build.gradle.kts

@@ -2,7 +2,7 @@ plugins {
     id("scientifik.publish") apply false
 }
 
-val kmathVersion by extra("0.1.4-dev-7")
+val kmathVersion by extra("0.1.4-dev-8")
 
 val bintrayRepo by extra("scientifik")
 val githubProject by extra("kmath")

doc/buffers.md

@@ -2,7 +2,7 @@
 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.

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> {
@@ -24,6 +24,7 @@ sourceSets {
 }
 
 dependencies {
+    implementation(project(":kmath-ast"))
     implementation(project(":kmath-core"))
     implementation(project(":kmath-coroutines"))
     implementation(project(":kmath-commons"))
@@ -33,8 +34,8 @@ dependencies {
     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

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/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
         }

kmath-ast/README.md

@@ -0,0 +1,62 @@
+# AST-based expression representation and operations (`kmath-ast`)
+
+This subproject implements the following features:
+
+- Expression Language and its parser.
+- MST as expression language's syntax intermediate representation.
+- Type-safe builder of MST.
+- Evaluating expressions by traversing MST.
+
+## Dynamic expression code generation with OW2 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;
+    private final Object[] constants;
+
+    public AsmCompiledExpression_1073786867_0(RealField algebra, Object[] constants) {
+        this.algebra = algebra;
+        this.constants = constants;
+    }
+
+    public final Double invoke(Map<String, ? extends Double> arguments) {
+        return (Double)this.algebra.add(((Double)MapIntrinsics.getOrFail(arguments, "x", (Object)null)).doubleValue(), 2.0D);
+    }
+}
+
+```
+
+### Example Usage
+
+This API is an extension to MST and MstExpression APIs. You may optimize both MST and MSTExpression: 
+
+```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 +1,37 @@
+plugins {
+    id("scientifik.mpp")
+}
+
+repositories {
+    maven("https://dl.bintray.com/hotkeytlt/maven")
+}
+
+kotlin.sourceSets {
+//    all {
+//       languageSettings.apply{
+//            enableLanguageFeature("NewInference")
+//       }
+//    }
+    commonMain {
+        dependencies {
+            api(project(":kmath-core"))
+            implementation("com.github.h0tk3y.betterParse:better-parse-multiplatform:0.4.0-alpha-3")
+            implementation("com.github.h0tk3y.betterParse:better-parse-multiplatform-metadata:0.4.0-alpha-3")
+        }
+    }
+
+    jvmMain {
+        dependencies {
+            implementation("com.github.h0tk3y.betterParse:better-parse-jvm:0.4.0-alpha-3")
+            implementation("org.ow2.asm:asm:8.0.1")
+            implementation("org.ow2.asm:asm-commons:8.0.1")
+            implementation(kotlin("reflect"))
+        }
+    }
+
+    jsMain {
+        dependencies {
+            implementation("com.github.h0tk3y.betterParse:better-parse-js:0.4.0-alpha-3")
+        }
+    }
+}

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

@@ -0,0 +1,67 @@
+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 unparsed string
+     */
+    data class Symbolic(val value: String) : MST()
+
+    /**
+     * A node containing a number
+     */
+    data class Numeric(val value: Number) : MST()
+
+    /**
+     * A node containing an unary operation
+     */
+    data class Unary(val operation: String, val value: MST) : MST() {
+        companion object {
+            const val ABS_OPERATION = "abs"
+            //TODO add operations
+        }
+    }
+
+    /**
+     * A node containing binary operation
+     */
+    data class Binary(val operation: String, val left: MST, val right: MST) : MST() {
+        companion object
+    }
+}
+
+//TODO add a function with positional arguments
+
+//TODO add a function with named arguments
+
+fun <T> Algebra<T>.evaluate(node: MST): T {
+    return 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))
+        }
+    }
+}
+
+fun <T> MST.compile(algebra: Algebra<T>): T = algebra.evaluate(this)

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

@@ -0,0 +1,72 @@
+package scientifik.kmath.ast
+
+import scientifik.kmath.operations.*
+
+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)
+}
+
+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)
+}
+
+object MstRing : Ring<MST>, NumericAlgebra<MST> {
+    override val zero: MST = number(0.0)
+    override val one: MST = number(1.0)
+
+    override fun number(value: Number): MST = MstAlgebra.number(value)
+    override fun symbol(value: String): MST = MstAlgebra.symbol(value)
+    override fun add(a: MST, b: MST): MST = binaryOperation(SpaceOperations.PLUS_OPERATION, a, b)
+
+    override fun multiply(a: MST, k: Number): MST =
+        binaryOperation(RingOperations.TIMES_OPERATION, a, MstSpace.number(k))
+
+    override fun multiply(a: MST, b: MST): MST = binaryOperation(RingOperations.TIMES_OPERATION, a, b)
+
+    override fun 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)
+}
+
+object MstField : Field<MST> {
+    override val zero: MST = number(0.0)
+    override val one: MST = number(1.0)
+
+    override fun symbol(value: String): MST = MstAlgebra.symbol(value)
+    override fun number(value: Number): MST = MstAlgebra.number(value)
+    override fun add(a: MST, b: MST): MST = binaryOperation(SpaceOperations.PLUS_OPERATION, a, b)
+
+    override fun multiply(a: MST, k: Number): MST =
+        binaryOperation(RingOperations.TIMES_OPERATION, a, MstSpace.number(k))
+
+    override fun multiply(a: MST, b: MST): MST = binaryOperation(RingOperations.TIMES_OPERATION, a, b)
+    override fun divide(a: MST, b: MST): MST = binaryOperation(FieldOperations.DIV_OPERATION, a, b)
+
+    override fun binaryOperation(operation: String, left: MST, right: MST): MST =
+        MstAlgebra.binaryOperation(operation, left, right)
+
+    override fun unaryOperation(operation: String, arg: MST): MST = MstAlgebra.unaryOperation(operation, arg)
+}

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

@@ -0,0 +1,55 @@
+package scientifik.kmath.ast
+
+import scientifik.kmath.expressions.Expression
+import scientifik.kmath.expressions.FunctionalExpressionField
+import scientifik.kmath.expressions.FunctionalExpressionRing
+import scientifik.kmath.expressions.FunctionalExpressionSpace
+import scientifik.kmath.operations.*
+
+/**
+ * The expression evaluates MST on-flight. Should be much faster than functional expression, but slower than ASM-generated expressions.
+ */
+class MstExpression<T>(val algebra: Algebra<T>, val mst: MST) : Expression<T> {
+
+    /**
+     * Substitute algebra raw value
+     */
+    private inner class InnerAlgebra(val arguments: Map<String, T>) : NumericAlgebra<T> {
+        override fun symbol(value: String): T = arguments[value] ?: algebra.symbol(value)
+        override fun unaryOperation(operation: String, arg: T): T = algebra.unaryOperation(operation, arg)
+
+        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)
+}
+
+
+inline fun <reified T : Any, A : Algebra<T>, E : Algebra<MST>> A.mst(
+    mstAlgebra: E,
+    block: E.() -> MST
+): MstExpression<T> = MstExpression(this, mstAlgebra.block())
+
+inline fun <reified T : Any> Space<T>.mstInSpace(block: MstSpace.() -> MST): MstExpression<T> =
+    MstExpression(this, MstSpace.block())
+
+inline fun <reified T : Any> Ring<T>.mstInRing(block: MstRing.() -> MST): MstExpression<T> =
+    MstExpression(this, MstRing.block())
+
+inline fun <reified T : Any> Field<T>.mstInField(block: MstField.() -> MST): MstExpression<T> =
+    MstExpression(this, MstField.block())
+
+inline fun <reified T : Any, A : Space<T>> FunctionalExpressionSpace<T, A>.mstInSpace(block: MstSpace.() -> MST): MstExpression<T> =
+    algebra.mstInSpace(block)
+
+inline fun <reified T : Any, A : Ring<T>> FunctionalExpressionRing<T, A>.mstInRing(block: MstRing.() -> MST): MstExpression<T> =
+    algebra.mstInRing(block)
+
+inline fun <reified T : Any, A : Field<T>> FunctionalExpressionField<T, A>.mstInField(block: MstField.() -> MST): MstExpression<T> =
+    algebra.mstInField(block)

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

@@ -0,0 +1,59 @@
+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.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 common
+ */
+private object ArithmeticsEvaluator : Grammar<MST>() {
+    val num by token("-?[\\d.]+(?:[eE]-?\\d+)?".toRegex())
+    val lpar by token("\\(".toRegex())
+    val rpar by token("\\)".toRegex())
+    val mul by token("\\*".toRegex())
+    val pow by token("\\^".toRegex())
+    val div by token("/".toRegex())
+    val minus by token("-".toRegex())
+    val plus by token("\\+".toRegex())
+    val ws by token("\\s+".toRegex(), ignore = true)
+
+    val number: Parser<MST> by num use { MST.Numeric(text.toDouble()) }
+
+    val term: Parser<MST> by number or
+            (skip(minus) and parser(this::term) map { MST.Unary(SpaceOperations.MINUS_OPERATION, it) }) or
+            (skip(lpar) and parser(this::rootParser) and skip(rpar))
+
+    val powChain by leftAssociative(term, pow) { a, _, b ->
+        MST.Binary(PowerOperations.POW_OPERATION, a, b)
+    }
+
+    val divMulChain: Parser<MST> by leftAssociative(powChain, div or mul use { type }) { a, op, b ->
+        if (op == div) {
+            MST.Binary(FieldOperations.DIV_OPERATION, a, b)
+        } else {
+            MST.Binary(RingOperations.TIMES_OPERATION, a, b)
+        }
+    }
+
+    val subSumChain: Parser<MST> by leftAssociative(divMulChain, plus or minus use { 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
+}
+
+fun String.tryParseMath(): ParseResult<MST> = ArithmeticsEvaluator.tryParseToEnd(this)
+fun String.parseMath(): MST = ArithmeticsEvaluator.parseToEnd(this)

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

@@ -0,0 +1,60 @@
+package scientifik.kmath.asm
+
+import scientifik.kmath.asm.internal.AsmBuilder
+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 scientifik.kmath.operations.NumericAlgebra
+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 -> loadVariable(node.value)
+
+            is MST.Numeric -> {
+                val constant = if (algebra is NumericAlgebra<T>)
+                    algebra.number(node.value)
+                else
+                    error("Number literals are not supported in $algebra")
+
+                loadTConstant(constant)
+            }
+
+            is MST.Unary -> buildAlgebraOperationCall(
+                context = algebra,
+                name = node.operation,
+                fallbackMethodName = "unaryOperation",
+                arity = 1
+            ) { visit(node.value) }
+
+            is MST.Binary -> buildAlgebraOperationCall(
+                context = algebra,
+                name = node.operation,
+                fallbackMethodName = "binaryOperation",
+                arity = 2
+            ) {
+                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 +1,518 @@
+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 java.util.*
+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.
+ *
+ * @param T the type of AsmExpression to unwrap.
+ * @param algebra the algebra the applied AsmExpressions use.
+ * @param className the unique class name of new loaded class.
+ * @param 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 [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<Type>().apply { push(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")
+    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)
+            )
+
+            visitField(
+                access = ACC_PRIVATE or ACC_FINAL,
+                name = "algebra",
+                descriptor = tAlgebraType.descriptor,
+                signature = null,
+                value = null,
+                block = FieldVisitor::visitEnd
+            )
+
+            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),
+                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)
+                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
+                )
+
+                visitLocalVariable("constants", OBJECT_ARRAY_TYPE.descriptor, null, l0, l4, constantsVar)
+                visitMaxs(0, 3)
+                visitEnd()
+            }
+
+            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()
+            }
+
+            visitEnd()
+        }
+
+        val new = classLoader
+            .defineClass(className, classWriter.toByteArray())
+            .constructors
+            .first()
+            .newInstance(algebra, constants.toTypedArray()) 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) typeStack.push(tType) else typeStack.push(primitiveMask)
+            return
+        }
+
+        loadConstant(value as Any, tType)
+    }
+
+    /**
+     * Boxes the current value and pushes it.
+     */
+    private fun box(): Unit = invokeMethodVisitor.invokestatic(
+        tType.internalName,
+        "valueOf",
+        Type.getMethodDescriptor(tType, primitiveMask),
+        false
+    )
+
+    /**
+     * Unboxes the current boxed value and pushes it.
+     */
+    private fun unbox(): Unit = invokeMethodVisitor.invokevirtual(
+        NUMBER_TYPE.internalName,
+        NUMBER_CONVERTER_METHODS.getValue(primitiveMask),
+        Type.getMethodDescriptor(primitiveMask),
+        false
+    )
+
+    /**
+     * Loads [java.lang.Object] constant from constants.
+     */
+    private fun loadConstant(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)
+    }
+
+    /**
+     * 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()
+                invokeMethodVisitor.checkcast(tType)
+            }
+
+            return
+        }
+
+        loadConstant(value, boxed)
+
+        if (!mustBeBoxed) unbox()
+        else invokeMethodVisitor.checkcast(tType)
+    }
+
+    /**
+     * 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)
+        else
+            aconst(null)
+
+        invokestatic(
+            MAP_INTRINSICS_TYPE.internalName,
+            "getOrFail",
+            Type.getMethodDescriptor(OBJECT_TYPE, MAP_TYPE, OBJECT_TYPE, OBJECT_TYPE),
+            false
+        )
+
+        checkcast(tType)
+
+        val expectedType = expectationStack.pop()
+
+        if (expectedType.sort == Type.OBJECT)
+            typeStack.push(tType)
+        else {
+            unbox()
+            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 {
+            unbox()
+            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 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/codegenUtils.kt

@@ -0,0 +1,148 @@
+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 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)
+
+/**
+ * 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 {
+    val l = Label()
+    visitLabel(l)
+    return l
+}
+
+/**
+ * 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)
+
+/**
+ * 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, arity: Int): Boolean {
+    val theName = methodNameAdapters[name to arity] ?: name
+    val hasSpecific = context.javaClass.methods.find { it.name == theName && it.parameters.size == arity } != null
+    val t = if (primitiveMode && hasSpecific) primitiveMask else tType
+    repeat(arity) { expectationStack.push(t) }
+    return hasSpecific
+}
+
+/**
+ * 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, arity: Int): Boolean {
+    val theName = methodNameAdapters[name to arity] ?: name
+
+    context.javaClass.methods.find {
+        var suitableSignature = it.name == theName && it.parameters.size == arity
+
+        if (primitiveMode && it.isBridge)
+            suitableSignature = false
+
+        suitableSignature
+    } ?: return false
+
+    val owner = context::class.asm
+
+    invokeAlgebraOperation(
+        owner = owner.internalName,
+        method = theName,
+        descriptor = Type.getMethodDescriptor(primitiveMaskBoxed, *Array(arity) { primitiveMask }),
+        expectedArity = arity,
+        opcode = INVOKEVIRTUAL
+    )
+
+    return true
+}
+
+/**
+ * Builds specialized algebra call with option to fallback to generic algebra operation accepting String.
+ */
+internal fun <T> AsmBuilder<T>.buildAlgebraOperationCall(
+    context: Algebra<T>,
+    name: String,
+    fallbackMethodName: String,
+    arity: Int,
+    parameters: AsmBuilder<T>.() -> Unit
+) {
+    loadAlgebra()
+    if (!buildExpectationStack(context, name, arity)) loadStringConstant(name)
+    parameters()
+
+    if (!tryInvokeSpecific(context, name, arity)) 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/instructionAdapters.kt

@@ -0,0 +1,10 @@
+package scientifik.kmath.asm.internal
+
+import org.objectweb.asm.Label
+import org.objectweb.asm.commons.InstructionAdapter
+
+internal fun InstructionAdapter.label(): Label {
+    val l = Label()
+    visitLabel(l)
+    return l
+}

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

@@ -0,0 +1,7 @@
+@file:JvmName("MapIntrinsics")
+
+package scientifik.kmath.asm.internal
+
+internal fun <K, V> Map<K, V>.getOrFail(key: K, default: V?): V {
+    return 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 +1,46 @@
+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))
+    }
+}

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 +1,26 @@
+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 mst = "2+2*(2+2)".parseMath()
+        val res = ComplexField.expression(mst)()
+        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/ParserTest.kt

@@ -0,0 +1,25 @@
+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.Complex
+import scientifik.kmath.operations.ComplexField
+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)
+    }
+}

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/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/build.gradle.kts

@@ -8,4 +8,4 @@ kotlin.sourceSets {
             api(project(":kmath-memory"))
         }
     }
-}
+}

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

@@ -0,0 +1,15 @@
+package scientifik.kmath.domains
+
+import scientifik.kmath.linear.Point
+
+/**
+ * A simple geometric domain
+ */
+interface Domain<T : Any> {
+    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 +1,67 @@
+/* 
+ * 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 = 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 +1,65 @@
+/* 
+ * 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 +1,36 @@
+/* 
+ * 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 +1,48 @@
+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 +1,23 @@
+package scientifik.kmath.expressions
+
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.Ring
+import scientifik.kmath.operations.Space
+
+/**
+ * Create a functional expression on this [Space]
+ */
+fun <T> Space<T>.spaceExpression(block: FunctionalExpressionSpace<T, Space<T>>.() -> Expression<T>): Expression<T> =
+    FunctionalExpressionSpace(this).run(block)
+
+/**
+ * Create a functional expression on this [Ring]
+ */
+fun <T> Ring<T>.ringExpression(block: FunctionalExpressionRing<T, Ring<T>>.() -> Expression<T>): Expression<T> =
+    FunctionalExpressionRing(this).run(block)
+
+/**
+ * Create a functional expression on this [Field]
+ */
+fun <T> Field<T>.fieldExpression(block: FunctionalExpressionField<T, Field<T>>.() -> Expression<T>): Expression<T> =
+    FunctionalExpressionField(this).run(block)

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

@@ -1,14 +1,21 @@
 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> {
     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)
 }
 
 operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke(mapOf(*pairs))
@@ -16,77 +23,14 @@ operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke
 /**
  * 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 +1,146 @@
+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> =
+        FunctionalBinaryOperation(algebra, 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> =
+        FunctionalBinaryOperation(algebra, 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> =
+        FunctionalBinaryOperation(algebra, 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)
+}
+
+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()

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

@@ -30,11 +30,11 @@ object RealMatrixContext : GenericMatrixContext<Double, RealField> {
     override val elementContext 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>(
@@ -102,7 +102,7 @@ infix fun BufferMatrix<Double>.dot(other: BufferMatrix<Double>): BufferMatrix<Do
     val array = DoubleArray(this.rowNum * other.colNum)
 
     //convert to array to insure there is not memory indirection
-    fun Buffer<out Double>.unsafeArray(): DoubleArray = if (this is DoubleBuffer) {
+    fun Buffer<out Double>.unsafeArray(): DoubleArray = if (this is RealBuffer) {
         array
     } else {
         DoubleArray(size) { get(it) }
@@ -119,6 +119,6 @@ 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/LUPDecomposition.kt

@@ -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")
                 }
 

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

@@ -90,20 +90,20 @@ abstract class AutoDiffField<T : Any, F : Field<T>> : Field<Variable<T>> {
 
     // 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/operations/Algebra.kt

@@ -6,9 +6,43 @@ annotation class KMathContext
 /**
  * Marker interface for any algebra
  */
-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
+}
+
+/**
+ * An algebra with numeric representation of members
+ */
+interface NumericAlgebra<T> : Algebra<T> {
+    /**
+     * Wrap a number
+     */
+    fun number(value: Number): T
+
+    fun leftSideNumberOperation(operation: String, left: Number, right: T): T =
+        binaryOperation(operation, number(left), right)
+
+    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)
 
 /**
  * Space-like operations without neutral element
@@ -24,14 +58,34 @@ interface SpaceOperations<T> : Algebra<T> {
      */
     fun multiply(a: T, k: Number): T
 
-    //Operation to be performed in this context
+    //Operation to be performed in this context. Could be moved to extensions in case of KEEP-176
     operator fun T.unaryMinus(): T = multiply(this, -1.0)
 
+    operator fun T.unaryPlus(): T = this
+
     operator fun T.plus(b: T): T = add(this, b)
     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
+
+    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 {
+        const val PLUS_OPERATION = "+"
+        const val MINUS_OPERATION = "-"
+        const val NOT_OPERATION = "!"
+    }
 }
 
 
@@ -60,22 +114,48 @@ interface RingOperations<T> : SpaceOperations<T> {
     fun multiply(a: T, b: T): T
 
     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 {
+        const val TIMES_OPERATION = "*"
+    }
 }
 
 /**
  * The same as {@link Space} but with additional multiplication operation
  */
-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)
+    }
+
+
+    operator fun T.plus(b: Number) = this.plus(number(b))
+    operator fun Number.plus(b: T) = b + this
+
+    operator fun T.minus(b: Number) = this.minus(number(b))
+    operator fun Number.minus(b: T) = -b + this
 }
 
 /**
@@ -85,6 +165,15 @@ interface FieldOperations<T> : RingOperations<T> {
     fun divide(a: T, b: T): T
 
     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 {
+        const val DIV_OPERATION = "/"
+    }
 }
 
 /**

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

@@ -8,10 +8,12 @@ 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
  */
-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)
@@ -30,9 +32,11 @@ 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))
@@ -50,6 +54,12 @@ object ComplexField : ExtendedFieldOperations<Complex>, Field<Complex> {
     operator fun Complex.minus(d: Double) = add(this, -d.toComplex())
 
     operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
+
+    override fun symbol(value: String): Complex = if (value == "i") {
+        i
+    } else {
+        super.symbol(value)
+    }
 }
 
 /**

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

@@ -7,12 +7,32 @@ import kotlin.math.pow as kpow
  * Advanced Number-like field 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)
+    }
+}
+
+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.
@@ -44,6 +64,10 @@ object RealField : ExtendedField<Double>, Norm<Double, Double> {
 
     override inline fun sin(arg: Double) = kotlin.math.sin(arg)
     override inline fun cos(arg: 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())
 
@@ -75,6 +99,10 @@ object FloatField : ExtendedField<Float>, Norm<Float, Float> {
 
     override inline fun sin(arg: Float) = kotlin.math.sin(arg)
     override inline fun cos(arg: Float) = kotlin.math.cos(arg)
+    override inline fun tan(arg: Float) = kotlin.math.tan(arg)
+    override inline fun acos(arg: Float) = kotlin.math.acos(arg)
+    override inline fun asin(arg: Float) = kotlin.math.asin(arg)
+    override inline fun atan(arg: Float) = kotlin.math.atan(arg)
 
     override inline fun power(arg: Float, pow: Number) = arg.pow(pow.toFloat())
 

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

@@ -13,16 +13,33 @@ package scientifik.kmath.operations
 interface TrigonometricOperations<T> : FieldOperations<T> {
     fun sin(arg: T): T
     fun cos(arg: T): T
+    fun tan(arg: T): T
 
-    fun tg(arg: T): T = sin(arg) / cos(arg)
+    companion object {
+        const val SIN_OPERATION = "sin"
+        const val COS_OPERATION = "cos"
+        const val TAN_OPERATION = "tan"
+    }
+}
 
-    fun ctg(arg: T): T = cos(arg) / sin(arg)
+interface InverseTrigonometricOperations<T> : TrigonometricOperations<T> {
+    fun asin(arg: T): T
+    fun acos(arg: T): T
+    fun atan(arg: T): T
+
+    companion object {
+        const val ASIN_OPERATION = "asin"
+        const val ACOS_OPERATION = "acos"
+        const val ATAN_OPERATION = "atan"
+    }
 }
 
 fun <T : MathElement<out TrigonometricOperations<T>>> sin(arg: T): T = arg.context.sin(arg)
 fun <T : MathElement<out TrigonometricOperations<T>>> cos(arg: T): T = arg.context.cos(arg)
-fun <T : MathElement<out TrigonometricOperations<T>>> tg(arg: T): T = arg.context.tg(arg)
-fun <T : MathElement<out TrigonometricOperations<T>>> ctg(arg: T): T = arg.context.ctg(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> tan(arg: T): T = arg.context.tan(arg)
+fun <T : MathElement<out InverseTrigonometricOperations<T>>> asin(arg: T): T = arg.context.asin(arg)
+fun <T : MathElement<out InverseTrigonometricOperations<T>>> acos(arg: T): T = arg.context.acos(arg)
+fun <T : MathElement<out InverseTrigonometricOperations<T>>> atan(arg: T): T = arg.context.atan(arg)
 
 /* Power and roots */
 
@@ -34,6 +51,11 @@ interface PowerOperations<T> : Algebra<T> {
     fun sqrt(arg: T) = power(arg, 0.5)
 
     infix fun T.pow(pow: Number) = power(this, pow)
+
+    companion object {
+        const val POW_OPERATION = "pow"
+        const val SQRT_OPERATION = "sqrt"
+    }
 }
 
 infix fun <T : MathElement<out PowerOperations<T>>> T.pow(power: Double): T = context.power(this, power)
@@ -42,9 +64,14 @@ fun <T : MathElement<out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
 
 /* Exponential */
 
-interface ExponentialOperations<T>: Algebra<T> {
+interface ExponentialOperations<T> : Algebra<T> {
     fun exp(arg: T): T
     fun ln(arg: T): T
+
+    companion object {
+        const val EXP_OPERATION = "exp"
+        const val LN_OPERATION = "ln"
+    }
 }
 
 fun <T : MathElement<out ExponentialOperations<T>>> exp(arg: T): T = arg.context.exp(arg)
@@ -54,4 +81,4 @@ interface Norm<in T : Any, out R> {
     fun norm(arg: T): R
 }
 
-fun <T : MathElement<out Norm<T, R>>, R> norm(arg: T): R = arg.context.norm(arg)
+fun <T : MathElement<out Norm<T, R>>, R> norm(arg: T): R = arg.context.norm(arg)

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

@@ -37,9 +37,9 @@ interface Buffer<T> {
 
     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 +51,7 @@ 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>
@@ -93,7 +93,7 @@ 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>
@@ -109,12 +109,11 @@ 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) })
         }
     }
 }
 
-
 inline class ListBuffer<T>(val list: List<T>) : Buffer<T> {
 
     override val size: Int
@@ -163,57 +162,6 @@ class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
 
 fun <T> Array<T>.asBuffer(): ArrayBuffer<T> = ArrayBuffer(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
 

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

@@ -79,6 +79,13 @@ class ComplexNDField(override val shape: IntArray) :
 
     override fun cos(arg: NDBuffer<Complex>) = map(arg) { cos(it) }
 
+    override fun tan(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) { tan(it) }
+
+    override fun asin(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) { asin(it) }
+
+    override fun acos(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) {acos(it)}
+
+    override fun atan(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) {atan(it)}
 }
 
 

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

@@ -1,13 +1,8 @@
 package scientifik.kmath.structures
 
-import scientifik.kmath.operations.*
+import scientifik.kmath.operations.ExtendedField
 
-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>
+interface ExtendedNDField<T : Any, F : ExtendedField<T>, N : NDStructure<T>> : NDField<T, F, N>, ExtendedField<N>
 
 
 ///**

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

@@ -0,0 +1,53 @@
+package scientifik.kmath.structures
+
+import kotlin.experimental.and
+
+enum class ValueFlag(val mask: Byte) {
+    NAN(0b0000_0001),
+    MISSING(0b0000_0010),
+    NEGATIVE_INFINITY(0b0000_0100),
+    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) = getFlag(index) != 0.toByte()
+
+fun FlaggedBuffer<*>.hasFlag(index: Int, flag: ValueFlag) = (getFlag(index) and flag.mask) != 0.toByte()
+
+fun FlaggedBuffer<*>.isMissing(index: Int) = 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/IntBuffer.kt

@@ -0,0 +1,20 @@
+package scientifik.kmath.structures
+
+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)

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

@@ -0,0 +1,19 @@
+package scientifik.kmath.structures
+
+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)

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

@@ -1,6 +1,6 @@
 package scientifik.kmath.structures
 
-inline class DoubleBuffer(val array: DoubleArray) : MutableBuffer<Double> {
+inline class RealBuffer(val array: DoubleArray) : MutableBuffer<Double> {
     override val size: Int get() = array.size
 
     override fun get(index: Int): Double = array[index]
@@ -12,23 +12,23 @@ inline class DoubleBuffer(val array: DoubleArray) : MutableBuffer<Double> {
     override fun iterator() = array.iterator()
 
     override fun copy(): MutableBuffer<Double> =
-        DoubleBuffer(array.copyOf())
+        RealBuffer(array.copyOf())
 }
 
 @Suppress("FunctionName")
-inline fun DoubleBuffer(size: Int, init: (Int) -> Double): DoubleBuffer = DoubleBuffer(DoubleArray(size) { init(it) })
+inline fun RealBuffer(size: Int, init: (Int) -> Double): RealBuffer = RealBuffer(DoubleArray(size) { init(it) })
 
 @Suppress("FunctionName")
-fun DoubleBuffer(vararg doubles: Double): DoubleBuffer = DoubleBuffer(doubles)
+fun RealBuffer(vararg doubles: Double): RealBuffer = RealBuffer(doubles)
 
 /**
  * Transform buffer of doubles into array for high performance operations
  */
 val MutableBuffer<out Double>.array: DoubleArray
-    get() = if (this is DoubleBuffer) {
+    get() = if (this is RealBuffer) {
         array
     } else {
         DoubleArray(size) { get(it) }
     }
 
-fun DoubleArray.asBuffer() = DoubleBuffer(this)
+fun DoubleArray.asBuffer() = RealBuffer(this)

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

@@ -9,145 +9,172 @@ import kotlin.math.*
  * A simple field over linear buffers of [Double]
  */
 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]) })
 }
 
 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

@@ -16,7 +16,7 @@ class RealNDField(override val shape: IntArray) :
     override val one 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
@@ -74,6 +74,13 @@ class RealNDField(override val shape: IntArray) :
 
     override fun cos(arg: NDBuffer<Double>) = 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) }
 }
 
 
@@ -82,7 +89,7 @@ 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))
 }
 
 /**
@@ -96,7 +103,7 @@ inline fun RealNDElement.mapIndexed(crossinline transform: RealField.(index: Int
  */
 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))
 }
 
 /**

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

@@ -0,0 +1,20 @@
+package scientifik.kmath.structures
+
+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)

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/jvmMain/kotlin/scientifik/kmath/operations/BigNumbers.kt

@@ -1,10 +1,12 @@
 package scientifik.kmath.operations
 
-import scientifik.kmath.structures.*
 import java.math.BigDecimal
 import java.math.BigInteger
 import java.math.MathContext
 
+/**
+ * A field wrapper for Java [BigInteger]
+ */
 object JBigIntegerField : Field<BigInteger> {
     override val zero: BigInteger = BigInteger.ZERO
     override val one: BigInteger = BigInteger.ONE
@@ -18,6 +20,9 @@ object JBigIntegerField : Field<BigInteger> {
     override fun divide(a: BigInteger, b: BigInteger): BigInteger = a.div(b)
 }
 
+/**
+ * A Field wrapper for Java [BigDecimal]
+ */
 class JBigDecimalField(val mathContext: MathContext = MathContext.DECIMAL64) : Field<BigDecimal> {
     override val zero: BigDecimal = BigDecimal.ZERO
     override val one: BigDecimal = BigDecimal.ONE

kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/streaming/BufferFlow.kt

@@ -5,7 +5,7 @@ import kotlinx.coroutines.flow.*
 import scientifik.kmath.chains.BlockingRealChain
 import scientifik.kmath.structures.Buffer
 import scientifik.kmath.structures.BufferFactory
-import scientifik.kmath.structures.DoubleBuffer
+import scientifik.kmath.structures.RealBuffer
 import scientifik.kmath.structures.asBuffer
 
 /**
@@ -45,7 +45,7 @@ fun <T> Flow<T>.chunked(bufferSize: Int, bufferFactory: BufferFactory<T>): Flow<
 /**
  * Specialized flow chunker for real buffer
  */
-fun Flow<Double>.chunked(bufferSize: Int): Flow<DoubleBuffer> = flow {
+fun Flow<Double>.chunked(bufferSize: Int): Flow<RealBuffer> = flow {
     require(bufferSize > 0) { "Resulting chunk size must be more than zero" }
 
     if (this@chunked is BlockingRealChain) {
@@ -61,13 +61,13 @@ fun Flow<Double>.chunked(bufferSize: Int): Flow<DoubleBuffer> = flow {
             array[counter] = element
             counter++
             if (counter == bufferSize) {
-                val buffer = DoubleBuffer(array)
+                val buffer = RealBuffer(array)
                 emit(buffer)
                 counter = 0
             }
         }
         if (counter > 0) {
-            emit(DoubleBuffer(counter) { array[it] })
+            emit(RealBuffer(counter) { array[it] })
         }
     }
 }

kmath-for-real/src/commonMain/kotlin/scientifik/kmath/real/RealVector.kt

@@ -7,31 +7,28 @@ import scientifik.kmath.operations.Norm
 import scientifik.kmath.operations.RealField
 import scientifik.kmath.operations.SpaceElement
 import scientifik.kmath.structures.Buffer
-import scientifik.kmath.structures.DoubleBuffer
+import scientifik.kmath.structures.RealBuffer
 import scientifik.kmath.structures.asBuffer
 import scientifik.kmath.structures.asIterable
 import kotlin.math.sqrt
 
+typealias RealPoint = Point<Double>
+
 fun DoubleArray.asVector() = RealVector(this.asBuffer())
 fun List<Double>.asVector() = RealVector(this.asBuffer())
 
-
 object VectorL2Norm : Norm<Point<out Number>, Double> {
     override fun norm(arg: Point<out Number>): Double = sqrt(arg.asIterable().sumByDouble { it.toDouble() })
 }
 
 inline class RealVector(private val point: Point<Double>) :
-    SpaceElement<Point<Double>, RealVector, VectorSpace<Double, RealField>>, Point<Double> {
+    SpaceElement<RealPoint, RealVector, VectorSpace<Double, RealField>>, RealPoint {
 
-    override val context: VectorSpace<Double, RealField>
-        get() = space(
-            point.size
-        )
+    override val context: VectorSpace<Double, RealField> get() = space(point.size)
 
-    override fun unwrap(): Point<Double> = point
+    override fun unwrap(): RealPoint = point
 
-    override fun Point<Double>.wrap(): RealVector =
-        RealVector(this)
+    override fun RealPoint.wrap(): RealVector = RealVector(this)
 
     override val size: Int get() = point.size
 
@@ -44,16 +41,12 @@ inline class RealVector(private val point: Point<Double>) :
         private val spaceCache = HashMap<Int, BufferVectorSpace<Double, RealField>>()
 
         inline operator fun invoke(dim: Int, initializer: (Int) -> Double) =
-            RealVector(DoubleBuffer(dim, initializer))
+            RealVector(RealBuffer(dim, initializer))
 
         operator fun invoke(vararg values: Double): RealVector = values.asVector()
 
-        fun space(dim: Int): BufferVectorSpace<Double, RealField> =
-            spaceCache.getOrPut(dim) {
-                BufferVectorSpace(
-                    dim,
-                    RealField
-                ) { size, init -> Buffer.real(size, init) }
-            }
+        fun space(dim: Int): BufferVectorSpace<Double, RealField> = spaceCache.getOrPut(dim) {
+            BufferVectorSpace(dim, RealField) { size, init -> Buffer.real(size, init) }
+        }
     }
 }

kmath-for-real/src/commonMain/kotlin/scientifik/kmath/real/realBuffer.kt

@@ -1,8 +1,8 @@
 package scientifik.kmath.real
 
-import scientifik.kmath.structures.DoubleBuffer
+import scientifik.kmath.structures.RealBuffer
 
 /**
- * Simplified [DoubleBuffer] to array comparison
+ * Simplified [RealBuffer] to array comparison
  */
-fun DoubleBuffer.contentEquals(vararg doubles: Double) = array.contentEquals(doubles)
+fun RealBuffer.contentEquals(vararg doubles: Double) = array.contentEquals(doubles)

kmath-for-real/src/commonMain/kotlin/scientifik/kmath/real/realMatrix.kt

@@ -5,8 +5,8 @@ import scientifik.kmath.linear.RealMatrixContext.elementContext
 import scientifik.kmath.linear.VirtualMatrix
 import scientifik.kmath.operations.sum
 import scientifik.kmath.structures.Buffer
-import scientifik.kmath.structures.DoubleBuffer
 import scientifik.kmath.structures.Matrix
+import scientifik.kmath.structures.RealBuffer
 import scientifik.kmath.structures.asIterable
 import kotlin.math.pow
 
@@ -27,6 +27,10 @@ typealias RealMatrix = Matrix<Double>
 fun realMatrix(rowNum: Int, colNum: Int, initializer: (i: Int, j: Int) -> Double): RealMatrix =
     MatrixContext.real.produce(rowNum, colNum, initializer)
 
+fun Array<DoubleArray>.toMatrix(): RealMatrix{
+    return MatrixContext.real.produce(size, this[0].size) { row, col -> this[row][col] }
+}
+
 fun Sequence<DoubleArray>.toMatrix(): RealMatrix = toList().let {
     MatrixContext.real.produce(it.size, it[0].size) { row, col -> it[row][col] }
 }
@@ -129,22 +133,22 @@ fun Matrix<Double>.extractColumns(columnRange: IntRange): RealMatrix =
 fun Matrix<Double>.extractColumn(columnIndex: Int): RealMatrix =
     extractColumns(columnIndex..columnIndex)
 
-fun Matrix<Double>.sumByColumn(): DoubleBuffer = DoubleBuffer(colNum) { j ->
+fun Matrix<Double>.sumByColumn(): RealBuffer = RealBuffer(colNum) { j ->
     val column = columns[j]
     with(elementContext) {
         sum(column.asIterable())
     }
 }
 
-fun Matrix<Double>.minByColumn(): DoubleBuffer = DoubleBuffer(colNum) { j ->
+fun Matrix<Double>.minByColumn(): RealBuffer = RealBuffer(colNum) { j ->
     columns[j].asIterable().min() ?: throw Exception("Cannot produce min on empty column")
 }
 
-fun Matrix<Double>.maxByColumn(): DoubleBuffer = DoubleBuffer(colNum) { j ->
+fun Matrix<Double>.maxByColumn(): RealBuffer = RealBuffer(colNum) { j ->
     columns[j].asIterable().max() ?: throw Exception("Cannot produce min on empty column")
 }
 
-fun Matrix<Double>.averageByColumn(): DoubleBuffer = DoubleBuffer(colNum) { j ->
+fun Matrix<Double>.averageByColumn(): RealBuffer = RealBuffer(colNum) { j ->
     columns[j].asIterable().average()
 }
 

kmath-histograms/src/commonMain/kotlin/scientifik/kmath/histogram/Histogram.kt

@@ -1,17 +1,9 @@
 package scientifik.kmath.histogram
 
+import scientifik.kmath.domains.Domain
 import scientifik.kmath.linear.Point
 import scientifik.kmath.structures.ArrayBuffer
-import scientifik.kmath.structures.DoubleBuffer
-
-/**
- * A simple geometric domain
- * TODO move to geometry module
- */
-interface Domain<T : Any> {
-    operator fun contains(vector: Point<out T>): Boolean
-    val dimension: Int
-}
+import scientifik.kmath.structures.RealBuffer
 
 /**
  * The bin in the histogram. The histogram is by definition always done in the real space
@@ -51,9 +43,9 @@ interface MutableHistogram<T : Any, out B : Bin<T>> : Histogram<T, B> {
 fun <T : Any> MutableHistogram<T, *>.put(vararg point: T) = put(ArrayBuffer(point))
 
 fun MutableHistogram<Double, *>.put(vararg point: Number) =
-    put(DoubleBuffer(point.map { it.toDouble() }.toDoubleArray()))
+    put(RealBuffer(point.map { it.toDouble() }.toDoubleArray()))
 
-fun MutableHistogram<Double, *>.put(vararg point: Double) = put(DoubleBuffer(point))
+fun MutableHistogram<Double, *>.put(vararg point: Double) = put(RealBuffer(point))
 
 fun <T : Any> MutableHistogram<T, *>.fill(sequence: Iterable<Point<T>>) = sequence.forEach { put(it) }
 

kmath-histograms/src/commonMain/kotlin/scientifik/kmath/histogram/RealHistogram.kt

@@ -1,8 +1,8 @@
 package scientifik.kmath.histogram
 
 import scientifik.kmath.linear.Point
-import scientifik.kmath.real.asVector
 import scientifik.kmath.operations.SpaceOperations
+import scientifik.kmath.real.asVector
 import scientifik.kmath.structures.*
 import kotlin.math.floor
 
@@ -21,7 +21,7 @@ data class BinDef<T : Comparable<T>>(val space: SpaceOperations<Point<T>>, val c
 
 class MultivariateBin<T : Comparable<T>>(val def: BinDef<T>, override val value: Number) : Bin<T> {
 
-    override fun contains(vector: Point<out T>): Boolean = def.contains(vector)
+    override fun contains(point: Point<T>): Boolean = def.contains(point)
 
     override val dimension: Int
         get() = def.center.size
@@ -50,7 +50,7 @@ class RealHistogram(
     override val dimension: Int get() = lower.size
 
 
-    private val binSize = DoubleBuffer(dimension) { (upper[it] - lower[it]) / binNums[it] }
+    private val binSize = RealBuffer(dimension) { (upper[it] - lower[it]) / binNums[it] }
 
     init {
         // argument checks

kmath-histograms/src/jvmMain/kotlin/scientifik/kmath/histogram/UnivariateHistogram.kt

@@ -16,7 +16,7 @@ class UnivariateBin(val position: Double, val size: Double, val counter: LongCou
 
     operator fun contains(value: Double): Boolean = value in (position - size / 2)..(position + size / 2)
 
-    override fun contains(vector: Buffer<out Double>): Boolean = contains(vector[0])
+    override fun contains(point: Buffer<Double>): Boolean = contains(point[0])
 
     internal operator fun inc() = this.also { counter.increment() }
 

kmath-memory/src/commonMain/kotlin/scientifik/memory/MemorySpec.kt

@@ -10,6 +10,7 @@ interface MemorySpec<T : Any> {
     val objectSize: Int
 
     fun MemoryReader.read(offset: Int): T
+    //TODO consider thread safety
     fun MemoryWriter.write(offset: Int, value: T)
 }
 

settings.gradle.kts

@@ -3,10 +3,12 @@ pluginManagement {
     val toolsVersion = "0.5.0"
 
     plugins {
+        id("kotlinx.benchmark") version "0.2.0-dev-8"
         id("scientifik.mpp") version toolsVersion
         id("scientifik.jvm") version toolsVersion
         id("scientifik.atomic") version toolsVersion
         id("scientifik.publish") version toolsVersion
+        kotlin("plugin.allopen") version "1.3.72"
     }
 
     repositories {
@@ -45,5 +47,6 @@ include(
     ":kmath-dimensions",
     ":kmath-for-real",
     ":kmath-geometry",
+    ":kmath-ast",
     ":examples"
 )