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/*
* Scala (https://www.scala-lang.org)
*
* Copyright EPFL and Lightbend, Inc.
*
* Licensed under Apache License 2.0
* (http://www.apache.org/licenses/LICENSE-2.0).
*
* See the NOTICE file distributed with this work for
* additional information regarding copyright ownership.
*/
package scala
package collection
package immutable
// TODO: Now the specialization exists there is no clear reason to have
// separate classes for Range/NumericRange. Investigate and consolidate.
/** `NumericRange` is a more generic version of the
* `Range` class which works with arbitrary types.
* It must be supplied with an `Integral` implementation of the
* range type.
*
* Factories for likely types include `Range.BigInt`, `Range.Long`,
* and `Range.BigDecimal`. `Range.Int` exists for completeness, but
* the `Int`-based `scala.Range` should be more performant.
*
* {{{
* val r1 = new Range(0, 100, 1)
* val veryBig = Int.MaxValue.toLong + 1
* val r2 = Range.Long(veryBig, veryBig + 100, 1)
* assert(r1 sameElements r2.map(_ - veryBig))
* }}}
*
* @author Paul Phillips
* @define Coll `NumericRange`
* @define coll numeric range
* @define mayNotTerminateInf
* @define willNotTerminateInf
*/
@SerialVersionUID(-5580158174769432538L)
abstract class NumericRange[T]
(val start: T, val end: T, val step: T, val isInclusive: Boolean)
(implicit num: Integral[T])
extends AbstractSeq[T] with IndexedSeq[T] with Serializable {
/** Note that NumericRange must be invariant so that constructs
* such as "1L to 10 by 5" do not infer the range type as AnyVal.
*/
import num._
// See comment in Range for why this must be lazy.
private lazy val numRangeElements: Int =
NumericRange.count(start, end, step, isInclusive)
override def length = numRangeElements
override def isEmpty = length == 0
override lazy val last: T =
if (length == 0) Nil.last
else locationAfterN(length - 1)
/** Create a new range with the start and end values of this range and
* a new `step`.
*/
def by(newStep: T): NumericRange[T] = copy(start, end, newStep)
/** Create a copy of this range.
*/
def copy(start: T, end: T, step: T): NumericRange[T]
override def foreach[U](f: T => U) {
var count = 0
var current = start
while (count < length) {
f(current)
current += step
count += 1
}
}
// TODO: these private methods are straight copies from Range, duplicated
// to guard against any (most likely illusory) performance drop. They should
// be eliminated one way or another.
// Tests whether a number is within the endpoints, without testing
// whether it is a member of the sequence (i.e. when step > 1.)
private def isWithinBoundaries(elem: T) = !isEmpty && (
(step > zero && start <= elem && elem <= last ) ||
(step < zero && last <= elem && elem <= start)
)
// Methods like apply throw exceptions on invalid n, but methods like take/drop
// are forgiving: therefore the checks are with the methods.
private def locationAfterN(n: Int): T = start + (step * fromInt(n))
// When one drops everything. Can't ever have unchecked operations
// like "end + 1" or "end - 1" because ranges involving Int.{ MinValue, MaxValue }
// will overflow. This creates an exclusive range where start == end
// based on the given value.
private def newEmptyRange(value: T) = NumericRange(value, value, step)
final override def take(n: Int): NumericRange[T] = (
if (n <= 0 || length == 0) newEmptyRange(start)
else if (n >= length) this
else new NumericRange.Inclusive(start, locationAfterN(n - 1), step)
)
final override def drop(n: Int): NumericRange[T] = (
if (n <= 0 || length == 0) this
else if (n >= length) newEmptyRange(end)
else copy(locationAfterN(n), end, step)
)
def apply(idx: Int): T = {
if (idx < 0 || idx >= length) throw new IndexOutOfBoundsException(idx.toString)
else locationAfterN(idx)
}
import NumericRange.defaultOrdering
override def min[T1 >: T](implicit ord: Ordering[T1]): T =
// We can take the fast path:
// - If the Integral of this NumericRange is also the requested Ordering
// (Integral <: Ordering). This can happen for custom Integral types.
// - The Ordering is the default Ordering of a well-known Integral type.
if ((ord eq num) || defaultOrdering.get(num).exists(ord eq _)) {
if (num.signum(step) > 0) head
else last
} else super.min(ord)
override def max[T1 >: T](implicit ord: Ordering[T1]): T =
// See comment for fast path in min().
if ((ord eq num) || defaultOrdering.get(num).exists(ord eq _)) {
if (num.signum(step) > 0) last
else head
} else super.max(ord)
// Motivated by the desire for Double ranges with BigDecimal precision,
// we need some way to map a Range and get another Range. This can't be
// done in any fully general way because Ranges are not arbitrary
// sequences but step-valued, so we have a custom method only we can call
// which we promise to use responsibly.
//
// The point of it all is that
//
// 0.0 to 1.0 by 0.1
//
// should result in
//
// NumericRange[Double](0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0)
//
// and not
//
// NumericRange[Double](0.0, 0.1, 0.2, 0.30000000000000004, 0.4, 0.5, 0.6000000000000001, 0.7000000000000001, 0.8, 0.9)
//
// or perhaps more importantly,
//
// (0.1 to 0.3 by 0.1 contains 0.3) == true
//
private[immutable] def mapRange[A](fm: T => A)(implicit unum: Integral[A]): NumericRange[A] = {
val self = this
// XXX This may be incomplete.
new NumericRange[A](fm(start), fm(end), fm(step), isInclusive) {
def copy(start: A, end: A, step: A): NumericRange[A] =
if (isInclusive) NumericRange.inclusive(start, end, step)
else NumericRange(start, end, step)
private lazy val underlyingRange: NumericRange[T] = self
override def foreach[U](f: A => U) { underlyingRange foreach (x => f(fm(x))) }
override def isEmpty = underlyingRange.isEmpty
override def apply(idx: Int): A = fm(underlyingRange(idx))
override def containsTyped(el: A) = underlyingRange exists (x => fm(x) == el)
override def toString = {
def simpleOf(x: Any): String = x.getClass.getName.split("\\.").last
val stepped = simpleOf(underlyingRange.step)
s"${super.toString} (using $underlyingRange of $stepped)"
}
}
}
// a well-typed contains method.
def containsTyped(x: T): Boolean =
isWithinBoundaries(x) && (((x - start) % step) == zero)
override def contains[A1 >: T](x: A1): Boolean =
try containsTyped(x.asInstanceOf[T])
catch { case _: ClassCastException => false }
final override def sum[B >: T](implicit num: Numeric[B]): B = {
if (isEmpty) num.zero
else if (numRangeElements == 1) head
else {
// If there is no overflow, use arithmetic series formula
// a + ... (n terms total) ... + b = n*(a+b)/2
if ((num eq scala.math.Numeric.IntIsIntegral)||
(num eq scala.math.Numeric.ShortIsIntegral)||
(num eq scala.math.Numeric.ByteIsIntegral)||
(num eq scala.math.Numeric.CharIsIntegral)) {
// We can do math with no overflow in a Long--easy
val exact = (numRangeElements * ((num toLong head) + (num toInt last))) / 2
num fromInt exact.toInt
}
else if (num eq scala.math.Numeric.LongIsIntegral) {
// Uh-oh, might be overflow, so we have to divide before we overflow.
// Either numRangeElements or (head + last) must be even, so divide the even one before multiplying
val a = head.toLong
val b = last.toLong
val ans =
if ((numRangeElements & 1) == 0) (numRangeElements / 2) * (a + b)
else numRangeElements * {
// Sum is even, but we might overflow it, so divide in pieces and add back remainder
val ha = a/2
val hb = b/2
ha + hb + ((a - 2*ha) + (b - 2*hb)) / 2
}
ans.asInstanceOf[B]
}
else if ((num eq scala.math.Numeric.FloatAsIfIntegral) ||
(num eq scala.math.Numeric.DoubleAsIfIntegral)) {
// Try to compute sum with reasonable accuracy, avoiding over/underflow
val numAsIntegral = num.asInstanceOf[Integral[B]]
import numAsIntegral._
val a = math.abs(head.toDouble)
val b = math.abs(last.toDouble)
val two = num fromInt 2
val nre = num fromInt numRangeElements
if (a > 1e38 || b > 1e38) nre * ((head / two) + (last / two)) // Compute in parts to avoid Infinity if possible
else (nre / two) * (head + last) // Don't need to worry about infinity; this will be more accurate and avoid underflow
}
else if ((num eq scala.math.Numeric.BigIntIsIntegral) ||
(num eq scala.math.Numeric.BigDecimalIsFractional)) {
// No overflow, so we can use arithmetic series formula directly
// (not going to worry about running out of memory)
val numAsIntegral = num.asInstanceOf[Integral[B]]
import numAsIntegral._
((num fromInt numRangeElements) * (head + last)) / (num fromInt 2)
}
else {
// User provided custom Numeric, so we cannot rely on arithmetic series formula (e.g. won't work on something like Z_6)
if (isEmpty) num.zero
else {
var acc = num.zero
var i = head
var idx = 0
while(idx < length) {
acc = num.plus(acc, i)
i = i + step
idx = idx + 1
}
acc
}
}
}
}
override lazy val hashCode = super.hashCode()
override def equals(other: Any) = other match {
case x: NumericRange[_] =>
(x canEqual this) && (length == x.length) && (
(length == 0) || // all empty sequences are equal
(start == x.start && last == x.last) // same length and same endpoints implies equality
)
case _ =>
super.equals(other)
}
override def toString = {
val empty = if (isEmpty) "empty " else ""
val preposition = if (isInclusive) "to" else "until"
val stepped = if (step == 1) "" else s" by $step"
s"${empty}NumericRange $start $preposition $end$stepped"
}
}
/** A companion object for numeric ranges.
*/
object NumericRange {
/** Calculates the number of elements in a range given start, end, step, and
* whether or not it is inclusive. Throws an exception if step == 0 or
* the number of elements exceeds the maximum Int.
*/
def count[T](start: T, end: T, step: T, isInclusive: Boolean)(implicit num: Integral[T]): Int = {
val zero = num.zero
val upward = num.lt(start, end)
val posStep = num.gt(step, zero)
if (step == zero) throw new IllegalArgumentException("step cannot be 0.")
else if (start == end) if (isInclusive) 1 else 0
else if (upward != posStep) 0
else {
/* We have to be frightfully paranoid about running out of range.
* We also can't assume that the numbers will fit in a Long.
* We will assume that if a > 0, -a can be represented, and if
* a < 0, -a+1 can be represented. We also assume that if we
* can't fit in Int, we can represent 2*Int.MaxValue+3 (at least).
* And we assume that numbers wrap rather than cap when they overflow.
*/
// Check whether we can short-circuit by deferring to Int range.
val startint = num.toInt(start)
if (start == num.fromInt(startint)) {
val endint = num.toInt(end)
if (end == num.fromInt(endint)) {
val stepint = num.toInt(step)
if (step == num.fromInt(stepint)) {
return {
if (isInclusive) Range.inclusive(startint, endint, stepint).length
else Range (startint, endint, stepint).length
}
}
}
}
// If we reach this point, deferring to Int failed.
// Numbers may be big.
val one = num.one
val limit = num.fromInt(Int.MaxValue)
def check(t: T): T =
if (num.gt(t, limit)) throw new IllegalArgumentException("More than Int.MaxValue elements.")
else t
// If the range crosses zero, it might overflow when subtracted
val startside = num.signum(start)
val endside = num.signum(end)
num.toInt{
if (startside*endside >= 0) {
// We're sure we can subtract these numbers.
// Note that we do not use .rem because of different conventions for Long and BigInt
val diff = num.minus(end, start)
val quotient = check(num.quot(diff, step))
val remainder = num.minus(diff, num.times(quotient, step))
if (!isInclusive && zero == remainder) quotient else check(num.plus(quotient, one))
}
else {
// We might not even be able to subtract these numbers.
// Jump in three pieces:
// * start to -1 or 1, whichever is closer (waypointA)
// * one step, which will take us at least to 0 (ends at waypointB)
// * there to the end
val negone = num.fromInt(-1)
val startlim = if (posStep) negone else one
val startdiff = num.minus(startlim, start)
val startq = check(num.quot(startdiff, step))
val waypointA = if (startq == zero) start else num.plus(start, num.times(startq, step))
val waypointB = num.plus(waypointA, step)
check {
if (num.lt(waypointB, end) != upward) {
// No last piece
if (isInclusive && waypointB == end) num.plus(startq, num.fromInt(2))
else num.plus(startq, one)
}
else {
// There is a last piece
val enddiff = num.minus(end,waypointB)
val endq = check(num.quot(enddiff, step))
val last = if (endq == zero) waypointB else num.plus(waypointB, num.times(endq, step))
// Now we have to tally up all the pieces
// 1 for the initial value
// startq steps to waypointA
// 1 step to waypointB
// endq steps to the end (one less if !isInclusive and last==end)
num.plus(startq, num.plus(endq, if (!isInclusive && last==end) one else num.fromInt(2)))
}
}
}
}
}
}
@SerialVersionUID(-5986512874781685419L)
class Inclusive[T](start: T, end: T, step: T)(implicit num: Integral[T])
extends NumericRange(start, end, step, true) {
def copy(start: T, end: T, step: T): Inclusive[T] =
NumericRange.inclusive(start, end, step)
def exclusive: Exclusive[T] = NumericRange(start, end, step)
}
@SerialVersionUID(-7058074814271573640L)
class Exclusive[T](start: T, end: T, step: T)(implicit num: Integral[T])
extends NumericRange(start, end, step, false) {
def copy(start: T, end: T, step: T): Exclusive[T] =
NumericRange(start, end, step)
def inclusive: Inclusive[T] = NumericRange.inclusive(start, end, step)
}
def apply[T](start: T, end: T, step: T)(implicit num: Integral[T]): Exclusive[T] =
new Exclusive(start, end, step)
def inclusive[T](start: T, end: T, step: T)(implicit num: Integral[T]): Inclusive[T] =
new Inclusive(start, end, step)
private[collection] val defaultOrdering = Map[Numeric[_], Ordering[_]](
Numeric.BigIntIsIntegral -> Ordering.BigInt,
Numeric.IntIsIntegral -> Ordering.Int,
Numeric.ShortIsIntegral -> Ordering.Short,
Numeric.ByteIsIntegral -> Ordering.Byte,
Numeric.CharIsIntegral -> Ordering.Char,
Numeric.LongIsIntegral -> Ordering.Long,
Numeric.FloatAsIfIntegral -> Ordering.Float,
Numeric.DoubleAsIfIntegral -> Ordering.Double,
Numeric.BigDecimalAsIfIntegral -> Ordering.BigDecimal
)
}
