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//===--- ApproximateEqualityTests.swift -----------------------*- swift -*-===//
//
// This source file is part of the Swift.org open source project
//
// Copyright (c) 2020 Apple Inc. and the Swift project authors
// Licensed under Apache License v2.0 with Runtime Library Exception
//
// See https://swift.org/LICENSE.txt for license information
// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
//
//===----------------------------------------------------------------------===//
import RealModule
import XCTest
import _TestSupport
final class ApproximateEqualityTests: XCTestCase {
func testSpecials<T: Real>(absolute tol: T) {
let zero = T.zero
let gfm = T.greatestFiniteMagnitude
let inf = T.infinity
let nan = T.nan
XCTAssertTrue(zero.isApproximatelyEqual(to: zero, absoluteTolerance: tol))
XCTAssertTrue(zero.isApproximatelyEqual(to:-zero, absoluteTolerance: tol))
XCTAssertFalse(inf.isApproximatelyEqual(to: gfm, absoluteTolerance: tol))
XCTAssertFalse(gfm.isApproximatelyEqual(to: inf, absoluteTolerance: tol))
XCTAssertTrue(inf.isApproximatelyEqual(to: inf, absoluteTolerance: tol))
XCTAssertTrue(inf.isApproximatelyEqual(to: inf, absoluteTolerance: tol))
XCTAssertFalse(nan.isApproximatelyEqual(to: nan, absoluteTolerance: tol))
}
func testSpecials<T: Real>(relative tol: T) {
let zero = T.zero
let gfm = T.greatestFiniteMagnitude
let inf = T.infinity
let nan = T.nan
XCTAssertTrue(zero.isApproximatelyEqual(to: zero, relativeTolerance: tol))
XCTAssertTrue(zero.isApproximatelyEqual(to:-zero, relativeTolerance: tol))
XCTAssertFalse(inf.isApproximatelyEqual(to: gfm, relativeTolerance: tol))
XCTAssertFalse(gfm.isApproximatelyEqual(to: inf, relativeTolerance: tol))
XCTAssertTrue(inf.isApproximatelyEqual(to: inf, relativeTolerance: tol))
XCTAssertTrue(inf.isApproximatelyEqual(to: inf, relativeTolerance: tol))
XCTAssertFalse(nan.isApproximatelyEqual(to: nan, relativeTolerance: tol))
}
func testSpecials<T: Real>(_ type: T.Type) {
XCTAssertTrue(T.zero.isApproximatelyEqual(to: .zero))
XCTAssertTrue(T.zero.isApproximatelyEqual(to:-.zero))
testSpecials(absolute: T.zero)
testSpecials(absolute: T.leastNormalMagnitude)
testSpecials(absolute: T.greatestFiniteMagnitude)
testSpecials(relative: T.zero)
testSpecials(relative: T.ulpOfOne)
testSpecials(relative: T(1).nextDown)
testSpecials(relative: T(1))
}
func testDefaults<T: Real>(_ type: T.Type) {
let e = T.ulpOfOne.squareRoot()
XCTAssertTrue(T(1).isApproximatelyEqual(to: 1 + e))
XCTAssertTrue(T(1).isApproximatelyEqual(to: 1 - e/2))
XCTAssertFalse(T(1).isApproximatelyEqual(to: 1 + 2*e))
XCTAssertFalse(T(1).isApproximatelyEqual(to: 1 - 3*e/2))
}
func testRandom<T>(_ type: T.Type) where T: FixedWidthFloatingPoint & Real {
var g = SystemRandomNumberGenerator()
// Generate a bunch of random values in a small interval and a tolerance
// and use them to check that various properties that we would like to
// hold actually do.
var x = [1] + (0 ..< 64).map {
_ in T.random(in: 1 ..< 2, using: &g)
} + [2]
x.sort()
// We have 66 values in 1 ... 2, so if we use a tolerance of around 1/64,
// at least some of the pairs will compare equal with tolerance.
let tol = T.random(in: 1/64 ... 1/32, using: &g)
// We're going to walk the values in order, validating that some common-
// sense properties hold.
for i in x.indices {
// reflexivity
XCTAssertTrue(x[i].isApproximatelyEqual(to: x[i]))
XCTAssertTrue(x[i].isApproximatelyEqual(to: x[i], relativeTolerance: tol))
XCTAssertTrue(x[i].isApproximatelyEqual(to: x[i], absoluteTolerance: tol))
for j in i ..< x.endIndex {
// commutativity
XCTAssertTrue(
x[i].isApproximatelyEqual(to: x[j], relativeTolerance: tol) ==
x[j].isApproximatelyEqual(to: x[i], relativeTolerance: tol)
)
XCTAssertTrue(
x[i].isApproximatelyEqual(to: x[j], absoluteTolerance: tol) ==
x[j].isApproximatelyEqual(to: x[i], absoluteTolerance: tol)
)
// scale invariance for relative comparisons
let scale = T(
sign:.plus,
exponent: T.Exponent.random(in: T.leastNormalMagnitude.exponent ..< T.greatestFiniteMagnitude.exponent),
significand: 1
)
XCTAssertTrue(
x[i].isApproximatelyEqual(to: x[j], relativeTolerance: tol) ==
(scale*x[i]).isApproximatelyEqual(to: scale*x[j], relativeTolerance: tol)
)
}
// if a ≤ b ≤ c, and a ≈ c, then a ≈ b and b ≈ c (relative tolerance)
var left = x.firstIndex { x[i].isApproximatelyEqual(to: $0, relativeTolerance: tol) }
var right = x.lastIndex { x[i].isApproximatelyEqual(to: $0, relativeTolerance: tol) }
if let l = left, let r = right {
for j in l ..< r {
XCTAssertTrue(x[i].isApproximatelyEqual(to: x[j], relativeTolerance: tol))
}
}
// if a ≤ b ≤ c, and a ≈ c, then a ≈ b and b ≈ c (absolute tolerance)
left = x.firstIndex { x[i].isApproximatelyEqual(to: $0, absoluteTolerance: tol) }
right = x.lastIndex { x[i].isApproximatelyEqual(to: $0, absoluteTolerance: tol) }
if let l = left, let r = right {
for j in l ..< r {
XCTAssertTrue(x[i].isApproximatelyEqual(to: x[j], absoluteTolerance: tol))
}
}
}
}
func testFloat() {
testSpecials(Float.self)
testDefaults(Float.self)
testRandom(Float.self)
}
func testDouble() {
testSpecials(Double.self)
testDefaults(Double.self)
testRandom(Double.self)
}
#if (arch(i386) || arch(x86_64)) && !os(Windows) && !os(Android)
func testFloat80() {
testSpecials(Float80.self)
testDefaults(Float80.self)
testRandom(Float80.self)
}
#endif
}
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