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//===--- ElementaryFunctionTests.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 XCTest
import ComplexModule
import RealModule
import _TestSupport
final class ElementaryFunctionTests: XCTestCase {
func testExp<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// exp(0) = 1
XCTAssertEqual(1, Complex<T>.exp(Complex( 0, 0)))
XCTAssertEqual(1, Complex<T>.exp(Complex(-0, 0)))
XCTAssertEqual(1, Complex<T>.exp(Complex(-0,-0)))
XCTAssertEqual(1, Complex<T>.exp(Complex( 0,-0)))
// In general, exp(Complex(r,0)) should be exp(r), but that breaks down
// when r is infinity or NaN, because we want all non-finite complex
// values to be semantically a single point at infinity. This is fine
// for most inputs, but exp(Complex(-.infinity, 0)) would produce
// 0 if we evaluated it in the usual way.
XCTAssertFalse(Complex<T>.exp(Complex( .infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex( .infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex( 0, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex(-.infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex(-.infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex(-.infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex( 0,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex( .infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex( .nan, .nan)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex( .infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex( .nan, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex(-.infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.exp(Complex( .nan,-.infinity)).isFinite)
// Find a value of x such that exp(x) just overflows. Then exp((x, π/4))
// should not overflow, but will do so if it is not computed carefully.
// The correct value is:
//
// exp((log(gfm) + log(9/8), π/4) = exp((log(gfm*9/8), π/4))
// = gfm*9/8 * (1/sqrt(2), 1/(sqrt(2))
let x = T.log(.greatestFiniteMagnitude) + T.log(9/8)
let huge = Complex<T>.exp(Complex(x, .pi/4))
let mag = T.greatestFiniteMagnitude/T.sqrt(2) * (9/8)
XCTAssert(huge.real.isApproximatelyEqual(to: mag))
XCTAssert(huge.imaginary.isApproximatelyEqual(to: mag))
// For randomly-chosen well-scaled finite values, we expect to have the
// usual identities:
//
// exp(z + w) = exp(z) * exp(w)
// exp(z - w) = exp(z) / exp(w)
var g = SystemRandomNumberGenerator()
let values: [Complex<T>] = (0..<100).map { _ in
Complex(T.random(in: -1 ... 1, using: &g),
T.random(in: -.pi ... .pi, using: &g))
}
for z in values {
for w in values {
let p = Complex.exp(z) * Complex.exp(w)
let q = Complex.exp(z) / Complex.exp(w)
XCTAssert(Complex.exp(z + w).isApproximatelyEqual(to: p))
XCTAssert(Complex.exp(z - w).isApproximatelyEqual(to: q))
}
}
}
func testExpMinusOne<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// expMinusOne(0) = 0
XCTAssertEqual(0, Complex<T>.expMinusOne(Complex( 0, 0)))
XCTAssertEqual(0, Complex<T>.expMinusOne(Complex(-0, 0)))
XCTAssertEqual(0, Complex<T>.expMinusOne(Complex(-0,-0)))
XCTAssertEqual(0, Complex<T>.expMinusOne(Complex( 0,-0)))
// In general, expMinusOne(Complex(r,0)) should be expMinusOne(r), but
// that breaks down when r is infinity or NaN, because we want all non-
// finite complex values to be semantically a single point at infinity.
// This is fine for most inputs, but expMinusOne(Complex(-.infinity, 0))
// would produce 0 if we evaluated it in the usual way.
XCTAssertFalse(Complex<T>.expMinusOne(Complex( .infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex( .infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex( 0, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex(-.infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex(-.infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex(-.infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex( 0,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex( .infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex( .nan, .nan)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex( .infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex( .nan, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex(-.infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.expMinusOne(Complex( .nan,-.infinity)).isFinite)
// Near-overflow test, same as exp() above.
let x = T.log(.greatestFiniteMagnitude) + T.log(9/8)
let huge = Complex<T>.expMinusOne(Complex(x, .pi/4))
let mag = T.greatestFiniteMagnitude/T.sqrt(2) * (9/8)
XCTAssert(huge.real.isApproximatelyEqual(to: mag))
XCTAssert(huge.imaginary.isApproximatelyEqual(to: mag))
// For small values, expMinusOne should be approximately the identity.
var g = SystemRandomNumberGenerator()
let small = T.ulpOfOne
for _ in 0 ..< 100 {
let z = Complex<T>(T.random(in: -small ... small, using: &g),
T.random(in: -small ... small, using: &g))
XCTAssert(z.isApproximatelyEqual(to: Complex.expMinusOne(z), relativeTolerance: 16 * .ulpOfOne))
}
}
func testLogOnePlus<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// log(onePlus: 0) = 0
XCTAssertEqual(0, Complex<T>.log(onePlus: Complex( 0, 0)))
XCTAssertEqual(0, Complex<T>.log(onePlus: Complex(-0, 0)))
XCTAssertEqual(0, Complex<T>.log(onePlus: Complex(-0,-0)))
XCTAssertEqual(0, Complex<T>.log(onePlus: Complex( 0,-0)))
// log(onePlus:) is the identity at infinity.
XCTAssertFalse(Complex<T>.log(onePlus: Complex( .infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex( .infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex( 0, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex(-.infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex(-.infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex(-.infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex( 0,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex( .infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex( .nan, .nan)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex( .infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex( .nan, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex(-.infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.log(onePlus: Complex( .nan,-.infinity)).isFinite)
// For randomly-chosen well-scaled finite values, we expect to have
// log(onePlus: expMinusOne(z)) ≈ z
var g = SystemRandomNumberGenerator()
let values: [Complex<T>] = (0..<1000).map { _ in
Complex(T.random(in: -2 ... 2, using: &g),
T.random(in: -2 ... 2, using: &g))
}
for z in values {
let w = Complex.expMinusOne(z)
let u = Complex.log(onePlus: w)
if !u.isApproximatelyEqual(to: z) {
print("log(onePlus: expMinusOne()) was not close to identity at z = \(z).")
print("expMinusOne(\(z)) = \(w).")
print("long(onePlus: \(w)) = \(u).")
XCTFail()
}
}
}
func testCosh<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// cosh(0) = 1
XCTAssertEqual(1, Complex<T>.cosh(Complex( 0, 0)))
XCTAssertEqual(1, Complex<T>.cosh(Complex(-0, 0)))
XCTAssertEqual(1, Complex<T>.cosh(Complex(-0,-0)))
XCTAssertEqual(1, Complex<T>.cosh(Complex( 0,-0)))
// cosh is the identity at infinity.
XCTAssertFalse(Complex<T>.cosh(Complex( .infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex( .infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex( 0, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex(-.infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex(-.infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex(-.infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex( 0,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex( .infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex( .nan, .nan)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex( .infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex( .nan, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex(-.infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.cosh(Complex( .nan,-.infinity)).isFinite)
// Near-overflow test, same as exp() above, but it happens later, because
// for large x, cosh(x + iy) ~ exp(x + iy)/2.
let x = T.log(.greatestFiniteMagnitude) + T.log(18/8)
let mag = T.greatestFiniteMagnitude/T.sqrt(2) * (9/8)
var huge = Complex<T>.cosh(Complex(x, .pi/4))
XCTAssert(huge.real.isApproximatelyEqual(to: mag))
XCTAssert(huge.imaginary.isApproximatelyEqual(to: mag))
huge = Complex<T>.cosh(Complex(-x, .pi/4))
XCTAssert(huge.real.isApproximatelyEqual(to: mag))
XCTAssert(huge.imaginary.isApproximatelyEqual(to: mag))
}
func testSinh<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// sinh(0) = 0
XCTAssertEqual(0, Complex<T>.sinh(Complex( 0, 0)))
XCTAssertEqual(0, Complex<T>.sinh(Complex(-0, 0)))
XCTAssertEqual(0, Complex<T>.sinh(Complex(-0,-0)))
XCTAssertEqual(0, Complex<T>.sinh(Complex( 0,-0)))
// sinh is the identity at infinity.
XCTAssertFalse(Complex<T>.sinh(Complex( .infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex( .infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex( 0, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex(-.infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex(-.infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex(-.infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex( 0,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex( .infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex( .nan, .nan)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex( .infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex( .nan, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex(-.infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.sinh(Complex( .nan,-.infinity)).isFinite)
// Near-overflow test, same as exp() above, but it happens later, because
// for large x, sinh(x + iy) ~ ±exp(x + iy)/2.
let x = T.log(.greatestFiniteMagnitude) + T.log(18/8)
let mag = T.greatestFiniteMagnitude/T.sqrt(2) * (9/8)
var huge = Complex<T>.sinh(Complex(x, .pi/4))
XCTAssert(huge.real.isApproximatelyEqual(to: mag))
XCTAssert(huge.imaginary.isApproximatelyEqual(to: mag))
huge = Complex<T>.sinh(Complex(-x, .pi/4))
XCTAssert(huge.real.isApproximatelyEqual(to: -mag))
XCTAssert(huge.imaginary.isApproximatelyEqual(to: -mag))
// For randomly-chosen well-scaled finite values, we expect to have
// cosh² - sinh² ≈ 1. Note that this test would break down due to
// catastrophic cancellation as we get further away from the origin.
var g = SystemRandomNumberGenerator()
let values: [Complex<T>] = (0..<1000).map { _ in
Complex(T.random(in: -2 ... 2, using: &g),
T.random(in: -2 ... 2, using: &g))
}
for z in values {
let c = Complex.cosh(z)
let s = Complex.sinh(z)
XCTAssert((c*c - s*s).isApproximatelyEqual(to: 1))
}
}
func testAcos<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// acos(1) = 0
XCTAssertEqual(0, Complex<T>.acos(1))
// acos(0) = π/2
XCTAssert(Complex<T>.acos(0).real.isApproximatelyEqual(to: .pi/2))
XCTAssertEqual(Complex<T>.acos(0).imaginary, 0)
// acos(-1) = π
XCTAssert(Complex<T>.acos(-1).real.isApproximatelyEqual(to: .pi))
XCTAssertEqual(Complex<T>.acos(-1).imaginary, 0)
// acos is the identity at infinity.
XCTAssertFalse(Complex<T>.acos(Complex( .infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex( .infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex( 0, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex(-.infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex(-.infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex(-.infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex( 0,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex( .infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex( .nan, .nan)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex( .infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex( .nan, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex(-.infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.acos(Complex( .nan,-.infinity)).isFinite)
// For randomly-chosen well-scaled finite values, we expect to have
// cos(acos(z)) ≈ z and acos(z) ≈ π - acos(-z)
var g = SystemRandomNumberGenerator()
let values: [Complex<T>] = (0..<1000).map { _ in
Complex(T.random(in: -2 ... 2, using: &g),
T.random(in: -2 ... 2, using: &g))
}
for z in values {
let w = Complex.acos(z)
XCTAssert(Complex.cos(w).isApproximatelyEqual(to: z))
XCTAssert(w.isApproximatelyEqual(to: Complex(.pi) - .acos(-z)))
}
}
func testAsin<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// asin(1) = π/2
XCTAssert(Complex<T>.asin(1).real.isApproximatelyEqual(to: .pi/2))
XCTAssertEqual(Complex<T>.asin(1).imaginary, 0)
// asin(0) = 0
XCTAssertEqual(0, Complex<T>.asin(0))
// asin(-1) = -π/2
XCTAssert(Complex<T>.asin(-1).real.isApproximatelyEqual(to: -.pi/2))
XCTAssertEqual(Complex<T>.asin(-1).imaginary, 0)
// asin is the identity at infinity.
XCTAssertFalse(Complex<T>.asin(Complex( .infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex( .infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex( 0, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex(-.infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex(-.infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex(-.infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex( 0,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex( .infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex( .nan, .nan)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex( .infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex( .nan, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex(-.infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.asin(Complex( .nan,-.infinity)).isFinite)
// For randomly-chosen well-scaled finite values, we expect to have
// sin(asin(z)) ≈ z and asin(z) ≈ -asin(-z)
var g = SystemRandomNumberGenerator()
let values: [Complex<T>] = (0..<1000).map { _ in
Complex(T.random(in: -2 ... 2, using: &g),
T.random(in: -2 ... 2, using: &g))
}
for z in values {
let w = Complex.asin(z)
XCTAssert(Complex.sin(w).isApproximatelyEqual(to: z))
XCTAssert(w.isApproximatelyEqual(to: -.asin(-z)))
}
}
func testAcosh<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// acosh(1) = 0
XCTAssertEqual(0, Complex<T>.acosh(1))
// acosh(0) = iπ/2
XCTAssert(Complex<T>.acosh(0).imaginary.isApproximatelyEqual(to: .pi/2))
XCTAssertEqual(Complex<T>.acosh(0).real, 0)
// acosh(-1) = iπ
XCTAssert(Complex<T>.acosh(-1).imaginary.isApproximatelyEqual(to: .pi))
XCTAssertEqual(Complex<T>.acosh(-1).real, 0)
// acosh is the identity at infinity.
XCTAssertFalse(Complex<T>.acosh(Complex( .infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex( .infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex( 0, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex(-.infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex(-.infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex(-.infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex( 0,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex( .infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex( .nan, .nan)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex( .infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex( .nan, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex(-.infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.acosh(Complex( .nan,-.infinity)).isFinite)
// For randomly-chosen well-scaled finite values, we expect to have
// cosh(acosh(z)) ≈ z
var g = SystemRandomNumberGenerator()
let values: [Complex<T>] = (0..<1000).map { _ in
Complex(T.random(in: -2 ... 2, using: &g),
T.random(in: -2 ... 2, using: &g))
}
for z in values {
let w = Complex.acosh(z)
XCTAssert(Complex.cosh(w).isApproximatelyEqual(to: z))
}
}
func testAsinh<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// asinh(1) = π/2
XCTAssert(Complex<T>.asin(1).real.isApproximatelyEqual(to: .pi/2))
XCTAssertEqual(Complex<T>.asin(1).imaginary, 0)
// asinh(0) = 0
XCTAssertEqual(0, Complex<T>.asin(0))
// asinh(-1) = -π/2
XCTAssert(Complex<T>.asin(-1).real.isApproximatelyEqual(to: -.pi/2))
XCTAssertEqual(Complex<T>.asin(-1).imaginary, 0)
// asinh is the identity at infinity.
XCTAssertFalse(Complex<T>.asinh(Complex( .infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex( .infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex( 0, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex(-.infinity, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex(-.infinity, 0)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex(-.infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex( 0,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex( .infinity,-.infinity)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex( .nan, .nan)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex( .infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex( .nan, .infinity)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex(-.infinity, .nan)).isFinite)
XCTAssertFalse(Complex<T>.asinh(Complex( .nan,-.infinity)).isFinite)
// For randomly-chosen well-scaled finite values, we expect to have
// sinh(asinh(z)) ≈ z
var g = SystemRandomNumberGenerator()
let values: [Complex<T>] = (0..<1000).map { _ in
Complex(T.random(in: -2 ... 2, using: &g),
T.random(in: -2 ... 2, using: &g))
}
for z in values {
let w = Complex.asinh(z)
let u = Complex.sinh(w)
if !u.isApproximatelyEqual(to: z) {
print("sinh(asinh()) was not close to identity at z = \(z).")
print("asinh(\(z)) = \(w).")
print("sinh(\(w)) = \(u).")
XCTFail()
}
}
}
func testAtanh<T: Real & FixedWidthFloatingPoint>(_ type: T.Type) {
// For randomly-chosen well-scaled finite values, we expect to have
// atanh(tanh(z)) ≈ z
var g = SystemRandomNumberGenerator()
let values: [Complex<T>] = (0..<1000).map { _ in
Complex(T.random(in: -2 ... 2, using: &g),
T.random(in: -2 ... 2, using: &g))
}
for z in values {
let w = Complex.atanh(z)
let u = Complex.tanh(w)
if !u.isApproximatelyEqual(to: z) {
print("tanh(atanh()) was not close to identity at z = \(z).")
print("atanh(\(z)) = \(w).")
print("tanh(\(w)) = \(u).")
XCTFail()
}
}
}
func testFloat() {
testExp(Float.self)
testExpMinusOne(Float.self)
testLogOnePlus(Float.self)
testCosh(Float.self)
testSinh(Float.self)
testAcos(Float.self)
testAsin(Float.self)
testAcosh(Float.self)
testAsinh(Float.self)
testAtanh(Float.self)
}
func testDouble() {
testExp(Double.self)
testExpMinusOne(Double.self)
testLogOnePlus(Float.self)
testCosh(Double.self)
testSinh(Double.self)
testAcos(Double.self)
testAsin(Double.self)
testAcosh(Double.self)
testAsinh(Double.self)
testAtanh(Double.self)
}
#if (arch(i386) || arch(x86_64)) && !os(Windows) && !os(Android)
func testFloat80() {
testExp(Float80.self)
testExpMinusOne(Float80.self)
testLogOnePlus(Float.self)
testCosh(Float80.self)
testSinh(Float80.self)
testAcos(Float80.self)
testAsin(Float80.self)
testAcosh(Float80.self)
testAsinh(Float80.self)
testAtanh(Float80.self)
}
#endif
}
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