }
 
-    override fun ln(arg: Buffer<Double>): DoubleBuffer {
+    override fun ln(arg: Buffer<Double>): RealBuffer {
         require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
         return RealBufferFieldOperations.ln(arg)
     }
-
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt

@@ -12,11 +12,11 @@ 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> =
-        DoubleBuffer(DoubleArray(size) { initializer(it) })
+        RealBuffer(DoubleArray(size) { initializer(it) })
 
     /**
      * Inline transform an NDStructure to
@@ -64,16 +64,23 @@ 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) }
+
+    override fun asin(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { asin(it) }
+
+    override fun acos(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { acos(it) }
+
+    override fun atan(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { atan(it) }
 }
 
 
@@ -82,27 +89,27 @@ class RealNDField(override val shape: IntArray) :
  */
 inline fun BufferedNDField<Double, RealField>.produceInline(crossinline initializer: RealField.(Int) -> Double): RealNDElement {
     val array = DoubleArray(strides.linearSize) { offset -> RealField.initializer(offset) }
-    return BufferedNDFieldElement(this, DoubleBuffer(array))
+    return BufferedNDFieldElement(this, RealBuffer(array))
 }
 
 /**
- * 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) =
+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]) }
-    return BufferedNDFieldElement(context, DoubleBuffer(array))
+    return BufferedNDFieldElement(context, RealBuffer(array))
 }
 
 /**
- * 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) }
 
 
@@ -111,13 +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 }
 
 /**

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ShortBuffer.kt

@@ -0,0 +1,50 @@
+package scientifik.kmath.structures
+
+/**
+ * Specialized [MutableBuffer] implementation over [ShortArray].
+ *
+ * @property array the underlying array.
+ */
+inline class ShortBuffer(val array: ShortArray) : MutableBuffer<Short> {
+    override val size: Int get() = array.size
+
+    override fun get(index: Int): Short = array[index]
+
+    override fun set(index: Int, value: Short) {
+        array[index] = value
+    }
+
+    override fun iterator(): ShortIterator = array.iterator()
+
+    override fun copy(): MutableBuffer<Short> =
+        ShortBuffer(array.copyOf())
+
+}
+
+/**
+ * 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)

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) =
+operator fun ShortNDElement.minus(arg: Short): ShortNDElement =
     context.produceInline { i -> (buffer[i] - arg).toShort() }

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure1D.kt

@@ -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)

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Structure2D.kt

@@ -14,7 +14,6 @@ interface Structure2D<T> : NDStructure<T> {
         return get(index[0], index[1])
     }
 
-
     val rows: Buffer<Buffer<T>>
         get() = VirtualBuffer(rowNum) { i ->
             VirtualBuffer(colNum) { j -> get(i, j) }
@@ -33,9 +32,7 @@ interface Structure2D<T> : NDStructure<T> {
         }
     }
 
-    companion object {
-
-    }
+    companion object
 }
 
 /**
@@ -58,22 +55,4 @@ fun <T> NDStructure<T>.as2D(): Structure2D<T> = if (shape.size == 2) {
     error("Can't create 2d-structure from ${shape.size}d-structure")
 }
 
-/**
- * Represent this 2D structure as 1D if it has exactly one column. Throw error otherwise.
- */
-fun <T> Structure2D<T>.as1D() = if (colNum == 1) {
-    object : Structure1D<T> {
-        override fun get(index: Int): T = get(index, 0)
-
-        override val shape: IntArray get() = intArrayOf(rowNum)
-
-        override fun elements(): Sequence<Pair<IntArray, T>> = elements()
-
-        override val size: Int get() = rowNum
-    }
-} else {
-    error("Can't convert matrix with more than one column to vector")
-}
-
-
 typealias Matrix<T> = Structure2D<T>

kmath-core/src/commonTest/kotlin/scientifik/kmath/expressions/ExpressionFieldTest.kt

@@ -9,7 +9,7 @@ import kotlin.test.assertEquals
 class ExpressionFieldTest {
     @Test
     fun testExpression() {
-        val context = ExpressionField(RealField)
+        val context = FunctionalExpressionField(RealField)
         val expression = with(context) {
             val x = variable("x", 2.0)
             x * x + 2 * x + one
@@ -20,7 +20,7 @@ class ExpressionFieldTest {
 
     @Test
     fun testComplex() {
-        val context = ExpressionField(ComplexField)
+        val context = FunctionalExpressionField(ComplexField)
         val expression = with(context) {
             val x = variable("x", Complex(2.0, 0.0))
             x * x + 2 * x + one
@@ -31,23 +31,23 @@ class ExpressionFieldTest {
 
     @Test
     fun separateContext() {
-        fun <T> ExpressionField<T>.expression(): Expression<T> {
+        fun <T> FunctionalExpressionField<T, *>.expression(): Expression<T> {
             val x = variable("x")
             return x * x + 2 * x + one
         }
 
-        val expression = ExpressionField(RealField).expression()
+        val expression = FunctionalExpressionField(RealField).expression()
         assertEquals(expression("x" to 1.0), 4.0)
     }
 
     @Test
     fun valueExpression() {
-        val expressionBuilder: ExpressionField<Double>.() -> Expression<Double> = {
+        val expressionBuilder: FunctionalExpressionField<Double, *>.() -> Expression<Double> = {
             val x = variable("x")
             x * x + 2 * x + one
         }
 
-        val expression = ExpressionField(RealField).expressionBuilder()
+        val expression = FunctionalExpressionField(RealField).expressionBuilder()
         assertEquals(expression("x" to 1.0), 4.0)
     }
 }

kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/MatrixTest.kt

@@ -17,7 +17,7 @@ class MatrixTest {
 
     @Test
     fun testBuilder() {
-        val matrix = Matrix.build<Double>(2, 3)(
+        val matrix = Matrix.build(2, 3)(
             1.0, 0.0, 0.0,
             0.0, 1.0, 2.0
         )
@@ -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])
         }
     }
 }