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ANKFullWidth+Multiplication.swift
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ANKFullWidth+Multiplication.swift
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//=----------------------------------------------------------------------------=
// This source file is part of the AwesomeNumbersKit open source project.
//
// Copyright (c) 2022 Oscar Byström Ericsson
// Licensed under Apache License, Version 2.0
//
// See http://www.apache.org/licenses/LICENSE-2.0 for license information.
//=----------------------------------------------------------------------------=
import ANKCoreKit
//*============================================================================*
// MARK: * ANK x Full Width x Multiplication
//*============================================================================*
extension ANKFullWidth {
//=------------------------------------------------------------------------=
// MARK: Transformations
//=------------------------------------------------------------------------=
@inlinable public mutating func multiplyReportingOverflow(by other: Self) -> Bool {
let pvo: PVO<Self> = self.multipliedReportingOverflow(by: other)
self = pvo.partialValue
return pvo.overflow as Bool
}
@inlinable public func multipliedReportingOverflow(by other: Self) -> PVO<Self> {
let lhsIsLessThanZero: Bool = self .isLessThanZero
let rhsIsLessThanZero: Bool = other.isLessThanZero
let minus = lhsIsLessThanZero != rhsIsLessThanZero
//=--------------------------------------=
var pvo = ANK.bitCast(self.magnitude.multipliedReportingOverflow(by: other.magnitude)) as PVO<Self>
//=--------------------------------------=
var suboverflow = (pvo.partialValue.isLessThanZero)
if minus {
suboverflow = !pvo.partialValue.formTwosComplementSubsequence(true) && suboverflow
}
pvo.overflow = pvo.overflow || suboverflow as Bool
//=--------------------------------------=
return pvo as PVO<Self>
}
//=------------------------------------------------------------------------=
// MARK: Transformations
//=------------------------------------------------------------------------=
@inlinable public mutating func multiplyFullWidth(by other: Self) -> Self {
let product: HL<Self, Magnitude> = self.multipliedFullWidth(by: other)
self = Self(bitPattern: product.low)
return product.high as Self
}
@inlinable public func multipliedFullWidth(by other: Self) -> HL<Self, Magnitude> {
let lhsIsLessThanZero: Bool = self .isLessThanZero
let rhsIsLessThanZero: Bool = other.isLessThanZero
var minus = lhsIsLessThanZero != rhsIsLessThanZero
//=--------------------------------------=
var product = self.magnitude.multipliedFullWidth(by: other.magnitude)
//=--------------------------------------=
if minus {
minus = product.low .formTwosComplementSubsequence(minus)
minus = product.high.formTwosComplementSubsequence(minus)
}
//=--------------------------------------=
return ANK.bitCast(product) as HL<Self, Magnitude>
}
}
//=----------------------------------------------------------------------------=
// MARK: + Unsigned
//=----------------------------------------------------------------------------=
extension ANKFullWidth where High == High.Magnitude {
//=------------------------------------------------------------------------=
// MARK: Transformations
//=------------------------------------------------------------------------=
@inlinable func multipliedReportingOverflow(by other: Self) -> PVO<Self> {
switch High.Magnitude.self == Low.self {
case true: return self.multipliedReportingOverflowAsKaratsubaAsDoubleWidthOrCrash(by: other)
case false: return self.multipliedReportingOverflowAsNormal(by: other) }
}
@inlinable func multipliedReportingOverflowAsKaratsubaAsDoubleWidthOrCrash(by other: Self) -> PVO<Self> {
(self as! ANKFullWidth<Low, Low>).multipliedReportingOverflowAsKaratsuba(by:(other as! ANKFullWidth<Low, Low>)) as! PVO<Self>
}
//=------------------------------------------------------------------------=
// MARK: Transformations x Full Width
//=------------------------------------------------------------------------=
@inlinable func multipliedFullWidth(by other: Self) -> HL<Self, Magnitude> {
switch High.Magnitude.self == Low.self {
case true: return self.multipliedFullWidthAsKaratsubaAsDoubleWidthOrCrash(by: other)
case false: return self.multipliedFullWidthAsNormal(by: other) }
}
@inlinable func multipliedFullWidthAsKaratsubaAsDoubleWidthOrCrash(by other: Self) -> HL<Self, Magnitude> {
(self as! ANKFullWidth<Low, Low>).multipliedFullWidthAsKaratsuba(by:(other as! ANKFullWidth<Low, Low>)) as! HL<Self, Magnitude>
}
}
//=----------------------------------------------------------------------------=
// MARK: + Unsigned x Normal
//=----------------------------------------------------------------------------=
extension ANKFullWidth where High == High.Magnitude {
//=------------------------------------------------------------------------=
// MARK: Transformations
//=------------------------------------------------------------------------=
@inlinable func multipliedReportingOverflowAsNormal(by other: Self) -> PVO<Self> {
let product = self.multipliedFullWidthAsNormal(by: other) as HL<Self, Magnitude>
return PVO(product.low, !product.high.isZero)
}
//=------------------------------------------------------------------------=
// MARK: Transformations x Full Width
//=------------------------------------------------------------------------=
@inlinable func multipliedFullWidthAsNormal(by other: Self) -> HL<Self, Magnitude> {
self.multipliedFullWidthAsNormal(by: other).descending
}
@inlinable func multipliedFullWidthAsNormal(by other: Self) -> ANKFullWidth<Self, Magnitude> {
ANKFullWidth<Self, Magnitude>.fromUnsafeMutableWords { product in
self .withUnsafeWords { this in
other.withUnsafeWords { other in
//=----------------------------------=
let subrange = this.indices
//=----------------------------------=
for productIndex in subrange {
product[productIndex] = UInt.zero
}
//=----------------------------------=
for lhsIndex in subrange {
var carry = UInt.zero
let lhsWord = this[lhsIndex]
for rhsIndex in subrange {
let rhsWord = other[rhsIndex]
let productIndex = lhsIndex &+ rhsIndex
var subproduct = lhsWord.multipliedFullWidth(by: rhsWord)
carry = UInt(bit: subproduct.low.addReportingOverflow(carry))
carry &+= UInt(bit: product[productIndex].addReportingOverflow(subproduct.low))
carry &+= subproduct.high
}
product[subrange.endIndex &+ lhsIndex] = carry
}
}}}
}
}
//=----------------------------------------------------------------------------=
// MARK: + Unsigned x Karatsuba
//=----------------------------------------------------------------------------=
extension ANKFullWidth where High == Low {
//=------------------------------------------------------------------------=
// MARK: Transformations x Transformations
//=------------------------------------------------------------------------=
/// An adaptation of Anatoly Karatsuba's multiplication algorithm.
@inlinable func multipliedReportingOverflowAsKaratsuba(by other: Self) -> PVO<Self> {
var ax = self.low .multipliedFullWidth(by: other.low)
let ay = self.low .multipliedReportingOverflow(by: other.high)
let bx = self.high.multipliedReportingOverflow(by: other.low )
let by = !(self.high.isZero || other.high.isZero)
//=--------------------------------------=
let o0 = ax.high.addReportingOverflow(ay.partialValue) as Bool
let o1 = ax.high.addReportingOverflow(bx.partialValue) as Bool
//=--------------------------------------=
let overflow = by || ay.overflow || bx.overflow || o0 || o1
//=--------------------------------------=
return PVO(Self(descending: ax), overflow)
}
//=------------------------------------------------------------------------=
// MARK: Transformations x Full Width
//=------------------------------------------------------------------------=
/// An adaptation of Anatoly Karatsuba's multiplication algorithm.
///
/// ### Order of operations
///
/// The order of operations matters a lot, so don't reorder it without a profiler.
///
@inlinable func multipliedFullWidthAsKaratsuba(by other: Self) -> HL<Self, Magnitude> {
var ax = self.low .multipliedFullWidth(by: other.low ) as HL<High, Low>
let ay = self.low .multipliedFullWidth(by: other.high) as HL<High, Low>
let bx = self.high.multipliedFullWidth(by: other.low ) as HL<High, Low>
var by = self.high.multipliedFullWidth(by: other.high) as HL<High, Low>
//=--------------------------------------=
let a0 = ax.high.addReportingOverflow(bx.low) as Bool
let a1 = ax.high.addReportingOverflow(ay.low) as Bool
let a2 = UInt(bit: a0) &+ UInt(bit: a1)
let b0 = by.low.addReportingOverflow(bx.high) as Bool
let b1 = by.low.addReportingOverflow(ay.high) as Bool
let b2 = UInt(bit: b0) &+ UInt(bit: b1)
//=--------------------------------------=
let lo = Magnitude(descending: ax)
var hi = Magnitude(descending: by)
let o0 = hi.low .addReportingOverflow(a2) as Bool
let _ = hi.high.addReportingOverflow(b2 &+ UInt(bit: o0)) as Bool
//=--------------------------------------=
return HL(high: hi, low: lo)
}
}