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Moved optimizations to branch refactor/polynomials

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Gleb Minaev 2022-06-25 16:01:18 +03:00
parent 9fc99a4c72
commit 403ff93f4a
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250
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/listUtilOptimized.kt
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@ -1,250 +0,0 @@
/*
* 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.functions
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.invoke
import kotlin.math.max
import kotlin.math.min
// TODO: Optimized copies of substitution and invocation
@UnstablePolynomialBoxingOptimization
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> copyTo(
origin: List<C>,
originDegree: Int,
target: MutableList<C>,
) {
for (deg in 0 .. originDegree) target[deg] = origin[deg]
}
@UnstablePolynomialBoxingOptimization
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> multiplyAddingToUpdater(
ring: Ring<C>,
multiplicand: MutableList<C>,
multiplicandDegree: Int,
multiplier: List<C>,
multiplierDegree: Int,
updater: MutableList<C>,
zero: C,
) {
multiplyAddingTo(
ring = ring,
multiplicand = multiplicand,
multiplicandDegree = multiplicandDegree,
multiplier = multiplier,
multiplierDegree = multiplierDegree,
target = updater
)
for (updateDeg in 0 .. multiplicandDegree + multiplierDegree) {
multiplicand[updateDeg] = updater[updateDeg]
updater[updateDeg] = zero
}
}
@UnstablePolynomialBoxingOptimization
@Suppress("NOTHING_TO_INLINE")
internal inline fun <C> multiplyAddingTo(
ring: Ring<C>,
multiplicand: List<C>,
multiplicandDegree: Int,
multiplier: List<C>,
multiplierDegree: Int,
target: MutableList<C>
) = ring {
for (d in 0 .. multiplicandDegree + multiplierDegree)
for (k in max(0, d - multiplierDegree)..min(multiplicandDegree, d))
target[d] += multiplicand[k] * multiplier[d - k]
}
@UnstablePolynomialBoxingOptimization
public fun <C> ListPolynomial<C>.substitute2(ring: Ring<C>, arg: ListPolynomial<C>) : ListPolynomial<C> = ring {
if (coefficients.isEmpty()) return ListPolynomial(emptyList())
val thisDegree = coefficients.lastIndex
if (thisDegree == -1) return ListPolynomial(emptyList())
val argDegree = arg.coefficients.lastIndex
if (argDegree == -1) return coefficients[0].asListPolynomial()
val constantZero = zero
val resultCoefs: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
resultCoefs[0] = coefficients[thisDegree]
val resultCoefsUpdate: MutableList<C> = MutableList(thisDegree * argDegree + 1) { constantZero }
var resultDegree = 0
for (deg in thisDegree - 1 downTo 0) {
resultCoefsUpdate[0] = coefficients[deg]
multiplyAddingToUpdater(
ring = ring,
multiplicand = resultCoefs,
multiplicandDegree = resultDegree,
multiplier = arg.coefficients,
multiplierDegree = argDegree,
updater = resultCoefsUpdate,
zero = constantZero
)
resultDegree += argDegree
}
return ListPolynomial<C>(resultCoefs)
}
/**
* Returns numerator (polynomial) of rational function gotten by substitution rational function [arg] to the polynomial instance.
* More concrete, if [arg] is a fraction `f(x)/g(x)` and the receiving instance is `p(x)`, then
* ```
* p(f/g) * g^deg(p)
* ```
* is returned.
*
* Used in [ListPolynomial.substitute] and [ListRationalFunction.substitute] for performance optimisation.
*/ // TODO: Дописать
@UnstablePolynomialBoxingOptimization
internal fun <C> ListPolynomial<C>.substituteRationalFunctionTakeNumerator(ring: Ring<C>, arg: ListRationalFunction<C>): ListPolynomial<C> = ring {
if (coefficients.isEmpty()) return ListPolynomial(emptyList())
val thisDegree = coefficients.lastIndex
if (thisDegree == -1) return ListPolynomial(emptyList())
val thisDegreeLog2 = 31 - thisDegree.countLeadingZeroBits()
val numeratorDegree = arg.numerator.coefficients.lastIndex
val denominatorDegree = arg.denominator.coefficients.lastIndex
val argDegree = max(numeratorDegree, denominatorDegree)
val constantZero = zero
val powersOf2 = buildList<Int>(thisDegreeLog2 + 1) {
var result = 1
for (exp in 0 .. thisDegreeLog2) {
add(result)
result = result shl 1
}
}
val hashes = powersOf2.runningReduce { acc, i -> acc + i }
val numeratorPowers = buildList<List<C>>(thisDegreeLog2 + 1) {
add(arg.numerator.coefficients)
repeat(thisDegreeLog2) {
val next = MutableList<C>(powersOf2[it + 1] * numeratorDegree + 1) { constantZero }
add(next)
val last = last()
multiplyAddingTo(
ring = ring,
multiplicand = last,
multiplicandDegree = powersOf2[it] * numeratorDegree + 1,
multiplier = last,
multiplierDegree = powersOf2[it] * numeratorDegree + 1,
target = next,
)
}
}
val denominatorPowers = buildList<List<C>>(thisDegreeLog2 + 1) {
add(arg.denominator.coefficients)
repeat(thisDegreeLog2) {
val next = MutableList<C>(powersOf2[it + 1] * denominatorDegree + 1) { constantZero }
add(next)
val last = last()
multiplyAddingTo(
ring = ring,
multiplicand = last,
multiplicandDegree = powersOf2[it] * denominatorDegree + 1,
multiplier = last,
multiplierDegree = powersOf2[it] * denominatorDegree + 1,
target = next,
)
}
}
val levelResultCoefsPool = buildList<MutableList<C>>(thisDegreeLog2 + 1) {
repeat(thisDegreeLog2 + 1) {
add(MutableList(hashes[it] * argDegree) { constantZero })
}
}
val edgedMultiplier = MutableList<C>(0) { TODO() }
val edgedMultiplierUpdater = MutableList<C>(0) { TODO() }
fun MutableList<C>.reset() {
for (i in indices) set(i, constantZero)
}
fun processLevel(level: Int, start: Int, end: Int) : List<C> {
val levelResultCoefs = levelResultCoefsPool[level + 1]
if (level == -1) {
levelResultCoefs[0] = coefficients[start]
} else {
levelResultCoefs.reset()
multiplyAddingTo(
ring = ring,
multiplicand = processLevel(level = level - 1, start = start, end = (start + end) / 2),
multiplicandDegree = hashes[level] * argDegree,
multiplier = denominatorPowers[level],
multiplierDegree = powersOf2[level] * denominatorDegree,
target = levelResultCoefs
)
multiplyAddingTo(
ring = ring,
multiplicand = processLevel(level = level - 1, start = (start + end) / 2, end = end),
multiplicandDegree = hashes[level] * argDegree,
multiplier = numeratorPowers[level],
multiplierDegree = powersOf2[level] * numeratorDegree,
target = levelResultCoefs
)
}
return levelResultCoefs
}
fun processLevelEdged(level: Int, start: Int, end: Int) : List<C> {
val levelResultCoefs = levelResultCoefsPool[level + 1]
if (level == -1) {
levelResultCoefs[0] = coefficients[start]
} else {
val levelsPowerOf2 = powersOf2[level]
if (end - start >= levelsPowerOf2) {
multiplyAddingTo(
ring = ring,
multiplicand = processLevelEdged(level = level - 1, start = start + levelsPowerOf2, end = end),
multiplicandDegree = hashes[level] * argDegree, // TODO: Ввести переменную
multiplier = numeratorPowers[level],
multiplierDegree = powersOf2[level] * numeratorDegree,
target = levelResultCoefs
)
multiplyAddingTo(
ring = ring,
multiplicand = processLevel(level = level - 1, start = start, end = start + levelsPowerOf2),
multiplicandDegree = hashes[level] * argDegree,
multiplier = edgedMultiplier,
multiplierDegree = max((hashes[level] and thisDegree) - powersOf2[level] + 1, 0) * denominatorDegree, // TODO: Ввести переменную
target = levelResultCoefs
)
if (level != thisDegreeLog2) {
multiplyAddingToUpdater(
ring = ring,
multiplicand = edgedMultiplier,
multiplicandDegree = max((hashes[level] and thisDegree) - powersOf2[level] + 1, 0) * denominatorDegree, // TODO: Ввести переменную
multiplier = denominatorPowers[level],
multiplierDegree = powersOf2[level] * denominatorDegree,
updater = edgedMultiplierUpdater,
zero = constantZero
)
}
} else {
copyTo(
origin = processLevelEdged(level = level - 1, start = start + levelsPowerOf2, end = end),
originDegree = hashes[level] * argDegree, // TODO: Ввести переменную
target = levelResultCoefs
)
}
}
return levelResultCoefs
}
return ListPolynomial(
processLevelEdged(
level = thisDegreeLog2,
start = 0,
end = thisDegree + 1
)
)
}

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kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/misc.kt
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@ -6,16 +6,6 @@
package space.kscience.kmath.functions
/**
* Marks operations that are going to be optimized reimplementations by reducing number of boxings but currently is
* under development and is not stable (or even ready to use).
*/
@RequiresOptIn(
message = "It's copy of operation with optimized boxing. It's currently unstable.",
level = RequiresOptIn.Level.ERROR
)
internal annotation class UnstablePolynomialBoxingOptimization
/**
* Marks declarations that give access to internal entities of polynomials delicate structure. Thus, it allows to
* optimize performance a bit by skipping standard steps, but such skips may cause critical errors if something is