An MIT licensed pure tone generator in Swift. A single function is provided with internal comments. Complexity calculation is not done, but is at least O(n) with the duration being the data.

pure_tone.swift

//
//
//  Swift Pure Tone Generation
//
/*
Copyright (c) 2021 Lee Barney
 Permission is hereby granted, free of charge, to any person obtaining a
 copy of this software and associated documentation files (the "Software"),
 to deal in the Software without restriction, including without limitation the
 rights to use, copy, modify, merge, publish, distribute, sublicense,
 and/or sell copies of the Software, and to permit persons to whom the Software
 is furnished to do so, subject to the following conditions:
 
 The above copyright notice and this permission notice shall be
 included in all copies or substantial portions of the Software.
 
 
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
 INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
 PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
 CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE
 OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/

import Foundation
import AVFoundation

func playPureTone(frequencyInHz: Int, amplitude: Float, durationInMillis: Int, completion: @escaping ()->Void) {
    //Use a semaphore to block until the tone completes playing
    let semaphore = DispatchSemaphore(value: 1)
    //Run async in the background so as not to block the current thread
    DispatchQueue.global().async {
        //Build the player and its engine
        let audioPlayer = AVAudioPlayerNode()
        let audioEngine = AVAudioEngine()
        semaphore.wait()//Claim the semphore for blocking
        audioEngine.attach(audioPlayer)
        let mixer = audioEngine.mainMixerNode
        let sampleRateHz = Float(mixer.outputFormat(forBus: 0).sampleRate)
        
        guard let format = AVAudioFormat(commonFormat: AVAudioCommonFormat.pcmFormatFloat32, sampleRate: Double(sampleRateHz), channels: AVAudioChannelCount(1), interleaved: false) else {
            return
        }
        // Connect the audio engine to the audio player
        audioEngine.connect(audioPlayer, to: mixer, format: format)
        
        
        let numberOfSamples = AVAudioFrameCount((Float(durationInMillis) / 1000 * sampleRateHz))
        //create the appropriatly sized buffer
        guard let buffer  = AVAudioPCMBuffer(pcmFormat: format, frameCapacity: numberOfSamples) else {
            return
        }
        buffer.frameLength = numberOfSamples
        //get a pointer to the buffer of floats
        let channels = UnsafeBufferPointer(start: buffer.floatChannelData, count: Int(format.channelCount))
        let floats = UnsafeMutableBufferPointer<Float>(start: channels[0], count: Int(numberOfSamples))
        //calculate the angular frequency
        let angularFrequency = Float(frequencyInHz * 2) * .pi
        // Generate and store the sequential samples representing the sine wave of the tone
        for i in 0 ..< Int(numberOfSamples) {
            let waveComponent = sinf(Float(i) * angularFrequency / sampleRateHz)
            floats[i] = waveComponent * amplitude
        }
        do {
            try audioEngine.start()
        }
        catch{
            print("Error: Engine start failure")
            return
        }

        // Play the pure tone represented by the buffer
        audioPlayer.play()
        audioPlayer.scheduleBuffer(buffer, at: nil, options: .interrupts){
            DispatchQueue.main.async {
                completionBlock()
                semaphore.signal()//Release one claim of the semiphore
            }
        }
        semaphore.wait()//Wait for the semiphore so the function doesn't end before the playing of the tone completes
        semaphore.signal()//Release the other claim of the semiphore
    }
}