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Divmod Int.swift
Raw
Int.swift
extension Int {
internal func divMod(other:Int) -> (quotient:Int, modulus:Int) {
let quotient = self / other
let remainder = self % other
if (quotient > 0) || (remainder == 0) {
return (quotient, remainder)
} else if quotient == 0 && (self > 0) && (other < 0) {
let div = quotient - 1
let result = (div * other) - self
return (div, -result)
} else {
let signSituation = ((self > 0) || (other < 0))
let div = ((quotient == 0) && signSituation) ? quotient : quotient - 1
let result = abs((div * other) - self)
return (div, (other < 0) ? -result : result)
}
}
internal func quotRem(other:Int) -> (quotient:Int, remainder:Int) {
return (self / other, self % other)
}
}
Raw
IntTests.swift
//
// IntTests.swift
// Rational
//
// Created by TJ Usiyan on 3/25/16.
// Copyright © 2016 Buttons and Lights LLC. All rights reserved.
//
import XCTest
import SwiftCheck
@testable import Symbolic
@warn_unused_result public func ==(lhs:(quotient: Int, modulus: Int), rhs:(quotient: Int, modulus: Int)) -> Bool {
return (lhs.quotient == rhs.quotient) && (lhs.modulus == rhs.modulus)
}
@warn_unused_result public func ==(lhs:(quotient: Int, remainder: Int), rhs:(quotient: Int, remainder: Int)) -> Bool {
return (lhs.quotient == rhs.quotient) && (lhs.remainder == rhs.remainder)
}
class IntTests: XCTestCase {
func testAll() {
property("(x ‘quot‘ y)⋆y + (x ‘rem‘ y) == x ") <- forAll { (x: Int, y: Int) in
return (y != 0) ==> {
let (quot, rem) = x.quotRem(y)
if (quot * y) + rem == x {
return true
} else {
return false
}
}
}
property("(x ‘div‘ y)⋆y + (x ‘mod‘ y) == x ") <- forAll { (x: Int, y: Int) in
return (y != 0) ==> {
let (div, mod) = x.divMod(y)
if (div * y) + mod == x {
return true
} else {
return false
}
}
}
}
func testDivMod() {
XCTAssertTrue((-25).divMod( 12) == (quotient: -3, modulus: 11))
XCTAssertTrue((-24).divMod( 12) == (quotient: -2, modulus: 0))
XCTAssertTrue((-23).divMod( 12) == (quotient: -2, modulus: 1))
XCTAssertTrue((-22).divMod( 12) == (quotient: -2, modulus: 2))
XCTAssertTrue((-21).divMod( 12) == (quotient: -2, modulus: 3))
XCTAssertTrue((-20).divMod( 12) == (quotient: -2, modulus: 4))
XCTAssertTrue((-19).divMod( 12) == (quotient: -2, modulus: 5))
XCTAssertTrue((-18).divMod( 12) == (quotient: -2, modulus: 6))
XCTAssertTrue((-17).divMod( 12) == (quotient: -2, modulus: 7))
XCTAssertTrue((-16).divMod( 12) == (quotient: -2, modulus: 8))
XCTAssertTrue((-15).divMod( 12) == (quotient: -2, modulus: 9))
XCTAssertTrue((-14).divMod( 12) == (quotient: -2, modulus: 10))
XCTAssertTrue((-13).divMod( 12) == (quotient: -2, modulus: 11))
XCTAssertTrue((-12).divMod( 12) == (quotient: -1, modulus: 0))
XCTAssertTrue((-11).divMod( 12) == (quotient: -1, modulus: 1))
XCTAssertTrue((-10).divMod( 12) == (quotient: -1, modulus: 2))
XCTAssertTrue(( -9).divMod( 12) == (quotient: -1, modulus: 3))
XCTAssertTrue(( -8).divMod( 12) == (quotient: -1, modulus: 4))
XCTAssertTrue(( -7).divMod( 12) == (quotient: -1, modulus: 5))
XCTAssertTrue(( -6).divMod( 12) == (quotient: -1, modulus: 6))
XCTAssertTrue(( -5).divMod( 12) == (quotient: -1, modulus: 7))
XCTAssertTrue(( -4).divMod( 12) == (quotient: -1, modulus: 8))
XCTAssertTrue(( -3).divMod( 12) == (quotient: -1, modulus: 9))
XCTAssertTrue(( -2).divMod( 12) == (quotient: -1, modulus: 10))
XCTAssertTrue(( -1).divMod( 12) == (quotient: -1, modulus: 11))
XCTAssertTrue(( 0).divMod( 12) == (quotient: 0, modulus: 0))
XCTAssertTrue(( 1).divMod( 12) == (quotient: 0, modulus: 1))
XCTAssertTrue(( 2).divMod( 12) == (quotient: 0, modulus: 2))
XCTAssertTrue(( 3).divMod( 12) == (quotient: 0, modulus: 3))
XCTAssertTrue(( 4).divMod( 12) == (quotient: 0, modulus: 4))
XCTAssertTrue(( 5).divMod( 12) == (quotient: 0, modulus: 5))
XCTAssertTrue(( 6).divMod( 12) == (quotient: 0, modulus: 6))
XCTAssertTrue(( 7).divMod( 12) == (quotient: 0, modulus: 7))
XCTAssertTrue(( 8).divMod( 12) == (quotient: 0, modulus: 8))
XCTAssertTrue(( 9).divMod( 12) == (quotient: 0, modulus: 9))
XCTAssertTrue(( 10).divMod( 12) == (quotient: 0, modulus: 10))
XCTAssertTrue(( 11).divMod( 12) == (quotient: 0, modulus: 11))
XCTAssertTrue(( 12).divMod( 12) == (quotient: 1, modulus: 0))
XCTAssertTrue(( 13).divMod( 12) == (quotient: 1, modulus: 1))
XCTAssertTrue(( 14).divMod( 12) == (quotient: 1, modulus: 2))
XCTAssertTrue(( 15).divMod( 12) == (quotient: 1, modulus: 3))
XCTAssertTrue(( 16).divMod( 12) == (quotient: 1, modulus: 4))
XCTAssertTrue(( 17).divMod( 12) == (quotient: 1, modulus: 5))
XCTAssertTrue(( 18).divMod( 12) == (quotient: 1, modulus: 6))
XCTAssertTrue(( 19).divMod( 12) == (quotient: 1, modulus: 7))
XCTAssertTrue(( 20).divMod( 12) == (quotient: 1, modulus: 8))
XCTAssertTrue(( 21).divMod( 12) == (quotient: 1, modulus: 9))
XCTAssertTrue(( 22).divMod( 12) == (quotient: 1, modulus: 10))
XCTAssertTrue(( 23).divMod( 12) == (quotient: 1, modulus: 11))
XCTAssertTrue(( 24).divMod( 12) == (quotient: 2, modulus: 0))
XCTAssertTrue(( 25).divMod( 12) == (quotient: 2, modulus: 1))
XCTAssertTrue((-25).divMod(-12) == (quotient: 2, modulus: -1))
XCTAssertTrue((-24).divMod(-12) == (quotient: 2, modulus: 0))
XCTAssertTrue((-23).divMod(-12) == (quotient: 1, modulus: -11))
XCTAssertTrue((-22).divMod(-12) == (quotient: 1, modulus: -10))
XCTAssertTrue((-21).divMod(-12) == (quotient: 1, modulus: -9))
XCTAssertTrue((-20).divMod(-12) == (quotient: 1, modulus: -8))
XCTAssertTrue((-19).divMod(-12) == (quotient: 1, modulus: -7))
XCTAssertTrue((-18).divMod(-12) == (quotient: 1, modulus: -6))
XCTAssertTrue((-17).divMod(-12) == (quotient: 1, modulus: -5))
XCTAssertTrue((-16).divMod(-12) == (quotient: 1, modulus: -4))
XCTAssertTrue((-15).divMod(-12) == (quotient: 1, modulus: -3))
XCTAssertTrue((-14).divMod(-12) == (quotient: 1, modulus: -2))
XCTAssertTrue((-13).divMod(-12) == (quotient: 1, modulus: -1))
XCTAssertTrue((-12).divMod(-12) == (quotient: 1, modulus: 0))
XCTAssertTrue((-11).divMod(-12) == (quotient: 0, modulus: -11))
XCTAssertTrue((-10).divMod(-12) == (quotient: 0, modulus: -10))
XCTAssertTrue(( -9).divMod(-12) == (quotient: 0, modulus: -9))
XCTAssertTrue(( -8).divMod(-12) == (quotient: 0, modulus: -8))
XCTAssertTrue(( -7).divMod(-12) == (quotient: 0, modulus: -7))
XCTAssertTrue(( -6).divMod(-12) == (quotient: 0, modulus: -6))
XCTAssertTrue(( -5).divMod(-12) == (quotient: 0, modulus: -5))
XCTAssertTrue(( -4).divMod(-12) == (quotient: 0, modulus: -4))
XCTAssertTrue(( -3).divMod(-12) == (quotient: 0, modulus: -3))
XCTAssertTrue(( -2).divMod(-12) == (quotient: 0, modulus: -2))
XCTAssertTrue(( -1).divMod(-12) == (quotient: 0, modulus: -1))
XCTAssertTrue(( 0).divMod(-12) == (quotient: 0, modulus: 0))
XCTAssertTrue(( 1).divMod(-12) == (quotient: -1, modulus: -11))
XCTAssertTrue(( 2).divMod(-12) == (quotient: -1, modulus: -10))
XCTAssertTrue(( 3).divMod(-12) == (quotient: -1, modulus: -9))
XCTAssertTrue(( 4).divMod(-12) == (quotient: -1, modulus: -8))
XCTAssertTrue(( 5).divMod(-12) == (quotient: -1, modulus: -7))
XCTAssertTrue(( 6).divMod(-12) == (quotient: -1, modulus: -6))
XCTAssertTrue(( 7).divMod(-12) == (quotient: -1, modulus: -5))
XCTAssertTrue(( 8).divMod(-12) == (quotient: -1, modulus: -4))
XCTAssertTrue(( 9).divMod(-12) == (quotient: -1, modulus: -3))
XCTAssertTrue(( 10).divMod(-12) == (quotient: -1, modulus: -2))
XCTAssertTrue(( 11).divMod(-12) == (quotient: -1, modulus: -1))
XCTAssertTrue(( 12).divMod(-12) == (quotient: -1, modulus: 0))
XCTAssertTrue(( 13).divMod(-12) == (quotient: -2, modulus: -11))
XCTAssertTrue(( 14).divMod(-12) == (quotient: -2, modulus: -10))
XCTAssertTrue(( 15).divMod(-12) == (quotient: -2, modulus: -9))
XCTAssertTrue(( 16).divMod(-12) == (quotient: -2, modulus: -8))
XCTAssertTrue(( 17).divMod(-12) == (quotient: -2, modulus: -7))
XCTAssertTrue(( 18).divMod(-12) == (quotient: -2, modulus: -6))
XCTAssertTrue(( 19).divMod(-12) == (quotient: -2, modulus: -5))
XCTAssertTrue(( 20).divMod(-12) == (quotient: -2, modulus: -4))
XCTAssertTrue(( 21).divMod(-12) == (quotient: -2, modulus: -3))
XCTAssertTrue(( 22).divMod(-12) == (quotient: -2, modulus: -2))
XCTAssertTrue(( 23).divMod(-12) == (quotient: -2, modulus: -1))
XCTAssertTrue(( 24).divMod(-12) == (quotient: -2, modulus: 0))
XCTAssertTrue(( 25).divMod(-12) == (quotient: -3, modulus: -11))
}
func testQuotRem() {
XCTAssertTrue((-25).quotRem( 12) == (quotient: -2, remainder: -1))
XCTAssertTrue((-24).quotRem( 12) == (quotient: -2, remainder: 0))
XCTAssertTrue((-23).quotRem( 12) == (quotient: -1, remainder: -11))
XCTAssertTrue((-22).quotRem( 12) == (quotient: -1, remainder: -10))
XCTAssertTrue((-21).quotRem( 12) == (quotient: -1, remainder: -9))
XCTAssertTrue((-20).quotRem( 12) == (quotient: -1, remainder: -8))
XCTAssertTrue((-19).quotRem( 12) == (quotient: -1, remainder: -7))
XCTAssertTrue((-18).quotRem( 12) == (quotient: -1, remainder: -6))
XCTAssertTrue((-17).quotRem( 12) == (quotient: -1, remainder: -5))
XCTAssertTrue((-16).quotRem( 12) == (quotient: -1, remainder: -4))
XCTAssertTrue((-15).quotRem( 12) == (quotient: -1, remainder: -3))
XCTAssertTrue((-14).quotRem( 12) == (quotient: -1, remainder: -2))
XCTAssertTrue((-13).quotRem( 12) == (quotient: -1, remainder: -1))
XCTAssertTrue((-12).quotRem( 12) == (quotient: -1, remainder: 0))
XCTAssertTrue((-11).quotRem( 12) == (quotient: 0, remainder: -11))
XCTAssertTrue((-10).quotRem( 12) == (quotient: 0, remainder: -10))
XCTAssertTrue(( -9).quotRem( 12) == (quotient: 0, remainder: -9))
XCTAssertTrue(( -8).quotRem( 12) == (quotient: 0, remainder: -8))
XCTAssertTrue(( -7).quotRem( 12) == (quotient: 0, remainder: -7))
XCTAssertTrue(( -6).quotRem( 12) == (quotient: 0, remainder: -6))
XCTAssertTrue(( -5).quotRem( 12) == (quotient: 0, remainder: -5))
XCTAssertTrue(( -4).quotRem( 12) == (quotient: 0, remainder: -4))
XCTAssertTrue(( -3).quotRem( 12) == (quotient: 0, remainder: -3))
XCTAssertTrue(( -2).quotRem( 12) == (quotient: 0, remainder: -2))
XCTAssertTrue(( -1).quotRem( 12) == (quotient: 0, remainder: -1))
XCTAssertTrue(( 0).quotRem( 12) == (quotient: 0, remainder: 0))
XCTAssertTrue(( 1).quotRem( 12) == (quotient: 0, remainder: 1))
XCTAssertTrue(( 2).quotRem( 12) == (quotient: 0, remainder: 2))
XCTAssertTrue(( 3).quotRem( 12) == (quotient: 0, remainder: 3))
XCTAssertTrue(( 4).quotRem( 12) == (quotient: 0, remainder: 4))
XCTAssertTrue(( 5).quotRem( 12) == (quotient: 0, remainder: 5))
XCTAssertTrue(( 6).quotRem( 12) == (quotient: 0, remainder: 6))
XCTAssertTrue(( 7).quotRem( 12) == (quotient: 0, remainder: 7))
XCTAssertTrue(( 8).quotRem( 12) == (quotient: 0, remainder: 8))
XCTAssertTrue(( 9).quotRem( 12) == (quotient: 0, remainder: 9))
XCTAssertTrue(( 10).quotRem( 12) == (quotient: 0, remainder: 10))
XCTAssertTrue(( 11).quotRem( 12) == (quotient: 0, remainder: 11))
XCTAssertTrue(( 12).quotRem( 12) == (quotient: 1, remainder: 0))
XCTAssertTrue(( 13).quotRem( 12) == (quotient: 1, remainder: 1))
XCTAssertTrue(( 14).quotRem( 12) == (quotient: 1, remainder: 2))
XCTAssertTrue(( 15).quotRem( 12) == (quotient: 1, remainder: 3))
XCTAssertTrue(( 16).quotRem( 12) == (quotient: 1, remainder: 4))
XCTAssertTrue(( 17).quotRem( 12) == (quotient: 1, remainder: 5))
XCTAssertTrue(( 18).quotRem( 12) == (quotient: 1, remainder: 6))
XCTAssertTrue(( 19).quotRem( 12) == (quotient: 1, remainder: 7))
XCTAssertTrue(( 20).quotRem( 12) == (quotient: 1, remainder: 8))
XCTAssertTrue(( 21).quotRem( 12) == (quotient: 1, remainder: 9))
XCTAssertTrue(( 22).quotRem( 12) == (quotient: 1, remainder: 10))
XCTAssertTrue(( 23).quotRem( 12) == (quotient: 1, remainder: 11))
XCTAssertTrue(( 24).quotRem( 12) == (quotient: 2, remainder: 0))
XCTAssertTrue(( 25).quotRem( 12) == (quotient: 2, remainder: 1))
XCTAssertTrue((-25).quotRem(-12) == (quotient: 2, remainder: -1))
XCTAssertTrue((-24).quotRem(-12) == (quotient: 2, remainder: 0))
XCTAssertTrue((-23).quotRem(-12) == (quotient: 1, remainder: -11))
XCTAssertTrue((-22).quotRem(-12) == (quotient: 1, remainder: -10))
XCTAssertTrue((-21).quotRem(-12) == (quotient: 1, remainder: -9))
XCTAssertTrue((-20).quotRem(-12) == (quotient: 1, remainder: -8))
XCTAssertTrue((-19).quotRem(-12) == (quotient: 1, remainder: -7))
XCTAssertTrue((-18).quotRem(-12) == (quotient: 1, remainder: -6))
XCTAssertTrue((-17).quotRem(-12) == (quotient: 1, remainder: -5))
XCTAssertTrue((-16).quotRem(-12) == (quotient: 1, remainder: -4))
XCTAssertTrue((-15).quotRem(-12) == (quotient: 1, remainder: -3))
XCTAssertTrue((-14).quotRem(-12) == (quotient: 1, remainder: -2))
XCTAssertTrue((-13).quotRem(-12) == (quotient: 1, remainder: -1))
XCTAssertTrue((-12).quotRem(-12) == (quotient: 1, remainder: 0))
XCTAssertTrue((-11).quotRem(-12) == (quotient: 0, remainder: -11))
XCTAssertTrue((-10).quotRem(-12) == (quotient: 0, remainder: -10))
XCTAssertTrue(( -9).quotRem(-12) == (quotient: 0, remainder: -9))
XCTAssertTrue(( -8).quotRem(-12) == (quotient: 0, remainder: -8))
XCTAssertTrue(( -7).quotRem(-12) == (quotient: 0, remainder: -7))
XCTAssertTrue(( -6).quotRem(-12) == (quotient: 0, remainder: -6))
XCTAssertTrue(( -5).quotRem(-12) == (quotient: 0, remainder: -5))
XCTAssertTrue(( -4).quotRem(-12) == (quotient: 0, remainder: -4))
XCTAssertTrue(( -3).quotRem(-12) == (quotient: 0, remainder: -3))
XCTAssertTrue(( -2).quotRem(-12) == (quotient: 0, remainder: -2))
XCTAssertTrue(( -1).quotRem(-12) == (quotient: 0, remainder: -1))
XCTAssertTrue(( 0).quotRem(-12) == (quotient: 0, remainder: 0))
XCTAssertTrue(( 1).quotRem(-12) == (quotient: 0, remainder: 1))
XCTAssertTrue(( 2).quotRem(-12) == (quotient: 0, remainder: 2))
XCTAssertTrue(( 3).quotRem(-12) == (quotient: 0, remainder: 3))
XCTAssertTrue(( 4).quotRem(-12) == (quotient: 0, remainder: 4))
XCTAssertTrue(( 5).quotRem(-12) == (quotient: 0, remainder: 5))
XCTAssertTrue(( 6).quotRem(-12) == (quotient: 0, remainder: 6))
XCTAssertTrue(( 7).quotRem(-12) == (quotient: 0, remainder: 7))
XCTAssertTrue(( 8).quotRem(-12) == (quotient: 0, remainder: 8))
XCTAssertTrue(( 9).quotRem(-12) == (quotient: 0, remainder: 9))
XCTAssertTrue(( 10).quotRem(-12) == (quotient: 0, remainder: 10))
XCTAssertTrue(( 11).quotRem(-12) == (quotient: 0, remainder: 11))
XCTAssertTrue(( 12).quotRem(-12) == (quotient: -1, remainder: 0))
XCTAssertTrue(( 13).quotRem(-12) == (quotient: -1, remainder: 1))
XCTAssertTrue(( 14).quotRem(-12) == (quotient: -1, remainder: 2))
XCTAssertTrue(( 15).quotRem(-12) == (quotient: -1, remainder: 3))
XCTAssertTrue(( 16).quotRem(-12) == (quotient: -1, remainder: 4))
XCTAssertTrue(( 17).quotRem(-12) == (quotient: -1, remainder: 5))
XCTAssertTrue(( 18).quotRem(-12) == (quotient: -1, remainder: 6))
XCTAssertTrue(( 19).quotRem(-12) == (quotient: -1, remainder: 7))
XCTAssertTrue(( 20).quotRem(-12) == (quotient: -1, remainder: 8))
XCTAssertTrue(( 21).quotRem(-12) == (quotient: -1, remainder: 9))
XCTAssertTrue(( 22).quotRem(-12) == (quotient: -1, remainder: 10))
XCTAssertTrue(( 23).quotRem(-12) == (quotient: -1, remainder: 11))
XCTAssertTrue(( 24).quotRem(-12) == (quotient: -2, remainder: 0))
XCTAssertTrue(( 25).quotRem(-12) == (quotient: -2, remainder: 1))
}
}
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