Merge pull request #118 from mipt-npm/hyp-trig-functions

Implement hyperbolic functions for various Algebras

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

@@ -84,9 +84,9 @@ object MstExtendedField : ExtendedField<MST> {
 
     override fun sin(arg: MST): MST = unaryOperation(TrigonometricOperations.SIN_OPERATION, arg)
     override fun cos(arg: MST): MST = unaryOperation(TrigonometricOperations.COS_OPERATION, arg)
-    override fun asin(arg: MST): MST = unaryOperation(InverseTrigonometricOperations.ASIN_OPERATION, arg)
+    override fun asin(arg: MST): MST = unaryOperation(TrigonometricOperations.ASIN_OPERATION, arg)
-    override fun acos(arg: MST): MST = unaryOperation(InverseTrigonometricOperations.ACOS_OPERATION, arg)
+    override fun acos(arg: MST): MST = unaryOperation(TrigonometricOperations.ACOS_OPERATION, arg)
-    override fun atan(arg: MST): MST = unaryOperation(InverseTrigonometricOperations.ATAN_OPERATION, arg)
+    override fun atan(arg: MST): MST = unaryOperation(TrigonometricOperations.ATAN_OPERATION, arg)
     override fun add(a: MST, b: MST): MST = MstField.add(a, b)
     override fun multiply(a: MST, k: Number): MST = MstField.multiply(a, k)
     override fun multiply(a: MST, b: MST): MST = MstField.multiply(a, b)

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

@@ -17,7 +17,6 @@ class DerivativeStructureField(
 ) : ExtendedField<DerivativeStructure> {
 
     override val zero: DerivativeStructure by lazy { DerivativeStructure(order, parameters.size) }
-
     override val one: DerivativeStructure by lazy { DerivativeStructure(order, parameters.size, 1.0) }
 
     private val variables: Map<String, DerivativeStructure> = parameters.mapValues { (key, value) ->
@@ -60,10 +59,18 @@ class DerivativeStructureField(
 
     override fun sin(arg: DerivativeStructure): DerivativeStructure = arg.sin()
     override fun cos(arg: DerivativeStructure): DerivativeStructure = arg.cos()
+    override fun tan(arg: DerivativeStructure): DerivativeStructure = arg.tan()
     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 sinh(arg: DerivativeStructure): DerivativeStructure = arg.sinh()
+    override fun cosh(arg: DerivativeStructure): DerivativeStructure = arg.cosh()
+    override fun tanh(arg: DerivativeStructure): DerivativeStructure = arg.tanh()
+    override fun asinh(arg: DerivativeStructure): DerivativeStructure = arg.asinh()
+    override fun acosh(arg: DerivativeStructure): DerivativeStructure = arg.acosh()
+    override fun atanh(arg: DerivativeStructure): DerivativeStructure = arg.atanh()
+
     override fun power(arg: DerivativeStructure, pow: Number): DerivativeStructure = when (pow) {
         is Double -> arg.pow(pow)
         is Int -> arg.pow(pow)
@@ -71,9 +78,7 @@ class DerivativeStructureField(
     }
 
     fun power(arg: DerivativeStructure, pow: DerivativeStructure): DerivativeStructure = arg.pow(pow)
-
     override fun exp(arg: DerivativeStructure): DerivativeStructure = arg.exp()
-
     override fun ln(arg: DerivativeStructure): DerivativeStructure = arg.log()
 
     override operator fun DerivativeStructure.plus(b: Number): DerivativeStructure = add(b.toDouble())

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

@@ -139,15 +139,9 @@ open class FunctionalExpressionExtendedField<T, A>(algebra: A) :
     ExtendedField<Expression<T>> where A : ExtendedField<T>, A : NumericAlgebra<T> {
     override fun sin(arg: Expression<T>): Expression<T> = unaryOperation(TrigonometricOperations.SIN_OPERATION, arg)
     override fun cos(arg: Expression<T>): Expression<T> = unaryOperation(TrigonometricOperations.COS_OPERATION, arg)
-
+    override fun asin(arg: Expression<T>): Expression<T> = unaryOperation(TrigonometricOperations.ASIN_OPERATION, arg)
-    override fun asin(arg: Expression<T>): Expression<T> =
+    override fun acos(arg: Expression<T>): Expression<T> = unaryOperation(TrigonometricOperations.ACOS_OPERATION, arg)
-        unaryOperation(InverseTrigonometricOperations.ASIN_OPERATION, arg)
+    override fun atan(arg: Expression<T>): Expression<T> = unaryOperation(TrigonometricOperations.ATAN_OPERATION, arg)
-
-    override fun acos(arg: Expression<T>): Expression<T> =
-        unaryOperation(InverseTrigonometricOperations.ACOS_OPERATION, arg)
-
-    override fun atan(arg: Expression<T>): Expression<T> =
-        unaryOperation(InverseTrigonometricOperations.ATAN_OPERATION, arg)
 
     override fun power(arg: Expression<T>, pow: Number): Expression<T> =
         binaryOperation(PowerOperations.POW_OPERATION, arg, number(pow))

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

@@ -153,7 +153,7 @@ object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex> {
      */
     operator fun Double.times(c: Complex): Complex = Complex(c.re * this, c.im * this)
 
-    override fun norm(arg: Complex): Complex = arg.conjugate * arg
+    override fun norm(arg: Complex): Complex = sqrt(arg.conjugate * arg)
 
     override fun symbol(value: String): Complex = if (value == "i") i else super.symbol(value)
 }

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

@@ -1,5 +1,6 @@
 package scientifik.kmath.operations
 
+import scientifik.kmath.operations.RealField.pow
 import kotlin.math.abs
 import kotlin.math.pow as kpow
 
@@ -7,19 +8,28 @@ import kotlin.math.pow as kpow
  * Advanced Number-like semifield that implements basic operations.
  */
 interface ExtendedFieldOperations<T> :
-    InverseTrigonometricOperations<T>,
+    FieldOperations<T>,
+    TrigonometricOperations<T>,
+    HyperbolicOperations<T>,
     PowerOperations<T>,
     ExponentialOperations<T> {
 
     override fun tan(arg: T): T = sin(arg) / cos(arg)
+    override fun tanh(arg: T): T = sinh(arg) / cosh(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)
+        TrigonometricOperations.ACOS_OPERATION -> acos(arg)
-        InverseTrigonometricOperations.ASIN_OPERATION -> asin(arg)
+        TrigonometricOperations.ASIN_OPERATION -> asin(arg)
-        InverseTrigonometricOperations.ATAN_OPERATION -> atan(arg)
+        TrigonometricOperations.ATAN_OPERATION -> atan(arg)
+        HyperbolicOperations.COSH_OPERATION -> cosh(arg)
+        HyperbolicOperations.SINH_OPERATION -> sinh(arg)
+        HyperbolicOperations.TANH_OPERATION -> tanh(arg)
+        HyperbolicOperations.ACOSH_OPERATION -> acosh(arg)
+        HyperbolicOperations.ASINH_OPERATION -> asinh(arg)
+        HyperbolicOperations.ATANH_OPERATION -> atanh(arg)
         PowerOperations.SQRT_OPERATION -> sqrt(arg)
         ExponentialOperations.EXP_OPERATION -> exp(arg)
         ExponentialOperations.LN_OPERATION -> ln(arg)
@@ -32,6 +42,13 @@ interface ExtendedFieldOperations<T> :
  * Advanced Number-like field that implements basic operations.
  */
 interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T> {
+    override fun sinh(arg: T): T = (exp(arg) - exp(-arg)) / 2
+    override fun cosh(arg: T): T = (exp(arg) + exp(-arg)) / 2
+    override fun tanh(arg: T): T = (exp(arg) - exp(-arg)) / (exp(-arg) + exp(arg))
+    override fun asinh(arg: T): T = ln(sqrt(arg * arg + one) + arg)
+    override fun acosh(arg: T): T = ln(arg + sqrt((arg - one) * (arg + one)))
+    override fun atanh(arg: T): T = (ln(arg + one) - ln(one - arg)) / 2
+
     override fun rightSideNumberOperation(operation: String, left: T, right: Number): T = when (operation) {
         PowerOperations.POW_OPERATION -> power(left, right)
         else -> super.rightSideNumberOperation(operation, left, right)
@@ -46,12 +63,13 @@ interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T> {
  * TODO inline does not work due to compiler bug. Waiting for fix for KT-27586
  */
 inline class Real(val value: Double) : FieldElement<Double, Real, RealField> {
+    override val context: RealField
+        get() = RealField
+
     override fun unwrap(): Double = value
 
     override fun Double.wrap(): Real = Real(value)
 
-    override val context: RealField get() = RealField
-
     companion object
 }
 
@@ -60,12 +78,22 @@ inline class Real(val value: Double) : FieldElement<Double, Real, RealField> {
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object RealField : ExtendedField<Double>, Norm<Double, Double> {
-    override val zero: Double = 0.0
+    override val zero: Double
+        get() = 0.0
+
+    override val one: Double
+        get() = 1.0
+
+    override fun binaryOperation(operation: String, left: Double, right: Double): Double = when (operation) {
+        PowerOperations.POW_OPERATION -> left pow right
+        else -> super.binaryOperation(operation, left, right)
+    }
+
     override inline fun add(a: Double, b: Double): Double = a + b
-    override inline fun multiply(a: Double, b: Double): Double = a * b
     override inline fun multiply(a: Double, k: Number): Double = a * k.toDouble()
 
-    override val one: Double = 1.0
+    override inline fun multiply(a: Double, b: Double): Double = a * b
+
     override inline fun divide(a: Double, b: Double): Double = a / b
 
     override inline fun sin(arg: Double): Double = kotlin.math.sin(arg)
@@ -75,27 +103,24 @@ object RealField : ExtendedField<Double>, Norm<Double, Double> {
     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): Double = arg.kpow(pow.toDouble())
+    override inline fun sinh(arg: Double): Double = kotlin.math.sinh(arg)
+    override inline fun cosh(arg: Double): Double = kotlin.math.cosh(arg)
+    override inline fun tanh(arg: Double): Double = kotlin.math.tanh(arg)
+    override inline fun asinh(arg: Double): Double = kotlin.math.asinh(arg)
+    override inline fun acosh(arg: Double): Double = kotlin.math.acosh(arg)
+    override inline fun atanh(arg: Double): Double = kotlin.math.atanh(arg)
 
+    override inline fun power(arg: Double, pow: Number): Double = arg.kpow(pow.toDouble())
     override inline fun exp(arg: Double): Double = kotlin.math.exp(arg)
     override inline fun ln(arg: Double): Double = kotlin.math.ln(arg)
 
     override inline fun norm(arg: Double): Double = abs(arg)
 
     override inline fun Double.unaryMinus(): Double = -this
-
     override inline fun Double.plus(b: Double): Double = this + b
-
     override inline fun Double.minus(b: Double): Double = this - b
-
     override inline fun Double.times(b: Double): Double = this * b
-
     override inline fun Double.div(b: Double): Double = this / b
-
-    override fun binaryOperation(operation: String, left: Double, right: Double): Double = when (operation) {
-        PowerOperations.POW_OPERATION -> left pow right
-        else -> super.binaryOperation(operation, left, right)
-    }
 }
 
 /**
@@ -103,12 +128,22 @@ object RealField : ExtendedField<Double>, Norm<Double, Double> {
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object FloatField : ExtendedField<Float>, Norm<Float, Float> {
-    override val zero: Float = 0f
+    override val zero: Float
+        get() = 0.0f
+
+    override val one: Float
+        get() = 1.0f
+
+    override fun binaryOperation(operation: String, left: Float, right: Float): Float = when (operation) {
+        PowerOperations.POW_OPERATION -> left pow right
+        else -> super.binaryOperation(operation, left, right)
+    }
+
     override inline fun add(a: Float, b: Float): Float = a + b
-    override inline fun multiply(a: Float, b: Float): Float = a * b
     override inline fun multiply(a: Float, k: Number): Float = a * k.toFloat()
 
-    override val one: Float = 1f
+    override inline fun multiply(a: Float, b: Float): Float = a * b
+
     override inline fun divide(a: Float, b: Float): Float = a / b
 
     override inline fun sin(arg: Float): Float = kotlin.math.sin(arg)
@@ -118,108 +153,118 @@ object FloatField : ExtendedField<Float>, Norm<Float, Float> {
     override inline fun asin(arg: Float): Float = kotlin.math.asin(arg)
     override inline fun atan(arg: Float): Float = kotlin.math.atan(arg)
 
-    override inline fun power(arg: Float, pow: Number): Float = arg.pow(pow.toFloat())
+    override inline fun sinh(arg: Float): Float = kotlin.math.sinh(arg)
+    override inline fun cosh(arg: Float): Float = kotlin.math.cosh(arg)
+    override inline fun tanh(arg: Float): Float = kotlin.math.tanh(arg)
+    override inline fun asinh(arg: Float): Float = kotlin.math.asinh(arg)
+    override inline fun acosh(arg: Float): Float = kotlin.math.acosh(arg)
+    override inline fun atanh(arg: Float): Float = kotlin.math.atanh(arg)
 
+    override inline fun power(arg: Float, pow: Number): Float = arg.kpow(pow.toFloat())
     override inline fun exp(arg: Float): Float = kotlin.math.exp(arg)
     override inline fun ln(arg: Float): Float = kotlin.math.ln(arg)
 
     override inline fun norm(arg: Float): Float = abs(arg)
 
     override inline fun Float.unaryMinus(): Float = -this
-
     override inline fun Float.plus(b: Float): Float = this + b
-
     override inline fun Float.minus(b: Float): Float = this - b
-
     override inline fun Float.times(b: Float): Float = this * b
-
     override inline fun Float.div(b: Float): Float = this / b
 }
 
 /**
- * A field for [Int] without boxing. Does not produce corresponding field element
+ * A field for [Int] without boxing. Does not produce corresponding ring element.
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object IntRing : Ring<Int>, Norm<Int, Int> {
-    override val zero: Int = 0
+    override val zero: Int
+        get() = 0
+
+    override val one: Int
+        get() = 1
+
     override inline fun add(a: Int, b: Int): Int = a + b
-    override inline fun multiply(a: Int, b: Int): Int = a * b
     override inline fun multiply(a: Int, k: Number): Int = k.toInt() * a
-    override val one: Int = 1
+
+    override inline fun multiply(a: Int, b: Int): Int = a * b
 
     override inline fun norm(arg: Int): Int = abs(arg)
 
     override inline fun Int.unaryMinus(): Int = -this
-
     override inline fun Int.plus(b: Int): Int = this + b
-
     override inline fun Int.minus(b: Int): Int = this - b
-
     override inline fun Int.times(b: Int): Int = this * b
 }
 
 /**
- * A field for [Short] without boxing. Does not produce appropriate field element
+ * A field for [Short] without boxing. Does not produce appropriate ring element.
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object ShortRing : Ring<Short>, Norm<Short, Short> {
-    override val zero: Short = 0
+    override val zero: Short
+        get() = 0
+
+    override val one: Short
+        get() = 1
+
     override inline fun add(a: Short, b: Short): Short = (a + b).toShort()
-    override inline fun multiply(a: Short, b: Short): Short = (a * b).toShort()
     override inline fun multiply(a: Short, k: Number): Short = (a * k.toShort()).toShort()
-    override val one: Short = 1
+
+    override inline fun multiply(a: Short, b: Short): Short = (a * b).toShort()
 
     override fun norm(arg: Short): Short = if (arg > 0) arg else (-arg).toShort()
 
     override inline fun Short.unaryMinus(): Short = (-this).toShort()
-
     override inline fun Short.plus(b: Short): Short = (this + b).toShort()
-
     override inline fun Short.minus(b: Short): Short = (this - b).toShort()
-
     override inline fun Short.times(b: Short): Short = (this * b).toShort()
 }
 
 /**
- * A field for [Byte] values
+ * A field for [Byte] without boxing. Does not produce appropriate ring element.
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object ByteRing : Ring<Byte>, Norm<Byte, Byte> {
-    override val zero: Byte = 0
+    override val zero: Byte
+        get() = 0
+
+    override val one: Byte
+        get() = 1
+
     override inline fun add(a: Byte, b: Byte): Byte = (a + b).toByte()
-    override inline fun multiply(a: Byte, b: Byte): Byte = (a * b).toByte()
     override inline fun multiply(a: Byte, k: Number): Byte = (a * k.toByte()).toByte()
-    override val one: Byte = 1
+
+    override inline fun multiply(a: Byte, b: Byte): Byte = (a * b).toByte()
 
     override fun norm(arg: Byte): Byte = if (arg > 0) arg else (-arg).toByte()
 
     override inline fun Byte.unaryMinus(): Byte = (-this).toByte()
-
     override inline fun Byte.plus(b: Byte): Byte = (this + b).toByte()
-
     override inline fun Byte.minus(b: Byte): Byte = (this - b).toByte()
-
     override inline fun Byte.times(b: Byte): Byte = (this * b).toByte()
 }
 
 /**
- * A field for [Long] values
+ * A field for [Double] without boxing. Does not produce appropriate ring element.
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object LongRing : Ring<Long>, Norm<Long, Long> {
-    override val zero: Long = 0
+    override val zero: Long
-    override inline fun add(a: Long, b: Long): Long = (a + b)
+        get() = 0
-    override inline fun multiply(a: Long, b: Long): Long = (a * b)
+
+    override val one: Long
+        get() = 1
+
+    override inline fun add(a: Long, b: Long): Long = a + b
     override inline fun multiply(a: Long, k: Number): Long = a * k.toLong()
-    override val one: Long = 1
+
+    override inline fun multiply(a: Long, b: Long): Long = a * b
 
     override fun norm(arg: Long): Long = abs(arg)
 
     override inline fun Long.unaryMinus(): Long = (-this)
-
     override inline fun Long.plus(b: Long): Long = (this + b)
-
     override inline fun Long.minus(b: Long): Long = (this - b)
-
     override inline fun Long.times(b: Long): Long = (this * b)
 }

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

@@ -1,12 +1,11 @@
 package scientifik.kmath.operations
 
 /**
- * A container for trigonometric operations for specific type. They are limited to semifields.
+ * A container for trigonometric operations for specific type.
  *
- * The operations are not exposed to class directly to avoid method bloat but instead are declared in the field.
+ * @param T the type of element of this structure.
- * It also allows to override behavior for optional operations.
  */
-interface TrigonometricOperations<T> : FieldOperations<T> {
+interface TrigonometricOperations<T> : Algebra<T> {
     /**
      * Computes the sine of [arg].
      */
@@ -22,31 +21,6 @@ interface TrigonometricOperations<T> : FieldOperations<T> {
      */
     fun tan(arg: T): T
 
-    companion object {
-        /**
-         * The identifier of sine.
-         */
-        const val SIN_OPERATION: String = "sin"
-
-        /**
-         * The identifier of cosine.
-         */
-        const val COS_OPERATION: String = "cos"
-
-        /**
-         * The identifier of tangent.
-         */
-        const val TAN_OPERATION: String = "tan"
-    }
-}
-
-/**
- * A container for inverse trigonometric operations for specific type. They are limited to semifields.
- *
- * The operations are not exposed to class directly to avoid method bloat but instead are declared in the field.
- * It also allows to override behavior for optional operations.
- */
-interface InverseTrigonometricOperations<T> : TrigonometricOperations<T> {
     /**
      * Computes the inverse sine of [arg].
      */
@@ -63,6 +37,21 @@ interface InverseTrigonometricOperations<T> : TrigonometricOperations<T> {
     fun atan(arg: T): T
 
     companion object {
+        /**
+         * The identifier of sine.
+         */
+        const val SIN_OPERATION: String = "sin"
+
+        /**
+         * The identifier of cosine.
+         */
+        const val COS_OPERATION: String = "cos"
+
+        /**
+         * The identifier of tangent.
+         */
+        const val TAN_OPERATION: String = "tan"
+
         /**
          * The identifier of inverse sine.
          */
@@ -98,20 +87,121 @@ fun <T : MathElement<out TrigonometricOperations<T>>> tan(arg: T): T = arg.conte
 /**
  * Computes the inverse sine of [arg].
  */
-fun <T : MathElement<out InverseTrigonometricOperations<T>>> asin(arg: T): T = arg.context.asin(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> asin(arg: T): T = arg.context.asin(arg)
 
 /**
  * Computes the inverse cosine of [arg].
  */
-fun <T : MathElement<out InverseTrigonometricOperations<T>>> acos(arg: T): T = arg.context.acos(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> acos(arg: T): T = arg.context.acos(arg)
 
 /**
  * Computes the inverse tangent of [arg].
  */
-fun <T : MathElement<out InverseTrigonometricOperations<T>>> atan(arg: T): T = arg.context.atan(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> atan(arg: T): T = arg.context.atan(arg)
+
+/**
+ * A container for hyperbolic trigonometric operations for specific type.
+ *
+ * @param T the type of element of this structure.
+ */
+interface HyperbolicOperations<T> : Algebra<T> {
+    /**
+     * Computes the hyperbolic sine of [arg].
+     */
+    fun sinh(arg: T): T
+
+    /**
+     * Computes the hyperbolic cosine of [arg].
+     */
+    fun cosh(arg: T): T
+
+    /**
+     * Computes the hyperbolic tangent of [arg].
+     */
+    fun tanh(arg: T): T
+
+    /**
+     * Computes the inverse hyperbolic sine of [arg].
+     */
+    fun asinh(arg: T): T
+
+    /**
+     * Computes the inverse hyperbolic cosine of [arg].
+     */
+    fun acosh(arg: T): T
+
+    /**
+     * Computes the inverse hyperbolic tangent of [arg].
+     */
+    fun atanh(arg: T): T
+
+    companion object {
+        /**
+         * The identifier of hyperbolic sine.
+         */
+        const val SINH_OPERATION: String = "sinh"
+
+        /**
+         * The identifier of hyperbolic cosine.
+         */
+        const val COSH_OPERATION: String = "cosh"
+
+        /**
+         * The identifier of hyperbolic tangent.
+         */
+        const val TANH_OPERATION: String = "tanh"
+
+        /**
+         * The identifier of inverse hyperbolic sine.
+         */
+        const val ASINH_OPERATION: String = "asinh"
+
+        /**
+         * The identifier of inverse hyperbolic cosine.
+         */
+        const val ACOSH_OPERATION: String = "acosh"
+
+        /**
+         * The identifier of inverse hyperbolic tangent.
+         */
+        const val ATANH_OPERATION: String = "atanh"
+    }
+}
+
+/**
+ * Computes the hyperbolic sine of [arg].
+ */
+fun <T : MathElement<out HyperbolicOperations<T>>> sinh(arg: T): T = arg.context.sinh(arg)
+
+/**
+ * Computes the hyperbolic cosine of [arg].
+ */
+fun <T : MathElement<out HyperbolicOperations<T>>> cosh(arg: T): T = arg.context.cosh(arg)
+
+/**
+ * Computes the hyperbolic tangent of [arg].
+ */
+fun <T : MathElement<out HyperbolicOperations<T>>> tanh(arg: T): T = arg.context.tanh(arg)
+
+/**
+ * Computes the inverse hyperbolic sine of [arg].
+ */
+fun <T : MathElement<out HyperbolicOperations<T>>> asinh(arg: T): T = arg.context.asinh(arg)
+
+/**
+ * Computes the inverse hyperbolic cosine of [arg].
+ */
+fun <T : MathElement<out HyperbolicOperations<T>>> acosh(arg: T): T = arg.context.acosh(arg)
+
+/**
+ * Computes the inverse hyperbolic tangent of [arg].
+ */
+fun <T : MathElement<out HyperbolicOperations<T>>> atanh(arg: T): T = arg.context.atanh(arg)
 
 /**
  * A context extension to include power operations based on exponentiation.
+ *
+ * @param T the type of element of this structure.
  */
 interface PowerOperations<T> : Algebra<T> {
     /**
@@ -163,6 +253,8 @@ fun <T : MathElement<out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
 
 /**
  * A container for operations related to `exp` and `ln` functions.
+ *
+ * @param T the type of element of this structure.
  */
 interface ExponentialOperations<T> : Algebra<T> {
     /**
@@ -200,6 +292,9 @@ fun <T : MathElement<out ExponentialOperations<T>>> ln(arg: T): T = arg.context.
 
 /**
  * A container for norm functional on element.
+ *
+ * @param T the type of element having norm defined.
+ * @param R the type of norm.
  */
 interface Norm<in T : Any, out R> {
     /**

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

@@ -15,7 +15,6 @@ class ComplexNDField(override val shape: IntArray) :
     ExtendedNDField<Complex, ComplexField, NDBuffer<Complex>> {
 
     override val strides: Strides = DefaultStrides(shape)
-
     override val elementContext: ComplexField get() = ComplexField
     override val zero: ComplexNDElement by lazy { produce { zero } }
     override val one: ComplexNDElement by lazy { produce { one } }
@@ -45,6 +44,7 @@ class ComplexNDField(override val shape: IntArray) :
         transform: ComplexField.(index: IntArray, Complex) -> Complex
     ): ComplexNDElement {
         check(arg)
+
         return BufferedNDFieldElement(
             this,
             buildBuffer(arg.strides.linearSize) { offset ->
@@ -61,6 +61,7 @@ class ComplexNDField(override val shape: IntArray) :
         transform: ComplexField.(Complex, Complex) -> Complex
     ): ComplexNDElement {
         check(a, b)
+
         return BufferedNDFieldElement(
             this,
             buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
@@ -69,23 +70,25 @@ class ComplexNDField(override val shape: IntArray) :
     override fun NDBuffer<Complex>.toElement(): FieldElement<NDBuffer<Complex>, *, out BufferedNDField<Complex, ComplexField>> =
         BufferedNDFieldElement(this@ComplexNDField, buffer)
 
-    override fun power(arg: NDBuffer<Complex>, pow: Number): ComplexNDElement = map(arg) { power(it, pow) }
+    override fun power(arg: NDBuffer<Complex>, pow: Number): ComplexNDElement =
+        map(arg) { power(it, pow) }
 
     override fun exp(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { exp(it) }
-
     override fun ln(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { ln(it) }
 
     override fun sin(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { sin(it) }
-
     override fun cos(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { cos(it) }
-
     override fun tan(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { tan(it) }
-
     override fun asin(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { asin(it) }
-
     override fun acos(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { acos(it) }
-
     override fun atan(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { atan(it) }
+
+    override fun sinh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { sinh(it) }
+    override fun cosh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { cosh(it) }
+    override fun tanh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { tanh(it) }
+    override fun asinh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { asinh(it) }
+    override fun acosh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { acosh(it) }
+    override fun atanh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { atanh(it) }
 }
 
 

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

@@ -10,14 +10,15 @@ import kotlin.math.*
  */
 object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
     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} " }
+        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 RealBuffer && b is RealBuffer) {
             val aArray = a.array
             val bArray = b.array
             RealBuffer(DoubleArray(a.size) { aArray[it] + bArray[it] })
-        } else
+        } else RealBuffer(DoubleArray(a.size) { a[it] + b[it] })
-            RealBuffer(DoubleArray(a.size) { a[it] + b[it] })
     }
 
     override fun multiply(a: Buffer<Double>, k: Number): RealBuffer {
@@ -26,12 +27,13 @@ object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
         return if (a is RealBuffer) {
             val aArray = a.array
             RealBuffer(DoubleArray(a.size) { aArray[it] * kValue })
-        } else
+        } else RealBuffer(DoubleArray(a.size) { a[it] * kValue })
-            RealBuffer(DoubleArray(a.size) { a[it] * kValue })
     }
 
     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} " }
+        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 RealBuffer && b is RealBuffer) {
             val aArray = a.array
@@ -42,34 +44,31 @@ object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
     }
 
     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} " }
+        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 RealBuffer && b is RealBuffer) {
             val aArray = a.array
             val bArray = b.array
             RealBuffer(DoubleArray(a.size) { aArray[it] / bArray[it] })
-        } else
+        } else RealBuffer(DoubleArray(a.size) { a[it] / b[it] })
-            RealBuffer(DoubleArray(a.size) { a[it] / b[it] })
     }
 
     override fun sin(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
         RealBuffer(DoubleArray(arg.size) { sin(array[it]) })
-    } else {
+    } else RealBuffer(DoubleArray(arg.size) { sin(arg[it]) })
-        RealBuffer(DoubleArray(arg.size) { sin(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
+    } else RealBuffer(DoubleArray(arg.size) { cos(arg[it]) })
-        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
+    } else RealBuffer(DoubleArray(arg.size) { tan(arg[it]) })
-        RealBuffer(DoubleArray(arg.size) { tan(arg[it]) })
 
     override fun asin(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
@@ -90,23 +89,50 @@ object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
     } else
         RealBuffer(DoubleArray(arg.size) { atan(arg[it]) })
 
+    override fun sinh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { sinh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { sinh(arg[it]) })
+
+    override fun cosh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { cosh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { cosh(arg[it]) })
+
+    override fun tanh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { tanh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { tanh(arg[it]) })
+
+    override fun asinh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { asinh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { asinh(arg[it]) })
+
+    override fun acosh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { acosh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { acosh(arg[it]) })
+
+    override fun atanh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { atanh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { atanh(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
+    } else RealBuffer(DoubleArray(arg.size) { arg[it].pow(pow.toDouble()) })
-        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
+    } else RealBuffer(DoubleArray(arg.size) { exp(arg[it]) })
-        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
+    } else RealBuffer(DoubleArray(arg.size) { ln(arg[it]) })
-        RealBuffer(DoubleArray(arg.size) { ln(arg[it]) })
 }
 
 /**
@@ -168,6 +194,36 @@ class RealBufferField(val size: Int) : ExtendedField<Buffer<Double>> {
         return RealBufferFieldOperations.atan(arg)
     }
 
+    override fun sinh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.sinh(arg)
+    }
+
+    override fun cosh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.cosh(arg)
+    }
+
+    override fun tanh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.tanh(arg)
+    }
+
+    override fun asinh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.asinh(arg)
+    }
+
+    override fun acosh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.acosh(arg)
+    }
+
+    override fun atanh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.atanh(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)

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

@@ -40,6 +40,7 @@ class RealNDField(override val shape: IntArray) :
         transform: RealField.(index: IntArray, Double) -> Double
     ): RealNDElement {
         check(arg)
+
         return BufferedNDFieldElement(
             this,
             buildBuffer(arg.strides.linearSize) { offset ->
@@ -71,16 +72,18 @@ class RealNDField(override val shape: IntArray) :
     override fun ln(arg: NDBuffer<Double>): RealNDElement = map(arg) { ln(it) }
 
     override fun sin(arg: NDBuffer<Double>): RealNDElement = map(arg) { sin(it) }
-
     override fun cos(arg: NDBuffer<Double>): RealNDElement = map(arg) { cos(it) }
+    override fun tan(arg: NDBuffer<Double>): RealNDElement = map(arg) { tan(it) }
+    override fun asin(arg: NDBuffer<Double>): RealNDElement = map(arg) { asin(it) }
+    override fun acos(arg: NDBuffer<Double>): RealNDElement = map(arg) { acos(it) }
+    override fun atan(arg: NDBuffer<Double>): RealNDElement = map(arg) { atan(it) }
 
-    override fun tan(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { tan(it) }
+    override fun sinh(arg: NDBuffer<Double>): RealNDElement = map(arg) { sinh(it) }
-
+    override fun cosh(arg: NDBuffer<Double>): RealNDElement = map(arg) { cosh(it) }
-    override fun asin(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { asin(it) }
+    override fun tanh(arg: NDBuffer<Double>): RealNDElement = map(arg) { tanh(it) }
-
+    override fun asinh(arg: NDBuffer<Double>): RealNDElement = map(arg) { asinh(it) }
-    override fun acos(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { acos(it) }
+    override fun acosh(arg: NDBuffer<Double>): RealNDElement = map(arg) { acosh(it) }
-
+    override fun atanh(arg: NDBuffer<Double>): RealNDElement = map(arg) { atanh(it) }
-    override fun atan(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { atan(it) }
 }
 
 
@@ -130,6 +133,5 @@ operator fun RealNDElement.minus(arg: Double): RealNDElement =
 /**
  * Produce a context for n-dimensional operations inside this real field
  */
-inline fun <R> RealField.nd(vararg shape: Int, action: RealNDField.() -> R): R {
+
-    return NDField.real(*shape).run(action)
+inline fun <R> RealField.nd(vararg shape: Int, action: RealNDField.() -> R): R = NDField.real(*shape).run(action)
-}

kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/ComplexFieldTest.kt

@@ -1,7 +1,10 @@
 package scientifik.kmath.operations
 
+import kotlin.math.PI
+import kotlin.math.abs
 import kotlin.test.Test
 import kotlin.test.assertEquals
+import kotlin.test.assertTrue
 
 internal class ComplexFieldTest {
     @Test
@@ -34,6 +37,25 @@ internal class ComplexFieldTest {
         assertEquals(Complex(Double.NaN, Double.NaN), ComplexField { Complex(1, 1) / Complex(0, 0) })
     }
 
+    @Test
+    fun testSine() {
+        assertEquals(ComplexField { i * sinh(one) }, ComplexField { sin(i) })
+        assertEquals(ComplexField { i * sinh(PI.toComplex()) }, ComplexField { sin(i * PI.toComplex()) })
+    }
+
+    @Test
+    fun testInverseSine() {
+        assertEquals(Complex(0, -0.0), ComplexField { asin(zero) })
+        assertTrue(abs(ComplexField { i * asinh(one) }.r - ComplexField { asin(i) }.r) < 0.000000000000001)
+    }
+
+    @Test
+    fun testInverseHyperbolicSine() {
+        assertEquals(
+            ComplexField { i * PI.toComplex() / 2 },
+            ComplexField { asinh(i) })
+    }
+
     @Test
     fun testPower() {
         assertEquals(ComplexField.zero, ComplexField { zero pow 2 })
@@ -43,4 +65,9 @@ internal class ComplexFieldTest {
             ComplexField { i * 8 }.let { it.im.toInt() to it.re.toInt() },
             ComplexField { Complex(2, 2) pow 2 }.let { it.im.toInt() to it.re.toInt() })
     }
+
+    @Test
+    fun testNorm() {
+        assertEquals(2.toComplex(), ComplexField { norm(2 * i) })
+    }
 }