dlib C++ Library - kiss_fft.h

    /*
     *  Copyright (c) 2003-2010, Mark Borgerding. All rights reserved.
     *  This file is part of KISS FFT - https://github.com/mborgerding/kissfft
     *
     *  SPDX-License-Identifier: BSD-3-Clause
     *  See COPYING file for more information.
     */

    #ifndef DLIB_KISS_FFT_H
    #define DLIB_KISS_FFT_H

    #include <complex>
    #include <vector>
    #include <cmath>
    #include <stdexcept>
    #include <algorithm>
    #include <unordered_map>
    #include <mutex>
    #include <numeric>
    #include "fft_size.h"
    #include "../hash.h"
    #include "../assert.h"

    #define C_FIXDIV(x,y) /*noop*/

    namespace dlib
    {
        namespace kiss_details
        {
            struct plan_key
            {
                fft_size dims;
                bool is_inverse;

                plan_key(const fft_size& dims_, bool is_inverse_)
                :   dims(dims_), is_inverse(is_inverse_)
                {}

                bool operator==(const plan_key& other) const
                {
                    return std::tie(dims, is_inverse) == std::tie(other.dims, other.is_inverse);
                }

                uint32 hash() const
                {
                    using dlib::hash;
                    uint32 ret = 0;
                    ret = hash(dims, ret);
                    ret = hash((uint32)is_inverse, ret);
                    return ret;
                }
            };

            template<typename T>
            struct kiss_fft_state
            {
                long nfft;
                bool inverse;
                std::vector<int> factors;
                std::vector<std::complex<T>> twiddles;

                kiss_fft_state() = default;
                kiss_fft_state(const plan_key& key);
            };

            template<typename T>
            struct kiss_fftnd_state
            {
                fft_size dims;
                std::vector<kiss_fft_state<T>> plans;

                kiss_fftnd_state() = default;
                kiss_fftnd_state(const plan_key& key);
            };

            template<typename T>
            struct kiss_fftr_state
            {
                kiss_fft_state<T> substate;
                std::vector<std::complex<T>> super_twiddles;

                kiss_fftr_state() = default;
                kiss_fftr_state(const plan_key& key);
            };

            template<typename T>
            struct kiss_fftndr_state
            {
                kiss_fftr_state<T> cfg_r;
                kiss_fftnd_state<T> cfg_nd;

                kiss_fftndr_state() = default;
                kiss_fftndr_state(const plan_key& key);
            };

            template<typename T>
            inline void kf_bfly2(
                std::complex<T> * Fout,
                const size_t fstride,
                const kiss_fft_state<T>& cfg,
                const int m
            )
            {
                const std::complex<T> * tw1 = &cfg.twiddles[0];
                std::complex<T> t;
                std::complex<T> * Fout2 = Fout + m;

                for (int i = 0 ; i < m ; i++)
                {
                    t = Fout2[i] * tw1[i*fstride];
                    Fout2[i] = Fout[i] - t;
                    Fout[i] += t;
                }
            }

            template<typename T>
            inline std::complex<T> rot_PI_2(std::complex<T> z)
            {
                return std::complex<T>(z.imag(), -z.real());
            }

            template<typename T>
            inline void kf_bfly3 (
                std::complex<T> * Fout,
                const size_t fstride,
                const kiss_fft_state<T>& cfg,
                const size_t m
            )
            {
                const size_t m2 = 2*m;
                const std::complex<T> *tw1,*tw2;
                std::complex<T> scratch[5];
                const std::complex<T> epi3 = cfg.twiddles[fstride*m];

                tw1=tw2=&cfg.twiddles[0];

                constexpr T half = 0.5;

                for (size_t k = 0 ; k < m ; k++)
                {
                    C_FIXDIV(Fout[k],3); C_FIXDIV(Fout[k+m],3); C_FIXDIV(Fout[m2+k],3); //noop for float and double

                    scratch[1] = Fout[k+m]  * tw1[k*fstride];
                    scratch[2] = Fout[k+m2] * tw2[k*fstride*2];

                    scratch[3] = scratch[1] + scratch[2];
                    scratch[0] = scratch[1] - scratch[2];

                    Fout[m+k] = Fout[k] - half * scratch[3];

                    scratch[0] *= epi3.imag();

                    Fout[k] += scratch[3];

                    Fout[k+m2] = Fout[k+m] + rot_PI_2(scratch[0]);
                    Fout[k+m] -= rot_PI_2(scratch[0]);
                }
            }

            template<typename T>
            inline void kf_bfly4(
                std::complex<T> * Fout,
                const size_t fstride,
                const kiss_fft_state<T>& cfg,
                const size_t m
            )
            {
                const std::complex<T> *tw1,*tw2,*tw3;
                std::complex<T> scratch[6];
                const size_t m2=2*m;
                const size_t m3=3*m;

                tw3 = tw2 = tw1 = &cfg.twiddles[0];

                for (size_t k = 0 ; k < m ; k++)
                {
                    C_FIXDIV(Fout[k],4); C_FIXDIV(Fout[m],4); C_FIXDIV(Fout[m2+k],4); C_FIXDIV(Fout[m3+k],4);

                    scratch[0] = Fout[m+k]  * tw1[k*fstride];
                    scratch[1] = Fout[m2+k] * tw2[k*fstride*2];
                    scratch[2] = Fout[m3+k] * tw3[k*fstride*3];

                    scratch[5] = Fout[k] - scratch[1];
                    Fout[k]  += scratch[1];
                    scratch[3] = scratch[0] + scratch[2];
                    scratch[4] = scratch[0] - scratch[2];
                    Fout[m2+k] = Fout[k] - scratch[3];

                    Fout[k] += scratch[3];

                    if(cfg.inverse) {
                        Fout[m+k]  = scratch[5] - rot_PI_2(scratch[4]);
                        Fout[m3+k] = scratch[5] + rot_PI_2(scratch[4]);
                    }else {
                        Fout[m+k] =  scratch[5] + rot_PI_2(scratch[4]);
                        Fout[m3+k] = scratch[5] - rot_PI_2(scratch[4]);
                    }
                }
            }

            template<typename T>
            inline void kf_bfly5(
                std::complex<T> * Fout,
                const size_t fstride,
                const kiss_fft_state<T>& cfg,
                const int m
            )
            {
                std::complex<T> scratch[13];
                const std::complex<T> * twiddles = &cfg.twiddles[0];
                const std::complex<T> ya = twiddles[fstride*m];
                const std::complex<T> yb = twiddles[fstride*2*m];

                std::complex<T> *Fout0=Fout;
                std::complex<T> *Fout1=Fout0+m;
                std::complex<T> *Fout2=Fout0+2*m;
                std::complex<T> *Fout3=Fout0+3*m;
                std::complex<T> *Fout4=Fout0+4*m;

                const std::complex<T> *tw = &cfg.twiddles[0];

                for (int u=0; u<m; ++u )
                {
                    scratch[0] = Fout0[u];

                    scratch[1] = Fout1[u] * tw[u*fstride]; //C_MUL(scratch[1] ,*Fout1, tw[u*fstride]);
                    scratch[2] = Fout2[u] * tw[2*u*fstride]; //C_MUL(scratch[2] ,*Fout2, tw[2*u*fstride]);
                    scratch[3] = Fout3[u] * tw[3*u*fstride]; //C_MUL(scratch[3] ,*Fout3, tw[3*u*fstride]);
                    scratch[4] = Fout4[u] * tw[4*u*fstride]; //C_MUL(scratch[4] ,*Fout4, tw[4*u*fstride]);

                    scratch[7]  = scratch[1] + scratch[4]; //C_ADD( scratch[7],scratch[1],scratch[4]);
                    scratch[10] = scratch[1] - scratch[4]; //C_SUB( scratch[10],scratch[1],scratch[4]);
                    scratch[8]  = scratch[2] + scratch[3]; //C_ADD( scratch[8],scratch[2],scratch[3]);
                    scratch[9]  = scratch[2] - scratch[3]; //C_SUB( scratch[9],scratch[2],scratch[3]);

                    Fout0[u] += scratch[7] + scratch[8];

                    scratch[5].real(scratch[0].real() + scratch[7].real() * ya.real() + scratch[8].real() * yb.real());
                    scratch[5].imag(scratch[0].imag() + scratch[7].imag() * ya.real() + scratch[8].imag() * yb.real());

                    scratch[6].real(scratch[10].imag() * ya.imag() + scratch[9].imag() * yb.imag());
                    scratch[6].imag(-scratch[10].real() * ya.imag() - scratch[9].real() * yb.imag());

                    Fout1[u] = scratch[5] - scratch[6]; //C_SUB(*Fout1,scratch[5],scratch[6]);
                    Fout4[u] = scratch[5] + scratch[6]; //C_ADD(*Fout4,scratch[5],scratch[6]);

                    scratch[11].real(scratch[0].real() + scratch[7].real()*yb.real() + scratch[8].real()*ya.real());
                    scratch[11].imag(scratch[0].imag() + scratch[7].imag()*yb.real() + scratch[8].imag()*ya.real());
                    scratch[12].real(- scratch[10].imag()*yb.imag() + scratch[9].imag()*ya.imag());
                    scratch[12].imag(scratch[10].real()*yb.imag() - scratch[9].real()*ya.imag());

                    Fout2[u] = scratch[11] + scratch[12];
                    Fout3[u] = scratch[11] - scratch[12];
                }
            }

            /* perform the butterfly for one stage of a mixed radix FFT */
            template<typename T>
            inline void kf_bfly_generic(
                std::complex<T> * Fout,
                const size_t fstride,
                const kiss_fft_state<T>& cfg,
                const int m,
                const int p
            )
            {
                int u,k,q1,q;
                const std::complex<T> * twiddles = &cfg.twiddles[0];
                std::complex<T> t;
                const int Norig = cfg.nfft;

                std::vector<std::complex<T>> scratch(p);

                for ( u=0; u<m; ++u ) {
                    k=u;
                    for ( q1=0 ; q1<p ; ++q1 ) {
                        scratch[q1] = Fout[ k  ];
                        C_FIXDIV(scratch[q1],p);
                        k += m;
                    }

                    k=u;
                    for ( q1=0 ; q1<p ; ++q1 ) {
                        int twidx=0;
                        Fout[ k ] = scratch[0];
                        for (q=1;q<p;++q ) {
                            twidx += fstride * k;
                            if (twidx>=Norig) twidx-=Norig;
                            t = scratch[q] * twiddles[twidx];
                            Fout[ k ] += t;
                        }
                        k += m;
                    }
                }
            }

            template<typename T>
            inline void kf_work(
                const kiss_fft_state<T>& cfg,
                const int* factors,
                std::complex<T>* Fout,
                const std::complex<T>* f,
                const size_t fstride,
                const int in_stride
            )
            {
                std::complex<T> * Fout_beg = Fout;
                const int p=*factors++; /* the radix  */
                const int m=*factors++; /* stage's fft length/p */
                const std::complex<T> * Fout_end = Fout + p*m;

                if (m==1) {
                    do{
                        *Fout = *f;
                        f += fstride*in_stride;
                    }while(++Fout != Fout_end );
                }else{
                    do{
                        // recursive call:
                        // DFT of size m*p performed by doing
                        // p instances of smaller DFTs of size m,
                        // each one takes a decimated version of the input
                        kf_work(cfg, factors, Fout , f, fstride*p, in_stride);
                        f += fstride*in_stride;
                    }while( (Fout += m) != Fout_end );
                }

                Fout=Fout_beg;

                // recombine the p smaller DFTs
                switch (p) {
                    case 2: kf_bfly2(Fout,fstride,cfg,m); break;
                    case 3: kf_bfly3(Fout,fstride,cfg,m); break;
                    case 4: kf_bfly4(Fout,fstride,cfg,m); break;
                    case 5: kf_bfly5(Fout,fstride,cfg,m); break;
                    default: kf_bfly_generic(Fout,fstride,cfg,m,p); break;
                }
            }

            /*  facbuf is populated by p1,m1,p2,m2, ...
                where
                p[i] * m[i] = m[i-1]
                m0 = n                  */
            inline void kf_factor(int n, std::vector<int>& facbuf)
            {
                int p=4;
                const double floor_sqrt = std::floor( std::sqrt((double)n) );

                /*factor out powers of 4, powers of 2, then any remaining primes */
                do {
                    while (n % p) {
                        switch (p) {
                            case 4: p = 2; break;
                            case 2: p = 3; break;
                            default: p += 2; break;
                        }
                        if (p > floor_sqrt)
                            p = n;          /* no more factors, skip to end */
                    }
                    n /= p;
                    facbuf.push_back(p);
                    facbuf.push_back(n);
                } while (n > 1);
            }

            template<typename T>
            inline kiss_fft_state<T>::kiss_fft_state(const plan_key& key)
            {
                constexpr double twopi = 6.283185307179586476925286766559005768394338798;
                nfft       = key.dims[0];
                inverse    = key.is_inverse;
                twiddles.resize(nfft);

                for (int i = 0 ; i < nfft ; ++i)
                {
                    double phase = -twopi*i / nfft;
                    if (inverse)
                        phase *= -1;
                    twiddles[i] = std::polar(1.0, phase);
                }

                kf_factor(nfft,factors);
            }

            template<typename T>
            void kiss_fft_stride(const kiss_fft_state<T>& cfg, const std::complex<T>* in, std::complex<T>* out,int fin_stride)
            {
                if (in == out)
                {
                    DLIB_ASSERT(out != nullptr, "out buffer is NULL!");
                    std::vector<std::complex<T>> tmpbuf(cfg.nfft);
                    kiss_fft_stride(cfg, in, &tmpbuf[0], fin_stride);
                    std::copy(tmpbuf.begin(), tmpbuf.end(), out);
                }
                else
                {
                    kf_work(cfg, &cfg.factors[0], out, in, 1, fin_stride);
                }
            }

            template<typename T>
            inline kiss_fftnd_state<T>::kiss_fftnd_state(const plan_key& key)
            {
                dims = key.dims;
                for (size_t i = 0 ; i < dims.num_dims() ; i++)
                    plans.push_back(std::move(kiss_fft_state<T>(plan_key({dims[i]}, key.is_inverse))));
            }

            template<typename T>
            void kiss_fftnd(const kiss_fftnd_state<T>& cfg, const std::complex<T>* in, std::complex<T>* out)
            {
                const std::complex<T>* bufin=in;
                std::complex<T>* bufout;
                std::vector<std::complex<T>> tmpbuf(cfg.dims.num_elements());

                /*arrange it so the last bufout == out*/
                if ( cfg.dims.num_dims() & 1 )
                {
                    bufout = out;
                    if (in==out) {
                        std::copy(in, in + cfg.dims.num_elements(), tmpbuf.begin());
                        bufin = &tmpbuf[0];
                    }
                }
                else
                    bufout = &tmpbuf[0];

                for (size_t k=0; k < cfg.dims.num_dims(); ++k)
                {
                    int curdim = cfg.dims[k];
                    int stride = cfg.dims.num_elements() / curdim;

                    for (int i=0 ; i<stride ; ++i )
                        kiss_fft_stride(cfg.plans[k], bufin+i , bufout+i*curdim, stride );

                    /*toggle back and forth between the two buffers*/
                    if (bufout == &tmpbuf[0])
                    {
                        bufout = out;
                        bufin = &tmpbuf[0];
                    }
                    else
                    {
                        bufout = &tmpbuf[0];
                        bufin = out;
                    }
                }
            }

            template<typename T>
            inline kiss_fftr_state<T>::kiss_fftr_state(const plan_key& key)
            {
                DLIB_ASSERT((key.dims[0] & 1) == 0, "real FFT must have even dimension");

                const int nfft = key.dims[0] / 2;
                substate = kiss_fft_state<T>(plan_key({nfft}, key.is_inverse));
                super_twiddles.resize(nfft/2);

                for (size_t i = 0 ; i < super_twiddles.size() ; ++i)
                {
                    double phase = -3.141592653589793238462643383279502884197169399 * ((double) (i+1) / nfft + .5);
                    if (key.is_inverse)
                        phase *= -1;
                    super_twiddles[i] = std::polar(1.0, phase);
                }
            }

            template<typename T>
            void kiss_fftr(const kiss_fftr_state<T>& plan, const T* timedata, std::complex<T>* freqdata)
            {
                DLIB_ASSERT(!plan.substate.inverse, "bad fftr plan : need a forward plan. This is an inverse plan");

                const int nfft_h = plan.substate.nfft; //recall that the FFT size is actually half the original requested FFT size, i.e. the size of timedata

                /*perform the parallel fft of two real signals packed in real,imag*/
                std::vector<std::complex<T>> tmpbuf(nfft_h);
                kiss_fft_stride(plan.substate, reinterpret_cast<const std::complex<T>*>(timedata), &tmpbuf[0], 1);
                /* The real part of the DC element of the frequency spectrum in st->tmpbuf
                 * contains the sum of the even-numbered elements of the input time sequence
                 * The imag part is the sum of the odd-numbered elements
                 *
                 * The sum of tdc.r and tdc.i is the sum of the input time sequence.
                 *      yielding DC of input time sequence
                 * The difference of tdc.r - tdc.i is the sum of the input (dot product) [1,-1,1,-1...
                 *      yielding Nyquist bin of input time sequence
                 */

                freqdata[0]         = std::complex<T>(tmpbuf[0].real() + tmpbuf[0].imag(), 0);
                freqdata[nfft_h]    = std::complex<T>(tmpbuf[0].real() - tmpbuf[0].imag(), 0);

                constexpr T half = 0.5;

                for (int k = 1 ; k <= nfft_h / 2 ; ++k)
                {
                    const auto fpk  = tmpbuf[k];
                    const auto fpnk = std::conj(tmpbuf[nfft_h-k]);
                    const auto f1k = fpk + fpnk;
                    const auto f2k = fpk - fpnk;
                    const auto tw  = f2k * plan.super_twiddles[k-1];
                    freqdata[k]         = half * (f1k + tw);
                    freqdata[nfft_h-k]  = half * std::conj(f1k - tw);
                }
            }

            template<typename T>
            void kiss_ifftr(const kiss_fftr_state<T>& plan, const std::complex<T>* freqdata, T* timedata)
            {
                DLIB_ASSERT(plan.substate.inverse, "bad Ifftr plan : need an inverse plan. This is a forward plan")

                const int nfft_h = plan.substate.nfft; //recall that the FFT size is actually half the original requested FFT size, i.e. the size of timedata

                std::vector<std::complex<T>> tmpbuf(nfft_h);

                tmpbuf[0] = std::complex<T>(freqdata[0].real() + freqdata[nfft_h].real(),
                                            freqdata[0].real() - freqdata[nfft_h].real());

                for (int k = 1; k <= nfft_h / 2; ++k)
                {
                    std::complex<T> fk   = freqdata[k];
                    std::complex<T> fnkc = std::conj(freqdata[nfft_h - k]);
                    auto fek = fk + fnkc;
                    auto tmp = fk - fnkc;
                    auto fok = tmp * plan.super_twiddles[k-1];
                    tmpbuf[k] = fek + fok;
                    tmpbuf[nfft_h - k] = std::conj(fek - fok);
                }

                kiss_fft_stride (plan.substate, &tmpbuf[0], (std::complex<T>*)timedata, 1);
            }

            template<typename T>
            inline kiss_fftndr_state<T>::kiss_fftndr_state(const plan_key& key)
            {
                const long realdim = key.dims.back();
                const fft_size otherdims = pop_back(key.dims);
                cfg_r  = kiss_fftr_state<T>(plan_key({realdim}, key.is_inverse));
                cfg_nd = kiss_fftnd_state<T>(plan_key(otherdims, key.is_inverse));
            }

            template<typename T>
            void kiss_fftndr(const kiss_fftndr_state<T>& plan, const T* timedata, std::complex<T>* freqdata)
            {
                const int dimReal  = plan.cfg_r.substate.nfft*2; //recall the real fft size is half the length of the input
                const int dimOther = plan.cfg_nd.dims.num_elements();
                const int nrbins   = dimReal/2+1;

                std::vector<std::complex<T>> tmp1(std::max<int>(nrbins, dimOther));
                std::vector<std::complex<T>> tmp2(plan.cfg_nd.dims.num_elements()*dimReal);

                // take a real chunk of data, fft it and place the output at correct intervals
                for (int k1 = 0; k1 < dimOther; ++k1)
                {
                    kiss_fftr(plan.cfg_r, timedata + k1*dimReal , &tmp1[0]); // tmp1 now holds nrbins complex points
                    for (int k2 = 0; k2 < nrbins; ++k2)
                       tmp2[k2*dimOther+k1] = tmp1[k2];
                }

                for (int k2 = 0; k2 < nrbins; ++k2)
                {
                    kiss_fftnd(plan.cfg_nd, &tmp2[k2*dimOther], &tmp1[0]);  // tmp1 now holds dimOther complex points
                    for (int k1 = 0; k1 < dimOther; ++k1)
                        freqdata[ k1*(nrbins) + k2] = tmp1[k1];
                }
            }

            template<typename T>
            void kiss_ifftndr(const kiss_fftndr_state<T>& plan, const std::complex<T>* freqdata, T* timedata)
            {
                const int dimReal  = plan.cfg_r.substate.nfft*2; //recall the real fft size is half the length of the input
                const int dimOther = plan.cfg_nd.dims.num_elements();
                const int nrbins   = dimReal/2+1;

                std::vector<std::complex<T>> tmp1(std::max<int>(nrbins, dimOther));
                std::vector<std::complex<T>> tmp2(plan.cfg_nd.dims.num_elements()*dimReal);

                for (int k2 = 0; k2 < nrbins; ++k2)
                {
                    for (int k1 = 0; k1 < dimOther; ++k1)
                        tmp1[k1] = freqdata[ k1*(nrbins) + k2 ];
                    kiss_fftnd(plan.cfg_nd, &tmp1[0], &tmp2[k2*dimOther]);
                }

                for (int k1 = 0; k1 < dimOther; ++k1)
                {
                    for (int k2 = 0; k2 < nrbins; ++k2)
                        tmp1[k2] = tmp2[ k2*dimOther+k1 ];
                    kiss_ifftr(plan.cfg_r, &tmp1[0], timedata + k1*dimReal);
                }
            }

            struct hasher
            {
                size_t operator()(const plan_key& key) const {return key.hash();}
            };

            template<typename plan_type>
            const plan_type& get_plan(const plan_key& key)
            {
                static std::mutex m;
                static std::unordered_map<plan_key, plan_type, hasher> plans;

                std::lock_guard<std::mutex> l(m);
                auto it = plans.find(key);
                if (it != plans.end())
                {
                    return it->second;
                }
                else
                {
                    plans[key] = plan_type(key);
                    return plans[key];
                }
            }
        }

        template<typename T>
        void kiss_fft(const fft_size& dims, const std::complex<T>* in, std::complex<T>* out, bool is_inverse)
        /*!
            requires
                - T must be either float or double
                - dims represents the dimensions of both `in` and `out`
                - dims.num_dims() > 0
            ensures
                - performs an FFT on `in` and stores the result in `out`.
                - if `is_inverse` is true, a backward FFT is performed,
                  otherwise a forward FFT is performed.
        !*/
        {
            using namespace kiss_details;
            static_assert(std::is_floating_point<T>::value, "template parameter needs to be a floating point type");
            DLIB_ASSERT(dims.num_dims() > 0, "dims can't be empty");

            const fft_size squeezed_dims = squeeze_ones(dims);

            if (squeezed_dims.num_elements() == 1)
            {
                if (in != out)
                {
                    out[0] = in[0];
                }
            }
            else if (squeezed_dims.num_dims() == 1)
            {
                const auto& plan = get_plan<kiss_fft_state<T>>({squeezed_dims, is_inverse});
                kiss_fft_stride(plan, in, out, 1);
            }
            else
            {
                const auto& plan = get_plan<kiss_fftnd_state<T>>({squeezed_dims,is_inverse});
                kiss_fftnd(plan, in, out);
            }
        }

        /*
         *  in  has dims[0] * dims[1] * ... * dims[-2] * dims[-1] points
         *  out has dims[0] * dims[1] * ... * dims[-2] * (dims[-1]/2+1) points
         */
        template<typename T>
        void kiss_fftr(const fft_size& dims, const T* in, std::complex<T>* out)
        /*!
            requires
                - T must be either float or double
                - dims represent the dimensions of `in`
                - `out` has dimensions {dims[0], dims[1], ..., dims[-2], dims[-1]/2+1}
                - dims.num_dims() > 0
                - dims.back() must be even
            ensures
                - performs a real FFT on `in` and stores the result in `out`.
        !*/
        {
            using namespace kiss_details;
            static_assert(std::is_floating_point<T>::value, "template parameter needs to be a floating point type");
            DLIB_ASSERT(dims.num_dims() > 0, "dims can't be empty");
            DLIB_ASSERT(dims.back() % 2 == 0, "last dimension needs to be even");

            const fft_size squeezed_dims = squeeze_ones(dims);

            if (squeezed_dims.num_dims() == 1)
            {
                const auto& plan = get_plan<kiss_fftr_state<T>>({squeezed_dims,false});
                kiss_fftr(plan, in, out);
            }
            else
            {
                const auto& plan = get_plan<kiss_fftndr_state<T>>({squeezed_dims,false});
                kiss_fftndr(plan, in, out);
            }
        }

        /*
         *  in  has dims[0] * dims[1] * ... * dims[-2] * (dims[-1]/2+1) points
         *  out has dims[0] * dims[1] * ... * dims[-2] * dims[-1] points
         */
        template<typename T>
        void kiss_ifftr(const fft_size& dims, const std::complex<T>* in, T* out)
        /*!
            requires
                - T must be either float or double
                - dims represent the dimensions of `out`
                - `in` has dimensions {dims[0], dims[1], ..., dims[-2], dims[-1]/2+1}
                - dims.num_dims() > 0
                - dims.back() must be even
            ensures
                - performs an inverse real FFT on `in` and stores the result in `out`.
        !*/
        {
            using namespace kiss_details;
            static_assert(std::is_floating_point<T>::value, "template parameter needs to be a floating point type");
            DLIB_ASSERT(dims.num_dims() > 0, "dims can't be empty");
            DLIB_ASSERT(dims.back() % 2 == 0, "last dimension needs to be even");

            const fft_size squeezed_dims = squeeze_ones(dims);

            if (squeezed_dims.num_dims() == 1)
            {
                const auto& plan = get_plan<kiss_fftr_state<T>>({squeezed_dims,true});
                kiss_ifftr(plan, in, out);
            }
            else
            {
                const auto& plan = get_plan<kiss_fftndr_state<T>>({squeezed_dims,true});
                kiss_ifftndr(plan, in, out);
            }
        }

        inline int kiss_fft_next_fast_size(int n)
        {
            while(1) {
                int m=n;
                while ( (m%2) == 0 ) m/=2;
                while ( (m%3) == 0 ) m/=3;
                while ( (m%5) == 0 ) m/=5;
                if (m<=1)
                    break; /* n is completely factorable by twos, threes, and fives */
                n++;
            }
            return n;
        }

        inline int kiss_fftr_next_fast_size_real(int n)
        {
            return kiss_fft_next_fast_size((n+1)>>1) << 1;
        }
    }

    #endif // DLIB_KISS_FFT_H