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//===--- main.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 Numerics
import _TestSupport
#if DEBUG
fatalError("Run this test in Release configuration")
#else
var componentError = Double(Float.ulpOfOne/2)
var complexError = Double(Float.ulpOfOne/2)
var componentMaxInput = Complex<Float>.zero
var complexMaxInput = Complex<Float>.zero
func test(_ z: Complex<Float>) {
let tst = Complex.log(z)
// TODO: we _should_ be able to say Complex<Double>(z), but that goes through
// the slow, generic path for BinaryFloatingPoint conversion; once we get
// that resolved in the standard library, we can replace the conversion on
// this and the next line. Currently it dominate testing time if we do that.
let ref = Complex.log(Complex(Double(z.real), Double(z.imaginary)))
if tst == Complex(Float(ref.real), Float(ref.imaginary)) { return }
let thisError = relativeError(tst, ref)
if thisError > complexError {
complexMaxInput = z
complexError = thisError
}
let thisComponentError = componentwiseError(tst, ref)
if thisComponentError > componentError {
componentMaxInput = z
componentError = thisComponentError
}
}
func testWithSymmetries(_ x: Float, _ y: Float) {
test(Complex( x, y))
test(Complex( y, x))
test(Complex(-y, x))
test(Complex(-x, y))
test(Complex(-x,-y))
test(Complex(-y,-x))
test(Complex( y,-x))
test(Complex( x,-y))
}
// The hardest to evaluate cases for log are those close to the unit circle,
// where log(z) is nearly zero. We want to have plausibly dense test coverage
// close to the circle.
let radii: [Float] = [0.9,
0.95,
0.99,
0.999,
0.9999,
1 - 10 * .ulpOfOne,
1,
1 + 10 * .ulpOfOne,
1.0001,
1.001,
1.01,
1.05,
1.1]
for r in radii {
for x in Interval(from: 1/Float.sqrt(2), to: r) {
// Generate the two y values that put us closest to the circle of radius r
let base = Double.sqrt(Double(r).addingProduct(Double(-x), Double(x)))
let a, b: Float
if Double(Float(base)) < base { a = Float(base); b = a.nextUp }
else { b = Float(base); a = b.nextDown }
testWithSymmetries(x, a)
testWithSymmetries(x, b)
}
}
// Away from the unit circle is "easy" but we still want to get some coverage.
// Generate 1 million uniform random points inside the circle, and then test
// both z and 1/z.
var g = SystemRandomNumberGenerator()
var count = 0
while count < 1_000_000 {
let z = Complex<Float>(.random(in: -1 ... 1, using: &g), .random(in: -1 ... 1, using: &g))
if z.length > 1 { continue }
count += 1
test(z)
test(1/z)
}
print("Worst complex norm error seen for log was \(complexError)")
print("For input \(complexMaxInput).")
print("Reference result: \(Complex.log(Complex<Double>(complexMaxInput)))")
print(" Observed result: \(Complex.log(complexMaxInput))")
print("Worst componentwise error seen for log was \(componentError)")
print("For input \(componentMaxInput).")
print("Reference result: \(Complex.log(Complex<Double>(componentMaxInput)))")
print(" Observed result: \(Complex.log(componentMaxInput))")
#endif
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