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[NBKCoreKit] Cleanup and some long division stuff.
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Sources/NBKCoreKit/Private/NBKStrictUnsignedInteger+Division+Long.swift
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| //=----------------------------------------------------------------------------= | ||
| // This source file is part of the Numberick open source project. | ||
| // | ||
| // Copyright (c) 2023 Oscar Byström Ericsson | ||
| // Licensed under Apache License, Version 2.0 | ||
| // | ||
| // See http://www.apache.org/licenses/LICENSE-2.0 for license information. | ||
| //=----------------------------------------------------------------------------= | ||
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| //*============================================================================* | ||
| // MARK: * NBK x Strict Unsigned Integer x Division x Long | ||
| //*============================================================================* | ||
| //=----------------------------------------------------------------------------= | ||
| // MARK: + where Base is Unsafe Buffer Pointer | ||
| //=----------------------------------------------------------------------------= | ||
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| extension NBK.StrictUnsignedInteger where Base: MutableCollection { | ||
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| //=------------------------------------------------------------------------= | ||
| // MARK: Initializers | ||
| //=------------------------------------------------------------------------= | ||
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| /// Initializes `base` to the [long][algorithm] `quotient` of dividing the | ||
| /// `dividend` by the `divisor` and forms the `remainder` in the `dividend`. | ||
| /// | ||
| /// - Parameter base: A nonempty buffer of size `dividend.count - divisor.count`. | ||
| /// | ||
| /// - Parameter dividend: The normalized `dividend`. It must be wider than | ||
| /// the `divisor` and less than `divisor << (Element.bitWidth * base.count)` | ||
| /// to ensure that the `quotient` fits. | ||
| /// | ||
| /// - Parameter divisor: The normalized `divisor`. Its last element's most significant | ||
| /// bit must be set to ensure that the initial `quotient` element approximation does | ||
| /// not exceed the real `quotient` by more than 2. | ||
| /// | ||
| /// - Important: The `base` must be uninitialized, or its elements must be trivial. | ||
| /// | ||
| /// [algorithm]: https://en.wikipedia.org/wiki/long_division | ||
| /// | ||
| /// ## Example Usage in Long Division Algorithm | ||
| /// | ||
| /// ```swift | ||
| /// // try fast path | ||
| /// // normalization | ||
| /// | ||
| /// var quotient = uninitialized(remainder.count - divisor.count) { | ||
| /// initializeToQuotientFormRemainderByLongAlgorithm2111MSB(&$0, dividing: ÷nd, by: divisor) | ||
| /// } | ||
| /// | ||
| /// // normalization | ||
| /// // return values | ||
| /// ``` | ||
| /// | ||
| @inlinable public static func initializeToQuotientFormRemainderByLongAlgorithm2111MSB<T>( | ||
| _ base: inout Base, dividing dividend: inout Base, by divisor: UnsafeBufferPointer<T>) | ||
| where Base == UnsafeMutableBufferPointer<T> { | ||
| //=--------------------------------------= | ||
| Swift.assert(base.count >= 1 && base.count == dividend.count - divisor.count, | ||
| "the dividend must be wider than the divisor") | ||
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| Swift.assert(NBK.SUISS.compare(dividend.dropFirst(base.count), to: divisor).isLessThanZero, | ||
| "the quotient must fit in dividend.count - divisor.count elements") | ||
| //=--------------------------------------= | ||
| for index in base.indices.reversed() { | ||
| let digit = NBK.SUI.formRemainderWithQuotientByOneLongIteration2111MSB( | ||
| dividing: ÷nd[index ..< index &+ divisor.count &+ 1], by: divisor) | ||
| base.baseAddress!.advanced(by: index).initialize(to: digit) | ||
| } | ||
| } | ||
| } | ||
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| //=----------------------------------------------------------------------------= | ||
| // MARK: + where Base is Mutable Collection | ||
| //=----------------------------------------------------------------------------= | ||
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| extension NBK.StrictUnsignedInteger where Base: MutableCollection { | ||
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| //=------------------------------------------------------------------------= | ||
| // MARK: Transformations | ||
| //=------------------------------------------------------------------------= | ||
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| /// Forms the `remainder` of dividing the `dividend` by the `divisor`, | ||
| /// then returns the `quotient`. Its arguments must match the arguments | ||
| /// of one long division iteration. | ||
| /// | ||
| /// - Parameter dividend: The current iteration's `remainder` slice from the `quotient` | ||
| /// element's index. It must be exactly one element wider than the `divisor`. | ||
| /// | ||
| /// - Parameter divisor: The normalized `divisor`. Its last element's most significant | ||
| /// bit must be set to ensure that the initial `quotient` element approximation does | ||
| /// not exceed the real `quotient` by more than 2. | ||
| /// | ||
| /// ## Example Usage in Long Division Algorithm | ||
| /// | ||
| /// ```swift | ||
| /// // try fast path | ||
| /// // normalization | ||
| /// | ||
| /// var quotient = uninitialized(dividend.count - divisor.count) { | ||
| /// for index in $0.indices.reversed() { | ||
| /// let digit = formRemainderWithQuotientByOneLongIteration2111MSB( | ||
| /// dividing: ÷nd[index ..< index &+ divisor.count &+ 1], by: divisor) | ||
| /// $0.baseAddress!.advanced(by: index).initialize(to: digit) | ||
| /// } | ||
| /// } | ||
| /// | ||
| /// // normalization | ||
| /// // return values | ||
| /// ``` | ||
| /// | ||
| @inlinable public static func formRemainderWithQuotientByOneLongIteration2111MSB( | ||
| dividing dividend: inout Base, by divisor: some RandomAccessCollection<Base.Element>) -> Base.Element { | ||
| //=--------------------------------------= | ||
| Swift.assert(divisor.last!.mostSignificantBit, | ||
| "the divisor must be normalized") | ||
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| Swift.assert(dividend.count == divisor.count + 1, | ||
| "the dividend must be exactly one element wider than the divisor") | ||
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| Swift.assert(NBK.SUISS.compare(dividend.dropFirst(), to: divisor).isLessThanZero, | ||
| "the quotient of each iteration must fit in one element") | ||
| //=--------------------------------------= | ||
| let numerator = NBK.TBI<Base.Element>.suffix2(dividend) | ||
| let denominator = NBK.TBI<Base.Element>.suffix1(divisor ) | ||
| //=--------------------------------------= | ||
| var quotient: Base.Element = denominator == numerator.high | ||
| ? Base.Element.max // the quotient must fit in one element | ||
| : denominator.dividingFullWidth((((numerator)))) .quotient | ||
| //=--------------------------------------= | ||
| if quotient.isZero { return quotient } | ||
| //=--------------------------------------= | ||
| var overflow = (NBK).SUISS.decrementInIntersection(÷nd, by: divisor, times: quotient).overflow | ||
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| decrementQuotientAtMostTwice: while overflow { | ||
| quotient = quotient &- 1 as Base.Element | ||
| overflow = !NBK .SUISS.increment(÷nd, by: divisor).overflow | ||
| } | ||
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| Swift.assert(NBK.SUISS.compare(dividend, to: divisor).isLessThanZero) | ||
| return quotient as Base.Element | ||
| } | ||
| } |