Optimised existing substitution function. Prototyped substitution for RFs.
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Gleb Minaev
parent
86553e9f35
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@ -50,24 +50,36 @@ public inline fun <C, A, R> A.scalablePolynomial(block: ScalablePolynomialSpace<
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}
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@Suppress("NOTHING_TO_INLINE")
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internal inline fun <C> iadd(
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ring: Ring<C>,
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augend: MutableList<C>,
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addend: List<C>,
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degree: Int
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) = ring {
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for (deg in 0 .. degree) augend[deg] += addend[deg]
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internal inline fun <C> copyTo(
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origin: List<C>,
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originDegree: Int,
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target: MutableList<C>,
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) {
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for (deg in 0 .. originDegree) target[deg] = origin[deg]
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}
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@Suppress("NOTHING_TO_INLINE")
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internal inline fun <C> addTo(
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internal inline fun <C> multiplyAddingToUpdater(
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ring: Ring<C>,
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augend: List<C>,
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addend: List<C>,
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degree: Int,
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target: MutableList<C>
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) = ring {
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for (deg in 0 .. degree) target[deg] = augend[deg] + addend[deg]
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multiplicand: MutableList<C>,
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multiplicandDegree: Int,
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multiplier: List<C>,
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multiplierDegree: Int,
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updater: MutableList<C>,
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zero: C,
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) {
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multiplyAddingTo(
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ring = ring,
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multiplicand = multiplicand,
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multiplicandDegree = multiplicandDegree,
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multiplier = multiplier,
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multiplierDegree = multiplierDegree,
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target = updater
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)
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for (updateDeg in 0 .. multiplicandDegree + multiplierDegree) {
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multiplicand[updateDeg] = updater[updateDeg]
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updater[updateDeg] = zero
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}
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}
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@Suppress("NOTHING_TO_INLINE")
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@ -107,32 +119,29 @@ public fun <C> Polynomial<C>.substitute(ring: Ring<C>, arg: C): C = ring {
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return result
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}
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public fun <C> Polynomial<C>.substitute(ring: Ring<C>, arg: Polynomial<C>) : Polynomial<C> = ring.polynomial {
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if (coefficients.isEmpty()) return zero
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public fun <C> Polynomial<C>.substitute(ring: Ring<C>, arg: Polynomial<C>) : Polynomial<C> = ring {
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if (coefficients.isEmpty()) return Polynomial(emptyList())
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val thisDegree = degree
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if (thisDegree == -1) return zero
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val argDegree = arg.degree
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val thisDegree = coefficients.indexOfLast { it != zero }
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if (thisDegree == -1) return Polynomial(emptyList())
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val argDegree = arg.coefficients.indexOfLast { it != zero }
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if (argDegree == -1) return coefficients[0].asPolynomial()
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val constantZero = constantZero
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val constantZero = zero
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val resultCoefs: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
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val resultCoefsUpdate: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
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var resultDegree = 0
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for (deg in thisDegree downTo 0) {
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resultCoefsUpdate[0] = coefficients[deg]
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multiplyAddingTo(
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multiplyAddingToUpdater(
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ring = ring,
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multiplicand = resultCoefs,
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multiplicandDegree = resultDegree,
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multiplier = arg.coefficients,
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multiplierDegree = argDegree,
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target = resultCoefsUpdate
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updater = resultCoefsUpdate,
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zero = constantZero
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)
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resultDegree += argDegree
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for (updateDeg in 0 .. resultDegree) {
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resultCoefs[updateDeg] = resultCoefsUpdate[updateDeg]
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resultCoefsUpdate[updateDeg] = constantZero
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}
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}
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return Polynomial<C>(resultCoefs)
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}
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@ -5,9 +5,12 @@
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package space.kscience.kmath.functions
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import space.kscience.kmath.operations.Field
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import space.kscience.kmath.operations.Ring
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import space.kscience.kmath.operations.invoke
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import kotlin.contracts.InvocationKind
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import kotlin.contracts.contract
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import kotlin.math.max
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/**
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@ -24,6 +27,177 @@ public inline fun <C, A : Ring<C>, R> A.rationalFunction(block: RationalFunction
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return RationalFunctionSpace(this).block()
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}
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/**
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* Evaluates the value of the given double polynomial for given double argument.
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*/
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public fun RationalFunction<Double>.substitute(arg: Double): Double =
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numerator.substitute(arg) / denominator.substitute(arg)
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/**
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* Evaluates the value of the given polynomial for given argument.
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*
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* It is an implementation of [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).
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*/
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public fun <C> RationalFunction<C>.substitute(ring: Field<C>, arg: C): C = ring {
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numerator.substitute(ring, arg) / denominator.substitute(ring, arg)
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}
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/**
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* Returns numerator (polynomial) of rational function gotten by substitution rational function [arg] to the polynomial instance.
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* More concrete, if [arg] is a fraction `f(x)/g(x)` and the receiving instance is `p(x)`, then
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* ```
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* p(f/g) * g^deg(p)
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* ```
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* is returned.
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*
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* Used in [Polynomial.substitute] and [RationalFunction.substitute] for performance optimisation.
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*/ // TODO: Дописать
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internal fun <C> Polynomial<C>.substituteRationalFunctionTakeNumerator(ring: Ring<C>, arg: RationalFunction<C>): Polynomial<C> = ring {
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if (coefficients.isEmpty()) return Polynomial(emptyList())
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val thisDegree = coefficients.indexOfLast { it != zero }
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if (thisDegree == -1) return Polynomial(emptyList())
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val thisDegreeLog2 = 31 - thisDegree.countLeadingZeroBits()
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val numeratorDegree = arg.numerator.coefficients.indexOfLast { it != zero }
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val denominatorDegree = arg.denominator.coefficients.indexOfLast { it != zero }
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val argDegree = max(numeratorDegree, denominatorDegree)
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val constantZero = zero
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val powersOf2 = buildList<Int>(thisDegreeLog2 + 1) {
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var result = 1
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for (exp in 0 .. thisDegreeLog2) {
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add(result)
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result = result shl 1
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}
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}
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val hashes = powersOf2.runningReduce { acc, i -> acc + i }
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val numeratorPowers = buildList<List<C>>(thisDegreeLog2 + 1) {
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add(arg.numerator.coefficients)
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repeat(thisDegreeLog2) {
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val next = MutableList<C>(powersOf2[it + 1] * numeratorDegree + 1) { constantZero }
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add(next)
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val last = last()
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multiplyAddingTo(
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ring = ring,
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multiplicand = last,
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multiplicandDegree = powersOf2[it] * numeratorDegree + 1,
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multiplier = last,
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multiplierDegree = powersOf2[it] * numeratorDegree + 1,
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target = next,
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)
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}
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}
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val denominatorPowers = buildList<List<C>>(thisDegreeLog2 + 1) {
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add(arg.denominator.coefficients)
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repeat(thisDegreeLog2) {
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val next = MutableList<C>(powersOf2[it + 1] * denominatorDegree + 1) { constantZero }
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add(next)
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val last = last()
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multiplyAddingTo(
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ring = ring,
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multiplicand = last,
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multiplicandDegree = powersOf2[it] * denominatorDegree + 1,
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multiplier = last,
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multiplierDegree = powersOf2[it] * denominatorDegree + 1,
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target = next,
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)
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}
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}
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val levelResultCoefsPool = buildList<MutableList<C>>(thisDegreeLog2 + 1) {
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repeat(thisDegreeLog2 + 1) {
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add(MutableList(hashes[it] * argDegree) { constantZero })
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}
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}
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val edgedMultiplier = MutableList<C>(0) { TODO() }
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val edgedMultiplierUpdater = MutableList<C>(0) { TODO() }
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fun MutableList<C>.reset() {
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for (i in indices) set(i, constantZero)
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}
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fun processLevel(level: Int, start: Int, end: Int) : List<C> {
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val levelResultCoefs = levelResultCoefsPool[level + 1]
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if (level == -1) {
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levelResultCoefs[0] = coefficients[start]
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} else {
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levelResultCoefs.reset()
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multiplyAddingTo(
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ring = ring,
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multiplicand = processLevel(level = level - 1, start = start, end = (start + end) / 2),
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multiplicandDegree = hashes[level] * argDegree,
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multiplier = denominatorPowers[level],
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multiplierDegree = powersOf2[level] * denominatorDegree,
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target = levelResultCoefs
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)
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multiplyAddingTo(
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ring = ring,
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multiplicand = processLevel(level = level - 1, start = (start + end) / 2, end = end),
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multiplicandDegree = hashes[level] * argDegree,
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multiplier = numeratorPowers[level],
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multiplierDegree = powersOf2[level] * numeratorDegree,
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target = levelResultCoefs
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)
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}
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return levelResultCoefs
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}
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fun processLevelEdged(level: Int, start: Int, end: Int) : List<C> {
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val levelResultCoefs = levelResultCoefsPool[level + 1]
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if (level == -1) {
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levelResultCoefs[0] = coefficients[start]
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} else {
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val levelsPowerOf2 = powersOf2[level]
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if (end - start >= levelsPowerOf2) {
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multiplyAddingTo(
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ring = ring,
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multiplicand = processLevelEdged(level = level - 1, start = start + levelsPowerOf2, end = end),
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multiplicandDegree = hashes[level] * argDegree, // TODO: Ввести переменную
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multiplier = numeratorPowers[level],
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multiplierDegree = powersOf2[level] * numeratorDegree,
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target = levelResultCoefs
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)
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multiplyAddingTo(
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ring = ring,
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multiplicand = processLevel(level = level - 1, start = start, end = start + levelsPowerOf2),
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multiplicandDegree = hashes[level] * argDegree,
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multiplier = edgedMultiplier,
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multiplierDegree = max((hashes[level] and thisDegree) - powersOf2[level] + 1, 0) * denominatorDegree, // TODO: Ввести переменную
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target = levelResultCoefs
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)
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if (level != thisDegreeLog2) {
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multiplyAddingToUpdater(
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ring = ring,
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multiplicand = edgedMultiplier,
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multiplicandDegree = max((hashes[level] and thisDegree) - powersOf2[level] + 1, 0) * denominatorDegree, // TODO: Ввести переменную
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multiplier = denominatorPowers[level],
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multiplierDegree = powersOf2[level] * denominatorDegree,
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updater = edgedMultiplierUpdater,
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zero = constantZero
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)
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}
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} else {
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copyTo(
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origin = processLevelEdged(level = level - 1, start = start + levelsPowerOf2, end = end),
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originDegree = hashes[level] * argDegree, // TODO: Ввести переменную
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target = levelResultCoefs
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)
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}
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}
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return levelResultCoefs
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}
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return Polynomial(
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processLevelEdged(
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level = thisDegreeLog2,
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start = 0,
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end = thisDegree + 1
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)
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)
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}
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//operator fun <T: Field<T>> RationalFunction<T>.invoke(arg: T): T = numerator(arg) / denominator(arg)
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//
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//fun <T: Field<T>> RationalFunction<T>.reduced(): RationalFunction<T> =
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