soxr additional source notices

Additional source notices for libsoxr 0.1.3. LGPL terms in LICENCE and COPYING.LGPL also apply. These exact notices are retained without changing or expanding their grants. Exact original notice comments from the source/header inputs correlated to the macOS, iOS and simulator contrib archives. All listed full source hashes agree across the three configured trees. Full primary license documents are also retained. Conditional code and shared headers may be conservative inclusions; this attribution inventory is not final-link retention, patent clearance or complete distribution approval.

src/aliases.h:1-2
src/cr.h:1-2
src/cr32.c:1-2
src/cr32s.c:1-2
src/cr64.c:1-2
src/data-io.c:1-2
src/dev32s.h:1-2
src/filter.c:1-2
src/internal.h:1-2
src/math-wrap.h:1-2
src/rint-clip.h:1-2
src/rint.h:1-2
src/std-types.h:1-2
src/util-simd.c:1-2
src/util32s.c:1-2
src/util32s.h:1-2
src/vr-coefs.h:1-2

/* SoX Resampler Library      Copyright (c) 2007-16 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details. */

src/avfft32.c:1-2
src/avfft32s.c:1-2
src/data-io.h:1-2
src/fft4g_cache.h:1-2
src/fft4g.h:1-2
src/fft4g64.c:1-2
src/fifo.h:1-2
src/filter.h:1-2
src/half-coefs.h:1-2
src/rdft_t.h:1-2
src/rdft.h:1-2

/* SoX Resampler Library      Copyright (c) 2007-13 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details. */

src/ccrw2.h:1-4

/* SoX Resampler Library      Copyright (c) 2007-13 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details. */

/* Concurrent Control with "Readers" and "Writers", P.J. Courtois et al, 1971 */

src/cr-core.c:1-4

/* SoX Resampler Library      Copyright (c) 2007-18 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details.
 *
 * Constant-rate resampling engine-specific code. */

src/cr.c:1-4

/* SoX Resampler Library      Copyright (c) 2007-16 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details.
 *
 * Constant-rate resampling common code. */

src/dbesi0.c:1-7

/*  Copyright(C) 1996 Takuya OOURA

You may use, copy, modify this code for any purpose and
without fee.

Package home:  http://www.kurims.kyoto-u.ac.jp/~ooura/bessel.html
*/

src/fft4g.c:1-282

/* Copyright Takuya OOURA, 1996-2001.

You may use, copy, modify and distribute this code for any
purpose (include commercial use) and without fee.  Please
refer to this package when you modify this code.

Package home:  http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html

Fast Fourier/Cosine/Sine Transform
    dimension   :one
    data length :power of 2
    decimation  :frequency
    radix       :4, 2
    data        :inplace
    table       :use
functions
    cdft: Complex Discrete Fourier Transform
    rdft: Real Discrete Fourier Transform
    ddct: Discrete Cosine Transform
    ddst: Discrete Sine Transform
    dfct: Cosine Transform of RDFT (Real Symmetric DFT)
    dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
function prototypes
    void cdft(int, int, double *, int *, double *);
    void rdft(int, int, double *, int *, double *);
    void ddct(int, int, double *, int *, double *);
    void ddst(int, int, double *, int *, double *);
    void dfct(int, double *, double *, int *, double *);
    void dfst(int, double *, double *, int *, double *);


-------- Complex DFT (Discrete Fourier Transform) --------
    [definition]
        <case1>
            X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
        <case2>
            X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
        (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
    [usage]
        <case1>
            ip[0] = 0; // first time only
            cdft(2*n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            cdft(2*n, -1, a, ip, w);
    [parameters]
        2*n            :data length (int)
                        n >= 1, n = power of 2
        a[0...2*n-1]   :input/output data (double *)
                        input data
                            a[2*j] = Re(x[j]),
                            a[2*j+1] = Im(x[j]), 0<=j<n
                        output data
                            a[2*k] = Re(X[k]),
                            a[2*k+1] = Im(X[k]), 0<=k<n
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n/2-1]   :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            cdft(2*n, -1, a, ip, w);
        is
            cdft(2*n, 1, a, ip, w);
            for (j = 0; j <= 2 * n - 1; j++) {
                a[j] *= 1.0 / n;
            }
        .


-------- Real DFT / Inverse of Real DFT --------
    [definition]
        <case1> RDFT
            R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
            I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
        <case2> IRDFT (excluding scale)
            a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
                   sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
                   sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            rdft(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            rdft(n, -1, a, ip, w);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        <case1>
                            output data
                                a[2*k] = R[k], 0<=k<n/2
                                a[2*k+1] = I[k], 0<k<n/2
                                a[1] = R[n/2]
                        <case2>
                            input data
                                a[2*j] = R[j], 0<=j<n/2
                                a[2*j+1] = I[j], 0<j<n/2
                                a[1] = R[n/2]
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/2)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n/2-1]   :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            rdft(n, 1, a, ip, w);
        is
            rdft(n, -1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
    [definition]
        <case1> IDCT (excluding scale)
            C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DCT
            C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            ddct(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            ddct(n, -1, a, ip, w);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        output data
                            a[k] = C[k], 0<=k<n
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/2)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/4-1] :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            ddct(n, -1, a, ip, w);
        is
            a[0] *= 0.5;
            ddct(n, 1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DST (Discrete Sine Transform) / Inverse of DST --------
    [definition]
        <case1> IDST (excluding scale)
            S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DST
            S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            ddst(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            ddst(n, -1, a, ip, w);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        <case1>
                            input data
                                a[j] = A[j], 0<j<n
                                a[0] = A[n]
                            output data
                                a[k] = S[k], 0<=k<n
                        <case2>
                            output data
                                a[k] = S[k], 0<k<n
                                a[0] = S[n]
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/2)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/4-1] :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            ddst(n, -1, a, ip, w);
        is
            a[0] *= 0.5;
            ddst(n, 1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
    [definition]
        C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
    [usage]
        ip[0] = 0; // first time only
        dfct(n, a, t, ip, w);
    [parameters]
        n              :data length - 1 (int)
                        n >= 2, n = power of 2
        a[0...n]       :input/output data (double *)
                        output data
                            a[k] = C[k], 0<=k<=n
        t[0...n/2]     :work area (double *)
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/4)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/4+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/8-1] :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a, t, ip, w);
        is
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a, t, ip, w);
            for (j = 0; j <= n; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
    [definition]
        S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
    [usage]
        ip[0] = 0; // first time only
        dfst(n, a, t, ip, w);
    [parameters]
        n              :data length + 1 (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        output data
                            a[k] = S[k], 0<k<n
                        (a[0] is used for work area)
        t[0...n/2-1]   :work area (double *)
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/4)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/4+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/8-1] :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            dfst(n, a, t, ip, w);
        is
            dfst(n, a, t, ip, w);
            for (j = 1; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


Appendix :
    The cos/sin table is recalculated when the larger table required.
    w[] and ip[] are compatible with all routines.
*/

src/half-fir.h:1-5

/* SoX Resampler Library      Copyright (c) 2007-16 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details. */

/* Decimate by 2 using a FIR with odd length (LEN). */
/* Input must be preceded and followed by LEN >> 1 samples. */

src/pffft.c:1-56

/* https://bitbucket.org/jpommier/pffft/raw/483453d8f7661058e74aa4e7cf5c27bcd7887e7a/pffft.c
 * with minor changes for libsoxr. */

/* Copyright (c) 2013  Julien Pommier ( pommier@modartt.com )

   Based on original fortran 77 code from FFTPACKv4 from NETLIB
   (http://www.netlib.org/fftpack), authored by Dr Paul Swarztrauber
   of NCAR, in 1985.

   As confirmed by the NCAR fftpack software curators, the following
   FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
   released under the same terms.

   FFTPACK license:

   http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html

   Copyright (c) 2004 the University Corporation for Atmospheric
   Research ("UCAR"). All rights reserved. Developed by NCAR's
   Computational and Information Systems Laboratory, UCAR,
   www.cisl.ucar.edu.

   Redistribution and use of the Software in source and binary forms,
   with or without modification, is permitted provided that the
   following conditions are met:

   - Neither the names of NCAR's Computational and Information Systems
   Laboratory, the University Corporation for Atmospheric Research,
   nor the names of its sponsors or contributors may be used to
   endorse or promote products derived from this Software without
   specific prior written permission.

   - Redistributions of source code must retain the above copyright
   notices, this list of conditions, and the disclaimer below.

   - Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions, and the disclaimer below in the
   documentation and/or other materials provided with the
   distribution.

   THIS 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 CONTRIBUTORS OR COPYRIGHT
   HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
   EXEMPLARY, OR CONSEQUENTIAL 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 WITH THE
   SOFTWARE.


   PFFFT : a Pretty Fast FFT.

   This file is largerly based on the original FFTPACK implementation, modified in
   order to take advantage of SIMD instructions of modern CPUs.
*/

src/pffft.h:1-51

/* https://bitbucket.org/jpommier/pffft/raw/483453d8f7661058e74aa4e7cf5c27bcd7887e7a/pffft.h
 * with minor changes for libsoxr. */

#if !defined PFFT_MACROS_ONLY

/* Copyright (c) 2013  Julien Pommier ( pommier@modartt.com )

   Based on original fortran 77 code from FFTPACKv4 from NETLIB,
   authored by Dr Paul Swarztrauber of NCAR, in 1985.

   As confirmed by the NCAR fftpack software curators, the following
   FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
   released under the same terms.

   FFTPACK license:

   http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html

   Copyright (c) 2004 the University Corporation for Atmospheric
   Research ("UCAR"). All rights reserved. Developed by NCAR's
   Computational and Information Systems Laboratory, UCAR,
   www.cisl.ucar.edu.

   Redistribution and use of the Software in source and binary forms,
   with or without modification, is permitted provided that the
   following conditions are met:

   - Neither the names of NCAR's Computational and Information Systems
   Laboratory, the University Corporation for Atmospheric Research,
   nor the names of its sponsors or contributors may be used to
   endorse or promote products derived from this Software without
   specific prior written permission.

   - Redistributions of source code must retain the above copyright
   notices, this list of conditions, and the disclaimer below.

   - Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions, and the disclaimer below in the
   documentation and/or other materials provided with the
   distribution.

   THIS 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 CONTRIBUTORS OR COPYRIGHT
   HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
   EXEMPLARY, OR CONSEQUENTIAL 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 WITH THE
   SOFTWARE.
*/

src/poly-fir.h:1-5

/* SoX Resampler Library      Copyright (c) 2007-16 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details. */

/* Resample using an interpolated poly-phase FIR with length LEN. */
/* Input must be followed by FIR_LENGTH-1 samples. */

src/poly-fir0.h:1-5

/* SoX Resampler Library      Copyright (c) 2007-16 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details. */

/* Resample using a non-interpolated poly-phase FIR with length LEN. */
/* Input must be followed by FIR_LENGTH-1 samples. */

src/soxr.c:1-2

/* SoX Resampler Library      Copyright (c) 2007-18 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details. */

src/soxr.h:1-20

/* SoX Resampler Library      Copyright (c) 2007-18 robs@users.sourceforge.net
 *
 * This library is free software; you can redistribute it and/or modify it
 * under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2.1 of the License, or (at
 * your option) any later version.
 *
 * This library is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser
 * General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this library; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */



/* -------------------------------- Gubbins --------------------------------- */

src/vr32.c:1-4

/* SoX Resampler Library      Copyright (c) 2007-16 robs@users.sourceforge.net
 * Licence for this file: LGPL v2.1                  See LICENCE for details. */

/* Variable-rate resampling. */