examples/build.gradle.kts

@@ -27,6 +27,7 @@ dependencies {
     implementation(project(":kmath-nd4j"))
     implementation(project(":kmath-tensors"))
     implementation(project(":kmath-symja"))
+    implementation(project(":kmath-units"))
     implementation(project(":kmath-for-real"))
 
     implementation("org.nd4j:nd4j-native:1.0.0-beta7")
@@ -52,12 +53,13 @@ kotlin.sourceSets.all {
     with(languageSettings) {
         useExperimentalAnnotation("kotlin.contracts.ExperimentalContracts")
         useExperimentalAnnotation("kotlin.ExperimentalUnsignedTypes")
+        useExperimentalAnnotation("kotlin.time.ExperimentalTime")
         useExperimentalAnnotation("space.kscience.kmath.misc.UnstableKMathAPI")
     }
 }
 
 tasks.withType<org.jetbrains.kotlin.gradle.tasks.KotlinCompile> {
-    kotlinOptions{
+    kotlinOptions {
         jvmTarget = "11"
         freeCompilerArgs = freeCompilerArgs + "-Xjvm-default=all" + "-Xopt-in=kotlin.RequiresOptIn"
     }

examples/src/main/kotlin/space/kscience/kmath/units/main.kt

@@ -0,0 +1,37 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.units
+
+import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.units.*
+
+fun main() {
+    var res = with(DoubleField.measurement()) {
+        val a = (2.0 * kg) / (3.0 * m) / (2.0 * with(MeasureAlgebra) { s * s })
+        val b = (23.0 * Pa)
+        a + b
+    }
+
+    println(res)
+
+    res = with(DoubleField.measurement()) {
+        val a = (2.0 * G(m)) + (3.0 * M(m))
+        val b = (3.0 * au)
+        a + b
+    }
+
+    println(res)
+
+    res = with(DoubleField.measurement()) {
+        val P = 100000.0 * Pa
+        val V = 0.0227 * (m pow 3)
+        val nu = 1.0 * mol
+        val T = 273.0 * K
+        P * V / (nu * T)
+    }
+
+    println(res)
+}

examples/src/main/kotlin/space/kscience/kmath/units/perf.kt

@@ -0,0 +1,33 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.units
+
+import space.kscience.kmath.operations.DoubleField
+import kotlin.random.Random
+import kotlin.time.measureTime
+
+fun main() {
+    var rng = Random(0)
+    var sum1 = 0.0
+
+    measureTime {
+        repeat(10000000) { sum1 += rng.nextDouble() }
+    }.also(::println)
+
+    println(sum1)
+
+    rng = Random(0)
+
+    with(DoubleField.measurement()) {
+        var sum2 = 0.0 * Pa
+
+        measureTime {
+            repeat(10000000) { sum2 += rng.nextDouble() * Pa }
+        }.also(::println)
+
+        println(sum2)
+    }
+}

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SplineIntegrator.kt

@@ -10,6 +10,7 @@ import space.kscience.kmath.functions.integrate
 import space.kscience.kmath.interpolation.PolynomialInterpolator
 import space.kscience.kmath.interpolation.SplineInterpolator
 import space.kscience.kmath.interpolation.interpolatePolynomials
+import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.Field
@@ -23,6 +24,7 @@ import space.kscience.kmath.structures.map
 /**
  * Compute analytical indefinite integral of this [PiecewisePolynomial], keeping all intervals intact
  */
+@PerformancePitfall
 @UnstableKMathAPI
 public fun <T : Comparable<T>> PiecewisePolynomial<T>.integrate(algebra: Field<T>): PiecewisePolynomial<T> =
     PiecewisePolynomial(pieces.map { it.first to it.second.integrate(algebra) })

kmath-units/build.gradle.kts

@@ -0,0 +1,15 @@
+import ru.mipt.npm.gradle.Maturity
+
+plugins {
+    id("ru.mipt.npm.gradle.mpp")
+}
+
+kotlin.sourceSets.commonMain {
+    dependencies {
+        api(project(":kmath-core"))
+    }
+}
+
+readme {
+    maturity = Maturity.PROTOTYPE
+}

kmath-units/src/commonMain/kotlin/space/kscience/kmath/units/units.kt

@@ -0,0 +1,276 @@
+package space.kscience.kmath.units
+
+import space.kscience.kmath.operations.*
+import kotlin.jvm.JvmName
+import kotlin.math.PI
+import kotlin.math.pow
+
+/**
+ * Represents base units of International System of Units.
+ */
+public enum class BaseUnits {
+    /**
+     * The base unit of time.
+     */
+    SECOND,
+
+    /**
+     * The base unit of length.
+     */
+    METER,
+
+    /**
+     * The base unit of mass.
+     */
+    KILOGRAM,
+
+    /**
+     * The base unit of electric current.
+     */
+    AMPERE,
+
+    /**
+     * The base unit of thermodynamic temperature.
+     */
+    KELVIN,
+
+    /**
+     * The base unit of amount of substance.
+     */
+    MOLE,
+
+    /**
+     * The base unit of luminous intensity.
+     */
+    CANDELA;
+}
+
+/**
+ * Represents a unit.
+ *
+ * @property chain chain of multipliers consisting of [BaseUnits] unit and its power.
+ * @property multiplier a scalar to multiply an element applied to this unit.
+ */
+public data class Measure internal constructor(
+    val chain: Map<BaseUnits, Int> = emptyMap(),
+    val multiplier: Double = 1.0,
+)
+
+internal fun Measure(vararg chain: Pair<BaseUnits, Int>, multiplier: Double = 1.0): Measure =
+    Measure(mapOf(*chain), multiplier)
+
+public data class Measurement<out T>(val measure: Measure, val value: T)
+
+public object MeasureAlgebra : Algebra<Measure> {
+    public const val MULTIPLY_OPERATION: String = "*"
+    public const val DIVIDE_OPERATION: String = "/"
+
+    public fun multiply(a: Measure, b: Measure): Measure {
+        val newChain = mutableMapOf<BaseUnits, Int>()
+
+        a.chain.forEach { (k, v) ->
+            val cur = newChain[k]
+            if (cur != null) newChain[k] = cur + v
+            else newChain[k] = v
+        }
+
+        b.chain.forEach { (k, v) ->
+            val cur = newChain[k]
+            if (cur != null) newChain[k] = cur + v
+            else newChain[k] = v
+        }
+
+        return Measure(newChain, a.multiplier * b.multiplier)
+    }
+
+    public fun divide(a: Measure, b: Measure): Measure =
+        multiply(a, b.copy(chain = b.chain.mapValues { (_, v) -> -v }))
+
+    public operator fun Measure.times(b: Measure): Measure = multiply(this, b)
+    public operator fun Measure.div(b: Measure): Measure = divide(this, b)
+
+    override fun binaryOperationFunction(operation: String): (left: Measure, right: Measure) -> Measure =
+        when (operation) {
+            MULTIPLY_OPERATION -> ::multiply
+            DIVIDE_OPERATION -> ::divide
+            else -> super.binaryOperationFunction(operation)
+        }
+}
+
+/**
+ * A measure for dimensionless quantities with multiplier `1.0`.
+ */
+public val pure: Measure = Measure()
+
+/**
+ * A measure for [BaseUnits.METER] of power `1.0` with multiplier `1.0`.
+ */
+public val m: Measure = Measure(BaseUnits.METER to 1)
+
+/**
+ * A measure for [BaseUnits.KILOGRAM] of power `1.0` with multiplier `1.0`.
+ */
+public val kg: Measure = Measure(BaseUnits.KILOGRAM to 1)
+
+/**
+ * A measure for [BaseUnits.SECOND] of power `1.0` with multiplier `1.0`.
+ */
+@get:JvmName("s-seconds")
+public val s: Measure = Measure(BaseUnits.SECOND to 1)
+
+/**
+ * A measure for [BaseUnits.AMPERE] of power `1.0` with multiplier `1.0`.
+ */
+public val A: Measure = Measure(BaseUnits.AMPERE to 1)
+
+/**
+ * A measure for [BaseUnits.KELVIN] of power `1.0` with multiplier `1.0`.
+ */
+public val K: Measure = Measure(BaseUnits.KELVIN to 1)
+
+/**
+ * A measure for [BaseUnits.MOLE] of power `1.0` with multiplier `1.0`.
+ */
+public val mol: Measure = Measure(BaseUnits.MOLE to 1)
+
+/**
+ * A measure for [BaseUnits.CANDELA] of power `1.0` with multiplier `1.0`.
+ */
+public val cd: Measure = Measure(BaseUnits.CANDELA to 1)
+
+public val rad: Measure = pure
+public val sr: Measure = pure
+public val degC: Measure = K
+public val Hz: Measure = MeasureAlgebra { pure / s }
+public val N: Measure = MeasureAlgebra { kg * m * (pure / (s * s)) }
+public val J: Measure = MeasureAlgebra { N * m }
+public val W: Measure = MeasureAlgebra { J / s }
+public val Pa: Measure = MeasureAlgebra { N / (m * m) }
+public val lm: Measure = MeasureAlgebra { cd * sr }
+public val lx: Measure = MeasureAlgebra { lm / (m * m) }
+public val C: Measure = MeasureAlgebra { A * s }
+public val V: Measure = MeasureAlgebra { J / C }
+public val Ohm: Measure = MeasureAlgebra { V / A }
+public val F: Measure = MeasureAlgebra { C / V }
+public val Wb: Measure = MeasureAlgebra { kg * m * m * (pure / (s * s)) * (pure / A) }
+
+@get:JvmName("T-tesla")
+public val T: Measure = MeasureAlgebra { Wb / (m * m) }
+
+@get:JvmName("H-henry")
+public val H: Measure = MeasureAlgebra { kg * m * m * (pure / (s * s)) * (pure / (A * A)) }
+
+public val S: Measure = MeasureAlgebra { pure / Ohm }
+public val Bq: Measure = MeasureAlgebra { pure / s }
+public val Gy: Measure = MeasureAlgebra { J / kg }
+public val Sv: Measure = MeasureAlgebra { J / kg }
+public val kat: Measure = MeasureAlgebra { mol / s }
+
+public val g: Measure = Measure(BaseUnits.KILOGRAM to 1, multiplier = 0.001)
+public val min: Measure = Measure(BaseUnits.SECOND to 1, multiplier = 60.0)
+public val h: Measure = Measure(BaseUnits.SECOND to 1, multiplier = 3600.0)
+public val d: Measure = Measure(BaseUnits.SECOND to 1, multiplier = 86_400.0)
+public val au: Measure = Measure(BaseUnits.METER to 1, multiplier = 149_597_870_700.0)
+public val deg: Measure = Measure(multiplier = PI / 180.0)
+public val arcMin: Measure = Measure(multiplier = PI / 10_800.0)
+public val arcS: Measure = Measure(multiplier = PI / 648_000.0)
+public val ha: Measure = Measure(BaseUnits.METER to 2, multiplier = 10000.0)
+public val l: Measure = Measure(BaseUnits.METER to 3, multiplier = 0.001)
+public val t: Measure = Measure(BaseUnits.KILOGRAM to 1, multiplier = 1000.0)
+public val Da: Measure = Measure(BaseUnits.KILOGRAM to 1, multiplier = 1.660_539_040_202_020 * 10e-27)
+public val eV: Measure = J.copy(multiplier = 1.602_176_634 * 10e-19)
+
+public fun Y(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e24)
+public fun Z(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e21)
+public fun E(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e18)
+public fun P(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e15)
+public fun T(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e12)
+public fun G(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e9)
+public fun M(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e6)
+public fun k(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e3)
+public fun h(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e2)
+public fun da(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e1)
+
+public fun y(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-24)
+public fun z(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-21)
+public fun a(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-18)
+public fun f(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-15)
+public fun p(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-12)
+public fun n(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-9)
+public fun u(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-6)
+public fun m(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-3)
+public fun c(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-2)
+public fun d(measure: Measure): Measure = measure.copy(multiplier = measure.multiplier * 1e-1)
+
+public infix fun Measure.pow(power: Int): Measure =
+    copy(chain = chain.mapValues { (_, v) -> IntRing.power(v, power.toUInt()) }, multiplier = multiplier.pow(power))
+
+public open class MeasurementAlgebra<T>(public open val algebra: Algebra<T>) : Algebra<Measurement<T>> {
+    public operator fun T.times(m: Measure): Measurement<T> = Measurement(m, this)
+    public operator fun Measurement<T>.times(m: Measure): Measurement<T> =
+        copy(measure = MeasureAlgebra { measure * m })
+
+    public override fun bindSymbol(value: String): Measurement<T> = algebra.bindSymbol(value) * pure
+}
+
+public fun <T> Algebra<T>.measurement(): MeasurementAlgebra<T> = MeasurementAlgebra(this)
+
+public open class MeasurementSpace<T, out A>(public override val algebra: A) : MeasurementAlgebra<T>(algebra),
+    Group<Measurement<T>>, ScaleOperations<Measurement<T>> where A : Group<T>, A : ScaleOperations<T> {
+    public override val zero: Measurement<T>
+        get() = Measurement(pure, algebra.zero)
+
+    public override fun add(a: Measurement<T>, b: Measurement<T>): Measurement<T> {
+        require(a.measure.chain == b.measure.chain) {
+            "The units are incompatible. The chains are ${a.measure.chain} and ${b.measure.chain}"
+        }
+
+        return a.copy(value = algebra { a.value * a.measure.multiplier + b.value * b.measure.multiplier })
+    }
+
+    public override fun scale(a: Measurement<T>, value: Double): Measurement<T> =
+        Measurement(a.measure, algebra { a.value * value })
+
+    override fun Measurement<T>.unaryMinus(): Measurement<T> = copy(value = algebra { -value })
+}
+
+public fun <T, A> A.measurement(): MeasurementSpace<T, A> where A : Group<T>, A : ScaleOperations<T> = MeasurementSpace(this)
+
+public open class MeasurementRing<T, out A>(override val algebra: A) : MeasurementSpace<T, A>(algebra),
+    Ring<Measurement<T>> where A : ScaleOperations<T>, A : Ring<T> {
+    public override val one: Measurement<T>
+        get() = Measurement(pure, algebra.one)
+
+    public override fun multiply(a: Measurement<T>, b: Measurement<T>): Measurement<T> =
+        Measurement(MeasureAlgebra { a.measure * b.measure }, algebra { a.value * b.value })
+}
+
+public fun <T, A> A.measurement(): MeasurementRing<T, A> where A : Ring<T>, A : ScaleOperations<T> = MeasurementRing(this)
+
+public open class MeasurementField<T>(public override val algebra: Field<T>) : MeasurementRing<T, Field<T>>(algebra),
+    Field<Measurement<T>> {
+    public override fun divide(a: Measurement<T>, b: Measurement<T>): Measurement<T> =
+        Measurement(MeasureAlgebra { a.measure / b.measure }, algebra { a.value / b.value })
+}
+
+public fun <T> Field<T>.measurement(): MeasurementField<T> = MeasurementField(this)
+
+public open class MeasurementExtendedField<T>(public override val algebra: ExtendedField<T>) :
+    MeasurementField<T>(algebra),
+    ExtendedField<Measurement<T>> {
+    public override fun number(value: Number): Measurement<T> = Measurement(pure, algebra.number(value))
+    public override fun sin(arg: Measurement<T>): Measurement<T> = Measurement(arg.measure, algebra.sin(arg.value))
+    public override fun cos(arg: Measurement<T>): Measurement<T> = Measurement(arg.measure, algebra.cos(arg.value))
+    public override fun tan(arg: Measurement<T>): Measurement<T> = Measurement(arg.measure, algebra.tan(arg.value))
+    public override fun asin(arg: Measurement<T>): Measurement<T> = Measurement(arg.measure, algebra.asin(arg.value))
+    public override fun acos(arg: Measurement<T>): Measurement<T> = Measurement(arg.measure, algebra.acos(arg.value))
+    public override fun atan(arg: Measurement<T>): Measurement<T> = Measurement(arg.measure, algebra.atan(arg.value))
+
+    public override fun power(arg: Measurement<T>, pow: Number): Measurement<T> =
+        (this as Field<Measurement<T>>).power(arg, pow.toInt())
+
+    public override fun exp(arg: Measurement<T>): Measurement<T> = Measurement(arg.measure, algebra.exp(arg.value))
+    public override fun ln(arg: Measurement<T>): Measurement<T> = Measurement(arg.measure, algebra.ln(arg.value))
+}
+
+public fun <T> ExtendedField<T>.measurement(): MeasurementExtendedField<T> = MeasurementExtendedField(this)

settings.gradle.kts

@@ -36,6 +36,7 @@ include(
     ":kmath-kotlingrad",
     ":kmath-tensors",
     ":kmath-jupyter",
+    ":kmath-units",
     ":kmath-symja",
     ":kmath-jafama",
     ":examples",