sqrt an array

// FFT.swift
//
// Copyright (c) 2014–2015 Mattt Thompson (http://mattt.me)
//
// 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 Accelerate

// MARK: Fast Fourier Transform

public func fft(input: [Float]) -> [Float] {
    var real = [Float](input)
    var imaginary = [Float](count: input.count, repeatedValue: 0.0)
    var splitComplex = DSPSplitComplex(realp: &real, imagp: &imaginary)

    let length = vDSP_Length(floor(log2(Float(input.count))))
    let radix = FFTRadix(kFFTRadix2)
    let weights = vDSP_create_fftsetup(length, radix)
    vDSP_fft_zip(weights, &splitComplex, 1, length, FFTDirection(FFT_FORWARD))

    var magnitudes = [Float](count: input.count, repeatedValue: 0.0)
    vDSP_zvmags(&splitComplex, 1, &magnitudes, 1, vDSP_Length(input.count))

    var normalizedMagnitudes = [Float](count: input.count, repeatedValue: 0.0)
    vDSP_vsmul(sqrt(magnitudes), 1, [2.0 / Float(input.count)], &normalizedMagnitudes, 1, vDSP_Length(input.count))

    vDSP_destroy_fftsetup(weights)

    return normalizedMagnitudes
}

public func sqrt(x: [Float]) -> [Float] {
    var results = [Float](count: x.count, repeatedValue: 0.0)
    vvsqrtf(&results, x, [Int32(x.count)])

    return results
}