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SelectivityCombiner.scala
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SelectivityCombiner.scala
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/*
* Copyright (c) 2002-2017 "Neo Technology,"
* Network Engine for Objects in Lund AB [http://neotechnology.com]
*
* This file is part of Neo4j.
*
* Neo4j is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
package org.neo4j.cypher.internal.compiler.v3_4.planner.logical.cardinality
import java.math
import org.neo4j.cypher.internal.util.v3_4.Selectivity
trait SelectivityCombiner {
def andTogetherSelectivities(selectivities: Seq[Selectivity]): Option[Selectivity]
// A ∪ B = ¬ ( ¬ A ∩ ¬ B )
def orTogetherSelectivities(selectivities: Seq[Selectivity]): Option[Selectivity]
}
case object IndependenceCombiner extends SelectivityCombiner {
override def andTogetherSelectivities(selectivities: Seq[Selectivity]): Option[Selectivity] =
selectivities.reduceOption(_ * _)
/**
* We transform the disjunction to a negation of a the conjunction of negations
* ∪{s ∈ selectivities} = ¬ ∩{ ¬ s | s ∈ selectivities}
* Where conjunction is computed through multiplication of the factors,
* and negation is computed as (1 - s.factor).
* Making the total formula:
* r = 1 - ∏{s ∈ selectivities}(1 - s.factor)
* Through expanding this formula we realize an iterative way to compute it:
* selectivities = {a} ⇒ r1 = 1 - (1-a) = a
* selectivities = {a, b} ⇒ r2 = 1 - (1-a)(1-b) = a + b - a * b = r1 + b - r1 * b
* selectivities = {a, b, c} ⇒ r3 = 1 - (1-a)(1-b)(1-c) = a + b + c - a*b - a*c - b*c + a*b*c = r2 + c - r2 * c
* Making the iterative formula:
* r[i] = r[i-1] + s[i].factor - r[i-1] * s[i].factor
* We then implement this formula with reduce.
*/
override def orTogetherSelectivities(selectivities: Seq[Selectivity]): Option[Selectivity] = {
selectivities.map(_.factor).reduceLeftOption((result, value) => result + value - result * value).flatMap(Selectivity.of)
}
}
object BigDecimalCombiner {
def orTogetherBigDecimals(bigDecimals: Seq[math.BigDecimal]): Option[math.BigDecimal] = {
val inverses = bigDecimals.map(negate)
andTogetherBigDecimals(inverses).map(negate)
}
def andTogetherBigDecimals(bigDecimals: Seq[math.BigDecimal]): Option[math.BigDecimal] = {
bigDecimals.reduceOption(_ multiply _)
}
def negate(bigDecimal: math.BigDecimal): math.BigDecimal = {
math.BigDecimal.ONE.subtract(bigDecimal)
}
}